Geofoam Applications in the Design and Construction of Highway Embankments (2004)

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5- 1 CHAPTER 5 EXTERNAL (GLOBAL) STABILITY EVALUATION OF GEOFOAM EMBANKMENTS Contents Introduction...................................................................................................................................5-4 Embankment Geometry ................................................................................................................5-5 Cross-Sectional Geometry........................................................................................................5-5 Longitudinal Geometry.............................................................................................................5-7 Embankment Cover ......................................................................................................................5-7 Trapezoidal Embankments .......................................................................................................5-8 Vertical Embankments .............................................................................................................5-9 Settlement of Embankment.........................................................................................................5-10 Introduction ............................................................................................................................5-10 Settlement Due to End-Of-Primary (EOP) Consolidation......................................................5-11 Settlement Due to Secondary Consolidation ..........................................................................5-13 Settlement Due to Long-Term Vertical Deformation (Creep) of the Fill Mass .....................5-14 Allowable Settlement .............................................................................................................5-16 Stress Distribution for Total Settlement Calculations ............................................................5-17 Stress Distribution at Center of Embankment ........................................................................5-18 Stress Distribution at Edge of Embankment...........................................................................5-21 Steps in EOP Consolidation Settlement Calculation ..............................................................5-23 Remedial Procedures for Excessive Total Settlements ..........................................................5-24 External Bearing Capacity of Embankment................................................................................5-25 Introduction ............................................................................................................................5-25 Stress Distribution Theory......................................................................................................5-28

5- 2 Interpretation of External Bearing Capacity Design Chart.....................................................5-32 Remedial Procedures ..............................................................................................................5-32 External Slope Stability of Trapezoidal Embankments ..............................................................5-33 Introduction ............................................................................................................................5-33 Typical Cross-Section.............................................................................................................5-33 Static Stability Analysis Procedure ........................................................................................5-34 Material Properties .................................................................................................................5-35 Location of Critical Static Failure Surface .............................................................................5-40 Design Charts .........................................................................................................................5-42 Interpretation of External Slope Stability Design Chart.........................................................5-44 Remedial Procedures ..............................................................................................................5-44 External Seismic Stability of Trapezoidal Embankments...........................................................5-45 Introduction ............................................................................................................................5-45 Seismic Shear Strength Parameters ........................................................................................5-47 Horizontal Seismic Coefficient ..............................................................................................5-48 Seismic Stability Analysis Procedure.....................................................................................5-53 Design Charts .........................................................................................................................5-54 Interpretation of Seismic Slope Stability Design Chart..........................................................5-57 Remedial Procedures ..............................................................................................................5-58 External Slope Stability of Vertical Embankments ....................................................................5-59 Introduction ............................................................................................................................5-59 Typical Cross-Section.............................................................................................................5-59 Static Stability Analysis Procedure ........................................................................................5-60 Material Properties .................................................................................................................5-61 Location of Critical Static Failure Surface .............................................................................5-62 Design Charts .........................................................................................................................5-65

5- 3 Interpretation of External Slope Stability Design Charts .......................................................5-67 Remedial Procedures ..............................................................................................................5-68 External Seismic Stability of Vertical Embankments.................................................................5-68 Introduction ............................................................................................................................5-68 Seismic Stability Analysis Procedure.....................................................................................5-69 Design Charts .........................................................................................................................5-70 Remedial Procedures ..............................................................................................................5-73 Overturning.............................................................................................................................5-73 Hydrostatic Uplift (Flotation) .....................................................................................................5-75 Introduction ............................................................................................................................5-75 Remedial Procedures ..............................................................................................................5-83 Translation and Overturning Due to Water (Hydrostatic Sliding and Overturning)...................5-84 Introduction ............................................................................................................................5-84 Translation..............................................................................................................................5-84 Overturning.............................................................................................................................5-89 Remedial Procedures ..............................................................................................................5-90 Translation and Overturning Due to Wind .................................................................................5-91 Introduction ............................................................................................................................5-91 Translation..............................................................................................................................5-91 Overturning.............................................................................................................................5-98 Remedial Procedures ..............................................................................................................5-99 References...................................................................................................................................5-99 Figures ......................................................................................................................................5-104 Tables........................................................................................................................................5-164 ______________________________________________________________________________

5- 4 INTRODUCTION Design for external (global) stability of the overall EPS-block geofoam embankment involves consideration of how the combined fill mass and overlying pavement system interact with the foundation soil. External stability consideration in the proposed design procedure includes consideration of Serviceability Limit State (SLS) issues, such as total and differential settlement caused by the soft foundation soil and Ultimate Limit State (ULS) issues, such as bearing capacity, slope stability, seismic stability, hydrostatic uplift (flotation), translation due to water (hydrostatic sliding), and translation due to wind (see Table 3.1). All of these external stability considerations are described in this chapter and illustrated in design examples in Chapter 7. These external stability considerations together with other project-specific design inputs, such as right-of-way constraints, limiting impact on underlying and/or adjacent structures, and construction time, largely govern the overall cross-sectional geometry of the embankment as well as the relative amount of geofoam used within the embankment. Because EPS-block geofoam is typically a more expensive material than soil on a cost-per-unit-volume basis, it is desirable to optimize the design to minimize the volume of EPS used yet still satisfy design criteria concerning settlement and stability. Therefore, it is not necessary for the EPS blocks to extend the full height vertically from the top of the soil subgrade to the bottom of the pavement system. The overburden stress imposed by the pavement system and fill mass on the soft foundation soil may decrease the stability of some of the external failure mechanisms, e.g., settlement, bearing capacity, slope stability, and seismic stability, while increasing the stability of others, e.g., hydrostatic uplift, translation due to water, and translation due to wind. Therefore, overall design optimization of an embankment incorporating EPS-block geofoam requires iterative analyses to achieve a technically acceptable design at the lowest overall cost. In order to minimize iterative analyses, the design flowchart shown in Figure 3.3 was developed to obtain a technically optimal design using a trial and error process. The design procedure considers a pavement system with the minimum required thickness, a fill mass with a minimum thickness of

5- 5 EPS-block geofoam, and the use of an EPS block with the lowest possible density. Therefore, the design procedure starts with the least expensive pavement/embankment system in the anticipation that a cost efficient design will be produced. Design for external stability begins with the selection of a cross-section geometry of the overall embankment in a plane perpendicular to the proposed road alignment. The type of cross- section selected will dictate the type of cover that will be required, such as facing panels for a vertical embankment and usually soil cover for a trapezoidal embankment. The cover system will impose vertical stresses directly on the EPS blocks or on the foundation soil. These vertical stresses due to the weight of the cover system must be included in calculations for the various external stability failure mechanisms. Steps 1 through 3 of the design process involve (1) background investigation, (2) selection of preliminary pavement system, and (3) preliminary arrangement of the fill mass (see Figure 3.3) and are presented in Chapter 3. In this chapter, the external (global) stability failure mechanisms, Steps 4 through 10 of the design process in Figure 3.3, are discussed. This chapter presents detailed background information on the external stability aspect of the EPS-Block geofoam design methodology. An abbreviated form of the external stability design procedure can be found in the provisional design guideline included in Appendix B. EMBANKMENT GEOMETRY The cross-sectional geometry in the direction transverse (perpendicular) to the road alignment is the critical geometry for performing external stability analysis because conventional settlement and two-dimensional limit equilibrium stability analyses utilize the transverse cross- section. However, the longitudinal geometry of the embankment along the road alignment must also be considered for construction and settlement purposes as described subsequently. Cross-Sectional Geometry The designer must choose the type of embankment, e.g., trapezoidal (sloped-side fill) or vertical (vertical-face fill), that will be most feasible for the project. These types of embankments

5- 6 are shown in Figure 3.4. Unlike other types of lightweight and soil fills, EPS is actually a solid material with internal strength. Therefore, each block is self-stable and collectively the blocks are also inherently self-stable to a certain extent even when the blocks are vertically stacked. Consequently, a benefit of EPS-block geofoam compared to other types of lightweight fills and traditional soil embankments is that a vertical embankment, also referred to as a geofoam wall (1), can be used. There are several benefits of using a geofoam wall over a traditional trapezoidal embankment. First, the volume of fill material, especially of EPS blocks, is minimized. This results in reduction of both material cost and construction time. Second, the footprint of the embankment is smaller and consequently the amount of right-of-way required is minimized. This can minimize cost as well as have positive environmental benefits. However, there are also some disadvantages of using a geofoam wall, which may offset the benefits mentioned above. These disadvantages include the need to cover the vertical faces of the exposed EPS blocks with a facing material that typically consists of a structural material. Types of facing materials available for geofoam walls are subsequently discussed in the “Embankment Cover” section of this chapter. The facing panel will place a concentrated vertical stress on the soft foundation soil and must be considered in overall stability and settlement analyses. Additionally, a portland cement concrete (PCC) slab on top of the EPS may be required in a vertical embankment for the function of providing anchorage for the facing panels or road hardware. If a trapezoidal embankment is used, a maximum overall slope angle of two horizontal to one vertical (2H:1V) should be used to accommodate the maintenance of vegetation typically placed for erosion control on the sloped sides of the embankment. Further discussion on the types of cover materials typically used to cover the EPS blocks in a trapezoidal embankment is provided subsequently in the “Embankment Cover” section of this chapter.

5- 7 Longitudinal Geometry Two aspects of the geometry of the embankment in the longitudinal direction (parallel to the roadway) that need to be considered during design include orientation of the EPS blocks and the transition zone between the geofoam and non-geofoam sections of the roadway. The top surface of the assemblage of EPS blocks should always be parallel with the final pavement surface (2) to facilitate construction and performance. Thus, any desired change in elevation (grade) along the road alignment must be accommodated by sloping the foundation soil surface as necessary prior to placement of the first layer of EPS blocks. Additionally, the upper surface of the EPS blocks should always be horizontal when viewed in transverse cross-section so any crown desired in the final pavement surface should be achieved by varying the thickness of the pavement system (2). In the longitudinal cross-section, the transition zone between geofoam and soil should be gradual to minimize differential settlement. The EPS blocks could be stepped as shown in Figure 5.1 to ease the transition. However, the specific pattern should be determined on a project- specific basis based on calculated differential settlements such as the criteria given in (3) which suggests that the calculated gradient within the transition zone should not exceed 1:200 (vertical: horizontal). Figure 5.1. Typical EPS block transition to a soil subgrade (1). EMBANKMENT COVER The EPS blocks should be permanently covered to protect against ultraviolet (UV) radiation. Although EPS does not suffer UV deterioration to the extent that many other geosynthetics do (the surface of the EPS will just yellow and become chalky after some weeks or months of exposure), it is still recommended that the surface of the EPS be covered as rapidly as possible after block placement. The type of covering system selected will depend on the type of embankment cross-sectional geometry that will be used.

5- 8 Trapezoidal Embankments For a trapezoidal fill embankment, the covering system typically consists of a thin layer of soil placed directly over the stepped edges of the EPS blocks. Vegetation is incorporated on the surface of the soil layer for erosion control. The angle of a trapezoidal embankment is governed by the stability of the soil cover as well as by maintenance requirements. Typically, the steepest slope angle used is two horizontal to one vertical (2H:1V), or 26.6 degrees which is similar to the maximum of 25 degrees recommended in the recent PIARC guidelines (2). However, steeper slopes may be possible if geosynthetics such as geotextiles, geogrids, geocells, or erosion-control geosynthetics are utilized. The current Norwegian design standards (4) and the recent PIARC guidelines (2) require a minimum thickness of soil cover of 250 mm (10 in.). This minimum thickness has been in use for more than 25 years. However, a thicker soil cover of 500 to 1,000 mm (20 to 39 in.) has been incorporated in the current United Kingdom design guidelines (5). The recommended thicker soil cover amount may be based on the following three reasons: • The results from full-scale fire tests in Japan (6) show that 500 mm (20 in.) of soil cover is adequate to prevent the EPS blocks from melting even after a one- hour fire consisting of burning kerosene on the sloped surface of the test embankment. However, these tests did not explore if less than 500 mm (20 in.) of soil would have also been satisfactory. • The desire to provide increased soil depth for surface vegetation roots. • The desire to provide greater protection to the EPS against unspecified hazards. Selection of the soil cover thickness is important because costs increase with increasing soil cover and the vertical stress imposed on the soft foundation soil increases. Based on the recommended thickness ranges from existing design standards and guidelines, it is recommended that the minimum thickness of the soil cover should be in the range of 300 to 500 mm (12 to 20 in.). The soil cover on the sides of a trapezoidal embankment can be assumed to be 400 mm (16

5- 9 in.) thick with a total (moist) unit weight of 18.8 kN/m³ (120 lbf/ft³) for preliminary design purposes. Vertical Embankments For vertical geofoam embankment walls, the exposed sides should be covered with a facing. The facing does not have to provide any structural capacity to retain the blocks because the blocks are self-stable so the primary function is to protect the blocks from environmental factors. The selection of the type of facing system to use is based on three general criteria: • facing must be self-supporting or physically attached to the EPS blocks, • architectural/aesthetic requirements, and • cost. The following materials have been successfully used for facing geofoam walls: • prefabricated metal (steel or aluminum) panels, • precast PCC panels, either full height or segmental (such as used in mechanically stabilized earth walls, MSEWs), • segmental retaining wall (SRW) blocks which are typically precast PCC, • shotcrete, and • geosynthetic vegetative mats. Other materials that might be suitable for facing geofoam walls include: • wood panels or planks, • the stucco-like finish used for exterior insulation finish systems (EIFS), and • EPS-compatible paint for temporary fills Regardless of the facing used, the resulting vertical stress on the foundation soil must be considered in the calculations for settlement and global stability. The weight of the facing elements needs to be obtained from a supplier or estimated because of the various types of vertical wall systems.

5- 10 SETTLEMENT OF EMBANKMENT Introduction Settlement is the amount of vertical deformation that occurs from immediate or elastic settlement of the fill mass or foundation soil, consolidation and secondary compression of the foundation soil, and long-term creep of the fill mass at the top of a highway embankment. Settlement caused by lateral deformation of the foundation soil at the edges of an embankment is not considered because (7) presents inclinometer measurements that show the settlements from lateral deformation are generally small compared with the five previously mentioned settlement mechanisms if the factor of safety against external instability during construction remains greater than about 1.4. If the factor of safety remains greater than 1.4, settlement caused by lateral deformation is likely to be less than 10 percent of the end-of primary settlement (7). The proposed design procedure recommends a factor of safety against bearing capacity failure and slope instability greater than 1.5. Therefore, settlement resulting from lateral deformations is not considered herein. However, lateral creep deformations should be considered if the proposed embankment will be placed near structures such as underground utilities. A discussion on lateral creep deformations can be found in (7,8). Total settlement of an EPS-block geofoam embankment considered herein, Stotal, consists of five components as shown by Equation (5.1): Stotal = Sif + Si + Sp + Ss + Scf (5.1) where Sif = immediate or elastic settlement of the fill mass, Si = immediate or elastic settlement of the foundation soil, Sp = end-of-primary (EOP) consolidation of the foundation soil, Ss = secondary consolidation of the foundation soil, and Scf = long-term vertical deformation (creep) of the fill mass. Immediate or elastic settlement of both the fill mass and foundation soil occur during construction and will not impact the condition of the final pavement system. Therefore,

5- 11 immediate settlements are not typically included in the total settlement estimate and the settlement analysis presented herein focuses on primary and secondary consolidation of the foundation soil and creep of the fill mass. However, immediate settlement of the foundation soil should be considered if the embankment will be placed over existing utilities. Immediate settlement can be estimated by elastic theory and is discussed in (9). Differential settlements may occur in clays with a desiccated crust even if the clay thickness and induced stresses are the same below the embankment because of random variations in compressibility and preconsolidation pressure within the clay and the desiccated crust. A method for estimating settlement of clay deposits that have a desiccated crust can be found in (10). Settlement Due to End-of-Primary (EOP) Consolidation The EOP consolidation of the foundation soil is the amount of compression that occurs during the period of time required for the excess porewater pressure to dissipate for an increase in effective stress. Equation (5.2) can be used to estimate the EOP consolidation of the foundation soil which allows for overconsolidated and normally consolidated soil deposits (7): p c vfr p o o o vo o p σ C σCS L log L log 1 e σ 1 e σ ′ ′= +′ ′+ + (5.2) where Sp = settlement resulting from one-dimensional EOP consolidation, Cr = recompression index, σ′p = preconsolidation pressure, σ′vo = in situ effective vertical stress, effective overburden pressure, eo = in situ void ratio under effective overburden pressure σ′vo, Cc = compression index, Lo = preconstruction thickness of the compressible layer with void ratio eo, σ′vf = final effective vertical stress = σ′vo + ∆ σ′Z , and ∆σ′Z = change in effective vertical stress.

5- 12 Soils that have not been subjected to effective vertical stresses higher than the present effective overburden pressure are considered normally consolidated and have a value of σ'p/σ'vo of unity. For normally consolidated foundation soil, Equation (5.2) can be simplified c vf p o o p C σS L log 1 e σ ′= ′+ (5.3) If the estimated settlement of the proposed EPS block embankment exceeds the allowable settlement, one expedient soft ground treatment method that can be utilized is to partially overexcavate the existing soft foundation soil and to place EPS blocks in the overexcavation. This treatment method decreases settlement by decreasing the final effective vertical stress. Note that Lo to be used in Equation (5.3) is the preconstruction thickness. If an overexcavation procedure is performed, Lo will be the thickness of the soft foundation soil prior to the overexcavation procedure. If the foundation soil is overconsolidated, i.e., σ′p /σ′v > 1, but the proposed final effective vertical stress will be less than or equal to the preconsolidation pressure, i.e., σ′vf ≤ σ′p, Equation (5.2) can be simplified to vfr p o o vo σCS L log 1+e σ ′= ′ (5.4) Values of Cr, Cc, and σ'p are determined from the results of laboratory consolidation tests as described in (11). However, empirical correlations can be used to obtain preliminary estimates of the input parameters for an EOP consolidation settlement analysis. Empirical correlations between Cc and in situ water content are provided in (7,9,11). Two widely used equations for estimating Cc are: c oC 1.15(e 0.35)= − (5.5) cC 0.009(LL-10)= (5.6) where LL = liquid limit of the soil.

5- 13 Equation (5.5) (12) is applicable to all clays and Equation (5.6) (13) is applicable to clays of low- to-medium sensitivity (sensitivity less than 4) (11). Most values of Cr/Cc are in the range of 0.02 to 0.2 with the lower values corresponding to highly structured and bonded soft clay and silt deposits and the higher values corresponding to micaceous silts and fissured stiff clays and shales (7). A widely used approximation Cr/Cc is 0.1. Therefore, Cr can be estimated by multiplying the value of Cc by 0.1. Settlement Due to Secondary Consolidation Secondary consolidation of the foundation soil is the amount of compression that occurs after the dissipation of the excess porewater pressure induced by an increase in effective stress occurs and thus secondary consolidation occurs under the final effective vertical stress σ'vf. Equation (5.7) can be used to estimate the secondary consolidation of the foundation soil (7). c c s o o p [C / C ] C tS L log 1 e t α ×= + (5.7) where Ss = settlement resulting from one-dimensional secondary compression, Cα = secondary compression index, eo = in situ void ratio under effective overburden pressure, σvo, Lo = preconstruction thickness of the compressible layer with void ratio eo, t = time, and tp = duration of primary consolidation. Cα is determined from the results of laboratory consolidation tests. However, for preliminary settlement analyses, empirical values of Cα/Cc , such as those provided in Table 5.1, can be used to estimate Cα. The validity of the Cα/Cc concept has been verified using field case histories (14,15). Table 5.1 Values of Cα/Cc for Soils (7).

5- 14 Field values of tp for layers of soil that do not contain permeable layers and peats can range from several months to many years. However, for the typical useful life of a structure, the value of the t/ tp rarely exceeds 100 and is often less than 10 (7). The determination of secondary settlement is important in high water content materials, such as peats, for the following three reasons (16): (1) peat materials exist at high natural water contents and void ratios; (2) peat materials have high Cα/Cc values; and (3) the duration of EOP consolidation for peat or other highly organic materials is very short because peat materials have a high initial permeability. The application of the Cα/Cc concept for high-water content material with and without surcharging can be found in (16). The Cα/Cc concept can also be used to predict the behavior of postsurcharge secondary settlement (14). Settlement Due to Long-Term Vertical Deformation (Creep) of the Fill Mass The creep behavior of EPS-block geofoam is discussed in Chapter 2 and as indicated, current creep models do not provide reliable estimates of the time-dependent total vertical strains. Further research is required to either refine current creep models or develop a new model. The current state of practice for considering creep strains in the design of EPS block embankments and bridge approaches is to base the design on laboratory creep tests on small specimens trimmed from an EPS block that will be used in construction or to base the design on published observations of the creep behavior of EPS, such as: • If the applied stress produces an immediate strain of 0.5 percent or less, the creep strains, εc, will be negligible even when projected for 50 years or more. The stress level at 0.5 percent strain corresponds to approximately 25 percent of the compressive strength defined at a compressive normal strain of 1 percent or 33 percent of the yield stress. • If the applied stress produces an immediate strain between 0.5 percent and 1 percent, the geofoam creep strains will be tolerable (less than 1 percent) in

5- 15 lightweight fill applications even when projected for 50 years or more. The stress level at 1 percent strain corresponds to approximately 50 percent of the compressive strength or 67 percent of the yield stress. • If the applied stress produces an immediate strain greater than 1 percent, creep strains can rapidly increase and become excessive for lightweight fill geofoam applications. The stress level for significant creep strain corresponds to the yield stress which is approximately 75 percent of the compressive strength. In summary, the compressive stress at a vertical strain of 1 percent, i.e., the elastic-limit stress, appears to correspond to a threshold stress level for the development of significant creep effects. As a result, the field applied stresses should not exceed the elastic limit stress until more reliable creep models are developed (1). Based on these observations, it is concluded that creep strains within the EPS mass under sustained loads are expected to be within acceptable limits (0.5 percent to 1 percent strain over 50 years) if the applied stress is such that it produces an immediate strain between 0.5 percent and 1 percent (1). The load bearing design recommended as part of internal stability in Chapter 6 is based on selecting an EPS block that will provide an immediate or elastic vertical strain of less than 1 percent. Therefore, the contribution of settlement due to geofoam creep is neglected in Equation (5.1) and Equation (5.1) reduces to the following for design purposes because Sif, Si, and Scf are likely to be negligible: total p sS S S= + (5.8) The initial (immediate) or elastic vertical strain of the EPS-block geofoam can be estimated from Equation (5.9) to determine if the vertical strain is between 0.5 percent and 1 percent which will result in negligible creep effects: o ti σε = E (5.9) where εo = immediate or elastic vertical strain of the geofoam in decimal format, σ = applied stress over the EPS, and

5- 16 Eti = initial tangent Young’s modulus of the EPS. Values of Eti can be estimated from Table 4.1 that presents values of Eti for different geofoam densities. This procedure only considers the long-term deformation of the EPS-block geofoam. If conventional soil fill is placed between the foundation soil and the EPS-blocks, both primary and secondary settlement of the soil fill needs to be estimated to obtain the total settlement of the fill mass. Allowable Settlement Tolerable settlements for highway embankments are not well established in practice nor is information concerning tolerable settlements readily available in the geotechnical literature. Postconstruction settlements of 0.3 to 0.6 m (1 to 2 ft) during the economic life of a roadway are generally considered tolerable provided the settlements are uniform, occur slowly over a period of time, and do not occur next to a pile-supported structure (17). If postconstruction settlement occurs over a long period of time, any pavement distress caused by settlement can be repaired when the pavement is resurfaced. Although rigid pavements have performed well after 0.3 to 0.6 m (1 to 2 ft) of uniform settlement, flexible pavements are usually selected where doubt exists about the uniformity of postconstruction settlements and some states utilize a flexible pavement when predicted settlements exceed 150 mm (6 in.) (17). Tolerable settlements of bridge approach embankments depend on the type of structure, location, foundation conditions, operational criteria, etc. (8). The following references are recommended for information on tolerable abutment movements: (18-21). The transition zone between geofoam and embankment soil should be gradual to minimize differential settlement. The EPS blocks should be stepped as shown in Figure 5.1 as the embankment transitions from a soft foundation soil that requires geofoam to a stronger foundation soil that can support the soil embankment. However, a minimum of two layers of blocks is recommended to minimize the potential of the blocks to shift under traffic loads. The

5- 17 only exception to this is the final step of the geofoam embankment, which can consist of one block as shown in Figure 5.1. The specific layout of the EPS blocks should be determined on a project-specific basis based on calculated differential settlements such as the criteria given in (3) which suggests that the calculated settlement gradient within the transition zone should not exceed 1:200 (vertical: horizontal). An allowable differential settlement of less than 10 cm (4 in.) is recommended by (22) to minimize the potential for detrimental shifting of the EPS blocks. However, the distance over which this recommended differential settlement value is based on is not provided. Stress Distribution for Total Settlement Calculations Based on Equation (5.8), the main contributors to embankment settlement are EOP consolidation and secondary consolidation of the foundation soil. Of these two mechanisms, the largest component of total settlement is EOP consolidation which occurs from an increase in effective vertical stress on the foundation soil. Therefore, reliable estimates of EOP consolidation settlement require knowledge of the stress distribution within the embankment and foundation soil. Although solutions for the determination of vertical stresses under embankments have been developed (23), these solutions were developed for conventional earth fill embankments and are based on the assumption that the embankment consists of one type of fill with a single unit weight. However, an EPS-block geofoam embankment typically consists of EPS-block geofoam, soil or a facing over the sides of the EPS blocks, and the pavement system above the EPS blocks (see Figure 3.6). Additionally, some amount of soil fill may also be used between the foundation soil and the bottom of the EPS blocks for overall economy and/or leveling purposes. Thus, an EPS-block geofoam embankment will consist of more than one type of material with varying unit weights. The soil cover on the sides of a slope-side embankment can be assumed to be 400 mm (16 in.) thick with a total (moist) unit weight of 18.8 kN/m³ (120 lbf/ft³). This is equivalent to a surcharge of 7.7 kPa (160 lbs/ft2). No guidance on the weight of the facing elements of a vertical-

5- 18 side embankment (geofoam wall) is provided because of the various types of facing systems so this weight must be estimated or provided by the supplier. The effect of vehicle loads on the road surface is generally negligible compared to the dead load of the pavement system and thus can typically be ignored in global settlement calculations. However, traffic loads are occasionally considered for embankments of low height that will experience a large volume of traffic (22). The critical locations along the embankment cross section for calculating total settlements are at the center and edge. These two locations will typically yield the greatest and least settlement magnitudes, respectively, and consequently yield the greatest differential settlement. Computation of stresses induced by the overall embankment on the foundation soil can be facilitated by dividing the embankment into three zones as shown in Figure 5.2. To calculate the increase in stress at the center and edge of the embankment, a new stress distribution procedure was developed herein to allow for a non-homogenous embankment. The next section presents the derivation or the stress distribution method for the center of the embankment and the following section describes the stress distribution method for the edge of the embankment. These solutions are based on the assumptions that the embankment is flexible and in full contact with the foundation soil. Figure 5.2. Zones of EPS embankment for stress distribution analyses. Stress Distribution at Center of Embankment To estimate the increase in vertical stress at the centerline of the geofoam embankment the effect of the stresses applied by zones I, II, and III in Figure 5.2 must be evaluated at the embankment centerline. The law of superposition allows the increase in vertical stresses for zone II to be considered and then multiplied by 2 to estimate the increase in vertical stress caused by zones II and III. The increase in vertical stress caused by zone I is added to the vertical stress increases caused by zones II and III to obtain the increase in vertical stress caused by the entire embankment. The increase in vertical stress caused by zone I is estimated by:

5- 19 ( ) I I Z qσ sin where is in radians, α α απ∆ = + (5.10) b 2 * arctan where is calculated in radians, Z α α =    (5.11) and the variables are defined in Figure 5.3. The surcharge from the center of embankment, qI, is estimated by the following expression: I fill pavementq q q= + (5.12) where fill EPS EPSq * T ,γ= (5.13) pavement pavement pavementq * T ,γ= (5.14) Tpavement = thickness of the pavement system in m, TEPS = maximum thickness of EPS block geofoam in embankment in m (see Figure 5.5), γEPS = unit weight of the EPS block geofoam in kN/m3, and γpavement = unit weight of the pavement system in kN/m3. If other materials are included in the embankment besides EPS, they can be included in the estimate of qI by multiplying the unit weight by the thickness of the material. Figure 5.3. Geometry and variables for the surcharge induced by Zone I at the embankment center. The increase in vertical stress caused by zones II or III, i.e., the triangular loads of the side of the embankment in Figure 5.2, is estimated by: a b arctan - where and is calculated in radians, Z α δ δ α+ =    (5.17) b arctan where is calculated in radians, Z δ δ =    (5.16) II II Z q xσ sin 2 where , are in radians, 2 0.5*a α δ α δπ  ∆ = −   (5.15)

5- 20 and the other variables are defined in Figure 5.4. The surcharge induced at the center of the embankment from the triangular loaded areas, i.e., zones II and III, is estimated below for zone II because the law of superposition and the symmetry of the embankment allows consideration of only one side of the embankment: qII = qfill + qcover (5.18) where qfill is given by Equation (5.13), covercover cover Tq = γ * cosθ (see Figure 5.5), (5.19) γcover = unit weight of cover soil in kN/m3, Tcover = thickness of soil cover over the geofoam in m, and θ= angle embankment slope makes with the horizontal in degrees. Figure 5.4. Geometry and variables for the surcharge induced by Zone II at the embankment center. Figure 5.5. Components of surcharges that are applied to the foundation soil. For example, if a 0.6 m (2 ft) thick soil cover with a unit weight of 18.8 kN/m3 (120 lbf/ft³) is used on the sides of an embankment with a slope of 4H: 1V (θ = 14 degrees), the vertical thickness of the soil cover is given by TCover/cosθ which is 0.62 m (2 ft) and the value of qcover is 11.7 kPa (244 lbs/ft³). If other materials are included in zones II and III besides EPS, these materials can be included in the estimates of qII by multiplying the unit weight by the thickness of the material. Therefore, the total increase in vertical stress at the center of a trapezoidal embankment is estimated as follows: ( )@center I IIZ Z Zσ σ 2 * σ ∆ = ∆ + ∆ (5.20)

5- 21 where IIZ σ∆ is multiplied by 2 to account for the vertical stress increase caused by zone III. The total increase in vertical stress at the center of a vertical embankment is only due to the vertical stress increase applied by zone I, i.e., no contributions from zones II and III because of the vertical sides of the embankment, and is estimated as follows: @center IZ Z σ σ∆ = ∆ (5.21) The thickness of the soil cover, Tcover, is defined herein as the thickness measured from the outer edge of the EPS blocks as shown in Figure 5.5 (b). The weight of the soil wedges between the inner and outer edges of the EPS blocks will add an additional surcharge to the surcharge value determined using Equation (5.19). An effective thickness of the soil cover, T′cover, can be determined and used instead of Tcover in Equation (5.19). The surcharge induced by the soil wedge will depend on the block thickness and the slope of the embankment. Additionally, note that the soil wedges only occupy half the cross-sectional area of the embankment between the outer and inner EPS block edges. Therefore, the additional thickness of soil cover that will impose a surcharge is approximately ½ of the thickness formed between the outer and inner EPS block edges. Therefore, 12cover cover block edgesT T ( * T )′ = + . For embankment slopes ranging from 2H:1V to 4H:1V and for a block thickness of 760 mm (30 in.), the additional thickness to be added to Tcover to obtain T′cover will range between 340 mm (13 in.) to 370 mm (15 in.). Stress Distribution at Edge of Embankment The increase in vertical stress at the edge of the embankment is complex because the embankment is not symmetric for stress distribution purposes. Therefore, the increase in vertical stress for zones I, II, and III in Figure 5.2 must be considered separately. The vertical stress increase at the edge of the embankment caused by zone II can be estimated by Figure 5.6 and Equations (5.22) and (5.23) provide the solution for determining the increase in vertical stress, IIZ ∆σ , at the edge of the embankment from a vertical loading increasing linearly.

5- 22 ( ) II II Z q∆σ sin 2 2π δ= where δ is in radians, (5.22) aarctan Z δ  =    where δ is calculated in radians, (5.23) and the variables are defined in Figure 5.6. The surcharge, qII, is estimated as shown in Equation (5.18). Figure 5.6. Geometry and variables for the surcharge induced by Zone II at the edge of the embankment. Figure 5.7 illustrates the solution for determining the increase in vertical stress, IIIZ ∆σ , at the edge of the embankment by zone III, which is located at the opposite end of the embankment. III III Z q xσ sin 2 2π 0.5 a α δ ∆ = − ∗  where α, δ are in radians, (5.24) a 2barctan Z δ + =    where δ is calculated in radians, (5.25) 2a 2barctan Z α δ+ = −   where δ and α is calculated in radians, (5.26) and the variables are defined in Figure 5.7. The value of surcharge induced by zone III, qIII , is equal to qII and can be estimated as shown in Equation (5.18). Figure 5.7. Geometry and variables for the surcharge induced by Zone III at the edge of the embankment. Figure 5.8 illustrates the solution for determining the increase in vertical stress, IZ ∆σ , at the edge of the embankment caused by zone I or the center of the embankment. The value of surcharge induced by zone I, qI , is estimated as shown in Equation (5.12). ( ) I I Z q sin cos 2 π  ∆σ = α + α α + δ  where α, δ are in radians, (5.27) aarctan Z δ  =    where δ is calculated in radians, (5.28)

5- 23 a 2barctan Z α δ+ = −   where δ and α is calculated in radians, (5.29) and the variables are defined in Figure 5.8. Therefore, the total increase in stress at the edge of a trapezoidal embankment is estimated as follows: I II IIIZ@edge Z Z Z ∆σ =∆σ +∆σ +∆σ . (5.30) The total increase in vertical stress at the edge of a vertical embankment is estimated as follows: IZ@edge Z ∆σ =∆σ (5.31) Note comparing Figures 5.8 and 5.9, the angle δ depicted in Figure 5.8 is set equal to zero in Figure 5.9 because of the vertical sides of the embankment. Figure 5.8. Geometry and variables for the surcharge induced by Zone I at the edge of a trapezoidal embankment. Figure 5.9. Geometry and variables for the surcharge induced by Zone I at the edge of a vertical embankment. If stresses from traffic loads are to be considered, the procedure for stress distribution through the fill mass described in the load bearing section of Chapter 6 can be used. Steps in EOP Consolidation Settlement Calculation The steps that can be used to estimate the EOP consolidation settlement are summarized below: 1. Divide soft soil stratum into sublayers using at least two sublayers depending on the thickness of the soft layer. For example, a 3 m (10 ft) thick soft layer could be subdivided into three 1 m (3.3 ft) thick sublayers. 2. Determine geostatic effective vertical stress at the mid-height of each sublayer. For a normally consolidated clay, this effective vertical stress, σ′vo equals the preconsolidation pressure, σ′p. .

5- 24 3. Determine the final effective vertical stress, σ′vf , at the mid-height of each sublayer, which includes the change in effective vertical stress, ∆ σ′Z. Equations (5.20) and (5.30) provide ∆ σ′Z at the center and edge of the embankment, respectively. σ′vf = σ′vo +∆ σ′Z (5.32) 4. Calculate the EOP consolidation settlement of each sublayer using Equation (5.2), (5.3), or (5.4). 5. Determine total EOP consolidation settlement of the soft soil stratum by summing the EOP consolidation settlement of each sublayer. n p pi 1 S S i− = ∑ (5.33) 6. Determine total settlement by adding Ss to the value of Sp from Equation (5.33). Remedial Procedures for Excessive Total Settlements If the estimated total settlement of the proposed embankment is excessive, the geotechnical engineer can consider reducing the load of the embankment by replacing any soil fill that is being proposed between the EPS blocks and foundation soil or a portion of the foundation soil materials with EPS-block geofoam. The replacement height or excavation depth is based on the required decrease in effective vertical stress or incremental stress that will yield tolerable settlements. If removal of soil fill or foundation soil and replacement with EPS blocks is not suitable, a ground improvement technique can be performed in conjunction with the use of EPS- block geofoam. An overview of ground improvement methods is presented in Chapter 1. As indicated above, in order to limit the magnitude of postconstruction settlement, it may be beneficial to partially excavate a portion of the soft foundation soil and replace the excavated material with EPS-block geofoam to limit the final effective vertical stress, σ′vf, to a tolerable level. This removal and replacement procedure is actually a combination of the following initial

5- 25 two categories of soft ground treatment methods indicated in Table 1.1: reducing the load by using EPS-block geofoam and replacing the problem materials by more competent materials. If the foundation soil is partially excavated, the excavation will typically need to be widened from the toe of the embankment so that the excavation side slopes remain stable during construction. Typically, the overexcavation should be widened a minimum of 1H:1V as measured from the bottom of the excavation to the toe of the embankment (8). Several key issues should be considered with a partial excavation procedure. First, temporary dewatering and/or adequate overburden may be required above the EPS blocks during construction to minimize the potential for hydrostatic uplift of the EPS blocks due to a relatively high groundwater level or accumulation of surface runoff within the excavation. Second, partial excavation of the foundation soil may not be desirable if a dessicated layer of soil is present at the surface of the foundation soil because the dessicated layer may contribute to the bearing capacity of the foundation soil and may decrease the magnitude of settlement of the embankment. (8). EXTERNAL BEARING CAPACITY OF EMBANKMENT Introduction This section presents an evaluation of bearing capacity as a potential external failure mode of an EPS-block geofoam embankment. Bearing capacity failure occurs if the applied stress exceeds the bearing capacity of the foundation soil which is related to the shear resistance of the soil. Failure is only considered through the foundation soil in this chapter because Chapter 6 addresses internal stability or load bearing failure through the geofoam embankment. If an external bearing capacity failure occurs, the embankment can undergo excessive vertical settlement and impact adjacent property. The general expression for the ultimate bearing capacity of soil, qult, is defined by (24) as: ult c f q W γq =cN +γD N +γB N (5.34)

5- 26 where: c = Mohr-Coulomb shear strength parameter termed cohesion, kN/m2, Nc, Nγ, Nq = Terzaghi shearing resistance bearing capacity factors, γ = unit weight of soil, kN/m3, BW = bottom width of embankment, m, and Df = depth of embedment, m. It is anticipated that most, if not all, EPS-block geofoam embankments will be founded on soft, saturated cohesive soils, because traditional fill material cannot be used in this situation without pre-treatment. Narrowing the type of foundation soil to soft, saturated cohesive soils allows Equation (5.34) to be simplified. The Mohr-Coulomb parameter termed undrained angle of internal friction, φ, is equal to zero, and the cohesion, c, equals the undrained shear strength, su, for a soft, saturated cohesive soil tested under undrained triaxial compression conditions. The undrained shear strength, su, of the cohesive soil is defined herein as the average su between the bottom of the embankment and a depth below the bottom of the embankment equal to the bottom width of the embankment, BW. This procedure is valid if su is fairly uniform with depth. Because φ equals zero, Nγ = 0, Nq = 1, and Equation (5.34) reduces to: ult f u cq =γD +s N (5.35) The EPS embankment is usually placed on the ground surface, which means that Df (depth of embedment) equals zero and thus Equation (5.35) simplifies to: ult u cq = s N (5.36) The following expression for Nc was developed in (25): W f c W B DN =5 (1+0.2 )(1+0.2 ) L B (5.37) where: L = length of the embankment, m, and

5- 27 because Df equals zero, Equation (5.37) simplifies to: W c BN =5 (1+0.2 ) L (5.38) For design purposes, an EPS-block geofoam embankment is assumed to be modeled as a continuous footing; and thus, the length of the embankment can be assumed to be significantly larger than the width such that the term BW/L in Equation (5.38) approaches zero. Upon including the BW/L simplification in Equation (5.38), Nc reduces to 5. Typical shallow foundation design requires a factor of safety, FS, of 3 against external bearing capacity failure (26), and the same factor of safety is used herein for EPS-block geofoam embankment design. By applying a FS of 3, the allowable soil pressure, qa, is: ua s *5q = 3 (5.39) where: su = 0.5 *qu qu = undrained unconfined compressive strength, kPa. By transposing Equation (5.39), the following expression is obtained: n@0m u 3 σ s 5 ∗= (5.40) where: σn@0m = normal stress applied by the embankment at the ground surface or at a depth of 0 metres, kPa = σn, pavement@0m + σn, traffic@0m + σn,geofoam@0m , (5.41) σn, pavement@0m = normal stress applied by pavement system at the ground surface, kPa, σn, traffic@0m = normal stress applied by traffic surcharge at the ground surface, kPa, σn,geofoam@0m = normal stress applied by weight of EPS geofoam at the ground surface, kPa

5- 28 = γEPS * TEPS , (5.42) γEPS = unit weight of the EPS-block geofoam, kN/m³, and TEPS = thickness or total height of the EPS-block geofoam, m. Stress Distribution Theory The following sections detail how the values comprising σn@0m are estimated for the design process. To evaluate the factor of safety against an external bearing capacity failure through the underlying soft, saturated cohesive soil, the normal stress applied by the pavement system, traffic, and embankment must be evaluated at the ground surface and not at the top of the embankment. This requires stress distribution theory to be used to transfer the pavement and traffic stresses from the top of the embankment to the bottom of the embankment. This stress distribution differs from the stress distribution analysis presented for EOP consolidation settlement analyses because this stress distribution analysis is estimating the amount of stress dissipated by the geofoam to determine the increase in vertical stress at the top of the foundation due to the overlying embankment. The stress distribution for the EOP consolidation settlement analyses is used to evaluate the increase in stress in the foundation soil due to the overlying embankment assuming that the embankment loads are placed directly on the surface of the foundation soil and not at the top of the embankment. This is a conservative approach because it results in greater increases in vertical stress in the foundation soil and thus greater EOP consolidation settlements. The transfer of the pavement and traffic stresses from the top of the embankment to the top of the foundation soil is accomplished using the 2V:1H stress distribution method (11) as follows: n, pavement n, traffic W n, pavement@0m n, traffic@0m W EPS ( + ) T + = (T +T ) σ σ ∗σ σ (5.43) where:

5- 29 σn, pavement = normal stress applied by pavement at top of embankment, kPa, σn, traffic = normal stress applied by traffic surcharge at top of embankment, kPa, and TW = top width of embankment, m. The 2V:1H stress distribution method was used because full-scale instrumented geofoam embankments in Norway (27,28), which were analyzed during this study, show that the stresses at the base of the embankment correspond to a stress distribution pattern of approximately 2V:1H. Further discussion on the full-scale tests can be found in Chapter 2. Boussinesq (29) stress distribution theory for an embankment-type loading is used herein to transfer the stress applied by the geofoam to the top of the foundation soil. The Boussinesq analysis reveals that the normal stress at the ground surface (0 m) due to the weight of the geofoam embankment, σn,EPS@0m, has a maximum value of ½ (γEPS * TEPS). This solution for embankment-type loading is presented in (11). Incorporating σn,EPS@0m and Equation (5.43) into Equation (5.41) yields the following: ( ) ( ) ( )n,pavement n,traffic W EPS EPS n@0m W EPS T T T T 2 σ + σ ∗ γ ∗σ = ++ (5.44) Incorporating Equation (5.44) into Equation (5.38), the undrained shear strength required to satisfy a factor of safety of 3 for a particular embankment height is as follows: n,pavement n,traffic W EPS EPS u W EPS ( + ) T (γ T )3s = + 5 (T +T ) 2  σ σ ∗  ∗ ∗       (5.45) Pavement systems range in thickness from 610 – 1,500 mm (24 – 59 in.), with 1,000 mm (39 in.) being a typical thickness. The various component layers of the pavement system can be assumed to have a total unit weight of 20 kN/m³ (130 lbf/ft³). Therefore, the stress induced by the pavement system, σn, pavement, can range from 12 kPa (250 lbs/ft²) to 30 kPa (626 lbs/ft²), with 20 kPa (418 lbs/ft²) being typical. However, a more conservative estimate of 21.5 kPa (450 lbs/ft²)

5- 30 was used in the development of the external bearing capacity design chart presented subsequently. In accordance with (30), 0.67 m (2 ft) of a 18.9 kN/m3 (120 lbf/ft³) surcharge material is used to model the design traffic stress, σn,traffic, of 11.5 kPa (240 lbs/ft²) at the top of the embankment. As indicated in Chapter 3, γEPS can be assumed to be 1 kN/m3 (6.37 lbf/ft3) to conservatively allow for potential long-term water absorption. Substituting the design values of σn,pavement , and σn,traffic, and γEPS into Equation (5.45) yields the following expression for the undrained shear stress required to satisfy a factor of safety of 3 for a particular embankment height: ( ) ( ) ( )3 EPSW u W EPS 1 kN/m T21.5 kPa 11.5 kPa T3s 5 T T 2   + ∗ = ∗ +  +     (5.46) which simplifies to: W u EPS W EPS 99 Ts = +0.3 T 5 (T +T ) (5.47) Based on Equation (5.47) and various values of TEPS, Figure 5.10 presents the minimum thickness of geofoam required for values of foundation soil undrained shear strength. The results show that if the foundation soil exhibits a value of su greater than or equal to 19.9 kPa (415 lbs/ft²), external bearing capacity will not control the external stability of the EPS embankment. However, if the value of su is less than 19.9 kPa (415 lbs/ft²), the allowable thickness of the EPS- block geofoam can be estimated from Figure 5.10 to prevent bearing capacity failure. Figure 5.10 also shows that as the number of lanes supported by the EPS embankment increases, the required height of EPS-block geofoam increases for a given undrained shear strength. The pavement widths used in the parametric study correspond to a 2-lane roadway (11 m or 36 ft) that consists of 2 lanes and with 2-shoulders that are 1.8 m (6 ft) wide, a 4-lane roadway (23 m or 76 ft) consists of 2-exterior shoulders that are 3 m (10 ft) wide and 2-interior

5- 31 shoulders that are 1.2 m (4 ft) wide, and a 6-lane roadway (34 m or 112 ft) consists of 4- shoulders that are 3 m (10 ft) wide. Each lane is assumed to be 3.66 m (12 ft) wide. The use of EPS blocks as lightweight fill benefits the external bearing capacity of an EPS-block geofoam embankment underlain by soft clay or other low-strength soils in two ways. First, the EPS-blocks induce a much smaller stress on the weak foundation than a traditional soil fill. Second, the height of the EPS-block embankment decreases the normal stress applied to the top of the foundation soil, because it distributes the pavement and traffic stresses over its height via stress distribution. As a result, the larger the thickness of EPS or higher the embankment, the lower the applied pavement and traffic surcharge stresses at the base of the embankment. Likewise, the larger the stresses at the base of the embankment or the lower the undrained shear strength, the thicker the EPS or higher the embankment must be to maintain a FS of 3. For example, at a su value less than 19.9 kPa (415 lbs/ft²) the thickness of EPS or height of the embankment must be greater than zero to distribute the applied stress to maintain a factor of safety of 3. As the value of su decreases the minimum thickness of EPS or embankment height required increases to distribute the applied stresses to a low enough level that satisfies a factor of safety of 3. Figure 5.10 also illustrates that the benefit of using an EPS-block geofoam embankment decreases with increasing road width, TW. An increased road width results in the pavement system and the traffic stress of 21.5 kPa (450 lbs/ft²) and 11.5 kPa (240 lbs/ft²), respectively, being applied over a larger width or area at the top of the embankment. This larger area reduces the amount of stress that is dissipated via the 2V:1H stress distribution theory because the value of TW increases relative to TEPS in Equation (5.43). As TW increases, the impact of TEPS on the normal stress at the base of the embankment is reduced because the TW term in the numerator and denominator override the value of TEPS. Despite reducing the stress-distribution effect of the EPS embankment with increasing road width, the EPS-block still provides a better alternative to soil

5- 32 materials that have higher unit weights because the reduction of stress-distribution effects with increasing road width will also occur in these materials. Figure 5.10 Design chart for obtaining the minimum thickness or height of geofoam, TEPS, for a factor of safety of 3 against external bearing capacity failure of a geofoam embankment. Interpretation of External Bearing Capacity Design Chart As can be observed from Figure 5.10, the critical external bearing capacity scenario involves a 6-lane embankment (34 m or 112 ft). For the 6-lane embankment, the lowest value of su that can accommodate this embankment is approximately 18.3 kPa (382 lbs/ft²) for a minimum height of EPS foam equal to 12.2 m (40 ft). This means that for a 6-lane embankment and an su value of 18.3 kPa (382 lbs/ft²), the required TEPS will be 12.2 m (40 ft). Conversely, if the height of the EPS embankment desired is 4.6 m (15 ft), an su of 18.9 kPa (394 lbs/ft²) would be required. If the available su of the foundation soil is less than 18.3 kPa (382 lbs/ft²), the height of the geofoam embankment would have to exceed 15.3 m (50 ft) to satisfy a factor of safety greater than 3. A geofoam embankment height of 15.3 m (50 ft) is not common and thus foundation improvement measures would have to be undertaken to increase the value of su to 18.9 kPa (394 lbs/ft²). Another example involves estimating the foundation soil su value required for a 2-lane highway and an embankment height of 6.1 m (20 ft). From Figure 5.10, the required su value is 15 kPa (304 lbs/ft²) which can also be calculated from Equation (5.45) for the 2-lane embankment width of 11 m (36 ft) as shown below: 3 2 u 3 33 kPa 11 m (1.27 kN/m 6.1 m)s = + =15 kPa (304 lbs/ft ) 5 (11 m+6.1 m) 2   ∗ ∗       (5.48) Remedial Procedures Remedial procedures that can be considered to increase the factor of safety against external bearing capacity failure are similar to the remedial procedures for decreasing the magnitude of settlement. In addition, the analyses indicate that increasing the thickness of EPS or

5- 33 height of the embankment will also increase the external bearing capacity because the pavement and traffic stresses are distributed over a larger height which reduces the increase in vertical stress at the top of the foundation soil resulting in an increase in bearing capacity resistance. EXTERNAL SLOPE STABILITY OF TRAPEZOIDAL EMBANKMENTS Introduction This section presents an evaluation of external slope stability as a potential failure mode of EPS-block geofoam trapezoidal embankments or embankments with sloped sides. A supplemental section of Chapter 5 considers external slope stability of vertical embankments. A slope stability failure occurs if the driving shear stresses equal or exceed the shear resistance of material(s) along the failure surface. If a slope stability failure occurs, the embankment can undergo substantial vertical settlement and impact adjacent property. Serious safety hazards, even death, and economic implications are associated with a slope stability failure. The general expression for the limit equilibrium factor of safety, FS, is given as: Shear ResistanceFS= Driving Shear Stresses (5.49) The driving shear stresses in this case are due to the overlying soil cover, EPS block, and the traffic and pavement surcharges. The shear resistance is primarily attributed to the undrained shear strength of the foundation soil and EPS blocks. Typical Cross-Section A typical cross-section through an EPS embankment with side-slopes of 2H:1V is shown in Figure 5.11. It can be seen that a soil cover is placed over the entire embankment including the top to facilitate input of the geometry in the slope stability software and to increase numerical stability. If the soil cover layer was terminated at the top of the embankment, this would cause a discontinuity in this soil layer in the slope stability software which caused some numerical difficulties. As a result, the soil cover is extended across the top of the embankment even though in a typical embankment it is terminated at the top of the embankment and the pavement system

5- 34 is placed on top of the embankment. The soil cover is 0.46 m (1.5 ft) thick, which is typical for the side slopes, and is assigned a moist unit weight of 18.9 kN/m3 (120 lbf/ft³). Because the soil cover is not usually placed on top of the embankment, the traffic and pavement surcharges were simply reduced by the weight of 0.46 m (1.5 ft) of soil cover or 8.7 kPa (181.7 lbs/ft²). As discussed in the section on external bearing capacity of the embankment in this chapter, the pavement system is modeled using a surcharge of 21.5 kPa (450 lbs/ft²). This surcharge is based on a typical pavement system thickness of 1,000 mm (39.4 in.) and a total unit weight of 20 kN/m3 (127.3 lbf/ft³), which yields a typical stress of 20 kPa (418 lbs/ft²) so the use of 21.5 kPa (450 lbs/ft²) is slightly conservative. The traffic surcharge is 11.5 kPa (240 lbs/ft²) based on the AASHTO recommendations (30) of using 0.67 m (2 ft) of a 18.9 kN/m3 (120 lbf/ft3) soil to represent the traffic surcharge at the top of the embankment. Therefore, the total surcharge used to represent the pavement and traffic surcharges is 21.5 kPa (450 lbs/ft²) plus 11.5 kPa (240 lbs/ft²) or 33.0 kPa (690 lbs/ft²). Because the soil cover artificially placed on top of the embankment for analysis purposes corresponds to 8.7 kPa (181.7 lbs/ft²), the surcharge placed on top of the embankment for the static slope stability analyses is 33.0 kPa (690 lbs/ft²) minus 8.7 kPa (181.7 lbs/ft²) or 24.3 kPa (508.3 lbs/ft²) as shown in Figure 5.11. Figure 5.11. Typical cross-section used in static external slope stability analyses of trapezoidal embankments. Static Stability Analysis Procedure Static slope stability analyses were conducted on a range of embankment geometries to investigate the effect of various embankment heights (3.1 m (10 ft) to 15.3 m (50 ft)), slope inclinations (2H:1V, 3H:1V, and 4H:1V), and road widths of 11, 23, and 34 m (36, 76, and 112 ft) on external slope stability. The results of these analyses were used to develop design charts to facilitate design of roadway embankments that utilize geofoam. The static analysis of each geometry or cross-section was conducted in two-steps. This first step involved locating the critical static failure surface and the second step involved calculating the factor of safety for the

5- 35 critical static failure surface. The Simplified Janbu stability method (31) was used to locate the critical static failure surface because a rotational failure mode surface was assumed for the external stability analyses, versus a translational failure mode for the internal stability analyses, and the microcomputer program XSTABL Version 5 (32) only allows searches for the critical failure surface using the Simplified Janbu method or Simplified Bishop (33) stability method. After locating the critical static failure surface using the Simplified Janbu stability method, the critical static factor of safety for this failure surface was calculated using Spencer’s (34) two-dimensional stability method because the method satisfies all conditions of equilibrium and provides the best estimate of the limit equilibrium factor of safety (35). Spencer’s method could not be used initially to locate the critical static failure surface because XSTABL only allows searches for the critical failure surface using the Simplified Janbu and Simplified Bishop stability methods. Material Properties The input parameters, i.e., unit weight and shear strength, used in the external slope stability analyses are presented in Table 5.2. It can be seen that Mohr-Coulomb shear strength parameters were used to represent the shear strength of the embankment and foundation materials. The foundation soil is represented using total stress shear strength parameters because the soft foundation soil material is assumed to behave in an undrained condition. Therefore, the angle of internal friction, φ, is assumed to be zero and the cohesion is assumed to equal the undrained shear strength, su, because the foundation soil is assumed to consist of soft and saturated cohesive soil. At most EPS-block geofoam sites, the phreatic surface is located at or near the ground surface and the foundation soil is saturated. The shear strength and unit weight values for the cover soil on the side slopes of the embankment are also shown in Table 5.2 and it can be seen that the soil cover is modeled using an effective stress friction angle of 28 degrees because it is anticipated that the soil cover will not be saturated at all times nor loaded rapidly and thus it will not experience an undrained failure.

5- 36 Selection of the shear strength parameters for the EPS-block geofoam within the embankment revealed some uncertainties in the modeling of geofoam in slope stability analyses. The lack of field case histories that illustrate the actual failure mode of the geofoam during an external slope stability failure resulted in uncertainty in whether during such a failure sliding occurs between the EPS blocks or through the EPS blocks. If sliding occurs between the EPS blocks, the applicable shear strength is the EPS/EPS interface friction angle of 30 degrees reported in Chapter 2. If failure occurs through the EPS bocks, the applicable shear strength is the strength of an individual block. The lack of field guidance as to whether sliding occurs between the EPS blocks or through the EPS blocks prompted an analysis to determine which shear strength produced the desired failure through the foundation soil. Because the external stability analyses focus on the soft, saturated foundation soil versus the internal stability analyses in Chapter 6 that focus on the EPS-block geofoam embankment, it was anticipated that circular failure surfaces through the foundation soil is the appropriate failure mode for the external stability analyses. As a result, the geofoam shear strength parameters that yielded the best approximation of failure through the foundation soil were selected. Considerable stability analyses were conducted to investigate how to represent the geofoam embankment to yield failure through the foundation soil. Some of the scenarios considered involve conservatively modeling the geofoam embankment with a friction angle of one degree and a cohesion of zero so the Table 5.2. Input parameters for external slope stability analysis with XSTABL. embankment did not contribute significantly to the factor of safety because of the uncertainties in estimating how much shear resistance the geofoam actually contributes in the field. Although this scenario is commonly used in practice, this scenario resulted in the critical failure surface being located in the embankment and not the foundation soil because of the small shear strength assigned to the geofoam. As a result, this approach was not accepted because it did not result in failure through the foundation soil. Another scenario was to apply a surcharge to the surface of the foundation soil that approximates the weight of the embankment and the pavement and traffic

5- 37 surcharges so the strength of the geofoam did not have to be considered. This approach was not selected because it could not be used for seismic stability analyses because the seismic force is applied at the center of gravity of the slide mass (see following section of this chapter) and if only a surcharge is used a seismic force cannot be applied. The third scenario involved assuming failure occurred between the EPS blocks, and thus sliding occurring along EPS/EPS interfaces, and using an interface friction angle of 30 degrees. This approach also resulted in the critical failure surface occurring through the embankment and not the foundation soil because the shear resistance provided by the geofoam even with a friction angle of 30 degrees is small. The shear resistance is small because the normal stress, σn, applied to any failure surface passing through the embankment is low because of the low unit weight of the geofoam and the failure surface is nearly vertical through the geofoam, which results in the normal stress on the failure surface being similar to the horizontal earth pressure of the geofoam. The horizontal earth pressure is low, which is one of the reasons geofoam is used for bridge abutments and vertical embankments, and results in a low normal stress being applied to the failure surface. If the normal stress on the failure surface is low, the shear resistance, τ, is low because of the following expression: nτ = c + σ tan φ (5.50) It can be seen that the shear resistance is directly related to the normal stress and thus a low normal stress results in a small shear resistance. The shear resistance is further impacted because the normal stress is multiplied by the tangent of the friction angle. As a result, the impact of a high friction angle is reduced because the tangent of the friction angle is used to estimate the shear resistance. In summary, modeling the geofoam using a friction angle did not result in the critical failure surfaces being located in the foundation soil so a scenario in which the geofoam was modeled using a cohesion value was sought so the strength would be independent of the normal stress and result in failure through the foundation soil. A friction angle of 30 degrees can

5- 38 be used to model the geofoam in the internal stability analyses in Chapter 6 because failure is assumed to occur between the EPS blocks and thus the EPS/EPS interface strength is applicable. The scenario used to model the geofoam strength for external slope stability analyses assumes that failure occurs through the EPS blocks and thus a cohesion value that adequately represents the shear strength of a geofoam block was sought. From Figure 2.15 and an EPS density of 20 kg/m3 (1.25 lbf/ft3) the internal shear strength of an individual block of geofoam is 145.1 kPa (3,030 lbs/ft²). This shear strength can be represented using a Mohr-Coulomb friction angle of zero and a cohesion value of 145.1 kPa (3,030 lbs/ft²). The geofoam is not continuous and thus the effect of joints or discontinuities between the blocks had to be considered to estimate a global shear strength of the EPS embankment. Based on typical block layouts observed in the case histories studied herein (see Chapter 11), it was estimated that a failure surface passing through the embankment would consist of 25 percent shearing through intact EPS blocks and 75 percent shearing through joints between the blocks. Therefore, the representative cohesion value for the global shear strength of the geofoam is estimated to be one-quarter of the compressive strength of the geofoam, i.e., 145.1 kPa (3,030 lbs/ft²), or 36.3 kPa (758 lbs/ft²) as shown in Table 5.2. The representative cohesion value needs to be corrected for the strain incompatibility between the soft foundation soil and the EPS-block geofoam and thus the potential for progressive failure of the embankment. Figure 5.12 shows a schematic of the stress-strain relationships for the geofoam and foundation soil and it can be seen that the failure through the geofoam results in a brittle failure and a post-peak strength loss at a small strain while the foundation soil exhibits a plastic failure and a peak shear strength at a large strain. Therefore, if the strains mobilized in the embankment and foundation are equal, failure would occur through the geofoam when only a fraction of the foundation strength had been mobilized. Conversely, after the peak strength of the foundation soil had been mobilized, the strength of the geofoam would correspond to a post-peak value. Thus, the peak strength of the geofoam should not be

5- 39 used in conjunction with the peak strength of the foundation soil in order to prevent progressive failure of the embankment. Progressive failure can occur when one material fails, e.g., the geofoam, and the stresses that were being resisted by that material are transferred to the another material, e.g., the foundation soil, which can result in overstressing of this material especially if it does not mobilize its peak strength at the same strain as the failed material. Therefore, the main geofoam issue is the determination of the shear strength of the geofoam and foundation soil that can be relied on because the stress-strain behavior for these two materials are not compatible. Figure 5.12. Typical stress-strain behaviors of geofoam and soft foundation soil (36). Chirapuntu and Duncan (36) used nonlinear finite element analyses to develop shear strength reduction factors for a compacted soil embankment overlying a soft clay foundation. The reduction factor for a compacted soil embankment is presented in Chirapuntu and Duncan (36) in graphical form but was converted to the following equation herein: E E F SR 0.89 0.089 S  = −    (5.51) where RE = embankment strength reduction factor SE = average embankment shear strength, kN/m2 SF = average foundation soil shear strength, kN/m2 For a geofoam embankment, the strength of the geofoam is reduced to account for the strain incompatibility with the foundation soil while the peak strength of the foundation soil is used. The value of embankment strength used in this expression is assumed to be as 36.3 kPa (758 lbs/ft²) as discussed earlier and shown in Table 5.2. The ratio of the embankment strength to the foundation strength was calculated for the various values of undrained shear strength used to model the foundation soil. After determining this ratio, the embankment strength reduction factor was estimated from the above expression. Typical values of RE for values of foundation soil undrained shear strength are shown in Table 5.3 and it can be seen that RE ranges from 0.62 to 0.82.

5- 40 Therefore, consideration of strain incompatibility results in a reduction of the cohesion value used to represent the shear strength of the geofoam of approximately 20 to 40 percent. The value of cohesion shown in Table 5.2 was reduced by the appropriate reduction factor and the resulting value was used in the external slope stability analyses to model the geofoam. Table 5.3. Typical reduction factors for geofoam to account for strain incompatibility. Location of Critical Static Failure Surface The first step in the external slope stability analyses was to locate the critical static failure surface in the foundation soil. Because the analysis involves soft, saturated foundation soil, only circular failure surfaces were analyzed in the external stability analysis. Figure 5.13 presents a cross-section through a 12.2 m (40 ft) high EPS embankment with side-slopes of 2H:1V and a road width of 34 m (112 ft). The behavior of the critical static failure surface depicted in this figure is typical of the other geometries considered and is used to illustrate the effect of the foundation soil shear strength on the location of the critical failure surface. It can be seen that as the value of undrained shear strength increases, the depth of the critical failure surface decreases. In other words, as the value of su increases, it is more likely that the critical failure will remain in the geofoam embankment because the strength of the foundation soil is approaching the strength of the embankment. If the critical failure surface remained in the foundation soil it was termed an external failure mode while it was termed an internal failure if the critical surface remained in the embankment. It can be seen when the value of su reaches 36 kPa (752 lbs/ft2), the critical failure surface remains in the embankment. The focus of this section is external stability so the subsequent design charts and seismic stability analyses only utilize critical failure surfaces that remained completely in the foundation soil because seismic internal stability of the geofoam embankment is addressed in Chapter 6. It can also be seen that as the critical failure surface changes from the foundation soil to the embankment, the failure surface exits on the embankment slope and the failure surface through the geofoam is no longer near vertical.

5- 41 The transition from the critical failure surface remaining in the foundation soil versus remaining in the embankment can be used to identify the value of su for the foundation soil that corresponds to internal stability being more critical than external stability. For example, if the su value for the foundation soil at a particular site is equal to or greater than 36 kPa (752 lbs/ft2) and the embankment geometry corresponds to Figure 5.13, internal stability will control the design of the geofoam embankment. If the su value for the foundation soil at a particular site is less than 36 kPa, (752 lbs/ft2) external stability will control the design of the geofoam embankment. Therefore, the subsequent design charts for external slope stability terminate at the value of su that corresponds to the transition from the critical failure surface remaining in the foundation soil versus moving into the embankment. This results in a different relationship for each embankment geometry because the transition point is a function of embankment geometry and su of the foundation soil. The value of su at which each relationship terminates signifies the transition from external slope stability being critical to internal stability being critical. However, if internal stability is determined to be critical, a static internal slope stability analysis does not have to be performed to locate the critical failure surface because there is little or no static driving force applied to any of the three potential failure modes described in the internal seismic stability section in Chapter 6 and shown in Figure 6.2. The driving force is small because the horizontal portion of the internal failure surfaces is assumed to be completely horizontal. Therefore, if Figures 5.14 through 5.16 indicate that internal static stability controls, i.e., su of the foundation soil exceeds the value of su at which a relationship shown in the figure terminates, the factor of safety against a slope stability failure is expected to exceed 1.5. The fact that embankments with vertical sides can be constructed demonstrates this conclusion. Figure 5.13. Behavior of critical static failure surface of a trapezoidal embankment as a function of the undrained shear strength of the foundation soil.

5- 42 Design Charts The results of the stability analyses were used to develop the static external slope stability design charts in Figures 5.14 through 5.16 for a 2-lane (road width of 11 m (36 ft)), 4-lane (road width of 23 m (76 ft)), and 6-lane (road width of 34 m (112 ft)) roadway embankment, respectively. Figure 5.14 presents the results for a 2-lane geofoam embankment and the three graphs correspond to the three slope inclinations considered, i.e., 2H:1V, 3H:1V, and 4H:1V, for various values of su for the foundation soil. It can be seen that for a 2H:1V embankment the affect of geofoam thickness or height, TEPS, is small where as geofoam height is an important variable for a 4H:1V embankment. The geofoam height corresponds to only the height of the geofoam and thus the total height of the embankment is TEPS plus the thickness of the pavement system. In the graph for the 4H:1V embankment, it can be seen that each relationship terminates at a different su value for the foundation soil. The value of su at which each relationship terminates signifies the transition from external slope stability being critical to internal stability being critical. For example, for a geofoam height of 12.2 m (40 ft), external slope stability controls for su values less than approximately 40 kPa (825 lbs/ft²). Therefore, a design engineer can enter this figure with an average value of su for the foundation soil and determine whether external or internal stability controls the design. If internal stability is determined to be critical, a static internal slope stability analysis does not have to be performed as previously discussed because the factor of safety against internal slope stability failure is expected to exceed 1.5. If external stability controls, the designer can use this figure to estimate the critical static factor of safety for the embankment, which must exceed a value of 1.5. It can be seen from Figures 5.14 through 5.16 that the critical static factor of safety for the embankment for the 2-lane, 4-lane, and 6-lane roadway embankment, respectively, all exceed a value of 1.5 for values of su greater than or equal to 12 kPa (250 lbs/ft²). These results indicate that external static slope stability will be satisfied, i.e., factor of safety greater than 1.5, if the foundation undrained shear strength exceeds 12 kPa (250 lbs/ft²). If the undrained shear strength

5- 43 of the foundation soil exceeds the value that corresponds to the maximum value of the appropriate relationship in Figures 5.14 through 5.16, internal stability is more critical than external stability. In summary, external slope stability does not appear to be the controlling external failure mechanism, instead it appears that settlement will be the controlling external failure mechanism. However, Figures 5.14 through 5.16 can be used to quickly estimate the critical static factor of safety for 2-lane, 4-lane, and 6-lane roadway embankments, respectively, to facilitate the design process. Figures 5.14 through 5.16 can also be used to investigate the behavior of geofoam embankments. It can be seen for 4-lane and 6-lane roadway embankments, Figures 5.15 and 5.16, respectively, that the critical static factor of safety decrease as the embankment height increases. In addition, as the embankment height decreases the value of su that corresponds to the transition between external and internal stability being critical decreases. Therefore, a higher foundation soil shear strength will be required to support higher 4-lane and 6-lane geofoam embankments. The opposite of the behavior was observed for the 2-lane roadway embankment (Figure 5.14) because with a narrower roadway a smaller length of the failure surface is being subjected to the pavement and traffic surcharges and the greater embankment height results in a greater contribution of the cohesion value that is used to represent the shear strength of the geofoam. As a result, the critical static factor of safety increases as the embankment height increases instead of decreasing as in Figures 5.15 and 5.16. It can be seen from Figure 5.14 that the 12.2 m (40 ft) high embankment has a higher factor of safety than the 6.1 m (20 ft) and 3.1 m (10 ft) high embankments. In the 4-lane and 6-lane geofoam embankments the critical failure surface extends at or near the full width of the roadway (see Figure 5.13) and thus a larger portion of the failure surface is subjected to the pavement and traffic surcharges.

5- 44 Interpretation of External Slope Stability Design Chart Comparison of the factors of safety in Figures 5.14 through 5.16 also reveals that the critical case for external slope stability is a 6-lane embankment (34.1 m or 112 ft) with a 2H:1V slope and a height of EPS block equal to 12.2 m (40 ft) because this case yields factors of safety of 1.6 to 3.2 for the entire range of su values. This is important because the static stability controls the seismic external stability. The greater the static external stability the greater the seismic external stability. The results of the seismic stability analyses will be presented in the next section. Figures 5.14 through 5.16 can be used for the design of a geofoam embankment by entering the appropriate graph with a value of su, e.g., 15 kPa (315 lbs/ft²), EPS-block geofoam thickness or height, TEPS, of 12.2 m (40 ft), and a required slope inclination of 3H:1V and obtaining a critical static factor of safety of approximately 1.9 for a 6-lane roadway embankment (see Figure 5.16). Remedial Procedures The main remedy procedure that can be used to increase the factor of safety against external slope instability is to increase the undrained shear strength of the foundation soil by using a ground improvement method. A discussion on ground improvement is provided in Chapter 1. However, the external slope stability analyses indicate that settlement will control the design of a geofoam embankment and not external slope stability, which is in agreement with the lack of field case histories involving external slope instability. Figure 5.14. Static external slope stability design chart for trapezoidal embankments with a 2-lane roadway with a total road width of 11 m (36 ft). Figure 5.15. Static external slope stability design chart for a trapezoidal embankment with a 4-lane roadway with a total road width of 23 m (76 ft). Figure 5.16. Static external slope stability design chart for a trapezoidal embankment with a 6-lane roadway with a total road width of 34 m (112 ft).

5- 45 EXTERNAL SEISMIC STABILITY OF TRAPEZOIDAL EMBANKMENTS Introduction Seismic loading is a short-term event that must be considered in geotechnical problems including road embankments. Seismic loading can affect both external and internal stability of an embankment containing EPS-block geofoam. This section of Chapter 5 considers external seismic slope stability of EPS-block geofoam trapezoidal embankments or embankments with sloped sides while internal seismic stability is addressed in Chapter 6. A supplemental section of Chapter 5 considers external seismic slope stability of EPS block vertical embankments. Most of the considerations for static and seismic external stability analyses are the same for embankments constructed of geofoam or earth materials. These considerations include various SLS and ULS mechanisms such as seismic settlement and liquefaction that are primarily independent of the nature of the embankment material because they depend on the seismic risk at a particular site and the nature and thickness of the natural soil overlying the bedrock. A discussion of these topics can be found in (37). Mitigation of seismic induced subgrade problems by ground improvement techniques prior to embankment construction is beyond the scope of this study. However, a discussion on ground improvement to reduce potential seismic-induced subgrade problems can be found in (8,37-39). This section focuses on the effect of seismic forces on the external slope stability of EPS- block geofoam embankments. This issue is addressed using a pseudo-static slope-stability analysis (37) involving circular failure surfaces through the foundation soil. Terzaghi (40) developed the pseudo-static stability analysis to simulate earthquake loads on slopes and the analysis involves modeling the earthquake shaking with a horizontal force that acts permanently, not temporarily, and in one direction on the slope. Thus, the primary difference between a pseudo-static and static external stability analyses is that a horizontal force is permanently applied to the center of gravity of the critical slide mass and in the direction of the exposed slope. If a stability method is used that involves dividing the slide mass into vertical slices, the horizontal

5- 46 force is applied to the center of gravity of each vertical slice that simulates the inertial forces generated by horizontal shaking. This horizontal force (F) equals the slide mass or the mass of the vertical slide (m) multiplied by the seismic acceleration (a), i.e., F=m*a. The seismic acceleration is usually derived by multiplying a seismic coefficient, k, by gravity. The pseudo-static horizontal force must be applied to the slide mass that is delineated by the critical static failure surface. Therefore, the steps in a pseudo-static analysis are: 1. Locate the critical static failure surface, i.e., the static failure surface with the lowest factor of safety, that passes through the foundation soil, i.e., external failure mechanism, using a slope stability method that satisfies all conditions of equilibrium, e.g., Spencer’s (34) stability method. This value of factor of safety should satisfy the required value of static factor of safety of 1.5 before initiating the pseudo-static analysis. 2. Modify the static shear strength values for cohesive or liquefiable soils situated along the critical static failure surface to reflect a strength loss due to earthquake shaking, which is discussed subsequently. 3. Determine the appropriate value of horizontal seismic coefficient (discussed subsequently) that will be multiplied by gravity to determine the horizontal seismic acceleration and applied to the center of gravity of the critical static failure surface. A search for a new critical failure surface should not be conducted with a seismic force applied because the search may and usually does not converge. The search may not converge because a failure surface that delineates a larger slide mass will result in a larger seismic force being applied to the slope and usually a lower factor of safety. It is reasonable to simply apply the horizontal seismic force to the critical static failure because if an earthquake occurs, the most vulnerable failure surface is the critical static failure surface.

5- 47 4. Calculate the pseudo-static factor of safety, FS’, for the critical static failure surface and ensure it meets the required value. In (41) it is indicated that for transient loads, such as earthquakes, safety factors as low as 1.2 or 1.15 may be tolerated. It is indicated in (42) that in southern California, a minimum factor of safety of 1.1 to 1.15 is considered acceptable for a pseudo-static slope stability analysis. A factor of safety between 1.0 and 1.2 is indicated in (37). The safety of factor required will most likely vary from state to state. Therefore, local Departments of Transporation factor of safety requirements for seismic stability should be used. The seismic design charts included in this report are based on a factor of safety of 1.2. A factor of safety of 1.2 was used for seismic stability to keep the factor of safety uniform for all temporary loading conditions, which includes design for hydrostatic uplift and translation (sliding). Seismic Shear Strength Parameters The static shear strength parameters should not be changed for a pseudo-static stability analysis unless a cohesive soil or liquefiable soil is involved. If a cohesive soil is located along the critical static failure surface, the peak shear strength of this material can be reduced by as much as 20 percent of the static peak undrained shear strength by seismic loading (43). As a result, in (43), the use of an undrained shear strength for a cohesive soil that is 80 percent or more of the static peak undrained shear strength is recommended. Thus, the value of su used to represent the foundation soil under the geofoam embankment should be reduced by not more than 20 percent. If a cohesionless soil is situated along the critical failure surface and is predicted to liquefy due to the earthquake shaking, this material should be assigned a liquefied shear strength as proposed in (44). Based on the geofoam interface strength testing described in Chapter 2, the value of static EPS shear strength shown in Table 5.2 can be used for the pseudo-static analyses. This conclusion is also supported by the results of shake table tests on geosynthetic interfaces (45) that showed the seismic interface strength of geosynthetic interfaces exceeds the static

5- 48 interface strength. However, this value of shear strength should be reduced for strain incompatibility with the foundation soil as was described for the external slope stability analyses. Horizontal Seismic Coefficient The horizontal seismic coefficient, kh,, at the center of gravity of the slide mass is estimated using the seismic acceleration at the base (subgrade level) and top of the embankment and linearly interpolating between these two values to obtain kh, at the center of gravity. This analysis approach is based on the assumption that the horizontal acceleration within the embankment can be assumed to vary linearly between the base and top of the embankment values. At any level within the embankment, the interpolated value of horizontal acceleration can be divided by gravity to determine the horizontal seismic coefficient which can be inputted into slope stability software to conduct a pseudo-static analysis. If a circular failure surface is used for the static stability analysis, the center of gravity of the sliding mass is usually located near the center or mid-height of the sliding mass. This location can be used in the linear interpolation process to estimate the seismic acceleration, and thus seismic coefficient, at the center of gravity of the critical static slide mass. One difficulty with this process is that estimating the seismic acceleration at the base and top of the geofoam embankment is difficult because a geofoam embankment is not rigid. The base acceleration must be estimated first and then this acceleration is transferred from the base to the top of the embankment to estimate the acceleration at the embankment crest. Because this project is focused on geofoam embankments, most, if not all, of the embankments will not be founded on bedrock. Therefore, the bedrock horizontal acceleration must be transmitted from the underlying bedrock through the overlying soil deposit at the base of the geofoam embankment. The base acceleration can be estimated from the bedrock acceleration in two primary ways: (1) conducting a one-dimensional site response analysis in which a representative earthquake record is inserted at the bedrock elevation and propagated vertically through the overlying soil to estimate the acceleration at the base of the geofoam embankment or (2) using empirical

5- 49 relationships that relate the bedrock acceleration to the ground surface acceleration for different soil types. If a one-dimensional site response analysis is conducted using a program such as SHAKE (46), the acceleration at the base and top of the embankment can be calculated and the horizontal seismic coefficient at the center of gravity of the slide mass can be estimated using the following expression presented in (47): h h τ *gk = γ*z' (5-52) where: z’ = depth from the top of the geofoam embankment at which the seismic coefficient is to be estimated γ = average unit weight of the material above depth z g = gravity, and τh = horizontal shear stress at depth z calculated by a one-dimensional site response analysis. The main issues encountered in conducting a site response analysis are determining representative earthquake records to propagate though the soil deposit overlying the bedrock and the seismic properties of the soil layers comprising the soil deposit. An extensive discussion of one-dimensional site response analyses for man-made embankments is presented by (48). If a site response analysis is conducted, the values of initial tangent Young’s modulus, Poisson’s ratio, and shear modulus indicated in Table 5.4 can be assumed for the EPS-block geofoam. Any portion of the EPS blocks that is permanently submerged under normal ground water conditions is assumed to have a total unit weight of 1,000 N/m³ (6.37 lbf/ft³), not the dry unit weight value of 200 N/m³ (1.25 lbf/ft³) suggested for general gravity stress calculations, to conservatively allow for long-term water absorption in the geofoam. Table 5.4. Seismic Material Properties for EPS-Block Geofoam for Site Response Analyses.

5- 50 Additional discussion of one-dimensional site response analyses for geofoam embankments is beyond the scope of this project. Thus, the use of existing empirical relationships for estimating the base acceleration from the bedrock acceleration is discussed in detail. Empirical site response relationships, developed using one-dimensional site response analyses and field observations, are typically used to estimate the ground surface acceleration. However, on large projects it may be prudent to conduct a site-specific response analyses to accurately estimate the acceleration at the ground surface and top of the embankment accelerations. Figure 5.17 presents relationships between bedrock acceleration and ground surface acceleration, i.e., acceleration at the base of the embankment, for various soil types. To utilize this chart, the peak horizontal bedrock acceleration needs to be estimated from local information or from seismic hazard maps prepared by the U.S. Geological Survey (USGS) (49). The USGS maps presents contours of peak horizontal bedrock acceleration for various probabilities of exceedance and return periods. For example, the maps corresponding to a probability of exceedance of 10 percent in 50 years is frequently used for civil engineering design purposes and can be used to estimate the bedrock peak horizontal acceleration for a particular location in the United States. This bedrock acceleration and Figure 5.17 can be used to estimate the ground surface acceleration, which can be assumed to be equal to the acceleration at the base of the geofoam embankment. This assumption appears valid for geofoam embankments because the normal stress applied to the subsurface soils by a geofoam embankment is small and thus probably has little, if any, effect on the response of the subsurface soils. This may not be a valid assumption for soil embankments because the applied normal stress can be significant. One important note concerning the relationships in Figure 5.17 is that the figure should not be used for soft soil sites such as soft clays or peats. Field observations of site response since publication of the site response relationships in Figure 5.17 has shown that soft soil sites can amplify the bedrock acceleration, especially at bedrock accelerations less than 0.4g. Thus, if the majority of the subsurface soils with depth at the EPS-block geofoam embankment site are

5- 51 characterized as a soft clay or peat, the site response relationship in Figure 5.18 should be used to estimate the ground surface acceleration from the bedrock acceleration. It can be seen that the median relationship at bedrock accelerations less than 0.4g predicts ground surface accelerations that are greater than the bedrock accelerations with a maximum amplification factor of approximately two. This amplification of the bedrock acceleration at soft soil sites has been verified by case histories such as the 1985 Mexico City and 1989 Loma Prieta earthquakes (see Figure 5.18). For example, in the 1985 Mexico City earthquake the ground surface acceleration was 1.5 to 2 times greater than the bedrock acceleration (see Figure 5.18). It has been postulated that this amplification contributed to the significant damage caused by the earthquake (50). For comparison with geofoam project sites, Mexico City is located on 100 to 200 feet thick soft clay deposits that fill an old lakebed (50). Figure 5.17. Relationship between bedrock and ground surface horizontal acceleration for various soil types (51). Figure 5.18. Relationship between bedrock and ground surface horizontal acceleration for soft soil sites (52). After estimating the base acceleration, the acceleration at the top of the embankment must be estimated so the acceleration at the center of gravity of the slide mass be estimated from linearly interpolating the accelerations at the base and top of the embankment. If the geofoam embankment was rigid the acceleration at the top would equal the acceleration at the base of the embankment. Japanese research (53) demonstrates that the seismic response of a geofoam embankment is not rigid but flexible. Therefore, the acceleration at the top generally will not equal the base acceleration. The acceleration at the top of the embankment could be greater or less than the base acceleration depending on the response of the embankment. However, it is anticipated that the top acceleration will be less than the base acceleration because of the potential for shear deformation to occur between geofoam blocks as the seismic shear waves propagate

5- 52 vertically through the embankment. Amplification has been observed in soil embankments (37) but no published accounts of amplification in EPS-block geofoam embankments were located during this study. The acceleration at the top of a geofoam embankment will primarily affect the factor of safety against lateral sliding of the pavement system on the top of the EPS mass. As with the base acceleration, there are two primary ways for estimating the acceleration at the top of the geofoam embankment: (1) conducting a one-dimensional site response analysis that models the foundation soils as well as the geofoam embankment and thus directly calculating the acceleration at the top of the embankment and at the center of gravity or (2) using empirical relationships to relate the base acceleration to the top acceleration. As mentioned previously, empirical site response relationships are frequently used to estimate the ground surface acceleration and it is proposed herein that they be used to estimate the top acceleration. On large projects it may be prudent to conduct a site-specific response analyses that models the geofoam embankment to accurately estimate acceleration at the center of gravity of the slide mass. To utilize empirical site response relationships, it must be determined what soil type should be used to approximate the geofoam. It is proposed herein that the geofoam be assumed to behave as the deep cohesionless soil depicted in Figure 5.17. The deep cohesionless soil behavior was chosen because the geofoam embankment will probably not behave as rock or a stiff soil because of the slippage that can occur between blocks. This slippage will result in some dissipation of shear stress as the seismic waves propagate through the embankment. The deep cohesionless soil relationship will yield accelerations at the top of embankment that are less than the base accelerations because the relationship does not indicate amplification (see Figure 5.17). A deep cohesionless soil was also selected because the shear resistance is frictional which is in agreement with the frictional nature of the EPS/EPS interface strengths reported in Chapter 2. It was also decided that modeling the geofoam embankment as a soft soil, and thus assuming amplification, probably would be too conservative. Finally, the stiff clay and sand relationship

5- 53 was disregarded because of the potential for slippage between the blocks and the deep cohesionless soil relationship provides a more conservative design. In summary, Figure 5.17 can be used with the base acceleration to estimate the acceleration at the top of the embankment and linear interpolation can be used to estimate the acceleration, and thus horizontal seismic coefficient, at the center of gravity of the critical static slide mass. The base acceleration should be used on the horizontal axis in Figure 5.17 and the acceleration at the top of the embankment should be estimated from the vertical axis using the deep cohesionless soil relationship. Seismic Stability Analysis Procedure Pseudo-static slope stability analyses were conducted on the range of embankment geometries used in the external static stability analyses to investigate the effect of various embankment heights (3.1 m (10 ft) to 12.2 m (40 ft)), slope inclinations (2H:1V, 3H:1V, and 4H:1V), and road widths of 11, 23, and 34 m (36, 76, and 112 ft) on external seismic slope stability. The results of these analyses were used to develop design charts to facilitate seismic design of roadway embankments that utilize geofoam. The seismic analyses utilized the critical static failure surfaces identified for each geometry in the external static stability analyses. A pseudo-static analysis was conducted on only the critical failure surfaces that passed through the foundation soil because external stability is being evaluated. As a result, the design charts for seismic stability terminate at the su value for the foundation soil that corresponds to the transition from a critical failure surface in the foundation soil to the geofoam embankment determined during external static stability analysis. This resulted in the seismic stability design charts terminating at the same value of su as the static stability charts in Figures 5.14 through 5.16. A typical cross-section through an EPS embankment with side-slopes of 2H:1V used in the pseudo-static stability analyses is shown in Figure 5.19. This cross-section differs from the cross-section used for the static analyses in Figure 5.11 because the surcharge used to represent the pavement and traffic surcharges is replaced by assigning the soil cover layer on top of the

5- 54 embankment a unit weight of 71.8 kN/m3 (460 lbf/ft³). The soil cover is 0.46 m (1.5 ft) thick so the stress applied by this soil cover equals 0.46 m times the increased unit weight or 33.0 kPa (690 lbs/ft²). A stress of 33.0 kPa (690 lbs/ft²) corresponds to the sum of the design values of pavement surcharge (21.5 kPa (450 lbs/ft²)) and traffic surcharge (11.5 kPa (240 lbs/ft²)) used previously for external bearing capacity and slope stability. The surcharge in Figure 5.11 had to be replaced because a seismic coefficient is not applied to a surcharge in limit equilibrium stability analyses only material layers because the horizontal force that represents the seismic loading must be applied at the center of gravity of the material layer. Figure 5.20 illustrates the location and magnitude of the pseudo-static forces used to represent earthquake loading for a particular value of horizontal seismic coefficient. The length of the horizontal arrows corresponds to the relative magnitude of the horizontal force for a given horizontal seismic coefficient. It can be seen that the pavement and traffic surcharges yields the largest horizontal force because the weight of the soil layer used to model the surcharge results in the largest weight. The soil cover and EPS exhibit a small weight and thus the horizontal seismic Figure 5.19. Typical cross-section used in seismic external slope stability analyses of trapezoidal embankments. Figure 5.20. Typical cross-section showing location and relative magnitude of pseudo-static forces used to represent an earthquake loading in a trapezoidal embankment. force is small for both materials. The weight is small for these materials because the thickness of the soil cover is small and the unit weight of the EPS is small, respectively. The foundation soil also contributes a significant horizontal seismic force because of the unit weight of the material. Design Charts The results of the stability analyses were used to develop the seismic external slope stability design charts for a 2-lane (road width of 11 m (36 ft)), 4-lane (road width of 23 m (76 ft)), and 6-lane (road width of 34 m (112 ft)) roadway embankment. Three seismic coefficients, low (0.05), medium (0.10), and high (0.20), were used for each roadway embankment. Values of

5- 55 seismic coefficient greater 0.20 indicate a severe seismic environment and a site-specific seismic analysis, including a site response analysis, should be conducted instead of using simplified design charts. The pseudo-static factor of safety for the critical static failure surfaces previously identified using the Simplified Janbu stability method was calculated for each geometry considered for the development of the design charts. The factor of safety was calculated using Spencer’s slope stability method (34) as coded in the microcomputer program XSTABL Version 5 (32) because it satisfies all conditions of equilibrium. The analyses were conducted without reducing the shear strength of the foundation soil 80 percent as discussed above because the design charts present the pseudo-static factor of safety for the critical versus undrained shear strength (see Figure 5.21) and a design engineer can utilize these charts with an su value that reflects any strength loss that might occur during earthquake shaking. Figures 5.21 through 5.23 present the seismic external stability results for a 2-lane geofoam roadway embankment with a total road width of 11 m (36 ft) and the three values of horizontal seismic coefficient, i.e., 0.05, 0.10, and 0.20, respectively. Comparison of these figures results in the following conclusions about the seismic performance of a 2-lane geofoam embankment: (1) Seismic stability is not a concern for a horizontal seismic coefficient less than or equal to 0.05 because all of the computed values of factor of safety exceed the required value of 1.2 (see Figure 5.21). (2) A horizontal seismic coefficient of 0.10 results in values of FS’ that do not satisfy the required value of 1.2 for embankment inclinations of 3H:1V and 4H:1V (see Figure 5.22). The flatter embankments are more critical than the 2H:1V embankment because the weight of the materials above the critical static failure surface is greater which results in a greater seismic force being applied in the 3H:1V and 4H:1V embankments versus the 2H:1V embankment.

5- 56 (3) A horizontal seismic coefficient of 0.20 results in values of FS’ that do not satisfy the required value of 1.2 for all embankment inclinations (see Figure 5.23). Again the flatter embankments are more critical and thus a higher undrained shear strength will be required to satisfy the required factor of safety of 1.2 especially for the 4H:1V embankment. Figure 5.21. Seismic external slope stability design chart for trapezoidal embankments with a 2-lane roadway with a total road width of 11 m (36 ft) and a kh of 0.05. Figure 5.22. Seismic external slope stability design chart for trapezoidal embankments with a 2-lane roadway with a total road width of 11 m (36 ft) and a kh of 0.10. Figure 5.23. Seismic external slope stability design chart for trapezoidal embankments with a 2-lane roadway with a total road width of 11 m (36 ft) and a kh of 0.20. Figures 5.24 through 5.26 present the seismic external stability results for a 4-lane geofoam roadway embankment with a total road width of 23 m (76 ft) and the three values of horizontal seismic coefficient, i.e., 0.05, 0.10, and 0.20, respectively. Comparison of these figures results in the following conclusions about the seismic performance of a 4-lane geofoam embankment: (1) Seismic stability is a concern even for a horizontal seismic coefficient less than or equal to 0.05 because some of the computed values of factor of safety do not satisfy the required value of 1.2 (see Figure 5.24) at the lowest value of undrained shear strength (12.0 kPa or 250 lbs/ft²). The reason for the decreased seismic stability from the 2-lane geofoam embankment is the wider roadway results in a larger critical slide mass and thus a larger weight above the critical failure surface. The larger the weight of the slide mass above the critical static failure surface the greater seismic force being applied in the analysis. (2) The increased roadway width results in large values of undrained shear strength being required for the foundation soil to achieve the required value of pseudo-static

5- 57 factor of safety of 1.2. It can been seen in Figure 5.26 that an su of at least 36 kPa (750 lbs/ft²) will be required for a 4H:1V embankment and a horizontal seismic coefficient of 0.20. Figure 5.24. Seismic external slope stability design chart for trapezoidal embankments with a 4-lane roadway with a total road width of 23 m (76 ft) and a kh of 0.05. Figure 5.25. Seismic external slope stability design chart for trapezoidal embankments with a 4-lane roadway with a total road width of 23 m (76 ft) and a kh of 0.10. Figure 5.26. Seismic external slope stability design chart for trapezoidal embankments with a 4-lane roadway with a total road width of 23 m (76 ft) and a kh of 0.20. Figures 5.27 through 5.29 present the seismic external stability results for a 6-lane geofoam roadway embankment with a total road width of 34 m (112 ft) and the three values of horizontal seismic coefficient, i.e., 0.05, 0.10, and 0.20, respectively. The 6-lane roadway results in the most critical seismic stability condition because the widest roadway results in the largest critical slide mass and thus the largest horizontal seismic force. This results in seismic stability concerns for the smallest horizontal seismic coefficient (see Figure 5.27), the shortest embankment height of 3.1 m (10 feet) (see Figure 5.28), and the flattest slope inclination of 4H:1V (see Figure 5.29). Figure 5.27. Seismic external slope stability design chart for trapezoidal embankments with a 6-lane roadway with a total road width of 34 m (112 ft) and a kh of 0.05. Figure 5.28. Seismic external slope stability design chart for trapezoidal embankments with a 6-lane roadway with a total road width of 34 m (112 ft) and a kh of 0.10. Figure 5.29. Seismic external slope stability design chart for trapezoidal embankments with a 6-lane roadway with a total road width of 34 m (112 ft) and a kh of 0.20. Interpretation of Seismic Slope Stability Design Chart Figures 5.21 through 5.29 can be used for the design of a geofoam embankment by entering the appropriate graph, which is determined by the horizontal seismic coefficient and

5- 58 slope inclination, using a value of su that reflects seismic loading and the thickness or height of EPS used in the embankment to obtain the pseudo-static factor of safety. For example, a 6-lane geofoam roadway embankment is proposed for a soft foundation soil that exhibits an undrained shear strength of 20 kPa (418 lbs/ft²). The height of EPS geofoam height is 6.1 m (20 ft) and the required slope inclination is 4H:1V. The critical pseudo-static factor of safety for this scenario with a horizontal seismic coefficient of 0.20 can be obtained from Figure 5.29 and is approximately 0.75 for a 6-lane roadway embankment. If the undrained shear strength of 20 kPa (418 lbs/ft²) is reduced by 80 percent to reflect strength loss during seismic loading as proposed in (43), the critical pseudo-static factor of safety Figure 5.29 is approximately 0.58. In summary, seismic external slope stability can control the design of a geofoam roadway embankment depending on the width, or number of roadway lanes, on the embankment and the magnitude of the horizontal seismic coefficient. Most of the geometries considered herein are safe for a horizontal seismic coefficient of less than or equal to 0.10. If the particular embankment is expected to experience a horizontal seismic coefficient greater than or equal to 0.20, seismic external slope stability could control the design of the embankment. Observations of EPS-block geofoam embankments after various earthquakes has revealed little or no series damage to the EPS embankments (6,54), which is in agreement with these findings. These observations include damage assessments after the 1993 Kushiro-Oki earthquake (Japan Meteorological Agency Intensity Scale (JMA)=5), 1993 Noto-Hanto-Oki earthquake (JMA=5), and 1995 Hyogo-Ken Nanbu earthquake (JMA= 7). Damage assessments made on nine EPS embankments after the 1995 Hyogo-Ken Nanbu earthquake, also known as the Kobe earthquake, revealed little or no damage except for one embankment which settled about 10 cm (3.9 in.) due to liquefaction of the embankment foundation soils. Remedial Procedures The main remedial procedure that can be used to increase the factor of safety against external seismic instability is to increase the undrained shear strength of the foundation soil by

5- 59 using a ground improvement method. A discussion on ground improvement is provided in Chapter 1. EXTERNAL SLOPE STABILITY OF VERTICAL EMBANKMENTS Introduction As shown by Figure 3.4 (b), an embankment with vertical side walls, sometimes referred to as a geofoam wall, can be constructed with EPS-block geofoam. The use of a vertical embankment minimizes the amount of right-of-way needed and the impact of embankment loads on nearby structures, which is an important advantage over other lightweight fills. This section presents an evaluation of external slope stability as a potential failure mode of EPS-block geofoam fill embankments with vertical walls. The general expression for the limit equilibrium factor of safety, FS, against a slope stability failure is given by Equation 5.49. As indicated by this equation, a slope stability failure occurs if the driving shear stresses equal or exceed the shear resistance of the material(s) along the failure surface. The driving shear stresses of an EPS-block geofoam vertical embankment are due to the weight of the EPS blocks and the overlying pavement and the traffic loads. The shear resistance is primarily attributed to the undrained shear strength of the foundation soil and/or EPS blocks. Typical Cross-Section The typical cross-section through an EPS vertical embankment with vertical walls used in the external static stability analyses is shown in Figure 5.30. This cross-section differs from the cross-section used for the static analyses of trapezoidal embankments in Figure 5.11 because the surcharge used to represent the pavement and traffic surcharges is replaced by placing a 0.61 m (2 ft) soil layer on top of the embankment with a unit weight of 54.1 kN/m3 (345 lbf/ft³). The soil layer is 0.61 m (2 ft) thick to represent the minimum recommended pavement section thickness discussed in Chapter 4. Therefore, the vertical stress applied by this soil layer equals 0.61 m (2 ft) times the increased unit weight of 54.1 kN/m3 (345 lbf/ft3) or 33.0 kPa (690 lbs/ft²). A vertical stress of 33.0 kPa (690 lbs/ft²) corresponds to the sum of the design values of pavement surcharge

5- 60 (21.5 kPa (450 lbs/ft²)) and traffic surcharge (11.5 kPa (240 lbs/ft²)) used previously for external bearing capacity and slope stability of trapezoidal embankments. Figure 5.30. Typical cross-section used in static and seismic external slope stability analyses of vertical embankments. The pavement and traffic surcharge in Figure 5.11 was replaced by an equivalent soil layer because a seismic slope stability analysis can only be performed with material layers and not surcharge loads as discussed in the next section. In a pseudo-static analysis a seismic coefficient cannot be applied to a surcharge in limit equilibrium stability analyses only material layers because the horizontal force that represents the seismic loading must be applied at the center of gravity of the material layer. The equivalent soil layer, which is equivalent to the pavement and traffic surcharge, was also used for the static stability analyses of embankments with vertical walls instead of a surcharge to minimize the number of stability analyses that would be required if two models were utilized, i.e., an embankment modeled with a surcharge and one modeled with a soil layer. A slight difference in the critical factor of safety value and the location of the critical failure surface may result between the two different models because surcharge forces exert an additional force at the top of each slice in the computer program XSTABL (32) while the force exerted by the weight of the soil layer is located at the center of each slice. In summary, the surcharge of the pavement system and traffic loads were modeled as a soil layer for both static and seismic slope stability analysis of embankments with vertical walls. Static Stability Analysis Procedure Static slope stability analyses were conducted on a range of embankment geometries to investigate the effect of various embankment heights (3.1 m (10 ft) to 12.2 m (40 ft)) and road widths of 11, 23, and 34 m (36, 76, and 112 feet) on external slope stability. The results of these analyses were used to develop design charts to facilitate design of roadway embankments that utilize geofoam. The static stability analysis of each geometry or cross-section was conducted in two-steps. This first step involved locating the critical static failure surface and the second step

5- 61 involved calculating the factor of safety for the critical static failure surface. The Simplified Janbu stability method (31) was used to locate the critical static failure surface because a rotational failure mode surface was assumed for the external stability analyses, versus a translational failure mode for the internal stability analyses. In addition, the microcomputer program XSTABL Version 5 (32) only allows searches for the critical failure surface using the Simplified Janbu method or Simplified Bishop (33) stability method. After locating the critical static failure surface using the Simplified Janbu stability method, the critical static factor of safety for this failure surface was calculated using Spencer’s (34) two-dimensional stability method because the method satisfies all conditions of equilibrium and provides the best estimate of the limit equilibrium factor of safety (35). Spencer’s method could not be used initially to locate the critical static failure surface because XSTABL only allows searches for the critical failure surface using the Simplified Janbu and Simplified Bishop stability methods. However, for the narrow and tall embankment with a width of 11 m (36 ft) and height of 12.2 m (40 ft), Spencer’s method yielded an unreasonable location of interslice forces. For these embankment geometries, the factor of safety value was determined using Bishop’s simplified method because Bishop’s simplified method provides similar values of factor of safety as Spencer’s method (35) for circular failure surfaces. Material Properties The same material input parameters, i.e., unit weight and shear strength, used in the external slope stability analyses of embankments with sloped sides, which are presented in Table 5.2, were used for external stability analysis of vertical embankments. However, since embankments with vertical walls do not have a soil cover on the side walls, the soil cover material parameters shown in Table 5.2 were not used. A friction angle of 0 degrees was used for the soil layer on top of the EPS-block geofoam that was used to model the pavement and traffic surcharges. The value of undrained shear strength for the EPS-block geofoam shown in Table 5.2 was reduced by the appropriate reduction factor shown in Table 5.3 to account for strain

5- 62 incompatibility as discussed previously in the sub-section entitled “Material Properties” and in the section entitled “External Slope Stability of Trapezoidal Embankments.” The phreatic surface was located at or near the ground surface and the foundation soil was assumed to be saturated as is typically the case at most EPS-block geofoam sites. Location of Critical Static Failure Surface The first step in the external slope stability analyses was to locate the critical static failure surface in the foundation soil. The critical failure surface is the failure surface that yields the lowest factor of safety for each foundation soil undrained shear strength investigated. Because the analysis involves soft, saturated foundation soil, only circular failure surfaces were analyzed in the external stability analysis. During the search for the critical circular failure surface, it was observed that the critical failure surface was located within the EPS-block geofoam for all foundation shear strengths analyzed. However, a critical failure surface within the EPS blocks is not representative of actual field conditions because stress distribution through the EPS blocks from the pavement and traffic loads is not considered. Additionally, analysis of a failure surface within only the EPS blocks should not be performed with the reduced shear strength values because strain incompatibility between the EPS blocks and the foundation soil is not an issue. Additionally, if internal stability is determined to be critical, a static internal slope stability analysis does not have to be performed to locate the critical failure surface because there is little or no static driving force applied to any of the three potential internal stability failure modes shown in Figure 6.7. The driving force is small because the horizontal portion of the internal failure surfaces is assumed to be completely horizontal along the surface of a row of blocks. The fact that embankments with vertical sides can be constructed demonstrates this conclusion. The focus of this section is external stability so the subsequent design charts and seismic stability analyses only utilize critical failure surfaces that remain completely in the foundation soil because seismic internal stability of the geofoam embankment is addressed in Chapter 6. Therefore, the

5- 63 search for the critical failure surface was limited to critical failure surfaces that extend into the foundation soil. Figure 5.31(a) and 5.31(b) presents a cross-section through a 12.2 m (40 ft) high EPS embankment with a road width of 11 m (36 ft) and 34 m (112 ft), respectively. For the 11 m (36 ft) wide embankment, as the undrained shear strength (su) of the foundation soil decreases, the critical failure surface extends further out from the toe of the embankment and terminates near the top outer edge of the embankment as shown in Figure 5.31(a). For the 34 m (112 ft) wide embankment, the su of the foundation soil does not have a significant impact on the location of the failure surface except at an su of 48 kPa (1,000 lbs/ft3) where the failure surface extends further out from the toe of the embankment. The behavior of the critical static failure surface depicted in Figure 5.31 is typical of the other geometries considered and is used to illustrate the effect of the foundation soil shear strength on the location of the critical failure surface within the foundation soil. It can be seen by comparing Figures 5.31(a) and 5.31(b) that no general conclusions can be made about the influence of foundation soil undrained shear strength on the location of the critical failure surface. As noted previously, the critical failure surface was located within the EPS-block geofoam for all foundation shear strengths analyzed. Thus, unlike the behavior of the critical static failure surface for trapezoidal embankments depicted in Figure 5.13, the transition from the critical failure surface remaining in the foundation soil versus remaining in the embankment cannot be used to identify the value of foundation su that corresponds to internal stability being more critical than external stability in embankments with vertical walls. Thus, a value of su cannot be identified at which the transition from external slope stability being critical to internal stability being critical occurs. Figure 5.32 presents cross-sections through a 12.2 m (40 ft) high EPS embankment with vertical walls for the three road widths investigated at an su of the foundation soil of 48 kPa (1,000 lbs/ft3). At embankment widths of 23 m (76 ft) and 34 m (112 ft), the factors of safety are

5- 64 similar and the failure surface originates near the toe of the embankment and terminates near the center of the embankment. At the smaller embankment width of 11 m (36 ft), the failure surface extends further out from the toe of the embankment and terminates near the top outer edge of the embankment. The narrower embankment width of 11 m (36 ft) also produces a higher factor of safety because the heavier foundation soil below the toe of the embankment provides more of the resisting load to the failure surface than the wider embankments for a given height. The failure surface extends further out because if the shape of the failure surface is assumed to be circular, the failure surface must extend further out for narrow and tall embankments to accommodate the circular failure surface. Additionally, a narrower embankment yields a smaller length of the failure surface that is subjected to the pavement and traffic driving stresses. (a) Road width = 11 m (36 ft) (b) Road width = 34 m (112 ft) Figure 5.31. Behavior of critical static failure surface of a vertical embankment as a function of the undrained shear strength of the foundation soil. Figure 5.32. Behavior of critical static failure surface of a vertical embankment as a function of the width of the embankment. Figure 5.33 presents a cross-section through an 11 m (36 ft) wide embankment with vertical walls for the three heights investigated at a foundation su of 48 kPa (1,000 lbs/ft3). Note that the factor of safety decreases when the embankment height is increased from 3.1m (10 ft) to 6.1 m (20 ft) but then increases when the embankment height is increased from 6.1 m (20 ft) to 12.2 m (40 ft). At embankment heights of 3.1 m (10 ft) and 6.1 m (20 ft), the failure surface originates near the toe of the embankment and terminates near the center of the embankment while for the taller embankment with a height of 12.2 m (40 ft), the failure surface extends further out from the toe of the embankment and terminates near the top outer edge of the embankment. Although a taller embankment results in a greater contribution of EPS undrained shear strength to the shear resistance along the failure surface, the factor of safety is less for an embankment height

5- 65 of 6.1 m (20 ft) than 3.1 m (10 ft) because the length of the failure surface within the embankment is larger for the higher embankment and thus a larger percentage of the failure surface is subjected to the pavement and traffic loads. However, the taller embankment height of 12.2 m (40 ft) produces a higher factor of safety because the failure surface extends further out from the toe of the embankment and, consequently, the heavier foundation soil below the toe of the embankment provides more resisting force to the failure surface than the shorter embankments for a given width. The failure surface extends further out because if the failure surface is assumed to be circular, the failure surface must extend out for narrow and tall embankments to accommodate the circular failure surface. In summary, no general conclusions can be made about the influence of foundation undrained shear strength on the location of the critical static failure surface because there is little affect of s u on failure surface location. Unlike the behavior of the critical static failure surface for trapezoidal embankments, a value of su cannot be identified for vertical embankments at which the transition from external stability being critical to internal stability being critical occurs. However, narrow and tall embankments with vertical walls will yield larger factors of safety because the failure surface will extend further out from the toe of the embankment and, consequently, the heavier foundation soil below the toe of the embankment provides more of the resisting load to the failure surface. The failure surface extends further out because if the failure surface is assumed to be circular, the failure surface must extend further out for narrow and tall embankments to accommodate the circular failure surface. Figure 5.33. Behavior of critical static failure surface of a vertical embankment as a function of the height of the embankment. Design Charts The results of the stability analyses were used to develop the static external slope stability design charts in Figures 5.34 and 5.35. Figure 5.34 presents the results for a 2-lane (road width of 11 m (36 ft)), 4-lane (road width of 23 m (76 ft)), and 6-lane (road width of 34 m (112 ft))

5- 66 roadway embankment, respectively, and the three graphs correspond to the three embankment heights considered, i.e., 3.1 m (10 ft), 6.1 m (20 ft), and 12.2 m (40 ft), for various values of foundation soil su. As shown in Figure 5.34 as the foundation su increases, the overall embankment slope stability factor of safety increases. It can be seen that for a 23 m (76 ft) and 34 m (112 ft) wide embankment, as the geofoam thickness or height, TEPS, increases for a given foundation su , the critical factor of safety decreases. The geofoam height corresponds to only the height of the geofoam and thus the total height of the embankment is TEPS plus the thickness of the pavement system. However, for the narrower embankment of 11 m (36 ft), the geofoam height of 12.2 m (40 ft) yielded a larger factor of safety than the shorter embankments of 3.1 m (10 ft) and 6.1 m (20 ft). As discussed in the previous section, narrow and tall embankments yield larger factors of safety because the failure surface will extend further out from the toe of the embankment and, consequently, the heavier foundation soil below the toe of the embankment provides more resisting force to the failure surface. The failure surface extends further out because if the failure is assumed to be circular, the failure surface must extend further out for narrow and tall embankments to accommodate the circular failure surface. Figure 5.34. Effect of embankment height on static external slope stability for vertical embankments and a road width of 11 m (36 ft), 23 m (76 ft), and 34 m (112 ft). Figure 5.35 presents the static external slope stability results for the three embankment widths considered, i.e., a 2-lane (road width of 11 m (36 ft)), 4-lane (road width of 23 m (76 ft)), and 6-lane (road width of 34 m (112 ft)), and various values of foundation su, for a given embankment height. Figure 5.35 shows that roadway width has little influence on the critical factor of safety for short embankments, e.g., at a height of 3.1 m (10 ft), but the influence of embankment width increases with increasing embankment height. This conclusion is supported by the observation made previously on the behavior of the critical static failure surface that narrow and tall embankments with vertical walls will yield larger factors of safety because the failure surface will extend further out from the toe of the embankment and, consequently, the

5- 67 heavier foundation soil below the toe of the embankment provides more of the resisting load to the failure surface. Figure 5.35. Effect of embankment width on static external slope stability for vertical embankments at heights of 3.1 m (10 ft), 6.1 m (20 ft), and 12.2 m (40 ft). The results of static external slope stability analyses performed for trapezoidal embankments, which are shown in Figures 5.14 through 5.16, show that as the slope inclination increases, the critical factor of safety decreases for each of the three embankment widths considered. A comparison between Figure 5.34 and Figures 5.14 through 5.16 also supports this observation because for a given embankment width, an embankment with vertical walls yields lower factors of safety values than an embankment with a 2H:1V side slope. It can be seen from Figures 5.34 and 5.35 that the critical static factors of safety for an embankment with vertical walls and with a width of 11 m (36 ft), 23 m (76 ft), and 34 m (112 ft) all exceed a value of 1.5 for su greater than or equal to 12 kPa (250 lbs/ft²). These results indicate that external static slope stability will be satisfied, i.e., factor of safety greater than 1.5, if the foundation undrained shear strength exceeds 12 kPa (250 lbs/ft²). In summary, external slope stability does not appear to be the controlling external failure mechanism of geofoam embankments with vertical walls, instead it appears that settlement will be the controlling external failure mechanism. However, Figures 5.34 or 5.35 can be used to quickly estimate the critical static factor of safety to facilitate the design process. Interpretation of External Slope Stability Design Charts Comparison of the factors of safety in Figures 5.34 and 5.35 also reveals that the critical case for external slope stability for vertical embankments and with widths of 23 m (76 ft) and 34 m (112 ft) is an embankment with a height of 12.2 m (40 ft) over a foundation soil with an su of less than 12 kPa (250 lbs/ft²). This case may yield factors of safety that are less than 1.5. For a vertical embankment with a narrow width of 11m (36 ft), the critical case for external slope stability is an embankment height of 6.1 m (20 ft) and a foundation su of less than 12 kPa (250

5- 68 lbs/ft²) because this case may yield factors of safety of less than 1.5. Knowledge of these critical cases is important because the static stability controls the seismic external stability. The greater the static external stability, the greater the seismic external stability. The results of the seismic stability analyses will be presented in the next section. Figure 5.34 can be used for the design of a geofoam embankment by entering the appropriate graph with a value of su, e.g., 36 kPa (750 lbs/ft²), geofoam height of 6.1 m (20 ft), and obtaining a critical static factor of safety of approximately 2.7 for a roadway embankment width of 34 m (112 ft) (see Figure 5.34). Remedial Procedures As with trapezoidal embankments, the main remedy procedure that can be used to increase the factor of safety against external slope instability of embankments with vertical walls is to increase the undrained shear strength of the foundation soil by using a ground improvement method. A discussion on ground improvement is provided in Chapter 1. However, the external slope stability analyses indicate that settlement will control the design of a vertical geofoam embankment and not external slope stability, which is in agreement with the lack of field case histories involving external slope instability. EXTERNAL SEISMIC STABILITY OF VERTICAL EMBANKMENTS Introduction This section focuses on the effect of seismic forces on the external slope stability of vertical EPS-block geofoam embankments. This analysis uses the same pseudo-static slope stability analysis used for external seismic stability of trapezoidal embankments and circular failure surfaces through the foundation soil. The pseudo-static stability analysis is used to simulate earthquake loads on slopes and involves modeling the earthquake shaking with a horizontal force that acts permanently, not temporarily, and in one direction on the slope. The pseudo-static horizontal force is applied to the slide mass that is delineated by the critical static failure surface.

5- 69 The same steps outlined in this chapter in the sub-sections entitled “Introduction,” “Seismic Shear Strength,” and “Horizontal Seismic Coefficient” of the section entitled “External Seismic Stability of Trapezoidal Embankments” are used in an external pseudo-static stability analysis of EPS-block geofoam vertical embankments. In seismic design of vertical embankments the following two analyses should be performed: 1) psuedo-static slope-stability analysis involving circular failure surfaces through the foundation soil, and 2) overturning of the entire embankment about one of the bottom corners of the embankment at the interface between the bottom of the assemblage of EPS blocks and the underlying foundation soil due to pseudo-static horizontal forces acting on the embankment especially for tall and narrow vertical embankments. Seismic Stability Analysis Procedure Pseudo-static slope stability analyses were conducted on the range of vertical embankment geometries used for the external static stability analyses to investigate the effect of various embankment heights (3.1 m (10 ft) to 12.2 m (40 ft)) and road widths of 11, 23, and 34 m (36, 76, and 112 ft) on external seismic slope stability. The results of these analyses were used to develop design charts to facilitate seismic design of vertical roadway embankments that utilize geofoam. The seismic analyses utilize the critical static failure surfaces identified for each geometry in the external static stability analyses. A pseudo-static analysis was conducted on only the critical failure surfaces that passed through the foundation soil because external stability is being evaluated. The same typical cross-section through an EPS embankment used in the static slope stability analysis of embankments with vertical walls was also used for the pseudo-static stability analyses and is shown in Figure 5.30. Figure 5.36 illustrates the location and magnitude of the pseudo-static forces used to represent earthquake loading for a particular value of horizontal seismic coefficient. The length of the horizontal arrows corresponds to the relative magnitude of the horizontal force for a given

5- 70 horizontal seismic coefficient. It can be seen that the pavement and traffic surcharges yield the largest horizontal force because the weight of the soil layer used to model the surcharge results in the largest weight. The EPS exhibits a small weight and thus the horizontal seismic force is small for the EPS blocks. The foundation soil also contributes a significant horizontal seismic force because of the unit weight of the material. Figure 5.36. Typical cross-section showing location and relative magnitude of pseudo-static forces used to represent an earthquake loading in a vertical embankment. Design Charts The results of the seismic stability analyses were used to develop the seismic external slope stability design charts for a 2-lane (road width of 11 m (36 ft)), 4-lane (road width of 23 m (76 ft)), and 6-lane (road width of 34 m (112 ft)) roadway embankment in Figures 5.37 to 5.39. Three seismic coefficients, low (0.05), medium (0.10), and high (0.20), were used for each roadway embankment. Values of seismic coefficient greater 0.20 indicate a severe seismic environment and a site-specific seismic analysis, including a site response analysis, should be conducted instead of using the enclosed simplified design charts. The pseudo-static factor of safety for the critical static failure surfaces previously identified using the Simplified Janbu stability method was calculated for each geometry considered to develop the design charts. The factor of safety was calculated using Spencer’s slope stability method (34) as coded in the microcomputer program XSTABL Version 5 (32) because it satisfies all conditions of equilibrium. However, for some of the narrow embankment widths with large heights such as at an embankment width of 11 m (36 ft) and height of 12.2 m (40 ft), Spencer’s method yielded an unreasonable location of interslice forces. For these narrow embankments, the factor of safety value was calculated using Bishop’s simplified method because for circular failure surfaces it provides similar factors of safety as Spencer’s method (35). Additionally, at a seismic coefficient of 0.2, Spencer’s (34) slope stability method did not

5- 71 converge for the vertical wall embankment geometries investigated and Bishop’s simplified method was also used for these cases. The seismic analyses were conducted without reducing the shear strength of the foundation soil to account for strain incompatibility or seismic loading as discussed in this chapter in the sub-section entitled “Material Properties” of the section entitled “External Slope Stability of Trapezoidal Embankments” because the design charts present the pseudo-static factor of safety for the critical versus undrained shear strength (see Figure 5.37) and a design engineer can utilize these charts with an su value that reflects any strength loss that might occur during earthquake shaking. Figures 5.37 through 5.39 present the seismic external stability results for an 11 m (36 ft), 23 m (76 ft), and 34 m (112 ft) geofoam roadway embankment with vertical walls, respectively. Each figure shows the critical factor of safety versus foundation su for the three values of horizontal seismic coefficient, i.e., 0.05, 0.10, and 0.20. Comparison of these figures results in the following conclusions: (1) Seismic stability is not a concern for vertical embankments with the geometries considered and horizontal seismic coefficients of 0.05, 0.10, and 0.20 because all of the computed values of factor of safety exceed the required value of 1.2. The factor of safety values obtained for embankments with vertical walls is greater than the embankment with 2H:1V side slopes. This conclusion is in agreement with the conclusion made for trapezoidal embankments that flatter embankments are more critical than the 2H:1V embankment because the weight of the soil cover materials above the critical static failure surface increases as the side slope becomes flatter which results in a greater seismic force being applied in the 3H:1V and 4H:1V embankments versus the 2H:1V embankment. The flatter embankments are more critical and thus a higher foundation undrained shear strength will be

5- 72 required to satisfy a factor of safety of 1.2 especially for the 4H:1V embankment. (2) Unlike the observations made for trapezoidal embankments, a wider roadway does not necessarily result in a decrease in seismic stability. Based on the static external stability results shown in Figure 5.32, the factors of safety are similar and the failure surface originates near the toe of the embankment and terminates near the center of the embankment for embankment widths of 23 m (76 ft) and 34 m (112 ft). At the smaller embankment width of 11 m (36 ft), the failure surface extends further out from the toe of the embankment and terminates near the top outer edge of the embankment. (3) The narrower embankment width of 11 m (36 ft) produces a higher factor of safety because the heavier foundation soil below the toe of the embankment provides more resisting force to the failure surface than the wider embankments for a given height. The failure surface extends further out because if the shape of the failure surface is assumed to be circular, the failure surface must extend further out for narrow and tall embankments to accommodate the circular failure surface. Additionally, a narrower embankment yields a smaller length of the failure surface that is subjected to the pavement and traffic driving stresses. This same behavior is exhibited in the external seismic stability analysis shown in Figures 5.37 through 5.39. At embankment widths of 23 m (76 ft) and 34 m (112 ft), the seismic factors of safety are similar. However, the narrower embankment with a width of 11 m (36 ft) yields a higher factor of safety. Figure 5.37. Seismic external stability design chart for a 2-lane roadway vertical embankment and a total width of 11 m (36 ft). Figure 5.38. Seismic external stability design chart for a 4-lane roadway vertical

5- 73 embankment and a total width of 23 m (76 ft). Figure 5.39. Seismic external stability design chart for a 6-lane roadway vertical embankment and a total width of 34 m (112 ft). Remedial Procedures As with trapezoidal embankments, the main remedy to increase the external seismic factor of safety for vertical embankments is to increase the undrained shear strength of the foundation soil by using a ground improvement method. A discussion on ground improvement is provided in Chapter 1. Overturning For tall and narrow vertical embankments the overturning of the entire embankment at the interface between the bottom of the assemblage of EPS blocks and the underlying foundation soil as a result of pseudo-static horizontal forces should be considered. These horizontal forces create an overturning moment about the toe at point O as shown in Figure 5.40. Figure 5.40. Variables for determining the factor of safety against overturning of a vertical embankment due to pseudo-static horizontal forces used to represent an earthquake loading. Vertical loads such as the weight of the EPS blocks and the pavement system and traffic surcharges will provide a stabilizing moment. A factor of safety against overturning of 1.2 is recommended for design purposes because overturning due to earthquake loading is a temporary loading condition. The factor of safety against overturning is expressed as follows: ( ) ( ) W EPS pavement & traffic surcharges h EPS EPS pavement h pavement & traffic surcharges stabilizing momentsFS overturning moments 1( T ) (W +W ) 2 1 1H k W T + T k W 2 2 ∑= ∑ ∗ ∗ =        ∗ ∗ ∗ + ∗ ∗ ∗              (5.54)

5- 74 The soil pressure under a vertical embankment is a function of the location of the vertical and horizontal forces. It is generally desirable that the resultant of the vertical and horizontal forces be located within the middle third of the base of the embankment, i.e., eccentricity, e ≤ (TW/6), to minimize the potential for overturning. If e = 0, the pressure distribution is rectangular. If e < (TW/6), the pressure distribution is trapezoidal, and if e = (TW/6), the pressure distribution is triangular. Therefore, as e increases, the potential for overturning of the embankment increases. Note that if e > (TW/6), the minimum soil pressure will be negative, i.e., the foundation soil will be in tension. Therefore, separation between the vertical embankment and foundation soil may occur, which may result in overturning of the embankment, because soil cannot resist tension. This is the primary reason for ensuring that e ≤ (TW/6). Equation (5.55) can be used to determine the location of the resultant a distance x from the toe of the embankment and Equation (5.56) can be used to determine e. Equation (5.57) can be used to estimate the maximum and minimum pressures under the embankment. stabilizing moments- overturning momentsx N ∑ ∑= ∑ (5.55) where x = location of the resultant of the forces from the toe of the embankment ΣN = summation of normal stresses WTe= x 2 − (5.56) where e = eccentricity of the resultant of the forces with respect to the centerline of the embankment TW = top width of the embankment W W a N 6eq= 1 q T T  ± ≤   ∑ (5.57) where q = soil pressure under the embankment qa = allowable soil pressure

5- 75 The soil pressures should not exceed the allowable soil pressure, qa, which is given by Equation (5.39). HYDROSTATIC UPLIFT (FLOTATION) Introduction EPS-block geofoam used as lightweight fill usually has a density that is approximately 1 percent of the density of earth materials. Because of this extraordinarily low density, the potential for hydrostatic uplift (flotation) of the entire embankment at the interface between the bottom of the assemblage of EPS blocks and the foundation soil must be considered in external stability evaluations. The factor of safety against upward vertical movement of the entire embankment due to a rise in the ground water table is the ratio of the total vertical stress from the embankment applied to the foundation soil (the unit weight of EPS is conservatively taken as the dry value, i.e., 0.2 kN/m³ (1.25 lbs/ft³)) divided by the uplift water pressure under some extreme event as shown in Equation (5.58). Figures 5.41 and 5.47 show the two cases of uplift of the embankment, equal water and non-equal water on both sides of the embankment, respectively, that were analyzed herein. In both cases, it is assumed that the EPS blocks extend down to the foundation soil and uplift will occur at the EPS block/foundation soil interface. U NFS ∑ ∑= (5.58) where ∑ N = summation of normal forces = WWEPS WWW ′++ ∑ U = summation of uplift forces, U, at base of embankment EPSW = weight of EPS-block geofoam embankment WW = vertical component of weight of water on the embankment face above the base of the embankment on the accumulated water side. WW′ = vertical component of weight of water on the face of the embankment on

5- 76 the tailwater side. With postconstruction settlements of 0.3 to 0.6 m (1 to 2 ft) generally considered tolerable for highway embankments during the economic life of a roadway as discussed in “Settlement of Embankments” in this chapter, the long-term total settlement might have a significant effect on the factor of safety against flotation. Therefore, the estimated total settlement as defined by Equation (5.1) should be included in the calculation of uplift force, U. The height of the embankment will remain the same after settlement occurs. However, the total depth of the design water level will increase. Thus, U should be based on the vertical height of accumulated water or tailwater, h or h’, respectively, to the bottom of the embankment at the start of construction, plus the estimated total settlement, Stotal, as indicated by Equations (5.59) and (5.60). The water pressures, P and P’, are derived from the vertical height of accumulated water at the start of construction plus the estimated total settlement, h+Stotal, and the vertical height of tailwater at the start of construction plus the estimated total settlement, h’+Stotal, and result in triangular pressure distributions acting on the sides of the embankment with a magnitude of γW * (h+Stotal) or γW * (h’+Stotal). For the case of the vertical height of accumulated water to the bottom of the embankment at the start of construction, h, equal to the vertical height of tailwater to the bottom of the embankment at the start of construction, h’, (see Figure 5.41), Equation (5.58) becomes: ( ) EPS W W REQ total W W W W W O FS h S Bγ ′+ + += ∗ + ∗ (5.59) where = Wγ unit weight of water, Stotal =total settlement as defined by Equation (5.1), BW = bottom embankment width, and =REQO additional overburden force required above the EPS blocks to obtain the desired factor of safety.

5- 77 Figure 5.41. Variables for determining hydrostatic uplift for the case of water equal on both sides of the embankment. Figure 5.41 defines the forces and pressures acting on a generic trapezoidal embankment with a side-slope inclination of θ, height of H, and top-width of TW. It can be seen that the water is at the same level on each side of the embankment, which represents the worst case scenario because the water on each side of the embankment creates a uniform uplift pressure at the base of the embankment. These water pressures create an uplift force, U, on the bottom of the embankment that equals: U = γW * BW * (h+Stotal) = γW * BW * (h’+Stotal) (5.60) The water pressures represent static water level pressures. Seepage pressures are not considered herein. The value of OREQ is the additional overburden force required above the EPS blocks to obtain the desired factor of safety in Equation (5.59). The components usually contributing to OREQ are the weight of the pavement system and the cover soil on the embankment side slopes. The weight of pavement system can be taken to be equal to the pavement surcharge of 21.5 kPa (450 lbs/ft²) used previously for external bearing capacity and slope stability or it can be calculated by multiplying the unit weight of the pavement system, γpavement, by the pavement thickness, Tpavement, and width, TW. The traffic surcharge of 11.5 kN/m2 (240 lbs/ft²) used previously is not included in OREQ because it is a live or transient load and may not be present at the time of the design hydrostatic uplift condition. The weight of the cover soil imposes overburden weight on the EPS blocks on both side slopes of the embankment and can be calculated using the variables in Figure 5.42 and the following expressions: ( )cover cover cover coverW 2 L Hγ= ∗ ∗ ∗ (5.61) where EPScover TL and sin = θ (5.62)

5- 78 covercover TH . cos = θ (5.63) Substituting Equations (5.62) and (5.63), Equation (5.61) becomes EPS cover cover cover T TW =γ 2 * * sin cos   θ θ  (5.64) Equation (5.64) utilizes the slope length of the cover soil, TEPS/sinθ, times the vertical thickness of the cover soil, Tcover/cosθ, and the unit weight of the cover soil to estimate the weight of the cover soil per length of the geofoam embankment. Therefore, to ensure the desired factor of safety used in Equation (5.59) is satisfied for hydrostatic uplift, the calculated value of OREQ should be less than the sum of the pavement and cover soil weights as shown below: OREQ < (γpavement * Tpavement * TW) + Wcover (5.65) Note that the pavement weight is γpavement * Tpavement * TW. If other weights, Wother, are applied to the embankment besides the pavement system and the soil cover, these weights can be included in Equation (5.65) and used to increase the applied vertical stress to meet the required value of OREQ as shown below: OREQ < (γpavement * Tpavement * TW) + Wcover +Wother (5.66) The design charts, which will be presented subsequently, are based on the assumption that the EPS blocks extend for the full height of the embankment, i.e., H = TEPS. Therefore, the weight of the EPS equivalent to the height of the pavement system times the unit weight of the EPS must be subtracted in the result of OREQ in Equation (5.65) as shown below: ( ) ( )REQ pavement pavement W EPS pavement W coverO T T T T Wγ γ< ∗ ∗ − ∗ ∗ + (5.67) Figure 5.42. Variables for the weight induced by the soil cover. If other weights, Wother, are applied to the embankment besides the pavement system and soil cover, Equation (5.67) becomes ( ) ( )REQ pavement pavement W EPS pavement W cover otherO T T T T W Wγ γ< ∗ ∗ − ∗ ∗ + + (5.68)

5- 79 Equation (5.59) also can be rearranged and used to obtain the value of OREQ required to obtain the desired factor of safety of 1.2. A factor of safety against hydrostatic uplift of 1.2 is recommended for design purposes because hydrostatic uplift is a temporary loading condition and a factor of safety of 1.2 is being used for other temporary loading conditions in the design procedure, such as seismic loading. Therefore, the value of OREQ corresponding to a factor of safety of 1.2 and the various embankment geometries considered during this study was calculated to develop design charts for hydrostatic uplift. This rearrangement results in the following expression: ( ) [ ]totalREQ W W EPS W WO 1.2*( h S B ) (W W W )γ ′ = ∗ + ∗ − + +  (5.69) Design charts were prepared for each embankment geometry because calculation of WEPS, WW, and W’W is cumbersome. The design charts simplify the process because a design engineer can enter a design chart and obtain the value of OREQ corresponding to a factor of safety of 1.2. The values of OREQ provided by the design charts are based on the assumption that the EPS blocks extend for the full height of the embankment and that the accumulated water level is the sum of the vertical accumulated water level to the bottom of the embankment at the start of construction and the estimated total settlement, h+Stotal. The design engineer then compares this value of OREQ with the weight of the pavement system and cover soil as shown in Equation (5.67). For example, Figure 5.43 presents the hydrostatic uplift design charts for a 4H:1V (14 degrees) embankment and the tailwater level equal to the upstream water level. If the proposed geofoam embankment has a 4-lane roadway (middle chart), a height of 12 m (40 feet), and a ratio of accumulated water level to embankment height of 0.2, which means the total water depth to include the estimated total settlement is 20 percent of the embankment height, the required value of OREQ is approximately 936 kN/m (64,150 lbs/ft) length of embankment. If the typical pavement system with a Tpavement of 1,000 mm (39 in.) used in previous external stability calculations is used the pavement weight, Wpavement, equals the surcharge times the pavement width:

5- 80 Wpavement = 21.5 kN/m2 * 23.2 m = 498.8 kN/m of roadway (5.70) Note that Wpavement is the initial part of Equation (5.67), i.e., γpavement * Tpavement. * TW. If the typical cover soil thickness of 0.46 m (1.5 feet) and moist unit weight of 18.9 kN/m3 (120 lbf/ft3) (see Table 5.2) used in previous external stability calculations is used, the cover soil weight equals: 3EPS covercover cover T T 12 m 0.46 mW 2 2 18.9 kN/m 889 kN/m sin cos sin14 cos14    = ∗ γ ∗ ∗ = ∗ ∗ ∗ =  θ θ    o o (5.71) From Equation (5.67) and assuming an EPS40, 936 kN/m = OREQ = < 498.8 kN/m –(0.16 kN/m³ ∗1 m ∗ 23 m) + 889 kN/m (5.72) 936 kN/m = OREQ < 1,384.1 kN/m of roadway Thus, the pavement and cover soil will provide sufficient overburden for a factor of safety of 1.2. Equal water level on both sides of the embankment is the worst-case scenario and construction measures should be taken to try avoid the situation of equal water level being created on both sides of the embankment. It will be shown in the following paragraphs that limiting the accumulation of water to one side of the embankment greatly reduces the value of OREQ for a factor of safety of 1.2. Figures 5.43 through 5.46 present the design charts for all of the embankment geometries considered during this study for equal upstream and tailwater levels and uplift at the EPS block/foundation soil interface. The values of OREQ shown in Figures 5.43 through 5.46 is the required weight of material over the EPS blocks in kN per linear meter of embankment length. Embankment top widths of 11m (36 ft), 23 m (76 ft), and 34 m (112 ft), side slope inclinations of 0H:1V, 2H:1V, 3H:1V, 4H:1V, and six heights between 1.5 m (4.92 ft) and 16 m (52.49 ft) were used in developing the charts. The accumulated water level is the total water depth to include the estimated total settlement, i.e., h+Stotal. The design charts only extend to a maximum ratio of accumulated water level to embankment height of 0.5, which means the total water depths to include the estimated total settlement is limited to 50 percent of the embankment height, because an embankment with a high accumulated water level is essentially a

5- 81 dam structure that may require unreasonable overburden forces on top of the EPS blocks to obtain the desired factor of safety. The design charts were only created for EPS40 and not EPS50, 70, or 100 because the results of a sensitivity analysis revealed that the value of OREQ required on top of an EPS-block geofoam embankment for a factor of safety of 1.2 is not sensitive to the density of the EPS geofoam. Therefore, the lighter EPS40 (density = 16 kg/m³ (1 lbf/ft³)) was used in determining the values of OREQ for the design charts. Because some embankments may utilize various types of EPS-blocks, the use of EPS40 for design against hydrostatic uplift will yield a worst-case scenario, which is desirable for ULS calculations. Even if a higher density is used, the value of OREQ did not change significantly because the density does not change significantly. For example, the density for EPS50 is 20 kg/m³ (1.25 lbf/ft³) versus 16 kg/m³ (1 lbf/ft³) for EPS40. Figure 5.43. Hydrostatic uplift (flotation) design for a factor of safety of 1.2 with tailwater level equal to upstream water level, 4H:1V embankment slope, and three road widths. Figure 5.44. Hydrostatic uplift (flotation) design for a factor of safety of 1.2 with tailwater level equal to upstream water level, 3H:1V embankment slope, and three road widths. Figure 5.45. Hydrostatic uplift (flotation) design for a factor of safety of 1.2 with tailwater level equal to upstream water level, 2H:1V embankment slope, and three road widths. Figure 5.46. Hydrostatic uplift (flotation) design for a factor of safety of 1.2 with tailwater level equal to upstream water level, vertical embankment (0H:1V), and three road widths. Figure 5.47. Variable for determining hydrostatic uplift analysis for the case of water on one side of the embankment only.

5- 82 For the case of the total vertical height of tailwater, h’+Stotal, equals zero (see Figure 5.47), Equation (5.59) becomes: ( ) EPS W REQ total W W W W O FS 1 * h S B 2 γ + += ∗ + ∗ (5.73) It can be seen that the weight of the tailwater is removed from the numerator and the uplift force corresponds to the resultant force of the water pressure diagram on the upstream side of the embankment. Equation (5.73) also can be rearranged and used to obtain the value of OREQ required to obtain the desired factor of safety of 1.2 against hydrostatic uplift. Therefore, the value of OREQ corresponding to a factor of safety of 1.2 and the various embankment geometries considered during this study was calculated to develop design charts for hydrostatic uplift with zero tailwater as shown below: ( ) [ ]totalREQ W W EPS W1O 1.2*( * h S B ) (W W )2 γ = ∗ + ∗ − +   (5.74) Figures 5.48 through 5.51 present the design charts for all of the embankment geometries considered during this study for a total tailwater depth of zero. These charts can be used to estimate the value of OREQ required to obtain the desired factor of safety of 1.2 against hydrostatic uplift at the EPS block/foundation soil interface. The same conditions used to generate the design charts for the equal upstream and tailwater levels were used to develop the design charts for zero tailwater Figure 5.48. Hydrostatic uplift (flotation) design for a factor of safety of 1.2 with no tailwater, 4H:1V embankment slope, and three road widths. Figure 5.49. Hydrostatic uplift (flotation) design for a factor of safety of 1.2 with no tailwater, 3H:1V embankment slope, and three road widths. Figure 5.50. Hydrostatic uplift (flotation) design for a factor of safety of 1.2 with no tailwater, 2H:1V embankment slope, and three road widths.

5- 83 Figure 5.51. Hydrostatic uplift (flotation) design for a factor of safety of 1.2 with no tailwater, vertical embankment (0H:1V), and three road widths. The design charts, i.e., Figures 5.43-5.46 and 5.48-5.51, are based on a factor of safety against hydrostatic uplift of 1.2. The Japanese design manual also recommends a minimum factor of safety of 1.2 (22) but the Norwegian design manual (4) recommends a minimum factor of safety of 1.3 for estimating the values of OREQ. The values of OREQ can be adjusted to other values of factor of safety by multiplying OREQ by the ratio of the factors of safety. For example, if the desired of factor of safety is 1.3, the value of OREQ obtained from one of the design charts should be multiplied by 1.3/1.2 or 1.08. However, a better estimate of OREQ can be obtained by using Equations (5.59) and (5.73). Because the design guidelines developed herein utilize a factor of safety of 1.2 for temporary loading conditions, the design charts utilize a safety factor of 1.2. As reported in (55) and (56), in 1987 the first EPS embankment built in Norway in 1972 failed due to hydrostatic uplift (flotation). Although the embankment was designed against the potential for uplift, the design water level used was 0.85 m (2.8 ft) lower than the flood level that occurred in 1987. Thus, the largest uncertainty in design against hydrostatic uplift is the selection of an appropriate flood elevation to utilize in the calculation and the water level on each side of the embankment. In addition to designing the completed embankment against uplift, it is important that proper temporary dewatering be maintained during construction to prevent hydrostatic uplift due to groundwater rise or surface water intrusion that may collect along the embankment during a heavy rainfall. A project in Orland Park, Illinois partially failed during construction due to hydrostatic uplift during a heavy rainfall (57). Remedial Procedures Remedial procedures that can be considered to increase the factor of safety against hydrostatic uplift of the entire embankment include: • If conventional soil fill is being proposed between the EPS blocks and the natural subgrade, a portion of this proposed soil fill can be removed and substituted with

5- 84 pavement system materials on top of the EPS thereby increasing the overburden over the EPS blocks. • A drainage system can be incorporated to minimize the potential for water to accumulate along the embankment. • An anchoring system that anchors the EPS blocks to the underlying foundation soil can be utilized. Details of a typical anchoring system that has used to resist hydrostatic uplift of an EPS-block geofoam embankment is included in Chapter 10. TRANSLATION AND OVERTURNING DUE TO WATER (HYDROSTATIC SLIDING AND OVERTURNING) Introduction Because of the extraordinarily low density of EPS-block geofoam, the potential for translation (horizontal sliding) of the entire embankment at the interface between the bottom of the assemblage of EPS blocks and the underlying foundation soil due to an unbalanced water pressure must be considered. This scenario is similar to the hydrostatic uplift case with zero tailwater but the failure mode is sliding and not uplift. Additionally, for vertical geofoam embankments, the potential for overturning of the entire embankment about one of the bottom corners of the embankment at the interface between the bottom of the assemblage of EPS blocks and the underlying foundation soil due to an unbalanced water pressure must be considered. Translation The short-term tendency of the entire embankment, such as during construction or immediately after construction, to slide under an unbalanced water pressure is resisted primarily by the undrained shear strength, su, of the foundation soil if it is a soft clay. However, the long- term tendency of the entire embankment to slide under an unbalanced water pressure is resisted primarily by EPS/foundation soil interface friction. Although the friction angle, δ, for this interface is relatively high (it approaches the Mohr-Coulomb angle of internal friction, φ, of the

5- 85 foundation soil), the resisting force (which equals the dead weight times the tangent of δ) is small because the dead weight of the overall embankment is small. Consequently, the potential for the entire embankment to slide under an unbalanced water pressure loading is a possible failure mechanism and the potential for translation (horizontal sliding) of the entire embankment in a direction perpendicular to the proposed road alignment should be considered. The factor of safety against horizontal sliding of the entire embankment is the ratio of shearing resistance along the EPS/foundation soil interface to the total horizontal driving force as shown in Equation (5.75). The total horizontal driving force is the net unbalanced water pressure, shown in Figure 5.47, which equals the resultant force of the triangular water pressure diagram or ½ (γW)h2 where h equals the vertical height of accumulated water to bottom of embankment. ( )c*A+ N- U tanhorizontal resisting forces FS= horizontal driving forces HF δ= ∑ ∑∑∑ ∑ (5.75) where c = interface cohesion along the horizontal sliding surface A = area of the horizontal sliding surface being considered ΣN = summation of normal forces = WEPS + WW +OREQ ΣU = summation of uplift forces = ½ * ( Wγ * h+Stotal) * (BW) δ = interface friction angle along the sliding surface ΣHF = summation of horizontal forces Rp=horizontal component of accumulated water on side slope above base of embankment on accumulated water side. The horizontal force, Rp=½*( Wγ * h²), is located ⅓ * h above the base of the embankment Wγ = unit weight of water h = vertical height of accumulated water to bottom of embankment at the start of construction

5- 86 Stotal=total settlement as defined by Equation (5.1) BW = bottom of embankment width As described for the analysis of hydrostatic uplift, OREQ is the additional overburden force required above the EPS blocks to obtain the desired factor of safety. In this case the desired factor of safety pertains to horizontal sliding because the resistance to horizontal sliding is controlled by the vertical normal force acting on the sliding interface just as uplift is controlled by the vertical normal force acting on the base of the embankment. For the case of no interface cohesion along the sliding surface, which is typical for geosynthetic interfaces (see Chapter 2), the expression for factor of safety against hydrostatic sliding simplifies to the following: ( ) ( )( ) ( )( ) ( )( ) 1EPS REQ totalW W W2 21 totalW2 W +W O h S γ B tan FS= γ h S δ + − + ∗ ∗ ∗  ∗ + (5.76) A factor of safety against hydrostatic sliding of 1.2 is recommended for design purposes because hydrostatic sliding is also a temporary loading condition and a factor of safety of 1.2 is being used for other temporary loading conditions in the design guidelines, such as seismic loading and hydrostatic uplift. For a factor of safety of 1.2 and solving for OREQ, Equation (5.76) becomes: ( )( ) ( )( ) ( )( )21 totalW2 1REQ total EPSW W W21.2( ) γ h SO = h S γ B -W - W tanδ∗ + + + ∗ ∗ (5.77) Equation (5.77) can be used to obtain the required value of OREQ for a factor of safety of 1.2 against hydrostatic sliding. Figures 5.53 through 5.56 present the design charts for all of the embankment geometries considered during this study for horizontal sliding caused by accumulation of water on one-side of the embankment. These charts can be used to estimate the value of OREQ per linear meter of embankment length required to obtain the desired factor of

5- 87 safety of 1.2 against hydrostatic sliding at the EPS block/foundation soil interface as was demonstrated for the hydrostatic uplift design charts. Embankment top widths of 11m (36 ft), 23 m (76 ft), and 34 m (112 ft), side slope inclinations of 0H:1V, 2H:1V, 3H:1V, 4H:1V, and six heights between 1.5 m (4.9 ft) and 16 m (52.5 ft) were used in developing the charts. For example, the design charts in each figure signify a different slope inclination where Figures 5.53 through 5.56 correspond to slope inclinations of 4H:1V, 3H:1V, 2H:1V, and 0H:1V, respectively. As described in the section on hydrostatic uplift, the value of OREQ is the additional overburden force required above the EPS blocks to obtain the desired factor of safety of 1.2. The components usually contributing to OREQ are the weight of the pavement system and the cover soil on the embankment side slopes. Therefore, to ensure the desired factor of safety, the calculated value of OREQ should be less than the sum of the pavement and cover soil weight as shown in Equation (5.65). If other weights, Wother, are applied to the embankment besides the pavement system and the soil cover, Equation (5.66) can be used to ensure that the desired factor of safety is obtained. The design charts, which will be presented subsequently, are based on the assumption that the EPS blocks extend for the full height of the embankment. Therefore, Equations (5.67) or (5.68) should be used to estimate the weight provided by the pavement system and soil cover. The design charts were only created for EPS40 and not EPS50, 70, or 100 because the results of a sensitivity analysis revealed that the value of OREQ required on top of an EPS-block geofoam embankment for a factor of safety of 1.2 is not sensitive to the density of the EPS geofoam. Therefore, the lighter EPS40 (density = 16 kg/m³ (1 lbf/ft³)) was used in determining the values of OREQ for the design charts. Because some embankments may utilize various types of EPS-blocks, the use of EPS40 for design against hydrostatic uplift will yield a worst-case scenario. However, even if a higher density is used, the value of OREQ did not change significantly because the density does not change significantly. The accumulated water level used in the design charts is the sum of the vertical accumulated water level to the bottom of the embankment at the

5- 88 start of construction and the estimated total settlement, i.e., h+Stotal. The design charts only extend to a maximum ratio of accumulated water level to embankment height of 0.5, which means the total water depth plus the estimated total settlement is limited to 50 percent of the embankment height. The maximum ratio is limited to 50 percent of the embankment height because a greater percentage may require an unreasonable overburden force on top of the EPS blocks to obtain the desired factor of safety. A factor of safety against hydrostatic sliding of 1.2 is recommended for design purposes because hydrostatic sliding is a temporary loading condition. However, other values of minimum factor of safety have been used for horizontal sliding such as 1.5 for mechanically stabilized earth (MSE) walls for design against sliding (58). A minimum factor of safety of 1.5 is also recommended for retaining walls for design against sliding in (7,59). However, since the potential for translation due to an unbalanced water head is an extreme event, a temporary loading condition, and the value of OREQ is sensitive to the design factor of safety, it was decided to use a minimum factor of safety of 1.2 for design of geofoam embankments against hydrostatic sliding. However, the values of OREQ can be adjusted to other values of factor of safety by multiplying OREQ by the ratio of the factors of safety. For example, if the desired of factor of safety is 1.3, the value of OREQ obtained from one of the design charts should be multiplied by 1.3/1.2 or 1.08. However, a better estimate of OREQ can be obtained by using Equation (5.76). Various sliding interfaces may need to be evaluated during design depending on the types of materials that are placed, if any, between the EPS blocks and the foundation soil. Chapter 2 discussed interface friction values between EPS and dissimilar materials as well as between EPS and EPS. A representative value of interface friction angle should be measured using laboratory direct shear testing, e.g., ASTM D 5321, and used in Figures 5.53 through 5.56 to obtain the required value of OREQ to resist horizontal sliding. The design charts are based on an EPS/other material interface friction angle between 20 degrees and 40 degrees, which covers the typical range of interface friction angle for geofoam embankments.

5- 89 Overturning For vertical embankments, the tendency of the entire embankment to overturn at the interface between the bottom of the assemblage of EPS blocks and the underlying foundation soil is a result of an unbalanced water pressure acting on the embankment. Overturning may be critical for tall and narrow vertical embankments. These horizontal forces create an overturning moment about the toe at point O as shown in Figure 5.52. The worst case scenario is for water accumulating on only one side of the embankment as shown in Figure 5.52. Vertical loads, such as the weight of the EPS blocks, the pavement system, and traffic surcharges, will provide a stabilizing moment. As described for the analysis of hydrostatic uplift, OREQ is the additional overburden force required above the EPS blocks to obtain the desired factor of safety. Figure 5.52. Variables for determining the factor of safety against overturning due to hydrostatic horizontal forces for the case of water on one side of the embankment. The factor of safety against overturning due to horizontal hydrostatic forces is expressed as ( ) W EPS REQ total p 1( T ) (W +O )stabilizing moments 2FS 1overturning moments h+S R 3 ∗ ∗∑= =∑ ∗ (5.78) A factor of safety against hydrostatic overturning of 1.2 is recommended for design purposes because hydrostatic overturning is a temporary loading condition and a factor of safety of 1.2 is being used for other temporary loading conditions, such as hydrostatic uplift and sliding and seismic loading. For a factor of safety of 1.2 and solving for OREQ, Equation (5.78) becomes ( ) ( )total p REQ EPS W 11.2 h+S R 3O = W 1 T 2  ∗ ∗ ∗   − ∗   (5.79)

5- 90 Equation (5.79) can be used to obtain the required value of OREQ for a factor of safety of 1.2 to resist hydrostatic overturning. The resultant of the vertical and horizontal forces should be checked to verify that the resultant is located within the middle third of the base, i.e., eccentricity, e ≤ (Bw/6), to minimize the potential for the wall to overturn. Equations (5.55) and (5.56) can be used to determine e. Additionally, the maximum and minimum soil pressures under the embankment should not exceed the allowable soil pressure, qa, which is given by Equation (5.39). Equation (5.57) can be used to determine the maximum and minimum pressures under the embankment. Remedial Procedures Remedial procedures that can be considered to increase the factor of safety against hydrostatic sliding and overturning include: • Removing any separation material that is being proposed between the EPS blocks and the foundation soil and replacing with an alternative separation material that will provide a larger interface friction angle. This remedial procedure will reduce the potential for sliding. • If conventional soil fill is being proposed between the EPS blocks and the foundation soil, a portion of this proposed soil fill can be removed and substituted with heavier pavement system materials on top of the EPS thereby increasing the overburden over the EPS blocks. This remedial procedure will reduce the potential for both horizontal sliding and overturning. • A drainage system can be incorporated to minimize the potential for water to accumulate along a side of the embankment. This will reduce the potential for horizontal sliding and overturning, as well as hydrostatic uplift. • If an anchoring system is used to resist hydrostatic uplift, this system will also provide resistance against horizontal sliding and overturning.

5- 91 Figure 5.53. Hydrostatic sliding (translation due to water) design for a factor of safety of 1.2 with no tailwater, 4H:1V embankment slope, and three road widths for various interface friction angles. Figure 5.54. Hydrostatic sliding (translation due to water) design for a factor of safety of 1.2 with no tailwater, 3H:1V embankment slope, and three road widths for various interface friction angles. Figure 5.55. Hydrostatic sliding (translation due to water) design for a factor of safety of 1.2 with no tailwater, 2H:1V embankment slope, and three road widths for various interface friction angles. Figure 5.56. Hydrostatic sliding (translation due to water) design for a factor of safety of 1.2 with no tailwater, vertical embankment (0H:1V), and three road widths for various interface friction angles. TRANSLATION AND OVERTURNING DUE TO WIND Introduction As discussed in Chapter 3, translation due to wind is an external stability ULS failure mechanism that is unique to embankments containing EPS-block geofoam because of the extremely low density of EPS blocks compared to other types of lightweight fill. Additionally, for vertical geofoam embankments, the potential for overturning of the entire embankment about one of the bottom corners of the embankment at the interface between the bottom of the assemblage of EPS blocks and the underlying foundation soil due to horizontal wind forces must be considered. Translation The factor of safety against translation of the entire embankment due to wind is the ratio of the shearing resistance along the EPS/foundation soil interface to the total horizontal driving force as shown in Equation (5.75). Equation (5.75) was presented in the previous section of this chapter during the discussion of “Translation Due to Water.” Equation (5.75) is restated below

5- 92 with the variable definitions re-defined for calculating wind forces instead of hydrostatic forces. Figure 5.57 defines the forces and pressures acting on a generic trapezoidal embankment with a side-slope inclination of θ, height of H, and top-width of TW. ( )c*A+ N- U tanhorizontal resisting forces FS= horizontal driving forces HF δ= ∑ ∑∑∑ ∑ (5.75) where c = interface cohesion along the horizontal sliding surface A = area of the horizontal sliding surface being considered ΣN = summation of normal stresses = WEPS + OREQ ΣU = summation of uplift forces δ = interface friction angle along the sliding surface ΣHF = summation of horizontal forces = RU + RD RU = upwind force = pU * H RD = downwind force = pD * H H = height of embankment = TEPS + TPavement Figure 5.57. Variables for determining wind analysis. It can be seen that the wind is acting on the left side of the embankment tending to push the embankment to the right and the horizontal resisting force acting along the base of the embankment is acting in the opposite direction and counteracting the wind. The worst-case scenario involves the wind acting on only one-side of the embankment as shown in Figure 5.57 and is considered herein. The resultant wind forces, RU and RD, are obtained from wind pressure diagrams. It can be seen from Figure 5.57 that the wind is modeled with a uniform pressure distribution with a magnitude of pU or pD. The expressions used to calculate pU or pD were obtained from the French national design guide (60) for EPS-block geofoam road embankments, are discussed in Chapter 3, and are re-stated below: 2U Up 0.75V sin= θ (3.4)

5- 93 2D Dp 0.75V sin= θ (3.5) with V = the wind speed in meters per second, pU and pD have units of kilopascals and the other variables are defined in Figure 5.57. Both of these equations treat a side-sloped embankment as a vertical wall. Therefore, the wind pressures are conservative in that the wind pressures are assumed to be horizontal instead of perpendicular to the side-slope. The wind driving forces come from applied stresses on both the windward and leeward sides of the embankment as shown in Figure 5.57. The downwind (leeward side) pressure diagram is due to suction while the windward pressure diagram is due to the wind. For the case of no interface cohesion along the basal sliding surface, c = 0, which is typical for geosynthetic interfaces (see Chapter 2), and no uplift wind forces, U = 0, the expression for factor of safety against translation due to wind in Equation (5.75) simplifies to the following: Equation (5.80) can be used to obtain the required value of OREQ for a factor of safety of 1.2 against translation due to wind. A factor of safety against sliding of 1.2 is recommended for design purposes because sliding due to wind is another temporary loading condition and a factor of safety of 1.2 is being used for other temporary loading conditions in the design guidelines, such as seismic loading and hydrostatic uplift. In addition, low safety factors (1.0 to 1.2) are considered acceptable for this load case because of the low probability of occurrence of the event. For a factor of safety of 1.2 and solving for OREQ, Equation (5.80) becomes: ( ) U D EPS REQW +O tan FS= R +R δ∗ (5.80) U DREQ EPS 1.2*(R +R ) O = W tanδ − (5.81)

5- 94 The components usually contributing to OREQ are the weight of the pavement system and the cover soil on the embankment side slopes. Therefore, to ensure the desired factor of safety, the calculated value of OREQ should be less than the sum of the pavement and cover soil weights as shown in Equation (5.65). If other weights, Wother, are applied to the embankment besides the pavement system and the soil cover, Equation (5.66) can be used to ensure that the desired factor of safety is obtained. Figure 5.58 presents the design charts for the embankment geometries considered during this study for translation due to wind. These charts can be used to estimate the value of OREQ per linear meter of embankment length required to obtain the desired factor of safety of 1.2 against translation due to wind. Figure 5.58 is based on the assumption that the EPS blocks extend down to the EPS/foundation soil interface and thus occurs at the EPS block/foundation soil interface. The charts differ from the hydrostatic uplift and sliding charts because the charts only correspond to a 2-lane road width (11m (36 ft)) but are applicable to 4-lane (23 m (76 ft)) and 6-lane embankments (34 m (112 ft)). This applicability is caused by the interface cohesion being assumed equal to zero, embankment width has a small influence on WEPS because of the small density of EPS, and the assumption that the wind acts on a vertical wall. The application of the design charts in Figure 5.58 to 4-lane and 6-lane roadways was verified with a comparison of the three top embankment widths for the 2H:1V case that showed little difference in the value of OREQ. Therefore, the slightly more conservative results for the 2-lane (11 m (36 ft)) roadway width are presented in Figure 5.58. The charts are a function of embankment heights between 1.5 m (4.92 ft) and 16 m (52.5 ft), side-slope inclinations of 0H:1V, 2H:1V, 3H:1V, 4H:1V, and two wind velocities (40 and 60 m/s (90 and 135 miles/hr)). It can also be seen that the design charts in Figure 5.58 utilize an interface friction angle, δ, of 20 degrees to 40 degrees for the EPS/foundation soil interface. The design charts correspond to EPS40, which has a density of 16 kg/m³ (1 lbf/ft³). Other densities were not considered because the value of OREQ for a factor of

5- 95 safety of 1.2 against translation to wind is not sensitive to other values of EPS density as noted previously in the hydrostatic uplift and hydrostatic sliding sections of this chapter. Figure 5.58. Design against translation due to wind for factor of safety of 1.2 and a road width of 11 m (36 ft) and four embankment slopes. The value of OREQ obtained from Figure 5.58 is the additional overburden force in kN per linear meter of embankment length required above the weight of the EPS blocks to obtain the desired factor of safety of 1.2. Figure 5.58 is based on the assumption that the EPS blocks extend for the full height of the embankment. Therefore, Equations (5.67) or (5.68) should be used to estimate the weight provided by the pavement system and soil cover. Various sliding interfaces may need to be evaluated during design depending on the types of materials that are placed, if any, between the EPS blocks and the foundation soil. Chapter 2 discussed interface friction values between EPS and dissimilar materials as well as between EPS and EPS. A representative value of interface friction angle should be measured using laboratory direct shear testing, e.g., ASTM D 5321, and used in Figure 5.58 to obtain the required value of OREQ to resist translation due to wind. The design wind speed can be obtained from local building codes or from references such as (61). Based on the wind speed contour map included in (61), wind speeds of 40 and 60 m/s (90 and 135 miles/hour) were used in developing Figure 5.58 because this is the range of wind speeds that predominate in the continental U.S. except for some coastal regions. However, as indicated in Chapter 3, no guidance is provided in (60) on the proper selection of wind speed. The wind pressures obtained from Equations (3.4) and (3.5) may be too conservative because there is no documented sliding failure of an embankment containing EPS-block geofoam due to wind loading. As shown in Table 5.5, for a relatively low embankment height of 2 m (6.6 ft), an overburden on top of the EPS-block geofoam equivalent to a pavement system thickness of 7.2 m (24 ft) would be required for an embankment with side slopes of 4H:1V, an EPS/foundation interface friction angle of 40 degrees, and a cover soil thickness of 0.46 m (1.5 ft)

5- 96 to provide sufficient stability against a 40 m/s (90 mph) wind speed. This pavement system thickness is greater than the typical pavement system thickness range of 0.6 to 1.5 m (2 to 4.9 ft). Table 5.5 also shows that the required value of OREQ increases dramatically for a vertical embankment and a decrease in the interface friction angle from 40 to 20 degrees. Table 5.5. Required overburden force and equivalent pavement system thickness for wind loading example problems. A comparison of Equations (3.4) and (3.5) with the ANSI/ASCE 7-95 wind load provisions for buildings revealed the following three potential problems with the use of Equations (3.4) and (3.5) for the design of geofoam embankments: • A draft version (60) of (61) used the coefficient 0.5, not 0.75 in Equation (3.5). A review of the ANSI/ASCE 7-95 (62) wind design parameters for the case of a building with a flat roof, which would be comparable to an embankment with vertical walls, revealed that the French design guideline pressure coefficients of 0.75 and 0.5 for the windward and leeward cases, respectively, are the same as the ANSI/ASCE 7-95 pressure coefficients for buildings with a length to width ratio ranging from 0 to 1 where the width of the building is perpendicular to the wind direction. This ratio would be applicable to most roadway embankments. However, unlike the ANSI/ASCE 7-95 design procedure, the French design guideline does not consider suction pressures on top of the structure. Suction pressures will decrease with the horizontal distance from the windward edge and will tend to decrease the translational stability of a vertical embankment. Therefore, the larger 0.75 downwind pressure coefficient that appeared in the later French guideline may compensate for the suction pressures on top of the structure. • Equations (3.4) and (3.5) treat a side-sloped embankment as a vertical wall. Therefore, the wind pressures are conservative in that the wind pressures are

5- 97 assumed to be horizontal instead of perpendicular to the side-sloped surface, which would yield both a horizontal and a vertical component to the wind pressure. • No guidance is provided in (60) or (61) on the selection of wind speed. The ANSI/ASCE 7-95 design procedure includes a wind speed contour map of the United States that does not include tornado winds because of their rare occurrence. However, the ANSI/ASCE building design equations include an exposure velocity pressure coefficient which reflects change in wind speed with height and terrain roughness, a topographic factor which accounts for wind speed up and over hills and escarpments, a gust effect factor, and an importance factor which adjusts wind speed to a 50-year mean recurrence interval. Based on the results in Table 5.5, the design charts in Figure 5.58, the potential problems presented herein with the use of Equations (3.4) and (3.5), and the absence of documented sliding failure due to wind loading, it is recommended that the translation due to wind failure mechanism not be considered until further research is performed on the applicability of Equations (3.4) and (3.5) to EPS-block geofoam embankments. However, the analysis procedure was presented herein for completeness and because future research may develop lower coefficients for Equations (3.4) and (3.5) that are in better agreement with field observations and the analysis presented above can be utilized with the lower coefficients. It is recommended that a more realistic procedure be developed for evaluating the potential for basal translation (sliding) due to wind loading especially under Atlantic hurricane conditions. An evaluation of the applicability of roof design shapes and procedures to side-sloped EPS-block geofoam embankments is recommended. Development of new wind pressure coefficients was outside the scope of this project but is listed as a topic for future research.

5- 98 Overturning For vertical embankments, the entire embankment can overturn at the interface between the bottom of the assemblage of EPS blocks and the underlying foundation soil due to horizontal wind forces acting on the embankment. These wind forces can create an overturning moment about the toe at point O as shown in Figure 5.59. Vertical loads such as the weight of the EPS blocks and any overburden material placed on top of the blocks such as the pavement system and traffic surcharges will provide a stabilizing moment. As described for the analysis of hydrostatic uplift, OREQ is the additional overburden force required above the EPS blocks to obtain the desired factor of safety. Figure 5.59. Variables for determining the factor of safety against overturning due to horizontal wind forces. The factor of safety against overturning due to wind is expressed as ( ) W EPS REQ U D 1( T ) (W +O )stabilizing moments 2FS 1overturning moments H R +R 2 ∗ ∗∑= =∑  ∗ ∗   (5.82) A factor of safety against hydrostatic overturning of 1.2 is recommended for design purposes because overturning due to wind is a temporary loading condition and a factor of safety of 1.2 is being used for other temporary loading conditions, such as hydrostatic uplift and sliding and seismic loading. For a factor of safety of 1.2 and solving for OREQ, Equation (5.82) becomes ( )U D W EPS REQ W 1 11.2 H R +R T W 2 2O = 1 T 2    ∗ ∗ ∗ − ∗ ∗        ∗   (5.83) Equation (5.83) can be used to obtain the required value of OREQ for a factor of safety of 1.2 to resist overturning by wind forces. The resultant of the vertical and horizontal forces should be checked to verify that the resultant is located within the middle third of the base, i.e., eccentricity, e ≤ (Bw/6), to minimize

5- 99 the potential for the wall to overturn. Equations (5.55) and (5.56) can be used to determine e. Additionally, the maximum and minimum soil pressures under the embankment should not exceed the allowable soil pressure, qa, which is given by Equation (5.39). Equation (5.57) can be used to determine the maximum and minimum pressures under the embankment. Remedial Procedures Remedial procedures that can be considered to increase the factor of safety against translation due to wind are similar to those for increasing the factor of safety against hydrostatic sliding discussed in the previous section except that the use of a drainage system would not apply to wind loading. REFERENCES 1. Horvath, J. S., Geofoam Geosynthetic, Horvath Engineering, P.C., Scarsdale, NY (1995) 229 pp. 2. “Matériaux Légers pour Remblais/Lightweight Filling Materials.” Document No. 12.02.B, PIARC-World Road Association, La Defense, France (1997) 287 pp. 3. Briaud, J.-L., James, R. W., and Hoffman, S. B., “Settlement of Bridge Approaches (The Bump at the End of the Bridge).” NCHRP Synthesis 234, Transportation Research Board, Washington, D.C. (1997) 75 pp. 4. “Expanded Polystyrene Used in Road Embankments - Design, Construction and Quality Assurance.” Form 482E, Public Roads Administration, Road Research Laboratory, Oslo, Norway (1992) 4 pp. 5. Sanders, R. L., and Seedhouse, R. L., “The Use of Polystyrene for Embankment Construction.” Contractor Report 356, Transport Research Laboratory, Crowthorne, Berkshire, U.K. (1994) 55 pp. 6. Miki, G., “Ten Year History of EPS Method in Japan and its Future Challenges.” Proceedings of the International Symposium on EPS Construction Method (EPS Tokyo '96), Tokyo, Japan, (1996) pp. 394-410. 7. Terzaghi, K., Peck, R. B., and Mesri, G., Soil Mechanics in Engineering Practice, 3rd, John Wiley & Sons, Inc., New York (1996). 8. Holtz, R. D., “Treatment of Problem Foundations for Highway Embankments.” NCHRP Synthesis 147, Transportation Research Board, Washington, D.C. (1989) 72 pp. 9. “Settlement Analysis.” Technical Engineering and Design Guides as Adapted From the U.S. Army Corps of Engineers, No. 9, ASCE, New York (1994) 144 pp. 10. Duncan, J. M., Javete, D. F., and Stark, T. D., “The Importance of a Desiccated Crust on Clay Settlements.” Soils and Foundations, Vol. 31, No. 3 (1991) pp. 77- 90. 11. Holtz, R. D., and Kovacs, W. D., An Introduction to Geotechnical Engineering, Prentice Hall, Englewood Cliffs,NJ (1981) 733 pp.

5- 100 12. Nishida, Y., “A brief note on compression index of soil.” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 82, No. SM3 (1956) pp. 1027- 1 - 1027-14. 13. Terzaghi, K., and Peck, R. B., Soil Mechanics in Engineering Practice, 2nd, John Wiley and Sons, New York (1967) 729 pp. 14. Mesri, G., “Discussion: Postconstruction Settlement of An Expressway Built on Peat by Precompression by Samson, L.” Canadian Geotechnical Journal, Vol. 23, No. 3 (1986) pp. 403-407. 15. Mesri, G., and Choi, Y. K., “Settlement Analysis of Embankments on Soft Clays.” Journal of Geotechnical Engineering, Vol. 111, No. 4 (1985) pp. 441- 464. 16. Mesri, G., Stark, T. D., Ajlouni, M. A., and Chen, C. S., “Secondary Compression of Peat With or Without Surcharging.” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 123, No. 5, May 1997 (1997) pp. 411-421. 17. “Treatment of Soft Foundations for Highway Embankments.” NCHRP Synthesis 29, Transportation Research Board, Washington, D.C. (1975) 25 pp. 18. “Bridge Approach Design and Construction Practices.” NCHRP Synthesis of Highway Practice 2, Transportation Research Board, Washington, D.C. (1969) 30 pp. 19. Wahls, H. E., “Shallow Foundations for Highway Structures.” NCHRP Synthesis of Highway Practice 107, Transportation Research Board, Washington, D.C. (1983) 38 pp. 20. Moulton, L. K., GangaRao, H. V. S., and Halvorsen, G. T., “Tolerable Movement Criteria for Highway Bridges.” FHWA/RS-85/107, Federal Highway Administration, Washington D.C. (1985). 21. Moulton, L. K., “Tolerable Movement Criteria for Highway Bridges.” FHWA-TS- 85-228, Federal Highway Administration, Washington, D.C. (1986) 93 pp. 22. “Design and Construction Manual for Lightweight Fill with EPS.” The Public Works Research Institute of Ministry of Construction and Construction Project Consultants, Inc., Japan (1992) Ch. 3 and 5. 23. Osterberg, J. O., “Influence Values for Vertical Stresses in a Semi-Infinite Mass Due to an Embankment Loading.” Proc. 4th Int. Conf. Soil Mech., London, Vol. 1 (1957) pp. 393-394. 24. Prandtl, L., “Über die Eindringungsfestigkeit (Härte) plastischer Bauttoffe und die Festigkeit von Schneiden (On the penetrating strengths (hardness) of plastic construction materials and the strength of cutting edges).” Zeit. angew. Math. Mech., Vol. 1, No. 1 (1921) pp. 15-20. 25. Skempton, A. W., “The bearing capacity of clays.” Proc. British Bldg. Research Congress, Vol. 1 (1951) pp. 180-189. 26. Peck, R. B., Hanson, W. E., and Thornburn, T. H., Foundation Engineering, 2nd, John Wiley & Sons, NY (1974). 27. Aabøe, R., “Deformasjonsegenskaper og spenningsforhold i fyllinger av EPS (Deformation and stress conditions in fills of EPS).” Intern Rapport Nr. 1645, Public Roads Administration (1993) 22 pp. Norwegian. 28. Aabøe, R., “Long-term performance and durability of EPS as a lightweight fill.” Nordic Road & Transport Research, Vol. 12, No. 1 (2000) pp. 4-7.

5- 101 29. Boussinesq, J., Application des Potentiels à l' Étude de l' Équilibre et du Mouvement des Solides Élastiques, Gauthier-Villard, Paris (1885). 30. American Association of State Highway and Transportation Officials, Standard Specifications for Highway Bridges, 16th, American Association of State Highway and Transportation Officials, Washington, D.C. (1996). 31. Janbu, N., “Slope Stability Computations.” Embankment Dam Engineering, Hirschfield and Poulos, eds., John Wiley & Sons, New York (1973) pp. 47-86. 32. Sharma, S., XSTABL: An Integrated Slope Stability Analysis Program for Personal Computers, Interactive Software Designs, Inc., Moscow, Idaho (1996) 150 pp. 33. Bishop, A. W., “The Use of the Slip Circle in the Stability Analysis of Slopes.” Geotechnique, Vol. V. No. 1, pp. 7-17. 34. Spencer, E., “A Method of Analysis of the Stability of Embankments Assuming Parallel Inter-slice Forces.” Geotechnique, Vol. 17, No. 1 (1967) pp. 11-26. 35. Duncan, J. M., and Wright, S. G., “The Accuracy of Equilibrium Methods of Slope Stability Analysis.” International Symposium on Landslides, New Delhi, India, (1980) pp. 247-254. 36. Chirapuntu, S., and Duncan, J. M., “The Role of Fill Strength in the Stability of Embankments on Soft Clay Foundations.” TE 75-3, Department of Civil Engineering, Institute of Transportation and Traffic Engineering, University of California, Berkeley (1975) 231 pp. 37. Kavazanjian, E., Jr., Matasovic, N., Hadj-Hamou, T., and Sabatini, P. J., “Geotechnical Engineering Circular No. 3; Design Guidance: Geotechnical Earthquake Engineering for Highways; Volume I - Design Principles.” FHWA- SA-97-076, U.S. Department of Transportation, Federal Highway Administration, Washington, D.C. (1997) 186 pp. 38. Elias, V., Welsh, J., Warren, J., and Lukas, R., “Ground Improvement Technical Summaries.” FHWA-SA-98-086, U.S. Department of Transportation, Federal Highway Adminstration, Washington, D.C. (1999). 39. Elias, V., Welsh, J., Warren, J., and Lukas, R., “Ground Improvement Technical Summaries.” FHWA-SA-98-086, Vol. 2, 2 Vols, U.S. Department of Transportation, Federal Highway Adminstration, Washington, D.C. (1999). 40. Terzaghi, K., “Mechanisms of Landslides.” Application of Geology to Engineering Practice, Berkey Vol., Geological Society of America (1950) pp. 83- 123. 41. “Soil Mechanics, Design Manual 7.01 Revalidated by Change 1 September 1986.” Naval Facilities Engineering Command, Alexandria, VA (1986) 364 pp. 42. Day, R. W., Geotechnical Earthquake Engineering Handbook, McGraw-Hill, New York (2002). 43. Makdisi, F., and Seed, H. B., “Simplified Procedure for Estimating Dam and Embankment Earthquake-Induced Deformations.” Journal of Geotechnical Engineering Division ASCE, Vol. 104, No. 7 (1978) pp. 849-867. 44. Stark, T. D., and Mesri, G., “Undrained Shear Strength of Liquefied Sands for Stability Analysis.” Journal of Geotechnical Engineering Division ASCE, Vol. 118, No. 11 (1992) pp. 1727-1747.

5- 102 45. Yegian, M. K., and Lahlaf, A. M., “Dynamic Interface Shear Strength Properties of Geomembranes and Geotextiles.” ASCE Journal of Geotechnical Engineering, Vol. 118, No. 5 (1992) pp. 760-779. 46. Schnabel, P., Lysmer, J., and Seed, H. B., “SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites.”, Earthquake Engineering Research Center, University of California at Berkeley, Richmond, CA, (1972). 47. Chopra, A. K., “Earthquake Effects on Dams,” Doctor of Philosophy thesis, University of California at Berkeley, Berkeley, CA (1966). 48. Hashash, M. A. Y., Stark, T. D., and Abdulamit, A., “Equivalent Linear Dynamic Response Analysis of Geosynthetic Lined Landfills.” Industrial Fabrics Association International, St. Paul, MN, Vol. February, 2001 (2001). 49. Algermissen, S. T., Perkins, D. M., Thenhaus, P. C., Hanson, S. L., and Bender, B. L., “Probabilistic Earthquake Acceleration and Velocity Maps for the United States and Puerto Rica.” Open-File Report 97-131, U.S. Geological Survey, Open-File Services Section, Denver, CO (1997). 50. Seed, H. B., Romo, M. P., Sun, J., Jaime, A., and Lysmer, J., “Relationships Between Soil Conditions and Earthquake Ground Motions in Mexico City in the Earthquake of Sept. 19, 1985.” UCB/EERC-87/15, University of California at Berkeley, Earthquake Engineering Research Center, Berkeley, CA (1987) 112 pp. 51. Seed, H. B., and Idriss, I. M., “Ground Motions and Soil Liquefaction During Earthquakes.”, Earthquake Engineering Research Center, University of California at Berkeley, Berkeley, CA, (1982). 52. Idriss, I. M., “Response of Soft Soil Sites During Earthquakes.” Proceedings of the H. Bolton Seed Memorial Symposium, Richmond, British Columbia, Vol. tel. 604-277-4250, fax 604-277-8125 (1990). 53. EDO, “(untitled).” Proceedings of International Geotechnical Symposium on Polystyrene Foam in Below Grade Applications, March 30, 1994, Honolulu, HI, Vol. May 1994, Research Report No. CE/GE-94-1 (1994) pp. 168. 54. Hotta, H., Nishi, T., and Kuroda, S., “Report of Results of Assessments of Damage to EPS Embankments Caused by Earthquakes.” Proceedings of the International Symposium on EPS Construction Method (EPS Tokyo '96), Tokyo, Japan, (1996) pp. 307-318. 55. Frydenlund, T. E., and Aaboe, R., “Expanded Polystyrene - A Light Solution.” International Symposium on EPS Construction Method (EPS Tokyo '96), Tokyo, Japan, (1996) pp. 31-46. 56. Horvath, J. S., “Lessons Learned from Failures Involving Geofoam in Roads and Embankments.” Research Report No. CE/GE-99-1, Manhattan College, Bronx, NY (1999) 18 pp. 57. Taccola, L. J., Telephone conversation with Arellano, D. 16 November 1999. 58. Elias, V., and Christopher, B. R., “Mechanically Stabilized Earth Walls and Reinforced Soil Slopes, Design and Construction Guidelines.” FHWA-SA-96-071, Federal Highway Administration, Washington, D.C. (1997) 371 pp. 59. “Foundations & Earth Structures, Design Manual 7.02 Revalidated by Change 1 September 1986.” Naval Facilities Command, Alexandria, VA (1986) 253 pp.

5- 103 60. Magnan, J.-P., “Recommandations pour L'Utilisation de Polystyrene Expanse en Remblai Routier.” Laboratoire Central Ponts et Chaussées, France (1989) 20 pp. 61. “Utilisation de Polystyrene Expanse en Remblai Routier; Guide Technique.” Laboratoire Central Ponts et Chaussées/SETRA, France (1990) 18 pp. 62. Minimum Design Loads for Buildings and Other Structures, ANSI/ASCE 7-95, Approved June 6, 1996, American Society of Civil Engineers, New York (1996).

FIGURE 5.1 PROJ 24-11.doc 5-104

FIGURE 5.2 PROJ 24-11.doc 5-105

FIGURE 5.3 PROJ 24-11.doc α Ι 5-106

FIGURE 5.4 PROJ 24-11.doc α δ ΙΙ 5-107

FIGURE 5.5 PROJ 24-11.doc Pavement System So il c ov er coverT EPST EPS Soil coverEPST ba ab Centeredge θ θ (a) EPS Inner Edge of Outer edge of Soil Cover T T Block Thickness Step Length EPS Blocks EPS Blocks block edges cover (b) 5-108

FIGURE 5.6 PROJ 24-11.doc δ ΙΙ 5-109

FIGURE 5.7 PROJ 24-11.doc δ α ΙΙΙ 5-110

FIGURE 5.8 PROJ 24-11.doc αδ Ι 5-111

FIGURE 5.9 PROJ 24-11.doc α Ι 5-112

FIGURE 5.10 PROJ 24-11.doc M in im u m th ic kn es s o f E PS -b lo ck g eo fo am , T E PS (m ) 10 11 12 13 14 15 16 17 18 19 20 Undrained Shear Strength, s u (kPa) 0 2 4 6 8 10 12 14 16 18 23 m (75 feet)11 m (36 feet) roadway 34 m (112 feet) 5-113

FIGURE 5.11 PROJ 24-11.doc 0.46 m 0.46 m Soil Cover EPS T EPS Traffic and Pavement Surcharge 2 1 2 1 Not to Scale (soil cover thickness exaggerated) 5-114

FIGURE 5.12 PROJ 24-11.doc 5-115

FIGURE 5.13 PROJ 24-11.doc 5-116

FIGURE 5.14 PROJ 24-11.doc Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct or o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Fa ct or o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 11 m pavement, static Undrained Shear Strength, su (kPa) 10 20 30 40 50 Fa ct or o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 FS = 1.5 FS = 1.5 FS = 1.5 2H:1V embankment 3H:1V embankment 4H:1V embankment TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 12.2 m = 6.1 m = 3.1 m 5-117

FIGURE 5.15 PROJ 24-11.doc Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, F S 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 23 m pavement, static Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, F S 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 2H:1V embankment TEPS = 3.1 m = 6.1 m = 12.2 m 3H:1V embankment 4H:1V embankment TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m FS = 1.5 FS = 1.5 FS = 1.5 5-118

FIGURE 5.16 PROJ 24-11.doc Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 34 m pavement, static Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, F S 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 2H:1V embankment 3H:1V embankment 4H:1V embankment TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m FS = 1.5 FS = 1.5 FS = 1.5 5-119

FIGURE 5.17 PROJ 24-11.doc Maximum Acceleration on Rock, g 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 M ax im u m A cc el er at io n , g 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Rock Stiff Soils Deep Cohesionless Soils Medium Stiff Clay and Sand 5-120

FIGURE 5.18 PROJ 24-11.doc 5-121

FIGURE 5.19 PROJ 24-11.doc γ 5-122

FIGURE 5.20 PROJ 24-11.doc 5-123

FIGURE 5.21 PROJ 24-11.doc 11 m pavement, kh=0.05 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, F S' 0.0 1.0 2.0 3.0 4.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic , Fa ct o r o f S af et y FS ' 0.0 1.0 2.0 3.0 4.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 2H:1V embankment 3H:1V embankment 4H:1V embankment FS' = 1.2 FS' = 1.2 FS' = 1.2 TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 3.1 m =6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m 5-124

FIGURE 5.22 PROJ 24-11.doc 11 m pavement, kh=0.10 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct or o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 FS' = 1.2 FS' = 1.2 FS' = 1.2 2H:1V embankment 3H:1V embankment 4H:1V embankment TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m 5-125

FIGURE 5.23 PROJ 24-11.doc 11 m pavement, kh=0.20 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct or o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 FS' = 1.2 FS' = 1.2 FS' = 1.2 2H:1V embankment 3H:1V embankment 4H:1V embankment TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 3.1 m = 6.1 m = 3.1 m TEPS = 3.1 m = 6.1 m = 3.1 m 5-126

FIGURE 5.24 PROJ 24-11.doc 23 m pavement, kh=0.05 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 2H:1V embankment 3H:1V embankment 4H:1V embankment FS' = 1.2 FS' = 1.2 FS' = 1.2 TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m 5-127

FIGURE 5.25 PROJ 24-11.doc 23 m pavement, kh=0.10 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Se ism ic Fa ct o r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 2H:1V embankment 3H:1V embankment 4H:1V embankment FS' = 1.2 FS' = 1.2 FS' = 1.2 TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m 5-128

FIGURE 5.26 PROJ 24-11.doc 23 m pavement, kh=0.20 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 2H:1V embankment 3H:1V embankment 4H:1V embankment FS' = 1.2 FS' = 1.2 FS' = 1.2 TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m 5-129

FIGURE 5.27 PROJ 24-11.doc 34 m pavement, kh=0.05 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Se is m ic F ac to r o f S af et y, FS 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Se ism ic F ac to r o f S af et y, FS 0.0 1.0 2.0 3.0 4.0 5.0 2H:1V embankment TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m 3H:1V embankment 4H:1V embankment TEPS = 3.1 m = 6.1 m = 12.2 m FS' = 1.2 FS' = 1.2 FS' = 1.2 5-130

FIGURE 5.28 PROJ 24-11.doc 34 m pavement, kh=0.10 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se is m ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 2H:1V embankment TEPS = 3.1 m = 6.1 m = 12.2 m 3H:1V embankment 4H:1V embankment TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m FS' = 1.2 FS' = 1.2 FS' = 1.2 5-131

FIGURE 5.29 PROJ 24-11.doc 34 m pavement, kh=0.20 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Se ism ic F ac to r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 2H:1V embankment TEPS = 3.1 m = 6.1 m = 12.2 m 3H:1V embankment 4H:1V embankment TEPS = 3.1 m = 6.1 m = 12.2 m TEPS = 3.1 m = 6.1 m = 12.2 m FS' = 1.2 FS' = 1.2 FS' = 1.2 5-132

FIGURE 5.30 PROJ 24-11.doc γ 5-133

FIGURE 5.31A PROJ 24-11.doc 5-134

FIGURE 5.31B PROJ 24-11.doc 5-135

FIGURE 5.32 PROJ 24-11.doc 5-136

FIGURE 5.33 PROJ 24-11.doc 5-137

FIGURE 5.34 PROJ 24-11.doc Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 6.0 7.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 6.0 7.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 6.0 7.0 11 m road width 23 m road width 34 m road width FS = 1.5 FS = 1.5 FS = 1.5 TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m 5-138

FIGURE 5.35 PROJ 24-11.doc Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 15 20 25 30 35 40 45 50 Fa ct o r o f S af et y, FS 1.0 2.0 3.0 4.0 5.0 FS = 1.5 FS = 1.5 FS = 1.5 Road width = 34 m Road width = 23 m Road width = 11 m Road width = 34 m Road width = 23 m Road width = 11 m Road width = 34 m Road width = 23 m Road width = 11 mTEPS =12.2 m TEPS =6.1 m TEPS =3.1 m 5-139

FIGURE 5.36 PROJ 24-11.doc 5-140

FIGURE 5.37 PROJ 24-11.doc Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic , Fa ct o r o f S af et y FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 FS' = 1.2 FS' = 1.2 FS' = 1.2 kh = 0.05 kh = 0.1 TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m kh = 0.2 5-141

FIGURE 5.38 PROJ 24-11.doc Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic , Fa ct o r o f S af et y FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, F S' 0.0 1.0 2.0 3.0 4.0 5.0 FS' = 1.2 FS' = 1.2 FS' = 1.2 kh = 0.05 kh = 0.1 TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m kh = 0.2 5-142

FIGURE 5.39 PROJ 24-11.doc Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic , Fa ct o r o f S af et y FS ' 0.0 1.0 2.0 3.0 4.0 5.0 Undrained Shear Strength, su (kPa) 10 20 30 40 50 Se ism ic Fa ct o r o f S af et y, F S' 0.0 1.0 2.0 3.0 4.0 5.0 FS' = 1.2 FS' = 1.2 FS' = 1.2 kh = 0.05 kh = 0.1 TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m TEPS = 12.2 m TEPS = 6.1 m TEPS = 3.1 m kh = 0.2 5-143

FIGURE 5.40 PROJ 24-11.doc 5-144

FIGURE 5.41 PROJ 24-11.doc θ θ 5-145

FIGURE 5.42 PROJ 24-11.doc θ 5-146

FIGURE 5.43 PROJ 24-11.doc 2-Lane Road Width = 11 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 2000 4000 6000 8000 10000 12000 14000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 4-Lane Road Width = 23 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 2000 4000 6000 8000 10000 12000 14000 H=16 m H=12 m H=8 m H=4 m H=2 m H=1.5 m = h + Stotal H 6- Lane Road Width = 34 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 2000 4000 6000 8000 10000 12000 14000 H=16 m H=12 m H=8 m H=4 m H=2 m H=1.5 m = h + Stotal H 5-147

FIGURE 5.44 PROJ 24-11.doc 2-Lane Road Width = 11 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 2000 4000 6000 8000 10000 12000 14000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 4-Lane Road Width = 23 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 2000 4000 6000 8000 10000 12000 14000 H=16 m H=12 m H=8 m H=4 m H=2 m H=1.5 m = h + Stotal H 6-Lane Road Width = 34 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 2000 4000 6000 8000 10000 12000 14000 H=16 m H=12 m H=8 m H=4 m H=2 m H=1.5 m = h + Stotal H 5-148

FIGURE 5.45 PROJ 24-11.doc 2 Lane Road Width = 11 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 2000 4000 6000 8000 10000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 4-Lane Road Width = 23 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 2000 4000 6000 8000 10000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 6-Lane Road Width = 34 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 2000 4000 6000 8000 10000 H=16 m H=12 m H=8 m H=4 m H=2 m H=1.5 m = h + Stotal H 5-149

FIGURE 5.46 PROJ 24-11.doc 2-Lane Road Width = 11 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 500 1000 1500 2000 2500 3000 3500 4000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 4-Lane Road Width = 23 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 500 1000 1500 2000 2500 3000 3500 4000 H=16 m H=12 m H=8 m H=4 m H=1.5 m H=2 m = h + Stotal H 6-Lane Road Width = 34 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 500 1000 1500 2000 2500 3000 3500 4000 H=16 m H=12 m H=8 m H=4 m H=2 m H=1.5 m = h + Stotal H 5-150

FIGURE 5.47 PROJ 24-11.doc θ θ 5-151

FIGURE 5.48 PROJ 24-11.doc 2-Lane Road Width = 11 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 1000 2000 3000 4000 5000 6000 7000 8000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 4-Lane Road Width = 23 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 1000 2000 3000 4000 5000 6000 7000 8000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 6-Lane Road Width = 34 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 1000 2000 3000 4000 5000 6000 7000 8000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 5-152

FIGURE 5.49 PROJ 24-11.doc 2-Lane Road Width = 11 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 1000 2000 3000 4000 5000 6000 7000 8000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 4-Lane Road Width = 23 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 1000 2000 3000 4000 5000 6000 7000 8000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 6-Lane Road Width = 34 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 1000 2000 3000 4000 5000 6000 7000 8000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 5-153

FIGURE 5.50 PROJ 24-11.doc H=16 m H=12 m H=8 m H=1.5 m, H=2 m H=4 m 2-Lane Road Width = 11 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 1000 2000 3000 4000 5000 6000 = h + Stotal H H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m 4-Lane Road Width = 23 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 1000 2000 3000 4000 5000 6000 H=16 m H=12 m H=8 m H=4 m H=1.5 m,2 m = h + Stotal H 6-Lane Road Width = 34 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 1000 2000 3000 4000 5000 6000 H=16 m H= 12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 5-154

FIGURE 5.51 PROJ 24-11.doc 2-Lane Road Width = 11 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 500 1000 1500 2000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H 4-Lane Road Width = 23 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 500 1000 1500 2000 H=16 m H=12 m H=8 m H=4 m H=1.5 m H=2 m = h + Stotal H 6-Lane Road Width = 34 m Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c U p l i f t ( k N / m o f r o a d w a y ) 0 500 1000 1500 2000 H=16 m H=12 m H=8 m H=4 m H=1.5 m H=2 m = h + Stotal H 5-155

FIGURE 5.52 PROJ 24-11.doc 5-156

FIGURE 5.53 PROJ 24-11.doc 2-Lane Road Width = 11 m δ = 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= 4-Lane Road Width = 23 m δ = 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = 6-Lane Road Width = 34 m δ = 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m = h + Stotal H δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=2 m H=1.5 m h + Stotal H = 5-157

FIGURE 5.54 PROJ 24-11.doc 2-Lane Road Width = 11 m δ = 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = 4-Lane Road Width = 23 m δ = 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = 6-Lane Road Width = 34 m δ = 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=2 m H=1.5 m h + Stotal H = 5-158

FIGURE 5.55 PROJ 24-11.doc Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m 2-Lane Road Width = 11 m δ = 40o h + Stotal H = 4-Lane Road Width = 23 m δ= 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= 6-Lane Road Width = 34 m δ= 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = 5-159

FIGURE 5.56 PROJ 24-11.doc 2-Lane Road Width = 11 m δ = 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= 4-Lane Road Width = 23 m δ = 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= 6-Lane Road Width = 34 m δ = 40o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = δ = 30o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=4 m H=1.5 m, H=2 m H=8 m h + Stotal H = δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H= δ = 20o Accumulated Water Level Embankment Height 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R e q u i r e d O v e r b u r d e n F o r F a c t o r o f S a f e t y o f 1 . 2 A g a i n s t H y d r o s t a t i c S l i d i n g ( k N ) 0 1000 2000 3000 4000 5000 6000 7000 H=16 m H=12 m H=8 m H=4 m H=1.5 m, H=2 m h + Stotal H = 5-160

FIGURE 5.57 PROJ 24-11.doc θ θ 5-161

FIGURE 5.58 PROJ 24-11.doc 0(H):1(V) Embankment Height (m) 0 5 10 15 20 25 R eq ui re d O ve rb ur de n fo r Fa ct o r o f S af et y o f 1. 2 A ga in st W in d Tr an sla tio n (k N ) 0 50000 100000 150000 200000 250000 300000 δ=20 deg, V=60 m/s δ=30 deg, V=60 m/s δ=20 deg, V=40 m/s δ=30 deg, V=40 m/s δ=40 deg, V=40 m/s δ=40 deg, V=60 m/s 2(H):1(V) Embankment Height (m) 0 5 10 15 20 25 R eq u ire d O v er bu rd en fo r Fa ct o r o f S af et y o f 1. 2 A ga in st W in d Tr an sla tio n (k N ) 0 50000 100000 150000 200000 250000 300000 δ=20 deg, V=60 m/s δ=30 deg, V=60 m/s δ=40 deg, V=60 m/s δ=20 deg, V=40 m/s δ=30 deg, V=40 m/s δ=40 deg, V=40 m/s 3(H):1(V) Embankment Height (m) 0 5 10 15 20 25 R eq u ire d O v er bu rd en fo r Fa ct o r o f S af et y o f 1. 2 A ga in st W in d Tr an sla tio n (kN ) 0 50000 100000 150000 200000 250000 300000 δ=20 deg, V=60 m/s δ=30 deg, V=60 m/s δ=40 deg, V=60 m/s δ=20 deg, V=40 m/s δ=30 deg, V=40 m/s δ=40 deg, V=40 m/s 4(H):1(V) Embankment Height (m) 0 5 10 15 20 25 R eq u ire d O v er bu rd en fo r Fa ct o r o f S af et y o f 1. 2 A ga in st W in d Tr an sla tio n (k N ) 0 50000 100000 150000 200000 250000 300000 δ=20 deg, V=60 m/s δ=30 deg, V=60 m/s δ=40 deg, V=60 m/s δ=20 deg, V=40 m/s δ=30 deg, V=40 m/s δ=40 deg, V=40 m/s 5-162

FIGURE 5.59 PROJ 24-11.doc 5-163

TABLE 5.1 PROJ 24-11.doc Material Cα/Cc Inorganic clays and silts 0.04 ± 0.01 Organic clays and silts 0.05 ± 0.01 Peat and Muskeg 0.06 ± 0.01 5-164

TABLE 5.2 PROJ 24-11.doc Total Stress Shear Strength Parameters Effective Stress Shear Strength Parameters Material Moist Unit Weight, γmoist kN/m3 (lbf/ft3) Saturated Unit Weight, γsat kN/m3 (lbf/ft3) Friction Angle, φ, (ο) Undrained Shear Strength, su kPa (lbs/ft2) Friction Angle, φ' (ο) Cohesion, c’ kPa (lbs/ft2) Soil cover 18.9 (120) 19.6 (125) N/A N/A 28 0 EPS-block Geofoam 1 (6.4) 1 (6.4) N/A 36.3 (758) N/A N/A Soft underlying clay 15.7 (100) 15.7 (100) 0 12.0, 23.9, 35.9, 47.9 (250, 500, 750, 1,000) N/A N/A Note: N/A = not applicable 5-165

TABLE 5.3 PROJ 24-11.doc Undrained Shear Strength, su kPa (lbs/ft2) SE / SF RE 12.0 (250) 3.0 0.62 17.0 (375) 2.0 0.71 23.9 (500) 1.5 0.75 35.9 (750) 1.0 0.80 47.9 (1,000) 0.75 0.82 5-166

TABLE 5.4 PROJ 24-11.doc Material Designation Dry Density/Unit Weight for Block as a Whole, kg/m3 (lbf/ft3) Initial Tangent Young's Modulus, MPa (lbs/in2) Poisson’s Ratio Shear Modulus G MPa(lbs/in2) EPS40 16 (1.0) 4 (580) 0.09 1.8 (266) EPS50 20 (1.25) 5 (725) 0.11 2.3 (327) EPS70 24 (1.5) 7 (1015) 0.14 3.1 (445) EPS100 32 (2.0) 10 (1450) 0.18 4.2 (614) Note: Shear modulus is based on the following equation: tiEG . 2(1 )ν= + (5.53) 5-167

TABLE 5.5 PROJ 24-11.doc δ Slope (H:V) TW m (ft) H m (ft) V m/s (mi/hr) OREQ* kN/m (kip/ft) Equivalent Pavement System thickness ** m (ft) 20˚ 4:1 11 (36) 2 (6.6) 40 (90) 3,870 (265) 17.2 (56) 20˚ 0:1 11 (36) 2 (6.6) 40 (90) 15,990 (1,096) 72.3 (237) 40˚ 4:1 11 (36) 2 (6.6) 40 (90) 1,656 (114) 7.2 (24) 40˚ 0:1 11 (36) 2 (6.6) 40 (90) 6,852 (470) 30.8 (101) Note: *OREQ at FS = 1.2 ** Based on an equivalent overall pavement system unit weight of 20 kN/m³ (125 lbf/ft3). 5-168