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

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6- 1 CHAPTER 6 INTERNAL STABILITY EVALUATION OF GEOFOAM EMBANKMENTS Contents Introduction...................................................................................................................................6-3 Block Interlock .............................................................................................................................6-4 Block Layout ............................................................................................................................6-4 Inter-Block Shear Resistance....................................................................................................6-4 Translation Due To Water (Hydrostatic Sliding)..........................................................................6-7 Remedial Procedures ................................................................................................................6-8 Translation Due To Wind .............................................................................................................6-8 Remedial Procedures ................................................................................................................6-9 Internal Seismic Stability of Trapezoidal Embankments..............................................................6-9 Introduction ..............................................................................................................................6-9 Typical Cross-Section.............................................................................................................6-11 Stability Analysis Procedure ..................................................................................................6-12 Material Properties .................................................................................................................6-15 Location of Critical Failure Mode ..........................................................................................6-16 Design Charts .........................................................................................................................6-17 Remedial Procedures ..............................................................................................................6-20 Internal Seismic Stability of Vertical Embankments ..................................................................6-20 Introduction ............................................................................................................................6-20 Typical Cross-Section.............................................................................................................6-21 Stability Analysis Procedure ..................................................................................................6-22 Material Properties .................................................................................................................6-23

6- 2 Location of Critical Failure Mode ..........................................................................................6-24 Design Charts .........................................................................................................................6-25 Remedial Procedures ..............................................................................................................6-29 Load Bearing...............................................................................................................................6-29 Introduction ............................................................................................................................6-29 Design Procedures ..................................................................................................................6-33 Loads Used in Developing Design Vertical Stress Charts .................................................6-38 Pavement Systems Used in Developing Design Vertical Stress Charts.............................6-39 Asphalt Concrete Pavement System. .............................................................................6-39 Portland Cement Concrete. ............................................................................................6-40 Composite Pavement System. .......................................................................................6-41 Conversion of Circular Loaded Areas To Rectangular Loaded Area ................................6-41 Remedial Procedures ..............................................................................................................6-49 Abutment Design ........................................................................................................................6-50 Introduction ............................................................................................................................6-50 Gravity Loads .........................................................................................................................6-51 Seismic Loads.........................................................................................................................6-52 Durability ....................................................................................................................................6-53 Construction Damage .............................................................................................................6-53 Long-Term Changes ...............................................................................................................6-53 Other Internal Design Considerations.........................................................................................6-55 Site Preparation ......................................................................................................................6-55 Slope Cover ............................................................................................................................6-55 Utilities ...................................................................................................................................6-55 References...................................................................................................................................6-56 Figures ........................................................................................................................................6-59

6- 3 Tables..........................................................................................................................................6-81 ______________________________________________________________________________ INTRODUCTION Design for internal stability of an EPS-block geofoam embankment involves consideration of EPS block behavior under various loadings, which are discussed in this chapter and illustrated via the design examples in Chapter 7. Internal stability in the proposed design procedure includes consideration of Serviceability Limit State (SLS) issues such as the proper selection and specification of EPS properties so the geofoam mass can provide adequate load bearing capacity to the overlying pavement system without excessive settlement and Ultimate Limit State (ULS) issues such as translation due to water (hydrostatic sliding), translation due to wind, and seismic stability (See Table 3.1). The evaluation of these three internal ULS failure mechanisms involves determining whether the geofoam embankment will behave as a single, coherent mass when subjected to external loads. This is determined by the shear resistance between the pavement system and the upper surface of the EPS mass and the interface friction between adjacent EPS blocks. Therefore, a discussion of methods that can be used to insure adequate block interlock is presented prior to describing the various internal stability analyses for translation due to water and wind and seismic shaking. Another internal stability issue involves the long-term durability of EPS blocks. To the extent that durability affects the in-situ and long-term mechanical properties of the EPS blocks, it must be considered as part of the internal stability assessment of an embankment and is discussed in this chapter. Other issues that impact internal stability include site preparation, type of cover material placed on the sides of the embankment, and utility placement. This Chapter presents detailed background information on the internal stability aspect of the EPS-block geofoam design methodology. An abbreviated form of the internal stability design procedure can be found in the provisional design guideline included in Appendix B.

6- 4 BLOCK INTERLOCK Although a lightweight fill embankment constructed using EPS-block geofoam will consist of a large number of individual blocks, current design procedures assume that the geofoam acts as a single, coherent mass when subjected to external loads (1,2). An EPS-block geofoam embankment will behave as a coherent mass if the individual EPS blocks exhibit vertical and horizontal interlock. Sufficient interlock between blocks involves consideration of the overall block layout (which primarily controls interlocking in a vertical direction) and inter-block shear (which primarily controls interlocking in the horizontal direction), both of which are discussed subsequently. Block Layout Guidelines for an appropriate layout of EPS blocks to obtain adequate interlocking in the vertical direction are summarized in Chapter 8. These guidelines include recommended block placement patterns for roadway embankments and inter-block resistance as described below. Inter-Block Shear Resistance EPS/EPS interface shear resistance and any interlocking along the horizontal interfaces between layers of EPS blocks are the primary mechanisms for resisting horizontal loads. Although the Mohr-Coulomb interface friction angle, δ, for EPS/EPS interface sliding is comparable to that of sand (δ ~ 30 degrees) as shown in Chapter 2, the shear resistance, σ′n * tan δ, is generally small in magnitude because the effective vertical normal stress, σ′n , is relatively small. This resistance may be insufficient to resist significant driving forces that result from horizontal loads such as unbalanced water head, wind, or seismic shaking. Recommended analysis procedures to evaluate the potential for horizontal sliding under these loads are described later in this chapter. If the calculated resistance forces along the horizontal planes between EPS blocks are insufficient to resist the horizontal driving forces, additional resistance between EPS blocks is

6- 5 generally provided by adding mechanical inter-block connectors (typically prefabricated barbed metal plates) along the horizontal interfaces between the EPS blocks. The use of mechanical connectors between layers of EPS blocks can be modeled by considering the horizontal interface between blocks follows the classical Mohr-Coulomb failure criterion: a nc tan′τ = + σ δ (6.1) where: ca = pseudo cohesion produced by connectors expressed as an average value per unit area, δ = EPS/EPS interface friction angle which testing conducted herein suggests is 30 degrees, σ′n = effective vertical normal stress at the interface, and τ = total shear resistance at the interface expressed as an average value per unit area. Equation (6.1) is illustrated conceptually in Figure 6.1 where it can be seen that mechanical connectors provide a pseudo cohesion to the otherwise frictional interface resistance. Experience in the U.K. (2) and elsewhere suggests that mechanical connectors are not required for typical gravity and vehicle-braking loads. However, mechanical connectors may be required where seismic or other lateral loads are deemed to be significant (3). The design chart for internal seismic stability discussed subsequently in this chapter shows that the critical interface for horizontal sliding is usually the pavement system/EPS interface and mechanical connectors are not required for a horizontal seismic coefficient less than or equal to 0.2. At the present time, all mechanical connectors available in the U.S. are of proprietary designs. Therefore, the resistance provided by such connectors and placement location must be obtained from the supplier or via independent testing. The designer should determine if the mechanical connector shear strength data provided is based on a rapid loading rate or long-term loading rate. Test data from short-term loading is appropriate for evaluating the shear resistance under transient or short-term loading such as earthquakes and is not suitable for sustained loads.

6- 6 Long-term shear resistance data should be obtained to evaluate connector shear resistance under sustained loads. Because the connector plates are propriety the cost of installing the plates may be significant. Therefore, unless the internal stability analyses indicate their necessity, the plates do not have to be installed. To overcome the proprietary nature of the common metal connector plates, new mechanical connectors such as barbed timber fasteners, special barbed geofoam connector plates, and sections of steel reinforcing bars are being developed and is a topic for future research. In addition to their role in resisting design loads, mechanical connectors have proven useful in keeping EPS blocks in place when subjected to wet, icy, or windy working conditions during construction (4) and to prevent shifting under traffic loads when only a few layers of blocks are used (5). At present, there is no consensus on where mechanical connectors should be used. One recommended practice is to place the connectors across every horizontal joint between blocks (3,6). Connectors are also used across horizontal joints on the outside face of the EPS block. A minimum of two timber fasteners per block was specified by the Washington Department of Transportation for the SR 516 project. In (7), it is recommended that a minimum of two plates for each 1.2 m (4 ft) by 2.4 m (8 ft) area of EPS be used. The resistance provided by mechanical connectors will depend on the type of connector used. In (7), it is indicated that each 102 mm by 102 mm (4 in by 4 in) plate exhibits a design pseudo cohesion of 267 N (60 lbs). This resistance is based on tests performed on EPS block with a density of 16 kg/m³ (1 lbf/ft³) in accordance with ASTM C 578 and includes a factor of safety of two. However, the effectiveness of mechanical connectors, especially under reverse loading conditions has been disputed in (2,8). Figure 6.1. Interface shear strength of EPS blocks with mechanical connectors.

6- 7 TRANSLATION DUE TO WATER (HYDROSTATIC SLIDING) Internal stability for translation due to water consists of verifying that adequate shear resistance is available between EPS block layers and between the pavement system and the EPS blocks to withstand the forces of an unbalanced water head. Equation (5.76) can be used to determine the factor of safety against hydrostatic sliding at various heights of the EPS embankment. Alternatively, Equation (5.77) can be used to determine the required overburden force, OREQ, to achieve a factor of safety of 1.2 against horizontal sliding. As discussed in Chapter 5, a minimum factor of safety of 1.2 is recommended for design of geofoam embankments against hydrostatic sliding. The vertical height of accumulated water to the bottom of the embankment at the start of construction, h, should be taken as the height of the accumulated water level to the interface that will be analyzed for hydrostatic sliding. As described in the section on hydrostatic sliding as part of external stability in Chapter 5, 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 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. Figures 5.53 through 5.56 can be used to determine the required overburden force, OREQ, to achieve a factor of safety of 1.2 against horizontal sliding. The accumulated water level used in the design charts is the sum of the height from the top of the accumulated water level to the interface that will be analyzed and the estimated total settlement, i.e., h+Stotal. Figures 5.53 through 5.56 are based on the assumption that the EPS blocks extend 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 as shown by Equations (5.67) and (5.68).

6- 8 The thickness of EPS blocks typically range between 610 mm (24 in.) to 1,000 mm (39 in.). Therefore, if the water level to be analyzed is less than about 610 mm (24 in.), an internal stability analysis for hydrostatic sliding is not required. Remedial Procedures Remedial procedures that can be used to increase the factor of safety against hydrostatic sliding include: • including a drainage system to minimize the potential for water to accumulate along the embankment. • install mechanical connectors between blocks. • 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 pavement system materials on top of the EPS thereby increasing the overburden acting on the EPS blocks. TRANSLATION DUE TO WIND Internal stability for translation due to wind consists of verifying that adequate shear resistance is available between EPS block layers and between the pavement system and EPS blocks to withstand the design wind forces. Equation (5.80) can be used to determine the factor of safety against translation due to wind. Alternatively, Equation (5.81) can be used to determine the required overburden for a factor of safety of 1.2. The bottom of the embankment should be taken as the same level as the interface that will be analyzed for translation due to wind. As described in the section on translation due to wind as part of external stability in Chapter 5, 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 sideslopes. 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

6- 9 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 can be used to determine the required overburden for a factor of safety of 1.2. The bottom of the embankment should be taken as the same level as the interface that will be analyzed for translation due to wind. Figure 5.58 is based on the assumption that the EPS blocks extend to 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 as shown by Equations (5.67) and (5.68). Remedial Procedures Remedial procedures that can be used to increase the factor of safety against translation due to wind are similar to those for increasing the factor of safety against hydrostatic sliding presented in the previous section except the use of a drainage system. INTERNAL SEISMIC STABILITY OF TRAPEZOIDAL EMBANKMENTS Introduction This section focuses on the effect of seismic forces on the internal stability of EPS-block geofoam trapezoidal embankments or embankments with sloped sides. The internal seismic response of an EPS-block geofoam embankment is discussed in the design loads section of Chapter 3. The main difference in this analysis and the external seismic stability analysis in Chapter 5 is that sliding is assumed to occur only within the geofoam embankment or along an EPS interface. This analysis uses a pseudo-static slope stability analysis, discussed in Chapter 5, and non-circular failure surfaces through the EPS or the EPS interface at the top or bottom of the embankment. 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

6- 10 slide mass that is delineated by the critical static failure surface. Therefore, the steps in an internal pseudo-static stability analysis are: 1. Identify the potential critical static failure surfaces, i.e., the static failure surface with the lowest factor of safety, that passes through the EPS embankment or an EPS interface at the top or bottom of the EPS. This is accomplished by measuring the interface strength between EPS blocks and the interfaces at the top and bottom of the EPS blocks and determining which of the interfaces yield the lowest factor of safety. In the analyses presented subsequently, it was found that the critical interface varies as the interface friction angle varies. Therefore, the factor of safety for all three interfaces should be calculated unless one of the interfaces exhibits a significantly lower interface friction angle than the other two interfaces and can be assumed to control the internal stability. 2. Determine the appropriate value of horizontal seismic coefficient (discussed in Chapter 5) that will be multiplied by gravity to determine the horizontal seismic acceleration and applied to the center of gravity of the slide mass delineated by the critical static failure surface. The horizontal seismic force is obtained by multiplying the horizontal seismic acceleration by the slide mass. As discussed in Chapter 5, estimation of the horizontal seismic coefficient can utilize empirical site response relationships and the horizontal acceleration within the embankment can be assumed to vary linearly between the base and crest values. At any level within the embankment, the interpolated value of horizontal acceleration can be multiplied by the mass of material (pavement system, EPS, etc.) above that level to determine the horizontal driving force due to seismic loading.

6- 11 3. Calculate the internal seismic factor of safety, FS’, for the critical internal static failure surface and ensure that it meets the required value of 1.2. A minimum factor of safety of 1.2 is recommended for internal seismic stability of EPS geofoam embankments because earthquake shaking is a temporary loading. The seismic factor of safety for the EPS/pavement system interface is calculated using a sliding block analysis and a pseudo-static stability analysis is used for the EPS/EPS and EPS/foundation soil interfaces. The pseudo-static factor of safety should be calculated using a slope stability method that satisfies all conditions of equilibrium, e.g., Spencer’s (9) stability method. Typical Cross-Section A typical cross-section through a 12.2 m (40 ft) high EPS trapezoidal embankment with side-slopes of 2H:1V that was used in the pseudo-static internal stability analyses is shown in Figure 6.2. It can be seen that a soil cover material is placed over the entire embankment. The material layer at the top of the embankment is used to model the pavement and traffic surcharges as discussed in Chapter 5. The pavement and traffic surcharges are modeled with a material layer on top of the embankment that has 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 unit weight of 71.8 kN/m3 (460 lbf/ft³) 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 in the external seismic slope stability analyses in Chapter 5. The pavement and traffic surcharges had to be modeled with a high unit weight soil layer instead of a surcharge. A surcharge could not be used because a seismic coefficient cannot be applied to a surcharge in limit equilibrium stability analyses because the horizontal seismic force must be applied at the center of gravity of a material layer. In summary, a pseudo-static force cannot be applied at the center of gravity of a surcharge because the surcharge does not have a center of gravity. The soil cover on the side-slopes of the embankment is also 0.46 m (1.5

6- 12 ft) thick, which is typical for the side slopes, and is assigned a typical moist unit weight of 18.9 kN/m3 (120 lbf/ft³). Figure 6.2 also presents the three failure surfaces or modes considered in the internal seismic stability analyses. It can be seen that the first failure mode, i.e., Mode I, corresponds to translational sliding at the pavement system/EPS interface at the top of the EPS blocks. This interface could involve a separation material such as a geomembrane placed over the EPS to protect the EPS against hydrocarbon spills or a geotextile to provide separation between the pavement system and the EPS. If a geosynthetic is not used on the top of the EPS blocks, the interface would consist of a pavement system material overlying the EPS blocks or a separation layer material that is not a geosynthetic placed between the pavement system and EPS blocks. The second failure mode, i.e., Mode II, corresponds to translational sliding between adjacent layers of EPS blocks, e.g., at the top of the last layer of EPS blocks, and thus consists of sliding along an EPS/EPS interface. The third failure mode, i.e., Mode III, corresponds to translational sliding at the EPS/foundation soil surface at the base of the EPS blocks. If a geosynthetic is not used at the base of the EPS blocks, the interface would consist of EPS overlying either a leveling soil or the in situ foundation soil. All three of these failure modes were assumed to initiate at or near the embankment centerline because it is anticipated that a pavement joint or median will exist near the embankment centerline in the field and provide a discontinuity that allows part of the embankment to displace. In addition, the embankment is symmetric. Figure 6.2. Typical trapezoidal cross-section used in seismic internal slope stability analyses with the three applicable failure modes. Stability Analysis Procedure Slope stability analyses were conducted on a range of trapezoidal embankment geometries to investigate the effect of embankment height (3.1 m (10 ft) to 12.2 m (40 ft)), slope inclination (2H:1V, 3H:1V, and 4H:1V), and roadway width (11 m (36 ft), 23 m (76 ft), and 34 m (112 ft)) on internal seismic slope stability. The results of these analyses were used to develop

6- 13 design charts to facilitate internal design of trapezoidal roadway embankments that utilize geofoam. Failure mode I in Figure 6.2 was modeled using a sliding block analysis in which a block slides on a surface with a frictional resistance equal to tan(φ). A similar analysis is used for retaining wall design to investigate the potential for sliding at the wall/soil interface. The weight of the block cancels out of the numerator and denominator leaving the seismic sliding factor of safety equal to: ( ) h tan φ FS'= k (6.2) where kh = horizontal seismic coefficient. The seismic factor of safety for Mode I depends only on the shear resistance of the pavement system/EPS interface and the magnitude of the horizontal seismic coefficient, i.e., size of the earthquake. The small amount of resistance that will be contributed in the field by the passive resistance of the soil cover at the edge of the pavement system was assumed to be negligible. This passive resistance could be mobilized if the pavement system slides toward the face of the side slope. This resistance was neglected in the calculations because it corresponds to approximately 165 kg (364 lbs) of passive resistance from a soil wedge weighing 102 kg (225 lbs) compared to 2,625 kg (5,790 lbs) of shear resistance developed along the pavement system interface with an interface friction angle of 25 degrees from a pavement weighing 5,634 kg (12,420 lbs). In summary, the passive resistance of the soil cover appears to be negligible and was not included in the analysis of pavement sliding along the top of the EPS and thus the seismic factor of safety is given by Equation (6.2). Failure modes II and III involve a failure surface that initiates at or near the centerline of the pavement, extends into the EPS embankment to a certain depth, and then travels horizontally until it terminates either on the embankment slope face or near the toe of the embankment, respectively. This is caused by the high intact shear strength of the EPS blocks (cohesion of 145

6- 14 kPa (3,030 lbs/ft²) from Chapter 2) and low unit weight of the EPS, which results in failure developing between the EPS blocks instead of through the EPS blocks. Therefore, the failure surface in Figure 6.2 for failure modes II and III follow pre-existing discontinuities between EPS blocks because the internal strength of the blocks is greater than the EPS/EPS interface strength. The shear resistance along these discontinuities corresponds to the EPS/EPS interface shear strength parameters of φ=30 degrees and c = 0 as shown in Table 6.1 and described in Chapter 2. These two failure modes result in a steep failure surface through the EPS blocks (see Figure 6.2) and the failure modes model a failure surface descending between adjacent blocks and not through EPS blocks. This results in a stair-stepped failure surface through the EPS that was modeled in the slope stability program XSTABL (10) by identifying the exact geometry of the failure surface through the EPS. A typical EPS block size of 760 mm (30 in.) high and 4,900 mm (193 in.) long was used to model the failure surfaces extending through the EPS blocks because this size was recently used on the Interstate-15 geofoam projects near Salt Lake City, Utah (8). It was assumed that the EPS blocks are offset laterally in the field so a continuous failure surface cannot develop through the blocks without generating any horizontal resistance through the EPS. The overall stair-stepped angle was assumed to be inclined at 45 degrees + φEPS/EPS/2 from the horizontal to simulate an active earth pressure condition where φEPS/EPS is the interface friction angle between two blocks of EPS. Thus, for a φEPS/EPS=30 degrees, the stair-stepped inclination was assumed to be 60 degrees. This inclination results in a minimum lateral earth pressure condition and a minimum shear resistance along the horizontal segments of the EPS blocks during failure. For a 0.76 m (2.5 ft) high EPS block and a 60 degrees overall stair-stepped inclination, the lateral offset of the failure surface is 0.76 * tan-1 (60˚) or 0.44 m (1.4 ft). Thus, it can be seen in Figure 6.2 that as the failure surface extends through the EPS, it creates a stair-stepped pattern to reflect the blocks being laterally offset. On the vertical portions of the stair-stepped pattern no shear resistance was applied in the stability analyses, however an

6- 15 interface friction angle of 30 degrees was assigned to the horizontal segments to reflect sliding between EPS blocks. The stair-stepped failure surface could travel horizontally along a horizontal joint between adjacent rows of EPS blocks (mode II) or continue to the base of the EPS and travel along the EPS/foundation interface (mode III). The factor of safety for failure mode II is a function of the depth at which the failure surface travels along a horizontal joint between adjacent rows of EPS blocks. The analyses conducted herein show that the seismic factor of safety decreases as the failure mode II extends further into the EPS and the critical failure surface was found to be located at the top of the bottom row of EPS blocks. As a result, failure mode II is similar to mode III with the only difference being that failure mode III extends to the EPS/foundation soil interface and the applicable interface friction angle along the horizontal portion of the failure surface is controlled by the EPS/foundation soil interface strength or by the type of geosynthetic or soil used between the EPS and the foundation soil instead of simply the EPS/EPS interface strength. Material Properties The input parameters, i.e., unit weight and shear strength, used in the internal slope stability analyses are presented in Table 6.1. It can be seen that Mohr-Coulomb shear strength parameters were used to represent the shear strength of the cover soil and the EPS interfaces. 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. Based on the geofoam shear strength testing described in Chapter 2, the value of EPS/EPS interface shear strength of 30 degrees can be used for the internal seismic analyses and does not have to be adjusted for seismic loading. This conclusion is also supported by the results of shake table tests on geosynthetic interfaces (11) that show the seismic strength of geosynthetic interfaces is at least as great as the static interface strength. It can be seen from Chapter 2 that the geofoam interface friction angle ranges from 24 degrees (geofoam/geotextile interface) to 52 degrees (geofoam/geomembrane interface) for

6- 16 EPS/geosynthetic interfaces and thus the design charts presented subsequently were developed for an interface friction angle ranging from 10 to 40 degrees (see Table 6.1). The design charts do not extend to an interface friction of 52 degrees because the analyses show that stability is not an issue with an interface friction angle greater than 40 degrees because the design chart relationships (discussed subsequently) are independent of interface friction angle at angles greater than 40 degrees. Sometimes a sand layer is placed between the geotextile and the geofoam at the bottom of an embankment and thus the geofoam/geotextile interface may not be present. In this case, an EPS/sand interface strength should be used and can be measured using direct shear tests (ASTM D 5321) to obtain a representative interface friction angle for use in the design charts. In summary, for the internal stability analysis performed for this study, an effective stress friction angle of 28 degrees was used for the soil cover and an interface friction angle of 30 degrees was used for the EPS/EPS interface in all of the analyses. Only the pavement system/EPS and EPS/foundation soil interface was varied between 10 and 40 degrees. Table 6.1. Input Parameters for Internal Slope Stability Analyses. Location of Critical Failure Mode Location of the critical failure mode, e.g., I, II, or III, for a particular embankment geometry was found to be a function of the three interface friction angles used to model these three failure modes. Failure modes I, II, and III depend on the interface friction angle between the pavement system and EPS, EPS and EPS, and EPS and the foundation geosynthetic or soil, respectively. The effect of the interface friction angle on the location of the critical failure surface is illustrated in Figure 6.3, which presents the seismic factor of safety for a 6-lane roadway on a 12.2 m (40 ft) high embankment for the three values of horizontal seismic coefficient (0.05, 0.10, and 0.20) used in Chapter 5. It can be seen for a horizontal seismic coefficient of 0.05, failure mode I, i.e., failure at the EPS/pavement system interface, is critical for an interface friction angle equal to or less than 15 to 20 degrees. For interface friction angles between 15 and about 30 degrees, failure mode III, i.e., failure at the EPS/foundation interface, is critical. For interface

6- 17 friction angles greater than about 30 degrees, failure mode II, i.e., failure within the embankment along an EPS/EPS interface, is critical. Therefore, the critical internal failure mode will vary depending on the design value of internal friction angle. A similar change in critical failure surface with changes in interface friction angle has been observed by (12) for the design of geosynthetic composite liner systems for landfills. As a result, the seismic factor of safety relationships presented subsequently in the design chart for failure modes II and III are combined because it can be seen that failure mode III is critical until an interface friction angle of approximately 30 degrees is reached. At interface friction angles greater than approximately 30 degrees, failure mode II controls because the friction angle for an EPS/EPS interface is 30 degrees. The effect of the interface friction angle on the seismic factor of safety is important because if the interface friction angle is increased on one interface, a different interface may become critical and might have to be strengthened to achieve the required factor of safety. For example, if the interface friction angle for failure mode I is increased from 10 to 15 degrees for a horizontal seismic coefficient of 0.2, the seismic factor of safety increases from approximately unity to greater than the required value of 1.2 (see Figure 6.3). However, if the interface friction angle for either failure mode II or III is 10 degrees, these interfaces will exhibit a seismic factor of safety at or below 1.2 and be critical. This may require the interface friction angle to be increased for failure mode III but probably not for failure mode II because the EPS/EPS interface friction angle usually exceeds 10 degrees as described in Chapter 2. Figure 6.3. Effect of interface friction angle and slope inclination on seismic factor of safety, for 12.2 m high EPS-block geofoam trapezoidal embankment with a 6-lane roadway with a total road width of 34 m (112 ft). Design Charts Figure 6.3 also illustrates the sensitivity of the seismic internal factor of safety to the inclination of the side slopes of the embankment. For all slope inclinations considered (2H:1V,

6- 18 3H:1V, and 4H:1V), the internal seismic factor of safety for failure mode I is not a function of the side slope inclination because the analysis simply involves a sliding block along a horizontal plane at the pavement system/EPS interface. For failure modes II and III, the slope inclination does not significantly influence the seismic internal factor of safety especially at horizontal seismic coefficients of 0.1 and 0.2. In addition, the largest variation of seismic factor of safety occurs at large values of factor of safety, i.e., kh = 0.05, with factors of safety of approximately 8 which is well above the required value of 1.2. As a result, the subsequent design chart is based on the most critical slope inclination of 2H:1V and thus the design chart is independent of inclination of the embankment side slopes. It can be seen that the sensitivity studies were conducted for a 6- lane roadway with a total road width of 34 m (112 ft) on top of a 12.2 m (40 ft) high EPS embankment in Figure 6.3. Figure 6.4 illustrates the sensitivity of the seismic internal factor of safety to the width of the embankment for a 12.2 m (40 ft) high EPS embankment with side-slope inclinations of 2H:1V. It can be seen that the critical failure mode is again a function of the interface friction angle with failure mode I controlling at low interface friction angles and mode II controlling at high values of interface friction angle. It can also be seen that roadway width does not significantly influence the seismic internal factor of safety especially at horizontal seismic coefficients of 0.1 and 0.2. At a horizontal seismic coefficient of 0.05, it can be seen that the seismic internal factor of safety is influenced by the difference in embankment width for a 2-lane (11 m (36 ft) wide) and a 6-lane (34 m (112 ft) wide) roadway with the 2-lane roadway being slightly more critical than the 6-lane roadway. However, the seismic factor of safety varies from approximately 7 to 8, which is well above the required value of 1.2 and thus will not control the embankment design. As a result, the subsequent design chart is based on the most critical slope inclination and roadway width of 2H:1V and 11 m (36 ft), 2-lane roadway. Figure 6.4. Effect of roadway width on seismic factor of safety for 12.2 m high trapezoidal embankment with a side-slope inclination of 2H:1V.

6- 19 Figure 6.5 illustrates the final sensitivity study used to develop the design chart, which involves the effect of embankment height on the seismic internal factor of safety. Based on the sensitivity studies in Figures 6.3 and 6.4, a 12.2 m (40 ft) high EPS embankment with a side- slope inclination of 2H:1V and a 2-lane roadway were used for this sensitivity study. It can be seen that embankment height does not significantly influence the seismic internal factor of safety especially at horizontal seismic coefficients of 0.1 and 0.2. At a horizontal seismic coefficient of 0.05, it can be seen that the seismic internal factor of safety is influenced by the difference in embankment height from 3.1 m (10 ft) to 12.2 m (40 ft). However, the seismic factor of safety varies from approximately 7 to about 9.5, which is well above the required value of 1.2 and thus will not control the embankment design. As a result, the subsequent design chart is based on the most critical slope inclination (2H:1V) and roadway width (11 m (36 ft) or 2-lane roadway). In addition, the relationship for failure modes II and III in the design chart depict the critical embankment height which varies from 3.1 m (10 ft) at an interface friction angles less than about 20 degrees to 12.2 m (40 ft) at an interface friction angles greater than or equal 20 degrees. The difference in the seismic factor of safety for heights of 3.1 m (10 ft) and 12.2 m (40 ft) is small, thus the design chart can be used for any embankment height between 3.1 m (10 ft) and 12.2 m (40 ft). Figure 6.5. Effect of EPS embankment height on seismic factor of safety for a trapezoidal embankment with a side-slope inclination of 2H:1V and a 2-lane roadway. The internal seismic stability design chart in Figure 6.6 presents the seismic factor of safety for each seismic coefficient as a function of interface friction angle. Based on the previously described parametric study, this chart can be used for any of the geometries considered during this study, i.e., embankment heights of 3.1 m (10 ft) to 12.2 m (40 ft), slope inclinations of 2H:1V, 3H:1V, and 4H:1V, and roadway widths of 11 m, 23 m, and 34 m (36, 76, and 112 feet), even though it is based on a side-slope inclination of 2H:1V, a 2-lane roadway, and an embankment height from 3.1 m (10 ft) to 12.2 m (40 ft). It can be seen that an EPS embankment

6- 20 will exhibit a suitable seismic factor of safety if the minimum interface friction angle exceeds approximately 15 degrees. However, an important aspect of Figure 6.6 is to develop the most cost-effective internal stability design by selecting the lowest interface friction angle for each interface that results in a seismic factor of safety of greater than 1.2. For example, a lightweight geotextile can be selected for the EPS/foundation interface because the interface only needs to exhibit a friction angle greater than 10 degrees. More importantly, the EPS/EPS interface within the EPS also only needs to exhibit a friction angle greater than 10 degrees, which suggests that mechanical connectors are not required between EPS blocks for internal seismic stability because the interface friction angle for an EPS/EPS interface is approximately 30 degrees (see Chapter 2). In summary, it appears that internal seismic stability will be controlled by the shear resistance of the pavement system/EPS interface. Figure 6.6. Design chart for internal seismic stability of EPS trapezoidal embankments. Remedial Procedures Remedial procedures that can be used to increase the factor of safety against internal seismic instability are decreasing the pavement system thickness, using pavement system materials with a lower unit weight, increasing the interface resistance at the pavement system/EPS interface and EPS/geosynthetic or soil interface at the bottom of the EPS blocks, and possibly using inter-block mechanical connectors to increase the interface strength between the EPS blocks. INTERNAL SEISMIC STABILITY OF VERTICAL EMBANKMENTS Introduction As shown by Figure 3.4 (b), an embankment with vertical sides, sometimes referred to as a geofoam wall, can be utilized with EPS- block geofoam. The use of an embankment with vertical walls 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 focuses on the effect of seismic forces on the internal stability of EPS-block geofoam

6- 21 embankments with vertical walls. The main difference in this analysis and the analysis for external seismic stability of embankments with vertical walls in Chapter 5 is that sliding is assumed to occur only within the geofoam embankment or along an EPS interface. This analysis uses the same pseudo-static slope stability analysis used for internal seismic stability of trapezoidal embankments and non-circular failure surfaces through the EPS or the EPS interface at the top or bottom of the embankment. 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 center of gravity of the slide mass that is delineated by the critical static failure surface. The same steps outlined in the “Introduction” sub-section of the “Internal Seismic Stability of Trapezoidal Embankments” section of this chapter can be used to conduct an internal pseudo-static stability analysis of vertical geofoam embankments. Typical Cross-Section A typical cross-section through a vertical EPS embankment used in the internal static stability analyses is shown in Figure 6.7. This cross-section is similar to the cross-section used for static analyses of vertical embankments in Figure 5.29 but differs from the cross-section used for the static analyses of trapezoidal embankments in Figure 5.10 because the surcharge used to represent the pavement and traffic surcharges is replaced by placing a 0.61 m (2 ft) thick soil layer on top of the embankment with a unit weight of 54.1 kN/m3 (345 lbs/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 times the increased unit weight or 33.0 kN/m2 (690 lbs/ft²). A vertical stress of 33.0 kN/m2 (690 lbs/ft²) corresponds to the sum of the design values of pavement surcharge (21.5 kN/m2 (450 lbs/ft²)) and traffic surcharge (11.5 kN/m2 (240 lbs/ft²)) used previously for external bearing capacity and static slope stability of trapezoidal embankments in Chapter 5.

6- 22 The surcharge in Figure 5.10 had to be replaced by an equivalent soil layer for the seismic slope stability analysis because a seismic coefficient cannot be applied to a surcharge in limit equilibrium stability analyses. The horizontal force that represents the seismic loading must be applied at the center of gravity of a material layer and not on a surcharge because a surcharge does not have a center of gravity. As noted in Chapter 5, this soil layer, which is equivalent to the pavement and traffic surcharge, was also used for the static stability analyses of vertical embankments instead of a surcharge to minimize the number of stability analyses that would be required to determine the critical static factor of safety and critical static failure surface for each model, 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 vertical slice in the limit equilibrium analysis while the force exerted by the weight of the soil layer is located at the center of each vertical slice. In summary, a pseudo-static seismic force cannot be applied at the center of gravity of a surcharge so the pavement system and traffic loads were modeled as an equivalent soil layer and not a surcharge. Figure 6.7. Typical cross-section used in seismic internal slope stability analyses for vertical embankments with the three applicable failure modes. Figure 6.7 also presents the three failure modes considered in the internal seismic stability analyses for vertical geofoam embankments. These failure modes are similar to the three failure modes analyzed in seismic internal slope stability analysis of trapezoidal embankments and a description of each is included in the “Typical Cross-Section” and “Stability Analysis Procedure” sub-sections of the “Internal Seismic Stability of Trapezoidal Embankments” section of this chapter. Stability Analysis Procedure Slope stability analyses were conducted on a range of vertical embankment geometries to investigate the effect of embankment height (3.1 m (10 ft) to 12.2 m (40 ft)) and roadway width

6- 23 (11 m (36 ft), 23 m (76 ft), and 34 m (112 ft)) on internal seismic slope stability. The results of these analyses were used to develop design charts to facilitate internal design of roadway embankments with vertical walls that utilize geofoam. The three failure modes shown in Figure 6.7 are similar to the three failure modes used in the analysis of trapezoidal embankments shown in Figure 6.2. Therefore, the analysis procedures used to model the three failure modes are similar to the procedures used in seismic internal slope stability analyses of trapezoidal embankments and are described in the “Stability Analysis Procedure” sub-section of the “Internal Seismic Stability of Trapezoidal Embankments” section of this chapter. However, Spencer’s (9) slope stability method did not converge for the vertical wall embankment geometries investigated. Therefore, Simplified Janbu’s method (13) was used to perform the internal slope stability analyses shown in Figures 6.8 through 6.12. The factor of safety obtained using the Simplified Janbu’s method is based on horizontal and vertical force equilibrium. Moment equilibrium is not satisfied, which is undesirable, but more importantly horizontal force equilibrium is satisfied which allows the seismic force to be directly incorporated into the analysis. Spencer’s (9) stability method, which satisfies all conditions of equilibrium, was used to obtain the seismic factor of safety, FS’, values for trapezoidal embankments shown in Figures 6.3 through 6.6. Therefore, a quantitative comparison cannot be made between the trapezoidal embankment design charts shown in Figures 6.3 through 6.6 and the vertical embankment design charts shown in Figures 6.8 through 6.12 but qualitative comparisons are suitable. Material Properties The same input parameters, i.e., unit weight and shear strength, used in the internal seismic stability analyses of trapezoidal embankments, which are presented in Table 6.1, were used for the internal seismic stability analysis of embankments with vertical walls. The basis for these input material parameters is presented in the “Material Properties” sub-section of the “Internal Seismic Stability of Trapezoidal Embankments” section of this chapter. However, since vertical embankments do not have a soil cover on the side walls, the soil cover material

6- 24 parameters shown in Table 6.1 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 phreatic surface is located at or near the ground surface and the foundation soil is saturated as is typically the case at most EPS-block geofoam sites. Location of Critical Failure Mode Location of the critical failure mode, e.g., either I, II, or III, for a particular embankment geometry was found to be a function of the three interface friction angles used to model these three failure modes. This behavior is similar to the behavior observed for trapezoidal embankments. Failure modes I, II, and III depend on the interface friction angle between the pavement system and EPS, EPS and EPS, and EPS and the foundation geosynthetic or soil, respectively. The effect of the interface friction angle on the location of the critical failure surface is illustrated in Figure 6.8, which presents the seismic factor of safety for a 6-lane roadway with a width of 34 m (112 ft) on a 12.2 m (40 ft) high embankment for the three values of horizontal seismic coefficient (0.05, 0.1, and 0.2). It can be seen for a horizontal seismic coefficient of 0.05, failure mode I or failure at the EPS/pavement system interface, is critical for an interface friction angle less than or equal to 11 degrees (see Figure 6.8). For interface friction angles between 10 and about 30 degrees, failure mode III, i.e., failure at the EPS/foundation interface, is critical. For interface friction angles greater than 30 degrees, failure mode II, i.e., failure within the embankment along an EPS/EPS interface, is critical. Therefore, the critical internal failure mode depends on the design value of internal friction angle. A similar change in critical failure surface with changes in interface friction angle has been observed by (12) for the design of geosynthetic composite liner systems for landfills and for trapezoidal embankments as shown in Figure 6.3. As a result, the seismic factor of safety relationships presented subsequently in the design chart for failure modes II and III are combined because it can be seen that failure mode III is critical until an interface friction angle of approximately 30 degrees is reached. At interface friction

6- 25 angles greater than approximately 30 degrees, failure mode II controls because the friction angle for an EPS/EPS interface is 30 degrees. A similar behavior was observed for seismic coefficients of 0.10 and 0.20 with only the transition from failure mode I and failure modes II and III occurring at a higher interface friction angle (see Figure 6.8). The effect of the interface friction angle on the seismic factor of safety is important because an increase in interface friction angle on one interface may result in a different interface being critical. The resulting critical interface may have to be strengthened to achieve the required factor of safety. For example, if the interface friction angle for failure mode I is increased from 10 to 15 degrees for a horizontal seismic coefficient of 0.2, the seismic factor of safety increases from approximately unity to greater than the required value of 1.2 (see Figure 6.8). Design Charts Failure mode I in Figure 6.7 was modeled using a sliding block analysis with the same procedure utilized for internal seismic stability of trapezoidal embankments. The seismic factor of safety, which is given by Equation 6.2, depends only on the shear resistance of the pavement system/EPS interface and the magnitude of the horizontal seismic coefficient, i.e. size of the earthquake. As was shown by Figure 6.3, the internal seismic factor of safety for failure mode I is not a function of the side slope inclination for the case of trapezoidal embankments. Therefore, the factor of safety for failure mode I for the case of vertical embankments in Figure 6.8 is similar to the factor of safety for the case of trapezoidal embankments in Figure 6.3 because the analysis for failure mode I simply involves a sliding block along a horizontal plane at the pavement system/EPS interface. For failure modes II and III within a trapezoidal embankment, the slope inclination influences the seismic internal factor of safety at a horizontal seismic coefficient of 0.05 but this influence decreases with increasing value of horizontal seismic coefficient (see Figure 6.3). Slope inclination does not significantly influence the seismic internal factor of safety at horizontal seismic coefficients of 0.1 and 0.2. Figure 6.3 also shows that for a given horizontal seismic

6- 26 coefficient, the seismic factor of safety decreases as the side slope becomes steeper. Although a quantitative comparison cannot be made between the internal seismic stability results of vertical embankments and trapezoidal embankments, e.g., between Figures 6.8 and 6.3, respectively, the seismic factor of safety values shown by modes III/II for vertical embankments in Figure 6.8 are less than the factor of safety values for trapezoidal embankments in Figure 6.3, with the difference becoming smaller with increasing horizontal seismic coefficient. The qualitative comparison of design charts also shows the difference in seismic factor of safety between a vertical wall and a 2H:1V sloped embankment is greater than between a 2H:1V and a 3H:1V sloped embankment. This difference is attributed to the difference in the slope stability method and the small passive resistance that the soil cover may contribute in a trapezoidal embankment. In addition, the traffic and pavement surcharges were modeled using a 0.61 m (2 ft) soil layer for the embankment with vertical walls case while the trapezoidal case was modeled using a 0.46 m (1.5 ft) soil layer, which is equivalent to the thickness of soil cover. This difference in soil layer thickness between the two models would have an impact on the location of the center of gravity of the soil layer where the horizontal force that represents the seismic loading is located. Also, for the vertical wall model, the soil layer had a shear strength of 0 degrees while for the sloped embankment model, the soil layer had a shear strength of 28 degrees, which is the same as the soil cover. Figure 6.8. Effect of interface friction angle on seismic factor of safety for 12.2 m high vertical embankment and with a 6-lane roadway with a total road width of 34 m (112 ft). Figures 6.9 and 6.10 illustrate the sensitivity of the seismic internal factor of safety to the width of the vertical embankment for a 3.1 m (10 ft) and 12.2 m (40 ft) high EPS embankment, respectively. It can be seen that the critical failure mode is a function of the interface friction angle. For a 3.1 m (10 ft) high embankment (Figure 6.9), failure mode III controls at low interface friction angles except at a horizontal seismic coefficient of 0.2 where failure mode I is

6- 27 slightly more critical. However, for a 12.2 m (40 ft) high embankment (Figure 6.10), failure mode I controls at low interface friction angles. A similar observation was made for trapezoidal embankments as shown by Figure 6.4. Mode II controls at high values of interface friction angles for both a 3.1 m (10 ft) and 12.2 m (40 ft) high embankment. For the 3.1 m (10 ft) high embankment (Figure 6.9), it can be seen that the seismic internal factor of safety is influenced by the difference in embankment width for an 11 m (36 ft) and 34 m (112 ft) wide roadway with the 11 m (36 ft) wide roadway being more critical than the 34 m (112 ft) roadway for failure modes II and III. For the 12.2 m (40 ft) high embankment (Figure 6.10), an embankment width of 11 m yields similar or lower seismic factors of safety than the 11 m (36 ft) wide embankment for failure mode II. Because a 11 m (36 ft) roadway is more critical for both embankment heights investigated, the subsequent design chart (Figure 6.12) is based on an 11 m (36 ft) wide, 2-lane roadway. Figure 6.11 illustrates the final sensitivity study used to develop the design chart, which involves the effect of embankment height on the seismic internal factor of safety. An embankment width of 11.1 m (36 ft) or a 2-lane roadway was used for this sensitivity study because the sensitivity studies in Figures 6.9 and 6.10 indicate that a 2-lane roadway is critical. It can be seen that the seismic internal factor of safety is influenced by the difference in embankment height from 3.1 m (10 ft) to 12.2 m (40 ft) for the three horizontal seismic coefficients investigated with the difference becoming less with an increase in horizontal seismic coefficient. Although the seismic factor of safety at interface friction angles of less than 30 degrees could not be determined for failure mode III for an embankment height of 12.2 m, it is anticipated that for a given width, an embankment height 12.2 m (40 ft) will provide larger seismic factors of safety than the shorter embankment of 3.1m (10 ft). Therefore, the subsequent design chart is based on the most critical embankment height of 3.1 m (10 ft). As indicated by Figure 6.10, no data is shown for failure mode III for the 12.2 m (40 ft) high and 11 m (36 ft) wide embankment because the critical failure mode could not be modeled.

6- 28 Based on the assumed stair-stepped internal failure surface used in the analyses with an overall inclination of 60 degrees to the horizontal, the internal failure surface will terminate within the EPS for tall and narrow embankments and will not extend to the EPS/foundation soil interface. Although slope stability analyses could not be performed for failure mode III for the 12.2 m (40 ft) high and 11 m (36 ft) wide embankment, based on the results shown in Figure 6.9 for the 3.1 m (10 ft) high embankments, it is anticipated that an embankment width of 11 m (36 ft) will provide less shear resistance within the blocks than the 34 m (112 ft) wide embankment and, consequently, the 11 m (36 ft) wide embankment will yield lower seismic factor of safety values for failure mode III than the 34 m wide (112 ft) embankment. This conclusion is in accordance with the previous conclusion made above that the critical embankment width is 11 m (36 ft) for both the 3.1 m (10 ft) and 12.2 m (40 ft) high embankments. Additionally, Figure 6.11 indicates that the critical embankment height is 3.1 m (10 ft). Therefore, failure mode III for the 12.2 m (40 ft) high embankment is not critical. Figure 6.9. Effect of roadway width on seismic factor of safety for 3.1 m high vertical embankment. Figure 6.10. Effect of roadway width on seismic factor of safety for 12.2 m high vertical embankment. Figure 6.11. Effect of EPS embankment height on seismic factor of safety for a vertical embankment with a 2-lane roadway with a width of 11 m (36 ft). The internal seismic stability design chart for vertical embankments in Figure 6.12 presents the seismic factor of safety for each seismic coefficient as a function of interface friction angle. Based on the previously described parametric study, this chart provides estimates of seismic internal factor of safety for vertical embankments with any of the geometries considered during this study, i.e., embankment heights of 3.1 m (10 ft) to 12.2 m (40 ft) and roadway widths

6- 29 of 11 m, 23 m, and 34 m (36, 76, and 112 feet), even though it is based on a roadway width of 11 m (36 ft) and an embankment height from 3.1 m (10 ft). It can be seen that an EPS embankment will exhibit a suitable seismic factor of safety if the minimum interface friction angle exceeds approximately 15 degrees, which is similar for trapezoidal embankments (see Figure 6.6). However, an important aspect of Figure 6.12 is that it can be used to develop the most cost-effective internal stability design by selecting the lowest interface friction angle for each interface that results in a seismic factor of safety of greater than 1.2. For example, a lightweight geotextile can be selected for the EPS/foundation interface because the interface only needs to exhibit a friction angle greater than 15 degrees. More importantly, the EPS/EPS interface within the EPS also only needs to exhibit a friction angle greater than 15 degrees, which suggests that mechanical connectors are not required between EPS blocks for internal seismic stability because the interface friction angle for an EPS/EPS interface is approximately 30 degrees (see Chapter 2). In summary, as with trapezoidal embankments, it appears that internal seismic stability will be controlled by the shear resistance of the pavement system/EPS interface. Remedial Procedures Remedial procedures that can be used to increase the factor of safety against internal seismic instability are decreasing the pavement system thickness, using pavement system materials with a lower unit weight, increasing the interface resistance at the pavement system/EPS interface and EPS/geosynthetic or soil interface at the bottom of the EPS blocks, and possibly using inter-block mechanical connectors to increase the interface strength between the EPS blocks. Figure 6.12. Design chart for internal seismic stability of EPS vertical embankments. LOAD BEARING Introduction

6- 30 The primary internal stability issue for EPS-block geofoam embankments is the load bearing of the EPS geofoam mass. A load bearing capacity analysis consists of selecting an EPS type with adequate properties to support the overlying pavement system and traffic loads without excessive EPS compression that could lead to excessive settlement of the pavement surface. Therefore, a knowledge of the mechanical (stress-strain-time-temperature) properties of block- molded EPS is required to understand the basis for past and current load bearing analysis procedures. The mechanical properties at small strains are the most relevant otherwise the settlements may become excessive if the large strain properties of the EPS block are mobilized. The three design goals for a load bearing analysis to ensure adequate performance of the EPS-block geofoam are: • The initial (immediate) deformations under dead or gravity loads from the overlying pavement system must be within acceptable limits. • Long-term (for the design life of the fill) creep deformations under the same gravity loads must be within acceptable limits. • Non-elastic or irreversible deformations under repetitive traffic loads must be within acceptable limits. Two load bearing analysis procedures have been used with EPS-block geofoam embankments to achieve these design goals. The first approach used in the early use of EPS-block geofoam as lightweight fill in the 1970s and 1980s consists of limiting the maximum applied vertical stress under any combination of loads to some fraction or percentage of the "compressive strength" of the EPS without regard to the level of deformation. This empirical approach is based solely on the ULS (collapse failure) design concept with no consideration of SLS design (deformations). Although this approach has resulted in EPS-block geofoam fills that have performed satisfactorily, it is not the most desired or theoretically sound because it can result in smaller deformations than can be tolerated.

6- 31 The current design approach, which is recommended herein, is an explicit deformation- based design methodology. It is based on the recognition that the compressive strength of EPS does not quantify the deformation characteristics of the geofoam. Consequently, the parameter of compressive strength is not used for a load bearing analysis but is still used for MQC/MQA purposes. The small-strain analysis utilizes the elastic limit stress, σe , and the initial tangent Young’s modulus, Eti , both of which are fully defined in Chapter 2, to evaluate the three settlement issues presented above. As shown in Chapter 2, current creep models for EPS-block geofoam do not provide reliable estimates of long-term vertical strain. However, creep strains within the EPS mass under sustained loads (primarily due to the overlying pavement system) are within acceptable limits (0.5 percent to 1 percent strain over 50 years) if the applied vertical stress produces an immediate strain between 0.5 percent and 1 percent. Consequently, if the applied vertical stress produces an immediate strain greater than 1 percent in laboratory testing, the EPS creep strains will rapidly increase and be considered excessive for lightweight fill applications. The initial (immediate) settlement can be estimated by dividing the applied vertical stress by the initial Young’s modulus (see Equation (5.9) in Chapter 5). Results of uniaxial compression tests (rapid loading, repetitive traffic loading, and creep) on specimens of EPS block test specimens indicate that if the maximum applied vertical stress under repetitive traffic loading has a magnitude not exceeding the elastic limit stress, the non- elastic or irreversible deformations will be tolerable and there will be no degradation of the initial Young’s modulus of the EPS. Table 6.2 provides the minimum recommended values of elastic limit stress for various EPS densities. The use of the elastic limit stress values indicated in Table 6.2 is slightly conservative because the elastic limit stress of the block as a whole is somewhat greater than these minimums, but this conservatism is not unreasonable and would ensure that no part of a block (where the density might be somewhat lower than the overall average) would become

6- 32 overstressed. Table 6.2 also contains recommended values of initial tangent Young’s modulus for determination of the initial (immediate) deformations. Table 6.2. Minimum allowable values of elastic limit stress and initial tangent Young’s Modulus for the proposed AASHTO EPS material designations. One advantage of a deformation-based design procedure is that the calculation of stresses and strains within the EPS mass allows the density of the EPS blocks to be optimized and thus specified for various portions of the embankment. In the 1970s and 1980s, there was a tendency to use EPS blocks of a single density for every project. The most commonly used density was 20 kg/m3 (1.25 lbf/ft3) (sometimes referred to as "EPS20" in European literature). EPS of this density was found to produce acceptable results so there was a tendency to simply replicate this on every project which resulted in an empirical approach. As a result, there was no rational basis for varying from a density that produced acceptable results. However, with a deformation-based design it is possible to select an EPS density that provides adequate load-bearing capacity within tolerable settlements without requiring an inefficient density. Because the applied vertical stress decreases with depth under the pavement and side slopes, it is possible to use multiple densities of EPS blocks in an embankment. For example, lower density blocks can be used at greater depths and/or under side slopes than higher density blocks that have to be used under the pavement system. The reason for not wanting to use an excessively high density of EPS is that the manufacturing cost of EPS block is significantly linked to the relative amount of raw material (expandable polystyrene) used. For example, an EPS block with an overall average density of 32 kg/m3 (2.0 lbf/ft3) would use twice as much raw material as an EPS block with an overall average density of 16 kg/m3 (1.0 lbf/ft3). In the U.S., raw material cost accounts for one half or more of the manufacturing cost of an EPS block so the impact of EPS density on project costs can be significant. Thus, there is an incentive to rationally select one or more EPS densities to use on a given project, with blocks of different density placed according to the applied vertical stresses. It is now routine in the U.K. to use three or four EPS densities within a given road embankment

6- 33 cross section. However, for constructability it is recommended that no more than two different density EPS blocks be used on the same project. As indicated in Chapter 4, the use of EPS40 directly below the pavement system is not recommended because the elastic limit stress of 40 kPa (5.8 lbs/in2) has been found to result in excessive settlements directly under a pavement system. Design Procedures The procedure for evaluating the load bearing capacity of EPS as part of internal stability is outlined in the following thirteen steps: 1. Estimate traffic loads. 2. Add impact allowance to traffic loads. 3. Estimate traffic stresses at top of EPS blocks. 4. Estimate gravity stresses at top of EPS blocks. 5. Calculate total stresses at top of EPS blocks. 6. Determine minimum required elastic limit stress for EPS under pavement system. 7. Select appropriate EPS block to satisfy the required EPS elastic limit stress for underneath the pavement system, e.g., EPS50, EPS70, or EPS100. 8. Select preliminary pavement system type and determine if a separation layer is required. 9. Estimate traffic stresses at various depths within the EPS blocks. 10. Estimate gravity stresses at various depths within the EPS blocks. 11. Calculate total stresses at various depths within the EPS blocks. 12. Determine minimum required elastic limit stress at various depths. 13. Select appropriate EPS block to satisfy the required EPS elastic limit stress at various depths in the embankment. The load bearing design procedure can be divided into two parts. Part 1 consists of Steps 1 through 8 and focuses on the determination of the traffic and gravity load stresses applied by

6- 34 the pavement system to the top of the EPS blocks and selection of the type of EPS that should be used directly beneath the pavement system (see steps above). Part 2 consists of Steps 9 through 13 and focuses on the determination of the traffic and gravity load stresses applied at various depths within the EPS blocks and selection of the appropriate EPS for use at these various depths within the embankment. Each of the design steps are subsequently described in detail. Additionally, in Chapter 7, Tables 7.6 through 7.8 are provided that summarize the load bearing design procedure for an example problem. In summary, the basic procedure for designing against load bearing failure is to calculate the maximum vertical stresses at various levels within the EPS mass (typically the pavement system/EPS interface is most critical) and select the EPS that exhibits an elastic limit stress that is greater than the calculated or required elastic limit stress at the depth being considered. Step 1: Estimate Traffic Loads Traffic loads are a major consideration in the load bearing capacity calculations. There are three procedures for considering the effects of traffic loading, traffic frequency (number of repetitions), and traffic configuration in the load bearing analysis: (1) fixed traffic, (2) fixed vehicle, and (3) variable traffic and vehicle (14). In the fixed traffic procedure, the thickness of the pavement is based on the heaviest single-wheel load anticipated and the number of load repetitions is not considered. Loads from axles with multiple wheels such as dual tires are converted to an equivalent single-wheel load (ESWL) (14) in this procedure. In the fixed vehicle procedure the pavement design is based on the number of repetitions of a standard vehicle or axle load such as the 80-kN (18-kip) single-axle load used in the AASHTO design procedure. In the variable traffic and vehicle procedure, loading magnitude, configuration, and number of load repetitions are considered by dividing the loads into a number of groups and determining the stresses, strains, and deflections under each load group. The recommended procedure for use in the geofoam load bearing design procedure presented below is the fixed traffic procedure because the design procedure limits static and

6- 35 dynamic loads to less than the elastic limit stress, which should result in tolerable deformations and the number of load repetitions do not have to be considered.. Figure 6.13 shows the wheel configuration of a typical semitrailer truck with a tandem axle with dual tires at the rear. Trucks with a tridem axle, each spaced at 122 to 137 cm (48 to 54 in.) apart, with dual tires also exists. The largest live or traffic load expected on the roadway above the embankment should be used for design. The magnitude and vehicle tire configuration that will provide the largest live load is typically not known during the preliminary design phase. Therefore, the AASHTO standard classes of highway loading (15) can be used for preliminary load bearing analyses. Figure 6.13. Wheel configuration of a typical semitrailer truck (14). Step 2: Add impact allowance to traffic loads Allowance for impact forces from dynamic, vibratory, and impact effects of traffic are generally only considered where they act across the width of the embankment or adjacent to a bridge abutment. In (1) an impact coefficient of 0.3 is recommended for design of EPS-block geofoam. Equation (6.3) can be used to include the impact allowance to the live loads estimated in Step 1 if impact loading is deemed necessary for design: Q=LL (1+I)∗ = 1.3 (LL) (6.3) where Q = traffic load with an allowance for impact, LL = live load for traffic from AASHTO standard classes of highway loading (15) obtained in Step 1, and I = impact coefficient = 0.3. Step 3: Estimate traffic load stresses at top of EPS blocks The objective of this step is to estimate the dissipation of vertical stress through the pavement system so that an estimate of the traffic stresses at the top of the EPS blocks can be obtained. The vertical stress at the top of the EPS is used to evaluate the load bearing capacity of the blocks directly under the pavement system. Various pavement systems, with and without a

6- 36 separation layer between the pavement system and the EPS blocks, should be evaluated to determine which alternative is the most cost effective. The three main procedures to determine the vertical stress at the top of the EPS are the Boussinesq solution (16), 1 (horizontal): 2 (vertical) stress distribution solution, and Burmister’s elastic layered solution (17). In each method the pavement system is assumed to behave as a linearly elastic material. The Boussinesq stress distribution solution does not accommodate layers with different elastic stress-strain properties and thus the stiffer pavement system over the softer EPS-blocks cannot be simulated. As a result, the Boussinesq solution is not recommended for estimating dissipation of vertical stress through the pavement system. The 1(horizontal): 2(vertical) stress distribution solution assumes that the applied vertical stress on the pavement surface is distributed over an area of the same shape as the loaded area on the surface, but with dimensions that increase by an amount equal to the depth below the surface as shown in Figure 6.14 (18). For example, for a rectangular shaped loaded area with dimensions of B x L at the surface, the vertical stress at a depth z is assumed to be distributed over an area (B + z) by (L + z). The vertical stress is assumed to be uniform over the stressed area and is determined by dividing the total applied loads at the surface by the stressed area. The load distribution through typical pavement system materials (asphalt concrete, Portland Cement Concrete, granular materials) will generally exceed the distribution of 1(horizontal): 2(vertical) or 26.6 degrees. Hunt (19) indicates that (20) suggests an angle of 30 degrees within relatively weak soil and 45 degrees for relatively strong soil. Greater load-spreading in the range of 35 to 45 degrees may be obtained through stiffer materials such as well-compacted granular fill over soft clay (21). Therefore, a 1(horizontal): 1(vertical) or 45 degree load distribution can be assumed through pavement materials except for concrete. Concrete can be substituted for granular material using a 1 concrete to 3 gravel ratio (22,23).

6- 37 The third and recommended procedure for estimating the stress at the top of the EPS is Burmister's elastic layered solution (24). Burmister's elastic layered solution is based on a uniform pressure applied to the surface over a circular area on top of an elastic half-space mass. Each layer has a finite thickness except for the lowest layer which is assumed to be infinite in thickness and each layer is assumed to be homogeneous, isotropic, and linearly elastic. The primary advantage of Burmister’s theory is that it considers the influence of layers with different elastic properties within the system being considered. The primary disadvantage is that vertical stress calculations are time consuming if not performed by computer. However, design charts are presented below that alleviate the use of computer software to utilize Burmister's elastic layered solutions. Figure 6.14. Approximate stress distribution by the 1(horizontal): 2 (vertical) method. In summary, Burmister’s elastic layered solution (24) is recommended to estimate the stress distribution through the pavement system to obtain the applied vertical stress at the top of the EPS-block fill due to a load applied to the pavement surface. To facilitate estimation of stresses on top of the EPS blocks from traffic and impact loads, stress design charts (see Figures 6.15 through 6.17) were developed during this study for various vehicle tire loads and pavement systems. The computer program KENLAYER (14), which is based on Burmister’s solution, was used to calculate vertical stresses through various thicknesses of the following types of pavement systems: asphalt concrete, portland cement concrete (PCC), and a composite pavement system. A composite pavement system is defined here as an asphalt concrete pavement system with a PCC slab separation layer placed between the asphalt concrete pavement system and the EPS-block geofoam. The main assumption in the KENLAYER analysis is that the interface of the various pavement system layers and the interface between the pavement system and the EPS blocks are frictionless. This assumption yields more conservative values of applied vertical stress on top of the EPS. The vertical stress charts in Figures 6.15 through 6.17 can be used to estimate the applied vertical stress on top of the EPS due to a tire load on top of an asphalt concrete, PCC, and

6- 38 composite pavement system, respectively. For example, the vertical stress applied to the top of the EPS blocks under a 178 mm (7 in.) thick asphalt pavement with a total wheel load of 100 kN (22,481 lbs) is approximately 55 kPa (8 lbs/in2) (see Figure 6.15). This value of 55 kPa (8 lbs/in2) is then used in the load bearing analysis described subsequently. Loads Used in Developing Design Vertical Stress Charts Axle loads ranging between 89 to 445 kN (20,000 and 100,000 lbs) were analyzed because this is the range of axle loads provided in the tables of axle load equivalency factors for calculating equivalent single-axle loads (ESALs) for single and tandem axles in the AASHTO 1993 pavement design guide (25). Based on these axle loads and on a tire pressure of 689 kPa (100 lbs/in²), a range of circular contact areas were obtained for both an axle system with two single tires and an axle system with two sets of dual tires using the equations shown below. These circular areas were used in KENLAYER. Both a single tire and a set of dual tires was modeled as a single contact area. Therefore, both a single tire and a set of dual tires can be represented by the total load of a single tire or on the dual tires and a contact area. The contact pressure is typically assumed to be equal to the tire pressure (14) and the tire and pavement surface interface is assumed to be free of shear stress. Typical tire pressures for legal highway trucks with single and dual tires range from of 414 to 621 kPa (60 to 90 lbs/in²) (26). A tire pressure of 689 kPa (100 lbs/in²) appears to be representative and is recommended for preliminary design purposes. This tire pressure is near the high end of typical tire pressures but is used for analysis purposes by transportation software such as ILLI-PAVE (27). The contact pressure is converted to a traffic load by multiplying by the contact area of the tire. For the case of a single axle with a single tire, the contact area is given by Equation (6.4) and the radius of the contact area is given by Equation (6.5): t C QA = q (6.4)

6- 39 1 2 CAr = π     (6.5) where AC = contact area of one tire, Qt = live load on one tire, q = contact pressure = tire pressure, and r = radius of contact area For the case of a single axle with dual tires, the contact area can be estimated by converting the set of duals into a singular circular area by assuming that the circle has an area equal to the contact area of the duals as indicated by Equation (6.6). The radius of contact is given by Equation (6.7). Equation (6.6) yields a conservative value, i.e., smaller area, for the contact area because the area between the duals is not included. D CD QA = q (6.6) 1 2 CDAr = π     (6.7) where ACD = contact area of dual tires QD = live load on dual tires q = contact pressure on each tire = tire pressure Pavement Systems Used in Developing Design Vertical Stress Charts Asphalt Concrete Pavement System. Based on the design catalog for flexible pavements, see Table 4.2, an asphalt thickness ranging from 76 to 178 mm (3 to 7 in.) was utilized with a corresponding crushed stone base thickness equal to 610 mm (24 in.) less the thickness of the asphalt. This provides the minimum recommended pavement system thickness of 610 mm (24 in.) to minimize the potential for differential icing and solar heating. For the asphalt concrete, a typical unit weight of 23 kN/m³ (148 lbf/ft³), Poisson's ratio of 0.46, and modulus of elasticity of 689 MPa (100 x 103 lbs/in²) were utilized (14). For the crushed stone base, a unit weight of 22

6- 40 kN/m³ (138 lbf/ft³), Poisson's ratio of 0.35, and modulus of elasticity of 21 MPa (3,000 lbs/in²) was utilized in KENLAYER. The unit weight and Poisson's ratio was obtained from average values reported in (14). The modulus of elasticity was conservatively based on average values reported in (19) for a loose sand and gravel. The resulting vertical stress at the top of the EPS, σLL, obtained from Figure 6.15 increases with the modulus of elasticity of the EPS. To maximize design values of σLL the properties of EPS100 geofoam, which is the stiffest EPS considered herein, were used in the analysis. The properties of EPS100 include a unit weight of 0.31 kN/m³ (2.0 lbf/ft³), Poisson's ratio of 0.18, and modulus of elasticity of 9,997 kPa (1,450 lbs/in²). Figure 6.15 presents values of σLL obtained from the analysis due to a single or dual wheel loads on an asphalt concrete pavement system. Figure 6.15. Vertical stress on top of the EPS blocks, σLL, due to traffic loads on top of a 610 mm (24 in.) asphalt concrete pavement system. Portland Cement Concrete. Based on the design catalog for rigid pavements, see Tables 4.6 and 4.7, a PCC thickness ranging from 127 to 229 mm (5 to 9 in.) was utilized with a crushed stone base thickness equal to 610 mm (24 in.) less the thickness of the PCC. This provides a minimum recommended pavement system thickness of 610 mm (24 in.) to minimize the potential for differential icing and solar heating. For the PCC, an average unit weight of 23.5 kN/m³ (150 lbf/ft³), Poisson's ratio of 0.15, and modulus of elasticity of 20,684 MPa (3 x 106 lbs/in²) were utilized from (14). The same properties for the crushed stone base and EPS fill used in the analysis of an asphalt concrete pavement system were utilized to develop the vertical stress applied by a PCC pavement system. Figure 6.16 presents the design vertical stress chart of a single or dual wheel acting on a PCC pavement system which can be used to estimate the vertical stress due to traffic loads, σLL, at the top of the EPS. Figure 6.16. Vertical stress on top of the EPS blocks, σLL, due to traffic loads on top of a

6- 41 610 mm (24 in.) portland cement concrete pavement system. Composite Pavement System. The asphalt concrete pavement system used to create the design chart in Figure 6.15 was utilized for this scenario except that a 102 mm (4 in.) concrete separation layer was added between the crushed stone base and the EPS blocks. A crushed stone base thickness equal to 610 mm (24 in.) less the thickness of the asphalt concrete and the separation slab was used to complete the remainder of the composite pavement system. This also provides a minimum recommended pavement system thickness of 610 mm (24 in.) to minimize the potential for differential icing and solar heating. The material properties utilized for the analysis of the composite pavement system are the same as those used for the asphalt concrete and PCC pavement systems in Figures 6.15 and 6.16, respectively. Figure 6.17 presents the design charts for vertical stress, σLL, on top of the EPS block due to a single or dual wheel acting on this composite pavement system. Figure 6.17. Vertical stress on top of the EPS blocks, σLL, due to traffic loads on top of a 610 mm (24 in.) asphalt concrete pavement system with a 102 mm (4 in.) concrete separation layer between the pavement system and EPS blocks. Conversion of Circular Loaded Areas to Rectangular Loaded Area It is more convenient to use a rectangular loaded area at the top of the EPS to calculate the vertical stresses acting on the EPS block in Step 9 of the load bearing analysis. This is similar to converting single and dual tire loadings to a single loaded circular area to estimate the stress through the pavement system. To perform the conversion the tire contact pressure on top of the pavement system is distributed over a circular area. The Portland Cement Association 1984 method as described in (14) can be used to convert the circular loaded area to an equivalent rectangular loaded area, as shown in Figure 6.18. The rectangular area shown is equivalent to a circular contact area that corresponds to a single axle with a single tire, AC , or a single axle with

6- 42 dual tires, ACD. The values of AC and ACD can be obtained from Equations (6.4) and (6.6), respectively, using the following procedure: 1) Estimate σLL from Figure 6.15, 6.16, or 6.17 depending on the pavement system being considered. 2) Use σLL in Equation (6.4) or (6.6) as the contact pressure, q, and the recommended traffic loads from Step 1 to estimate the live load in Equation (6.4) or (6.6) for a single axle with a single tire or a single axle with dual tires, respectively, to calculate AC or ACD . 3) Use the values of AC or ACD to calculate the value of L′ in Figure 6.18 by equating AC or ACD to 0.5227L′² and solving for L′. After solving for L′, the dimensions of the rectangular loaded area in Figure 6.18, i.e., 0.8712L′ and 0.6L′, can be calculated. Figure 6.18. Method for converting a circular contact area into an equivalent rectangular contact area (14). Step 4: Estimate gravity stresses at top of EPS blocks Stresses resulting from the gravity load of the pavement system and any road hardware placed on top of the roadway must be added to the traffic stresses obtained in Step 3 to conduct a load bearing analysis of the EPS. The gravity stress from the weight of the pavement system is given by: =DL pavement pavementT γσ ∗ (6.8) where σDL = gravity stress due to dead loads Tpavement = pavement system thickness, and γpavement = average unit weight of the pavement system. As discussed in Chapter 4, the various components of the pavement system can be assumed to have an average unit weight of 20 kN/m3 (130 lbf/ft3). Because the traffic stresses in

6- 43 Figures 6.15 through 6.17 are based on a pavement system with a total thickness of 610 mm (24 in.), a value of Tpavement equal to 610 mm (24 in.) should be used to estimate σDL to ensure consistency. Step 5: Calculate total stresses at top of EPS blocks The total vertical stress at the top of EPS blocks underlying the pavement system from traffic and gravity loads, σtotal, is given by: = LL DLtotal +σ σ σ (6.9) Step 6: Determine minimum required elastic limit stress for EPS under pavement system The minimum required elastic limit stress of the EPS block under the pavement system can be calculated by multiplying the total vertical stress from Step 5 by a factor of safety as shown by Equation (6.10). e total FSσ ≥ σ ∗ (6.10) where σe = minimum elastic limit stress of EPS FS = factor of safety = 1.2 The main component of σtotal is the traffic stress and not the gravity stress from the pavement. Because traffic is a main component of σtotal and traffic is a transient load like wind loading, a factor of 1.2 is recommended for the load bearing analysis. This is the same value of factor of safety recommended for other transient or temporary loadings such as wind, hydrostatic uplift, and sliding, and seismic used for external stability analyses. Step 7: Select appropriate EPS block to satisfy the required EPS elastic limit stress for underneath the pavement system, e.g., EPS50, EPS70, or EPS100 Select an EPS type from Table 6.2 that exhibits an elastic limit stress greater than or equal to the required σe determined in Step 6. The EPS designation system in Table 6.2 defines the minimum elastic limit stress of the block as a whole in kilopascals. For example, EPS50 will have a minimum elastic limit stress of 50 kPa (7.2 lbs/in2). The EPS selected will be the EPS

6- 44 block type that will be used directly beneath the pavement system for a minimum depth of 610 mm (24 in.) in the EPS fill. This minimum depth is recommended because it is typically the critical depth assumed in pavement design for selection of an average resilient modulus for design of the pavement system (14). Thus, the 610 mm (24 in.) depth is only an analysis depth and is not based on the thickness of the EPS blocks. Of course, if the proposed block thickness is greater than 610 mm (24 in.), the block selected in this step will conservatively extend below the 610 mm (24 in.) zone. The use of EPS40 is not recommended directly beneath paved areas because an elastic limit stress of 40 kPa (5.8 lbs/in2) has resulted in pavement settlement problems. Step 8: Select preliminary pavement system type and determine if a separation layer is required A cost analysis should be performed in Step 8 to preliminarily select the optimal pavement system that will be used over the type of EPS blocks determined in Step 7. The cost analysis can focus on one or all three of the pavement systems evaluated in Step 3, i.e., asphalt concrete, portland cement concrete, and a composite pavement system. The EPS selected for a depth of 610 m (24 in.) below the pavement system is a function of the pavement system selected because the vertical stress induced at the top of the EPS varies with the pavement system as shown in Figures 6.15 through 6.17. Therefore, several cost scenarios can be analyzed, e.g., a PCC versus asphalt concrete pavement system and the accompanying EPS for each pavement system, to determine the optimal combination of pavement system and EPS. The cost analysis will also determine if a concrete separation layer between the pavement and EPS is cost effective by performing a cost analysis on the composite system. The resulting pavement system will be used in Steps 9 through 13. If a concrete separation slab will be used, the thickness of the concrete slab can be estimated by assuming the slab to be a granular material and will dissipate the traffic stresses to a desirable level at 1(horizontal): 1(vertical) stress distribution. Concrete can then be substituted for granular material using the 1 concrete to 3 gravel ratio previously discussed in Step 3 to estimate

6- 45 the required thickness of granular material. For example, a 102 mm (4 in.) thick concrete separation layer can be used to replace 306 mm (12 in.) of granular material. Therefore, a 927 mm (36.5 in.) thick asphalt concrete pavement system that consists of 127 mm (5 in.) of asphalt and 800 mm (31.5 in.) of crushed stone base will be 927 mm (36.5 in.) thick less 306 mm (12 in.) of crushed stone base which is replaced by 102 mm (4 in.) thick concrete separation layer. However, as discussed in Chapter 4, it is recommended that a minimum pavement system thickness of 610 mm (24 in.) be used to minimize the potential for differential icing and solar heating. Step 9: Estimate traffic stresses at various depths within the EPS blocks This step estimates the dissipation of the traffic induced stresses through the EPS blocks within the embankment. Utilizing the pavement system and separation layer, if included, from Step 8, the vertical stress from the traffic loads at depths greater than 610 mm (24 in.) in the EPS is calculated. The vertical stress is usually calculated at every 1 m (3.3 ft) of depth below a depth of 610 mm (24 in.). Block thickness is typically not used as a reference depth because the block thickness that will be used on a given project will typically not be known during the design stage of the project. The first depth at which the vertical stress will be estimated is 610 mm (24 in.) because in Step 7 the EPS selected to support the pavement system will extend to a depth of 610 mm (24 in.). The traffic vertical stresses should also be determined at any depth within the EPS blocks where the theoretical 1(horizontal): 2(vertical) stress zone overlaps as shown in Figure 6.19. These vertical stress estimates will be used in Step 12 to determine if the EPS type selected in Step 8 for directly beneath the pavement system is adequate for a depth of greater than 610 mm (24 in.) into the EPS and to determine if an EPS block with a lower elastic limit stress, i.e., lower density and lower cost, can be used at a greater depth. Based on an analysis performed during this study and the results of a full-scale model creep test that was performed at the Norwegian Road Research Laboratory (28,29) to investigate the time-dependent performance of EPS-block geofoam, a 1 (horizontal) to 2 (vertical)

6- 46 distribution of vertical stresses through EPS blocks was found to be in agreement with the measured vertical stresses, which showed a stress distribution of 1 (horizontal) to 1.8 (vertical). The test fill had a height of 2 m (6.6 ft) and measured 4 m (13.1 ft) by 4 m (13.1 ft) in plan at the bottom of the fill decreasing in area with height approximately at a ratio of 2 (horizontal) to 1 (vertical) to about 2 m (6.6 ft) by 2 m (6.6 ft) at the top of the fill. A load of 105 kN (23.6 kips) was applied through a 2 m (6.6 ft) by 1 m (3.3 ft) plate at the top of the fill resulting in an applied stress of 52.5 kPa (1,096 lbs/ft2). The fill consisted of four layers of full-size EPS blocks with dimensions 1.5 m (4.9 ft) by 1 m (3.3 ft) by 0.5 m (1.6 ft) and densities of 20 kg/m3 (1.25 lbf/ft³). The stress at the bottom of the fill was measured using four pressure cells. An average pressure of 7.8 kPa (163 lbs/ft2) was measured in the pressure cells during the 1,270 day test. Based on this average pressure measured at the bottom of the test fill and the stress of 52.5 kPa (1,096 lbs/ft2) applied at the top of the fill, the stress distribution within the EPS fill was approximately 1 (horizontal) to 1.8 (vertical). The measured stress distribution is slightly wider but still in agreement with a 1 (horizontal) to 2 (vertical) stress distribution. Thus, the measured stress with depth is slightly less than the typically assumed stress distribution, which results in a slightly conservative design. In summary, Burmister’s layered solution is only applicable to stress distribution through the pavement and thus the 1 (horizontal): 2 (vertical) stress distribution theory is used to estimate the vertical stress within the EPS. In order to use the 1 (horizontal): 2 (vertical) stress distribution method to calculate the vertical stresses applied through the depth of EPS block using hand calculations, it is easier to assume a rectangular loaded area at the top of the EPS and to assume that the total applied load at the surface of the EPS is distributed over an area of the same shape as the loaded area on top of the EPS, but with dimensions that increase by an amount equal to 1(horizontal): 2(vertical) (see Figure 6.14). As shown in Figure 6.14, at a depth z below the EPS, the total load Q applied at the surface of the EPS is assumed to be uniformly distributed over an area (B+z) by (L+z). The increase in vertical pressure, σZ, at depth z due to an applied live load

6- 47 such as traffic is given by Equation (6.11). Figure 6.19 demonstrates the use of the 1 (horizontal): 2(vertical) to estimate overlapping stresses from closely spaced loaded areas such as from adjacent sets of single or dual tires. Figure 6.19. Approximate stress distribution of closely spaced loaded areas by the 1 (horizontal): 2(vertical) method. Z,LL Q= (B+z)(L+z) σ (6.11) where σZ,LL = increase in vertical stress at depth z caused by traffic loading, Q = applied traffic load, B = width of the loaded area, L = length of the loaded area. To use the 1(horizontal): 2(vertical) stress distribution method to calculate the vertical stresses through the depth of the EPS block, the assumed circular loaded area below a tire used to determine σLL in Figures 6.15, 6.16, or 6.17 should be converted to an equivalent rectangular area as discussed previously in Step 3. Alternatively, Equation (6.11) can be modified to determine σZ,LL directly from the σLL, which is determined from Figures 6.15, 6.16, or 6.17 as shown below: LL rectQ A= σ ∗ (6.12) where σLL is obtained from Figures 6.15, 6.16 or 6.17. From Figure 6.18, 1 2rectAL = 0.5227  ′    (6.13) B=0.6 L′∗ (6.14) L=0.8712 L′∗ (6.15) Substituting Equations (6.12) through (6.15) into (6.11),

6- 48 ( )( )LL rectZ,LL A 0.6L + z 0.8712L + z σ ∗σ = ′ ′ (6.16) where Arect is either AC or ACD determined from Equations (6.4) or (6.6), respectively. Step 10: Estimate gravity stresses at various depths within the EPS blocks Stresses resulting from the gravity load of the pavement system, any road hardware placed on top of the roadway, and the EPS blocks must be added to the traffic stresses to evaluate the load bearing capacity of the EPS within the embankment. The procedure described in the Stress Distribution at Center of Embankment section of Chapter 5 can be used to obtain an estimate of the increase in vertical stress at the centerline of the geofoam embankment at various depths due to the increase in gravity stress of the pavement system. For example, Equations (5.10), (5.11), and (5.12) can be modified as shown below to determine the increase in vertical stress caused by the gravity load of the pavement system: ( )tZ,DL q sin where is in radians∆σ = α + α απ (6.17) b2 arctan where is calculated in radians z α α = ∗    (6.18) t pavement pavement pavementq q Tγ= = ∗ (6.19) where ∆σZ,DL = increase in vertical stress at depth z due to pavement system dead load in m, γpavement = unit weight of the pavement system in kN/m³, Tpavement = thickness of the pavement system in m, and the other variables are defined in Figure 5.3. The total gravity stress from the pavement system and the EPS blocks is given by: = EPSZ,DL Z,DL( ) + (z γ )σ ∆σ ∗ (6.20) where σZ,DL = total vertical stress at depth z due to dead loads in kN/m², z = depth from the top of the EPS in m, γEPS = unit weight of the EPS blocks in kN/m³.

6- 49 As discussed in Step 5, the various components of the pavement system can be assumed to have an average unit weight of 20 kN/m3 (130 lbf/ft3). Because the traffic stresses in Figures 6.15 through 6.17 are based on a pavement system with a total thickness of 610 mm (24 in.), a value of Tpavement equal to 610 mm (24 in.) should be used to estimate qt to ensure consistency. It is recommended that the unit weight of the EPS be assumed to be 1,000 N/m3 (6.37 lbf/ft3), to conservatively allow for long-term water absorption in the calculation of σZ,DL. Step 11: Calculate total stresses at various depths within the EPS blocks The total vertical stress induced by traffic and gravity loads at a particular depth within the EPS is given by: total Z,LL Z,DL = +σ σ σ (6.21) Step 12: Determine minimum required elastic limit stress for EPS at various depths Determine the minimum required elastic limit stress of the EPS block at each depth that is being considered using the same equations from Step 6 which is shown below: e total 1.2σ ≥ σ ∗ (6.22) Step 13: Select appropriate EPS block to satisfy the required EPS elastic limit stress at various depths in the embankment Select an EPS type from Table 6.2 that exhibits an elastic limit stress greater than or equal to the required σe determined in Step 12. EPS40 is not recommended for directly beneath the pavement system (see Step 7) but can be used at depths below 610 mm (24 in.) in the embankment if the required elastic limit stress is less than 40 kPa (5.8 lbs/in2). However, for constructability reasons, it is recommended that no more than two different EPS block types be used Remedial Procedures

6- 50 Remedial procedures that can be used to increase the factor of safety against load bearing failure includes adding a separation layer, such as a concrete slab, between the pavement system and the EPS blocks. If an EPS with an elastic limit stress greater than 100 kPa or 14.5 lbs/in2 (EPS100) is required, consideration can be given to contacting local molders to determine if EPS- block geofoam with an elastic limit stress greater than 100 kPa (14.5 lbs/in2) can be molded for the project. ABUTMENT DESIGN Introduction In applications where the EPS-block geofoam is used as part of a bridge approach, the EPS blocks should be continued up to the drainage layer that is placed along the back of the abutment. A geosynthetic sheet drain, not natural aggregate, should be used for this drainage layer to minimize the vertical and lateral earth pressure on the subgrade and abutment, respectively, as well as facilitate construction. The design requirements for abutments as well as design examples can be found in (30). The procedure for design of retaining walls and abutments consists of the following steps (30): 1. Select preliminary proportions of the wall. 2. Determine loads and earth pressures. 3. Calculate magnitude of reaction force on base. 4. Check stability and safety criteria: (a) location of normal component of reactions, (b) adequacy of bearing pressure, and (c) safety against sliding. 5. Revise proportions of wall and repeat Steps 2 through 4 until stability criteria are satisfied; then check: (a) settlement within tolerable limits and (b) safety against deep-seated foundation failure.

6- 51 6. If proportions become unreasonable, consider a foundation supported on driven piles or drilled shafts. 7. Compare economics of completed design with other wall systems. For a bridge approach consisting of EPS-block geofoam backfill, earth pressures, which are required for Step 2 of the abutment design process, generated by the following two sources should be considered: • the gravity load of the pavement system, WP, and EPS blocks WEPS (usually small) pressing directly on the back of the abutment (see Figure 6.20) and • the active earth pressure from the soil behind the geofoam fill (see Figure 6.20) that can be transferred through the geofoam fill to the back of the abutment. Figure 6.20. Loads on an EPS-block geofoam bridge approach system. The magnitude of these loads vary depending on whether gravity and/or seismic loading is evaluated. The procedure for estimating the gravity and seismic loads are discussed in the following sections. Gravity Loads The assumed components of the gravity loads acting on a vertical wall or abutment are (see Figure 6.21): • the uniform horizontal pressure acting over the entire depth of the geofoam caused by the vertical stress applied by the pavement system to the top of the EPS, which can be estimated from Figures 6.15 through 6.17, • the horizontal pressure generated by the vertical stress imposed by the pavement system, which can be assumed to be equal to 1/10 times the vertical stress, • the horizontal stress from the EPS blocks is neglected because it is negligible, and

6- 52 • the lateral earth pressure, PA, generated by the soil behind the EPS/soil interface, which is conservatively assumed to be transmitted without dissipation through the geofoam to the back of the abutment. The active earth pressure acting along this interface is calculated using a coefficient of active earth pressure, KA because it is assumed that enough lateral deformation will occur to mobilize an active earth pressure condition in the soil behind the geofoam. The active earth pressure coefficient can be determined from the following equation, which is based on Coulomb’s classical earth-pressure theory (31). Figure 6.21. Gravity load components on a vertical wall. ( ) ( ) ( ) ( )( ) A 2 1sin -φ sinK = sin φ+δ sin φ sin +δ sin    θ   θ   θ + θ  (6.23) where δ is the friction angle of the EPS/soil interface, which is analogous to the soil/wall interface in typical retaining wall design. The value of δ can be assumed to be equal to the friction angle of the soil, φ. Equation (6.23) is applicable only to horizontally level backfills. The active earth pressure force is expressed in Equation (6.24) as: 2 A Soil A 1P γ H K 2 = (6.24) where γSoil = unit weight of the soil backfill. Seismic Loads The following seismic loads acting on the back of an abutment must be added to the gravity loads in Figure 6.22 to safely design a bridge abutment in a seismic area: • inertia forces from seismic excitation of the pavement system and the EPS blocks (usually negligible). These inertial forces should be reduced by the horizontal

6- 53 sliding resistance, tan (φ) developed along the pavement system/EPS interface; and • seismic component of the active earth pressure generated by the soil behind the EPS/soil interface, which can be calculated using the solution presented by Mononobe-Okabe (32). Figure 6.22. Seismic load components on a wall. DURABILITY Consideration of durability can be divided into construction damage and long-term changes that may occur once the EPS blocks are buried in the ground. Both can affect product performance and therefore need to be considered during design. A recent (1999) state-of-art assessment of failures of all types of geosynthetics concluded that construction damage is the more important of these two durability categories by a significant margin (33). A more-specific assessment of geofoam failures came to the same broad conclusion (34). Both of these durability factors are discussed in the following paragraphs. Construction Damage Construction damage is considered to be physical damage to the geofoam product during its shipment to the project site; its placement on site; or during subsequent placement of other materials above the geofoam. A summary of recommended procedures to minimize construction damage to the EPS blocks is presented in the block shipment, handling, and storage; block placement; and pavement construction sections of Chapter 8. Long-Term Changes Long-term in-situ durability relates to chemical changes to or within the polymer that comprises the geofoam. Experience with actual in-ground use of EPS geofoam since the 1960s indicates that there is little or no chemical change or deterioration of EPS due to contact with the ground or ground water because EPS is relatively inert. Although EPS will absorb water to a limited extent once placed in the ground, the absorbed water causes no change in the physical

6- 54 dimensions of the EPS block or changes in any physical properties that are relevant to lightweight fill applications. However, there are three issues regarding EPS durability that can affect the long- term durability of geofoam in roadway embankments and should be considered in design: • The surface of EPS must be covered for protection 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 in the ground. • Liquid petroleum hydrocarbons (gasoline, diesel fuel/heating oil) will dissolve EPS if the EPS is inundated with the liquid. This consideration in the design process is discussed in the pavement system design section of Chapter 4. • Although EPS is not a food source for any known living organism, in below- grade residential insulation applications, EPS (and other polymeric foams such as XPS as well) has been found to be damaged by certain types of insects (termites and carpenter ants) tunneling through or nesting in the EPS. There are no known occurrences of this with EPS in any lightweight fill applications. However, an inorganic, natural mineral additive has been approved by the U.S. Environmental Protection Agency for use in EPS that renders the EPS resistant to such insect attack. This additive does not affect the engineering properties of the EPS although it can affect the cost as well as limit those who can supply the material because not all EPS block molders in the U.S. have a license to use this material. A license is required because this additive is covered by at least two U.S. patents (35). Experience indicates that some U.S. designers of EPS-block geofoam fills have opted to specify treated EPS block to be cautious and conservative. However, it is recommended that the insect additive be used only after careful

6- 55 evaluation because there is no documented need for the additive and it is proprietary which affects cost. OTHER INTERNAL DESIGN CONSIDERATIONS Site Preparation Proper site preparation prior to placing the EPS blocks is important for both internal stability as well as overall constructability. This is important because each layer of blocks should be placed as level as possible to avoid high spots that will cause stress concentrations and rocking of the blocks. If the first block layer is not sufficiently level, block-alignment problems will tend to be compounded with each succeeding layer. Recommended site preparation details are provided in the site preparation section of Chapter 8. Slope Cover An assessment of the stability of the slope cover, e.g., a soil or a structural material, must be made. For a soil cover, this assessment generally requires a sufficiently flat side slope (typically two horizontal to one vertical or flatter) to be used so the soil is inherently stable and not easily eroded. For a structural material cover, the material must either be self stable or physically attached to the assemblage of EPS blocks. Utilities Where possible, utilities that are either part of the road structure (e.g. storm drains, electrical conduit) or crossed by the road should be buried either within the pavement system or below the EPS blocks. If this is not possible, utilities may be buried within the EPS mass by creating trenches (either by judicious block placement or cutting out of a trench with a chain saw after placement) and placing the utility line within the trench using a conventional soil bed. The volume of soil placed under and around the utility line should be minimized to minimize the localized stress concentration on the underlying EPS and foundation soil. Normal EPS block placement can be continued above the utility line.

6- 56 Whether a utility line is buried beneath or within the EPS mass, a concern is sometimes expressed as to how such a utility line will be accessed should service, maintenance, or upgrading be required. This cannot be answered definitively because there is no documented knowledge on this problem. In the interim, it would seem reasonable to saw-cut (using a chain saw) a vertical trench through the overlying EPS blocks as necessary to access the utility line. After the required utility work has been performed, the cut pieces of EPS (and not soil or other standard-weight material) should be placed within the trench, taking care not to leave voids between the replaced pieces. Consideration should be given to using an EPS-compatible glue to physically attach the cut pieces to the in-place EPS as well as each other. Alternatively, it might be possible to fill the trench with a geofoam material such as polyurethane that is compatible chemically and mechanically with the EPS and can be formed in place. REFERENCES 1. “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. 2. 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. 3. “EPS.” Expanded Polystyrol Construction Method Development Organization, Tokyo, Japan (1993) 310 pp. 4. Horvath, J. S., “A Concept for an Improved Inter-Block Mechanical Connector for EPS-Block Geofoam Lightweight Fill Applications: 'The Ring's the Thing',” In Manhattan College-School of Engineering, Center for Geotechnolgy [web site]. [updated 8 September 2001; cited 20 September2001]. Available from http://www.engineering.manhattan.edu/civil/CGT/T2olrgeomat2.html; INTERNET. 5. Duskov, M., “EPS as a Light Weight Sub-base Material in Pavement Structures; Final Report.” Report Number 7-94-211-6, Delft University of Technology, Delft, The Netherlands (1994). 6. Horvath, J. S., Geofoam Geosynthetic, Horvath Engineering, P.C., Scarsdale, NY (1995) 229 pp. 7. “AFM ® Gripper TM Plate.” AFM ® Corporation, Excelsior, MN (1994). 8. Bartlett, S., Negussey, D., Kimble, M., and Sheeley, M., “Use of Geofoam as Super-Lightweight Fill for I-15 Reconstruction (Paper Pre-Print).” Transportation Research Record 1736, Transportation Research Board, Washington, D.C. (2000).

6- 57 9. 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. 10. Sharma, S., XSTABL: An Integrated Slope Stability Analysis Program for Personal Computers, Interactive Software Designs, Inc., Moscow, Idaho (1996) 150 pp. 11. 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. 12. Stark, T. D., and Poeppel, A. R., “Landfill Liner Interface Strengths From Torsional-Ring-Shear Tests.” ASCE Journal of Geotechnical Engineering, Vol. 120, No. 3 (1994) pp. 597-615. 13. Janbu, N., “Slope Stability Computations.” Embankment Dam Engineering, Hirschfield and Poulos, eds., John Wiley & Sons, New York (1973) pp. 47-86. 14. Huang, Y. H., “Pavement Analysis and Design.”, Prentice-Hall, Inc., Englewood Cliffs, NJ, (1993) 805. 15. 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). 16. Boussinesq, J., Application des Potentiels à l' Étude de l' Équilibre et du Mouvement des Solides Élastiques, Gauthier-Villard, Paris (1885). 17. Burmister, D. M., “The Theory of Stresses and Displacements in Layered Systems and Applications to the Design of Airport Runways.” Proceedings, Highway Research Board,1958, Vol. 23 pp. 126-144. 18. “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. 19. Hunt, R. E., Geotechnical Engineering Analysis and Evaluation, McGraw-Hill, Inc., New York (1986) 729 pp. 20. Sowers, G. F., Introductory Soil Mechanics and Foundations: Geotechnical Engineering, 4th, Macmillan Publishing, NY (1979). 21. Jewell, R. A., Soil Reinforcement with Geotextiles, Construction Industry Research and Information Association, London (1996). 22. Refsdal, G., “Frost Protection of Road Pavements.” Frost Action in Soils - No. 26, Committee on Permafrost, ed., Oslo, Norway (1987) pp. 3-19. 23. “Matériaux Légers pour Remblais/Lightweight Filling Materials.” Document No. 12.02.B, PIARC-World Road Association, La Defense, France (1997) 287 pp. 24. Burmister, D. M., “The Theory of Stresses and Displacements in Layered Systems and Applications to the Design of Airport Runways.” Proceedings, Highway Research Board, Vol. 23, (1943) pp. 126-144. 25. American Association of State Highway and Transportation Officials, AASHTO Guide for Design of Pavement Structures, 1993, American Association of State Highway and Transportation Officials, Washington, D.C. (1993). 26. Schroeder, W. L., Soils In Construction, 3rd, Wiley, NY (1984) 330 pp. 27. Raad, L., and Figueroa, J. L., “Load Response of Transportation Support Systems.” Transportation Engineering Journal, ASCE, Vol. 106, No. TE1 (1980) pp. 111-128.

6- 58 28. 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. 29. 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. 30. Barker, R. M., Duncan, J. M., Rojiani, K. B., Ooi, P. S. K., Tan, C. K., and Kim, S. G., “Manuals for the Design of Bridge Foundations, NCHRP Report 343.” Transportation Research Board, National Research Council, Washington, D.C. (1991) 308 pp. 31. Coulomb, C. A., “Essai sur une Application des Règles des Maximis et Minimis à quelques Problèmes de Statique Relatifs à l' Architecture (An attempt to apply the rules of maxima and minima to several problems of stability related to architecture).” Mém. Acad. Roy. des Sciences, Paris (1776) 343-382 pp. 32. 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. 33. Giroud, J.-P., “Lessons Learned from Failures Associated with Geosynthetics.” Proceedings of Geosythetics '99,1999, Vol. I pp. 1-66. 34. 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. 35. Savoy, T., “Building Material, with Protection from Insects, Molds, and Fungi.” U.S. Patent No. 5,194,323 (1993).

FIGURE 6.1 PROJ 24-11.doc 6-59

FIGURE 6.2 PROJ 24-11.doc γ III II I 6-60

FIGURE 6.3 PROJ 24-11.doc 34 m road width, 12.2 m high embankment Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I 4H:1V 3H:1V 2H:1V FS' = 1.2 kh = 0.05 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I 4H:1V 3H:1V 2H:1V FS' = 1.2 kh = 0.10 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I 4H:1V 3H:1V 2H:1VFS' = 1.2 kh = 0.20 Mode IIMode III Mode IIMode III Mode IIMode III 6-61

FIGURE 6.4 PROJ 24-11.doc 2H:1V slope, 12.2 m high embankment Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I 34 m 11 m FS' = 1.2 kh = 0.05 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I FS' = 1.2 kh = 0.10 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I 34 m 11 mFS' = 1.2 kh = 0.20 Mode IIMode III Mode IIMode III Mode IIMode III 34 m 11 m 6-62

FIGURE 6.5 PROJ 24-11.doc 11 m pavement, 2H:1V slope Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I 3.1 m 12.2 m FS' = 1.2 kh = 0.05 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I FS' = 1.2 kh = 0.10 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I 3.1 m 12.2 mFS' = 1.2 kh = 0.20 Mode IIMode III Mode IIMode III Mode IIMode III 3.1 m 12.2 m 6-63

FIGURE 6.6 PROJ 24-11.doc Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I FS' = 1.2 Mode IIMode III kh = 0.05 kh = 0.10 kh = 0.20 I II&III kh = 0.05 = 0.10 = 0.20 6-64

FIGURE 6.7 PROJ 24-11.doc γ 6-65

FIGURE 6.8 PROJ 24-11.doc 34 m road width, 12.2 m high embankment Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic Fa ct o r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I FS' = 1.2 kh = 0.05 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I FS' = 1.2 kh = 0.10 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I FS' = 1.2 kh = 0.20 Mode IIMode III Mode IIMode III Mode IIMode III 6-66

FIGURE 6.9 PROJ 24-11.doc 3.1 m high embankment Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic Fa ct o r o f S af et y, F S' 0 2 4 6 8 10 Failure Mode I 34 m FS' = 1.2 kh = 0.05 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic Fa ct o r o f S af et y, F S' 0 2 4 6 8 10 Failure Mode I FS' = 1.2 kh = 0.10 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I 34 m 11 mFS' = 1.2 kh = 0.20 Mode IIMode III Mode IIMode III Mode IIMode III 34 m 11 m 11 m 6-67

FIGURE 6.10 PROJ 24-11.doc 12.2 m high embankment Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, F S' 0 2 4 6 8 10 Failure Mode I 34 m 11 m FS' = 1.2 kh = 0.05 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic Fa ct o r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I FS' = 1.2 kh = 0.10 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, F S' 0 2 4 6 8 10 Failure Mode I 11 m 34 mFS' = 1.2 kh = 0.20 Mode IIMode III Mode IIMode III Mode IIMode III 34 m 11 m 6-68

FIGURE 6.11 PROJ 24-11.doc 11 m wide pavement Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I 12.2 m 3.1 mFS' = 1.2 kh = 0.05 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I FS' = 1.2 kh = 0.10 Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, FS ' 0 2 4 6 8 10 Failure Mode I 12.2 m 3.1 mFS' = 1.2 kh = 0.20 Mode IIMode III Mode IIMode III Mode IIMode III 12.2 m 3.1 m 6-69

FIGURE 6.12 PROJ 24-11.doc Interface Friction Angle, δ (degrees) 5 10 15 20 25 30 35 40 Se ism ic F ac to r o f S af et y, F S' 0 2 4 6 8 10 Failure Mode I FS' = 1.2 Mode IIMode III kh = 0.05 kh = 0.10 kh = 0.20 I II&III kh = 0.05 = 0.10 = 0.20 6-70

FIGURE 6.13 PROJ 24-11.doc 7 m (23 ft) 4 m (13 ft) Tractor Single Axle with Single Tire 4 ft Longitudinal wheel Spacing = 1.8 m Transverse Wheel Spacing = Trailer Single Axle with Dual Tireswith Dual Tires Tandem Axle Dual Spacing = 0.3 - 0.36 m (6 ft) (12-14 in) 6-71

FIGURE 6.14 PROJ 24-11.doc 1 1 2 2 Q z L + z B + z B L 6-72

FIGURE 6.15 PROJ 24-11.doc Total Load on Single Wheel or Dual Wheels (kN) 0 50 100 150 200 250 V er tic al St re ss o n to p of EP S Bl o ck s, σ LL (kP a) 0 20 40 60 80 100 120 140 160 180 Asp halt Thi ckn ess = 102 mm Asp halt Thi ckn ess =12 7 m m Asp halt Thic knes s=1 52 m m Asph alt T hick nes s=17 8 mm Asp halt Thi ckn ess = 76 m m 6-73

FIGURE 6.16 PROJ 24-11.doc Total Load on Single Wheel or Dual Wheels (kN) 0 50 100 150 200 250 V er tic al St re ss o n to p o f E PS B lo ck s, σ LL (kP a) 0 10 20 30 40 Con cre te T hick nes s=1 52 m m Conc rete Thic knes s=17 8 mm Conc rete T hickn ess= 203 m m Concre te Thic kness= 229 mm Co nc ret e T hic kne ss= 127 mm 6-74

FIGURE 6.17 PROJ 24-11.doc Total Load on Single Wheel or Dual Wheels (kN) 0 100 200 300 400 V er tic al S tre ss o n to p of EP S Bl o ck s, σ LL (kP a) 10 20 30 40 50 60 Asphalt Thickness=76 mm Asphalt Thickness=102 mm Asphalt Thickness=127 mm Asphalt Thickness=152 mm Asphalt Thickness=178 mm 6-75

FIGURE 6.18 PROJ 24-11.doc 6-76

FIGURE 6.19 PROJ 24-11.doc 2 1 B + B + z + S B Q Q S1 B2 1 2 z 1 2 6-77

FIGURE 6.20 PROJ 24-11.doc 6-78

FIGURE 6.21 PROJ 24-11.doc 6-79

FIGURE 6.22 PROJ 24-11.doc 6-80

TABLE 6.1 PROJ 24-11.doc 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' or δ (degrees) Cohesion, c’ kPa (lbs/ft2) Soil cover 18.9 (120) 19.6 (125) 28 0 EPS/EPS interface 1 (6.4) 1 (6.4) 30 0 Pavement System/EPS and/or EPS/Foundation Soil Interface 1 (6.4) 1 (6.4) 10 – 40 0 Note: φ' = friction angle of a natural soil. δ = interface friction angle of a geosynthetic interface to include EPS blocks with another geosynthetic or natural soil. 6-81

TABLE 6.2 PROJ 24-11.doc Material Designation Dry Density of Each Block as a Whole, kg/m3 (lbf/ft3) Dry Density of a Test Specimen, kg/m3 (lbf/ft3) Elastic Limit Stress, kPa (lbs/in²) Initial Tangent Young's Modulus, MPa (lbs/in²) EPS40 16 (1.0) 15 (0.90) 40 (5.8) 4 (580) EPS50 20 (1.25) 18 (1.15) 50 (7.2) 5 (725) EPS70 24 (1.5) 22 (1.35) 70 (10.1) 7 (1015) EPS100 32 (2.0) 29 (1.80) 100 (14.5) 10 (1450) 6-82