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Recommended Design Guideline

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1 RECOMMENDED DESIGN GUIDELINE RECOMMENDED DESIGN GUIDELINE 1 INTRODUCTION Projects," which was administered by the Transportation Re- search Board (TRB). The report provides the commentary This design guideline is intended to provide design guid- accompanying this guideline and the design charts and equa- ance to civil engineers experienced in geotechnical engineer- tions used in the guideline. It is suggested that users of this ing and pavement engineering when designing lightweight guideline review the report, published as NCHRP Web Doc- fills that incorporate expanded polystyrene (EPS)-block geo- ument 65, for the necessary technical background. This guide- foam. The proposed design guideline is limited to embank- line is intended to be used in conjunction with the recom- ments that have a transverse (cross-sectional) geometry such mended standard that follows. that the two sides are more or less of equal height (see Fig- The design charts developed as part of this research and ure 1). Applications where the fill sides are markedly different included herein are based on embankment models with the geo- and closer to those shown in Figure 2 (sometimes referred to metric and material parameters described in the report. How- as side-hill fills) are excluded from this study because they are ever, most design charts are based on embankment sideslopes the subject of a separate study (1). It should be noted from of 0 (horizontal, H):1 (vertical, V), 2H:1V, 3H:1V, and 4H:1V. Figure 1 (b) that, unlike other types of lightweight fill Widths at the top of the embankment of 11 m (36 ft), 23 m embankments, a vertical embankment can be utilized with (76 ft), and 34 m (112 ft) were evaluated. These widths are EPS-block geofoam. The use of a vertical embankment, some- based on a two-lane roadway with 1.8-m (6-ft) shoulders, four- times referred to as a geofoam wall, will minimize the amount lane roadway with two 3-m (10-ft) exterior shoulders and of right-of-way needed and will also minimize the impact of two 1.2-m (4-ft) interior shoulders, and a six-lane roadway the embankment loads on nearby structures. The types of fills with four 3-m (10-ft) shoulders. Each lane was assumed to be considered in this document are also limited to approaches 3.66 m (12 ft) wide. Embankment heights ranging between with conventional jointed-deck bridges (including fill behind 1.5 m (4.9 ft) and 16 m (52 ft) were evaluated. For simplicity, the abutments of such bridges). In both the embankment and the fill mass was assumed to consist entirely of EPS blocks. bridge approach cases, the underlying foundation soil consists This design guideline is expected to be suitable for the pre- of soft soil defined as relatively compressible and weak. For liminary design of most typical projects (projects with either the purposes of this design guideline, such earthworks will be critical or noncritical conditions) and for final design for referred to simply as embankments on soft soil. projects with predominantly noncritical conditions. Exam- Both the Système International d'Unités (SI) and inch-pound ples of critical and noncritical design conditions are provided (I-P) units have been used in this guideline. SI units are shown in Table 1. Engineering judgment is required to determine first, and I-P units are shown in parentheses within text. Numer- if critical or noncritical design conditions exist for a specific ous figures are included for use in design. Therefore, only SI project situation. More detailed design is required for units are provided in some of the figures to avoid duplication of embankments with critical conditions than those with non- figures. Additionally, in some cases figures have been repro- critical conditions. duced that use either all SI or all I-P units. These figures have With regard to who actually designs the block layout, tra- not been revised to show both sets of units. However, Sec- ditionally this was done by the design engineer for the proj- tion 7 presents factors that can be used to convert between SI ect. However, this is appropriate only if the designer knows and I-P units. The one exception to the dual SI and I-P unit the exact block dimensions beforehand. In current U.S. prac- usage involves the quantities of density and unit weight. Den- tice, there will generally be more than one EPS block molder sity is the mass per unit volume and has units of kg/m3 who could potentially supply a given project. In most cases, (slugs/ft3), and unit weight is the weight per unit volume and block sizes will vary somewhat between molders because of has units of kN/m3 (lbf/ft3). Although density is the preferred different make, model, and age of molds. Therefore, the trend quantity in SI, unit weight is still the common quantity in geot- in U.S. practice is to leave the exact block layout design to echnical engineering practice. Therefore, the quantity of unit the molder. The design engineer simply weight will be used herein except when referring to EPS-block geofoam. The geofoam manufacturing industry typically uses · Shows the desired limits of the EPS mass on the contract the quantity of density with the SI units of kg/m3 but with the drawings, specifying zones of different EPS densities as I-P quantity of unit weight with units of lbf/ft3. Therefore, the desired; same dual-unit system of density in SI and unit weight in I-P · Includes the above conceptual guidelines in the contract units will be used when referring to EPS-block geofoam. specifications for use by the molder in developing shop This guideline was prepared as part of the National Cooper- drawings; and ative Highway Research Program (NCHRP) Project HR 24-11, · Reviews the submitted shop drawings during con- titled "Guidelines for Geofoam Applications in Embankment struction.

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2 RECOMMENDED DESIGN GUIDELINE EPS block (typical) (a) Sloped-side fill. EPS block (typical) (a) Sloped-side fill. EPS block (typical) (b) Vertical-face fill. Figure 1. Typical EPS-block geofoam applications EPS block (typical) involving embankments (2). (b) Vertical-face fill. Figure 2. Typical EPS-block geofoam applications 2 DESIGN GUIDELINE involving side-hill fills (2). 2.1 Major Components of an EPS-Block Geofoam Embankment which serves as the finished road surface, is usually either As indicated in Figure 3, an EPS-block geofoam embank- asphaltic concrete or portland cement concrete (PCC) to ment consists of three major components: provide a smooth traveling surface for motor vehicles. Asphalt concrete appears to be the predominant road sur- · The existing foundation soil, which may or may not have face type because asphalt concrete pavements tend to undergone ground improvement prior to placement of tolerate postconstruction settlements better than PCC the fill mass. pavements and because asphalt concrete pavements are · The proposed fill mass, which primarily consists of EPS- less expensive. However, in certain applications (e.g., block geofoam, although some amount of soil fill is often vehicle escape ramps in mountainous regions and logging used between the foundation soil and the bottom of the roads), an unbound gravel or crushed-rock surface layer EPS blocks for overall economy. In addition, depending may be used. on whether the embankment has sloped sides (trape- zoidal embankment) or vertical sides (vertical embank- 2.2 Design Phases ment), there is either soil or structural cover over the sides of the EPS blocks. At the present time, earthworks incorporating EPS-block · The proposed pavement system, which is defined as geofoam are only designed deterministically using service including all material layers, bound and unbound, placed loads and the traditional Allowable Stress Design (ASD) above the EPS blocks. The uppermost pavement layer, methodology with safety factors. The embankment overall TABLE 1 Examples of critical and noncritical embankment design and construction conditions (3) Condition Critical Noncritical Stability Large, unexpected, Slow, creep movements catastrophic movements Structures involved No structures involved Evidence of impending No evidence of impending instability failure instability failure Settlements Large total and differential Small total and differential Occur over relatively short Occur over large distances distances Rapid, direction of traffic Slow, transverse to direction of traffic Repairs Repair cost much greater than Repair cost less than original original construction cost construction cost

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3 RECOMMENDED DESIGN GUIDELINE Pavement System Fill Mass (EPS Blocks & Soil Cover, if any) Foundation Soil Figure 3. Major components of an EPS-block geofoam embankment. as well as its components individually must be designed to pre- pavement system--as defined by rutting, cracking, or a vent failure. As used herein, the term failure includes both of similar criterion--which is an SLS type of failure. Also, the following: when designing the pavement cross section, overall con- sideration should be given to providing sufficient support, · Serviceability failure (e.g., excessive settlement of the either by direct embedment or by structural anchorage, embankment or premature failure of the pavement sys- for any road hardware (e.g., guardrails, barriers, median tem). In this document, this will be referred to as the ser- dividers, lighting, signage, and utilities). viceability limit state (SLS). · Collapse or ultimate failure (e.g., slope instability of the edges of the embankment). In this document, this will 2.3 Design Procedure be referred to as the ultimate limit state (ULS). The design procedure for an EPS-block geofoam roadway embankment over soft soil considers the interaction between The overall design process is divided into the following the three major components of the embankment: foundation three phases: soil, fill mass, and pavement system. Because of this inter- action, the three-phased design procedure involves inter- · Design for external (global) stability of the overall connected analyses among these three components. For embankment, which considers how the combined fill example, some issues of pavement system design act oppo- mass and overlying pavement system interact with the sitely to some of the design issues involving internal and exter- existing foundation soil. External stability includes con- nal stability of a geofoam embankment (i.e., the thickness of sideration of serviceability failure issues, such as global the pavement system will affect both external and internal total and differential settlement, and collapse failure stability of the embankment). Additionally, the dead load issues, such as bearing capacity and slope stability under imposed by the pavement system and fill mass may decrease various load cases (e.g., applied gravity, seismic loading, the factor of safety of some failure mechanisms (e.g., slope and water and wind loading). These failure considera- stability) while increasing it in others (e.g., uplift). Because tions, together with other project-specific design inputs, of the interaction among these components, overall design such as right-of-way constraints, limiting impact on optimization of a roadway embankment incorporating EPS- underlying and/or adjacent structures, and construction block geofoam requires an iterative analysis to achieve a time, usually govern the overall cross-sectional geome- technically acceptable design at the lowest overall cost. In try of the fill. Because EPS-block geofoam typically has order to minimize the iterative analysis, the design procedure a higher material cost per volume than soil, it is desirable shown in Figure 4 was developed to obtain an optimal to optimize the design to minimize the volume of EPS design. The design procedure considers a pavement system used yet still satisfy design criteria concerning settlement with the minimum required thickness, a fill mass with the and stability. Therefore, it is not necessary for the EPS minimum thickness of EPS-block geofoam, and the use of an blocks to extend the full height vertically from the top of EPS block with the lowest possible density. Therefore, the the foundation soil to the bottom of the pavement system. design procedure will produce a cost-efficient design. Fig- · Design for internal stability within the embankment ure 4 also presents remedial measures that can be employed if mass. The primary consideration is the proper selection one of the design criteria is not satisfied. and specification of EPS properties so that the geofoam The design procedure is similar for both trapezoidal and mass can support the overlying pavement system with- vertical embankments except that overturning of the entire out excessive immediate and time-dependent (creep) embankment at the interface between the bottom of the assem- compression that can lead to excessive settlement of the blage of EPS blocks and the underlying foundation soil as a pavement surface. result of horizontal forces should be considered for vertical · Design of an appropriate pavement system for the sub- embankments as part of seismic stability (Step 7), translation grade provided by the underlying EPS blocks. This due to water (Step 9), and translation due to wind (Step 10) design criterion is to prevent premature failure of the analysis during the external stability design phase.

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4 RECOMMENDED DESIGN GUIDELINE Main Procedure 1 Background investigation 2 Proceed to Select preliminary type 10 remedial procedure C of EPS and assume a Translation No preliminary pavement and overturning due to system design wind (external) FS>1.2? 3 Yes Determine a preliminary fill mass arrangement 11 Translation No due to 4 water (internal) FS>1.2? No Settlement acceptable? Yes Proceed to remedial procedure D 12 Yes Translation No due to 5 wind (internal) Bearing FS>1.2? No capacity Yes FS>3? Proceed to 13 remedial procedure E Proceed to Yes Seismic No remedial procedure A stability (internal) 6 Slope FS>1.2? No stability Yes FS>1.5? Proceed to 14 remedial procedure F Yes No Load bearing 7 FS>1.2? No Seismic stability and overturning (external) Yes FS>1.2? 15 Yes Pavement system Proceed to design remedial procedure B 8 Hydrostatic No uplift (flotation) 16 Proceed to FS>1.2? Does required remedial procedure G pavement system result in Yes Yes a significant change in overburden Proceed to stress compared to the preliminary remedial procedure C 9 pavement system design Translation developed in step No and overturning due to 2? water (external) FS>1.2? No significant change 17 Yes Final embankment design FS = Factor of Safety. Figure 4. Flow chart of design procedure for an EPS-block geofoam roadway embankment.

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5 RECOMMENDED DESIGN GUIDELINE Start of Remedial Procedure A A-1 Can the thickness of any soil fill that may be A-2 proposed between the EPS blocks and soil subgrade be decreased to increase Satisfy current step Select a supplemental No the thickness of EPS? Yes requirements and proceed ground improvement or to the next step in main technique to be used in Can the foundation soil be partially excavated to procedure. conjunction with EPS a depth that will decrease the effective lightweight fill. vertical stress that will yield tolerable settlements or adequate stability? Proceed to step 1 Start of Remedial Procedure B B-1 If conventional soil fill is being proposed between the EPS blocks and the foundation Satisfy current step Yes requirements and proceed soil, can a portion of the proposed soil fill be removed and substituted to the next step in main procedure. with pavement system materials on top of the EPS blocks? No B-2 Is a drainage Satisfy current step No Yes requirements and proceed Proceed to step A-2 system or a ground anchoring suitable? to the next step in main procedure. Start of Remedial Procedure C Can any separation material being proposed between the fill mass and foundation soil be replaced with an alternative separation material that will provide a larger interface friction angle? or Satisfy current step No If conventional soil fill is being proposed between the Yes requirements and proceed Proceed to step A-2 EPS blocks and the foundation soil, can a portion to the next step in main of the proposed soil fill be removed and substituted with procedure. pavement system materials on top of the EPS blocks? or Is a drainage system suitable (for the translation due to water failure mechanism)? Start of Remedial Procedure D If conventional soil fill is being proposed between the EPS blocks and the foundation soil, can a portion of the proposed soil fill be removed and substituted with pavement system Satisfy current step No materials on top of the EPS blocks? Yes requirements and proceed Proceed to step A-2 or to the next step in main Is the use of inter-block connectors suitable? procedure. or Is a drainage system suitable (for the translation due to water failure mechanism)? Note: These remedial procedures are not applicable to overturning of a vertical embankment about the toe of the embankment at the embankment and foundation soil interface. If the factor of safety against overturning of a vertical embankment is less than 1.2, consideration can be given to adjusting the width or height of the vertical embankment. Figure 4. (Continued )

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6 RECOMMENDED DESIGN GUIDELINE Start of Remedial Procedure E Is the use of inter-block connectors suitable? or Can the pavement system thickness be decreased and/or can pavement system materials with a lower unit weight be used? Is decreasing the pavement system and/or Yes using pavement system materials No Satisfy current step Proceed to step 8 requirements and proceed with a lower unit weight being considered? to step 14 . Start of Remedial Procedure F Modify the pavement system by adding a separation layer or modifying the one currently being proposed. Can also inquire if EPS blocks with a larger elastic limit stress can be locally produced. If the pavement system greater was modified, is the less Proceed to step 4 resulting overburden stress greater, Proceed to step 8 less, or near the same as the previous overburden stress? No significant change Proceed to step 15 Start of Remedial Procedure G Did the required pavement system result decrease in an increase or decrease Proceed to step 8 in overburden stress? increase Can the thickness of any soil fill between the EPS blocks and foundation soil be Yes Satisfy current step decreased so that the EPS block thickness requirements and proceed can be increased to offset to step 17 the increase in pavement system overburden? No Proceed to step 4 Note: These remedial procedures are not applicable to overturning of a vertical embankment about the toe of the embankment at the embankment and foundation soil interface. If the factor of safety against overturning of a vertical embankment is less than 1.2, consideration can be given to adjusting the width or height of the vertical embankment. Figure 4. (Continued )

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7 RECOMMENDED DESIGN GUIDELINE 2.3.1 Step 1--Background Investigation Steps 4­10 in the flow chart in Figure 4. The tolerable crite- ria for each operation are also shown in Figure 4. The The first step in the design procedure is background inves- design methodology and tolerable criteria for external (global) tigation, which involves obtaining the subsurface information stability are described in more detail in Section 4. at the project site, estimating the loads that the embankment system will be subjected to, and determining the geometrical parameters of the embankment. Background investigation is 2.3.5 Steps 11­14--Internal Stability discussed in detail in Chapter 3 and was not the focus of this research so this information is not included in the guideline. After external stability, internal stability (e.g., translation The guideline focuses on the steps for designing the EPS por- due to water and wind, seismic stability, and load bearing) tion of the embankment. of the embankment is evaluated. This evaluation is illus- trated in Steps 11­14 in the flow chart in Figure 4 with the accompanying tolerable criteria. More detail of the internal 2.3.2 Step 2--Preliminary Selection of EPS stability evaluation and tolerable criteria is presented in and Pavement System Section 5. The second step of the design procedure is to select a pre- liminary type of EPS-block geofoam and pavement system. 2.3.6 Step 15--Pavement System Design Although the pavement system has not been designed at this point, it should be equal to or greater than 610 mm (24 in.) Step 15 involves designing the pavement system and ver- in thickness to minimize the effects of differential icing and ifying that the EPS type selected in Step 14 directly below solar heating. The design procedure depicted in Figure 4 is the pavement system will provide adequate support for the based on obtaining a pavement system that transmits the pavement system. Pavement system design is described in least amount of vertical stress to the EPS-block geofoam Section 3. embankment to satisfy internal and external stability require- ments. Therefore, it is recommended that the preliminary pavement system be assumed to be 610 mm (24 in.) thick and 2.3.7 Step 16--Comparison that the various component layers of the pavement system of Applied Vertical Stress be assumed to have a total (moist) unit weight of 20 kN/m3 (130 lbf/ft3). Chapter 4 presents the methodology for selecting Step 16 involves verifying that the vertical stress applied a preliminary pavement system. by the preliminary pavement system (Step 2) and the final pavement system (Step 15) are in agreement. If the vertical stress of the final pavement system is greater than the verti- 2.3.3 Step 3--Select Preliminary cal stress imposed by the preliminary pavement, the design Embankment Arrangement procedure may have to be repeated at Step 4 with the higher vertical stress, as shown by Remedial Procedure G of Fig- The third step of the design procedure is to determine a pre- ure 4. If the applied vertical stress from the final pavement liminary embankment arrangement. Because EPS-block geo- system is less than the applied vertical stress from the pre- foam typically has a higher material cost per volume than soil liminary pavement system, the design procedure will have to has, it is desirable to optimize the volume of EPS used yet still be repeated at Step 8, as shown by Remedial Procedure G satisfy design criteria concerning settlement and stability. of Figure 4. If the applied vertical stress from the final pave- Therefore, to achieve the most cost-effective design, a design ment system is in agreement with that from the preliminary goal is to use the minimum number of EPS blocks necessary pavement system, the resulting embankment design can be to meet the external and internal stability requirements. The used for construction purposes. design failure mechanisms that will dictate the maximum stress that can be imposed on the soft foundation soil, which dictates the minimum thickness of EPS blocks needed, include 3 PAVEMENT SYSTEM DESIGN settlement, bearing capacity, slope stability, and external seis- PROCEDURE mic stability. 3.1 Introduction 2.3.4 Steps 4­10--External (Global) Stability The objective of pavement system design is to select the most economical arrangement and thickness of pavement After the design loads, subsurface conditions, embankment materials that will be founded on EPS blocks. The design cri- geometry, preliminary type of EPS, preliminary pavement terion is to prevent premature failure of the pavement system design, and preliminary fill mass arrangement have been (as defined by rutting, cracking, or a similar criterion). obtained, the design continues with external (global) sta- Traditional pavement design procedures may be used by bility evaluation. External (global) stability is illustrated in considering the EPS to be an equivalent soil subgrade. The

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8 RECOMMENDED DESIGN GUIDELINE resilient modulus or equivalent California Bearing Ratio (CBR) 3. The designs are based on a 50- or 75-percent level of value of the EPS can be used in the design procedure. A sum- reliability, which AASHTO considers acceptable for mary of these design parameters is provided in Table 2. low-volume road design. As part of the research reported herein, pavement design 4. The designs are based on the resilient modulus values catalogs were developed to facilitate pavement system design. indicated in Table 2 for the three typical grades of A design catalog is a means for designers to obtain expedient EPS: EPS50, EPS70, and EPS100. pavement layer thicknesses that can be used to design the pave- 5. The designs are based on an initial serviceability index ment system. The following sections present the design cata- of 4.2 and a terminal serviceability index of 2. The aver- logs for flexible and rigid pavement systems. The American age initial serviceability at the American Association of Association of State Highway and Transportation Officials State Highway Officials (AASHO) road test was 4.2 for (AASHTO) 1993 design procedure (4 ) was used to develop flexible pavements. AASHTO recommends a terminal the flexible and rigid pavement design catalogs. serviceability index of 2 for highways with less traffic than major highways. 6. The designs are based on a standard deviation of 0.49 3.2 Flexible Pavement System to account for variability associated with material prop- Design Catalog erties, traffic, and performance. AASHTO recommends The design catalog for a flexible pavement system, shown a value of 0.49 for the case where the variance of pro- in Table 3, is based on the following assumptions (4 ): jected future traffic is not considered. 7. The designs do not consider the effects of drainage 1. All designs are based on the structural requirement for levels on predicted pavement performance. one performance period, regardless of the time interval. The performance period is defined as the period of Table 3 is similar in format to the design catalogs provided time for which an initial (or rehabilitated) structure will in the 1993 AASHTO Guide for Design of Pavement Struc- last before reaching its terminal serviceability (4). tures (4 ). Although the design catalog in Table 3 is for low- 2. The range of traffic levels for the performance period volume roads, the use of EPS-block geofoam is not limited to is limited to between 50,000 and 1 million 80-kN low-volume roads; EPS-block geofoam has been used for (18-kip) equivalent single-axle load (ESAL) applica- high-volume traffic roads such as Interstate highways. tions. An ESAL is the summation of equivalent 80-kN Once a design structural number (SN) is determined, appro- (18-kip) single-axle loads and is used to convert mixed priate flexible pavement layer thicknesses can be identified traffic to design traffic for the performance period (4 ). that will yield the required load-carrying capacity indicated by TABLE 2 Equivalent soil subgrade values of EPS-block geofoam for pavement design Design Values of Engineering Parameters Proposed Initial Tangent AASHTO Minimum Allowable California Young's Resilient Material Full-Block Density, Bearing Ratio, Modulus, Eti, Modulus, MR, Designation kg/m3(lbf/ft3) CBR (%) MPa(lbs/in2) MPa(lbs/in2) EPS50 20 (1.25) 2 5 (725) 5 (725) EPS70 24 (1.5) 3 7 (1015) 7 (1015) EPS100 32 (2.0) 4 10 (1450) 10 (1450) Note: The use of EPS40 directly beneath paved areas is not recommended and thus does not appear in this table because of the potential for settlement problems. The minimum allowable block density is based on density obtained on either a block as a whole unit or an actual full-sized block. The proposed AASHTO material type designation system is based on the minimum elastic limit stress of the block as a whole in kilopascals (see Table 8). TABLE 3 Flexible pavement design catalog for low-volume roads Traffic Level R EPS Low Medium High (%) Type 50,000 300,000 400,000 600,000 700,000 1,000,000 50 EPS50 4* 5.1 5.3 5.5 5.7 5.9 EPS70 3.5 4.6 4.7 5 5.1 5.3 EPS100 3.1 4.1 4.2 4.5 4.6 4.8 75 EPS50 4.4 5.6 5.8 6.1 6.2 6.5 EPS70 3.9 5 5.2 5.5 5.6 5.9 EPS100 3.5 4.5 4.7 5 5.1 5.3 R = Reliability level. * design structural number, SN.

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9 RECOMMENDED DESIGN GUIDELINE the SN in accordance with the following AASHTO flexible sented in Tables 5 and 6. The rigid pavement design cata- pavement design equation: logs are similar to the rigid pavement design catalogs pro- vided in the AASHTO 1993 procedure (4 ) except that the SN = a 1D1 + a 2 D 2 + a 3 D 3 (1) designs herein are based on the resilient modulus values representative of an EPS subgrade, which are shown in Where Table 2. Tables 5 and 6 can be used by design engineers to obtain a concrete thickness with a geofoam embank- a1, a2, and a3 = layer coefficients for surface, base, and ment. As with the design catalogs provided in the AASHTO subbase course materials, respectively, 1993 procedure, Tables 5 and 6 are based on the following and assumptions: D1, D2, and D3 = thickness (in inches) of surface, base, and subbase course, respectively. · Slab thickness design recommendations apply to all six Layer coefficients can be obtained in the 1993 AASHTO U.S. climatic regions. Guide for Design of Pavement Structures (4 ) or from state · The procedure is based on the use of dowels at trans- department of transportation (DOT) design manuals. How- verse joints. ever, layer coefficient values for PCC slabs are not provided · The range of traffic loads for the performance period is in the 1993 AASHTO pavement design guide (4 ). If a re- limited to between 50,000 and 1,000,000 applications of inforced PCC slab is considered as a separation layer between 80-kN (18-kip) ESALs. An ESAL is the summation of the top of the EPS blocks and the overlying pavement sys- equivalent 80-kN (18-kip) single-axle loads used to con- tem, it may be possible to incorporate the PCC slab into the vert mixed traffic to design traffic for the performance AASHTO 1993 flexible pavement design procedure by deter- period (4 ). mining a suitable layer coefficient to represent the PCC slab. · The designs are based on a 50-percent or 75-percent level NCHRP Report 128 (5) indicates that, based on test results of reliability, which AASHTO considers acceptable for performed in Illinois, a PCC base with a 7-day strength of low-volume road design. 17.2 MPa (2,500 lbs/in2) exhibits a layer coefficient of 0.5. · The designs are based on a minimum thickness of high- It can be seen that, for a given set of layer coefficients, quality material subbase equivalent to 610 mm (24 in.) Equation 1 does not provide a unique solution for the thickness less the PCC slab thickness used. This thickness min- of the surface, base, and subbase. However, AASHTO rec- imizes the potential for differential icing and solar ommends the minimum thickness values indicated in Table 4 heating. for asphalt concrete and aggregate base to overcome place- · The designs are based on the resilient modulus values ment impracticalities, ensure adequate performance, and lower indicated in Table 2 for EPS70 and EPS100. costs. This recommendation provides guidance in fixing val- · The designs are based on a mean PCC modulus of rupture ues of D1 and D2 so D3 can be estimated in Equation 1. In addi- ) of 4.1 or 4.8 MPa (600 or 700 lbs/in2). (Sc tion, it is recommended herein that a minimum pavement sys- · The designs are based on a mean PCC elastic modulus tem thickness of 610 mm (24 in.) be used over EPS-block (Ec) of 34.5 GPa (5,000,000 lbs/in2). geofoam to minimize the potential for differential icing and · Drainage (moisture) conditions (Cd) are fair (Cd = 1.0). solar heating. After various layer thickness combinations have · The 80-kN (18-kip) ESAL traffic levels are as follows: been determined and checked against construction and main- ­ High: 700,000­1,000,000. tenance constraints, a cost-effective layer thickness combina- ­ Medium: 400,000­600,000. tion is typically selected. ­ Low: 50,000­300,000. 3.3 Rigid Pavement System Design Catalog Even though the design catalogs in Tables 5 and 6 are for low-volume roads, EPS-block geofoam can be and has Design catalogs for rigid pavements developed herein been used for high-volume traffic roads, such as Interstate and based on the AASHTO 1993 design procedure are pre- highways. TABLE 4 Minimum practical thicknesses for asphalt concrete and aggregate base ( 4 ) Minimum Thickness , mm (in.) Traffic, ESALs Asphalt Concrete Aggregate Base Less than 50,000 25 (1.0) 100 (4.0) 50,001­150,000 50 (2.0) 100 (4.0) 150,001­500,000 64 (2.5) 100 (4.0) 500,001­2,000,000 76 (3.0) 150 (6.0) 2,000,001­7,000,000 90 (3.5) 150 (6.0) More than 7,000,000 100 (4.0) 150 (6.0)

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RECOMMENDED DESIGN GUIDELINE TABLE 5 Rigid concrete thickness for low-volume roads for inherent reliability of 50 percent LOAD TRANSFER EPS DEVICES No Yes RESILIENT INHERENT MODULUS EDGE SUPPORT No Yes No Yes RELIABILITY EPS MPa (lbs/in2) 2 % TYPE S'c MPa (lbs/in ) 4.1 (600) 4.8 (700) 4.1 (600) 4.8 (700) 4.1 (600) 4.8 (700) 4.1 (600) 4.8 (700) Traffic (ESALs) Rigid Concrete Thickness (in.) 50 EPS70 7 (1015) 50,000 5 5 5 5 5 5 5 5 EPS100 10 (1450) 5 5 5 5 5 5 5 5 EPS70 7 (1015) 300,000 6.5 6 6 6 6 5.5 5.5 5 EPS100 10 (1450) 6.5 6 6 6 6 5.5 5.5 5 EPS70 7 (1015) 400,000 7 6.5 6.5 6 6 5.5 6 5.5 EPS100 10 (1450) 7 6.5 6.5 6 6 5.5 6 5.5 EPS70 7 (1015) 600,000 7.5 7 7 6.5 6.5 6 6 5.5 EPS100 10 (1450) 7.5 7 7 6.5 6.5 6 6 5.5 EPS70 7 (1015) 700,000 7.5 7 7 6.5 6.5 6 6 6 EPS100 10 (1450) 7.5 7 7 6.5 6.5 6 6 6 EPS70 7 (1015) 1,000,000 8 7.5 7.5 7 7 6.5 6.5 6 EPS100 10 (1450) 8 7.5 7.5 7 7 6.5 6.5 6

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41 RECOMMENDED DESIGN GUIDELINE 30 m 10 I II&III Failure Mode I kh = 0.05 Seismic Factor of Safety, FS' kh = 0.10 25 m = 54.1 kN/m3 (345 lbf/ft3) 8 kh = 0.20 20 m I 6 kh 12.2 m (40 ft) Mode III Mode II 15 m 4 II = 0.05 10 m 2 = 0.10 III Foundation Soil = 0.20 FS' = 1.2 EPS/geosynthetic 5m Interface 0 5 10 15 20 25 30 35 40 Interface Friction Angle, (degrees) 0m 0m 10 m 20 m 30 m 40 m 50 m 60 m Figure 39. Design chart for internal seismic stability of Figure 38. Typical cross section used in seismic internal EPS vertical embankments. slope stability analyses for vertical embankments with the three applicable failure modes. for trapezoidal embankments (see Figure 7). However, an important aspect of Figure 39 is that it can be used to develop (690 lbs/ft2) corresponds to the sum of the design values of the most cost-effective internal stability design by selecting the pavement surcharge (21.5 kN/m2 [450 lbs/ft2]) and traffic sur- lowest interface friction angle for each interface that results in charge (11.5 kN/m2 [240 lbs/ft2]) used previously for exter- a seismic factor of safety of greater than 1.2. For example, a nal bearing capacity and static slope stability of trapezoidal lightweight geotextile can be selected for the EPS/foundation embankments. The surcharge in Figure 6 had to be replaced interface because the interface only needs to exhibit a friction by an equivalent soil layer for the seismic slope stability analy- angle greater than 15 degrees. More importantly, the EPS/EPS sis because a seismic coefficient cannot be applied to a sur- interface within the EPS also only needs to exhibit a friction charge in limit equilibrium stability analyses. angle greater than 15 degrees, which suggests that mechanical Figure 7 also presents the three failure modes considered in connectors are not required between EPS blocks for internal the internal seismic stability analyses for vertical geofoam seismic stability because the interface friction angle for an embankments. These failure modes are similar to the three EPS/EPS interface is approximately 30 degrees. In summary, failure modes analyzed in the seismic internal slope stability as with trapezoidal embankments, it appears that internal seis- analysis of trapezoidal embankments, and a description of mic stability will be controlled by the shear resistance of the each is included in Section 5.4.1.1. pavement system/EPS interface. Slope stability analyses were conducted on a range of ver- tical embankment geometries to investigate the effect of 5.5 Load Bearing embankment height (3.1 m [10 ft] to 12.2 m [40 ft]) and road- way width (11 m [36 ft], 23 m [76 ft], and 34 m [112 ft]) on 5.5.1 Introduction internal seismic slope stability. The results of these analyses were used to develop design charts to facilitate internal design The primary internal stability issue for EPS-block geo- of roadway embankments with vertical walls that use geo- foam embankments is the load bearing of the EPS-geofoam foam. Three seismic coefficients--low (0.01), medium (0.10), mass. A load-bearing capacity analysis consists of selecting and high (0.20)--were used for each roadway embankment. an EPS type with adequate properties to support the over- lying pavement system and traffic loads without excessive 5.4.2.2 Design Chart. The internal seismic stability EPS compression that could lead to excessive settlement design chart for vertical embankments in Figure 39 presents of the pavement surface. The design approach used herein the seismic factor of safety for each seismic coefficient as a is an explicit deformation-based design methodology. It function of interface friction angle. This chart provides esti- is based on the elastic limit stress, e, to evaluate the load mates of seismic internal factors of safety for vertical embank- bearing of EPS. ments with any of the geometries considered during this Table 8 provides the minimum recommended values of study--i.e., embankment heights of 3.1 m (10 ft) to 12.2 m elastic limit stress for various EPS densities. The use of the (40 ft) and roadway widths of 11 m, 23 m, and 34 m (36, 76, elastic limit stress values indicated in Table 8 is slightly con- and 112 ft)--even though the chart is based on a roadway width servative because the elastic limit stress of the block as a of 11 m (36 ft) and an embankment height from 3.1 m (10 ft). whole is somewhat greater than these minimums, but this It can be seen that an EPS embankment will exhibit a suit- conservatism is not unreasonable and will ensure that no part able seismic factor of safety if the minimum interface friction of a block (where the density might be somewhat lower than angle exceeds approximately 15 degrees, which is similar the overall average) becomes overstressed.

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42 RECOMMENDED DESIGN GUIDELINE TABLE 8 Minimum allowable values of elastic limit stress and initial tangent Young's modulus for the proposed AASHTO EPS material designations Dry Density of Each Block as a Dry Density of a Elastic Limit Material Whole, kg/m3 Test Specimen, Stress, kPa Initial Tangent Young's Designation (lbf/ft3) kg/m3 (lbf/ft3) (lbs/in2) 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) 5.5.2 Design Procedure elastic limit stress that is greater than the calculated or required elastic limit stress at the depth being considered. The load- The procedure for evaluating the load-bearing capacity of bearing design procedure can be divided into two parts. Part 1 EPS as part of internal stability is outlined in the following consists of Steps 1 through 8 and focuses on the determination thirteen steps: of the traffic and gravity load stresses applied by the pavement system to the top of the EPS blocks and selection of the type 1. Estimate the traffic loads. of EPS that should be used directly beneath the pavement sys- 2. Add impact allowance to the traffic loads. tem (see steps above). Part 2 consists of Steps 9 through 13 and 3. Estimate traffic stresses at the top of EPS blocks. focuses on the determination of the traffic and gravity load 4. Estimate gravity stresses at the top of EPS blocks. stresses applied at various depths within the EPS blocks and 5. Calculate total stresses at the top of EPS blocks. selection of the appropriate EPS for use at these various depths 6. Determine the minimum required elastic limit stress within the embankment. Each of the design steps are sub- for EPS under the pavement system. sequently described. 7. Select the appropriate EPS block to satisfy the required EPS elastic limit stress for underneath the pavement 5.5.2.1 Step 1: Estimate the Traffic Loads. Figure 40 system, e.g., EPS50, EPS70, or EPS100. shows the wheel configuration of a typical semitrailer truck 8. Select the preliminary pavement system type and with a tandem axle with dual tires at the rear. Trucks with determine whether a separation layer is required. a tridem axle, each spaced at 122 to 137 cm (48 to 54 in.) 9. Estimate traffic stresses at various depths within the apart, and dual tires also exist. The largest live or traffic load EPS blocks. expected on the roadway above the embankment should be 10. Estimate gravity stresses at various depths within used for design. The magnitude and vehicle tire configuration the EPS blocks. that will provide the largest live load is typically not known 11. Calculate total stresses at various depths within the during the preliminary design phase. Therefore, the AASHTO EPS blocks. standard classes of highway loading (12) can be used for pre- 12. Determine the minimum required elastic limit stress liminary load-bearing analyses. at various depths. 13. Select the appropriate EPS block to satisfy the re- quired EPS elastic limit stress at various depths in the 5.5.2.2 Step 2: Add Impact Allowance to the Traffic embankment. Loads. Allowance for impact forces from dynamic, vibra- tory, and impact effects of traffic is generally only considered The basic procedure for designing against load-bearing fail- where these forces act across the width of the embankment or ure is to calculate the maximum vertical stresses at various lev- adjacent to a bridge abutment. An impact coefficient of 0.3 is els within the EPS mass (typically the pavement system/EPS recommended for design of EPS-block geofoam (15 ). Equa- interface is most critical) and select the EPS that exhibits an tion 31 can be used to include the impact allowance to the live 7 m (23 ft) 4 m (13 ft) Longitudinal Wheel Spacing = 4 ft Transverse Wheel Dual Spacing = 0.3 - 0.36 m Spacing = 1.8 m (12-14 in) Trailer Tractor Single Axle (6 ft) with Single Tire Tandem Axle Single Axle with Dual Tires with Dual Tires Figure 40. Wheel configuration of a typical semitrailer truck (14).

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43 RECOMMENDED DESIGN GUIDELINE loads estimated in Step 1 if impact loading is deemed neces- 1 r= A CD 2 sary for design: (35) Q = LL (1 + I ) = LL 1.3 (31) Where Where ACD = contact area of dual tires, Q = traffic load with an allowance for impact, QD = live load on dual tires, and LL = live load for traffic from AASHTO standard classes q = contact pressure on each tire = tire pressure. of highway loading (12) obtained in Step 1, and The recommended procedure for estimating the stress at the I = impact coefficient = 0.3. top of the EPS is Burmister's elastic layered solution (17 ). Burmister's elastic layered solution is based on a uniform pres- 5.5.2.3 Step 3: Estimate Traffic Stresses at the Top of sure applied to the surface over a circular area on top of an EPS Blocks. The objective of this step is to estimate the dis- elastic half-space mass. The primary advantage of Burmister's sipation of vertical stress through the pavement system so that theory is that it considers the influence of layers with different an estimate of the traffic stresses at the top of the EPS blocks elastic properties within the system being considered. Design can be obtained. The vertical stress at the top of the EPS charts are presented in Figures 41 through 43 that alleviate the is used to evaluate the load-bearing capacity of the blocks use of computer software to use Burmister's elastic layered directly under the pavement system. Various pavement sys- tems, with and without a separation layer between the pave- solutions. The procedure used to obtain the results shown in ment system and the EPS blocks, should be evaluated to deter- these figures is presented in Chapter 6. mine which alternative is the most cost-effective. Figure 41 presents values of vertical stress on top of the The contact pressure applied by a tire to the top of the pave- EPS blocks due to a single or dual wheel load, LL, on an ment is typically assumed to be equal to the tire pressure (14 ), asphalt concrete pavement system. The asphalt concrete and the tire and pavement surface interface is assumed to be pavement system represented by Figure 41 consists of the free of shear stress. A tire pressure of 689 kPa (100 lbs/in2) indicated asphalt thickness with a corresponding crushed appears to be representative and is recommended for prelimi- stone base thickness equal to 610 mm (24 in.) less the thick- nary design purposes. This tire pressure is near the high end of ness of the asphalt. Figure 42 presents values of LL on a typical tire pressures, but is used for analysis purposes by portland cement concrete (PCC) pavement system. The PCC transportation software such as ILLI-PAVE (16 ). pavement system represented in Figure 42 consists of the The contact pressure is converted to a traffic load by mul- indicated PCC thickness with a corresponding crushed stone tiplying by the contact area of the tire. For the case of a sin- base thickness equal to 610 mm (24 in.) less the thickness of gle axle with a single tire, the contact area is given by Equa- the PCC. Figure 43 presents values of LL on a composite tion 32, and the radius of the contact area is given by pavement system defined here as an asphalt concrete pave- Equation 33: ment system with a PCC slab separation layer placed between the asphalt concrete pavement system and the EPS-block geo- Qt foam. The composite pavement system represented in Fig- AC = (32) q ure 43 consists of the indicated asphalt thickness plus a 102-mm (4-in.) concrete separation layer with a correspond- 1 ing crushed stone base thickness equal to 610 mm (24 in.) less r= AC 2 (33) the thickness of the asphalt concrete and the separation slab. In all three figures, the minimum recommended pave- ment system thickness of 610 mm (24 in.) to minimize the Where potential for differential icing and solar heating was used. AC = contact area of one tire, Both a single tire and a set of dual tires were modeled as a sin- Qt = live load on one tire, gle contact area. Therefore, both a single tire and a set of dual q = contact pressure = tire pressure, and tires can be represented by the total load of a single tire or of r = radius of contact area. the dual tires and a contact area. In summary, the vertical stress charts in Figures 41 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 through 43 can be used to estimate the applied vertical stress circular area by assuming that the circle has an area equal to on top of the EPS due to a tire load, LL; on top of an asphalt the contact area of the duals, as indicated by Equation 34. The concrete, PCC system; and on top of a composite pavement radius of contact is given by Equation 35. Equation 34 yields system, respectively. For example, the vertical stress a conservative value, i.e., smaller area, for the contact area applied to the top of the EPS blocks under a 178-mm (7-in.)- because the area between the duals is not included. thick asphalt pavement with a total wheel load of 100 kN (225 kips) is approximately 55 kPa (8 lbs/in2) (see Figure QD 41). This value of 55 kPa (8 lbs/in2) is then used in the load- A CD = (34) q bearing analysis described subsequently.

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44 RECOMMENDED DESIGN GUIDELINE 180 m 6m Vertical Stress on top of EPS Blocks, LL (kPa) s s =7 mm 160 e kn =102 hic ss mm alt T ckne 27 140 ph As alt T hi e s s=1 ick n mm ph 52 As alt Th s s =1 120 ph ne mm As ick 78 lt Th e s s=1 pha ick n 100 As t Th s p hal A 80 60 40 20 0 0 50 100 150 200 250 Total Load on Single Wheel or Dual Wheels (kN) Figure 41. Vertical stress on top of the EPS blocks, LL, due to traffic loads on top of a 610-mm (24-in.) asphalt concrete pavement system. 40 Vertical Stress on top of EPS Blocks, LL (kPa) mm 1 27 ss= kne 30 T hic re te nc m Co 2m 15 ss= i ckne h eT mm 20 nc ret 178 Co k ness= hi c m eT 3m cret s=20 Con hi c knes mm eT 229 cret ness= Con ete Thick r 10 Conc 0 0 50 100 150 200 250 Total Load on Single Wheel or Dual Wheels (kN) Figure 42. Vertical stress on top of the EPS blocks, LL, due to traffic loads on top of a 610-mm (24-in.) portland cement concrete pavement system. 5.5.2.4 Step 4: Estimate Gravity Stresses at the Top of The various components of the pavement system can EPS Blocks. Stresses resulting from the gravity load of the be assumed to have an average unit weight of 20 kN/m3 pavement system and any road hardware placed on top of (130 lbf /ft3). Because the traffic stresses in Figures 41 the roadway must be added to the traffic stresses obtained in through 43 are based on a pavement system with a total thick- Step 3 to conduct a load-bearing analysis of the EPS. The grav- ness of 610 mm (24 in.), a value of Tpavement equal to 610 mm ity stress from the weight of the pavement system is as follows: (24 in.) should be used to estimate DL to ensure consistency. DL = Tpavement pavement (36) 5.5.2.5 Step 5: Calculate Total Stresses at the Top of EPS Blocks. The total vertical stress at the top of EPS blocks Where underlying the pavement system from traffic and gravity loads, DL = gravity stress due to dead loads, total, is as follows: Tpavement = pavement system thickness, and pavement = average unit weight of the pavement system. total = LL + DL (37)

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45 RECOMMENDED DESIGN GUIDELINE 60 Asphalt Thickness=76 mm Vertical Stress on top of EPS Blocks, LL (kPa) Asphalt Thickness=102 mm Asphalt Thickness=127 mm Asphalt Thickness=152 mm 50 Asphalt Thickness=178 mm 40 30 20 10 0 100 200 300 400 Total Load on Single Wheel or Dual Wheels (kN) Figure 43. Vertical stress on top of the EPS blocks, LL, due to traf- fic loads on top of a 610-mm (24-in.) asphalt concrete pavement sys- tem with a 102-mm (4-in.) concrete separation layer between the pavement system and EPS blocks. Where defines the minimum elastic limit stress of the block as a whole in kilopascals. For example, EPS50 will have a mini- LL = vertical stress applied to the top of EPS-block geo- mum elastic limit stress of 50 kPa (7.2 lbs/in2). The EPS foam due to traffic loads under a particular pave- selected will be the EPS block type that will be used directly ment system. beneath the pavement system for a minimum depth of 610 mm (24 in.) in the EPS fill. This minimum depth is recommended 5.5.2.6 Step 6: Determine the Minimum Required because it is typically the critical depth assumed in pavement Elastic Limit Stress for EPS Under the Pavement System. design for selection of an average resilient modulus for design The minimum required elastic limit stress of the EPS block of the pavement system (14 ). Thus, the 610-mm (24-in.) depth under the pavement system can be calculated by multiplying is only an analysis depth and is not based on the thickness of the total vertical stress from Step 5 by a factor of safety, as the EPS blocks. Of course, if the proposed block thickness is shown in Equation 38: greater than 610 mm (24 in.), the block selected in this step will conservatively extend below the 610-mm (24-in.) zone. e total FS (38) The use of EPS40 is not recommended directly beneath paved areas because an elastic limit stress of 40 kPa (5.8 lbs/in2) has Where resulted in pavement settlement problems. e = minimum elastic limit stress of EPS and 5.5.2.8 Step 8: Select the Preliminary Pavement Sys- FS = factor of safety = 1.2. tem Type and Determine Whether a Separation Layer Is The main component of total is the traffic stress and not the Required. A cost analysis should be performed in Step 8 to gravity stress from the pavement. Because traffic is a main preliminarily select the optimal pavement system that will be component of total and traffic is a transient load like wind used over the type of EPS blocks determined in Step 7. The loading, a factor of safety of 1.2 is recommended for the load- cost analysis can focus on one or all three of the pavement bearing analysis. This is the same value of factor of safety rec- systems evaluated in Step 3--i.e., asphalt concrete, PCC, and ommended for other transient or temporary loadings, such as a composite pavement system. The EPS selected for a depth wind, hydrostatic uplift, sliding, and seismic loading used for of 610 m (24 in.) below the pavement system is a function of external stability analyses. the pavement system selected because the vertical stress induced at the top of the EPS varies with the pavement sys- 5.5.2.7 Step 7: Select the Appropriate EPS Block to tem, as shown in Figures 41 through 43. Therefore, several Satisfy the Required EPS Elastic Limit Stress for cost scenarios can be analyzed--e.g., a PCC versus asphalt Underneath the Pavement System, e.g., EPS50, EPS70, or concrete pavement system and the accompanying EPS for EPS100. Select an EPS type from Table 8 that exhibits an each pavement system--to determine the optimal combi- elastic limit stress greater than or equal to the required e deter- nation of pavement system and EPS. The cost analysis will mined in Step 6. The EPS designation system in Table 8 also determine whether a concrete separation layer between

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46 RECOMMENDED DESIGN GUIDELINE the pavement and EPS is cost-effective by performing a cost type selected in Step 8 for directly beneath the pavement sys- analysis on the composite system. The resulting pavement tem is adequate for a depth of more than 610 mm (24 in.) into system will be used in Steps 9 through 13. the EPS and to determine if an EPS block with a lower elastic If a concrete separation slab will be used, the thickness of limit stress, i.e., lower density and lower cost, can be used at the concrete slab can be estimated by assuming that the slab a greater depth. is a granular material and will dissipate the traffic stresses to Based on an analysis performed during this study and the a desirable level at 1(horizontal): 1(vertical) stress distribu- results of a full-scale model creep test that was performed at the tion. Concrete can then be substituted for granular material Norwegian Road Research Laboratory (18, 19), a 1(horizon- using the 1 concrete to 3 gravel ratio previously discussed in tal): 2(vertical) distribution of vertical stresses through EPS Step 3 to estimate the required thickness of granular material. blocks, as shown in Figure 44, should be used to estimate the For example, a 102-mm (4-in.)-thick concrete separation applied vertical stress at various depths in the geofoam. layer can be used to replace 306 mm (12 in.) of granular ma- In order to use the 1(horizontal): 2(vertical) stress distribu- terial. Therefore, a 927-mm (36.5-in.)-thick asphalt concrete tion method to calculate the vertical stresses applied through pavement system that consists of 127 mm (5 in.) of asphalt the depth of the EPS block using handheld calculations, it is and 800 mm (31.5 in.) of crushed stone base will be 927 mm easiest to assume a rectangular loaded area at the top of the (36.5 in.) thick less 306 mm (12 in.) of crushed stone base, EPS and to assume that the total applied load at the surface of which is replaced by a 102-mm (4-in.)-thick concrete separa- the EPS is distributed over an area of the same shape as the tion layer. However, it is recommended that a minimum pave- loaded area on top of the EPS, but with dimensions that ment system thickness of 610 mm (24 in.) be used to mini- increase by an amount equal to 1(horizontal): 2(vertical) (see mize the potential for differential icing and solar heating. Figure 44). Therefore, the live load vertical stress, LL, obtained from Figures 41 through 43 should be converted 5.5.2.9 Step 9: Estimate Traffic Stresses at Various from the assumed circular area to a rectangular area. The Depths Within the EPS Blocks. This step estimates the dis- Portland Cement Association 1984 method, as described by sipation of the traffic-induced stresses through the EPS blocks Huang (14 ), can be used to convert the circular loaded area to within the embankment. Using the pavement system and sep- an equivalent rectangular loaded area, as shown in Figure 45. aration layer, if included, from Step 8, the vertical stress from The rectangular area shown is equivalent to a circular contact the traffic loads at depths greater than 610 mm (24 in.) in the area that corresponds to a single axle with a single tire, AC, or EPS is calculated. The vertical stress is usually calculated at a single axle with dual tires, ACD. The values of AC and ACD every 1 m (3.3 ft) of depth below a depth of 610 mm (24 in.). can be obtained from Equations 32 and 34, respectively, using Block thickness is typically not used as a reference depth the following procedure: because the block thickness that will be used on a given proj- ect will typically not be known during the design stage of the 1. Estimate LL from Figure 41, 42, or 43 depending on project. The first depth at which the vertical stress will be esti- the pavement system being considered. mated is 610 mm (24 in.) because in Step 7 the EPS selected 2. Use LL in Equation 32 or 34 as the contact pressure, q, to support the pavement system will extend to a depth of and the recommended traffic loads from Step 1 to esti- 610 mm (24 in.). The traffic vertical stresses should also be mate the live load on one tire in Equation 32 or 34 for determined at any depth within the EPS blocks where the a single axle with a single tire or a single axle with dual theoretical 1(horizontal): 2(vertical) stress zone overlaps, as tires, respectively, to calculate AC or ACD. will be shown subsequently (see Figure 44). These vertical 3. In Figure 45, use the values of AC or ACD to calculate stress estimates will be used in Step 12 to determine if the EPS the value of L, the length of a rectangle used to repre- sent a circular contact area for a tire AC if the axle has one tire and ACD if the axle has two tires. Equate AC or Q ACD to 0.5227L2 and solve for L. After solving for L, the dimensions of the rectangular loaded area in Fig- ure 45, i.e., 0.8712L and 0.6L, can be calculated. L z B 2 Area = 0.5227 L2 0.6 L 1 2 L+z 1 0.8712 L B+z Figure 44. Approximate stress distribution by the 1(hori- Figure 45. Method for converting a circular contact area zontal): 2(vertical) method. into an equivalent rectangular contact area (14).

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47 RECOMMENDED DESIGN GUIDELINE As shown in Figure 44, at a depth z below the EPS, the total L = 0.8712 L ( 43) load Q applied at the surface of the EPS is assumed to be uni- formly distributed over an area (B + z) by ( L + z). The Substituting Equations 40 through 43 into 39, increase in vertical pressure, Z, at depth z due to an applied live load such as traffic is given by Equation 39. Figure 46 LL A rect demonstrates the use of the 1(horizontal): 2(vertical) method Z,LL = ( 44) (0.6 L + z)(0.8712L + z) to estimate overlapping stresses from closely spaced loaded areas, such as from adjacent sets of single or dual tires. Where Arect is either AC or ACD, as determined from Equa- Q tions 32 or 34, respectively. Z,LL = (39) (B + z)( L + z) 5.5.2.10 Step 10: Estimate Gravity Stresses at Various Where Depths Within the EPS Blocks. Stresses resulting from Z,LL = increase in vertical stress at depth z caused by traf- the gravity load of the pavement system, any road hardware fic loading, placed on top of the roadway, and the EPS blocks must be Q = applied traffic load, added to the traffic stresses to evaluate the load-bearing B = width of the loaded area, capacity of the EPS within the embankment. Equations 45, z = depth, and 46, and 47 can be used to determine the increase in vertical L = length of the loaded area. stress caused by the gravity load of the pavement system: To use the 1(horizontal): 2(vertical) stress distribution qt Z,DL = ( + sin ) where is in radians ( 45) method to calculate the vertical stresses through the depth of the EPS block, the assumed circular loaded area below a tire used to determine LL in Figures 41, 42, or 43 should be con- verted to an equivalent rectangular area, as discussed previ- = 2 arctan (b z) where is calculated in radians ( 46) ously. Alternatively, Equation 39 can be modified to deter- mine Z,LL directly from the LL, which is determined from Where Figures 41, 42, or 43, as shown below: b = one-half the width of the roadway. Q = LL A rect ( 40) q t = q pavement = pavement Tpavement ( 47) Where Where Arect = area of equivalent rectangle to represent a circu- qpavement = vertical stress applied by the pavement system, lar contact area for a tire. kN/m3; Z,DL = increase in vertical stress at depth z due to pave- LL is obtained from Figures 41, 42, or 43. ment system dead load, m; From Figure 45, pavement = unit weight of the pavement system, kN/m3; and Tpavement = thickness of the pavement system, m. 1 L = A rect 2 Figure 47 shows the geometry and variables for determining 0.5227 ( 41) the increase in vertical stress with depth. B = 0.6 L ( 42) b b Q1 Q2 qI X Center B1 S B2 1 z 2 Z B1 + B 2 + z + S Figure 47. Geometry and variables for determining the Figure 46. Approximate stress distribution of closely increase in vertical stress with depth. (qI = stress applied to spaced loaded areas by the 1(horizontal): 2(vertical) method. the surface.)

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48 RECOMMENDED DESIGN GUIDELINE The total gravity stress from the pavement system and the limit stress is less than 40 kPa (5.8 lbs/in2). However, for con- EPS blocks is as follows: structability reasons, it is recommended that no more than two different EPS block types be used. Z,DL = ( Z,DL ) + (z EPS ) ( 48) Where 6 ABUTMENT DESIGN Z,DL = total vertical stress at depth z due to dead loads, 6.1 Introduction kN/m2; z = depth from the top of the EPS, m; and In applications where the EPS-block geofoam is used as EPS = unit weight of the EPS blocks, kN/m3. part of a bridge approach, the EPS blocks should be contin- ued up to the drainage layer that is placed along the back of As discussed in Step 5, the various components of the the abutment. A geosynthetic sheet drain, not natural aggre- pavement system can be assumed to have an average unit gate, should be used for this drainage layer to minimize the weight of 20 kN/m3 (130 lbf/ft3). Because the traffic stresses vertical and lateral earth pressure on the subgrade and abut- in Figures 41 through 43 are based on a pavement system ment, respectively, as well as to facilitate construction. The with a total thickness of 610 mm (24 in.), a value of Tpave- design requirements for abutments as well as design examples ment equal to 610 mm (24 in.) should be used to estimate qt to can be found in NCHRP Report 343 (20). The procedure for ensure consistency. It is recommended that the unit weight designing retaining walls and abutments consists of the fol- of the EPS be assumed to be 1,000 N/m3 (6.37 lbf/ft3) to con- lowing steps (20): servatively allow for long-term water absorption in the cal- culation of Z,DL. 1. Select preliminary proportions of the wall. 2. Determine loads and earth pressures. 5.5.2.11 Step 11: Calculate Total Stresses at Various 3. Calculate the magnitude of reaction force on the base. Depths Within the EPS Blocks. The total vertical stress 4. Check stability and safety criteria: induced by traffic and gravity loads at a particular depth within (a) location of normal component of reactions, the EPS, total, is as follows: (b) adequacy of bearing pressure, and (c) safety against sliding. total = Z,LL + Z,DL ( 49) 5. Revise proportions of wall, and repeat Steps 2 through 4 until stability criteria are satisfied; then check the 5.5.2.12 Step 12: Determine the Minimum Required following: Elastic Limit Stress at Various Depths. Determine the (a) settlement within tolerable limits and minimum required elastic limit stress, e, of the EPS block at (b) safety against deep-seated foundation failure. each depth that is being considered using the same equation 6. If proportions become unreasonable, consider a foun- from Step 6: dation supported on driven piles or drilled shafts. 7. Compare economics of completed design with other e total 1.2 (50) wall systems. 5.5.2.13 Step 13: Select the Appropriate EPS Block to For a bridge approach consisting of EPS-block geofoam Satisfy the Required EPS Elastic Limit Stress at Various backfill, earth pressures, which are required for Step 2 of Depths in the Embankment. Select an EPS type from the abutment design process, generated by the following two Table 8 that exhibits an elastic limit stress greater than or sources should be considered: equal to the required elastic limit stress determined in Step 12. EPS40 is not recommended for directly beneath the pave- · The gravity load of the pavement system, WP, and of ment system (see Step 7), but can be used at depths below EPS blocks, WEPS (usually small), pressing directly on 610 mm (24 in.) in the embankment if the required elastic the back of the abutment (see Figure 48) and Figure 48. Loads on an EPS-block geofoam bridge approach system.

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49 RECOMMENDED DESIGN GUIDELINE · The active earth pressure from the soil behind the geo- ( ) 2 1 foam fill (see Figure 48) that can be transferred through sin ( - ) KA = sin the geofoam fill to the back of the abutment. (51) sin( + ) + sin( + ) sin sin The magnitude of these loads varies depending on whether gravity and /or seismic loading is evaluated. The procedure for estimating the gravity and seismic loads is discussed in Where is the friction angle of the EPS/soil interface, which the following sections. is analogous to the soil/wall interface in typical retaining wall design. The value of can be assumed to be equal to the fric- tion angle of the soil, . Equation 51 is applicable only to hor- 6.2 Gravity Loads izontally level backfills. The active earth pressure force, PA, is expressed in Equation 52: The assumed components of the gravity loads acting on a vertical wall or abutment are as follows (see Figure 49): 1 PA = soil H 2 K A (52) 2 · The uniform horizontal pressure acting over the entire depth of the geofoam caused by the vertical stress applied Where by the pavement system to the top of the EPS, which can be estimated from Figures 41 through 43; soil = unit weight of the soil backfill and · The horizontal pressure generated by the vertical stress H = height of the soil backfill behind the vertical wall. imposed by the pavement system, which can be assumed to be equal to 1/10 times the vertical stress; and 6.3 Seismic Loads · The lateral earth pressure, PA, generated by the soil behind the EPS/soil interface, which is conservatively The following seismic loads acting on the back of an abut- assumed to be transmitted without dissipation through ment must be added to the gravity loads in Figure 50 to the geofoam to the back of the abutment. The active safely design a bridge abutment in a seismic area: earth pressure acting along this interface is calculated using a coefficient of active earth pressure, KA, · Inertia forces from seismic excitation of the pavement because it is assumed that enough lateral deformation system and the EPS blocks (usually negligible). These will occur to mobilize an active earth pressure condi- inertial forces should be reduced by the horizontal sliding tion in the soil behind the geofoam. The active earth resistance, tan, developed along the pavement system/ pressure coefficient can be determined from Equation 51, EPS interface. which is based on Coulomb's classical earth-pressure · The seismic component of the active earth pressure gen- theory (21). erated by the soil behind the EPS/soil interface, which can be calculated using the solution presented by Mononobe- The horizontal stress from the EPS blocks is neglected Okabe (13). because it is negligible. Figure 49. Gravity load components on a vertical wall. Figure 50. Seismic load components on a wall. (FB = (F = resisting force against sliding.) resisting force against sliding and m = seismic moment.)

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50 RECOMMENDED DESIGN GUIDELINE 7 CONVERSION FACTORS Stress, Pressure, Modulus of Elasticity: 1 lb/ft2 = 47.88 Pa 7.1 Introduction 1 lb/ft2 = 0.04788 kPa 1 U.S. ton/ft2 = 95.76 kPa Both the Système International d'Unités (SI) and inch- 1 kip/ft2 = 47.88 kPa pound (I-P) units have been used in this report. SI units are 1 lb/in2 = 6.895 kPa shown first, and I-P units are shown in parentheses within Density: 1 slug/ft3 = 16.018 kg/m3 text. Numerous figures are included for use in design. There- Unit Weight: 1 lbf/ft3 = 0.1572 kN/m3 fore, only SI units are provided in some of the figures to avoid 1 lbf/in3 = 271.43 kN/m3 duplication of figures. Additionally, in some cases figures have been reproduced that use either all SI or all I-P units. Moment: 1 lb-ft = 1.3558 N m 1 lb-in. = 0.11298 N m These figures have not been revised to show both sets of units. The one exception to the dual SI and I-P unit usage in- Temperature: 1°F = use 5/9 (°F - 32) to obtain °C volves the quantities of density and unit weight. Density is the General Note: 1 mil = 10-3 in. mass per unit volume and has units of kg/m3 (slugs/ft3), and unit weight is the weight per unit volume and has units of kN/m3 (lbf/ft3). Although density is the preferred quantity in 7.3 Conversion Factors from the Système SI, unit weight is still the common quantity in geotechnical International d'Unités (SI Units) to Inch-Pound Units (I-P Units) engineering practice. Therefore, the quantity of unit weight will be used herein except when referring to EPS-block geofoam. Length: 1m = 3.281 ft The geofoam manufacturing industry typically uses the quan- 1 cm = 3.281 × 10-2 ft tity of density with the SI units of kg/m3, but the quantity of 1 mm = 3.281 × 10-3 ft unit weight with the I-P units of lbf/ft3. Therefore, the same 1m = 39.37 in. 1 cm = 0.3937 in. dual-unit system of density in SI units and unit weight in I-P 1 mm = 0.03937 in. units will be used when referring to EPS-block geofoam. 1m = 1.094 yd 1 cm = 0.01094 yd 1 mm = 1.094 × 10-3 yd 7.2 Conversion Factors from Inch-Pound Units 1 km = 0.621 mi (I-P Units) to the Système International d'Unités (SI Units) Area: 1 m2 = 10.764 ft2 1 cm2 = 10.764 × 10-4 ft2 Length: 1 ft = 0.3048 m 1 mm2 = 10.764 × 10-6 ft2 1 ft = 30.48 cm 1 m2 = 1550 in2 1 ft = 304.8 mm 1 cm2 = 0.155 in2 1 in. = 0.0254 m 1 mm2 = 0.155 × 10-2 in2 1 in. = 2.54 cm 1 m2 = 1.196 yd2 1 in. = 25.4 mm 1 cm2 = 1.196 × 10-4 yd2 1 yd = 0.9144 m 1 mm2 = 1.196 × 10-6 yd2 1 yd = 91.44 cm Volume: 1 m3 = 35.32 ft3 1 yd = 914.4 mm 1 cm3 = 35.32 × 10-4 ft3 1 mi = 1.61 km 1 m3 = 61,023.4 in3 Area: 1 ft2 = 929.03 × 10-4 m2 1 cm3 = 0.061023 in3 1 ft2 = 929.03 cm2 1 m3 = 1.308 yd3 1 ft2 = 929.03 × 102 mm2 1 cm3 = 1.308 × 10-6 yd3 1 in2 = 6.452 × 10-4 m2 1 in2 = 6.452 cm2 Force: 1N = 0.2248 lb 1 in2 = 645.16 mm2 1 kN = 224.8 lb 1 yd2 = 836.1 × 10-3 m2 1 kgf = 2.2046 lb 1 yd2 = 8361 cm2 1 kN = 0.2248 kip 1 yd2 = 8.361 × 105 mm2 1 kN = 0.1124 U.S. ton 1 metric ton = 2204.6 lb Volume: 1 ft3 = 28.317 × 10-3 m3 1 N/m = 0.0685 lb/ft 1 ft3 = 28.317 cm3 1 in3 = 16.387 × 10-6 m3 Stress, Pressure, Modulus 1 in3 = 16.387 cm3 of Elasticity: 1 yd3 = 0.7646 m3 1 Pa = 20.885 × 10-3 lb/ft2 1 yd3 = 7.646 × 105 cm3 1 kPa = 20.885 lb/ft2 Force: 1 lb = 4.448 N 1 kPa = 0.01044 U.S. ton/ft2 1 lb = 4.448 × 10-3 kN 1 kPa = 20.885 × 10-3 kip/ft2 1 lb = 0.4536 kgf 1 kPa = 0.145 lb/in2 1 kip = 4.448 kN Density: 1 kg/m3 = 0.0624 slugs/ft3 1 U.S. ton = 8.896 kN 1 lb = 0.4536 × 10-3 metric ton Unit Weight: 1 kN/m3 = 6.361 lbf/ft3 1 lb/ft = 14.593 N/m 1 kN/m3 = 0.003682 lbf/in3

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51 RECOMMENDED DESIGN GUIDELINE Moment: 1Nm = 0.7375 lb-ft etrating Strengths (Hardness) of Plastic Construction Materials 1Nm = 8.851 lb-in. and the Strength of Cutting Edges)." Zeit. Angew. Math. Mech., Temperature: 1°C = use 9/5 (°C) + 32 to obtain °F Vol. 1, No. 1 (1921), pp. 15­20. 12. American Association of State Highway and Transportation General Note: 1 Pa = 1 N/m2 Officials, Standard Specifications for Highway Bridges, 16th. Washington, D.C. (1996). 13. Kavazanjian, E., Jr., Matasovic, N., Hadj-Hamou, T., and Saba- 8 REFERENCES tini, P. J., "Geotechnical Engineering Circular No. 3; Design Guidance: Geotechnical Earthquake Engineering for High- 1. "Slope Stabilization with Geofoam" (in prep). Syracuse Uni- ways; Volume I--Design Principles." FHWA-SA-97-076, U.S. versity and the Society of Plastics Industries. Department of Transportation, Federal Highway Administra- 2. Horvath, J. S., Geofoam Geosynthetic. Horvath Engineering, tion, Washington, D.C. (1997), 186 pp. P.C., Scarsdale, NY (1995), 229 pp. 14. Huang, Y. H., "Pavement Analysis and Design." Prentice-Hall, 3. Holtz, R. D., NCHRP Synthesis of Highway Practice 147: Treat- Inc., Englewood Cliffs, NJ (1993), 805. ment of Problem Foundations for Highway Embankments. Trans- 15. "Design and Construction Manual for Lightweight Fill with portation Research Board, Washington, D.C. (1989), 72 pp. EPS." The Public Works Research Institute of Ministry of Con- 4. American Association of State Highway and Transportation struction and Construction Project Consultants, Inc., Japan Officials, AASHTO Guide for Design of Pavement Structures, (1992), Ch. 3 and 5. 1993. Washington, D.C. (1993). 16. Raad, L., and Figueroa, J. L., "Load Response of Transporta- 5. Van Til, C. J., McCullough, B. F., Vallerga, B. A., and Hicks, tion Support Systems." Transportation Engineering Journal, R. G., NCHRP Report 128: Evaluation of AASHO Interim Guides ASCE, Vol. 106, No. TE1 (1980), pp. 111­128. for Design of Pavement Structures. Transportation Research 17. Burmister, D. M., "The Theory of Stresses and Displacements Board, Washington, D.C. (1972). in Layered Systems and Applications to the Design of Airport 6. Terzaghi, K., Peck, R. B., and Mesri, G., Soil Mechanics in Runways." Proceedings, Highway Research Board, Vol. 23 Engineering Practice, 3rd. John Wiley & Sons, Inc., New York (1943), pp. 126­144. (1996). 18. Aabøe, R., "Deformasjonsegenskaper og Spenningsforhold i 7. "Settlement Analysis." Technical Engineering and Design Fyllinger av EPS (Deformation and Stress Conditions in Fills Guides as Adapted from the U.S. Army Corps of Engineers, No. of EPS)." Intern Rapport Nr. 1645, Public Roads Administra- 9. ASCE, New York (1994), 144 pp. tion (1993), 22 pp. Norwegian. 8. Mesri, G., and Choi, Y. K., "Settlement Analysis of Embank- 19. Aabøe, R., "Long-Term Performance and Durability of EPS as ments on Soft Clays." Journal of Geotechnical Engineering, a Lightweight Fill." Nordic Road & Transport Research, Vol. 111, No. 4 (1985), pp. 441­ 464. Vol. 12, No. 1 (2000), pp. 4­7. 9. Mesri, G., "Discussion: Postconstruction Settlement of an 20. Barker, R. M., Duncan, J. M., Rojiani, K. B., Ooi, P. S. K., Tan, Expressway Built on Peat by Precompression by Samson, L." C. K., and Kim, S. G., NCHRP Report 343: Manuals for the Canadian Geotechnical Journal, Vol. 23, No. 3 (1986), Design of Bridge Foundations. Transportation Research Board, pp. 403­407. National Research Council, Washington, D.C. (1991), 308 pp. 10. NCHRP Synthesis of Highway Practice 29: Treatment of 21. Coulomb, C. A., "Essai sur une Application des Règles des Max- Soft Foundations for Highway Embankments. Transportation imis et Minimis à quelques Problèmes de Statique Relatifs à Research Board, Washington, D.C. (1975), 25 pp. l'Architecture (An Attempt to Apply the Rules of Maxima and 11. Prandtl, L., "Über die Eindringungsfestigkeit (Härte) Plastis- Minima to Several Problems of Stability Related to Architec- cher Bauttoffe und die Festigkeit von Schneiden (On the Pen- ture)." Mém. Acad. Roy. des Sciences, Paris (1776), pp. 343­382.