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

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2-1 CHAPTER 2 RELEVANT ENGINEERING PROPERTIES OF BLOCK-MOLDED EPS Contents Background...................................................................................................................................2-3 Introduction...............................................................................................................................2-3 Manufacturing (Molding) EPS .................................................................................................2-3 Overview...............................................................................................................................2-3 Block Molding ......................................................................................................................2-5 Physical Properties and Issues ......................................................................................................2-8 Introduction...............................................................................................................................2-8 Density ......................................................................................................................................2-9 Fusion......................................................................................................................................2-11 Block Dimensions...................................................................................................................2-11 Color .......................................................................................................................................2-13 Flammability ...........................................................................................................................2-13 Durability ................................................................................................................................2-15 Environmental Effects ............................................................................................................2-17 Mechanical Properties.................................................................................................................2-18 Introduction.............................................................................................................................2-18 Compression ...........................................................................................................................2-19 Introduction.........................................................................................................................2-19 Rapid Loading Testing........................................................................................................2-20 Compatibility with MQC/MQA Testing.........................................................................2-26 Monotonic. ......................................................................................................................2-27

2-2 Cyclic ..............................................................................................................................2-32 Poisson’s Ratio................................................................................................................2-33 Time-Dependent Behavior (Creep and Relaxation)................................................................2-34 Introduction.........................................................................................................................2-34 Testing ................................................................................................................................2-35 Constitutive Modeling of the Stress-Strain-Time Behavior of EPS ...................................2-38 Introduction.................................................................................................................2-38 Laboratory Creep Tests...............................................................................................2-40 Full-Scale Model Creep Test ......................................................................................2-43 Full-Scale Field Monitoring........................................................................................2-44 Summary of Comparison of Measured and Calculated Values of Total Strain. .............2-45 Temperature – Dependent Behavior ...................................................................................2-47 Introduction.....................................................................................................................2-47 Constitutive Modeling of the Stress-Strain-Time-Temperature Behavior of EPS .........2-47 Recommended Procedure for Considering Creep Strains...................................................2-48 Tension....................................................................................................................................2-49 Flexure ....................................................................................................................................2-50 Shear .......................................................................................................................................2-51 Introduction.........................................................................................................................2-51 Internal ................................................................................................................................2-51 External ...............................................................................................................................2-51 Introduction to External (Interface) Properties.. .............................................................2-51 EPS/EPS Interface.. ........................................................................................................2-52 EPS/Dissimilar Material Interfaces.................................................................................2-54 Interface Shear Testing Procedure ..............................................................................2-56 Geofoam And Geosynthetic Specimen Preparation Procedure...................................2-57

2-3 Comparison of Large-Scale Direct Shear and Torsional Ring Shear Tests ................2-59 Geofoam/GC Geomembrane Interface Test Results...................................................2-60 Geofoam/Nonwoven Geotextile Interface Test Results..............................................2-61 Summary of EPS Interface Strengths..........................................................................2-62 Thermal Properties......................................................................................................................2-62 References...................................................................................................................................2-63 Figures ........................................................................................................................................2-68 Tables..........................................................................................................................................2-89 ______________________________________________________________________________ BACKGROUND Introduction This chapter presents an overview of the engineering properties of EPS. A knowledge of the physical, mechanical (stress-strain-time-temperature), and thermal properties of block-molded EPS is required to understand the basis for past design methodologies as well as to understand the recommended design methodology that is summarized in Chapter 3 and incorporated in the provisional design guideline in Appendix C. The properties of block-molded EPS of interest for the function or application of lightweight fill include: • physical, • mechanical (stress-strain-time-temperature), and • thermal. These properties are discussed subsequently. However, the EPS block molding process can significantly influence the quality and other performance aspects of EPS-block geofoam to include the physical, mechanical, and thermal properties. Therefore, a knowledge of the key elements of the molding process is useful and is initially discussed. Manufacturing (Molding) EPS

2-4 Overview There are two distinct steps involved in manufacturing (molding) EPS: • A manufacturer called a resin supplier produces the raw material that is formally called expandable polystyrene but colloquially referred to as beads or resin. Expandable polystyrene consists of fine to medium sand-size spherical particles of solid polystyrene with a naturally occurring petroleum hydrocarbon, almost always pentane (Japan is the only known country where an alternative, butane, is used routinely), mixed in as a blowing agent. The expandable polystyrene may also contain other additives that are discussed subsequently. Most resin suppliers are large, multi-national chemical companies with a broad range of products. • A manufacturer called a molder buys the expandable polystyrene and, in a multi- stage process, transforms it into expanded polystyrene (EPS). The final EPS products are broadly categorized as either being prismatic blocks (block-molded EPS) or some type of custom shape (shape-molded EPS). Block molders traditionally were relatively small, privately, locally owned businesses serving a relatively limited geographical area. This is changing in the U.S.A. to ownership by larger corporations with multiple plant locations. Although there are still more than approximately 100 block molders, no one molder serves the entire country. EPS blocks can be used for a wide variety of purposes and applications, one of which is EPS-block geofoam. In the U.S.A. at present, EPS-block geofoam is most often marketed by and purchased directly from a local block molder although sale through distributors who handle other geosynthetics and/or construction products as well as large retail chains selling construction materials is becoming more common. Practices vary widely in this regard at the present time, even within a given area where one molder might sell directly to an owner and a competitor will only sell through a distributor. End users should be aware of the fact that purchasing EPS-block

2-5 geofoam through a distributor generally results in a greater unit cost for the product because of distributor markup for their overhead and profit. In many cases, there is no value added by a distributor. In typical road construction in the U.S.A. at the present time, EPS-block geofoam is purchased by the general contractor from a molder or a distributor. Block Molding Manufacturing EPS-block geofoam is basically a two-step process. The first step is called pre-expansion of the expandable polystyrene. The expandable polystyrene (a.k.a. beads, resin) raw material is placed into a large container called a pre-expander and then heated with steam. The steam causes the blowing agent that is dissolved in each bead of expandable polystyrene to phase change into a gas and expand the polystyrene in the process to approximately 50 times its initial volume, a diameter increase of the order of three to four times. The expanded spheres of polystyrene is colloquially referred to as pre-puff. Each pre-puff particle contains numerous closed cells with about 98 percent of the total volume consisting of gas-filled voids. Initially, the gas is a mixture of the residual blowing agent and air. The density of the pre-puff can be varied within certain limits which will affect the density of the final product. As will be discussed subsequently, the density of EPS-block geofoam can be an important and useful index property. The pre-puff is then moved to temporary storage in large fabric bags to allow it to stabilize thermally and chemically. After several hours of storage (the overall quality of the final product is sensitive to storage time), the pre-puff is placed into a mold which is essentially a closed steel box that is rectangular parallelepiped in shape. Steam is injected into the sealed mold and this simultaneously resoftens the polystyrene and causes some further expansion of the pre- puff. As a result, the spheres of pre-puff fuse thermally and distort somewhat in shape to more of a polyhedral shape to fill most of the void spaces between the originally spheroidal pre-puff particles. The block is then released from the mold and allowed to "season", i.e. stabilize thermally (dimensional changes of the block occur during cooling) and chemically (residual blowing agent remaining in the cells of the EPS outgasses and is replaced by air). The block also

2-6 dries during this seasoning period as a relatively significant amount of water vapor and liquid (which can artificially increase the apparent density of the EPS) that is condensed steam from molding remains in the block at the end of molding. The duration of the seasoning can vary widely from hours to weeks depending on the desired stability of the final product. A minimum seasoning time of three days (72 hours) at ambient room temperature is recommended and will be discussed subsequently in the “Flammability” section of this chapter. Seasoning is often accelerated by short-term storage in a room with temperatures that are elevated relative to ambient conditions within the molding plant. However, not all EPS molders in the U.S.A. have such storage rooms. At the end of the seasoning period, a block can be trimmed, cut, or used as desired. There has been insufficient study to date to be able to quantify the effects of time and temperature on the mechanical and thermal properties of EPS-block geofoam. The primary reasons for the lack of data is primarily due to the numerous variables related to seasoning, including time and temperature, that affect the mechanical and thermal properties of EPS. For example, in (1) it is suggested that resin type and molding technique affect the rate of pentane emissions. The issue of pentane emissions is further discussed in the “Flammability” section of this chapter. The recommended seasoning requirement of three days (72 hours) is based primarily on safety concerns related to the outgassing of residual pentane blowing agent and is based on an assessment of the little industry information available on this subject. Thus, the seasoning recommendation represents the state of knowledge at this time and no further quantitative information can be provided. The final EPS product has the visual texture of individual, fused particles (the former pre- puff particles, each of which is still roughly spherical in shape). Because of this, EPS was, and sometimes still is, occasionally referred to in literature as molded expanded polystyrene or molded-bead expanded polystyrene although these terms are typically not used in current U.S. practice. This macrofabric of EPS is also the reason that it has been and still is sometimes referred

2-7 to colloquially as beadboard, a term that the EPS industry in the U.S.A. appears to deprecate because of an-often negative connotation associated with this term. There is a variation of the above manufacturing procedure that is worth mentioning. The above process is the typical process when the molder is using 100 percent virgin raw material (expandable polystyrene). However, EPS molding always generates some in-plant scrap or waste material. Consequently, to reduce their costs for both waste disposal as well as raw material purchase, most block molders in the U.S.A. try to reuse at least some of this scrap. This is accomplished by grinding it up into pieces that are generally sand-size to produce what is called regrind. The regrind is mixed in with virgin pre-puff during the final block molding process. Because the regrind has long since lost any residual pentane, it does not react the same way as virgin pre-puff during the final molding process. Therefore, block-molded EPS containing regrind will, all other variables being equal, have poorer properties (the mechanical properties which are the ones of greatest importance in geofoam applications as lightweight road fill are particularly affected) than block-molded EPS made with 100 percent virgin prepuff. For example, the percentage of regrind, if any, can affect the compressive properties of block-molded EPS, especially the design-critical initial tangent Young's modulus, Eti (2,3). The effect of increasing regrind content on the small strain stiffness is further discussed in the “Compression” section of this chapter. The degradation in mechanical properties occurs gradually as the relative proportion of regrind is increased. Below are several reasons why regrind negatively affects the quality of the finished EPS- block geofoam that were provided in (4): • The grinding process tears and crushes the original cellular structure of the EPS. Torn and crushed cells have much lower stiffness than the intact cells in virgin prepuff. • Regrind has long since lost all of its hydrocarbon blowing agent. As a result, during the final molding process it does not soften and fuse together in the same

2-8 way that virgin prepuff does so that the overall bead fusion of the finished EPS is poorer than if all virgin prepuff were used. The resulting new EPS with regrind has a more crumbly texture. • All EPS is inherently white regardless of density and flame retardancy. It is thus possible that regrind of incorrect density and/or material that is not flame retardant may be mixed in and compromise the density and/or flame retardancy of the new EPS. • If post-consumer regrind is used, plastic foams other than EPS may be mixed in and further contaminate the new EPS. The final quality (in terms of geotechnical relevant mechanical properties in particular) of an EPS block is influenced by numerous factors and procedures at each of the above steps of the manufacturing process, including what percentage, if any, of regrind is used. However, an appropriate material standard for EPS-block geofoam does not have to explicitly address any of the quality issues at intermediate stages of manufacturing, including maximum allowable regrind content. Rather, it is sufficient to specify minimum quality parameters for the final product and then leave it to the molder to take appropriate measures at each step in the manufacturing process to ensure that final quality parameters are met. PHYSICAL PROPERTIES AND ISSUES Introduction The physical properties of EPS-block geofoam can be thought of as being conceptually similar to the traditional index properties of soil (description, classification, particle size, Atterberg Limits, etc.) and thus useful, within a certain context, during the design process. Soil index properties are those properties that are used to classify or discriminate among the different kinds of soil in a given category (5). A material property is a good index property if the property is simple to express, e.g., numerical values, measurement is quick, measurement is simple, measurement is reproducible, and property is significant, i.e., property is a measure of or

2-9 correlates with a significant engineering property of soils (6). Density and fusion are two key index properties of EPS-block geofoam. However, other physical properties, such as block dimensions, color, flammability, durability, and environmental effects, can also affect cost, design, or construction. Density As noted previously, it is possible to manufacture EPS blocks within a range of densities, primarily through controlling the density of the pre-puff created during the first stage of manufacturing (the pre-expansion process). The overall range in EPS density possible is between approximately 10 to 100 kg/m3 (0.62 to 6.24 lbf/ft3) although for practical purposes the range available for lightweight fill applications is much smaller, of the order of 16 to 32 kg/m3 (1.0 to 2.0 lbf/ft3). The relevance of EPS density is that the density of EPS-block geofoam can be a very useful index property only if the EPS meets certain minimum quality parameters. Assuming that the appropriate quality standards are met, density of EPS-block geofoam has been shown to correlate well with both geotechnical relevant mechanical and thermal properties. For example, compression behavior in general exhibits a primary dependency on EPS density. Therefore, EPS- block geofoam density can be used as an index property to estimate some mechanical and thermal properties provided the EPS meets a set of minimum standards, such as those specified in the provisional American Association of State Highway and Transportation Officials (AASHTO) standard included in Appendix C. There are several additional issues regarding the density of EPS-block geofoam. First, a given production run of EPS blocks will always exhibit some variability of final product density from block to block, even if appropriate manufacturing quality controls are being employed. This simply reflects inherent variability in the EPS manufacturing process and can easily be checked by weighing each block to determine its nominal (average) density.

2-10 Second, there will be density variations (called density gradients in the industry) within every block, also a result of inherent variability in the EPS manufacturing process. Density gradients up to approximately ±10 percent relative to some nominal (average) value are often given in the literature as typical. In addition, it is generally assumed that densities are largest at the center of a block and smallest at the edges. However, with molding equipment currently in use it appears that neither of these statements is universally true any more. Density gradients can, in fact, exceed ±10 percent (the range appears to increase with increasing average density of the block) and can potentially have complex patterns of variation. Thus the density of a relatively small specimen cut from a block can be significantly different than the gross density of the entire block. This is significant because the compressive behavior of block-molded EPS is most dependent on density (7-11). The density of specimens cut from a block can be determined in accordance with ASTM D 1622 (12). The use of a hot-wire cutter may yield more consistent density values than the use of a fine-tooth band saw because a hot-wire cutter produces a cleaner and smoother surface than a fine-tooth band saw. Third, most block molders in the U.S. are set up to manufacture EPS to five standard densities specified in the ASTM standard used for this purpose (13). Thus it is always most cost effective to develop a design based on these densities whenever possible. It is important to note that this ASTM standard is written from the perspective of specifying minimum acceptable values of product density and several other parameters. This has apparently led to certain misconceptions within the EPS industry regarding product quality. These misconceptions are discussed in Chapter 9. Several issues need to be noted with regard to measuring block density which is generally viewed as being a trivial measurement: • For relatively freshly molded EPS, density is sensitive to time to outgassing of both residual pentane blowing agent as well as moisture from condensed steam.

2-11 Therefore, the date of molding for the block from which a test specimen is obtained should always be recorded as part of the test data. • Density can be affected by absorbed atmospheric moisture. Therefore, density should be determined immediately prior to testing and only after an appropriate seasoning protocol (referred to aging and conditioning in the EPS industry). A typical protocol essentially requires a minimum of 40 hours under standard laboratory conditions (13). Fusion Another index of overall EPS quality is called fusion. This refers to the thermal fusion between pieces of prepuff (and regrind when used) that occurs during the second stage of manufacturing (final block molding). Experience and testing indicates that fusion does not so much influence the mechanical and thermal properties as it does the overall durability and robustness of the finished product. Tensile loading is an indicator of EPS fusion. However, flexural strength correlates well with tensile strength and can also provide an indirect indicator of EPS fusion. Both tensile and flexural testing are discussed subsequently as part of the “Mechanical Properties” section of this chapter. Block Dimensions The dimensions of an EPS block do not affect its geotechnical engineering properties. However, other design issues such as product unit cost (including delivery to a job site) and in situ block layout are influenced by block dimensions. The dimensions of an EPS block are governed primarily by the mold used during manufacturing. There is no standard mold size used worldwide or even within the U.S.A. so some variation between molders must be expected. However, there is an overall trend, at least within the U.S.A., toward using molds that produce somewhat larger blocks (primarily with respect to the smallest (thickness) and largest (length) dimensions) than in the past. Where possible, it is generally desirable to try to use EPS blocks in their full as-molded size, assuming that the blocks

2-12 meet certain dimensional quality criteria for straightness, etc. Although it is possible to factory cut a seasoned block into a smaller size, such cutting can add significantly to the unit cost of the final EPS-block geofoam product. For many years, the typical dimensions of EPS-block geofoam available in the U.S.A. were 610 x 1,220 x 2,440 mm (24 x 48 x 96 in.). The first trend that developed during the 1990s was toward longer blocks, typically 4,880 mm (192 in.) in length. More recently, the trend has been toward thicker blocks, with the thickness dimension increasing from 610 mm (24 in.) to between 760 and 1,000 mm (30 and 39 in.) depending on the particular mold used. Thus, many EPS blocks currently produced in the U.S.A. are almost square in cross-section. Fortunately, in most lightweight fill applications, it is possible to use these larger blocks for at least most of the fill. However, some factory and field cutting of blocks is generally necessary on every project. There are basically two ways to deal with the variability in dimensions of EPS-block geofoam (keep in mind that there are more than 100 EPS block molders in the U.S.A.): • Select a supplier (molder or distributor) of the EPS-block geofoam during the design phase of a project and determine what is the standard block size available from that supplier. The design professional of record for the project then develops the explicit block layout for the project and this information is shown on the design drawings. • The design professional produces design drawings that show the overall geometry and dimensions of the desired mass of EPS-block geofoam, as well as specifies certain key conceptual elements of the block layout (minimum number of layers, overall geometry of each layer, etc.). The construction contractor on the project is then required to submit shop drawings depicting the actual block dimensions and layout proposed for use. These shop drawings are typically prepared by the EPS molder and would be reviewed and approved per the normal process used for years in many other aspects of engineered construction.

2-13 The first alternative is generally not feasible for government projects such as road construction. In addition, experience in the latter part of the 1990s has indicated that more and more EPS block molders in the U.S.A. are developing the capability to provide shop drawings so this alternative is proving to be feasible in practice. Color EPS is inherently white in color although it is possible, for a cost, to tint it another color during the manufacturing process. There is no technical merit or benefit in geofoam applications to a color other than white. The only benefit would be for product identification and marketing purposes. Although EPS-block geofoam of a color other than white is sold in several countries (e.g. certain proprietary products are brown in Canada and pink in the United Kingdom), such products are not known to be available in the U.S.A. This is perhaps partially due to the fact that the most common and obvious colors (blue, green, pink and yellow) have already been used and legally identified (through registered trademark) with extruded polystyrene (XPS) products that are manufactured in the U.S.A. What has seen sporadic use in the U.S.A. is for a molder to stencil or otherwise mark some or all blocks of EPS-block geofoam with their name or a logo for product identification or marketing purposes. Such markings can also have a technical benefit to identify (by using different colors for the markings) EPS blocks of different density shipped to the same project site (this is done in the U.K. for example). More common, however, for cost reasons, is the use of simple color markings to identify EPS blocks of different density shipped to the same project site. Flammability Flammability of a polymeric material such as polystyrene is often measured or expressed by its oxygen index (OI). The OI is the minimum relative proportion (expressed as a percent) of oxygen in some mixture of gases that is required to support continuous combustion. Air at sea level contains approximately 21 percent oxygen so if a material has an OI less than 21 percent it

2-14 will burn freely in air until all the material is consumed provided there is an initial ignition source. If the OI of the material is greater than 21 percent, it will not support continuous combustion after initial ignition (this is generally referred to as being self extinguishing) although it may still melt as well as support combustion if an ignition source is continuously present. Polystyrene has an OI of 18 percent which means that normal EPS is inherently flammable. However, it is possible to incorporate an inorganic, bromine-based chemical into the expandable polystyrene raw material used to manufacture EPS so that final block product is flame retardant and self extinguishing. Such raw material is referred to as modified bead or resin. EPS made with modified bead can still melt, however, at a temperature between approximately +150 and +260°C (300° and 500°F) although +95°C (200°F) is generally recommended as a maximum working value. In the U.S.A., ASTM specifications (13) for flame-retardant EPS call for a minimum OI of 24 percent which is 3 percent greater than the OI of air. It is of interest to note that flame-retardant EPS cannot be identified visually nor are any other physical, mechanical or thermal properties affected by the bromine additive. In general, flame-retardant EPS block reportedly may cost up to 10 percent more than EPS block that is not flame retardant because of higher raw-material costs. Therefore, on a global basis, use of flame-retardant EPS block for geofoam applications has not been universal and should never be assumed. For example, in Norway which pioneered the use of EPS-block geofoam as lightweight fill in 1972, flame-retardant EPS-block geofoam is reportedly rarely specified. However, in some countries such as the U.S.A., it has become routine to supply only flame-retardant EPS-block geofoam. There are at least two reasons for this. First, whenever ASTM C 578 is used as a material specification, only flame-retardant material will be supplied. Second, if a molder uses normal or regular (non-flame-retardant) raw material, it will contaminate the various components of the manufacturing equipment (mold, etc.) and thus potentially compromise a subsequent manufacturing run of flame-retardant EPS. Thus, most molders find it easier to simply always manufacture flame-retardant EPS block.

2-15 There is another flammability issue separate from the inherent flammability of the EPS block. It is related to the outgassing of the blowing agent used in the manufacturing process. The blowing agents used for EPS, primarily pentane but butane in some countries (chiefly Japan), are inherently flammable and potentially explosive. In addition, the blowing agents are heavier than air and tend to pool or settle around a block as opposed to freely dispersing into the atmosphere. After an EPS block is released from the mold during the second and final stage of manufacturing, the closed cells within the fused pre-puff will still contain some blowing agent. The remaining blowing agent will naturally outgass from the cells and be replaced by air within a relatively short period of time. The exact duration of this outgassing process depends on many factors, especially temperature, but the duration is usually on the order of days. However, based on available published information (14) as well as anecdotal information obtained by personal communication with both resin suppliers and block molders in the U.S.A., an interim recommendation of three days of seasoning at ambient room temperature is proposed. As discussed in (15), there was a lightweight fill project in Japan where the EPS blocks were being delivered to the job site and reportedly placed with very little seasoning time after molding due to project needs (this is not uncommon and is known to have occurred on several projects in the U.S.A.). On this specific project in Japan, the outgassed butane blowing agent accumulated in the joints between blocks and was ignited in situ by some on-site ignition source (welding or flame cutting of metal that was unrelated to the geofoam usage or even personal tobacco smoking). Durability The overall durability of EPS-block geofoam encompasses a range of issues. Flammability was addressed separately in the preceding section as it is primarily a manufacturing issue and not directly related to post-manufacturing durability. Considered in this section are the external factors related to construction and the in situ environment that may affect the physical, mechanical, or thermal properties of EPS-block geofoam after it leaves the molding plant. The

2-16 effect of EPS-block geofoam on the in situ environment is discussed separately in the following section. In general, EPS-block geofoam has proven to be a very robust geosynthetic product, much more problem-free on the whole compared to many other types of geosynthetics where there is a potential for significant physical damage to and detrimental chemical changes within the geosynthetic during and after construction. EPS is inherently non-biodegradable and will not dissolve, deteriorate, or change chemically in the ground and ground water. Although EPS will absorb some ground water over time, the product will not change dimensionally and its mechanical properties are unaffected. The EPS will, however, lose some of its thermal efficiency which is irrelevant per se to most lightweight fill applications. EPS provides no nutritive food source to any living organism or animal. However, certain burrowing insects such as termites and carpenter ants have been found to either tunnel through EPS or nest in it. This has only been observed for relatively thin (of the order of several tens of millimeters thick) geofoam panels used as thermal insulation in residential construction where there is an abundance of dead wood. There is no known case in the world where insect damage has been detected for EPS-block geofoam used as lightweight fill. There was an active discussion of this topic at Session 6 of the International Symposium on EPS Construction Method (EPS Tokyo ’96) that was held in Tokyo, Japan in 1996 and reported in the final report (16) for this symposium. It is worth noting that an inorganic chemical additive with the tradename Timbor was developed in the U.S.A. toward the end of the 20th century for EPS. The reported benefit of this additive is that it acts as a deterrent to insect infestation of block-molded EPS. The use of this additive in EPS block is proprietary and is available only from certain EPS block molders in the U.S.A. and Puerto Rico at the present time. EPS block manufactured with this additive is marketed under various tradenames including Bug Block-R, Perform Guard, Teps and possibly others. Some design professionals have elected to specify EPS-block geofoam treated

2-17 with Timbor for lightweight fill applications. The additive does not affect any of the geotechnical relevant physical, mechanical or thermal properties of the EPS. Specifiers of this additive should, however, be aware of the fact that requiring this additive in EPS-block geofoam will, in most parts of the U.S., restrict the number of molders who can bid on and supply a project. Because of this elimination of competition plus the inherent cost of the additive itself, the unit cost of the EPS blocks would be expected to be higher, possibly significantly so, than otherwise. However, it is not possible to quantify the likely relative cost increase because there are many intangible business issues involved. There are relatively few conditions against which EPS-block geofoam needs protection. When exposed to ultraviolet (UV) radiation from sunlight, the surface of an EPS block will turn yellow in color and become somewhat brittle and chalky. However, this process takes from months to years to develop and is limited to the surface (degradation does not progress into the block) so it is only necessary to protect EPS-block geofoam from long-term UV radiation. Relatively brief exposure such as during construction is not a problem. There are relatively few liquids that will dissolve EPS. The only ones likely to be encountered in lightweight fill geofoam applications are fuels such as gasoline and diesel fuel. The need and design methodology for dealing with this potential exposure is discussed in detail as part of separation materials in Chapter 4. Environmental Effects Environmental effects related to EPS-block geofoam fall into several categories. First, regarding the material itself, polystyrene is not inherently harmful or hazardous. Solid polystyrene is used for eating utensils and food containers, and EPS is used for beverage containers (the ubiquitous white foam coffee cup is a shape-molded EPS product) as well as food packaging. The blowing agents used to manufacture EPS are naturally occurring hydrocarbons, not a synthetic fluorocarbon-family gas which is used as a blowing agent for most other plastic foams. Thus, there are no gases that are potentially harmful to the Earth’s upper-atmosphere

2-18 ozone layer that are associated with manufacturing EPS. Furthermore, because the cells within EPS are completely filled with air within a few days after molding, there is no concern about long-term outgassing of potentially toxic and hazardous gases as has been a problem with other types of plastic foam. EPS will not interact in any way with the ground or ground water, and will not leach any chemical into the ground or ground water. If EPS is burned, either accidentally or intentionally as part of a waste-to-energy program, the products of combustion are primarily carbon dioxide and water. In addition, flame-retardant EPS (as would typically be used for lightweight fill geofoam in U.S. practice) will also emit traces of hydrogen bromide. The residual ash from burned EPS contains no heavy metals or other substances generally considered to be toxic or hazardous. Note that the above comments regarding environmental impact of EPS only apply to "normal" EPS. Information concerning the impact(s), if any, associated with EPS treated with the insecticide noted above would have to be obtained from the proprietary supplier of such EPS. MECHANICAL PROPERTIES Introduction The mechanical properties of EPS-block geofoam for the use as lightweight fill are important during the design because they affect both external and internal stability as well as pavement design. The mechanical properties of block-molded EPS primarily involve its stress- strain response under various modes and duration of loading. The temperature of the EPS can also affect the mechanical behavior but is generally a secondary issue. As noted previously, water absorption, if any, has no effect on the mechanical properties of the EPS. In particular, two distinct categories of mechanical properties that need to be addressed include: • The properties of the EPS itself under vertical stress. This information is used during the internal stability assessment phase to determine the appropriate EPS density to support the applied dead- and live- loads as well as to provide equivalent soil property information for pavement design.

2-19 • The interface shear properties, both between EPS blocks as well as between EPS and dissimilar materials (both soil and non-soil). This information is used during external and internal stability assessment, particularly under conditions that produce lateral loading during an extreme event involving either wind, an unbalanced water head, or seismic loading. Therefore, the compression and interface shear properties of EPS will be discussed. However, tension and flexure properties of EPS are also briefly discussed because both tensile and flexural loading tests can be useful manufacturing quality control and manufacturing quality assurance (MQC/MQA) tests. Although the thermal insulation function of EPS-block geofoam is not a primary concern for the function of lightweight fill, some knowledge of the geothermal properties of EPS is necessary to understand the issues of differential icing and solar heating that need to be considered during design of the pavement system. Modern analysis and design methods for EPS-block geofoam as lightweight fill are based on explicit deformations of the geofoam mass. Therefore, the most important properties of block- molded EPS to test for are those related to the overall mechanical (stress-strain-time-temperature) behavior of an entire EPS block in compression as this is what will be loaded in the final embankment. However, given the typical dimensions of EPS blocks, precision testing of an entire block is not feasible on a routine basis although some testing of this nature is highly desirable as discussed subsequently. Therefore, any testing must be performed on specimens prepared from samples cut from blocks. Thus, there is always going to be some approximation or error involved in testing of such specimens, simply because what is being tested is not what is being placed in the actual fill. This approximation or error is not "fatal" or insurmountable. In fact, for most construction materials, whether natural (e.g., soil) or manufactured, only relatively small specimens relative to the final product are typically tested. Compression Introduction

2-20 Loading in unconfined uniaxial compression has been and remains the primary mode of loading for tests performed on EPS-block geofoam for both quality control and research purposes. This is because compression is by far the predominant mode of loading for EPS in load-bearing applications, including when used as lightweight fill. Thus, as indicated previously, the most important properties of block-molded EPS to test for are those related to the overall mechanical (stress-strain-time-temperature) behavior of an entire EPS block in compression as this is what will be loaded in the final embankment. Also, as indicated previously, blocks of EPS tend to have density gradients (variations) that are inherent in the manufacturing process. Therefore, the density of a relatively small specimen cut from a block can be significantly different than the gross density of the entire block and thus not representative of behavior of the entire block. This is significant as fundamental research has shown that the compressive behavior of block-molded EPS is most dependent on density (7-11,16). Although research has been performed on the relative effect of specimen shape and dimensions on test results (17), studies where laboratory tests were performed on both small specimens and full-size blocks to evaluate the absolute difference in measured results is lacking. Additionally, there is also a lack of comparison between the deformation measurements of full- scale fills with calculated values. Both of these comparisons are required to better understand and predict the behavior of full size blocks. Rapid Loading Testing The primary variables to consider for rapid-loading tests are: • test specimen shape, • test specimen dimensions, • test specimen age, • use of strain versus stress controlled loading, • loading rate,

2-21 • confining stress (if any) on the test specimen, and • ambient temperature and relative humidity in the laboratory where the test is performed. The effect of each of these variables on overall stress-strain behavior has been studied to varying degrees over the years. As a result, it is possible to draw some broad conclusions as to the relative effect of each of these variables. Although there is variation in practice for each of the above variables, there is a combination of variables that are most commonly used and thus can be viewed as the de facto standard against which other variations can be compared. The de facto standard is: • Cube-shaped specimens 50 mm (2 in.) wide. • Strain-controlled unconfined axial compression at a strain rate of 10 percent per minute. • Standard laboratory conditions of approximately +23°C (73° F) and 50 percent humidity. Using this combination of variables for reference, the observed variations in test variables and recommendations for practice are provided. As will be discussed, standardization currently does not exist for testing of EPS- block specimens. Standardization is recommended because test data from standardized testing procedures are needed in developing mathematical models for EPS behavior (18) and implementing the design methodology presented herein. Overall, there appears to be no compelling reason to deviate significantly from past practices until such time as fundamental research is performed to compare results between compression testing of full-size blocks versus relatively small laboratory test specimens. In an effort to develop guidelines for future testing, recommendations are provided for the following test variables to develop future standard test protocols. • Specimen shape.

2-22 Observation: There has been a trend since about the 1980s toward occasional use of specimens that are right circular cylindrical in shape with dimensions similar to soil specimens used in triaxial tests, i.e. approximately 150 mm (5.9 in.) in height and 70 mm (2.75 in.) in diameter. Presumably this shape has been used to accommodate use of geotechnical laboratory testing equipment. Both the initial tangent Young's modulus and elastic limit stress for such specimens reportedly decrease compared to values measured using the de facto standard specimens (which would appear to be contradictory to the above statement that stiffness increases with increasing specimen size) (19). On the other hand, recent testing on cylindrical specimens of different dimensions (approximately 25 mm (1 in.) high and 60 mm (2.36 in.) in diameter which is similar to soil specimens used for oedometer (one-dimensional consolidation) tests showed no practical difference from the "standard" 50 mm (2 in.) cubes (20). Recommendation: A square as opposed to circular cross-section is desirable to simplify trimming of test specimens from EPS samples taken from blocks. Care should be taken when preparing a test specimen, regardless of its shape and dimension. No surface of the specimen should include any portion of a face of the block from which the specimen sample was cut to avoid any localized edge effects. Experience indicates that a hot-wire cutter produces the cleanest and smoothest surfaces for test specimens so this method of cutting is recommended. The alternative using a fine-tooth band saw tends to leave a rougher surface. • Specimen dimensions. Observation: Specimen thickness (height) appears to have relatively less influence than width on the compression test results. In general, as specimen dimensions increase so does the initial tangent Young's modulus, Eti. Compression test results on 400 mm (16 in.) cubes and the typical 50 mm (2 in.)

2-23 cubes indicate that the larger specimens are approximately 50 percent stiffer compared to the smaller specimens at small strains (17). This suggests that an entire block might tend to behave stiffer than any small test specimen would indicate. However, this is speculative at this time and needs to be evaluated by detailed research. ASTM D 1621 (21) has been specified in the past for performing rapid-loading unconfined uniaxial compression tests. This test procedure allows the use of square or circular test specimens with a cross- sectional area ranging between 25.8 cm² (4 in.²) and 232 cm² (36 in.²). The specimen height can range from 25.4 mm (1 in.) to a maximum height no greater than the width or diameter of the specimen. Therefore, if cube-shaped specimens are utilized, specimens ranging in dimensions from 50 mm (2 in.) to 203 mm (8 in.) can be used per ASTM D 1621. One trend that appears to be developing in the EPS industry is to utilize specimens of increasing dimensions within the allowable ASTM D 1621 dimensions until the specimens meet the required compressive strength parameters. Therefore, it is recommended that determination of the uniaxial compression behavior between specimens of various sizes to full-size blocks be considered a high priority for future research. Recommendation: The width of the specimen should be such that it can be accommodated by typical end platens used in geotechnical compression test machines. This suggests a 50 mm (2 in.) width which is just accommodated by the standard 71 mm (2.8 in.) diameter platen. With regard to specimen thickness (height), the thickest specimen possible should be used to increase the vertical displacement to achieve an axial strain of 1 percent. This is because the strain range of interest for most lightweight fill applications is focused on the region from 0 percent to 1 percent axial strain. The thicker the specimen the greater the precision in strain measurement for a fixed precision in deformation

2-24 measurement (as most test apparatus would be expected to have). In addition, any end effects are minimized with a thicker specimen. Of course, if the thickness-to- width ratio is too large inadvertent specimen buckling during testing could be a problem. Based on experience with triaxial compression tests on soils, a two-to- one height to width ratio should be used, which implies a 100 mm (3.9 in.) maximum specimen thickness. A research project should be initiated to evaluate the possible switch to using test specimens that are 50 mm (2 in.) square in cross-section and 100 mm (3.9 in.) thick (high) with all other test variables unchanged. The measured properties of such specimens should be compared to those from 50 mm (2 in.) cubes for a range in EPS densities. In addition, there should be large-scale laboratory testing (most likely in a solid mechanics or structural engineering laboratory to be able to utilize large compression testing machines in an environment with the same temperature as a geotechnical laboratory) involving full-size blocks to compare the measured performance to that of both the 50 mm (2 in.) and 100 mm (3.9 in.) thick specimens. • Specimen age. Observation: This variable has not been explored in any systematic or extensive research program. Assuming that the specimen is at least several days old so that the effects of molding have disappeared, there are indications that specimen age has no influence (17). There are some indications based on testing of EPS-block geofoam that had been in the ground for approximately 24 years that there was no significant difference in material behavior from that measured prior to installation (22). This also suggests excellent long-term durability of EPS-block geofoam.

2-25 Recommendation: A minimum specimen age is desirable to ensure that the test specimen has undergone at least most of its seasoning and facilitate comparison of test results. Based on informal discussions with EPS block molders in the U.S.A., it appears that for the pentane blowing agent content and mold sizes in common use, a minimum age of three days is sufficient. • Strain rate. Observation: Not surprisingly for a polymeric material such as EPS, strain rate has a profound effect on the measured stress-strain behavior. The de facto standard rate of 10 percent per minute appears to be at the high end of the range used in past research. Rates one or more orders of magnitudes lower have been used at various times and by various researchers. It appears that stress-strain behavior under relatively small strains (the range of interest in lightweight fill applications) is most affected by strain rate (17), with the initial tangent Young's modulus either increasing or decreasing as strain rate is increased or decreased, respectively. Recommendation: There appears to be no compelling reason not to use a strain rate of 10 percent per minute for axial compression tests on EPS geofoam. • Specimen confining stress. Observation: A relatively few number of researchers (e.g., (23,24)) have tried to emulate "true" triaxial compression testing of soils by subjecting right-circular- cylindrical specimens of EPS to an isotropic confining stress prior to increasing the axial stress. There does not appear to be any benefit from doing so as the horizontal confining stresses in roadway embankments are generally small in magnitude to the point of being negligible in most cases. In addition, there has been no systematic study that compares laboratory behavior of EPS and full-scale performance in lightweight fills to indicate that testing of EPS specimens that

2-26 includes a radial confining stress provides a more accurate estimate of EPS mechanical behavior. Recommendation: There appears to be no compelling reason not to use unconfined compression tests to measure the compressive strength and initial tangent Young’s modulus. • Temperature. Observation: The vast majority of testing of EPS has been at the normal ambient laboratory temperature of +23°C ± (73°F±). Thus there has been relatively little study of the effect of temperature on the mechanical properties of EPS in the small-strain range of interest for lightweight fill applications and only slightly more testing of the effects at larger strains. However, existing data suggests stiffer geofoam behavior with decreasing temperature and softer behavior with increasing temperature compared to the de facto standard laboratory conditions. For example, data in (25) indicates that the initial tangent Young's modulus is either unchanged or slightly larger in magnitude under lower than ambient laboratory temperatures. Based on the present knowledge, there is insufficient information to incorporate temperature into any analysis or design procedure for EPS-block geofoam as lightweight fill. Recommendation: There appears to be no compelling reason not to use ambient conditions typical of most laboratories (+23°C ± (73°F±) and 50 percent ± humidity). Compatibility with MQC/MQA Testing. If possible without compromising the goals of either research or manufacturing quality control and assurance testing, specimen and test parameters for the two areas of testing should be the same for both simplicity and comparison of results.

2-27 Monotonic. The most commonly performed test on EPS specimens involves strain- controlled compression loading at a relatively rapid rate, typically 10 percent per minute, with the load applied in a monotonically increasing fashion until a desired strain level is reached. Figure 2.1 illustrates the typical stress-strain response from such a test that was performed on a 50 mm (2 in.) cubic specimen and a strain rate of 10% per minute to an unusually large strain level (approximately 90 percent) to illustrate the entire range of EPS compression behavior. The test was performed on a block-molded EPS specimen with a density of 21 kg/m3 (1.3 lbf/ft3). However, the stress-strain response for other densities are qualitatively similar (18). The primary item of note is that the EPS does not fail in the traditional sense of other solid materials used in construction (metals, concretes, wood) by a physical rupture of the material. Nor does the EPS behave like soil or other particulate materials where inter-particle slippage occurs and a steady state or residual strength develops at large strains. Rather, the EPS essentially crushes one dimensionally (Poisson's ratio of EPS is discussed in detail subsequently) back to its original solid polystyrene state, and the behavior is continuously work (strain) hardening in nature. The stress-strain behavior of EPS shown in Figure 2.1 can be divided into the following four zones (18): • Zone 1: initial linear response. • Zone 2: yielding. • Zone 3: linear and work hardening in nature. • Zone 4: non linear but still work hardening in nature. Figure 2.1. Stress-strain behavior of 21 kg/m3 (1.3 lbf/ft3) EPS block under rapid, strain- controlled, unconfined axial compression (18,26). The limit of Zone 1, i.e., the initial linear stress-strain behavior, extends to strains between 1 percent and 1.5 percent with the larger strain at the end of the linear region occurring with an increase in EPS density (18). An initial slightly curved, concave upward, response has

2-28 been observed within Zone 1 prior to the linear portion (18). However, it has been suggested that this curvature is the result of the testing equipment and procedures and not a fundamental characteristic of EPS (18). In particular, errors related to seating of the end platens due to surface irregularities of the test specimen introduced during trimming and mechanical slack in the loading system will introduce errors in the deformation measurements. These errors can be minimized by making deformation measurements directly on the test specimens with the use of extensometers (18). It is indicated in (18) that data in (25) suggests that the initial portion of the stress-strain curve is slightly curved, concave downward, in the 0 percent to 1 percent strain range even after correcting for seating effects. This appears to be similar to the small-strain behavior of soil. Research results in (27) suggest that behavior is linear only up to a strain level of about 0.5 percent. In summary, the consensus that has evolved worldwide is that the stress-strain behavior of EPS-block geofoam is both linear and elastic up to a compressive strain of 1 percent. As a result, a new material parameter for EPS-block geofoam called the elastic limit stress, σe, has been suggested (18). This is defined as the compressive stress at 1 percent strain as measured in a standard rapid-loading compression test. Furthermore, the slope of the initial (approximately) linear portion of the stress-strain curve (see Zone 1) is defined as the initial tangent Young’s modulus, Eti. As shown in Figure 2.2, for all practical purposes there is a linear empirical relationship between EPS density and Eti assuming that the EPS is of appropriate quality (for the purposes of this proposal, material satisfying the provisional AASHTO standard included in Appendix C). The data shown in Figure 2.2 was obtained from (17,28-31) Equation (2.1) provides an average Eti based on the data of Figure 2.2: Eti = 450 ρ - 3000 (2.1) where Eti has units of kilopascals (kPa) and ρ = EPS density in kg/m3.

2-29 From Hooke’s law relation, σ = (Eti)∗(ε), where σ is the applied stress and ε is strain after stress application, Equation (2.1) can be extended to form an expression for the elastic limit stress at an axial strain of 1 percent that is sufficiently accurate for routine analysis and design purposes: σe = (450 ρ – 3000)∗(0.01) = 4.5 (ρ) - 30 (2.2) where σe has units of kPa and ρ = EPS density in kg/m3. The data used to create Figure 2.2 and Equations (2.1) and (2.2) are based on testing relatively small specimens prepared from samples cut from full-size blocks of EPS. There is a lack of information at the present time concerning the stress-strain behavior of full-size EPS blocks although limited unpublished information suggests that full size blocks may be somewhat stiffer, i.e. have a larger initial tangent Young's modulus, than either Figure 2.2 or Equation (2.1) would imply. Figure 2.2. Correlation between density and initial tangent Young’s modulus for block- molded EPS (18). Zone 2 of a typical stress-strain curve (see Figure 2.1) is called yielding. The zone of yielding is dependent on density and extends to strains between 3 percent and 5 percent (18). After the zone of yielding, the behavior is linear again. The radius of curvature inside the zone of yielding is dependent on the density of EPS but in general, the greater the density, the smaller (sharper) the radius of curvature and the smaller the strain at which linear post-yield behavior resumes (18). Even though EPS loaded in compression does not fail in the traditional sense of a physical rupture and yielding occurs over a range of stresses, it has been and still is traditional nonetheless to define a material parameter called compressive strength of EPS, σc. Compressive strength of EPS is defined as the compressive stress at some arbitrary strain level. There is no universal agreement as to what this arbitrary strain level is. ASTM and most other standards organizations around the world define it as 10 percent so in this report the compressive strength

2-30 of EPS is given the notation σc10. This point on the stress-strain curve is shown in Figure 2.1. In Norway, where much of the early use of EPS-block geofoam occurred, the strain criterion used for σc is 5 percent. Referring to Figure 2.1, it can be seen that there is nothing particularly noteworthy about a strain level of 10 percent (or 5 percent for that matter) other than that it occurs after a zone of initial yielding of the EPS. This is an important point because early geofoam design methods were based on compressive strength. In many ways, the use of a parameter called "strength" for EPS is unfortunate as it implies an ultimate condition (ULS type failure) involving material rupture. In fact, neither aspect is exhibited by EPS geofoam. Compressive strength increases linearly with increasing EPS density (18) and the following equation has been suggested (18,32): (2.3) where σc10 = compressive strength using the 10 percent-strain criterion in kPa and ρ = EPS density in kg/m3. As indicated previously, compressive strength occurs after a zone of initial yielding of the EPS and is defined at a strain level beyond the yield range. Therefore, a parameter called the "plastic stress" (σp) (30) or "yield stress" (σy) (18) has been proposed to define the stress corresponding to the onset of yielding. Figure 2.3 shows the definition of yield stress. The yield stress can be determined graphically or by the use of empirical equations. Graphically, the yield stress can be determined by forward extrapolation of the initial linear portion (Zone 1) and backward extrapolation of the post-yield linear portion of the stress-strain curve (Zone 3) as shown in Figure 2.3 (18). The stress at the intersection of the two lines is the yield stress. The following three empirical equations have also been suggested to estimate the yield stress (18): (2.4) (2.5) c10σ 8.82ρ 61.7= − y y σ 6.41ρ 35.2 σ 6.62ρ 46.3 = − = −

2-31 yσ 6.83ρ 48.4= − (2.6) where σy = yield stress in kPa and ρ = EPS density in kg/m3. Figure 2.3. Definition of yield (plastic) stress (18). Figure 2.4 shows a comparison of the three empirical equations. Equation (2.4) was obtained from (18,30) and Equations (2.5) and (2.6) were obtained from (18). By definition the yield stress is less than the compressive strength. This is generally depicted in Figure 2.4 except for Equation (2.4) for low-density EPS. Thus, it is possible to estimate the yield stress from the recommended compression testing with sufficient accuracy in practice even if project-specific testing is not performed (18). In general, the magnitude of yield stress is approximately 75 percent of the magnitude of the compressive strength and the strain corresponding to the yield stress is approximately 1.5 percent, which is slightly greater than 1 percent which corresponds to σe, over a wide range of EPS densities (18). Figure 2.4. Comparison of empirical relationships between yield stress and density for block-molded EPS (18). As shown in Table 2.1, compressive strength varies with temperature (18,32). The percentage (if any) of in-plant regrind and post-consumer recycled material and how it is fused into blocks may have varying affects on the compressive strength, elastic limit stress, and initial tangent Young's modulus in compression of block-molded EPS, especially the initial tangent Young’s modulus (2,3). For example, tests have Table 2.1. Compressive Strength Variation with Temperature (18,32). revealed that EPS with an average density on the order of 16 kg/m3 (1.0 lbf/ft3) had virtually the same compressive strength with up to 50 percent regrind content yet the initial tangent Young's modulus was reduced by a factor of approximately two between samples with no regrind and 50

2-32 percent regrind (33). Figure 2.5 shows a qualitative description of the effect of regrind content on the small-strain region of the stress-strain region of EPS, which is the most critical region for load-bearing applications. Both the initial tangent Young’s modulus and elastic limit stress decrease with increasing regrind content. However, the compressive strength is affected only slightly by regrind content. Figure 2.5. Effect of regrind content on the stress-strain behavior of EPS-block geofoam (4). Cyclic. For the purposes of this report, cyclic loading is defined as loads that are applied, removed, and reapplied in a fairly rapid and repetitive manner. Research to date indicates that as long as the maximum applied stress has a magnitude not exceeding the elastic limit stress, σe, there is: • no plastic (permanent) strain upon stress removal and • no degradation of the initial tangent Young’s modulus with cyclic loading. However, as shown in Figure 2.6, if the stress level goes beyond the elastic range there is both plastic deformation as well as a degradation of modulus. The latter can be seen by the progressive flattening of the unload-reload curves. Figure 2.6 is based on testing performed on a 50 mm (2 in.) cubical specimen with a density of 13 kg/m3 (0.81 lbf/ft³) subjected to rapid cycles of loading and unloading in the post-yield range, i.e., the applied stress exceeds the elastic limit stress (18). As shown in Figure 2.6, the average tangent Young's modulus of each unload-reload cycle is smaller than the initial tangent Young's modulus and decreases in magnitude with increasing strain. At very large strains, the unload-reload cycles become sharply curved as the EPS stiffens. Figure 2.6. Cyclic load behavior for 13 kg/m3 (0.81 lbf/ft3) block-molded EPS (18). The mechanical properties of EPS, including cyclic loading behavior, are dependent primarily on the shape of the polyhedra (18,32). As indicated in the manufacturing (molding)

2-33 section of this chapter, the pre-puff changes from spherical shape to a more polyhedral shape after the pre-puff is further expanded in the second step of the manufacturing process. Each face of a polyhedron represents a contact plane with an adjacent polyhedron. However, the contacts are not perfect and some void space may exist between polyhedra. Fusion between polyhedra occurs from the cooling of the softened polystyrene at these contact planes. Each polyhedron retains the numerous closed cells. The deformation of the polyhedra is elastic within the elastic range which is defined as axial strains up to approximately 1 percent. It is reported in (18) that research performed in (31) indicates that no change in the tangent Young's modulus occurred after 2 x 106 cycles of loading on a strain-controlled cyclic test between 0 percent and 1 percent strain on a specimen with a density of 20 kg/m3 (1.25 lbf/ft³). Beyond the elastic range, the cellular polyhedra undergo permanent shape change from polyhedral to ellipsoidal, with the short axis of the ellipsoids parallel to the direction of loading (18). This permanent change in shape is represented by plastic, non-recoverable, deformation and a lower tangent modulus. In summary, cyclic loading, e.g., traffic loading, should not adversely impact the geofoam unless the maximum applied stress exceeds the elastic limit stress. These observations and conclusions concerning behavior under cyclic loads are based on testing relatively small specimens prepared from samples cut from full-size blocks of EPS. There is a lack of information at the present time concerning the cyclic loading behavior of full-size EPS blocks. Poisson’s Ratio. The following findings regarding the Poisson’s ratio, ν, of EPS block are provided: • Within the elastic range, ν is relatively small (of the order of 0.1) and often taken to be zero for practical design purposes, e.g. in the French national design manual (34). However, if a more accurate estimate of ν is desired, the following empirical relationship, which indicates that ν increases slightly with increasing EPS density, can be used:

2-34 ν = 0.0056 ρ + 0.0024 (2.7) where ρ = EPS density in kg/m3. This equation is based on research performed in Japan (19). • If an estimate of the coefficient of lateral earth pressure at rest, Ko, is desired, the following equation, which is valid for any elastic material, can be used: 0K 1 v v = − (2.8) This means that under confined (at-rest) conditions horizontal stresses will be approximately one-tenth the vertical stresses, a fact that has been confirmed by full-scale case-history observations (35) and highlights a benefit of using EPS- block geofoam as backfill behind retaining structures. • Beyond the elastic range, ν rapidly decreases to zero. For example, testing performed on EPS with a density of 20 kg/m3 (1.25 lbf/ft3) shows, ν decreases from 0.12 within the elastic range (strains between 0 percent and 1 percent) to 0.03 at a strain of 5 percent (18,19). In some tests necking of the test specimens (which implies a negative Poisson's ratio) has been observed (32). The above observations and conclusions concerning Poisson's ratio are also based on testing relatively small specimens prepared from samples cut from full-size blocks of EPS. There is limited information available at the present time concerning the stress-strain behavior of full- size EPS blocks although case history observations, primarily in Norway, suggest that Poisson's ratio is indeed relatively small in magnitude compared to most other civil engineering materials. Time-Dependent Behavior (Creep and Relaxation) Introduction Another area of research in recent years has been the time-dependent response of EPS- block geofoam to compressive loads. Five variables that affect the time-dependent behavior of EPS include density, stress, strain, time, and temperature (18). Only the time-dependent behavior

2-35 is discussed here. The temperature dependent behavior is discussed separately. Two time- dependent behaviors of EPS are: • Creep which is the additional strain or deformation that occurs with time under an applied stress or load of constant magnitude. • Relaxation which is the reduction in applied stress or load with time under a constant magnitude of strain or deformation. For the function of lightweight fill, creep is the only time-dependent behavior of concern. Thus, relaxation will not be addressed here. Testing A review of published creep test results (27,30,31,36-41) performed for this study reveal a lack of a standard creep test method for geofoam. About the only common denominator in creep tests performed around the world to date is that they are almost always performed under ambient laboratory conditions of approximately +23°C (+73°F) and 50 percent humidity. In addition, there has been no direct comparison of creep tests performed using different combinations of test variables so an assessment of variable variation is impossible to conduct at the present time. It is recommended that a standard test method be developed for performing creep tests on EPS-block geofoam so creep models can be developed and reliably evaluated. The best that can be accomplished at this time is to discuss the test variations used in practice and make recommendations based on judgment and indirect comparative testing. The primary variables that need to be considered for creep tests are: • test specimen shape, • test specimen dimensions, • test specimen age, • applied stress level, • confinement of the test specimen,

2-36 • test duration, and • ambient temperature in the laboratory where the test is performed. Using the above list of variables for reference, the observed variations in test variables and recommendations for creep testing in practice are as follows: • Specimen shape and dimensions. Specimen shapes that have been reported in the literature include a cube, right-circular cylinder, and disc. Cube-shaped specimens are typically 50 mm (2 in.) cubes. Right-circular cylinder specimens with heights of 38, 50, 200, and 300 mm (1.5, 2, 8, and 12 in.) and diameters of 76, 50, 100, and 150 mm (3, 2, 4, and 6 in.), respectively, have been utilized. Disc-shaped specimens typically replicate the dimensions of soil oedometer (one- dimensional consolidation) test specimens (i.e., 25 mm ( 1 in.) thick and 65 mm (2.5 in.) ± in diameter). Figure 2.7 shows creep test results from three different specimen sizes with a density of 20 kg/m³ (1.25 lbf/ft³) tested at a sustained stress of 20 kPa (417 lbs/ft²). These results as well as comparisons made from specimens tested at stresses of 30 and 50 kPa (625 and 1,045 lbs/ft²) indicate that disc shaped specimens may yield higher creep strains than cylindrical specimens. • Specimen age. This has not been studied but it is desirable that all specimens in a given suite of tests (creep tests tend to be performed in groups or suites of tests on EPS of the same density and subjected to different stress levels) have the same age and, in fact, be prepared from samples taken from the same EPS block. As an absolute standard, it appears that the minimum specimen age of three days as for rapid-loading compression tests is appropriate for creep tests as well. Figure 2.7. Comparison of laboratory compression creep test data for an EPS density of 20 kg/m3 (1.25 lbf/ft3) and applied stress of 20 kPa (417 lbs/ft2) and the creep equations. (42)

2-37 • Applied stress level. This will be dependent on the stress that the EPS-block will be subjected to in the particular load-bearing application. • Specimen confinement. When geotechnical oedometer equipment is used, tests have been performed both with and without the metal confinement ring although no direct comparison of results has been reported. Given the relatively small magnitude of the Poisson ratio of EPS under small strains, the results between the two test protocols are expected to be similar. However, the unconfined test is arguably more representative of actual conditions; should yield somewhat greater deformations (and thus be more conservative); is easier to perform; and removes concern over friction between the EPS specimen and ring. Thus, unconfined creep tests are recommended. • Test duration. This parameter has seen the greatest variation in practice. Many early creep tests only lasted several hundred hours. It is now recognized that this is inadequate and can produce potentially misleading results as tertiary creep can be totally missed (39). As a result, 10,000 hours (approximately 13 months) is now considered to be the absolute minimum test duration with 15,000 hours (approximately 20 months) or more preferred (tests in excess of 19,000 hours (approximately two years) have been performed). The justification for these longer duration tests is that it is believed that the creep performance of EPS can only be projected for 30 times the creep test duration which is somewhat more generous than the factor of 10 suggested for polymeric geosynthetics in general (43). This suggests that creep test durations of at least 15,000 hours (20 months) is required using the extrapolation factor of 30 for a 50-year design life (which is not unreasonable for a geotechnical highway structure).

2-38 • Temperature. Little creep testing has been conducted at temperatures other than de facto standard laboratory conditions. Creep at temperatures greater than +23°C± (73°F±) has been found to accelerate with increasing temperature. • Specimen Preparation. The same care in specimen preparation discussed previously for rapid-loading compression tests is recommended for creep tests. The general time-dependent behavior of EPS is similar to other engineering materials and exhibits primary, secondary, and tertiary creep as shown in Figure 2.8. Creep tests on EPS-block geofoam are typically depicted as shown in Figure 2.9. However, experience indicates that the most useful way to portray creep-test data is by constructing a family of isochronous stress-strain relations for tests performed on EPS specimens of the same density. An isochronous curve is the estimated stress-strain behavior for a range of applied stresses for a specific duration of time. Figure 2.10 illustrates a typical family of isochronous stress-strain curves together with a portion of the standard rapid-loading compression test for comparison. However, the approximate stress- strain relation for the standard rapid loading compression test and the isochronous curves are not strictly comparable because they represent different loading conditions of sustained versus constantly changing load (18,44). Isochronous stress-strain curves for different durations of loading are useful in geotechnical applications where sustained loads are typically involved (18). Figure 2.8. Regions of behavior in creep (45). Figure 2.9. Results of typical unconfined axial compression creep tests on block-molded EPS (18). Figure 2.10. Isochronous stress-strain curves for 23.5 kg/m3 (1.47 lbf/ft³) block-molded EPS based on unconfined axial compression creep tests (18,26). Constitutive Modeling of the Stress-Strain-Time Behavior of EPS Introduction. Two time-dependent stress-strain (creep) models that have been suggested for predicting the vertical strain or deformation of EPS blocks that occurs under an applied stress

2-39 include the general power-law equation and the Findley equation (39). An initial overview of the theory and application of both equations is presented. The total vertical strain predicted by these two equations consist of two components as shown below. where ε = total strain at some time period t after stress application, εo = immediate strain upon stress application, and εc = time-dependent strain (creep) at some time period t after stress application. Based on the assumption that εo is linear-elastic and based on empirical relationships established through laboratory creep-test data, the Laboratoire Ponts et Chaussess (LCPC) derived the following General Power-Law equation for the total strain of EPS blocks (30,39): where ε = total strain at some time period t after stress application (in decimal form, not as a percent), σ = applied stress in kPa, σp = plastic stress of EPS in kPa, Eti = initial tangent modulus in kPa, and t = time in hours after stress application. The LCPC established the following two empirical relationships based on laboratory testing to facilitate use of Equation (2.10): σp = 6.41ρ - 35.2 (2.11) Eti = 479ρ - 2875 (2.12) where σp = plastic stress in kPa, Eti = initial tangent modulus in kPa, and o c ε=ε +ε (2.9) 10 p i σ2.47 0.9log 1 σ t p σ σε 0.00209 t E σ     − −             = +            (2.10)

2-40 ρ = EPS-block geofoam density in kg/m3. However, it was found in (39) that Equation (2.12) yields values of initial tangent modulus that are higher than typically reported in the literature. The consequence of using Equation (2.12) to estimate the initial tangent modulus is discussed subsequently. Equation (2.1), which is based on averaging other published relationships by (18) can also be used to estimate Eti. The Findley equation (46,47) is also used to predict the total time-dependent vertical strain of geofoam. The Findley equation has been modified by (39) based on creep test results that extend for nearly 19,000 hours (2.2 years) as shown below: where ε = total strain at some time t after a stress application (in percent), σ = applied stress in kPa, and t = time in hours after stress application. Equation (2.13) is based on three tests performed on 50 mm (2 in.) cube-shaped EPS specimens with a density of 20 kg/m3 (1.25 lbf/ft³) at stresses of 30, 40, and 50 kPa (625, 835, and 1,045 lbs/ft²). Therefore, the modified Findley equation, i.e., Equation (2.13), is applicable to EPS block with a density of 20 kg/m3 (1.25 lbf/ft³) subjected to stresses between 30 and 50 kPa (625 and 1,045 lbs/ft²). The applicability of Equation (2.13) at stress levels not between 30 and 50 kPa (625 and 1,045 lbs/ft²) is investigated herein to determine the potential benefit of refining Equation (2.13) so that it can be used for other stress levels. Both the general power-law and modified Findley equations will be compared with laboratory measured results on full-size EPS blocks to assess their accuracy. Laboratory Creep Tests. As indicated previously, there is a lack of a standard creep test method for geofoam. Therefore, a qualitative, not quantitative, comparison is made between σ σ 0.20ε 1.1sinh( ) 0.0305sinh( )(t) 54.2 33.0 = + (2.13)

2-41 published laboratory creep test results and the calculated strain values derived from the general power-law and modified Findley equations to assess the accuracy of these equations. Figures 2.7 and 2.11 provide a qualitative comparison between various size EPS specimens with a density of 20 kg/m3 (1.25 lbf/ft³) at stresses of 20 kPa (417 lbs/ft²) and 70 kPa (1,460 lbs/ft²) and the calculated results based on the general power-law and the modified Findley equations. The laboratory test results shown in these figures are limited to specimens with a density of 20 kg/m3 (1.25 lbf/ft3) and to stress levels of 20 kPa (417 lbs/ft²) and 70 kPa (1,460 lbs/ft²) because this is the density and stress range of EPS blocks that are used in the full-size block and full-scale model tests. Laboratory test data utilized in deriving the general power-law and modified Findley equations are not shown to provide non-bias comparisons. At the lower stress level of 20 kPa (417 lbs/ft²), see Figure 2.7, both equations predict strains that are in agreement with the measured values from cylindrical EPS specimens. However, the modified Findley equation predicts slightly larger strains than the general power-law equation. Neither equation predicts strains near the measured values obtained on a disc-shaped specimen at an applied stress of 20 kPa (417 lbs/ft²). A disc-shaped specimen is usually used when creep testing is performed with an oedometer, which is typically used to simulate one-dimensional compression of soils in the laboratory. At the higher stress level of 70 kPa (1,460 lbs/ft²), see Figure 2.11, the power-law equation and the modified Findley equation predict larger and smaller total strains, respectively, than the measured values. It is indicated in (36) that the creep test was performed with a standard consolidation test machine. Thus, it can be inferred that a disc-shaped specimen typically used in soil oedometer (one-dimensional consolidation) testing, which is typically on the order of 25 mm (1 in.) thick and 65 mm (2.5 in.) ± in diameter, was used. The general power-law equation indicates a relationship between the time-dependent behavior of EPS and the plastic stress and initial tangent modulus, see Equation (2.10). Therefore, it is recommended that compressive strength tests be performed on similar specimens that will be used for creep testing so values of plastic stress and initial tangent modulus can be obtained from

2-42 the same test sample. It is also recommended that the elastic-limit stress be determined from compressive strength tests because, as will be discussed later, the elastic-limit stress may be a useful guide for estimating the onset of significant creep effects (18). It is also recommended that axial strain data be obtained immediately upon stress application and frequently for the first hour after load application to better estimate the immediate strain, εo, (39). A good estimate of εo is critical to estimating the total strain because εo contributes more to the total strain than the creep- induced strain, εc. Full-Size EPS Block Creep Test. A full-size block with a density of 20 kg/m3 (1.25 lbf/ft³) and dimensions of 1.5 m (4.9 ft) by 1 m (3.3 ft) by 0.5 m (1.6 ft) was loaded under a stress of 71 kPa (1,480 lbs/ft²) for 61 days (48). A stress of 27 kPa (564 lbs/ft²) was initially applied for four days. An additional stress of 19 kPa (397 lbs/ft²) (total stress equal to 46 kPa (961 lbs/ft²)) was applied for seven days and an additional stress of 25 kPa (522 lbs/ft²) (total stress equal to 71 kPa (1,483 lbs/ft²)) was applied for 50 days. The stress at the bottom of the block was Figure 2.11. Comparison of compression laboratory creep test data for an EPS density of 20 kg/m3 ( 1.25 lbf/ft³) and applied stress of 70 kPa (1,460 lbs/ft2) and the creep equations. measured using seven pressure cells and an average pressure of 34, 55, and 79 kPa (710, 1,149, and 1,650 lbs/ft²) was measured in the pressure cells for days 1 through 5, 5 through 12, and 12 through 62, respectively. These average stresses are used in calculating the vertical strains using the power-law and modified Findley equations. Figure 2.12 shows a comparison between the calculated and measured total strains for compressive stresses of 34, 55, and 79 kPa (710, 1,149, and 1,650 lbs/ft²). At the initial stress levels of 34 and 55 kPa (710 and 1,149 lbs/ft²), both the general power-law and modified Findley equations predict total strains that are in agreement with the measured strains. At the largest stress of 79 kPa (1,650 lbs/ft²), the power-law equation significantly overestimates the measured strains

2-43 and the modified Findley equation underestimates the measured strains. However, the modified Findley equation provides the best agreement with the measured values especially as the time, t, increases. Full-Scale Model Creep Test. A full-scale model creep test was performed at the Norwegian Road Research Laboratory (48,49) to investigate the time-dependent performance of EPS-block geofoam. 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). Figure 2.12. Comparison of full-size EPS block creep test data and the creep equations for an EPS density of 20 kg/m3 (1.25 lbf/ft³) and an applied stress of 34 kPa (710 lbs/ft2) for days 1-5, 55 kPa (1,149 lbs/ft2) for days 5-12, and 79 kPa (1,650 lbs/ft2) for days 12-62. 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). This is in agreement with a stress distribution of 1 (horizontal) to 2 (vertical), which is typically assumed in design calculations incorporating EPS- block geofoam structures. The measured stress distribution is slightly wider but still in agreement with 1 (horizontal) to 2 (vertical). Thus, the measured stress with depth is slightly less than the typically assumed stress distribution, which results in a slightly conservative design when a 1 (horizontal) to 2 (vertical) stress distribution is assumed. Therefore, it is recommended that a 1

2-44 (horizontal) to 2 (vertical) stress distribution be utilized in design calculations for EPS-block geofoam embankments. Figure 2.13 shows a comparison of the total strain measured in the EPS blocks of the full- scale test fill and the calculated total strains based on the power-law and modified Findley equations. In calculating the total strains, the fill was divided into the same number of horizontal layers as EPS block layers used, four. The total strain of each layer was determined based on the average stress calculated at the middle of each block using the measured 1 (horizontal) to 1.8 (vertical) stress distribution. Thus, the stress used for each layer from top to bottom was 36.2, 20.4, 13.1, and 9.1 kPa (756, 426, 274, and 190 lbs/ft²). As indicated in Figure 2.13, both the general power-law and modified Findley equations underestimate the strains measured in the full- scale test fill. The power-law predictions are lower than the modified Findley predictions and thus the Findley equation provides the best agreement. Figure 2.13. Comparison of full-scale model creep test data and the creep equations for an EPS density of 20 kg/m3 (1.25 lbf/ft³). Full-Scale Field Monitoring. A field monitoring program was implemented as part of the Løkkeberg bridge project built in Norway in 1989 (48,49). EPS blocks were used to construct a bridge approach embankment and to support the bridge foundation. Pressure cells were installed at various locations within the embankment and settlement monitoring rods were installed at four locations to measure the total settlement of the embankment and the vertical strains at various depths in the embankment. The height of the embankment is 4.5 m (14.7 ft). EPS blocks with an unconfined compressive strength of 240, 180, and 100 kPa (5,012, 3,759, 2,089 lbs/ft²), were used in the top 1.2 m (3.9 ft), middle, and bottom 2.1 m (6.9 ft) of the embankment, respectively. A 10 cm (3.9 in.) concrete slab was placed between the 180 and 100 kPa (3,759 and 2,089 lbs/ft²) blocks to further distribute the stresses within the 100 kPa (2,089 lbs/ft²) blocks. Figure 2.14 shows the total vertical strain measured in the lowest block layer. The density of the bottom row of EPS blocks is 20 kg/m3 (1.25 lbf/ft³) and the original thickness of the EPS

2-45 blocks is 0.6 m (2 ft). Three pressure cells were installed below the first row of blocks. An average pressure of 67 kPa (1,399 lbs/ft²) was recorded in the three pressure cells during the period that the vertical strain was being obtained from the settlement rods. As shown in Figure 2.14, the power-law and modified Findley equations significantly overestimate and underestimate the measured total strains, respectively. However, the total strains predicted by the modified Findley equation are again in better agreement with the measured values than the power-law equation. Figure 2.14. Comparison of total vertical strain measured in the lowest EPS block layer of the field test fill and the general power-law and modified Findley equations. Summary of Comparison of Measured and Calculated Values of Total Strain. For stresses between 10 and 55 kPa (209 and 1,149 lbs/ft²), both the power-law and modified Findley equations yield total strain values similar to or less than the measured values obtained on the full- size block and full-scale creep test fills. In general, the power-law equation predicts total strains smaller than the modified Findley equation for compressive stresses between 10 and 55 kPa (209 and 1,149 lbs/ft²). A similar observation was made in (39). In (39) it is suggested that the power- law equation predicts smaller total strains than laboratory measured values, especially for short time durations, because the test specimens used by the LCPC to derive the power-law equation yield larger values of initial tangent modulus than other specimens reported in the literature. This is apparent by comparing Equations (2.12) and (2.1). It is also suggested in (39) that the values of Eti obtained from the LCPC relationship in Equation (2.12) are approximately 40 percent larger than the values from Equation (2.1), which is based on averaging other published relationships. In summary, the modified Findley equation is recommended to predict total vertical strains for compressive stresses between 10 and 55 kPa (209 and 1,149 lbs/ft²). Further refinement of the modified Findley equation for stresses outside the 30 to 50 kPa (627 and 1,044 lbs/ft²) stress range that was used in developing the equation may result in better predictions.

2-46 At larger compressive stresses of 67, 70, and 79 kPa (1,399, 1,462 and 1,650 lbs/ft²), the total strains determined by the power-law equation and the modified Findley equation significantly overestimate and underestimate, respectively, the measured full-size block and full- scale test fill values. The modified Findley equation provides better agreement than the power- law equation, especially as the elapsed time increases. Further refinement of the modified Findley equation for stresses outside 30 to 50 kPa (627 to 1,044 lbs/ft²) stress range that was used in developing the equation may result in better predictions. As noted in (39), the power-law equation may provide unusually high strain values at large compressive stresses, especially at longer durations of applied stress, because the power-law equation was developed from creep tests of insufficient duration. This results in greater strains because the total strains decrease with increasing elapsed time as shown in Figures 2.7 and 2.11 through 2.14. The time-dependent behavior obtained on one layer of blocks in the full-scale field test is similar to the behavior obtained during the full-size block test. After a time equal to 1,440 hours (60 days), the difference in total strain measured was approximately 3.2 percent, with the full-size block test producing the larger total strain because the average total stress measured in the full- size block test was 79 kPa (1,650 lbs/ft²) compared to 67 kPa (1,399 lbs/ft²) for the full-scale field test. Therefore, it appears that creep tests based on a full-size EPS block may provide reasonable predictions of total vertical strain with time for full-scale projects utilizing EPS-block geofoam as lightweight fill. This reduces the need for constructing full-scale model test fills to develop time- dependent data and validate or modify existing creep models. Therefore, a standard test method could be developed either using a full-size block or comparing the results from smaller specimens with the results of full-size blocks. At present, the general power-law and modified Findley equations do not provide a reliable estimate of the time-dependent total strains. Further research is required to either refine these expressions or develop new expressions based on other creep models. In particular, the power-law equation should be refined to include results from specimens with lower values of Eti

2-47 and tests of longer duration. The modified Findley equation should be refined to include test results from compressive stresses outside the 30 to 50 kPa (627 to 1,044 lbs/ft²) stress range that was used to develop the relationship. The results of the full-scale model test conducted at the Norwegian Road Research Laboratory indicates that the typically assumed 1 (horizontal) to 2 (vertical) distribution of compressive stresses through a geofoam embankment is reasonable, albeit slightly conservative because the measured stress showed a stress distribution of 1 (horizontal) to 1.8 (vertical), for design calculations. Temperature – Dependent Behavior Introduction. In general, the stress-strain behavior of polymeric materials, such as EPS- block geofoam, is temperature dependent (50). Available information suggests that very little creep testing of EPS block has been conducted at temperatures other than ambient in a typical laboratory environment (+23°C± (+73°F±). The limited testing at elevated (relative to typical laboratory) temperatures indicates that the behavior of EPS block is consistent with trends of polymeric materials in general, i.e. creep rates increase with increasing temperature. The data shown in Table 2.2 and discussed in (18) shows this trend. Table 2.2. General Temperature-Dependent Behavior for EPS (18). A likely reason for the lack of creep tests at elevated temperatures is the fact that most EPS-block geofoam applications were, until the 1990s, in relatively cool Northern Hemisphere locations where annual average air temperatures are of the order of +5°C (+41°F) to +15°C (+59°F) maximum. Creep at these temperatures would be expected to be somewhat less than at ambient laboratory temperatures and long-term case history observations (mostly from Norway) confirm that. Constitutive Modeling of the Stress-Strain-Time-Temperature Behavior of EPS. The availability of a mathematical model for the stress-strain-time-temperature behavior for EPS is

2-48 currently unavailable. Such a model would be useful in practice to estimate creep behavior beyond the duration of creep tests. The variables of test duration and temperature are of particular interest for future improvements in test protocols. Consideration should be given to using time- temperature superposition procedures or a combination of both conventional testing procedures and time-temperature superposition procedures (stepped isothermal methods) to measure creep behavior. These alternate methods have been used to study creep behavior of other geosynthetic materials (43) and can accelerate acquisition of meaningful creep data. The resulting creep data could be used to develop a stress-strain-time-temperature mathematical model for EPS block. Such a model would enable better predictions of creep strains at temperatures other than the conventional laboratory ambient conditions. Recommended Procedure for Considering Creep Strains The current state of practice for considering creep strains in the design of EPS block embankments and bridge approaches is to base the design on laboratory creep tests on small specimens trimmed from the same EPS block that will be used in construction or to base the design on published observations of the creep behavior of EPS such as: • If the applied stress produces an immediate strain of 0.5 percent or less, the creep strains, εc, will be negligible even when projected for 50 years or more. The stress level at 0.5 percent strain corresponds to approximately 25 percent of the compressive strength defined at a compressive normal strain of 1 percent or 33 percent of the yield stress. • If the applied stress produces an immediate strain between 0.5 percent and 1 percent, the geofoam creep strains will be tolerable (less than 1 percent) in lightweight fill applications even when projected for 50 years or more. The stress level at 1 percent strain corresponds to approximately 50 percent of the compressive strength or 67 percent of the yield stress.

2-49 • If the applied stress produces an immediate strain greater than 1 percent, creep strains can rapidly increase and become excessive for lightweight fill geofoam applications. The stress level for significant creep strain corresponds to the yield stress which is approximately 75 percent of the compressive strength. The approximate compressive strengths indicated above are based on empirical relationships. Compressive strength, which is dependent on the strain level, e.g., 5 percent or 10 percent, does not provide fundamental knowledge into the creep behavior of EPS because it is determined in a rapid load compression test (18). It should be noted that material stressed at or near the compressive strength will exhibit large creep deformations almost immediately (18). Therefore, to produce acceptable strain levels in lightweight fill applications, stress levels must be kept low relative to compressive strength. This is illustrated in Figure 2.10. Lower density EPS tends to creep more than higher density EPS at the same relative stress level defined as the same fraction of the yield stress or compressive strength with creep effects increasing significantly for EPS with a density equal to or less than 16 kg/m3 (1 lbf/ft3) (18). In summary, the compressive stress at a vertical strain of 1 percent, i.e., the elastic-limit stress, appears to correspond to a threshold stress level for the development of significant creep effects and the field applied stresses should not exceed the elastic-limit stress until more reliable creep models are developed (18). Based on these observations, it is concluded that creep strains within the EPS mass under sustained loads are expected to be within acceptable limits (0.5 percent to 1 percent strain over 50 to 100 years) if the applied stress is such that it produces an immediate strain between 0.5 percent and 1 percent (18). Tension Although tensile loading generally does not occur when EPS block is used in geofoam applications, tensile loading is an important mode of loading for evaluating EPS fusion, a manufacturing quality parameter. Thus, tensile loading can be an important MQC/MQA test. However, tensile testing is not typically performed because of the difficulty in fabricating the

2-50 hourglass-shaped test specimens required for tensile testing per the ASTM C 1623 standard test method (51) and the availability of other types of tests (most notably flexure which is discussed subsequently) that essentially test for the same behavior and are easier to perform. Laboratory tests for tensile loading are performed at a standard speed of testing such that rupture occurs in 3 to 6 min. Tensile strength is defined as the tensile stress at which physical material rupture occurs. Figure 2.15 illustrates the linear relationship between tensile strength and EPS density. Also shown for comparison is the relationship for compressive strength using the ASTM criterion of 10 percent strain. The tensile strength data shown in Figure 2.15 was obtained from (52) which did not indicate strain rate, specimen dimensions, or the magnitude of axial strain at which tensile failure occurred (18). No test data was located concerning long-term tensile behavior of EPS (18). Flexure Although tensile strength is the fundamental indicator of EPS fusion and thus a useful MQC/MQA parameter, the test itself is somewhat cumbersome as discussed in the previous section. As a result, flexural tests on beam-shaped specimens are typically performed for testing the tensile strength of EPS. The relevant ASTM standard, ASTM C 203 (53), test setup used is such to produce maximum bending moment and, therefore, maximum tension in the extreme bottom fiber of the EPS beam. A beam-type specimen on the order of 100 mm (4 in.) wide, and 300 mm (12 in.) long, and 25 mm (1 in.) thick is subjected to transverse load (18). However, the test method also provides recommended test specimen sizes based on the geometric setup of the test apparatus. As with other basic tests, the loading rate to failure (physical rupture of the EPS beam) is fairly rapid. The ASTM test method allows for some variation in strain rates (18). The flexural strength is defined as the calculated maximum-fiber stress at the time of rupture of the specimen (18). As can be seen in Figure 2.15, flexural strength correlates well with tensile strength which validates the assumption that flexural tests can be used routinely as a measure of bead fusion during the manufacture of EPS. No information is available regarding actual

2-51 specimen dimensions and strain rates used to obtain the data in Figure 2.15. No long-term test data is known to exist for the flexure mode of loading (18). Figure 2.15. Strength of block-molded EPS in various test modes as a function of density (18). Shear Introduction There are two modes of shear that are of interest: • internal shear strength within a specimen of EPS and • external shear strength (sliding resistance) between EPS blocks or between an EPS block and a dissimilar material (soil, other geosynthetic, etc.). These modes of shear are discussed separately. Internal The internal shear strength of EPS is measured by loading a test specimen fairly rapidly until the maximum shear stress is reached, whether or not this stress produces a physical rupture of the test specimen. ASTM test method C 273 (54) addresses internal shear strength of geofoam. However, this standard test method addresses the testing of cores of structural “sandwiches” or composites (18). The correlation between shear strength of EPS block and EPS density is shown in Figure 2.15. The test values for shear strength were obtained by (18) from (29). Specimen dimensions and testing strain rate are not provided in (18). Because the shear strength of EPS block exhibits a correlation with compressive strength, experience indicates that the shear strength test is rarely performed in practice for either MQC/MQA or engineering design. External Introduction to External (Interface) Properties. Interface friction, primarily along horizontal surfaces, is an important consideration in external and internal stability assessments under horizontal loads such as wind, unbalanced water head, or seismic shaking. Thus, tests to

2-52 assess interface friction between the surface of EPS blocks and a variety of other materials is of interest in projects where significant horizontal design loads or internal sliding can occur. Two types of interfaces that are of interest for EPS-block geofoam in lightweight fill applications include an EPS/EPS interface and an EPS/dissimilar material interface. EPS/EPS Interface. The interface friction between two pieces of EPS has been studied by a number of researchers (19). Unfortunately, the lack of a standard test method has meant that a range of test variables (specimen size, specimen preparation, smoothness of specimen surface, test setup, loading rate, etc.) have been used. In particular, a large effect on the EPS/EPS interface strength is the smoothness of the EPS surface. The smoothest surface is obtained from a relatively smooth molded face of a full-size block and the roughest from a piece of EPS cut from a block. Although there is no standard method for EPS/EPS interface tests, the typical procedures that have been used involve placing two pieces of EPS in contact along a single horizontal surface; subjecting the contact to a vertical normal stress; then horizontally shearing one piece of EPS (typically the upper one) relative to the other while measuring the horizontal displacement and force required for movement, which is similar to direct shear testing (ASTM D 5321) in soils and geosynthetics testing. Based on a review of existing shear strength data between two pieces of EPS (19), the shearing resistance can be defined adequately by the classical Coulomb (dry) friction equation: τ = σn ∗ (µ) =σn ∗ (tanδ) (2.14) where τ = interface shear resistance, σn = applied normal stress on interface, µ = friction coefficient = tan δ, and δ = EPS/EPS interface friction angle. When the interface shear resistance, τ , is plotted against normal stress, a linear relationship indicative of a classical Coulomb behavior is obtained. The data does not show a

2-53 post-peak strength loss and thus a residual interface friction angle is not reported. Previous testing also indicates that the value of δ is independent of EPS density because shearing occurs on the surface of the specimen, although the normal stress is assumed to be low enough that excessive deformation of the EPS did not occur (19). Because of variations in specimen dimensions, displacement rate, roughness of the EPS surfaces, and other factors, a range in EPS/EPS interface friction angles have been reported. All reported values fall within the range between µ = 0.5 to 0.7, with µ = 0.64 the value reported in the most extensive and detailed published study to date that was performed in Japan (19). The corresponding values of δ are 27 degrees to 35 degrees with δ = 32 degrees found for the Japanese study (19). For routine design, it is recommended that δ = 30 degrees be used. As indicated by Equation (2.14), shear stress is dependent on the applied normal stress. The normal stress that will act between blocks of EPS for lightweight fill applications will typically be small (18). Therefore, the corresponding shear resistance between blocks will also be small. Consequently, the use of mechanical connectors are sometimes required to increase the shear resistance between blocks. The use of mechanical connectors is discussed in Chapter 6. In view of the lack of a standardized test protocol, it is recommended that the standard test method for geosynthetic interface friction, D 5321 (55) be adopted for determining the EPS/EPS interface friction. However, ASTM D 5321 allows other direct shear devices (ASTM D 3080 (56)) to be used for geosynthetic shear testing if the device yields similar results as the large-scale direct shear box. It should be further required that test specimens should be prepared so that shearing occurs only along the relatively smooth molded exterior surfaces of the EPS block to produce a conservative estimate of the interface friction angle. The surfaces of the EPS also should be free of any small indentations or projections that can be created by the walls of the steel block mold.

2-54 EPS/Dissimilar Material Interfaces. A significant gap in the published literature exists for interface friction values between EPS block and other materials likely to be encountered in lightweight fills such as planar geosynthetics (chiefly geotextiles and geomembranes) as well as poured-in-place portland cement concrete (PCC). Two locations within the embankment where these dissimilar materials may be utilized include as a separation layer between the pavement system and the EPS blocks and as a separation layer between the EPS blocks and the natural foundation soil. The use of separation materials between the top of the EPS blocks and the overlying pavement system is discussed in Chapter 4. Materials that are sometimes utilized between the pavement system and the EPS blocks include a geotextile, geomembrane, a PCC slab, geogrid, geocell with soil or PCC fill, soil cement, and pozzolanic stabilized materials. Materials that are sometimes utilized between the EPS blocks and the natural foundation soil include granular material such as sand and geotextiles. The only published data on interface friction with dissimilar materials involves EPS/sand interfaces and the results indicate that δ equals the Mohr-Coulomb angle of internal friction (φ) of the sand (57,58). Whether this is the peak or constant-volume (critical state) value of φ for the sand was not identified. However, it appears reasonable that the choice would depend on the relative magnitude of shear strain, with a peak value (which is stress dependent) appropriate for small strains and a constant-volume value (which is usually assumed to be stress independent) for large strains. For design purposes a peak value of the sand friction angle can be used because it is undesirable for the embankment to undergo large strains. A friction coefficient, µ, of 0.5 was reported for a sand with similar grain shape and gradation of Ottawa sand (59). This is equivalent to a friction angle of 27 degrees. An average friction angle of 33 degrees was obtained from interface shear strength tests performed between EPS and bedding sand tested over a stress range of 25 kPa (522 lbs/ft2) to 40 kPa (835 lbs/ft2) (58). In summary, the EPS/sand interface friction appears to range from 27 degrees to 33 degrees which is typical for the φ of a sand. In (60), it is

2-55 suggested that the friction coefficient between EPS blocks and soil is approximately 0.5 (δ=27 degrees). However, the type of soil was not indicated. Various sliding situations may need to be evaluated during design depending on the types of materials that are placed, if any, between the EPS blocks and the natural foundation soil. For example, if a sand layer is placed between the EPS blocks and natural foundation soil, the friction between the EPS and sand as well as the sand and foundation soil will need to be considered. The interface friction angle between the sand and the underlying natural foundation soil will be dependent on the type of natural soil as well as type of sand. However, it is suggested that for preliminary design of retaining walls where well compacted sharp-grained sand or sand with gravel is placed between the foundation of a retaining wall and a natural silt or clay that a friction angle of 20 degrees can be assumed between the sand and the underlying silt or clay (5). Because the use of an EPS-block geofoam embankment will typically be used over soft soils, the case of sliding occurring within the soft soil must also be considered. It is indicated in (5) that if the undrained shear strength, su, of the underlying soil is less than the frictional resistance beneath any part of a retaining wall base, sliding will occur by undrained shear within the soil at some distance below the base. Additional sliding cases will need to be considered if geosynthetics are used between the EPS blocks and the natural soil which can be measured using site specific interface shear testing. Geosynthetic interface testing was conducted during this study to evaluate the interface shear resistance between EPS-block geofoam and a nonwoven geotextile and a gasoline containment (GC), i.e., gasoline resistant, geomembrane. These interfaces are common in EPS- block geofoam embankments and thus are considered in the internal stability analysis described in Chapter 6. Large-scale direct shear and torsional ring shear tests were conducted on EPS-block geofoam/nonwoven geotextile and EPS-block geofoam/GC geomembrane interfaces. The geosynthetics used in the interface shear testing are listed below.

2-56 • Geofoam: EPS-block geofoam with a unit weight of 20 kg/m3 (1.25 lbf/ft3). This geofoam was manufactured by Wisconsin EPS, Inc. in Fond Du Lac, Wisconsin. • Nonwoven Geotextile: A nonwoven, polypropylene geotextile with a mass per unit area of 205 g/m2 (6 oz/yd2). This geotextile was manufactured by Polyfelt Americas of Atlanta, Georgia. • Gasoline Containment (GC) Geomembrane: A minimum 0.76 mm (30 mils) thick, smooth tri-polymer alloy geomembrane that is manufactured by Seaman Corporation of Wooster, Ohio. The geomembrane can contain both diesel fuel and gasoline. The shear testing was conducted to simulate the stress conditions in EPS-block geofoam embankments and thus three effective normal stresses were used for the testing, 12, 20 or 21, and 26 kPa (250, 426 or 436, 550 lbs/ft²). Therefore, at least three interface shear tests were conducted for each geotextile and geomembrane interface. Interface Shear Testing Procedure Large-scale direct shear and torsional ring shear tests were conducted on the geofoam interfaces. To facilitate the required testing, it is desirable to use a ring shear device instead of the large-scale direct shear box required by ASTM D 5321. ASTM D 5321 allows other shear devices to be used for geosynthetic shear testing if they yield similar results as the large-scale direct shear box. To investigate this substitution, large-scale direct shear tests were conducted on the same geofoam interfaces that were tested in the torsional ring shear device. The direct shear tests were performed in accordance with ASTM D 5321 using a 305 mm (12 in.) by 305 mm (12 in.) upper geosynthetic specimen that was sheared over a 305 mm (12 in.) by 356 mm (14 in.) lower geosynthetic specimen. The direct shear normal stresses are applied pneumatically and the same shear displacement rate 0.37 mm/min (0.0144 in./min) that was used for the ring shear tests

2-57 were used for the direct shear tests to avoid displacement rate-related discrepancies in the test results. The successful use of a torsional ring shear apparatus to measure the shear strength of geosynthetic/geosynthetic and geosynthetic/soil interfaces is described in (61-63). The torsional ring shear apparatus is much easier to use than the large-scale direct shear box and allows: (a) unlimited continuous shear displacement to occur in one direction, resulting in the development of a true residual strength condition; (b) a constant cross-sectional area during shear; (c) minimal laboratory supervision; and (d) data acquisition techniques to be readily used. A modified Bromhead ring shear apparatus was used to measure the shear strength of the geofoam/geosynthetic interfaces. A modified specimen container was used to hold the bottom interface component in place. In tests on geosynthetic/geosynthetic interfaces, the knurled porous stone in the specimen container is replaced with a plastic insert to secure the appropriate geosynthetic. The insert is fastened to the specimen container using four screws. Specifically, an annular geofoam specimen with an inside and outside diameter of 40 and 100 mm (1.6 and 3.9 in.), respectively, is secured to the plastic insert using an adhesive. The other interface component is adhered to the top (loading) platen. The normal stress is applied by dead weight to the top platen, which sits on top of the specimen container. During shearing, the bottom interface component moves with respect to the stationary top interface component. All of the shear displacement values and shear displacement rates reported herein were calculated using a diameter of 70 mm (2.8 in.), which is the average diameter of the annular specimen. Geofoam And Geosynthetic Specimen Preparation Procedure The EPS-blocks were cut into square and annular shapes using a hot-wire cutter for the direct shear and torsional ring shear testing, respectively. The geofoam was always placed in the specimen container and the geomembrane or geotextile was secured to the top platen. The molded exterior surface was used as the shearing interface to produce an estimate of the field interface shear resistance.

2-58 The geomembrane specimens were cut from a geomembrane sheet using a hydraulic jack and steel die that is the same size and shape as the required specimen. An adhesive was used to secure the geomembrane specimen to a plastic insert that fits into the top platen of the direct shear box. The geofoam specimen was cut so that it fit into the 305 mm (12 in.) by 356 mm (14 in.) lower container. A thin coat of epoxy was used to adhere the geofoam and geomembrane to a plastic insert for the bottom specimen container and the top platen, respectively, of the torsional ring shear device. The epoxy was allowed to cure for 24 hours under a normal stress of 12 kPa (250 lbs/ft2). The curing normal stress did not exceed the normal stress at which the tests were conducted and thus the specimens were normally consolidated at the time of testing. The curing normal stress aided bonding of the geosynthetics and minimized vertical displacement caused by the epoxy adhering procedure during testing. The geomembrane and specimen container/top platen were marked to ensure that the geomembrane did not slip during shearing. The geotextile specimens were cut into square and annular shapes using scissors and/or a razor blade knife. The nonwoven geotextile specimens were secured to the top platen in the direct shear or torsional ring shear devices. To secure the geotextile in the direct shear box, the geotextile was wrapped around the edges of the upper platen and secured using a metal bar that is screwed into the top platen. To secure the geotextile to the top platen in the torsional ring shear device, the geotextile was initially glued to a smooth high-density polyethylene (HDPE) geomembrane ring that was cut to the same size as the geomembrane specimen. The geotextile was cut in a circle with a diameter of approximately 160 mm (6.3 in.), which is larger than the outside diameter of the ring shear specimen (100 mm (3.9 in.)). A small circular hole (roughly 20 mm (0.8 in.)) was cut in the center of the geotextile specimen so that the centering pin of the ring shear apparatus was not interfered with. The HDPE geomembrane ring was then glued to the geotextile using a thin coat of epoxy. A 2-3 kg (4.4-6.6 lb) mass was placed on the geotextile/geomembrane ring to aid adhesion. After about 15 minutes of drying, the geotextile extending beyond the edge of the

2-59 geomembrane ring was cut so that eight wedges or flaps of geotextile that were equal in size and spacing remained. Epoxy was applied to the back of the smooth geomembrane and the eight geotextile wedges were folded over and adhered to the backside of the smooth geomembrane. The 2-3 kg (4.4-6.6 lb) mass was reapplied for roughly 45 minutes. This wrapping of the geotextile around the geomembrane ring prevented geotextile fibers from readily pulling out during shearing. This procedure was also used so epoxy did not contaminate the geotextile fibers that would be in contact with the geofoam and thus produce dubious values of shear resistance. The geotextile/geomembrane ring system was secured to the top platen using a thin coat of epoxy. The side with the eight wedges was adhered to the top platen. The top platen with the attached geotextile specimen was then placed in the ring shear apparatus on top of the specimen container, to which the geofoam specimen was adhered. A sacrificial geotextile cushion was placed between the geofoam and geotextile so that there was no contact between the interface components before shearing. The epoxy was allowed to cure for 24 hours under a normal stress (12 kPa (250 lbs/ft2)) that did not exceed the normal stress at which the test was to be conducted. The top platen and geotextile were also marked to ensure that the geotextile did not slip during shearing. After allowing the epoxy to cure for 24 hours, the sacrificial geotextile was removed and the two interface components were placed in contact such that no relative displacement occurred between them prior to shearing. The ring shear apparatus was then loaded to the shearing normal stress using a load increment ratio of 1.0. Once the desired normal stress was applied, the interface system was allowed to equilibrate for about 20 minutes before shearing started. Comparison of Large-Scale Direct Shear and Torsional Ring Shear Tests Large-scale direct shear tests were conducted at one normal stress for comparison with results on the same interfaces tested in the torsional ring shear device. Figure 2.16 presents a comparison between the shear stress-displacement relationships obtained from the large-scale direct shear and ring shear tests on the geofoam/GC geomembrane interface at a normal stress of

2-60 21 kPa (436 lbs/ft²). It can be seen that both test procedures produce similar shear stress- displacement relationships up to a shear displacement of about 100 mm (3.9 in.). At this displacement, the direct shear test is stopped because the travel of the direct shear box is limited. However, this is enough shear displacement to measure the peak shear resistance and the peak friction angle. The direct shear and ring shear tests yielded peak friction angles of 53 and 56 degrees, respectively, for this normal stress. These friction angles are in agreement and a similar agreement was obtained for the geofoam/nonwoven geotextile interface. This agreement is expected because shearing occurred on the surface or outside of the EPS. As a result, the torsional ring shear device was used for the majority of the testing of the two geofoam interfaces. The main difference between the ring shear and direct shear test methods is in the values obtained for the residual friction angle and shear displacement at the residual strength. The direct shear test terminates at a shear displacement of approximately 100 mm (3.9 in.) and, thus, the resulting friction angle does not correspond to a residual friction angle whereas the ring shear test was conducted until a constant minimum, i.e., residual, strength was reached. In summary, it was assumed that the ring shear device yields similar results to the large- scale direct shear apparatus for the normal stresses and geomembrane and geotextile interfaces considered herein and could be used as a substitute for the direct shear apparatus as suggested in ASTM D 5321. The ring shear device was chosen because ring shear tests are easier and more cost effective to perform than large-scale direct shear tests. This is mainly due to the fact that a much larger specimen is required for the direct shear test. Figure 2.16. Comparison of large-scale direct shear and torsional ring shear tests on geofoam/GC geomembrane interface at a normal stress of 21 kPa (436 lbs/ft2). Geofoam/GC Geomembrane Interface Test Results Figure 2.17 presents a comparison between the shear stress-displacement relationships obtained from the ring shear tests on the geofoam/GC geomembrane interface at a normal stresses of 12.0, 21, and 26 kPa (250, 436, 550 lbs/ft²). It can be seen that the geofoam/geomembrane

2-61 interface exhibits a peak and residual strength at each of the three normal stresses. These three shear stress-displacement relationships were used to develop the peak and residual failure envelopes for this interface that are presented in Figure 2.18. It can be seen that the failure envelopes correspond to peak and residual interface friction angles of approximately 55 and 43 degrees, respectively. Therefore, the shear strength of the geofoam/GC geomembrane interface is extremely high, which is attributed to the bonding or sticking that was observed between the geomembrane and the surface of the EPS specimen. Figure 2.17. Shear stress-displacement relationships for the geofoam/GC geomembrane interface at normal stresses of 12, 21, and 26 kPa (250, 436, 550 lbs/ft²). Figure 2.18. Peak and residual failure envelopes for the geofoam/GC geomembrane interface at normal stresses of 12, 21, and 26 kPa (250, 436, 550 lbs/ft2). Geofoam/Nonwoven Geotextile Interface Test Results Figure 2.19 presents a comparison between the shear stress-displacement relationships obtained from the ring shear tests on the geofoam/nonwoven geotextile interface at a normal stresses of 12, 20, and 26 kPa (250, 426, 550 lbs/ft²). It can be seen that the geofoam/nonwoven geotextile interface also exhibited a peak and residual strength at each of the three normal stresses. As shown in Figure 2.20, these three shear stress-displacement relationships correspond to peak and residual friction angles of approximately 25 and 18 degrees, respectively. The shear strength of the geofoam/nonwoven geotextile is significantly lower than the geofoam/GC geomembrane interface because the geotextile did not stick or bond to the geofoam. As a result, a geofoam/nonwoven geotextile interface is more critical than a geofoam/geomembrane interface for internal stability analyses. Figure 2.19. Shear stress-displacement relationships for the geofoam/geotextile interface at normal stresses of 12, 20, and 26 kPa (250, 426, 550 lbs/ft2). Figure 2.20. Peak and residual failure envelopes for the geofoam/geotextile at

2-62 normal stresses of 12, 20, and 26 kPa (250, 426, 550 lbs/ft2). Summary of EPS Interface Strengths The following conclusions are based on the data and interpretations of the interface friction data presented in this section: • It is recommended that an EPS/EPS interface friction angle of 30 degrees be used for design • It is recommended that an EPS/nonwoven geotextile interface friction angle of 25 degrees be used for design if the geotextile is the same or substantially similar to the geotextile used in this study. • It is recommended that an EPS/GC geomembrane interface friction angle of 52 degrees be used for design if the geomembrane is the same or substantially similar to the GC geomembrane used in this study. • Based on the results reported in (58,59) an interface friction angle of 30 degrees can be used for an EPS/sand interface for preliminary analysis. • Site specific interface testing should be conducted to ensure that representative values of interface friction angle are being used for external and internal stability calculations. EPS interface friction tests can be conducted using ASTM standard test method D 5321. If preferred, the test results obtained herein suggest that torsional ring shear tests can be substituted for the large-scale direct shear tests specified in ASTM D 5321. THERMAL PROPERTIES Although the thermal insulation function of EPS-block geofoam is not a primary concern for the function of lightweight fill, some knowledge of the geothermal properties of EPS is necessary to understand the potential problems of differential icing and solar heating. These

2-63 problems are discussed in Chapter 4. The key aspects of the thermal behavior of EPS-block geofoam are: • The coefficient of thermal conductivity of EPS block in the as-molded (dry) state varies with both EPS density and ambient temperature as shown in Figure 2.21. Thermal conductivity defines the rate of heat flow through the EPS. The smaller the coefficient of thermal conductivity, the more efficient the EPS is as a thermal insulator. Figure 2.21. Coefficient of thermal conductivity, k, for dry, block-molded EPS (18). • EPS block will absorb water with time once placed in the ground. The magnitude of absorbed water (which is traditionally expressed on a relative volume basis, not relative weight basis as for soil) can vary widely and is a function of many variables, with thickness of the piece of geofoam one of the more important variables. Therefore, it is not possible to give typical values or even a range of values for absorbed water that apply to EPS-block geofoam usage in roadway embankments. However, the coefficient of thermal conductivity is expected to increase with increasing water content, which means that the EPS loses some of its thermal efficiency with increasing water content. • Overall, EPS-block geofoam is a very efficient thermal insulator compared to soil. A general rule is that dry EPS-block geofoam is 30 to 40 times more efficient thermally compared to soil, e.g. 1 mm (0.04 in.) of EPS will have the same thermal-insulation effect as 30 to 40 mm (1.2 to 1.6 in.) of soil. REFERENCES 1. “Pentane Emissions during Processing.” Technical Bulletin N-840, BASF Corporation, Jamesburg, New Jersey (1999) 4 pp. 2. Bartlett, P. A., “Expanded Polystyrene Scrap Recovery & Recycling.” ARCO Chemical Company (undated) . 3. Bartlett, P. A., “Letter report to unnamed customer 11 September.” ARCO Chemical Company, Newtown Square, PA (1986) .

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2-65 23. Preber, T., Bang, S., Chung, Y., and Cho, Y., “Behavior of Expanded Polystyrene Blocks.” Transportation Research Record No. 1462, Transportation Research Board, Washington, D.C. (1994) pp. 36-46. 24. Athanasopoulos, G. A., Pelekis, P. C., and Xenaki, V. C., “Dynamic Properties of EPS Geofoam: An Experimental Investigation.” Geosythetics International, Vol. 6, No. 3 (1999) pp. 171-194. 25. Duskov, M., “Materials Research on Expanded Polystyrene Foam (EPS).” Report 7-94- 211-2, Delft University of Technology, Delft, The Netherlands (1993) . 26. Horvath, J. S., “Discussion: Status of ASCE Standard on Design and Construction of Frost Protected Shallow Foundations by L.S. Danyluk and J.H. Crandell.” Journal of Geotechnical and Geoenvironmental Engineering, , (1999) . 27. Duskov, M., “EPS as a Light-Weight Sub-Base Material in Pavement Structures,” Doctor of Engineering thesis, Delft University of Technology, Delft, The Netherlands (1998). 28. “Earthwork; Soil Stabilization.” SPEC-DATA  Section 02200, AFM Corporation, Excelsior, Minn. (1994) 4 pp. 29. “Styropor®; Construction; Highway Construction/Ground Insulation.” BASF, AG, Ludwigshafen, Germany (1991) 12 pp. 30. Magnan, J.-P., and Serratrice, J.-F., “Propriétés mécaniques du polystyréne expansé pour ses applications en remblai routier.” Bulletin Liaison Laboratoire Ponts et Chaussées, , No. 164 (1989) pp. 25-31. 31. van Dorp, T., “Expanded Polystyrene Foam as Light Fill and Foundation Material in Road Structures (preprint paper).” The International Congress on Expanded Polystyrene: Expanded Polystyrene- Present and Future, Milan, Italy (1988) . 32. “Styropor®; Processing; Measurements/Tests.” Technical Information Bulletin No. 0- 220e, BASF AG, Ludwigshafen, Germany (1990) 4 pp. 33. Horvath, J. S., Personal Communication. 34. “Utilisation de Polystyrene Expanse en Remblai Routier; Guide Technique.” Laboratoire Central Ponts et Chaussées/SETRA, France (1990) 18 pp. 35. Kutara, K., Aoyama, N., and Takeuchi, T., “Earth Pressure Test of Retaining Wall Using EPS as Back-filling Material.” Technical Reports of Construction Method Using Expanded Polystrol, Expanded Polystyrol Construction Method Development Organization, Tokyo (1989) . 36. “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. 37. Negussey, D., and Jahanandish, M., “Comparison of some engineering properties of expanded polystyrene with those of soils.” Transportation Research Record, Vol. 1418, (1993) pp. 43-48. 38. Zou, Y., and Leo, C. J., “Laboratory Studies on the Engineering Properties of Expanded Polystyrene (EPS) Materials for Geotechnical Applications.” 2nd International Conference on Ground Improvement Techniques: 8-9 October 1998,1998, Singapore, pp. 581-588. 39. Horvath, J. S., “Mathematical Modeling of the Stress-Strain-Time Behavior of Geosythetics Using the Findley Equation: General Theory and Application to EPS-Block Geofoam.” Research Report No. CE/GE-98-3, Manhattan College, Bronx, N. Y. (1998) . 40. Sun, M. C.-W., “Engineering Behavior of Geofoam (Expanded Polystyrene) and Lateral Pressure reduction in Substructures,” M.S. thesis, Syracuse University, Syracuse (1997). 41. Wu, Y., “An Investigation of Long-Term Deformation Behavior of EPS Block Under Static & Repeated Loads,” M.S. thesis, South Dakota School of Mines and Technology, Rapd City (1996).

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FIGURE 2.1 PROJ 24-11.doc 2-68

FIGURE 2.2 PROJ 24-11.doc EPS Density (kg/m3) 5 10 15 20 25 30 35 40 45 In iti al Ta n ge n t Y o u n g's M o du lu s (M Pa ) 0 5 10 15 20 AFM [28] Eriksson & Trank [17] Equation 2.1 Magnan & Serratrice [30] van Dorp [31] BASF [29] 2-69

FIGURE 2.3 PROJ 24-11.doc 2-70

FIGURE 2.4 PROJ 24-11.doc EPS Density (kg/m3) 0 5 10 15 20 25 30 35 40 45 St re ss (k Pa ) 0 50 100 150 200 250 300 Compressive Strength (Eq.2.3) Yield (Eq. 2.4) Yield (Eq. 2.5) Yield (Eq. 2.6) 2-71

FIGURE 2.5 PROJ 24-11.doc 2-72

FIGURE 2.6 PROJ 24-11.doc Compressive strain (%) 0 10 20 30 40 50 60 Co m pr es siv e st re ss (k Pa ) 0 10 20 30 40 2-73

FIGURE 2.7 PROJ 24-11.doc Time, t (days) -100 0 100 200 300 400 500 To ta l S tr ai n, ε (% ) 0 1 2 3 D=Specimen Diameter H=Specimen Height Wu [41], Disc, H=25 mm, D=47 mm Modified Findley Equation General Power-Law Equation Duskov [27], Cylindrical, H=300 mm, D=150 mm Duskov [27], Cylindrical, H=200 mm, D=100 mm 2-74

FIGURE 2.8 PROJ 24-11.doc t ε Primary Secondary Tertiary σ x Rupture 2-75

FIGURE 2.9 PROJ 24-11.doc Density = 14.5 kg/m3 Time, t (days) 0.1 1 10 100 1000 To ta l S tr ai n, ε (% ) 0 2 4 6 8 10 12 14 Compressive stress = 35 kPa 30 kPa 15 kPa Density = 23.5 kg/m3 Timet, t (days) 0.1 1 10 100 1000 To ta l S tr ai n, ε (% ) 0 2 4 6 8 10 12 14 Compressive stress = 70 kPa 50 kPa 30 kPa Density = 32.5 kg/m3 Time, t (days) 0.1 1 10 100 1000 To ta l S tr ai n, ε (% ) 0 1 2 3 4 5 Compressive Stress = 100 kPa 60 kPa 80 kPa 2-76

FIGURE 2.10 PROJ 24-11.doc 2-77

FIGURE 2.11 PROJ 24-11.doc Time, t (days) 0 100 200 300 400 500 To ta l S tr ai n , ε (% ) 0 5 10 15 20 25 30 Public Work s Inst itute [3 6] Gene ral Po wer - Law Equa tion Modified Findley Equation Disc-shaped specimen 2-78

FIGURE 2.12 PROJ 24-11.doc Time, t (days) 0 10 20 30 40 50 60 70 To ta l S tr ai n, ε (% ) 0 5 10 15 20 25 30 Ge ne ra l P ow er - La w Eq ua tio n Average Measur ed (Aabφ e [48]) Modified Findley Equation 2-79

FIGURE 2.13 PROJ 24-12.doc Time, t (days) 0 200 400 600 800 1000 1200 1400 To ta l S tr ai n , ε (% ) 0 1 2 3 4 General Power-Law Equation Modified Findley Equation Average Measured (Aaboe [48], [49]) 2-80

FIGURE 2.14 PROJ 24-11.doc Time, t (days) 0 1000 2000 3000 4000 5000 To ta l S tr ai n , ε (% ) 0 5 10 15 20 25 30 Ge ne ra l P ow er - La w Eq ua tio n Modified Findley Equation Average Measured (Aaboe [48]) 2-81

FIGURE 2.15 PROJ 24-12.doc EPS density (kg/m3) 10 15 20 25 30 35 40 St re n gt h (kP a) 0 100 200 300 400 500 tension flexure shear compression (10% strain criterion) 2-82

FIGURE 2.16 PROJ 24-12.doc 2-83

FIGURE 2.17 PROJ 24-12.doc 2-84

FIGURE 2.18 PROJ 24-12.doc 2-85

FIGURE 2.19 PROJ 24-12.doc 2-86

FIGURE 2.20 PROJ 24-12.doc 2-87

FIGURE 2.21 PROJ 24-12.doc EPS density (kg/m3) 20 40 60 80 100 Co ef fic ie n t o f t he rm al co n du ct iv ity (m W /m - K ) 0 10 20 30 40 50 + 40 C - 40 C 0 C 2-88

TABLE 2.1 PROJ 24-11.doc Temperature Range Rate of Change Comment less than 0°C (+32°F) 0% Remains approximately constant +23°C (+73°F) to 0°C (+32°F) +7% per 10°C (18°F) Increases linearly with decreasing temperature +23°C (+73°F) to +60°C (+140°F) -7% per 10°C (18°F) Decreases linearly with decreasing temperature Note: EPS does not become brittle even at -196°C (-321°F). EPS melts between +150°C (+302°F) and +260°C (+500°F). 2-89

TABLE 2.2 PROJ 24-11.doc Density Temperature Stress Duration Strain Strain Increase 20 kg/m3 (1.25 lbs/ft3) +23 °C (+73°F) 30 kPa (626 lbs/ft²) 2,400 hours (approx. 3 months) 0.8% 0% +60 °C (+140 °F) 1.5% 88% +23 °C (+73 °F) 40 kPa (835 lbs/ft²) 2,400 hours (approx. 3 months) 1.1% 0% +60 °C (+140 °F) 3.25% 195% 2-90