Numerical modeling of EPS geofoam used with swelling soil

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Geotextiles and Geomembranes 15 (1997) 133-146 © 1998 Elsevier Science Limited

Printed in Great Britain. All fights reserved 0266-1144/97 $17.00

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Numerical Modeling of EPS Geofoam used with Swelling Soil

Mustafa Aytekin

Civil Engineering Department , Karadeniz Technical University, Trabzon TR-61080, Turkey

A BSTRA CT

The cost associated with damage due to swelling soils is more than double the cost associated with damage from floods, hurricanes, tornadoes, and earth- quakes. This paper illustrates the numerical modeling of block molded expanded polystyrene, (EPS) geofoam, used as a compressible inchtsion between expansive soils and a retaining structure. In several hypothetical cases, the reduction on the transmitted lateral pressures on a retaining structure is determined with different thieknesses of EPS. The reduction on the transmitted lateral pressures are compared with the reduction of granular backfill. © 1998 Elsevier Science Ltd.

INTRODUCTION

Many basement walls and earth retaining structures, with the exception of fully embedded walls in natural ground, support soil that has been placed against the structure. If the backfill is compressible enough, transmitted lateral pressure on the structure would be reduced. Otherwise, the transmitted lateral pressure could be very high so that design loads would make the structure uneconomical.

Traditionally, high-quality granular material has been used as backfill to retaining structures. However, in some areas, granular materials are becoming scarce, and the use of lower quality cohesive materials may result in significant savings in backfill costs (Symons et al., 1989). The properties of cohesive soil vary with its water content and due to low permeability of cohesive soil, changes in volume of the backfill and in lateral earth pressure acting on a retaining structure

133

134 M. Aytekin

could continue for many years after construction is completed. When cohesive soils are used as backfill material, additional uncertainties are introduced into design. Thus, materials such as EPS geofoam with known properties could be used as backfill between retaining structures and expansive soil.

In order to consider volume change of expansive soil behind earth retaining structures a finite element code was developed by Aytekin (Aytekin, 1992; Aytekin et al., 1994). When soil swell occurs against a rigid structural member such as a retaining wall, the unexpected lateral forces can cause damage. The forces induced must be controlled within acceptable limits and the structural member designed to withstand the expected forces. To reduce and control the lateral pressure distribution behind the structure, a soil investigation prior to the start of construction will identify the extent of soil expansion to be expected, and this information can be used to select the required dimensions of compressible fill material required.

MECHANISMS OF SWELLING IN EXPANSIVE SOILS

Van der Waal forces include three types of weak electrical attractive forces, namely dipole-dipole attraction forces, induction effect forces, and London forces (Snethen, 1979). The influence of van der Waal forces is rapidly overcome by the development of the double layer (White, 1979) under conditions where water is attracted to the clay mineral.

In most cases, three mechanisms are primary sources of expansion. It has been concluded that for samples compacted with a moisture content more than optimum water content, swelling is caused by osmotic repulsive pressures, and for samples compacted dry of optimum water content, swelling is influenced by factors, such as cation hydration and attraction of the clay particle surface for water, London van der Waal forces, elastic rebound, particle orientation, and presence of air, in addition to osmotic pressures (Ladd, 1960). Ladd also points out a type of categorization of the range of the basic mechanisms in a very general sense. In other words, his concept of osmotic repulsion controlling volume change above optimum water content and cation hydration and clay particle attraction plus the other less significant factors having a greater influence below optimum water content was a major step toward a better understanding of the volume change phenomenon. Any volume increase in the saturated clay can be considered as an equal increase in the volume of water in the clay. In Fig. 1, a clay particle is immersed in pure water. Sufficient exchangeable cations surround the particle so that the cations plus the particle constitute an electrically neutral system. This system is designated the clay 'micelle'. The ions and water within the micelle constitute the double layer.

Numerical modeling of EPS geofoam used with swelling soil

- - Boundary of double layer

" ~ (Z) '2

Y @,,IG " i (!) '~, ", / e e,,le

\ ~.\ \ \ /II

Exchangeable cations

Fig. 1. The clay micelle in pure water.

135

The pressures between clay particles basically responsible for swelling are R, the repulsive pressure that arises f rom the interaction of the double layers associated with the two clay particles, and A, the total at tract ion pressure as seen in Fig. 2.

The magni tude of rebound of an unloaded specimen in a s tandard conso- l idation test is directly related to the decrease in effective stress. The effective

A

!

¢--

R

2d Fig. 2. Pressures between two clay particles.

136 M. Aytekin

stress can be related to physico-chemical forces acting between clay particles:

a ' - ~ R - A , (1)

where o-'= effective stress. The value of R must be greater than the value of A for swelling to occur in an expansive soil. It is generally believed that this repulsive pressure has several components:

(1) The most important component is caused by an osmotic pressure arising from the higher ion concentration in the double layer of the clay micelle than in the free pore water.

(2) The effect of secondary valance or London van der Waal's forces on the water surrounding clay particles.

(3) The effect of the negative electric field on the double layer of water.

There are no data in the technical literature from which a definite conclusion can be drawn relative to the magnitude of influence of the last two factors on swelling.

The rest of the mechanisms that affect the swelling phenomenon are cation hydration, capillary imbibition, and elastic relaxation. Physical hydration of cations are substituted into or attached to the clay particle. When cations hydrate, their ionic radii increase, resulting in a net volume change of the soil mass. Movement of water into a mass of clay is called capillary imbibition. Compressive forces are applied to the clay particles by the menisci of the water in the pores. When free water becomes available to the unsaturated clay mass, the pore water menisci begin to enlarge and compressive forces exerted on the clay particles are relaxed. The capillary film will enlarge and result in a volume change of soil or act as water source for one of the other swelling mechanisms. The last mechanism affecting the swelling of clays is elastic relaxation, which is readjustment of clay particles due to some change in the diagenetic factors. Because of particle reorientation and changes in soil structure, volume changes of soil mass occur.

In the field, most of the process involving soil-water interaction occur while the soil is in an unsaturated condition. The formulation and solution of unsaturated soil problems very often require the use of indirect methods of analysis, based on approximations or numerical techniques. For this reason, the development of rigorous theoretical and experimental methods for treating these problems was rather late in coming.

FORCES DUE TO SWELLING OF SOIL MASS

Boundaries of an expansive soil must not be restrained if the soil is to increase in volume, i.e. to swell. The ground surface increases in elevation as expansive soil swells vertically. The ground also swells laterally as well as

Numerical modeling of EPS geofoam used with swelling soil 137

vertically. If the ground surface is cracked and fissured, the lateral increase in volume is accommodated by the cracks or fissures closing as the soil mass expands into the voids of the cracks. However, when there are no cracks or fissures or when they are very small, the soil becomes restrained in the lateral directions. Thus, no volume change occurs and a lateral swelling pressure develops. Using the well-known Finite Element Method (FEM), a soil mass can be divided into small sub regions. Each sub-region is termed as an element.

In order to calculate the swelling forces of each element, swelling strains, which are dependent upon variations of soil suction, must be determined. Thus, the soil suction change in two extreme cases, the driest and the wettest seasons of an average year, must be known. Soil suction envelopes in the two extreme cases can be easily estimated (Aytekin, 1995). Once the initial and the final soil suction values are known for every nodal point on a soil element, average soil suction change for the soil element can be calculated as follows (Aytekin, 1992).

1 ~ ( h f - hi)k, (2) ApF = k=l

where hi and hr are the initial and the final soil suction values in pF for a quadrilateral soil element, respectively. In engineering practice, soil suction is expressed as a positive value in units of pF, which is defined as the logarithm of head in centimeters of water. The pF scale was first introduced by Scho- field (Schofield, 1935) by analogy with pH. The symbol 'p' indicates the logarithmic character, while the symbol 'F' denotes free energy difference measured on a gravity scale. The swelling forces at nodal points are determined as follows.

{Q}sF = [B]T[D]{~swe'l}lJI dsdt, (3)

where {Q}sF is swelling force vector, [D] is the constitutive matrix, and ]J] is the determinant of the Jacobian matrix.

USE OF EXPANDED POLYSTYRENE (EPS) GEOFOAM

A compressible inclusion, in general, is any material that is significantly more compressible than other materials that are in contact with the compressible material. In geotechnical applications, a compressible inclusion is placed between a below-ground structure and the surrounding ground. The compressible inclusion would deform more readily than the other system components under an applied stress or displacement. This phenomenon produces several benefits such as a reduced stress on the

138 M. Aytekin

structure. In many cases, the use of a compressible inclusion is a more cost-effective alternative than designing the structure to withstand the stresses.

In geotechnical applications, usage of EPS geofoam as a compressible inclusion can be categorized as follows:

(1) behind earth retaining structures (2) beneath a grade beam or structural slab (3) above pipes or culverts.

There could be some other applications of EPS as compressible inclusion such as the liner of a tunnel. However, EPS geofoams are used for thermal insulation, lightweight fill, and small-amplitude wave damping. Drainage also can be provided by using a geocomposite consisting of a prefabri- cated drainage composite laminated to one or more faces of a solid EPS block (Horvath, 1995a). A summary of geofoam materials is given by Horvath (Horvath, 1995b). Stiffness of the geofoam in the direction of primary deformation is the most relevant property for compressible inclusion applications. The lowest density of EPS for compressible inclusion applications is desirable as the initial tangent Young's modulus and compressive stress (at 5-10% strain) both decrease with decreasing density of EPS geofoam. The minimum density of EPS block that can be produced depends on several factors related to manufacturing but is in the order of 10kg/m 3. Since there are some difficulties in the usage of EPS geofoam with minimum density, in geotechnical applications, a density somewhat above the minimum but with a greater durability is used. In the USA practice, it has proved useful to use ASTM Standard C578 as an interim standard. The lowest density EPS block covered by this standard is referred as to ASTM type XI. It has a nominal density of 12 kg/m 3 and a minimum density of 11 kg/m 3 (Horvath, 1992).

Elasticity properties of EPS block can be determined by unconfined axial compression test in which (50×50×50)mm 3 specimens are used. In Fig. 3, the curve shows the stress-strain relation of a specimen of Type XI material, which has an actual specimen density of 13 kg/m 3 as would be used for compressible inclusion in the numerical simulation. The stress-strain relation of EPS in Fig. 3 shows 'elasticized' EPS, which is normal EPS that has been modified by an additional manufacturing step.

In geotechnical applications, engineers should request stress-strain data for any EPS product from the supplier. In practice, usage of a compressible inclusion represents a highly indeterminate system that should be analyzed as a soil-structure interaction problem. In order to solve the problem, a numerical technique such as the finite element method should be used.


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NUMERICAL MODELING OF THE PROBLEM

Since the main objective of this paper is to estimate the lateral expansion and transmitted lateral swelling pressure of EPS geofoam backfills behind a retaining structure or a basement wall, a finite element code developed by Aytekin (Aytekin, 1992) is modified and used here.

In the code, the finite element solution technique with an isopara- metric four-node quadrilateral element is used. Volume changes of expansive soils are taken as dependent upon soil suction in pF units.

140 M. Aytekin

Therefore, an analogous comparison to thermal expansion of solids is made.

Complications that the code is programmed to handle include the follow- ing: each finite element may have its own modulus of elasticity, Poisson's ratio, and unit weight different from each other. The code considers initial strains due to swelling of soils as well as the strains due to external loads. Body forces, and surcharge boundary loading (if there is any) are also taken into account.

In order to start off, it is essential to plot the geometry of the problem to scale on a rectangular coordinate grid. Coordinate axes must be chosen carefully such that the total problem is defined within the first quadrant (Fig. 4a). This enables the user to prepare input without any trouble. It is suggested that one nodal point of the problem's geometry should be in the origin of the rectangular coordinate axes. The nodal points of an element must be numbered in sequence counterclockwise. This is the standard local nodal numbering scheme in the program (Fig. 4b). Also, each element must have an assigned number, called an element number. Some- times, plotting the geometry of the problem to scale, numbering the elements and their nodal points, and giving XY-coordinates for each element are somewhat time-consuming. To make this work easier, another

O : N u m b e r o f nodal points

n : Ntanber ot e lements

Retaining wall

D n

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(a)

q

p : node number i ' element number

(b)

Fig. 4. Numbering of finite elements and the nodal points (a) Coordinate axes of a problem, and (b) Local numbering of nodes of the element.

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|11 I l l Retaining wall ,,.~ 11

I l l I l l I l l I l l 111

Fig. 5. The actual finite element mesh with assumed boundary conditions used here to solve the hypothetical considerations.

computer program called MESH has been developed to generate a finite element mesh for the geometry of the problem in the hypothetical cases. The actual finite element mesh used here to solve the hypothetical considerations is seen in Fig. 5.

The program can be used for different geometrical shapes of other problems if little modifications are made. In usage of MESH, a user does not have to plot the geometry of the problem to scale. Only a schematic plotting of the problem is enough.

Before beginning analysis using the program, distributed boundary loads applied to the ground surface or at any other locations in the soil system must be determined as equivalent nodal forces, and must be applied on specified nodal points by defining their direction of application. The direction of application must be horizontal or vertical. No inclined line of action is acceptable to the finite element code. Inclined forces (if there are) must be divided in two components that are vertical and lateral. In the determination of body forces, two-point Gauss quadrature formula is used. In the formu- lae, the weighting functions are unity, and the Gauss points are located at natural coordinates,

Although LATEXP2D has been developed to estimate transmitted lateral swelling pressures generated by a cohesive swelling, cohesive non-swelling, granular soil, expanded polystyrene (EPS) geofoam backfills, etc., acting on retaining structures, it has other capabilities too. For instance, the code can be used to solve the thermal expansion of solid materials with known boundary conditions. However, the material does not have to be homo- genous, the modulus of elasticity may vary within the domain, and problems in a domain that has composed materials like expanded polystyrene (EPS) geofoam as backfill can be solved by the finite element code with or without an expansion.

142 M. Aytekm

HYPOTHETICAL CONSIDERATION OF EPS BACKFILL

Several hypothetical cases are considered to see how the transmitted lateral pressures are affected by the thickness of elasticized EPS backfill as a compressible inclusion between expansive soil and a retaining structure. For this purpose, a rectangular EPS backfill with different thicknesses is considered. The rectangular backfills considered in the hypothetical cases had thicknesses of X = HI20, H/10, and HI5, where H is the height of retaining structure that has been considered in the numerical modeling as seen in Fig. 6. Also, a granular (sand) backfill with a thickness of 1-1/5 m is simulated in the code in order to see the reduction differences on the transmitted lateral pressures. Thus, the reductions due to granular backfill with a thickness of HI5 m and the reductions due to EPS backfills with the thicknesses of/ / /20, H/10, and HI20 m could be compared.

First of all, an unyielding retaining structure has been considered in an in- situ expansive soil without considering any backfill material, and the transmitted lateral swelling pressure distributions on the retaining structure due to expansion of the natural soil has been determined. Then, the same soil and problem was solved with narrow (X=H/20, and X=H/IOm), and wide (X= 1-1/5 m) zones of EPS backfills. Also, X--11/5 m of sand backfill (depth of the retaining wall, H, remained a constant of 3.00 m) has been considered. The shape of the EPS backfills, and granular backfill simulated in the numerical model is seen in Fig. 6.

The modulus of elasticity of soils (Es) is dependent upon water content (Barkan, 1962) and depth (Gibson, 1967) of soil.

Es = Eo + mz, (4)

where the coefficient m is equal to half of the modulus of subgrade reaction

Retaini

l Fig. 6. Rectangular EPS backfill as compressible inclusion.


(ks) of the soil, Eo is the modulus of elasticity of soil at the surface, and z is the depth.

ks m = -- (5) 2

Therefore, in the calculations, the modulus of elasticity for expansive soil is assumed to be a value equal to that of the soil's wet state since the larger swelling pressure would occur when the soil is in the wet state, and Es varies linearly with depth. For an expansive soil, a typical value of Poisson's ratio, vs = 0.3 (Amir & Sokolov, 1980) has been used. The unit weight of expansive soil was taken as 20 kN/m 3. Another soil parameter is the coefficient of the suction change compressibility (Th). In the hypothetical considerations, natural expansive soil is assumed to have 50% of montmorillonite so that the suction compression index (~'h) has been calculated as 0.02367. The suction compression index (Vh) can be calculated as a function of the type and amount of clay in the soil (Aytekin, 1992). Although soil suction change decreases with depth (Aytekin, 1995) in the soil domain, a constant soil suction difference (ApF = 3.0 pF) within the depth of retaining structure has been taken in the hypothetical cases since no climatic and local conditions are considered. Once boundary values of soil suction at the surface, and equilibrium suction at the depth of active zone in situ are measured for a field condition, soil suction difference (ApF) can be considered as its real value for each finite element of the soil domain. The finite element mesh, which is used in the numerical simulation for rectangular backfills, is seen in Fig. 5. In the mesh, 236 nodal points and 202 finite elements have been employed.

The modulus of elasticity for elasticized EPS was taken from Fig. 3, as 222 kPa for a maximum stress level of 100 kPa. This stress level was checked after transmitted lateral stresses were determined. It was seen that maximum lateral stress applied to EPS backfill is no more than 100 kPa. The elasticized stress-strain curve is used in the determination of lateral pressure distribution, and as a consequence, the results are conservative. As a matter of fact, the stress-strain relations given in Fig. 3 are based on rapid loading test results; on the contrary, the swelling process of expansive soil takes a long time to develop swelling pressure behind the retaining structure. Based on unpublished test results, elasticized EPS is even more compressible under sustained loads. It was found that elasticized EPS under 1 year of sustained load was approximately three times more compressible than in rapid loading because of creep (Horvath, pers. commun., 1996).

Transmitted lateral swelling pressure distributions due to expansion of the natural soil on the retaining structure with various rectangular backfills of elasticized EPS geofoam with no wall movement being permitted have been estimated. The transmitted lateral pressure distributions from each of the

144 M. Aytekin

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-2.00

-2.50

- 3 . 0 0 0.00

I L 3 ~ L t _ _ ~ /

50.00 100.00 150.00 200.00 250.00 Transmitted Lateral Pressure (kPa)

F i g . 7. Transmitted lateral swelling pressure distributions with different thicknesses of EPS, and granular backfills.

different backfill problems are shown in Fig. 7. In Fig. 7, the reductions on the lateral pressures within a depth of more than 11/2 m is more than in the upper part of the retaining wall. The reason for this is the magnitude of the stress level is larger in these depths. Thus, backfill materials distribute the lateral pressures from lower elevations to upper elevations. Although this distribution is seen for EPS backfills, it is very clear that the lateral pressures on the retaining structure are transferred to upper part of the retaining wall when granular material is used as backfill (see Fig. 7). If creep behavior of EPS is considered, the required thickness of EPS could be one-third of that shown in Fig. 7. For instance, transmitted lateral pressure on the retaining structure with a thickness of H/5 EPS backfill could be achieved with the thickness of H/15 EPS backfill.

As illustrated in Fig. 7, the reduction on the transmitted lateral pressure distributions becomes more and more uniform with depth when the thickness of


the EPS geofoam backfills is increased. The maximum reduction on the transmitted lateral pressure occurs at the bottom of the retaining structure.

Transmitted lateral earth pressure on the retaining structure for the at-rest condition is also shown in Fig. 7. It should be noted that the lateral pressures due to swelling soil are much more than the lateral pressures due to at-rest condition.

CONCLUSIONS

The lateral swelling pressure transmitted to a retaining structure by swelling soil can be reduced by using EPS geofoam as compressible backfill material. When the backfill thickness of EPS geofoam material is increased, transmitted lateral swelling pressure decreases. When the thickness of EPS backfill is 1-1/5, the transmitted lateral swelling pressure is more uniformly distributed behind the retaining structure. The stress-strain relations given in Fig. 3 are based on rapid loading test results; on the contrary, the swelling process of expansive soil takes a long time to develop swelling pressure behind the retaining structure. Since elasticized EPS under 1 year of sustained load was approximately three times more compressible than in rapid loading because of creep, transmitted lateral pressure on the retaining structure with a thickness of H/5 EPS backfill could be achieved with the thickness of H/15 EPS backfill.

As shown in Fig. 7, the transmitted lateral pressure on the retaining wall is much more when granular (sand) backfill with a thickness of 1-1/5 m is used instead of the same thickness of EPS backfill. The maximum difference that occurred at a depth of 3.00 m is approximately 146-0 kPa. This result shows that a 565% reduction on the transmitted lateral pressure would occur when EPS backfill is used with a thickness of HI5 m instead of the same thickness of granular backfill.

It can be concluded that some simplified design procedure can be developed from the finite element code introduced briefly in this paper. In the design procedure, practitioners would use some tables and/or graphs to determine the thickness of EPS backfill to achieve a given reduction in the lateral earth pressure due to swelling soil. Thus, practitioners would calculate the thickness of EPS backfill without any difficulty.

ACKNOWLEDGEMENTS

The author is indebted to Professor J. S. Horvath for encouraging work on this subject, providing EPS geofoam material that was sent from Germany, and editing the manuscript.

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R E F E R E N C E S

Amir, J. M. & Sokolov, M. S. (1980) Analog model for piles in expansive clay. In Proceedings, 4th International Conference on Expansive Soils. Denver, CO, pp. 582-595.

Aytekin, M. (1992) Finite element modeling of lateral swelling pressure distributions behind earth retaining structures. PhD thesis, Texas Tech University, Lubbock, TX.

Aytekin, M., Wray, K. W. & Vallabhan, C. V. G. (1994) Swelling pressures on retaining structures. In Proceedings of Eighth International Conference on Computer Methods and Advances in Geomechanics. Morgantown, West Virginia, pp. 2423-2428.

Aytekin, M. (1995). Determination of soil suction envelopes. Tech. J. Turkish Chamber Civil Eng., 6(2), 937-945.

Barkan, D. D. (1962) Dynamics of Bases and Foundations, translated from Russian by L. Drashevska, ed. G. P. Tschebotarioff. McGraw Hill Series in Soils Engi- neering and Foundations, New York, pp. 1-53.

Gibson, R. E. (1967). Some results concerning displacements and stresses in a non- homogeneous elastic half space Geotechnique, 17(1), 58-67.

Horvath, J. S. (1992) Dark No Sugar: A well known material enters the geosynthetic mainstream. Geotechnical Fabrics Report, 18-23.

Horvath, J. S. (1995a). Geoinclusion: a new multifunctional geocomposite. Geotech. Fabric Rep., 19, 8-9.

Horvath, J. S. (1995b). EPS geofoam: new products and marketing trends. Geosyn- thetic World, 3(1), 15-17.

Ladd, C. C. (1960) Mechanisms of swelling by compacted clay. Bulletin of the Highway Research Board, No. 245.

Schofield, R. K. (1935) The pF of the water in soil. In Transactions, 3rd International Congress of Soil Science, Vol. 2, pp. 37-48.

Snethen, D. R. (1979) Technical guidelines For Expansive Soils in Highway Subgrades. FWHA-RD-79-51, Federal Highway Administration, Washington, DC.

Symons, I. F., Clayton, C. R. I. & Darley, P. (1989) Earth Pressures Against an Experimental Retaining Wall Backfilled with Heavy Clays. Transport and Road Research Lab., Research Report No. 192, Crowthorne, UK.

White, R. E. (1979) Introduction to the Principle and Practice of Soil Science. Wiley, New York.

Numerical modeling of EPS geofoam used with swelling soil

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