Geofoam introduced in recent years has provided solutions to a number of engineering problems. One of these problems is the slope stability problem. In a slope stability problem a slip surface develops between two portions of the soil as in figure 4-1. One portion tends to slip over the other making it unsafe for engineering constructions on the top or at the toe of the slope.

A sliding mass can be partitioned unto two main blocks: the driving block and the resisting block as shown in figure 4-1. If the mass of the driving block increases shear stress along the slip surface increases and the equilibrium in the slope is reduced. If the mass of the resisting block increases the equilibrium in the slope increases as the shear strength along the slip surface in the resisting mass block increases. One way to increase the factor of safety of a slope is to reduce the driving mass by replacing an amount of soil by foam.

Two techniques of analyses are used in this study; the limiting equilibrium method and finite difference method. Each method is used in separate numerical simulation softwares. Results by the two methods are compared for cases with and without geofoam. A parametric study was done to provide guidance for practical applications.

Figure 4‑1 Driving and Resisting Blocks in a Failure Zone

Different values of horizontal seismic coefficients were applied to simulate earthquake effects on slope equilibrium. Important results of this study and a case history are presented in this chapter.

4.2 Geofoam Block Alignment

Generally, the cross section of a geofoam stabilized slope embankment contains layers of foam blocks, each layer being about 0.6m-0.83m thick. These layers rest on a leveling course of 0.15m thick sand or filter. The geofoam fill is usually capped with reinforced concrete slab of about 0.15m thickness. The concrete slab acts as a load distributing layer as well as a protection for the foam. The paving material and sub base layers are placed and compacted over the top of the concrete slab.

Two configurations for the distribution of foam blocks within the slope were studied. Figure 4-2 shows a configuration where the foam blocks are arranged such that the edge of the blocks nearest the face is inclined at an angle equivalent to that of the slope. The back edge of the geofoam configuration is vertical. In this case, the soil is either excavated to its normal angle of repose or supported with temporary sheeting while excavating and constructing the embankment. This arrangement may be required by specific projects or constraints. The vibratory driver for installation and withdrawn of the sheeting can trigger additional movement. The sheeting itself is expensive, making the geofoam solution less economical. Installation and the extraction of the sheeting is also time consuming. The advantage of a vertical back face with sheeting, though, is that the excavated space is less and the usable space during construction is more.

The configuration shown in figure 4-3 does not require sheeting. The shape of the foam back slope tends to be parallel to the repose angle of the soil.

A number of parameters can affect the factor of safety of a geofoam-stabilized slope. The characteristics of the soil such as its shear strength, density, and hydraulic conductivity constitute the most important factors. The geometry of the slope itself, such as height and inclination also affect the factor of safety. The geometry and position of the foam fill also control the factor of safety.

Figure 4‑1 Typical Cross Section of a Geofoam Stabilized Slope

Figure 4‑2 Arrangement of Geofoam Blocks with Two Inclined Edges

4.3 Methods Of Analysis

4.3.1 The Limiting Equilibrium Method

GeoSlope software (GEOCOMP Corp., 1992) calculates the factor of safety and draws the slip surface of a slope. Soil Characteristics such as density, cohesion, and friction angle are required input for GeoSlope and other limit equilibrium methods of analysis.

Foam is idealized either as a stiff clay with very low density or the slope is treated as a bench neglecting the presence of the foam. Different magnitudes of horizontal seismic coefficients of horizontal seismic coefficients were applied to a range of earthquake magnitudes. Bishop circular option of analysis in GeoSlope was used in the parametric study.

4.3.2 The Finite Difference Analysis Method

Fast Lagrangian Analyses of Continua (FLAC) software (Coetzee et al., 1998) was used to analyze slope stability problems using the finite difference method. In the FLAC model, the cross section of the problem is divided into a mesh of preferably square elements. Mohr-Coulomb model is used to represent the soil. Cohesion, friction angle, dilation angle, density, shear modulus and bulk modulus are required input for the model.

Geofoam is represented in the model as an elastic material. Density, shear and bulk moduli were assigned for the elastic model. Values of these properties were chosen so as to cover the range of practical interest. The limits of the problem or boundary were selected to be sufficiently away from the region of critical slip surfaces. Failure was interpreted to initiate when the solution began to diverge. The safety factor of the cross section was calculated by dividing the shear strength of the soil by the shear strength at failure. The critical slip surface was defined by taking zones where the shear strain increment is maximum.

4.4 Effect of Using Geofoam in Increasing the Factor of Safety

Slopes with circular critical surfaces were found to have the same factor of safety and identical slip surfaces using either FLAC or GeoSlope. This is examined for both cases, with foam and without foam. GeoSlope and FLAC gave the same factor of safety and the same starting point of the circular slip surface for slopes (not having geofoam) as given by Taylor charts.

4.4.1 Cohesionless Soil

Failure surfaces for homogenous cohesionless soils are generally shallow (McCarthy, 1998) and forms near surface as shown in figure 4-4. The limit equilibrium analysis gave essentially the same critical surfaces as the finite difference analysis. The factor of safety and failure surface does not change unless geofoam can be configured to replace soil in the shallow failure zone.

Geofoam does not contribute to addressing the stabilization problem represented in figure 4-5. The failure zones develop in the area between the foam and the slope face.

Figure 4‑1 Shear Strain Contours in a Cohesionless Soil Slope

Figure 4‑2 Shear Strain Contours in a Geofoam-Stabilized Cohesionless Soil Slope

4.4.2 Cohesive Soil

The slip surface for a general slope of a homogeneous cohesive soil is either a deep-seated circle or a toe circle (McCarthy, 1998). In both cases, a large amount of soil next to the slope edge acts in the driving force. Figure 4-6 shows the failure zones for a clay soil obtained using FLAC. The soil profile of this cross section is a cohesive soil over stiffer or hard soil. For such cases, the failure surface almost touches the stiff soil interface. Approximately the same failure surface develops with GeoSlope analysis.

By using geofoam in the cross section, the surface with a minimum factor of safety is deeper and below foam blocks. The surface is no longer circular. The limiting equilibrium search must be made general to include non-circular surfaces. Results from FLAC analysis indicate that the factor of safety increases by using geofoam and that the failure zones surround the foam as shown in figure 4-7.

Figure 4‑1 Shear Strain Contours in a Cohesive Soil Slope

Figure 4‑2 Shear Strain Contours in a Geofoam-Stabilized Cohesive Soil Slope

4.4.3 Increasing The Factor of Safety

One way to increase the factor of safety of a slope is to decrease the inclination by either flattering or benching. This would result in reduction of usable space at the crest. Geofoam stabilization however maintains the inclination of the original slope and while increasing the factor of safety. In some cases, the slope can even be made steeper with improvement in factor of safety, as shown in figure 4-8. The more the amount of foam that is added, the larger the failure area becomes resulting in a higher factor of safety. From the figure it can be seen that the increase in the factor of safety is large up to a certain width value. Increasing the width further will result in a slight increase in the factor of safety depending on the slope value. The distribution of a certain amount of foam will affect the factor of safety as shown in figure 4-9. The closer is the shape of the foam fill to the slip surface shape the higher is the factor of safety. This holds as long as the foam does not encroach upon the area of the stabilizing force.

Figure 4‑1 Effect of EPS Width on the Factor of Safety for various Slopes

Figure 4‑2 Effect of EPS Width on the Factor of Safety for Different EPS Configurations

Figures 4-10 shows the variation of the factor of safety for both static and dynamic conditions, with the width and the depth of the foam fill. From the figure it can be seen that the increase in the factor of safety is large up to a certain width value for the one layer. Increasing the width further will result in slight increase in the factor of safety. At a certain width the factor of safety tends to be constant where the failure likely to occur in the slope side of the foam. Figure 4-11 shows that the factor of safety for the case of foam is higher than that for the case of no foam. The purpose of presenting figures 4-8 to 4-11 is to show the benefit of using geofoam to increase the factor of safety.

Figure 4‑3 Effect of EPS Width on the Factor of Safety for Two Thicknesses

Figure 4‑4 Effect of Using Geofoam on the Factor of Safety for Different Horizontal Accelerations

4.5 Route 23A

4.5.1 Background

Geofoam was used for stabilizing a nearby 100m long section of Route 23A east of the Village of Jewett Center in Greene County, NY (Jutkofsky, 1998). In 1966 New York State Department of Public Works reconstructed the portion of Route 23A between the Village of Hunter and Jewett Center. Shortly after the reconstruction, a 100-m-long section of the roadway embankment began to move laterally towards Schoharie Creek, as shown in figure 4-12. A scarp developed on the pavement as shown in photo 4-1. Frequent patching was required to maintain a normal grade through the following years.

In 1978, a subsurface exploration program began. The general subsurface profile up to a maximum explored depth of 21 m, consist of compact gravelly silt (clayey); over layered clayey silt (silty clay); underlain by clayey silt gravelly. Ground water was observed to vary from at 1.5 to 5m below surface. In 1979, a cluster of 22 horizontal drains was installed in a fan-shaped pattern along the toe of the slope in an attempt to reduce the movement by lowering the water table. At the same time, a monitoring program began. Inclinometer A, shown in figure 4-13, was installed near the center of the failure area to determine the zone and the rate of movement. Inclinometer reading was taken for the following 14 years.

Photo 4‑1 Main Crack before 1996

Figure 4‑1 Cross Section before and after 1996 (after Sheeley 2000)

Figure 4‑2 Positions of the Slope Indicators

As the results of the inclinometer showed progressive movement, the horizontal drain treatment (figure 4-12) was considered unsuccessful. That was partly due to the low hydraulic conductivity nature of clayey soils and also their low strength. In 1994, a permanent treatment was pursued. The solution was utilizing EPS geofoam on a horizontal sand filter as shown in figure 4-14. Utilizing EPS geofoam reduced the driving force while using a sand filter provided a positive drainage that lowered the water table to strengthen the soil. This results in fast reconstruction, without property- taking from the adjoining homeowners and maintaining the same geometry of the slope.

A 15m long sheeting was required to handle two construction problems; retaining surrounding soils during excavation and functioning as a safety barrier for the detour traffic during construction. The excavation level was chosen to be the 100-year flood level at 5m below surface and geofoam was placed above elevation 426.72m. A typical cross section in figure 4-14 shows 0.6m crushed stone - filter below 5 layers of foam. Besides functioning as a drainage blanket the horizontal sand layer established a clean stabilized working platform over the soft saturated soils. A 0.6m wide crushed stone column extends between the foam blocks and the sheeting as shown. The main purpose of this arrangement was to lower the water table to the bottom drainage layer. The vertical layer functioned as a protection to the foam from damage as the sheeting was extracted. That filled the voids when the sheeting was vibrated out.

Figure 4‑3 Typical Cross Section in Route 23A

Photo 4‑2 The Crushed Stone Filter

Photo 4‑3 Pouring the Concrete Slab

Photo 4‑4Backfilling over the Foam Side

The foam used was type VIII Expanded Polystyrene with nominal density of 20 kg/m³. The blocks were 0.6m X 1.2m X 2.4m. The minimum shear strength of such type was between 159kpa (ASTM D732). The minimum compressive strength at 10% deformation according to ASTM D1621 was 90 kg/m³. A 0.1m reinforced concrete slab was placed on the top of the 3m height foam blocks to serve as a protection from petroleum spilling and to distribute the traffic load on the foam.

In August 1995 inclinometer B, shown in figure 4-14, was installed. In October sheet pile driving began. Excavation started after about 70 percent of the sheeting was installed. In November the foam blocks were placed. Backfilling began after several geofoam courses were placed. Earth fill was placed over the stepped face of the block mass. This operation continued as geofoam courses were added up to the finish grade. Only the earth fill was compacted.

By December 1995, the first half of the blocks was in place and ready to receive the concrete slab as shown in photo 4-3. The graded sub base crushed stone was placed after concrete curing and backfilling as shown in photo 4-4. The sheeting was removed in January 1996. Placing of 0.23 m asphalt pavement was completed in April 1996. The total thickness of the base and the subbase ranged from 0.6m to 1.2m because of the road banking and inclined geometry. Figure 4-15 shows the construction sequence.

Figure 4‑4 Construction Time Line

4.5.2 Field Results

Figures 4-16 through 4-27 show the results obtained from inclinometer A. The inclinometer gives the displacement in two directions, the main direction and the secondary direction. The main direction is the North/South direction as shown in figure 4-13. The secondary direction is the East/West direction, which is the direction out of plane of figure 4-13. The total displacement is calculated by taking the square root of sum of squares of the displacement in the main and secondary directions. The angle that the total direction makes with the North/South direction is 6 degrees based on the maximum North/South displacement and its correspondence in the East/West direction. The results were obtained for a 20.72m depth each 0.6m from the top surface, elevation 439.83, all the way down to elevation 419.09m. The results were obtained from September 4^th 1979 up to October 7^th 1993. The twelve figures show that there is a movement but of a slow rate. An overall failure did not occur. The factor of safety can be considered to be 1.0.

Figure 4-16 is the North/South direction creep. The movement for the zone between elevation 419.09m and 428.85m can be considered zero with no creep effect. Up to 0.6m above this zone, i.e. between elevations 428.85m and 429.46m, displacement increases with time. The top zone between elevations 429.46m and elevation 439.8m has the same trend of increasing displacement. Thus a slip surface can be considered passing between the two zones and at elevation 429.46 at inclinometer A position. Figure 4-17 shows the East/West direction creep. The displacement values are generally a tenth of those in the North/South direction. Two zones appear in this figure. Below elevation 428.85m, the soil has less creep. Above this zone, the displacements are almost equal for all monitored elevations with more creep effect.

Figure 4‑1 In Plane Creep at Different Elevations

Figure 4‑2 Out of Plane Creep at Different Elevations

Total creep measured by inclinometer A is shown in figure 4-18. The maximum displacement is equal to 0.2m, which is almost equal to what was measured in the North/South direction. Comparison of figure 4-18 with figure 4-16 shows that the effect of the out of plane movement can be neglected.

Figures 4-19, 4-20 and 4-21 show the vertical distribution of the horizontal displacement at three different times in the 14-year period. Figure 4-19 is for the North/South direction, figure 4-20 is for the East/West Direction and figure 4-21 is the resultant. Base readings were taken in 1979. There is essentially no movement below elevation 428.85m over the period of record. A sudden increase started at elevation 429.46m.

Figure 4‑3 Total Creep at Different Elevations

Figure 4‑4 In Plane Movement in 14 Years

Figure 4‑5 Out of Plane Movement in 14 Years

Figure 4‑6 Total Movements in 14 Years

Movements above elevation 429.46m are almost equal. Movements in the East/West direction are a tenth of that in the North/South direction. Results at three instants were presented in these figures. For the East/West, movement was towards the east up to April 1982 and after that it moved towards the west. The maximum movement was less than 2 cm. Movements in the North/South direction was towards the south throughout the 14 years (i.e. towards the creek).

Figures 4-22, 4-23 and 4-24 represent the displacement rate with time for the North/South, the East/West and the resultant directions at inclinometer A position, respectively. The values in East/West direction are one half that in the North/South direction. There was an increase in the displacement rate from 1979 to 1986 when a peak of 0.06 mm/day was reached. Between 1986 and 1992, there was a reduction in the displacement rate.

Figure 4‑7 In Plane Displacement Rate at Different Elevations

Figure 4‑8 Out of Plane Displacement Rate at Different Elevations

Figure 4‑9 Total Displacement Rate for Different Elevations at Inclinometer A

After 1992, the results gave a large increase in the displacement rate. As mentioned before, this is an indication that the factor of safety is equal to 1.0, as in this case any small changes in the applied loads can jump the situation from stable to unstable equilibrium or vise versa.

Figures 4-25, 4-26 and 4-27 show the incremental strain distribution over a 20m height for the North/South, East/West and the resultant directions. The increment strain distribution is for the period between 1979 and 1993. For the three directions, there are large strains in the 2.44m thick zone between elevations 428.24m and 430.68m. Both the total and the North/South strain increment exceeded a 20% strain value. The East/West direction reached only a 3.5% strain increment. Strain values were calculated by dividing the difference in displacement at the ends of the 0.6m deep intervals by the thickness. The peak strain for the three directions is at elevation 429.46.

Figure 4‑10 In Plane Shear Strain in 14 Years

Figure 4‑11 Out of Plane Shear Strain in 14 Years

Figure 4‑12 Total Strain in 14 Years

Results obtained from inclinometer B are shown in figures 4-28 to 4-39. The results were for the period from August 1995 to June 1999. Parts of the results were obtained during the construction period, August 1995 to April 1996.

Figures 4-28, 4-29 and 4-30 show the creep behavior for the three directions the North/South, the East/West and the resultant respectively. The results were shown for different elevations. For all three directions, the displacement increase from zero to a certain level until construction is done after which there was no increase in the displacement values. Both the North/South and the East/West directions show comparable maximum displacement values. The North/South direction reached a max value of about 8 cm while the East/West reached about 7 cm displacement until construction was completed.

Figure 4‑13 In Plane Creep at Different Elevations after 1995

Figure 4‑14 Out of Plane Creep at Different Elevation Before 1995

Figure 4‑15 Total Creep at Different Elevations Before 1995

Figures 4-31, 4-32 and 4-33 represent the movement distribution over the 12m depth from the surface for the North/South, the East/West, and the resultant direction, respectively. Three dates are shown in this figure; November 1995 was during construction, August 1996 was when the first readings were available after construction and the third date is one for which the most recent reading is available. Three zones can be determined in these figures; the first zone is below elevation 426.1m, the second zone is between elevations 426.1m and 429.1m and the third zone is above elevation 429.1m. No movement showed up in the lower zone for the 4-year period during and after construction. The top zone has uniform movement all over the height of the zone during and after construction. The movement in the top zone occurred mostly during the construction period. The middle zone has linear movement distribution all the zone height. All the movement in this zone ceased after construction.

Figure 4‑16 In Plane Movement after 1995

Figure 4‑17 Out of Plane Movement after 1995

Figure 4‑18 Total Movement after 1995

Figures 4-34, 4-35, and 4-36 show the displacement rate for the North/South, East/West and the resultant directions, respectively. After the construction is done in April 1996, the displacement rate is equal to zero for the three directions. In the three figures, there are two distinct period of movement. Peak in the East/West direction occurred in the first period at 1.4mm/day. Peak in the North/South direction occurred in the second period at 2 mm/day. The displacement rate was calculated by dividing the difference in two successive dates by the duration between them and was plotted at the initial date.

Figure 4‑19 In Plane Displacement Rate at Different Elevations after 1995

Figure 4‑20 Out of Plane Displacement Rate at Different Elevations after 1995

Figure 4‑21 Total Displacement Rate at Different Elevations after 1995

Figures 4-37, 4-38 and 4-39 represent the strain distribution obtained from inclinometer B in the North/South, the East/West and the resultant direction respectively. The results are for a 4 years period. Three dates were presented in these figures during construction and just after construction and three years after construction. A maximum strain of 3.8% was obtained in the North/South direction. This amount was obtained during construction.

Figures 4-40 through 4-51 show the same results for figures 4-28 through 4-39 with the results for the period after April 1996, i.e. after the construction was ended. Figure 4-52 shows the creep trend over 20 years.

Figure 4‑22 In Plane Strain at Different Elevations after 1995

Figure 4‑23 Out of Plane Strain at Different Elevations after 1995

Figure 4‑24 Total Strain at Different Elevations after 1995

Figure 4‑25 In Plane Creep after Construction

Figure 4‑26 Out of Plane Creep after Construction

Figure 4‑27 Total Creep after Construction

Figure 4‑28 In Plane Displacement after Construction

Figure 4‑29 Out of Plane Displacement after Construction

Figure 4‑30 Total Displacement after Construction

Figure 4‑31 In Plane Displacement Rate after Construction

Figure 4‑32 Out of Plane Displacement Rate after Construction

Figure 4‑33 Total Displacement Rate after Construction

Figure 4‑34 In Plane Strain after Construction

Figure 4‑35 Out of Plane Strain after Construction

Figure 4‑36 Total Strain after Construction

Figure 4‑37 Creep Trend before and after Utilizing Geofoam

Four extensometers were installed between geofoam layers to monitor movements of geofoam blocks as shown in figure 4-53. Extensometers A and B were located between the vertical stone drainage gallery and the blocks. Extensometers C and D were located within the blocks. Figure 4-54 shows the results of extensometers B and D. Movement occurred during the construction period. Extensometer B moved about 6 cm towards the creek while extensometer D moved 2.5 cm only. The movement is believed to be the closing of the gaps between the blocks. The difference in the value can be explained to be due to the position of the extensometer within the geofoam mass. More gaps are required to be closed for the case of extensometer B. After construction no movement was measured by both extensometers. Extensometers A and C measured negligible movement.

Figure 4‑38 Positions of the Extensometers

Figure 4‑39 Extensometers B & D Readings

4.5.3 Numerical Analysis

The Rt23A geofoam stabilized cross-section is next numerically modeled. A finite difference mesh is shown in figure 4-55. The problem is simulated as an in plane problem. The dimensions of the cross-section are chosen such that the boundaries are sufficiently away from the stressed zones. A plastic model, Mohr-Coulomb is used to simulate the soil. Material properties are represented by density, shear and bulk moduli for deformation and friction angle and cohesion for strength of the soil. Strength parameters are back calculated using FLAC and GeoSlope to meet the assumed slip surface (Figure 4-56). After applying loads and boundary conditions, the numerical analysis software is run in a large strain mode. Large strain mode adjusts the dimensions of the mesh after each solution step to take account of the deformations that occur. Even with failure and large deformations, the solution process continues until either equilibrium occurs with a new grid dimensions or the aspect ratio of any rectangular element reaches a value of 10. In the latter case the program will stop running. The problem can also be solved in a small strain mode. In the small strain mode, the initial dimensions of the grid are maintained during stepping. In the case of no failure; implying very small movements, convergence will occur. The solution will stop if there develop large deformations and changes in the dimensions of the elements. Large strain mode can converge even after deformations of the order of 10 meters. Figure 4-57 shows the grid distortion for the cross-section before 1996 as well as the boundary of the cross section before starting the solution achieved in small strain mode. The grid is magnified 60 times. The maximum displacement is 8 cm. This is a static equilibrium situation. No creep effect is encountered in this solution. Slightly reducing the strength, the displacement increases to an order of meters and may not converge. That means, the factor of safety is close to one for the situation before 1996. The failure surface can be figured from figure 4-57 by tracing the skew rectangle elements where excessive shear has strain taken place. Small deformation can be seen in the first three rows where the soil in these rows is stiffer than the upper rows. The upper line of the exaggerated grid profile shows settlement in the road area as well as high deformation in the north side of the road where the scarp occurred.

Figure 4‑1 The Finite Difference Grid

Figure 4‑2Strength Parameters for Factor of Safety Equals One

Displacement vectors are shown in figure 4-58. The directions of the arrows represent the direction of the movement. The movements are due to two reasons; self-weight and the effect of the sloped edge. Only vertical movements occurred near the north vertical boundary implying that the boundary was far enough from the zone of the slope effect. On the other side very small diagonal arrow shows up on the south vertical boundary. Although moving that boundary few meters to the south will increase the accuracy of the results the current solution gives good results with reasonable solution time. The failure surface can be determined by the large change in the length of the two adjacent arrows.

Figure 4‑3 Exaggerated Grid Distortion before 1996

Figure 4‑4 Displacement Vectors before 1996

Three zones are shown in figure 4-59. The zone with small circles at the top of slope has tension failure. The zone with the mark (*) is a shear failure zone. No failure occurred in the rest of the cross section. A scarp occurred in the tension failure zone. A failure surface would pass through the tension and shear failure zones. As can be seen from the flat-based shear failure zone next to the lower stiff layer, it may not be a circular surface.

Figure 4-60 shows the shear strain distribution before 1996. The values are due to static equilibrium, which means that no creep effect is taken into consideration. Comparing this figure with figure 4-24, it can be seen that at horizontal distance equals to 26m where inclinometer A is located, maximum strain occurs at elevation 429.5m for both figures. Again, the difference in values is equal to that due to the creep effect. The maximum shear strain in the cross section occurs at distance 42m and is too close to the stiffer lower layers. An inclinometer may give very high readings if installed in this location. A failure surface can be traced by passing a line through the points of highest strain at each vertical section.

Figure 4-61 shows the horizontal displacement contours. The failure surface can be easily identified by the contour B, the first nonzero contour. Again, it is not a circular surface, and the creep effect is not included in these results. Comparing the in plane horizontal distribution in figure 4-19 with a vertical section at horizontal distance 26m, the position of inclinometer A, one can find that both distributions start with a zero value and continue up to 427m-428 m. A rapid change of the horizontal displacement with height occurs in the upper 3 meters. The horizontal displacement does not change much above an elevation of 431m.

The vertical displacement contours are shown in figure 4-62. The movement is the result of self-weight and slope effect. The maximum settlement will occur beneath the road. Before 1996, it was essential to repave the settled portion of the road to maintain leveled driving surface from time to time. Creep effect was the main reason of this progressive settlement. Two material models are used for the case after 1996 as shown in figure 4-63. Elastic model is used for foam. Young’s Modulus, Poisson’s ratio and the density are the parameters required in the elastic model. Mohr-Coulomb is used for soil. No interface elements between the geofoam blocks and the soil or between the foam blocks are modeled in this solution. From the results that are shown later, shear stresses are too low to produce slippage.

To reach the case after 1996 cross-section, construction sequence is modeled in this solution. After reaching equilibrium using the soil cross-section, the sheet pile is added to the model, excavation is done and the drainage filter, foam blocks and back filling are followed by final removal of sheet pile. In each construction step, the solution has to reach equilibrium before proceeding to the following step.

Figure 4-64 shows the displacement vectors after excavation. A lateral movement of 0.6m of the sheet pile was reported. It was noticed that “several inches” of settlement occurred behind the sheet pile as soil was removed. In the FLAC model, 0.2m settlement occurred just after excavation. The exact value from the field is not known as the road behind the sheet pile was re-graded to maintain safe driving surface.

After removing the sheet pile in the FLAC model, the solution was allowed to reach convergence to study the geofoam-stabilized slope. Figure 4-65 shows the shear strain distribution in the cross section. The maximum value reached is 0.1% compared to the 0.4% reached in figure 4-37. In both figures, the shear strain can be considered zero. Inclinometer B is located at a distance of 35.5 m from the edge of the model.

Figure 4‑5 Failure Zones before 1996

Figure 4‑6 Shear Strain Contours before 1996

Figure 4‑7 Horizontal Displacement Contours before 1996

Figure 4‑8 Vertical Displacement Contours before 1996

Figure 4‑9 Material Models

Figure 4‑10 Displacement Vectors after Excavation

Figure 4‑11 Shear Strain Contours after 1996

Figure 4-66 shows the horizontal displacement contours after 1996. The maximum value of horizontal displacement is 0.5 cm. Figure 4-42 gives the same results all over the body of the inclinometer with the peak at the top. The horizontal movement in the numerical model shows up near the sloped surface.

Figure 4-67 shows the vertical displacement contours after 1996. The maximum value is 1.8 cm. The settlement is due to the elasticity of both the soil and the foam. The main load for this settlement is the fill on the top of the foam as the self-weight of the foam is negligible.

Ground water is considered in the numerical solution. FLAC calculates the pore pressure. Figure 4-68 shows the pore pressure contours before 1996. The drainage blanket changes the water pressure profile as shown in figure 4-69.

Figure 4‑12 Horizontal Displacement Contours after 1996

Figure 4‑13 Vertical Displacement Contours after 1996

Figure 4‑14 Pore Pressure Contours before 1996

Figure 4‑15 Pore Pressure Contours after 1996

Figures 4-70 through 4-82 show the stresses in three directions: vertical direction, in plane horizontal direction and out-of-plane direction. All stresses are shown for the two cases (total stresses and effective stresses). The figures are shown for the two cases before and after 1996.

The total horizontal in plane stresses in the foam zone is reduced after 1996 as shown in figure 4-70 compared to figure 4-71. The effective stresses are also reduced (figures 4-72 and 4-73).

The total Vertical stresses in the foam zone and below it is reduced after 1996 as shown in figure 4-74 compared to figure 4-75. This is due to the effect of the lightweight fill. In front and on the back of the foam blocks the stresses are the same before and after 1996. The same distribution can be observed in figures 4-76 and 4-77 but with reduction in the stresses because of the effect of the pore water pressure.

The total and the effective shear stress contours are identical, as Mohr circle at each point will have the same radius for both cases. Figure 4-78 shows the in plane shear stress for the case before 1996. The maximum value reached for the zone between the weak and the stiffer soil is 35 kPa. For the case after 1996 the same spot has a 30 kPa stress as shown in figure 4-79. The factor of safety of the slope will be 35/30. 1.17 as a factor of safety would have been increased by redistribution of the same foam amount in the cross section as mentioned earlier. The out of plane stresses behaved like the in plane horizontal stresses. As shown in figures 4-80 and 4-81 the total stresses are less before 1996 for the geofoam zone. For the same zone, the effective stresses are also reduced (figures 4-82 and 4-83).

Figure 4‑16 Horizontal Stress Contours before 1996

Figure 4‑17 Horizontal Stress Contours after 1996

Figure 4‑18 Effective Horizontal Pressure Contours before 1996

Figure 4‑19 Effective Horizontal Stress after 1996

Figure 4‑20 Vertical Stress Contours before 1996

Figure 4‑21 Vertical Stress Contours after 1996

Figure 4‑22 Effective Vertical Stress Contours before 1996

Figure 4‑23 Effective Vertical Stress Contours after 1996

Figure 4‑24 Shear Stress Contours before 1996

Figure 4‑25 Shear Stress Contours after 1996

Figure 4‑26 Out of Plane Stress Contours before 1996

Figure 4‑27 Out of Plane Stress Contours after 1996

Figure 4‑28 Out of Plane Effective Stress Contours before 1996

Figure 4‑29 Out of Plane Effective Stress Contours after 1996

4.6 Summary

· The factor of safety of slopes can be increased using geofoam stabilization for both static and dynamic conditions.

· A number of parameters including the amount and the distribution of foam blocks, soil characteristics, geometry of slope affect the factor of safety of a geofoam stabilized slope.

· The effect of amount and distribution of foam on the factor of safety are controlled by the type of soil.

· Using geofoam blocks in cohesionless soil slopes, where shallow failure surface occurs, will not affect the factor of safety at all.

· Modeling geofoam blocks as cohesive soil with a very high cohesion value using the limiting equilibrium analysis is same as modeling geofoam blocks as elastic material using finite difference analysis.

· For cohesive soil, the failure surface of geofoam-stabilized slopes is deep, either surrounding the whole amount of foam or forming on the slope side of the foam.

· For geofoam stabilized cohesive soil where failure surface tends to develop only on one side of the foam, increasing the amount and the distribution of foam will increase the factor of safety of the slope until the slip surface occurs. Any further amount of foam will not increase the factor of safety of the slope.

· For geofoam stabilized cohesive soil slopes in which the failure surface develops on one side of the foam and ends on the other side of the foam, increasing the amount of foam increases the factor of safety up to a certain amount. Beyond this point, the slip surface starts to form only on one side of the slope. Any further amount of foam will not increase the factor of safety of the slope.

· For cohesive soil with an amount of friction particles, the failure surface of geofoam-stabilized slopes is shallow and develops on the slope side of the foam. Any increase in the amount of the foam in this case does not affect the factor of safety.

· In general, the more the amount of foam, the more the factor of safety as long as the slip surface does not develop on the slope side of the foam.

· For the same amount of foam, the closer is the foam to the slope side the higher is the factor of safety, as long as the failure surface does not develop on the foam slope side.

· For the same amount of foam, the closer is the distribution of the foam to the circular shape (i.e. with two inclined edges) the higher is the factor of safety, so long as the failure surface does not develop on the slope side of the foam.

· Parameters affecting the factor of safety of geofoam-stabilized slopes under static loading will affect the factor of safety under dynamic loading.

· Geofoam stabilization leads to a steeper slope whose factor of safety is higher. A steep slope also increases the usable space.

Selected Engineering Properties and Applications of EPS Geofoam

Ahmed Fouad Elragi, PhD

4 Slope Stabilization With EPS Geofoam

4.1 Introduction