Selected Engineering Properties and Applications
of EPS Geofoam

Ahmed Fouad Elragi, PhD

4 Slope Stabilization With EPS Geofoam

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).