ample sizes from 0.05m cubes up to 0.6m cubes were tested in this study. Stacked arrangements of blocks up to 2.4m height were also tested. As was mentioned earlier sensors were mounted over the height of the specimens to monitor the deformations at different levels. The configuration of the stacked blocks and sensor positions are shown in figure. 3-38.

Figure 3‑1 Positions of the LVDTs on the 0.6m Cube and the Stacked Blocks

            Corrected stress-strain curves for a 0.15m height, Type IX EPS geofoam, cylindrical sample is shown in figure 3-39. Global displacements monitored by an LVDT resulted in an initial modulus of 9.3MPa. The stress-strain curve derived from displacement measurement with an extensometer mounted at the middle of the sample resulted in a modulus of 13.4MPa. Thus depending on the sample height and location of deformation observation the inferred modulus for the same density geofoam was found to be different. As the modulus increased with height and with the position of displacement observation, the possibility of end effects being the cause of discrepancy was examined by testing a 0.6m block sample.

Figure 3‑2 Initial Modulus for Cylindrical Type IX Sample

            Results from a test on a 0.6m cube specimen where displacements were observed at various locations over the height are shown in figure 3-40. The initial modulus for the middle third of the sample is 18.1MPa. The modulus corresponding to the global or total deformation measurement for this large sample is the same 9.3MPa as determined from measurement of deformation by extensometer observation for the cylindrical sample. The modulus based on deformation of the bottom 0.05m segment is 2.5MPa and lower than the 7.7MPa for 0.05m cube sample. As the reference height for the lower 0.05m is the same as for the 0.05m cube sample, and the platen contact was only on one end, a higher modulus was anticipated for the 0.05m segment of the large block. However, repeated tests consistently showed the 0.05m cube sample modulus to be higher. This may be due in part to differences in contact surface roughness and relative severity of end restraint between large and small end areas. The modulus of 1.2MPa for the top 0.025m segment is the lowest. The strain distribution over the height of the test block was not uniform. End segments of the sample and adjacent to the loading platens were undergoing much greater deformation as compared to the mid-segment of the sample. 

            Results from compression testing of four stacks of 0.6m geofoam blocks are shown in figure 3-41. Each block layer is referred to as a stage with the first being at the bottom or lowest elevation. The strain rate at which the stacked blocks were tested was 2 percent per min and less than the 10 percent per min strain rate used for the individual block tests. The initial modulus determined for the middle third of the second stage geofoam block is 15.9MPa. The modulus based on the combined deformation of all four stages is 13.1MPa. The modulus value obtained for a gauge length of 0.075m straddling between the interface of stages two and three is 10.6MPa. Even though the stacked blocks were tested at a lower strain rate, all three moduli are larger than the value of 9.3MPa obtained from separate testing of an individual block and considering total deformations. The extent of any crushing or damage at geofoam to geofoam interfaces was much limited relative to the deformation noted to have occurred in zones adjacent to the rigid end platens.

These results indicate cell damage and crushing was occurring in the zone of geofoam immediately adjacent to the rigid loading platens. Consequently, Young's modulus values derived from tests on small samples underestimate the likely performance of geofoam fills. This observation may explain some of the discrepancy reported by Duskov (1997) between laboratory-determined modulus and values obtained from field monitoring and back analysis. Underestimation of model parameters may also partly explain the large difference between the model prediction and actual observations for the test fill reported by Frydenlund and Aabfe (1996).

Figure 3‑3 Initial Modulus for a 0.6m Type IX Cube

Figure 3‑4 Initial Modulus for a 2.4m Type IX in Stack Blocks

            Initial modulus values determined for 0.05m cubes and the mid-third of 0.6m cubes of different densities are summarized in figure 3-42. Both sets of data show an increasing trend in initial modulus with density. For each density, the initial modulus derived from testing conventional 0.05m cube samples is about half the corresponding value obtained for the mid-segment of 0.6m blocks. The upper line in figure 3-42, for the mid-section of single blocks, represents the behavior of stacked blocks better than the lower curve for the 0.05m cube samples. 

Horizontal deformation measurements on opposite sides and at the middle of 0.6m cube samples enabled simultaneous determination of lateral and vertical strains. The trend of lateral strain with increasing axial strain both for the whole sample and also for the middle segment is shown in figure 3-43. In the initial stages of compression loading, the lateral strain is negative and is directed outward. As loading continued, the direction of lateral deformation began to reverse. Figure 3-44 represents Poisson's ratio values determined in a range of 0 to 2 percent vertical strain. The upper curve is from evaluation using vertical strain for the middle third segment of the sample. The lower curve is from evaluation using vertical strain for the entire sample. The two results are markedly different particularly in the region below 1 percent vertical strain. Crushing and damage at the upper and lower boundaries that are adjacent to the metal loading platens exaggerate the vertical strains derived from the overall height of the sample. Whereas vertical strains determined for the middle third of the specimen were less affected by edge damage and were correspondingly lower. The Poisson's ratio values associated with the mid-section vertical strains are therefore correspondingly higher. This phenomenon of edge damage mostly explains why previously reported values for EPS geofoam on the basis of testing small samples and total vertical strain have generally been of the order of 0.15 or less. Initial modulus and Poisson's ratio values are desired to simulate the behavior of EPS geofoam as an elastic material. The appropriate region of interest for estimating desired elastic parameters is generally below 1 percent vertical strain. In this region, Poisson's ratio values attributed to EPS geofoam should be higher instead of lower than 0.15. 

Figure 3‑5 Initial Modulus for Different Densities

Figure 3‑6 Strain States for a 0.6m Cube Type IX

Figure 3‑7 Poisson’s Ratio for Different Vertical Strain Levels