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A study on the response of clay layers subjected to differential deformations by centrifuge <br /> model tests was presented by Jessberger, et. al..(9). In this study, the effects of overburden and <br /> choice of clay liner material on the response of a model liner subjected to deformations were <br /> investigated. The test results show no tension cracks at the surface. Jessberger, et al. suggested <br /> that the suppression of tension cracking can be explained, in part, by a simple elastic <br /> interpretation of the material response, as illustrated in Figure 2. The incrvased initial lateral <br /> stresses generated within the liner as a result of the overburden allowed greater differential <br /> settlement of the clay liner to occur before tensile stresses could be generated. However, before <br /> reaching such stress levels, localized dislocation would take place to form multiple shear <br /> ruptures in the areas of greatest liner deformation. 'Consequently, tensile stresses did not arise <br /> and no tension cracks were created once rupturing occurred.. It was observed from the test that <br /> the presence of shear ruptures did not affect the performance 'of the-liner as an effective <br /> hydraulic barrier. <br /> Differential Settlement Approximation On a Sloped Surface. To evaluate the impact of <br /> differential`settlement on the liner grade, it is necessary to define the configuration of the <br /> deformed liner surface on a sloped plane. However, the Elastic Method was developed for <br /> horizontal surfaces. The model does not evaluate differential settlements on sloped surfaces. <br /> To evaluate the surface deformation of a sloped liner surface, an approximation was made <br /> by projecting the differential settlements calculated on a horizontal surface to a sloped surface. <br /> This results in a conservative approximation because the distances between the points along the <br /> sloping surface and the void are always greater than or equal to those in the horizontal case. <br /> Therefore, the differential settlements so calculated in the sloped surface will be slightly higher <br /> than those in the horizontal case. <br /> Poisson's Ratio. Tsur-Lavie, et. al. (15) compared the maximum differential settlement <br /> calculated with the analytical elastic model with field measurements for mining subsidence. <br /> With a Poisson's ratio of 0.5, the results of the analysis were close to the field results obtained <br /> with a void found at shallow depths. Tsur-Lavie, et. al. thus concluded that the differential <br /> settlement resulting from shallow voids was associated with a state of failure extending into the <br /> medium surface. This resulted in an increase in volume (dilatancy) and, therefore, was best <br /> represented by a model with a large Poisson's ratio. Following Tsur-Lavie, et. al's <br /> recommendations, a Poisson's ratio of 0.5 was used in the design example presented in this <br /> paper. <br /> Calculation Procedures. An example of the application of the elastic model to design a liner <br /> system for an actual case where the vertical expansion of an existing landfill is being planned, <br /> is presented below. <br /> EXAMPLE CALCULATION FOR THE DESIGN OF A SLOPED LINER SYSTEM <br /> Design Problem. A void 0.9 m (3 feet) long by 0.9 m (3 feet) wide by 1.8 m (6 feet) deep is <br /> Geosynthetics'93-Vancouver,Canada-1503 <br />