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A study on the response c <br />model tests was presented by Je; <br />choice of clay liner material on <br />investigated. The test results she <br />that the suppression of tensioi <br />interpretation of the material res <br />stresses generated within the Iii <br />settlement of the clay liner to occ <br />reaching such stress levels, loc <br />ruptures in the areas of greatest l <br />and no tension cracks were creat <br />the presence of shear. ruptures <br />hydraulic barrier. <br />clay layers subjected to differential deformations by centrifuge <br />berger, et. al..(9). In' study, the effects of overburden and <br />he response of a model liner subjected to deformations were <br />v no tension cracks at the surface. Jessberger, et al. suggested <br />cracking can be explained, in part, by a simple elastic <br />onse, as illustrated in Figure 2. The increased initial lateral <br />.r as a result of the overburden allowed grater differential <br />r before tensile stresses could be generated. However, before <br />lized dislocation would take place to form multiple shear <br />zer deformation. -Consequently, tensile stresses did not arise <br />I once rupturing. occurred.- It was observed from the test that <br />id not affect the performance --of the -liner as an effective <br />rifer :ntial e m n "m To evaluate the impact of <br />differential _ settlement on the lin r grade, it is necessary . to , define the configuration of the <br />deformed liner surface on a sloy ed plane. However, the Elastic Method was developed for <br />horizontal surfaces. The model oes not evaluate differential settlements on sloped surfaces. <br />. To evaluate the surface def <br />by projecting the differential sett <br />This results in a conservative apr <br />sloping surface and the void are <br />Therefore, the differential settlen <br />than those in the horizontal case. <br />Poisson's Ratio. Tsur-Lav <br />calculated with the analytical ela <br />With a Poisson's ratio of 0.5, the <br />with a void found at shallow der <br />settlement resulting from shallow <br />medium surface. This resulted i <br />represented by a model with F <br />recommendations, a Poisson's rai <br />tion of a sloped liner surface, an approximation was made <br />its calculated on a horizontal surface to a sloped surface. <br />nation because the distances between the points along the <br />ys greater than or equal to those in the horizontal case. <br />so calculated in the sloped surface will .be slightly higher <br />, et. al. (15) compared the maximum differential settlement <br />is model with field measurements for mining subsidence. <br />sults of the analysis were close to the field results obtained <br />is. Tsur-Lavie, et. al. thus concluded that the differential <br />)ids was associated with a state of failure extending into the <br />an increase in volume (dilatancy) and, therefore, was best <br />large Poisson's ratio. Following Tsur-Lavie, -et. al's <br />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 tl�e 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 />i <br />Design Problem A void 0.9 m (4 feet) long by 0.9 m (3 feet) wide by 1.8 m (b feet) deep is <br />Gcosptbetics'93 - Vancouver, Canada -1503 <br />11 <br />