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7 <br /> A study on the response®clay layers subjected to differential deformations by centrifuge <br /> model tests was presented by Jesiberger, 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 increased initial Iateral <br /> stresses generated within the li* as a result of the overburden allowed grc!ater differential <br /> settlement of the clay liner tobefore tensile stresses could be generated. However, before <br /> reaching such stress Levels, 1 dislocation would take place to form multiple shear <br /> ruptures in the areas of greatest l ner deformation. -Consequently, tensile stresses did not arise <br /> and no tension cracks were. crcatd once rupturing.ocacurred.= It was observed from the test that <br /> the presence of shear. rupturii di not affect the performance of the.liner as an effective <br /> hydraulic barrier. - <br /> iffer : tial Settlement AJ2b=i '6* . d To evaluate the impact of <br /> differential settlement on the lin grade., it is necessary.to_defi_ne the configuration of the <br /> deformed liner surface on a sI 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 r nation of a sloped finer 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 app ximation because the distances between the points along the <br /> sloping surface and the void are always greater .aor equal to those in the horizontal case. <br /> Therefore, the differential settlem-,nts so calculated in the sloped surface will be slightly higher <br /> than those in the horizontal case. <br /> Poisson's Ratio Tsur Lav , et. al. (15) compared the maximum differential settlement <br /> calculated with the analytical elti.c model with field measurements for mining subsidence. <br /> With a Poisson's ratio of 0.5, the - ults of the analysis were close to the field results obtained <br /> with a void found at shallow de s. Tsu-r-Lavie, et. al. thus concluded that the differential <br /> settlement resulting from shallowoids was associated with a state of failure extending into the <br /> medium surface. This resulted i. 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 radio of 0.5 was used in the design example presented in this <br /> s <br /> paper. <br /> • s <br /> Calculation Procedures An exar#ple of the application of the elastic model to design a liner <br /> system for an actual case where toe 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 (J feet) long by 0.9 m (3 feet) wide by 1.8 m (6 feet) deep is <br /> I <br /> I <br /> Goosynthetics-93-Vawouvrs,Canada-1503 <br />