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1 <br /> A study on the nse o$clay layers subjected.to-differential deformations by c entri <br /> model tests was prase by J ber-ger,et. al..(9). In this study, the effects of overburden <br /> choice of clay liner- m tenial on a response of a model: liner subjected to deformations were <br /> -- investigated. The test ults sho no tension cracks at-the surface. Jessberger, et al. suggested <br /> that the suppression f tensiocracidng can be explained, in part, by a simple elastic <br /> interpretation of the m terial res nse, as illustrated in Figure 2. The increased initial lateral <br /> stresses generated wid in the Ii r as a result of the overburden allowed greater differential <br /> settlement of the clay li ier to before tensile susses could be generated. However, before <br /> reaching such stress hvels, 1 dislocation would take place to form multiple shear <br /> ruptures in the areas of greatest finer deformation. -Consequently, tensile stresses did not arise <br /> and no tension cracks re crew once'rupturing.occurred.-- It was observed from the test that <br /> the presence of shear. ptu�,cs tlid not affect the performance of the°liner as an effective <br /> hydraulic barrier. <br /> � mmt.Av roximation To evaluate the impact of <br /> differential'seitlement c n the lin it is necessary.to.define the configuration of the <br /> deformed liner surface n a sI : d plane. However, the-Elastic Method was developed for <br /> horizontal surfaces. Th model oes not evaluate differential settlements on sloped surfaces. <br /> -To eval urate the suface def rmation of a sloped finer surface, an approximation was made <br /> by projecting the differential seW. ments calculated on a horizontal surface to a sloped surface. <br /> This results in a conservo five app ximation because the distances between the points along th( <br /> sloping surface and the void are dways greater than or equal to those in the horizontal cas <br /> Therefore, the differentia settlem is so calculated in the sloped surface wilf.be slightly highe <br /> than those in the Horizon al case. <br /> Poisson's Ratio I sur-Lav e, et. al. (I5) compared tfre maximu-m differential settlement <br /> calculated with the anal ,"cal elastic model with field measurements for mining subsidence. <br /> With a Poisson's ratio of 0.5, the results of the ana-lysis were close to the field results obtained <br /> with a void found at shat ow dcp s. Tsur=Lavie, et. al. thus concluded that the differential <br /> settlement resulting from hallow oils was associated with a state of failure extending into the <br /> medium surface. This r. sulted i an increase in volume (dilatancy) and, therefore, was best <br /> represented by a model with s large Poisson's ratio. Following Tsur-Lavie, -et. al's <br /> recommendations, a Poiss n's radio of 0.5 was used in the design example presented in this <br /> paper. <br /> Calculation Procedures n example of the application of the elastic model to design a liner <br /> System for an actual case vthere the vertical expansion of an existing landfill is being planned, <br /> is presented below. <br /> EXAMPLE CALCULA ON F�R THE DESIGN OF A SLOPED LINER SYSTEM <br /> i <br /> Design Problem A void 9 m (I feet) long by-0.9 m (3 feet) wide by 1.8 m (6 feet) deep is <br /> _ 1 <br /> Geesynttyctics'93-Vancouver.Canada-1503 <br />