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the model tests appear to confirm one another. <br /> Drumm, E. C., et. al. also used finite element analysis to evaluate the deformation of <br /> highly plastic soils in contact with cavitose bedrock. The calculated settlements were presented <br /> as a function of cavity size in a paper titled "Analysis of Plastic Soil in Contact with Cavitose <br /> Bedrock" (5). <br /> Displacement Method. "Closed-form" solutions for the strain field in an initially isotropic and <br /> homogeneous incompressible soil due to near-surface ,ground loss were presented by Sagaseta, <br /> C. (11). The differential settlement of a point on a plane.is calculated in this method, as a <br /> function of the displacement of other points. The applications of the closed form solutions to <br /> 'te well with e <br /> some typical problems indicate that the calculated movements agree <br /> merical m s�cperimental <br /> observations and compare favorably with other commonly u <br /> sed Elastic Solution. In the Conference of Engineering Geology of Underground Movements, in <br /> September 1987, an analytical elastic method to evaluate settlements caused by voids at depth <br /> was presented by Y. Tsur-Lavie, et. al. The method can be used to calculate the surface <br /> settlement as a function of the dimension of the void, thickness of medium (soil/rock) over the <br /> void, and Poisson's ratios. The method presented is based on a solution developed by Goleeld <br /> (7,8) for stresses and displacements in an infinite homogeneous elastic half space, with <br /> discontinuous step-like uniform boundary displacement representing the collapsing of a void. <br /> The displacement in the surrounding medium and the resulting differential settlement at t' <br /> medium surface is then calculated by the elastic method. <br /> The results obtained from the analytical elastic method were compared with British <br /> National Coal Board (NCB) mining subsidence field measurement data by Tsur-Lavie, et. al., <br /> and are in close agreement with one another. <br /> ummary. Several analytical and numerical methods are presented in <br /> the <br /> previous se from the <br /> the methods discussed are capable of calculating differential settlements <br /> existence of a void at depth. <br /> The numerical methods discussed, i.e., the finite element and the finite difference <br /> methods, are suitable for the analysis of problems with nonhomogeneous, anisotropical <br /> materials. However, the displacement method and the elastic solution method discussed above, <br /> require little or no material properties for the analysis, and therefore can be readily applied to <br /> a vertical expansion design. Of these two methods, the elastic solution has the advantage that <br /> it has been calibrated by field measurements and it allows the performance of sensitivity analyses <br /> based on different soil or waste characteristics. The elastic solution method is easier to apply <br /> than the finite element analysis, and since it neglects arching in the waste, it also provides <br /> conservative results. <br /> The following section discusses how Tsur-l-avie, et. al's Elastic Solution Method w.., <br /> 1500- Vancouver,Canada -Geosynthetics'93 <br />