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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 />- <br />C. (11). The differential settlement of a point.on a plant is calculated in this method, as a <br />displacement of -other points. The applications o <br />function of the f the closed form solutions to <br />well with experimental <br />some typical problems indicate that the calculated movements agree quite <br />methods. <br />observations and compare favorably with other commonly used numerical <br />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 surf -ace 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 />Surnma-U. Several analytical and numerical methods are presented in the previous sections. All <br />the methods discussed are capable of calculating differential settlements resulting from the <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-Lavie, et. al's Elastic Solution Method wa-, <br />1500 - Vancouver, Canada - Geosynthetics'93 <br />