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the model tests aPPS' to confirm one another. ~ Drumm, E. C., et. lal. also used finite element analysis to evaluate the deformation of- highly plastic soils in contact with cavitose bedrock. The oculated settlements were presented as a function of cavity size- in a paper titled "Analysis of Plastic Soil in Contact with Cavitose 4 Bedrock" (5). p ml-woment Method "Closed-form" solutions for the strain field in an initially isotropic and homogeneous incompressible soil due to near-surface ground loss were presented by Sagaseta, C. (11). The differential kettlement of a point.on a plane is calculated in this method, as x function of the-displacement of other points. The applications of the closed form solutions !o some-typical problems indicate that the calculated movements-agree quite well with experimental observations and compare fi orably with other commonly used numerical methods. Elastic Solation, 1n the Conference of Engineering Geology. of Underground Movements, in September 1987, an analytical elastic mothod to evaluate settlements caused by voids at depth was presented by Y. Tsur=Lavie, et. al. The method can -be used to calculate the surface settlement as a function of the dimension of the void. thickness of me&um (soil/rock) over the void, and Poisson's ratios. ;The method presented is based on a solution developed by Golecki (7,$) for stresses and displacements in an infinite homogeneous elastic half space, with discontinuous step-like uniform boundary displacement.representing the collapsing of a void. The displacement in the suirrounding medium and the resulting differential settlement at t' - medium surface is then cal"ated by the elastic method. The results obtained, from the analytical elastic method were compared with British National Coal Board (NCB) mining subsidence field measurement data by Tsur-Lavie, et. al., and are in close agreement with one another. 5ummary. Several analytical and numerical methods are presented in the previous sections. All the methods discussed are capable of calculating differential settlements resulting from the existence of a void at depth: The numerical methods discussed, i.e., the finite element and the finite difference methods, are suitable for the analysis of problems with nonhomogeneous, anisotropical materials. However, the displacement method and the elastic solution method discussed above, require little or no material :properties for the analysis, and therefore can be readily applied to a vertical expansion design. Of these two methods, the elastic solution has the advantage that it has been calibrated by field measurements and it allows the performance of Sensitivity analyses based on different soil or waste characteristics. The elastic solution method is easier to apply than the finite element analysis, and since it neglects arching in the waste, it also provides conservative results. The following section discusses how Tsur-Lavie, et. al's Elastic Solution Method wt.,, 1500- Vancouver.Canada -Geosynthetics'93