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Approach. A computer .program was developed to solve the three-dimensional equation <br /> presented in Tsur-Lavie, et al's analytical elasticity solution. This computer program is canabi <br /> of evaluating the differential settlement caused by voids at depth. The input variables <br /> program consist of the following: <br /> • The void size (defined by L,= x 4 x D); <br /> • The soil thickness over the void M; and, _ <br /> • Poisson's ratio of the subsiding material. <br /> The computer program was verified by comparing its output with the characteristic curve <br /> presented in Tsur-Lavie, et. al's paper. <br /> Assumptions. Three basic assumptions were made to model the deformation of a surface due <br /> to the presence of a void at depth. These assumptions are as follows: <br /> • The liner surface is stress free; _ <br /> • Differential settlement on a horizontal plane is projected to a graded surface; an( <br /> • A constant Poisson's ratio. <br /> Each of the assumptions listed above is further discussed in the following sections. <br /> Stress Free Surface. A stress free surface is one of the assumptions made in the solutior <br /> of the Elastic Model. This is a conservative assumption because the strains at the liner sr- - <br /> are reduced by the arching effect of the material, i.e., waste, overlaying it. Mathematiti __.y, <br /> incorporating the waste above the liner could reduce the magnitude of the settlement b) <br /> approximately half. <br /> Overburden <br /> �l Gay <br /> Sand <br /> Cracks <br /> ano propped <br /> rvptwe trapdoor Ruptures <br /> <0 00 op rro +oe> 0 <br /> ♦ 4 1+1\ <br /> Initial Bend,ng Initial Bending <br /> Stress stress stress stress <br /> Figure 2 Influence of overburden on lateral stress level <br /> (After Jessberger and Stone, 1991) <br /> I <br /> 1502-Vancouver,Canada-Geosynthetics`93 <br />