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geogrid deflects into the depression as tensile stresses develop in.the geogrid. <br /> The otherr ethod, stabilizing existing refuse areas, includes surcharging, deep dynam, <br /> compaction, and li e/fly ash slurry injection, among others (2). Time and/or field constrain <br /> often vender these rr ethods impractical for the development of vertical expansions. <br /> t <br /> All the methods currently in use are based on the assumption that "void-induced <br /> settlement will impair the liner. Since none of these methods require the calculation of th <br /> settlement, it is unlaiown whether "void-induced" settlement is a real or perceived problerr <br /> And, whether other alternatives such as providing a thick buffer, or a strain-transition zon <br /> -;.offers as effective a solution as those..methods currently in use. The. calculation of "void <br /> -induced" settlement, d the evaluation of an alternative design methodology are the subjects o <br /> this paper.: <br /> REVIEW OF ME1711ODS FOR FSIIMMNG DNEMENUAL SEIILEMNT <br /> 1 <br /> To date, the authors are not aware of a specific methodology used to quantify the <br /> settlement resulting from the presence of a void within a landfill. However, similar situation: <br /> are often encountered in raining and classical geotechnical fields. Several methods to analyze <br /> "void-induced" settle ent have been developed and am documented in mining and geotwinica <br /> journals and conferej ice proceedings. The following four methods of analysis am briefl} <br /> discussed in this pap- : <br /> -� 0 Mining Subsidence Empirical Methods (3,4), which include influence and profile <br /> functions; <br /> • Numeriad Methods (5,18), which include finite element (FE) and finite difference <br /> (FD) me ods; <br /> • <br /> Displacement Method (11); <br /> • Two-dire nsional and Three-dimensional Elastic Solutions (15, 16). <br /> Mining Subsidence Em irical Methods. A mechanism similar to the collapse of a large object <br /> within an existing la.nc fill and the resulting differential settlement at the surface of a liner <br /> System exists in mining (3,4). Mining subsidence occurs in a bowl-shaped pattern. Empirical <br /> methods have been developed to analyze the subsidence of "long-wall" mines, an underground <br /> mining technique mainly used in rock formations. The method applied in a specific geographical <br /> region is unique, based on the geological characteristics of the region. Because there is no <br /> generic solution available for all geographical regions, this method is not suitable for the analysis <br /> of differential settlem ents for a landfill vertical expansion configuration. <br /> numerical Meth <br /> ods3 Fi Re element analyses of a void within a soli layer have been conducted <br /> in several research fields other than landfill engineering. Wang, M. C., et. al. used a finite <br /> element analysis and a physical model to analyze the bearing capacity of a shallow footing above <br /> a void embedded in clay (18). The results of Wang's finite element analysis and the insults of <br /> Geosyntbctics'93-Vancouver.Canada-1499 <br />