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geogrid deflects into the depression as tensile stresses develop in-the geogrid. <br /> The other method stabilizing existing_ � g refuse areas, includes surcharging, deep dynam <br /> compaction, and lime/fly ash slurry injection, among others (2). Time and/or field constrain- <br /> often render these methods impractical for the development of vertical expansions. <br /> , <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 unknown whether "void-induc od" settlement is a real or perceived problem <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, and the evaluation of an alternative design methodology are the subjects o <br /> this paper. <br /> REVIEW OF METHODS FOR ES TING DUTERENIIAL SETTLEMENT <br /> To date, the authors are not aware of a specific methodology used to quantify tht <br /> ` settlement resulting from the presence of a void within a landfill. However, similar situation: <br /> are often encountered in mining and classical geotechnical fields. Several methods to analyze <br /> "void-induced" settlement have been developed and are documented in mining and geotechnica <br /> journals and conference proceedings. The following four methods of analysis are briefl} <br /> discussed in this paper: <br /> Mining Subsidence Empirical Methods (3,4), which include influence and profile <br /> functions; . <br /> • Numerical Methods (5,18), which include finite element (FE) and finite difference <br /> (FD) methods; <br /> • Displacement Method (11); <br /> • Two-dimensional and Three-dimensional Elastic Solutions (15, 16). <br /> Mining Subsidence Empirical Methods. A mechanism similar to the collapse of a large object <br /> within an existing landfill 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 settlements for a landfill vertical expansion configuration. <br /> Numerical Methods, Finite element analyses of a void within a soil 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 results of <br /> ceosynthetics'93-Vancouver.Canada-1499 <br />