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geogrid deflects into the depression as tensile stresses develop in-the geogrid. <br /> The other rim thud, stabilizing existing refuse areas, includes surcharging, deep dynam. <br /> compaction, and lie/fly ash slurry injection, among others (2). Time and/or field constrain- <br /> often vender these rriethods 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 u own whether 'void-induc od' settlement is a real or perceived problen: <br /> And, whether other ternatives such as providing a thick buffer, or a strain-transition zon <br /> -t.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 AMn IODS FOR E:S' IT9G DUTERENTLAL SETTLEMENT <br /> To date, the thors 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 I in mining and classical geotechnical fields. Several methods to analyzt <br /> "void-induced" settlement have been developed and are documented in mining and geotwIniea <br /> journals and conference proceedings. The following four methods of analysis are brieflg <br /> discussed in this paper: <br /> • Mining Subsidence Empirical Methods (3,4), which include influence and profile <br /> functions; - <br /> • Numeri Methods (5,18), which include finite element (FE) and finite difference <br /> (FD) methods; <br /> • Displacement Method (11); <br /> ® Two-dim nsional and Three-dimensional Elastic Solutions (15, I6). <br /> Mining Subsidence Em. irical Methods. A mechanism similar to the collapse of a large object <br /> within an existing land fill and the resulting differential settlement at the surface of a liner <br /> system exists in miming (3,4). Mining subsidence occurs in a bowl-shaped pattern. Empirical <br /> methods have been dev loped to analyze the subsidence of "long-wail" mines, an underground <br /> mining technique maim used in rock formations. The method applied in a specific geographical <br /> region is unique, bas I on the geological characteristics of the region. Because there is no <br /> generic solution availabl 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 <br /> 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 pI ysical 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 010 <br /> Geosynthetics'93-Vancouver,Canada-1499 <br />