Laserfiche WebLink
9.3 CONTINUUM MECHANICS THEORIES 291 <br /> i.o <br /> w o.o <br /> ao <br /> o.. <br /> az <br /> 0 1 2 a . 6 • <br /> TYao Inwnt►s) Fig. 9.2.8 "rime factor for soft strata(13). <br /> was definitely time-dependent in both longwall and room-and-pillar min- <br /> ing. However, the conclusions reached in recent studies differ considera- <br /> bly. For example,Gentry(5)tends to agree with the critical area concept, <br /> while Dahl and Choi (7) found that surface subsidence is time- <br /> independent. <br /> 9.3 CONTINUUM MECHANICS THEORIES <br /> Continuum mechanics theories have been developed for almost every <br /> kind of material behavior, including elastic (14-16), viscoelustic (17, 18) <br /> and elastic-elastoplastic(19). In the following discussions,only represen- <br /> tative theories that have been field-tested will be presented, mainly be- <br /> cause of the complexity of mathematical derivation involved. <br /> 9.3.1 FAustic Theory <br /> Berry (18) analyzed elastic ground movement for three kinds of under- <br /> ground excavation closure development: (1) nonclosure (floor and roof <br /> never met), (2) partial closure, and (3) complete closure (Fig. 9.3.1). <br /> Excavations were treated as displacement discontinuities by using a com- <br /> plex potential method for partial closure. The results were then extended <br /> to nonclosure and complete closure as the limits. It was found that surface <br /> subsidence calculated for isotropic material was smaller than actual mea- <br /> surements. Therefore, the theory for transversely isotropic ground was <br /> developed in two dimensions such that the vertical surface subsidence Sa <br /> is given by the equation <br /> —So 2112AW(K, + KJ112 (9.3.1) <br /> s zr(KIW + 2K,h2x3 + h4) <br /> A is the cross-sectional area of the closure,the maximum of which is wm, <br /> where w is the width of the opening and m is the thickness of the coal <br />