土木专业外文翻译---简要的分析斜坡稳定性的方法-建筑结构(编辑修改稿)

土木专业外文翻译---简要的分析斜坡稳定性的方法-建筑结构(编辑修改稿)内容摘要：

n of the slope stability problem addressed in this paper achievable and some of these assumptions would lead to restrictions in terms of applications ( pressure on retaining walls). However, analytical solutions have a special usefulness in engineering practice, particularly in terms of obtaining approximate solutions. More rigorous methods, . finite element technique, can then be used to pursue a detail solution. Bishop39。 s rigorous method5 introduces a further numerical procedure to permit specialcation of interslice shear forces Xl and Xr . SinceXl and Xr are internal forces, ()lrXX must be zero for the whole section. Resolving prerpendicularly and parallel to EF, one gets sin c osT hd x k hd x    （ 9） c os c si nN hd x k hd x    （ 10） 22a r c sin ,xa r a br    （ 11） The force N can produce a maximum shearing resistance when failure occurs: se c ( c os si n ) t a nR c dx hdx k       （ 12） The equations of lines AC, CB, and ABY are given by y 221 2 3ta n , , ( )y x y h y b r x a      （ 13） The sums of the disturbing and resisting moments for all slices can be written as 01 3 2 30( si n c o s )( ) ( si n c o s ) ( ) ( si n c o s )()lsllLscM r h k d xr y y k d x r y y k d xr I k I             (14)  02300232sec ( c os si n ) t a nsec ( ) ( c os si n ) t a n( ) ( c os si n ) t a nt a n ( )lrlllLcsM r c h k dxr c dx r y y k dxr y y k dxr c r I k I                       (15) 22c o t , ( )L H l a r b H     （ 16） a r c si n a r c si nl a arr  （ 17） 1 3 2 3022( ) sin ( ) sin1( c o t ) se c23Lls LI y y d x y y d xH a b Hr      （ 18） 1 3 2 30222 2 2 22 2 2( ) c os ( ) c ost a n t a n2 ( ) ( ) ( )6 2 3( t a n ) a r c si n ( t a n ) a r c si n221( ) a r c si n( ) 4 ( ) ( )26Lls LI y y dx y y dxb r br L a r L arrr L a r aa H a brrr l ab H r l ab l a H arr                             （ 19） The safety factor for this case is usually expressed as the ratio of the maximum available resisting moment to the disturbing moment, that is ta n ( )() csrs s s cc r I k IMF M I k I    (20) When the slope inclination exceeds 543, all failures emerge at the toe of the slope, which is called toe failure, as shown in Figure 2. However, when the slope heightH is relatively large pared with the undrained shear strength or when a hard stratum is under the top of the slope of clayey soil with 03 , the slide emerges from the face of the slope, which is called Face failure, as shown in Figure 3. For Face failure, the safety factor Fs is the same as 185。 oe failure1s using 0()Hh instead of H. For flatter slopes, failure is deepseated and extends to the hard stratum forming the base of the clay layer, which is called Base failure, as shown in Figure ,3 Following the same procedure as that for 185。 oe failure, one can get the safety factor for Base failure:  39。 39。 39。 39。 ta n ( )css scc r I k IF I k I    （ 21） where t is given by equation (17), and 39。 sI and39。 cI are given by      010039。 0 3 1 3 2 3032 2 201sin sin sinc o t ( ) ( ) ( 2 ) ( 3 3 )1 2 2 2 3l l ls llI y y x d x y y x d x y y x d xH H b l Hl l l l l a b b H Hr r r                (22)          222222032310 30c4612c o ta r c s i n2t a na r c s i n21a r c s i n2c o t412c o sc o sc o s1100aHalablrrrHHarrarbraHbrHrrHldyydyydyyI xllxllxl      （ 23） 其中，   221 2 30 , ta n , ,y y x y H y b r x a       （ 24）   220201c o t , c o t ,22l a H l a H l a r b H        (25) It can be observed from equations (21)~(25) that the factor of safety Fs for a given slope is a function of the parameters a and b. Thus, the minimum value of Fs can be found using the Powell39。 s minimization technique. For a given single function f which depends on two independent variables, such as the problem under consideration here, minimization techniques are needed to find the value of these variables where f takes on a minimum value, and then to calculate the corresponding value of f. If one starts at a point P in an Ndimensional space, and proceed from there in some vector direction n, then any function of N variables f (P) can be minimized along the line n by onedimensional methods. Different methods will difer only by how, at each stage, they choose the next direction n. Powell rst discovered a direction set method which producesN mutually conjugate , a problem of linear dependence was observed in Powell39。 s algorithm. The modiffed Powell39。 s method avoids a buildup of linear dependence. The closedform slope stability equation (21) allows the application of an optimization technique to locate the center of the sliding circle (a, b). The minimum factor of safety Fs min then obtained by substituting the values of these parameters into equations (22)~(25) and the results into equation (21), for a base failure problem (Figure 4). While using the Powell39。 s method, the key is to specify some initial values of a and b. Wellassumed initial values of a and b can result in a quick convergence. If the values of a and b are given inappropriately, it may result。