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'~ -~ i) <br />1. 1. .\ ti'1' r <' 1? 11 1' I I. 1 I1 It I l' \I . 1' II . X <br />IIMII <br />IIM <br />~r <br />III <br />a = a~` <br />lll` <br />3n° <br />20" ;o° lill° <br />a <br />la) <br />~H <br />calculations made with logarithmic spiral and circular arc as failure surfaces <br />give very close results. Cx[ensive studies by Swedish engineers of slope failures <br />in clay during the early part of this century also revealed that the failure <br />surface closely approaches the circular arc. The analysis of slope stability <br />using a circular slip surface was developed by Fellenius' (1976) and others <br />and is often referred to as the S,rerlisb circle method. Figure S.'_'_ shows the <br />displacement of the soil mass produced by a slope failwe. <br />K sin m <br />h'. <br />II' <br />F <br />n <br />(n) <br />i cl (7Q <br />Fip. N:_'l. Circular arc method of slope amllysis. <br /> <br /> <br /> <br /> <br />~ ~~ ---D/H = I <br /> <br /> <br /> <br /> <br /> ~ ~ <br /> ~ i ~ <br />~ <br />~ <br /> <br /> <br /> ~ ~ <br /> <br /> <br /> <br /> 3ll° m = a5° <br /> <br />ar .1 u' liu' <br />Q <br />~nl <br />Fip. 6.911. 13eann6 capably numbers fur lounda- <br />lions with inclined loads. [.4fler ~teyerholi(1957).] <br />Circular arc nu•dlod. Figure S.?I(u) shows a soil mass bounded by the <br />slip surface uhnl. Since the circular arc is an assumed slip sur(act, its position <br />is not determinate. The arc ubrd is therefore an arbitrarily assumed arc The <br />forces acting un the soil mass nbn/are the weight of the wil moss tr' and the <br />force on (he failure surface. The force on any element hr• of the slip surface <br />is composed of a normal cmuponent r7F„ and shear or tangential Component <br />dF, parallel to it. At (allure, dF, must be @qual to the shear strength of the <br />soil as expressed by Eq. (7.2), which in this case can be written :+i <br />1, <br />r <br />m dF. <br />c dl <br />df' <br />dF,=cell+dF„tangy <br />