Slope Stability Analysis with Rigid-Plastic Finite Element Method

Abstract

Rigid plastic finite element method was formulated for slope stability assessment by introducing the shear strength reduction coefficient to define the factor of safety used in slope stability. The framework of the proposed method was clarified in comparison with the limit equilibrium method based on slice method. The limit equilibrium method was shown to coincide with the upper bound theory in limit analysis and the process of minimizing the factor of safety for possible slip line was clarified to be important from the viewpoint of limit analysis. Rigid plastic FEM analysis has the advantages of (1) no need to assume the failure mode prior to analysis, (2) mathematical minimization of factor of safety, (3) use of constitutive equation and (4) taking account of dilatancy property of geo-material. The factor of safety was examined with simple slope for various conditions. It shows the good agreement with conventional methods and the applicability of proposed method was clarified. Case studies shows non-linear slip lines were well obtained corresponding to geometry and geology of slopes in the analysis. In some cases the sliding mass included several shearing zones inside and this fact suggests the existence of complicated failure mode not to be covered in the conventional methods. Keywords: stability analysis, finite element method, Rigid-Plastic FEM, Limit equilibrium method, limit analysis ˜a • ¶-v Ž|-{˜_ • ¶ ‚Í •"'Y•«-L OEÀ-v 'f-@ ‚Ì ŽÎ-ʈÀ'è‰ð •Í ‚Ö‚Ì 'è Ž® ‰» ‚ðŽ¦ ‚µ,‚» ‚Ì "K-p •« ‚ð-¾‚ç‚©‚É ‚µ‚½•B•" 'Y•«-L OEÀ-v 'f-@ ‚Ì 'è Ž® ‰» ‚Å‚Í ‹É OEÀ •½•t-@‚AE "äŠr ‚· ‚é ‚± ‚AE ‚É ‚ae‚è,-¼Žè-@ ‚ª ‹ÉOEÀ ‰ð •Í ‚Ì •ã ŠE'è-•‚ÉŠî ‚Ã‚-‚± ‚AE ‚ðŽ¦ ‚µ‚½•B•" 'Y•«-L OEÀ-v 'f-@‚Ì "Á'¥ ‚Í(1)‚· ‚× ‚è•ü ‚Ì ‰¼ 'è ‚ª •s-v,(2)ˆÀ'S-¦ ‚Ì •" Šw"I ‚È•Å•¬‰» ‰‰ ŽZ,(3)•\ •¬Ž®‚Ì-˜-p ‚É‚ae‚é•s •Ã'è-â'è ‚Ì ‰ð •Á,(4)ƒ_ ƒCƒOE ƒCƒ^ ƒ"ƒV•[ ‚Ì •l-¶ ‚ð‚ ‚° ‚ç‚ê ‚é•BŽ-á ‰ð •Í ‚É‚ae‚è‰ð •Í-@ ‚Ì ŽÎ-ʈÀ'è‚Ö‚Ì "K-p •« ‚ð-¾‚ç‚©‚É‚µ‚½•B ƒL•[ ƒ••[ ƒh:ˆÀ 'è ‰ð •Í,-L OEÀ-v 'f-@,•" 'Y•«,‹É OEÀ •½•t-@,‹É OEÀ ‰ð •Í 1.‚Í ‚ ¶ ‚ß ‚É ŽÎ-Ê ‚̈À‚̈À 'è ‰ð •Í ‚Í •ª Š"-@‚É'ã •\ ‚³ ‚ê ‚é ‹É OEÀ •½•t-@‚ª •• •L ‚-p‚¢ ‚ç ‚ê ‚Ä ‚« ‚½•B ‚± ‚Ì •û-@‚Ì "Á'¥ ‚Í ‚· ‚× ‚è•ü ‚ð "± "ü ‚· ‚é ‚± ‚AE‚É ‚ae ‚Á‚Ä‚· ‚× ‚è"y ‰ò ‚Ì ‰^ "® ‚ð •I ‚Ý ‚ɉð •Í ‚· ‚é "_ ‚É ‚ ‚é •B •ª Š"-@‚É ‚ae ‚é ‰ð•Í ‚Í ‚· ‚× ‚è"y‰ò‚ð ‚¢ ‚-‚ ‚©‚Ì •" 'Ì ƒu ƒ• ƒb ƒN‚É •ª Š" ‚µ ‚Ä‚· ‚× ‚è "y ‰ò‚Ì ‰^ "® ‚ð ‹L •q ‚· ‚é •B OE •X‚Ì •" 'Ì ƒu ƒ• ƒbƒN‚Ì ‰^ "®‚Ì ‹L •q ‚É ‚Í •ì-p-Í‚ª-¾‚ç ‚© ‚É ‚³ ‚ê ‚é •K-v‚ª ‚ ‚è,•ì-p-Í‚Ì •" ‚AE •ì-p-Í‚ð 'è ‚ß ‚é ‚½‚ß ‚Ì •û 'ö Ž®‚É ŠÖ‚· ‚é ‹c˜_‹c˜_ ‚ª •]-ˆ‚ae ‚è•· ‚ñ ‚É •s ‚í ‚ê ‚Ä ‚« ‚½(-á ‚¦ ‚Î,-] OEŽ‚ç1),‹ß "¡ ‚ç2),'n "Õ•HŠwƒn ƒ" ƒhƒu ƒbƒN3)‚È‚Ç)•B ‚µ ‚© ‚µ,ŽÀ-± ‚É ‚Ä-p‚¢ ‚ç ‚ê ‚é ‰ð •Í Žè-@‚͈ê@‚͈ê "Ê ‚ÉŠÈ•Ö ‚ÈŽè-@‚ª-p‚¢ ‚ç ‚ê ‚é ‚± ‚AE‚ª '½ ‚-,‹É OEÀ •½•t-@‚É ŠÖ‚· ‚é OE¤‹ † ‚Ì •¬ ‰Ê ‚ª ŽÀ-± ‚É•\ •ª ‚ÉŠÒOE³‚³ ‚ê ‚Ä‚¨‚ç‚Ä‚¨‚ç ‚¸,‚» ‚Ì ‚½‚ß ‚É ‹É OEÀ •½•t-@‚Ì "K-p •« ‚É ŠÖ‚· ‚é •M-Š •« ‚ª 'á ‰º‚· ‚é ‚± ‚AE‚AE‚È ‚Á‚Ä ‚¢ ‚é •B ‚± ‚Ì "wOEi‚É ‚Í ‹É OEÀ •½•t-@‚ð-p‚¢ ‚½Žè-@‚ª ‚¢ ‚-‚‚© 'ñ ˆÄ ‚³ ‚ê ‚Ä‚¨‚è‚Ä‚¨‚è,‚Ç ‚Ì •û-@‚ð-p‚¢ ‚ê ‚Î ‚ae ‚¢ ‚Ì ‚©‚ªˆê‚©‚ªˆê "Ê ‚É "F 'm ‚³ ‚ê ‚Ä‚¢ ‚È ‚¢ ‚± ‚AE‚ª ‚ ‚° ‚ç ‚ê ‚é •B ‚Ü‚½•ª Š"-@‚É ‚ae ‚é ‹É OEÀ •½•t-@‚Í ‚· ‚× ‚è •ü ‚ð •Ï ‰»‚³ ‚¹ ‚éˆÀ‚éˆÀ'S-¦‚Ì •Å•¬ ‰» ‰‰ ŽZ ‚ð •s ‚¤ •K-v ‚ª ‚ ‚è,‚· ‚× ‚è•ü ‚ð OEÅ 'è ‚µ ‚½‚· ‚× ‚è "y‰ò‚̈Ày‰ò‚̈À 'S-¦OEvŽZ ‚Í ŠÈ-ª‚Å‚ ‚é ‚Ì ‚É'Î ‚µ ‚Ä,‚· ‚× ‚è•ü ‚É ŠÖ‚· ‚é •ê • ‡ ‚Ì •" ‚Í "V• ¶ Šw"I •" Žš ‚É ‚È ‚é ‚½‚ß ‚ÉOEvŽZ-Ê ‚Í-c 'å ‚AE‚È ‚é-â'è ‚ª ‚ ‚é •B •Å•¬ ‰» ‰‰ ŽZ‚É ŠÖ‚· ‚é ƒAƒ‹ ƒS ƒŠƒYƒ€ ‚Ì OE¤‹ † ‚à •s ‚í ‚ê ‚Ä‚¢ ‚é ‚ª(-á ‚¦ ‚Î,ŽR •ã ‚ç4)),'S "Ê "I ‚ɉð •Í Žè-@ ‚É ŠÖ‚· ‚é •M-Š •« 'á ‰º‚Ì ‚½‚ß ‚ÉŠÈ-ª‰» ‚ª-D •ae ‚³ ‚ê ‚Ä‚¢ ‚é ‚Ì ‚ª OE»•ó ‚AEŽv ‚í ‚ê ‚é •B ‹É OEÀ •½•t-@‚Ì ‚ae ‚¤ ‚É ‚· ‚× ‚è•ü ‚AE•" 'Ì ƒu ƒ• ƒbƒN‚𠉼 'è ‚· ‚é •û-@‚AEˆÙ ‚È ‚é ‰ð •Í Žè-@‚ɘA'± 'Ì-•˜_ ‚ÉŠî ‚Ã ‚-L OEÀ-v 'f ‰ð •Í ‚ª ‚ ‚é •B •" 'Y•«-L OEÀ-v 'f-@‚Í 'n "Õ‚Ì ‹É OEÀ •ó 'Ô ‚ð '¼•Ú ‰ð •Í ‚· ‚é ‹É OEÀ ‰ð •Í ‚Ì •ã ŠE'è-•‚ÉŠî ‚Ã‚¢ ‚ÄŠJ"-‚³ ‚ê ‚½‰ð •Í Žè-@‚Å‚ ‚è,Žå ‚AE‚µ ‚Ä‹à '® ‚Ì 'Y•« ‰Á •H ‚Ì •ª-ì ‚Å"K-p‚³ ‚ê ‚Ä ‚« ‚½(-á ‚¦ ‚Î,•x "c5))•B 'n "Õ‚Ì •Þ-¿ "Á•« ‚ð •ã Žè ‚-•\ OE» ‚· ‚é ‚ae ‚¤ •\ •¬ ŠÖOEW ‚ð Šg'£ ‚· ‚é ‚± ‚AE‚É ‚ae ‚è,'n "Õ•HŠw‚Ì •ª-ì ‚Å ‚à 'n "Ղ̈ÀՂ̈À 'è •« •] ‰¿‚É-p‚¢ ‚ç ‚ê ‚é ‚ae ‚¤ ‚É ‚È ‚Á‚Ä‚¢ ‚é