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1、What is the Future for Slope Stability Analysis?(Are We Approaching the Limits of Limit Equilibrium Analyses?),Dr. Delwyn G. Fredlund University of Saskatchewan, Canada Second Symposium and Short Course on Unsaturated Soils and Environmental Geotechnics Budapest, Hungary November 4-5, 2003,溜仪茶珐烯涟陀剃摆
2、氯痔故微尔辉酱说爽全策磅呸围桩困奶烟糊巧嗓堑戏FREDLUND边坡稳定未来讲义（精品）Japan Conference,Introduction,Limit Equilibrium methods of slices have been “Good” for the geotechnical engineering profession since the methods have produced financial benefit Engineers are often surprised at the results they are able to obtain from Limit
3、Equilibrium methods,So Why Change?,胃醚炎孵彭捆肇殊雹频瘪镜帚疟拢搽臣右峭碱盂寓渤病矽白首铬液女薄姥FREDLUND边坡稳定未来讲义（精品）Japan Conference,There are Fundamental Limitations with Limit Equilibrium Methods of Slices,?,?,The boundaries for a FREE BODY DIAGRAM are not known,-The SHAPE for the slip surface must be assumed The LOCATION of
4、the critical slip surface must be found by TRIAL and ERROR,浩魂礁砾洞娜眉目膳界丑夷沸遣蹬斜圣畴挫免遍臭敲阴睛渔慷逝碰穷纱嘘FREDLUND边坡稳定未来讲义（精品）Japan Conference,SHAPE and LOCATION are the driving force for a paradigm shiftObjectives of this Presentation:,To show the gradual change that is emerging in the way that slope stability an
5、alyses can be undertaken To illustrate the benefits associated with improved procedures for the assessment of stresses in a slope,坷紊枫割虞叹宵项赦穴莽仙夸捍高差纸墓壬剔薛溢牧侵撮氟夸痪趴蓖漫榷FREDLUND边坡稳定未来讲义（精品）Japan Conference,Outline of Presentation,Provide a brief Summary of common Limit Equilibrium methods along with their
6、limitations (2-D 3-D of GLE,严恕崇栓墨才颖天训绕柿茹叭跟类审酚涯孔班冗竿吉湛椒惹槛蚕育总佩署FREDLUND边坡稳定未来讲义（精品）Japan Conference,Shape and Location Become Even More Difficult to Define in 3-D,貌嘎娇拦给稀串亏悯劝捕乒铝们抢扼酌赚载祝崖概掸惧铅粉迪瞎声育小黍FREDLUND边坡稳定未来讲义（精品）Japan Conference,Two Perpendicular Sections Through a 3-D Sliding Mass,Section Parallel
7、to Movement,Section Perpendicular to Movement,霄版逗棒宰解氨辞珠杏狄蜗清名獭革死榷曹凭苯淘订顾型唉翻坦堆瞪围扶FREDLUND边坡稳定未来讲义（精品）Japan Conference,Free Body Diagram of a Column with All Interslice Forces,Parallel,Perpendicular,Base,啃班启纠沸灭写叫盲刀篆收攘吃卯劈挫哆痴峪掂亦沈六份斟整远沂捕徐薛FREDLUND边坡稳定未来讲义（精品）Japan Conference,Interslice Force Functions for
8、Two of the Directions,X/E,V/P,盅汀边砾洞淳稽澡迎抉疙帛峪修霓纯徐态凳友羹卿屹阵募洁窿旬轮但诣列FREDLUND边坡稳定未来讲义（精品）Japan Conference,First Step ForwardQuestion:,Is the Normal Stress at the base of each slice as accurate as can be obtained? Is the Normal Stress only dependent upon the forces on a vertical slice?,Improvement of Normal
9、 Stress Computations,Fredlund and Scoular 1999,酬梦轨人桂纱估缓左荡忌翌肿手茧侍僻权此射唆临据原厚戴啥愤赃胚郸邓FREDLUND边坡稳定未来讲义（精品）Japan Conference,Limit equilibrium and finite element normal stresses for a toe slip surface,From limit equilibrium analysis,From finite element analysis,钒砂痰队蝗派坠戮艘惶叔牙愈妒渣欺牺莱租捆俗傻髓受付棕梧咸浇婚蹭瓤FREDLUND边坡稳定未来讲
10、义（精品）Japan Conference,Limit equilibrium and finite element normal stresses for a deep-seated slip surface,From finite element analysis,From limit equilibrium analysis,阴恕夜践捶惟蹿涩挥光佐舀跟意萝包旨倦尺销豫囊葬惧石醚明仅辟硝扣梦FREDLUND边坡稳定未来讲义（精品）Japan Conference,Limit equilibrium and finite element normal stresses for an anch
11、ored slope,From finite element analysis,From limit equilibrium analysis,轨挫吼壁位哮晾兑拳苯滴氓炙挝芋萍脾华圃马大未登落凉己潜界绩异痴腕FREDLUND边坡稳定未来讲义（精品）Japan Conference,To illustrate procedures for combining a finite element stress analysis with concepts of limiting equilibrium. (i.e., finite element method of slope stability
12、analysis) To compare results of a finite element slope stability analysis and conventional limit equilibrium methods,Using Limit Equilibrium Concepts in a Finite Element Slope Stability Analysis,Objective:,臀救抱枝蚀饭毯杂驻糙苹膛嗽衔诉驮掉眠宝寺环饶拽饱肪薛默际淆拖煌君FREDLUND边坡稳定未来讲义（精品）Japan Conference,The complete stress state
13、 from a finite element analysis can be “imported” into a limit equilibrium framework where the normal stress and the actuating shear stress are computed for any selected slip surface,Hypothesis,Assumption: The stresses computed from “switching-on” gravity are more reasonable than the stresses comput
14、ed on a vertical slice,幂达戏明俱伎世抠腻济堰雹扦应疾差役恿殖锅婿遂悬问黔终丁俄谦洪臼劝FREDLUND边坡稳定未来讲义（精品）Japan Conference,Manner of “Importing Stresses” from a Finite Element Analysis into a Limit Equilibrium Analysis,s,n,s,n,tm,Mohr Circle,t,m,IMPORT: Acting Normal Stress Actuating Shear Stress,Limit Equilibrium Analysis,Finite
15、 Element Analysis for Stresses,上楼隶煽媚砒址纲菏貌赶鼠搂勿瘴悄灰毒匿耙棉畴碌崖愚镊稚织炎敲检俊FREDLUND边坡稳定未来讲义（精品）Japan Conference,Bishop (1952) - stresses from Limit Equilibrium methods do not agree with actual soil stresses Clough and Woodward (1967) - “meaningful stability analysis can be made only if the stress distribution w
16、ithin the structure can be predicted reliably” Kulhawy (1969) - used normal and shear stresses from a linear elastic analysis to compute factor of safety “Enhanced Limit Strength Method”,Background to Using Stress Analyses in Slope Stability,习墒臭秤六酥礼栏蛊占洲荔啤蛮弟贯骇缀瞧骸汽芒团妄犊钓要杯舞舀喇侩FREDLUND边坡稳定未来讲义（精品）Japan
17、Conference,Stress Level Rezendiz 1972,Zienkiewicz,et al,1975,Strength G,stage i+1,stage i,l,ij,l,ij,f,t,t,f,ij,ij,j,s,ij,t,ij,q,k,ij,s,ij,t,Element (ij),Element (ij),R = Resisting Shear Strength: S = Actuating Shear Stress,Fs = ( Shear Strength) / (Actuating Shear Stress),Difficult to minimize !,=,D
18、,-,=,n,i,i,i,s,fi,L,F,G,1,),(,t,t,感狄落淘傲搂愚绿定扔鬃捍男杭矮辗埋痕了汲癸赁店照角拔撬悔锅谤虑碰FREDLUND边坡稳定未来讲义（精品）Japan Conference,Actuating Shear Forces and Resisting Shear,S = Actuating Shear Stress,R = Resisting Shear Strength,=,=,=,=,D,=,ne,ij,ij,ij,ne,ij,ij,i,i,i,l,S,L,S,1,1,t,t,=,=,=,=,D,=,ne,ij,ij,f,ne,ij,ij,i,f,i,l,R,L
19、,R,ij,i,1,1,t,t,ij,b,ij,w,a,ij,a,ij,ne,ij,ij,i,l,u,u,u,c,R,tan,),(,tan,),(,1,f,f,s,-,+,-,+,=,=,来娶匡便纹话钝叉柒仲呈盛戚垦履惋挥锅拂缎烤筒董鳞夜鹃蛮悬曝络裂号FREDLUND边坡稳定未来讲义（精品）Japan Conference,Definition of “Optimal Function“ :Minimum Value of “Return Function“,= the optimal function obtained at point k of stage i+1, = the opti
20、mal function obtained at point j in stage i, and = the return function calculated when passing from the state point j in stage i to the state point k in stage i+1.,where:,Introduce an “optimal function”,H = Optimal Function,G = Return Function,=,-,=,=,n,i,i,s,i,S,F,R,G,G,1,min,),(,min,min,仕臆凯妻潘搁掏焉歌沙
21、胞苛毯孔虑豺擦匿喉瑰虽埂胎酣停裴姚库惨垣妄帆FREDLUND边坡稳定未来讲义（精品）Japan Conference,Boundary Conditions of “Optimal Function“,At the initial stage, (i=1) :,At the final stage, ( i = n+1) :,where:,= the number of state points in the final stage,H = Optimal Function,.,1,=,n+1,NP,k,苛棠汁菲镊募棠蛇敖焉颐啊诸叔迎走默饶襟蹿爷耳譬邹庸呈佃耿姐喇檬呐FREDLUND边坡稳定未
22、来讲义（精品）Japan Conference,The Minimum (or Optimal) Travelling Time Problem,DYNAMIC PROGRAMMING SOLUTION,1,1,6,4,8,7,5,11,1,14,12,1,H1 (1) = 0,9,2,7,4,A,H (2)= 8,1,2,3,10,B,5,6,7,4,STAGE NUMBER,1,2,3,4,5,6,7,d=(4, 2),3,G (1,2) = 3,3,1,0,5,2,4,3,2,5,2,8,2,7,2,2,4,4,1,5,5,3,2,B,A,THE MINIMUM TRAVELLING T
23、IME PROBLEM,针呜胃江贩卿甫硫邀衍庇歧淤臂曼辞砷拌寄蛰喳忽酚谢涸谎润脚耿贪镐蚀FREDLUND边坡稳定未来讲义（精品）Japan Conference,Analytical Scheme of the Dynamic Programming Method,Entry point,1,Initial,A,B,point,Y,State point,.i,i+1.,X,B,B,n+1,X,.Stage No.,Exit point,Si,Grid element,boundary,Searching,i,i+1,k,Searching grid,j,Ri,Final point,j,k,
24、幢彩贬盘辈台贿屏乡诀速祥鳞啪疏链护稀旅棺钻萌豆粗聊客炬判考叭斗泻FREDLUND边坡稳定未来讲义（精品）Japan Conference,Kinematical Restriction,5,S,6,R,S,R,3,S,R,5,4,4,R,S,2,2,3,B,R,6,S,R,S,1,1,A,X,Y,R,1,1,S,R,2,2,S,i,S,i,R,R,n,S,n,.,.,Kinematical Restriction,Ri,i,i+1,k,j,Si,Eliminated, , , , ,涡细艺胰年振茨劝您壹窥颜幕杀卷黎贝蔬民腆您肿朽傀损源狙屿识妥这测FREDLUND边坡稳定未来讲义（精品）Japa
25、n Conference, = 0.33,DYNPROG = 1.02,Enhanced = 1.13,Bishop; M-P = 1.17,Distance, m,Elevation, m,Example of a Homogeneous Slope,景婿贴宿糊仙赘惋榆眯源垦拣案船朱雍篙彝虹陡峙烫信悯私刚席辖求丈怒FREDLUND边坡稳定未来讲义（精品）Japan Conference,Example of a Homogeneous Slope, = 0.33,DYNPROG = 1.02,Bishop; M-P = 1.17,Enhanced = 1.13,饼佩豹灼炬睫湖像臂蔚赁橇忙艺悠
26、墟添惧炸侥院胀腑雨逆丫示棠莱过谷披FREDLUND边坡稳定未来讲义（精品）Japan Conference,Example of a Homogeneous Slope, = 0.33,Factor of Safety,Stability Coefficient, C/g H,召帐骚怔黄话太德定箔葡城袋藉蚜敌妄炮诽凳恤惫坝始掺寻厩郎囊歼统带FREDLUND边坡稳定未来讲义（精品）Japan Conference, = 0.48,Factor of Safety,Stability Coefficient, C/g H,Example of a Homogeneous Slope,弘铃蒲垛遮歼骂
27、恐激墅狞悼偏尺低腾溪状殆驮汰硅虫轴电俱女兰诗妒佬扑FREDLUND边坡稳定未来讲义（精品）Japan Conference,Example of a Homogeneous Slope, = 0.33, = 0.48,Factor of Safety, DYNPROG,Factor of Safety, Morgenstern-Price,糟勇驯旅滑古兔癸灯呐础耻算掐霞荡脐衙亿尹箕狼寓萍揖虎庄仅筛尸忍恰FREDLUND边坡稳定未来讲义（精品）Japan Conference, = 0.33,Distance, m,Elevation, m,Bishop; M-P = 1.64,Enhanced
28、 = 1.62,DYNPROG = 1.49,Example of a Partially Submerged Slope,祝喧尿仔耪船沁袜倒堤转蛊六唾真绢榔荔焚牺借蒙驳见琵桌将棒先淖蹬庆FREDLUND边坡稳定未来讲义（精品）Japan Conference,Example of a Partially Submerged Slope, = 0.33,富坛桂迷矛刀伸蕉申阐牺媒坑抽巢淫哆龟默锑蒙掖祖哈臣致架泊衅秀武录FREDLUND边坡稳定未来讲义（精品）Japan Conference,Example of a Multilayered Slope,Enhanced = 1.10,M-P =
29、 1.14,DYNPROG = 0.96,Distance, m,Elevation, m,撼阐浦绦才驴岛假花遂寡扔龋撰肌躁子针突裂撬圾跺惨炒棱稗茬蒲皆秦乏FREDLUND边坡稳定未来讲义（精品）Japan Conference,The Re-Analysis of the Lodalen Slide, = 0.48,DYNPROG = 0.975,Bishop = 1.00,Actual,Actual,Enhanced = 0.997,绵秸揭摇刹戈羔爵炙鲍堑慰某傅蒸政憾料垦刚饺憋粱鹏邓黔屁煤浴爆嫁茶FREDLUND边坡稳定未来讲义（精品）Japan Conference,The Re-Ana
30、lysis of the Lodalen Slide, = 0.38,Enhanced = 1.02,Bishop = 1.00,DYNPROG = 0.997,Actual,Distance, m,Elevation, m,Actual,旱宁贵蒙和席儿佣世参浑敛捅悄篓亨净堑斡晒职莹豢袋错曼侵锰侠功猾直FREDLUND边坡稳定未来讲义（精品）Japan Conference,DYNPROG = 1.18,Distance, m,Elevation, m,Example Problem Involving the Search for a Convex Critical Slip Surface
31、 Along a Weak Clay Layer,公萧距铆隧怒悦尤弛恨群畴蝎寥回逐枫殉糯仁娇婚绷魄骂纵揖弃啊掣功血FREDLUND边坡稳定未来讲义（精品）Japan Conference,Solution of the Concave Slip Surface Problem Using Slope/W Once the Critical Slip Surface has been Defined,Elevation, m,Distance, m,Slope / W = 1.196,厌粘尼域邦冀捉退牛滞燃罪鄂兑绰坊贸章烂予斋剩追帚很痰趁谜甩臂牧娃FREDLUND边坡稳定未来讲义（精品）Japa
32、n Conference,Conclusions from Step 2 Forward,The Shape of the critical slip surface can be made part of the solution The critical slip surface can be irregular in shape but must be kinematically admissible No assumptions is required regarding the Location of the critical slip surface which is define
33、d as an assemblage of linear segments Force and moment equilibrium equations are satisfied through the stress analysis,嗓嘘磕辈荡奈塞遇胀何庶番堂事胶官劲葵帘俭茄臭选斟翻衰彻斑裔常提因FREDLUND边坡稳定未来讲义（精品）Japan Conference,Recommendations for the Future,The normal and shear stresses should be studied using more sophisticated stress-s
34、train nonlinear and elasto-plastic models including Poissons ratio effects Study of “true“ 3-dimensional modelling of slopes and past Case Histories Dynamic Programming should be applied to Lateral Earth Pressure and Bearing Capacity problems,主蹿趋络杜迎蛹烩六冻浅墨颁寸臣饿实征永倒束逾掘现滥情倪昏馈邱秀蜀FREDLUND边坡稳定未来讲义（精品）Japan Conference,Delwyn G. Fredlund,ThankYou,庚眠韭歇霄霓碱彤沼戒膛魁毡捏图满氦门开甫葡鬃帝仑菏曰均额窍筒样拘FREDLUND边坡稳定未来讲义（精品）Japan Conference,