[中英文翻譯]邊坡穩(wěn)定匯編

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1、土木建筑學(xué)院 土木0302班 學(xué)生邵明志 外文翻譯 第2頁共14頁 邊坡穩(wěn)定 重力和滲透力易引起天然邊坡、開挖形成的邊坡、堤防邊坡和土壩的不穩(wěn)定性。最重 要的邊坡破壞的類型如圖9.1所示。在旋滑中，破壞面部分的形狀可能是圓弧或非圓弧線。 總的來說，勻質(zhì)土為圓弧滑動(dòng)破壞，而非勻質(zhì)土為非圓弧滑動(dòng)破壞。平面滑動(dòng)和復(fù)合滑動(dòng) 發(fā)生在那些強(qiáng)度差異明顯的相鄰地層的交界面處。 平面滑動(dòng)易發(fā)生在相鄰地層處于邊坡破壞面以下相對(duì)較淺深度的地方：破壞面多為平 面，且與邊坡大致平行。復(fù)合滑動(dòng)通常發(fā)生在相鄰地層處于深處的地段，破壞面由圓弧面 和平面組成。 滑動(dòng)邊坡 圖瓦1邊坡破壞類型

2、在實(shí)踐中極限平衡法被用于邊坡穩(wěn)定分析當(dāng)中。它假定破壞面是發(fā)生在沿著一個(gè)假想 或已知破壞面的點(diǎn)上的。土的有效抗剪強(qiáng)度與保持極限平衡狀態(tài)所要求的抗剪強(qiáng)度相比， 就可以得到沿著破壞面上的平均安全系數(shù)。問題以二維考慮，即假想為平面應(yīng)變的情況。 二維分析為三維（碟形）面解答提供了保守的結(jié)果。 在這種分析方法中，應(yīng)用總應(yīng)力法，適用于完全飽和粘土在不條件排水下的情況。如 建造完工的瞬間情況。這種分析中只考慮力矩平衡。此間，假定潛在破壞面為圓弧面。圖 9.2展示了一個(gè)試驗(yàn)性破壞面（圓心 O,半徑r,長度La）。潛在的不穩(wěn)定性取決于破壞面 以上土體的總重量（單位長度上的重量 W。為了達(dá)到平衡，必須沿著破壞面?zhèn)?/p>

3、遞的抗剪強(qiáng) 度表小如下： 其中F是就抗剪強(qiáng)度而言的安全系數(shù).關(guān)于 O點(diǎn)力矩平衡: %"吟" 因此 圖9.2 mu情況的分析 (9.1) ~Wd~ 其它外力的力矩必須亦予以考慮。在張裂發(fā)展過程中，如圖 9.2所示，如果裂隙中充 滿水，弧長La會(huì)變短，超孔隙水壓力將垂直作用在裂隙上。有必要用一系列試驗(yàn)性破壞面 來對(duì)邊坡進(jìn)行分析，從而確定最小的安全系數(shù)。 FyH 基于幾何相似原理，泰勒［9.9］發(fā)表了《穩(wěn)定系數(shù)》，用于在總應(yīng)力方面對(duì)勻質(zhì)土邊坡 進(jìn)行分析。對(duì)于一個(gè)高度為 H的邊坡，沿著安全系數(shù)最小的破壞面上的穩(wěn)定系數(shù) （Ns）為： (9.2) 對(duì)于（h =0的情況，

4、Ns的值可以從圖9.3中得到。尺值取決于邊坡坡角B和高度系 數(shù)D,其中DH是到穩(wěn)固地層的深度。 吉布森和摩根斯特恩［9.3］發(fā)表了《不排水強(qiáng)度cu（ 4u=0）隨深度線性變化的正常固結(jié) 粘土邊坡的穩(wěn)定系數(shù)》。 在這種方法中，潛在破壞面再次被假定為以 。為圓心，以r為半徑的圓弧。試驗(yàn)性破 壞面（AQ以上的土體（ABCD,如圖9.5所示，被垂直劃分為一系列寬度為 b的條塊。 每個(gè)條塊的底邊假定為直線。對(duì)于任何一個(gè)條塊來說，其底邊與水平線的夾角為 a ,它的 高，從中心線測(cè)量，為h。安全系數(shù)定義為有效抗剪強(qiáng)度（Pf）與保持邊限平衡狀態(tài)的抗剪 強(qiáng)度（Pm）的比值，即： F h % 濟(jì)南大學(xué)畢

5、業(yè)設(shè)計(jì)用紙 土木建筑學(xué)院 土木0302班 學(xué)生邵明志 外文翻譯 第4頁共14頁 圖9. 5條分法 每個(gè)條塊的安全系數(shù)取相同值，表明條塊之間必須互相支持，即條塊間必須有力的作 用。 作用于條塊上的力（條塊每個(gè)單元維上法向力）如下： 1 .條塊總重量，W= b h （適當(dāng)時(shí)用Tsat） 2 .作用于底邊上總法向力，N （等于目）。總體上，這個(gè)力有兩部分：有效法向力N（等 于-1 ）和邊界孔隙水壓力U （等于ul）,其中u是底邊中心的孔隙水壓力，而l是底邊 長度。 3 .底邊上的剪力，T=r ml o 4 .側(cè)面上總法向力，E i和巳。 5 .側(cè)面上總剪力，Xi和X

6、2 任何的外力也必須包含在分析之中。 這是一種靜不定問題，為了得到解決，就必須對(duì)于條塊間作用力 E和X作出假定：安 全系數(shù)的最終解答是不準(zhǔn)確的。 考慮到圍繞。點(diǎn)的力矩，破壞弧AC上的剪力T的力矩總和，必須與土體 ABCDM量所 產(chǎn)生的力矩相等。對(duì)于任何條塊，W的力臂為rsin a , 因此 ETr=EWr sin a 則， 對(duì)于有效應(yīng)力方面的分析： E W sins 或者 此 + ian式卬 其中La是弧AC的長度。公式9.3是準(zhǔn)確的，但是當(dāng)確定力N’時(shí)引入了近似。對(duì)于給定 的破壞面，F(xiàn)的取值將決定于力N的計(jì)算方法。 在這種解法中，假定對(duì)于任何一個(gè)條塊，條間

7、的相互作用力為零。解答包括了解出每 個(gè)條塊垂直于底邊的作用力，即： N=WCO S -ul 因此，在有效應(yīng)力方面的安全系數(shù)（公式 9.3）,由下式計(jì)算： 也 + tan/(Wcosot 一 皿) Ursina (9.4) 對(duì)于每個(gè)條塊，Wcosx和Wsin a可以通過圖表法確定。a的取值可以通過測(cè)量或計(jì)算 得到。同樣地，也必須選擇一系列試驗(yàn)性的破壞面來獲得最小的安全系數(shù)。這種解法所得 的安全系數(shù)：與更精確的分析方法相比，其誤差通常為 5-2%。 應(yīng)用總應(yīng)力法分析時(shí)，使用參數(shù) Cu和（|）u,公式9.4中u取零。如果小u=0,那么安全系 數(shù)為： LIV sin a (9.5)

8、 因?yàn)镹’沒有出現(xiàn)在公式9.5中，故得到的安全系數(shù)F值是精確的 在這種解法中，假定條塊側(cè)面的力是水平的，即: X -X2=0 為了達(dá)到平衡，任何一個(gè)條塊底邊上的剪力為： 7 = / k" + N tan 解答垂直方向上的力: , c7 N 國［ Ncosa + ulcosa + Tsina + -tan^sini \ H f ） 很方便得到： l=b sec a 從公式9.3,通過一些重新整理， (9.6) F = rN 仲 + W-郵砌 sec a tan a tan (9.7) 孔隙水壓力通過孔壓比，可以與任何點(diǎn)的與總“填充壓力”相聯(lián)系，定義為: (

9、9.8) 濟(jì)南大學(xué)畢業(yè)設(shè)計(jì)用紙 土木建筑學(xué)院 土木0302班 學(xué)生邵明志 外文翻譯 第15頁共14頁 （適當(dāng)時(shí)用Y sat）.對(duì)于任何條塊, U % "麗 因此公式9.7可寫為： 「士麗占 ｛般+呷一..樹「湫:不 一一一 F」（9.9） 因?yàn)榘踩禂?shù)出現(xiàn)在公式 9.9的兩邊，必須使用一系列近似，才能獲得解答，但收斂 很快。 基于計(jì)算的重復(fù)性，需要選擇充分?jǐn)?shù)量的試驗(yàn)性破壞面。條分法特別適合于計(jì)算機(jī)解 答?？梢砸敫鼜?fù)雜的邊坡幾何學(xué)和不同的土層。 在大多數(shù)問題中，孔壓力比的取值 ru在整個(gè)破壞面上是不一致的，但一旦存在獨(dú)立的 高孔壓區(qū)，通常在設(shè)計(jì)中采用平均值（單位面

10、積上的荷重） 。同樣的，這種方法確定的安 全系數(shù)過低，但誤差不超過7%,多數(shù)情況下小于2%0 斯班瑟[9.8] 提出了一種分析方法，在此法中，條塊間的作用力是水平的，且滿足 力和力矩平衡。斯班瑟得到了只滿足力矩平衡的畢肖普簡化解，其精確度取決于邊坡條塊 間作用力力矩平衡的不敏感性。 基于公式9.9的勻質(zhì)土邊坡的穩(wěn)定系數(shù)，是由畢肖普和摩根斯特恩 [9.2]發(fā)表的。由此 可見，對(duì)于給定坡角和給定土性的邊坡，安全系數(shù)隨 Tu線性變化，因此可以表示為： F=m-T u （9.10） 其中m和n是穩(wěn)定系數(shù)。系數(shù) m和n是0 ,小‘，c/ 丫及深度系數(shù)D的函數(shù)。 假定潛在破壞面與邊坡面平行，所在

11、深度與邊坡長度相比很小。那么，邊坡可以看作無 限長，忽略端部效應(yīng)。邊坡與水平線成B角，破壞面深度為z如圖9.7中所示。水位線在破 壞面以上高度 mz （0

12、坡面與破壞面間的土 接下來的特殊情況是需要引起注意的。如果 是不完全飽和的)，那么： F =步 (9.11) tan fl 如果c =0和m=1仰水位線與邊坡面一致)，那么: (9.12) 應(yīng)當(dāng)注意的是，當(dāng)c =0時(shí)，安全系數(shù)是與深度無關(guān)的。如果 c大于零，那么安 . 一一 ,?一 、 、 , ? ? ?一一 、一 一、 ? 一 全系數(shù)就是z的函數(shù)，如果z比規(guī)定值還小的話，B可能會(huì)超過小。 應(yīng)用總應(yīng)力分析法，需使用抗剪強(qiáng)度參數(shù) cu和一，而u取值為零。 摩根斯特恩和普萊斯［9.4］提出了一般分析法，此法滿足所有的邊界條件和平衡條件， 破壞面可以是任何形狀，圓弧，

13、非圓弧或符合型。破壞面以上的土體被劃分為一系列垂直 的平面，問題通過假定每部分之間垂直邊界上的作用力 E和X的關(guān)系 而轉(zhuǎn)化為靜定。這 個(gè)假定的形式為 X=f(x)E (9.13) 其中f(x)是描述隨土體而變化的比值 X/E的形式的任意函數(shù)，而入是尺寸效應(yīng)系數(shù)。 入的值是在解安全系數(shù)F時(shí)一同獲得的。在每個(gè)垂直邊界上能夠確定作用力 E和X的值及 作用點(diǎn)。對(duì)于任意的假定函數(shù)f(x),有必要仔細(xì)地檢查解答，以確定其在物理學(xué)上的合 理性(即破壞面以上土體中沒有剪切破壞或張力)。函數(shù)f(x)的選擇對(duì)于F的計(jì)算值的影 響不能超過5% ,通常假定f(x)=l 。 這種分析包含了人和F值相互作用的復(fù)

14、雜過程，如摩根斯特恩和普萊斯 ［9.5］所描述的 那樣，計(jì)算機(jī)的運(yùn)用是必不可少的。 貝爾［9.1］提出了一種滿足所有平衡情況，假定破壞面可能是任何形狀的分析方法。 土體被劃分成一系列垂直的條塊，通過沿著破壞面上的法向作用力的假想分配，轉(zhuǎn)化為靜 定問題。 薩爾瑪［9.6］ 基于條分法發(fā)展了一種方法，在此法中，產(chǎn)生極限平衡所要求的臨界地 震加速度是確定的。這種分析方法在分析中假定了條塊間垂直作用力的分配。同樣的，滿 足所有的平衡條件，破壞面可以是任何形狀。靜安全系數(shù)是土的抗剪強(qiáng)度必須減小，以致 于臨界加速度為零時(shí)的系數(shù)。 計(jì)算機(jī)的使用對(duì)于貝爾法和薩爾瑪法來說，是必不可少的。所有的解答必須要檢

15、查， 以確保它們?cè)谖锢韺W(xué)上是可以接受的。 Stability of Slopes by Gravitational and seepage forces tend to cause instability in natural slopes, in slopes formed by excavation and in the slopes of embankments and earth dams. The most important types of slope failure are illustrated in Fig.9.1.In rotational slips the s

16、hape of the failure surface in section may be a circular arc or a non-circular curve. In general, circular slips are associatedwith homogeneous soil conditions and non-circular slips with non-homogeneous conditions. Translational and compound slips occur where the form of the failure surface is infl

17、uenced the presence of an adjacent stratum of significantlydifferent strengt h Translational slips tend to occur where the adjacent stratum is at a relatively shallow depth below the surface of the slope:the failure surface tends to be plane and roughly parallel to the slope.Compound slips usually

18、 occur where the adjacent stratum is at greater depth the failure surface consisting of curved and plane section, s Tyjm of Sge failure In practice, limiting equilibrium methods are used in the analysis of slope stability. It is considered that failure is on the point of occurring along an assum

19、ed or a known failure surface. The shear strength required to maintain a condition of limiting equilibrium is compared with the available shear strength of the soil giving the average factor of safety along the failure surface. The problem is considered in two dimensions, conditions of plane strain

20、being assumed It has been shown that a two-dimensional analysis gives a conservative result for a failure on a three-dimensional(dish-shaped) surfac e This analysis, in terms of total stress, covers the case of a fully saturated clay under undrained conditions, i.e. For the condition immediately af

21、ter construction. Only moment equilibrium is considered in the analysis In section, the potential failure surface is assumed to be a circular arc. A trial failure surface(centre O, radius r and length La)is shown in Fig.9.2. Potential instability is due to the total weight of the soil mass(W per uni

22、t Length) above the failure surface. For equilibrium the shear strength which must be mobilized along the failure surface is expressed as t ==— 冊(cè) F F where F is the factor of safety with respect to shear strength Equating moments about O Therefore Kg 91 The e.二 0 anwhsis. Wd (9.1) The mome

23、nts of any additional forces must be taken into account In the event of a tension crack developing , as shown in Fig.9.2, the arc length La is shortened and a hydrostatic force will act normal to the crack if the crack Ills with water . It is necessary to analyze the slope for a number of trial fail

24、ure surfaces in order that the minimum factor of safety can be determine d Based on the principle of geometric similarity, Taylor[9.9]published stability coefficients for the analysis of homogeneous slopes in terms of total stres s For a slope of height H the stability coefficient (Ns) for the fail

25、ure surface along which the factor of safety is a minimum is (9.2) For the case of u =0^ values of Ns can be obtained from Fig.93The coefficient N depends on the slope angle 0 and the depth facwh ere DH is the depth to a firm stratum. Gibson and Morgenstern [9.3] published stability coefficients

26、for slopes in normally consolidated clays in which the undrained strength u( u =0) varies linearly with depth. I- ig. 7、 1 tie mel tiocE of slices In this method the potential failure surface in section, is again assumed to be a circular arc with centre O and radius r. The soil mass (ABCD) above a

27、 trial failure surface (AC) is divided by vertical planes into a series of slices of width b, as shown in Fig.9.5.The base of each slice is assumed to be a straight lineFor any slice the inclination of the base to the horizontal is height, measured on the centre-1ine,is h. The factor of safety is de

28、fined as the ratio of the available shear strength( f)tor the shear strength( m) iwhich must be mobilized to maintain a condition of limiting equilibrium, i.e. The factor of safety is taken to be the same for each slice, implying that there must be mutual support between slices i.e. forces must ac

29、t between the slices The forces (per unit dimension normal to the section) acting on a slice are 1 .The total weight of the slice, W=y b h (sat/where appropriate) 2 .The total normal force on the base N (equal to . dn) general this force has two components, the effective normal force N(equal to

30、o- l ) and the boundary water force U(equal to ul ), where u is the pore water pressure at the centre of the base and l is the length of the base 3 .The shear force on the base T= iml. 4 .The total normal forces on the sides, E and E2. 5 .The shear forces on the sides Xi and X2. Any external fo

31、rces must also be included in the analysis The problem is statically indeterminate and in order to obtain a solution assumptions must be made regarding the interslice forces E and X the resulting solution for factor of safety is not exact. Considering moments about Q the sum of the moments of the

32、shear forces T on the failure arc AC must equal the moment of the weight of the soil mass ABCD For any slice the lever arm of W is rsin a , therefore E Tr= E Wr sin a Now, T = r/=? I F =工亞血工 .卬 For an analysis in terms of effective stres s ES + rftan 修 I 二—lIVsina Or cLb + lan (9.3) Sllsi

33、nx where La is the arc length AC . Equation 9.3 is exact but approximations are introduced in determining the forces N. For a given failure arc the value of F will depend on the way in which the forces N are estimated In this solution it is assumed that for each slice the resultant of the intersli

34、ce forces is zero The solution involves resolving the forces on each slice normal to the ba ei.e. N=WCOS -ul Hence the factor of safety in terms of effective stress (Equation 9.3) is given by Iosina crLf + tan W cos - ui) (9.4) for each The components WCOS and Wsin a can be determined graphi

35、cally 濟(jì)南大學(xué)畢業(yè)設(shè)計(jì)用紙 slice. Alternatively , the value of a can be measured or calciAgtein, a series of trial failure surfaces must be chosen in order to obtain the minimum factor of safety. This solution underestimates the factor of safet ythe error, compared with more accurate methods of analy

36、sis is usually within the range 5-2%. For an analysis in terms of total stress the parameters Cand 而 are used and the value of u in Equation 9.4 is zero. If u=0 ,the factor of safety is given by (9.5) As N does not appear in Equation 9.5 an exact value of F is obtained In this solution it is ass

37、umed that the resultant forces on the sides of the slices are horizontal, i.e. Xl-X2=0 For equilibrium the shear force on the base of any slice is 丁 = / + 卻tan 在) Resolving forces in the vertical direction: 力 V Nc&s i + ulcos i + —sin i + — tan i1 疝 a F F 一卜=修一機(jī)觸，正005!! COSI + F f It is

38、 convenient to substitute l=b sec a From Equation 9.3, after some rearrangemen,t (9.6) 琲加產(chǎn) :+吧吧 The pore water pressure can be related to the total point by means of the dimensionless pore pressure rat jo defined as u 「調(diào) (sat where appropriate). For any slice, u r - ,— "W/b Hence Equation

39、 9.7 can be written: (9.7) fill pressure (9.8) F (9.9) at any As the factor of safety occurs on both sides of Equation 99a process of successive approximation must be used

40、to obtain a solution but convergence is rap id Due to the repetitive nature of the calculations and the need to select an adequate number of trial failure surfaces, the method of slices is particularly suitable for solution by computer More complex slope geometry and different soil strata can be in

41、troduce d In most problems the value of the pore pressure ratio ru is not constant over the whole failure surface but, unless there are isolated regions of high pore pressure, an average value(weighted on an area basis) is normally used in design. Again, the factor of safety determined by this meth

42、od is an underestimate but the error is unlikely to exceed % and in most cases is less than 2 . Spencer [9.8] proposed a method of analysis in which the resultant Interslice forces are parallel and in which both force and moment equilibrium are satisfied. Spencer showed that the accuracy of the Bis

43、hop simplified method, in which only moment equilibrium is satisfied, is due to the insensitivity of the moment equation to the slope of the interslice force s Dimensionless stability coefficients for homogeneous slopes based on Equation 9.9 have been published by Bishop and Morgenstern [9.2].It ca

44、n be shown that for a given slope angle and given soil properties the factor of safety varies linearly with u and can thus be expre ssed as F=m-n u (9.10) where, m and n are the stability coefficients. The coefficients, m and n are functions of p the dimensionless number c/ 丫 and the depth factor

45、D. Using the Fellenius method of slices, determine the factor of safety, in terms of effective stress, of the slope shown in Fig.9.6 for the given failure surface The unit weight of the soil, both above and below the water table is 20 kN /m and the relevant shear strength parameters are c =10 kN/m

46、nd[=29. The factor of safety is given by Equation 9.4.The soil mass is divided into slices l.5 m wide. The weight (W) of each slice is given by W=T bh=20X51 油=30h kN/m The height h for each slice is set off below the centre of the base and the normal and tangential components hcos a and hsin a r

47、espectively are determined graphicaas shown in Fig.9.6.Then Wcosa =30h cos a W sin a =30h sin a The pore water pressureat the centre of the base of each slice is taken to b碰zw, where zw y is the vertical distance of the centre point below the water table (as shown in figure). This procedure slig

48、htly overestimates the pore water pressure which strictly should be/ze, where ze is the vertical distance below the point of intersection of the water table and the equipotential through the centre of the slice base The error involved is on the safe side The arc length (La) is calculated as 14.35 m

49、m The results are given in Table 9.1 E Wcosa =30 x 17.50=525kNm EW sin a =30X8.45=254km E (wcos -M)=525 —132=393kN/m *。工“ + tan 力E(Wc口sot — u/) EWsinot (tO x 14 35) + (0 554 x 393) 254 1435 + 218 ，小 「昨9看 Table 9.! Slux h COS Q h sin j i ui no ㈣ 1叫 IkN m2] 向卜 ikNym) 1 0

50、75 -0 15 5-9 1-55 91 2 1 80 -0 10 b5U 17 7 3 2 70 0 40 162 155 25 4 32S r do 1*1 1 60 5 J 45 b75 J7 1 1 70 29 1 6 MO 2-35 心 1 95 22 0 7 1 90 225 0 255 O 8 055 0-95 0 245 0 1750 H45 1435 It is assumed that the potential failure surface is p

51、arallel to the surface of the slope and is at a depth that is small compared with the length of the slope. The slope can then be considered as being of infinite length , with end effects being ignored. The slope is inclined at angle 0 to the horizontal and the depth of the failure plane is z. as sh

52、own in section in Fig.97The water table is taken to be parallel to the slope at a height of mz (0

53、ns are the same at every point on the failure plane. J-ifL 胃? FLinc cr^rivlali^niLil

54、8s2# T = {(1 -帥 + IM、)工品?ssf u = mzyw cos7 The following special cases are of interest If c =0 and m=0 (i.e. the so between the surface and the failure plane is not fully saturated),then A— tan 由 tan /? (9.11) If c lan fi =0 and m=1(i.e. the water table coincides with the surface of the

55、 s [opeen： (9.12) m may ex It should be noted that when c =0 the factor of safety is independent of the depth z. If c is greater than zetbe factor of safety is a function of z, and provided z is less than a critical value For a total stress analysis the shear strength parameters^ ond 加 are used

56、 with a zero value of u. Morgenstern and Price[9.4]developed a general analysis in which all boundary and equilibrium conditions are satisfied and in which the failure surface may be any shap e circular, non-circular or compound. The soil mass above the failure plane is divided into sections by a n

57、umber of vertical planes and the problem is rendered statically determinate by assuming a relationship between the forces E and X on the vertical boundaries between each section This assumption is of the form X=X f(x)E (9.13) where f(x)is an arbitrary function describing the pattern in which the r

58、atio X/E varies across the soil mass and 入 is a scale factoralue of 入 is obtained as part of theioo along with the factor of safety F . The values of the forces E and X and the point of application of E can be determined at each vertical boundary For any assumed function f(x) it is necessary to exam

59、ine the solution in detail to ensure that it is physically reasonable (i.e. no shear failure or tension must be implied within the soil mass above the failure surface). The choice of the function f(x) does not appear to influence the computed value of F by more than about 5% and f(x)=l is a common a

60、ssumption. The analysis involves a complex process of iteration for the values of , described by 入 and F Morgenstern and Price[9.5], and the use of a computer is essential. Bell [9.1] proposed a method of analysis in which all the conditions of equilibrium are satisfied and the assumed failure sur

61、face may be of any shape The soil mass is divided into a number of vertical slices and statical determinacy is obtained by means of an assumed distribution of normal stress along the failure surface Sarma [9.6] developed a method, based on the method of slices, in which the critical earthquake acce

62、leration required to produce a condition of limiting equilibrium is determined. An assumed distribution of vertical interslice forces is used in the analysis Again , all the conditions of equilibrium are satisfied and the assumedfailure surface may be of any shape. The static factor of safety is the factor by which the shear strength of the soil must be reduced such that the critical acceleration is zero The use of a computer is also essential for the Bell and Sarma methods and all solutions must be checked to ensure that they are physically acceptab le 來源： (巖土英語)