[中英文翻譯]邊坡穩(wěn)定匯編

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(yè)共14頁(yè)邊坡穩(wěn)定重力和滲透力易引起天然邊坡、開(kāi)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(lèi)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(xiàn)。 總的來(lái)說(shuō)，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?；瑒?dòng)邊坡圖瓦1邊坡破壞類(lèi)型在實(shí)踐中極限平衡法被用于邊坡穩(wěn)定分析當(dāng)中。它假定

2、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(wèn)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(zhǎng)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(zhǎng)度上的重量 w。為了達(dá)到平衡，必須沿著破壞面?zhèn)鬟f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

3、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(guò)程中，如圖 9.2所示，如果裂隙中充 滿(mǎn)水，弧長(zhǎng)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(lái)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，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

4、摩根斯特恩9.3發(fā)表了不排水強(qiáng)度cu（ 4u=0）隨深度線(xiàn)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(xiàn)。對(duì)于任何一個(gè)條塊來(lái)說(shuō)，其底邊與水平線(xiàn)的夾角為a ,它的高，從中心線(xiàn)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(yè)共14頁(yè)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

5、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）?？傮w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(zhǎng)度。3 .底邊上的剪力，t=r ml o4 .側(cè)面上總法向力，e i和巳。5 .側(cè)面上總剪力，xi和x2任何的外力也必須包含在分析之中。這是一種靜不定問(wèn)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?？紤]到圍繞。點(diǎn)的力矩，破壞弧ac上的剪力

6、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l(wèi)a是弧ac的長(zhǎng)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)

7、對(duì)于每個(gè)條塊，wcosx和wsin a可以通過(guò)圖表法確定。a的取值可以通過(guò)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(lái)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)因?yàn)閚沒(méi)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(guó) n&#

8、39;cosa + ulcosa + tsina + -tansini h f ）很方便得到：l=b sec a從公式9.3,通過(guò)一些重新整理，(9.6)f = £rn 仲 + w-郵砌sec atan a tan(9.7)孔隙水壓力通過(guò)孔壓比，可以與任何點(diǎn)的與總“填充壓力”相聯(lián)系，定義為:(9.8)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(yè)共14頁(yè)（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(xiě)為：士麗占£ 般+呷一.樹(shù)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

9、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(wèn)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（單位面積上的荷重） 。同樣的，這種方法確定的安 全系數(shù)過(guò)低，但誤差不超過(guò)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(mǎn)足 力和力矩平衡。斯班瑟得到了只滿(mǎn)足力矩平衡的畢肖普簡(jiǎn)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

10、9.2發(fā)表的。由此 可見(jiàn)，對(duì)于給定坡角和給定土性的邊坡，安全系數(shù)隨tu線(xiàn)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，所在深度與邊坡長(zhǎng)度相比很小。那么，邊坡可以看作無(wú) 限長(zhǎng)，忽略端部效應(yīng)。邊坡與水平線(xiàn)成b角，破壞面深度為z如圖9.7中所示。水位線(xiàn)在破 壞面以上高度 mz （0<m<1）處,與邊坡平行。假定穩(wěn)定滲流發(fā)生在與邊坡平行的方向上。任 何垂直條塊側(cè)面上白力是等值反向的，且破壞面上任意一點(diǎn)的應(yīng)力狀態(tài)是相同的.圖9. 7平面層滑應(yīng)用有效應(yīng)力法，沿著破壞面上的土的抗剪

11、強(qiáng)度為0 = c' + (tr - u)tan 0'安全系數(shù)為:b=1 一m)y +西九職上cos'°t = (i - m)y + zsinflcos/? h = /nzywcos2 flc' =0和m=0 (即坡面與破壞面間的土接下來(lái)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(xiàn)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(wú)關(guān)的。如果c'大于零，那么安. 一一 ,一 、 、 , 一一 、一 一、 '

12、一 '全系數(shù)就是z的函數(shù)，如果z比規(guī)定值還小的話(huà)，b可能會(huì)超過(guò)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(mǎn)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，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(wèn)題通過(guò)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

13、(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(méi)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(guò)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)雜過(guò)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(mǎn)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(guò)沿著破壞面上的法向作用力的假想分配，轉(zhuǎn)化為靜 定問(wèn)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

14、。同樣的，滿(mǎn) 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(lái)說(shuō)，是必不可少的。所有的解答必須要檢查， 以確保它們?cè)谖锢韺W(xué)上是可以接受的。stability of slopesbygravitational 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 mo

15、st important types of slope failure are illustrated in fig.9.1.in rotational slips the shape 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 conditio

16、ns. translational and compound slips occur where the form of the failure surface is influencedthe presence of an adjacent stratum of significantlydifferent strengt htranslational slips tend to occur where the adjacent stratum is at a relatively shallow depth below the surface of the slope:the failur

17、e surface tends to be plane and roughly parallel to the slope.compound slips usually occur where the adjacent stratum is at greater depth the failure surface consisting of curved and plane section, styjm of sge failurein practice, limiting equilibrium methods are used in the analysis of slope stabil

18、ity. it is considered that failure is on the point of occurring along an assumed 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 sur

19、face. the problem is considered in two dimensions, conditions of plane strain 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 ethis analysis, in terms of total stress, covers the case of a fully satu

20、rated clay under undrained conditions, i.e. for the condition immediately after 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.

21、 potential instability is due to the total weight of the soil mass(w per unit length) above the failure surface. for equilibrium the shear strength which must be mobilized along the failure surface is expressed ast =冊(cè) f fwhere f is the factor of safety with respect to shear strength equating moments

22、 about othereforekg 91 the e.二 0 anwhsis.wd(9.1)the moments 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 n

23、ecessary to analyze the slope for a number of trial failure surfaces in order that the minimum factor of safety can be determine dbased on the principle of geometric similarity, taylor9.9published stability coefficients for the analysis of homogeneous slopes in terms of total stres s for a slope of

24、height h the stability coefficient (ns) for the failure 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 morgen

25、stern 9.3 published stability coefficients 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 slicesin this method the potential failure surface in section, is again assumed to be a circular arc with centre o and

26、radius r. the soil mass (abcd) above a 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

27、-1ine,is h. the factor of safety is defined 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

28、 between slices i.e. forces must act between the slicesthe forces (per unit dimension normal to the section) acting on a slice are1 .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 thisforce has two components, the effecti

29、ve normal force n'(equal too- 'l ) and the boundarywater 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 base3 .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

30、 xi and x2.any external forces must also be included in the analysisthe 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

31、of the moments of the 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 , thereforee tr= e wr sin anow,t = r/=? i f=工亞血工.卬for an analysis in terms of effective stres ses + rftan 修 i 二livsinaorclb + lan(9.3)sllsin

32、xwhere 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 estimatedin this solution it is assumed that for each slice the resultant of the int

33、erslice forces is zero the solution involves resolving the forces on each slice normal to the ba§ ei.e.n'=wcos -ulhence the factor of safety in terms of effective stress (equation 9.3) is given byiosinacrlf + tan w cos « - ui)(9.4)for eachthe components wcos andwsin a can be determined

34、 graphically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 solutionunderestimates the factor of safet ythe error, compared with more accurate methods of analysis i

35、s 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 obtainedin this solution it is assumed tha

36、t the resultant forces on the sides of theslices are horizontal, i.e.xl-x2=0for equilibrium the shear force on the base of any slice is丁 =/ + 卻'tan 在)resolving forces in the vertical direction:力vn'c&s i + ulcos i + sin i + tan i1 疝 aff一卜=修一»機(jī)觸，正005! cosi +' ffit is convenient to

37、 substitutel=b sec afrom equation 9.3, after some rearrangemen,t(9.6)琲加產(chǎn):+吧吧the pore water pressure can be related to the totalpoint by means of the dimensionless pore pressure rat jo defined asu調(diào)(sat where appropriate). for any slice, u r -,"w/bhence equation 9.7 can be written:(9.7)fill press

38、ure(9.8)f(9.9)at anyas the factor of safety occurs on both sides of equation 99a process of successive approximation must be used to obtain a solution but convergence is rap iddue to the repetitive nature of the calculations and the need to select an adequate number of trial failure surfaces, the me

39、thod of slices is particularly suitable for solution by computer more complex slope geometry and different soil strata can be introduce din 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 pressur

40、e, an average value(weighted on an area basis) is normally used in design. again, the factor of safety determined by this method 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 for

41、ces are parallel and in which both force and moment equilibrium are satisfied. spencer showed that the accuracy of the bishop 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 sdimensionless stabi

42、lity coefficients for homogeneous slopes based on equation 9.9 have been published by bishop and morgenstern 9.2.it can 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 asf=m-n u(9.10)where, m and n are the stabili

43、ty coefficients. the coefficients, m and n are functions of p the dimensionless number c'/丫 and the depth factor 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 th

44、e soil, both above and below the water table is 20 kn /m and the relevant shear strength parameters are c ' =10 kn/mnd=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 byw=t bh=20x51 油=30h kn/mthe height

45、h for each slice is set off below the centre of the base and the normal and tangential components hcos a and hsin a respectively are determined graphicaas shown in fig.9.6.thenwcosa =30h cos aw sin a =30h sin athe pore water pressureat the centre of the base of each slice is taken to b碰zw, where zwy

46、is the vertical distance of the centre point below the water table (as shown in figure). this procedure slightly 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 c

47、entre of the slice base the error involved is on the safe sidethe arc length (la) is calculated as 14.35 mm the results are given in table 9.1e wcosa =30 x 17.50=525knmew sin a =30x8.45=254kme (wcos -m)=525 132=393kn/m*。工“ + tan 力'e(wc口sot u/) ewsinot(to x 14 35) + (0 554 x 393)2541435 + 218 ，小昨

48、9看table 9.!sluxh cos qh sin jiuino1叫ikn m2向卜iknym)1075-0 155-91-559121 80-0 10b5u17 732 700 4016215525 »432sr do1*11 605j 45b75j7 11 7029 16mo2-35心1 9522 071 902250255o80550-95024501750h451435it is assumed that the potential failure surface is parallel to the surface of the slope and is at a de

49、pth 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 angle0 to thehorizontal and the depth of the failure plane is z. as shown in section in fig.97the water table is taken to b

50、e parallel to the slope at a height of mz (0<m<1)above the failure plane. steady seepage is assumed to be taking place in a direction parallel to the sloperhe forces on the sides of any vertical slice are equal and opposite and the stress conditions are the same at every point on the failure p

51、lane.j-ifl 胃 flinc crrivlalinilil <lipin terms of effective stress, the shear strength of the soil along the failure plane ist/=c' + (<r u)tanand the factor of safety isf = %the expressions for o-, r and ii are:仃=(1 - tn)y + 用%j 2 8s2#t = (1 -帥 + im、)工品?ssfu = mzyw cos7the following specia

52、l cases are of interest if c =0 and m=0 (i.e. the sobetween the surface and the failure plane is not fully saturated),thena'tan 由'tan /?(9.11)if clan fi=0 and m=1(i.e. the water table coincides with the surface of the s opeen：(9.12)m may exit should be noted that when c=0 the factor of safet

53、y is independent ofthe depth z. if c is greater than zetbe factor of safety is a function of z, and provided z is less than a critical valuefor a total stress analysis the shear strength parameters ond 加 are used with a zero value of u.morgenstern and price9.4developed a general analysis in which al

54、l 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 number 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 formx=x f(x)e(9.13)where f(x)is