土木專業(yè)外文翻譯---簡(jiǎn)要的分析斜坡穩(wěn)定性的方法

1、<p>　　INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS</p><p>　　Int. J. Numer. Anal. Meth. Geomech., 23, 439}449 (1999)</p><p>　　SHORT COMMUNICATIONS</p>&l

2、t;p>　　ANALYTICAL METHOD FOR ANALYSIS OF SLOPE</p><p><b>　　STABILITY</b></p><p>　　JINGGANG CAOs AND MUSHARRAF M. ZAMAN*t</p><p>　　School of Civil Engineering and Envir

3、onmental Science, University of Oklahoma, Norman, OK 73019, U.S.A.</p><p><b>　　SUMMARY</b></p><p>　　An analytical method is presented for analysis of slope stability involving cohesi

4、ve and non-cohesive soils.Earthquake effects are considered in an approximate manner in terms of seismic coe$cient-dependent forces. Two kinds of failure surfaces areconsidered in this study: a planar failure surface, an

5、d a circular failure surface. The proposed method can be viewed as an extension of the method of slices, but it provides a more accurate etreatment of the forces because they are represented in an i</p><p>　

6、　The factors of safety obtained by the analytical method are found to be in good agreement with those determined by the local minimum factor-of-safety, Bishop's, and the method of slices. The proposed method is strai

7、ghtforward, easy to use, and less time-consuming in locating the most critical slip surface and calculating the minimum factor of safety for a given slope. Copyright ( 1999) John Wiley & Sons, Ltd.</p><p&g

8、t;　　Key words: analytical method; slope stability; cohesive and non-cohesive soils; dynamic effect; planar failure surface; circular failure surface; minimization technique; factor-of-safety.</p><p>　　INTROD

9、UCTION</p><p>　　One of the earliest analyses which is still used in many applications involving earth pressure was proposed by Coulomb in 1773. His solution approach for earth pressures against retaining wal

10、ls used plane sliding surfaces, which was extended to analysis of slopes in 1820 by Francais. By about 1840, experience with cuttings and embankments for railways and canals in England and France began to show that many

11、failure surfaces in clay were not plane, but signi"cantly curved. In 1916, curved failure</p><p>　　circular and non-circular sliding surfaces . In recent years, numerical methods have also been used in

12、the slope stability analysis with the unprecedented development of computer hardware and software. Optimization techniques were used by Nguyen,10 and Chen and Shao. While finite element analyses have great potential for

13、modelling field conditions realistically, they usually require signi"cant e!ort and cost that may not be justi"ed in some cases.</p><p>　　The practice of dividing a sliding mass into a number of sl

14、ices is still in use, and it forms the basis of many modern analyses.1,9 However, most of these methods use the sums of the terms for all slices which make the calculations involved in slope stability analysis a repetiti

15、ve and laborious process.</p><p>　　Locating the slip surface having the lowest factor of safety is an important part of analyzing a slope stability problem. A number of computer techniques have been develope

16、d to automate as much of this process as possible. Most computer programs use systematic changes in the position of the center of the circle and the length of the radius to find the critical circle.</p><p>　

17、　Unless there are geological controls that constrain the slip surface to a noncircular shape, it can be assumed with a reasonable certainty that the slip surface is circular.9 Spencer (1969) found that consideration of c

18、ircular slip surfaces was as critical as logarithmic spiral slip surfaces for all practical purposes. Celestino and Duncan (1981), and Spencer (1981) found that, in analyses where the slip surface was allowed to take any

19、 shape, the critical slip surface found by the search was ess</p><p>　　The circular slip surfaces are employed for analysis of clayey slopes, within the framework of an analytical approach, in this study. Th

20、e proposed method is more straightforward and simpler than that developed by Chen and Liu. Earthquake effects are included in the analysis in an approximate manner within the general framework of static loading. It is ac

21、knowledged that earthquake effects might be better modeled by including accumulated displacements in the analysis. The planar slip surfaces are </p><p>　　STABILITY ANALYSIS CONDITIONS AND SOIL STRENGTH</p

22、><p>　　There are two broad classes of soils. In coarse-grained cohesionless sands and gravels, the shear strength is directly proportional to the stress level:</p><p><b>　?。?）</b></p

23、><p>　　where is the shear stress at failure, the effective normal stress at failure, and the effective angle of shearing resistance of soil.</p><p>　　In fine-grained clays and silty clays, the st

24、rength depends on changes in pore water pressures or pore water volumes which take place during shearing. Under undrained conditions, the shear strength cu is largely independent of pressure, that is=0. When drainage is

25、permitted, however, both &cohesive' and &frictional' components are observed. In this case the shear strength is given by</p><p><b>　　(2)</b></p><p>　　Consideration o

26、f the shear strengths of soils under drained and undrained conditions, and of the conditions that will control drainage in the field are important to include in analysis of slopes. Drained conditions are analyzed in term

27、s of effective stresses, using values of determined from drained tests, or from undrained tests with pore pressure measurement. Performing drained triaxial tests on clays is frequently impractical because the required te

28、sting time can be too long. Direct shear test</p><p>　　Stability analysis involves solution of a problem involving force and/or moment equilibrium.The equilibrium problem can be formulated in terms of (1) to

29、tal unit weights and boundary water pressure; or (2) buoyant unit weights and seepage forces. The first alternative is a better choice, because it is more straightforward. Although it is possible, in principle, to use bu

30、oyant unit weights and seepage forces, that procedure is fraught with conceptual diffculties.</p><p>　　PLANAR FAILURE SURFACE</p><p>　　Failure surfaces in homogeneous or layered non-homogeneous

31、sandy slopes are essentially planar. In some important applications, planar slides may develop. This may happen in slope, where permeable soils such as sandy soil and gravel or some permeable soils with some cohesion yet

32、 whose shear strength is principally provided by friction exist. For cohesionless sandy soils, the planar failure surface may happen in slopes where strong planar discontinuities develop, for example in the soil beneath

33、t</p><p>　　Figure 1 shows a typical planar failure slope. From an equilibrium consideration of the slide body ABC by a vertical resolution of forces, the vertical forces across the base of the slide body mus

34、t equal to weight w. Earthquake effects may be approximated by including a horizontal acceleration kg which produces a horizontal force k= acting through the centroid of the body and neglecting vertical inertia.1 For a

35、slice of unit thickness in the strike direction, the resolved forces of normal and t</p><p><b>　?。?）</b></p><p><b>　?。?）</b></p><p>　　where is the inclinati

36、on of the failure surface and w is given by</p><p><b>　?。?）</b></p><p>　　where is the unit weight of soil, H the height of slope, is the inclination of the slope. Since the length

37、of the slide surface AB is , the resisting force produced by cohesion is cH/sin a. The friction force produced by N is . The total resisting or anti-sliding force is thus given by</p><p><b>　?。?）</b

38、></p><p>　　For stability, the downslope slide force ¹ must not exceed the resisting force R of the body. The factor of safety, Fs , in the slope can be defined in terms of effective force by ratio R/

39、T, that is</p><p><b>　?。?）</b></p><p>　　It can be observed from equation (7) that Fs is a function of a. Thus the minimum value of Fs can be found using Powell's minimization tec

40、hnique18 from equation (7). Das reported a similar expression for Fs with k=0, developed directly from equation (2) by assuming that , where is the average shear strength of the soil, and the average shear stress devel

41、oped along the potential failure surface.</p><p>　　For cohesionless soils where c=0, the safety factor can be readily written from equation (7) as</p><p><b>　?。?）</b></p><

42、p>　　It is obvious that the minimum value of Fs occurs when a=b, and the failure becomes independent of slope height. For such cases (c=0 and k=0), the factors of safety obtainedfrom the proposed method and from Das ar

43、e identical.</p><p>　　CIRCULAR FAILURE SURFACE</p><p>　　Slides in medium-stif clays are often deep-seated, and failure takes place along curved surfaces which can be closely approximated in two

44、dimensions by circular surfaces. Figure 2 shows a potential circular sliding surface AB in two dimensions with centre O and radius r. The first step in the analysis is to evaluate the sliding' or disturbing moment

45、Ms about the centre of the</p><p>　　circle O. This should include the self-weight w of the sliding mass, and other terms such as crest loadings from stockpiles or railways, and water pressures acting externa

46、lly to the slope. Earthquake effects is approximated by including a horizontal acceleration kg which produces a horiazontal force kd=acting through the centroid of each slice and neglecting vertical inertia. When the soi

47、l above AB is just on the point of sliding, the average shearing resistance which is required along AB for li</p><p><b>　?。?）</b></p><p><b>　?。?0）</b></p><p>

48、;<b>　　（11）</b></p><p>　　The force N can produce a maximum shearing resistance when failure occurs:</p><p><b>　?。?2）</b></p><p>　　The equations of lines AC, C

49、B, and ABY are given by y</p><p><b>　　（13）</b></p><p>　　The sums of the disturbing and resisting moments for all slices can be written as</p><p><b>　　(14)</b>

50、;</p><p><b>　　(15)</b></p><p><b>　?。?6）</b></p><p><b>　?。?7）</b></p><p><b>　?。?8）</b></p><p><b>　?。?9

51、）</b></p><p>　　The safety factor for this case is usually expressed as the ratio of the maximum available resisting moment to the disturbing moment, that is</p><p><b>　　(20)</b>

52、;</p><p>　　When the slope inclination exceeds 543, all failures emerge at the toe of the slope, which is called toe failure, as shown in Figure 2. However, when the slope heightH is relatively large compared

53、 with the undrained shear strength or when a hard stratum is under the top of the slope of clayey soil with, the slide emerges from the face of the slope, which is called Face failure, as shown in Figure 3. For Face fail

54、ure, the safety factor Fs is the same as ¹oe failure1s using instead of H.</p><p>　　For flatter slopes, failure is deep-seated and extends to the hard stratum forming the base of the clay layer, which

55、is called Base failure, as shown in Figure 4.1,3 Following the same procedure as that for ¹oe failure, one can get the safety factor for Base failure:</p><p><b>　?。?1）</b></p><p&g

56、t;　　where t is given by equation (17), andandare given by</p><p><b>　　(22)</b></p><p><b>　?。?3）</b></p><p>　　其中， （24）</p><p><

57、;b>　　(25)</b></p><p>　　It can be observed from equations (21)~(25) that the factor of safety Fs for a given slope is a function of the parameters a and b. Thus, the minimum value of Fs can be found

58、using the Powell's minimization technique.</p><p>　　For a given single function f which depends on two independent variables, such as the problem under consideration here, minimization techniques are nee

59、ded to find the value of these variables where f takes on a minimum value, and then to calculate the corresponding value of f. If one starts at a point P in an N-dimensional space, and proceed from there in some vector d

60、irection n, then any function of N variables f (P) can be minimized along the line n by one-dimensional methods. Different method</p><p>　　The closed-form slope stability equation (21) allows the application

61、 of an optimization technique to locate the center of the sliding circle (a, b). The minimum factor of safety Fs min then obtained by substituting the values of these parameters into equations (22)~(25) and the results i

62、nto equation (21), for a base failure problem (Figure 4). While using the Powell's method, the key is to specify some initial values of a and b. Well-assumed initial values of a and b can result in a quick conver<

63、/p><p>　　(16)~(20) could be used to compute the Fs .min for toe failure (Figure 2) and face failure (Figure 3),except is used instead of H in the case of face failure.</p><p>　　Besides the Powell m

64、ethod, other available minimization methods were also tried in this study such as downhill simplex method, conjugate gradient methods, and variable metric methods. These methods need more rigorous or closer initial value

65、s of a and b to the target values than the Powell method. A short computer program was developed using the Powell method to locate the center of the sliding circle (a, b) and to find the minimum value of Fs . This approa

66、ch of slope stability analysis is straig</p><p>　　RESULTS AND COMMENTS</p><p>　　The validity of the analytical method presented in the preceding sections was evaluated using two well-established

67、 methods of slope stability analysis. The local minimum factor-of-safety (1993) method, with the state of the effective stresses in a slope determined by the finite element method with the Drucker-Prager non-linear stres

68、s-strain relationship, and Bishop's (1952) method were used to compare the overall factors of safety with respect to the slip surface determined by the proposed analy</p><p>　　The cases are chosen from t

69、he toe failure in a hypothetical homogeneous dry soil slope having a unit weight of 18.5 kN/m3. Two slope configurations were analysed, one 1 : 1 slope and one 2 : 1 slope. Each slope height H was arbitrarily chosen as 8

70、 m. To evaluate the sensitivity of strength parameters on slope stability, cohesion ranging from 5 to 30 kPa and friction angles ranging from 103 to 203 were used in the analyses (Table I). A number of critical combinati

71、ons of c and were found to be uns</p><p>　　To examine the e!ect of dynamic forces, the analytical method is chosen to analyse a toe failure in a homogeneous clayey slope (Figure 2). The height of the slope H

72、 is 13.5 m; the slope inclination b is arctan 1/2; the unit weight of the soil c is 17.3 kN/m3; the friction angle is 17.3KN/m; and the cohesion c is 57.5 kPa. Using the conventional method of slices, Liu obtained the m

73、inimum safety factor Using the proposed method, one can get the minimum value of safety factor from equation (20) a</p><p>　　CONCLUDING REMARKS</p><p>　　An analytical method is presented for an

74、alysis of slope stability involving cohesive and noncohesive soils. Earthquake e!ects are considered in an approximate manner in terms of seismic coe$cient-dependent forces. Two kinds of failure surfaces are considered i

75、n this study: a planar failure surface, and a circular failure surface. Three failure conditions for circular failure surfaces</p><p>　　namely toe failure, face failure, and base failure are considered for c

76、layey slopes resting on a hard stratum.</p><p>　　The proposed method can be viewed as an extension of the method of slices, but it provides a more accurate treatment of the forces because they are represente

77、d in an integral form. The factor of safety is obtained by using theminimization technique rather than by a trial and error approach used commonly.</p><p>　　The factors of safety obtained from the proposed m

78、ethod are in good agreement with those determined by the local minimum factor-of-safety method (finite element method-based approach), the Bishop method, and the method of slices. A comparison of these methods shows that

79、 the proposed analytical approach is more straightforward, less time-consuming, and simple to use. The analytical solutions presented here may be found useful for (a) validating results obtained from other approaches, (b

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103、><p>　　33. Chen (1970).</p><p>　　34. Baker and Garber (1977).</p><p>　　35. Bishop (1952).</p><p>　　簡(jiǎn)要的分析斜坡穩(wěn)定性的方法</p><p>　　JINGGANG CAOs 和 MUSHARRAF M. ZAMAN