边坡稳定外文文献翻译.doc

1、青岛理工大学毕业设计（论文）外文文献翻译一、原文Stability of Slopes9.1 IntroductionGravitational 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

2、slips the shape of the failure surface in section may be a circular arc or a non-circular curveIn general，circular slips are associated with homogeneous soil conditions and non-circular slips with non-homogeneouconditionsTranslational and compound slips occur where the form of the failure surface is

3、 influenced by the presence of an adjacent stratum of significantly different strength . 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 s

4、lips usually occur where the adjacent stratum is at greater depth，the failure surface consisting of curved and plane sectionsIn 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 assumed or a known f

5、ailure surfaceThe 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 surfaceThe problem is considered in two dimensions，conditions of plane strain being assumedIt has

6、been shown that a two-dimensional analysis gives a conservative result for a failure on a three-dimensional(dish-shaped) surface9.2 Analysis for the Case of u =0This analysis, in terms of total stress，covers the case of a fully saturated clay underfund rained conditions, i.e. For the condition immed

7、iately after constructionOnly moment equilibrium is considered in the analysisIn 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 pe

8、r unit Length) above the failure surfaceFor equilibrium the shear strength which must be mobilized along the failure surface is expressed aswhere F is the factor of safety with respect to shear strengthEquating moments about O： Therefore (9.1) The moments of any additional forces must be taken into

9、accountIn 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 fills with waterIt is necessary to analyze the slope for a number of trial failure surfaces in order that the minimum factor of safe

10、ty can be determined Based on the principle of geometric similarity，Taylor9.9published stability coefficients for the analysis of homogeneous slopes in terms of total stressFor a slope of height H the stability coefficient (Ns) for the failure surface along which the factor of safety is a minimum is

11、 (9.2)For the case ofu =0，values of Ns can be obtained from Fig.9.3.The coefficient Ns depends on the slope angle and the depth factor D，where DH is the depth to a firm stratumGibson and Morgenstern 9.3 published stability coefficients for slopes in normally consolidated clays in which the undrained

12、 strength cu(u =0) varies linearly with depthExample 9.1A 45slope is excavated to a depth of 8 m in a deep layer of saturated clay of unit weight 19 kNm3:the relevant shear strength parameters are cu =65 kNm2 andu =0Determine the factor of safety for the trial failure surface specified in Fig.9.4.In

13、 Fig.9.4, the cross-sectional area ABCD is 70 m2.Weight of soil mass=7019=1330kNmThe centroid of ABCD is 4.5 m from OThe angle AOC is 89.5and radius OC is 12.1 mThe arc length ABC is calculated as 18.9mThe factor of safety is given by： This is the factor of safety for the trial failure surface selec

14、ted and is not necessarily the minimum factor of safetyThe minimum factor of safety can be estimated by using Equation 9.2.From Fig.9.3，=45and assuming that D is large，the value of Ns is 0.18.Then9.3 The Method of SlicesIn this method the potential failure surface，in section，is again assumed to be a

15、 circular arc with centre O and radius rThe 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 isa

16、nd the height, measured on the centre-1ine,is h. The factor of safety is defined as the ratio of the available shear strength(f)to the shear strength(m) which 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

17、that there must be mutual support between slices，i.e. forces must act between the slicesThe forces (per unit dimension normal to the section) acting on a slice are：1.The total weight of the slice，W=b h (sat where appropriate)2.The total normal force on the base，N (equal to l)In general thisforce has

18、 two components，the effective normal force N(equal tol ) 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 base3.The shear force on the base，T=ml.4.The total normal forces on the sides, E1 and E2.5.The shear forces on

19、 the sides，X1 and X2.Any external forces 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

20、 O，the sum of the moments of the shear forces T on the failure arc AC must equal the moment of the weight of the soil mass ABCDFor any slice the lever arm of W is rsin,thereforeTr=Wr sinNow, For an analysis in terms of effective stress，Or (9.3)where La is the arc length ACEquation 9.3 is exact but a

21、pproximations are introduced in determining the forces NFor a given failure arc the value of F will depend on the way in which the forces N are estimated The Fellenius SolutionIn this solution it is assumed that for each slice the resultant of the interslice forces is zeroThe solution involves resol

22、ving the forces on each slice normal to the base，i.e.N=WCOS-ulHence the factor of safety in terms of effective stress (Equation 9.3) is given by (9.4)The components WCOS and Wsin can be determined graphically for each sliceAlternatively，the value of can be measured or calculatedAgain，a series of tri

23、al failure surfaces must be chosen in order to obtain the minimum factor of safetyThis solution underestimates the factor of safety：the error，compared with more accurate methods of analysis，is usually within the range 5-2%. For an analysis in terms of total stress the parameters Cu andu are used and

24、 the value of u in Equation 9.4 is zeroIf 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 obtainedThe Bishop Simplified SolutionIn this solution it is assumed that the resultant forces on the sides of theslices are horizontal，i.e.Xl-X2=0For equi

25、librium the shear force on the base of any slice is Resolving forces in the vertical direction: (9.6)It is convenient to substitute l=b secFrom Equation 9.3，after some rearrangement， (9.7) The pore water pressure can be related to the total fill pressure at anypoint by means of the dimensionless por

26、e pressure ratio，defined as (9.8)(sat where appropriate)For any slice, Hence Equation 9.7 can be written: (9.9) As the factor of safety occurs on both sides of Equation 9.9,a process of successive approximation must be used to obtain a solution but convergence is rapid Due to the repetitive nature o

27、f the calculations and the need to select an adequate number of trial failure surfaces，the method of slices is particularly suitable for solution by computerMore complex slope geometry and different soil strata can be introducedIn most problems the value of the pore pressure ratio ru is not constant

28、 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 designAgain，the factor of safety determined by this method is an underestimate but the error is unlikely to exceed 7and in most cases is less th

29、an 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 satisfiedSpencer showed that the accuracy of the Bishop simplified method，in which only moment equilibrium is satisfied, is due to the insensitivity

30、 of the moment equation to the slope of the interslice forces Dimensionless stability 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 expressed asF=m-nu (9.10)where，m and n are the stability coefficientsThe coefficients，m and n arefunctions of,，the dimensionless number c/and the depth factor D.Example 9.2Using the Fellenius method of slices，determine the factor of safety，in terms of