【文章內(nèi)容簡(jiǎn)介】 r of safety :the error, pared with more accurate methods of analysis, is usually within the range of 520﹪.For an analysis in terms of total stress the parameters cu and u are used and the value of u in equation is zero. If u=0 the factor of safety is given by: F= ()As N′does not appear in equation an exact value of F is obtained.The Bishop Simplified SolutionIn this solution it is assumed that the resultant forces on the sides of the slices are horizontal, . X1X2=0For equilibrium the shear force on the base of any slice is: T= Resolving forces in the vertical direction: ∴ ()It is convenient to substitute: l= From equation , after some rearrangement: ()The pore water press can be related to the total‘fill pressure’ at any point by means of the dimensionless pore press ratio, defined as: ()( where appropriate )For any slice, Hence equation can be written: ()As the factor of safety occurs on both sides of equation a process of successive approximation must be used to obtain a solution but convergence is rapid. The method is very suitable for solution on the puter. In the puter program the slope geometry can be made more e plex, with soil strata having different properties and pore pressure conditions being introduced.In most problems the value of the pore pressure ratio is not constant over the whole failure surface but, unless there are isolates 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 method is an underestimate but the error is unlikely to exceed 7﹪ and in most cases is less than 2﹪.Spencer [] 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 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 forces.Dimensionless stability coefficients for homogeneous slopes, based on equation , have been published by Bishop and Morgenstern[]. It can be shown that for a given slope angle and given soil properties the factor of safety varies linearly with and can thus be expressed as: ()where m and n are the stability coefficients m and n are functions of , the dimensionless number and the depth factor D.Example Using the Fellenius method of slices, determined the factor of safety in terms of effective stress of the slope shown in for the given failure surface. The distribution of pore water pressure along the failure surface is given in the figure. The unit weight of the soil is 20 kN/m3 and the relevant shear strength parameters are =10kN/m2 and =29176。.The factor of safety is given by equation . The soil mass is divided into slices wide. The weight(W) of each slice is given by: The height h for each slice is set off bellow the centre of the base and the normal and tangential ponents and respectively are determined graphically, as shown in .Then: and Figure Example .The arc length (La) is calculated as . The results are tabulated below: Analysis of a Plane Translational SlipIt is assumed that potential failure surface is parallel to the surface of the slope and is at a depth that is small pared 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 to the horizontal and the depth of the failure plane z, as shown in section in . The water table is taken to be 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 slope. The 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 plane. Figure Plane translational slip.In terms of effective stress, the shear strength of the soil along the failure plane is: and the factor of safety is: The expressions for , and u are as follows: The following special cases are of interest. If =0 and m=0(. the soil between the surface and the surface plane is not fully saturated), then: （）If =0 and m=1(. the water table conditions with the surface of the slope),then: If should be noted that when =0 the factor of safety is independent of the depth z. If is greater to zero, the factor of safety is a function of z, and may exceed provided z is less than a critical value.For a total stress analysis the shear strength parameters and are used and the value of u is zero.A long natural slope in fissured overconsolidated clay is inclined at 12176。 to the horizontal. The water table is at the surface and seepage is roughly parallel to the slope. A slip has developed on a plane parallel to the surface at a depth of saturated unit weight of the clay is 20 kN/m3. The peak strength parameters are =10kN/m2 and =26176。 the residual strength parameters are =0 and =18176。. Determine the factor of safety along the slip plane(a) in terms of the peak strength parameters, (b) in terms of the residual strength parameters.With the water table at the surface (m=1), at any point on the slip plane: