1. Chapter 7 Slope Stability 7.1 General For the analysis of the stability of slopes of arbitrary shape and composition various approximate methods have been developed. Most of these assume a circular slip surface.

2. Limiting equilibrium methods are normally used in the analysis of slope stability in which it is considered that failure is on the point of occurring along an assumed or a known failure surface. In the traditional approach the shear strength required to maintain a condition of limiting equilibrium is compared with the available shear strength of the soil, giving the average (lumped) factor of safety along the failure surface.

3. In slope stability analysis we determine the Factor of Safety as a ratio of resisting forces to driving forces F s = Resisting / Driving Theoretically, any slope with a Factor of Safety less than one will fail and any slope with a factor of safety greater than one will not. Design focuses on the soil parameters and geometry that will provide the maximum factor of safety. Sometimes, the analysis of an existing slope will be what is called a parametric study – that is establishing a factor of safety and performing an analysis that back calculates the strength parameters. The engineer will then determine his/her confidence level as to whether or not the soil has that strength through experience, lab, and/or field data.

4. W T T  N Stable condition ： T>T Inner friction angle Stability factor 7.2 Sandy Soil Slope

5. 7.3 Clay Soil Slope Fellenius, Taylor, Bishop, Morgenstern-Price, Spencer, Janbu, among others N f W R O B C A (1) Sweden Arc Method For equilibrium the shear strength which must be mobilized along the failure surface is expressed as

6. Example 1 A slope is excavated to a depth of 8m in a deep layer of saturated clay of unit weight 19 kN/m3: the relevant shear strength parameters are cu=65 kN/m2 and U=0. Determine the factor of safety for the trial failure surface specified in Figure 9.4. Check that no loss of overall stability will occur according to the limit state approach. Solution:

7. a b c d i βiβi O C R A B H (2) Slice Arc Method For any slice the inclination of the base to the horizontal is and the height, measured on the centreline, is h. The analysis is based on the use of a lumped factor of safety (F ), 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. c d b a lili XiXi PiPi X i+1 P i+1 NiNi TiTi WiWi

9. Example 2 某土坡如图所示。已知土坡高 度 H=6m ，坡角  =55° ，土的重度  =18.6kN/m 3 ，内摩擦角  =12° ， 粘聚力 c =16.7kPa 。试用条分法验 算土坡的稳定安全系数

10. Solution ①按比例绘出土坡，选择圆心，作出相应的滑动圆弧 ②将滑动土体分成若干土条，对土条编号 ③量出各土条中心高度 h i 、宽度 b i ，列表计算 sin  i 、 cos  i 以及土条重 W i ，计算 该圆心和半径下的安全系数 ④对圆心 O 选不同半径，得到 O 对应的最小安全系数； ⑤在可能滑动范围内，选取其它圆心 O 1 ， O 2 ， O 3 ， … ，重复上述计算，求出最 小安全系数，即为该土坡的稳定安全系数

11. 0.60 1.80 2.85 3.75 4.10 3.05 1.50 1 1 1 1 1 1 1.15 11.16 33.48 53.01 69.75 76.26 56.73 27.90 11.0 32.1 48.5 59.41 58.33 36.62 12.67 12345671234567 编号中心高度 (m) 条宽 (m) 条重 W i kN/m β1(o)β1(o) W i sin  i 9.5 16.5 23.8 31.6 40.1 49.8 63.0 W i cos  i 1.84 9.51 21.39 36.55 49.12 43.33 24.86 合计 186.60258.63

12. (3) Taylor Method

13. 7.4 Discussion Slopes in overconsolidated fissured clays require special consideration. A number of cases are on record in which failures in this type of clay have occurred long after dissipation of excess pore water pressure had been completed. Analysis of these failures showed that the average shear strength at failure was well below the peak value.