Comparison of Three Dimensional Translational and Rotational Mechanisms in Seismic Slope Stability Analyses by Upper Bound Limit Analysis

In this paper, seismic stability of slopes in three dimensional cases is investigated, using rotational and translational failure mechanisms and compared based on the upper bound limit analysis method. Definition of lateral surfaces of three dimensional failure mechanisms in upper bound method requires considering the associated flow rule, which makes it necessary that particular equations be satisfied. To develop further studies on three dimensional stability of slopes using translational and rotational mechanisms, the present work compares the results of a translational mechanism with a rotational one. In order to compare the factor of safety in slopes stability problems between translational and rotational mechanisms under body forces due to the weight of the soil mass and horizontal acceleration of the earthquake, the parameter λφc is used, where γ is the unit weight of the soil, H is the height of slope and c and ϕ are the soil shear strength parameters. This comparison is carried out for different slope inclination angles (30◦, 60◦, 90◦), two ratios of the width of the failure mechanism (L) to the slope height (H), i.e. 1 and 8, and for cohesive (λφc = 0) and non-cohesive soils (λφc ≠ 0). L/H = 1 and L/H = 8 are used to model the three dimensional and two dimensional mechanisms, respectively. By an increase in the parameter of λφc, the soil behaves more frictional. Some of the most important results of this research are as follows: - Generally, the importance of three dimensional analyses is more in seismic states. - The trend of variations of the safety factor of slopes is almost the same by increase in the coefficient of horizontal earthquake acceleration for both rotational and transitional mechanisms. - The results of this study show that in rotational mechanisms, in most cases, especially in vertical slopes, the safety factors are smaller than translational mechanisms. - Translational mechanisms results (safety factors) are usually lower in cohesive soils. - The difference between the results of two translational and rotational mechanisms is less in cohesive soils and more in frictional soils. - By an increase in inclination angle of the slope, the difference between the results of the two mechanisms becomes more. Regardless of the kind of the mechanism, in assessing the effect of different parameters on the factor of safety of slopes stability, the following general points can be noted: - The increase in the coefficient of horizontal earthquake acceleration (from 0 to 0.3) contributes to the decrease in the factor of safety. The reductions for cohesive soils and inclination angle equal to 30 degrees are about 69 and 40 percent, respectively for two dimensional and three dimensional mechanisms. The mentioned reductions for frictional soils in vertical slopes, are about 35 and 20 percent. These results indicate that the effect of earthquake is more in lower slopes with cohesive soil. - As the failure mechanism widens, the safety factor decreases, and at higher kh values, this decrease becomes more pronounced. This indicates the greater impact of earthquakes on reducing the stability of two-dimensional mechanisms. - The difference between the results of two dimensional and three dimensional mechanisms in cohesive soils is more than frictional soils. - The factors of safety of slopes in three dimensional mechanisms are more than two dimensional. This is due to the fact that the contribution of lateral surfaces in 3D mechanisms is more outstanding than the bottom logarithmic spiral surface. It contributes to the increase in the rate of dissipated work and consequently the factor of safety of the slope increases.