Stability Analysis Of Anchored Slopes Subjected To Seismic Loadings Based On Upper Bound Approach

Based on the upper bound theory of limit analysis, upper bound approach applied to the seismic stability analysis of anchored slopes is developed in this paper.With the log-spiral failure mechanism, considering seismic loadings, anchorage load, and nonlinear failure criterion of materials, the stability of homogeneous slopes under complex conditions is analyzed. On the basis, considering the complexity of soil layers and slope gemetries, the combined log-spiral failure mechanism is built. Meanwhile, numerical integration method is used to solved the factor of safety of complicated multistep and multilayer slopes with upper bound approach. Furthermore, the method is extend to the stability analysis of anchored complex slopes subjected to seismic loadings. The paper includes four aspects:(1) Firstly, analytical expressions of the rate of external work and internal energy dissipation are derived for simple homogeneous slopes. Combined the strength reduction technique with optimization method, both the factor of safety and the critical sliding surface are solved. Then, both the factor of safety and the yield acceleraion coefficient are solved considering seismic loadings, as well as the permanent displacement. To verify the correctness of the method, various examples are carried out. Parameter studies are also carried out to discuss effect of the direction of seismic loadings. Results show that, with a specified seismic loading, the most unfavorable direction can be considered as direction of the slope.(2) Seismic stability analysis of slopes reinforced with pre-stressed anchors based on upper bound approach is conducted. Parametric studies show that:under the condition of single row of anchors, the most favorable direction of anchors have a trend to increase as the anchor position near the toe of slope, but overall remain within the range 0°～15°; while the anchor positions were close to the toe of slope, the stability of the slope would improved, but should pay attention to local stability of the slope, and prevent adverse local buckling; when a slope reinforced with multi-row of anchors, direction of the upper anchors should be set horizontal as much as possiable, while direction of the lower anchors should be set within 0° 15° with horizontal; horizontal seismic loading has significant effect on the stability of slopes, when horizontal seismic loading is larger enough, the adverse impact of vertical siesmic loading on stability of slopes should be considered.(3) Considering the nonlinear Hoek-Brown failure criterion with the "outside tangent method", seismic stability analysis of slopes reinforced with pre-stressed anchors based on upper bound approach is conducted. Parametric studies show that:all of the Hoek-Brown parameters, including GSI, mi and D, have remarkalbe influences on slope stability, particularly the most significant impact parameter is GSI, D followed, and mi does the minimal impact; when rocks of slopes have better overall quality and less external disturbances, the stability of slopes decreases much more significantly while subjected to seismic loadings; the optimal anchor direction is within 0°～15° while slopes reinforced with single row of anchors, and the closer the anchor position is to the toe of slope, the better results the reinforcement does, but attention should be paid to local stability of the slope, and multi-row of anchors could be used to avoid local buckling.(4) With multi-stage and multi-layer slope as the research object, using Cartesian coordinates to model the slope, integral expressions of the rate of external forces on potential landslide are derived. With the introduction of numerical integration techniques and the selection of Cartesian coordinates of the rotation center and the starting point of slide as independent variables, the stability of complex slopes are analyzed based on upper bound approach. On this basis, considering seismic loadings and anchorage loading, the seismic stability analysis of complex slopes are carried out. Comparative analysis of numerical examples illustrate the validity of this method, thus a new idea is proposed to the stability analysis of complex slopes.