Seismic stability analysis of slopes with pre-existing slip surfaces

In analyzing seismic stability of a slope with upper bound limit analysis method, the slip surface is often assumed as a log-spiral or plane slip surface. However, due to the presence of a weak layer and unfavorable geological structural surface or a bedrock interface with overlying soft strata, the preexisting slip surface of the slope may be irregular and composed of a series of planes rather than strictly logspiral or plane shape. A computational model is developed for analyzing the seismic stability of slopes with pre-existing slip surfaces. This model is based on the upper bound limit analysis method and can consider the effect of anchor bolts. The soil or rock is deemed to follow the Mohr-Coulomb yield criterion. The slope is divided into multiple block elements along the slip surface. According to the displacement compatibility and the associated flow rule, a kinematic velocity field of the slope can be obtained computationally. The proposed model allows not only calculation of the rate of external work owing to the combined effect of self-weight and seismic loading, but also that of the energy dissipation rate caused by the slip surface, interfaces of block elements and anchorage effect of the anchors. Considering a direct relationship between the rate of external work and the energy dissipation rate, the expressions of yield acceleration and permanent displacement of anchored slopes can be derived. Finally, the validity of this proposed model is illustrated by analysis on three typical slopes. The results showed that the proposed model is more easily formulated and does not need to solve complex equations or time consuming iterations compared with previous methods based on the conditions of force equilibrium.

Predicting seismic permanent displacement of soil walls under surcharge based on limit analysis approach

Seismic permanent displacement of the soil walls plays an important role in design of these structures. Due to the increase in growth of urban areas and the limitations in use of flat grounds, many structures are built near slopes and retaining walls. During earthquakes, these structures can apply an additional surcharge on the wall. The intensity and location of the surcharge is of considerable importance on the seismic displacements of the soil wall. In this study, by using the limit analysis and upper bound theorem, seismic permanent displacement of the soil wall under surcharge has been analyzed. Thus, a formulation is presented for calculating the yield acceleration and seismic displacement for different surcharge conditions. The effect of seismic acceleration, surcharge intensity, its location and soil properties is investigated. A parameter called the ＂displacement coefficient＂ is proposed, and is a potential modification for Newmark’s sliding-block method.

Analytical expressions for determining the stability of cohesionless soil slope under generalized seismic conditions

In recent major earthquakes, the researchers have found the need for consideration of vertical seismic acceleration for the stability analysis of the man-made and natural slopes. However, in most past studies, the performance of slopes has been assessed by accounting only the horizontal seismic component of the ground motion, without giving due weightage to the effect of vertical component. In the present study, analytical expressions are derived to determine the factor of safety, yield seismic coefficient and consequently the seismic displacement of cohesionless soil slope under combined horizontal and vertical components of the ground motion. The derivation uses the Newmark's sliding block approach, in which the soil slope with a planar failure surface within the framework of conventional pseudo-static analysis is assumed to follow the Mohr-Coulomb failure criterion. The effects of vertical seismic coefficient on the stability of cohesionless slope have been studied through a set of graphical presentations for a specific range of soil parameters. It is observed that overlooking the effect of the vertical component of the ground motion on factor of safety and the displacement while designing the slope may be detrimental, resulting in the slope failure. The general expressions presented in this paper may be highly useful in the field of earthquake geotechnical engineering practice for designing the cohesionless soil slopes under combined horizontal and vertical seismic loads.