A Dynamic Method to Predict the Earthquake-Triggered Sliding Displacement of Slopes

The earthquake-induced permanent displacement is an important index of the potential damage to a slope during an earthquake. The Newmark method assumes that a slope is a rigid-plastic body, and the seismic responses of sliding masses or seismic forces along the slide plane are ignored. The decoupled method considers no relative displacement across the sliding plane, so it overpredicts the seismic response of the sliding mass. Both dynamic and sliding analyses are performed in the coupled method, but when Ts/Tm is large, the results are unconservative. In this paper, a method is proposed to predict the earthquake-triggered sliding displacement of slopes. The proposed method is based on the Newmark rigid method, coupled method, and decoupled method considering both the forces at the sliding interface and the system dynamics under critical conditions. For the flexible system, the displacements are calculated with different stiffness values, and the results show that as the stiffness increases and tends to infinity, the critical acceleration and displacements of the proposed method are close to those of the Newmark method. The proposed method is also compared with the Newmark method with the period ratio Ts/Tm. At small values of Ts/Tm, the flexible system analysis results of the displacement are more conservative than those of the rigid block model; at larger values of Ts/Tm, the rigid block model is more conservative than the flexible system.

On two improved numerical algorithms for vibration analysis of systems involving fractional derivatives

Zhang and Shimizu (1998) proposed a numerical algorithm based on Newmark method to calculate the dynamic response of mechanical systems involving fractional derivatives. On the basis of Runge-Kutta-Nyström method and Newmark method, the present study proposes two new numerical algorithms, namely, the improved Newmark algorithm using the second order derivative and the improved Runge-Kutta-Nyström algorithm using the second order derivative to solve the fractional differential equations of vibration systems. The accuracy of new algorithms is investigated in detail by numerical simulation. The simulation result demonstrated that the Runge-Kutta-Nyström algorithm using the second order derivative for the vibration analysis of systems involving fractional derivatives is more effective than the Newmark algorithm of Zhang and Shimizu.

Influence of the Slope Shape on Seismic Stability of a Slope

The slope shape is one of the most intuitive factors affecting the seismic stability of a slope. However, current research on this subject is mainly focused on statistical analysis and seismic response law, and the influence on seismic stability evaluation of the slope is rarely discussed. Furthermore, slope shapes are often simplified for easy numerical model building. In view of this, five slope models with different slope shapes are considered, and the time-history analysis method and Newmark method are chosen to evaluate the seismic stability of these slope models under different amplitudes. The purpose of this paper is to compare the seismic stability of slopes with different slope shapes and to study the feasibility of simplifying the slope shape when evaluating the seismic stability of a slope.