Search Results (4)

Currently, the study of analytical solutions for the seismic stability of slopes under anchorage conditions is one of the hottest subjects in engineering. In this paper, an analytical solution for the seismic safety of the three-dimensional (3D) two-stage rock slope reinforced with prestressed anchor cables governed by the nonlinear Hoek–Brown criterion was deduced, in which the analyses of seismicity were performed by the latest modified pseudo-dynamic method. This method supplements the consideration of the damping effect of the rock medium on seismic waves, which is more in line with the real seismic situation. A mathematical geometric model was developed for calculating the external forces work and internal energy dissipation acting on 3D rotating rock masses reinforced with prestressed anchor cables, in which the seismic work rate was calculated using a new layer-by-layer superposition summation method. The analytical solution of the safety factor could be collated as an explicit function of several variables, and then, the optimal value was obtained by the Particle Swarm Optimization (PSO) algorithm. To corroborate the accuracy of new analytical solutions, the results were contrasted with those of the pertinent literature. The results of the two comparisons were very close. Ultimately, the sensitivity analyses and coupling effects of seismic pseudo-dynamic factors and prestressing anchorage factors were carried out. It was found that even small seismic intensities had a large effect on the stability of rock slopes with developed joints. Increasing the number of steps and prestressing anchors can effectively improve the stability of rock slopes under seismic effects. The conclusions have significant implications for the anchorage design of the 3D two-stage rock slope as seismic events occur. Full article

This work assesses the seismic stability of tunnel faces advanced in heterogeneous and anisotropic soils based on the plastic limit theorem. A discretized kinematic velocity field respecting the normal flow rule is generated via a point-to-point discretization technique. The distribution of soil parameters in the depth direction including cohesion, friction angle, and unit weight are considered by four kinds of profiles. The variation in cohesion with shear direction caused by consolidation and sedimentation is considered by including an anisotropy coefficient. The seismic acceleration is represented by the modified pseudodynamic method (MPD) rather than the conventional pseudodynamic method (CPD). Based on the energy equilibrium equation, an upper-bound solution is derived. The accuracy and rationality of the proposed procedure are substantiated by comparing with the solutions obtained by conventional log-spiral mechanism and CPD. A parametric study indicates that nonlinear profiles tend to predict a smaller required face pressure than the constant and linear profiles due to the convexity of nonlinear profiles. The over-consolidated soil is more sensitive to the anisotropy coefficient than normally consolidated soil. Moreover, the adverse effect of horizontal seismic acceleration is much greater than that of vertical acceleration, and the resonance effect is more prone to happen, especially for shallow-buried tunnels. Full article

In engineering mathematics, the unsaturated nature of soil has a significant impact on the seismic bearing capacity solution. However, it has generally been neglected in the published literature to date. Based on the kinematic approach of limit analysis, the present study proposes a method for calculating the bearing capacity of shallow strip footings located in unsaturated soils, taking four common types of soils as examples. The modified pseudo-dynamic (MPD) approach is used to calculate the seismic forces varying with time and space, and the layerwise summation method is used to derive the power generated by the seismic forces. In the calculation of internal energy dissipation, this paper introduces the effective stress based on the suction stress to derive the cohesion expression at different depths. The analytical formula of bearing capacity is obtained by the principle of virtual work, and its value is optimized by the Sequential Quadratic Programming (SQP) algorithm. In order to verify the validity of the proposed method, the present results are compared with the solutions published so far and a good agreement is obtained. Finally, a parametric study is performed to investigate the influence of different types of parameters on the bearing capacity. Full article

Seismic events are an active factor in causing slope instability, and the existing pseudo-dynamic method ignores some practical engineering conditions. In this paper, the seismic stability of three-dimensional (3D) two-step slopes is evaluated utilizing the modified pseudo-dynamic method based on the kinematical approach of limit analysis, in which the nonlinear characteristics of soil are considered using the generalized tangent technique. A 3D horn-like rotational failure mechanism is established to solve internal energy dissipation and external force work, in which the seismic work is considered in addition to the soil weight work and obtained by the layer-wise summation method. Based on the force-increase technique, the analytical expression for the safety factor (FS) of 3D two-step slopes is derived more readily. To verify the reliability of the new expression, the present results are compared with already posted solutions and the original pseudo-dynamic solutions. Ultimately, the sensitivity discussions are carried out to investigate the impacts of various factors on slope stability. This has some significance for the design and safety of 3D two-step slopes. Full article