L. Li’s research while affiliated with Central South University and other places

Slope displacement and factor of safety (FOS) of a slope are two aspects that reflect the stability of a slope. However, the traditional limit equilibrium (LE) methods only give the result of the slope FOS and cannot be used to solve for the slope displacement. Therefore, developing a LE method to obtain the results of the slope FOS and slope displacement has significance for engineering applications. Based on a force-displacement coupled mode, this work expands the LE MorgensternPrice (M-P) method. Except for the mechanical equilibrium conditions of a sliding body adopted in the traditional M-P method, the present method introduces a nonlinear model of the shear stress and shear displacement. Moreover, the energy equation satisfied by a sliding body under a small slope displacement is also applied. Therefore, the double solutions of the slope FOS and horizontal slope displacement are established. Furthermore, the flow chart for the expanded LE M-P method is given. By comparisons and analyses of slope examples, the present method has close results with previous research and numerical simulation methods, thus verifying the feasibility of the present method. Thereafter, from the parametric analysis, the following conclusions are obtained: (1) the shear displacement parameters of the soil affect the horizontal slope displacement but have little effect on the slope FOS; and (2) the curves of the horizontal slope displacement vs. the minimum slope FOS could be fitted by a hyperbolic model, which would be beneficial to obtain the horizontal slope displacement for the slope in the critical state.

Based on the effective stress principle, a new formula for shear strength of unsaturated soil is derived under the general nonlinear Mohr-Coulomb (M-C) strength criterion to improve the classical strength criterion of unsaturated soil. Meanwhile, the simple irrigation model under steady seepage is adopted to obtain the distribution of the matrix suction or the degree of saturation (DOS) above the groundwater table in the slope. Then, combined with the improved strength criterion of unsaturated soil and the simple irrigation model under steady seepage, the limit equilibrium (LE) solutions for the unsaturated slope stability are established according to the global LE conditions of the entire sliding body with assumption of the stresses on the slip surface. Compared to the classical strength criterion of unsaturated soil, not only the cohesion soil but also the internal friction angle is affected by the matric suction or the DOS in the improved strength criterion. Moreover, the internal friction angle related to the matric suction has the nonlinear characteristics, particularly for a small of the matric suction. Thereafter, the feasibility of the present method is verified by comparison and analysis on some slope examples. Furthermore, stability charts are also drawn to quickly analyze the unsaturated slope stability.

Due to the seepage of groundwater, the resisting force of slopes decreases and the sliding force increases, resulting in significantly reduced slope stability. The instability of most natural slopes is closely related to the influence of groundwater. Therefore, it is important to study slope stability under groundwater seepage conditions. Thus, using a simplified seepage model of groundwater combined with the analysis of stresses on the slip surface, the limit equilibrium (LE) analytical solutions for two- and three-dimensional slope stability under groundwater seepage are deduced in this work. Meanwhile, the general nonlinear Mohr-Coulomb (M-C) strength criterion is adopted to describe the shear failure of a slope. By comparing the results with the traditional LE methods on slope examples, the feasibility of the proposed method is verified. In contrast to traditional LE methods, the proposed method is more suitable for analyzing slope stability under complex conditions. In addition, to facilitate the optimization of drainage design in the slope, stability charts are drawn for slopes with different groundwater tables. Furthermore, the study concluded that: (1) when the hydraulic gradient of groundwater is small, the effect on slope stability is also small for a change in the groundwater table; and (2) compared with a slope without a groundwater table, a slope with a groundwater table has a larger failure range under groundwater seepage.

In the stability analyses of a reinforced slope with a grid beam anchored by cables, the anchoring force of the cable is usually simplified as the concentrated force acting on the slip surface to calculate the reinforcement effect. The anchoring force actually acts on the slope surface as stress because of the effect of the grid beam. Therefore, this work proposes two new calculation modes of anchoring force: stresses with rectangular and curved distribution acting on the slope surface. In addition, the analysis considered the presence of a cavity, which results in a void underneath the grid beam near the slope surface. Then, two types of slip surfaces and the Morgenstern-Price method were adopted to study slope stability. Thus, the following conclusions were obtained: (1) three calculation modes have nearly similar solutions with less than 5% difference; (2) the arbitrary curved slip surface is suggested to be used as the critical slip surface that shows a noncircular shape; and (3) the void causes anchorage cable failure, which reduces slope stability significantly.

Through simple calculation of the normal stress on slip surface and the Mohr-Coulomb strength criterion, various calculation parameters are introduced and the stresses on slip surface are properly assumed, from which the limit equilibrium solution for three-dimensional slope stability is derived based on the static equilibrium conditions that three-dimensional sliding body satisfies Meanwhile, in stability analysis of three-dimensional slope, the direction of shear stress on slip surface is also assumed based on the previous research results, and the nonstrict method, quasi-strict method and strict method are adopted for three-dimensional slope stability analysis. By comparing with the classical results, the proposed method is validated, and the differences among various methods are analyzed. It is shown that the nonstrict method yields the smallest factor of safety, i.e., a conservative result; the quasi-strict method is similar to the strict method, yielding reliable results in calculating the safety factor of slope. In the proposed method, reasonable assumptions are made for the stresses on slip surface, and the simple solution process can be easily implemented into a computer code.

Automata theory is an important branch of theoretical computer science. ω-automaton is an important part of automata theory. The judgment standard for the equivalence of two automata is the equivalence of their acceptance language. Acceptance conditions for automata are expressed with state set. This paper tries to use path to express acceptance conditions for ω-automaton that is convenient for judging the automatons equivalence property and transforming between different types of automata. With the help of Path ω-automaton, Muller automaton is transformed into Büchi automaton. Compared with the existing algorithm, the state scale of Büchi automaton has been reduced and the problem of state space explosion has been relieved. The research findings in this paper contribute to enrich the existing ω-automaton theory and provide a new idea for ω-automaton theory and application research.

Based on the upper bound limit analysis method and by considering the seismic load effect, the stability of two sets of jointed consequent rock slope is analyzed. Then, by integrating a strength reduction technique, a calculation formula of the safety factor of two sets of jointed consequent rock slope is put forward, and the objective function of the safety factor Fs is optimized by means of the nonlinear sequential quadratic programming method. Finally, under different seismic loads, the slope safety factor obtained through the upper bound limit analysis method is compared with the results obtained through the discrete element method. It is found that the two kinds of results are close to each other, with a relative error of less than 4%, and the corresponding sliding surfaces are also similar, which demonstrates the rationality and reliability of the proposed method. Parametric analysis shows that the slope height, the internal friction angle of the joints, the joint angle combination and the seismic loading all have significant effects on the slope safety factor and the potential critical slip surface. © 2016, Editorial Department, Journal of South China University of Technology. All right reserved.

Ground water level fluctuations have greatly influence on stability of slopes with cracks. Pore-water pressure as the external force was involved in the calculation of energy consumption based on the upper bound limit analysis and strength reduction technique. The effect of pore-water pressure on stability of slopes with cracks was analysed. However, the change rules of critical depth or position of cracks under the effect of ground water level and slope angle was the focus of this paper. Results show that the critical position and depth of cracks significantly depend on the ground water level and slope angle. The increase in ground water level makes the critical crack close to slope crest in the case that ground water level is low. It is also observed that the influence of ground water level on critical depth of cracks presents different regularity for the case of crack position known and both crack position and depth unknown. Research results provide a new method for obtaining critical crack located on the upper surface of slopes under the complex condition. © 2016, Editorial Department of Journal of Beijing University of Technology. All right reserved.

The stress wave method is difficult to be applied to obtain effective stress wave signal that reflects the section change of anchorage body in the long anchor cable. Based on the actual models of anchorage body with three special types, i.e. full-length grouting anchorage body, full-length grouting anchorage body with existence of defective segment, and non full-length grouting anchorage body with existence of free segment, and using two stress wave excitation modes, i.e. stress wave signal exciting respectively on top or bottom of anchor cable, the reliability of stress wave method to detect anchorage quality was verified through comparing the theoretical vibration velocity of the stress wave with the measured ones. Then, by combining the above two stress wave excitation modes, the feasibility of stress wave signal exciting simultaneously on top and bottom of anchor cable to detect anchorage quality of anchor cable was studied. The results show that the excitation mode of stress wave signal simultaneously on top and bottom of anchor cable can effectively detect anchorage quality of anchor cable, and signal received on top of anchor cable in this mode is the stress wave signal with the shortest propagation path for reflecting change positions of anchorage body sections. Meanwhile, the two kinds of stress wave signals are suggested to adopt different frequencies to distinguish stress wave signals exciting respectively on top and bottom of anchor cable.

Based on the cavity expansion theory, the influences of the geometric parameter (edge angle), the rock mechanical parameters (compressive strength and Poisson's ratio) on the radius of elastic-plastic interface in rocks under wedge cutting conditions are studied. The results show that the smaller the blade angle, the larger the damaged area and the larger the elastoplastic radius when the contact width between the blade and rock is constant. When the other factors remain unchanged, the increase of the Poisson's ratio or the increase of the compressive strength leads to a decrease in the radius of elastoplastic interface. The sensitivity of the three factors is studied by the sensitivity analyzing method. Under a certain contact width, the blade angle has the most significant influence on the damaged area. A numerical model of the penetration of indentation is developed by using the software ABAQUS. The numerical results show that the changes of the blade angle can significantly influence the spatial position of the point with the maximum tensile stress and the direction of minimum gradient.