Guanhua Sun

Combined Finite-Discrete Element Method for Simulation of Hydraulic Fracturing

Hydraulic fracturing is widely used in the exploitation of unconventional gas (such as shale gas).Thus, the study of hydraulic fracturing is of particular importance for petroleum industry. The combined finite-discrete element method (FDEM) proposed by Munjiza is an innovative numerical technique to capture progressive damage and failure processes in rock. However, it cannot model the fracturing process of rock driven by hydraulic pressure. In this study, we present a coupled hydro-mechanical model based on FDEM for the simulation of hydraulic fracturing in complex fracture geometries, where an algorithm for updating hydraulic fracture network is proposed. The algorithm can carry out connectivity searches for arbitrarily complex fracture networks. Then, we develop a new combined finite-discrete element method numerical code (Y-flow) for the simulation of hydraulic fracturing. Finally, several verification examples are given, and the simulation results agree well with the analytical or experimental results, indicating that the newly developed numerical code can capture hydraulic fracturing process correctly and effectively.

A global procedure for evaluating stability of three-dimensional slopes

In the setting of the three-dimensional limit equilibrium method, a procedure for bounding the factor of safety is proposed under the constraint of the reasonable conditions on the system of forces suggested by Morgenstern and Price. No assumption is made regarding the internal forces but the system of forces resulted from the procedure satisfies the reasonable conditions as well as all the equilibrium conditions. The optimization problem proposed has weak nonlinearity but no numerical problems inherent in the methods of columns and can be solved using those conventional optimization techniques. Through some typical examples, it is illustrated that even for complicated failure surfaces the proposed procedure gives rise to a very narrow interval of the factor of safety with a low degree of computational complexity.

Huangtupo landslide stability under water level fluctuations of the Three Gorges reservoir

The Huangtupo riverside slope, which extends an area of 1.35u2009×u2009106xa0m2 and has a total volume of 6.934u2009×u2009107xa0m3, is one of the most noted large-scale landslides with great concern about the safety of immigrants in the Three Gorges reservoir area of China. During the normal operation, the reservoir water level fluctuates periodically. Water level fluctuation will soften the strength of the geologic materials on the banks, induce underground water fluctuation, and in turn affect the slope stability. On the basis of the thorough engineering geological survey, the analysis of engineering geological conditions and deformation mechanism is conducted primarily. Then, the Huangtupo landslide is divided into four minor landslides, all of which have typical three-dimensional characteristics. To these landslides, a three-dimensional rigorous limit equilibrium method is proposed, which can accommodate failure surfaces of any shape, and satisfies all the equilibrium conditions. In terms of the strength parameters of geologic materials, the stability evolution of the four minor landslides at the Huangtupo landslide under periodical water level fluctuation is investigated in detail. From the results, the 3D safety factors turned out to be somewhat bigger than the 2D results even though they displayed the same trends. The differences between 2D and 3D results are about 2.92–6.11xa0%. The maximum reduction in safety factors with the rapid down of water level is 0.11. It is suggested that the safety margin of the two minor landslides near the riverside is insufficient and might become instable under periodical water level fluctuation.

Strain softening of nano-scale fuzzy interfaces causes Mullins effect in thermoplastic polyurethane

The strain-induced softening of thermoplastic polyurethane elastomers (TPUs), known as the Mullins effect, arises from their multi-phase structure. We used the combination of small- and wide- angle X-ray scattering (SAXS/WAXS) during in situ repeated tensile loading to elucidate the relationship between molecular architecture, nano-strain, and macro-scale mechanical properties. Insights obtained from our analysis highlight the importance of the ‘fuzzy interface’ between the hard and soft regions that governs the structure evolution at nanometre length scales and leads to macroscopic stiffness reduction. We propose a hierarchical Eshelby inclusion model of phase interaction mediated by the ‘fuzzy interface’ that accommodates the nano-strain gradient between hard and soft regions and undergoes tension-induced softening, causing the Mullins effect that becomes apparent in TPUs even at moderate tensile strains.

Extremum solutions to the limit equilibrium method subjected to physical admissibility

In the slope stability analysis, the interslice force calculated by the method of slices is the internal force of the slope in the limit equilibrium state, which is vital to the design of reinforcement. However, none of the existing methods can guarantee a priori the interslice force is reasonable. Starting from the global analysis procedure, an optimization problem for maximizing the factor of safety is posed under the constraints that the system of forces in the sliding body is physically admissible. In the problem, both the factor of safety and the normal stress along the slip surface are taken as the independent variables. With weak nonlinearity and no numerical problems inherent in the methods of slices, the optimization problem can be solved by those conventional optimization techniques. No assumption is made regarding the interslice forces, but the system of forces from the optimization problem is physically admissible. To bracket the factor of safety, meanwhile, the minimum of the factor of safety is calculated through a minimization process under the same constraints as the maximization process. It is illustrated that for smooth slip surfaces, the solutions to the maximum and the minimum almost coincide, and for non-smooth slip surfaces, the interval of the solution is very narrow.

Mechanisms of Interaction Between an Arch Dam and Abutment Slope Using Physical Model Tests

In southwestern China, the stability of high-steep slopes in large-scale hydropower projects has become a key technical challenge that constrains the safety of construction and operation. Based on a geological survey of the large-scale rock block in the Jinping-I Hydropower Station left bank, the entire system of the dam and its abutment slope is defined as the study subject. The mechanisms of interaction between the arch dam and the abutment slope during the construction stage, the impoundment stage and the structural plane strength-weakening stage are investigated using physical model tests. (1) During the excavation stage, the early-stage excavation has a significant impact on the huge rock block, whereas the impact of later-stage excavation is relatively small. (2) During the impoundment stage, the dam foundation is under hydraulic load. Therefore, the huge rock block moves away from the slope due to the arch thrust. (3) During the structural plane strength-weakening stage, both sides of the structural planes develop a relative displacement, and the massive rock block slips slightly. Moreover, the strain of the dam is slightly different from the situation in the normal impoundment stage. The majority of the downstream plane is under tension, indicating that a decline in the bedrock strength of the left bank dam abutment results in deformation of the dam towards the mountain body, the riverbed and the top part of the dam crest.

3D DDA Based on Variational Inequality Theory and Its Solution Scheme

The advantage of 3D discontinuous deformation analysis (3D DDA) is the rigorous contact conditions on the interaction of 3D blocks. These conditions are enforced by the penalty function convention; however, inappropriate penalty parameters easily generate numerical instability. To avoid the introduction of the penalty parameters, the contact conditions in 3D DDA are described as variational inequalities in this study, and the extra-gradient method is employed to solve this new formulation of 3D DDA. The proposed computation scheme is more flexible and dispenses with large scale matrix inversion. Some practical examples originally designed by Shi are analysed, verifying the effectiveness and precision of the new scheme.

A Simplified Solution for Calculating the Phreatic Line and Slope Stability during a Sudden Drawdown of the Reservoir Water Level

On the basis of the Boussinesq unsteady seepage differential equation, a new simplified formula for the phreatic line of slopes under the condition of decreasing reservoir water level is derived by means of the Laplacian matrix and its inverse transform. In this context, the expression of normal stress on the slip surface under seepage forces is deduced, and a procedure for obtaining the safety factors under hydrodynamic forces is proposed. A case study of the Three Gorges Reservoir is used to analyze the influences of the water level, decreasing velocity and the permeability coefficient on slope stability.

A Three-Node Triangular Element with Continuous Nodal Stress (Trig3-CNS) for Geometry Nonlinear Solid Mechanics Problems

This paper investigates the performance of the three-node triangular element with continuous nodal stress (Trig3-CNS) for geometry nonlinear solid mechanic problems. This Trig3-CNS element was recently proposed to improve accuracy of the finite element method (FEM). By synergizing the individual strengths of meshfree method and FEM, the Trig3-CNS element achieves higher accuracy and convergence rate. Furthermore, Trig3-CNS presents high tolerance to mesh distortion. Therefore, it is potentially useful for geometry nonlinear solid mechanics problems in which mesh distortion takes place. Compared with the traditional hybrid “FE-Meshfree” elements, Trig3-CNS naturally processes CNS without requiring any extra operation in post-processing. Numerical tests in the present work show that for geometry nonlinear analysis, the results of the Trig3-CNS element are better than the 3-node triangular element (Trig3) and 4-node isoparametric quadrilateral element (Quad4). In addition, the performance of Trig3-CNS is com...

Optimization Model for Determining Safety Factor and Thrust Line in Landslide Assessments

AbstractWhen the limit-equilibrium method is employed in the stability assessment of complicated landslides, some eccentric results are often encountered with the use of rigorous methods. These eccentric results may be attributable to irrationally assumed interslice forces. Furthermore, engineers should verify the rationality of the thrust-line position in a landslide after the safety factor of the landslide is solved with the use of such rigorous methods. In this paper, a new global analysis method is proposed based on the Morgenstern–Price assumption for interslice forces. The global equilibrium equations, normal stresses on the sliding surface, and position of the thrust line were employed as constraint conditions to construct an optimization model. The relationships between the constraint conditions and the safety factors and thrust line were investigated through the analysis of some typical landslides with some interesting results.