Once an earth slope is led to the limit equilibrium state by means of the finite element–strength reduction technique, a plastic zone will go through the slope from the toe to the top. Based on the ...observation that the critical slip surface will be within the plastic zone and be composed of the points at which the equivalent plastic strain arrives at the maximum in the vertical direction. First, some vertical lines are arranged along the horizontal direction. Then, along each of the vertical lines the point with the maximum equivalent plastic strain is found out. All such points take on a shape of wave and form the functional data. Finally, the functional data are smoothed by the least squares and the position of the critical slip surface is determined. The proposed procedure is verified through comparison with other procedures.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
•A PU-based four-node tetrahedral element with continuous nodal stress is proposed.•Performance of the proposed element is investigated for 3D elastic problems.•Performance of the proposed element is ...much better than Tetr4 and Hexa8 elements.•The proposed element could obtain continuous nodal stress.
Formulation of a partition of unity (PU) based four-node tetrahedral element with continuous nodal stress (Tetr4-CNS) and its applications to the analysis of linear elasticity problems in three-dimension are presented in this paper. By simply using the same mesh as the classical tetrahedral element (Tetr4), Tetr4-CNS element is able to obtain continuous nodal stress without recourse to stress smoothing operation in the post-processing process, and to construct high order global approximation without adding extra nodes or nodal DOFs. Moreover, it is free from the linear dependence problem which cripples many of the PU-based methods. A series of numerical tests are carried out to evaluate the performance of the Tetr4-CNS element. The numerical results show that accuracy through the proposed element is superior to that through Tetr4 element and eight-node hexahedral element (Hexa8). More importantly, the proposed element has excellent mesh distortion tolerant capabilities.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
This paper presents the frictional contact formulation for frictional crack in elastic solids at small strains based on the Penalty method in the framework of the virtual element method. For normal ...direction of contact interface, the Karush-Kuhn-Tucker conditions (or KKT-conditions) is engaged to handle the contact problem. The Coulomb's law is exerted to respond to the crack interface's stick-slip condition for the tangential direction of the contact interface. The frictional contact constraints are forced by the classical Penalty method and the node-to-segment approach is applicated to compute the contact element on the contact interface. Several numerical examples with Voronoi meshes are offered to display the contact algorithm accuracy compared with existing results in the imitation of a variety of contact conditions. In the last numerical simulations, the contact algorithm is also suitable for the rock mass with multiple cracks.
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GEOZS, IMTLJ, KILJ, NLZOH, NUK, OILJ, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK
In the current context of global climate change, geohazards such as earthquakes and extreme rainfall pose a serious threat to regional stability. We investigate a three-dimensional (3D) slope dynamic ...model under earthquake action, derive the calculation of seepage force and the normal stress expression of slip surface under seepage and earthquake, and propose a rigorous overall analysis method to solve the safety factor of slopes subjected to combined with rainfall and earthquake. The accuracy and reliability of the method is verified by two classical examples. Finally, the effects of soil permeability coefficient, porosity, and saturation on slope stability under rainfall in a project located in the Three Gorges Reservoir area are analyzed. The safety evolution of the slope combined with both rainfall and earthquake is also studied. The results indicate that porosity has a greater impact on the safety factor under rainfall conditions, while the influence of permeability coefficient and saturation is relatively small. With the increase of horizontal seismic coefficient, the safety factor of the slope decreases significantly. The influence of earthquake on slope stability is significantly greater than that of rainfall. The corresponding safety factor when the vertical seismic action is vertically downward is smaller than that when it is vertically upward. When considering both horizontal and vertical seismic effects, slope stability is lower.
•The improved VEM is proposed for the excavation analysis of the stony soil slope.•The excavation algorithms are implemented to simulate the excavation processes.•The improved shear strength ...reduction technique is adopted and implemented into the VEM.•Compared to the FEM, VEM has shape independent and can flexible choice of nodes number in an element which can be changed easily during the simulation process.•The advantages of the VEM in discretization and accuracy are demonstrated.
This study improved two parts of the virtual element method (VEM) to ensure that the stability of a stony soil slope, especially under excavation conditions, could be better studied. One of the improvements was the specific realization of the excavation algorithm, including the determination of how to identify polygonal elements that needed to be excavated, and the “deactivate and reactivate polygonal elements” used to calculate the excavation load during the slope excavation process. The second improvement was the calculation of the factor of safety (FOS) of a slope by combining shear strength reduction and the φ−ν inequality so that the stability of the stony soil slope could be better evaluated. The principal goal was to extend the latest developed virtual element method to the analysis and calculation of the excavation of a stony soil slope. Because the VEM was shape independent, it also allowed the number of nodes in an element to be chosen flexibly and fluidly, so the number of nodes could be changed easily during a simulated procedure. Two numerical examples of the one-step excavation of a homogeneous slope and the two-step excavation of a stony soil slope were solved with the improved VEM. The numerical results showed that the VEM could accurately simulate the excavation process of the slope.
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GEOZS, IMTLJ, KILJ, NLZOH, NUK, OILJ, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK
In geotechnical analysis, the factor of safety (FOS) is crucial for slope stability assessment. Traditional methods often overlook the nuances of partial slope instability. Accurately determining ...geotechnical parameters for FOS in complex simulations is challenging and resource-intensive. The limit equilibrium method (LEM), considering unit weight, cohesion, and internal friction angle, is used to address this. This study focuses on the Jiuxianping landslide, analyzing its stability and failure behavior. Utilizing the Bayesian theorem, the study back-analyzes shear strength parameters, considering partial instability and uncertainties in the Janbu corrected method. The parameters’ posterior distribution is determined using the Markov Chain Monte Carlo (MCMC) method and Multivariate Adaptive Regression Splines (MARS) for efficient sampling. These parameters are then used for precise FOS calculation at the critical point of partial instability, corroborated by 2021 data from the Jiuxianping landslide. The study finds that while the entire slope remains stable, partial instability caused by long-term water erosion significantly lowers the FOS about 10.9%, highlighting its critical impact on overall slope stability.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Summary
The rotation degree of freedom in discontinuous deformation analysis (DDA) may cause false volume expansion when a block undergoes a large rotation. We propose a block displacement function ...to prevent this defect. Specifically, the degrees of freedom in a block are redefined by incremental displacements at its vertices, and displacement is formulated based on the mean value coordinates. In addition, the finite element method with updated Lagrangian formulation is employed to derive the equilibrium equations, while the contact analysis and implicit time integration for dynamics is maintained from the original DDA. After each time step, the block configuration is updated by adding the new degrees of freedom to the previous coordinates of the block vertices. Results from numerical examples confirm the effectiveness of the proposed approach to prevent false volume expansion, ensure correctness of contact analysis, and provide realistic stress results when simulating large rotations.
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
Abstract
The virtual element method (VEM) is commonly used in engineering due to its ability to solve arbitrary node meshes. In this study, we propose a method to determine the free surface of the ...unconfined seepage problem in soil–rock mixtures slope using the advantages of the VEM. By cutting meshes in the iteration, our method overcomes the limitation of fixed mesh in solving the free surface, and the numerical tests confirm the accuracy of the proposed method in predicting the location of the seepage surface. Moreover, the results demonstrate that the presence of rock blocks significantly impacts the unconfined seepage behavior of soil–rock mixtures slope, revealing the importance of considering rock blocks in the analysis of such systems.
This paper introduces the Goodman contact element based on the virtual element method framework. Since the virtual element method can calculate polygonal elements with any number of nodes, the ...limitation of mesh matching of the contact part required by the Goodman contact element is overcome by adding nodes to the contact element. Combine the virtual element method with the Goodman contact element to enable the Goodman contact element to solve practical problems in geotechnical engineering. In this paper, first, we derive the elastoplastic virtual element equations, and then, the Goodman contact stiffness matrix based on the virtual element method is calculated. Finally, several numerical examples are shown. In numerical models, the sensitivity of the virtual element method to mesh distortion is studied. We also investigate the shape sensitivity of the algorithm and the convergence of the Voronoi element through several frictionless contact examples. And then, the contact examples under friction state and elastic–plastic constitutive law are carried out. Finally, the contact force between soil and wall under the non-matching mesh in the gravity retaining wall commonly used in geotechnical engineering is presented.
