Computation of the safety factor for slope stability using discontinuous deformation analysis and the vector sum method

Fu, Xiaodong; Sheng, Qian; Zhang, Yonghui; Chen, Jian; Zhang, Shankai; Zhu, Zhenping

doi:10.1016/j.compgeo.2017.07.026

Cited by 46 publications

(20 citation statements)

References 38 publications

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“…The open-close iteration based on Equation 17eliminates contact misjudgments due to false volume expansion 47 and ensures that the contact state of a contact pair remains unchanged when the block configuration is finally updated. The total stress and strain velocity are first calculated using Equations (5) and (8), and then transformed using the Mohr's circle of stress and strain.…”

Section: Revisiting Original Dda and Remedies To Prevent False Volumementioning

confidence: 99%

“…(4) Assembling Equation (31) of all blocks, obtain the equilibrium equations of the block system as Equation (43). (5) Obtain Δa I for each block by executing the open-close iteration, which is essential in DDA to ensure the correctness of contact states for the contact pairs. First, obtain interim Δa I by solving Equation (43).…”

Section: Algorithmmentioning

confidence: 99%

“…As shown in Figure 12, the resulting stresses either remain unchanged or change with the rotation angle. The DDA modification in Reference 41 induces unchanging stresses, as shown in Figure 12A, thus providing clearly incorrect stress results possibly attributed to the use of Equation (5) to update the stress of the rotating block. Figure 12B shows the stresses calculated using the other three DDA modifications, demonstrating their agreement with the analytic solution, despite the different stress updates.…”

Section: Stress Accumulation In Rotating Triangular Blockmentioning

confidence: 99%

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Novel displacement function for discontinuous deformation analysis based on mean value coordinates

Jiang

Zheng

et al. 2020

Numerical Meth Engineering

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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. K E Y W O R D S discontinuous deformation analysis (DDA), false volume expansion, mean value coordinates 1 INTRODUCTION Discontinuous deformation analysis (DDA), originally proposed by Shi, 1 allows to effectively analyze the mechanical behavior of a discrete block system subject to large displacements. 2 In addition, DDA can handle discontinuity and has been adopted to address diverse geotechnical problems, such as landslide simulations, 3,4 rock slope stability evaluation, 5,6 rockfall trajectory tracking, 7 blasting effect evaluation, 8 shear creep deformation analysis of structural planes, 9 crack propagation modeling, 10,11 and seismic wave propagation modeling. 12 Various enhancements have been 4768

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Section: Revisiting Original Dda and Remedies To Prevent False Volumementioning

confidence: 99%

Section: Algorithmmentioning

confidence: 99%

Section: Stress Accumulation In Rotating Triangular Blockmentioning

confidence: 99%

See 1 more Smart Citation

Novel displacement function for discontinuous deformation analysis based on mean value coordinates

Jiang

Zheng

et al. 2020

Numerical Meth Engineering

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“…Fan et al [28,29] used virtual work theory to improve the accuracy of deformation and large rotation error estimation and proposed a new method to identify and analyze the contact blocks. Fu et al [30] applied the vector sum method (VSM) to the DDA to calculate the slope stability safety factor based on the actual stress state and vector and algorithm. ere is a lack of studies regarding the stability analysis of a slope with multiple sliding surfaces using these methods.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Slope with Multiple Sliding Surfaces Based on Dynamic Strength‐Reduction DDA Method

Wang

Zhu

Wang

et al. 2019

Advances in Civil Engineering

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The present study aims to elucidate the problem of a rock mass structural plane with a range of damage degrees and the numerical model selection for analysis of a slope with multiple sliding surfaces. Based on the relative displacement between blocks, the dynamic strength reduction-discontinuous deformation analysis (hereinafter referred to as DSR-DDA) method is proposed for studying slopes with multiple sliding surfaces. The slope-slider classic case was used to test the displacement threshold. The model was applied to the stability analysis of multiple sliding surfaces of a high rock slope in the Fushun West Open-Pit Mine. The results show that when the displacement threshold is set to 1 mm, the error between the DSR-DDA results and the theoretical solution is within 0.5%, which satisfies the calculation requirements. The most dangerous slip surface in the Fushun West Open-Pit Mine slope was identified. Based on the numerical slope model after the first landslide, the position of the secondary slip surface was then identified. The failure mode is traction sliding failure, and the middle and lower oil shales play a key role in the slope stability. This study recommends that mining of the remaining oil shale should stop to avoid causing large-scale landslides in the upper part of the slope and landslides at the pit-city boundary.

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“…is approach is the seepage-softening-stability analysis method, which is generally applied in the stability analysis of soft rock slopes rather than loess slopes [7,8]. In this framework, the failure mechanism of a loess slope can be revealed if the vector sum analysis method can be introduced into the stability analysis of the loess slope because the safety factor of the vector sum analysis method has a more concrete meaning [9,10]. e stability analysis of loess slopes with a rising groundwater level integrates unsaturated and transient seepage, stress analysis, and stability prediction.…”

Section: Introductionmentioning

confidence: 99%

Vector Sum Analysis Method of Loess Slope Stability under Rising Groundwater Level Conditions

Xue

Dang

et al. 2019

Advances in Civil Engineering

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e stability analysis of loess slopes with a rising groundwater level is a problem that integrates unsaturated and transient seepage, stress analysis, and stability prediction. For this purpose, a sequentially coupled method of seepage-softening-stability was used. First, seepage analysis of a loess slope with a rising groundwater level was conducted according to unsaturated and transient seepage analysis theory. Second, the spatial distribution of the deformation and strength parameters of the soil, both of which were based on the calculated results of the seepage analysis, were adjusted according to the water-induced structural deterioration equation. ird, the vector sum analysis method of loess slope stability, which was based on the temporal-spatial distribution laws of effective unit weight, elastic modulus, Poisson's ratio, cohesion, internal friction angle, and seepage force, was performed by the body force method. To verify the proposed method, the limit equilibrium method of loess slope stability was conducted by the surface force method. Finally, the progressive failure process of a loess slope with a rising groundwater level on the White Deer Plain was presented as an example. A comparison analysis of the calculated results of the two methods revealed that the proposed method was reasonable and reliable.

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Computation of the safety factor for slope stability using discontinuous deformation analysis and the vector sum method

Cited by 46 publications

References 38 publications

Novel displacement function for discontinuous deformation analysis based on mean value coordinates

Novel displacement function for discontinuous deformation analysis based on mean value coordinates

Stability Analysis of Slope with Multiple Sliding Surfaces Based on Dynamic Strength‐Reduction DDA Method

Vector Sum Analysis Method of Loess Slope Stability under Rising Groundwater Level Conditions

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