Simulating stress wave with flat-top partition of unity based high-order discontinuous deformation analysis

Liu, Xiaoying; Zhao, Zhiye; Ma, Shuqi

doi:10.1016/j.enganabound.2018.03.015

Cited by 10 publications

(4 citation statements)

References 37 publications

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“…The unique values of a, b, and c can be obtained by solving Equation ( 16), and the correction functions of acceleration, velocity, and displacement can be obtained by substituting them into Equations ( 13)- (15). In the process of obtaining Equations ( 14) and ( 15) by integrating Equation ( 13), the accurate integration of continuous function is adopted.…”

Section: Pre-processing Methodsmentioning

confidence: 99%

“…However, the original DDA method also has limitations in dealing with many problems, such as high-precision stress field in a rock block, stratified rock mass, and so on. In order to solve these problems, many scholars have carried out in-depth research, and the theoretical research can be roughly summarized as parameter selection, block contact, accurate block stress, dynamic calculation, multiscale analysis, and 3D simulation [15,16]. Meanwhile, the DDA method has also been widely used in practical engineering, including slopes, dams, tunnels, and so on [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Investigation of 2D Seismic DDA Method for Numerical Simulation of Shaking Table Test of Rock Mass Engineering

Kang

Sheng

et al. 2022

Mathematics

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Since the basic theory of the discontinue deformation analysis (DDA) method was proposed, the DDA open source has gone through a long development process. At present, different kinds of programs have been widely applied in rock mass engineering such as slope, dam, and tunnel. This paper introduces the solution principle of DDA motion equations in detail, as well as the development status of the 2D open-source program. Numerical simulation of shaking table test of rock mass engineering using 2D DDA program is highlighted, and investigations of seismic wave pre-processing and seismic input method are carried out. First, based on the Newmark integration scheme, the integration algorithms of synthetic or measured seismic wave time history, correction function of seismic wave, and DDA simulation are unified. Then, three seismic input methods are implanted in the DDA program, and the applicability of various seismic input methods is discussed. On this basis, using the improved seismic 2D DDA program, a shaking table test of typical rock mass engineering is simulated. Through the comparison between the theoretical/test data and simulation results, the reliability of the improved DDA program in seismic response analysis is verified; the large mass method and the large stiffness method are more suitable for rigid foundation, such as shaking table test; the propagation of the seismic wave presents a significant amplification effect due to the reflection, refraction, and diffraction in the tunnel. The research results provide DDA theory and an open-source program for analyzing the seismic response of rock mass engineering.

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Section: Pre-processing Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Investigation of 2D Seismic DDA Method for Numerical Simulation of Shaking Table Test of Rock Mass Engineering

Kang

Sheng

et al. 2022

Mathematics

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“…Discontinuous Deformation Analysis (DDA) [ 1 ], a novel numerical method for analyzing the dynamic mechanical behavior of a block system in cases of large displacement, was verified as an effective tool in solving a variety of discontinuities in rock problems [ 2 , 3 ]. In rock-mass engineering, DDA has been employed to handle a great deal of problems, e.g., landslide process simulations [ 4 , 5 ], slope stability assessments [ 6 , 7 ], blasting effect evaluation [ 8 ], crack propagation simulation [ 9 , 10 ], seismic wave propagation analysis [ 11 ], and rock burst prediction [ 12 ]. Applications of 2D DDA in the modeling of rock-mass dynamics until 2017 were summarized by Ning [ 13 ].…”

Section: Introductionmentioning

confidence: 99%

Vertex Displacement-Based Discontinuous Deformation Analysis Using Virtual Element Method

et al. 2021

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To avoid disadvantages caused by rotational degrees of freedom in the original Discontinuous Deformation Analysis (DDA), a new block displacement mode is defined within a time step, where displacements of all the block vertices are taken as the degrees of freedom. An individual virtual element space V1(Ω) is defined for a block to illustrate displacement of the block using the Virtual Element Method (VEM). Based on VEM theory, the total potential energy of the block system in DDA is formulated and minimized to obtain the global equilibrium equations. At the end of a time step, the vertex coordinates are updated by adding their incremental displacement to their previous coordinates. In the new method, no explicit expression for the displacement u is required, and all numerical integrations can be easily computed. Four numerical examples originally designed by Shi are analyzed, verifying the effectiveness and precision of the proposed method.

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“…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 proposed for improving the DDA efficiency in engineering applications.…”

Section: Introductionmentioning

confidence: 99%

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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Simulating stress wave with flat-top partition of unity based high-order discontinuous deformation analysis

Cited by 10 publications

References 37 publications

Investigation of 2D Seismic DDA Method for Numerical Simulation of Shaking Table Test of Rock Mass Engineering

Investigation of 2D Seismic DDA Method for Numerical Simulation of Shaking Table Test of Rock Mass Engineering

Vertex Displacement-Based Discontinuous Deformation Analysis Using Virtual Element Method

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

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