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1.
The discontinuous deformation analysis (DDA) with second‐order displacement functions was derived based on six‐node triangular mesh in order to satisfy the requirement for the accurate calculations in practical applications. The matrices of equilibrium equations for the second‐order DDA were given in detail for program coding. By close comparison with widely used finite element method and closed form solutions, the advantages of the modified DDA were illustrated. The program coding was carried out in C++ environment and the new code applied to three examples with known analytical solutions. A very good agreement was achieved between the analytical and numerical results produced by the modified DDA code. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
2.
《Geomechanics and Geoengineering》2013,8(2):147-153
With high-order numerical manifold method (NMM) or high-order discontinuous deformation analysis method (DDA), computational accuracy of structure deformation can be improved greatly. However, poor accuracy is obtained and even computation is not convergent while treating large deformation problems, due to inaccurate or incorrect high-order initial stress formulae. Based on 2D triangular mathematical meshes and polynomial cover functions in high-order NMM, exact formulae for high-order initial stresses are deduced to depict configuration change of structures under large deformations. The formulae are expressed in polynomial forms so as to be used in simplex integrations. The approach is also extended to high-order DDA. Comparing with analytical solutions, accurate results for large deformation of a cantilever beam prove the validity of the proposed formulae. 相似文献
3.
Over the last decade, researchers in the discontinuous deformation analysis (DDA) community have dedicated a great deal of effort to document the accuracy of the method by performing validation studies. This paper contains a summary of more than 100 published and unpublished validation studies which comprise the body of DDA validation information to which the authors have access. The studies are grouped into three general categories: (a) validation with respect to analytical solutions, (b) validation with respect to results of other numerical techniques, and (c) validation with respect to laboratory and field data. Three general techniques for validation are described: qualitative assessment visually examining runtime behaviour of simulations, semi‐quantitative assessment comparing numerical results of simulations, and quantitative where numerical simulation results are evaluated in detail with respect to similar analytical, laboratory or field results. We find that for many of the problems addressed by the papers in this review, DDA performs more than adequately for engineering analysis. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
4.
As a hybrid method, the nodal‐based discontinuous deformation analysis (NDDA) greatly improves the stress accuracy within each DDA block by coupling a well‐defined finite element mesh inside the DDA block; at the same time, the NDDA inherits the unique block kinematics of the standard DDA method. Each finite element mesh line inside the DDA block is treated as a potential crack, which enables the transformation of the block material from continuum to discontinuum through the tensile and shear fracturing mechanism. This paper introduces a double minimization procedure into the NDDA method to further improve the accuracy of the stresses evaluated at the finite element mesh lines and thus to obtain a more realistic fracture model. Three numerical examples are employed to demonstrate the improved stress accuracy by the implemented double minimization procedure and the accuracy and capability of the enhanced NDDA method in capturing brittle fracturing process. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
5.
Validating the ability of the discontinuous deformation analysis method to model normal P‐wave propagation across rock fractures 
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下载免费PDF全文 The effects of fractures on wave propagation problems are increasingly abstracting the attention of scholars and engineers in rock engineering field. This study aims to fully validate the ability of discontinuous deformation analysis (DDA) to model normal P‐wave propagation across rock fractures. The effects of a single fracture and multiple parallel fractures are all tested. The results indicate that DDA can accurately reflect the fracture effects, including the fractures stiffness, the fracture spacing and the fracture number, and the effects of incident wave frequency on one‐dimensional P‐wave propagation problems. Thus, DDA is able to deal well with normal incident P‐wave propagation problems. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
6.
A New Viscous Boundary Condition in the Two-Dimensional Discontinuous Deformation Analysis Method for Wave Propagation Problems 总被引：1，自引：1，他引：0
Viscous boundaries are widely used in numerical simulations of wave propagation problems in rock mechanics and rock engineering. By using such boundaries, reflected waves from artificial boundaries can be eliminated; therefore, an infinite domain can be modeled as a finite domain more effectively and with a much greater accuracy. Little progress has been made, thus far, with the implementation and verification of a viscous boundary in the numerical, discrete element, discontinuous deformation analysis (DDA) method. We present in this paper a new viscous boundary condition for DDA with a higher absorbing efficiency in comparison to previously published solutions. The theoretical derivation of the new viscous boundary condition for DDA is presented in detail, starting from first principles. The accuracy of the new boundary condition is verified using a series of numerical benchmark tests. We show that the new viscous boundary condition works well with both P waves as well as S waves. 相似文献
7.
Investigation of highly efficient algorithms for solving linear equations in the discontinuous deformation analysis method 下载免费PDF全文
下载免费PDF全文 Large‐scale engineering computing using the discontinuous deformation analysis (DDA) method is time‐consuming, which hinders the application of the DDA method. The simulation result of a typical numerical example indicates that the linear equation solver is a key factor that affects the efficiency of the DDA method. In this paper, highly efficient algorithms for solving linear equations are investigated, and two modifications of the DDA programme are presented. The first modification is a linear equation solver with high efficiency. The block Jacobi (BJ) iterative method and the block conjugate gradient with Jacobi pre‐processing (Jacobi‐PCG) iterative method are introduced, and the key operations are detailed, including the matrix‐vector product and the diagonal matrix inversion. Another modification consists of a parallel linear equation solver, which is separately constructed based on the multi‐thread and CPU‐GPU heterogeneous platforms with OpenMP and CUDA, respectively. The simulation results from several numerical examples using the modified DDA programme demonstrate that the Jacobi‐PCG is a better iterative method for large‐scale engineering computing and that adoptive parallel strategies can greatly enhance computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
8.
The scaled boundary finite‐element method is derived for elastostatic problems involving an axisymmetric domain subjected to a general load, using a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system. The method is particularly well suited to modelling unbounded problems, and the formulation allows a power‐law variation of Young's modulus with depth. The efficiency and accuracy of the method is demonstrated through a study showing the convergence of the computed solutions to analytical solutions for the vertical, horizontal, moment and torsion loading of a rigid circular footing on the surface of a homogeneous elastic half‐space. Computed solutions for the vertical and moment loading of a smooth rigid circular footing on a non‐homogeneous half‐space are compared to analytical ones, demonstrating the method's ability to accurately model a variation of Young's modulus with depth. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
9.
A meshfree node‐based smoothed point interpolation method (NS‐PIM), which has been recently developed for solid mechanics problems, is applied to obtain certified solutions with bounds for hydraulic structure designs. In this approach, shape functions for displacements are constructed using the point interpolation method (PIM), and the shape functions possess the Kronecker delta property and permit the straightforward enforcement of essential boundary conditions. The generalized smoothed Galerkin weak form is then applied to construct discretized system equations using the node‐based smoothed strains. As a very novel and important property, the approach can obtain the upper bound solution in energy norm for hydraulic structures. A 2D gravity dam problem and a 3D arch dam problem are solved, respectively, using the NS‐PIM and the simulation results of NS‐PIM are found to be the upper bounds. Together with standard fully compatible FEM results as a lower bound, we have successfully determined the solution bounds to certify the accuracy of numerical solutions. This confirms that the NS‐PIM is very useful for producing certified solutions for the analysis of huge hydraulic structures. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
Boundary setting method for the seismic dynamic response analysis of engineering rock mass structures using the discontinuous deformation analysis method 下载免费PDF全文
下载免费PDF全文 Large deformations and discontinuous problems can be calculated using the discontinuous deformation analysis (DDA) method by solving time steps, and this method is suitable for simulating the seismic dynamic response of engineering rock mass structures. However, the boundary setting must be carefully analyzed. In this paper, four boundary settings for the DDA method are investigated. First, the contributions to the DDA equations for nonreflecting boundaries (including the viscous boundary and the viscoelastic boundary) are deduced based on the Newmark method. Second, a free‐field boundary is introduced in the DDA method with boundary grid generation and coupling calculation algorithms to accurately simulate external source wave motion, such as earthquakes. Third, seismic input boundary treatments are intensively examined, and the force input method is introduced based on nonreflecting boundaries. Finally, the static‐dynamic unified boundary is implemented to ensure consistent boundary transformation. The boundary setting method in the DDA method is discussed, and the suggested treatments are used to analyze the seismic dynamic response of underground caverns. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
11.
The discontinuous deformation analysis (DDA) is a discontinuum‐based method, which employs a penalty method to represent the contact between blocks. The penalty method is easy to be implemented in the program, but the contact constraint is only approximately satisfied. Penetrations between contacting blocks are unavoidable even if the penalty value is very large. To improve the contact precision in the DDA, an augmented Lagrangian method is introduced, which can make use of advantages of both the Lagrangian multiplier method and the penalty method. This paper provides a detailed implementation of the augmented Lagrangian method in the DDA program and compares it with the standard DDA on the computational efficiency and contact precision. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
12.
基于DDA方法一种流-固耦合模型的建立及裂隙体渗流场分析和应用 总被引：1，自引：0，他引：1
以非连续变形分析方法（DDA）为基础并采用稳态流体计算方法将二者结合进行裂隙岩体流-固耦合分析。利用DDA方法生成裂隙岩体模型,在此基础上采用矩阵搜索等方法形成新的裂隙水通网络模型。采用稳态迭代算法和立方定律求得裂隙水压力,并把裂隙水压力作为线载荷施加到块体边界,在DDA算法中每个迭代步完成后更新裂隙开度和水压值,与DDA算法结合研究裂隙水与块体之间相互作用关系。利用以上裂隙岩体流-固耦合计算方法研究了某水封油库开挖和运行过程洞室围岩流量和密封性,为该工程预测水封效果提供了有益的主要依据,也是国内首次采用DDA方法做大型工程的流-固耦合模型分析。 相似文献
13.
Jian‐Hong Wu 《国际地质力学数值与分析法杂志》2007,31(5):649-666
Chiu‐fen‐erh‐shan landslide is a remarkable slope failure occurred during the Chi‐Chi earthquake in 1999. In November of 2002, abnormal geomorphologic features, including buckling and ground subsidence, were observed on the lower slope of the Chiu‐fen‐erh‐shan landslide. This study attempts to assess the constrained area of a future collapsing on the slope using a dynamic discrete numerical analysis method, discontinuous deformation analysis (DDA). The simulation results show that the depression in front of the toe of the slope provides a space for arresting the whole sliding rocks when only the unstable lower slope fails. However, as the whole slope slides, the rock fragments move farther into the memorial park and can impact other facilities resulting in the enlarging of constrained area. The authority should prohibit people from entrancing the constrained area in the rainy season. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
14.
Disk clusters are developed to represent the shape of granular materials more precisely (compared to circular particles) and to minimise excessive rolling. Investigating the behaviour of dynamic disk-based discontinuous deformation analysis (DDA) with disk clusters is very important to evaluate the applicability of disk-based DDA to dynamic problems in geomechanics. In this paper, the accuracy of disk-based DDA under dynamic conditions is studied by a comprehensive sensitivity analysis. The results obtained by disk-based DDA are compared with the analytical solutions of a disk cluster on an incline subjected to gravitational force only, and three different accelerations of increasing complexity with sinusoidal input functions as well as gravitational load. In this research, the effects of time step size and interface friction angles on the results are studied. Overall, most of the error for both velocity and displacement occurs at the beginning of the solution. With increasing friction angle, the initial perturbation of the solution increases in the case of sliding under gravitational force only, and decreases in the case of sliding under dynamic loads. This study shows that disk-based DDA predicts accurately the velocities and displacements derived with respect to the frictional resistance offered by the inclines. 相似文献
15.
The role of interface friction is studied by slow direct shear tests and rapid shaking table experiments in the context of dynamic slope stability analysis in three dimensions. We propose an analytical solution for dynamic, single and double face sliding and use it to validate 3D‐DDA. Single face results are compared with Newmark's solution and double face results are compared with shaking table experiments performed on a concrete tetrahedral wedge model, the interface friction of which is determined by constant velocity and velocity stepping, direct shear tests. A very good agreement between Newmark's method on one hand and our 3D analytical solution and 3D‐DDA on the other is observed for single plane sliding with 3D‐DDA exhibiting high sensitivity to the choice of numerical penalty value. The results of constant and variable velocity direct shear tests reveal that the tested concrete interface exhibits velocity weakening. This is confirmed by shaking table experiments where friction degradation upon multiple cycles of shaking culminated in wedge run out. The measured shaking table results are fitted with our 3D analytical solution to obtain a remarkable linear logarithmic relationship between friction coefficient and sliding velocity that remains valid for five orders of magnitude of sliding velocity. We conclude that the velocity‐dependent friction across rock discontinuities should be integrated into dynamic rock slope analysis to obtain realistic results when strong ground motions are considered. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
16.
Jian-Hong Wu 《Computers and Geotechnics》2010,37(1-2):153-163
This work calculates the integrations of convex and concave polyhedrons in three-dimensional discontinuous deformation analysis (3D DDA) using a novel method. With this novel method, mathematical topology is applied to the integration, and the numerical mesh used by the Finite Element Method (FEM) is not needed to subdivide polyhedrons into tetrahedrons or hexahedrons. Examples demonstrate the accuracy of the proposed method for integrating convex and concave polyhedrons with planar boundaries. 相似文献
17.
David M. Doolin 《国际地质力学数值与分析法杂志》2005,29(12):1199-1207
Displacement boundary constraints in discontinuous deformation analysis (DDA) are applied using stiff penalty springs. A co‐ordinate‐free formulation for displacement boundary constraints is presented here for DDA, which unifies previous derivations for points of fixity, and for points constrained to induce or prohibit block motion in specified directions as a function of location or time. Examples for each type of constraint are used to illustrate the behaviour of the algorithm and provide a link with previous formulations for each case. The new, unified formulation has five benefits: (1) simple to express algorithmically; (2) easy to program and verify; (3) penalty values in different directions may be chosen to allow fixed points, lines, curves or planes; (4) formulation works for 2D and 3D; (5) displacement constraint may be a function of time or location or both. Feedback in the algorithm may induce internal resonance in homogeneously deformable discrete elements used in DDA, and resonance in block‐to‐block contact interactions. Consequently, high mass problems with insufficient damping may suffer from excessive ‘vibrational hammering’, inducing physically implausible behaviour such as elastic rebound. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
18.
Unbounded plane stress and plane strain domains subjected to static loading undergo infinite displacements, even when the zero displacement boundary condition at infinity is enforced. However, the stress and strain fields are well behaved, and are of practical interest. This causes significant difficulty when analysis is attempted using displacement‐based numerical methods, such as the finite‐element method. To circumvent this difficulty problems of this nature are often changed subtly before analysis to limit the displacements to finite values. Such a process is unsatisfactory, as it distorts the solution in some way, and may lead to a stiffness matrix that is nearly singular. In this paper, the semi‐analytical scaled boundary finite‐element method is extended to permit the analysis of such problems without requiring any modification of the problem itself. This is possible because the governing differential equations are solved analytically in the radial direction. The displacement solutions so obtained include an infinite component, but relative motion between any two points in the unbounded domain can be computed accurately. No small arbitrary constants are introduced, no arbitrary truncation of the domain is performed, and no ill‐conditioned matrices are inverted. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
19.
Accurate estimation of rockfall trajectory and motion behaviors is essential for rockfall risk assessment and the design and performance evaluation of preventive structures. Numerical simulation using discontinuous deformation analysis (DDA) is effective and helpful in rockfall analysis. Up to now, there have been many reports on application of two-dimensional (2-D) DDA programs. In this paper, the major advantages of rockfall analysis using 2-D and extensions to three-dimensional (3-D) analysis are presented. A practical 3-D DDA code is demonstrated to be capable of simulating free falling, rolling, sliding, and bouncing with high accuracy. Because rockfall trajectories and motion behaviors can be described as combinations of these four types, this demonstration indicates that the implemented code is capable of providing reliable rockfall analysis. Finally, specific tests are conducted to compare 2-D and 3-D DDA rockfall analysis in predicting trajectory and dynamic behavior. The results indicate that 3-D DDA simulations are more appropriate for rough tree-laden inclined slopes in providing detailed spatial distribution, whereas 2-D DDA simulations have better efficiency for slopes dominated by valleys and ravines. These results can help in selecting the appropriate DDA simulation for rockfall analysis. 相似文献
20.
Solutions are presented for the problem of isothermal dessiccation shrinkage in a double‐layer porous partially saturated medium. The rheological model taken into account is linear poroelastic. Hence the analysis is mainly focused on hydromechanical coupling effects and contrasts of mechanical and hydraulic properties between two materials: a low thickness skin comprised between the outer boundary and the reference porous material. Three one‐dimensional ideal structures are taken into account: a wall of finite thickness (cartesian geometry), a thick cylinder and a thick sphere. The solution of the time‐dependent problem is arrived at by applying Laplace transforms to the field variables. Exact solutions are obtained in Laplace transform space using Mathematica© to solve the field equations whilst taking into account the continuity equations at the interface and the boundary conditions. The Talbot's modified algorithm has been performed to invert the Laplace transform solutions. A bibliographical and numerical study shows that this method is remarkably precise, stable and close to the analytical inversion. Results are presented using poroelastic data representative of a concrete material and involve a strong coupling effect between hydraulical and mechanical behaviours. A first approach elastic modelling of degradation process have been presented using a thin outer layer. Apart from emphasising the semi‐explicit solution utility due to accurate speed calculation, this paper deals with more complex problems than those which can be solved using purely analytical solutions. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献