Discontinuous Deformation Analysis Code Research Articles

Dynamic process analysis of the Niumiangou landslide triggered by the Wenchuan earthquake using the finite difference method and a modified discontinuous deformation analysis

The Niumiangou landslide was the largest landslide triggered by the 2008 Wenchuan earthquake, which was significantly affected by the amplification effect of seismic acceleration. The ring-shear experiments indicated that the materials in the source area of the Niumiangou landslide were subjected to friction degradation under a big shear displacement, which may result in rapid movement of the landslide. In order to better understand the landslide movement and study the effect of the friction degradation on movement mechanisms, the dynamic process of Niumiangou landslide was simulated with a new numerical method, which combines the finite difference method (FDM) and the discontinuous deformation analysis (DDA). First, the FDM was used to study the initiation time, amplification effect and velocity of the landslide. Afterwards, these initiation velocities were applied to the blocks in the DDA model by corresponding coordination in the FDM model. A displacement-dependent friction model of the sliding surface was incorporated into DDA code to further understand the kinetic behavior of the landslide. The results show that the displacement-dependent friction strongly decreases the friction coefficient of sliding surface under a big displacement, which can obviously promote the run-out and velocity of landslide. The model output well matches the topographic map formed by the landslide. This implies that the proposed model can be applied to the simulation of earthquake-induced landslides with amplification effect, and the friction degradation model is important to clarify the movement mechanism of high-speed and long-distance landslides.

Development of a Coupled DDA–SPH Method and its Application to Dynamic Simulation of Landslides Involving Solid–Fluid Interaction

Landslides involving solid–fluid interaction such as submarine landslides and landslide dams occur frequently around the world, which may bring severe damage to human lives and properties. Investigation of such landslides is thus of significance to hazard prevention and mitigation. To conduct the analysis, there are three key points to be addressed: (a) the landslide failure process, (b) the free surface flow, and (c) the solid–fluid interaction process. Discontinuous deformation analysis (DDA) method is suitable for analyzing discontinuous blocky systems and has outstanding advantages in simulating the landslide failure process. Meanwhile, smoothed particle hydrodynamics (SPH) method is well-suited for modeling the free surface flow. However, the consideration of solid–fluid interaction in these two methods is seldom, which somehow restricts their applications. With the aim to take advantages of these two methods, a coupled DDA–SPH method in two-dimensional case is proposed, in which the solid–fluid interaction is forced using a penalty approach. The SPH formulations are implemented into DDA code. Several numerical examples are presented to check the validity of the proposed method. A dam-break test is first investigated to show the success of implementing SPH into DDA code for modeling the fluid flow in later simulations of fluid–solid systems. Subsequently, the performance of the coupled DDA–SPH method is validated through a submarine rigid landslide, and the simulation results are in good agreement with the experimental data. Further, an extension study on the submarine deformable landslide is performed, in which the landslide mass consists of multiple blocks and a sensitivity analysis on the interface friction angle between blocks is conducted. Finally, a designed landslide dam is simulated to show the applicability and feasibility of the coupled DDA–SPH method.

A method for microscopic unsaturated soil-water interaction analysis based on DDA

Unsaturated soil is a three-phase discontinues system, and microscopic analysis can provide an intrinsic understanding for macroscopic mechanical behavior of the soil. Discontinuous Deformation Analysis (DDA) has the advantage for analyzing the material like granular aggregates. Based on capillary mechanics, a newly developed algorithm is applied in conventional DDA code, which treats a DDA element as an ideal soil particle and exerts capillary force among elements. Then, to validate the extended method, an ideal microscopic soil model is established, and the simulation results are in good agreement with typical analytical solutions. It indicates that the developed DDA is reliable and applicable to explore unsaturated soil behaviors microscopically.

Implementation of displacement-dependent Barton-Bandis rock joint model into discontinuous deformation analysis

Discontinuous deformation analysis (DDA) has been widely applied in analyzing various rock engineering problems. As the joint strength play a vital role in the stability of jointed rock mass, this paper makes an attempt to implement the Barton-Bandis rock joint model into the DDA code to replace the original Mohr-Coulomb joint model. The developed Barton-Bandis joint model which is characterized by displacement-dependent shear strength is verified by experimental direct shear tests. An example of a block sliding on an inclined plane is used to demonstrate the capacity of the DDA-BB model in predicting the dynamic motion behavior of sliding blocks.

Numerical Simulation in Rockfall Analysis: A Close Comparison of 2-D and 3-D DDA

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.

The vertex-to-vertex contact analysis in the two-dimensional discontinuous deformation analysis

In the two-dimensional discontinuous deformation analysis (DDA), contacts can be generalized into three types: vertex to edge, edge to edge, and vertex to vertex. In the vertex–edge contact, the contact reference edge is clearly and uniquely defined, while the contact reference edge for the vertex–vertex contact is not unique, which will lead to an indeterminate state. The indeterminacy of the vertex–vertex contact is a well-known problem in both the continuum-based methods and the discontinuum-based methods. The standard DDA employs the shortest path method to deal with the indeterminacy in the vertex–vertex contact, which is sensitive to the choice of analysis parameters, such as the time step size, the maximum displacement ratio and the contact spring stiffness. Two enhancements to the shortest path method are introduced in this paper. The first enhancement employs a temporary vertex–vertex contact spring to determine the moving tendency among two contact blocks. The second enhancement uses the trajectory of the vertex during a time step to find the entrance edge when the moving vertex invades into the target block. Examples show that these two enhancements to the standard DDA code work well.

Two-Dimensional DDA Contact Constitutive Model for Simulating Rock Fragmentation

Due to the difficulties of fracture mechanics in dealing with multicrack problems, the continuum-based numerical methods always encounter mathematical problems when modeling rock fragmentation, so the alternative discontinuum-based numerical approaches are worth trying. This paper presents a new two-dimensional contact constitutive model for the discontinuous deformation analysis (DDA) method to simulate the fragmentation of jointed rock. This contact constitutive model consists of a two-phase force-displacement relation in the nomal direction and the Mohr-Coulomb criterion in the shear direction. The two-phase force-displacement relation is imposed in the normal direction of the block interface, instead of the penalty contacting spring. The first phase functions as the original penalty spring, and the second phase serves as a cohesive component. This new contact constitutive model was incorporated into the original DDA code, and four examples were computed for verification. The simulated results agree favorably with those obtained from physical tests and other numerical simulation, showing that the proposed method can simulate the whole process of rock fragmentation and can deal with cases of intact rock, rock mass with nonpenetrative joints, and even blocky rock structures. Furthermore, due to the nature of the triangular block shape, the proposed model can avoid the mesh dependence problem. DOI: 10.1061/(ASCE)EM.1943-7889.0000319. (C) 2012 American Society of Civil Engineers.

An alternative scheme for the corner–corner contact in the two-dimensional Discontinuous Deformation Analysis

Formulated based on the discrete block system, the Discontinuous Deformation Analysis (DDA) requires an accurate contact analysis between discrete blocks. Among the various contacts, the modeling of the corner-corner contact is the most challenging one as the contact reference edges in the corner-corner contact are not unique, which may lead to an indeterminate state in the numerical analysis. The algorithm in the original DDA employs the penetration distance to determine the contact edge in the corner-corner contact, which may not work for cases where two corners are detected in contact but without a penetration. An enhanced algorithm for choosing the initial contact edge of the corner-corner contact in the DDA is presented in the paper, in which a special contact spring that works like a weak ''pin joint'' is added between the contact corners. The relative moving tendency is determined under the special contact spring, so that the program can automatically choose a reasonable contact reference edge for the corner-corner contact. Three numerical examples are used to illustrate the advantage of this alternative method over the original DDA code.

Discontinuous deformation analysis with second-order finite element meshed block

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.

Modelling burden size and strata dip effects on the surface blasting process

Abstract The objective of this paper is to introduce the development of a dynamic blasthole expansion model, which is coupled to the discontinuous deformation analysis (DDA) code of Shi (Ph.D. Thesis, University of California at Berkely, Berkely, 1988). The developed model considers the effects of blast geometry (blasthole shape, angle, and location), the physical properties of the intact rock and existing discontinuities, the distribution and orientation of pre-existing discontinuities, and the blasthole pressure on the processes of burden breakage, fragment throw and muckpile formation. The newly modified DDA code (DDA_BLAST) describes the expansion of the blast chamber as a function of blast chamber volume and time. It is assumed in the code that the rock is already fragmented in situ due to the intersection of pre-existing discontinuities and the passage of stress wave. Hence, the model only considers the gas pressurization phase of the blasting process. Moreover, the proposed model for blasthole expansion assumes an adiabatic expansion of explosion products and variations in explosion pressure upon expansion of blast chamber is calculated from an equation of state. Furthermore, a rigid-body damping algorithm, based on energy approach, was developed and implemented to the original DDA code. Accordingly, the newly modified DDA_BLAST code was employed to simulate typical blasting problems in jointed media and delve into the mechanisms involved (in a macro scale) in the gas pressurization phase of the blasting process, burden breakage, and the effects of discontinuities on the process of burden breakage.

Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method

This paper presents a numerical model for coupled hydro-mechanical processes in fractured hard rocks using the discontinuous deformation analysis (DDA) method. Detailed descriptions were given to the governing equations, basic assumptions, algorithms and their computer implementations, and verification results. The emphasis was on the physical behaviour of the coupled stress/deformation and fluid flow interaction in rock fractures . The strain-block geometry incompatibility in some DDA formulations was overcome by proper internal discretization of deformable blocks using triangle or quadrilateral elements . For the first time, explicit expressions for contributions from fluid pressure to the global stiffness matrix and load vectors of the discrete block systems were derived systematically for rigid blocks, triangle elements and quadrilateral elements, respectively, by closed-form integration. The flow algorithm used a residual flow method for locating the free surfaces in unconfined flow problems, which was then coupled to the mechanical equations of motion for the coupled hydro-mechanical analysis, also for the first time. A laboratory experiment of fluid flow in a 2-D rectangular network was simulated to verify the residual flow algorithm in the new DDA code, with an acceptable agreement between the measured and calculated results.

Modelling the effects of discontinuity orientation, continuity, and dip on the process of burden breakage in bench blasting

The objective of this paper is to introduce the development of a dynamic blasthole expansion model, which is coupled to the discontinuous deformation analysis (DDA) code of Shi (1988). The developed model considers the effects of blast geometry (blasthole shape, angle, and location), the physical properties of the intact rock and existing discontinuities, the distribution and orientation of pre-existing discontinuities, and the blasthole pressure on the processes of burden breakage, fragment throw and muckpile formation. The newly modified DDA code (DDA_BLAST) describes the expansion of the blasthole as a function of blast chamber volume and time. It is assumed in the code that the rock is already fragmented in-situ due to the intersection of pre-existing discontinuities and the passage of stress wave. Hence, the model only considers the gas pressurization phase of the blasting process. Moreover, the proposed model for the blasthole expansion assumes an adiabatic expansion of explosion products and variations in the explosion pressure upon expansion of the blast chamber are calculated from an equation of state. Accordingly, the newly modified DDA_BLAST code was used to simulate typical blasting problems in jointed media and delve into the mechanisms involved (in a macro scale) in the gas pressurization phase of the blasting process, burden breakage, and the effects of the discontinuity properties on the process of rock breakage by blasting.

Modelling of blasthole expansion and explosive gas pressurization in jointed media

The objective of this paper is to introduce the development of a dynamic blasthole expansion model, which is coupled to the discontinuous deformation analysis (DDA) code of Shi (Ph.D. Thesis, University of California at Berkely, Berkely, 1988). The developed model considers the effects of blast geometry (blasthole shape, angle, and location), the physical properties of the intact rock and existing discontinuities, the distribution and orientation of pre-existing discontinuities, and the blasthole pressure on the processes of burden breakage, fragment throw and muckpile formation. The newly modified DDA code (DDA_BLAST) describes the expansion of the blast chamber as a function of blast chamber volume and time. It is assumed in the code that the rock is already fragmented in situ due to the intersection of pre-existing discontinuities and the passage of stress wave. Hence, the model only considers the gas pressurization phase of the blasting process. Moreover, the proposed model for blasthole expansion assumes an adiabatic expansion of explosion products and variations in explosion pressure upon expansion of blast chamber is calculated from an equation of state. Furthermore, a rigid-body damping algorithm, based on energy approach, was developed and implemented to the original DDA code. Accordingly, the newly modified DDA_BLAST code was employed to simulate typical blasting problems in jointed media and delve into the mechanisms involved (in a macro scale) in the gas pressurization phase of the blasting process, burden breakage, and the effects of discontinuities on the process of burden breakage.