Discontinuous Deformation Analysis Research Articles

Improved contact approaches for irregular polygonal or polyhedral blocks and their applications

Correct mathematical description and mechanical solution towards contact of polygonal or polyhedral blocks are fundamental issues in discontinuous deformation analysis of fractured rock masses. Encountering irregular polygonal or polyhedral shapes (such as blocks with small edges or tiny faces), traditional contact detection and solution approaches may predict incorrect or inaccurate results due to the inappropriate choice of contact parameters or algorithmic robustness problems. Aimed to solve the above disadvantages of conventional contact detection and solution approaches in treating irregular polygonal or polyhedral block shapes, we developed several improved approaches, including (1) the new cover-based contact detection approach to establish inequality constraints for irregular polygons, and (2) the improved potential-based penalty function approaches to compute contact forces for irregular blocks. These improved approaches were proposed based on the contact theory proposed by Shi and the penalty function approach proposed by Munjiza. Several new algorithms, such as the contact trace tracking algorithm, block overlap examination algorithm, intersection block construction algorithm, contact force integration algorithm, were developed. The correctness of proposed approaches was first verified by several benchmarking tests. Several specially designed cases showed that these improved approaches can correctly treat the contact scenarios involving irregular blocks while previous approaches may fail or produce inaccurate results. The proposed approaches were further applied to several application cases which involves a large number of blocks. The proposed approaches and several embedded algorithms enriched the algorithm database for discontinuum-based computational methods.

Three-Dimensional Discontinuous Deformation Analysis of Failure Mechanisms and Movement Characteristics of Slope Rockfalls

Three-Dimensional Discontinuous Deformation Analysis of Failure Mechanisms and Movement Characteristics of Slope Rockfalls

Efficient Investigation of Rock Crack Propagation and Fracture Behaviors during Impact Fragmentation in Rockfalls Using Parallel DDA

The study of the rock crack propagation and fracture behaviors during impact fragmentation is important and necessary for disaster evaluation of rockfalls. Discontinuous Deformation Analysis (DDA) incorporating virtual joints can offer a powerful tool to solve such a problem. In the analysis process, the computational efficiency is critical because the mesh must be very dense to make crack propagation more realistic. Thus, parallel DDA using OpenMP is applied. The flattened and precrack Brazilian disc tests are first reproduced, respectively, to verify the accuracy and efficiency of the parallel DDA with virtual joints. Then, the impact fragmentation process is simulated and validated with corresponding laboratory experiments in terms of crack propagation results. Furthermore, the effects of joint-slope angle, joint connectivity rate, and impact velocity on rock fracture behaviors are investigated. It is concluded that the peak number of cracks occurs when the joint-slope angle ranges between 30° and 45°; the higher impact velocity and joint connectivity rate tend to cause more cracks and larger damages to the specimen.

Stability of caisson-type breakwater subjected to strong hydrodynamic impacts using discontinuous deformation analysis method

A numerical study using the Discontinuous Deformation Analysis (DDA) method is proposed to analyze the effect of the caisson sliding subjected to a hydrodynamic loading in the stability of the rear side of the caisson-type breakwater. The study takes into account the slope inclination of the breakwater as well as the contact between the armour units constituting the shoreward of the breakwater, where the contact stresses are imposed through a penalty method. A dimensionless displacement parameter, [Formula: see text], is defined to investigate the instability of armor units. The results of the simulation show that the shape of the armour units plays an important role in the stability of the breakwater, where the tetrapods and the acropods give better stability than the cubic shapes, with a clear superiority of the tetrapods. They also show that the reduction in the slope clearly contributes to the stability of caisson up to a slope of 1: 2, but below this ratio of 1: 2 this stability is no longer obvious. Furthermore, a new relation of the displacement of the armour units according to the slope is established.

Techniques for Progressive Failure Simulation of Hard Brittle Surrounding Rockmass: Taking the URL Test Tunnel as an Example

Accurate simulation of the failure process of hard brittle surrounding rockmass is very important for the analysis and control of the structural stability in deep underground engineering. In order to simulate the progressive failure process of the hard brittle surrounding rockmass, a continuous discontinuous deformation analysis method that couples the finite element and discrete element is adopted. Taking the URL test tunnel in Canada as an engineering case, the constitutive model of the contact considering the effects of cohesion weakening and friction strengthening is applied, and the 2D approximation to 3D excavation by applying elastic modulus reduction technology is adopted to simulate the range and depth of crack growth of the surrounding rockmass. Then, the comparison between simulated results and on-site monitoring results is performed, which shows good consistency. At the same time, the key factors in the numerical simulation of progressive failure in hard brittle rockmass are identified, including the number of elements, excavation effects, and constitutive models. The results show that the constitutive model determines the basic form of crack propagation, but in order to accurately simulate the progressive propagation of cracks, the number of elements must be sufficient enough and the effects of 3D excavation must be considered. The analysis accurately simulates the progressive failure characteristics of hard brittle surrounding rockmass under high stress, achieving the purpose of reasonably grasping the degree of damage to the surrounding rockmass, and provides technical reference and support on how to accurately simulate the failure of hard brittle surrounding rockmass using the finite discrete element method.

Discontinuous deformation analysis with distributed bond for the modelling of rock deformation and failure

Fracture and fragmentation of rock under various loadings or in multi-field conditions are important topics in many rock engineering scenarios. Numerical tools are commonly applied to evaluate the rock deformation and progressive failure process, while the accuracy and efficiency of the analysis are closely related to the applied fracture models. In this paper, an improved discontinuous deformation analysis (DDA) program with the distributed bond (DB) is proposed for rock deformation and rock fragmentation analysis. The jointed rock model is regarded as an assembly of triangular elements connected with DBs and contacts. The DB uses distributed constraints to bond the co-edge elements for continuous deformation modeling, and the fracturing and fragmentation of rock material is fulfilled by progressive DB failure with linear and nonlinear bond constitutive models. The theory, formulation, and implementation of DB in DDA framework are given in detail. The feasibility and accuracy of the proposed DB in simulating rock deformation and failure process are verified by several examples.

Three-dimensional discontinuous deformation analysis with explicit contact formulation and block-wise multicore CPU acceleration

In this study, an explicit three-dimensional discontinuous deformation analysis (3D-DDA) is parallelized. Using explicit contact force circumvents the open-close iteration and makes the global stiffness matrix block-diagonal. Post-judgment of contacts is split into two parts to unify the data access pattern, constant acceleration Newmark method is adopted to guarantee unconditional stability of time integration, and square-root-free Cholesky decomposition is adopted to solve small linear equations efficiently. To exploit the multicore CPU with few changes in code and achieve good modularity, block-wise parallelization is adopted, which can realize the full-stage parallelization with just several lines of OpenMP directives. There is no need to modify block specific algorithms, such as contact detection and block information update, for the proposed parallelization, which results in the most efficient parallelization scheme to date. Correctness and efficiency are validated using several numerical examples. The speed-up ratio of 5.0–6.5 is achieved on an 8-core CPU.

Micro-scale analysis on shear characteristics of unsaturated soil by considering capillary suction and adsorption suction based on DDA

In this research, Discontinuous Deformation Analysis (DDA) is extended to analyze shear characteristics of unsaturated soil by separately considering capillary suction and adsorption suction at micro-scale. First, the developed matric suction model is validated by comparing simulation results with the analytical solution. Then, the shear characteristics of unsaturated cohesionless soil are simulated and compared with experimental results. The “peak effect” of the shear strength is reproduced, and it is quantitively explained by the proposed micro parameter CSN (number of the capillary bridge). Further, in the high suction range of cohesive soil, adsorption suction is the dominant factor for apparent cohesion. As the contact area of the clay layer decreases slightly in the high suction range, adsorption suction controls shear strength, therefore, there is seldom a “peak effect” of the shear strength for cohesive soil. The extended DDA provides an innovative approach to analyze the micro mechanism of matric suction in a wide suction range.

A bound water model for numerical simulation of SWCC in the wide suction range based on DDA

In this study, Discontinuous Deformation Analysis (DDA) method is extended to simulate Soil-Water Characteristic Curve (SWCC) by considering both capillary water and bound water at the micro-scale. First, a simple and practical bound water model is proposed and incorporated into DDA program to simulate SWCC in the high suction range. Then, to prove the availability of the developed program, the extended DDA is used to simulate the SWCCs of two types of fine sand with kaolin clay in a wide suction range. The simulation results agree with the experimental results, which demonstrate that the extended DDA is an alternative method for simulating and analyzing SWCC of both cohesionless soil and cohesive soil. Finally, one of the influential factors specific surface area is theoretically analyzed. This study provides an approach to simulate the matric suction of unsaturated soil, and the extended DDA could be a potential tool for unsaturated soil research.

Parallelization of spherical discontinuous deformation analysis (SDDA) for geotechnical problems based on cloud computing environment

Parallelization of spherical discontinuous deformation analysis (SDDA) for geotechnical problems based on cloud computing environment

MICROSCOPIC DISCONTINUITY DEFORMATION ANALYSIS OF CAPILLARY IN UNSATURATED SOIL

Capillary action is one of significant sources of matric suction in the unsaturated soil. So we propose a new method based on two-dimensional Discontinuous Deformation Analysis(DDA)to simulate the distribution of capillary water and to calculate soil water characteristic curve(SWCC)under different saturation. Firstly,the radius of capillary water meniscus is calculated with iterative algorithm method,and circle center trajectory intersection method is used to determine capillary water distribution in this algorithm. Then,the matric suction,calculated with Young-Laplace equation,is taken into account in the control equation of the original DDA method with the surface tension. Moreover,in order to verify the accuracy of the algorithm,an ideal loess structure model is established. In this model,the soil particles used are mainly coarse particles with high content of loess. The particle size distribution and shape accord with the actual values. And then,the model is used to simulate the distribution of capillary water and to calculate soil water characteristic curve(SWCC). The results show that simulated SWCC contains boundary effect stage,transition stage and residual stage. The distribution of capillary water is simulated at each stage. In addition,the result comparison between the numerical simulation and the experimental data shows the simulation results agree well with experimental data,which suggest that this method is available for simulating capillary action in unsaturated soil.

Improvement of Discontinuous Deformation Analysis Incorporating Implicit Updating Scheme of Friction and Joint Strength Degradation

Improvement of Discontinuous Deformation Analysis Incorporating Implicit Updating Scheme of Friction and Joint Strength Degradation

Improvement of vertex-to-vertex contact processing in two-dimensional DDA

This paper proposes a new critical concept for contact processing in the original two-dimensional discontinuous deformation analysis (DDA). A new critical concept that is inside or outside the reference line is proposed to enhance contact processing in the original DDA. When the vertex P is inside of one reference line, the reference line is shifted to the other edge so that P is now outside. The original rules are applicable only when both vertices are outside or inside of both the possible edges. The new critical concept is a stricter algorithm that remedies the indeterminacy of detecting the candidate reference line for vertex-to-vertex contact in the original DDA. The accuracy and effectiveness of the contact-improved DDA were studied using various numerical examples. The simulation results showed that the proposed method is more accurate and useful compared to original method after contact improvement and can be better applied to models with arbitrary vertex-to-vertex contact states.

Analysis of Rainfall-induced Landslide Using the Extended DDA by Incorporating Matric Suction

Rainfall-induced landslide is a common natural hazard, and one of the disaster-causing factors is the loss of apparent cohesion that is mainly caused by the dissipation of matric suction. To analyze the rainfall-induced landslide, especially the post-failure behaviors, a matric suction model is proposed and incorporated into the Discontinuous Deformation Analysis (DDA). In this model, the matric suction is simplified as an equivalent line load and updated at each time step. The safety factor of the simple sliding model simulated by the extended DDA (DDA_c) showed a good agreement with the limit equilibrium method. The simulated relationship between runout distance and the degree of saturation of the multi-block sliding model was validated by the experimental results. Finally, a rainfall-induced landslide in Fukuchi-machi was simulated using the extended DDA. The results illustrated that the apparent cohesion loss is an important mechanism for landslide initiation and a crucial reason for the long-runout distance. The presented DDA_c can be served as a qualified tool to analyze shallow slope stability and post-failure behavior involving apparent cohesion.

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.

Stability and Failure Analysis of Zhaoshuling Landslide under the Reservoir Water and Earthquake

Due to the reservoir impoundment, the geological environment in Three Gorges Reservoir area deteriorates, consequently inducing a series of geological hazards. Zhaoshuling landslide is one of the most important landslides in Three Gorges Reservoir area, and its safety seriously affects the planning and construction of the new-established Badong city. The unfavourable change of hydraulic condition, accompanied with earthquake, may cause landslide instability. In this paper, the stability and failure features of Zhaoshuling landslide under the reservoir water and earthquake are researched by discontinuous deformation analysis (DDA) method. The simulated results show that Zhaoshuling landslide is globally stable under the reservoir water and VII earthquake, while considering the degradation effect of rainfall and reservoir water on the strength of the sliding zone, the landslide may be damaged. The landslide damages more seriously at a low water level, the failure mode is creep and traction, and the failure mainly happens at the head and middle of landslide. Therefore, the head and middle of landslide is the key section of prevention and treatment.

Study on the Dynamic Response of Landslide Subjected to Earthquake by the Improved DDA Method

Majiagou landslide, a major ancient landslide in Three Gorges Reservoir region, is located in the high earthquake area of southwest China. The 2013 Badong earthquake caused an obvious deformation of landslide monitored by the sliding inclinometer. A strong earthquake may induce the reactivation of ancient landslide. So, it is necessary to research the seismic dynamic response of Majiagou landslide. For this purpose, discontinuous deformation analysis (DDA), improved by introducing the artificial joint and viscous boundary, is applied in this study. The displacements at monitoring points caused by Badong earthquake are calculated and compared with the field data, verifying the numerical method and model. Further, a strong earthquake with the peak acceleration of 1 g is assumed to act on the landside, the initiation and evolution process of landslide is simulated, and the movement features of landslide are discussed. The dynamic failure of landslide and the local amplification of seismic wave can be embodied, indicating that the improved DDA provides an alternative approach for analyzing the seismic dynamic response of jointed rock.

Vertex Displacement-Based Discontinuous Deformation Analysis Using Virtual Element Method.

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.

Verification and application of 2-D DDA-SPH method in solving fluid–structure interaction problems

The study of fluid–structure interaction (FSI) is a challengeable topic, which concerns a coupled system with consideration of not only the behaviors of the fluid and the structure, but also the interaction process between both. In this paper a coupled method is introduced to simulate FSI problems in two-dimensional (2-D) case. In this coupled method (2-D DDA-SPH), the smoothed particle hydrodynamics (SPH) based on kernel approximation and particle approximation is employed to represent the fluid domain governed by Navier–Stokes equations and the discontinuous deformation analysis (DDA) based on the minimum total potential energy principle is used to model the real solid structure (with rigidity or elasticity) through virtual joints. A coupling scheme bridging both methods is used based on a penalty-force method, and an improved contact detection between particle and block is proposed. Several challenging examples, including breaking dam flow through an elastic plate, breaking dam flow on a rigid barrier or an elastic barrier are investigated to demonstrate the capability of the 2-D DDA-SPH method to capture the entire FSI process. Finally, two application examples, failure of gravity dam induced by water pressure, and dynamic response of armor blocks on breakwater under incident wave, are studied by using 2-D DDA-SPH. The simulation results show satisfactory agreements with available experimental, numerical, and analytical results, suggesting the applicability of the 2-D DDA-SPH method to solve FSI problems.

Experimental Verifications and Applications of 3D-DDA in Movement Characteristics and Disaster Processes of Rockfalls

Rockfalls are a major hazard in mountain areas and along engineering slopes. It is important to fully understand the characteristics and processes of rockfall movements, both for hazard assessment and countermeasure design. This study focused on the movement characteristics and disaster processes of rockfalls by three-dimensional discontinuous deformation analysis (3D-DDA), the effectiveness of which was verified by outdoor experiments. An apparatus specifically built for the experiments was established, which included a releasing device and a binocular camera stereovision system. Blocks of three different shapes and sizes were released on slopes with three different inclinations on the campus of Tibet University. The indices of the movement characteristics of the blocks, such as lateral deviation, resting position, jumping height, and kinetic energy evolution, were investigated. The experimental results were compared with those of the 3D-DDA, so as to study the rockfall movement characteristics. On this basis, the 3D-DDA was applied to simulate a large-scale slope rockfall on the Tibetan Plateau, and the rockfall failure processes and movement characteristics were further analyzed. The results showed that the 3D-DDA method could effectively simulate the entire rockfall process in time and space, including instability and movement. Through the 3D-DDA numerical simulations, rockfall phenomena and behaviors could be fully understood. Furthermore, by analyzing the trajectories and kinetic energies of a rockfall, the prediction of rockfall disasters and the reasonable design of protective countermeasures could be realized.