Discontinuous Deformation Analysis Method Research Articles

Modified discontinuous deformation analysis for rock failure: Crack propagation

Deformation of rock masses is not only related to rock itself, but also related to discontinuities, the latter maybe greater. Study on crack propagation at discontinuities is important to reveal the damage law of rock masses. DDARF is a discontinuous deformation analysis method for rock failure and some modified algorithms are proposed in this study. Firstly, coupled modeling methods of AutoCAD-DDARF and ANSYS-DDARF are introduced, which could improve the modeling efficiency of DDARF compared to its original program. Secondly, a convergence criterion for automatically judging the computation equilibrium is established, it could overcome subjective drawbacks of ending one calculation by time steps. Lastly but not the least, relationship between the super relaxation factor and the calculation convergence is analyzed, and reasonable value range of the super relaxation factor is obtained. Based on these above modified programs, influences on crack propagation of joint angle, joint parameters and geo-stresses

Advances in micromechanical modelling of asphalt mixtures: a review

This paper carries out a survey on available methods for micromechanical modelling on asphalt mixture. Focus is placed on models based on different concepts as well as different computational methods in numerical implementation. The major topics covered include: models based on discrete element method, micromechanical finite element models, disturbed state concept, the discontinuous deformation analysis method, integration of mechanics on different scales, etc. A brief description of some fundamental algorithms in discrete element and finite element methods are also included due to the modelling accuracy and thus wide interest in them. Simple case studies are included to illustrate the methods in discussion wherever space allows.

Modelling Coastal Cliff Recession Based on the GIM–DDD Method

The unpredictable and instantaneous collapse behaviour of coastal rocky cliffs may cause damage that extends significantly beyond the area of failure. Gravitational movements that occur during coastal cliff recession involve two major stages: the small deformation stage and the large displacement stage. In this paper, a method of simulating the entire progressive failure process of coastal rocky cliffs is developed based on the gravity increase method (GIM), the rock failure process analysis method and the discontinuous deformation analysis method, and it is referred to as the GIM–DDD method. The small deformation stage, which includes crack initiation, propagation and coalescence processes, and the large displacement stage, which includes block translation and rotation processes during the rocky cliff collapse, are modelled using the GIM–DDD method. In addition, acoustic emissions, stress field variations, crack propagation and failure mode characteristics are further analysed to provide insights that can be used to predict, prevent and minimize potential economic losses and casualties. The calculation and analytical results are consistent with previous studies, which indicate that the developed method provides an effective and reliable approach for performing rocky cliff stability evaluations and coastal cliff recession analyses and has considerable potential for improving the safety and protection of seaside cliff areas.

Simulation of Sidewall Failure in Coal Mine Roadways Using an Extended Continuous Joint Model

Coal is well developed with beddings, and the beddings play an important role in the stability of tunnel stability of coal mine. This study focused on jointed rock mass with two sets of joint and proposed an extended ubiquitous model and associated numerical implementation accounting for joint spacing to represent geometric features of coal. The failure criteria of two sets of joint proposed in this paper not only accounted for joint spacing, but also contained the ubiquitous joint model. This extended theory was validated against the discontinuous deformation analysis method, the plane of weakness theory and experimental results for jointed coal with different joint fabric. The model is also used to analyze tunnel stability of roadways in coal mine with different joint spacing. The ubiquitous joint model could simulate jointed coal with small joint spacing, but for that with larger joint spacing, the ubiquitous joint model is not applicable and the joint model containing joint spacing proposed by this paper should be used. A series of comparisons demonstrated that the proposed model was capable of considering the influence of joint spacing on jointed coal tunnel with two sets of joint.

Scaling rockburst hazard using the DDA and GSI methods

We examine the influence of rock mass quality, as scaled by the Geological Strength Index (GSI), on energy redistribution in tunnels driven through discontinuous rock masses. We assume that in blocky rock masses rockbursts develop asabrupt motion of finite rigid blocks along pre-existing discontinuities rather than by fracture of intact rock elements. We begin by formulating analytically the local energy density around a tunnel in continuous, homogenous, isotropic, linear-elastic medium and demonstrate the significance of the initial principal stress ratio on the result. We then introduce discontinuities into the rock mass and find analytically the peak acceleration of an ejected keyblock when it flies into the tunnel space, to demonstrate the viability of this mechanism asa potential rockbursting source. Using the numerical discontinuous deformation analysis (DDA) method we find the total kinetic energy released during rockbursting and validate our DDA results using monitored seismic energy emissions detected during an intensive rockburst event encountered while excavating one of the headrace tunnels at Jinping II hydroelectric project in China. Utilizing an analytical solution we published earlier for the redistribution of energy components due to tunneling, we explore the effect of rock mass quality as scaled by GSI on the elastic strain energy, dissipated energy, and kinetic energy. We find that the elastic strain energy and the energy dissipated by shear generally decrease with increasing GSI value. The kinetic energy of rockbursts however shows a more complicated behavior. It is low at low quality rock masses, peaks at GSI value of about 60, and decreases again with increasing rock mass quality. This result is supported by documented rockbursts during excavation of the deep tunnels of the Jinping II hydropower project, where the majority of rockbursts were recorded in tunnel segments with characteristic GSI values between 60 and 75.

Rock strata movement and subsidence based on MDDA, an improved discontinuous deformation analysis method in mining engineering

In this paper, a new program MDDA (mining discontinuous deformation analysis) has been developed to simulate the continuous excavation process in mining engineering based on the existing discontinuous deformation analysis (DDA). Through MDDA simulation, both the real-time stress distribution and evolution of rock strata movement during the mining process could be effectively obtained. A simple example was used to test the effectiveness of MDDA. The calculation results from MDDA well agreed with the theoretical results of the example. MDDA was applied to simulate roof falling and stress field evolution during mining process. The lateral pressure coefficient almost had no influence on rock strata subsidence in spite of some influence on roof fracture mechanics. What is more, the strata subsidence laws of MDDA simulation were approximately consistent with the Universal Distinct Element Code (UDEC) and similar simulation results.

Discontinuous deformation analysis of super section tunnel surrounding rock stability based on joint distribution simulation

Based on binocular stereo photography measurement technology, the actual distribution information of joints and fractures in the tunnel face were obtained via image processing and feature extraction, and the preliminary evaluation of surrounding rock stability of Laohushan tunnel was conducted according to surrounding rock classification method. Since all available surrounding rock classification approaches didn’t consider the influences of the size effect of tunnel excavation span and unfavorable geologic bodies such as weak-fracture zones, an improved discontinuous deformation analysis (DDARF) method was adopted to conduct a numerical simulation of the deformation and fracture processes of the surrounding rock. Using the traveling wave method, triangle DDA blocks were automatically generated in the calculation zone, and the block boundaries were divided into real joints and virtual joints. Based on the real joint information obtained via aforementioned photographic measurement, the real joints in the tunnel face were dynamically modified, in order to achieve the simulation of joint distribution. The results revealed that the fracture evolution regularity, deformation failure mechanism, and block dropping phenomenon that the DDARF joint simulation model calculated are in good agreement with actual conditions, while those obtained based on conventional models present differences from field situation. Additionally, focusing on the localised rockfall phenomenon of Laohushan tunnel, the crack extension rate was introduced to conduct a quantitative comparison of the rock crack evolution process with or without anchor supporting. The research results offer practical guidance for field construction and anchorage support scheme optimization.

The failure processes analysis of rock slope using numerical modelling techniques

Abstract The slope failure process includes crack initiation, propagation and coalescence during the formation of a slip surface (small deformation stage) and block movement, rotation and fragmentation during the sliding process (large deformation stage). Neither the finite element method (FEM) nor the discontinuous deformation analysis method (DDA) can solve such problems satisfactorily due to the complex mechanical behaviour of slope failure. To study the entire process of slope failure, we develop here a model that combines the FEM and DDA approaches. The main concept of this approach is to first apply FEM to model crack growth behaviour and then automatically switch to the DDA module to model the post-failure process when the slip surface forms. The efficiency and simplicity of this approach lies in keeping the FEM and DDA algorithms separate and solving each equation individually. The heterogeneous nature of the slope material at the mesoscopic level is considered by assuming that the mechanical properties of individual elements follow a Weibull statistical distribution. The slope models are progressively destabilized by the critical gravity approach, and both the failure onset and the slope collapse process are analysed. Our modelling reveals that shear cracks first initiate at the toe of slope and subsequently promote the propagation of tensile fractures due to the stress accumulation at the shear crack tips. Throughout the entire failure process, failure in tension occurs at a higher rate than shear failure and plays a dominant role in the formation of the slip surface. The effects of slope angle and pre-formed cracks on the post-failure process are studied using the proposed method. This study demonstrates that the modelling approach outlined herein is able to tackle the fundamental problems of rock slope failure and offers a better understanding of the slope failure mechanisms at both the macroscopic and microscopic levels.

Time-Frequency Analysis of Seismic Wave Propagation across a Rock Mass Using the Discontinuous Deformation Analysis Method

To investigate the wave (including P-wave and S-wave) propagation across a rock mass, the seismic discontinuous deformation analysis (DDA) method is used, and a time-frequency analysis of the DDA simulation results is performed in this paper. First, compared with the theoretical solution, the correctness of the DDA to simulate the seismic wave propagation across both the interlayer and interface is validated. Second, the propagation effects of the seismic wave across the jointed rock mass are studied, showing that the joint stiffness, joint spacing, and joint number have different effects on the attenuation of seismic waves. Last, to analyze seismic wave propagation across a rock mass, the engineering site of the underground cavern complex of the Dagangshan hydropower station in southwest China is used as a typical case study. A number of valuable results are obtained by time-frequency analysis; an obvious topographic amplification effect and a joint abnormal area are found. From the analysis of the time-space effect, it may be concluded that the relative displacement of the rock mass is easily encountered under earthquake, which adversely affects the stability of the engineering site. The spectrum characteristics of the seismic dynamic responses at different locations are significantly different, and a weak area of the peak acceleration may be caused by the joint attenuation effect. Based on the joint time-frequency analysis, it is suggested that adjustments for both the peak acceleration and spectrum be made before taking the ground motion record as the incident wave.

Validating the ability of the discontinuous deformation analysis method to model normal P‐wave propagation across rock fractures

SummaryThe 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.

GPU-based parallel computation for discontinuous deformation analysis (DDA) method and its application to modelling earthquake-induced landslide

Graphic Processing Unit (GPU), as a computing device, has upgraded from single-subject graphical processors to multi-core processors with tremendous computational horsepower. This paper proposes to accelerate the DDA using parallel Jacobi Preconditioned Conjugate Gradient (JPCG) technique on GPUs. Based on the results of two numerical examples, the calculation accuracies of the DDA with serial and parallel solvers are validated, and we found that the DDA with parallel solvers exhibits a much higher execution efficiency. The movement process of Daguangbao landslide triggered by the Wenchuan earthquake is replicated and the modeled deposit pattern coincides well with the actual topography after earthquake.

Improvement of contact calculation in spherical discontinuous deformation analysis

Discontinuous deformation analysis (DDA) method is a newly developed discrete element method which employs the implicit time-integration scheme to solve the governing equations and the open-close iteration (OCI) method to deal with contact problem, its computational efficiency is relatively low. However, spherical element based discontinuous deformation analysis (SDDA), which uses very simple contact type like point-to-point contact, has higher calculation speed. In the framework of SDDA, this paper presents a very simple contact calculation approach by removing the OCI scheme and by adopting the maximal displacement increment (MDI). Through some verification examples, it is proved that the proposed method is correct and effective, and a higher computational efficiency is obtained.

Shear Creep Simulation of Structural Plane of Rock Mass Based on Discontinuous Deformation Analysis

Numerical simulations of the creep characteristics of the structural plane of rock mass are very useful. However, most existing simulation methods are based on continuum mechanics and hence are unsuitable in the case of large displacements and deformations. The discontinuous deformation analysis method proposed by Genhua is a discrete one and has a significant advantage when simulating the contacting problem of blocks. In this study, we combined the viscoelastic rheological model of Burgers with the discontinuous deformation analysis (DDA) method. We also derived the recurrence formula for the creep deformation increment with the time step during numerical simulations. Based on the minimum potential energy principle, the general equilibrium equation was derived, and the shear creep deformation in the structural plane was considered. A numerical program was also developed and its effectiveness was confirmed based on the curves obtained by the creep test of the structural plane of a rock mass under different stress levels. Finally, the program was used to analyze the mechanism responsible for the creep features of the structural plane in the case of the toppling deformation of the rock slope. The results showed that the extended DDA method is an effective one.

Boundary Element based Discontinuous Deformation Analysis

SummaryA Boundary Element based Discontinuous Deformation Analysis (BE‐DDA) method is developed by implementing the improved dual reciprocity boundary element method into the open close iterations based DDA. This newly developed BE‐DDA is capable of simulating both the deformation and movement of blocks in a blocky system. Based on geometry updating, it adopts an incremental dynamic formulation taking into consideration initial stresses and dealing with external concentrated and contact forces conveniently. The boundaries of each block in the discrete blocky system are discretized with boundary elements while the domain of each block is divided into internal cells only for the integration of the domain integral of the initial stress term. The contact forces among blocks are treated as concentrated forces and the open–close iterations are applied to ensure the computational accuracy of block interactions. In the current method, an implicit time integration scheme is adopted for numerical stability. Three examples are used to show the effectiveness of the algorithm in simulating block movement, sliding, deformation and interaction of blocks. At last, block toppling and tunnel stability examples are conducted to demonstrate that the BE‐DDA is applicable for simulation of blocky systems. Copyright © 2016 John Wiley & Sons, Ltd.

Latest advances in discontinuous deformation analysis method

Latest advances in discontinuous deformation analysis method

Discontinuous deformation analysis method and its applications to disaster prevention

Discontinuous deformation analysis method and its applications to disaster prevention

Slope-Slide Simulation with Discontinuous Deformation and Displacement Analysis

Abstract The discontinuous deformation and displacement (DDD) analysis method, a combination of the realistic failure-process analysis (RFPA) and discontinuous deformation analysis (DDA) methods, offers an appropriate approach for whole rock failure-process analysis involving both the small deformation and large displacement stages. A high rock-slope slide at the Alpetto Mine in Cesana Brianza, Italy, was simulated with the DDD method, and the results are consistent with site observations and previous numerical results, which validates the DDD code for this kind of geotechnical problem. Moreover, this study verified the two main advantages of the DDD method, i.e., the critical failure surface can be obtained directly without any assumptions with the RFPA module before using the DDA module, and computing efficiency is improved significantly because the large displacement elements are the only elements that need to be calculated by the DDA module. The DDD method has proved to be an effective and efficient a...

Three-Dimensional Spherical DDA Method for Modeling Friction Problems

AbstractThree-dimensional (3D) discontinuous deformation analysis (DDA) is very suitable for simulating large-displacement behavior of rock masses. One fundamental issue commonly encountered in 3D DDA is 3D friction problems. In this paper, a friction contact model based on 3D spherical DDA (SDDA) and the determination method of friction force direction is proposed for modeling 3D friction problems. Simulation results of three verification examples with available analytical solutions demonstrate the correctness of the friction contact model in 3D SDDA. Meanwhile, the simulation result of one application example, namely, a 3D-sphere natural-accumulation simulation, indicates that the friction problems of a 3D-sphere system can be modeled well by the proposed friction contact model. This work is helpful for solving 3D friction problems in discrete blocky systems.

Method for Estimating Normal Contact Parameters in Collision Modeling Using Discontinuous Deformation Analysis

AbstractThis paper presents a contact parameter estimation method for collision modeling using discontinuous deformation analysis (DDA). Most DDA codes and discrete element method (DEM) codes use the viscoelastic contact model for contact-stress calculation. The contact parameters of the viscoelastic contact model, such as normal stiffness and damping constant, affect the computation results observably. Although the DDA method has been proposed for more than 20 years, the contact parameters in DDA modeling are still difficult to determine. In collision dynamics, the coefficient of restitution (COR) is considered the critical parameter for describing the changes of motion state after collision between two objects. In the proposed method, the normal COR is used for evaluating calculation results of rockfall modeling with three-dimensional DDA. The normal COR of the two-object model is obtained by tests or empirical methods. The relation curve of contact parameters and the normal COR is generated on the basi...

Extension of the Discontinuous Deformation Analysis Method to Simulate Seismic Response of a Large Rock Cavern Complex

AbstractThe discontinuous deformation analysis (DDA) method calculates large deformations and discontinuous problems using time-step solving and provides an effective tool for analyzing the seismic response of rock mass engineering. In this paper, extensions of the DDA method to simulate the seismic response of a large rock cavern complex are carried out. First, applicability of the existing seismic input methods, including the multiblock Newmark method, large mass method, and large stiffness method, are discussed. Second, considering the characteristics of the seismic response of a large rock cavern complex, a new seismic DDA model that includes a coupling model and a force-input method is presented. Last, the extended DDA method is used for a case study. Simulations of the quasi-static and seismic dynamic stages for the large rock cavern complex of the Dagangshan hydropower station in southwest China are carried out. Considering the stress and displacement distributions in the quasi-static stage, the mo...