Discontinuous Deformation Analysis Method Research Articles

Investigations of sequential excavation and reinforcement in tunnels based on the extended three-dimensional discontinuous deformation analysis method

The unloading effect of excavation is the key factor leading to rock mass instability, and bolt support is the key means of controlling the stability. However, the original three-dimensional discontinuous deformation analysis method (3D DDA) can only simulate rock mass instability and bolt support after the tunnel is excavated, which makes it difficult to study the effect of tunnel excavation and bolt support on rock mass stability. Therefore, an algorithm to confirm the excavated blocks and reinforced blocks based on the volume judgment method (VJM) was proposed in this paper. Sequential excavation and reinforcement in tunnels can be simulated by introducing the time variables of block excavation and bolt deployment into the 3D DDA method. By embedding these two algorithms in the 3D DDA method, an extended 3D DDA method for sequential excavation and reinforcement in tunnels was developed, named the 3D DDA_ES method. Based on the 3D DDA_ES method, the collapse that occurred during the construction of the Huangjiazhuang Tunnel was simulated, and the displacement of key blocks and the axial force of the bolts were analyzed. According to the simulation results, the axial force on the bolts is strongly related to the position of the key blocks, and the axial force on the bolts at the tunnel roof is much greater than that at the tunnel arch shoulder. In this regard, these bolts with axial forces less than 1 kN are removed during the simulation, and the key blocks remain stable with a maximum displacement of 12 cm. The research results can provide a theoretical basis for tunnel construction and reinforcement parameter optimization for similar projects.

Evolution of Shear Rupture Along a Prescribed Interface Using the Discontinuous Deformation Analysis Method

Evolution of Shear Rupture Along a Prescribed Interface Using the Discontinuous Deformation Analysis Method

A hybridized DDA-DDM for modeling jointed rock masses

The complexity of geo-materials’ behaviors surpass the capabilities of conventional numerical methods alone, particularly when realistically modeling rock structures. Coupling methods can enhance the realism of numerical modeling. Discontinuous deformation analysis (DDA) and displacement discontinuity method (DDM) are combined to model block displacement and crack propagation mechanisms in a blocky rock mass. DDA calculates stresses, strains, rotations, and displacements of the blocks, while DDM predicts crack propagation paths based on specified boundary conditions. The displacements result from DDA are transformed into stresses, followed by investigating crack propagation mechanisms within each block using Kelvin's solution. Boundary stresses are adjusted as cracks propagate, updating stress boundary conditions in DDA. This iterative process continues until crack propagation halts or a new block emerges. In this paper, the complete failure process of a rock slab with one pre-existing non-persistent joint located on the crest of a rock slope and compression test on the rock-like specimen with a single random crack with a 45° slope angle is simulated using the proposed numerical approach. The proposed numerical solution is compared with existing numerical results. This comparison confirms the accuracy and effectiveness of the proposed procedure, as the predicted crack propagation paths from the coupled numerical method align well with the corresponding numerical results from the rock-like samples.

Modeling the failure process of rock masses using a 3D nodal-based continuous-discontinuous deformation analysis method

A three-dimensional nodal-based continuous-discontinuous deformation analysis method (3D-NCDDAM) is developed in this study for modeling the failure process of rock masses. In the 3D-NCDDAM, four-node tetrahedral elements which can be automatally generated are used to discretize the problem domain. To reduce computational cost, and effectively model the failure process of rock masses at concerned regions, the problem domain is devided into two types of regions, namely, the “non-destructive region” and “possible destructive region”. The non-destructive region is mainly used to reduce the boundary effects on the numerical results, and is regarded transitional zone in which the failure of rock masses is not considered. For the possible destructive region, artificial joint elements are inserted, and the failure of these joint elements is used to represent fracture initiation and propagation in rock masses. Additionally, the contact potential which is initially proposed in finite-discrete element method (FDEM) is incorporated into the 3D-NCDDAM to simuate the opening and slipping of discontinuous structural planes involved in rock masses’ failure process. Note that the difficultly in determing contact types in the traditional 3D discontinuous deformation analysis (3D-DDA) method is avoided in the 3D-NCDDAM. The proposed 3D-NCDDAM can be treated as a hybrid method, which inherite both the advantage of DDA method and FDEM. To validate the 3D-NCDDAM, seven numerical examples are conducted. The numerical results indicte that the 3D-NCDDAM can effectively model the failure process of rock masses in both experimental scale and engineering scale.

A modified discontinuous deformation analysis method considering the bonding effect for the simulation of structural loess

A modified discontinuous deformation analysis method considering the bonding effect for the simulation of structural loess

An extended 3D discontinuous deformation analysis method considering bolt supports and its application in tunnels

Implementing bolt supports is the main means of controlling block instability. However, the original three-dimensional discontinuous deformation analysis method (3D ODDA) is still unable to simulate bolt supports, making it difficult to study the control effect of bolt supports on block instabilities. Therefore, an extended three-dimensional discontinuous deformation analysis method (3D EDDA) that can simulate the effect of bolt supports is proposed in this article. Based on the 3D ODDA method, we proposed a simulation algorithm for bolt supports, which improves the constitutive model of the bolt in the original DDA method. Then, we analysed the failure process of a bolt between two blocks and compared the numerical simulation results with the theoretical analysis results to verify the accuracy of the bolt support algorithm in the 3D EDDA method. With the 3D EDDA method, we simulated the failure process of the surrounding rock in a jointed rock mass tunnel at the engineering scale under conditions with bolt supports and without bolt supports. By comparing the results of these two conditions, we deduced the evolution law of the block displacement and bolt axial force around the tunnel and determined the anisotropic characteristics of these items. Specifically, the axial force of the local bolts is relatively small and has a small control effect on the stability of the block in the area. During actual construction, the length or strength of these bolts can be reduced, which can provide a theoretical basis for the design of tunnel bolt support parameters.

Implementation of Viscoelastic Artificial Boundary and Seismic Motion Input Method in Three-Dimensional Discontinuous Deformation Analysis Method

Implementation of Viscoelastic Artificial Boundary and Seismic Motion Input Method in Three-Dimensional Discontinuous Deformation Analysis Method

Study on rock block seismic sliding using three‐dimensional discontinuous deformation analysis

AbstractThe seismic sliding of rock masses is an important phenomenon that is widely involved in earthquake geological hazards. Practical seismic sliding is a three‐dimensional problem, namely, the seismic loads may act in any direction and the rock masses may move in an arbitrary direction relative to the sliding plane. In the present work, the functions of two different seismic loading methods, that is, loading as body force time histories to the sliders or as displacement time histories to the base, are added to the program of the three‐dimensional discontinuous deformation analysis (3D‐DDA) method that is based on the contact theory to study the seismic sliding of rock blocks. The theoretical solutions of single‐block sliding on an incline under the two seismic loading methods are derived. By comparing the 3D‐DDA results of single‐block seismic sliding with the corresponding theoretical results, and comparing the 3D‐DDA results of seismic sliding of three‐stacked‐blocks under the two seismic loading methods, the correctness of 3D‐DDA for seismic sliding simulations is validated. Thereafter, the influence of three‐dimensional seismic components on single‐block sliding, and the movement of block groups under different seismic load conditions are investigated by 3D‐DDA simulations, which indicate the importance to consider rock mass seismic sliding as a three‐dimensional problem and the capability of 3D‐DDA for its analysis. This work builds a meaningful basis for the further numerical simulation study on the earthquake‐induced rock mass movements by 3D‐DDA.

Verification of 3D DDA-SPH coupling method and its application in the analysis of geological disasters

At present, discontinuous deformation analysis (DDA) is in an active development stage and its application in the field of geohazards is expanding. Recently, the DDA method has been coupled with smooth particle hydrodynamics (SPH) to analyze some geohazards involving fluid-solid interactions (FSI) and has shown good prospects in the field. However, the interaction between rocks and water in geological disasters is extremely complex and the comprehensive verifications of the simulation results between the block and fluid under different interactive modes are never found. To solve this problem, we first introduced the basic principle of the DDA and SPH method, followed by the coupling algorithm of the two methods. Then, the correctness of the coupling method was verified through analyses of fluid and solid movement by adopting the dam break test, Scott Russell's wave generator experiment, water entry test of a single sphere, and landslide-generated impulsive wave, which represent different interaction modes between blocks and fluids respectively. Finally, based on the 3D DDA-SPH method, this paper simulated the chain disasters of the water inrush induced by tunnel collapse and the dam instability induced by slope sliding, and analyzed the chain mechanism between the different disasters, which illustrates the feasibility of 3D DDA-SPH coupling method in simulating the FSI problem in geotechnical engineering.

Extension of discontinuous deformation analysis method for coupled reactive transport problems

Fluid flow and the accompanying reactant transport in fractured rock masses are key concerns for understanding the performance and safety assessments of subsurface engineering problems, particularly in waste disposal and tunneling project. Nevertheless, predicting solute transport behavior remains a great challenge due to computational sophistication and numerical instability if numerous discontinuities and chemical reaction is taken into consideration. In this study, the partial differential equation describing the reactive transport of solute is solved and coupled with the Discontinuous Deformation Analysis (DDA) method. First, the extended DDA method is validated by simulating an indoor dissolution test on the single rock fracture. Then, it is applied to establish a discrete fracture network (DFN), and be further employed to investigate the reactive transport behavior and geochemical evolution in a case of acidic mine drainage in a fractured stratum. The study analyzes the effects of stress field, reaction speed, and diffusion coefficient on the reactive transport. Numerical results indicate that the conclusions reached are consistent with current findings, combined with its prominent features in simulating the mechanical behavior of discontinuities, demonstrating that the extended method is a promising tool for the coupled hydro-mechanical-chemo analysis.

Development of a Composite Implicit Time Integration Scheme for Three-Dimensional Discontinuous Deformation Analysis

Discontinuous deformation analysis (DDA) is a discontinuum-based and implicit method for investigating the deformational behavior of block systems. The constant acceleration integration (CAI) scheme characterized by unconditional stability is employed in the traditional DDA. In this study, the problems of the CAI scheme regarding the time step in DDA are pointed out. A too large or too small time step size adopted in the CAI scheme will have adverse effects on the DDA computation. To overcome the weaknesses, an alternative composite implicit time integration (CITI) scheme, which is a combination of the trapezoidal rule and the three-point backward Euler method, is implemented in the three-dimensional (3D) DDA method. Verification examples and slope numerical simulations are presented to illustrate the accuracy and effectiveness of the proposed methodology. The results showed that the CITI scheme can overcome the numerical error caused by the large time step size, and the algorithm damping is closely related to the time step size and the selected splitting parameter.

Dynamic Process Study of Earthquake-Induced Landslides Applying an Improved Discontinuous Deformation Analysis Method Considering Site Response

Dynamic Process Study of Earthquake-Induced Landslides Applying an Improved Discontinuous Deformation Analysis Method Considering Site Response

Study on the effect of hydro‐chemical dissolution on shear properties of rock fractures using the improved discontinuous deformation analysis

AbstractHydro‐chemical erosion has critical effects on the short‐ and long‐term stability of fractured rock masses in subsurface engineering. Attempts have been made to study this water‐rock interaction process using numerical approaches. However, the majority of the existing approaches quantify the degradation based on the homogeneity hypothesis, which leads to unrealistic results in the case of rock mass with discontinuities. In this study, the hydro‐chemical degradation is represented through geometrical variation of a single crack and reflected in the modified bilinear constitutive model by introducing the hydro‐chemical damage factor. Then, discontinuous deformation analysis (DDA) method embedded in such improvements is chosen to implement the direct shearing process of the rock fracture after hydro‐chemical erosion. The results reveal that the peak shear strength decrease with the increase in the acidity solutions, and a logarithmic relation is found between the decreasing percentage of shear properties and soaking time, which are consistent with the laboratory results. Besides, based on the proposed method, the change in peak shear strength presents synchronism with the variation in the mineral ion and concentration, shown to be in good agreement with the basic understanding of the dissolution process. In addition, the failure patterns of the sheared samples under different normal stress are studied. This research provides an effective tool to quantify the hydro‐chemical damage from the microscale and will be a significant complement to the coupled numerical analysis of the water‐rock interaction process.

A Nodal-Based 3D Discontinuous Deformation Analysis Method with Contact Potential for Discrete Rock Block System

A Nodal-Based 3D Discontinuous Deformation Analysis Method with Contact Potential for Discrete Rock Block System

DDA simulation study on fracturing failure reproducibility of heterogenous rock

The mesoscale heterogeneity of rock determines its macroscale mechanical performance to a large extent. In this paper, a sub-block element discontinuous deformation analysis (DDA) method coupled with a statistic heterogeneity model was used to simulate the fracturing failure of pre-notched rock specimens. The simulation recreated the macroscale whole-process nonlinear deformation and fracturing failure of pre-notched disc and rectangular specimens with some important features explored in experiments or other numerical simulations. Combing intact heterogeneous rock specimen simulations in previous work, the effect of the heterogeneity on the reproducibility of macroscale strength and failure patterns of the specimens were investigated. Results indicate that the influence degree of the heterogeneity on the macroscale equivalent strength and fracturing failure pattern reproducibility varies with the specimen particularities (disc or rectangular, pre-notched or intact, and inclination of the pre-existing flaw), and the reason behind was discussed from the point view of stress concentration. This work is meaningful for the understanding of the result discreteness of rock specimen experiments, and assures the importance to consider the rock heterogeneity in practical rock engineering.

Improved discontinuous deformation analysis method for modeling tensile cracking in quasi-brittle materials

Tensile cracks in quasi-brittle geomaterials can degrade the stability of tunnels, pavements, and other infrastructures; however, effective modeling of the tensile fracture and subsequent collapse of such structures remains a challenging issue. The purpose of this study is to present an improved discontinuous deformation analysis (DDA) algorithm that efficiently and accurately considers the complex fracture responses of geotechnical structures composed of quasi-brittle materials. A piecewise linear cohesive contact model (PLCM) based on the fracture mechanics theory is proposed; it considers the post-peak softening behaviors of quasi-brittle materials. Then, the PLCM is integrated into the source code of the original DDA by adjusting the modeling, contact computation and open-close iteration to overcome the limitation of the original DDA in simulations of quasi-brittle fracture problems. Finally, the accuracy and validity of the improved DDA for the analysis of quasi-brittle fractures are demonstrated by comparing the predicted results with the experimental results and other results based on exact solutions or other existing numerical methods.

Numerical simulation scheme of jointed rock masses using UAV photogrammetry and a disk-based discontinuous deformation analysis model

<abstract><p>The use of unmanned aerial vehicles (UAVs) for photogrammetry allows the rapid acquisition of high-resolution images of geological masses in complex landforms. However, effective analysis of the acquired image information remains a key research issue. At K158 + 837 on the Chongqing-Huaihua Railway, Baima jointed rock masses were reconstructed with high accuracy using UAV close-range photogrammetry technology, and rock discontinuities were extracted from the projected image. The proposed modeling algorithm for jointed rock masses enables the preprocessing of two-dimensional jointed rock mass slopes. Numerical simulations using the disk-based discontinuous deformation analysis method show that the discontinuity network formed by initial cutting significantly affects the subsequent crack development. Meanwhile, simulation results under different scenarios indicate the importance of the pre-reinforcement measures applied to unstable rock masses. The workflow developed based on these results can serve as a reference for the comprehensive acquisition, recognition and numerical modeling analysis of similar jointed rock masses.</p></abstract>

An improved 3D DDA method considering the unloading effect of tunnel excavation and its application

Tunnel excavation unloading is the primary factor in disasters such as collapse and large deformations of surrounding rock. Therefore, it is a key issue to study the deformation mechanism of the surrounding rock in the process of tunnel excavation unloading. However, the original three-dimensional discontinuous deformation analysis method (3D DDA) can only simulate the displacement of the surrounding rock after the completion of tunnel excavation, which is not suitable for studying the mechanism of the surrounding rock’s deformation caused by tunnel excavation. Therefore, this paper proposes a virtual block removal algorithm that moves the blocks out of the calculation area while ensuring the consistency of the array and develops an improved 3D DDA method (3D DDA_exc) by embedding the algorithm into the original 3D DDA program, which is suitable for the simulation of tunnel excavation. In addition, based on the free fall models of static and sliding blocks, we compare the results of the 3D DDA_exc simulation with theoretical calculation results, which are basically the same. Then, both the 3D DDA_exc method and the discrete element method (DEM) are used to simulate the excavation of the tunnel in a blocky rock mass, and the rock displacements around the tunnel hole are basically the same, which further illustrates the accuracy of the 3D DDA_exc method in simulating tunnel excavation. Finally, taking the Huangjiazhuang Tunnel of the Rizhao-Lankao high-speed railway as a case study, we simulated block collapse during the excavation process of the tunnel using the centre diaphragm method (CD method). Compared with the result of the 3D DDA method without the process of tunnel excavation, block collapse can be avoided if the dangerous blocks are supported and reinforced during the excavation of part ① and part ② of the tunnel, which was of guiding significance to the safe construction of the tunnel.

Analysis method of the water inrush and collapse in jointed rock mass tunnels: A case study

Water inrush disaster occurs easily when the tunnel is close to the water rich fault fracture zone. To clarify the disaster evolution process and the critical thickness of the water-resistant rock mass is the key problem of the prevention and control of water inrush disaster in jointed rock tunnel. However, the water inrush disaster in jointed rock tunnels involves solid-fluid interaction, and the conventional single-phase numerical method is difficult to realize the real simulation of the disaster. To solve this problem, we gave full play to the advantages of the discontinuous deformation analysis method (DDA) in simulating solid motion and the smoothed particle hydrodynamics method (SPH) in simulating fluid motion, and the two-dimensional DDA-SPH (2D DDA-SPH) method was used to simulation the solid-fluid interaction in the water inrush disasters. Firstly, the 2D DDA-SPH method was used to replicate the solitary wave experiment, named Scott Russell's wave generator, and the result of the simulation was almost the same with experiment, which verified the accuracy of 2D DDA-SPH method in simulating solid-fluid interaction dynamic problems. Secondly, taking the Yonglian Tunnel as the research object, we simulated the water inrush disaster in the F2 fault of Yonglian Tunnel under the condition of different thickness of water-resistant rock mass. Based on the results of the simulation, the critical thickness of water-resistant rock mass was determined, which was about 5m. Lastly, we analyzed the process of the water inrush disasters based on the movement state of the fluid near the water-resistant rock mass. And we divided the process of the water inrush disasters in the jointed rock mass into three stage, which were mutation stage, cataclysmic stage and stable stage, which provided a theoretical basis for the prevention and control of water inrush in jointed rock tunnel.

A new SDDA-based numerical approach for simulating rock cracking induced by temperature stresses

Temperature-induced rock failure occurs in geothermal exploitation, nuclear disposal, and other underground engineering scenarios. In this paper, the conventional spherical discontinuous deformation analysis (SDDA) method is extended to simulate the temperature-induced rock failure problems. Firstly, an improved bonded sphere algorithm is proposed to precisely modeling rock failure behavior in the SDDA framework. Secondly, a heat conduction model based on the thermal conductivity pipe between spheres is proposed and further implemented in the SDDA program through an explicit thermal–mechanical coupling procedure. Thirdly, three typical examples are selected to verify the accuracy of the heat conduction model by comparing the temperature evolution between numerical and analytical results. Finally, the improved SDDA model was applied to analyze several experimental cases involving thermal cracking, including lab-scale experiments and field-scale examples. The simulation results show that the improved SDDA approach is effective for the simulation of the temperature-induced crack propagation process.