Discontinuous Deformation Analysis Research Articles

Impact failure and disaster processes associated with rockfalls based on three‐dimensional discontinuous deformation analysis

AbstractRockfalls, a common geohazard in mountainous areas, have destructive impact capacity and may cause failure of dangerous rock masses in their runout range. For slope risk assessment, a thorough understanding of the impact failure processes and dynamic characteristics associated with rockfall movements is necessary. The aim of this study is to investigate the impact of rockfall failure behaviours and disaster processes on the dangerous rock mass along the way through three‐dimensional discontinuous deformation analysis (3D DDA). To validate the reliability and applicability of 3D DDA, numerous laboratory experiments are performed on the impact of downward moving blocks on the unstable block and block system (i.e. single block–single block, single block–block system and block column–block system models) by comparing the displacements, kinetic energies and movement states of blocks. Using the G318 national road in Tibet as an example, 3D DDA simulates the impact and disaster processes associated with upper rockfalls sourced from a complete giant block and multiple discrete blocks on lower dangerous rock mass. Further, rockfall failure modes, movement characteristics, block interactions and impact phenomena are investigated. Results show that 3D DDA can effectively simulate block movement and impact interaction. The upper rockfalls impact the initially stable lower dangerous rock mass, which is the triggering factor for failure of the lower dangerous rock mass. The blocks from the upper rockfalls interact and merge to move downward, increasing the total volume and impact capacity of the rockfalls. It has been discovered that the rockfall disaster caused by the impact of an upper rockfall comprising discrete blocks on a lower dangerous rock mass is more severe than that resulting from the impact of a complete block. Overall, the results of this research can be used to help predict and prevent rockfall disasters.

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

Numerical simulation of wedge failure of rock slopes using three-dimensional discontinuous deformation analysis

Numerical simulation of wedge failure of rock slopes using three-dimensional discontinuous deformation analysis

Meta-contact analysis based on contact theory in three-dimensional discontinuous deformation analysis

Accurate contact analysis between nonspherical blocks, such as polyhedral blocks, is crucial for modeling jointed rock masses. The Contact Theory provides a rigorous foundation for contact detection. However, designing a robust and efficient algorithm that conforms to the original Contact Theory remains challenging. This study introduces the meta-contact concept for polyhedral blocks, which corresponds to the contact cover on the entrance block of the Contact Theory. Using the meta-contact concept, contact type identification, determination of contact points and plans, and contact force calculation can be formulated while retaining the advantages of Contact Theory in dealing with irregular blocks with small edges and large penetration.

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.

Directivity effect of the spatial distribution of co-seismic landslides affected by near-fault ground motions

Numerous co-seismic landslides occur in near-fault areas, and their spatial distribution seems to correlate well with the distribution of the energy and pulse of near-fault ground motions (NFGMs) in all directions. To confirm the relationship between the energy and pulse characteristics of NFGMs and the spatial distribution of co-seismic landslides, three-dimensional discontinuous deformation analysis (3D-DDA) was used to investigate the effect of NFGMs on initiating co-seismic landslides through an octagonal platform model and a generalized landslide. This model was subjected to the influence of two sets of representative three-component NFGMs. The outcomes derived from the block sliding processes revealed pronounced variations in the displacements of blocks in different spatial orientations. The greatest difference was up to 4.2 times, and the sliding blocks were more prone to large displacements in the direction with large energy and pulse. This study confirmed that the distribution characteristics of co-seismic landslides are related to the energy and pulse of NFGMs and provided evidence to illuminate the special distribution characteristics phenomenon of co-seismic landslides and theoretical support for the selection of factors for landslide hazard assessment.

An extended discontinuous deformation analysis (DDA) for simulation of grouting reinforcement in a water-rich fractured rock tunnel

Grouting has been the most effective approach to mitigate water inrush disasters in underground engineering due to its ability to plug groundwater and enhance rock strength. Nevertheless, there is a lack of potent numerical tools for assessing the grouting effectiveness in water-rich fractured strata. In this study, the hydro-mechanical coupled discontinuous deformation analysis (HM-DDA) is inaugurally extended to simulate the grouting process in a water-rich discrete fracture network (DFN), including the slurry migration, fracture dilation, water plugging in a seepage field, and joint reinforcement after coagulation. To validate the capabilities of the developed method, several numerical examples are conducted incorporating the Newtonian fluid and Bingham slurry. The simulation results closely align with the analytical solutions. Additionally, a set of compression tests is conducted on the fresh and grouted rock specimens to verify the reinforcement method and calibrate the rational properties of reinforced joints. An engineering-scale model based on a real water inrush case of the Yonglian tunnel in a water-rich fractured zone has been established. The model demonstrates the effectiveness of grouting reinforcement in mitigating water inrush disaster. The results indicate that increased grouting pressure greatly affects the regulation of water outflow from the tunnel face and the prevention of rock detachment face after excavation.

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

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

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

Numerical simulation for microstructure evolution of magnetorheological fluid based on combined disk DDA-LBM approach

In order to investigate the microstructure evolution characteristic of the magnetorheological fluid (MRF), a novel combined model coupling the disk discontinuous deformation analysis (disk DDA) model with the lattice Boltzmann method (LBM) called the disk DDA-LBM model is developed in this paper, and its acceptability is verified. After that, this new combined model is used to simulate the microstructure evolution process of the MRF. The simulation results clearly demonstrate the chain-process of the MRF, indicating that the proposed method exhibits a satisfactory accuracy in describing the microstructure evolution of the MRF. Simultaneously, a highly effective chain identification technique called Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is introduced to quantify the number of particle chains within the MRF. The results demonstrate that this method can accurately identify magnetic chains in the MRF and tracks changes of the chain number throughout the entire chain-process of the MRF.

Quantitative investigation of rock dynamic failure using Voronoi-based discontinuous deformation analysis

Dynamic failure widely exists in rock engineering, such as excavation, blasting, and rockburst. However, the quantitative measurement of the dynamic damage process using experimental methods remains a challenge. In this study, a SHPB modeling technique is established based on Voronoi-based DDA to study the damage evolution of Fangshan granite under dynamic loading. The assessment of cracking along the artificial joints among Voronoi sub-blocks is conducted using the modified contact constitutive law. A calibration procedure has been implemented to investigate the rock dynamic properties quantitatively. The dispersion and damping effect can be effectively eliminated by regular discretization in SHPB bars, based on which the dynamic stress equilibrium can be satisfied. To reproduce the loading rate effect of the dynamic compressive strength, which has been observed in the experiment, a modification strategy considering the influence of the rate effect on the strength meso-parameters is proposed. Using this strategy, the peak stresses of the transmitted waves predicted by DDA match well with those obtained from experiments conducted at different loading rates. The simulation results show that more microcracks are generated and the proportion of tensile cracks decreases as the loading rate increases. Furthermore, the dynamic mechanical behavior and fracturing process have also been discussed and compared with the experiments. The results show that the established SHPB system is a powerful tool for quantitative analysis of rock dynamics problems and can handle more complex problems in the future.

A continuous-discontinuous deformation analysis method for research on the mechanical properties of coarse granular materials

The mechanical properties of coarse granular materials play a crucial role in the safety of rockfill dams. From a mesoscopic viewpoint, the macroscopic mechanical properties of these materials are a result of the interactions between particles and the progression of particle breakage. Traditional continuum-based numerical methods struggle to accurately analyze the mechanical properties of coarse granular materials. Discontinuous deformation analysis (DDA) is a more suitable algorithm for studying these properties due to its significant benefits in block displacement mode and open-close iteration for contact handling. In this paper, a continuous-discontinuous deformation analysis method (CDDA) based on the conventional DDA is developed for the numerical investigation of coarse granular materials' mechanical properties. This method incorporates critical kinetic damping, multi-stageloading, stricter displacement convergence criteria and particle breakage simulation. It can provide a comprehensive representation of deformation, particle breakage, force chain, shear zone, and stress–strain curve evolutions. The CDDA results are found to be consistent with indoor test results and can more effectively disclose the deformation and failure mechanism of coarse granular materials. Furthermore, CDDA is employed to examine the impacts of particle size and end friction, leading to valuable insights regarding these effects.

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.

Dynamic Coupled Hydromechanical Approach for Fractured Rock Mass Seepage Using Two-Dimensional Discontinuous Deformation Analysis

Dynamic Coupled Hydromechanical Approach for Fractured Rock Mass Seepage Using Two-Dimensional Discontinuous Deformation Analysis

Dynamic modeling of block-in-matrix rock (bimrock) focusing on tensile behavior based on the modified 2D DDA-SPH method

In recent decades, numerous geotechnical hazards, including landslides, foundation settlements, and tunnel collapses, have been linked to block-in-matrix rock (bimrock), resulting in substantial damage. The examination and analysis of the engineering properties and mechanical behavior of both the rock and soil have become increasingly intriguing research areas. However, analyzing bimrock remains a formidable challenge due to its inherent heterogeneity. In this study, to investigate the tensile behavior of the bimrock, the numerical method that couples discontinuous deformation analysis (DDA) and smoothed particle hydrodynamics (SPH) is improved. First, a tension damage model is implemented in SPH for simulating the tensile behavior of the soil. The effectiveness of the presented model is verified through the direct tensile test model and the Brazil disc split model as an indirect tensile test. The contact algorithm of DDA-SPH is then modified by adding a tensile contact spring to introduce tensile strength at the interface between the matrix and the rock in the bimrock. Through a simple pulling numerical model, the accuracy of this modification has been verified, and the appropriate tensile contact stiffness is discussed. Furthermore, using the proposed method, the overall tensile strength of the bimrock with respect to the interface tensile strength is investigated. Finally, the proposed numerical method is applied to the simulation of geoengineering problems, demonstrating the capacity to analyze the stability and large deformation of bimrocks.

An implicit thermo-mechanical coupling model for heat conduction and thermal cracking in brittle materials

In this paper, an implicit thermo-mechanical coupling model is developed to simulate heat conduction and thermal cracking in brittle materials. In the thermal analysis, an implicit particle heat conduction model (PHCM) is proposed. A linear algebraic system of heat conduction equations is derived based on the temperatures of the particle system and the heat flux among adjacent particles. An analytical expression is introduced for the involved correction coefficient, with which the macroscopic thermal conductivity coefficient can be directly adopted without calibration. Furthermore, a thermal conductivity reduction coefficient is introduced to account for the thermal resistance of the cracks. In the mechanical analysis, particle discontinuous deformation analysis (PDDA), which is an implicit variant of the discrete element method, is employed. The PHCM is first verified against analytical and finite element solutions for transient heat conduction problems. The results show that the PHCM is an effective and accurate heat conduction model that readily reflects the thermal resistance of cracks. Then, the thermo-mechanical coupling model is verified by the expansion of heated specimens under different conditions. Finally, the successful application of the coupling model in the simulation of thermal shock tests demonstrates its effectiveness for thermal cracking problems.

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.