Continuum-based Discrete Element Method Research Articles

Progressive Failure of Surrounding Rock in Underground Engineering and Size Effect of Numerical Simulation

The analysis and simulation of progressive failure of surrounding rock is very important for analyzing the stability of surrounding rock in underground engineering. Size effect is also a key problem worth further study in engineering. Taking the underground powerhouse on the right bank of Baihetan as an example, the acoustic test results are collected and the relaxation and failure characteristics of the surrounding rock are summarized. Then, the numerical simulation of progressive failure of surrounding rock of underground powerhouse is carried out by using the finite discrete element method CDEM (continuum-based discrete element method). The results are compared with the acoustic test results of the surrounding rock relaxation layer, and the stress and displacement of surrounding rock characteristic points are analyzed. At the same time, the size effect of grid and mechanical parameter in the process of numerical simulation are discussed. The calculated fracture depth of surrounding rock is in good agreement with the acoustic test results, which shows the reliability of progressive failure simulation of surrounding rock of the underground powerhouse. When CDEM is used to simulate the excavation of tunnels with different tunnel diameters, the minimum grid size should be about 1% of the tunnel diameter. The mechanical parameters of rock mass have significant size effect, which needs to be analyzed in detail. The research results prove the superiority of the CDEM method in simulating the progressive failure of hard surrounding rock and its unique size effect characteristics, which can provide technical reference for the application of the CDEM method in other similar engineering problems.

Influence of reservoirs/interlayers thickness on hydraulic fracture propagation laws in low-permeability layered rocks

In this study, the hydraulic fracture propagation mechanism in low-permeability layered rocks was investigated using the true triaxial hydraulic fracturing test system and the Continuum-based Discrete Element Method. Firstly, the mechanical properties of natural cores in reservoirs and interlayers were determined using uniaxial and triaxial testing machines. Secondly, the Kaiser stress effect method was employed to calculate the in-situ stress. To characterize the thickness distribution characteristics of reservoirs/interlayers in layered rocks, the concept of reservoir thickness ratio kδ was proposed. The influence law of kδ on the fracture pressure Pf of layered rocks was explored. The fracture elongation r was proposed to describe the extension state of fractures in reservoirs and interlayers, and the effect of kδ on fracture elongation r were analyzed. The spatial morphology and geometrical characteristics of fractures were characterized based on the 3D fractal dimension and fracture opening. The 3D damage variable DV was defined to reveal the damage evolution law of layered rocks during fracture propagation. The research results reveal the fracture propagation mechanism in hydraulic fracturing of layered rocks and provide theoretical guidance for the effective implementation of hydraulic fracturing technology. This study is important for the efficient reconstruction of low-permeability reservoirs with layered media and improving oil and gas recovery.

Study on Progressive Failure of Hard Rock Tunnel After Excavation Under High Stress

The analysis and simulation of brittle failure of hard rock tunnels under high stress is essential for understanding and mastering the brittle failure characteristics of rock masses and for analyzing and regulating the stability of surrounding rocks in underground projects. The rupture and deformation of hard brittle basalt in the dam site area is one of the key problems faced by Baihetan Hydropower Station. In the paper, the spalling characteristics of the surrounding rock on the right bank of the exploratory tunnel are summarized. CDEM (continuum-based discrete element method) is used to carry out the numerical simulation and the fracture energy model considering cohesive force weakening and friction angle strengthening is adopted. The indoor test simulations are conducted first to verify the effectiveness of the model. Then the simulation of the right bank exploratory tunnel is conducted to study the brittle failure of the surrounding rock. The results are compared with the field exposure, and the stress and displacement of characteristic points of the surrounding rock are analyzed. The numerical results are in good agreement with the damage situation in the field and reflect the brittle failure characteristics of basalt under high-stress conditions, which helps to reasonably grasp the damage situation of the surrounding rock and take corresponding support measures, and also proves the superiority of CDEM method in solving hard rock fracture, providing a technical reference for similar hard rock brittle failure problems in engineering.

Stability evaluation method for assessing bedrock and overburden layer slope (BOLS) under seismic load

Seismic load is a type of dynamic load that can easily induce the failure of the foundation slope. Using the continuum-based discrete element method in continuum mechanics, herein, the rupture degree and permanent displacement are defined and their evaluation steps are proposed. The sensitivity of rupture degree and the permanent displacement of overburden under seismic force are also analyzed. A new stability evaluation method for an overburden layer under seismic load, which considers rupture degree and permanent displacement, is established. The results showed that the overburden layer and the interface between bedrock and overburden are damaged to a certain extent under the action of a small-intensity earthquake (a peak = 0.03–0.06 g), although the overburden surface is not damaged. With the increase of seismic frequency and slope height, the permanent displacement of overburden decreases, although it increases with the increase of peak acceleration and slope angle. Furthermore, duration has little to no influence on the permanent displacement of the overburden under the condition of a small or moderate earthquake. In the case of a large earthquake, the permanent displacement of overburden increases linearly with the increase in duration.

Numerical analysis of deep hole multi-stage cut blasting of vertical shaft using a continuum-based discrete element method

Due to the high in situ stress of the deep rock mass and the restraining effect of the surrounding rock, the deep hole blasting of vertical shaft faces the problems of low borehole utilization rate and poor blasting effect. In this regard, this paper proposes a deep hole multi-stage cut blasting technology of vertical shaft. Preliminary engineering practice shows that such cut blasting technology can make better use of explosive energy, reduce the restraining effect of surrounding rock, and increase the borehole utilization rate. Furthermore, based on the continuum-based discrete element method (CDEM), the fractal damage, fragmentation, and blasting cavity characteristics of deep hole multi-stage cut blasting of vertical shaft are studied and analyzed. The results show that in the multi-stage cut blasting of vertical shaft, if the length proportion of the first stage is too small or too large, it will lead to poor cavity formation along the cut direction. Characteristic parameters such as fractal damage of blasting cavity, fracture degree of element, and fracture degree of interface show a trend of first increasing and then decreasing as the length proportion of the first stage increases, and the length proportion of the first stage has an optimal value. Under the conditions of rock parameters, explosive performance and linear charge density set by the numerical simulation in this paper, when the length proportion of the first stage accounts for 0.42, the multi-stage cut blasting of vertical shaft can make better use of explosive energy and achieve the best blasting effect.

Effects of bedding planes on the fracture characteristics of coal under dynamic loading

To investigate the influence of bedding planes on its fracture characteristics under dynamic loading, testing and numerical simulations are carried out on semi-circular bend specimens of coal. It is shown that the fracture load and dynamic initiation fracture toughness decrease as the increase of bedding-plane angle. The crack propagation direction is jointly controlled by the maximum principal stress and bedding planes. Based on the digital speckle correlation method, it is found out that, due to stress concentration, strain at the initial loading stage concentrates around crack tip. After crack initiation, there is a specific strain gradient with a candle flame-like shape on the surface of a specimen. The opening displacements at crack tip can be divided into stable and linearly increasing phases. Further, a continuum-based discrete element method is applied to virtually reproduce these fracture characteristics, which are instructive to study dynamic anisotropy in fracture of coal.

Numerical investigation of the effect of holes on dynamic fracturing in multi‐flawed granite

AbstractA numerical study is conducted using the improved continuum‐based discrete element method (CDEM) to investigate the effect of holes on the dynamic fracturing of multi‐flawed rocks. The specimen geometries contain a perpendicular crack‐like flaw, a hole‐like flaw, and an inclined crack‐like flaw. A fracture model is implemented into the improved CDEM that combines the nonlinear pressure‐dependent shear strength and tensile strength of rocks. The digital image correlation method combined with ultra‐high‐speed photography is applied in a split Hopkinson pressure bar system to verify the accuracy of the proposed model. The experimental results show that the improved CDEM accurately reproduces dynamic crack behavior in rocks. The simulation results show that hole‐like flaws significantly affect crack behavior compared with the two investigated crack‐like flaws. However, this effect gradually weakens with increasing loading stresses. This study provides important insight into the dynamic fracturing of multi‐flawed rocks.

Fragmented chip formation mechanism in high-speed cutting from the perspective of stress wave effect

In this study, fragmented chip formation mechanism in high speed cutting (HSC) process is explored by using continuum-based discrete element method (DEM) based on the stress wave theory. The continuum-based DEM model established with Godunov frame is suitable for capturing multiple cracks propagation under high-speed impact. The chip forming mechanism based on stress wave theory is quantitatively analysed by DEM simulations against experimental data, which shows that the unloading wave reflected by the free surface of chips under high-speed conditions has a fundamental influence on chip formation.

Experimental observation and numerical investigation on propagation and coalescence process of multiple flaws in rock-like materials subjected to hydraulic pressure and far-field stress

In this paper, a newly developed rock-like material (cement mortar) was proposed. Multiple flaws (including horizontal and inclined flaws) were prefabricated in the testing specimens, and a number of specimens subjected to hydraulic pressure and far-field stress were performed to study the crack propagation and coalescence process. Experimental results show as following. (1) Under uniaxial compressive condition, the propagation path and direction of preexisting flaws change obviously after the inclined flaws meet the horizontal flaws during the propagation process, and the phenomenon of ‘displacement jumping’ appears. (2) Under biaxial compressive condition, the increase of lateral pressure suppresses the initiation of cracks and secondary cracks at the ends of the inclined flaws. Under the condition of high lateral pressure, these inclined flaws would not propagate through the horizontal flaws and the failure mode changes from splitting to shear failure. The shielding effect of horizontal flaws on stress transfer is gradually increased. (3) Under the combined action of internal water pressure and far-field stress, with the increase of internal water pressure, the maximum principal stress distribution at the tip of wing crack in uniaxial compression gradually decreases, and the initiation stress, initiation angle and peak strength are also gradually reduced. The crack propagation and coalescence laws obtained by numerical simulation based on Continuum-based Discrete Element Method (CDEM) are basically in good agreement with the experimental results. The numerical analysis of the inclined flaws with different internal water pressures penetrating through the horizontal flaws without water pressure is also carried out. With the increase of internal water pressure, the inclined flaws firstly initiates the coplanar crack and then generates the wing crack. When the wing crack propagates though the horizontal flaw, the propagation path also changes. Under the combined action of internal water pressure and far-field stress, the lateral pressure also suppresses the initiation of the wing crack. The increase of internal water pressure weakens the restraint effect of lateral pressure on wing cracks.

Analysis of Criteria for Assessing Safety Distance for Focused Warhead Fragments Based on CDEM

This study uses the continuum-based discrete element method (CDEM) to build a new model for warhead safety distance, simulating the fragment fields over space and time for tungsten alloy and steel fragment focused warheads to derive respective safety distances for personnel. Regarding the effects of different warhead attitudes and fragment effectiveness definitions, it is found that, for single-shot focused warheads, the fragmentation risk is significantly higher for horizontal placement than for vertical placement; the fragment safety distance inneed increases nonlinearly as the threshold energy decreases. Meanwhile, the safety distance is less affected by the threshold energy for high-density-casing charges than for low density.

Numerical analysis of the dynamic evolution of mining-induced stresses and fractures in multilayered rock strata using continuum-based discrete element methods

In this study, the continuum-based discrete element method (CDEM) was adopted to simulate the evolution of mining-induced stress and fracturing during roadway tunnelling and mining in multilayered heterogeneous rock strata. The CDEM integrates the finite element method (FEM) and the discrete element method (DEM) to characterize the mining-induced stress evolution, the discontinuous fractures, separations, and caving that occur in the interfaces between multilayered rock strata. The maximum tensile-stress criterion and the Mohr–Coulomb strength criterion were used to evaluate the tensile and shear failure of the material elements. The CDEM model for rock strata was constructed by employing image processing and reconstruction approaches, using the geometrical and physical parameters that were measured from a real coal mining site. The stress evolution and compression deformation of the roof and floor strata were computed to evaluate the criticality of mining-induced disasters. The constructed model was employed to simulate and analyse the immediate roof collapse, immediate floor bulges, and the compaction of the collapse blocks, as well as the large deformation, separation, and collapse between the immediate roof and the main roof during coal seam mining. It was shown that the proposed method could predict ranges for the caving zone and fracture zone in the rock roofs that were in good agreement with the observation results from the real coal mining site.

Numerical analysis of the hydrofracturing behaviours and mechanisms of heterogeneous reservoir rock using the continuum-based discrete element method considering pre-existing fractures

The continuum-based discrete element method was applied to probe 3D hydrofracturing behaviours. The interaction between hydrofracturing cracks and pre-existing fractures was modelled. Glutenite, a typical heterogeneous rock, was numerically reconstructed using physical parameter tests, computed tomography and imaging processing methods. The effect of pre-existing fractures on hydrofracture propagation was characterized, and the effects of material heterogeneity and horizontal in situ stress differences on fracturing were characterised using fractal theory. Investigation of hydraulic fracture (HF) propagation in heterogeneous rock, and of the mechanism by which complex hydrofracturing crack networks form through numerical simulation, revealed four typical influencing factors. These four, namely mineral particles, in situ stress difference, natural fracture (NF) density, and NF aperture inside the glutenite, were analysed to determine their effect on the HF propagation pattern, and the mechanism of complex fracture network formation in glutenite was determined. A 3D fractal dimension was proposed to characterize the spatial distribution of complex fracture networks. With increasing aperture and density of NFs, the hydrofracturing crack network becomes more complex. Mineral particles hinder the propagation of HFs; analogously, the higher the volume percentage of mineral particles is; the more complex is the hydrofracturing crack network that forms. The HFs generate and propagate near the bilateral tips of the NFs. The HFs will propagate along the direction of maximum horizontal in situ stress, and they are prone to turn into a single crack with greater in situ stress difference. The 3D fractal dimensions were computed and quantitatively reflected the above phenomena.

Numerical Analysis of Hydrofracturing Behaviors and Mechanisms of Heterogeneous Reservoir Glutenite, Using the Continuum‐Based Discrete Element Method While Considering Hydromechanical Coupling and Leak‐Off Effects

AbstractHydrofracturing technology has been widely used to stimulate the tight hydrocarbon reservoirs that usually comprise heterogeneous glutenites. Hydromechanical coupling and leak‐off are essential characteristics of this process and need to be properly addressed in numerical simulation, which plays an important role in quantitatively evaluating the efficiency of this technology. Due to the challenges in accurately representing the complex structure and physical properties of heterogeneous glutenites as well as hydraulic‐driven crack propagation, however, the hydromechanical coupling, leak‐off, and material heterogeneity have not yet been handled satisfactorily. To overcome these challenges, we use the continuum‐based discrete element method (CDEM) to simulate the hydraulic fracturing of heterogeneous glutenites, considering hydromechanical coupling and leak‐off effects. The CDEM models are constructed using the geometrical and physical parameters that were extracted from natural heterogeneous glutenites using computed tomography, X‐ray diffraction, and triaxial tests, based on image processing and reconstruction approaches. The CDEM models are composed of hydraulic fractures and microscale pores, and Darcy's law was integrated within the model to govern fluid leak‐off; this is a nontraditional approach to leak‐off effects. The coupled finite element‐discrete element‐finite volume approach is used to determine the fracturing behaviors of heterogeneous models. The fracturing crack propagation and distribution patterns of homogeneous and heterogeneous models under various horizontal in situ stress differences are characterized by fractal theory, and the models are compared to assess the influences of material heterogeneity and in situ stresses on the hydraulic fracturing of heterogeneous glutenites.

Numerical modelling of the contact condition of a Brazilian disk test and its influence on the tensile strength of rock

The stress distribution and failure process in the Brazilian test disk are numerically studied using the continuum-based discrete element method. The stress distribution in the immediate contact vicinity between disk and jaws with two types of contact conditions are compared, and the position of failure initiation is determined based on the generalised Griffith criteria. Moreover, the whole process of the Brazilian test is modelled for disks with various material properties under two contact conditions and the modelled Brazilian tensile strengths of the disks are obtained. Numerical simulations show that the distribution of stress components in the vicinity of the contact have remarkable differences between the two contact conditions, and the difference increase with the increasing of loading level and disk's elastic modulus. However, the stress distributions exhibit almost no difference on the disk's centre area. The disk's elastic modulus and the ratio of compressive strength to tensile strength are the main factors that influence the distribution of stresses in the vicinity of the contact, thereby affecting the failure initiation and tensile strength, especially under no-cushion contact conditions. The thin plastic cushion can alleviate the stress concentration in the vicinity of the contact between the disk and jaws, and cracks initiating from the vicinity of the contact can be avoided for almost all of the rock-like materials. However, the enlarging contact ranges will result in a larger deviation between the test results and the real tensile strength. An improved Brazilian test method considering two contact conditions of with and without cushions for rock and rock-like material is proposed.

A case study integrating numerical simulation and GB-InSAR monitoring to analyze flexural toppling of an anti-dip slope in Fushun open pit

Toppling failure of rock slopes is a complicated mode due to a combination of both continuous and discontinuous deformation, especially in dealing with anti-dip rock slopes. In this paper, a novel continuum-based discrete element method (CDEM), which is useful in modeling the entire progressive process from continuous to discontinuous deformation, is proposed to analyze the deformation characteristics, the failure mechanism and the evolution process of a large-scale open pit slope with a typical anti-dip structure. To simulate the slope deformation, the shear strength reduction method (SSR) is adopted to represent the strength degradation of rock mass in the deterioration process. The simulated results are validated using data obtained from a field investigation and continuous monitoring by employing an advanced remote sensing technique called ground-based interferometric synthetic aperture radar (GB-InSAR). To analyze the evolution trend of the anti-dip slope, the subsequent toppling failure mode is predicted using the validated CDEM models. Based on a case study of a slope at the Fushun open pit mine (in Fushun, China), the unique geological structure with various joints and discontinuities, groundwater, intense rainfall, and mining activities are identified as the main triggers for different failure stages. The comparison between the field data and the simulation shows that CDEM accurately depicts the rock deformation and the failure pattern of the studied slope. The proposed numerical modeling techniques can be used for predicting failures of other similar excavated rock slopes. The simulated evolution process and the recorded deformation patterns help engineers to gain a better understanding of rock mass movement of anti-dip slopes, and the presented methodology could be utilized for similar studies and engineering designs.

Comparisons between centrifuge and numerical modeling results for slope toppling failure

This paper presents series studies on the toppling mechanism by centrifuge tests and numerical simulations. Two different discrete element methods, i.e., the continuum-based discrete element method (CDEM) and the discontinuous deformation analysis (DDA), are adopted. The modeling results show that both the methods can accurately capture the failure modes of the centrifuge tests, including three distinct zones and two failure surfaces. Comparisons are made between the physical test and numerical simulation results. The critical inclination angle of the tilting table where the slope models are fixed on can be moderately predicted by the two methods, with different degrees of precision. The error between the test results and the simulated results is within 1% for the slope models without rock-bridges by both CDEM and DDA. However, it is amplified for the staggered-joint models that simulate the rock-bridges. With DDA, the average error is about 5%, and the maximum error is up to 17%. While with CDEM, the errors for the aligned-joint models are ranged from 1% to 6%, and it is from 10% to 29% for the staggered- joint models. The two numerical methods show the capability in simulating toppling failure of blocky rock mass with and without rock-bridges. The model with rock-bridges which provides a certain bending resistance is more stable than the one without any rock-bridge. In addition, the two failure surfaces were observed, which is different from the common understanding that only one failure surface appears.

2D particle contact-based meshfree method in CDEM and its application in geotechnical problems

Purpose - Continuum-based discrete element method is an explicit numerical method, which is a combination of block discrete element method (DEM) and FEM. When simulating large deformation problems, such as cutting, blasting, water-like material flowing, the distortion of elements will lead to no convergence of the numerical system. To solve the convergence problem, a particle contact-based meshfree method (PCMM) is introduced in. The paper aims to discuss this issue. Design/methodology/approach - PCMM is based on traditional particle DEM, and use particle contacts to generate triangular elements. If three particles are contact with each other, the element will be created. Once elements are created, the macroscopic constitutive law could be introduced in. When large deformation of element occurs, the contact relationship between particles will be changed. Those elements that do not meet the contact condition will be deleted, and new elements that coincide with the relationship will be generated. By the deletion and creation of elements, the convergence problem induced by element distortion will be eliminated. To solve FEM and PCMM coupled problems, a point-edge contact model is introduced in, and normal and tangential springs are adopted to transfer the contact force between particles and blocks. Findings - According to the deletion and recreation of elements based on particle contacts, PCMM could simulate large deformation problems. Some numerical cases (i.e. elastic field testing, uniaxial compression analysis and wave propagation simulation) show the accuracy of PCMM, and others (i.e. soil cutting, contact burst and water-like material flowing) show the rationality of PCMM. Originality/value - In traditional particle DEM, contact relationships are used to calculate contact forces. But in PCMM, contact relationships are adopted to generate elements. Compared to other meshfree methods, in PCMM, the element automatic deletion and recreation technique is used to solve large deformation problems.

3D reconstruction of low-permeability heterogeneous glutenites and numerical simulation of hydraulic fracturing behavior

Based on microfocus computed tomography ( μ CT) imaging and X-ray diffraction techniques, a three-dimensional (3D) reconstruction model for heterogeneous glutenites was established by taking into account the mineral compositions and distribution characteristics of gravel particles. We employed the continuum-based discrete element method (CDEM) to simulate and analyze the initiation and propagation behavior of hydrofracturing cracks of heterogeneous glutenites subjected to various horizontal geostresses. The influences of various horizontal stress ratios and the characteristics of gravel particles on the initiation, growth, geometry, and spatial distribution of hydrofracturing cracks in heterogeneous glutenites were evaluated by comparing the properties of fractures with the simulation results of homogeneous sandstones. Additionally, we conducted a series of hydrofracturing experiments with physical models of the heterogeneous glutenites and homogeneous sandstones and compared the experimental data to the simulation results. Findings showed that the heterogeneity of glutenites significantly affects the hydrofracturing crack initiation and growth behavior. For identical geostress, the initiation pressure for hydrofracturing of heterogeneous glutenites was lower than that of homogeneous sandstones. The difference in initiation pressure between the heterogeneous glutenites and homogenous sandstones gradually decreased with an increase in the horizontal stress ratio, but overall, the change in the horizontal stress ratio had little effect on the initiation pressure for hydrofracturing of heterogeneous glutenites. The data from this investigation also indicate that for both heterogeneous glutenites and homogeneous sandstones, changes in the horizontal stress ratio can have an apparent impact on the spatial distribution and morphology of hydrofracturing cracks.

Application of Hilbert-Huang Transform to the analysis of the landslides triggered by the Wenchuan earthquake

A steep rock hill with two side slopes located at DK30+256 of National Road 213 was used as a prototype for analysis. The full process from initial deformation to sliding of the slope during ground shaking was simulated by using a new Continuum-based Discrete Element Method. During the earthquake, when shaking amplitudes were lower, the stress concentration points firstly appeared at the top of the slip mass, and then some tension failure points appeared, followed by shear failure points. At the same time, both the instantaneous frequencies of accelerations in the bedrock and that in the slip mass basically stayed in two different ranges. The energy transmittance coefficients of the sliding surface also stayed in a high range. As the ground shaking lasted, the number of failure points gradually increased until landslide occurrence. The instantaneous frequencies of accelerations in the slip mass and the energy transmittance coefficients of sliding surface gradually decreased, and both finally converged to a lower range. And then, the reasons triggering landslides are analysis in the joint time-frequency domain using Hilbert-Huang Transform, as follows: the differences of distribution and dissipation of the earthquake energy and the inconsistency of movements between the slip mass and the bedrock were the two major influence factors.

Strength characteristics of soil rock mixture under equal stress and cyclic loading conditions

Soil rock mixture (SRM) is a special geological material with non-uniform rock distribution, non-continuous cementation between rock and soil, and size effect structural characteristics, hence, possessing mechanical properties different from rock or soil. Field survey indicated that the surface layer of SRM above the rock slope was almost unstable under cyclic loading; however, at the same time, the slope itself was stable. This phenomenon exceeded initial judgments, thus it was important to study the mechanical characteristics of SRM under cyclic loading. Numerical simulation using continuum-based discrete element method was employed to study the strength degradation and failure mechanism of SRM under different frequencies, dynamic stress amplitudes and durations. Results show that the peak stress gradually increased with the increasing dynamic stress amplitude and frequency, but decreased with the increasing percentage of rock because the stiffness decreased greatly under cyclic loading. At the same time, the elasticity modulus decreased gradually with the dynamic stress amplitude and increasing frequency.