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Parameter selection is always a critical issue for the numerical modeling of many geotechnical problems. In this work, an idea of non-parameterized numerical analysis is demonstrated by incorporating tri-axial data as the input into the distinct lattice spring model (DLSM). An automatic parameter acquisition procedure is developed to determine the parameters of a modified Duncan–Chang (DC) model which is implemented in the DLSM through the further development of an incremental DLSM and a fabric stress calculation scheme. These newly developed algorithms are verified against available numerical results and experimental counterparts. Then, the discrete feature of the DC-DLSM is explored and discussed through the numerical modeling of large-scale tri-axial tests and a fracturing test. Finally, a real rockfill dam project is analyzed by using the DC-DLSM with the available tri-axial data as the input, and a reasonable fitting is obtained, which shows the possibility for the numerical modeling of the DLSM with no parameter selection burden.

Digital image correlation (DIC) is used to investigate crack initiation and propagation in discs of transversely isotropic Hawkesbury sandstone subjected to the Brazilian test . To verify DIC's validity and precision a simple calibration method is presented. It involves adjusting the size and spacing of subsets of pixels within images of a specimen's surface from which local deformations and strains are quantified, achieving agreement between strains measured by DIC and gauges attached to the surface. Using DIC the tensile and shear strain fields, crack opening displacements (CODs) and displacement vectors are determined at all stages of loading. The development of the fracture process zone is also identified prior to a major crack initiation. Also, a range of load contact configurations is considered, including the loads being applied via flat rigid platens and across finite strips with widths controlled by small (3 mm wide) and big (5 mm wide) wooden cushions placed between the load applicators and discs. It is observed that, for 0° and 90° anisotropy angles (representing layering normal to and parallel to diameters connecting load contacts) and for both the flat platen and small wooden cushion, cracks initiate far from the disc centres. Also, for the 45° anisotropy angle and all load configurations, cracks initiate at the disc centres. Furthermore, when the loads are applied via big wooden cushions, cracks initiate at the disc centres regardless of the anisotropy angle. Also, specimens loaded via big wood cushions exhibited the largest COD while the specimens loaded via small wood cushions exhibited the smallest. Also, specimens loaded via flat platens failed at smaller loads compared to those using wooden cushions. This study confirms transverse isotropy has strong effect on crack development. It also demonstrates important parameters including time and location of initiation, as well as COD, may be determined using DIC.

In this work, the distinct lattice spring model (DLSM) and the lattice Boltzmann method (LBM) are coupled together to simulate hydraulic fracturing problems. As the DLSM and LBM are both lattice modelling methods, the lattice meshes in these two systems are simply overlapped, which results in the same resolution in both the DLSM and LBM. The momentum exchange bounce-back algorithm is used to evaluate the forces exerted on the solid particles. Moreover, the calculation step in the LBM and DLSM is synchronised for prompt updates of fluid–solid interactions. The coupled model is further validated through a series of benchmarks. Finally, the coupled model shows its ability to simulate hydraulic fracturing in formations with complex discrete fracture networks.

In this work, a general framework is developed for the incorporation of elasto-plastic constitutive models into the Distinct Lattice Spring Model (DLSM). Within this framework, a smoothed non-associative Drucker-Prager (DP) model is implemented. To verify the model, a number of numerical examples are examined, and the results are compared to the analytical solution, numerical solution based on the Finite Volume Method (FVM), and the experimental results, where available. It is shown that the proposed framework is numerically stable and is capable of solving elasto-plastic problems while maintaining the general advantages of the LSM technique in tacking material fracturing.

A fundamental study on the tensile failure of rock is conducted using the three-dimensional lattice spring model. The model covers three aspects: (1) the relationship between the mesoscopic tensile/shear failure and the corresponding macroscopic tensile failure; (2) the effects of the size, shape, and location of the initial defect on the macroscopic tensile failure; and (3) the effects of the porosity, heterogeneity, crystal structure, mesoscopic constitutive model, and model scale on its macroscopic tensile responses. Through investigation, this study reveals that the mesoscopic strength heterogeneity affects the macroscopic pre-peak response of rock, and the initial defect could control its macroscopic post-peak response. The post-peak characteristics of the mesoscopic constitutive model influence both the macroscopic pre-peak and post-peak responses, which are scale independent and scale dependent, respectively. Based on these investigations, a parameter-selection method for the mesoscopic constitutive model is established to fully utilize the macroscopic tensile experimental data.

This paper studies the propagation and attenuation of blasting wave induced by explosion in underground rock cavern by employing the newly developed four-dimensional lattice spring model (4D-LSM). The non-reflection viscous boundary condition was implemented in the 4D-LSM to reduce the computing resources of full-scale simulation of blasting wave propagation in the practical engineering. Then, a number of damping models were developed and implemented in the 4D-LSM to describe the attenuation of blasting wave in the rock mass. In addition, the influence of the loading form of blast load and damping models on the propagation and attenuation of blasting wave were studied by comparing with the field test data in details. It was found that the loading form of a triangular blast stress wave with an equivalent pressure wave and the coupled damping model could lead the 4D-LSM producing a reasonable fitting over the field test data in terms of both the blasting waveform recorded at a given measuring point and attenuation results from a number of measuring points. Our study provides a basis for the further application of the 4D-LSM as an alternative numerical tool in modeling the blasting wave propagation problems in rock engineering.

Recently, a four-dimensional lattice spring model (4D-LSM) was developed to overcome the Poisson's ratio limitation of the classical LSM by introducing the fourth-dimensional spatial interaction. In this work, some aspects of the 4D-LSM on solving problems in geomechanics are investigated, such as the ability to reproduce elastic properties of geomaterials, the capability of solving heterogeneous problems, the accuracy on modelling stress wave propagation, the ability to solve dynamic fracturing and the parallel computational efficiency. Our results indicate that the 4D-LSM is promising to deal with problems in geomechanics.

The spontaneous crack growth in an infinite domain is studied using the distinct lattice spring model (DLSM). The kinetic energy, strain energy, crack opening, and crack branching during the crack growth are investigated numerically using a simple spring model. The discrete simulation satisfactorily reproduces the experimental observations and the theoretical predictions of the fracture energy increase even without considering the crack tip damage zone and crack bifurcation. Moreover, from analysis of the intrinsic fracture energy release rate, it was concluded that the observed fracture energy increase should originate from the distribution of kinetic energy during self-similar crack growth.

In this work, comprehensive numerical modelling was conducted on the full-scale linear cutting test with a TBM disc cutter. Several numerical techniques, including local particle refinement and the coupling of different numerical methods (4D-LSM, DDA, and NMM), were adopted to more realistically reproduce the actual experimental loading conditions. The coupled numerical method was first calibrated against the normal cutting force of the normal linear cutting test with large blocks of granite. Following the calibration, numerical predictions of the inclined cutting and double-channel continuous cutting processes were conducted, and the numerical results showed good agreement with previous experimental observations. The influences of cutting speed, particle size, and multiscale coupling techniques were further discussed, and some suggestions were derived on the selection of proper numerical parameters and techniques in the numerical simulation of 3D large-scale TBM disc cutting lab tests.

In this work, toppling failure of a jointed rock slope is studied by using the distinct lattice spring model (DLSM). The gravity increase method (GIM) with a sub-step loading scheme is implemented in the DLSM to mimic the loading conditions of a centrifuge test. A classical centrifuge test for a jointed rock slope, previously simulated by the finite element method and the discrete element model, is simulated by using the GIM-DLSM. Reasonable boundary conditions are obtained through detailed comparisons among existing numerical solutions with experimental records. With calibrated boundary conditions, the influences of the tensional strength of the rock block, cohesion and friction angles of the joints, as well as the spacing and inclination angles of the joints, on the flexural toppling failure of the jointed rock slope are investigated by using the GIM-DLSM, leading to some insight into evaluating the state of flexural toppling failure for a jointed slope and effectively preventing the flexural toppling failure of jointed rock slopes.

With the rapid development of high-performance computing, Lattice Spring Models (LSMs) using a simple fracturing law demonstrate many prospects for simulating crack propagation in brittle solids. In this paper, a comprehensive study on crack propagation in brittle material is conducted using the distinct lattice spring model (DLSM) with high-performance computing and physical tests on crack propagation in brittle material from this work and the literature. The relationship between the simple fracturing law and the fracture criterion based on linear elastic fracture mechanics is investigated for the first time. The work involved includes the correlation between the Stress Intensity Factor (SIF) and spring deformation, the influence of the particle size on fracture toughness, and the relationship between the micro-spring failure and the critical stress intensity factors. Our results indicate that the simple fracturing law based on spring deformation may be easier and more fundamental for understanding crack propagation in brittle materials than fracture-toughness-based criteria. The applicability of the simple fracturing law is further confirmed from numerical modelling of crack propagation and coalescence problems with complex pre-existing cracks. Our results show that models with an appropriate resolution can simulate the crack path reasonably. Finally, the advantages of using the simple fracturing law are highlighted through multiple dynamic crack propagation and three-dimensional fracturing.

The influence of original prefabricated empty hole on dynamic crack propagation was studied. The dynamic behavior of crack propagation due to the impacting of drop hammer on the defective PMMA medium of manufactured hole defect (different extent of left shift, respectively, for L = 110 mm, L = 111.25 mm and L = 112.5 mm) was conducted using the test system of digital laser dynamic caustics (DLDC). The stress intensity factor and velocity at the running crack tip were analyzed. Moreover, the recently developed distinct lattice spring model (DLSM) was validated using the experimental data. It was found that the numerical modeling can reproduce the experimentally observed phenomena. Combining the experimental and numerical results, it can be concluded that the influence of empty hole defects of brittle materials on dynamic fracturing is great.

In this work, a four-dimensional lattice spring model is developed for studying the mechanical responses of solids. Our results indicate that the Poisson’s ratio limitation of the classical lattice spring model defined in three-dimensional space can be released by introducing an extra fourth-dimensional interaction. The fourth-dimensional lattice spring model adopts central interactions only, and it can naturally represent the nonlinear dynamic responses of solids without special treatment of rigid body rotation or incremental integration of non-central/non-local interaction as used in the traditional methods. Applicability of the model is illustrated from a few numerical examples.

High-energy laser technology is expected to be applied into deep drilling and tunnel excavation due to its attractive prospects for enhanced hard rock breakage. However, there is still a lack of proper experimental methods and numerical tools to quantitatively evaluate the influence of laser radiation on rock fracture. Combined with our specially designed experimental tests, this work aims to provide a numerical tool to quantitatively investigate laser-induced rock damage. Using a specially designed experimental platform, we conducted direct tensile tests on rock samples in the shape of dog-bone to determine rock damage under the laser radiation of different parameters. The experimental results show that a high-energy laser beam can cause a significant loss in rock tensile strength. Then, a mathematical model was established to describe the temporal and spatial evolution of rock damage in a given path of laser scanning, which was implemented in a four-dimensional lattice spring model (4D-LSM) to simulate our experimental tests. Through a comparison between the numerical and experimental results, the multiparameter damage model was proven to be more suitable for the numerical simulation of laser-induced rock damage. Finally, by introducing a laser damage model, an orthogonal experimental design was used to analyse the influencing significance of different factors on the efficiency of rock breaking and the wear of cutter tools in laser-assisted rock cutting, showing the prospects for application of the proposed numerical model to laser-assisted tunnel boring machine (TBM) tunnelling in the future.

In this paper, fluid flow through natural fracture network is studied using computational fluid dynamics. To investigate the influence of fracture roughness, normal deformation and shear deformation on the fracture transmissivity/permeability, numerical tests of fluid flow through 3D rock fracture are conducted using the lattice Boltzmann method (LBM) in a middle size cluster. An empirical equation was obtained from the numerical results. Following this, natural fracture networks are built for fluid dynamics simulation of fluid flow through rock fracture network. It is found that the pipe network model enriched with the derived empirical equation can produce similar results compared with the LBM simulation which further confirms the empirical equation’s applicability. Finally, influences of fracture length, fracture density, and deformation of the fracture network on the fluid flow are studied preliminarily from coupling LBM with the discrete fracture network model and discrete element model.

Dynamic crack coalescence attracts great attention in rock mechanics. However, specimen preparation in experimental study is a time-consuming and difficult procedure. In this work, a gypsum-like material by powder bed and inkjet 3D printing technique was applied to produce specimens with preset cracks for split Hopkinson pressure bar (SHPB) test. From micro X-ray CT test, it was found that the 3D printing technique could successfully prepare specimens that contain preset cracks with width of 0.2 mm. Basic mechanical properties of the 3D printing material, i.e., the elastic modulus, the Poisson’s ratio, the density, the compressive strength, the indirect tensile strength, and the fracture toughness, were obtained and reported. Unlike 3D printed specimens using polylactic acid, these gypsum-like specimens can produce failure patterns much closer to those observed in classical rock mechanical tests. Finally, the dynamic crack coalescence of the 3D printed specimens with preset cracks were captured using a high-speed camera during SHPB tests. Failure patterns of these 3D printed specimens are similar to the specimens made by Portland cement concrete. Our results indicate that sample preparation by 3D printing is highly competitive due to its quickness in prototyping, precision and flexibility on the geometry, and high material homogeneity.

A new damage-plasticity constitutive model which takes account of the effect of confining pressure and strain rate on the strength and post-peak behaviour is proposed for rock subjected to dynamic loading. The model treats the compressive and tensile damages, both related to plastic and volumetric deformations, separately. The strain rate effect is considered by incorporating a newly developed dynamic increase factor formula, which reflects the pure rate sensitivity of rock, into the yield surface via radial enhancement approach. Fractionally-associated flow rule and lode-angle dependency are employed to capture the shear dilation behaviour of rock. The new model is then implemented into LS-DYNA via a user defined material subroutine to simulate the mechanical response of rock under various loading scenarios including triaxial compression, direct tension, Split Hopkinson Pressure Bar compression, oval-nose projectile penetration and explosive blast action, reported in literature. The robustness and accuracy of the new model are demonstrated by validating against available experimental results and by benchmarking with the reported simulations.

As a newly developed computational method, the four-dimensional lattice spring model (4D-LSM) is computationally intensive due to the introduction of extra-dimensional interactions. In this work, the 4D-LSM is parallelized to fully utilize the available computational resources of modern computers, namely, the multi-core CPU and the GPU. To utilize computing power of the multi-core CPU, OpenMP with a fork-join scheme is used to assign computational tasks to different CPU threads, whereas CUDA, with a granular computing scheme, is adopted to assign computations to thousands of GPU threads. A domain decomposition with a data communication scheme is proposed to utilize both the multi-core CPU and the GPU. The influence of digital precision and hardware on the parallel computing performance of the 4D-LSM are investigated through a number of numerical examples including elastic deformation, elastic bulking and dynamic fracturing. Finally, the multi-core CPU 4D-LSM is used to solve a crack propagation problem and is compared with existing experimental and numerical results.

The thermal damage evolution of rock closely relates to many important scientific and engineering problems, such as the mechanisms of earthquake and the effective extraction of deep geothermal energy. However, there is lack of rational thermal damage evolution model, and the mechanisms of thermal damage are still unclear especially during cooling. By use of a specially designed acoustic emission (AE) test system, we explored the thermal damage evaluation in a rock and established a thermal damage evolution model which takes into account both heating and cooling processes. The mechanisms of rock damage caused by heating and cooling were analyzed by using a lattice spring model, and two different microstructural explanations were found, i.e. heterogeneous microstructure and microdefect structure. The damage evolution model can be used for more accurate modeling of these problems which involve rock thermal damage, such as induced seismic activity during deep geothermal exploration.

Rock cutting and rock penetration are typical problems in civil, mining, petroleum, and geothermal engineering disciplines. They involve dynamic fracturing and fragmentation of rock, high-speed movements of a cutter/impactor, and complex dynamic contacts between the cutter/impactor and the rock. In this study a new three-dimensional (3D) coupled approach is developed to address these problems. The distinct lattice spring model (DLSM) is used to simulate the dynamic fracturing process of the rock, and the discontinuous deformation analysis (DDA) is adopted to model the high-speed motion of the cutter/impactor. An explicit-implicit coupling scheme is developed to bridge DLSM and DDA. Moreover, to take account of interaction between DLSM and DDA, a 3D simplex sphere-to-block contact method is introduced. Finally, a number of numerical examples are conducted to verify the implementation of the coupled approach and its ability to model rock cutting and rock penetration problems.

Dynamic indirect tensile tests were carried out by using a Split Hopkinson Pressure Bar (SHPB) for coal sampled from the Datong mine in China. The principal purpose was to explore the influence of bedding structure in the coal on its dynamic indirect tensile strength. However, to resolve some contradictions, X-ray micro CT, high speed optical imaging and a discrete element based modelling approach were combined to analyze the test results. The X-ray micro CT was used to detect the actual bedding structure in the coal; the high speed imaging captured failure patterns of the specimens with different bedding directions; and the numerical modelling was utilized to investigate the influence of different bedding structures on dynamic strength. The SHPB and numerical results illustrate that dynamic indirect tensile strength reliably correlates with impact velocity. In addition, the dynamic indirect tensile strength is not only influenced by the bedding direction but also by the roughness and discontinuity of the bedding. Based on these findings, a method is developed to further process the test data including a model to describe the dynamic indirect tensile strength of Datong coal.

Although lattice spring models (LSMs) have been increasingly applied in the study of rock fracturing and rock failure, it is still difficult to accurately reproduce high ratios of the uniaxial compressive strength to the tensile strength of rock materials. In this work, a feasible solution is developed for the four-dimensional lattice spring model (4D-LSM) that overcomes this shortcoming by incorporating a multibody failure criterion. The stress tensor of a spring bond is determined by the local deformation state between this bond and its neighboring spring bonds, which is further used to judge its failure state using a stress-based strength model. Then, a cohesive zone model is introduced to describe the postfailure stage of the spring bond. The performance of the proposed solution in reproducing the high ratio of the uniaxial compressive strength to the tensile strength of rock materials is demonstrated via numerical tests. Enriched by the multibody failure criterion, 4D-LSM is demonstrated to solve a broader range of practical problems that involve rock failure.

Brazilian tests are used to determine tensile strengths of rocks. Failure mechanisms, and the strengths determined, are influenced by the configuration of the load contacts. Most research on how to interpret Brazilian tests is only valid for isotropic rocks. This study addresses Brazilian tests on transversely isotropic rocks, experimentally and analytically, to identify failure conditions for a range of load contact types and anisotropy angles (representing orientations of the transversely isotropic planes with respect to direction normal to the loading). Stress fields are determined analytically and coupled with a failure criterion to infer locations where failure and crack initiations occur. The analytical results are compared with experimental observations using digital image correlation (DIC) for transversely isotropic Hawkesbury sandstone. It is found that anisotropy angles affect the locations of the crack initiations, with agreement between the experimental results and analytical solutions being observed. The study goes on to show that, for a wide range of transversely isotropic rocks and for planes parallel and perpendicular to the loading directions, cracks will always initiate at disc centres as long as the contact area is large (corresponding to a subtended angle at the disc centre of at least 25 ∘ ) . Failure and cracking at a disc centre enables reliable determination of the indirect tensile strength. The equation for strength, including a stress concentration factor for a range of transversely isotropic elastic properties, is presented for use by practitioners and laboratory technicians.

Understanding the dynamic responses and failure modes of stratified sedimentary rocks is critical to predict ground motion in sedimentary rock formations during underground excavation. We experimentally investigated the dynamic properties of sandstone specimens, siltstone specimens, and composite specimens with sealed sandstone-siltstone interfaces using a split Hopkinson pressure bar system. We also numerically examined the effects of rock type, strain rate, particle size, and interface cementation degree on the dynamic properties of sedimentary rock specimens using the discrete element method. Our results show that the dynamic strengths of sandstone and siltstone increase with higher strain rate in a similar manner, but the dynamic strength of sandstone is larger than that of siltstone at the same strain rate. Although the size of deposited particles may not affect the dynamic strength of lithified rocks, the fracture surface of sandstone with large particle size is relatively rough. The degree of cementation at the interface between siltstone and sandstone has a negligible effect on the dynamic strength of sedimentary rocks, but remarkably affects the failure modes. Micro-cracks first initiate in the low-strength siltstone, and coalesce with those subsequently developed in the sandstone and at the sealed interface to form meso-fractures.

This paper further extends the ability of the distinct lattice spring model (DLSM) to predict quasi-brittle crack propagation in concrete. In contrast to brittle crack propagation, most experimental results confirm that the crack propagation in concrete is quasi-brittle. The DLSM was originally developed to study the brittle fracturing of rock. Whether and how it could be applied to quasi-brittle crack propagation has not been systematically studied. In this work, considering aspects of the geometric non-uniformity, material heterogeneity and micro-mechanical constitutive model, the ability of the DLSM to solve quasi-brittle crack propagation has been systematically investigated. The main contributions of this work are that it (1) confirmed the necessary for the DLSM to have a new micro-mechanical constitutive model to solve the quasi-brittle crack propagation problem; (2) established a new micro-mechanical constitutive model for quasi-brittle crack propagation; and (3) proposed a formula for the relationship between the micromechanical and macroscopic material parameters of the concrete. The new micromechanical constitutive model proposed in this paper has been systematically verified by three-point bending experimental results of various grades of concrete. Finally, the new constitutive model has been adopted to analyse the cracking of the concrete lining.

In this paper, a model for damage and fracture, considering the heterogeneity of material properties, is validated and used to investigate the mechanism of spallation in fiber-reinforced concrete (FRC) slabs with various fiber and aggregate contents under impact loading. Numerical simulations show that there is a marked difference in the failure patterns among slabs with various fiber and aggregate contents, and the fibers can remarkably improve the tensile strength of the concrete slab, effectively prevent the initiation and propagation of cracks, and inhibit the occurrence of spallation. Moreover, numerical simulations capture the whole process of the propagation of incident compressive stress waves in the FRC and the reflection of stress waves upon concrete surfaces and the spallation failure of FRC induced by the reflected tensile stress wave, which is obviously different from the failure pattern of FRC under static loads. The results of this study can also provide a valuable reference for stu...

A full rate-dependent cohesive law is implemented in the distinct lattice spring method (DLSM) to investigate the dynamic fracturing behavior of brittle materials. Both the spring ultimate deformation and spring strength are dependent on the spring deformation rate. From the simulation results, it is found that the dynamic crack propagation velocity can be well predicted by the DLSM through the implemented full rate-dependent cohesive law. Furthermore, a numerical investigation on dynamic branching is also conducted by using the DLSM code.

In this paper, the ability of the distinct lattice spring model (DLSM) for modeling stress wave propagation in rocks was fully investigated. The influence of particle size on simulation of different types of stress waves (e.g. one-dimensional (1D) P-wave, 1D S-wave and two-dimensional (2D) cylindrical wave) was studied through comparing results predicted by the DLSM with different mesh ratios (lr) and those obtained from the corresponding analytical solutions. Suggested values of lr were obtained for modeling these stress waves accurately. Moreover, the weak material layer method and virtual joint plane method were used to model P-wave and S-wave propagating through a single discontinuity. The results were compared with the classical analytical solutions, indicating that the virtual joint plane method can give better results and is recommended. Finally, some remarks of the DLSM on modeling of stress wave propagation in rocks were provided.