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With the shift of coal seam mining to the deep, the in-situ stress of coal and rock mass increases gradually. High ground stress can limit the generation of rock cracks caused by blasting, and blasting usually shows different crushing states than low stress conditions. In order to study the blasting expansion rule of rock mass with cavity under high ground stress and the rock mass fracture state under different side stress coefficients. In this paper, the effective range of blasting and the stress distribution under blasting load are analyzed theoretically. The RHT (Riedel-Hiermaier-Thoma) model is used to numerically simulate the blasting process of rock mass with cavity under different ground stress, and the influence of ground stress and lateral pressure coefficient on the crack growth of rock mass is studied. The results show that when there is no ground stress, the damage cracks in rock mass are more concentrated in the horizontal direction and the fracture development tends to the direction where the holes are located, which confirms the guiding effect and stress concentration effect of the holes in rock mass, which helps to promote the crack penetration between the hole and the hole. The length difference of horizontal and vertical damage cracks in rock mass increases with the increase of horizontal and vertical stress difference. Under the same lateral stress coefficient, the larger the horizontal and vertical stress difference is, the stronger the inhibition effect on crack formation is. For blasting of rock mass with high ground stress, the crack formation length between gun holes decreases with the increase of stress level, and the crack extends preferentially in the direction of higher stress. Therefore, the placement of gun holes along the direction of greater stress and the shortening of hole spacing are conducive to the penetration of cracks between gun holes and empty holes. The research can provide reference for rock breaking behavior of deep rock mass blasting. [ABSTRACT FROM AUTHOR]

This paper presents a novel framework combining the state-based peridynamics (SBPD) with the extended finite element method (XFEM) for crack propagation in two-dimensional solids. Numerical examination is conducted fulfilling both the quasi-static and time-dependent loading conditions. The computational domain is partitioned into two regions: (a) SPBD region: the vicinity of crack tips and potential region where the crack is likely to propagate, and (b) XFEM region: the area behind the crack tip and the rest of the body. The salient features of the developed framework include: (a) avoiding requirement of a priori knowledge of enrichment functions like the conventional XFEM; (b) without fracture criteria for crack propagation; (c) no restriction on the value of Poisson's ratio like the bond-based peridynamics; and (d) higher computational efficiency than the pure peridynamics. The efficiency and accuracy of the proposed framework are systematically demonstrated through benchmark examples involving quasi-static crack growth and dynamic crack branching problems. [ABSTRACT FROM AUTHOR]

This paper presents a new damage detection strategy for structures, capable of identifying the defects from a set of energy density measurements, at medium and high frequencies. An inverse energetic approach, also called the inverse simplified energy method (IMES), is used for this purpose. It was first developed for the localization and the quantification of vibro-acoustic sources. The main novelty of this paper is to extend this inverse approach to the field of defects detection, to localize the flaw through the knowledge of the energy density field within the structure. A new numerical methodology is proposed in this paper for this purpose. Numerical simulations with different defect cases were performed to validate the presented method. Results show that IMES is an effective predictive tool in structural damage detection. [ABSTRACT FROM AUTHOR]

This paper deals with the computational homogenization and numerical model reduction of deformation driven pressure diffusion in fractured porous rock. Exposed to seismic waves, the heterogeneity of the material leads to local fluid pressure gradients which are equilibrated via pressure diffusion. However, a macroscopic observer is not able to measure the diffusion process directly but senses the intrinsic attenuation of an apparently monophasic viscoelastic solid. The aim of this paper is to establish a reliable, yet numerically efficient, computational homogenization method to identify the viscoelastic properties of the macroscopic substitute model. Inspired by the Nonuniform Transformation Field Analysis, we incorporate a Numerical Model Reduction procedure. The proposed method is validated for several scenarios ranging from pressure diffusion in an unfractured poroelastic matrix, via localized pressure diffusion in interconnected fractures embedded in an impermeable matrix, to the fully coupled pressure diffusion both in fractures and the embedding poroelastic matrix. [ABSTRACT FROM AUTHOR]

The work considers the deformation and fracture of a reinforced concrete slab under the effect of an air shock wave. The research involves data from the "Blind Blast Test" experimental case. The slab is loaded by detonating an explosive in a shock tube. The numerical and experimental results are compared quantitatively and qualitatively. Quantitative comparison is made for the history of movement of key points of the reinforced concrete slab during deformation. Qualitative comparison is made for photographs of the destruction of a real reinforced concrete slab and distribution of the damage fields obtained by calculation. The numerical simulation is carried out using LS-DYNA code and the finite element method with an explicit time integration scheme. The CSCM (Continuous Surface Cap Model) model is used to model the concrete material. This model assumes that that the material is isotropic and has a three-invariant yield surface. The strength characteristics of the material depend on the rate of loading, and its damage is considered separately for compressive and tensile loads, which allows taking into account the partial recovery of compressive strength. The mathematical description of the model is given as part of the paper. Steel reinforcement of the concrete slab is modeled explicitly with beam finite elements. Finite element meshes of the concrete volume and reinforcing elements are coupled by means of kinematic dependences, automatically created by the design code. The properties of the reinforcement material are specified within the classical theory of elastoplastic flow with the criterion of limiting states in the Huber–Mises form and taking into account viscoplastic effects. The influence of boundary conditions, practical mesh convergence, and the capability of the mathematical model to predict the location of zones of material failure, displacement, and deformation of the structure are studied. [ABSTRACT FROM AUTHOR]

Geological dynamic hazards during coal mining can be induced by the structural instability of a composite structure of roof rock, coal and floor rock layers, whereas the joint in coal plays a vital role in the corresponding structural instability. In this paper, the effects of coal persistent joint on the uniaxial compression failure of a roof rock-coal-floor rock composite sample were analyzed using PFC2D software. The results show that with an increase of included angle α between the loading direction and coal persistent joint plane, the uniaxial compressive stress (UCS) and peak strain of the composite sample decreased firstly and then increased. The change of elastic modulus was not obvious with α. The UCS and peak strain at α of 45° were the smallest. Additionally, the coal bodies in composite samples were mainly destructed as a shear failure. The roof or floor rock presented a tensile failure or no damage. And four failure patterns were observed for composite samples after failure, i.e., inverted V-shaped shear failure in coal and tensile failure in roof or floor rock, M-shaped shear failure in coal and tensile failure in floor rock, shear failure along the joint plane in coal and tensile failure in roof and floor rocks, shear failure along partial joint plane without obvious damage for roof or floor rock. [ABSTRACT FROM AUTHOR]

In this paper, the embedded discontinuity approach is applied in finite element modeling of rock in compression and tension. For this end, a rate-dependent constitutive model based on (strong) embedded displacement discontinuity model is developed to describe the mode I, mode II and mixed mode fracture of rock. The constitutive model describes the bulk material as linear elastic until reaching the elastic limit. Beyond the elastic limit, the rate-dependent exponential softening law governs the evolution of the displacement jump. Rock heterogeneity is incorporated in the present approach by random description of the mineral texture of rock. Moreover, initial microcrack population always present in natural rocks is accounted for as randomly-oriented embedded discontinuities. In the numerical examples, the model properties are extensively studied in uniaxial compression. The effect of loading rate and confining pressure is also tested in the 2D (plane strain) numerical simulations. These simulations demonstrate that the model captures the salient features of rock in confined compression and uniaxial tension. The developed method has the computational efficiency of continuum plasticity models. However, it also has the advantage, over these models, of accounting for the orientation of introduced microcracks. This feature is crucial with respect to the fracture behavior of rock in compression as shown in this paper. [ABSTRACT FROM AUTHOR]

In this paper, using a special class of nonlinear response relations between linearized strain and Cauchy stress tensors, we study a quasi-static mixed-mode (combination of mode-I and mode-II) fracture boundary value problem. A special subclass of such relations are strain-limiting in which the strains are guaranteed to be uniformly bounded in the neighborhood of crack-tip. In this article, we consider a finite element method based direct numerical simulation (DNS) of plane-strain mixed-mode fracture in a class of strain-limiting, transversely isotropic elastic bodies. We study the numerical solution of a nonlinear fracture boundary value problem with displacement as the primary unknown. The linearized version of the strong form was derived using damped Newton's method and the corresponding weak formulation was solved using a conforming finite element method. The results of this DNS indicate that even very near the crack tip, both stress and strain remain much smaller in magnitude than the corresponding predictions from the linearized elastic fracture mechanics (LEFM). While away from strain concentrating crack-tip region, the solution to the nonlinear, strain-limiting model agrees closely with the LEFM solution. This supports recent asymptotic theoretical studies of anti-plane and plane-strain fracture boundary value problems. Further, we also study the behavior of cleavage stress in the neighborhood of crack-tip. The numerical results indicate that the cleavage stress is largest along a line directly ahead of the crack-tip in agreement with the classical LEFM solution for pure mode I loading. [ABSTRACT FROM AUTHOR]

Overhanging rock instability is a serious geological problem in mountainous regions. The initiation and propagation of a controlling crack are the fundamental causes of overhanging rock failure. In the view of fracture mechanics, the instability of toppling overhanging rock can be equivalent to the effect of pure shear and pure bending moment. This paper analyzes the evolution of displacement-load curves and failure modes of overhanging rock models at different crack lengths, crack angles, and load distances based on fracture tests of the toppling overhanging rock model. Maximum circumferential stress theory is used as the fracture criterion of mixed mode I-II fractures to calculate the stress intensity factor (SIF) of the crack tip and the theoretical failure load of the overhanging rock model. The fracture mode mechanism is analyzed by the calculated SIF. We use the extended finite element method to simulate the crack propagation path and analyze the change process from equivalent stresses of the numerical model using propagation steps. Comparisons between the physical tests, theoretical calculations, and numerical simulations verify the rationality of the experimental results. [ABSTRACT FROM AUTHOR]

In this paper, crack growth simulation for arbitrarily shaped cracks was investigated based on the virtual crack closure technique. During simulations, the crack front was represented by an approximated zigzag line which had the same general shape as the given crack. For this approximated zigzag crack front, a modified approach was developed to determine the required nodal forces, virtually closed area and displacement opening. After the strain energy release rate G was calculated, crack growth was governed by the fracture criterion G/ GC = 1 at all the crack tip nodes. The important features of the proposed approach are that (i) a simple stationary finite element mesh can be used for arbitrarily shaped cracks and (ii) adaptive re-meshing technique is avoided in studying crack growth. Three cases having different initial crack shapes are presented to assess the validity of this approach and to evaluate the ease of use in tracking crack growth. Reasonable agreement between the present study and other approaches are obtained. The shape changes during crack propagation can also be tracked with ease. [ABSTRACT FROM AUTHOR]

Natural fractures are ubiquitous in the Earth’s crust and often deeply buried in the subsurface. Due to the difficulty in accessing to their three-dimensional structures, the study of fracture network geometry is usually achieved by sampling two-dimensional (2D) exposures at the Earth’s surface through outcrop mapping or aerial photograph techniques. However, the measurement results can be considerably affected by the coverage of forests and other plant species over the exposed fracture patterns. We quantitatively study such effects using numerical simulation. We consider the scenario of nominally isotropic natural fracture systems and represent them using 2D discrete fracture network models governed by fractal and length scaling parameters. The groundcover is modelled as random patches superimposing onto the 2D fracture patterns. The effects of localisation and total coverage of landscape patches are further investigated. The fractal dimension and length exponent of the covered fracture networks are measured and compared with those of the original non-covered patterns. The results show that the measured length exponent increases with the reduced localisation and increased coverage of landscape patches, which is more evident for networks dominated by very large fractures (i.e. small underlying length exponent). However, the landscape coverage seems to have a minor impact on the fractal dimension measurement. The research findings of this paper have important implications for field survey and statistical analysis of geological systems. [ABSTRACT FROM AUTHOR]

Grouting plays a crucial role in dam safety. Due to the concealment of grouting activities, complexity of fracture distribution in rock masses and rheological properties of cement grout, it is difficult to analyze the effects of grouting. In this paper, a computational fluid dynamics (CFD) simulation approach of dam foundation grouting based on a 3D fracture network model is proposed. In this approach, the 3D fracture network model, which is based on an improved bootstrap sampling method and established by VisualGeo software, can provide a reliable and accurate geometric model for CFD simulation of dam foundation grouting. Based on the model, a CFD simulation is performed, in which the Papanastasiou regularized model is used to express the grout rheological properties, and the volume of fluid technique is utilized to capture the grout fronts. Two sets of tests are performed to verify the effectiveness of the Papanastasiou regularized model. When applying the CFD simulation approach for dam foundation grouting, three technical issues can be solved: (1) collapsing potential of the fracture samples, (2) inconsistencies in the geometric model in actual fractures under complex geological conditions, and (3) inappropriate method of characterizing the rheological properties of cement grout. The applicability of the proposed approach is demonstrated by an illustrative case study—a hydropower station dam foundation in southwestern China. [ABSTRACT FROM AUTHOR]

In this paper, the numerical simulation of crack propagation inmicrostructures of Al2O3/SiCn nanocomposite ceramic tool materials is carried out by means of a micromechanical model based on the Voronoi tessellation and the cohesive element theory in order to explore the relationship between microstructure morphologies and mechanical properties. The residual stress initiated due to the mismatch of thermal expansion coefficients and elastic modulus betweenmatrix grains and nanoparticles is considered in the simulation. The effects of microstructure types and nanoparticle volume content on the residual stress field and the fracture behavior are analyzed, respectively. [ABSTRACT FROM AUTHOR]

Numerical simulations based on the bifurcation and imperfection versions of the strain localization theory are used in this paper to predict the failure loci of metals and applied to an advanced high strength steel subjected to proportional loading paths. The results are evaluated against the 3D unit cell analyses of Dunand and Mohr (J Mech Phys Solids 66(1):133–153, 2014. doi:10.1016/j.jmps.2014.01.008) available in the literature. The Gurson porous plasticity model (Gurson in J Eng Mater Technol 99(1):2–15, 1977. doi:10.1115/1.344340) is used to induce strain softening and drive the localization process. The effects of the void growth, void nucleation and void softening in shear are investigated over a large range of stress triaxialities and Lode parameters. A correlation between the imperfection and bifurcation results is established. [ABSTRACT FROM AUTHOR]

We consider a dense aggregate of elastic, frictional particles isotropically compressed and next uniaxial strained at constant pressure. We show how failure can be predicted if fluctuations in the kinematics of contacting particles are introduced. We focus on the second order work and the possibility that at some stressed states it becomes negative under proper perturbations. Our analysis involves both a theoretical model and numerical simulations based upon the distinct element method (DEM). The theoretical model deals with contacting particles with incremental relative displacements that deviate from the average deformation in order to ensure their equilibrium. Because of this, the macroscopic stiffness tensor of the aggregate, that relates increments in stress with increments in strain, does not have the major symmetry. Consequently, in the hardening regime, we predict stressed states in which the second order work vanishes. The model seems transparent, and it makes clear and illustrative the role played by the fluctuations introduced in the kinematics of contacting particles in relation to the vanishing of second order work in an aggregate of compressed particles. The comparison with numerical simulations data supports the model. Statistical representation of the aggregate: conditional average. [ABSTRACT FROM AUTHOR]

This paper investigated the mechanism of fracture in concrete due to the deflagration phenomenon. For this purpose, the electric discharge impulse crushing method was selected, with liquid nitromethane (NM) taken as the deflagration agent. Employing this technique, NM is set inside charge holes and initiated by electric discharge. The pressure generated by the deflagration of NM in a steel chamber was modeled using the Jones-Wilkins-Lee equation of state. The modeled and measured pressures agreed well and the applicability of the pressure model was validated. Then, assuming controlled splitting along the expected fracture surface in concrete, dynamic fracture process analysis (DFPA) based on two-dimensional dynamic finite element method was conducted. The results showed that fracture patterns predicted in the DFPAs agreed well with those obtained from experiments. The mechanism of fracture in concrete due to deflagration was then discussed in terms of the fracture process in the controlled splitting. Owing to stress interference from each charge hole, compressive stress zones (CSZs) formed above and below the middle regions between charge holes where maximum and minimum principle stresses were both in compression. The CSZs was found to be important in obtaining a flatter fracture surface in the case of controlled splitting. In conclusion, the proposed method was shown to be useful for the investigation of the fracture mechanism in the case of the use of deflagration agents and could be useful for the design optimization of such controlled splitting. [ABSTRACT FROM AUTHOR]

The crack propagation simulation is still an open problem in the mechanical simulation field. In the present work this problem is analyzed using a version of truss-like Discrete Element Method, that here we called DEM. This method has been used with success in several applications in solid mechanical problems where the simulation of fracture and fragmentation is relevant. The formulation of DEM explaining the way the process of rupture could be simulated in consistent form is showed. Also are described details about how the dynamical fracto-mechanical stress intensity factors are computed. The main aim of this paper is to show the ability of this method in simulating fracture and crack propagation in solids, for this, three examples with different levels of complexity are analyzed. The obtained results are presented in terms of the variation of dynamic stress intensity factor in the fracture process, the stress map and geometric configuration on different steps in the simulation of the fracture process, the crack speed and the energetic balance during all the process. These results are compared with experimental and numerical results obtained by other researchers and published in recognized scientific papers. Final commentaries about the performance of the version of lattice model considered are carried out. [ABSTRACT FROM AUTHOR]

Fracture toughness is one of the most important mechanical properties for sheet metal in many applications. However not enough attention has been paid to the effects of laser forming conditions on fracture toughness of sheet metal. This paper presents an integrated fracture toughness model to study fracture toughness of sheet metal after laser forming. Microstructure, distribution of residual stresses and geometry of sheet metal specimen are considered in the model. Results of residual stress from microstructure-integrated finite element modelling of laser forming are incorporated in the model. Low carbon steel is used in this paper to validate the model. The results from the fracture toughness study are found to be consistent with microstructure analysis . [ABSTRACT FROM AUTHOR]

In fractured-vuggy reservoirs, cracks are not only reservoir spaces but also seepage channels. They are more likely to be closed and cracked under the coupling of the seepage field and the stress field. Therefore in this paper fractured-vuggy reservoirs are analyze as the background to study the propagation and closure of cracks under the seepage-stress coupling model. Firstly, the hydraulic model of continuous-discrete medium is established. Secondly, the fracture mechanics method is used to obtain the expression of crack width in the process of propagation and closure with the consideration of the water pressure, and then the propagation and closure criterions are established. On this basis, a numerical simulation method of crack propagation and closure under the seepage-stress coupling model is proposed by using the XFEM, and it is realized in ABAQUS by the secondary development. The calculation of typical cracks shows that: (1) the numerical calculation method established in this study is effective to simulate the propagation and closure of cracks; (2) the direction of crack propagation under Darcy flow is parallel to the vertical stress, and the direction of the crack propagation under the non-Darcy flow is perpendicular to the original fracture. (3) Non-Darcy flow is more likely to cause the whole system to become unstable than the Darcy flow does. This research has great significance for the future experimental researches, theoretical analyses and engineering applications. [ABSTRACT FROM AUTHOR]

This paper touches upon the computer simulation of the propagation of elastic waves in three-dimensional multilayer fractured media. The dynamic processes are described using the defining system of equations in the partial derivatives of the deformed solid mechanics. The numerical solution of this system is carried out via the grid-characteristic method on curvilinear structural grids. The fractured nature of the medium is accounted for by explicitly selecting the boundaries of individual cracks and setting special boundary conditions in them. Various models of heterogeneous deformed media with a fractured structures are considered: a homogeneous medium, a medium with horizontal boundaries, a medium with inclined boundaries, and a medium curvilinear boundaries. The wave fields detected on the surface are obtained, and their structures are analyzed. It is demonstrated that it is possible to detect the waves scattered from fractured media even in the case of nonparallel (inclined and curvilinear) boundaries of geological layers. [ABSTRACT FROM AUTHOR]

Tracking algorithms constitute an efficient numerical technique for modelling fracture in quasi-brittle materials. They succeed in representing localized cracks in the numerical model without mesh-induced directional bias. Currently available tracking algorithms have an important limitation: cracking originates either from the boundary of the discretized domain or from predefined 'crack-root' elements and then propagates along one orientation. This paper aims to circumvent this drawback by proposing a novel tracking algorithm that can simulate cracking starting at any point of the mesh and propagating along one or two orientations. This enhancement allows the simulation of structural case-studies experiencing multiple cracking. The proposed approach is validated through the simulation of a benchmark example and an experimentally tested structural frame under in-plane loading. Mesh-bias independency of the numerical solution, computational cost and predicted collapse mechanisms with and without the tracking algorithm are discussed. [ABSTRACT FROM AUTHOR]

This paper shows a new approach to estimate the critical traction for Mode I crack opening before crack growth by numerical simulation. For quasi-static loading, Linear Elastic Fracture Mechanics predicts the critical traction before crack growth. To simulate the crack growth, we used bond-based peridynamics, a non-local generalization of continuum mechanics. We discretize the peridynamics equation of motion with a collocation by space approach, the so-called EMU nodal discretization. As the constitutive law, we employ the improved prototype micro brittle material model. This bond-based material model is verified by the Young's modulus from classical theory for a homogeneous deformation for different quadrature rules. For the EMU-ND we studied the behavior for different ratios of the horizon and nodal spacing to gain a robust value for a large variety of materials. To access this wide range of materials, we applied sparse grids, a technique to build high-dimensional surrogate models. Sparse grids significantly reduce the number of simulation runs compared to a full grid approach and keep up a similar approximation accuracy. For the validation of the quasi-static loading process, we show that the critical traction is independent of the material density for most material parameters. The bond-based IPMB model with EMU nodal discretization seems very robust for the ratio $${\delta }/{\varDelta X}=3$$ for a wide range of materials, if an error of 5 % is acceptable. [ABSTRACT FROM AUTHOR]

Many researchers have discussed contaminant migration in clay liners, but study of compacted clay with vertical fractures is rare. In this paper, an experimental model was developed to assess how a vertical fracture influences contaminant migration in a clay layer. Experimental results were compared with numerical simulation data. Dispersion parameters were calibrated according to measured and calculated concentrations from observation holes. Three factors, affecting the intact clay, different depths of landfill leachate, and fracture aperture, have been discussed using the calibrated parameters. Results show that contaminant migration in fractured clay is faster than in intact clay and the break-through time for the tracer was shorter than that in intact clay. The migration rate of the tracer in fractured clay first decreased and then increased with increasing landfill leachate depth. Furthermore, larger fracture apertures accelerated the rate of contaminant migration. [ABSTRACT FROM AUTHOR]

The use of stochastic non-linear computational mechanics in real-world applications faces a fundamental obstacle: the lack of knowledge regarding the stochastic properties of material parameters involved in the problem. The paper describes the results of an experimental program which was focused on the determination of fracture-mechanical parameters and their stochastic models of different concrete types after different hardening durations. The investigated types of concrete, C40/50 and C50/60, are used industrially for the production of pre-fabricated concrete elements (e.g. double T-shaped beam elements for roofing). The fracture-mechanical parameters were determined by wedge splitting tests on cubic specimens with notch. Moreover, numerical simulations were carried out for the identification of material parameters by using artificial neural networks. All results obtained from the individual tests will here be presented, compared and discussed. Finally, recommendations for stochastic models of selected parameters of the analysed concrete will be given. [ABSTRACT FROM AUTHOR]

This paper presents a review of studies of delayed fracture and fracture mechanics problems in which the hypotheses and ideas of Yu. N. Rabotnov and L. M. Kachanov on the mechanisms of delayed fracture under creep conditions are extended to describe fracture processes using scalar and tensor measures of damage. The results of current research in the theory of elasticity, the mathematical theory of plasticity and creep, the mechanics of composites, and linear and nonlinear fracture mechanics, with material damage taken into account. [ABSTRACT FROM AUTHOR]

The subject of the paper is the capabilities and problems of simulation in computational and experimental fracture mechanics as applied to description of the stress-strain state in the neighborhood of the crack tip and the fracture mechanics parameters considering specific features of the local deformation fixity (stress triaxiality). Simulation techniques are illustrated by evaluation of fracture mechanics parameters of substandard cracked or notched specimens by numerical and experimental methods. [ABSTRACT FROM AUTHOR]

This paper proposes for the first time an intrinsic enrichment for extremely curved cracks in a meshfree framework. The unique property of the proposed method lies in the exact geometric representation of cracks using non-uniform rational B-splines (NURBS). A distance function algorithm for NURBS is presented, resulting in a spatial field which is simultaneously discontinuous over the (finite) curved crack and continuous all around the crack tips. Numerical examples show the potential of the proposed approach and illustrate its advantages with respect to other techniques usually employed to model fracture, including standard finite elements with remeshing and the extended finite element method. This work represents a further step in an ongoing effort in the community to integrate computer aided design with numerical simulations. [ABSTRACT FROM AUTHOR]

This paper presents a scheme for adaptive mesh refinement on unstructured polygonal meshes to better capture crack patterns in dynamic cohesive fracture simulations. A randomly seeded polygonal mesh leads to an isotropic discretization of the problem domain, which does not bias crack patterns, but restricts the number of paths that a crack may travel at each node. An adaptive refinement scheme is proposed and investigated through a detailed set of geometric studies. The refinement scheme is selectively chosen to optimize the number of paths that a crack may travel, while still maintaining a conforming domain discretization. The details of the refinement scheme are outlined, along with the criterion used to determine the region of refinement and the method of interpolating nodal attributes. Extrinsic cohesive elements are inserted when and where necessary, and follow the constitutive response of the Park-Paulino-Roesler cohesive model. The influence of bulk and cohesive material heterogeneity is investigated through the use of a statistical distribution of material properties. The adaptive mesh modifications are handled through a compact topological data structure. Numerical examples highlight the features of adaptive refinement in capturing physical fracture patterns while addressing computational cost. Thus, the present approach is a step towards obtaining accurate dynamic fracture patterns and fields with polygonal elements. [ABSTRACT FROM AUTHOR]

Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach followed by a real 3D case study of the Habanero reservoir in the Cooper Basin, Australia. [ABSTRACT FROM AUTHOR]

The understanding and the prediction of the failure behaviour of materials with pronounced microstructural effects is of crucial importance. This paper presents a novel computational methodology for the handling of fracture on the basis of the microscale behaviour. The basic principles presented here allow the incorporation of an adaptive discretization scheme of the structure as a function of the evolution of strain localization in the underlying microstructure. The proposed quasi-discrete methodology bridges two scales: the scale of the material microstructure, modelled with a continuum type description; and the structural scale, where a discrete description of the material is adopted. The damaging material at the structural scale is divided into unit volumes, called cells, which are represented as a discrete network of points. The scale transition is inspired by computational homogenization techniques; however it does not rely on classical averaging theorems. The structural discrete equilibrium problem is formulated in terms of the underlying fine scale computations. Particular boundary conditions are developed on the scale of the material microstructure to address damage localization problems. The performance of this quasi-discrete method with the enhanced boundary conditions is assessed using different computational test cases. The predictions of the quasi-discrete scheme agree well with reference solutions obtained through direct numerical simulations, both in terms of crack patterns and load versus displacement responses. [ABSTRACT FROM AUTHOR]

The heat treatment of tire protection chains has a major influence on the final product because the high local stresses that arise during quenching may lead to material failure, i.e., quench cracks. The investigations presented in this paper aim at the identification of critical areas in the design of a tire chain link made of 50CrV4 (DIN 1.8159) steel. Parametric studies were conducted by means of finite element (FE) simulation. The FE model enables the calculation of the stress evolution in the chain link during heat treatment. The position of the cracks produced in laboratory quench experiments coincided with the position where the FE simulation model predicted the maximum tensile stress at the end of the quench. Hence, geometry optimization of the chain links is now possible by means of parametric FE studies aiming to minimize these tensile stresses. To identify the influence of the various input parameters on the calculated stress evolution during the quenching, a sensitivity analysis was performed. The influence of the mesh size, the heat transfer at the surface, and the thermo-mechanical properties of the material phases on the stress calculation was evaluated and trends were identified. Temperature measurements during quenching experiments were used to determine the heat transfer parameters. X-ray residual stress measurements on pre-defined positions after an instrumented laboratory quenching were used to validate the simulation results. [ABSTRACT FROM AUTHOR]

Different failure modes during fracture shearing have been introduced including dilation, sliding, asperity cut-off and degradation. Several laboratory studies have reported the complexity of these failure modes during shear tests performed under either constant normal load (CNL) or constant normal stiffness (CNS) conditions. This paper is concerned with the mechanical behaviour of synthetic fractures during direct shear tests using a modified shear cell and related numerical simulation studies. The modifications made to an existing true triaxial stress cell (TTSC) in order to use it for performing shear tests under CNL conditions are presented. The large loading capacity and the use of accurate hydraulic pumps capable of applying a constant shear velocity are the main elements of this cell. Synthetic mortar specimens with different fracture surface geometries are tested to study the failure modes, including fracture sliding, asperity degradation, and to understand failure during shearing. A bonded particle model of the direct shear test with the PFC2D particle flow code is used to mimic the tests performed. The results of a number of tests are presented and compared with PFC2D simulations. The satisfactory results obtained both qualitatively and quantitatively are discussed. [ABSTRACT FROM AUTHOR]

Different failure modes during fracture shearing have been introduced including normal dilation or sliding, asperity cut-off and degradation. Attempts have been made to study these mechanisms using analytical, experimental and numerical methods. However, the majority of the existing models simplify the problem, which leads to unrealistic results. With this in mind, the aim of this paper is to simulate the mechanical behaviour of synthetic and rock fracture profiles during direct shear tests by using the two-dimensional particle flow computer code PFC2D. Correlations between the simulated peak shear strength and the fracture roughness parameter D recently proposed by Rasouli and Harrison () are developed. Shear test simulations are carried out with PFC2D and the effects of the geometrical features as well as the model micro-properties on the fracture shear behaviour are studied. The shear strength and asperity degradation processes of synthetic profiles including triangular, sinusoidal and randomly generated profiles are analysed. Different failure modes including asperity sliding, cut-off, and asperity degradation are explicitly observed and compared with the available models. The D parameter is applied to the analysis of synthetic and rock fracture profiles. Accordingly, correlations are developed between D and the peak shear strength obtained from simulations and by using analytical solutions. The results are shown to be in good agreement with the basic understanding of rock fracture shear behaviour and asperity contact degradation. [ABSTRACT FROM AUTHOR]

This paper proposes a numerical method to simulate hydrogen-assisted stress corrosion cracking, via coupled diffusion elastic-plastic finite element damage analyses based on phenomenological stress-modified fracture strain model. For validation, simulated results using the proposed method are compared with published experimental data of FeE 690T compact tension tests under air and hydrogen condition with various constant load-line displacement rates. The simulated results agree well with experimental data. [ABSTRACT FROM AUTHOR]

This work presents an extension of grid generation techniques for finite-volume discretizations of density-driven flow in fractured porous media, in which fractures are considered as low-dimensional manifolds and are resolved by sides of grid elements. The proposed technique introduces additional degrees of freedom for the unknowns assigned to the fractures and thus allows to reconstruct jumps of the solution over a fracture. Through the concept of degenerated elements, the proposed technique can be used for arbitrary junctions of fractures but is sufficiently simple regarding the implementation and allows for the application of conventional numerical solvers. Numerical experiments presented at the end of the paper demonstrate the applicability of this technique in two and three dimensions for complicated fracture networks. [ABSTRACT FROM AUTHOR]

An elliptical front crack has been found to be more accurate and realistic for modeling the transverse surface crack in rotating machinery compared with the widely used straight front crack. When the shaft rotates, the elliptical crack opens and closes alternatively, due to gravity, and thus, a 'breathing effect' occurs. This variance in shaft stiffness is time-periodic, and hence, a parametrically excited system is expected. Therefore, the dynamic instability and steady-state response of a rotating shaft containing an elliptical front crack are studied in the paper. The local flexibility due to the crack is derived, and the governing equations of the crack shaft system are established using the assumed modes method. Utilizing the Bolotin's method and harmonic balance method, the boundaries of two typical instability regions and maximum response amplitude of the cracked shaft could be computed numerically. The elliptical crack parameters (depth, shape factor and position) and damping are, respectively, considered and discussed for their effects on the dynamic behavior of the elliptical cracked shaft. Some research results might be helpful for the crack detection in rotating machinery. [ABSTRACT FROM AUTHOR]

In this paper, we present a damage model and its numerical solution by means of Fast Fourier Transforms (FFT). The FFT-based formulation initially proposed for linear and non-linear composite homogenization (Moulinec and Suquet in CR Acad Sci Paris Ser II 318:1417-1423 ; Comput Methods Appl Mech Eng 157:69-94 ) was adapted to evaluate damage growth in brittle materials. A non-local damage model based on the maximal principal stress criterion was proposed for brittle materials. This non-local model was then connected to the Griffith criterion with the aim of predicting crack growth. By using the proposed model, we carried out several numerical simulations on different specimens in order to assess the fracture process in brittle materials. From these studies, we can conclude that the present FFT-based analysis is capable of dealing with crack initiation and crack growth in brittle materials with high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical model for analyzing the dynamic characteristic such as natural frequencies and vibration mode shapes of cracked gears. The influence of crack position and crack size on the dynamic characteristic of gears is thoroughly investigated using the proposed theoretical model as well as the finite element method (FEM) for the sake of model validation. The theoretical analysis and numerical simulation show that the influence of crack size and crack position on the dynamic responses of cracked gears is significant and that the influence of crack position is larger than that of crack size. The natural frequencies drop with the increase of crack size and the low order natural frequencies drop more notably. The natural frequencies drop more significantly when crack is located at tooth root than at tooth tip. The vibration mode shapes of cracked gear tooth are very different from those of gear tooth without crack, and the vibration amplitude increases significantly in crack neighborhood. These observations are very valuable for damage detection and fault diagnosis of gear system. [ABSTRACT FROM AUTHOR]

The current paper presents a theoretical study of the identification of cracks in an elastic medium based on optimization methods using harmonic elastic waves. A generalized crack model was used to determine the elastodynamic behaviour of an arbitrarily located and oriented crack subjected to a plane harmonic wave. Sensitivity analysis was conduced to evaluate the variation of stress and strain fields with various crack parameters using the direct differential method (DDM). These general results were then used to identify an unknown crack from known strain components at discrete locations. The BFGS optimization scheme based on the sensitivity analysis was used to determine the length, the orientation and the position of the crack. Numerical simulation was conducted and the results were presented to show the effectiveness of the sensitivity analysis and the optimization method. It was observed that starting from a set of arbitrarily determined initial values, the length, position and the orientation of the crack can be accurately determined. [ABSTRACT FROM AUTHOR]

This research aims to assess geoenvironmental risks and identify the primary deterioration drivers in ancient buildings in Najran City, utilizing various analytical tools to help make informed judgments. The samples extruded from historical buildings were examined using field inspection, experimental data, SEM, EDX, and XRD analyses, in addition to lab and field observations and meteorological data. The dissolution of clay minerals and salt crystallization are the key contributors to the degradation and cracking of historical buildings in Najran City, according to lab and field observations. When the daytime high temperature surpasses 44 °C, wind erosion and humidity might cause continuous wetting–drying cycles on the investigated building surfaces. Test results indicated that the average unconfined compressive strength of the extruded earthen wall samples was 2 MPa and the water absorption was within the upper allowed limit (i.e., 15%). A finite element model of a typical earthen historical building was developed using PLAXIS 3D software to assess the behavior and nonlinear response of the silty sand soil layer underlying the building and the earthen historical buildings themselves using a plastic material model. The field observations confirm the results of the simulation, which clearly explained the failure mechanism. The integrated geotechnical and numerical simulations could provide insights for assessing geoenvironmental risks, identify the primary deterioration drivers in ancient buildings, and provide an understanding of material qualities and failure causes not only in the studied area but in other similar regions elsewhere. [ABSTRACT FROM AUTHOR]

The effects of the dip angles of the echelon notches on the acoustic emission (AE) are studied under uniaxial compression. For this comprehensive analysis, discrete-element simulations are used. Therefore, model dimensions of 150×150 mm were specially prepared. These models contained three echelon cracks with different lengths of 4.5, 3, and 1.5 cm, and a 2 mm vertical distance between the cracks. The inclination angles of the middle crack varied as 0°, 15°, 30°, 60°, 75°, and 90° in the specimens containing echelon cracks with different configurations. Two neighboring cracks were perpendicular to the middle cracks. Twelve different models were designed and tested under uniaxial compression. It was observed that the failure process and crack propagation patterns in the rock-like material specimens were affected by changes in cracks' angles and their configurations. The AE events in the loaded specimens grew rapidly during the initial loading phase. Numerous AE events showed a decline in the induced stresses at the peak load states. [ABSTRACT FROM AUTHOR]

Three-dimensional model of fracture propagation is proposed. The model simultaneously accounts rock deformation in the vicinity of a fracture and a cavity, fluid flow inside the fracture and its propagation in the direction that is selected by a growth criterion. The results of the sensitivity analysis of model solution to the variation of model parameters are presented. [ABSTRACT FROM AUTHOR]

We analyze the applicability of a modified Leonov-Panasyuk-Dugdale model to the description of the propagation of a mode I crack in structured materials under plane stress conditions. For quasi-brittle materials, refined formulas of the critical length of the prefracture zone and the critical load containing a structural parameter are proposed. The Kornev model is extended to the case of quasi-ductile materials. Numerical simulation of plastic zones in square plates of a bimetal and a homogeneous material under quasi-static loading is performed. In the numerical model, the equations of deformable solid mechanics are expressed in the Lagrangian formulation, which is the most preferred for large-strain deformations of elastoplastic materials. The results of the numerical experiments are consistent with the results of calculations using the analytical model for the fracture of structured materials. [ABSTRACT FROM AUTHOR]

ymptotic solutions for fracture opening, volume and specific surface energy for small and large fracture radii are presented from the literature. By comparison to numerical simulation of static circular fractures subject to constant and uniform internal pressures, it is found that a good approximation for fracture opening, for intermediate fracture radii, is obtained from a power mean (with exponent 1/2) of the small and large fracture radii limiting cases. The power mean equation for fracture opening is used to derive corresponding equations for fracture volume, specific surface energy and mode I and II stress intensities. These are then combined to form an approximate solution to describe the propagation of circular toughness-dominated near-surface hydraulic fractures, suitable for small, large and intermediate fracture radii. The approximate solution is shown to closely approximate results from equivalent numerical simulation. [ABSTRACT FROM AUTHOR]

We analyze scaling and localization phenomena in the fracture of a random central-force spring lattice model with strong disorder by means of computer simulation. We investigate the statistical and topological properties of the developing damage pattern and the scaling behaviour of the threshold. Our observations show that from the beginning and up to the point of maximum stress, damage develops in a uniform manner, qualitatively like in a percolating lattice, but numerically different from random percolation. Beyond the maximum-stress point localization and anisotropy come into play, resulting in final crack formation. The fraction of broken bonds at which the lattice fails, as well as the strain corresponding to failure, scale with the lattice size via power laws. The roughness of the final crack scales as a power law of the crack length over three decades of lengthscale. [ABSTRACT FROM AUTHOR]

Defects widely exist in rock masses, which have great impacts on the rock mechanical properties. The pre-existing fissures and holes are two common rock defects. In order to study the influence of hole shapes and fissure geometries on the failure modes and mechanical properties of rock masses, the derivatives of kernel functions in the traditional SPH method have been improved by introducing a fracture mark ξ, and a novel numerical method named improved kernel of smoothed particle hydrodynamics (IKSPH) has been developed to realize the simulations of rock fracture processes. The Monte Carlo method has also been introduced into the proposed method to realize the formations of random fissures. The small-scale numerical rock specimens with different hole shapes as well as random fissures are established. The crack propagation processes, the failure modes and the mechanical properties under uniaxial compression are simulated, results show that: 'Wing cracks' initiate from the random fissures, whose locations and interaction modes differ according to the geometries of random fissures. For rectangle hole, the crack initiations mainly occur at the upper and lower edges as well as the corners; for circular hole, tensile cracks appear at the 6 and 12 o'clock directions, meanwhile, shear cracks initiate at the 5 and 7 o'clock direction after the tensile crack propagates to a certain extent; for trapezoid and triangle hole, crack initiations mostly appear at the corners of the hole; the length and quantity of pre-existing fissures have greater influences on the mechanical properties of rock masses than the hole shapes and fissure dip angles. The research results can provide guidance for the correct understandings of fractured rock mechanisms. Meanwhile, the proposed method can also provide references for the applications of SPH method into simulations of rock fracture mechanics. At the same time, future research focus should be put on the applications of IKSPH method into engineering practices and developing high-performance IKSPH programming. [ABSTRACT FROM AUTHOR]

Fracture toughness investigation provides a perception of required minimum stress to commence the existing crack in material. Over the years, many approaches are developed for estimation of fracture toughness of rock in Mode I. Among them, semi-circular bend (SCB) test is most popular due to easier sample preparation. In this study, sandstone rock was collected from two locations (Jhanjra and Kusunda mines) for conducting SCB test. This test is conducted by varying the notch length (16, 18, 20, 22 mm) and fracture toughness and fracture energy are determined. Further, fracture toughness is determined with different models based on tensile strength of rock. In ABAQUS, XFEM approach with cohesive zone model is applied to investigate the crack growth in rock by SCB test. The results of the numerical analysis are compared with the laboratory results and it was found that fracture toughness decreases with increase in notch length as the applied load has to travel less distance to reach the tip of the notch. [ABSTRACT FROM AUTHOR]

By introducing the shape functions of virtual node polygonal (VP) elements into the standard extended finite element method (XFEM), a conforming elemental mesh can be created for the cracking process. Moreover, an adaptively refined meshing with the quadtree structure only at a growing crack tip is proposed without inserting hanging nodes into the transition region. A novel dynamic crack growth method termed as VP-XFEM is thus formulated in the framework of fracture mechanics. To verify the newly proposed VP-XFEM, both quasi-static and dynamic cracked problems are investigated in terms of computational accuracy, convergence, and efficiency. The research results show that the present VP-XFEM can achieve good agreement in stress intensity factor and crack growth path with the exact solutions or experiments. Furthermore, better accuracy, convergence, and efficiency of different models can be acquired, in contrast to standard XFEM and mesh-free methods. Therefore, VP-XFEM provides a suitable alternative to XFEM for engineering applications. [ABSTRACT FROM AUTHOR]

Over the last decades, finite-volume discretisations for flow in porous media have been extended to handle situations where fractures dominate the flow. Successful discretisations have been based on the discrete fracture-matrix models to yield mass conservative methods capable of explicitly incorporating the impact of fractures and their geometry. When combined with a hybrid-dimensional formulation, two central concerns are the restrictions arising from small cell sizes at fracture intersections and the coupling between fractures and matrix. Focusing on these aspects, we demonstrate how finite-volume methods can be efficiently extended to handle fractures, providing generalisations of previous work. We address the finite-volume methods applying a general hierarchical formulation, facilitating implementation with extensive code reuse and providing a natural framework for coupling of different subdomains. Furthermore, we demonstrate how a Schur complement technique may be used to obtain a robust and versatile method for fracture intersection cell elimination. We investigate the accuracy of the proposed elimination method through a series of numerical simulations in 3D and 2D. The simulations, performed on fractured domains containing permeability heterogeneity and anisotropy, also demonstrate the flexibility of the hierarchical framework. [ABSTRACT FROM AUTHOR]

Numerical simulation and field monitoring are conducted in this study to investigate rock deformation and failure behaviors during excavation of underground cavern group under high in situ stresses in Jinping I Hydropower Station. According to the numerical simulation, large deformation and damage in the surrounding rock mass result in anchorage cable overlimit. The traditional elastoplastic model only considers plastic yielding in rock mass and does not consider the evolution of damage in rock mass, i.e., initiation, propagation and coalescence of cracks. It is found from the numerical results that the damage behaviors of rock masses subjected to high in situ stresses are characterized by the formation of multi-fractured zones, i.e., the zonal disintegration. Theoretical basis, general rules and reinforcement method for zonal disintegration of the surrounding rock masses under high in situ stresses are proposed. The proposed methods are applied to strengthen support measures for construction of Jinping I Hydropower Station. [ABSTRACT FROM AUTHOR]