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• Multi-scale dynamical responses of submerged particle jet impact drilling were investigated. • Correlation and nonlinear analysis of rock fracture were modelled and experimentally validated. • Rock fracture can be characterized as instantaneous stepwise temporal evolution and longitudinal expansion. • Dynamic responses are represented in terms of accumulative growths in macro-scale, radial cracks in micro-scale. Particle Impact Drilling (PID) technology is highly efficient for exploitation of unconventional energy resources in extra-deep and ultra-hard strata. The multi-scale dynamic responses and fracture mechanics analysis of rock formations in drilling using the PID are discussed in this paper. Firstly, rock fracture experiments and penetration performance under submerged particle jet impact were conducted to analyze fracture mechanisms in macro-scale. Then, the rock constitutive relation model and damage model for the submerged particle jet impacts using the damage and failure theory and correlation analysis model were constructed. On this basis, multi-scale dynamic responses and nonlinear analysis of failure performance with submerged particle jet impact were conducted. Our results indicate continuous damage growth in macro-scale and radial cracks development in micro-scale when submerged particles impact the drilled formation in a process of creating a well. [Display omitted] [ABSTRACT FROM AUTHOR]

• Dynamic mechanical properties were studied using true triaxial SHPB. • Under hydrostatic stress, the dynamic breaking of rocks requires more energy. • The increase in axial confining pressure promotes dynamic rock breakage. • Suggestion to arrange blastholes along the direction of maximum geostress. During rock blasting at deep depths, the rock is subjected to high geostress and explosion impact. Understanding the dynamic mechanical behaviour of rock induced by the combined static and dynamic loads is crucial for revealing the mechanism and improving the fragmentation of deep rock blasting. A true triaxial split Hopkinson pressure bar (SHPB) was used in this study to investigate the dynamic mechanical properties and fracture behaviour of red sandstone under multiaxial confining pressure and impact loading. Sieving tests and fractal dimension were used to quantitatively assess the effects of confining pressure and impact loads on the dynamic fracture characteristics of rock. The test results show that the dynamic peak stress, elastic modulus, incident energy and dissipated energy of rock fracture decrease with an increase in the axial confining pressure (σ x -st) along the impact loading direction. While these quantities associated with the dynamic mechanical properties and fracture increase with increasing the lateral confining pressure (σ y -st and σ z -st). The enhancing effect of σ y -st and σ z -st is dominated by the minimum pre-stress component. The dynamic strength and elastic modulus under an isobaric confining pressure condition are higher and more energy is required to dynamically fracture rock in comparison to anisobaric pre-stress states with the same average pressure. For red sandstone, the dynamic strength under multiaxial confinement is also strain rate dependent. Moreover, the strain rate effect is more significant under triaxial and anisobaric confining pressure. The size distribution and fractal dimension of rock fragments based on the sieving tests show that σ x -st promotes the dynamic rock fracture, while σ y -st and σ z -st have an inhibiting effect. As the impact load increases in a constant pre-stress state, the fractal dimension of rock fragments is positively and linearly related to the energy dissipated in the rock fracture. From the perspective of the promoting effect of σ x -st on dynamic rock fracture, rock fragmentation by blasting can be improved and accordingly explosives used in the blasting can be reduced if geostress conditions are well utilized. In this regard, it is recommended that the blastholes detonated simultaneously are arranged along the direction of the maximum geostress on the blasting work face. [ABSTRACT FROM AUTHOR]

Indentation testing has been widely used in laboratory environments to investigate the processes leading to rock fragmentation in drilling, mechanized tunneling, and mining. Rock specimens for laboratory testing are limited to finite size, potentially causing size effects that have to be accounted for when transferring results to in situ applications. We present an integrated experimental and theoretical investigation of the specimen size effect in indentation testing (a) to address the limited understanding of its causes and the lack of tools to analyze tests on variable specimen sizes and (b) to identify to what extent an indenter mimicking the shape of a cutter on a tunneling machine can be approximated by a conventional indenter geometry. We performed indentation tests on cylindrical specimens of a porous sandstone with aspect ratios (diameter/height) ranging from 0.3 to 1.7, using a blunt-truncated indenter and monitoring the fracturing process by the acoustic emission technique. A damage zone, enclosing a zone of crushed grains immediately below the indenter tip, forms and grows due to tool penetration. Eventually, all specimens failed as a result of the propagation of a sub-vertical fracture, initiated close to peak indentation pressure. Peak force, its corresponding penetration depth, and peak indentation pressure increase with specimen size, more significantly with specimen diameter than with height. We developed a semi-analytical model based on cavity-expansion theory and linear elastic fracture mechanics for the formation of the damage zone and the nucleation and propagation of the macroscopic vertical fracture, respectively, whose predictions are in good agreement with our experimental data. The observed increases of peak indentation pressure with specimen size can be explained by the effect of the free surfaces on damage zone growth rather than on fracture propagation. The model permits evaluating the specimen size effect through the ratio between two geometrical parameters, specimen diameter and tip width of the truncated indenter, which has to be larger than around 102 for the size effect to be insignificant. The model permits upscaling of experimental results to in situ conditions based on geometrical indenter parameters and commonly used material parameters. Highlights: The series of indentation tests performed with the aid of acoustic emission technique reveals the significant influence of specimen size on test results. The proposed novel semi-analytical model is proved useful to analyse indentation tests on variable specimen sizes and indenter geometries including indenters with a truncated tip. The presented detailed mechanistic analysis for indentation tests identifies key parameters controlling rock fragmentation process and permits transferring laboratory results to in-situ applications. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study on the effects of microwave irradiation on the mechanical properties of hard rock. More specifically, the weakening effect of microwave heating induced damage on the uniaxial compressive and tensile strength of granite-like rock is numerically evaluated. Rock fracture is modelled by means of a damage-viscoplasticity model with separate damage variables for tensile and compressive failure types. We develop a global solution strategy where the electromagnetic problem is solved first separately in COMSOL multiphysics software, and then provided into a staggered implicit solution method for the thermo-mechanical problem. The thermal and mechanical parts of the problem are considered as uncoupled due to the dominance of the microwave-induced heat source. The model performance is tested in 2D finite element simulations of heterogeneous numerical rock specimens subjected first to heating in a microwave oven and then to uniaxial compression and tension tests. According to the results, the compressive and tensile strength of rock can be significantly reduced by microwave heating pretreatment. [ABSTRACT FROM AUTHOR]

Peridynamics employs an integral form to deal with the discontinuity within the object, showing great advantages in analyzing material failure. However, in Peridynamics, many existing contact methods have some shortcomings in accurately calculating contact forces, leading to some unreasonable results when the problem involves contact. A more accurate contact model based on particle penetration is proposed by modifying the traditional particle-to-particle contact model. The proposed contact model is verified through two typical benchmark tests, and the calculated results are compared with the traditional pin-ball contact model and short-range-force contact model. The results demonstrate the correctness and advantages of the proposed model. Bond-Based Peridynamics equipment with the proposed contact model is used to analyze the Brazilian tensile test of rocks. The elastic deformation and fracture evolution show a high agreement with the analytical solution and experimental results, demonstrating the effectiveness and robustness of the proposed contact model. Based on the Brazilian tensile test, a method to verify the correctness of contact models is proposed. The differences in numerical results obtained with the proposed contact model and the short-range force model are compared, and the mechanism underlying the differences are investigated. In addition, Graphics Processing Units (GPU) are used to implement parallel computation to improve efficiency. This research contributes to the understanding of the mechanism of Brazilian tensile test. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study on thermal jet drilling of granite rock that is based on a thermal spallation phenomenon. For this end, a numerical method based on finite elements and a damage–viscoplasticity model are developed for solving the underlying coupled thermo-mechanical problem. An explicit time-stepping scheme is applied in solving the global problem, which in the present case is amenable to extreme mass scaling. Rock heterogeneity is accounted for as random clusters of finite elements representing rock constituent minerals. The numerical approach is validated based on experiments on thermal shock weakening effect of granite in a dynamic Brazilian disc test. The validated model is applied in three-dimensional simulations of thermal jet drilling with a short duration (0.2 s) and high intensity (approx. 3 MW m−2) thermal flux. The present numerical approach predicts the spalling as highly (tensile) damaged rock. Finally, it was shown that thermal drilling exploiting heating-forced cooling cycles is a viable method when drilling in hot rock mass. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on the modelling of mixed‐mode fracture using the conventional smoothed particle hydrodynamics (SPH) method and a mixed‐mode cohesive fracture law embedded in the particles. The combination of conventional SPH and a mixed‐mode cohesive model allows capturing fracture and separation under various loading conditions efficiently. The key advantage of this framework is its capability to represent complex fracture geometries by a set of cracked SPH particles, each of which can possess its own mixed‐mode cohesive fracture with arbitrary orientations. Therefore, this can naturally capture complex fracture patterns without any predefined fracture topologies. Because a characteristic length scale related to the size of the fracture process zone is incorporated in the constitutive formulation, the proposed approach is independent from the spatial discretisation of the computational domain (or mesh independent). Furthermore, the anisotropic fracture responses of materials can be naturally captured thanks to the orientation of the fracture process zone embedded at the particle level. The performance of the proposed approach demonstrates its potentials in modelling mixed‐mode fracture of rocks and similar quasi‐brittle materials. [ABSTRACT FROM AUTHOR]

The impact of changes in active‐layer thickness on the depth of pervasive macrofracturing (brecciation) in frost‐susceptible bedrock is unclear but important to understanding its physical properties and geohazard potential. Here we report results from a laboratory experiment to test the hypothesis that active‐layer deepening drives an increase in the depth of brecciation. The experiment simulated active‐layer deepening in 300 mm cubic blocks of limestone (chalk) and sandstone. Temperature, surface heave and strain at depth were measured during 16 freeze–thaw cycles. Macrocracks photographed at intervals were digitally analyzed to visualize crack growth and to quantify crack inclination and length. In chalk, an upper horizon of macrocracks developed first at about 100 mm depth in a shallow active layer during cycles 1–8, followed by a lower horizon at about 175–225 mm depth in a deeper active layer during cycles 9–16. The longest cracks (>35 mm) were most common at inclinations of 0–30° from the horizontal, and numerous cracks <5 to 15 mm long developed at inclinations of 40–50°, with some longer vertical to subvertical cracks linking the two brecciated horizons. Overall, the observations support the hypothesis that a thickening active layer drives deeper rock fracture by ice segregation. [ABSTRACT FROM AUTHOR]

This study numerically investigates the damage process in a granite using an inelastic multiminerallic block model in two‐dimensional Universal Distinct Element Code. In addition to the commonly considered calibration targets like uniaxial and triaxial strengths, tensile strength, and Young's modulus, attention was paid to reproduce additional attributes such as postpeak response, residual strengths, and confinement‐dependent dilatancy to minimize the nonuniqueness potential of the models. The fracture pattern transitioned from axial cracking to shear banding as the specimen confinement was increased from 0 to 60 MPa. Most notably, the model could exhibit the cohesion‐weakening‐frictional‐strengthening behavior that is typically associated with brittle rocks. The progressive damage mechanism in the unconfined bonded block model (BBM) was subsequently studied using the 2‐D digital image correlation (2‐D‐DIC) approach. To date, the application of the 2‐D‐DIC approach has been restricted only to real material testing; this study, therefore, is an attempt to extend its applicability to numerical models. It was found that 2‐D‐DIC is capable of imaging the simulated microcracking process very well and the results were similar to those observed from real testing on a different granitic rock. Lastly, the numerical‐based DIC results were analyzed to clarify that even if the point of axial stress‐axial strain nonlinearity does not coincide with the point of volumetric strain reversal in unconfined BBMs, the axial stress‐axial strain nonlinearity approach should always be used for determining the crack damage threshold in BBMs. Key Points: This study explores the capability of bonded block models to replicate the prepeak and postpeak attributes of a granitic rockThe model exhibited a degradation of specimen‐scale cohesion and mobilization of friction angle with increase in damageTwo‐dimensional digital image correlation analysis was conducted on the model results to evaluate the changes in strain field [ABSTRACT FROM AUTHOR]

Summary: This paper presents a numerical investigation on the effects of thermal shock as a pretreatment of rock prior to comminution. More specifically, the effect of heat shock‐induced cracks on the uniaxial compressive strength of rock is numerically studied. The chosen constitutive model of rock employs a (strong) embedded discontinuity finite element formulation to describe cracks. The thermomechanical problem that governs the heat shock pretreatment of rocks is considered as an uncoupled problem because of a highly dominating role of the external heat influx. Two solution methods of the global problem are presented: an explicit‐explicit dynamic scheme and an implicit‐implicit quasi‐static scheme. The model performance is tested in simulations on heterogeneous numerical rock samples subjected first to a heat shock pretreatment and then to a mechanical compression test. According to the results, the compressive strength of intact granite rock having the axial splitting failure mode can be substantially reduced by heat shock pretreatment. [ABSTRACT FROM AUTHOR]

The fracturing of six granite cubes (400 × 400 × 400 mm3) in response to blast loading was investigated using a combination of data collected from strain gauges and generated by digital image correlation (DIC) of pictures captured using a high-speed camera. This instrumentation permits the observation of the crack initiation, crack opening velocity, fracture pattern, full-field strain variation, and fragment movement at the cube's surface. In each experiment, an explosive charge was positioned at the center of the block in a vertical drill hole. Two charge weights, 6 g and 12 g, of pentaerythritol tetranitrate (PETN) were used. Using the high-speed camera, dominant vertical cracks were found to initiate on the surface of the cubes within 250 µs of the charge detonation. Two or three dominant vertical cracks appeared in specimens with a 12 g charge, while a single dominant vertical crack came into view in specimens with a 6 g charge. In addition, a single dominant horizontal crack was observed in all specimens, irrespective of charge weight. The maximum concentration of strain obtained from a DIC analysis agreed well with the dominant cracks and fracture patterns observed in the specimens. By combining the results from the strain gauges and the results from the DIC analysis for the specimen with a 12 g charge, the first crack initiation was found to occur at 67 µs after detonation. The crack opening velocities were determined using a boundary identification method and ranged from 5.0 to 7.6 m s−1, whereas the observed in-plane fragment velocities were slightly less. These experiments may contribute to a better understanding of the fundamental mechanisms of the rock fracture by blasting. [ABSTRACT FROM AUTHOR]

Abstract A new computational approach combining the Smooth Particle Hydrodynamics and a constitutive model that possesses an intrinsic length scale is proposed in this study for modelling rock fracture. In particular, a continuum-based size-dependent constitutive model with an embedded fracture process zone described by a cohesive model is adopted for modelling strain localisation in geomaterials. A length scale is introduced into the constitutive equations to describe the scale effect commonly observed in localised failure of geomaterials. The constitutive model is then employed in a mesh-free Taylor Smooth Particle Hydrodynamics (Taylor-SPH) framework to produce a new computational tool for rock fracture modelling. The key feature of the proposed numerical framework is that it describes the fracture geometry by a set of Lagrangian particles, which carry fracture information such as damage evolution and fracture orientation, thus bypassing the need to represent the fracture's topology and fracture orientation. To test the capability of this computational framework in simulating rock fracture behaviour, three mode-I numerical fracture tests including three-point bending test, Brazilian-disc test and semi-circular bending test are carried out and results validated with experimental data in the literature. The good agreement between numerical and experimental results suggests that the proposed method is a promising numerical approach to modelling rock fracture. [ABSTRACT FROM AUTHOR]

Abstract The physics of electromagnetic radiation due to rock facture is complex, and understanding of this phenomena and its relationship with the extent of rock damage is imperative and remains challenging. In this paper, the relationship between the electric dipole moment and the stress change rate at the crack tip and the crack propagation characteristics are established. The stress change process is divided into three stages, the characteristics of electric dipole moment of each stage are analyzed. Simulation studies showed that the dipole frequencies, the angles between the electric dipole and detectors have a significant influence on the detection of those radiations. Self-expanding destructive experiments were designed and carried out for different types of rocks to observe more details of this phenomenon. In the rupture process of the sample, a number of electromagnetic radiation signals were detected. The duration of the signal is about 2 to 3 ms, and the interval between signals varies from 23 to 210 ms. The spectrum of the signal is between 4 kHz and 50 kHz. The complex variation of the signal spectrum and amplitude are due to the different electric dipoles produced by the different stages of crack propagation, and the change in the distance and angle of the radiation source from the detector during the crack propagation. [ABSTRACT FROM AUTHOR]

Numerous rock engineering applications require a reliable estimation of fracture permeabilities to predict fluid flow and transport processes. Since measurements of fracture properties at great depth are extremely elaborate, representative fracture geometries typically are obtained from outcrops or core drillings. Thus, physically valid numerical approaches are required to compute the actual fracture geometries under in situ stress conditions. Hence, the objective of this study is the validation of a fast Fourier transform (FFT)-based numerical approach for a circular granodiorite fracture considering stress-dependent normal closure. The numerical approach employs both purely elastic and elastic-plastic contact deformation models, which are based on high-resolution fracture scans and representative mechanical properties, which were measured in laboratory experiments. The numerical approaches are validated by comparing the simulated results with uniaxial laboratory tests. The normal stresses applied in the axial direction of the cylindrical specimen vary between 0.25 and 10 MPa. The simulations indicate the best performance for the elastic-plastic model, which fits well with experimentally derived normal closure data (root-mean-squared error = 9 µm). The validity of the elastic-plastic model is emphasized by a more realistic reproduction of aperture distributions, local stresses and contact areas along the fracture. Although there are differences in simulated closure for the elastic and elastic-plastic models, only slight differences in the resulting aperture distributions are observed. In contrast to alternative interpenetration models or analytical models such as the Barton-Bandis models and the “exponential repulsion model”, the numerical simulations reproduce heterogeneous local closure as well as low-contact areas (< 2%) even at high normal stresses (10 MPa), which coincides with findings of former experimental studies. Additionally, a relative hardness value of 0.14 for granitic rocks, which defines the general resistance to non-elastic deformation of the contacts, is introduced and successfully applied for the elastic-plastic model. [ABSTRACT FROM AUTHOR]

Shear deformation-induced hydraulic conductivity change in fracture has been studied for decades. However, the existing models to link shear deformation and hydraulic behaviors are less accurate due to complex flow in rock fractures. This study presents an improved flow model for calculating nonlinear flow behaviors in rock fractures during shear. In this model, the linear and nonlinear coefficients in the Forchheimer equation were determined using mechanical aperture and fracture roughness coefficients. The mechanical aperture was equal to the initial aperture plus the change of the aperture due to shear-induced dilation. The dilation curve was divided into three stages and analytical expressions for modeling the dilation curve were established by incorporating the joint roughness coefficient (JRC) and the mobilized roughness coefficient (JRCmob). In addition, shear-flow tests were conducted on marble and granite fractures with normal stress between 0.5 and 3.0 MPa. The experimental data were used to verify the proposed model. The results show that the proposed model predicts flow in rock fractures well. [ABSTRACT FROM AUTHOR]

Monitoring and predicting crack propagation in rock using acoustic emission (AE) technology is integral to a variety of sub-disciplines in the geosciences. The utility of existing AE data, however, is severely limited by prevailing visualization techniques, which suffer from problems of occlusion. Here, we introduce a novel approach to visualize 3D data through time (4D data) using unfiltered individual (AE) event data collected from a granite boulder for a period over 3 years. We implement a 3D extension of Ripley’s K function to evaluate the magnitude of clustering, and use the scale at which clustering is strongest to parameterize three-dimensional kernel density estimation (3DKDE) of AE events. We develop a parallel approach that features a load balancing technique to decrease the computational effort for 3DKDE and hence, reduce execution time. The results from the 3DKDE allow for comprehensible visualization of high AE density areas—best reflecting the actual location of subcritical cracking—and their changes through time, which is a substantial improvement over most existing methods. Our framework is scalable and portable to a variety of other disciplines such as epidemiology, ecology, and any point data by extension. Assumptions and limitations are identified as well as possible future research directions. [ABSTRACT FROM AUTHOR]

This paper presents a systematic research for understanding mechanical shearing effects on the fluid flow and the solute transport behavior of rough fractures through a numerical simulation approach. The aperture fields were modeled based on a real rock fracture geometry and the normal displacement obtained from the shear-flow test. The fluid flow through the rough fracture under shear was simulated using a finite element code that solves the Reynolds equation, and the transport behavior through the rough fracture under shear was simulated calculating the advection–dispersion equation. The results show that the fracture apertures increase as the shear displacement increases, with a few major flow channels detected through the fracture. The shear-induced flow channels increase both flow connectivity and transport connectivity, which accelerate the movement of solutes in a particular direction and lead to early breakthrough of the contaminants. Adsorption, acting as a retardation term, has a decisive influence on the transport process. These results can give a basic knowledge of the hydromechanical and solute transport progress through fracture, and will be helpful to safety assessment for high-level radioactive waste disposal facilities. [ABSTRACT FROM AUTHOR]

The effect of water on the shear behavior of joints in rocks is critical for determining the global stability of fractured rock slopes subjected to changes in water levels, because the joint peak shear strength can be significantly lowered owing to wetting. The roles of the mechanical and the combined physical and chemical water-rock interactions in the deformation of reservoir bank slopes are studied using discrete element method. The numerical results showed that the joints that are subparallel to the slope surface mainly determine the displacements of rock blocks and that water-rock interaction-induced deterioration of joint shear stiffness and strength plays a critical role in the stability of reservoir bank slopes. The weakening of rock fractures induced by interactions between water and fracture walls can explain the monitored valley contraction during the impoundment of high dams. [ABSTRACT FROM AUTHOR]

A new resin material has been developed by massive formula exploration. The resin is thoroughly transparent and rock-like at low temperatures. Its tension-compression strength ratio is up to 1/6.6 in the temperature range of − 10 to − 15 °C. It can simulate quite a few kinds of engineering rocks. Specimens have been made with two internal cracks. The progressive failures under uniaxial and biaxial compressions are systematically studied. The uniaxial failure process is divided into four stages as conventional rock mechanics test. Several forms of secondary cracks, like anti-wing cracks in the biaxial experiment with high lateral pressure, have seldom been described by former scholars. Three-dimensional numerical simulation has been conducted using FLAC3D. A novel elastic-brittle constitutive model is developed and programed. Superfine mesh generation is demanded as well. Both uniaxial and biaxial results of the new numerical approach show excellent consistency with experimental results in this paper. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • 3D numerical modelling of rock fracture was developed by a hybrid finite and cohesive element method (FCEM). • Simulations of Brazilian disc and uniaxial compression test obtained rock micro-parameters. • Rock breaking mechanism and chip shape similarity were confirmed using FCEM. • Pick sharpness and self-rotation should be considered for reducing penetration force and pick-tip wear. Abstract To investigate the rock fracture, penetration force, and chip shape during rock breaking with a conical pick, a 3D numerical model was developed by inserting cohesive elements into finite elements. Mixed-mode cohesive traction response was applied to describe the micromechanics of rock cementation, which was also able to reflect the rock damage process and crack propagation associated with the zero-thickness elements. Simulations of Brazilian disc tests and uniaxial compression tests were used to verify the proposed numerical model and obtain rock micro-parameters, and a comparison of the penetration forces in the experimental and simulation results confirmed the accuracy and efficiency of the proposed method. Similar to the experimental phenomena of rock fracture with a conical pick, the rock crushing zone, microscopic radial cracks, macroscopic dominating crack, and main chip were produced successfully with the numerical model. Quantitative analysis of the rock fracture features (penetration force and chip shape) and breaking parameters of the conical pick revealed some valuable relationships between them, which can provide useful information for the optimal design of conical picks or breaking devices with multiple conical picks for mechanical excavation. [ABSTRACT FROM AUTHOR]

A multi-physics numerical model was developed to predict the fluid flow and mass transport behavior of rock fractures under coupled thermal-hydraulic-mechanical-chemical (THMC) conditions. In particular, the model was employed for the purpose of describing the evolution of permeability and reactive transport behavior within rock fractures by taking into account the geochemical processes of the free-face dissolution and the pressure dissolution. In order to examine the capability of the developed model, the model was applied to replicate the experimental measurements of the evolution in hydraulic aperture, permeability, and element concentrations obtained from two flow-through experiments using single granite and mudstone fractures. The model predictions for the granite experiment were able to follow the actual data for the evolution in hydraulic aperture and effluent element concentrations without adopting any fitting parameters that are often used in other THMC coupled models obtained from literature. Furthermore, the model succeeded in replicating the actual changes in fracture permeability and effluent element concentrations within the mudstone fracture. Although some uncertain mismatches between the experiments and the model predictions, such as changes in the concentrations of several elements (i.e., Na and K concentrations in the granite fracture and Al in the mudstone fracture) were remaining at this stage, the developed model should be valid for evaluating the evolution in the fluid flow and mass transport behavior within rock fractures induced by mineral dissolution under stress- and temperature-controlled conditions. [ABSTRACT FROM AUTHOR]

Fluid flow in single rock fractures considering the influences of fracture surface roughness, shearing process, normal loading, and so on has been extensively studied for several decades, yet the significant influence of fillings has not been systematically investigated due to the numerous difficulties such as determination of the physical parameters of fillings. The present study aims to estimate the hydraulic properties of single fractures filled with different graded and gap-graded fillings, based on a series of flow tests on rock-like samples using the MTS815.02 material testing system. With the increment of fracture aperture, the pressure drops before and after fillings are flowed away decrease, whereas the permeabilities before and after fillings are flowed away increase. When the ratio of mechanical aperture of fractures to maximum diameter of fillings decreases from 4 to 1.33, both pressure drop and permeability change significantly before the fillings are flowed away and then hold constant values after the fillings are flowed away. Due to the effects of fraction force and interlocking force between particles, the ratio of mechanical aperture to maximum diameter of fillings that equals to 2.67 is the inflection point, where the pressure drop has the maximum value and permeability has the minimum value. When the fractures are filled with gap-graded fillings, in which the ratio of mechanical aperture of fractures to mean diameter of fillings decreases from 5.76 to 1.45, the variations of both pressure drop and permeability before fillings are flowed away change more significantly than those after fillings are flowed away. The hydraulic aperture of fractures with fillings is approximately 2-3 orders of magnitude smaller than the mechanical aperture. [ABSTRACT FROM AUTHOR]

A better understanding of solute transport and retention mechanism in rock fractures has been challenging due to difficulty in their direct observations in microscale rough-walled fractures. Six representative troughs in a rough-walled fracture were selected for microscale observations of eddy formation with increasing flow velocity and its effect on spatiotemporal changes of solute concentration. This experimental study was enabled by a microscale visualization technique of micro particle image velocimetry. With increasing flow velocity (Re ≤ 2.86), no eddies were generated, and solutes along the main streamlines transported rapidly, whereas those near the wall moved slowly. A larger amount of solutes remained trapped at all troughs at Re = 2.86 than Re < 1. For Re = 8.57, weak eddies started to be developed at the troughs on the lee side, which little contributed to overall solute flushing in the fracture. Accordingly, a large of amount of water was needed for solute flushing. The flow condition of 1 < Re < 10, before a full development of eddies, was least favourable in terms of time and amount of remediation fluid required to reach a target concentration. After large eddies were fully developed at troughs on the lee side for Re = 17.13, solutes were substantially reduced by eddies with less amount of water. Fully developed eddies were found to enhance solute transport and recovery, as opposed to a general consensus that eddies trap and delay solutes. Direct inflow into troughs on the stoss side also made a great contribution to solute flushing out of the troughs. This study indicates that fully developed eddies or strong inflows at troughs are highly possible to form for Re > 10 and this flow range could be favourable for efficient remediation. [ABSTRACT FROM AUTHOR]

The convective heat transfer coefficient (HTC) is a useful indicator that characterizes the convective heat transfer properties between flowing fluid and hot dry rock. An analytical method is developed to explore a more realistic formula for the HTC. First, a heat transfer model is described that can be used to determine the general expression of the HTC. As one of the novel elements, the new model can consider an arbitrary function of temperature distribution on the fracture wall along the direction of the rock radius. The resulting Dirichlet problem of the Laplace equation on a semi-disk is successfully solved with the Green's function method. Four specific formulas for the HTC are derived and compared by assuming the temperature distributions along the radius of the fracture wall to be zeroth-, first-, second-, and third-order polynomials. Comparative verification of the four specific formulas based on the test data shows that the formula A corresponding to the zeroth-order polynomial always predicts stable HTC values. At low flow rates, the four formulas predict similar values of HTC, but at higher flow rates, formulas B and D, respectively, corresponding to the first- and third-order polynomials, predict either too large or too small values of the HTC, while formula C, corresponding to the second-order polynomial, predicts relatively acceptable HTC values. However, we cannot tell which one is the more rational formula between formulas A and C due to the limited information measured. One of the clear advantages of formula C is that it can avoid the drawbacks of the discontinuity of temperature and the singular integral of HTC at the points (± R, 0). Further experimental work to measure the actual temperature distribution of water in the fracture will be of great value. It is also found that the absorbed heat of the fluid, Q, has a significant impact on the prediction results of the HTC. The temperatures at the inlet and the outlet used for Q should be consistent with the assumptions adopted in the derivation of its corresponding HTC formula. A mismatched value of Q might be the reason that some existing HTC formulas predict negative or extremely large HTCs at high flow rates. [ABSTRACT FROM AUTHOR]

Based on a combined finite-discrete element method (FDEM), this study builds a coupled thermo-mechanical model (termed FDEM-TM) to simulate thermal cracking of rock. The coupled thermo-mechanical model consists of two major parts. In the first part the temperature distribution of the system is analyzed based on the heat conduction equation. In the second part the thermal stress caused by temperature change is added to perform mechanical fracture calculation. Based on these two parts, we can model rock fracture driven by thermo-mechanical coupling. Three examples with analytic solutions are used to verify the correctness of the model in dealing with the problems of steady-state heat conduction, unsteady-state conduction, and thermal-mechanic coupling, respectively. In addition, an example of thermal cracking is also given and compared with the experimental results. The simulation results are in excellent agreement with the analytical solutions or experimental results, verifying the correctness of the coupled thermo-mechanical model to simulate thermal cracking. The proposed method provides a new tool for thermal-mechanical coupling problems in geothermal exploitation. [ABSTRACT FROM AUTHOR]

The normal stiffness of a fracture is a key parameter that controls, for example, rock mass deformability, the change in hydraulic transmissivity due to stress changes, and the speed and attenuation of seismic waves that travel across the fracture. Non-linearity of normal stiffness as a function of stress is often attributed to plastic yield at discrete contacts. Similar surface-altering mechanisms occur due to pressure solution and precipitation over larger timescales. These processes partition the fracture surfaces into a flattened contact region, and a rough free surface that bounds the void space. Under low loads, contact occurs exclusively over the flattened part, leading to rapid, exponential stiffening. At higher loads, contact occurs over the rough surface fraction, leading to the conventional linear increase of stiffness with stress. It follows that a relationship exists between the history of in situ temperature and stress state of a rock fracture, and its subsequent deformation behavior. [ABSTRACT FROM AUTHOR]

A new rock-like resin has been developed after extensive formula research. This resin is completely transparent and low temperature brittle. Its tension-compression ratio can reach 1/6.6 in the −10 to −15 °C temperature range. It can simulate many kinds of engineering rocks. Specimens are made with a single internal crack. The progressive failure processes of specimens under uniaxial and biaxial compressions are investigated. The uniaxial failure process of specimens is divided into four stages. Some forms of secondary cracks, like anti-wing cracks in biaxial test, have never been reported in previous studies. 3-D numerical simulation is carried out using FLAC3D. A new elastic-brittle constitutive model is developed in the simulation. Superfine element division is also required. The uniaxial and biaxial numerical results of the new method possess an excellent consistency with experiment results in this paper. [ABSTRACT FROM AUTHOR]

Rock fractures are major conduits for fluid flow in fractured rocks, and the convective heat transfer between rock fracture surfaces and circulating fluid is a critical issue in heat recovery in fractured rocks. It has been demonstrated that fracture surface roughness has a significant influence on the mechanical, hydraulic, thermal and transport behavior of single fractures. This study aimed to assess the effects of local surface roughness of fractures on fluid flow and heat transfer processes at the macroscopic scale of fracture networks. Two distributions of Joint Roughness Coefficient (JRC) were determined based on the JRC data in Oskarshamn/Forsmark, Sweden and Bakhtiary, Iran. Two empirical models relating hydraulic apertures to mechanical apertures were considered. A total of ninety-one realizations that considered different JRC distributions and empirical models of mechanical-hydraulic apertures were studied. The results show that fracture surface roughness can affect the fluid flow and heat transfer processes in fracture networks to various extents, mainly depending on the empirical models of mechanical-hydraulic apertures. In other words, the role of fracture surface roughness in macroscopic fluid flow and heat transfer in fractured rocks is critical, when using a model of mechanical-hydraulic apertures that predicts significant reduced hydraulic apertures. Discrete fracture networks models with the normal distribution of JRC are less permeable than those with the lognormal distribution of JRC, using the fitting parameters of in-situ JRC data. [ABSTRACT FROM AUTHOR]

The friction factor is an important dimensionless parameter for fluid flow through rock fractures that relates pressure head loss to average flow velocity; it can be affected by both fracture geometry and flow regime. In this study, a theoretical formula form of the friction factor containing both viscous and inertial terms is formulated by incorporating the Forchheimer equation, and a new friction factor model is proposed based on a recent phenomenological relation for the Forchheimer coefficient. The viscous term in the proposed formula is inversely proportional to Reynolds number and represents the limiting case in Darcy flow regime when the inertial effects diminish, whereas the inertial term is a power function of the relative roughness and represents a limiting case in fully turbulent flow regime when the fracture roughness plays a dominant role. The proposed model is compared with existing friction factor models for fractures through parametric sensitivity analyses and using experimental data on granite fractures, showing that the proposed model has not only clearer physical significance, but also better predictive performance. By accepting proper percentages of nonlinear pressure drop to quantify the onset of Forchheimer flow and fully turbulent flow, a Moody-type diagram with explicitly defined flow regimes is created for rock fractures of varying roughness, indicating that rougher fractures have a large friction factor and are more prone to the Forchheimer flow and fully turbulent flow. These findings may prove useful in better understanding of the flow behaviors in rock fractures and improving the numerical modeling of non-Darcy flow in fractured aquifers. [ABSTRACT FROM AUTHOR]

The size of a fracture within a rock mass can be obtained using data sampled from boreholes or exposed surfaces. In this study, fracture sizes are estimated using data from multiple boreholes. The fractures are assumed to be elliptical, all having the same aspect ratio, but not necessarily occurring parallel to each other. Formulae for estimating the mean and standard deviation of the characteristic fracture size are developed by considering the number of intersections between the fractures and the boreholes. A method is proposed to infer the probability density function of the fracture size from the number of fractures, which is obtained by random sampling of fractures in adjacent boreholes; the fracture distribution is assumed to follow the form of a fractal, exponential, or lognormal distribution. The performance of the method is validated using Monte Carlo simulations with different inputs of size distribution, fracture density, orientation, and mean fracture size. [ABSTRACT FROM AUTHOR]

The article discusses the study on the use of the effective stress principle for partially saturated fractures in rocks. Topics include analysing the surface morphology and aperture distribution of rock fractures, introducing suction on partially saturated fractured rocks, and fluid distribution and effective stress principle in partially saturated rough-walled fractures.

The rock fracture detection by image analysis is significant for fracture measurement and assessment engineering. The paper proposes a novel image segmentation algorithm for the centerline tracing of a rock fracture based on Hessian Matrix at Multi-scales and Steger algorithm. A traditional fracture detection method, which does edge detection first, then makes image binarization, and finally performs noise removal and fracture gap linking, is difficult for images of rough rock surfaces. To overcome the problem, the new algorithm extracts the centerlines directly from a gray level image. It includes three steps: (1) Hessian Matrix and Frangi filter are adopted to enhance the curvilinear structures, then after image binarization, the spurious-fractures and noise are removed by synthesizing the area, circularity and rectangularity; (2) On the binary image, Steger algorithm is used to detect fracture centerline points, then the centerline points or segments are linked according to the gap distance and the angle differences; and (3) Based on the above centerline detection roughly, the centerline points are searched in the original image in a local window along the direction perpendicular to the normal of the centerline, then these points are linked. A number of rock fracture images have been tested, and the testing results show that compared to other traditional algorithms, the proposed algorithm can extract rock fracture centerlines accurately. [ABSTRACT FROM AUTHOR]

Summary This study focuses on experimental evaluation of the Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures. Water flow tests through twelve granite fracture samples with different roughness were conducted in a triaxial cell under confining stresses varying from 1.0 MPa to 30.0 MPa. A total of 2280 experimental data in the form of pressure gradient versus discharge were collected. Three representative types of nonlinear flow behaviors induced by inertial effect, fracture dilation and solid–water interaction, respectively, were observed. Regression analyses of the experimental data show that the Forchheimer equation adequately describes the non-Darcy flow behavior induced by significant inertial effect. Based on the experimental observations, two empirical equations were proposed for parametric expression of the Forchheimer’s nonlinear coefficient, one as a power function of hydraulic aperture and the other dependent on both hydraulic aperture and peak asperity of the fracture surface. A new criterion was presented for assessing the applicability of Darcy’s law, which relies on the ratio of discharge or pressure gradient predicted by the Forchheimer’s law incorporated with the single-parameter equation to that predicted by the Darcy’s law. A sensitivity analysis was performed using the double-parameter equation for examining the dependence of the Forchheimer’s nonlinear coefficient on peak asperity, demonstrating the importance of incorporating the fracture roughness in the development of non-Darcy flow models. The experimental results and the proposed models are useful for understanding and numerical modeling of the nonlinear flow behaviors in fractured aquifers. [ABSTRACT FROM AUTHOR]

Although uniaxial compression testing of rock is considered a simple technique for evaluation of rock strength, it induces a complicated fracture pattern in the specimen that is difficult to comprehend. In particular, axial splitting is observed in uniaxial compression tests. There have been some attempts to interpret the failure pattern in compression testing of rock. The rock non-homogeneity and existence of initial micro-cracks and pores have been considered the main causes for nucleation of axial cracks. Based on some physical uniaxial compression tests on Pennsylvania blue sandstone, we suggest another possible mechanism, which considers the rock–loading platen interaction for generation of axial cracks in rock. In particular, this failure mechanism can occur in rock pillars which are loaded by the roof or floor that is made of a rock with different elastic properties. The non-uniform penetration of specimen in the loading platens and the end friction produce shear strain that can be the cause of axial shear cracking at the specimen ends. Dislocation along these axial shear cracks and the induced material dilation generate radial stresses which result in confinement of the core of the specimen and radial cracks in the vicinity of the specimen end surfaces. As a consequence of axial and radial cracks, rock pieces in the form of cantilever beams are generated around the specimen free surface. These rock pieces can break in tension in mode I fracture due to the internal radial stresses. Based on the physical observations, a simple mathematical model is proposed to explain the fracture pattern observed in the physical tests. Furthermore, a bonded particle numerical model for rock, together with a finite element simulation of the loading machine, is used to show how the applied boundary conditions and loading machine stiffness can affect the failure pattern. [ABSTRACT FROM AUTHOR]

Fast closure of rock fractures has been commonly observed in the initial stage of fluid flow experiments at environmental temperatures under low or moderate normal stresses. To fully understand the mechanisms that drive this fast closure, the evolution of local stresses acting on contacting asperities on the fracture surfaces prior to fluid flow tests needs to be evaluated. In this study, we modeled numerically the asperity deformation and failure processes during initial normal loading, by adopting both elastic and elastic-plastic deformation models for the asperities on a real rock fracture with measured surface topography data, and estimated their impact on initial conditions for fluid flow test performed under laboratory conditions. Compared with the previous models that simulate the normal contact of a fracture as the approach of two rigid surfaces without deformations, our models of deformable asperities yielded smaller contact areas and higher stresses on contacting asperities at a given normal stress or normal displacement. The results show that the calculated local stresses were concentrated on the contacts of a few major asperities, resulting in crushing of asperity tips. With these higher contact stresses, however, the predicted closure rates by pressure solution are still several orders of magnitude lower than that of the experimental measurements at the initial stage of fluid flow test. This indicates that single pressure solution may not likely to be the principal compaction mechanism for this fast closure, and that the damages on contacting asperities that occur during the initial normal loading stage may play an important role. Copyright © 2015 John Wiley & Sons, Ltd. [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]

• FEMR is owing to the dangling bond atoms in the nonlinear field. • FEMR generation model is related to the two states of dipole oscillation. • An equivalent electromagnetic field source model of rock fracture is constructed. • The proposed frequency domain index effectively represents the FEMR directionality. The electromagnetic radiation generated during the fracturing process is generally regarded as vector field that holds an imperative significance in rock engineering and fracture mechanics. With this motive, based on the theory of fracture mechanics and electromagnetics, the nonlinear field at the crack tip and the atomic bond breaking condition are analyzed in this study. Considering the electromagnetic field pattern generated by the oscillating dipole, the generation process of the electromagnetic radiation signal is divided into two stages namely, initiation of the forced oscillation of the dipole and the damped dipole oscillation. Followed by this, the experimental investigations on limestone and shale under the condition of Brazilian tests are performed. In the whole loading process, four sets of three-axis electromagnetic antennas are used for simultaneous measurement in different directions. The experimental and theoretical results exhibit close resemblance. The superposition effect of the electromagnetic field from microcrack initiation to macro-fracture is analyzed further. Based on the obtained results, three indicators are proposed to characterize the directionality of the electromagnetic radiation generated by the rock fracture. It is observed that the changing law of the direction angles is consistent, showing a strong correlation with the symmetrical position. The direction of the magnetic flux density vector generated by rock Brazilian tests tends to be parallel to the crack surface. [ABSTRACT FROM AUTHOR]

• The modified cutter can generate more connections between the surface and internal cracks and form even larger number of chips. • The modified cutter consumes nearly the same amount of energy as the CCS cutter. • The tensile stress concentrations are responsible for internal and surface crack propagation. Connections between surface and internal cracks are critical to rock fractures between kerfs. To promote rock fracture, a modified cutter containing wedge-shaped cutting teeth was invented. Then, comparison linear cutting tests were performed using a CCS and a modified cutter. The results indicate that the modified cutter can promote surface crack incisions (most frequently initiating from the contact points between cutting teeth and rock) and generate an increased number of chips. The modified cutter consumes nearly the same energy as the CCS cutter. Thus, the cutting efficiency of the modified cutter is higher. To further investigate the underlying mechanism, the dynamic stress evolution between kerfs (using PFC 3D) is studied. The numerical results agree well with laboratory tests in rock fractures and indicate that tensile stress concentrations are responsible for the initiation of internal and surface cracks. In addition, theoretical analysis using elastic–plastic fracture mechanics properly explains the formation of the regularly distributed surface cracks caused by the modified cutter. [ABSTRACT FROM AUTHOR]

The article presents a study which described the impact of fracture surface roughness on solute transport and fluidic flow in fracture networks. The researchers simulated the flow and transport processes in two different fracture networks. It implied that understanding the fluid flow and solute migration in fracture networks for rocks may be critical to many applications, such as underground nuclear waste repositories, carbon dioxide sequestration, and enhanced geothermal systems.

The double-primer placement is based on the principle of shock wave collision. When two shock waves meet each other, the final pressure is greater than the sum of the initial two pressures. Stress analysis indicates that this should be favorable to rock fracture and fragmentation in blasting. This double-primer placement was tested in Malmberget mine by using electronic detonators, aiming to improve rock fragmentation. At the same time, another method, named DRB (Dividing Ring Blasting), was tested, too. Two production drifts in an ore body were taken as test drifts. In each test drift both methods were tried. For comparison, two nearest production drifts to the test drifts were taken as reference drifts. The results showed that on average the double-primer placement recovered more iron ore than either the DRB method or the ordinary method used in the reference drifts. In addition, fragmentation looked much finer and the eyebrow break became much less for the double-primer rings, compared with the reference rings. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with numerical and experimental research of percussive drilling. A finite element based modelling approach, developed earlier by the authors, was employed in the simulation of the dynamic bit-rock interaction process. The rock fracture in this approach was modelled with a damage-viscoplasticity model accounting for the main fracture types in the bit-rock interaction as well as the strain-rate effects. In the experimental part of the work, dynamic indentation tests were carried out on Kuru granite using a special triple-button drill bit where the buttons were inserted at the vertices of an equilateral triangle. The purpose of these experiments was to provide data on the fracture of the hard rock under percussive drilling action and to find the (experimental setup specific) striker impact velocity that leads to lateral chipping, i.e. material removal of rock between the adjacent bit-buttons. Despite the statistical nature of rock behaviour, which lead to the material removal at several striker impact velocities, these experiments provide a suitable validation problem for codes designed for numerical modelling of percussive drilling. The present modelling technique reproduced the experimental data with good accuracy in tests where the stress wave amplitude in the drill rod was up to 200 MPa. This stress level is seldom exceeded practical rock drilling. The simulation results deviated from the experimental results in the experiments with higher stress amplitude, which is probably due to the continuum assumption of the present modelling approach. [Copyright &y& Elsevier]

This study presents a methodology for estimating the unsaturated hydraulic properties of rock fractures under deformation conditions. The surface morphology of an artificial granite rock fracture was examined using a high-resolution three-dimensional laser scanner, and the aperture distribution of the fracture was found to follow a Gaussian distribution. By virtue of the aperture distribution function and applying the Young-Laplace equation to local apertures, a novel model was presented to predict the capillary pressure-saturation relationship and the relative hydraulic conductivity of rough-walled rock fractures subjected to normal and shear loading. The proposed model was partially validated against existing laboratory data on the unsaturated hydraulic properties of rock fractures, and can be readily applied to various engineering practices such as transport phenomena in fractures, landslide mitigation, or underground oil storage. [ABSTRACT FROM AUTHOR]

The objective is to assess the performance of sludge mixed with commercial grade Portland cement type I for use in minimizing the permeability of fractured rock mass. The fractures were artificially made by applying a line load to sandstone block specimens. The sludge comprises over 80% of quartz with grain sizes less than 75 µm. The results indicate that the mixing ratios of sludge:cement (S:C) of 1:10, 3:10, 5:10 with water:cement ratio of 1:1 by weight are suitable for fracture grouting. For S:C = 3:10, the compressive strength and elastic modulus are 1.22 MPa and 224 MPa which are comparable to those of bentonite mixed with cement. The shear strengths between the grouts and fractures surfaces are from 0.22 to 0.90 MPa. The S:C ratio of 5:10 gives the lowest permeability. The permeability of grouted fractures with apertures of 2, 10, and 20 mm range from 10-16 to 10-14 m² and decrease with curing time. [ABSTRACT FROM AUTHOR]

Abstract: Two analytical solutions are derived to model the heated flow-through experiments for granite fractures in the literature. The first model, which assumes an identical/continuous temperature between the bulk fluid and fracture surfaces, represents an upper bound solution of water temperature in rock fractures. The second model including the empirical parameter of heat transfer coefficient is used to calculate the average heat transfer coefficient based on the available experimental data. The obtained heat transfer coefficients are smaller than that from the thermal boundary layer theory for flat plates, but larger than the previous estimates. A power function is fitted to describe the relation between heat transfer coefficient and flow velocity. Both models show that water temperature increases non-linearly along fracture plane. [Copyright &y& Elsevier]

Abstract: The purpose of this study is to investigate the role of filling materials (e.g., quartz sand and kaolin clay) in the interaction between a P-wave and a rock fracture. The specific fracture stiffness reflects the seismic response of a filled fracture, while the wave transmission coefficient describes P-wave transmission across the filled fracture. A series of experimental tests using a split Hopkinson rock bar technique are conducted on artificial rock fractures that are filled with pure quartz sand, sand–clay mixtures with 30%, 50% and 70% clay weight fractions, and a pure clay matrix. The boundary conditions of the filled fracture, i.e., the displacement and stress discontinuities, are used in the method of characteristic lines to calculate the wave transmission coefficient in the time domain. The analytical results agree well with the experimental results. The specific fracture stiffness and the wave transmission coefficient decrease with increasing filling material thickness. When the clay matrix completely fills the void space of the quartz sand, the filled fracture exhibits the largest specific fracture stiffness and promotes P-wave transmission. In general, the wave transmission coefficient is strongly related to the specific fracture stiffness, regardless of the filling material composition or the filling material thickness. [Copyright &y& Elsevier]