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In this work, the color difference phase separation (CDPS) approach is proposed to segment the solid and pore phases. Pore‐scale variables are defined to describe the microstructural characteristics. Novel relations to quickly determine the deformation moduli and thermal conductivity are established. Digital–virtual modeling to investigate the mechanical and thermal properties is addressed. The correlation between pore‐scale variables and the mechanical and thermal properties is investigated. Results show that the calculated shear and Young's moduli decrease and the computed Poisson's ratio increases as porosity increases. The deformation moduli and thermal conductivity increase with increasing pore radius for different types of rocks. Excellent consistencies are found between the digital–virtual and realistic experimental results. The proposed method provides useful tools to fast and accurately determine the deformation moduli and thermal conductivity, which is helpful for the underground space and deep energy resource explorations. Highlights: Multiphase structure is segmented without overestimation or underestimation.Micro‐deformation moduli and thermal conductivity of rocks are fast determined.Thermo‐mechanical properties are effectively validated in microstructures of rocks. [ABSTRACT FROM AUTHOR]

Layered composite rocks (LCRs) are often encountered in underground excavation in which extensive deformation, buckling and local collapse near the layer interface frequently occur. However, there is limited advance knowledge of the failure mechanisms of LCRs to interpret the field observations due to the relative scarcity of polyaxial compression testing. To that end, this study conducts the true-triaxial experiments with the acoustic emission (AE) monitoring on the LCR specimens, with the emphases being on the effects of mechanical contrast (MC) between the layers on the fracture behaviors under true-triaxial stresses. First, the strength of LCRs is controlled by the weaker layer. Second, at the unstable fracturing phase, high AE event rate is faithfully recorded but intermittently interrupted by macrofracturing in granite but not in sandstone. Third, main failure planes of LCRs appear sub-orthogonally to σ3 (minimum principal stress), taken the form of delamination fracture and exhibited the mode of σ3-transverse-symmetric fracturing. As the distance from the unloaded surface increases, the fracturing transitions from σ3-transverse-symmetric spalling to σ3-transverse-symmetric shearing. Depending on the MC, both the fracture propagation through the interface and the fracture containment within sandstone are registered. Moreover, the interface effect is numerically revealed through a 3D finite-element modeling. This study gets insights into the failure mechanisms of LCRs with a changing mechanical property in individual layers under true-triaxial stresses. Highlights: True-triaxial experiment investigations of layered composite rocks in a brittle-brittle sequence. Quantitative interpretations of acousto-mechanical properties and fracturing behaviors in layered composite rocks. The fracture propagation through the interface is registered, as well as the fracture containment within the sandstone. The delamination fracture along σ3-unloading direction dominates the feature of σ3-transverse-symmetric fracturing. The interface effect is revealed by a 3D finite-element modelling. [ABSTRACT FROM AUTHOR]

True triaxial experiment with a synchronous acoustic emission (AE) monitoring system is a popular measure for the assessment of strength and cracking behaviors of brittle flawed rocks under anisotropic stress circumstances. This measure was employed to investigate the laboratory-scale brittle failure of flawed sandstone containing two different en echelon flaw configurations. Quantitative interpretations and comparisons of acousto-mechanical properties and cracking behaviors in intact and flawed sandstone have become available. Observations first revealed that en echelon flaws considerably weakened rock strength and deformability, and strongly affected the damage and failure processes. Second, intact specimen showed a quasi-2D spallation failure, while the failure of flawed specimens was dominated by the induced cracks initiated from en echelon flaws. Third, the two fundamental failure types of rock bridge including tensile-dominated failure and shear-dominated failure were registered. Whatever the failure type, micro-shear failure mechanism co-existed with micro-tensile failure mechanism. Moreover, AE amplitude distributions at the stable and unstable cracking phases follow a power law. The current findings provide insights into the brittle failure mechanisms of flawed rocks and have significant implications at scales relevant to seismicity and engineering applications. Highlights: True triaxial experiment investigations of brittle failure in flawed sandstone Quantitative interpretations and comparisons of acousto-mechanical properties and cracking behaviors in intact and flawed sandstone Quasi-2D spallation failure occurs in intact specimen, while the shear cracks initiated from the flaw tips dominate the failure in flawed specimens Co-existences of micro-shear failure mechanism with micro-tensile failure mechanism at the triggering processes of rock fracture AE amplitude distributions at the stable and unstable cracking stages follow a power law [ABSTRACT FROM AUTHOR]

• A novel fractional viscoelastic-viscoplastic (FVEVP) constitutive law is proposed. • A numerical implementation strategy of the FVEVP model by an explicit time integration scheme is proposed. • A unified progressive damage-rupture criterion is proposed. • A non-linear creep-damage-fracture kinematic-constraint-inspired non-ordinary state-based peridynamics (KC NOSBPD) formulation is proposed. • The time-dependent deformation and fracturing behaviors of intact, macrofractured, and surrounding rock mass around underground openings are reproduced. An in-depth understanding of the time-dependent deformation and failure behavior of rocks is essential for the long-term stability of surrounding rock mass around underground engineering. In this paper, the kinematic-constraint-inspired non-ordinary state-based peridynamic (KC NOSBPD) formulation is proposed to incorporate time dependence by adopting a fractional viscoelastic-viscoplastic (FVEVP) constitutive law to describe the non-linear creep deformation behavior and conjugating it with a time-independent progressive damage-rupture criterion to reproduce creep damage and subsequent creep fracture process. The FVEVP constitutive model is established by coupling a Hooke body, an Abel dashpot and a fractional viscoplastic body. Through the Grünwald-Letnikov (GL) definition of the fractional-order derivatives, finite increment formulations for the FVEVP constitutive model are derived to facilitate numerical implementation by an explicit time integration scheme. The unified progressive damage-rupture criterion is obtained by combining the damage criterion with the rupture criterion via a strain-dependent isotropic scalar damage variable. The novel model is employed to reproduce the time-dependent deformation and fracturing behaviors of intact salt rock, macrofractured sandstone specimens, and surrounding rock mass around the salt cavern gas storage. The proposed model agrees well with experimental data and numerical results from other published literature. To the authors' knowledge, the FVEVP model is first developed to simulate fracture behaviors. [ABSTRACT FROM AUTHOR]

The purpose of this review is to discuss the development and the contribution of the experiments and numerical simulations in compression‐induced failure characteristics of flawed rock specimens. Investigation is essential to understand the fundamental failures occurring in a rock bridge, for assessing anticipated and actual performances of the structures built on or in rock masses. The review begins by representing and discussing compression‐induced crack initiation and growth in flawed rocks and explaining the significance of studying these issues in Section 1. The crack initiation and growth behaviors in flawed rocks under uniaxial, biaxial, and triaxial compressions are described in depth in Section 2 where it is expected to distinguish 2‐D crack growth from 3‐D crack growth. After that, the failure characteristics of flawed rock specimens due to temperature treatments and hydraulic pressure are systematically reviewed. Numerical studies of the compression‐induced failure characteristics of flawed rock specimens based on different numerical theories and numerical models are comprehensively evaluated in Section 3. In Section 4, the new findings obtained recently from experimental and numerical studies are drawn. Finally, some aspects of prospective research and a brief summary are presented in Sections 5 and 6. [ABSTRACT FROM AUTHOR]

In this paper, a compressive-shear fracture model of the phase-field method is proposed to simulate the compressive-shear failure behaviours of pre-cracked rock materials and investigate their fracture mechanisms. In the proposed model, a modified Hoek–Brown criterion is incorporated into the driving term in the evolution equation of the phase field to control the crack phase field. Rock-like specimens containing single flaw and double flaws were used to validate the performance of the proposed numerical model in capturing compressive-shear fractures. The numerical results were in good agreement with the experimental observations. Subsequently the effects of flaw geometries, i.e. flaw inclination angle, spacing and continuity, on the cracking behaviours and mechanical properties of rock-like specimens containing double parallel flaws were investigated. Typical shear cracks, such as coplanar or quasi-coplanar secondary cracks and oblique secondary cracks as well as coalescence types of different shear cracks, were captured. The mechanical properties were also strongly related to the flaw geometry. These performances indicated that the proposed numerical model has ability to simulate compressive-shear cracks. [ABSTRACT FROM AUTHOR]

Understanding the mechanical properties plays pivotal roles in rock engineering. This work aims to establish novel relations linking the porosity, ultrasonic wave and fluid saturation to estimate the uniaxial compressive strength (UCS) fast and simply. The uniaxial compressive coupled with ultrasonic wave tests on sandstone samples are carried out to obtain the datasets of the UCS, P-wave and S-wave velocities. X-ray CT imaging technique is employed to capture the microstructure information. The color difference phase separation approach to segment the pore, water and solid phases is proposed, and pore-scale variables to describe the microstructure characteristics are defined. Novel relations to determine the micro velocities of P-wave and S-wave are established, and the modulus of deformation and the physical properties of rocks are evaluated. Novel relation to determine the UCS is established and validated by the real and virtual experiment datasets. Results show that the UCS, P-wave and S-wave velocities computed by the proposed method decrease with increasing fluid saturation. The errors between the calculated and experimental UCS, P-wave and S-wave velocities are all < 5%, showing excellent consistency with each other. The proposed method is effective to estimate the mechanical properties fast and accurately, simplifying the estimation of the UCS in rock engineering. [ABSTRACT FROM AUTHOR]

Uniaxial compression tests combined with nondestructive testing techniques are performed to explore the roles of non‐isometric flaws in crack developments in brittle rocks. The acoustic emission (AE) rate‐process theory is adopted to analyze fracture‐related AE event rate characteristics. The full‐field optical method is applied to detect cracking modes. Experimental results show that AE activity is quite active when the matrix microcracking is dominant, while after each macrocracking event, AE activity becomes inactive because of the stress release. Multiphysical data for each tested flaw configuration faithfully confirm the rupture progressivity. The larger the flaw length ratio, the lower the peak stress (also peak axial strain and elastic modulus), as well as the more progressive the cracking process. Moreover, ultimate failure is triggered by the shear fracturing from the relatively long flaw. The short flaw is conditionally involved in ultimate failure when the stress buildup effect dominates. Finally, the fracture mechanism of brittle rocks with non‐isometric flaws is revealed. [ABSTRACT FROM AUTHOR]

Highlights • A novel four-element fractional visco-plastic (FVP) model is proposed. • The closed-form solution of visco-plastic deformation of rock tunnels is derived. • The deformation of auxiliary tunnel of Jinping II hydropower station is analyzed. • The analytical deformation of auxiliary tunnel agrees well with the monitoring data. Abstract The squeezing of rock tunnels in soft strata is often encountered during and after excavation, which is closely related to the viscoplasticity of rock mass. However, previous studies involved multiple creep elements in the calculation of visco-plastic deformation, which cost much time to identify creep parameters. In this paper, a novel four-element fractional visco-plastic (FVP) model, which includes two Abel dashpots, one spring and one visco-plastic body, is established using fractional derivatives. Three-dimensional creep equation of the FVP model is first derived using the von Mises equivalent plastic stress-strain relationship. Then the closed-form solution of visco-plastic deformation of the surrounding rock around circular tunnels is derived by the FVP model combining with the non-associated flow rule and the Hoek-Brown criterion. Next, taking rock tunnels that are excavated in three different quality rock salt as examples, parametric investigations of time-dependent parameters and time-independent parameters are carried out. Visco-plastic deformation curves of rock tunnels, which includes (a) the displacement of tunnel wall versus time; (b) the displacement of visco-plastic zone versus depth, are analyzed. Finally, the auxiliary tunnel of Jinping II hydropower station is taken as a typical example for studying the time-dependent deformation of rock tunnels. The analytical results are in good agreement with the experimental and monitoring data. This paper may blaze a new trail to quickly evaluate the visco-plastic deformation of rock tunnels during the early design process. [ABSTRACT FROM AUTHOR]

• The investigations of the occurrence of tension and shear mechanisms in rock fracturing process. • The development of the integrated acousto-optic-mechanics multi-physics field characterization method for a crack. • Using the AF-RA-based Kernel density median criterion and the optical angular bisector criterion to distinct tension- vs shear-induced cracks. Rock macrofracturing often involves the tension-shear coexistence mechanism on the microscopic scale. This paper addresses the occurrence of tension and shear mechanisms in rock macrofracturing process based on the self-developed integrated acoustic-optic-mechanics (AOM) multi-physics field monitoring technique. With this advanced technique, three-point bending (3-p-b) tests with conventional loading and unconventional loading, as a control of the conditions that produce the different mechanisms, are first carried out on sandstone to establish AOM criteria for crack nature classifications. By using the AF-RA-based Kernel density median criterion and the optical angular bisector criterion, a coupled analysis of acoustical-optical data for the distinction of tension- vs shear-induced cracks in two different flaw configurations under uniaxial compression has been available. Results show that the crack initiation mode in tension-type rock bridge tests is dominated by the tension mechanism, while the ultimate failure pattern is shear-dominated. Comparably, failure of shear-type rock bridge is faithfully dominated by the shear mechanism. The paper, therefore, makes two contributions—a better understanding of rock fracturing process and providing a method of establishing the simple and intuitive criteria to justify the crack natures. [ABSTRACT FROM AUTHOR]

The crack initiation, growth, wrapping and coalescence of two 3D pre-existing cross-embedded flaws in PMMA specimens under uniaxial compression are investigated. The stress-strain curves of PMMA specimens with 3D cross-embedded flaws are obtained. The tested PMMA specimens exhibit dominant elastic deformation and eventual brittle failure. The experimental results show that four modes of crack initiation and five modes of crack coalescence are observed. The initiations of oblique secondary crack and anti-wing crack in 3D cracking behaviors are first reported as well as the coalescence of anti-wing cracks. Moreover, two types of crack wrapping are found. Substantial wrapping of petal cracks, which includes open and closed modes of wrapping, appears to be the major difference between 2D and 3D cracking behaviors of pre-existing flaws, which are also first reported. Petal crack wraps symmetrically from either the propagated wing cracks or the coalesced wing cracks. Besides, only limited growth of petal cracks is observed, and ultimate failure of specimens is induced by the further growth of the propagated wing crack. The fracture mechanism of the tested PMMA specimens is finally revealed. In addition, the initiation stress and the peak stress versus the geometry of two 3D pre-existing cross-embedded flaws are also investigated in detail. [ABSTRACT FROM AUTHOR]

In this paper, the kinematic-constraint-inspired non-ordinary state-based peridynamic formulation (KC-NOSBPD) is proposed to investigate the time-dependent behaviors of rocks, which play a critical role in evaluating the long-term stability of the surrounding rocks around underground opening quantitatively. The peridynamic differential operator (PDDO) is introduced to KC-NOSBPD to improve the precision of bond-associated deformation gradient and to suppress the skin effect. On this basis, a unified creep-damage-rupture KC-NOSBPD model is proposed, in which the Burgers-creep viscoplastic constitutive law, a visco-elastoplastic constitutive model, is used to describe the rheological deformation of rocks. A unified damage-rupture framework based on a strain-based isotropic scalar damage variable is established to simulate the creep damage and subsequent creep rupture. The fidelity of this proposed model without damage is verified by comparing it with the benchmark solution for the creep response of a 2D rock specimen subjected to various load histories. Further, the proposed model is employed to simulate uniaxial and triaxial compression creep tests. These present numerical results agree well with the experimental observation, implying that the proposed model successfully captures the accelerating creep behavior of rocks. Moreover, the proposed model performs the time-dependent deformation and failure analysis for the surrounding rocks around the tunnel. [ABSTRACT FROM AUTHOR]

• The developments and contributions of experimental studies on the FPZ in quasi-brittle materials are discussed. • Correlations of the cracking levels in quasi-brittle materials with the FPZ perspective is established. • The existence of apparent FPZs is the material basis for unstable crack growth in flawed granite. In the failure of quasi-brittle materials such as rocks, microstuctural damage always precedes macroscopic fracture and manifests itself in the formation of fracture process zones (FPZs). Investigations of the FPZ are of importance to a better understanding of quasi-brittle fracture behavior along with the size effect and failure forecast. The sensitivities of the FPZ to material microstructures, specimen geometries, loading conditions, ambient factors and monitoring techniques have been investigated extensively, as well as the effects of the FPZ on crack damage and strength/fracture toughness. The first purpose in this study is to discuss the developments and contributions of experimental studies on the FPZ in quasi-brittle materials. Besides, there is limited advance knowledge of the correlations of cracking levels with the FPZ evolution patterns due to the fact that researchers concern cracking levels seldom from the FPZ perspective. This study is also to establish a better understanding of stable and unstable crack growth in quasi-brittle materials from the FPZ perspective. Acousto-optic-mechanical data from uniaxial compression tests faithfully show that the existence of apparent FPZs is a material basis for unstable crack growth in flawed granite. [ABSTRACT FROM AUTHOR]

In this paper, a thermo-hydro-chemo-mechanical coupling peridynamic model of fractured rock mass is proposed to simulate the fluid-driven crack and the characteristics of water pressure and temperature under thermo-hydro-chemo-mechanical coupling condition. Firstly, the coupling model is employed to simulate the thermo-hydraulic coupling consolidation problem of rock samples, and its accuracy is verified by comparing with the analytical solution and the previous numerical results. Secondly, the coupling model is employed to simulate the problems of fluid-driven crack and chemical corrosion, and the present numerical results are in good agreement with those obtained by the phase field method. Finally, thermo-hydro-chemo-mechanical coupling peridynamic model is used to simulate the process of geothermal extraction, and to investigate water pressure and thermal field distribution. [ABSTRACT FROM AUTHOR]

In this paper, it is assumed the rock-like materials contain penny-shaped microcracks. The modes II and III stress intensity factors at tips of the three-dimensional penny-shaped microcracks are determined. The micro-failure orientation angle α is given out to describe the failure of rock-like materials. The formulation between the micro-failure orientation angle α and stress components is obtained from the mixed-mode fracture criterion. Failure characteristic parameters under true triaxial compression condition are defined, which are an invariant and are relative to the intermediate and minimum principal stresses. A three-dimensional nonlinear strength criterion of rock-like materials, in which the effects of the intermediate principal stress on the failure of rock-like materials is taken into account, is developed based on micromechanical methods. The theoretical nonlinear strength criterion is novel, which is not found in the previous references. By comparison with experimental data, it is shown that the present theoretical strength criterion is in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

• The dynamic mechanical properties, failure modes and energy evolution characteristics of persistent fractured granite are investigated. • The influence mechanism of joint configuration on rock dynamic failure is finally revealed. • Effects of different joint inclination angles and joint numbers on the energy absorption property of rocks are analyzed. The previous investigation on rock dynamics mainly focused on the intact and non-persistent fractured rocks, rather than the persistent fractured rocks, while understanding the dynamic mechanical properties and instability failure characteristics of persistent fractured rocks under impact loading remains defective. In this study, impact tests are performed to experimentally study the dynamic mechanical properties, failure modes and energy evolution characteristics of persistent fractured granite with a variety of joint configurations using the Split Hopkinson Pressure Bar (SHPB) apparatus. This paper especially concerns the effects of the loading rate on dynamic failure of persistent fractured granite and the energy evolutions in dynamic failure. Experimental results show that the dynamic strength and energy absorption of persistent fractured granite decrease with increasing joint number. Moreover, as the joint inclination angles increase from 30° to 90°, the failure mode gradually transits from shear to tensile, and the dynamic strength of persistent fractured granite first increases and then decreases. Based on the experimental observations and elastodynamics, the influence mechanism of joint configuration on dynamic failure is finally revealed. The findings can fill in the gap of dynamic failure mechanism with the incorporation of persistent fracture at different loading rates. [ABSTRACT FROM AUTHOR]

• True triaxial compression tests are conducted on coarse and fine sandstone. • The coupled effects of the microstructure and the pre-existing flaws are revealed. • Mechanisms of micro-shear cracking and micro-tensile cracking are revealed. • The micro-shear cracking is seldom generated in fine sandstone. Failure characteristics of flawed rocks subjected to true triaxial stress are not studied, and the cracking mechanism is not fully understood. Especially, the damage and failure mechanisms incorporating the effect of material properties such as grain diameter are seldom revealed. In this study, true triaxial compression tests are conducted on flaws-contained specimens of coarse and fine sandstone, to explore the coupled effects of the microstructure and the pre-existing flaws on cracking characteristics and further to reveal the cracking mechanism. Acoustic emission (AE) data and the mechanical data are the main experimental output. It is found that cracking characteristics are collectively affected by the microstructure features and the geometrical features of specimen-sized pre-existing flaws. When the confining pressure is relatively large, the mechanical interaction between coarse grains inhibits the specimen's rupture and contributes to the increase of the strength of coarse sandstone. Due to the complex interaction between grain-scale microcracks, the micro-shear cracking mechanism and the micro-tensile cracking mechanism are presented in the physical process of damage progression in coarse sandstone. However, the microcrack clustering phenomenon in fine sandstone is insignificant, and the interaction between grain-scale microcracks is weak. Accordingly, the micro-shear cracking is seldom generated in fine sandstone. [ABSTRACT FROM AUTHOR]

• Acoustic emission (AE) and photographic technologies are employed. • The dominant frequency and amplitude characteristics of rocks are investigated. • Four modes of AE signals are found during the cracking process of flawed rocks. • The fracture mechanism of flawed rocks is discussed. To study the time-varying dominant frequency distribution characteristics during the cracking process of intact and flawed rocks, uniaxial compression tests are carried out on three types of red sandstone specimens. Both acoustic emission (AE) and photographic technologies are performed to monitor the real-time cracking process of tested specimens. The relationship between the AE rate curve, the axial stress-time curve and the cracking process is first analyzed, which can be employed to evaluate the microscopic and macroscopic deformation characteristics of rocks. The time-varying dominant frequency and amplitude distribution characteristics in different cracking stages of tested rocks are investigated. Four modes of AE signals, i.e., AE signals with low-frequency and high-amplitude (LF-HA), AE signals with low-frequency and low-amplitude (LF-LA), AE signals with intermediate-frequency and low-amplitude (IF-LA) and AE signals with high-frequency and low-amplitude (HF-LA), are found. The coupling application of four modes of AE signals extracted from unstable deformation stages can be viewed as early warning for unstable failure of rocks. The fracture mechanism of intact and flawed rocks is discussed based on the statistical characteristics of dominant frequency during the cracking process. Micro-shear cracking mainly dominants the ultimate failure of all of tested rocks. [ABSTRACT FROM AUTHOR]

In this paper, a new fully coupled hydromechanical model in terms of bond-based peridynamics is proposed to simulate the pressured and fluid-driven fracturing process in fissured porous rocks. A fissured porous rock model is established based on the classic Biot poroelasticity theory. The coupled hydromechanical bond-based peridynamic model consists of two parts: fluid flow and mechanical deformation. A governing equation of fluid flow in terms of peridynamics is established along with an integral-differential equation of motion in the fissured porous medium. Moreover, a fracture criterion in the hydromechanical bond-based peridynamic model is introduced to simulate the failure caused by high fluid pressure. Finally, four numerical simulations are conducted to verify the accuracy and correctness of the proposed model. [ABSTRACT FROM AUTHOR]

• The real-time fracture process of fissured red sandstone specimen is monitored. • Two indices of RA and AF are performed to classify the different fracture modes. • The adequacy of the fracture mode classification is evaluated by Kernel Density Estimation (KDE). • KDE can identify and visualise the high concentration regions of RA and AF values. • RA values can serve as an early warning for ultimate failure of rocks. To study the classification of fracture modes of rocks during the cracking process, uniaxial compression tests were conducted on intact and flawed red sandstone specimens. Meanwhile, both acoustic emission (AE) and digital image correlation (DIC) technologies were adopted to monitor and record the real-time cracking process of the specimens tested. In this study, the interevent time function F (τ) (AE events rate) was utilized to distinguish the transition from microcracking to macrocracking for the tested specimens. An AE parameter analysis method based on two indices of RA (rise time/amplitude) and AF (AE counts/duration) values was performed to classify the different cracking modes during the loading process. The classification results of the cracking modes coincide with the cracking type of macrocracks captured by the photographic system. Moreover, the adequacy of the crack classification was also evaluated by the kernel density estimation (KDE) function, a nonparametric density estimation method. KDE is used as a parametric model to overcome the randomness found in the data set generated by AE testing and can well identify and visualize the high concentration regions of RA and AF values. A continuous increase of RA values (more than 400 ms/v) can serve as an early warning for the ultimate failure of red sandstone. The results of this present investigation can be applied in the health monitoring of rock engineering. [ABSTRACT FROM AUTHOR]