Abstract Experimental uniaxial compression loading tests and scanning electron microscope (SEM) tests are carried out on rock-like specimens containing single pre-existing cracks to study the mechanical properties and microscopic damage evolution. The present study has distinguished tensile or shear cracks based on different SEM observations on a micro scale. Specifically, six typical micro patterns are defined according to their geometry shapes, namely, flocculent, flaw, circle, flow, layered, and broken circle pattern. These micro patterns display distinct characteristics on structure surfaces, boundary lines, and the distribution of grain debris. Moreover, the microscopic damage of both tensile and shear cracks is quantitatively studied using the image post-processing technique. The damage evolution, which associates the macroscopic cracking processes, has been investigated. It is indicated that the microcracks develop from the pre-existing cracks prior to the initiation of any macroscopic observable cracks, and the damage is not rapidly accumulated after the initiation of both tensile and shear cracks. 1. Introduction Natural rock contains discontinuities, including fractures, pores, and other defects, which govern the fracturing behaviors of the rock masses under loading. Numerous theoretical, experimental, and numerical studies have been carried out to study mechanical properties of jointed rocks or other rock-like materials (Griffith, 1921; Brace and Bombolakis, 1963; Horii and Nematnasser, 1985; Bobet and Einstein, 1998; Wong and Einstein, 2009a; 2009b; 2009c; Park and Bobet, 2010; Zhang and Wong, 2012; 2013; Gonçalves da Silva and Einstein, 2013; Haeri et al., 2014; Yang et al., 2017; Zhao et al., 2018). In these researches, tensile and shear cracks are always be regarded as two basic crack types and fundamental of the rock mechanic. (Cheng and Wong, 2018). Bombolakis (1963) firstly observed the propagation of tensile wing cracks from straight cracks under uniaxial compression, which consists well with the Griffith theory. Lajtai (1974) carried out uniaxial compression loading tests on plaster of Paris, the results consist of five crack types, including both tensile and shear cracks. Petit and Barquins (1988) observed that shear zones develop extensively in addition to the occurrence of tensile wing cracks. Using scanning electron microscope (SEM), Sagong and Bobet (2003) investigated tensile and shear cracks in gypsum specimens on a micro scale. Li et al. (2005) conducted experimental tests on marble specimens, and they discovered two cracking phenomena: wing cracks and secondary quasi-coplanar cracks. Although the mechanical properties of these two cracks were not clearly identified by the authors, it is accepted that wing cracks are tensile cracks and secondary cracks are shear cracks. Wong and Einstein (2009a) systematically characterized the tensile/shear cracks which emanate from a single pre-existing crack. Seven different crack types (including three tensile types, three shear types, and one mixed type) were identified based on geometry and propagation mechanism. Subsequently, they studied the orientation of microcracking zones of the wing cracks (Wong and Einstein, 2009c). As a summary, the previous studies focused on the differences between tensile cracks and shear cracks in three main aspects (Cheng and Wong, 2018): First, the tensile/compressive stress concentration phenomenon around the pre-crack tips; Second, the initiation direction and propagation trajectories of observable cracks; Third, the microscopic observation of the crack surfaces.

Abstract The cracks on shale wellbore have an important influence on the borehole instability, and the study is an important significance. The article based on fracture mechanics, the propagation model of crack on shale wellbore was established with the in-situ stress, the hydration swelling stress and capillary force. The influences of the hydration stress and capillary force on the crack propagation were discussed. The result shows that the hydration swelling has a great influence on the stress intensity factor, the drilling fluid systems need to decrease the drilling fluid filter loss and increase the clay minerals hydrate inhibitor. The wetting behavior has a great influence on the wellbore stability, the drilling fluid systems need to reduce the drilling fluid interfacial tension and enlarge the wetting angle between drilling fluid and rock medium. The crack geometric characteristics and the spatial distribution characteristics of the crack in formation have larger difference on the stress intensity factor, the crack propagation mechanism of the wellbore rock with different scale varies. The drilling fluid should put some particles compatible with the micro-cracks in the hard brittle shale into avoid initiation and propagation of the crack in the drilling. The hole trajectory have larger difference on the stress intensity factor, the well deviation angle and the azimuth angle have adverse effect on the crack propagation, the well trajectory should be optimized to control the crack propagation. 1. Introduction Recently, with increased demand for energy and advances in exploration and development technologies, the exploitation of unconventional oil and gas reservoirs, especially shale gas reservoirs, has attracted the attention of many countries. In 2013, a study titled, "Technically Recoverable Shale Oil and Shale Gas Resources: An Assessment of 137 Shale Formations in 41 Countries Outside the United States", conducted by the U.S. DOE's Energy Information Administration, estimated shale gas resources of 36.1×10 12 m 3 in China and 17.75 × 10 12 m 3 in the Sichuan Basin (EIA, 2013). In the process of shale gas development, wellbore instability of shale gas well is one of the important and complex issue (Chee and Brian,1997; Li, 1999). Aimed at borehole stability of the hard brittle shale, some scholars have conducted the thorough research. Lou and Liu (1997) constructed mechanical calculation models of borehole stability in highly inclined shale formation based on the linear elastic mechanics theory. Jin et al. (1999a,1999b) discussed the factors affected sidewall stability of deviated and straight well in the fractural formation, used the weak surface model. However, Mclellan et al. (1996) reported that the elastic-plastic theory should be adopted to investigate sidewall stability in shale formation. The mechanism on instability of surrounding rocks affected by the fracture for shale has been studied by Germanovich and Dyskin (2000). Helstrup et al. (2004) investigated the effect of the parameters of in-situ stress and drilling fluid on the sidewall stability. Chen et al. (2003) and Zhan et al. (2006) established chemo-mechanical coupling model to analyze the impact of temperature and drilling fluid on the shale borehole stability. Liu et al. (1998) explored the factors affecting the wellbore stability in the fractured formation from the aspect of fracture mechanics. Combined Fracture Mechanics with Damage Mechanics, Tang et al. (2007) deduced the mechanical calculation model of the wall stabilization in the hard brittle shale formation. Liu et al. (2014) found the influence of the wettability of hard brittle shale on rock strength. However, the influence factors of hydration and wettability on the crack propagation of hard brittle shale has been analyzed by Liang et al. (2015a). And on this basis, Liang et al. (2015a) proposed the significantly impact of the time effect and the scale effect on crack propagation of hard brittle shale. The three researches above elucidate the physicochemical property of the hard brittle shale and its effect from the different angles. Some accomplishment of wellbore stability technology in hard brittle shale achieved by Mechanics, Chemistry, Chemo-mechanical coupling, Fracture Mechanics, Damage Mechanics, Damage-Fracture Mechanics and so on have been made. From the previous literatures (Liang et al., 2015b,c; Xiong et al., 2015), clay minerals in the shale gas reservoir are constituted by large amounts of illite and small amounts of illite-montmorillonite mixed-layer, as the weak swelling rock. The shrinkage phenomena resulted from hydration expansion rarely occur, whereas spalling and breaking are more concerning. Although the hydration expansion volume found for this kind of shale via laboratory experiments is small, the hydration stress there cannot be ignored. Therefore, the model of mechanical-chemical coupling and the coupling between drilling fluid and fluid or solid at the surface of rock was established considering the hydration and wetting behavior. According to the Fracture Mechanics, the crack propagation model was built considering the hydration and capillary effect. Besides, the influences of the hydration stress and capillary force on the crack propagation on the wall of the shale gas well were discussed and the mechanism of shale wellbore instability from the perspective of multi-field coupling were also investigated.

Abstract This paper presents a new method to accurately determine the strata while drilling. We developed an original prototype of instrumented drilling system, with it the measurement was performed on a hydraulic servo drilling rig. The drilling parameters (i.e., thrust or weight of drill strings, rotational speed, bit shift, torque as well as vibration of drilling rig) were recorded. According to the harmonious principle, a coding method for identification of sub-penetrating processes is established through the determination of parameter status. A slope coefficient searching identification algorithm is proposed for the penetrating data with the features of multiple pulses, noisy, huge data and nonlinear. Field drilling tests were carried out in three different sites. The results show that the approach well agrees with that of conventional drilling investigation, which provides a new method for in-situ intelligent survey in geological and geotechnical engineering. 1. Introduction In geological and geotechnical engineering investigation, the primary methods to obtain strata structure are drilling and related in-situ test techniques. For example, geophysical detecting techniques (GD), resistivity, magnetics, electromagnetic, seismic wave, seismic CT, gravity, sonic and ultrasonic methods have been extensively applied to the identification of strata interfaces at initial stage of geologic prospecting (1). In terms of technology, borehole penetrating test and coring are the most authentic and reliable for geotechnical investigation and geological survey. Unfortunately, the job of borehole logging, sampling, in-situ testing and indoor physical mechanical parameters testing is overloaded, time-consuming and expensive. According to incomplete survey, in drilling exploration of foundation, the time consuming ratio of net penetrating in the whole drilling is less than 30%, the costs of drilling exploration are generally accounted for 8%-28% of a project cost, this ratio will possibly increase with the increase of investigation depth. In geological drilling, the borehole depth generally reaches thousands of meters. At present, the maximum depth has reached over 4500 m in metal mining; for nearly 1/3 underground metal mines, the mined depth has exceeded 1000 m in China; in coal mines, the numbers of well over 1000 m in depth have made a substantial growth in recent 10 years; the constructed depth of tunnel has rose up to near 3000 m. In earth science drilling, this figure has exceeded 10 000 m, and among the earth science boreholes, there are dozens of boreholes over 4000 m in depth worldwide. Obviously, with the growth of drilling depth, the complexity of geological conditions will increase, processing time will greatly grow in non-drilling such as sampling, lifting and lowering of drill strings and in-situ testing. For example, the depth of core drilling in the earth drilling-CCSD-1 reached 5158 m, totally spent 16.6189 million Chinese Yuan, core length of 4400 m with a cored rate 85.30%, for nearly 4 years. On the other hand, the geophysical approaches have good prospect for application in field investigation, but can be easily interfered with external factors and the interpretation accuracy is not very high when a single method is applied. Due to uncertainty, multiplicity of interpretation, it needs a combination of various methods to recognize formations. Besides, it is hard to give all the required basic data for geotechnical and geological engineering, and is difficult for rock mass classification.

Abstract Intermittent jointed rocks, widely existing in various mining and civil engineering structures, are quite sensitive to dynamic cyclic loading conditions. Understanding the dynamic mechanical properties of jointed rocks is beneficial for the rational design and the long-term stability assessment of rock engineering projects. This study experimentally investigates the dynamic mechanical properties of synthetic jointed rock models under different cyclic conditions, regarding four loading frequencies, four maximum stresses and four amplitudes. Our experimental results reveal the influence of the three cyclic loading parameters on the mechanical properties of jointed rocks, including the fatigue deformation characteristics, the fatigue energy and damage evolution, and the fatigue progressive failure behavior. Under lower loading frequency or higher maximum stress and amplitude, the jointed rock is characterized by higher fatigue deformation moduli and higher dissipated hysteresis energy, leading to higher accumulative damage and lower fatigue life. The accumulative fatigue damage of jointed rocks exhibits an inverted S-shape with a three-stage evolution, i.e., initial, steady and accelerated stage. The fatigue failure modes of jointed rocks are independent of cyclic loading parameters; all tested jointed rocks feature a prominent tensile splitting failure mode. Three different crack coalescence patterns are classified between two adjacent joints. Furthermore, different from the progressive failure under static monotonic loading, the jointed rocks under cyclic compression fail more abruptly without evident preceding signs. The tensile cracks on the front surface of jointed rocks always initiate from the joint tips, and then propagate at a certain angle with the joints towards the direction of maximum compression. 1. Introduction The mechanical characteristics of intermittently jointed rocks play a dominant role in the overall mechanical behavior of many mining and civil engineering structures, such as underground tunnels, bridge abutments and road foundations. Since these rock structures are likely to be subjected to cyclic loading resulting from earthquakes, quarrying and rockbursts, it is thus crucial to characterize the fatigue properties and failure mechanism of intermittently jointed rocks for the rational design and long-term stability analysis of rock structures under different cyclic loading conditions.

Abstract This paper presents an extended three-dimensional discontinuous deformation analysis (3–D DDA) method for stability analyses of jointed rock tunnels. In the natural environment, rock masses are cut by finite joints into numerous polyhedral blocks with arbitrary shapes, including convex, concave, those with cavities and/or holes, and probably their unions. In stability analysis of rock-masses, especially for jointed rock tunnels, one of the primary bottlenecks is discontinuous computation of the contacts between arbitrarily shaped polyhedral blocks. The original contact detection approach proposed by the first author, entrance plane method (EPM), is extended to address this problem by integrating a novel method termed local convex decomposition (LCD). Rather than globally intersecting non-convex polyhedrons into a combination of convex polyhedrons, LCD only decomposes locally the non-convex vertex angles of polyhedrons into a set of convex vertex angles, which is much easier to implement. The decomposed vertices of these non-convex polyhedrons are separately detected for possible entrances in a geometrical way but then the whole polyhedron is treated as one in the mechanical calculation. The developed code is fully integrated in the original 3-D DDA program and then applied to a complex tunnel scenario. The whole failure process is exhibited dynamically, involving large displacement and rotation of multiple interaction blocks. Overall, the extended 3-D DDA could be potentially used to find the failure mechanism of jointed rock tunnels, such as to optimize the tunnel stabilization or protection design. 1. Introduction For structure design and disaster prevention, stability analyses are routinely performed to identify potentially unstable regions of tunnels, especially for those going through jointed rock masses. Practical rock tunnel stability problems are complicated because of complex topological geometry and mechanical behavior primarily resulting from joints. Numerical modeling techniques facilitate the approximate solutions, which would have never been possible by using the conventional techniques. However, the numerical methods for rock mechanics analysis are generally underdeveloped compared to its demand in practical rock tunnel engineering. Main barriers are as follows. In the natural environment, there exist a great number of various joints, each with finite extensions. Consequently, these finite joints, which are assumed to be planar, cut the rock mass into numerous polyhedral blocks with arbitrary shapes, including convex, concave, those with cavities and/or holes (see Fig. 1), and probably their unions. For example, some nonconvex blocks usually exist in the tunnel surface, and the other potentially unstable regions formed by pre-existing joint planes (Shi and Goodman, 1989). In most rock tunnel engineering cases, the behavior of rock masses is dominated by the geometrical configurations and mechanical properties of joints (Goodman, 1989). The numerical analysis accuracy depends mostly on properly treating interactions among joints, which can be referred to as a contact problem. Contact treatment is extremely difficult, especially in 3-D situations where the contacts between arbitrarily shaped polyhedral blocks can be highly non-linear, strongly non-smooth, and thus extremely indeterminable. The rock tunnel failure is a complex process which involves sliding along and opening/closure of joints and large displacements, deformations and rotations of discrete blocks. The underlying continuum assumption within conventional continuum-based methods often leads to difficult parameters to define and oversimplified geometry to be realistic, making them almost impossible to realize the whole failure process (Jing, 2003).

Abstract To consider the roughness effect on shear strength and deformation of rock joint, this research proposed a joint model for the discrete element method. The background theory of the proposed model is based on Barton's shear strength criterion which is widely used to describe non-cohesive joint with roughness. To implement Barton's criterion in DEM software, three calculation modifications were performed, including exceeded force recapture, contact area equalization, and stiffness adjustment. Through the modifications, the force of each joint contact could be calculated, which reasonably reflect the joint mechanical behavior under different normal stress. Afterward, the proposed model was verified by comparing to the theoretical model. The results indicated that the proposed model rationally describes the shear stiffness influenced by mobilized joint roughness coefficient during the shear process. The comparisons showed that the proposed model is versatile in simulating the shear displacement with loading-unloading-reloading cycles, normal closure, and shear dilation of joint. 1. Introduction The strength and deformability of rock mass are heavily influenced by the properties of joints. The joint exhibits highly non-linear behavior under applied stress and is influenced by surface roughness. To describe the joint behavior, Barton proposed a non-linear model for rock joint (Barton, 1973). It not only provided the description of the failure envelope but also considered the evaluation of shear-displacement and dilation relationships. Therefore, it is widely used in the analysis of rock mechanics. On the other hand, the discrete element method (DEM) has been widely adopted to explore the behavior of rock mass and successfully applied to rock engineering. Lots of models were developed to simulate joint behavior in DEM, including the bond-eliminate method, the smooth-joint method, and so on (Chiu et al., 2013). However, these methods can not reflect the phenomenon in experiments, such as shear-displacement curve and nonlinear failure envelope. To overcome this problem, this study proposed a rock joint model "rough-joint model". The theory of the proposed model is based on Barton's model. To implement Barton's criterion in DEM software, three calculation modifications were needed. After finishing the construction of the joint model, the direct shear test with reverse shearing has been simulated to show the performance. The failure envelope, shear-displacement curve, closure curve and dilation curve fit Barton's model very well. The above results show that rough-joint model can provide a way to simulated joint behavior with roughness in DEM, which is helpful for researchers to perform numerical analysis for the joint sliding problem.

Abstract Since its development, the grain-based model (GBM) has been demonstrated to be capable to capture the strength and deformation behavior and the micro-cracking process under different loading conditions. In the GBM, individual grains resemble the actual constituent minerals, while each grain comprises multiple bonded particles. Particle size is an important micro-parameter of bonded particle model used in the particle flow code (PFC) for studying the rock mechanical behavior. However, most of the previous studies simply select the particle size based on the consideration of computer capacity and efficiency, without comprehensively accounting for its effect on the simulation results. This paper numerically investigates the effect of grain size to particle size ratio on the simulation results using GBM. Numerical PFC specimen models with different grain sizes and particle sizes are first generated, on which numerical simulations of uniaxial compression test are then conducted. The results in this study show that both grain size and particle size have a significant influence on the strength and deformation parameters and the induced micro-cracking process. By correlating the simulated uniaxial compressive strength and Young's modulus with the grain size to particle size ratio, it is found that the two parameters increase with the grain size to particle size ratio, and their increase gradually diminishes when such ratio reaches a threshold. Due to such remarkable influences on numerical results, these two geometrical parameters should be properly determined during the parameter calibration stage. 1. Introduction A good understanding of the rock strength and deformation will facilitate cost-effective design and long-term stability maintenance of engineering structures constructed in or on rocks. Numerous laboratory test results have revealed that the deformation (failure) of rocks is mainly controlled by its inherent microstructure and the associated micro-cracking process (Brace et al., 1966; Bieniawski, 1967). The microstructures are usually associated with the different mineral aggregations and varying amounts of micro-defects such as micro-cracks, voids, and cleavage planes (Kranz, 1983). It is, therefore, of vital importance to comprehensively study the influence of inherent microstructures on the failure behavior and the induced micro-cracking process of rocks.

Abstract Compressed air energy storage (CAES) power plants are one of the most reliable systems available for energy storage, and they use conventional technology. A salt dome is usually used for the high-pressure air reservoir in the CAES plants currently in commercial operation. However, due to the complicated geological conditions in Japan, it is not easy to design and construct an underground high-pressure air storage tank there. To address this problem, the authors devised a mud slurry lining (MSL) system for storing compressed air underground. The MSL is a pressurized mud slurry injected into the gap between a reinforced concrete lining and bedrock that provides pre-stress on the lining. This report outlines the MSL design and considers the two central features affecting practical applications of MSL. The installation conditions are modeled in terms of the rock mechanics under high pressure, and the self-clogging behavior of the mud slurry is discussed with experimental results. If the maximum pressure is 3 MPa, analysis confirmed that a minimum installation depth of about 100 m is sufficient. Laboratory tests indicate that the critical pressure of the mud slurry is 3 MPa with an artificial joint width of about 3 mm. 1. Background Energy storage technology is essential for the widespread adoption of renewable energy generation, because the outputs of solar and wind generation plants tend to fluctuate. Compressed air energy storage (CAES) converts electrical energy into compressed air, and is a promising technology for grids that incorporate fluctuating renewable generation. Recently the storage efficiency of CAES plants has been improved with the application of effective heat energy storage technology referred to as adiabatic CAES (A-CAES 1) ). The concept of A-CAES is diagrammed in Fig. 1. An A-CAES plant can start up quickly and is responsive to load fluctuations. Further, since it only requires conventional equipment, it is highly reliable and has no risk of chemical deterioration. For A-CAES to be implemented widely, storage capacity must be maximized. Subsurface space is generally used to make the development of a large storage reservoir economically feasible.

Abstract Combined finite-discrete element method has become one of the most powerful numerical methods for modelling rock failure process in recent decades. However, most of studies focus on two-dimensional combined finite-discrete element modelling of the rock failure process. This paper further develops a hybrid finite-discrete element method proposed early by the authors for three-dimensional modelling of the rock failure processes in Brazilian tests and uniaxial compression test. The further developed three-dimensional hybrid finite-discrete element method is then parallelized using compute unified device architecture - based general purpose graphic processing unit parallel method to conduct a full-scale three-dimensional modelling of rock spalling failure process in the single Hopkinson pressure bar test. It is concluded that the three-dimensional hybrid finite-discrete element method provides a valuable numerical tools for modelling rock fracture and fragmentation and the parallelization makes it possible to be applied in the large-scale rock mass instability engineering application. 1. Introduction The study on rock failure process has been a challenging but hot topic since rock fracture has applications in not only breaking the rock mass for extracting valuable natural resources in mining, geothermal, and oil & gas industries but also preventing geotechnical engineering structures such as tunnels, slopes and dams from failure and collapse. In recent decades, numerical method has been one of the most powerful tools for studying rock failure process and the combined finite-discrete element method initially proposed by Munjiza (2004) has become one of the most powerful numerical methods for modelling the rock failure process. Compared with the finite element method, the combined finite-discrete element method is more robust in modelling rock failure, especially fracture, fragmentation, and fragment movements resulting in tertiary fractures. Compared with the discrete element method, the combined finite-discrete element method is more versatile in dealing with irregular-shaped, deformable and breakable particles. However, most of studies in literatures focus on modelling the rock failure process using two-dimensional (2D) finite-discrete element methods (Mahabadi et al., 2010; Liu, 2013; Lisjak et al., 2014; Liu et al., 2015 and 2016; Mahabadi et al., 2016; An et al., 2017). Thanks to the rapid development of computing power, interactive computer graphics and topological data structure, three-dimensional (3D) finite-discrete element modelling of the rock failure process has attracted the attention of more and more researchers. Rougier et al. (2014) simulated the dynamic rock failure process in dynamic Brazilian test using a 3D combined finite-discrete element method, i.e. the so-called MUNROU (Munjiza-Rougier) code running on a supercomputer with a few hundreds of CPUs at Los Alamos National Laboratory. Mahabadi et al. (2014) implemented a 3D combined finite-discrete element method to investigate the rock failure process in Brazilian disc test and uniaxial compression test although their 3D modelling of the uniaxial compression test is far from satisfactory. Hamdi et al. (2014) simulated the complete 3D fracture process during conventional laboratory testing including Brazilian indirect tension and uniaxial and biaxial compression using a combined finite-discrete element method called ELFEN developed Rockfield Ltd. In this study, a hybrid finite-discrete element method proposed by Liu et al. (2015) on the basis of Munjiza's (2004) open-source combined finite-discrete element libraries are further developed for three-dimensional modelling of the rock failure processes in Brazilian tests and uniaxial compression test, which extends a recent study on the 3D hybrid finite-discrete element modelling conducted by the authors (Liu et al., 2018). Moreover, the further developed 3D hybrid finite-discrete element method is parallelized using the GPGPU (general purpose graphic processing unit) parallel method initially implemented in the DFPA (dynamic failure process analysis) code (Fukuda et al., 2016) to conduct a full-scale 3D modelling of the single Hopkinson pressure bar test on the rock spalling failure process. Unlike Rougier et al.'s (2014) and probably Hamdi et al.'s (2014) (although unclear since not stated in their paper) modellings completed in the supercomputer with hundreds of CPUs, all of 3D modellings reported in this paper are completed in PC although the rock spalling test is modelled using a PC with a powerful GPU.

Abstract Barton's joint model is the most realistic model for predicting the nonlinear shear behavior of rock joints. This capability comes from the inclusion of a joint surface roughness parameter called the joint roughness coefficient (JRC) that is mobilized under shearing. Recently, a linearized implementation of Barton's model has been done to obtain the mobilized equivalent Mohr-Coulomb (M-C) parameters that account for generation and reduction of JRC as a function of shear displacement ∆ u . These equivalent parameters will allow the linear M-C model to capture nonlinearity in the shear behavior of rock joints. In the linearized Barton's model, the pre- and post-peak joint shear stiffness also contains mobilized JRC that is expressed as hyperbolic and logarithmic functions of ∆ u , respectively. This paper further explores the capability of the linearized Barton model to predict the shear behavior of rock joints. The model is verified against results from the experimental and numerical direct shear test on joint planes from various rock types. The verification shows that the linearized Barton's model can capture the nonlinearity in the shear stress-displacement and in the dilation-induced shear displacement behaviors of rock joints under variations normal stress and JRC values. In the future, the linearized Barton's model has the potential to be applied in computer codes for fractured rock modeling. By implementing this model, neither the simplicity of the linear M-C model nor the advanced capability of the nonlinear Barton's model is lost. 1. Introduction In a fractured rock mass, the shear behavior of rock joints is particularly important because it dominantly controls the deformability, strength, and hence the stability of the rock mass. Block sliding from a slope or block falling in an underground excavation are examples of joint shear behavior that is not only controlled by the shear strength of the particular joint but also by its dilation (Goodman, 1976; Barton, 1982). The dilation is caused by the mobilization of joint surface roughness, causing a nonlinearity in the shear behavior of rock joints in the form of strain hardening and strain softening under shearing.

Abstract The existence or many joints brings about the problems of interaction between joints. In this regard, it is very important to explore the interaction between two joints under shear loading condition. In this study, the shear performance of double joints was studied using the laboratory experiments, where the smooth cleavage joints were generated by sawing off and the rough joints were generated by the Brazilian Split test. The experimental results of double joints of sandstone show that, under lower normal stress the interlayer rock between two joints does not fracture, and the peak shear strength of the specimen is determined by the weaker joint. In contrast, under higher normal stress, the peak shear strength is attained when the tensile fractures initiate in the interlayer rock, and it has also relevancy to the JRC of double joints and interlayer thickness. Additionally, numerical simulation of the double-joint shear tests show that the direction of the cracks trends to be parallel with that of the maximum principal stress, and the stress concentration in the joint surfaces causes penetration between different joints, which leads to a lower strength. 1. Introduction Shear strength of a single joint can be effectively estimated by an empirical formula [1], However, the structural planes or joints in the real rock mass are usually not exist alone, the interaction between different joints has important influence on the overall strength. Yang et al. [2] studied the strength and deformation of rock specimens cut with parallel structures under the uniaxial compression conditions. It indicated that the failure modes of specimens with multiple structures can be divided into three types. The stress-strain characteristics of rock mass with multiple joints based on the double axial compression tests have been conducted by Yoshinaka and Yamabe [3], and the related constitutive equation was established. Through the true triaxial compression tests on large size multi-jointed rock specimens, Reik and Zacas [4] have found that the deformation and failure mode of jointed rock mass are both related to the direction of the joints and the stress state. Kulatilake et al.[5] deemed that the fracture tensor component can be used to establish a nonlinear relationship with the strength of rock mass with many groups of joints. Jaeger [6] and Bray [7] predicted the strength of rock mass containing one or two joints by the principle of stress superposition, and they considered that the weakest structure played a decisive role in the strength of rock mass. Hoek and Brown [8] have also set up a prediction formula of jointed rock mass strength based on the uniaxial compression test. In addition, the numerical simulation method is used to study the mechanical properties of the multi-jointed rock, and the results show that the direction, number and spacing of the structural planes have influence on the overall strength[9]-[11]. Generally speaking, the current understanding of the interaction between different joints is still not enough, especially on the interpenetration between two or more rough joints.

Abstract Entry driven along goaf-side (EDG), which is to develop the entry of the next longwall panel along the goaf-side and isolate the entry from goaf with a small-width yield pillar, has been widely employed in the past few decades in China. The width of such a yield pillar has a crucial effect in EDG layout in terms of ground control, isolation effect and recourse recovery rate. On the basis of a case study, this paper presents a methodology of evaluation, design and optimization of EDG and the yield pillar by considering results from numerical simulation and field practice. In order to analyze the ground stability rigorously, the numerical study begins with the simulation of goaf-side stress and the ground condition. Four global models with identical conditions except the width of the yield pillar are built and the effect of the pillar width on ground stability has been investigated with comparison in aspects of stress distribution, failure propagation, and displacement evolution in the entire service life of entry. On the basis of simulation results, the isolation effect of the pillar acquired from field practice is also taken into consideration. The suggested optimal yield pillar design is validated from a field test in the same mine. Thus the presented methodology provides references and can be utilized for evaluation, design and optimization of EDG and yield pillars under similar geological and geotechnical circumstances. 1. Introduction The stability of roadways is a long-standing issue in underground coal mines, especially for entries that serve and ensure the safe production of longwall panels. The ground stability and failure mechanisms of entries vary depending on stress, geological and geotechnical conditions. Entry driven along goaf-side (EDG), which is the development of an entry of the next longwall panel along the goaf-side and the isolation of the entry from the goaf with a small-width yield pillar, has been widely employed in China over the past several decades (Li et al. 2015; Wang et al. 2015, Zhang et al 2017). A yield pillar, which is designed to deform progressively during its service life, can transfer its load to adjacent abutments and control the mining-induced stress distribution around the entries (Peng 2008). Hence, it contributes to preventing coal bumps and excessive ground deformation by employing yield pillars, and it has been successfully applied in many coal mines of China and USA (Peng 2008; Li 2015; Chen et al. 2014). For instance, Carr et al. (1985) employed a yield-abutment-yield pillar layout to a four-entry longwall system in the Blue Creek seam in Alabama to control its severe floor deformation. The application of yield pillars in Utah coal fields has achieved a notable effect on preventing coal bumps (Peperakis, 1958; Agapito et al., 1988).

Abstract The semi-circular bending (SCB) test is one of the useful testing methods for determining mode-I fracture toughness of rocks. A SCB specimen with an artificial notch is loaded at three points including lower two points and upper single point in the test. In general, there are two types of geometry in artificial notch: straight notch and chevron notch. The straight notch in the SCB test is adopted in the suggested method for estimating of mode-I fracture toughness of rocks in ISRM. On the other hand, the cracked chevron notch SCB (CCNSCB) test using a specimen with a chevron notch has been proposed. However, the stress intensity factor on the CCNSCB test has not been made clear, sufficiently considering cracking such as initiation/propagation and geometry of critical crack front at maximum load. In this paper, by means of software ABAQUS, a cracking behavior from the tip of artificial notch on CCNSCB test is analyzed by XFEM in order to clarify the geometry of crack front in a process of cracking. Analyzing stress intensity factors of specimen with the calculated geometries of crack front during the cracking process by FEM, the relation between crack length and stress intensity factor is obtained precisely. Using this relation, the minimum stress intensity factor at a critical crack length is determined for estimating mode-I fracture toughness of rocks on CCNSCB test. 1. Introduction High-level nuclear waste disposal and caprock in carbon capture storage must be designed considering its long-term stability. For this purpose, it is important to consider the strength of the bedrock around these rockmass structures. For the design of such rockmass structures uniaxial compressive and tensile strengths are used as a rock strength. These are macroscopic mechanical properties. But it is necessary to understand the fracture behavior of rockmass for the design and stability evaluation. In fracture process of rock, fracture toughness, which is microscopic mechanical property and represents resistance to the crack propagation, should be considered. In order to measure the fracture toughness of rock, several methods have been proposed by the International Society for Rock Mechanics (ISRM): Chevron bend (CB) test and Short Rod (SR) test by Ouchterlony (1988); Cracked Chevron Notched Brazilian Disc (CCNBD) test by Fowell (1995); Semi-circular Bend (SCB) test by Kuruppu, Obara et al. (2014) and so on. The SCB testing method which was proposed originally by Chong and Kuruppu (1984) has recently received much attention by researchers. This specimen is a semi-circular disk and has a straight notch (Cracked Straight Through SCB: CSTSCB) or chevron notch (Cracked Chevron Notched SCB: CCNSCB). Among above methods, the chevron notch has an advantage over the straight notch. By concentrating stress on the chevron notch tip, it can be fractured at a relatively low load. Then, the propagated crack during the loading is natural rather than artificial. However, the preparation of the chevron notch is relatively difficult compared to that of the straight notch. If the fracture toughness obtained from CSTSCB test is the same as that from CCNSCB test, it is unnecessary to use CCNSCB specimen. However, in the case of CCNSCB specimen, the normalized stress intensity factor used for fracture toughness evaluation has not yet be determined, because that behavior of crack initiation/propagation from the artificial notch and geometry of critical crack front at maximum load have not been made clear. In this study, firstly, using software ABAQUS, a cracking behavior from the tip of the artificial notch on CCNSCB test is analyzed by an extend finite element method (XFEM) in order to clarify the geometry of crack front in a process of cracking. Secondly using FEM, the stress intensity factor is analyzed for the 3D models with various geometries of the crack front during loading obtained by the XFEM analyses. Then, the relation between the crack length and the stress intensity factor is obtained precisely. From these analyses, the geometry of the critical crack front at the maximum load as well as the minimum normalized stress intensity factor is determined for estimating the mode-I fracture toughness of rock specimens for CCNSCB test.

Abstract Pick cutters are usually used in mechanical excavators such as Tunnel Boring Machines (TBMs), roadheaders, longwall shearers, and trenchers. It is important task to estimate the effect of cutting parameters (i.e. penetration depth, cut spacing, attack angle, skew angle, etc.) on the cutting performance of a pick cutter for optimizing machine's design. This study focused on the effect of skew angle on the cutting performance (i.e. cutter force and specific energy) of a pick cutter. The linear cutting machine (LCM) tests were performed for Linyi sandstone from China with different penetration depths and skew angles. The results showed that the three-directional cutter forces (normal, cutting and side forces) and specific energy were significantly affected by skew angle of a pick cutter. The results from the study can be used for optimizing of design parameters of mechanical excavators, and they will be background database to understand the cutting mechanism of a pick cutter. 1. Introduction The demand and application of mechanized excavation of rock have been steadily increasing in many civil and mining projects while its key technologies have been rapidly growing (Jeong et al., 2016). There are many types of mechanical excavation machine that have different shapes and purposes. Among them, tunnel boring machine (TBM), roadheader, longwall shearer, and trencher are widely used in civil and mining projects. In the design stage of the machine, it is important to determine the cutter arrangement and operational parameters as well as to evaluate the performance of the machine. Different types of rock cutting tools are available, and they are mainly categorized into the disc cutter and pick cutter. The primary fragmentation mechanism is different for different tools; a disc cutter breaks rock in the indenting process. The primary force of the disc cutter related to rock breakage is the normal force. However, the primary force of a pick cutter is the cutting force (the same term with the rolling force of a disc cutter) that acts in the direction parallel to the rock surface. Thus, the primary mechanism of rock breakage of a pick cutter is dragging. It has been reported that pick cutters can be used for rocks with a uniaxial compressive strength up to 120 MPa (Copur et al., 2012). Many parameters are used to design a mechanized excavation machine and to determine the machine operation conditions. They include the cutter type, cutter dimension, cutter tip angle and shape, number of cutters, cutter (cut) spacing, penetration depth per revolution, installation angle of cutter, cutting speed, thrust, torque, and RPM. Of the parameters, it is important to estimate the forces that act on the cutting tool (i.e., normal, cutting or rolling, and side force) when cutting a particular type of rock to determine the operational parameters. The cutting forces are used to predict the penetration rate and to determine the optimum operational parameters of a machine for the given ground condition. The normal force that acts on the cutting tool determines the thrust, while the cutting (rolling) force determines the torque and power of a machine during operation, which are important factors in the cutter-head design and machine operation (Jeong et al., 2016).

Abstract Deep geological repositories are a feasible and reliable way to dispose of spent nuclear fuel, and the mechanical and thermal properties of the host rock are key factors in their long-term safety. The mechanical properties of rock, including uniaxial compressive strength, tension strength and elastic modulus are thermally-dependent - for example, the uniaxial compressive strength of rock will decrease with increasing temperature, as a result of thermally-induced cracks between mineral particles. However, thermally-induced cracks and the micro-mechanisms of rock damage are difficult to observe by experiments. We therefore used uniaxial compressive strength test and Brazilian disk PFC models with heterogeneous thermal expansion properties to reveal the micro-mechanisms of rock damage induced by thermal heating. Based on the mineral compositions of granite, heterogeneous models contained four particle types with different thermal expansion properties (quartz, potassium feldspar, plagioclase, and biotite). A series of heating simulations (temperature increment: ΔT = 80 – 300 °C) showed that thermally-induced cracks occurred when the temperature increment exceeded 250 °C, and that the main crack type was tension crack. In homogeneous PFC models no thermally-induced cracking occurred even at ∆T = 300 °C. In simulations of thermal-mechanical coupling, the heterogeneous PFC models have the advantage of revealing differences in radius expansion of various mineral particles with increasing temperature, resulting in the additional and uneven distribution of contact force, stress concentration between different particles and bond breaking, and it lead to decreases in uniaxial compressive strength, elastic modulus and initial crack stress. 1. Introduction In the construction and operation of deep geological repositories of nuclear waste, the physical and mechanical properties of host rock are influenced by excavations and decay heat induced by the installation of nuclear waste canisters. This may result in a variety of changes in rock porosity and seepage conditions in the rock mass, the formation of excavation damage zones and the occurrence of thermally-induced rock damage, etc. Thermally-induced damage results from heterogeneous thermal properties in rock - for example, the thermal expansion coefficient of quartz (24.3 × 10 −6 /°C) is three times that of biotite (8.0 × 10 –6 /°C), leading to the differential expansion of mineral volume and macro-mechanical properties of rock with increasing temperature. In order to understand and interpret the influences of thermally-induced damage on the mechanical behavior of rock, homogeneous and heterogeneous bonded particle models were adopted to simulate a uniaxial compressive test (UCS) and Brazilian indirect tensile test in this study.

Abstract In the process of engineering investigation of rock mass, it is of great significance to obtain precise rock structural surface properties for rational design of the project and prevention of geological disasters during construction. A new three-dimensional topological feature description method for the rock face was proposed. This method is based on the circular structural profile line observed in the borehole and digital borehole camera technology application in three-dimensional topographical feature of the rock structure plane. This paper is based on the borehole wall plane development graph as the basic data, the basic information such as the occurrence of rock structural planes on the borehole wall is analyzed, and the structural surface section lines extracted from the borehole plane development diagram of the digital image processing technology are used. According to the three-dimensional information feature of the profile line on the structural wall of the hole wall, the profile feature parameters of the profile lines in each direction are calculated, and the structural surface is formed by referring to the correspondence between the profile feature parameters and the structural surface roughness coefficient ( JRC ). Then the roughness coefficient rose diagram is made to describe the three-dimensional roughness of the rock structure surface. 1. Introduction In recent years, China has gradually attached importance to the use of underground space in cities and the exploration and development of deep resources. Many major projects have gradually been put on the agenda, and engineering safety issues have also increased. The use of test technology by engineering designers to obtain precise and accurate engineering properties of deep rock masses is of great significance to the rational design of the project and the prevention of geological disasters during construction. The study of rock structural planes is the basic work of analyzing the engineering properties of rock masses. Numerous studies and experiments have shown that the mechanical properties of the rock face are not only related to the characteristics of the wall rock and the combined state of the face, but also affected by the surface morphology of the face. For a hard structural surface with a small degree of filling, the surface morphology of the structural surface is the main influencing factor controlling the mechanical properties of the structural surface (Gao et al.,2010). However, obtaining information on deep rock structural planes by drilling and coring has many limitations. First, during the core drilling process, due to the rotational displacement of the core, the exact information of the rock structural plane is destroyed. Secondly, the disturbances such as high-speed rotation of the drill bit and the circulation of the drilling fluid in the coring tube generate a structural plane on the core affect the determination of structural surface closure (openness) and structural surface filling. It can be seen that using core data as a source of rock structural plane information is not accurate enough. Therefore, it is necessary to propose an in-situ measurement technique to directly measure the structural plane of the hole wall of the drilled hole and obtain the surface morphology information of structural plane on the hole wall.

Abstract This paper shows a modelling framework for simulation of thermal effect on the fracture behavior of a clay-rich sandstone. The framework was based on the particulate discrete element method (DEM), combined with a coupled thermal-mechanical scheme. Pure mode I and mode II, and mixed-mode (I+II) fracture toughness of the rock was measured under elevated temperatures (up to 600°C) using the ISRM-suggested semi-circular bend (SCB) specimens. The simulation results were validated against analytical predictions. 1. Introduction This study relates to thermal effect on fracture toughness of rock. Fracture toughness is a parameter of geo-materials that describes its ability to resist fracturing. This parameter is fundamentally important to rock and reservoir engineering applications, for example hydraulic fracturing for geothermal energy, oil and gas extractions (especially in the tight and low permeable formations), as well as wellbore stability assessment. Although fracture toughness is often deemed as an intrinsic property of rock, it still can with factors including geological anisotropy (e.g., Chandler, 2016), temperature and confinement (e.g., Funatsu et al., 2014), experimental setup and loading conditions (e.g., Shang et al., 2018a). Chong and Kuruppu (1987) experimentally investigated the fracture behvaiour of layered oil shale, where semi-circular bend (SCB) specimens (later suggested by ISRM) containing different proportions of organic matter were prepared. It was found that organic-rich shale specimens had a higher fracture toughness than leaner specimens. Chandler et al. (2016) reported fracture toughness measurements on Mancos shale in three principal crack orientations (i.e., arrester, divider and short-transverse) using a short-rod method, and found that fracture toughness of the divider oriented specimens was much higher (increased by a factor of 3.4) than that measured using the short-transverse oriented specimens. Temperature can be another important factor that affects fracture toughness of rock, especially in the deep underground. It is well accepted that fracture toughness of a rock material can increase under elevated temperatures until it reaches an elasto-plastic transition phase (Mahanta, 2016), after which a decrease in fracture toughness can be seen. The transition phase is rock type- and temperature-dependent, which is probably due to the variations in mineral composition leading to various thermal dilations, as well as due to mineral grain interactions at microscale. This paper reports a particulate DEM study on the thermal influence on mixed-mode fracture toughness of a clay-rich sandstone, where a fully coupled thermal-mechanical model was used. 2. Methodology In the study, a series of semi-circular bend (SCB) specimens with the ISRM-suggested dimensions were numerically manufactured using the Particle Flow Code (PFC) to measure the fracture toughness of rock under elevated temperatures (up to 600°C). Fig.1 shows a representative numerical sample used in the study, where main minerals in the Midgley Grit Sandstone (MGS, Shang, 2016) were differentiated by assigning particles with different thermal expansion coefficients (i.e. quartz, 24.3×10 −6 K −1 ; feldspar, 8.7×10 −6 K −1 ; biotite, 1.0×10 −6 K −1 ; clay, 3.6×10 −6 K −1 ) (Fei, 1995; Zhao, 2016). Thermal strains can be produced in the sample by accounting for the thermal expansion of the particles as well as the bonds which act as thermal pipes (only apply to parallel bond). Specific heat of each particle and thermal expansion per unit length were 1.0e 3 J/kg°C and 0.3°C/Wm, respectively. The DEM samples used in the study were first heated to desired temperatures up to 600°C, followed by three-point bending tests (without cooling phase) as shown in Fig. 1. It is worthwhile mentioning that a group of particles (green particles in Fig. 1) contacting the loading bar and the two supporting bars was generated and these particles were not heated (thus, no thermal expansion) so as to eliminate stress concertation which can be due to the different contact conditions arising from different expansion coefficients of the particles. Sample dimensions are shown in Fig. 1, in which sample radius R (50 mm), span length 2s (55 mm), thickness t (30 mm), and crack length a (25 mm) are constants, and the crack angle β varied from 0° to 46° to allow a complete modes of fracture toughness to be measured (Shang et al. 2018a). Table 1 shows the micro-parameters used in the study which have been calibrated by Shang et al. (2017).

Abstract In CO 2 geological storage, CO 2 /brine/rock chemical interactions may lead to changes in mechanical properties of rocks. These changes can have impacts on performance and integrity in storage depending on their intensities. In case of sandstones consisting mainly of quartz and feldspar grains, there may be little changes in the properties because of low reactivities of the minerals. On the other hand, significant changes may occur in case of volcanic sandstones because they contain high-reactivity volcanic glasses. However, influences of the chemical interactions on the properties of volcanic sandstones have not been investigated so far. Thus, we have conducted triaxial compression experiments on two cylindrical volcanic sandstone samples consisting mainly of andesite/basalt and scoria grains (porosity: ca. 33%) at a confining/axial pressure of 30 MPa, pore pressure of 15 MPa, CO 2 saturation of 50% or 77% and 60°C for several weeks. Bulk modulus, Young's modulus and Poisson's ratio were measured intermittently. Before and after the experiment, porosity and permeability were also measured on each sample, and initial and final brine chemistries were analyzed. Additionally, X-ray CT was conducted on the samples before and after the experiment. Changes in bulk modulus and Young's modulus were qualitatively similar whereas Poisson's ratio was almost constant. In case of one of the sample that contained relatively large scoria grains of high porosities, bulk modulus first decreased, then recovered partially, and finally became constant. In case of the other sample, bulk modulus first increased and then became constant. The decrease and increase in bulk modulus may have been caused respectively by dissolution-induced collapse of the relatively large scoria grains and by precipitations of some minerals such as silica minerals. Permeability of one of the samples increased while permeability of the other sample decreased, although porosity decreased for both samples. 1. Introduction To solve the global warming problem, many countries have attempted to reduce CO 2 emissions. CO 2 capture and storage (CCS) utilizing reservoir rocks such as porous sandstones at depth is considered as one of promising ways to reduce CO 2 emissions. Indeed, CCS demonstration tests have been conducted in various countries. A test has been conducted in Sleipner field (North Sea) since 1996 (Baklid et al., 1996), where CO 2 injection has averaged almost 1 Mt per year with more than 16 Mt successfully stored by 2016 (White et al., 2017). A test has also been conducted in Tomakomai, Japan. The storage potential in Japan by the proposed scheme is evaluated to be 71.6 Gt, which corresponds to the emission in Japan for 53.6 years (Suekane et al., 2007).

Abstract The sprayed waterproofing membrane has high adhesion to a substrate, such as excavated rock surface and shotcrete. Because it is easily sprayed and bonded on the substrate, the sprayed waterproofing membrane is being considered as an alternative method of a conventional sheet waterproofing membrane. The sprayed waterproofing membrane has high adhesion to the substrate, such as excavated rock surface and shotcrete. Also, because of its ductility and flexibility with high elongation, it can prevent the substrate from a brittle failure. The purpose of this study is to evaluate the sprayed waterproofing membrane as a possibility of auxiliary support system. First, the sprayed waterproofing membrane was mixed and produced. Next, physical properties of the membrane were evaluated. After that, inner surfaces of shield segments were coated by the sprayed waterproofing membrane with a thickness of 3, 5 and 7 mm. Finally, full-scale loading tests were carried out to evaluate a structural reinforcement of shield segments. From the test, it was confirmed that the structural loading capacity of the shield segment could be improved by a coating of the sprayed waterproofing membrane. 1. Introduction The sprayed waterproofing membrane is a kind of new waterproofing materials recently developed as an alternative measure of a conventional waterproofing sheet (ITAtech, 2013). Contrary to the waterproofing sheet, it shows characteristics of high adhesion and fully bonds to the substrate, such as rock surface and shotcrete. Because of these features, the sprayed waterproofing membrane can form an integrated composite structure with a concrete lining and function as a single-shell structure (Makhlouf and Holter, 2008; Thomas, 2009; Holter, 2016; Chang et al., 2016a; Chang et al., 2016b). In other words, the thickness of the concrete lining closely associated with the construction cost reduction can be decreased during the tunnel construction or reinforcement work. Also, issues about the repair and rehabilitation of deteriorated tunnel structures have been increasing recently in Europe. Particularly, in the case of cyclic reinforcements of existing tunnels, a new problem that inner sections of tunnels are gradually being reduced can emerge. Contrary to Thin-Spray-on Liner (TSL) developed for the use of rock support, the sprayed waterproofing membrane, as its name indicates, was initially developed for waterproofing, not for the support system. Moreover, any sources are not presented by ITAtech (2013) for the application of the sprayed waterproofing membrane as tunnel support or reinforcement. Nevertheless, because of its similarity to TSL in terms of a chemical composition and construction technique, various studies (Makhlouf and Holter, 2008; Ahn, 2011; Chang et al., 2015; Chang et al., 2016a; Lee et al., 2017) have attempted to review the applicability of sprayed waterproofing membrane as a new tunnel support system, not only for waterproofing. The object of this study is to evaluate the structural reinforcement of the shield segment coated by the sprayed waterproofing membrane through a full-scale loading test. Once the sprayed waterproofing membrane was being coated and hardened on the inner surface of the shield segment, full-scale loading tests were carried out to evaluate the reinforcing effect by measuring the early-age cracking load and the failure load of the shield segment.

Abstract In this paper, a coupled mechanical model is proposed to analyze the influence of the thermal stress, the non-uniform geologic stress and the fracture pressure on the mechanical characteristics of the cement during fracturing of shale gas wells. In this model, the casing-cement-formation assembly is described as a multilayer string system with elastic property. The system is subjected on a coupled effect of three kinds of load: the thermal stress generated by heat transfer from the wellbore to the formation, the hydraulic pressure from fracturing operation, and the non-uniform geologic stress. The analysis model is established and the governing equation is deduced based on the elastic mechanics. A computer program is developed to solve the equation. On this basis, the influence of cement thickness, elastic modulus, and Poisson's ratio on the mechanical characteristics of the cement sheath is discussed in detail. Analysis results show that temperature variation generates circumferential compression stress on the system. While the fracturing pressure and the non-uniform geologic stress produce a periodical circumferential stress and radial stress. Under the combined loads, the cement is inclined to tension failure. The temperature has a positive effect on the safety of the cement sheath. The orientation of the tension failure is determined by the non-uniform stress field, which is paralleled to the major principal stress. This study has a reference for the prediction and control of well integrity of shale gas wells during fracturing operation. 1. Introduction Due to the low porosity and low permeability of shale reservoirs, the multi-stage hydraulic fracturing is the important and irreplaceable techniques for shale gas development (Bai, 2014; Liu, 2014). During the operation, the fracturing fluid is pumped into the reservoir through the casing, which would induce well failure and cement sheath damage. The schematic diagram of multi-stage fracturing operation is shown in Fig. 1. Almost all shale gas wells have well integrity problems, such as sustained casing pressure (Ma, 2017; Zhu, 2016), casing collapse and cement failure, etc. Many published literatures have discussed the problems. Some papers (Tao, 2017; Chu, 2015; Liu, 2017; Shen, 2017) have proposed that the gas channeling from the reservoir to the wellhead through the damaged cement sheath is a main factor generating the well failure. In the fracturing operation, the cement sheath is suffered tension stress under the external loads. Mostly, the tension stress is much higher than the tension strength, which is just 3.2MPa-4.3MPa (Tao, 2017). Moreover, the tension strength would decline under cyclic fracturing pressure (Shadravan, 2015). Some laboratory tests (Shadravan, 2015; Bois, 2012; Goodwin, 1992) show that the radial crack generated by the tension stress is the main failure mode. Besides, the non-uniform geologic stress acting on casing and cement is another important reason for well failure. The influence of non-uniform geologic stress on the collapse strength of casing has been detailed discussed (Fang, 1995, 2015; Yin, 2006; Li, 2009; Wang, 2015).