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Hot dry rock (HDR) geothermal resource is a renewable green energy source with great exploitation potential. The burial depth of HDR generally exceeds 2500 m and is typically under high in situ stress conditions, resulting in an ultralow permeability of the rock formations. To enhance the permeability of these formations, hydraulic fracturing is widely used as a reservoir stimulation technique in HDR geothermal resource exploitation. The differences in burial depth, in situ stress, and geological environment require different engineering designs when implementing hydraulic fracturing. Therefore, the confining pressure and injection rate play significant roles in determining the effectiveness of hydraulic fracturing, as they affect the propagation and distribution of fractures in the rock formation. To quantify the impact of these factors on the effectiveness of hydraulic fracturing, simulation experiments, and permeability tests were conducted using granite specimens under various confining pressure and injection rate conditions. The results of these experiments revealed the relationships among the confining pressure, injection rate, breakdown pressure, and permeability enhancement of the granite. The breakdown pressure of granite increased with the confining pressure, while the injection rate had little effect on the breakdown pressure. The hydraulic fractured sample produced new penetrating fractures, which increased the reservoir permeability, and owing to the higher complexity of hydraulic fractures under low confining pressure, the increase of permeability is correspondingly higher. The research results can provide an important reference for efficient stimulation development technology of deep HDR geothermal resources. [ABSTRACT FROM AUTHOR]

During deep underground coal mining, coal is typically fractured under high in situ and mining-related stresses, thus increasing the risk for dynamic disasters. However, knowledge regarding the mechanical and permeability characteristics of initially fractured coal remains limited. In this study, laboratory investigations were performed to examine the anisotropic strength, failure modes, and permeability of initially fractured coal subjected to true triaxial stresses. The results indicated that initially fractured coal can be classified into semi-brittle Class I failure modes. A new failure plane can be formed for initially fractured coal samples after failure, which was different from the intact coal samples' failure mode. The peak strength of initially fractured coal was typically observed when the maximum principal stress was subjected perpendicular to the bedding planes, while minimum values were obtained when the maximum principal stress was subjected parallel to the butt cleats. The brittleness of initially fractured coal was increased with intermediate stress. The permeability evolution curves for initially fractured coal exhibited an L-shaped trend. The pulverized coal grains in initially fractured coal can block the gas flow channel contributing to the continuous decrease in permeability. Intermediate stress exerts a more significant effect on permeability reduction when deviatoric stresses are applied parallel to cleats in coal. [ABSTRACT FROM AUTHOR]

Outbursts comprise the predominant natural hazards in Chinese underground coal mines. Extracting high content gas within coal seams is one of the most effective ways to reduce the risk of triggering outbursts. However, with the depth increase of coal mining production, conventional gas drainage might be failed due to the low permeability of coal seams. Additional permeability enhancement methods should be adopted to improve the gas drainage efficiency. In this study, we proposed the application of liquid carbon dioxide fracturing for enhancing gas drainage in a underground coal mine in China with low permeability coal seams. By drilling cross-seam boreholes, liquid carbon dioxide fracturing was simultaneously performed in the two drilled fracturing boreholes. The effective damage radius of liquid carbon dioxide fracturing was further identified by continuously monitoring pure gas flow rates in different observation boreholes. After liquid carbon dioxide fracturing, there was no significant decrease in pure gas flow rate of observation boreholes for a period of 2 weeks. A conceptual model of liquid carbon dioxide fracturing was proposed for illustrating the mechanisms of improving gas drainage efficiency. Some methods for further optimizing gas drainage with the operation of liquid carbon dioxide fracturing under various thickness of coal seams and geological conditions were discussed. These results suggest that the application of liquid carbon dioxide fracturing are effective for gas control and hazards prevention in underground coal mines. [ABSTRACT FROM AUTHOR]

It is important to understand the gas flow properties in coal and sandstone under different stress conditions for underground carbon dioxide storage and coal bed gas drainage in underground engineering. In an actual project, the rock layers are complex and varied, and the in situ stress presents a significant three-dimensional anisotropy (σ 1 > σ 2 ≠ σ 3). Although a large amount of data on the permeability of coal have been reported previously, studies on the permeability of layered composite coal rock under true triaxial stress conditions are lacking. In this study, the permeability of layered composite coal rock under true triaxial stress conditions was measured by using a true triaxial apparatus. Under experimental stress conditions, the permeability always decreased as the principal stress increased. The thickness changes in coal seams and sandstone formations have major influences on the evolution of composite coal rock permeability. Furthermore, the normalized permeability increases with the thickness ratio of sandstone to coal. We analyzed the stress state of layered composite coal rock by considering the interaction of coal and sandstone under true triaxial stress conditions. Based on the anisotropy consideration of coal rock and the stress difference of composite coal rock masses, a permeability model for layered composite coal rock under true triaxial stress condition was proposed (TCP model: layered composite coal rock permeability model). It was found that this model can well reflect the permeability characteristics of composite coal rock under true triaxial stress conditions while simultaneously considering the effect of the three principal stresses and the mutual strain restraint effects of coal and sandstone. • Influence of intermediate principal stress on permeability of composite coal rock. • Effect of combination type and thickness ratio on permeability of coal-rock mass. • True triaxial stress state of layered composite coal rock. • New permeability model of layered composite coal rock. [ABSTRACT FROM AUTHOR]

It is critical to understand the gas flow behavior in coal under a reservoir stress condition for coal bed methane production, underground coal mining, and CO 2 -sequestration in deep coal seams. With respect to coal seams, the in-situ stress is anisotropic and generally exists under true triaxial stress ( σ 1  >  σ 2  >  σ 3 ) conditions. Additionally, the flow channels determining the permeability of coal are also anisotropic. This dual anisotropy produces difficulties in replicating the gas transport characteristics of coal at the laboratory scale, and there is a paucity of relevant studies. In this study, we performed a series of permeability measurements using cubic anthracite coal samples and changing the principal stresses and flow directions under various true triaxial stress conditions. The coal permeability exhibited greater anisotropy in the vertical direction as a result of the presence of minerals in cleats across the bedding plane. After each principal stress compression at a differential stress of 20 MPa, the permeability in each direction decreased by an order of magnitude. With an increase in the intermediate stress parameter, the permeability values of two horizontal cleats experienced higher decreasing rates compared with the vertical bedding permeability. This increased the significance of the horizontal permeability anisotropy. With respect to the true triaxial stress condition with a higher horizontal principal stress ( σ H  >  σ h  >  σ v ), a higher permeability reduction was observed during the principal stress loading period. The butt cleat plane was more sensitive to changes in the principal stress because of the lower connectivity of the flow channels induced by the closure of the face cleat that acted as a cross-linked pathway. The anisotropic permeability data measured under true triaxial stress conditions were well expressed by an exponential equation containing different mean cleat compressibility and stress terms. The cleat compressibility values in different directions were obtained by data fitting. [ABSTRACT FROM AUTHOR]

This study investigated the stress–strain–permeability relationship of a Chongqing coal under the stress path during the mining process. The abutment stress was first measured at the longwall (LW) face 3211 of Songzao Mine in Chongqing, China. The field monitoring results revealed that the concentration coefficient of the abutment stress was approximately 1.5–2.0 during protective layer mining. Then, triaxial compression tests for the gas-infiltrated coals were conducted under the above stress path and different gas pressures. These tests, with the simultaneous actions of unloading confining stress and loading axial stress, are called SUL tests. The triaxial compression tests revealed that the peak deviatoric stress and the corresponding strain of coal under SUL tests were lower than those under conventional triaxial compression (CTC) tests. Poisson's ratio was higher, but the elastic modulus was lower in SUL tests. The permeability evolution of coal under the SUL tests underwent four distinct stages: the increasing stage in the process of SUL, decreasing stage, slowly increasing stage beyond the yield point, and sharply increasing stage after the peak stress. With the increased gas pressure, the peak deviatoric stress and corresponding axial strain decreased, Poisson's ratio increased, and elastic modulus decreased. Further, the permeability of coal increased with increasing gas pressure in the complete deformation process. [ABSTRACT FROM AUTHOR]

Permeability evolution of sandstone is of great significance in the development of tight sandstone gas reservoirs. Traditional laboratory tests have the disadvantages of high cost and long testing time. Therefore, the present study employed use artificial intelligence systems, i.e., backpropagation neural network (BPNN), genetic programming (GP), and multiple regression analysis to construct prediction models of sandstone permeability based on the coupling effect of true triaxial stress field and pore pressure. The results showed that the permeability prediction obtained from the systems fit well with the experimental data, and evidenced that permeability increased with pore pressure and decreased with increase in principal stress. Sensitivity analysis showed that the pore pressure has the greatest influence on sandstone permeability under different true triaxial stress. The effect of anisotropic principal stress on permeability exhibited σ 1 > σ 2 > σ 3 under fixed pore pressure. Further assessment based on a combination of five evaluation indexes showed that the prediction accuracy of the BPNN model was better. • The permeability prediction models are built by BPNN, GP, and regression analysis. • The permeability prediction data fit well with the experimental data. • The pore pressure has the greatest influence on sandstone permeability. • Under true triaxial stress, the influence on permeability follows σ 1 > σ 2 > σ 3. • The BPNN model is more accurate than the GP and multiple regression models. [ABSTRACT FROM AUTHOR]

The effective stress principle plays an important role in the study of the permeability evolution and mechanical behavior of coal and rocks. A key to evaluating the effective stress is determining the evolution of the effective stress coefficient α. However, conventional triaxial stress-path tests are not suitable for reproducing the actual stress state of coal and rocks and thus determining the effective stress coefficient. Therefore, this study was conducted to investigate the anisotropic characteristics of the effective stress coefficient for sandstone under different true triaxial stress and pore pressure conditions. The results show that the effective stress coefficient exhibits anisotropy due to the different principal strains in three directions and the anisotropy of pore structure, and it is closely linked with the pore pressure and principal stress. An increase in pore pressure causes sandstone particles that block the seepage channel to migrate, which reduces the sensitivity of permeability to principal stress, increasing the effective stress coefficient. When principal stress increases, pores and fractures are compressed, which reduces the sensitivity of permeability to pore pressure, resulting in a decrease in α. However, as principal stress continues to increase, effective stress coefficients can increase in the directions of major and intermediate principal stresses, while an α 3 beyond unity appears in the direction of minor principal stress. This is related to the pore fluid flowing through highly compressible clay aggregates, in which the pore area is large, and the sensitivity of permeability to pore pressure is enhanced. The effective stress coefficient increases with an increase in permeability due to the effect of porosity. A new formula for calculating the volumetric strain of a linear elastic isotropic porous medium is established based on the anisotropy of the effective stress coefficient, which can be applied to experimental results. • Effective stress coefficient α exhibits anisotropy under true triaxial stress. • α increases with an increase in pore pressure. • α decreases first and then increases as the principal stress increases. • Clay minerals between quartz grains can increase α , even beyond unity. • As the permeability increases, α also increases due to the effect of porosity. [ABSTRACT FROM AUTHOR]

The extraction of coalbed methane can supply clean energy to society and improve the safety of subsurface coal mining. The low and ultra-low permeability of coal seams has resulted in the significantly low efficiency of methane production in surface and subsurface extraction systems. Fluid stimulation has been extensively applied for the enhancement of formation permeability. However, the response of coal seams to fluid stimulation may be different from other formations due to their unique structure and mechanical properties. Moreover, the presence of shear-fracturing stimulation and its effect on permeability enhancement is more significant in coal seams during fluid stimulation. In this study, a fluid injection-induced hydrofracturing treatment and shear-fracturing stimulation were separately investigated through laboratory experiments. The permeability of both intact and fractured specimens was used to directly evaluate the efficiency of these two types of fluid stimulations in different types of reservoirs. The experimental results indicated that the closure of hydraulic (i.e., tensile) fractures significantly inhibited the permeability enhancement of the hydrofracturing treatment in coal seams, and resulted in the permeability of fractured coal specimens were considerably lower than that of hard rocks (e.g., shale and sandstone). The results also demonstrated that fluid injection-induced shear stimulation in the coal specimens resulted in dilation behavior primarily associated with permeability enhancement. This was attributed to the fact that the exfoliated particles and masses prop shear fractures and increase their stiffness. It was found that, because of the weak mechanical and discontinuous properties of coal seams, an increase in the deviator stress improved the feasibility of shear-fracturing stimulation. Finally, fluid stimulation can be achieved using low viscosity fluids, such as L/Sc-CO 2 , as the fracturing fluid tended to form a shear dilation zone with high permeability in the coal seams. • The closure of hydraulic fractures inhibit the efficiency of hydrofracturing in coal seams. • The shear-dilation zone induced by fluid stimulation significantly enhance coal permeability. • The mechanical properties of coal and low viscosity fluid advance the feasibility of shear stimulation. [ABSTRACT FROM AUTHOR]

Because of periodic disturbance during coal seam excavation and support, the surrounding rock is subjected to cyclic unloading-reloading. To study the effect of pressure-relief on coal fields during gas drainage and mining, the permeability, acoustic emission (AE) and energy dissipation properties of coal under tiered cyclic unloading were experimentally investigated. Permeability enhancement rate (PER), AE signal change rate and a damage variable were defined to describe this process. Hysteresis, memory and Felicity effects are revealed. These results show that, the step-wise increase of strains and permeability display a hysteresis effect under tiered cyclic unloading. The axial residual strain increases exponentially, while the radial residual strain increases as a quadratic function, and the PER increases. The AE signals show Kaiser effect when the unloading capacity is small. Conversely, the Felicity effect is displayed when the unloading capacity is large. The cumulative AE signal and the axial strain exhibit good synchronisation and memory characteristics. The dissipated energy increases as a quadratic function, and the developed damage variable also increases, the critical damage variable of coal failure is estimated to be D c ≈ 0.8. • Seepage, AE and energy dissipation properties of coal and their intrinsic relationship are analysed. • Definition of PER and AE change rate for quantitative characterization of the effect of unloading confining pressure. • Hysteresis effect,Kaiser effect and Felicity effect under unloading confining pressure are revealed. • A new damage variable function based on dissipation energy is proposed under tiered cyclic unloading. [ABSTRACT FROM AUTHOR]

The permeability anisotropy of shales can be attributed largely to bedding planes. It is critical to study the bedding effect on permeability evolution for shales. We conducted an experiment on shale permeability anisotropy under true triaxial stress conditions. Even though the mean stress of shales was different, the permeability still exhibits obvious bedding dependent. In this study, we present a new permeability model considering bedding planes. The introduction of characteristic functions and parameters characterizes the transformation process from bedding to non-bedding during compression. Compared with the experimental data, we obtained a good fitting result. Owing to the increase in the resistance of the pressurized gas into the fracture system, Biot's coefficient α decreases with increasing mean stress. The porosity sensitivity exponent s parallel to the bedding planes are larger than those perpendicular to the bedding planes. In our opinion, owing to the smaller stiffness of the bedding plane, the relatively large amount of pore deformation is caused by the loading on the vertical bedding planes. Furthermore, we introduce η to characterize the effect of non-bedding and bedding on permeability. The permeability of shale or bedding is more sensitive at lower stress than at higher stress and the fluid flow through the non-bedding in shales cannot be ignored. • Characteristic functions and parameters show the deformation evolution of bedding. • We established the stress-dependent permeability model considering bedding effect. • Biot's coefficient α decreases with increasing mean stress. • The porosity sensitivity exponent s exhibits anisotropy. [ABSTRACT FROM AUTHOR]

Although the mechanical behaviors and flow aspects of sandstone have been previously investigated, studies of the effect of the intermediate principal stress (σ2) on the strength, deformation, and permeability of sandstone are lacking. In this work, the mechanical behaviors and permeability of sandstone under true triaxial stress conditions were investigated using a newly developed true triaxial geophysical apparatus. The experimental results showed that with increasing σ2, the peak strength, octahedral effective normal stress, and octahedral effective shear stress of the sandstone increased, and the rate of increase decreased. This is because a larger intermediate principal stress coefficient b has an inhibitory effect on rock strength. In our study, as the ratio of σ2/σ3 increased, the specimen entered compressive strain in the σ2 direction during the first stress drop. The stress and strain path deviations occur during rock failure. The amount of deviation increased as the σ2 increased before the peak stress. This phenomenon indicates that elastic mechanics are not suitable for understanding this sandstone rock during its failure. The permeability evolution of the sandstone under true triaxial stress conditions was measured and analyzed to investigate the effect of σ2. During the complete true triaxial stress-strain experiments, the variation we found in gas seepage velocity could be divided into two stages. Before the first pressure drop, the gas seepage velocity was mainly affected by volume strain. After the first pressure drop, the seepage velocity was affected by the deviator strain, which can change the seepage channels. [ABSTRACT FROM AUTHOR]

Coal belongs to sedimentary rock with obvious bedding planes. The existence of bedding weakens the continuity and integrity of coal. Deformation and permeability anisotropy of coals, to a certain extent, is attributed to the bedding planes. We performed experiments of deformation and permeability evolution of coals under true triaxial stress conditions. The experimental results indicate that the volumetric strain and bedding jointly affect permeability. An analytical model for stress-strain relationship of coals containing beddings is developed to quantify the bedding effects under true triaxial stress conditions. In the model, the deformation and permeability of the bedding and non-bedding are separated through bedding ratio and bedding elastic modulus. The bedding ratio is defined as the ratio of the total length of bedding to the total length of coal normal to bedding planes, which is a parameter closely related to the porosity. The elastic modulus is divided into four parts: a bedding elastic modulus and a non-bedding elastic modulus in the direction normal to bedding planes, and two elastic moduli in the direction parallel to bedding planes. The four elastic moduli are calculated by the analytical model. The bedding elastic modulus is relatively small, which shows that the bedding effect cannot be ignored. The permeability is highly sensitive to the bedding of coal with low stress in the direction normal to the bedding. The bedding ratio always affects the volumetric strain. The permeability of the coal is divided into bedding and non-bedding permeability. The ratio of the bedding permeability to the total permeability is different due to different stresses in the direction normal to bedding planes, which is linking with the compression of bedding. A permeability model which can reflect the different effects of beddings and non-beddings to the total permeability is proposed and verified. [ABSTRACT FROM AUTHOR]

Permeability is a crucial parameter for characterizing gas transport and exchange in coal seams and is fundamental for designing and optimizing gas extraction and control methods. However, the permeability of coal seams is mainly determined through laboratory tests, with few studies using in-situ tests. To address the limitations of laboratory tests, such as their small scale and poor ability to provide engineering guidance, this study proposes a novel in-situ permeability test (IPT) system to investigate the fluid-flow aspects of geological formations. The system comprises the water-injection sealing and gas-injection testing subsystems. By considering the coal seam surrounding a gas injection borehole interval as a filter, the equation for calculating the in-situ coal seam permeability was derived based on steady-state gas-seepage theory. The IPT system was then assembled and used to test the in-situ permeability of the JI 15 coal seam at the Pingdingshan XII coal mine. The study estimated the representative elementary volume (REV) of the tested coal seam permeability, analyzed the applicability of Darcy's law during the tests, and obtained the anisotropic permeability of the coal seam by drilling test boreholes in different directions within the coal seam. Finally, the reliability of the new test method was verified by comparing its results with laboratory and well test data. The results demonstrated the effectiveness and reliability of the novel IPT system and encouraged further investigations into efficient gas extraction and control in deep coal seams. • A novel in-situ permeability test system based on steady-state flow theory is proposed. • The anisotropic permeability of in-situ coal seams is tested at engineering scale. • Τhe tested in-situ permeability are compared with the laboratory and well test results. [ABSTRACT FROM AUTHOR]

Fracking to approach permeability enhancement is indispensable to enhance coalbed methane recovery, which can significantly reduce greenhouse gas emissions and produce substantial clean energy. To access efficient fracking, samples of Permian low permeable coal reservoir were cracked into different sizes or scales of blocks and particles with liquid nitrogen cryogenic freeze fracturing (FF) by maximizing the underlying heterogeneity of coal. To investigate the crack efficacy, this study systematically examined the permeability evolution and mesoscopic cracking behaviors of coal with different water contents and cleat–fracture systems in the context of cryogenic FF. Results showed that the permeability enhancement and microcracking tended to occur with increasing water content of coal sample; and the efficacy of cryogenic FF on the tighter coal sample was more remarkable. However, the permeability does not strictly increase with the cycles of cryogenic FF and has a close relationship with water content, structural plane direction, efficacy of cryogenic FF, and porosity compaction. The mesoscopic cracking behaviors indicate that numerous smaller pores are iteratively, not strictly sequentially, cracked and become connective in this process. The permeability evolution of coal sample is identified as significantly associated with the mesoscopic cracking behaviors. Notably, the first cycle of cryogenic FF acted on the detected several scales of pores and micro fissures, and partially caused these structures to be opened and interconnected to be permeable. Two main changes were observed in the microcracking of the coal samples in this study: 1) nonuniform shrinkage deformation and micro fissure expansion; and 2) pores opening mostly in the macropore and mesopore scale. It is reasoned that thermal cracking and intermittent opening of seepage pores due to the phase transition of free water in pores or micro fissures ultimately contribute to the permeability enhancement in low permeable and heterogeneous coal. [ABSTRACT FROM AUTHOR]

Investigations of the directional permeability evolution of intact and fractured coal are conducted under different simulated geological conditions. The effects of fracture geometry, water adsorption and stress conditions on the permeability evolution of coal as a function of stress are systematically studied. The results indicate that permeability anisotropy is more pronounced in fractured coal than in intact coal. The permeability order, i.e., the k fa > k bu > k be relationship, is maintained following the introduction of macrofractures into coal. The fracture compressibility in the butt cleat plane flow direction is higher than that in the other two flow directions for both intact and fractured coal. The presence of water in coal can reduce the permeability by up to one order of magnitude, and a more significant permeability decrease is observed in coal specimens containing rough macrofractures. Permeability hysteresis for both intact and fractured coal is somewhat dependent on the stress condition. The hysteresis effect of coal is more significant under triaxial stress conditions and less pronounced under true-triaxial stress conditions. [ABSTRACT FROM AUTHOR]

Highlights • Effects of intermediate principal stress and stress Lode angle on sandstone. • Influence of gas flow direction and principal stress direction on permeability. • The strength of the rock under true triaxial stress conditions is discussed. • Response of plastic strain to stress Lode angle was discussed based on MLC criterion. Abstract The magnitude and direction of geo-stress undergoes complex changes following disturbance by artificial excavation in underground engineering. Tests were conducted using the self-made multi-functional true triaxial geophysical apparatus to investigate the influence of stress Lode angle on deformation, deformation modulus, and permeability of sandstone under true triaxial stress conditions (σ 1 > σ 2 > σ 3). The results indicate that principal, volumetric, and deviatoric strains, as well as permeability varied with the stress Lode angle, and eventually increased/decreased at different levels. For constant deviatoric stress and variable mean stress, the plastic strain decreased with increasing M (ratio of deviatoric stress q to mean stress p), whereas the permeability increased. For constant mean stress and variable deviatoric stress, the principal, volumetric, and deviatoric strains, as well as the permeability decreased first and then increased with the increase in M ; the rock generated fracture surface when M was relatively large. The gas flow and stress axis directions significantly influence the value and changing trend of the permeability. With increasing stress Lode angle, the permeability increased first and then decreased. In our stress condition testing, the permeability value and variation range were maximum when the gas flow direction was parallel to σ 1 ; when it was parallel to σ 3 , the permeability demonstrated an upward trend, but with a smaller increase range. Conversely, when it was parallel to σ 2 , the permeability decreased and the variation range was minimized. Finally, based on the analysis of the experimental results, we developed a permeability model that is expressed by both volumetric and deviatoric strains. [ABSTRACT FROM AUTHOR]

The effective stress law and the permeability play a notable role in dealing with the gas-solid coupling problem of porous media. The key parameter to quantify the influence of pore pressure to effective stress is the effective stress coefficient α ij. However, current relevant researches are mainly focused on the pore elastic flow characteristics in the elastic stage or hydrostatic pressure under conventional triaxial stress state, which are difficult to reflect the actual formation stress condition. To this end, the present study was conducted to investigate the influence of induced damage on the effective stress coefficient and the permeability of sandstone under true triaxial stress. The results showed that the effective stress coefficient and the permeability were closely related to the damage evolution and fracture propagation. α ij exhibited obvious anisotropy, α 1 was larger than α 2 and α 3 , and α 3 > α 2 appeared in the horizontal direction. α ij increased with increasing the fracture density and opening, even greater than unity. Increasing the initial horizontal stress could reduce α ij under the damage state. The elastic modulus E ij also exerted anisotropy during loading, E 1 basically exhibited an increasing trend followed by a decrease as the axial strain increased, E 2 and E 3 were continue to degrade with increasing the axial strain. Loading the deviatoric stress could cause damage, which induced the initiation and propagation of microcracks, and in turn led to the nonlinear stress-strain relationship and volume expansion of the rock, so the permeability increased, and it had increased sharply before reaching the peak strength. Under the influence of σ 2 , α ij first increased and then decreased with increasing the intermediate principal stress coefficient b under the damage stage. The porosity effect also affected the relationship between α ij and the permeability related to the induced damage, and α ij revealed an increasing trend as the permeability increased. • Effective stress coefficient a ij increases with fracture growth, even beyond unity. • a ij and E ij exhibit anisotropy with loading. a 1 is the largest, and a 3 > a 2. • Increasing the horizontal stress can reduce a ij related to the induced damage. • a ij first decreases and then increases with increasing b under the damage state. • a ij increases with the increase in permeability attributed to the induced damage. [ABSTRACT FROM AUTHOR]