Intermediate Principal Stress Σ2 Research Articles

Numerical Simulation of Pressure Distribution Changes in Porous Rocks under the Action of High Pressure Fluid

The rock medium has the characteristics of heterogeneity, opacity and porosity. Fluid injection (such as hydraulic fracturing technology) can make the tight rock mass form a gas permeability enhancement zone near the borehole, which is conducive to unconventional natural gas extraction. Compared with experimental research, numerical simulation research has lower cost and higher efficiency, and has become an important method for research on fluid interaction and pore pressure. Based on this, this article mainly conducts a numerical simulation study on the changes in the internal pressure distribution of porous rocks under the action of high-pressure fluid (HPF). This article outlines the mechanism of quasi-static HPF fracturing coal and rock, and describes the classification of tensile fracture and shear fracture. In this paper, a numerical simulation method is used to construct a model of a porous rock sample, and a test of the internal pressure of the porous rock under the action of a HPF is carried out on the rock simulation sample. The experiment shows that when the intermediate principal stress σ2 is 20 MPa, the peak pressure of fluid is 12.5 MPa; when σ 2 is 25 MPa, the peak fluid pressure of is 12 MPa. This shows that the intermediate principal stress (or horizontal stress difference) is negatively related to the maximum fluid pressure.

Strength and deformation properties of frozen sand under a true triaxial stress condition

In recent years, the mechanical properties of frozen soils under complex stress states have attracted significant attention; however, limited by the test apparatus, true triaxial tests on frozen soils have rarely been conducted. To study the strength and deformation properties of frozen sand under a true triaxial stress state, a novel frozen soil testing system, i.e., a true triaxial apparatus, was developed. The apparatus is mainly composed of a temperature control system, a servo host system, a hydraulic servo loading system, and a digital control system. Several true triaxial tests were conducted at a constant minor principal stress (σ3) and constant intermediate principal stress ratio (b) to study the effect of intermediate principal stress (σ2) on the mechanical properties of frozen sand. The test results showed that the stress–strain curve can be mainly divided into three stages, with evidence of strain hardening characteristics. The strength, elastic modulus, and friction angle increased with the increase in b from 0 to 0.6, but decreased when increasing b from 0.6 to 1, whereas the cohesion varied little with the variation in b. The deformation in the direction of σ2 changed from dilative to compressive and that in the direction of σ3 remained dilative throughout.

Experimental study on mechanical and damage characteristics of coal under true triaxial cyclic disturbance

A true triaxial test system was used to study the mechanical and damage characteristics of coal under tiered cyclic maximum principal stress (σ1), intermediate principal stress (σ2), and minimum principal stress (σ3). The influence of each principal stress cycle on the deformation, energy evolution and damage characteristics of coal was systematically analyzed, and the mechanical evolution characteristics of coal under the disturbance action of true triaxial excavation were revealed. In the process of true triaxial tiered cyclic loading, it is found that: the stress-strain curves of different principal stress cycles processes are quite different, but they will all cause plastic deformation or plastic hysteresis loop of principal strain in each principal stress directions of coal, and the principal strain corresponding to the cyclic principal stress direction is the dominant deformation, and its deformation is relatively large. According to the true triaxial strength curve and experimental results, the cyclic loading or unloading σ2 may cause instability and failure of coal. The variation trend of residual deformation caused by σ1 and σ3 is the same: with the increase of the amplitude of true triaxial tiered cyclic loading, the absolute value of the cumulative maximum and minimum residual principal strains increase exponentially and quadratic parabola, respectively. And the absolute value of the relative maximum and minimum residual principal strains decrease first and then increase, showing U-shaped and arch shaped changes, respectively. While the changes of cumulative and relative residual intermediate principal strains are all small. The total dissipation energy of coal increases exponentially with the increase of the amplitude of true triaxial tiered cyclic loading. Combined with the energy dissipation characteristics, the damage variable equation of coal under true triaxial cyclic loading is newly defined. With the increase of the amplitude of true triaxial tiered cyclic loading, the damage variable presents an obvious S-type change trend of deceleration acceleration re-deceleration.

Effect of Unloading Direction on Rock Failure under True Triaxial Stress Conditions

Abstract Rock failures induced by excavation unloading in the direction of the minimum principal stress σ3 and the intermediate principal stress σ2 were numerically simulated and analyzed. The damage evolution process, the failure mode, and the failure mechanism under the two conditions were investigated. The results show that the unloading direction of the principal stress has a significant impact on the rock failure mode. Under the same triaxial stress level, when unloading σ3, rock failure is mainly caused by localized tensile-shear composite failure; when unloading σ2, rock failure is mainly caused by tensile buckling failure. When unloading σ3, the damage is mainly concentrated near the free surface; however, when unloading σ2, the damage range increases and develops toward the interior of the rock. The greater the intermediate principal stress is before unloading, the larger the number of splitting fractures and the magnitude of dilatation are, and the smaller the thickness of the splitting plate is. These results may shed light on the prevention and mitigation of rock instability in deep underground engineering.

Experimental Study of Size Effects on the Deformation Strength and Failure Characteristics of Hard Rocks under True Triaxial Compression

Size effect has always been the focus of rock mechanics as a bridge between laboratory test and engineering site. Previously, the research conditions and objects of the rock size effect have mostly focused on cylindrical rock samples with different height-to-diameter ratios (H/Ds) under uniaxial or conventional triaxial compression, while there has been little research on the rock size effect under true triaxial compression (TTC), especially rectangular rock samples with different sizes and the same length-to-width-to-height ratio. Based on this, the deformation, strength, and failure characteristics of Beishan (BS) granite and Baihetan (BHT) basalt with different sample sizes under TTC were studied by a comparative analysis method. The size effect of deformation and failure characteristics under TTC are not obvious, including stress-strain curves, Young’s modulus, peak strains, failure angles, and macrofailure mode. However, the damage stress (σcd) and peak strength (σp) have obvious size effect; that is, the smaller the sample size is, the higher the strength is. Additionally, the relationship among the peak strength, sample size, and intermediate principal stress (σ2) is power function. In addition, by comparing the peak strength increment caused by the sample size of the two types of rocks, the σp of the fine-grained BHT basalt is more sensitive to sample size than that of the coarse-grained BS granite. Finally, by analyzing the relationship between the size of the mineral grains or clusters in the two types of hard rocks and the complexity of crack propagation in the fracture surface under TTC, it is suggested that the minimum side length of rock samples should not be less than 10 times the maximum mineral clusters (such as feldspar phenocrysts in BHT basalt). In addition, the method of estimating elastic strain is established by analyzing the relationship between the size of the rock sample σ2 and the elastic strain under TTC.

Investigation of the influence of intermediate principal stress on the dynamic responses of rocks subjected to true triaxial stress state

Precisely understanding the dynamic mechanical properties and failure modes of rocks subjected to true triaxial stress state (σ1 > σ2 > σ3, where σ1, σ2, and σ3 are the major principal stress, intermediate principal stress, and minor principal stress, respectively) is essential to the safety of underground engineering. However, in the laboratory, it is difficult to maintain the constant true triaxial stress state of rocks during the dynamic testing process. Herein, a numerical servo triaxial Hopkinson bar (NSTHB) was developed to study the dynamic responses of rocks confronted with a true triaxial stress state, in which lateral stresses can maintain constant. The results indicate that the dynamic strength and elastic modulus of rocks increase with the rise of intermediate principal stress σ2, while the dynamic elastic modulus is independent of the dynamic strain rate. Simulated acoustic emission distributions indicate that the intermediate principal stress σ2 dramatically affects dynamic failure modes of triaxial confined rocks. As σ2 increases, the failure pattern switches from a single diagonal shear zone into two parallel shear zones with a small slant. Moreover, a recent triaxial Hopkinson bar experimental system using three bar pairs is also numerically established, and the measuring discrepancies are identified between the two numerical bar systems. The proposed NSTHB system provides a controllable tool for studying the dynamic triaxial behavior of rocks.

The Plastic Zone of Tunnel Surrounding Rock under Unequal Stress in Two Directions Based on the Unified Strength Theory

For the deficiencies that the existing calculation theory for the Plastic Zone of Tunnel Surrounding Rock (PZTSR) does not consider the effect of the intermediate principal stress σ2 and interaction between the surrounding rock and support structure on the PZTSR under unequal stress, the Unified Strength Theory (UST) for the rock is adopted to replace the often used Mohr-Coulomb (M-C) strength criterion to consider the effect of σ2 on the PZTSR. Meanwhile, the interaction mechanism between the surrounding rock and support structure is also considered in the proposed model. Finally, the effect of the initial elastic displacement of the surrounding rock, stiffness of the support structure, and the coefficient b of the intermediate principal stress on the plastic zone is discussed. The results show that the PZTSR will increase nonlinearly with increasing the initial elastic displacement of the surrounding rock, and when it increases to a certain value, its increase extent will be much obvious. With increasing the stiffness of the support structure, the PZTSR will gradually decrease nonlinearly, but the decrease extent is not very much. With increasing b, the PZTSR will decrease; namely, σ2 can improve the stress condition of the surrounding rock and reduce the PZTSR.

Development of a poly-axial platen for testing true-triaxial behavior of rocks

Mining at greater depths can lead to stress-induced failure, especially in areas of high horizontal in situ stress. The induced stresses around the opening are known to be in a poly-axial stress state where, σ1 ≠ σ2 ≠ σ3 with special case of σ3 = 0 and σ1, σ2 ≠ 0 at its boundary, where σ1, σ2, σ3 are major, intermediate, minor principal stress, respectively. The conventional triaxial testing does not represent the actual in situ strength of the rock in regions of high horizontal stress, as it ignores the influence of intermediate principal stress (σ2). The typical poly-axial testing (biaxial and true-triaxial tests) of intact rock mostly requires sophisticated and expensive loading systems. This study investigated the mechanical behavior of intact rock under a poly-axial stress state using a simple and cost-effective design. The apparatus consists of a biaxial frame and a confining device. The biaxial frame has two platens that apply equal stress in both directions (σ1 = σ2) on a 50.8 mm cubical specimen when placed inside the uniaxial loading device. The confining device performed separate biaxial tests under constant intermediate principal stress (σ2 = constant) and true-triaxial tests when used along with the biaxial frame. This study then compared the failure modes and peak strength of Berea sandstone specimens with other biaxial–triaxial devices to validate the design of the poly-axial apparatus. We also performed uniaxial tests on both standard cylindrical samples and prismatic specimens of different slenderness ratios. These tests provided a complete understanding of the failure mode transition from standard uniaxial compressive tests to triaxial stress conditions on cubical specimens. Additionally, this study determined best-fitted strength envelopes for biaxial and triaxial stress state. Based on regression analysis, we found a quadratic polynomial to be a good fit to biaxial strength envelope. For the true-triaxial strength envelope, we found the three-dimensional (3D) failure criterion to be a good fit with R2 of 0.964.

Mechanical and Acoustic Emission (AE) Characteristics of Rocks under Biaxial Confinements

The surrounding rocks of underground engineering are generally subjected to a biaxial compressive stress condition. The failure properties of rocks under such a stress condition are worthy of being studied to ensure the stability of surrounding rock. This study aims to investigate the mechanical characteristics and acoustic emission (AE) properties of granite, marble, and sandstone in biaxial compression tests. Under biaxial confinements, it is evident that the elastic moduli of the three types of rocks decrease, and the plasticity increases monotonously with the increase of the intermediate principal stress σ2. As σ2 increases, the biaxial compressive strength σbcs of rock increases initially and subsequently decreases. The lateral strain ε2 of rock under biaxial confinement is controlled by both σ1 and σ2, and the restrain degree in the development of microcracks and the constrain extent in the expansion along the direction of σ2 are both enhanced gradually with increase in σ2. The sharp increase points of AE hit and AE count indicate that the failure will occur soon. The AF-RA distribution of AE signals shows that the increase of σ2 causes more tensile cracks in rock. According to the dip failure angle of macro-cracks in rock under biaxial confinement, the failure modes of granite and marble are slabbing, while failure mode of sandstone is shear. In addition, the σ2 has a positive effect on the mass ratio of large size fragments after rock failure. An exponent relationship between the σbcs and σ2 was found, and the inner apices–inscribed Drucker–Prager criterion can be used to predict the σbcs of rock.

Focal mechanisms and the stress field in the aftershock area of the 2018 Hokkaido Eastern Iburi earthquake (MJMA\u2009=\u20096.7)

The tectonic stress field was investigated in and around the aftershock area of the Hokkaido Eastern Iburi earthquake (MJMA = 6.7) occurred on 6 September 2018. We deployed 26 temporary seismic stations in the aftershock area for approximately 2 months and located 1785 aftershocks precisely. Among these aftershocks, 894 focal mechanism solutions were determined using the first-motion polarity of P wave from the temporary observation and the permanent seismic networks of Hokkaido University, Japan Meteorological Agency (JMA), and High Sensitivity Seismograph Network Japan (Hi-net). We found that (1) the reverse faulting and the strike-slip faulting are dominant in the aftershock area, (2) the average trend of P- and T-axes is 78° ± 33° and 352° ± 51°, respectively, and (3) the average plunge of P- and T-axes is 25° ± 16° and 44° ± 20°, respectively: the P-axis is close to be horizontal and the T-axis is more vertical than the average of the P-axes. We applied a stress inversion method to the focal mechanism solutions to estimate a stress field in the aftershock area. As a result, we found that the reverse fault type stress field is dominant in the aftershock area. An axis of the maximum principal stress (σ1) has the trend of 72° ± 7° and the dipping eastward of 19° ± 4° and an axis of the intermediate principal stress (σ2) has the trend of 131° ± 73° and the dipping southward of 10° ± 9°, indicating that both of σ1- and σ2-axes are close to be horizontal. An axis of the minimum principal stress (σ3) has the dipping westward of 67° ± 6° that is close to be vertical. The results strongly suggest that the reverse-fault-type stress field is predominant as an average over the aftershock area which is in the western boundary of the Hidaka Collision Zone. The average of the stress ratio R = (σ1 − σ2)/(σ1 − σ3) is 0.61 ± 0.13 in the whole aftershock area. Although not statistically significant, we suggest that R decreases systematically as the depth is getting deep, which is modeled by a quadratic polynomial of depth.

A strength criterion for rocks

A simple strength criterion J2=α+βσ3 is investigated to describe the ultimate stress capacity of rocks. This criterion takes the intermediate principal stress σ2 into consideration. The nonlinear parabolic form on the meridian plane makes the present criterion is more suitable in rock mechanics than the linear Mohr–Coulomb failure criterion. The present criterion has only 3 corners on the π plane, resulting in higher efficiency and reliability in solving the corner problems in numerical analysis than Mohr-Coulomb and Hoek-Brown criteria. Comparison by the experimental results indicates that the proposed strength criterion gives a better agreement with experimental data than Mohr-Coulomb, Hoek-Brown, Drucker-Prager and modified Lade-Duncan criteria.

Effects of high differential stress and mineral properties on deformation and failure mechanism of hard rocks

To study the deformation and failure mechanism of hard rocks, true triaxial compression tests were conducted on four types of hard rocks to obtain the complete stress–strain curves and failure modes. Under true triaxial compression conditions, the shapes of the complete stress–strain curves can be divided into three types: elastic–brittle (EB), elastic–plastic–brittle (EPB), and elastic–plastic–ductile (EPD) types. According to the different post-peak deformation behaviours, the stress–strain curves of EPB type can be subdivided into three sub-categories: post-peak instantaneous brittle (EPB-I), post-peak multi-stage brittle (EPB-M), and post-peak delayed brittle (EPB-D). The stress–strain curves change from EPD to EPB-D, EPB-M, EPB-I, and finally EB with increasing differential stress (σ2– σ3). The deformation characteristics are dependent on intermediate principal stress σ2, minimum principal stress σ3, mineral compositions, and mineral textures of rock samples. An increase in σ3leads to an increased ductility, while an increase in σ2leads to an increased brittleness. Moreover, rocks with regular mineral textures and low mineral hardness are more prone to ductility. When the deformation curve is transformed from EPD to EPB and then to EB, the tensile crack gradually predominates, and the macroscopic failure angle gradually becomes steeper.

A method to remove end effect for the determination of intrinsic 3D rock strength envelopes

The strength of rock or rock mass is needed for the design of mining and geotechnical engineering structures. Pioneer laboratory works stimulated the interest of developing 3D rock failure criteria with the consideration of the effect of the intermediate principal stress (σ2). However, the variability among some of the test data obtained under different testing conditions hampered the usefulness of these test data. In this study, a FEM tool is utilized to quantify platen-induced σ2 effects in the σ2 range of σ3 ≤ σ2 ≤ 1/2σ1. It is proposed that the intrinsic 3D rock strength envelopes within the range of σ3 ≤ σ2 ≤ 1/2σ1 can be obtained by excluding the end-effect-induced strength increase from the laboratory true triaxial compression test results. The proposed method is checked against laboratory test results of two types of rocks where applied stresses were kept the same with different rock-platen contact conditions. In the end, an approach to determine 3D failure envelopes in the full σ2 range of σ3 ≤ σ2 ≤ σ1 is proposed. This study offers insight into how to better interpret laboratory true triaxial compression test results for developing 3D failure criteria of rock.

An Investigation on Failure Behaviour of a Porous Sandstone Using Single-Stage and Multi-stage True Triaxial Stress Tests

The deformational characteristics of a set of synthetic sandstones when subjected to true triaxial stress conditions were investigated in this study. The experimental results showed that the lateral stress anisotropy (σ2 ≠ σ3) significantly affected the rock’s compressive strength, elastic modulus, inelastic deformation, dilatancy and failure mode. By increasing the intermediate principal stress (σ2) over quasi-isotropic conditions (σ2 = σ3), the measured compressive strength increased more than twice in some cases, and the onset of dilatancy was suppressed to more than 80% of the peak stress. The obtained failure stresses were examined against a Mogi-type true triaxial criterion and indicated a good fit to the empirical model. Furthermore, multistage-true triaxial tests were carried out on the sandstones, and their results were compared against the single-stage test data to examine the suitability of this testing method for evaluation of the σ2 impact on the rock’s mechanical properties. Over the course of each multistage-true triaxial test, a sample was loaded to several levels of intermediate principal stress, while the minimum stress was held constant. Comparing the results of the multistage-true triaxial tests on the synthetic sandstones with the equivalent single-stage true triaxial measurements revealed noticeable differences between the resultant rock strengths and elastic properties. The findings of these tests are discussed and the potential mechanisms responsible for the observed disagreements are explained in this paper.

Failure properties of cubic granite, marble, and sandstone specimens under true triaxial stress

Cubic specimens of granite, marble, and sandstone, with side lengths of 50 mm, were prepared in the laboratory. True triaxial compression tests were conducted on each rock type with minor principal stress (σ3) magnitudes of 10, 20, 30, 50, and 100 MPa and the intermediate principal stress (σ2) varying from σ2 = σ3 to σ2 = σ1 (where σ1 represents the major principal stress). The experimental results demonstrated that the failure strength, fracture dip angle, non-linear behavior and failure mode of these rocks under true triaxial conditions were affected by both σ2 and σ3, as well as by the rock lithology. When σ3 was kept constant and σ2 increased, failure strength showed an initial increase followed by a decrease, whereas the fracture dip angle increased monotonically. The non-linear behavior before the peak strength point of granite became more apparent by the increase of σ3, whereas σ2 had an opposite effect on the non-linear behavior of granite under high σ3 (e.g. 100 MPa). The non-linear behavior before the peak strength point was always found in marble and sandstone for all of the stress state conditions. Analyses of fracture dip angle and failure mode showed that when σ3 = 10, 20, and 30 MPa and σ2/σ3 ≥ 5, 7.5, and 10, respectively, the failure mode of granite changed from shear to slabbing, whereas marble and sandstone always fractured in the shear direction. This study confirms that rocks may experience slabbing failure under true triaxial stress, and slabbing failure mode is likely to be induced in high-strength and brittle rocks under low σ3 with the stress ratio of σ2/σ3 exceeding a particular threshold value.

Dynamic strength and failure modes of sandstone under biaxial compression

Geomaterials are increasingly being subjected to the quasi-static confinements and dynamic loadings, and thus it is critical to characterise dynamic behaviour under the coupled static-dynamic loading conditions. In this study, a series of dynamic biaxial compression tests was performed on cubic specimens of sandstone by using a triaxial Hopkinson bar system, high-speed three-dimensional digital image correlation (3D-DIC) and synchrotron-based micro-computed-tomography (μCT). This testing apparatus allows for determining dynamic stress-strain behaviour of the specimen under biaxial static pre-stress (σ1, σ2) conditions and different impact velocities (i.e. 15, 20 and 26 m/s), corresponding to average axial strain rates of 80, 200 and 250 s−1. Both σ1 and σ2 applied in the tests varied from 0 to 40 MPa with an interval of 10 MPa. Dynamic strength and fracture behaviours of biaxially confined rocks were systematically characterised from macroscopic to microscopic, surface to interior and 2D to 3D by using the 3D-DIC and synchrotron-based μCT techniques. Experimental results show that, under the same biaxial pre-stresses, dynamic biaxial compressive strength of sandstone increases with strain rate, i.e. rate dependence. At a given impact velocity, dynamic biaxial compressive strength decreases with increasing pre-stress values (σ1) along the impact direction, while it enhances with the increase of intermediate principal stress (σ2) in the lateral direction, which is so-called confinement dependence. Besides, two types of dynamic stress-strain curves of rocks are observed under biaxial compression, which is associated with post-peak fracturing characteristics. High-speed 3D-DIC shows that rock fragments are ejected out of the free surface (σ3 = 0) with certain velocities including the translation and rotation, which resembles the rock ejection observed during drilling and blasting and even strong rockbursts. μCT reveals that the double “V” shapes of shear fractured zones are symmetrically generated under biaxial compression. The crack surface area, volume and dynamic fracture energy are also estimated under different confinements to characterise the damage of impacted rock.

Strength and deformability of a low-porosity sandstone under true triaxial compression conditions

True triaxial tests (σ1≥σ2≥σ3) were conducted on the Zigong sandstone with a relatively low porosity of ~6.5% with the aim of assessing the influence of the intermediate principal stress σ2 on the strength and deformability. Three series of true triaxial tests (σ3= 0, 20, and 60 MPa) were performed. Within each series, σ2 was planned to be varied from σ2=σ3 to σ2=σ1 from test to test. For each test, σ1 was raised monotonically to failure while σ2 and σ3 were kept constant and the post-peak behavior has been captured. It is found that the strain in the σ3-direction is always larger than that in the σ2-direction under true triaxial stresses, which is attributed to the stress-induced tensile microcracks aligned with the σ1-σ2 plane. For a constant σ3, the dilatant strain in the σ2-direction is progressively suppressed and becomes compactive as σ2 raises from σ2=σ3 to σ2=σ1. Based on a modified Hoek-Brown failure criterion with three stress invariants, the best fitting brittle strength envelope reveals that the σ2 effect on rock strength, i.e., the ascending-then-descending trend for a given σ3, is the combined effect of mean stress and Lode angle. In the series of biaxial tests (σ3=0 MPa), macro tensile fractures that parallel to the σ1-σ2 plane develop regardless of σ2, displaying a failure plane angle of approximately 90°. As σ3 is raised, failure plane angle generally decreases. When σ3 = 20 MPa, the failure plane angle generally increases with σ2 while there is no evident dependence on σ2 when σ3 = 60 MPa. Comparisons with the other two sandstones with higher porosity reveal that porosity exerts critical control on the brittle strength and that the σ2 effect on deformability is also the result of two competing effects induced by mean stress and Lode angle. It is also found that the residual strength data facilitate the prediction of brittle-ductile transition pressure when σ2=σ3 in spite of relatively low σ3 level, which matches well with the empirical relation proposed by Mogi.1

Generalized crack damage stress thresholds of hard rocks under true triaxial compression

The rock failure process can be characterized by several distinct stress thresholds: the crack closure stress σcc, crack initiation stress σci, crack damage stress σcd and peak stress σp. Seventy-one true triaxial compression tests were conducted to investigate the crack damage stress σcd, which is the stress at the onset of unstable crack development and dilation. Two empirical models are developed to predict the crack damage stress σcd using the intermediate principal stress σ2 and the minimum principal stress σ3. In addition, the proposed models are validated by ten results derived from the German Continental Deep Drilling Program (KTB) deep hole amphibolite. A comparison with other failure criteria also indicates the accuracy and simplicity of the proposed models. The proposed composite models show that the crack damage stress σcd gradually increases with increasing intermediate principal stress σ2 and minimum principal stress σ3. The physical meanings and ranges of six material parameters are analyzed and explained. Both the influence of the tangent Young’s modulus E and strain characteristics on the crack damage stress σcd and the inhomogeneity of the tested specimens are discussed in this paper.

Influence of gas migration on permeability of soft coalbed methane reservoirs under true triaxial stress conditions.

The permeability of the coal body is the key parameter restricting the efficient extraction of coalbed methane, and scholars have analysed it from two angles of the change of stress state and porosity of the coal body. However, there is still a lack of study on the mechanism of gas migration and movement in soft coalbed methane reservoir under the coupling between the true triaxial stress field (maximum principal stress σ1 > intermediate principal stress σ2 > minimum principal stress σ3) and the gas pressure field. In this paper, the coal gas adsorption and seepage experiments are conducted through the self-developed true triaxial ‘gas–solid’ coupled coal mass seepage system with gas as the adsorption and seepage medium and coal briquette taking the place of soft coalbed methane reservoirs. Furthermore, the coal gas adsorption deformation model and the permeability evolution model taking gas adsorption into account are developed. Through analysis of both experimental and theoretic results, the main conclusions are drawn as follows: (i) With the increase in gas pressure, the adsorption deformation variation of coal mass is divided into a slow growth zone, a stable growth zone and a rapid growth zone. (ii) The gas adsorption deformation model developed can predict the variation trend of coal mass adsorption volumetric strains for different types of soft coalbeds, and the fitting variance of experimental and theoretical volumetric strains is above 98%. (iii) With the increase in maximum principal stress difference, the coal permeability variation curve shows two obvious turning points, which can be divided into a slow reduction zone, a rapid reduction zone and a steady reduction zone. (iv) The permeability model of coal mass considering the gas adsorption effect can reflect the variation characteristics of permeability in the rapid reduction zone, and the overall fitting variance of experimental and theoretical permeabilities is above 91%. The above results could provide a reliable experimental and theoretical basis for improving coalbed methane extraction rates.

Permeability evolution under true triaxial stress conditions of Longmaxi shale in the Sichuan Basin, Southwest China

Shale permeability is considered the critical parameter for commercial gas production. In this work, we investigated the permeability evolution under true triaxial stress conditions of Longmaxi shale. The results showed that shale permeability decreased significantly with increasing intermediate principal stress σ2 and increased gradually with decreasing σ2. And permeability was larger when σ2 was perpendicular to the bedding than that when σ2 was parallel to the bedding. A theoretical model was derived to describe the permeability of shale with respect to effective stress and the results agreed well with the experiment. The matching results showed that the fracture was compressed more easily when σ2 was perpendicular to the bedding and the shale sample was generally compressed in the loading process while swelled during the unloading process. Strong hysteresis was observed for both permeability and strain results. It also warrants testing other gas shales to specifically determine this effect.