Triaxial Compression Conditions Research Articles

Compaction localization in geomaterials: A mechanically consistent failure criterion

Compaction bands play a key role in the deformation processes of porous rocks and explain different aspects of physical processes in geological formations. The state-of-the-art description of the localized strains that lead to compaction banding has limitations from the mechanical point of view. Thus, we describe the phenomenon using a consistent axiomatic formulation. We build a viscoplastic model using minimal assumptions; we base our model on six principles to study compaction band strain localization triggered by viscous effects. We analyze different stress states to determine the conditions that trigger compaction bands. Laboratory experiments show that a material undergoes different strain localizations depending on the confinement pressure; thus, we perform a series of numerical experiments that reproduce these phenomena under varying triaxial compression conditions. These simulations use a simple viscoplastic constitutive model for creep based on Perzyna’s viscoplasticity and show how confinement changes the strain localization type for different triaxial tests.

Study on failure characteristics and evaluation index of aquifer shale based on energy evolution

AbstractThe presence of abundant clay components and microporous structure in shale results in its high hydrophilicity, making a water-rich environment inevitable in petroleum exploration projects. Therefore, it is crucial to consider the influence of bedding structure, moisture content, confining pressure, and their combined effects on the geomechanical properties of shale. This article aims to investigate the mechanical properties of deep shale under varying water content conditions, elucidate the failure mode and failure mechanism of shale in actual engineering scenarios, and explores the interplay between stress, structure, moisture content, and other factors on its mechanical properties. The evaluation of wellbore stability and fracture propagation effects is proposed based on laboratory experiments using triaxial stress and strain data, along with the application of energy evolution theory. The experimental procedures encompass an analysis of shale's microscopic components and structure, as well as anisotropic shale triaxial compression tests conducted under different moisture contents and confining pressures. The results demonstrate that shale exhibits dense pores in its microstructure and displays pronounced anisotropic characteristics in its macrostructure. The presence of water within these pores, combined with the in situ stress within the formation, significantly influences the mechanical properties of shale. This anisotropy decreases with increasing moisture content, but the mechanical performance still decreases. Under triaxial compression conditions, the increase in confining pressure to some extent enhances the anisotropy of shale's deformation characteristics, which is related to the failure modes of shale. However, the detrimental effect of moisture content on shale's mechanical properties still persists. In order to quantify the impact of these factors, this study utilizes the elastic modulus as an indicator of the coupling effect. It combines the triaxial strain curve obtained from laboratory tests and proposes an evaluation index for shale mechanical properties based on the energy evolution theory. This index is suitable for assessing wellbore stability (the stability index called SIr) and crack expansion (the brittleness index called BIr). The calculation results reveal that, during the wellbore drilling process, excavating parallel to the direction of shale bedding while maintaining low moisture content and high confining pressure yields a higher SIr value, indicating better wellbore stability. On the other hand, during reservoir fracturing, fracturing perpendicular to the shale bedding direction and maintaining low confining pressure and moisture content result in a smaller BIr value. This approach is more beneficial for the expansion of shale fracture network in engineering.

Numerical investigation on the fracture and mechanical behaviors of marble containing two parallel fissures under triaxial compression conditions using FDEM

This paper aims to investigate the fracture and mechanical behaviors of fissured marble under triaxial compression. The two-dimensional models of marble with two parallel fissures and various rock bridge angles were established, and then the numerical simulations considering the effect of confining pressure were performed with the finite-discrete element method. The brittle-ductile transition and stress multi-peak characteristics are presented with the increase of the confining pressure. The characteristic strain, stress, and elastic strain energy exhibit various trends with the increment of the rock bridge angle, whilst increasing trend with the increment of the confining pressure. The cohesion presents the variation of first increasing and then decreasing with the increase of the rock bridge angle, and the friction angle presents the opposite trend to the cohesion. The proposed strength model can reflect the evolutions of the cohesion and the friction angle considering the effect of confining pressure and rock bridge angle. The elastic strain energy has the trends of nonlinear increase and fluctuation in the pre-peak and post-peak phases, respectively. The variation of kinetic energy is induced by the internal local fracture during the progressive failure. The failure pattern transforms from the tensile failure to the shear failure with the increase of the confining pressure. The coalescence behavior of cracks at the rock bridge can be classified into four modes.

A generalized nonlinear three-dimensional Hoek‒Brown failure criterion

To understand the strengths of rocks under complex stress states, a generalized nonlinear three-dimensional (3D) Hoek‒Brown failure (NGHB) criterion was proposed in this study. This criterion shares the same parameters with the generalized HB (GHB) criterion and inherits the parameter advantages of GHB. Two new parameters, β, and n, were introduced into the NGHB criterion that primarily controls the deviatoric plane shape of the NGHB criterion under triaxial tension and compression, respectively. The NGHB criterion can consider the influence of intermediate principal stress (IPS), where the deviatoric plane shape satisfies the smoothness requirements, while the HB criterion not. This criterion can degenerate into the modified HB criteria under triaxial compression condition and the HB criterion under triaxial compression and tension condition. This criterion was verified using true triaxial test data for different parameters, six types of rocks, and two kinds of in situ rock masses. For comparison, three existing 3D HB criteria were selected for performance comparison research. The result showed that the NGHB criterion gave better prediction performance than other criteria. The prediction errors of the strength of six types of rocks and two kinds of in situ rock masses were in the range of 2.0724%–33.5091% and 1.0144%–3.2321%, respectively. The proposed criterion lays a preliminary theoretical foundation for prediction of engineering rock mass strength under complex in situ stress conditions.

Fracture propagation and failure mode characteristics of lamellar lacustrine shale under true triaxial compression conditions

Fracture propagation and failure mode characteristics of lamellar lacustrine shale under true triaxial compression conditions

Brittleness index evaluation of gas-bearing sandstone under triaxial compression conditions

Brittleness is a critical property in gas-bearing rock excavation and reservoir fracturing. This paper analyzes the three types of brittleness indices in detail, proposes new indices, and conducts relevant conventional triaxial tests for analysis. A stress–strain curve-based brittleness index would be appropriate for the evaluation of brittleness if the parameters represented unique and certain stress–strain curves. Therefore, a new brittleness index is proposed. It consists of two components: the stress variation index and the strain variation index, which reflects the strain ratio of the stress drop and the relationship between elastic and post-peak strains, combining the stress variation and strain variation in the pre- and post-peak phases. Triaxial compression tests of sandstone under different confining pressures and gas pressures were conducted, and specific stress and strain parameters were collected. Based on the comparison and analysis of various brittleness indices, it is found that the newly proposed brittleness index can be a good measure of the brittle evolution of sandstones under different confining pressures and gas pressures, and it can provide a more accurate estimate of rock brittleness than the existing indices. The index is also used to further investigate the relationship between rock brittleness and confining and gas pressures. This has important implications for the assessment of rock brittleness in practical engineering.

Space-time evolution characteristics of loaded gas-bearing coal fractures based on industrial μCT

Abstract The space-time evolution characteristics of fractures in coal seams under external loads are of great significance for the exploration and development of coalbed methane and the safe mining of coal. In this study, the in situ industrial μCT scanning experiments of gas-bearing coal under triaxial compression conditions was carried out using a loaded coal rock industrial μCT scanning system. The computed tomography (CT) scan images of different deformation stages were obtained. The temporal characteristics and spatial evolution patterns of fractures during gas-bearing coal rupture were investigated by combining image retrieval techniques and fractal theory. The results show that (1) as the axial load increases, the maximum similarity of the CT images showed a gradually decreasing trend. (2) Under the triaxial compression conditions, the number of two-dimensional cracks in a coal-containing gas at different spatial positions exhibited a changing pattern in which it slowly decreased before rapidly increasing. (3) The patterns of change in the three-dimensional fracture rate, fracture density, and fractal dimension were quite similar, showing four stages of slow decline, slow growth, sharp growth, and slow growth again. In contrast, the Euler number exhibited the exact opposite pattern of change. (4) The coal sample space showed prominent zonal failure characteristics. The bottom of the coal sample space position (Area C) near the loading indenter had the most developed cracks and serious damage, the middle of the coal sample space position (Area B) was the second, and the upper of the coal sample space position (Area A) near the fixed indenter had slow fracture development and minimal damage.

Viscoelastic Strains of Palaeozoic Shales under the Burger’s Model Description

This article presents the results of creep studies of Palaeozoic shales from the Baltic Basin in which the exploitation of shale gas in Poland was planned. Knowledge of instantaneous and long-term properties investigated in triaxial stress conditions is important from the point of view of exploitation techniques related to hydraulic fracturing. Rheological phenomena also play an important role in the analysis of the initial stress in shales, the knowledge of which is indispensable in the hydraulic fracturing process. The tests were carried out on samples representing four siltstone–claystone lithostratigraphic units occurring in the Baltic Basin. The studies and analyses were aimed at determining the character of creep in shales, selection of the appropriate rheological model for the analyzed rocks, and determination of the threshold of the linear creep under triaxial compression conditions. An original approach together with analysis results are presented here, which enable the separation and monitoring of shear and volume creep effects, and on this basis, the determination of the significance of the contribution of volume creep in the entire creep process. A relatively simple methodology for determination of the parameters of the Burgers model using this division is presented. The original value of the article is also due to the test results themselves and the parameter values of the analyzed model for triaxial creep of shales, which are not numerous in the literature. The investigations were performed at various loading levels in relation to the triaxial strength of the shales. Depending on the load, at its low values up to 0.7 (σ1 − σ3)max, creep had a determined character and did not show features of progressive creep. The linear creep threshold was also analyzed in this range. The loading level of 0.7 (σ1 − σ3)max was the limit of linear creep. Exceeding this load resulted in the loss of the linear character of creep, which in consequence lead to the subsequent third creep phase ending with rock damage. Parameters of the Burger’s model for gas shales from the Baltic Basin (northern Poland) were identified. There are significant differences in the behavior of shales depending on the lithostratigraphic unit from which the samples were collected. The mineral composition of the shales also influenced their behavior.

An Experimental Investigation on the Foliation Strike-Angle Effect of Layered Hard Rock under Engineering Triaxial Stress Path.

Deep underground engineering encounters substantial layered hard rock formations, and the engineering triaxial stress path involves an increase in maximum principal stress, constant intermediate principal stress, and a decrease in minimum principal stress. However, previous research has focused on rock layer angles under conventional triaxial stress conditions, disregarding the influence of foliation strike angles in engineering triaxial stress scenarios. This study experimentally investigates the effects of foliation strike angles on layered hard rock under an engineering triaxial stress path. To account for the brittleness of layered hard rock, we propose a specific small sample-processing method tailored to the foliation strike angle. True triaxial loading tests are conducted on steep, thin slate samples with two different loading orientations, accompanied by acoustic emission monitoring. Results indicate that the strength under a traditional true triaxial compression condition is similar for specimens with 90° and 0° strike angles. Stress-strain curves show that larger deformations occur perpendicular to bedding planes, while surface fractures propagate exclusively along the bedding planes. Mechanical responses differ significantly between specimens subjected to the engineering triaxial stress path at 0° and 90° strike angles compared to conventional true triaxial loading tests, with a lower bearing capacity and differentiated intermediate and minimum principal strains in the 0° case. Conversely, the 90° case exhibits a higher bearing capacity, consistent deformation, and more acoustic emission events. Numerical simulations comparing plastic zone sizes during actual underground excavation support these conclusions. These findings highlight the effects of foliation strike angles, favoring the 90° strike-angle configuration for excavation activities and providing enhanced stability in the surrounding rock mass.

Critical State Characterization of New Zealand East Coast Sand for Numerical Modeling

This paper outlines the findings of a laboratory-based and numerical study to investigate the undrained flow failure behavior of East Coast Sand (ECS). ECS is a commonly encountered coastal deposit from the upper North Island of New Zealand. The study focused on establishing the undrained strength characteristics of ECS under static, triaxial compressive loading conditions, and at confining pressures in the range of typical engineering interest and for a range of soil densities considered in loosely deposited sands. The research objectives of establishing the basic soil properties and the intrinsic advanced geomechanical properties specific to ECS from Auckland were achieved through laboratory experiments and matching numerical simulations with an advanced critical-state compatible soil constitutive model (Norsand). The current work examined five different aspects of the ECS undrained behavior under static loads. It was shown that loosely deposited ECS within mean effective stresses ranging between 50 and 200 kPa was highly susceptible to expensive flow failures of structures built on or with them. The obtained approximate peak undrained shear strengths before failure and critical states were 29 kPa, 84 kPa, 130 kPa, and 200 kPa for test confining stresses of 50 kPa, 100 kPa, 200 kPa, and 300 kPa, respectively. Similarly, the corresponding excess pore water pressures were 48 kPa, 98 kPa, 200 kPa, and 240 kPa, respectively. The above results proved that the soil’s effective and confining stress are key determinants of the soil’s undrained shear strength characteristics which was consistent with the existing literature.

Investigation of Damage and Creep for Bedding's Carbonaceous Slate with Chemical Erosion Effect.

Tunnel projects in the southwestern mountainous area of China are in full swing. According to the tunnel burial depth, structural characteristics, and chemical erosion environments of the Lixiang railway tunnel, carbonaceous slate specimens obtained in the field were taken to experimentally investigate the physical, mechanical, and creep characteristics of the bedding's slate specimens after chemical erosion. The results of scanning electron microscopy (SEM) indicate that chemical erosion leads to internal damage in the carbonaceous slate specimens, and the internal damages are increasing with the increase of erosion days. Moreover, the specimens' ultrasonic test (UT) results prove that specimens with smaller bedding angles suffer a more serious erosion and induce more internal cracks. Under conventional triaxial compression conditions with 40 MPa of confining pressures, the conventional triaxial compressive strength (σs) decreases with the decrease of the bedding angle and the increase of erosion days, and the failure modes of the specimens are mainly controlled by oblique shear fractures and accompanied by the occurrence of slip dislocation fractures between the bedding inclination. Under creep conditions with 40 MPa of confining pressures, the final deformations of specimens are increasing with the increase of erosion days, which means the longer the erosion days, the greater the deformations. The failure modes of the specimens under creep conditions are controlled by shear fractures, and for the specimen with a 60° bedding angle and long-term erosion, there are block separations and many cavities along the shear planes. Therefore, more attention should be paid to prevent serious failure of the surrounding rock if the surrounding rock has a bedding angle of 60° or suffers long-term erosion.

Cracking property and brittleness evaluation of granite under high-temperature true triaxial compression in geothermal systems

Cracking property and brittleness are critically important to the drillability of injection and production wells of enhanced geothermal systems. This paper is devoted to evaluating the cracking property and brittleness of the Gonghe granite under high-temperature true triaxial compression conditions through a series of laboratory tests. Thermal–mechanical coupled true triaxial compression tests were conducted on Gonghe granite samples under four representative temperatures (20 °C, 120 °C, 180 °C, and 240 °C) and three different minimum (5, 10, and 30 MPa) and intermediate (40, 60, and 75 MPa) principal stresses that correspond to the in-situ conditions of Gonghe geothermal reservoir. The strength, deformation, and cracking characteristics of the Gonghe granite are quantitatively evaluated from macro- to micro-scales based on the experimental results. Meanwhile, a novel brittleness index evaluation method considering both energy and failure surface roughness is proposed to accurately assess the brittleness strength of the Gonghe granite. We found that the strength of Gonghe granite is reduced by more than 20% when the temperature increases from room temperature to 240 °C. Higher temperature contributes to a smoother fracture surface and reduced brittleness of the Gonghe granite under thermal–mechanical coupled true triaxial compression. Our findings provide new insights for brittleness evaluation of the Gonghe granite formation and assist in efficient wells drilling design of enhanced geothermal systems.

A Hybrid Anisotropic Elastoplastic Model for Layered Rock Mass and Numerical Implementation

An elastoplastic model that exhibits hybrid initial and stress-induced anisotropy is developed for layered rock masses. The formulation considers the thermodynamic aspect, and is consistent and rigorous. Both initial anisotropy and stress-induced deformation anisotropy are reflected by a hybrid anisotropic stiffness matrix influenced by the deterioration development degree (DDD) in different directions. By employing a combination of the strength criterion of rock material and rock bedding plane, an anisotropic failure formulation for layered rock mass has been established. The hybrid anisotropic model has been implemented in cellular automata software for the engineering rock mass fracturing process (CASRock). The performance of the anisotropic part is demonstrated by reproducing the deformation and failure characteristics of initial or stress-induced anisotropic behaviors for layered rocks under uniaxial, conventional triaxial, and true triaxial compression and Brazilian splitting conditions. Important features, such as the strength, mechanism, deformation, DDD, and fracturing process variation, can be captured by the proposed model. In addition, a numerical simulation of tunnel excavation in a layered rock mass is performed to study the anisotropic excavation-induced damage zone (EDZ) distribution in the field. The results indicate that the model is able to reproduce the observed failure mode satisfactorily.

Anisotropic Strength, Deformability, and Failure Behavior of Artificial Columnar Jointed Rock Masses under Triaxial Compression

Columnar jointed rock masses (CJRMs) have a complex network structure and, therefore, present a great challenge to geotechnical engineering design. A series of triaxial compression tests is performed on artificial CJRM specimens subjected to a confining pressure of 5 MPa, considering various pore pressures (pw=0 MPa, 2 MPa, and 4 MPa). In this work, the influence of the joint dip angles and pore pressure on the anisotropic strength, deformation, and failure modes of the CJRM is investigated. The anisotropic characteristic stresses, strength parameters (c and φ) and elastic modulus of the CJRM specimens show a U-shaped pattern with increasing joint dip angles (β), while Poisson’s ratio changes inversely. The elastic modulus has a stronger anisotropy than Poisson’s ratio. Moreover, with increasing pore pressure, the characteristic stresses decrease, while the anisotropy of stresses and deformations increases. Finally, three failure modes of CJRM specimens with different joint dip angles are observed under triaxial compression conditions.

Evolution of the force chain structure of partially saturated granular material under triaxial compression conditions

Saturation conditions play a significant role in the mechanical behavior of granular material and the evolution of an interparticle contact system during the loading process. Using data derived from discrete element simulations of granular assemblies subject to triaxial compression loading with different suctions, we examine the properties of an interparticle contact network and force chain structure to provide a comprehensive picture of the evolution of a particle-scale contact system. The study focuses on the evolution of the topological statistic features (including degree and triangles) and the force chain structure characteristics influenced by suction conditions. To comprehensively evaluate the characteristics of the force chain system, combined statistical parameters are proposed for describing the linearization and intensity of the force chain structure, which account for multiple features of force chains. Accordingly, a novel expression combined with multiscale properties is proposed for strength prediction that convincingly explains data results in the studied suction range. This study illustrates the consistency of the evolving force chain structure features with mechanical behavior that provides new insights for understanding the particle-scale force chain structure evolution from which these properties dominate the macroscopic response.

Оценка удароопасности скальных горных пород Ждановского месторождения (Кольский полуостров)

he paper presents the results of uniaxial and triaxial compression tests of hard rock samples from the Zhdanovskoe deposit. Two criteria were used to assess the tendency of rocks to fail in dynamic mode (rockburst hazard). In the first case, the A.N. Stavrogin's criterion was used, which requires testing of specimens using “rigid” presses. In the second case, the criterion developed at the Mining Institute of the Kola Scientific Center of the Russian Academy of Sciences was applied to estimate the rockburst hazard of rocks based on the test results of samples using the standard presses. It is shown that the studied rocks of the Zhdanovskoe deposit are prone to failure in dynamic mode according to the two criteria considered. It was found that with the transition from uniaxial to triaxial compression conditions at the lateral pressures up to 40 MPa, the tendency of rocks to dynamic failure is maintained.

A Model of Stress-Damage-Permeability Relationship of Weakly Cemented Rocks under Triaxial Compressive Conditions.

To unravel the permeability variation mechanism of weakly cemented rocks (WCR), the paper conducted triaxial permeability tests on weakly cemented sandstones (WCS) collected from the Jurassic formation in northwest China. The paper identified the correlation of WCS permeability versus porosity, cementation structure, and mineral composition, further developing a model to characterize the WCS stress-damage-permeability relationship. The research indicated that the WCS permeability was initially high due to the naturally high porosity, large pore diameter, and loose particle cementation, thus favoring a significant decline as pore convergence in the compaction stage. In the residual stage, kaolinite and montmorillonite minerals disintegrated into water and narrowed fractures, causing a slight permeability increase from the initial to the maximum and residual stages. The WCS matrix fracturing was phenomenologically accompanied by clay mineral disintegration. By assuming that the matrix can be compressed, jointed, and fractured, the paper defined a damage variable D and accordingly developed a stress-damage-permeability relationship model that incorporated matrix compression, jointing, and fracturing. The model can describe the WCS permeability regime regarding the high initial permeability and slight difference of the maximum and residual permeabilities versus the initial.

Further modification of a generalised 3D Hoek–Brown criterion: the GZZ criterion

This paper presents a further modification of the generalised three-dimensional (3D) Hoek–Brown (HB) criterion – the generalised 3D Zhang-Zhu (GZZ) criterion. Specifically, a modification was made by introducing a 3D version of effective mean stress to replace the original two-dimensional (2D) version of effective mean stress in the GZZ criterion. The modification overcomes the non-smoothness and non-convexity problems of the GZZ criterion and maintains a simple form of the criterion expression. The modified GZZ criterion can also reduce to the 2D HB criterion under both triaxial compression and extension conditions and thus inherits the advantages of and uses the same parameters as the HB criterion. Eleven sets of true triaxial test data were collected from publications to evaluate the newly modified GZZ criterion. The results indicate that the newly modified GZZ criterion has the highest or at least the same accuracy for strength prediction among the various 3D versions of the HB criterion that can reduce to the HB criterion and are smooth and convex. Moreover, of the various 3D versions of the HB criterion that can reduce to the HB criterion and are smooth and convex, only the newly modified GZZ criterion can be expressed explicitly.

Creep and breakage behavior of broken rock in the caved zone of abundant mines under triaxial compression condition

It is essential to deeply understand the deformation behavior of overburden above the goaf after mining for the ecological restoration of abandoned mines and the reuse of underground space. Due to the large voids and complex structures, the broken rock in the caved zone is sensitive to time effects, and the deformation behavior is the most complicated. Therefore, a self-made broken rock specimen was made which can freely deform in the lateral direction and withstand confining pressure. A series of rheological tests were performed on these specimens under various confining pressures, axial pressures, and gradations. The research results show that the creep behavior of broken rock undergoes decelerated creep or stable creep stages, depending on its level of axial pressure, and there is no accelerated creep stage. Compared with the confining pressure, the axial pressure plays the main role in the creep deformation of the specimen. Moreover, the broken rock gradation of the triaxial creep experiment affects the relative breakage index Br. When the proportion of rock blocks of the original gradation increases with the particle size of each group, the relative breakage index Br is the largest; on the contrary, it is the smallest. The relative breakage index Br is positively correlated with the confining pressure. In addition, a fractional-order creep model for broken rock in the caved zone of the goaf was proposed, and its fitting results are better than those of the classical Burgers model. Based on the proposed fractional-order creep model, a long-term subsidence prediction model of the caved zone after mining is also proposed, which can provide a theoretical basis for the long-term stability analysis of the abandoned mine.

Mechanical Constitutive and Seepage Theoretical Model of Water Storage Media Based on Fractional Derivative

Using an abandoned underground goaf in coal mines as water reservoirs has been successfully applied for protecting mine water resources in western China. The water storage media are composed of broken rock masses and the voids between the rock masses. It is critical for reservoir capacity calculation that the deformation characteristics and seepage evolution of the water storage media under triaxial stress are theoretically described. In this study, broken rock masses and the space among the rock masses are simplified as two springs in a series. The mechanical behavior of the broken rock mass is described by Hooke’s law of linear elasticity, and the deformation characteristics of the space among the rock masses are represented by a nonlinear elastic constitutive model. The nonlinear stress-strain constitutive model of the water storage media is established by combining Hooke’s law and the fractional derivative stress-strain model. Similarly, a non-Darcy seepage model of the water storage media is obtained. The nonlinear stress-strain model is verified by mechanical experiments, physical simulation tests, and field measured data, and parameter sensitivity analysis is performed. The non-Darcy seepage equation is fitted and analyzed by using the seepage experimental data of the broken rock mass under triaxial compression conditions. The fractional non-Darcy model rather than the Forchheimer equation can more accurately describe the nonlinear seepage process in water storage media.