Triaxial Compression Conditions Research Articles

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.

A modified rigid-body-spring method for modeling damage and failure of brittle rocks subjected to triaxial compression

A three-dimensional modified rigid-body-spring method (3D mRBSM) is presented to simulate the progressive damage and failure process of rocks under triaxial compressive conditions. Different from the original RBSM model, the mRBSM employs spring-set groups distributed on interfaces between blocks to approximately describe the progressive failure process of micro-cracks without increasing the size of governing equations. Firstly, the basic equations of 3D mRBSM are derived. A new randomly distributed Voronoi-based mesh technique is proposed to reproduce homogeneous and isotropic rock materials. Then, relationships between macro and micro elastic parameters are established, and a calibration procedure for parameters of failure criterion is adopted based on the trial-and-error procedure. Lastly, the new model is applied to simulate pseudo triaxial and true triaxial compression tests on brittle rocks. Results show that the proposed model correctly captures common mechanical properties of brittle rocks, such as nonlinear stress–strain relationship, brittle-ductile transition, confining pressure dependence of failure mode and medium principal stress effect. The above research demonstrates that the mRBSM is successfully upgraded to three-dimensional version. The new method is a promising tool for simulation of deformation and failure process of rocks under true triaxial stress conditions.

Assessment of Spatio-Temporal Kinematic Phenomena Observed along the Boundary of Triaxial Sand Specimens

This paper follows up on a reference paper that inspired MDPI’s topic “Stochastic Geomechanics: From Experimentation to Forward Modeling”, in which global and local deformation effects on sand specimens were fully described from high-resolution boundary displacement fields. This paper is supported by that study’s experimental database, which is open to the scientific community for further study. This paper focuses on the analysis of this experimental study to investigate strain localization effects on a subset of tests included in this database. Strain localization is defined here as associated with the non-homogeneous deformation process occurring in elastoplastic materials, including sands. Many experimental and numerical studies have been conducted during the last two decades to explore the characteristics of localization effects on sand, and to determine how these contribute to the failure mechanisms of specific sands. Under a triaxial compression condition, localization effects have been studied mainly with regard to particle kinematics and translational strain of the specimen’s displacement fields. However, to the best of the authors’ knowledge, there has been no 3D experimental kinematic analysis performed on sands to study the localization phenomena that can directly relate the impact of a specimen’s initial and boundary conditions to a failure mechanism during a triaxial test. In this paper, we introduce a full set of 3D kinematic operators under cylindrical coordinates to assess the boundary localization effects of deforming sand specimens under triaxial loading conditions. Furthermore, a set of experiments were carried out under varying experimental conditions to study the impact of variability in these localization effects. Results show that patterns of kinematic effects are quantifiable and can be used to assess likely failure-influencing factors, such as confining pressure, initial density, sample geometry, and sample heterogeneity, in the development of specific failure mechanisms. Spatio-temporal interdependencies between localization effects, such as the interactions between shear, expansion, and compaction bands observed during the specimen’s shearing process, were also studied. We therefore hypothesize that the proposed framework will serve as the basis for quantifying the uncertainty associated with the development of localization effects over the boundary of sand-deforming specimens.

A novel true triaxial test device with a high-temperature module for thermal-mechanical property characterization of hard rocks

Rock mechanical property testing under high-temperature true triaxial compression conditions is significantly important to understanding the stability of deep underground engineering rock masses where high temperature exists. This article presents the development, calibration and application of a self-designed true triaxial test system for investigating rock mechanical behaviors under coupled high-temperature and high-pressure conditions with cuboid rock samples. The test system is consisted of four independent parts, respectively for mechanical loading in three axis, thermal loading up to 250 °C, deformation and temperature measurement, and the data acquisition center. The key technology and calibration method of the measurement sensors were introduced. The primary testing results of Jinping marble, Bayu granite and Longchang sandstone under high-temperature and high-pressure coupled true triaxial conditions were obtained. It shows that the peak strength, elastic modulus and fracture mode vary with rock types and temperatures. The mechanical property of Jinping marble increases with the increase of temperature in the tested temperature range, while Longchang sandstone shows a decreasing trend, and the change of Bayu granite is relatively small. The fracture mode of Jinping marble, Bayu granite Longchang sandstone at different temperatures is compressive-shear fracture. The results verify the reliability of the test system, and provides a new platform for understanding the mechanical properties of rocks of deep underground engineering with high temperatures.

Experimental investigation of timber samples under triaxial compression conditions

Timber is re-emerging as a prominent structural material in construction due to its sustainability and aesthetic features. Timber is increasingly used in composite elements made along with steel and concrete. In the composite elements, timber is subjected to a triaxial confined stress state. However, the characteristics of timber under triaxial stress state are not well understood. An experimental campaign was carried out to characterise the triaxial confined behaviour of timber samples. Two types of timbers (soft and hardwood) were used in the experimental campaign. The selected timber samples were subjected to confined and unconfined axial compression loading conditions. In total, 50 samples were tested with five different lateral confining pressures (unconfined, 3, 5, 8 and 12 MPa). The experimental results are presented in terms of compressive strengths and axial compression stress-strain curves. The experimental data obtained was used to define the critical parameters of confined timber, such as confined strength, strain at peak stress and stress-strain behaviour. Test results demonstrate that the confinement pressure improves the strength and ductility, and the conventional Mohr-Coulomb criterion can be used to represent the confined timber strength and strain evolution. Finally, based on the data gathered, a suitable constitutive model to characterise the stress-strain behaviour of timber under the triaxial confined stress-state is proposed. This model is similar to the constitutive models typically used for concrete, mortar and rock under confined stress state. However, differences are highlighted in timber in terms of strength gain and ductility.

A quantitative model considering crack closure effect of rock materials

The crack closure effect of rock materials plays a key role in the evaluation of its compressive mechanical behavior. Based on the effective medium theory, an exponential model is proposed to describe the influence of the crack closure effect on the constitutive relation. The crack deformation is characterized by natural strain, and the crack propagation in the compaction phase and elastic phase can be captured by this quantitative model. Three model parameters can be determined from experimental data. The model was verified by our uniaxial compression tests on marble and other types of rocks from the published literature. The results show that the model can simulate the nonlinear phase of stress–strain curves of rocks under uniaxial and triaxial compression conditions. The crack closure behavior in the compression tests can be well reflected by this model. In addition, the microcrack volume ratio is positively correlated with the crack density parameters, and the material damage caused by microcracks can be identified and quantified by the microcrack volume ratio.

Effect of rarefied proppant monolayer on coal permeability

Effective gas drainage and intensification of coalbed methane recovery is a challenging problem in underground mining. One of the methods to increase coal permeability is hydraulic fracturing. Long-term conductivity of hydraulic fractures is ensured using wedging materials (proppants). The effect of partial filling of an artificial fracture by proppant on coal permeability is studied. The permeability tests of samples with a longitudinal fracture filled by a rarefied monolayer of proppant were performed under conditions of triaxial compression at 1-5 MPa. It is found that with a decrease in the surface density of the proppant by 2-4 times, the coal permeability is preserved and corresponds to the values obtained for a continuous proppant monolayer. The compressibility coefficients of the natural and artificial fractures in coal are estimated based on the permeability test results. The compressibility coefficient in the propped fractures is one order of magnitude lower than in the natural cracks.

Microscopic fabric evolution and macroscopic deformation response of gangue solid waste filler considering block shape under different confining pressures.

The irregular shape of gangue blocks will affect the coordination structure between blocks in the crushed gangue accumulation body, and then affect the engineering mechanical properties of crushed gangue in the process of load-bearing compression. In this paper, through CT scanning experiment, particle flow numerical simulation experiment, and comprehensive application of image processing, 3D reconstruction, FLAC/PFC3D continuum—discrete coupling technology, the gangue digital 3D model and the numerical model of crushed gangue particle flow under triaxial compression condition considering the real shape of the block were obtained. The microscopic fabric evolution law and macroscopic deformation response characteristics of crushed gangue considering triaxial compression condition and different confining pressures were studied. The results show that: (1) the bearing capacity of crushed gangue materials increases with the increase of confining pressure; (2) the block aggregate in the gangue sample is gradually compacted, and the lateral deformation of the sample is changed from “extruding to the axis” to “bulging to the periphery”; (3) the vertical movement of the block decreases gradually from the top to the bottom of the sample, and there is a “triangle area” of block displacement at the top and bottom of the sample; the larger the confining pressure, the smaller the vertical displacement range at the top of the sample; (4) the process of “instability and failure—optimization and reconstruction” of skeleton force chain structure occurs constantly; as confining pressure increases, the stability of skeleton force chain structure and the bearing capacity of crushed gangue sample increases; (5) under the same strain state, the greater the confining pressure, the higher the fragmentation degree of the sample. This study reveals the internal mechanism of macro deformation of crushed gangue under the triaxial compression from the perspective of the mesoscopic fabric evolution. The research results are of great significance for the selection of crushed gangue in engineering application. In addition, the research results also have a significant impact on promoting the reasonable disposal and resource utilization of gangue solid waste and protecting the ecological environment of mining areas.

Analyses of True-Triaxial Hydraulic Fracturing of Granite Samples for an Enhanced Geothermal System

Abstract The fracturing behavior of enhanced geothermal system (EGS) reservoirs merits investigation under field-relevant temperature and stress conditions, in order to understand the creation of an extensive fracture network that helps achieve a high heat exchange efficiency. In this work, hydraulic fracturing tests were conducted on two 300 mm sized cubic granite samples at room (32°C) and field-relevant (250°C) temperatures under true triaxial compression conditions. The failure behavior and fracturing plane were studied using acoustic emission (AE) testing, μm-scale computed tomography (μm-CT), and scanning electronic microscopy (SEM), in addition to the monitoring and analyses of pressure-flow curve during fracturing. The results show that (1) at the macroscale, the strength of the granite sample was weakened at high (field-relevant) temperature, as shown by a decrease in the breakdown pressure and increase in closure pressure from the pressure-flow curve; (2) at the microscale, the failure pattern of grains during fracturing did not differ much at high and room temperatures for both intergranular and transgranular fractures; and (3) due to upscaling issues from the laboratory to field, however, the laboratory experiment will not directly provide some critical parameters (e.g., mud window pressure needed for fracture initiation and borehole failure avoidance) needed for an EGS field exploration.

Damage constitutive model of gas-bearing coal using industrial CT scanning technology

Determining the deformation characteristics and mechanical behavior of gas-bearing coal is beneficial to understanding the phenomena and rules of dynamic disasters during coal mining. In this study, a computed tomography (CT) scanner and a triaxial loading seepage system were used to perform CT scanning tests on gas-bearing coal under triaxial compressive conditions. We processed the CT images in different deformation stages of the gas-bearing coal and analyzed them with a digital image processing technology to depict dynamic evolution damage trend. In addition, we employed a fracture area projection method to propose a new damage variable and theoretically constructed a new damage constitutive model. The results showed that the coal specimens became prone to increased instability and damage as gas pressure increased. The growth and expansion of fissures in gas-bearing coal were heterogeneous and anisotropic and mainly experienced three processes, that is, closure in the compaction stage and elasticity stage, expansion in the strain-hardening stage, and sharp propagation and interconnection in the post-peak stage. With the progression of fracture propagation, the degree of damage gradually decreased then increased. The proposed new damage variable was more suitable than the traditional damage variable for depicting the damage degree and damage evolution process. Furthermore, the proposed new damage constitutive model well mirrored the deformation behavior of gas-bearing coal under triaxial compressive loads.

Experimental investigation on stress-induced failure in D-shaped hard rock tunnel under water-bearing and true triaxial compression conditions

Experimental investigation on stress-induced failure in D-shaped hard rock tunnel under water-bearing and true triaxial compression conditions

Fracture evolution and nonlinear seepage characteristic of gas-bearing coal using X-ray computed tomography and the lattice Boltzmann method

Fracture is the primary channel of gas seepage in coal seams and controls the drainage efficiency of coal bed methane (CBM). However, the seepage characteristics and dynamic evolution law in the fractures of gas-bearing coal under external loads are yet to be clearly revealed. In this study, an industrial computer tomography (CT) scanner equipped with a triaxial loading system was used to conduct gas-seepage and CT scanning experiments under triaxial compression conditions. The results showed that the fracture volume and permeability decreased first and then increased during the complete stress–strain process of gas-bearing coal, displaying an approximate U-shaped variation trend involving a decrease stage, an increase stage, and a jump-increase stage. The lattice Boltzmann method (LBM) was applied to make the seepage processes of gas-bearing coal reappear, and a modified nonlinear permeability model was developed to represent non-Darcy seepage inside fractured coal. The LBM simulation results mirrored the dynamic evolution of the gas seepage field and gas permeability controlled by fracture propagation. The proposed modified nonlinear permeability model effectively reflected the nonlinear variation behaviour of gas permeability and was superior to the traditional Darcy's model in describing nonlinear seepage of gas-bearing coal.

Strength criterion of recycled aggregate concrete under triaxial Compression: Model calibration

Utilization of recycled aggregate concrete (RAC) can promote the development of green building materials since it can make full use of waste concrete. The mechanical properties and failure criterion of RAC under triaxial compression is the computational basis for design of RAC structural members. However, an explicit and unified approach for assessing the failure surface of RAC under both traditional triaxial compression and true triaxial compression condition is extremely limited. Aiming to provide a solution to figure out the above-mentioned technical bottleneck, firstly this study evaluated the applicability of existing failure criterion developed based on natural aggregate concrete using an experimental database including 123 cylindrical RAC specimens; and then an equation of compressive meridian (i.e., Lode angel is 60°) in octahedral stress space was proposed with the help of this database. Further, the formula for tensile meridian of RAC (i.e., Lode angel is 0°) was established based on 24 cubic RAC specimens collected from available literature. The influence of high temperature was also considered in both compressive meridian and tensile meridian formula. A complete failure surface of arbitrary stress condition (i.e., the Lode angle ranges from 0° to 60°) was determined. Finally, the proposed equations for failure surface of RAC in the cases of room temperature and high temperatures were validated with reference to experimental results.

Creep and Breakage Behavior of Broken Rock in Caving Zone of Abundant Mines Under Triaxial Compression Condition

Creep and Breakage Behavior of Broken Rock in Caving Zone of Abundant Mines Under Triaxial Compression Condition