Triaxial 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.

Experimental study on failure characteristics of single-sided unloading rock under different intermediate principal stress conditions

Investigation of unloading rock failure under different σ2 facilitates the control mechanism of excavation surrounding rock. This study focused on single-sided unloading tests of granite specimens under true triaxial conditions. The strength and failure characteristics were studied with micro-camera and acoustic emission (AE) monitoring. Furthermore, the choice of test path and the effect of σ2 on fracture of unloading rock were discussed. Results show that the increased σ2 can strengthen the stability of single-sided unloading rock. After unloading, the rock's free surface underwent five phases, namely, inoculation, particle ejection, buckling rupture, stable failure, and unstable rockburst phases. Moreover, at σ2≤30 MPa, the b value shows the following variation tendency: rising, dropping, significant fluctuation, and dropping, with dispersed damages signal. At σ2≥40 MPa, the tendency shows: a rise, a decrease, a slight fluctuation, and final drop, with concentrated damages signal. After unloading, AE energy is mainly concentrated in the micro-energy range. With the increased σ2, the micro-energy ratio rises. In contrast, low, medium and large energy ratios drop gradually. The increased tensile fractures and decreased shear fractures indicate that the failure mode of the unloading rock gradually changes from tensile-shear mode to tensile-split one. The fractional dimension of the rock fragments first increases and then decreases with an inflection point at 20 MPa. The distribution of SIF on the planes changes as σ2 increases, resulting in strengthening and then weakening of the rock bearing capacity.

Experimental study on nonlinear seepage characteristics of coal under true triaxial stress loading

The characteristics of coalbed methane flow are jointly determined by the fracture and stress environment. Previous studies conducted under conventional triaxial or uniaxial stress conditions cannot truly reflect the in situ stress environment and neglected the influence of intermediate principal stress on the nonlinear seepage characteristics of coal. For this study, coal seepage tests were performed under true triaxial stress, allowing the nonlinear seepage characteristics of coal to be analyzed under different principal stresses. This enables the applicability of nonlinear seepage characterization equations and the change laws of relevant parameters to be clarified. The results show that the nonlinear seepage characteristics of coal under true triaxial stress increase as the principal stresses and gas pressure gradient increase. Using the Forchheimer equation for characterization, the nonlinear effect factor, viscous permeability, and inertial permeability gradually decrease with increasing principal stress in all directions. Intermediate principal stress σ2 has the most significant effect on nonlinear effects and inertial permeability, whereas principal stress σ3 has the greatest effect on viscous permeability. Using the Izbash equation for characterization, the fitting coefficients λ, m increase with increasing principal stress. Principal stress σ2 has the most significant effect on m, whereas principal stress σ3 has the greatest influence on λ. Comparative analysis shows that both Forchheimer and Izbash equations accurately characterize the nonlinear seepage characteristics of coal under real triaxial stress. The Forchheimer equation requires more theoretical parameters to measure the degree of nonlinear seepage and thus better describes the evolution process of linear to nonlinear seepage.

Fractional creep model and experimental study of unsaturated silty clay in Fuyang

Due to the long-term overdraft of groundwater in Fuyang, silty clay in this area has been in an unsaturated state for a long time, which caused ground subsidence and threatened the safety of engineering construction. Creep is an important part of ground subsidence, but it is easily ignored in ground subsidence caused by groundwater overdraft. Therefore, in order to explore the creep behavior in this environment, a series of triaxial creep tests of unsaturated soil were conducted to research the effects of deviator stress, matrix suction and net confining pressure on creep. Then, based on analysis results of the geometric characteristics of the test creep curves, an improved fractional order Nishihara model of unsaturated soil under triaxial stress conditions was constructed by using fractional calculus theory. Finally, the effectiveness of improved fractional order Nishihara model was verified based on cooperation search algorithm and minimum mean square error principle. The simulation results show that the fitting curves of improved fractional order Nishihara model are in good agreement with the test curves, and it is feasible and effective to describe the creep characteristics of unsaturated silty clay in Fuyang.

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.

Investigation into the compression behaviour of unsaturated damaged Callovo-Oxfordian claystone

In this study, the compression behaviour of unsaturated damaged COx claystone is investigated by performing high pressure oedometer tests with controlled suction. The damaged oedometer samples were prepared by shearing the claystone in triaxial conditions. Four high pressure oedometer tests were conducted using different controlled suctions. The effects of suction and damage on the swelling and compression were investigated in oedometer. Results show that the intact claystone exhibits a larger swelling strain than that of the damaged one at the same imposed suction. The damaged claystone at a lower suction displays a smaller yield stress and higher compressibility, and exhibits a larger compression index Cc than the intact one, evidencing the effect of damage. In addition, the step compression index Cc* increases with the increase of vertical stress, while deceases with the decrease of suction. This indicates the dependencies of compression behaviour on vertical stress and suction.

Validation of the Crack Mode-Changing Stress in Circular Tunnels Under Generalized Triaxial Tensile Stress States

In the past century, mining depths have increased profoundly from a few hundred meters to several kilometres following improvements in drilling techniques and instrumentation methods. In highly-stressed tunnels, the predominant failure mechanism of underground rock is controlled by stress-induced fractures parallel to the excavation boundaries in terms of spalling failures or, in some severe cases, a violent slab ejection that forms a V-shaped notch around the excavation walls. Such failures can seriously affect production and shut down the operation temporarily or even permanently. To better characterize, predict, and prevent these catastrophic failures, many laboratory tests and scaled model tunnels have been conducted under uniaxial and biaxial loading conditions, with limited studies also available under true triaxial stress states. This paper extends the previous studies on the impact of true triaxial loading conditions on the spalling failure in high porosity sandstone and investigates further the validation of a new Crack Mode-Changing Stress (CMCS) parameter, defined as the minimum principal stress required to change rock fracturing from splitting to a sliding failure mode. The results revealed that the minor principal stress can significantly affect the propagation of the stress-induced fractures of spalling failure along the tunnel sidewall.

Effect of roughness and pore pressure on shear behavior of rock joint under true triaxial loading conditions

This paper presents the direct shear test to investigate the effect of the joint roughness and pore pressure on the shear behavior of rock joints. Recently, we have developed an experimental method for the direct shear test using true triaxial apparatus that can control three mutually perpendicular loads and pore pressure independently. The morphological properties of the joints were quantified using a non-contact 3D laser scanner to investigate the change in surface roughness due to shear and the effect of pore pressure. In addition, the time variation of shear load, normal displacement, and flow rate on the joint during shear sliding were measured, and the relationship with the change of the discontinuous surface after the experiment was discussed.

Evaluation of the mechanical properties of Inada granite under true triaxial conditions by discrete element method

Evaluation of the mechanical properties of Inada granite under true triaxial conditions by discrete element method

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.

A comparison of shear modulus of unsaturated sand in triaxial and simple shear tests under different strains and suctions

The shear modulus (G) in sands changes when subjected to variations in the degree of saturation. The matric suction in unsaturated sands increase the effective stress and consequently the shear modulus. The trend of G/Gsat variations is complicated as it is dependent on a number of parameters including stress state and therefore, requires more in-depth evaluations. Several isotropic cyclic triaxial as well as simple shear tests (K0 condition) are carried out under various degrees of saturation and strain amplitudes on a fine angular to sub-angular silica sand. The results show greater values of G from triaxial tests as compared to simple shear tests under similar vertical stress and void ratio, mainly due to a higher mean effective stress at isotropic triaxial condition. Besides, the two different stress states of isotropic and K0 conditions resulted in different curves of G/Gsat at the examined range of suction. Based on the measured values, G/Gsat variations versus matric suction cannot be well predicted solely by contribution of suction in the effective stress, but the variations of the degree of saturation with suction should be taken into account.

Coupled thermo-mechanical constitutive damage model for sandstone

Underground rock dynamic disasters are becoming more severe due to the increasing depth of human operations underground. Underground temperature and pressure conditions contribute significantly to these disasters. Therefore, it is important to understand the coupled thermo-mechanical (TM) behaviour of rocks for the long-term safety and maintenance of underground tunnelling and mining. Moreover, investigation of the damage, strength and failure characteristics of rocks under triaxial stress conditions is important to avoid underground rock disasters. In this study, based on Weibull distribution and Lemaitre’s strain equivalent principle, a statistical coupled TM constitutive model for sandstone was established under high temperature and pressure conditions. The triaxial test results of sandstone under different temperature and pressure conditions were used to validate the model. The proposed model was in good agreement with the experimental results up to 600 °C. The total TM damage was decreased with increasing temperature, while it was increased with increasing confining pressure. The model’s parameters can be calculated using conventional laboratory test results.

On the influence of drained cyclic preloadings on the cyclic behaviour of Zbraslav sand

This article experimentally evaluates the influence of directional drained cyclic preloadings on the subsequent undrained monotonic and cyclic response of Zbraslav sand. The cyclic tests were performed on dense samples and under triaxial conditions. The experiments considered several different preloading directions, magnitude of the maximum deviatoric stress reached during the drained preloading stage and deviatoric stress amplitudes during the undrained shearing stage. The experimental results suggested that the rate of strains and pore water pressure accumulation, and therefore, the number of cycles to reach initial liquefaction or failure conditions are remarkably affected by the direction of the drained preloading history. In addition, the preloading direction plays a major role on the contractive/dilative response during the subsequent undrained monotonic loading. In particular, directional drained cyclic preloadings toward positive deviatoric stresses at constant mean effective stress and isotropic compression led to more dilative responses. Contrary, preloadings toward negative deviatoric stresses at constant mean effective stress led to more contractive responses. The results suggest that these major variations cannot be associated to the rather small changes in the relative density of the samples but likely due to fabric changes and induced anisotropy caused by the drained preloading history.

Statistical Characterization of Boundary Kinematics Observed on a Series 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 the authors populated a spatio–temporal database of boundary displacement fields from a series of triaxial sand specimens using three-dimensional (3D) digital image correlation analysis. The database was curated and is currently available to the scientific community for further study. This paper uses a subset of this database, in which the experimental conditions were similar, to statistically investigate the dominant kinematic phenomena observed on the boundary of triaxial sand specimens under compression. The first-order 3D kinematic operators under the cylindrical coordinates, comprised of the divergence, curl, and gradient, were applied to the boundary displacement fields to illustrate the localization deformation patterns including the translational, rotational, shearing, and volumetric behaviors throughout the triaxial compression processes. Subsequently, the first-order statistics of the kinematic results are estimated, with the aim of revealing the evolution of associated localization effects as well as their corresponding uncertainties in space and time. The results of this research provide an innovative statistical interpretation of the localization effects on soil specimens under three-dimensional stress conditions. The proposed approach advances the interpretation of granular material’s responses under triaxial compression experimental conditions, while opening an opportunity to reproduce the material’s kinematic responses under the triaxial experimental conditions through constitutive modeling or machine learning techniques.

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.

The effect of grain size and porosity on the nature of compaction localisation in high-porosity sandstone

Compaction bands are a type of deformation band with negligible shear in porous rocks such as sandstones and are important because they can impede subsurface fluid flow. However, the microstructural properties which favour their growth are not fully understood. We experimentally investigate the effect of porosity and grain size on compaction localisation using synthetic sandstones that permit control of the starting porosity (27%, 32%, 37%) and mean grain size (ranging from 314 to 987 μm). Each sample is subjected to the same triaxial test conditions and shortened by 5% axial strain at an effective confining pressure of 85% of their grain crushing pressure (P*). Discrete compaction bands oriented normal to the axial loading direction are found only in the sample with the lowest starting porosity (27%) and smallest grain size (314 μm), while diffuse bands are observed for the same porosity at a larger grain size of 411 μm. No compaction bands are observed for any grain size in either the 32% or 37% starting porosity samples. Porosity analysis indicates grain size reduction does not necessarily correspond to porosity reduction indicating that compaction by grain rearrangement is as effective as localisation through comminution for these high-porosity synthetic sandstones.

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.

Experimental and numerical study on the mechanical properties of compressively precracked sandstone repaired by grouting

• A set of laboratory grouting devices was developed to grout the precracked rock specimen. • The strength of grouted rock is observed to be determined by the interface between rock and cement. • A numerical simulation method of grouting was developed based on the Fish language of PFC 2D . Grouting is a common reinforcement method that is widely used in various geotechnical engineering applications. Studying the mechanical properties of grouted rock masses under different stress conditions is of great significance to geotechnical engineering, so a set of laboratory grouting devices was developed for this study. The mechanical properties of compressively precracked sandstone before and after grouting were studied by triaxial compression tests with different confining pressures, and the crack and cementation morphologies of precracked specimens were revealed by X-ray CT (Computed Tomography) scanning. According to the findings of the study, grouting significantly improves the integrity and mechanical properties of cracked specimens. The grouted specimens exhibit higher strengths and Mohr–Coulomb parameters ( c and φ), and these increments vary with confining pressures. The strength of grouted specimens depends mainly on the micromechanical properties of the contact surface between sandstone and cement grout. Affected by the mechanical properties of cement grout, the elastic modulus of the grouted specimens is lower than that of uncracked sandstone, and the deformation of the grouted specimen also exhibits an obvious ideal plasticity state under triaxial stress conditions. Thus, the grouted sandstone does not break suddenly. In addition, a numerical method of grouting was also developed in the PFC 2D program to investigate the micro mechanisms of fracturing and grouting sandstone. The numerical simulations represent the strength and progressive failure process of both intact and grouted specimens very well and reveal the micromechanical behaviors of the grouted rock mass.