Triaxial Conditions Research Articles

Experimental study on seepage-induced concentrated leak erosion in sand under triaxial testing conditions

Experimental study on seepage-induced concentrated leak erosion in sand under triaxial testing conditions

Experiment and discrete element modeling of particle breakage in coral sand under triaxial compression conditions

Particle breakage is a major factor that determines the strength and deformation of coral sand. Consolidated drained triaxial compression tests under different confining pressures have been conducted on coral sands as a basis for 3D discrete element simulations, focusing on the particle breakage characteristics. Considering angular breakage and overall breakage in the numerical model, particle breakage is simulated with a fragment replacement method, and the particle size and the equivalent stress are combined as the criterion to judge the occurrence of particle crushing. The validation of the numerical model is proved by reproducing comparable stress-strain relations, evolutions of grain size distribution and relative breakage rate. The overall behavior of the specimen transit from strain softening to strain hardening with the increase in confining pressure from 100 kPa to 400 kPa. Meanwhile, the number of angular breakages increases at a decreasing rate, while the number of overall breakages increase at an increasing rate. This phenomenon implies that overall breakage overwhelms angular breakage and becomes the dominating particle breakage mechanism gradually with increasing confining pressure. Microscopic analyses reveal that higher confining pressure increases the overall contact force, the portion of strong contact force and the coordination number.

Elastoplastic analysis of the enhancing mechanism of tensile performance of ductile thin-walled circular tubes with internal support

Composite components with internal support, such as concrete-filled steel tubes (CFST), are widely applied in a variety of industries. Various experimental and numerical studies have revealed that internal supports could effectively enhance the tensile performance of ductile tubes. However, stress–deformation relations and strengthening mechanisms of thin-walled circular tubes under tension, (especially in plastic stages) have not been studied based on plastic increment theory. In this study, based on circumferential deformation coordination and generalized Hook’s law, the effects of internal support on yield strength and axial deformation of tubes were analyzed and the yield strength calculation equation of filled tubes was derived under true triaxial conditions. Based on plastic increment theory and isotropic linear hardening hypothesis, the differential relationship between the pressure increment of internal support and the axial plastic strain increment of steel tubes was established. The effects of elastic modulus, radius–thickness ratio and axial plastic strain on strength increase were also evaluated. Comparative analyze showed that the value of stress increase on filled tubes predicted by the proposed model was consistent with the results obtained from CFST tensile test and flexible support-filled thin-walled circular tube (FTWCT) test. In conclusion, a theoretical model was established for the first time for tensile strength enhancement mechanism of FTWCTs in plastic large-deformation stage, which was important in predicting the performance of ductile thin-walled structures under extreme loads.

New Insights into Failure Behaviors of Tectonic Coal Under Triaxial Conditions Using Reconstituted Coal Specimens

New Insights into Failure Behaviors of Tectonic Coal Under Triaxial Conditions Using Reconstituted Coal Specimens

Experimental Study on Percolation Rate Characteristics of Gas-Filled Coal Bodies Based on True Triaxial Condition

To research the percolation rate of gas-filled coal based on true triaxial condition, this paper uses the three-phase coupling true triaxial servo test device to carry out the seepage test of coal, and the percolation rate of coal under different conditions of three factors such as gas pressure was measured by Darcy’s law, and the variation of percolation rate of coal was studied based on the comprehensive consideration of thermal elastic swelling deformation, expansion deformation of adsorbed gas, and compression deformation of interstitial pressure. The results are as follows: (1) When the main stress and temperature maintain unchanged, the percolation rate presents the trend which first decreases and then becomes gentle with the gas pressure; when the gas pressure and main stress maintain unchanged, the percolation rate increases with the decrease of temperature; when the pressure and temperature maintain unchanged, the changes of percolation rate present a shape of “V” with the main stress. (2) The strain curve of gas-filled coal decreases at first and then increases; that is, the percolation rate decreases gradually when the strain increases at the compression phase and elastic phase, while the percolation rate increases with the increase of strain at the yield phase and failure phase. (3) In the process of increasing volume stress, the percolation rate decreases gradually in the pore compaction stage, the percolation rate increases gradually from crack propagation to peak failure stage, and then, the percolation rate increases significantly after the peak damage. According to the test results, the percolation rate and volume strain show an inverse proportion.

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.

An analytical model for the triaxial compressive Stress-strain relationships of Cemented Pasted Backfill (CPB) with different curing time

The strength of Cemented Pasted Backfill (CPB) is gradually enhanced with the increase of curing time. It is of great significance to study the stress-strain behaviors of CPB with different curing time under triaxial loading conditions. The triaxial compressive tests of CPB samples with 4 different curing time (1, 3, 7, and 28 days) were firstly conducted using GCTS (Geotechnical Consulting ＆ Testing System) loading system under 4 different lateral constraint ratios (σ3/UCS≈0%, 10%, 20%, and 30%). The experimental data were then used to develop a damage constitutive model in which the lateral constraint rations σ3/UCS plays a key role. The tested stress-strain curves from the experiments were used to verify the proposed damage constitutive model. The comparisons between the tests and the model prediction showed that the triaxial strength of CPB can be accurately predicted by the Mohr-Coulomb strength criterion. An obvious secondary elastic strengthening stage was identified in the stress-strain curves of CPB when σ3/UCS is high (≥20%). And the proposed damage constitutive model can accurately represent the stress-strain relationships of CPB with different curing time and σ3/UCS. The results presented in this study contribute to a better understanding of the triaxial mechanical behaviors of CPB.

Imaging Elastodynamic and Hydraulic Properties of In Situ Fractured Rock: An Experimental Investigation Exploring Effects of Dynamic Stressing and Shearing

AbstractWe describe laboratory experiments to elucidate the relationship between nonlinear elasticity and permeability evolution in fractured media subjected to local stress perturbations. This study is part of an effort to measure fluid pathways and fracture properties using active‐source acoustic monitoring during fluid injection and shear of rough fractures. Experiments were conducted with L‐shaped samples of Westerly granite fractured in situ under triaxial conditions with deionized water subsequently circulated through the resulting fractures. After in situ fracturing, we separately imposed oscillations of the applied normal stress and pore pressure with amplitudes ranging from 0.2 to 1 MPa and frequencies from 0.1 to 40 Hz. In response to normal stress and pore pressure oscillations, fractured Westerly granite samples exhibit characteristic transient softening, acoustic velocity fluctuations, and slow recovery, together with permeability enhancement or decay, informing us about the coupled nonlinear elastodynamic and poromechanical rock properties. Fracture interface properties (contact asperity stiffness, aperture) are then altered in situ by shearing, which generally decreases the measured elastic nonlinearity and permeability change for both normal stress and pore pressure oscillations.

Specific surface area: A reliable predictor of creep and stress relaxation in gas shales

In recent years, short-term creep parameters determined in the laboratory from cylindrical gas shale samples subjected to triaxial (in-situ) stress conditions have been used successfully to infer long-term deformation and stress relaxation at the reservoir scale across geologic time scales. Due to the viscoelastic formalism, both the laboratory creep response and field-scale stress relaxation can be modeled with power law functions of time involving the elastic compliance of the shale B, the time-dependence exponent n, and the amount of total strain ∊. Gas shales often exhibit a high specific surface area associated with their high content in clay minerals and/or total organic carbon (TOC). The low-pressure nitrogen adsorption technique can be used advantageously to estimate specific surface area (SN2); i.e., it is a relatively fast and cost-effective measurement conducted on powdered samples of shale material. A robust global empirical correlation between gas shale creep parameters and SN2 emerges from the analysis of laboratory data collected from multiple gas shale formations in Australia (the prospective Goldwyer Formation) and the United States (Barnett, Haynesville, and Eagle Ford formations), and spanning a broad range of clay content, organic matter, maturity, and porosity values. This data set also shows that the summed fractions of clay minerals, TOC, and porosity, the so-called weak phase fraction, correlates nearly as well with primary creep parameters. The weak phase fraction can also be estimated from faster and more cost-effective measurements or from well logs. To evaluate its predictive capacity, the key correlation between SN2 and creep parameters is used in a case study to predict the magnitude of present-day least principal stress Shmin across six depth intervals/lithologic layers in a prolific unconventional shale formation in the northeastern United States. Several Shmin measurements are available for verification, and our approach successfully captures the observed layered variation of stress with depth.

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.

Mechanical characteristics of red sandstone under cyclic wetting and drying

The bank slope of the Three Gorges Reservoir is affected by seasonal water level fluctuations, which leads to deterioration of the rock mass, resulting in a series of geological disasters such as landslides and mudslides. Therefore, to thoroughly understand the degradation mechanism of mechanical characteristics under wetting–drying cycles, uniaxial compression tests and triaxial compression tests were used to reveal the relationship between mechanical characteristics and wetting–drying cycles. The results of the uniaxial compression tests show that with the increase in the number of wetting–drying cycles, the mechanical characteristics show a declining trend, and the compaction stage of the sample increases considerably. It was found that the first ten wetting–drying cycles have a greater impact on the mechanical characteristics of red sandstone under the triaxial compression condition, the mechanical parameters such as deviatoric stress, elasticity modulus dropped rapidly under the first 10 cycles and then tend to be stable. Based on the testing data under wetting–drying cycle condition, the mechanical parameters of the statistics damage constitutive model were modified and the results show that the modified damage constitutive model has a high degree of fit with the test data, indicating that the modified mechanical parameters can better reflect the degradation of red sandstone after the wetting–drying cycles. This understanding of the degradation process of the mechanical characteristics under wetting–drying cycles can provide theoretical guidance for the protection of dangerous slopes in the drawdown zone of the Three Gorges Reservoir.

Roughness of fracture surfaces in numerical models and laboratory experiments

Abstract. We investigate the influence of stress conditions during fracture formation on the geometry and roughness of fracture surfaces. Rough fracture surfaces have been generated in numerical simulations of triaxial deformation experiments using the discrete element method and in a small number of laboratory experiments on limestone and sandstone samples. Digital surface models of the rock samples fractured in the laboratory experiments were produced using high-resolution photogrammetry. The roughness of the surfaces was analyzed in terms of absolute roughness measures such as an estimated joint roughness coefficient (JRC) and in terms of its scaling properties. The results show that all analyzed surfaces are self-affine but with different Hurst exponents between the numerical models and the real rock samples. Results from numerical simulations using a wide range of stress conditions to generate the fracture surfaces show a weak decrease of the Hurst exponents with increasing confining stress and a larger absolute roughness for transversely isotropic stress conditions compared to true triaxial conditions. Other than that, our results suggest that stress conditions have little influence on the surface roughness of newly formed fractures.

Effect of CO2 on coal P-wave velocity under triaxial stress

As P-wave velocity is sensitive to the variations in coal reservoir parameters, it is possible to monitor the injected CO2 through P-wave velocity during CO2 sequestration in coal. However, the effects of CO2 on the coal P-wave velocity under triaxial stress are not clearly discerned. In the present study, different boundary conditions and gases were utilised to investigate the factors affecting the P-wave velocity after the interaction of coal with CO2. Experiments with helium indicated that the pore pressure primarily affected the P-wave velocity by altering the effective stress. Experiments with CH4 and CO2 indicated that matrix swelling induced-cleats porosity decline significantly promoted P-wave velocity. Moreover, CO2 caused a wider scale and severe weakening of coal matrix than CH4, thereby significantly decreasing the P-wave velocity, and the decline in P-wave velocity increases with vitrinite content. Furthermore, experiments under different boundary conditions showed that with the boundary condition having more constraints, the decrement of pore pressure on P-wave velocity is more weaken, whereas the improvement of matrix swelling on P-wave velocity is more evident. This study contributes to understanding the mechanism of effect of CO2 on P-wave velocity under triaxial stress condition and provides guidance for monitoring CO2 sequestration in coal.

The Effect of Curing under Applied Stress on the Mechanical Performance of Cement Paste Backfill

After placing the Cement Paste Backfill (CPB) slurry in mined cavities underground, during the setting and hardening processes, the weight and hydrostatic pressure of the upper-layer CPB slurry applies an axial load over the bottom-layer CPB materials, which is called the self-consolidation of CPB slurry. Due to this phenomenon, the mechanical properties of in situ CPB could be considerably different from laboratory results. Hence, it is crucial to understand the effect of self-consolidation behaviour on the mechanical properties of backfill material. This paper presents an experimental study on the impact of axial applied stress (As) during curing, which represents the various self-consolidation conditions and curing times on the mechanical properties of CPB material prepared using the tailings of a copper mine in South Australia and a newly released commercially manufactured cement called Minecem (MC). A curing under pressure apparatus (CPA) is designed to cure CPB samples under axial applied stress. The equipment can apply and measure axial load during curing and measure the passive lateral stress due to axial load which represents the horizontal stresses at a certain depth of CPB stope on the retaining structure. The prepared samples with axially applied pressure during curing were tested under uniaxial and triaxial compressive loading conditions. Microstructural tests by scanning electron microscopy (SEM) were also used to study the fabric evolution in response to various applied stresses during curing. Overall, the increase in As during curing leads to higher resultant CPB peak strength and stiffness under uniaxial and triaxial compression tests. For instance, a sample cured under 3.6 MPa axial load for 28 days demonstrates a uniaxial compressive strength (UCS) value of five times more than a sample cured under atmospheric curing conditions. Passive lateral stress was measured during the curing period and was representative of underground barricade stress. Furthermore, during curing, the axial applied stress changed the initial CPB pore structure after placement. With the increase in applied stress, the stress compressed CPB samples at the macroscale, leading to much smaller pores or cracks prior to the hydration process. At an early stage, the increase in UCS due to axial applied stress mainly arises from a dense microstructure caused by the compression of tailings and cement particles. With the increase in curing time, the observation also shows that a CPB matrix with fewer pore spaces may improve the hydration progress; hence, the influence of axial applied stress becomes more pronounced in long-term UCS.

Stress-sensitivity analysis of rock mechanical and petrophysical properties of fractured tight sandstone under true-triaxial stresses in the laboratory

In the process of oilfield production, effective stresses usually increase continuously and act as unequal triaxial stresses on the reservoir. However, most studies on rock stress sensitivity are conducted under conventional triaxial or uniaxial stress conditions, which cannot truly represent the in situ stress environment. In this work, two groups of fractured tight sandstones sampled from northwestern China were tested under true-triaxial stress environments to study the stress sensitivity of mechanical and petrophysical properties. The sandstones are elastically deformed under experimental stress conditions, showing an apparent correlation with fracture angles. The acoustic wave velocity increases linearly with the stresses, and the shear wave velocity is strongly affected by fracture angle and anisotropic effective stresses. The permeabilities decrease exponentially and show significant anisotropy with increasing effective stress, which is less stress sensitive when the fracture strike is parallel to the maximum horizontal principal stress than when it is perpendicular. This work successfully reveals the stress sensitivity of anisotropic permeability, stress-strain behavior, and acoustic wave velocity of fractured tight sandstone during reservoir depletion. The testing results provide an innovative method to accurately measure the anisotropic rock properties, offer new ideas about fractures identification, and have profound significance for exploration and development of tight reservoirs.

Development and application of triaxial rock shear - self-supporting fracture conductivity experiment system

The structure and function of shear - self-supporting fracture conductivity test device in great detail were presented. This device system consists of five parts: vertical loading system, horizontal shear loading system, the servo control system, power system, shear box and its sealing system, digital control and acquisition system. It can provide vertical force up to 2000KN, shear force 500KN, lateral stress 50MPa and hydraulic pressure 40 MPa. Characteristics of the system are illustrated as follows. (1) The experimental research of rock shear failure can be performed under three axial stress conditions, the lateral stress is loaded by hydraulic oil and the vertical stress is loaded by pressing machine. (2) True triaxial and quasi-triaxial loading modes can be switched by using different sealing sleeves. (3) The shear seepage coupling and self-supporting fracture conductivity tests could be conducted under three axial stress conditions. (4) The stress and displacement loading modes under different loading rate can be realized by servo system. Based on this experimental system, shear - fracture conductivity test under three axial stress conditions was performed on shale specimen and its reliability was verified. The experimental system can be used to provide theoretical basis for the shear destruction mechanism and Self-supporting shear fracture conductivity test under true triaxial stress conditions. The research has an important guiding significance on the formation mechanism of unconventional reservoir shear fracture and the flow capacity of self-supporting shear fracture and its influencing factors.

Modeling investigation of coupling between damage and permeability for sandstone

Rock damage due to microcrack propagation leads to changes in seepage characteristics. Therefore, the coupled mechanism of rock damage and permeability plays a significant role in some underground engineering projects, such as mining, excavation, and hydraulic activity. In this study, a rock micro-unit is divided into damaged and undamaged parts. The damaged part only consists of cracks, and the undamaged part includes pores and matrices. A damage evolution function was proposed on the basis of statistical damage theory considering water pore pressure to demonstrate the mechanical behavior under triaxial compression conditions. The damage variable could be obtained with the Weibull distribution function. Then, a novel sandstone permeability model was developed by introducing the damage evolution function. The proposed coupled damage and permeability model covered the matrix and fracture permeabilities. A series of triaxial seepage experimental data of sandstone under different pore water pressures was cited to validate the coupled model. Results showed that the coupled damage and permeability model was remarkably consistent with experimental findings.

Effect of the Minor Principal Stress on Crack Initiation Stress Threshold

The rapid expansion of urban and mining infrastructures worldwide over the last two decades has seen an escalation of development in hard rock, including urban tunnels, deep open pits, and underground mines. However, despite many success stories, the pervasiveness of rock burst and spalling remains yet a major unresolved ground control problem in many deep mines and tunnels. Spalling is characterised as a sudden explosion-like rock failure that occurs spontaneously and could affect both the short-term and long-term viability of mining operations. Previous studies strongly show that the spalling strength in low-porosity rocks can be associated with the initiation of internal cracks in the sample. However, very limited studies are available that looks at the effect of all the principal stresses on rock crack initiation stress threshold. This paper investigates the previously ignored effect of the minor principal stress on the crack initiation stress level of sandstone cubes tested under true triaxial loading conditions. The results reveal that the minor principal stress has a profound effect on the crack initiation point. As a result of this study, a new crack mode-changing stress (CMCS) concept is also introduced which is defined as the corresponding minimum principal stress required to change rock fracturing from splitting to a sliding failure mode.

Consolidated drained (CID) behavior of fibre reinforced cemented Toyoura sand in triaxial loading conditions

The effects of fibre (0–3 %) and cement (0–3 %) additives, on Toyoura sand were examined under consolidated drained compression and extension loading conditions. All samples were prepared to a target dry density value (e.g., {rho }_{d}= 1.489 g/cm3) of Toyoura sand using under-compaction moist tamping technique. In compression, the unreinforced specimens exhibited a behavior of medium dense sand and reached a peak deviator stress (qp) at approximately 4 % axial strain ({epsilon }_{a}) for the varying mean effective stresses, pʹ (i.e. 50–400 kPa). The peak drained strength increases in fibre reinforced cemented specimens were found to be up to 132 % (lower effective stresses) and 243 % (higher effective stresses), while, the drained strength increases at critical state for the fibre reinforced cemented specimens were found to be up to 105 % (lower effective stresses) and 245 % (higher effective stresses). Overall, the fibre and cement additives increased the stiffness, peak and strength at critical state of pure Toyoura sand but were found to be least effective in extension loading. Moreover, the stress ratio, peak and critical state stress ratios increase with the addition of fibres and cement. The secant modulus shows limited increases for the fibre reinforced specimens. However, a significant improvement in the secant modulus is observed for the fibre reinforced cemented specimens. For both unreinforced and reinforced specimens there is a decrease in volumetric strain with greater effective stresses or in other words, the rate of dilation decreases with increases in effective stresses. The fibre and cement additives also increased the strength parameters (frictional angle, cohesion), dilatancy angle, slope of the critical state line, and decreased the state parameter of pure Toyoura sand.

Methane adsorption on shale under in situ conditions: Gas-in-place estimation considering in situ stress

Gas-in-place (GIP) is one of the essential indices for the resource evaluation of shale gas storage capacity. In this study, based on the simplified local density (SLD) theory, the shale adsorption capacity was investigated considering the effect of burial depth on the shale pore structure. Shale isotherm adsorption experiments under triaxial conditions were performed with a homemade adsorption test device, and CH4 adsorption isotherms under different shale reservoir conditions representative of different burial depths were obtained. By establishing the relationship between the SLD model regression parameters and burial depth, a shale GIP estimation model considering the influence of in situ stress was established. In situ stress controls the pore structure of shale and consequently affects the gas storage capacity of shale. The conventional method does not consider the influence of in situ stress, resulting in overestimation of the free gas content, underestimation of the adsorbed gas content, and overall overestimation of the GIP by 1.12–1.26 times. Taking into account the influence of the stress state, the contribution of the free gas content to GIP is weakened. In contrast, the adsorbed gas content plays a key role in GIP. The distribution of the shale reservoir GIP concentrates at depths of 2500–4500 m. These findings will be helpful in the future evaluation of shale gas reserves and improvement in shale gas content evaluation methods.