Triaxial Loading Research Articles

Experiment and DEM simulation study on mechanical behaviors of shale under triaxial cyclic loading and unloading conditions

During shale gas exploration, natural fractures in shale reservoirs may be induced by cyclic loads frequently encountered in different geological processes, including tectonic movements, seismic actions, and artificial construction interference (vertical and horizontal wells drilling and cyclic hydraulic fracturing). In this paper, experiments and PFC2D simulations are conducted to investigate the mechanical response and mechanism of shale specimens under cyclic loading and unloading. Using the experimental and simulation results, the strength and deformation characteristics and strain energy and damage evolutions during the cyclic loading-unloading process are quantified and analyzed. The damage variable characterized by plastic deformation, deformation modulus, and dissipated energy is thoroughly analyzed. Based on the PFC2D simulation, the micro-crack distribution and evolution are further studied, and the results can reflect the experiments well and reveal the damage mechanism under cyclic loading. Furthermore, the experiments and simulations indicate that the degree of fatigue damage is closely related to the number of cycles the specimens undergo, and a small number of cycles may not have a distinct effect on the strength.

A characterization method for equivalent elastic modulus of rock based on elastic strain energy

Energy is an internal variable during rock deformation and failure, and its dissipation and conversion law can reflect the rock’s internal damage and deterioration state. Analysis of rock deformation and failure process from the perspective of energy is helpful to deeply understand the mechanism of rock damage, fracture and instability failure, and has important theoretical and practical significance for the stability evaluation and support control of surrounding rock. In this study, through single cyclic loading and unloading (SCLU) experiments, cyclic triaxial loading and unloading (CTLU) experiments and conventional triaxial compression (CTC) experiments, the equivalent elastic modulus method based on elastic strain energy is proposed to analyze the energy conversion of rock. The results show that the error of the elastic strain energy calculated by the strain energy formula method is generally higher than 10% with the secant and tangent modulus of the loading and unloading curve as input parameters. Taking the equivalent elastic modulus proposed in this study as an input parameter, more accurate elastic strain energy can be obtained by the strain energy formula. During the rock failure process, the equivalent elastic modulus shows a three-stage characteristic of increase, steady and decrease. The equivalent elastic modulus can be estimated by the quadratic function between the equivalent elastic modulus and confining pressure and axial strain. Under the same deformation and deviatoric stress, the elastic strain energy stored in rock increases with increasing confining pressure. The local maximum energy dissipation rate corresponds to stress drop, and the peak energy dissipation rate appears near the peak strength. High energy dissipation mainly occurs in a short time after peak strength, and energy release and dissipation are more sudden and severe under high confining pressure.

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.

Liquefaction characteristics in triaxial tests under various gravity environments – DEM analyses

Liquefaction of sands occurs when the effective stress becomes zero during undrained loading, and the state of liquefaction is often considered that individual particles do not transmit contact forces. In shaking table model tests, seepage flows towards the surface occur during liquefaction; this potentially maintains individual particles floated as the gravitational forces can be cancelled out by the upward seepage forces. In laboratory element tests, however, undrained conditions induce no seepage flows during liquefaction. This raises a key question of how the individual particles behave during liquefaction in element tests, and how the macroscopic mechanical response is affected due to gravity. To answer these questions, this contribution conducts a series of triaxial loading simulations using the discrete element method (DEM) considering the effect of gravity on the mechanical response of spherical particle assemblies. The results reveal that the presence of gravity affects both packing properties and liquefaction characteristics. Inter-particle contacts are maintained during liquefaction under non-zero gravity conditions. Although the liquefaction resistance is merely affected due to gravity, the stress–strain relation and stress path are measurably altered. This contribution highlights the importance of considering the potential effect of gravity when laboratory or DEM results on liquefaction phenomena are interpreted.

Experimental Study on Silt Soil Improved by Microbial Solidification with the Use of Lignin.

At present, in the field of geotechnical engineering and agricultural production, with increasingly serious pollution an environmentally friendly and efficient means is urgently needed to improve the soil mass. This paper mainly studied the microbial induced calcium carbonate precipitation (MICP) technology and the combined effect of MICP technology and lignin on the improvement of silt in the Beijing area. Through unconfined compressive strength and dynamic triaxial test methods, samples improved by microorganisms were studied to obtain the optimal values of cement concentration and lignin under these two test schemes. The results show that after the incubation time of Sporosarcina pasteurii reached 24 h, the OD600 value was 1.7-2.0 and the activity value (U) was 930-1000 mM ms/min. In the unconfined static pressure strength test, after MICP treatment the optimal concentration of cementitious solution for constant temperature and humidity samples and constant-temperature immersion samples was 1.25 mol/L. The compressive strength of the constant temperature and humidity sample was 1.73 MPa, and the compressive strength of the constant-temperature immersion sample was 3.62 Mpa. At the concentration of 1.25 mol/L of cement solution, MICP technology combined with lignin could improve the constant temperature and humidity silt sample. The optimal addition ratio of lignin was 4%, and its compressive strength was 1.9 MPa. The optimal lignin addition ratio of the sample soaked at a constant temperature was 3%, and the compressive strength was 4.84 MPa. In the dynamic triaxial multi-stage cyclic load test, the optimal concentration of cementation solution for the constant temperature and humidity sample after MICP treatment was 1.0 mol/L, and the failure was mainly inclined cracks. However, in the condition of joint improvement of MICP and lignin, the sample mainly had a drum-shaped deformation, the optimal lignin addition ratio was 4%, and the maximum axial load that the sample could bear was 306.08 N. When the axial dynamic load reached 300 N, the strain accumulation of the 4% group was only 2.3 mm. In this paper, lignin, an ecofriendly material, was introduced on the basis of MICP technology. According to the failure shape and relevant results of the sample, the addition of lignin was beneficial for the improvement of the compressive strength of the sample.

A Study of Constitutive Model of Rock Damage under the Joint Effect of Load and Moisture

To study the mechanical damage characteristics of rock under the effect of subversion, a series of mechanical experiments, including both uniaxial and triaxial mechanical compression experiments under various levels of water content were performed. In this study, researchers investigate the impact of water content on the mechanical characteristics of rock, based on the compliance of the rock damage variants to the Weibull statistic distribution, and Drucker–Prager strength rule, aiming to construct a constitutive model under the joint effect of load and moisture. In addition, the established constitutive model is tested in the experiment. According to the test results, during the initial phase of the submersion, the water content in the rock increases following the exponential function until reaching the threshold. The water content remains stable after the threshold. Under the uniaxial and triaxial loads, the damage detected in the rock and the elasticity modulus decreases linearly as the water content increases. The rock’s mechanical parameters and the damage evolution rate are significantly impacted by the surrounding pressure. As the surrounding pressure increases, the weakening effect of the water in the rock decreases. The theoretic curves developed to describe the rock damage under the joint effect of the water and load are consistent with the curves drafted based on the test, indicating that the constitutive model can accurately describe the stress and strain behaviors of rock under various water contents and loading conditions.

Continuous Evaluation of Shear Wave Velocity from Bender Elements during Monotonic Triaxial Loading.

Few researchers have attempted to experimentally evaluate the low-strain shear wave velocity (Vs) of specimens undergoing large strain deformations. They report that the Vs is practically unaffected by the strains, and the reasons behind this behavior are not fully understood. This study presents the continuous measurement of low-strain Vs with bender elements (BE) during monotonic shearing of two sand specimens in a triaxial device. The results are analyzed using a micro-mechanical model based on contact theory. The results of this study confirm that the Vs values from BE measurements are unaffected by an increase in axial strains that are induced by a separate mechanism. The micro-mechanical model predictions of Vs agree well with the results of this study and with the results of previous studies. They show that the mean effective stress and increase in inter-particle stiffness controls the low-strain stiffness despite a global increase in strains during monotonic loading.

Strain Evolution and Fatigue Damage Characteristics Analysis of Sandstones During Multi-Level Triaxial Cyclic Loading and Unloading Under Varying Stress Limits

Strain Evolution and Fatigue Damage Characteristics Analysis of Sandstones During Multi-Level Triaxial Cyclic Loading and Unloading Under Varying Stress Limits

Deformation and Seepage Characteristics of Coal Under True Triaxial Loading–Unloading

Deformation and Seepage Characteristics of Coal Under True Triaxial Loading–Unloading

Displacement response characteristics of different sand tunnel excavation faces under true triaxial loading

During the construction of subway tunnels, the geotechnical body is affected by excavation to produce three-dimensional spatial deformation. The deformation of geotechnical bodies is an important safety hazard for project advancement, so it is important to understand the excavation disturbance range and deformation mechanism. The current related research is mainly about the theory of land subsidence and the two-dimensional plane displacement of the stratum, and there are few studies on the specific three-dimensional disturbance mode and its mechanism. In order to better understand the three-dimensional displacement characteristics of the tunnel excavation soil, a tunnel excavation model test was established based on a true triaxial stress loading system combined with three-dimensional scanning technology for a superimposed sandy soil. Based on the established model, the vector displacement response range and three-dimensional deformation characteristics of the excavation face were studied in the main displacement affected area around the excavation face. Meanwhile, the deformation characteristics, such as vertical settlement and horizontal displacement of the stratum in the main influence area were analyzed. The results show that the main influence area of tunnel excavation is elliptical and distributed within a range of twice the diameter of the tunnel axis. The main influence range is bell-shaped in the vertical direction and inverted wedge-shaped in the horizontal direction. The three-dimensional space presents a “W” deformation distribution. The three-dimensional deformation theoretical model of the excavation face established in this paper can provide some references for the excavation engineering of superimposed sand-soil tunnels.

Experimental and analytical investigations on strength and deformation behaviour of red sandstone under conventional triaxial compression

In this article, a series of conventional triaxial compression tests were carried out to investigate strength characteristics and deformation behaviour of red sandstone. According to experimental results, the initial yield stress, volume dilatation stress and peak strength of the red sandstone all increase with confining pressure. Moreover, with the increase in confining pressure, the failure modes of the specimens are changed from splitting failure to compressive-shear failure. The non-linear Hoek–Brown criterion is found suitable for fitting the strength data. An elastoplastic damage model with a unified plastic hardening/softening law is developed on the basis of the experiments. As an original contribution, analytical solutions to the constitutive equations are derived for the conventional triaxial loading path under consideration. The model is validated by comparing the analytical predictions with the experimental data.

Extending modified Cam-Clay to unsaturated soils by incorporating a scaled stress variable

This paper extends the modified Cam-Clay model to describe the behaviour of unsaturated soils by replacing the effective stress with the scaled stress. The scaled stress accounts for the mechanical effect of capillarity by factoring Bishop’s stress with a power function of degree of saturation. The extendedmodified Cam-Clay model postulates the existence of a yield curve in the mean scaled stress 𝑝̅– deviatoric scaled stress 𝑞̅ plane. Coherently with the modified Cam-Clay model, the stress-strain behaviour is predicted by means of an elastic law inside the yield curve. As the scaled stress state evolves onto the yield curve, the behaviour becomes elasto-plastic and this is modelled by a plastic flow rule combined with a volumetric hardening law. The extended modified Cam-Clay model is then validated against experimental data published in the literature. Results show that the proposed approach is capable of well predicting the mechanical behaviour of unsaturated soils during triaxial loading. Future work will be directed at further validating the present formulation along different stress paths as well as accounting for the combined effect of partial saturation and cementation within a critical state framework based on bounding surface plasticity.

Geotechnical justification of the stadium construction on water-saturated soils under seismic loading

One of the main issues in the design of bases and foundations on water-saturated soils in conditions of possible seismic impacts is the geotechnical substantiation of the possibil-ity of construction. Among the main influencing factors, one can single out the assessment of the ability of water-saturated sandy soil to resist vibration liquefaction. The paper presents the re-sults of studying the behavior of sandy soil samples under conditions of triaxial cyclic loading, which is equivalent in strength to seismic action. The urgency of the problem lies in the study of the process of vibration liquefaction with an assessment of the deformability of water-saturated soils under dynamic influences. The tests were carried out in a pneumatic stabilometer. A special technique has been developed that provides for the imposition of dynamic stresses on the static stress state of the samples. The criteria for vibration liquefaction have been determined. A ge-otechnical substantiation of the possibility of building a stadium on water-saturated sandy soils under conditions of seismic loading has been carried out. The parameters of the earthquake, in which the soils will show liquefaction, have been established.

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.

Study on the Constitutive Model and the Identification of Parameters of Granite Based on the Crack Closure Ratio

A large number of cracks exist inside brittle rocks, and the evolution and expansion of cracks inside rocks have adverse effects on the deformation and strength of rocks, leading to the reduction of mechanical properties of rocks and endangering the stability and safety of rock engineering. Taking the granite samples taken from underground plant of Yebatan hydropower station as the research object, conventional triaxial compression tests were carried out. The characteristics of crack evolution and expansion in granite is investigated, and the parameters of granite are analysed and identified for different mechanical states by using stress-crack strain evolution constitutive model. The stress-crack strain evolution constitutive model was embedded into FLAC3D for triaxial loading tests through secondary development. The results show that the stress-crack strain evolution constitutive model is reasonable and accurate enough to be applied in numerical simulation of underground power-house of Yebatan hydropower station.

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.

Parameter determination of the method of directional unloading of the reservoir based on physical modelling on a true triaxial loading setup

The article presents a theoretical and experimental substantiation of the method of directional unloading of the reservoir in fields with low-permeability reservoirs. The relevance of the article is due to the reduction of hydrocarbon resources in modern conditions and the need to create new efficient environmentally friendly technologies to develop hydrocarbon deposits with hard-to-recover reserves, primarily with low-permeability reservoirs. The results of a theoretical study of the stress-strain state in the vicinity of a well, both cased and open, are presented. They are necessary to develop programs for laboratory testing of core specimens from the studied fields. A technique for physical modelling of deformation processes in the bottomhole zone with a decrease in pressure at the well bottom in a true triaxial loading unit is described in order to determine the parameters of the process impact on the formation reservoir, leading to an increase in well productivity. The method was applied to the conditions of the low-permeability reservoir at the Verkhneviluchanskoye oil and gas condensate field in the southwest of the Republic of Sakha (Yakutia). Expe-rimental studies were carried out on a unique scientific unit for true triaxial loading, created at the IPMech RAS, the Triaxial Independent Loading Test System. The directional unloading method was adapted for the studied field, the process parameters of successful application of the method were determined: the bottomhole design, the drawdown values necessary to increase the permeability of the bottomhole formation zone.

Analysis of changes in the internal structure of low-permeability reservoir rocks by means of computed tomography after implementation of the directional unloading method

The article presents the results of comprehensive studies of changes in the internal structure and evolution of filtration properties of low-permeability rocks of the Astrakhan gas-condensate field when implementing the method of increasing well productivity – the directional unloading method. Physical modeling of the deformation and filtration processes on the unique Triaxial Independent Load Test System of the Institute for Problems in Mechanics of the Russian Academy of Sciences was carried out. A 3D scan of rocks after testing was performed using a ProCon CT-MINI high-resolution X-ray tomograph in order to analyze changes in the internal structure. A digital model of the rock was obtained, and numerical simulation of filtration flow in GeoDict software based on the results of microtomography scanning was performed. Velocity fields and permeability values for different computational models and computation optimization methods are calculated. The results obtained in different filtration models are compared with the laboratory measured value of permeability. The main differences in approaches to numerical estimation of rock permeability are described, and conclusions about the applicability of the modeling techniques used are made. The research results allow us to conclude that the directional unloading method can be successfully applied to the conditions of the Astrakhan gas-condensate field, allowing to significantly improve filtration properties of rocks in the vicinity of the well.

Energy Action Mechanism of Reinforced Sandstone under Triaxial Cyclic Loading and Unloading

In underground engineering, reinforcement is a necessary means to ensure the stability of surrounding rock. Due to the stress redistribution caused by excavation disturbances, the reinforced rock mass is frequently subjected to loading and unloading, and its mechanical properties change accordingly. Based on the above engineering practice, using pasted circular CFRP, an approximate simulation of the rock reinforcement effect of bolt and shotcrete support was performed. Triaxial cyclic loading and unloading tests of reinforced sandstone were carried out, and the influence of different reinforcement schemes on the mechanical properties was compared and analyzed. Furthermore, the strengthening mechanism, damage evolution, and energy transformation mechanism of CFRP are discussed. The results showed that the peak strength increased about 14.2% and 23.8% with the two reinforced schemes, and the residual strength increased about 27.3% and 52.8% with the increase in the area reinforced by CFRP. Under the same confining pressure and strain conditions, the characteristic energy density and elastic energy ratio increased with an increase in the reinforcement area, but the damage variable decreased. It is proved that CFRP can improve energy absorption efficiency, enhance the energy storage limit, and reduce dissipation efficiency. By inhibiting the propagation of internal fissures and limiting the energy dissipation during fractures, the rock mass can be restrained and strengthened.

Triaxial mechanical behaviour and energy conversion characteristics of deep coal bodies under confining pressure

To understand more about damage, failure, and transformation of coal, this paper performed triaxial loading tests on coal samples obtained from a deep coal mine in China. Results showed that the brittle failure characteristics of the specimens were obvious under single-axis loading, and that the ductile failure characteristics of the specimens increased as confining pressure increased. The ultimate strength and residual strength of the samples exhibited a sound linear growth relationship with confining pressure. And according to the change trend of damage variable with axial strain, the damage process of coal body is divided into four stages: initial damage stage, stable damage stage, rapid damage stage and damage failure stage. The energy conversion characteristics of the samples were thoroughly analysed and it was found that with the increase of confining pressure, the proportion of elastic energy of coal samples increases, while the proportion of dissipated energy decreases, indicating that confining pressure can inhibit the expansion of fractures and strengthen the energy storage capacity of coal samples. It was also discovered that the greater the confining pressure, the greater the ultimate elastic energy of the samples. This study is of great significance for mastering high energy level disasters in deep mines.