Triaxial Loading Research Articles

Investigation of fatigue failure and energy characteristics of rock exposed to complicated stress disturbance paths: Cyclic stress amplitude effect

AbstractTo deeply reveal the differences in geomechanical responses of rock during mining exposed to complicated stress disturbance of excavation unloading and cyclic loading conditions, cyclic triaxial fatigue loads with four cyclic stress amplitude (CSA) (60, 100, 130, and 160 MPa) were performed on deeply buried rock. Results show that rock deformation, energy evolution, and failure modes are all influenced by the CSA. Additionally, it is found that all the strain energy increases with increasing CSA during rock failure. Especially, the dissipated energy increases greatly at the confining stress unloading stage (CSUS) than the fatigue loading stage (FLS), indicating the influence of unloading on rock damage accumulation. Moreover, a damage evolution model reflecting a first slow and then quick increase pattern was established using the dissipated energy. Finally, a transition failure mode from the dominant tensile‐shear to pure shear is found. It is suggested that much more energy needs to be consumed to induce shear cracks than tensile cracks.

Influence of volume compression on the unloading deformation behavior of red sandstone under damage-controlled cyclic triaxial loading

A reasonable evaluation of unloading deformation characteristics is of great significance for the effective analysis of deformation and stability of surrounding rocks after underground excavation. In this study, the damage-controlled cyclic triaxial loading tests were conducted to investigate the pore compaction mechanism and its influences on the unloading deformation behavior of red sandstone, including Young's modulus, Poisson's ratio, volumetric strain, and irreversible strain. The experimental results show that the increases of volumetric and irreversible strains of rocks can be attributed to the compaction mechanism, which almost dominates the entire pre-peak deformation process. The unloading deformation consists of the reversible linear and nonlinear strains, and the irreversible strain under the influence of the porous grain structure. The pre-peak Young's modulus tends to increase and then decrease due to the influence of the unloading irreversible strain. However, it hardly changes with the increasing volumetric strain compaction under the influence of reversible nonlinear strain. Instead, the initial unloading tangent modulus is highly related to the volumetric strain, and clearly reflects the compaction state of red sandstone. Furthermore, both the reversible nonlinear and irreversible unloading deformations are independent of confining pressure. This study is beneficial for the theoretical modeling and prediction of cyclic unloading deformation behavior of red sandstone.

DEM investigation of strength and critical state behaviours of granular materials under true triaxial loadings

This paper investigates the strength and critical state (CS) behaviours of granular materials via DEM simulations of true triaxial drained tests under three different loading modes including constant b (intermediate stress ratio) tests with constant σ1′ (major principal stress), constant p′ (mean pressure) and constant σ3′ (minor principal stress) respectively. To this end, a series of samples are generated with the same particle size distribution, and with the confining stresses ranging from 100 kPa to 900 kPa. The CS is achieved for all samples. Both the macroscopic behaviours and the microscopic behaviours are examined and compared considering different loading modes, confining stresses and intermediate stress ratios (b). The critical state lines (CSLs) are found to be unique and independent of the loading modes, but dependent on the b values. The CSLs with b=0 and b=1 form the two boundaries of CSLs respectively beyond which CSLs under all other b tests cannot go beyond. Six different strength criteria are examined and compared in terms of both peak and CS failures. The Mohr–Coulomb strength criterion is found to be only suitable for axisymmetric loading conditions. The Lade-Duncan criterion is only suitable for describing peak strengths, which is dependent on the loading modes and confining stresses. The Satake criterion and Matsuoka-Nakai criterion are the more appropriate strength criteria for describing CS failures, indicating that the CS values of both the Satake parameter and the Matsuoka-Nakai parameter describe an inherent property that characterizes the CS failure for a given type of soil. The CS mechanical coordination number is fitted by a curved line for a given b value, which is unique regardless of the loading modes. The peak and CS values of both major and minor principal fabric tensors decrease with increasing b values, while they increase with increasing b values for the intermediate principal fabric tensor.

Multiscale identification and NTFA reduction of the elasto-viscoplastic polycrystalline behaviour of uranium dioxide (UO2) for wide range of loading conditions

This numerical study presents a micromechanical modelling of the behaviour of uranium dioxide fuel (UO2), a polycrystalline ceramic used in nuclear power plants, for loading condition typical of a reactivity initiated accident (RIA). Above a specific temperature, UO2 has an elasto-viscoplastic behaviour with strain hardening depending on both temperature and macroscopic strain rate (T,ε¯˙).In a first step, via a full-field approach, an inverse identification of the local single crystal evolution law is performed based on experimental data obtained at the macroscopic scale [4,5]. Beyond the macroscopic behaviour of the fuel pellet, it is sometimes necessary to go down in scale to study local phenomena. A first approach would be to perform a Finite Element Method squared to two (FEM2) resolution [37]. It consists to solve a thermomechanical problem on a first mesh defined at the pellet scale where at each integration point is solved another thermomechanical problem on a Representative Volume Element. The full-field approach guarantees access to the local field at the expense of relatively high computational time. It is not conceivable within industrial codes.In a second step it appeared necessary to replace the second full-field resolution by a model reduction method based on the Nonuniform Transformation Field Analysis (NTFA) approach. This method allows access to macroscopic quantities and local fields while drastically reducing the computational time. The NTFA model [21] with tangent second order (TSO) approximation [24,21] is developed and applied to the problem at hand. Two decompositions of the hardening variable are studied. It is taken as in the reference [21], as uniform per grain or taken as decomposed, like modes associated with the viscoplastic strain tensor. Then, work is done to integrate the specific loading conditions, i.e. temperatures and strain rates of the RIA, into the NTFA model while keeping the number of internal variables as low as possible. Finally, the results from the experimental, full-field and NTFA TSO models are compared. It is checked that the numerical results are not deteriorated either macroscopically or locally at the macroscopic and local scales for uniaxial and triaxial loading.

A nonlinear constitutive model for whole stress–strain behaviors of compressed rocks incorporating crack closure effect

AbstractThis paper is devoted to establishing a nonlinear constitutive model incorporating crack closure effect for capturing the whole process of rock deformation and failure behavior under compression. The model formulated in the framework of irreversible thermodynamics is based on the additive decomposition of the total strain into crack closure strain, elastic, and plastic parts. New specific criteria are proposed for the description of crack closure strain and plastic strain evolution. Notably, analytical solutions of the model under conventional triaxial compression loading conditions are derived. For application, a robust semi‐implicit return mapping (SRM) algorithm with a crack closure strain correction and a plastic strain correction is developed. The analytical solutions, herein, are subtly used to calibrate model parameters and as reference results for assessing the accuracy and robustness of the SRM algorithm. Validation of the model conducted by comparing with experimental data from the literature shows that the model can properly describe the nonlinear mechanical behaviors of rocks, including crack closure effect, strain hardening/softening, peak and residual strength, as well as volumetric compaction/dilation transition. In addition, a nonlocal formulation is introduced as an extension of the model to remedy the mesh dependency problem.

МОЖЛИВОСТІ ПРОЄКТУВАННЯ НЕУКРІПЛЕНИХ ОСНОВ НЕЖОРСТКИХ ДОРОЖНІХ ОДЯГІВ ЗА РЕЗУЛЬТАТАМИ ВИВЧЕННЯ ДЕФОРМАЦІЙНОЇ ПОВЕДІНКИ ДИСПЕРСНИХ СУМІШЕЙ

Introduction. The introduction to the paper highlights the role of the modeling of deformation behavior of unbound granular mixtures (UGMs) under repeated mechanical loading as the base aspect of designing flexible road pavement with an unbound base layers due to the fact that UGMs have been recognized as the most vulnerable materials of the flexible road pavement under action of negative climatic (seasonal) or technogenic factors. Problem statement. The issues of the paper concern the problems related to unstable deformation behavior of UGMs in unbound base/subbase layers during flexible road pavement designing and maintenance. Purpose. The main goal of the paper is to perform an analytical review of the theoretical background to the construction and calculation of an unbound base layer of the flexible road pavement according to the results of the study of UGMs’ deformation behavior with their following categorization. The results of the analytical review are intended to be used during implementation of a national standard concerning the method of testing of unbound granular mixtures by the triaxial cyclic loading identical to the related European standard. Results. The “shakedown concept” was reviewed which allows the categorization and also the appropriate selection of granular mixture during road pavement design and construction. It was established, that the “shakedown concept” sets up three types of permanent behavior of UGMs which, only after being tested via the triaxial cyclic loading method, can be categorized considering the design input data as stable or unstable ones. Also, an analytical comparison of various possible approaches to the UGMs’ categorization within the “shakedown concept” was fulfilled. By the standardized approach, the limits of three categories shall be established at progressively increasing stresses taking into consideration the restrictions on accumulated axial permanent strains. The other approach may be potentially effective for UGM selection and is based on the value of the permanent axial strain rate per one loading cycle. Further, the aspects of an empirical designing of flexible road pavements were reviewed where the parameters of deformation behavior of UGM were adopted, via the Finite Elements Method, to calculate the distribution of stresses and to model rutting in an unbound base layer considering variable thickness of asphalt pavement and variable climatic factors as well.

МЕТОДИ ВИПРОБУВАННЯ З ВИЗНАЧАННЯ ДЕФОРМАЦІЙНИХ ВЛАСТИВОСТЕЙ ДОРОЖНЬО-БУДІВЕЛЬНИХ ДИСПЕРСНИХ СУМІШЕЙ ВІДПОВІДНО ДО ВИМОГ ЄВРОПЕЙСЬКИХ СТАНДАРТІВ

Introduction. In the introduction to the paper, the effect of deformation behavior of unbound granular mixtures (UGMs), when used in an unbound base layer, on the construction of the flexible road pavement was outlined. Problem statement. The issues of the paper concern the problems related to the unstable deformation behavior of UGMs in unbound base/subbase layers during flexible road pavement designing and maintenance. Purpose. The main goal of the paper is to perform an analytical review of methods for testing and modeling of deformation behavior of UGMs. The results of the analytical review are intended to be used during implementation of a national standard concerning the method of testing of unbound granular mixtures by the triaxial cyclic loading identical to the related European standard. Results. The analytical reviewing led to the following results: it was revealed that at each stress level the most stable conditions are ensured to each UGM in its post-compaction period when the rate of accumulated permanent strains becomes negligible and the plot of permanent strain versus the number of loading cycles takes an asymptotic form; it was concluded that the main task of the UGM testing by triaxial cyclic loading shall be resolved as the evaluation of the loads (stresses) that, accepting all the input data, ensure the stable condition of the mixture in an unbound layer of the designed flexible road pavement; the test consists of applying the cyclic stresses corresponding to their expected limits to the cylindrical specimen of UGM and of measuring the axial and radial strains of the specimen induced by these stresses; it was stated that the effective prediction of deformation behavior of UGMs and also their classification to relate the category of deformation behavior of UGM to the expected stress level can be performed through various mathematical models based on “permanent deformation/stress” dependency.

Study on the Mechanical Behavior and Constitutive Model of Layered Sandstone under Triaxial Dynamic Loading

In construction engineering, rock is an important building material. During the construction process, layered rock masses are typically subjected to varying dynamic load disturbances under triaxial loads. It is thus essential to investigate the mechanical response of layered rocks under various disturbances of the triaxial loads. By using a three-dimensional SHPB, triaxial dynamic compression tests with various impact dynamic load disturbances and identical triaxial static loads were carried out on sandstones with differing bedding angles. The impact pressures were 0.8, 1.2, and 1.6 MPa, and the bedding angles were 0°, 30°, 45°, 60°, and 90°. The results showed that the ductility of the sandstone considerably increased under triaxial static loading. With the increasing bedding angle, the sandstone’s dynamic strength and coupling strength first declined and subsequently rose. As the impact pressure increased, the reflective energy ratio, peak strain, and dynamic growth factor of the sandstone essentially rose progressively. The bedding angles and dynamic loads had a major impact on the damage pattern of the layered sandstones. Additionally, a constitutive model considering bedding angle, dynamic load, and static load was established and verified. The constitutive model was able to accurately characterize the dynamic behavior of the rock under load disturbances.

Constitutive model for simulating the mechanical behaviour of rock under triaxial cyclic loading

To simulate the cyclic behaviour of rock comprehensively, relevant mechanical features were analysed sufficiently, including the massing effect, ratcheting effect, Kaiser effect and Felicity effect. A constitutive body was proposed based on the deformation mechanism and implemented by strain increment method. This body comprised three elements (elastic element Ee, plastic element Ep and friction element Ef), in which Ee and Ep were connected in series, and Ef was connected with them in parallel. Two kinds of triaxial cyclic loading experiments were conducted to determine the constitutive laws of these elements and the Poisson’s ratios of Ee and Ep; moreover, the simulation effect was validated against the experimental data. Results showed that the tangential modulus of Ee was nonlinear due to damage development and variation of particle dense state, the backwards movement of the yield surface involving Ep during reloading induced the ratcheting effect and Felicity effect, and the opposite role of Ef during loading and unloading caused the massing effect. The constitutive laws of Ee and Ep could be expressed by quadratic polynomial function and logistic equation, respectively; the Poisson’s ratio variations in Ee and Ep with axial plastic strain could be expressed by linear function and exponential function, respectively.

Zonal disintegration phenomenon based on triaxial dynamic load test of hollow cylindrical sandstone specimens

Zonal disintegration phenomenon based on triaxial dynamic load test of hollow cylindrical sandstone specimens

Mechanical properties and dynamic multifractal characteristics of shale under anisotropic stress using AE technology

The mechanical properties and failure mechanism of shale under anisotropic stress is the key to evaluate the stability of wellbore. Meanwhile, the fracture instability process of shale needs to be characterized by the reasonable monitoring technology. This paper performs a series of uniaxial, biaxial and true triaxial loading tests on shale specimens. A monitoring technology, Acoustic emission (AE), is adopted to record the fracture process of shale. The effects of anisotropic stress on the mechanical behaviors of shale are analyzed. The evolution characteristics of AE event rate are applied to describe the fracture process of shale. The transition from AE quite period to AE active period effectively characterizes the macro-cracking process within shale specimens. The multifractal theory is adopted to analyze the dynamic multifractal characteristics and to quantitatively characterize the fracture instability process of shale. The distribution difference of multifractal parameters can be served as an early warning information for the stable and unstable macro-cracking within shale. The anisotropic stress evidently affects the failure mechanism of shale. The results of this study will be important to ensure the production efficiency of shale gas and the stability of drilling operation.

Excess pore water pressure generation in fine granular materials under undrained cyclic triaxial loading

Understanding the mechanism of excess pore water pressure generation in subgrades is essential for not only designing but also further maintenance purposes. The primary goal of this research was to investigate excess pore water pressure generation in fine granular materials under cyclic loading. A series of undrained cyclic triaxial tests were performed to study the excess pore water pressure generation in two selected fine granular materials: (1) railway sand and (2) tailings. The excess pore water pressure response of these materials was evaluated in terms of density conditions, number of cycles, and applied cyclic stress ratios (CSR). As a result, excess pore water pressure accumulated over time due to cyclic loading. However, its accumulation was significantly dependent on the governing factors, i.e., densities, CSR values, and material types. The excess pore water pressure exhibited a slight increase at low CSR values, but a sharp increase was observed at higher CSR values, which ultimately led to a failure state after a certain number of cycles. In addition, under the same loading conditions, the samples that had higher relative compaction showed better resistance to cyclic loads as compared to those with lower relative compaction. Finally, a relationship between excess pore water pressure and cyclic axial strain of the fine granular materials was discovered.

Effect of Confining Pressure on Impact Reaction Threshold of Aluminum/Polytetrafluoroethylene Reactive Material

An impact reaction experiment is conducted with a modified split Hopkinson pressure bar (SHPB) apparatus to study the reaction threshold of aluminum/polytetrafluoroethylene (Al/PTFE) reactive materials under confining pressure. The dynamic compression behavior, impact damage characteristics, and impact reaction threshold of the Al/PTFE reactive material under the confining pressure are investigated. The results have presented that confining pressure makes the specimens suffer triaxial loading and improves the dynamic compressive strength of Al/PTFE reactive materials from 36.8 MPa (impact velocity is 14.64 m s−1) to 62.7 MPa (14.80 m s−1). Besides, the fractal dimension of the posttest specimen is decreased by confining pressure, which has proved that the confining pressure hinders damage under impact loading. Moreover, the impact reaction experiment demonstrates that the confining pressure increases the threshold of Al/PTFE, and the minimum specific incident energy for the reaction of the T10 (molding pressure is 10 MPa) specimen increases from to . This research not only reveals that Al/PTFE can be reacted by impact loading at confining pressure but also clarifies that confining pressure limits the impact damage of the Al/PTFE reactive material and increases the reaction threshold.

Mechanical behavior of coal under true triaxial loading test connecting the effect of excavation- and mining-induced disturbances

In order to understand the mechanical behavior of a stope and analyse the stress conditions of surrounding rocks after ventilation shaft excavation and the abutment stresses of the top coal mining layout. In situ uniaxial stress monitoring tests were performed to understand the field abutment pressure evolution. Furthermore, the variation of the stress concentration factor was studied using the Tongxin Mine 8309 mining face of the TongMei Group, China, as a case study. A loading model of coal rock under excavation- and mining-induced disturbances was proposed, and the stress path and experimental method were designed to investigate the high excavation-damaged zone (HDZ), excavation-damaged zone (EDZ), and undisturbed zone (UZ). Moreover, the mechanical characteristics and failure characteristics of coal rock in different zones under site disturbance were obtained and the mesoscopic analysis is carried out by acoustic emission test. The results indicated that the strengths of the UZ, EDZ, and HDZ samples declined gradually. The volume of the UZ sample continuously expanded. However, the volumes of the EDZ and HDZ samples were compressed first and then expanded. Furthermore, the shear bands presented in all three samples resulted in failure. The cubic triaxial tests performed without considering mining-induced pressure produced higher strengths and less damage compared with the results of the true triaxial tests. The stress path used in the laboratory with the mining-induced stress throughout the stope could optimally reproduce the in situ mining process, which is significantly safe and efficient for the mining of deep resources.

Experimental Study on Mechanical and Damage Evolution Characteristics of Coal during True Triaxial Cyclic Loading and Unloading

Research on the mechanical properties and damage evolution of coal during true triaxial cyclic loading and unloading is of great significance for maintaining the long-term safety and stability of underground engineering structures in coal mines. In this paper, firstly, the deformation, strength and fracturing characteristics of coal during true triaxial loading and true triaxial cyclic loading and unloading were analyzed. Then, the residual strain characteristics, energy distribution and evolution of coal were systematically studied. Additionally, the damage evolution laws of coal during cyclic loading and unloading were quantitatively analyzed from the perspectives of residual strain and energy dissipation, respectively. The damage evolution law based on residual strain showed that when the intermediate principal stress was high, the damage to coal was directional. With the increase in cyclic load, the coal damage variables in the directions of σ1 and σ3 increased exponentially, while that in the direction of σ2 increased quadratically. The damage evolution law based on energy dissipation showed that the coal damage variable increased exponentially with the increase in cyclic load. With the increase in σ2, the increasing speed of coal damage variable decreased first and then increased. The damage variables established based on residual strain and energy dissipation can both reveal the damage deterioration mechanism of coal during true triaxial cyclic loading and unloading, which is of great theoretical and engineering significance for scientifically evaluating the stability of underground coal and rock engineering and preventing the occurrence of major geological disasters.

Radial Depth Damage Properties of Coal Tunnels Surrounded by Rock under Excavation and Unloading

In order to study the mechanism of radial gradient damage of surrounding rock caused by deep elevated stress coal roadway excavation, a triaxial loading unloading uniaxial reloading coal sample damage test was carried out. Based on the defined damage factor and fractal theory, the wave velocity damage characteristics, fracture characteristics, three-dimensional fractal characteristics and uniaxial reloading strength characteristics of coal samples under different loading unloading paths were studied. The results show that the shift of wave velocity can better reflect the damage of coal samples. Under the same confining pressure, the damage amount of coal samples increases with the axial compression ratio index, and the confining pressure can inhibit the damage of coal samples to a certain extent; the fracture characteristics of coal samples are closely related to the loading history. The surface cracks of coal samples tend to become complex with the increase of axial compression ratio, but eventually develop to the shear plane fracture surface; the surface cracks of damaged coal samples under the radial stress gradient of surrounding rock have excellent fractal characteristics. The fractal dimension has a linear function relationship with axial compression loading ratio and wave velocity damage; from the angle of wave velocity damage and strength loss, it is expounded that the increase of confining pressure can inhibit low damage to a certain extent, but can promote the occurrence of extreme damage.

Three-invariant model and bifurcation analysis of deformation bands for a sandstone subjected to true triaxial loading paths

Three-invariant model and bifurcation analysis of deformation bands for a sandstone subjected to true triaxial loading paths

Deformation responses and strength criteria of different shotcrete-rock composites under triaxial cyclic compression

Understanding the mechanical performance of shotcrete-rock composites under cyclic loading is important for deep-buried underground projects. In this study, triaxial cyclic compressive tests were conducted on the shotcrete-rock composites (SC-G with granite and SC-S with sandstone) to investigate their cyclic failure mechanisms. The results showed that the confining pressure and rock type both had significant effects on the failure modes of the composite materials. Under triaxial cyclic loading, the failure process of the composites can be divided into five stages. Both the axial and lateral deformations of SC-S were larger than that of SC-G, but the elastic modulus of SC-S was smaller than that of SC-G. Besides, the volumetric deformations of the composites included both contraction and dilation stages, and the plasticity parameter was introduced to establish the dilatancy angle models for shotcrete-rock composites. In addition, considering the damage accumulation during triaxial cyclic loading, a yield surface model was proposed based on the M−C failure criterion to characterize the correlation of post-peak stress state, plasticity parameter, and strength parameters of the composite. The research findings can provide a great theoretical significance and engineering value for the safe design and construction of deep-buried tunnels.

Characterization and evaluation of brittleness of deep bedded sandstone from the perspective of the whole life-cycle evolution process

The quantitative determination and evaluation of rock brittleness are crucial for the estimation of excavation efficiency and the improvement of hydraulic fracturing efficiency. Therefore, a “three-stage” triaxial loading and unloading stress path is designed and proposed. Subsequently, six brittleness indexes are selected. In addition, the evolution characteristics of the six brittleness indexes selected are characterized based on the bedding effect and the effect of confining pressure. Then, the entropy weight method (EWM) is introduced to assign weight to the six brittleness indexes, and the comprehensive brittleness index Bc is defined and evaluated. Next, the new brittleness classification standard is determined, and the brittleness differences between the two stress paths are quantified. Finally, compared with the previous evaluation methods, the rationality of the proposed comprehensive brittleness index Bc is also verified. These results indicate that the proposed brittleness index Bc can reflect the brittle characteristics of deep bedded sandstone from the perspective of the whole life-cycle evolution process. Accordingly, the method proposed seems to offer reliable evaluations of the brittleness of deep bedded sandstone in deep engineering practices, although further validation is necessary.

Acoustic emission characteristics and energy evolution of salt rock for deep-salt-cavern engineering under triaxial loading and unloading

Acoustic emission characteristics and energy evolution of salt rock for deep-salt-cavern engineering under triaxial loading and unloading