Triaxial Compression Creep Tests Research Articles

An improved Burgers creep model of coal based on fractional-order

The instability and destruction of various types of coal pillars left in deep underground mining are frequently attributed to cumulative creep deformation exceeding the permissible limit, with high in situ stress playing a critical role in this phenomenon. To understand the complicated creep behavior of coal, triaxial compression creep tests were conducted. It has been proven that the coal specimens subjected to high confining pressure exhibit typical three-stage creep characteristics. Furthermore, with the increase in confining pressure, the creep threshold value increases while the creep threshold coefficient decreases. By fitting the creep strain-time results, an improved Burgers creep model based on fractional-order was proposed. This model can describe the primary, secondary, and tertiary stages and reflect the nonlinear behavior, contributing to the understanding of the long-term stability evaluation of deep coal pillars.

The Deformation Law of a Soft-Rock Cavern by Step Excavation in a Pumped Storage Power Station

The surrounding rock stability of large underground caverns in a pumped storage power station is one of the most crucial problems in hydropower project design and construction. In the construction of hydropower projects in Southwest China, many underground soft-rock caverns in are excavated. Influenced by the high sidewall, high ground stress, large burial depth, and hydrodynamic pressure action, the deformation of the cavern is special, especially in terms of its soft-rock distribution. At present, most research of underground engineering on soft-rock stability focuses on small-scale tunnel excavations in homogeneous geological conditions, with limited studies on the large-scale excavation of deeply buried underground powerhouses in complex geological structures, featuring extensive soft-rock-layer exposure on the cavern wall. Therefore, it is particularly important to investigate the excavation method of and support measures for soft-rock caverns under complex geological conditions. Based on laboratory rock mechanics testing (petrographic analysis, uniaxial compressive strength tests, shear tests, and triaxial compression creep tests) and the distribution characteristics of the surrounding soft-rock layer of the proposed underground powerhouse, obtained from the survey, we discuss the excavation and support measurements. These include the influence of support measures on the deformation of the underground excavated cavern considering the inclination of rock layers, the impact of the excavation under supported conditions on the deformation of the underground cavern, and the correlation between the lining thickness and stress variation within the lining.

Investigating time-dependent behavior of rocks using kinematic-constraint-inspired non-ordinary state-based peridynamics

In this paper, the kinematic-constraint-inspired non-ordinary state-based peridynamic formulation (KC-NOSBPD) is proposed to investigate the time-dependent behaviors of rocks, which play a critical role in evaluating the long-term stability of the surrounding rocks around underground opening quantitatively. The peridynamic differential operator (PDDO) is introduced to KC-NOSBPD to improve the precision of bond-associated deformation gradient and to suppress the skin effect. On this basis, a unified creep-damage-rupture KC-NOSBPD model is proposed, in which the Burgers-creep viscoplastic constitutive law, a visco-elastoplastic constitutive model, is used to describe the rheological deformation of rocks. A unified damage-rupture framework based on a strain-based isotropic scalar damage variable is established to simulate the creep damage and subsequent creep rupture. The fidelity of this proposed model without damage is verified by comparing it with the benchmark solution for the creep response of a 2D rock specimen subjected to various load histories. Further, the proposed model is employed to simulate uniaxial and triaxial compression creep tests. These present numerical results agree well with the experimental observation, implying that the proposed model successfully captures the accelerating creep behavior of rocks. Moreover, the proposed model performs the time-dependent deformation and failure analysis for the surrounding rocks around the tunnel.

Experimental Study on Creep Characteristics and Long–Term Strength of Anthracite

Coal pillars from old mines undergo creep, a type of time−dependent deformation. Research on underground engineering stability of coal mines has increasingly focused on long−term strength as an important mechanical index of the creep characteristics of coal pillars. This study performed conventional triaxial compression and triaxial creep tests of anthracite under different confining pressures. The creep law of anthracite and the long−term strength of anthracite was studied according to the test results. The test results demonstrated the following: (1) The conventional elastic modulus and peak strain of anthracite increased exponentially with the confining pressure. (2) Under low stress levels, anthracite exhibited only instantaneous deformation and attenuation creep. In contrast, anthracite exhibited instantaneous deformation, attenuation creep, and steady creep under high stress levels; accelerated creep occurred until failure when the stress reached a particular value. (3) By fitting the steady−state creep rate of anthracite under high stress levels, the functional relationship between axial stress and steady−state creep rate was established, and the threshold of the steady−state creep rate in high−stress−level areas was suggested as the optimum long−term strength of anthracite. (4) The ratio of the long−term strength to instantaneous strength under various confining pressure grades ranged from 70% to 91%.

Fluid-Structure Coupling Creep Characteristics of Red-Bed Soft Rock in South China

In order to study the creep characteristics and mechanism of red-bed soft rock under the water–rock interaction, fluid–structure coupling triaxial compression tests and creep tests under stepwise loading were carried out. Furthermore, the influences of seepage pressure and stress on creep deformation, long-term strength, Poisson’s ratio, and seepage velocity were analyzed. According to the experimental results, the influence of seepage on the creep of soft rock cannot be ignored. The results show that the seepage leads to a decrease in triaxial strength and long-term strength, and an increase in instantaneous deformation and creep deformation. The failure mode of triaxial compression changes from shear failure to tension-shear conjugate failure, whereas the long-term strength of fluid–structure coupling creep is 60%~70% of the triaxial strength. When the stress level and seepage pressure are relatively small, the Poisson’s ratio of creep increases with the increase of seepage pressure, and the radial creep deformation response lags behind the axial creep deformation. However, at a high stress level and osmotic pressure, the Poisson’s ratio and seepage velocity increase rapidly, and the duration of the accelerated creep is obviously shortened. Through the analysis of the influence of seepage pressure on the seepage velocity, with the increase in the seepage velocity, the seepage velocity changes and fluctuations are more obvious, which further confirms the damaging effect of seepage pressure and erosion on the internal structure. In the field monitoring of actual engineering, the rapid change of seepage velocity can be used as a precursor signal to predict the instability. Therefore, the water–rock interaction cannot be ignored in the analysis of mechanical properties and long-term stability of red-bed soft rocks.

Stress–Strain–Time Description and Analysis of Frozen–Thawed Silty Clay under Low Stress Level

The construction of high-speed railways in cold regions needs to consider the effects of freeze–thaw cycles (FTHs) on the long-term deformation of subgrades. However, at present, research on the creep characteristics of frozen–thawed rocks and soils is not extensive. In the limited studies on frozen–thawed soil creep properties, current research focuses more on high stress–strain–time responses, but for the subgrades, the inner stress is usually low. This paper presents the results of triaxial compression creep tests on remolded, frozen–thawed silty clay sampled in the Yichun-Tieli area and describes its stress–strain–time relationship in an arctan function-based mathematical model. Each creep test condition is studied using three specimens. Frozen–thawed silty clay exhibits attenuation creep under low-level stress. In general, from 4 FTHs to 11 FTHs, the mean elasticity modulus decreases first, and then, increases. The exerted stress is higher than the yield stress; the more FTHs the specimens experience, the more time they need to be deformed stably under the same axial deviatoric stress (ADS). Under the same mean ADS, the mean stable strain of 7 FTHs exceeds the other two FTH conditions and, in general, the mean stable strain of 4 FTHs exceeds 11 FTHs. By dissecting the phenomena, it can be concluded that with FTHs increasing, moisture and voids reconstitute in the process; the elastic strain accounts for most of the total strain and significantly decides the extent of creep deformation; the arctan function-based model is basically able to describe, but not perfectly predict, the stress–strain–time relationship of frozen–thawed silty clay.

Time-Dependent Deformation and Long-Term Strength of Carbonaceous Mudstone under Dry and Wet Cycles

Clarifying the time-dependent strength deterioration characteristics of carbonaceous mudstone under dry and wet cycles is of great significance to the design of expressway cut slopes. In this work, we conducted triaxial compression creep tests on carbonaceous mudstone specimens that had undergone different numbers of dry and wet cycles to investigate their creep properties. A function was established between the steady-state viscoplastic creep rate and axial compression. The threshold stress of the steady-state viscoplastic creep rate was assumed as the long-term strength, and the long-term strength deterioration law of carbonaceous mudstone under dry and wet cycles was studied. The results showed that the transient strain, viscoelastic creep, and viscoplastic creep of carbonaceous mudstone increased with the number of dry and wet cycles, and the creep failure stress and transient elasticity modulus decreased. Based on the steady-state viscoplastic creep rate method, the long-term strength of carbonaceous mudstone after n (n = 0, 3, 6, 9) dry and wet cycles was found to be 74.25%, 64.88%, 57.56%, and 53.16% of its uniaxial compression strength, respectively. Compared with the isochronous curve method and the transition creep method, the steady-state viscoplastic creep rate method can more accurately determine the long-term rock strength. The long-term strength of carbonaceous mudstone under dry and wet cycles decays exponentially, and the long-term strength decay rate during the first three dry and wet cycles is about 215 times the average decay rate.

Prediction of compressive creep behaviors of expansive soil exposed to freeze-thaw cycle using a disturbed state concept-based model

Expansive soils are discovered along the high-speed railways in typical cold regions of northeastern China. The long-term safety of slopes with expansive soil along the high-speed railways requires a detailed characterization of the time-dependent performances of expansive soils. In this study, X-ray diffraction, thermal analyses, and triaxial compressive creep tests are performed to explore the effect of freeze-thaw (F-T) cycle and montmorillonite (MMT) content on the creep characteristics of expansive soils collected along the high-speed railways near the stations of Binxi, Jiamusi, and Yanji. The results reveal that an accelerating creep stage in the creep process is observed for soil samples with higher MMT contents. For the expansive soils with higher MMT contents, the creep strain rates in the last creep stage show that there exists a threshold for creep-induced sample failure. The F-T cycle considerably affects the creep deformation of expansive soil and results in a creep failure of expansive soils. An accelerated creep stage is more likely to occur under the action of lower confining pressure. Additionally, by utilizing field investigation and microstructure analysis, the creep failure mechanism of the expansive soil slope after F-T cycle is preliminarily discussed. Finally, a suitable creep model for expansive soils subjected to F-T cycles is proposed based on the disturbed state concept to predict the primary and steady creep stages. The experimental results exhibit good agreement with the predicted values, confirming the validity of the proposed model. This work can provide reliable experimental data for the creep theory of expansive soil subjected to the F-T cycle.

AN ELASTO-VISCOPLASTIC MODEL FOR SOFT SEDIMENTARY ROCK BASED ON TIJ CONCEPT AND SUBLOADING YIELD SURFACE

In this paper, an elasto-viscoplastic constitutive model with strain softening is developed for soft sedimentary rock using a newly proposed evolution equation for subloading yield surface originally invented by Hashiguchi (1980). In the model, associated flow rule is adopted and tij concept, which can take into consideration the influence of intermediate stress on deformation and strength of geomaterials, is used. In the model, as is the same as Cam-clay model, plastic volumetric strain is used as hardening parameter, which is widely accepted by the researchers who specialize in the constitutive model for geomaterials. The application of the model to the experimental results of soft sedimentary rock indicates that the model not only can describe the time dependency, such as strain rate dependency and creep, but also the strain softening behavior of geologic materials. The material parameters involved in the model have clear physical meanings and can be easily determined with triaxial compression tests and creep tests.

Experimental study of creep Poisson ratio of hydraulic concrete under multi-age loading-unloading conditions

Elastic creep theory, which is widely used in concrete dam engineering, assumes that the elastic Poisson ratio and the creep Poisson ratio equal the effective creep Poisson ratio. However, differences in creep test conditions and stress state make this assumption controversial. To accurately clarify the Poisson effect of hydraulic concrete, uniaxial compression creep tests with four loading ages (3d, 14d, 28d, and 60d) and conventional triaxial compression creep tests with three loading ages (14d, 28d, and 60d) are conducted under unified test conditions. And high-precision creep data of transverse and longitudinal for multi-age loading and unloading are obtained. We then denoise the creep data by using a Savitzky-Golay filter. Furthermore, based on the denoised creep data, we calculate the Poisson ratio at each stage for uniaxial compression and conventional triaxial compression. Finally, we compare and analyze the Poisson ratio of each stage in different stress states. The results show that the creep tests have the same noise when conducted under the same test conditions, and the optimal denoising by the Savitzky-Golay filter is obtained with parameters W (window width) = 9 and N (polynomial order) = 6. Under different stress states, the elastic Poisson ratio, creep Poisson ratio and effective creep Poisson ratio are not equal to each other, and the elastic Poisson ratio is greater than the creep Poisson ratio. In addition, under the conventional triaxial stress state, the effective creep (creep recovery) Poisson ratio in each direction is different, which indicates that the creep (creep recovery) in each direction is dependent under multi-axial stress state.

Constitutive model of concrete creep damage considering the deterioration of creep parameters

The MTS815.03 rock test system is used to carry out mechanical property and triaxial compression creep tests on concrete specimens of the same specification under different confining pressure conditions to study the creep characteristics of concrete structures in deep high-stress level areas. The relationship between the creep strain rate of the concrete specimen and the stress level and the creep characteristics of the concrete specimen in the high-stress level area are analyzed. Based on the establishment of a creep damage model in the high-stress level zone of a concrete specimen, a method for determining creep parameters is proposed on the basis of the characteristics of the creep test curve. The degradation law of creep parameters under different stress levels is analyzed, and the relationship between creep parameters and stress is constructed. Finally, the expressions between each creep parameter and stress are substituted into the creep damage model, and an improved creep damage model is obtained. The correctness of the established model is verified by comparing the test curve and the model curve. Result shows that the agreement between the established creep model curve and the accelerated test curve is higher than that between the traditional Nishihara model curve and the accelerated test curve. The established creep damage creep model can be used to predict the deformation trend of surrounding concrete over time after chamber or tunnel excavation and provide theoretical basis for concrete support and lining construction.

A THERMODYNAMIC CONSISTENT ELASTOPLASTIC FRACTIONAL TIME-DEPENDENT DAMAGE MODEL FOR ROCK-LIKE MATERIALS

This paper aims at presenting a thermodynamically consistent elastoplastic fractional time-dependent damage model for describing short- and long-term behaviors of rock-like materials. The model utilizes generalized potential theory with a yield criterion, a non-associated flow rule and an isotropic plastic hardening function for describing the evolution of plasticity. A time-dependent Lemaitre-type damage is introduced through fractional derivative considering the short- and long-term evolution of microstructure, which leads to progressive degradation of elastic modulus and failure strength of material. In this context, both instantaneous and delayed deformations shall be well described within the unique constitutive model. For practical application, an efficient and convergent semi-implicit return mapping (SRM) algorithm involving a plasticity-damage decoupling corrector is developed. The proposed model is finally adopted to predict the mechanical and deformation behavior of several types of rocks under different loading conditions in conventional or quasi-static (different loading strain rate) triaxial compression tests, creep tests and relaxation tests. Comparisons between model predictions and experimental data demonstrate that the proposed model has the capability to reproduce main features of short and long-term behaviors of rock-like materials.

Experimental study of concrete creep under thermal-mechanical-hydric conditions

In this paper, the creep deformations of two representative concrete materials are investigated under thermal-mechanical-hydric conditions. Both basic and drying creeps are considered. Triaxial compression creep tests are first performed under a confining pressure of 5 MPa and three different values of temperature (T = 20 °C, 50 °C or 80 °C). Two different levels of differential stress are considered (50% and 80% of the peak strength at 20 °C). These tests are used for the characterization of basic creep. Then hydric creep tests are conducted on samples subjected to uniaxial compression condition with different prescribed values of axial stress (30%, 50% and 70% of the uniaxial compressive strength) and at constant temperature (20 °C). The samples are progressively dried by decreasing the relative humidity (RH) from 98 to 50%. The relative variations of sample mass are also measured during the drying process. It is found that the basic creep strain rate is enhanced by temperature and differential stress. The drying kinetics is strongly influenced by the compositions of concrete. The drying creep deformation is directly correlated with the mass loss kinetics.

Experimental study of the creep properties of coal considering initial damage

In underground tunnels, caverns or pillar goaf, the time-dependent deformation or failure of the rock or coal mass is a major safety concern, which affects the mechanical properties and stability of the coal and rock in the underground excavations. However, the damage surrounding rock or coal usually occurs from the time mining starts. This initial damage is rarely considered during the current creep tests used for coal. In the present study, an experimental specimen processing method to identify the initial damage to a coal deposit is suggested. The effect of the strain history on the deformation of coal samples with initial damage during multi-level loading triaxial compression creep tests was studied. The laboratory tests showed that the strain versus creep curve of the coal samples experiences three typical creep stages of deceleration creep in the early stage, constant velocity creep in the medium term and catastrophic accelerated creep in the later stage. With the increase in initial damage, it was observed the gradual decrease in total creep time, deviating stress of creep failure, stress threshold of accelerated creep and starting time of the volume expansion. When the initial damage value increased from 0.0 to 0.50, the deviating stress of creep failure, stress threshold of accelerated creep and starting time of the volume expansion of the coal decreased by 42.3%, 48.5% and 51.4%, respectively. The study is of great significance to conduct researches on the deformation, mechanical characteristics and long-term strength of coal pillar with initial damages under long-term pressure, and also provides insight into the underground excavations and the design of supports to the opneings under such disturbance.

Micro-Nano Fine Characterization of Coal Fracture Evolution During the Triaxial Compression Creep.

The production and evolution of fractures during coal creep will directly affect the occurrence, extraction and flow law of gas in a coal seam. The coal fracture evolution under creep conditions was studied by qualitative analysis and quantitative characterization. At a room temperature of 24 °C, triaxial compression creep tests of coal samples from the Zhaogu No. 2 coal mine in Jiaozuo were carried out under different loading conditions (0 MPa, 6 MPa, 9 MPa and 12 MPa), and low field nuclear magnetic resonance technique tests and industrial CT scanning experiments were performed. The obtained CT images were analyzed with the MATLAB software for equalization and binary image processing. The development and distribution of fractures in coal samples under different loading conditions were studied. The results show that the internal fractures are unevenly distributed and controlled by the main fracture, and the expansion direction of fractures is parallel to the direction of the maximum effective compressive stress. The number of fractures shows an increasing trend with the increase of axial stress, and the pace of growth of new fractures accelerates. The primary fractures in the coal body expand and generate new fractures, which improves the connectivity of the fractures in the coal body. The research results can provide a basis for studying the gas flow rule around the borehole and determining the influence range of the borehole.

A rheological constitutive model for damaged zone evolution of a tunnel considering strain hardening and softening

A rheological constitutive model for damaged zone evolution of a tunnel is proposed in this paper to describe the strain hardening and softening properties of the excavation-disturbed rock mass. Firstly, the one-dimension rheological model is introduced by connecting the improved St. Venant body with the Nishihara model, and this model can be used to describe the whole process including transient viscoplastic creep under a low-stress state, steady-state and accelerative creep under a high-stress state. Secondly, the constitutive equations of the rheological model under three-dimensional condition of the improved St. Venant body based on generalized plasticity potential theory are deduced, and the generic three-dimensional rheological model is developed. Thirdly, the creep and stress relaxation properties of the rheological model are studied and discussed. Furthermore, numerical analysis of triaxial compression tests and triaxial compression creep tests are conducted and the rheological model are validated. The results show that the rheological model can be used to study the evolution of excavation damaged zone in underground tunnel engineering.

A Theoretical and Experimental Study of Stress–Strain, Creep and Failure Mechanisms of Intact Coal

Deep mining and drilling activities typically trigger significant deformation of coal/rock roadway and even coal/rock dynamic hazards, which has attracted considerable attention. Hence, in this article, the mechanics and failure properties of intact coal are examined through triaxial compression tests and creep tests. First of all, triaxial compression experiments demonstrated that the complete stress–strain curves of intact coal are characterised by Class-I behaviour; and the post-peak modulus is negative. Second, with increasing confining pressure, peak strength and residual strength rise linearly, whereas elasticity modulus and peak strain increase as a power function form. Thirdly, compared with conventional triaxial load, tiered cyclic load can stiffen the strength of intact coal. Moreover, the data of creep tests are successfully fitted to the Burgers model. Maxwell elasticity modulus is significantly smaller than other creep parameters; Maxwell viscosity coefficient shows a positive correlation with deviatoric stress. Contrarily, Kelvin elasticity modulus and Kelvin viscosity coefficient drop with the rise in deviatoric stress. Additionally, with increasing deviatoric stress, single-step creep strain and average creep strain rate, proposed in this study, increase in a power function form. Finally, failure characteristics of intact coal under triaxial stress could be classified into four types (mainly shear failure and multiple shear fractures). The failure-plane angle generally linearly increases with the rise in confining pressure applied.

Mechanical behaviour and damage evolution of Beishan granite considering the transient and time-dependent effects of excavation unloading

A series of triaxial unloading tests on integrated rock, triaxial compression tests and creep tests on unloading-cracked rock were carried out on dry and saturated specimens. The spatial and temporal distribution of microcracking process were obtained with the help of 3D acoustic emission (AE) monitoring system. The experiment data revealed that the saturation had a degeneracy effect on the transient failure strength of integrated granite, and the failure strain at high confinement. The creep characteristics of unloading-cracked granite in lateral direction were found to be greater than in axial direction. At high confinement, the critical strain of creep failure, the creep deformation and the lateral creep strain rate were shown to be degraded by the saturation. When the applied stress surpassed the level of 90% of the compressive strength of unloading-cracked specimen, the variation of AE event showed a consistent tendency with the evolution of lateral strain, and the AE events were found to be mainly accumulated along the macroscopic failure surface. The AE signal was noticed to be more sensitive than the macroscopic deformation to the occurrence of creep failure. Before the appearance of large increase in lateral strain, the rapidly increase of AE activity had occurred.

Micromechanical modelling of short- and long-term behavior of saturated quasi-brittle rocks

This paper presents a physically-motivated micromechanical damage model for describing short- and long-term behaviors of saturated quasi-brittle rocks under drained condition. Rocks are considered composed of a pores-weakened elastic solid matrix and distributed microcracks. The system free energy is determined with the Mori-Tanaka homogenization method. Two main dissipative mechanisms, inelastic deformation due to frictional sliding and damage by crack propagation, are involved and strongly coupled in both stress-loading phases and creep phases under constant stresses. The effect of pore pressure is taken into account in the damage-friction coupling context. The microcracks induced rock damage is divided into two parts: instantaneous damage related directly to stress-induced microcrack growth, and time-dependent damage caused by subcritical cracking. The short- and long-term strengths of saturated brittle rocks are analytically deduced by damage-friction coupling analysis. By using the long-term strength, the creep parameter is calibrated in terms of a critical stress state identified in experiment. Comparisons between model’s predictions and laboratory tests are performed for two typical quasi-brittle rocks under triaxial compression tests and triaxial compression creep tests. It is shown that the proposed model can capture the main features of the mechanical behavior of quasi-brittle materials.

Creep behaviours of methane hydrate-bearing sediments

Natural gas hydrates, as a new energy source, are attracting more and more attention. Safe and efficient exploitation has become one of the hot issues in current studies. In order to investigate the creep behaviour of sediments containing methane hydrates, a series of triaxial compression tests and creep tests was conducted under various conditions. First, stress–strain curves were drawn, and then the failure strength of the sediments was obtained. Next, on the basis of creep tests, the creep curves were recorded. The results showed that the attenuation- and steady-creep stages always existed during creep, but the acceleration-creep stage just appeared under higher-temperature and higher-stress conditions. The creep test results indicated that the confining pressure, temperature and stress level affected the creep characteristics of sediments, such as the initial strain ε 0, the rheological initial time t m, the rheological initial strain ε m, the failure time t f and the failure strain ε f. The findings suggested that, during the creep tests, more hydrate dissociation accelerated the damage to the sediments’ strength under higher stress level, temperature or confining pressure.