Creep Behavior Of Rock Research Articles

A microscopic approach to brittle creep and time-dependent fracturing of rocks based on stress corrosion model

A brittle creep and time-dependent fracturing process model of rock is established by incorporating the stress corrosion model into discrete element method to analyze the creep behavior and microcrack evolution in brittle rocks at a micro-scale level. Experimental validation of the model is performed, followed by numerical simulations to investigate the creep properties and microcrack evolution in rocks under single-stage loading, multistage loading, and confining pressure, at various constant stress levels. The results demonstrate that as the stress level increases in single-stage creep simulations, the time-to-failure progressively decreases. The growth of microcracks during uniaxial creep occurs in three stages, with tensile microcracks being predominant and the spatial distribution of microcracks becoming more dispersed at higher stress levels. In multi-stage loading-unloading simulations, microcracks continue to form during the unloading stage, indicating cumulative damage resulting from increased axial stress. Additionally, the creep behaviour of rocks under confining pressure is not solely determined by the magnitude of the confining pressure, but is also influenced by the magnitude of the axial stress. The findings contribute to a better understanding of rock deformation and failure processes under different loading conditions, and they can be valuable for applications in rock mechanics and rock engineering.

Review of the creep constitutive models for rocks and the application of creep analysis in geomechanics

AbstractThe creep behavior of rocks has been broadly researched because of its extensive application in geomechanics. Since the time-dependent stability of underground constructions is a critical aspect of geotechnical engineering, a comprehensive understanding of the creep behavior of rocks plays a pivotal role in ensuring the safety of such structures. Various factors, including stress level, temperature, rock damage, water content, rock anisotropy, etc., can influence rocks’ creep characteristics. One of the main topics in the creep analysis of rocks is the constitutive models, which can be categorized into empirical, component, and mechanism-based models. In this research, the previously proposed creep models were reviewed, and their main characteristics were discussed. The effectiveness of the models in simulating the accelerated phase of rock creep was evaluated by comparing their performance with the creep test results of different types of rocks. The application of rock’s creep analysis in different engineering projects and adopting appropriate creep properties for rock mass were also examined. The primary limitation associated with empirical and classical component models lies in their challenges when it comes to modeling the tertiary phase of rock creep. The mechanism-based models have demonstrated success in effectively simulating the complete creep phases; nevertheless, additional validation is crucial to establish their broader applicability. However, further investigation is still required to develop creep models specific to rock mass. In this paper, we attempted to review and discuss the most recent studies in creep analysis of rocks that can be used by researchers conducting creep analysis in geomechanics.

A novel creep contact model for rock and its implement in discrete element simulation

The creep behavior of rocks significantly impacts projects' structural safety, including mining, tunneling, and hydraulic engineering. Numerous creep models used in numerical calculations incorporate basic elements, such as Burger's model. However, relying solely on series or parallel combinations of these basic components fails to account for the accelerated creep stage, prompting efforts toward developing enhanced creep models. Despite noted progress, a limited number of studies on the full-process simulation of graded creep loading and the consequent generation of cracks. To overcome this problem, an innovative creep model is proposed based on both the Parallel Bond and the Kelvin-Voigt contact models. This proposed creep model simulates the graded loading creep test of rocks under different load conditions and also conducts a parameter sensitivity analysis for the impact of the proportionate discrepancy between the two contact models. The results indicate that this new creep model could successfully simulate the comprehensive creep process, effectively capture crack progression, and represent ultimate failure modes during the creep process. Notably, to ensure the precision of simulations, it is recommended that the proportion of the Kelvin-Voigt contact model within the total contact is at most 25%.

A true triaxial creep constitutive model of rock considering the coupled thermo-mechanical damage

The main emphasis in contemporary mineral resource extraction has shifted towards deep Earth resources to address economic development requirements. The influence of temperature has emerged as an undeniable factor as engineering projects delve deeper into the Earth. The definition of a damage variable, which considers the coupled thermo-mechanical damage, has been proposed within the framework of damage mechanics. This definition aims to accurately describe the different stages of rock creep behavior in high-temperature environments. Furthermore, a constitutive model has been developed to describe the creep behavior of rocks under the combined influence of temperature and true triaxial stress. This model considers the series connection of the elastic body, nonlinear Kelvin body, Heard body, and visco-elastic-plastic body. The model has been parameterized and validated using available creep test data, and the equation for the yield surface of rocks under true triaxial stress has been derived through data fitting. The findings suggest that the developed constitutive model is capable of accurately describing the properties of rock creep behavior at different stages in high-temperature conditions, thus confirming its rationality and precision.

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.

Mechanical Properties of Gas Storage Sandstone under Uniaxial Cyclic Loading and Unloading Condition

In order to study the mechanical properties and damage evolution of the gas storage surrounding rock under the periodic injection-production process, the uniaxial cyclic loading and unloading tests of sandstone were carried out by TFD-2000 microcomputer servo-controlled rock triaxial testing machine. Results shown that the compressive strength of gas storage sandstone specimens were gradually decreases with increasing of the stress amplitude after 200 cycles. The stress-strain curve under uniaxial cyclic loading and unloading condition formed hysteresis loops, and the hysteresis loop presented sparse-dense-sparse when the stress amplitude was relative higher. The residual strains can be divided into three stages of decay deformation stage, stable deformation stage and accelerated deformation stage when the stress amplitude is 8~32 MPa, this phenomenon is very similar to the creep behavior of rocks. The energy evolution of sandstone under cyclic loading and unloading was analyzed and the damage evolution low of which was also discussed in detail, the damage variable defined by energy dissipative ratio accumulation can well reflect the damage development of sandstone under uniaxial cyclic loading and unloading. A nonlinear visco-plastic body was proposed by considering the accelerate stage of curves of the axial residual strains, and used the nonlinear visco-plastic body to replace the visco-plastic body of the traditional Nishihara model, a nonlinear viscoelastic-plastic model for cyclic loads was established and the applicability of the model is verified. The research results provide certain reference value for the construction and maintenance of gas storage.

A Chemical Damage Creep Model of Rock Considering the Influence of Triaxial Stress.

In order to accurately describe the characteristics of each stage of rock creep behavior under the combined action of acid environment and true triaxial stress, based on damage mechanics, chemical damage is connected with elastic modulus; thus, the damage relations considering creep stress damage and chemical damage are obtained. The elastic body, nonlinear Kelvin body, linear Kelvin body, and viscoelastic-plastic body (Mogi-Coulomb) are connected in series, and the actual situation under the action of true triaxial stress is considered at the same time. Therefore, a damage creep constitutive model considering the coupling of rock acid corrosion and true triaxial stress is established. The parameters of the deduced model are identified and verified with the existing experimental research results. The yield surface equation of rock under true triaxial stress is obtained by data fitting, and the influence of intermediate principal stress on the creep model is discussed. The derived constitutive model can accurately describe the characteristics of each stage of true triaxial creep behavior of rock under acid environment.

Creep Behavior of Rocks and Its Application to the Long-Term Stability of Deep Rock Tunnels

Since underground structures such as tunnels are inevitably surrounded by rocks, their long-term safety and stability are primarily governed by the comportment of these materials. Being able to express the time-dependent behavior of rocks, creep is one of the most interesting mechanical properties considered in the study of tunnels. Based on relevant research efforts, this article aims to provide a comprehensive review of pertinent information on rock creep and its potential influencing factors. It also presents the latest progress in constitutive models of rock creep and discusses their applicability to the long-term stability of deep underground structures. The results show that rock creep is significantly influenced by various potential factors both external and internal. These are mainly hydraulic pressure, stress level, water content, temperature, damage, and time-to-failure. For instance, the creep lifetime of andesite is drastically reduced by the presence of water. It is about 180 times shorter in wet conditions than in dry conditions, under the same stress conditions. By the combined influence of high stresses, high pressures, and high temperatures, creep rupture occurs in a semi-brittle manner for most types of hard rocks. The characteristics and installation period of the lining structures also have a strong influence on the evolution of creep in the rocks surrounding the underground structures. It is suggested that despite the colossal research efforts already made in this area, more accurate creep constitutive models are still needed for more adequate applications to the long-term stability of deep rock tunnels. Accordingly, key perspectives for future investigations are highlighted. This work can serve as a good reference in the establishment of new constitutive models of rock creep aimed at improving their accuracy, and facilitate appropriate actions to predict the long-term stability of deep tunnels in realistic situations.

Experiment and Numerical Simulation on Creep Mechanical Behaviors of Mudstone under Unloading Condition

The deep soft rock with complex occurrence conditions is easy to produce significant creep deformation under the influence of high in situ stress, high temperature, and disturbance, which has a great influence on the safety and long-term stability of structures with long service life, such as underground chambers and nuclear waste storage rooms. To study the creep effect of surrounding rock of deep chamber under the condition of excavation and unloading, creep tests of deep mudstone over 1000 meters in unloading confining pressure were carried out in this work. The experimental results show that high confining pressure has a significant inhibition effect on the creep behavior of rock, while high axial stress aggravates the creep behavior, which is manifested by the increase of creep deformation and the shortening of total creep time. When the axial stress is higher than the yield strength of the rock mass, the rock mass enters the tertiary creep stage (which is characterized by large deformation and instability failure in a short period of time). An improved nonlinear viscoelastic-plastic rock creep model, which can simulate three creep stages, is established (well verified). In addition, the creep deformation of surrounding rock after excavation is simulated based on this model, and the simulation results are consistent with the engineering practice: after 165 days of excavation, there is still a large deformation rate.

Influence of dynamic disturbance on rock creep from time, space and energy aspects

In order to explore the influence of dynamic disturbance on creep behavior of rock, the creep damage evolution in rock under the dynamic disturbance are reproduced with creep damage model. In this model, the constitutive law of rock under combined creep and dynamic loading condition is implemented based on elastic damage principle and Norton-Bailey equation in COMSOL Multiphysics. The numerical results show that the dynamic disturbance alters the creep behavior of rock in three aspects, i.e., time, space and energy. In temporal aspect, dynamic disturbance not only accelerates the creep damage evolution of rock, but also leads to the tensile damage accounting for the main damage mode. The tensile damage mode mainly occurs during the unloading stage of dynamic disturbance, and the tendency of transition becomes evident under more dynamic disturbances. In spatial aspect, the dynamic disturbance may facilitate the development of rock damage, resulting in unstable rock failure. In energy aspect, the dynamic disturbance causes creeping rock to absorb and release energy in a short time, which can be quantified with the energy dissipation rate. The residual deformation caused by the dynamic disturbance is also exponentially related to the energy dissipation rate.

Experimental Investigations on Creep Behavior of Coal under Combined Compression and Shear Loading

The creep behavior of rock has received much attention for analyzing the long-term response and stability of underground rock engineering structures. Numerous studies have been carried out on the creep properties of various rocks under pure compression conditions. However, little attention has been paid to the creep behavior of rocks in a combined compression-shear loading state. In this work, a novel combined compression and shear test (C-CAST) system was used to carry out inclined uniaxial compression tests and creep tests for various inclination angles (0°, 5°, 10°, and 15°). The results revealed that the peak strength of the coal decreased with the inclination angle of the specimen, which could provide the basis for setting up a creep test scheme. Multistage compression-shear creep tests were carried out on specimens with different inclination angles. Based on the analysis of the creep test data, the creep behavior of the coal in a combined compression-shear state was studied. It was found that the specimen inclination affected the time-dependent deformation, long-term strength (LTS), and time to failure. Compared with the specimen under pure compression, the inclination specimens tend to produce large shear strain with time, while they were more prone to shear failure. The reduction of the long-term strength was closely associated with the increase of the specimen inclination angle when the angle was more than 5°. Moreover, the ratio of the peak strength to the LTS was not affected by the specimen inclination, which is considered an inherent characteristic. We anticipate that the results obtained will assist in pillar design and long-term stability analysis.

An experimental and theoretical investigation of time-dependent cracking and creep behavior of rocks under triaxial hydro-mechanical coupling

Subcritical crack propagation and rock creep deformation are the main factors affecting the long-term stability and strength characteristics of rocks under hydro-mechanical coupling. Triaxial creep tests were performed on rock-like mortar specimens containing a pre-existing 3-D crack to investigate the time-dependent mechanical behavior of the cracked rock. A modified theoretical model for the irreversible deformation of rocks based on subcritical crack propagation was used to analyze the creep mechanism of the specimens and the effects of water pressure. The specimens with creep damage mainly exhibited a tensile-shear failure mode, and the macrofracture presented more tensile characteristics with increasing water pressure. The water pressure promoted the prefabricated crack propagation, inhibited the formation of microcracks, increased the creep rate, and accelerated specimen failure, which had a negative effect on the long-term stability of the specimens. The modified model accurately predicted the variation in irreversible axial strain and time required for specimen failure, especially under higher water pressures. The creep deformation of the specimens was much larger than the instantaneous deformation at the same crack propagation length, indicating that subcritical crack propagation is the main factor leading to the failure of rocks.

New Physical Model to Study Tunnels in Squeezing Clay-Rich Rocks

Abstract Squeezing ground conditions in tunnels are often associated with rock mineralogy, strength, ductility, excavation sequence, and the magnitude of in situ stresses. Numerous methodologies and empirical correlations have been proposed in the past to determine the level of ground squeezing conditions in tunnels, but most of them are problem specific and limited in scope. This paper presents a fundamental study of tunnel squeezing using a novel experimental approach to simulate tunnel boring machine (TBM) excavation in squeezing ground conditions. The proposed experimental setup employs a cubical specimen of synthetic mudstone, with each dimension being 300 mm and the six faces subjected to a true-triaxial state of stress, with different magnitudes of principal stresses and stress levels that correspond to realistic in situ conditions. A miniature TBM was designed, fabricated, and used to excavate a tunnel into the host rock (specimen) while the rock was subjected to a true-triaxial state of stress. Embedded strain gauges and acoustic emission sensors, which were coupled on the surface of the rock specimen, were also used to monitor the tunnel’s response during the excavation stage. The results from the experiment confirmed the capability of the physical model to provide a better understanding of tunnel squeezing and to delineate the damage and the deformation that occurs during instant stress release and creep behavior of rock around the tunnel boundary during tunnel excavation.

Cracking and Creep Behavior of Rocks Considering Propagation and Interaction of Adjacent Cracks Under Hydro-Mechanical Coupling

Cracking and Creep Behavior of Rocks Considering Propagation and Interaction of Adjacent Cracks Under Hydro-Mechanical Coupling

Time-dependent deformation and failure of granite based on the virtual crack incorporated numerical manifold method

Micro-cracks are known to greatly affect the mechanical properties of granite and subcritical crack growth (SCG) is considered to be the main mechanism of brittle creep in rocks, including granite. Here, we provide new uniaxial compressive strength and creep experiments for Lanhélin granite, and a new multi-crack numerical model to explain the experimental observations. We first thermally-stressed our granite samples to create thermal micro-cracks. Uniaxial compressive strength experiments were then used to find the uniaxial compression strength of the thermally-cracked granite, a pre-requisite for brittle creep experiments. We introduced a new model that combines SCG theory and the numerical manifold method (NMM) to link the local damage caused by micro-crack propagation and the macroscopic creep deformation observed in the granite samples. We also investigated the influence of virtual micro-crack length, confining pressure, and differential stress on brittle creep behavior. According to our model, we can numerically simulate the entire creep process, from the small deformation caused by micro-cracks to the large displacement characteristic of brittle creep. The fact that the numerical simulations are in good agreement with experimental results shows that the NMM combined with the SCG theory is a suitable method for modeling the creep behavior of rocks.

A full-stage creep model for rocks based on the variable-order fractional calculus

An accurate characterization of rocks for the modelling of creep is an essential step toward ensuring the safety with respect to reliability of underground rock engineering. In this work, a novel variable fractional order rheological model is established to describe the full-stage creep behavior of rocks. With simpler form and fewer parameters, the proposed model is verified to have the ability for the description of trimodal creep behavior of rocks. The evolution of mechanical properties during creep is quantitatively described by the variable fractional order including the creep hardening, softening and the transition part between them. Moreover, the physical significance of fractional order is further explored by the commonly accepted competition mechanism of creep hardening and softening for brittle creep, which indicates that the mechanical property of rocks during creep is harder with lower water contents but softens faster with larger applied stresses. Furthermore, the linear form of the variable order function is determined by applying the new variable order fractional operator. It is shown that the slope of order function confirms the creep strain rate and the intercept of order function primarily affects the critical time for entering the nonlinear creep phase. Finally, the rising tendency of fractional order reveals that the accelerating creep is a continuous softening process of mechanical properties since the larger values of fractional order exhibits the property of rocks is more viscous.

Micro-crack propagation and coalescence during time-dependent deformation of granite based on numerical manifold method

An understanding of influence of micro-cracks on time-dependent deformation in granite is of fundamental importance in many situations, such as nuclear waste storage facilities or the exploitation of geothermal resources. Time-dependent cracking is considered to be the main mechanism of brittle creep in granite. Creep strain rates are strongly influenced by the density of pre-existing defects that also exert a significant influence on rock physical properties. We introduce a new model that combines the subcritical crack growth (SCG) theory and the numerical manifold method (NMM) to link the local damage (using an exponential material softening law) caused by micro-crack propagation and the macroscopic creep deformation typically observed in granite specimens. In this model, each element contains a virtual micro-crack that can propagate sub-critically following Charles’ law. Once the virtual micro-crack length reaches a given value, it will convert to a real micro-crack, which can cut through adjacent elements, open, and slide according to the principle of NMM. We also investigated the influence of virtual micro-crack length, confining pressure and differential stress on creep behaviour. The fact that numerical simulations are in good agreement with experimental results shows that the NMM combined with the SCG theory is a suitable method for modelling the creep behaviour of rocks.

A time-dependent creep model for rock based on damage mechanics

A creep model based on the damage mechanics is proposed in this study to describe the three-stage creep deformation of rocks under conventional triaxial loading conditions. The proposed model has a simple form as it is based on the mechanism which assumes that the time-dependent creep behavior of rocks is solely described by the damage evolution. Verification of the proposed model against the creep tests shows that the model can reflect the three-stage creep behavior under higher stress levels as well as the elastic behavior under lower stress levels using the same model equations. The features of the proposed model include: (1) Simple mathematical form as it contains only one strain component without strain partitioning, and one set of equations to predict the creep deformation for all stress levels; and (2) The model requires only four parameters. All these features make the proposed model simple to use and easy to implement.

Creep and permeability evolution behavior of red sandstone containing a single fissure under a confining pressure of 30\u2009MPa

The long-term deformation and permeability evolution with time are key issues for geo-engineering applications such as radioactive waste disposal. Rock permeability concurrent with deformation is significantly influenced by cracking. This study investigated the creep-permeability evolution behavior of red sandstone specimens containing a single fissure under a confining pressure of 30 MPa. First, the effects of stress ratio (SR) and fissure dip angle on the creep behavior of rock were investigated. The more loading/unloading cyclic numbers, the larger the irrecoverable axial deformation. The instant elastic strains and visco-elastic strains linearly increased with SR for both the intact and fissured specimens, whereas the instant plastic strains showed different results. The visco-plastic strains nonlinearly increased. For fissured and intact specimens, the creep strains and the steady-state creep rates nonlinearly increased as SR increased. The instantaneous strains, instant elastic strains, and visco-elastic strains slightly varied when the fissure dip angle was less than 45° but notably decreased with increasing fissure dip angle beyond 45°. However, the fissure dip angle had no obvious effects on the plastic and creep strains. Damage (D) was defined using the ratio of non-elastic strains to the total strain. D increased approximately linearly with SR, but the fissure dip angle had no obvious influences. Subsequently, the long-term strength (LTS) of the red sandstone was determined using two different methods. The LTS first decreased when the fissure dip angle increased from 0 to 45° but increased with increasing dip angle. The triaxial and creep failure modes were mainly shear along anti-wing cracks for the fissured specimens but shear failure occurred for the intact specimen. Moreover, the permeability of the fissured red sandstone was governed by SR and deformation or time. During the multi-step loading/unloading creep process, the permeability first decreased and then had a sudden rise when tertiary creep occurred.

Indentation size and loading rate sensitivities on mechanical properties and creep behavior of solid bitumen

Creep behavior of rocks could impair fracture conductivity and wellbore stability during gas production from highly matured organic-rich shales in South China, of which the organic matter is mainly in the form as solid bitumen and is thought to be a major contributor for the creep deformation. To get a better insight into this phenomenon, this paper for the first time characterizes the mechanical properties and creep behavior of a millimeter-sized solid bitumen sample by using quasi-static state creep tests and Dynamic Mechanical Analysis in nanoindentation, and reports their dependences on indentation size and loading rate, respectively. Mechanical properties (including hardness and Young's modulus) are found to be negatively related with both indentation size and loading rate. The extremely small creep strain rate sensitivity (m) of solid bitumen indicates a localized shear flow inside. And m exhibits slightly positive dependences on indentation size and loading rate. The potential mechanisms controlling the deformation of solid bitumen under indentation are also discussed.