Deformation Behavior Of Rock Research Articles

A Time-Dependent Damage Constitutive Model for Brittle Rock Materials Based on Subcritical Damage Theory.

In the domain of geotechnical engineering, a profound understanding of the long-term mechanical deformation characteristics of rocks is indispensable for the design and construction of structures, dams, tunnels, and various engineering projects. The deformation behavior of rocks under long-term loads directly impacts the stability and safety of engineering structures. This study employs micromechanical methods to investigate the subcritical extension of microcracks under stress corrosion. By examining the accumulated damage resulting from this phenomenon, the research explores the patterns of aging damage development and establishes a constitutive model for aging that incorporates cumulative damage over the stress history. The accuracy of the proposed model is evaluated through a comprehensive comparison of numerical results with experimental data. The experimental data set encompasses traditional triaxial compression tests, single-stage creep, multistage creep, and single-stage relaxation tests conducted under varying confining pressures. The predicted results exhibit strong consistency with the entire data set. Furthermore, this paper employs crack damage stress as an indicator characterizing the long-term strength of rock. Through frictional damage coupling analysis and derivation, an analytical expression for the long-term strength of rock materials containing microcracks is provided, serving as a theoretical basis for investigating the long-term mechanical performance of brittle rock materials and ensuring the long-term stability of large-scale rock engineering projects.

Quantitative prediction of surrounding rock deformation via an energy-based damage model combining with microseismic monitoring

In this study, combined with microseismic (MS) monitoring and numerical simulation, a novel energy-based damage model is proposed for quantitatively predicting the surrounding rock deformation for the stability analysis of underground engineering. First, the rock damage range is delineated based on MS event location and source radius. Second, seismic efficiency is introduced to calculate the actual released energy, and the total releasable energy density and total stored energy density are derived from element stress information and stress–strain curves in numerical simulation. Finally, a novel energy-based damage model with definite physical significance is developed based on the above-mentioned three forms of energy. Our new model introduces MS source parameters into the classical damage variable based on dissipated energy, accurately reflecting the qualitative relationship between them, which is highly applicable to practical engineering. Moreover, this model comprehensively reflects the damage degree variation of surrounding rocks from in-situ stress state to different excavation stages and describes real-time deterioration of rock mechanical parameters. In addition, a new approach based on seismology formulation is applied to solve seismic efficiency, without requiring reference to the destruction situation. To validate our proposed model, a three-dimensional (3D) numerical simulation embedding the damage model is conducted to investigate the surrounding rock deformation behavior of underground caverns in the Lianghekou hydropower station. A reasonable consistency is observed between the simulated displacement field and source parameters distribution obtained from MS monitoring and field failure. Furthermore, compared to the original model without a damage variable, the energy-based damage model greatly improves the deformation prediction precision.

Experimental study of real-time temperature-dependent nonlinear deformation of sandstone

In contrast to thermal heating, the real-time heated rock exhibits significant nonlinearity during the elastic deformation stage. Hence, an experiment assembled by a high and low-temperature test chamber and a microcomputer-controlled rock direct shear instrument is built to evaluate the effect of real-time temperature on the nonlinear deformation behavior of rock. A set of nonlinear stress–strain relationships of forty sandstone samples under moderate real-time temperature conditions are obtained from experiments and agree well with the theoretical predictions from the two-part Hooke’s model (TPHM). The soft and hard parts respond to the real-time temperature are quite different. The ratio of the soft part (γt) increases and the elastic modulus of the hard part (Ee) decreases with the temperature below 125℃. On the contrary, γt decreases and Ee increases with the temperature above 125℃ up to 200℃. Thermally-induced and expandable microcracks (thermal weakening) incur structural damage of the hard part below 125℃, while thermal expansion (thermal strengthening) can lead to tighter compaction between grains above 125℃. Therefore, there is a threshold temperature 125℃ under real-time heating condition due to the thermal cracks and expansion. The elastic modulus of the soft part (Et) decreases continuously with increasing temperature, indicating inconsistent thermal expansion effects on the soft part with mixture of impurity particles and the hard part whose mineral particles are closely contacted at higher temperature. Based on the experimental data and TPHM, empirical relationships between the real-time temperature and nonlinear deformation are proposed. This study will provide support for the safe production and disaster prevention of geological engineering under thermo-mechanical coupling working condition.

Sintering and deformation properties of forsterite + diopside aggregates in an electrical field

A new technique called “flash sintering” has been proposed in the field of materials science. When a compact powder of oxide material is sintered in an electrical field, densification accelerates at a certain temperature, and the sintering is completed in a shorter time at a lower temperature as compared with conventional sintering experiments. In addition, tensile deformation experiments conducted on a dense oxide body in an electrical field have shown that plastic deformation can be enhanced at lower temperatures with lower stresses, as compared with conventional deformation experiments. Fluctuations in the magnetic and electrical fields derived from outside Earth, such as solar activity, induce an electrical field inside Earth. The strength of the electrical field in Earth's mantle is still debated, but it could be up to 10−6 V/cm. Although electrical fields inside Earth may affect the deformation behavior of rocks, no experimental studies have been conducted on geomaterials to assess this effect. Therefore, based on these recent findings in materials science, we conducted sintering and deformation experiments to examine the effects of an electrical field on high-temperature mass transport. We used forsterite + diopside crystal aggregates, which are good analogs for Earth's mantle. The sintering experiments demonstrated that the relative density increases with an increasing electrical field at a constant temperature. In the deformation experiment with a constant displacement rate, the samples in an electrical field of 1000 V/cm were deformed by 4.4× lower stress than for samples not in an electrical field. These features suggest that diffusional mass transport is enhanced in an electrical field. We propose that the presence of an electrical field within Earth may accelerate the deformation of mantle materials.

Quantifying the Rock Damage Intensity Controlled by Mineral Compositions: Insights from Fractal Analyses

Since each rock type represents different deformation characteristics, prediction of the damage beforehand is one of the most fundamental problems of industrial activities and rock engineering studies. Previous studies have predicted the stress–strain behaviors preceding rock failure; however, quantitative analyses of the progressive damage in different rocks under stress have not been accurately presented. This study aims to quantify pre-failure rock damage by investigating the stress-induced microscale cracking process in three different rock types, including diabase, ignimbrite, and marble, representing strong, medium-hard, and weak rock types, respectively. We demonstrate crack intensity at critical stress levels where cracking initiates (σci), propagates (σcd), and where failure occurs (σpeak) based on scanning electron microscope (SEM) images. Furthermore, the progression of rock damage was quantified for each rock type through the fractal analyses of crack patterns on these images. Our results show that the patterns in diabase have the highest fractal dimensions (DB) for all three stress levels. While marble produces the lowest DB value up to σci stress level, it presents greater DB values than those of ignimbrite, starting from the σcd level. This is because rock damage in ignimbrite is controlled by the groundmass, proceeding from such stress level. Rock texture controls the rock stiffness and, hence, the DB values of cracking. The mineral composition is effective on the rock strength, but the textural pattern of the minerals has a first-order control on the rock deformation behavior. Overall, our results provide a better understanding of progressive damage in different rock types, which is crucial in the design of engineering structures.

The novel strength criterion and the associated constitutive model based on the finite deformation behavior for the rock under the disturbance stress paths

To develop a novel 3D Hoek–Brown strength criterion and an associated constitutive model based on the finite deformation behavior of rock under the disturbance stress paths, a series of mechanical tests are initially conducted under designed disturbance stress paths (hydrostatic stress stage (HSS), initial loading–unloading stage (ILUS), and disturbance stage (DS)). Additionally, low disturbance (LD), medium disturbance (MD), and high disturbance (HD) modes are taken into consideration. Then, the finite deformation theory is employed to study the nonlinear behavior. This nonlinear behavior can be regarded as a nonlinear relationship between the stress and strain of rock under loading, especially the initial compression stage and plastic stage, as well as a complex deformation field, which is described by the finite deformation theory and featured by the mean rotation angle (Θ). Afterwards, the damage variable (DV) regarding Θ is proposed and used to establish a novel strength criterion (NSC) based on the current Hoek–Brown strength criterion. Finally, by considering the NSC, an associated elasto-plastic constitutive model is developed. The results show that the initial confining pressure (ICP) and disturbance mode have a significant effect on the elastic modulus (E). Meanwhile, the ICP has a higher effect on E than the disturbance mode. Then, the evolution of Θ is closely associated with the nonlinear deformation of rock masses because the σ1−Θ curves can be divided into three stages. Those stages can match well with the initial compression stage, elastic stage, and plastic stage, respectively. Regarding Θ as a parameter of the damage variable (DV), the NSC is established. Additionally, it can be observed that the failure envelopes of the NSC scale down gradually with increasing Θ on the deviatoric plane. Meanwhile, as the value of the coefficient of determination (DC) is higher than that of other strength criteria, the NSC may exhibit better agreement with the experimental data. Furthermore, a constitutive model based on the aforementioned strength criterion and the hardening function that takes Θ and the disturbance of rock masses (D) into account is proposed and validated as a solution to predict the nonlinear behavior of rock specimens under the disturbance stress paths.

Viscoelastic–plastic response of tunnels based on a novel damage creep constitutive model

Geomaterial rheology plays an important role in engineering stability and can be used to understand the deformation behavior of rocks. This study proposes a novel damage constitutive model to describe the rheological properties of rocks, which includes a Maxwell body, a Kelvin body, and a new damage-plastic element. A series of uniaxial rock creep tests were performed, and the experimental results can verify the proposed viscoelastic–plastic model. A closed-form analytical solution of surrounding rock creep in a circular tunnel is derived using the proposed model, and parametric studies are examined to determine the influence of parameters on the surrounding rock deformation. Dengjiashan tunnel in Sichuan, China is employed to verify the analytical solution. The results show that the proposed viscoelastic–plastic model well describes the entire rock creep process. The geological strength index has a significant influence on the surrounding rock deformation. The analytical results agree well with the experimental and monitoring data. The proposed analytical solution can therefore be applied to predict the creep deformation of surrounding rocks due to tunnel excavation.

Micromechanical behavior of jointed rock masses under uniaxial compression loading: a numerical study based on the discrete element method

The discrete element method is used to study the deformation process and failure mechanism of rock masses under uniaxial compression when the initial joint frequency increases. In this study, a systematic analysis is carried out to investigate failure mechanisms in rock masses with special emphasis on macroscopic deformation processes and the micromechanical origin. The influences of joints on strength, deformability, stress–strain relationship, and failure mode are studied at the macroscopic level. The tensile and shear crack distribution, fragment characteristics, and energy dissipation are also analyzed to advance the understanding of the deformation process and failure mechanism of jointed rock masses. The microevolution of fabric and forces anisotropy during loading and contact force distribution provide insights into the effect of increasing initial joint frequency on the macroscopic deformation behavior of rocks. The results reveal that with the increasing initial joint frequency, the specimen exhibits brittle-ductile characteristics, and the failure mode changes from splitting to sliding along the joint surfaces. They also show how the deceleration in the growth of fabric and contact forces anisotropy develops and confirm that the increase in initial joints and corresponding microstructural changes can suppress the development of anisotropy, thereby significantly reducing the strength of rock samples.

Numerical investigation of the effect of improved endochronic constitutive model on rock material deformation under cyclic loading

Abstract Rock materials are often subjected to cyclic loads during construction. A full understanding of the deformation behavior of rock under cyclic loads is of great significance in engineering. In this study, by using the endochronic constitutive model proposed by Valanis, the reinforcement function form and constitutive parameters of the endochronic model are improved. An endochronic plasticity constitutive program for rock based on the finite element method is used to study the mechanical properties of rock under different cyclic loading conditions (of maximum loading stress, amplitude, and confining pressure), and through the use of red sandstone, marble, and basalt, experimental and simulation results are compared to verify the model. The results show that the theory can better simulate the hysteresis loop width and cumulative plastic strain of rock under cyclic loading and, under different loading conditions, the numerical simulation results are consistent with the actual rock experimental law. Therefore, the endochronic plasticity constitutive model in this study can be applied to investigate the influence of cyclic loading on the dynamic deformation behavior of rock.

Estimating the rock mass deformation modulus: A comparative study of empirical methods based on 48 rock mass scenarios

Abstract The rock mass deformation modulus, Erm, is an input parameter for most numerical modeling to verify the deformation behavior of rocks due to rock engineering activities within/on it. Among the most common methodologies used for estimating this parameter, empirical correlations based on rock mass classification schemes (e.g., RQD, RMR, GSI, and Q) stand out the most, principally because of their low cost when compared to the other methods. Herein, the main correlations used in practice are evaluated and comparted for 48 different rock quality scenarios, previously characterized and classified according to rock mass classification systems. The results obtained by each of the empirical correlations demonstrated that normalized correlations, that is, based on the ratio of the rock mass and intact rock modulus, Erm/Ei, underestimate the Erm values when compared to those results obtained from not-normalized correlations in the scenarios of better quality rock masses. For poor quality rock mass scenarios, both non-normalized and normalized correlation presented similar results. The correlations proposed by Hoek and Diederichs (2006) and Galera et al. (2007) estimated more central Erm values when compared to the other correlations, for all quality scenarios, while the Mitri et al. (1994) and Sonmez et al. (2006) methods estimated most high and low values of Erm, respectively.

Shear Behavior and Anisotropy Characteristics of the Fracture Morphology of Sandstone with Different Water Contents

Hydromechanical coupling in rock masses is an important issue for many rock mechanics and hydrogeology applications. The change of a water-bearing state will induce the fracture of the intact rocks and further accelerate the shear slip instability of the sheared surface. To investigate the weakening effect of water content on the mechanical properties of a rock mass, laboratory direct shear tests combined with three-dimensional analysis of sheared surfaces were carried out on sandstone samples with different water contents. The variogram parameters, sill and range, were applied to quantify the morphology of shear fracture surfaces, to reflect the shear failure process of the intact rock, and to provide a basis for resliding instability of jointed rock. It was determined that the sill represents the height of the fluctuation body in the fracture surface and the range represents the single fluctuation body and may reflect the frequency of fluctuations. The test results revealed that the increase in water content had a clear weakening effect on the shear strength and deformation behavior of rock, especially under saturated conditions. Moreover, the distribution of water in the samples directly affected the crack initiation and propagation and characteristics of the fracture morphology.

Modeling time-dependent deformation behavior of brittle rock using grain-based stress corrosion method

This research presents a grain-based stress corrosion model to simulate time-dependent failure of brittle rock. Time-dependent deformation of rock is considered as the manifestation of stress corrosion that may occur inside grains and on grain boundaries. A damage-rate law is adopted and modified to describe continuous degradations of parallel-bond diameters and contact properties in the stress corrosion process. A detailed numerical scheme with self-adaptive determination of time step is used to simulate the time-dependent deformation behavior of rock. The results show that both the short-term mechanical properties and the fatigue test results of Lac du Bonnet granite can be reproduced by the proposed method. In addition, compared with the original parallel-bond stress corrosion method, the modified grain-based stress corrosion method predicts the failure time of rock better under low driving-stress ratios. With the increase of the driving-stress ratio, the failure time of the numerical specimen decreases, and the creep curves tend to have a stair-stepping shape. The numerical simulation results show that an increase of 15 MPa confining pressure under a driving-stress ratio of 0.6 can lengthen the failure time of the rock from 139 days to 11 years.

A comprehensive parametric study of grain-based models for rock failure process simulation

Grain and contact are the two key components in 3DEC-GBMs (grain-based models) because they control the micro-mechanical behavior and consequently the macro-mechanical behavior of rock. Three types of grains – rigid, elastic, and breakable grains – are considered in this study to explore the influence of grain properties on the mechanical behavior of rock. Equivalent 2D plane strain problems are solved using 3DEC to reduce computation time. A non-uniform distribution of grain size is used to generate numerical models using Neper, a software package for polycrystal generation and meshing. A comprehensive parametric study of properties of contact and grain of the three types of grains is conducted and calibration procedures are suggested for numerical modeling. The modeling results indicate that both the contact and the grain properties affect the macroscopic mechanical behavior of synthetic rock specimens. All the three types of grains produce reasonable results for pre-peak deformation (E and υ) and macroscopic strength (UCS, σt, C and ϕ) parameters. Each grain type has advantages and disadvantages in numerical modeling. Rigid grains cannot produce volumetric strain properly and a near-zero residual friction angle of contact is needed to capture post-peak deformation behavior due to the grain interlocking effect. Elastic grains also need a very low residual friction angle of contact and brittle rock deformation behavior cannot be captured. The complex calibration procedure and long computation time are the main issues of breakable grains, although it simulates well the volumetric strain, does not require a very low contact residual friction angle, and captures brittle rock behaviors better than other two types of grains. The findings from this study are useful for rock failure process simulation using the 3DEC-GBM modeling approach.

Influence of initial micro-crack damage on strength and micro-cracking behavior of an intrusive crystalline rock

Rocks inherently contain some micro-cracks. The existence of initial micro-cracks introduces weakness to the rock specimen and hence affects the strength and deformation behavior of rocks. This paper numerically investigates the influence of initial micro-crack damage on the strength and deformation behavior and the associated micro-cracking process of a crystalline rock using a previously-calibrated grain-based model (GBM), which is implemented in two-dimensional Particle Flow Code (PFC2D). The initial micro-crack damage is generated by loading/unloading of the model numerically, and a damage parameter is defined to quantify the degree of initial micro-crack damage. After the initial micro-crack damage is generated, compressive loading tests under different confining pressures are conducted. The simulation results reveal that the initial micro-crack damage has a significant influence on the simulated stress–strain curve, rock strength, elastic modulus, and total number of generated micro-cracks. In general, as the initial micro-crack damage increases in the numerical model, the simulated rock strength and elastic modulus gradually decrease. However, the decrease in rock property (strength and elastic modulus) will become significant only after sufficiently high initial micro-crack damage in the model is reached. The elastic modulus to UCS ratio (E/UCS) is not significantly affected by the initial micro-crack damage. Overall, the initial micro-crack damage weakens the model. The simulation results are in good agreement with previous laboratory tests results. The PFC2D-GBM approach in this study can be used to capture the strength and deformation behavior of damaged rocks, which are induced from initially-generated micro-cracks, e.g., rock drilling and coring, cyclic loading, and thermal loading.

Numerical analysis on nonlinear deformation behavior of rock considering compaction of pores

The nonlinear behavior of porous or fractured rocks plays an important role for analyzing the mechanical response and stability in many geological and geotechnical applications. A stress-strain relationship considering the porosity is established for modeling the nonlinear deformation. In the present paper, firstly, on the basis of nonlinear deformation mechanism of porous or fractured rocks, the typical stress-strain curve was divided into two parts factitiously. Then, two constitutive models were established for the two parts, respectively. In order to describe the effect of the change of porosity on deformation behavior of rock, a new microcracks closure factors D ϕ was proposed in the microcracks closure phase. For the other part, elastic damage mechanics is used to describe the constitutive law of meso-level elements, the maximum tensile strain criterion as well as the Mohr-Coulomb criterion is utilized as the damage threshold. The proposed model is implemented using finite element method by MATLAB programming under the environment of COMSOL Multiphysics. Then the model was validated by comparing the numerical simulations with our experimental result and the previously published experimental data. At last, numerical simulation on failure process of 6 rock specimens with different porosities but same rock matrix under uniaxial compression is presented. It is found that the established model accurately reproduces the typical stress-strain curve, the microcracks closure phase, especially. With the increase of porosity, the uniaxial compressive strength (UCS) decreases. And the elasticity modulus increases with the porosity decrease.

A new approach to time-load-deformation-stress hypersurface of rocks to stability analysis of underground openings

The most important developments in rock engineering are about time-dependent deformation behavior of rocks under different loads. Many studies have been done for the purpose of identifying mathematically time-load-deformation (TLD) characteristics of the rocks. These studies have made an important contribution to the research on the stability of constructions built in rock masses, and rock material is the main part of the rock mass in which the engineering constructions. When considered from this point of view, the time-dependent deformation behavior of the rocks under different loads is important to determine unstable conditions of the rock constructions in the long term. Researches in rock masses use surfaces based on TLD data. On the other hand, the strength of the rock is also part of these analyzes. The new model developed in this study has four variables such as time, load, deformation, and strength. Therefore, TLD surfaces developed for time-load-deformation has been associated with another variable and three-component (TLD) surfaces eventually transformed into four-component (time-load-deformation-strength; TLDS) hypersurfaces. Hypersurfaces, which illustrate new TLDS behaviors of the rocks, developed in underground openings in different rock constructions in different areas. It is thought that the TLDS hypersurfaces will especially be contributed to the numerical modeling studies of rock construction analysis.

Rock Deformation Behavior Near Excavations Under the Influence of High Tectonic Stress in Coal Seam V-12, “Severnaya” Mine, JSC “Urgalugol”

The article is devoted to determination of roof bolt parameters in coal mine excavations when there is rather high tectonic stress. The work was complicated by the presence of considerable number of fractures in the adjacent rock of seam V-12 in “Severnaya” mine (JSC “Urgalugol”) as well as variable stress field, low roof rock strength and heterogeneity, considerable rock shift during excavations development and maintenance. The article presents the results of horizontal and vertical stress measurements in the rock mass, physical and mechanical properties, roof rock structure and fracturing. According to the results of boreholes study by means of borehole endoscope the authors fully confirmed the forecasted parameters of areas with roof rock discontinuity, the boundaries of unstable rock. The article presents the measurement results of roof rock shift during development face advance. Based on the research, recommendations on excavations development and proper support using were given under conditions of seam V-12 in “Severnaya” mine (JSC “Urgalugol”).

Simulation of rock deformation behavior

Simulation of rock deformation behavior

Effects of Acoustic Emission and Energy Evolution of Rock Specimens Under the Uniaxial Cyclic Loading and Unloading Compression

Characteristics of energy accumulation, evolution, and dissipation in uniaxial cyclic loading and unloading compression of 30 sandstone rock specimens under six different loading rates were explored. Stress–strain relations and acoustic emission characteristics of the deformation and failure of rock specimens were analyzed. The densities and rates of stored energy, elastic energy, and dissipated energy under different loading rates were confirmed, and an effective approach for the equivalent energy surface was presented. The energy evolution of rock deformation and failure were revealed. It turns out that the rock deformation behavior under uniaxial cyclic loading and unloading compression remained almost unchanged compared with that of uniaxial compression. The degree of match between reloading stress–strain curves and previous unloading curves was high, thereby demonstrating the memory function of rock masses. The intensity of acoustic emission fluctuated continually during the entire cyclic process. Emissions significantly increased as the stress exceeded the unloading level. The peak of acoustic emission increased with increasing loading stress level. Relationships between energy density and axial load indicate that the rock mass possesses a certain energy storage limitation. The energy evolution of rock masses is closely related to the axial loading stress, rather than to the axial loading rate. With increasing axial loading stress, stored energy varied most rapidly, followed by that of the elastic energy, then dissipated energy. Energy accumulation dominates prior to the axial load reaching peak strength; thereafter, energy dissipation becomes dominant. The input energy causes the irreversible initiation and extension of microcracks in the rock body. Elastic energy release leads to sudden instability of rock bodies and drives rock damage.

Experimental and Numerical Study on Stress Relaxation of Sandstones Disturbed by Dynamic Loading

Time-dependent rheological deformation of rocks affects the stability of underground stopes or constructions. It may also be altered by dynamic disturbances, such as rock blasting. To study such effects, a new stress relaxation-disturbance testing machine was invented, capable of loading conditions for stress relaxation and dynamic disturbance. Effects of testing machine stiffness on rock deformation behavior were examined to confirm that rocks had undergone stress relaxation. Stress relaxation tests on specimens under uniaxial compression were carried out over 6 or more days. Under single-stage stress relaxation, axial stress relaxed within 5–7 days, stabilizing at constant strain. During two-stage stress relaxation, larger stress decay was observed under the higher strain level. A dynamic disturbance from a pendulum hammer was applied to specimens under stress relaxation to evaluate their response. In these tests, stress decline and strain increase were related to residual strain induced by the dynamic disturbance. The strain variation in specimens was found to be within 1.5 % of values before the disturbance. Finally, a damage-based constitutive model for rocks subjected to stress relaxation and dynamic disturbance is proposed. It reproduces the stress relaxation behavior of rock observed in our experiments. The model was used to quantify stress relaxation of rocks and the effects of dynamic disturbance on this process. The larger stress decay of rocks under higher strain is likely related to damage in the rock. Clearly, increases in strain and decreases in stress induced by dynamic loading, coupled with rock damage, are over-estimated in our numerical simulations.