Strain Equivalence Hypothesis Research Articles

Study on damage evolution and constitutive model of sandstone under the coupled effects of wetting-drying cycles and cyclic loading

A constitutive model for damage is proposed to describe the deformation and strength characteristics of sandstone under the coupled effects of wetting-drying cycles and cyclic loading. First, the microparameters of sandstone were calibrated by wetting-drying cycles and uniaxial compression tests. Subsequently, a discrete element model of the specimen was established by numerical simulation software (PFC2D), and a cyclic loading test was performed to obtain relevant test data. Second, assuming the microdamage of the sample is described by the Weibull distribution, the macrodamage can be described by a mechanical model. Based on the Lemaitre strain equivalence hypothesis, the coupled damage variable of the specimens was derived. Finally, the constitutive model of damage of sandstone under the coupled effects of wetting-drying cycles and cyclic loading was derived from the statistical mechanics theory of damage. In addition, the damage evolution process of sandstone under the coupled effects of wetting-drying cycles and cyclic loading was validated by an analysis of the microscopic force field and calculations of the damage variable. Compared with the existing models, the constitutive model proposed in this paper can better reflect the stress-strain relationship and damage evolution of sandstone under the coupled effects of wetting-drying cycles and cyclic loading.

Mechanical property deterioration characteristics and a new constitutive model for rocks subjected to freeze-thaw weathering process

The recurrence of freeze-thaw processes induced by day-night and seasonal temperature changes is one of the most important reasons for damage and instability of rock engineering structures in cold regions. The study of the constitutive relationship and the damage degradation of rocks subjected to freeze-thaw weathering process is therefore of critical scientific importance to solving the stability problem of rock excavations in these regions. In this work, the stress-strain relationships of rocks subjected to different number of freeze-thaw weathering cycles were investigated in details. Experimental results show that as the number of freeze-thaw cycles increases, the compaction stage of the stress-strain curve becomes longer with more pronounced nonlinear features, while the uniaxial compressive strength, full compaction stress, tangent deformation modulus and initial deformation modulus all decrease, but the peak strain and full compaction strain all increase. A new piecewise constitutive model based on the characteristics of compaction and post-compaction stages of the stress-strain curve was proposed using a statistical compaction model in combination with the conventional statistical damage mechanics model with the strain equivalence hypothesis. Compared with the reference model, the proposed constitutive model has been demonstrated to be much more effective in describing the stress-strain behaviour of rocks having freeze-thaw damages, particularly when the number of freeze-thaw weathering cycles is significant. For all the experimental cases presented in this work, the coefficients of determination, R2, based on the proposed model are always greater than 0.93, while those of the reference model never exceed 0.85. In addition to, the model parameters have been shown to have clear physical meanings closely related to the characteristics of the measured stress-strain curve.

Finite Element Analysis of Composite Matrix Material with Micro-damage Healing Ability

A novel constitutive model for modelling of polymer composite matrix material is proposed. Investigated material is an advanced ethylene/methacrylic acid (E/MAA) copolymer, DuPont™ Surlyn® 8940 thermoplastic resin, which exhibits intrinsic self-healing ability. The model incorporates damage evolution and healing model, and the von Mises linear isotropic hardening plasticity model and is validated with static tensile and two-cycle tensile tests on pure Surlyn® 8940 specimens. The concept of nominal and healing configurations is used in the development and numerical implementation of the model, which is additionally streamlined by the application of the strain equivalence hypothesis. Developed constitutive model enables accurate prediction of Surlyn® 8940 behaviour under tensile loading and precise prediction of accumulated plastic strain.

A Modified Model for Predicting the Strength of Drying-Wetting Cycled Sandstone Based on the P-Wave Velocity

The drying-wetting cycles caused by operation of the Three Gorges Reservoir have considerable effect on the deterioration of reservoir bank rock mass, and the degradation of reservoir rock mass by the drying-wetting cycle is becoming obvious and serious along with the periodic operation. At present, the strength of the rock prediction research mainly focuses on the uniaxial strength, and few studies consider the drying-wetting effect and confining pressure. Therefore, in this paper, typical sandstone from a reservoir bank in the Three Gorges Reservoir area is taken as the research object, while the drying-wetting cycle test, wave velocity test and strength test are carried out for the research on the strength prediction of sandstone under the action of the drying-wetting cycle. The results show that the ultrasonic wave velocity Vp of the sandstone has an exponential function relation with the drying-wetting cycle number n, and the initial stage of drying-wetting cycles has the most significant influence on the wave velocity. Under different confining pressures, the compressive strength of sandstone decreases linearly with the increase of the drying-wetting cycle numbers, and the plastic deformation increases gradually. The damage variable of the sandstone has a power function relation with the increase of drying-wetting cycle numbers. A traditional strength prediction model based on P-wave velocity was established combined with the damage theory and Lemaitre strain equivalence hypothesis; in view of the defects of the traditional strength prediction model, a modified model considering both the drying-wetting cycle number and confining pressures was proposed, where the calculated results of the modified model are closer to the test strength value, and the prediction error is obviously decreased. This indicated that the modified model considering the drying-wetting cycle number and confining pressure is reasonable and feasible.

Damage constitutive model of stirrup-confined recycled aggregate concrete after freezing and thawing cycles

The inferior quality of recycled coarse aggregates (RA) relative to natural coarse aggregates (NA) is usually considered as unfavorable for the freeze-thaw durability of concrete. In order to study the uniaxial compressive behavior and stress-strain relationship of stirrup-confined recycled aggregate concrete (RAC) after exposure to freeze-thaw cycles (FTCs), 48 short columns incorporating different levels of RA (γ% ;i.e., 0, 30%, 70% and 100%) were fabricated and subjected to different numbers of FTCs (N; i.e., 0, 100, 150 and 200), finally these specimens were submitted to uniaxial compression tests. The effect of RA substition and FTCs on the main mechanical parameters, such as compressive strength, peak strain and ductility coefficient were discussed. A uniaxial compression damage constitutive model based on the strain equivalence hypothesis and modified Loland damage theory was established, and the evolution rule of damage variables were also studied. It was shown that the concrete with RA exhibited good freezing resistance, but the peak strain of RAC was generally larger than that of NAC, and the ductility coefficient of RAC was less than that of NAC. Compared with the experimental data, the proposed damage constitutive model was shown to be applicable to confined RAC after different numbers of FTCs. For specimens with different levels of RA, the evolution law of damage variable as increasing of strain were similar. The growth rate of freezing-thawing damage variable increased as the increment of N when the RA replacement was less than 30%, but decreased when the RA replacement reached to 70% and 100%.

Analysis of Three‐Dimensional Damage Constitutive Model of Frozen Sand Based on the Influence of Intermediate Principal Stress and Temperature

To study the mechanical properties of frozen soil, it is necessary to understand the damage characteristics of frozen soil. Four types of three‐dimensional indoor tests of frozen sand were carried out at −5°C, −10°C, and −15°C to study the mechanical damage properties. These include different stress path tests with the principal stress coefficients of 0, 0.25, 0.5, and 0.75 while analyzing the entire failure process. First, the three‐dimensional compression test of frozen sand was studied to analyze the influence of temperature and intermediate principal stress coefficient on the large principal stress of frozen soil. The damage cost of frozen sand under the influence of different temperatures and intermediate principal stress coefficients was also established. Second, using the characteristics of discreteness and randomness of the distribution of the microelements inside the frozen soil and assuming that the failure of the microelement of the frozen soil obeys the Weibull distribution, the Drucker–Prager strength criterion was used as the statistical distribution variable of the microelement of the frozen soil based on the strain equivalence hypothesis, statistical theory, and continuous damage mechanics. This allows for a constitutive model of frozen sand damage under the three‐dimensional stress state to be established. Finally, the model parameter values through low‐temperature three‐dimensional test data were able to be determined. This model allows for the physical meaning of Weibull distribution parameters F0 and m to be analyzed, and the distribution parameters with temperature and intermediate principal stress coefficient can be modified to obtain a modified frozen sand damage constitutive model. The results show that the modified damage constitutive model can simulate the entire process curve of the large principal stress‐strain of frozen sand. It shows that the large principal stress of frozen sand increases with the increase of temperature and intermediate principal stress coefficient. Concurrently, the frozen sand damage constitutive model proposed in this paper can describe the deformation behavior of frozen soil under different temperature and stress paths and can be adapted to various other sediment types.

Mining-induced static and dynamic loading rate effect on rock damage and acoustic emission characteristic under uniaxial compression

To further understand rock damage mechanisms under loading, evaluate coal burst danger and ensure stopping safety during coal mining, uniaxial compression tests of rock samples at different mining-induced loading rates were carried out. A systematical analysis has been conducted on strain rate effect on rock mechanical properties, AE parameters response and damage evolution law. The results show that along with the increase of mining-induced loading rate, an increase of peak strength and elastic modulus of rock together with a decrease of peak strain and dynamic failure duration in post-peak period are shown. Several acoustic characteristics are found decreasing in power function when loading rate increases such as AE hits, counts and events, but an obvious increase of AE energy is shown. Peak frequencies of AE events are mostly between 95 ∼ 125 kHz and 270 ∼ 310 kHz. A well-defined correspondence between AE count curve and rock stress-strain curve is presented. Rock damage variable was derived based on accumulative AE count, and three stages of rock damage evolution at different loading rates can be divided: initial damage, steady evolution, and accelerated development. A constitutive damage equation has been established on the basis of equivalent strain hypothesis and AE count. Calculated results can basically reflect the characteristics of rock stress-strain curves at different strain rates. The conclusions of this paper can provide references for the issues of coal burst control and hazard assessment.

Damage Constitutive Model Based on Energy Dissipation for Frozen Sandstone Under Triaxial Compression Revealed by X-Ray Tomography

A series of triaxial compression tests, with real-time computed tomography (CT) scanning performed in the loading process, were conducted on frozen sandstones at confining pressures of 0, 1, 2, and 3 MPa at different temperatures of −2, −6, −10, and 20 °C, respectively. The experimental results indicate that the strength of frozen sandstone increases with a decrease in temperature. The strength of frozen sandstone increases with an increase in the confining pressure at freezing temperatures. In the loading process, the evolution law of the CT value of the whole sandstone is explored, and three-dimensional reconstruction of CT images, which denote postfailure models of frozen sandstone, is also performed. According to energy dissipation theory, an isotropic damage variable is introduced. Based on the CT value of the whole sandstone, the concept of the compaction coefficient K, which describes the compaction degree, is proposed to modify the damage model obtained by Lemaitre’s strain equivalence hypothesis. The validity of the model is verified by comparing its computed results with the experimental results obtained from triaxial compression tests. The results indicated that the modified damage model can adequately predict the stress-strain relationship of the frozen sandstone.

Dynamic constitutive model of penetrating jointed rock mass based on ZTW model

According to the characteristics of stress-strain curves of soft rock with through joints under dynamic loading and the related research results of existing dynamic constitutive models of soft rock, a dynamic uniaxial compression constitutive model for soft rock with through joints is established. The model is based on Zhu-Wang-Tang model, in which damage body, joint plane closure element and shear deformation element are connected in series to simulate the static compressive mechanical properties of jointed rock mass, and Maxwell composite element is connected in series to describe the strain rate effect of jointed rock mass. First, the micro-damage model is described assuming that the integrity of the intact rock mass follows the tensile strain criterion and the statistical damage of the micro-intensity and damage satisfying the Weibull distribution; Secondly, the Mohr-Coulomb strength criterion is introduced into the strength damage variable to modify the macroscopic damage variable according to the shear failure characteristics of the through-jointed rock mass along the Plane-straight joint plane under uniaxial compressive load. Thirdly, based on the Lemaitre equivalent strain hypothesis, a coupled damage variable (tensor) considering the macroscopic and microscopic effects is established, and then the damage viscoelastic dynamic constitutive model of the jointed soft rock is established. Finally, the model is used to discuss the effects of joint cohesion, joint internal friction angle and joint dip angle on the dynamic mechanical properties of rock mass. The results show that the uniaxial compression dynamic peak strength of jointed rock mass increases with the joint cohesion and the internal friction angle of the joint, and U-shaped with the increase of the joint inclination angle, and the minimum value is obtained at 60°.

Statistical Constitutive Model of Thermal Damage for Deep Rock considering Initial Compaction Stage and Residual Strength

From the theory of damage mechanics, based on the Hoek‐Brown strength criterion and Weibull distribution law of rock microelement strength, a statistical constitutive model of rock thermal damage is established by using equivalent strain hypothesis, and the theoretical model is modified by considering the compression coefficient and residual strength correction coefficient. The rationality of the modified model is verified by experimental data. The results show that the stress‐strain curves of rock can be divided into four stages: initial compaction, stable damage propagation, damage strengthening expansion, and damage failure according to the characteristics of rock damage evolution. The peak stress of rock increases exponentially with the increase of confining pressure, and the maximum damage evolution rate decreases exponentially with the increase of confining pressure, which indicates that confining pressure delays the development of cumulative damage. The peak stress and maximum damage evolution rate of rock decrease exponentially with the increase of temperature, which accelerates the damage of rock. The initial damage of rock is thermal damage caused by temperature, and the damage value increases with the increase of temperature. The revised theoretical curve reflects the characteristics of rock compaction stage and residual strength and improves the coincidence with the experimental curve. The research results provide a reference for the establishment of thermal damage constitutive model of rock in deep engineering.

Numerical analyses of novel prefabricated structural wall panels in residential buildings based on laboratory tests in scale 1:1

The paper presents experimental and numerical investigations on novel prefabricated composite building wall panels for residential building constructions. The wall panels were composed of reinforced concrete ribbed elements with the core from the EPS foam as the thermal insulation. The wall panels in the full-scale 1:1 were subjected to vertical loads. In the first step, the experiments were analysed with simple usual static methods. Next they were analysed numerically using the finite element method based on two different constitutive continuum models for concrete. First, an elasto-plastic model with the Drucker-Prager criterion defined in compression and with the Rankine criterion defined in tension was used. Second, a coupled elasto-plastic damage formulation based on the strain equivalence hypothesis was used. In order to properly describe strain localization in concrete, both models were enhanced in a softening regime by a characteristic length of micro-structure by means of a non-local theory. A satisfactory agreement between the experiments and FE analyses was achieved. In addition, the FE results with the non-local approach were compared with the crack band model.

A damage constitutive model for intermittent jointed rocks under cyclic uniaxial compression

A damage constitutive model is proposed to describe the deformation and strength characteristics of intermittent jointed rocks under cyclic uniaxial compression. First, a coupled damage tensor for intermittent jointed rocks is derived based on the Lemaitre strain equivalence hypothesis, which combines the Weibull statistical damage model for micro-flaws and the fracture mechanics model for macro-joints. Second, a fatigue constitutive model with an internal variable (i.e., irreversible plastic strain) is proposed to reproduce the degradation behaviors in fatigue deformation and strength of rocks under cyclic loading. Finally, a damage constitutive model with a definite physical significance is constructed for the intermittent jointed rocks under cyclic uniaxial compression. Our new model comprehensively reflects the coupled damage induced by micro-flaws and macro-joints, in which the geometric parameters and the mechanical properties of intermittent joints are considered simultaneously. Moreover, this model is able to reproduce the hysteretic stress-strain curves and the cumulative fatigue plastic deformation of rock materials under cyclic loading. In addition, a compaction coefficient, which is defined as the ratio of the secant modulus to the Young's modulus, is proposed to reflect the compaction stage of rock materials during the first loading process. To validate this new model, nine cyclic uniaxial compression tests are conducted on both intact and jointed rock samples prepared with synthetic rock-like materials. A reasonable consistency is observed between the theoretical and experimental results for the cyclic stress-strain curves and the fatigue deformation modulus.

A finite deformation viscoelastic–viscoplastic constitutive model for self-healing materials

In this paper, employing the Hencky strain, viscoelastic–viscoplastic response of self-healing materials is investigated. Considering the irreversible thermodynamics and using the effective configuration in the Continuum Damage-Healing Mechanics (CDHM), a phenomenological finite strain viscoelastic–viscoplastic constitutive model is presented. Considering finite viscoelastic and viscoplastic deformations, total deformation gradient is multiplicatively decomposed into viscoelastic and viscoplastic parts. Due to mathematical advantages and physical meaning of Hencky strain, this measure of strain is employed in the constitutive model development. In this regard, defining the damage and healing variables and employing the strain equivalence hypothesis, the strain tensor is determined in the effective configuration. Satisfying the Clausius–Duhem inequality, the evolution equations are introduced for the viscoelastic and viscoplastic strains. The damage and healing variables also evolve according to two different prescribed functions. To employ the proposed model in different loading conditions, the model is discretized in the semi-implicit form. Material parameters of the model are identified employing experimental tests on asphalt mixes available in the literature. Finally, capability of the model is demonstrated comparing the model predictions in the creep-recovery and repeated creep-recovery with the experimental results available in the literature and a good agreement between predicted and test results is revealed.

Finite element analysis of dynamic progressive failure of plastic composite laminates under low velocity impact

This paper studies dynamic mechanical responses and damage mechanisms of plastic fiber-reinforced polymer matrix composite laminate under low velocity impact. First, the plastic damage model is introduced for intralaminar damage, where Puck’s failure criteria and strain based damage evolution laws for fiber and matrix are used, and the bilinear cohesive model is adopted for delamination. Second, an uncoupled numerical scheme for dealing with the intralaminar plastic deformation and damage evolution by finite element analysis (FEA) is originally proposed based on the strain equivalence hypothesis, in which the effective stresses and strains are first solved using the backward Euler algorithm and then the nominal stresses and damage variables are updated independently. Finally, the proposed algorithm is implemented using ABAQUS-VUMAT by the time stepping algorithm. For two composite specimens under transverse impact, the impact force-time curve, the impact displacement-time curve and the dissipated energy at different impact energies are studied by comparing the results using experiments and FEA. Numerical results show the plastic damage model leads to higher precision than the elastic damage model as the impact energy becomes relatively large.

Long-term performance of prestressed concrete bridges under the intertwined effects of concrete damage, static creep and traffic-induced cyclic creep

The current progress towards sustainable transportation demands for a prolonged lifespan, i.e., over 100years, for large-span bridges. To accomplish this goal, realistic prediction of the long-term performance of bridges plays an indispensable role in bridge engineering. In this study, the long-term deflection and the deflection-induced damage growth are investigated for the large-span prestressed concrete bridges carrying busy traffic flows. A unified constitutive model, taking into account the coupled effects of concrete viscoelastic behavior and concrete tensile cracking and plastic softening, is developed to estimate the bridge performance. Here the static creep of concrete is approximated by a series of Kelvin units. The elasto-plastic damage of concrete is described by the plasticity yield surfaces hinging on the flow rules and anisotropic damage laws anchored at the strain equivalence hypothesis. In addition to the static creep, the cyclic creep of concrete induced by vehicles is integrated in the nonlinear stress-strain incremental relation based on the fatigue growth of microcracks. With the aid of the 3D rate-type formulation, the proposed unified model is implemented in ABAQUS and a large-span prestressed concrete bridge carrying heavy traffic loads is analyzed. Compared to the inspection reports, the deflection history at the midspan, the deformed profile of the whole bridge and the distribution of concrete cracking are all adequately captured in the simulations. Further sensitivity investigation on bridge deflection finds that the cyclic load-induced damage accumulation process plays a non-negligible role and traffic management plans are needed for heavy trucks to mitigate the risk of excessive deflection and concrete degradation.

Investigation of isothermal and thermo-mechanical fatigue behavior of the nickel-base superalloy IN738LC using standardized and advanced test methods

The uniaxial and biaxial-planar isothermal fatigue behavior as well as the uniaxial thermo-mechanical fatigue behavior of the nickel-base superalloy IN738LC was investigated at high temperatures using standardized and advanced test technologies. Small scale specimens’ tests were carried out in order to study the specimen size effect and biaxial-planar tests under equibiaxial and shear loading to investigate the influence of the multiaxial stress state on the isothermal fatigue behavior both at 750°C. Standardized specimens were used to determine the uniaxial isothermal and thermo-mechanical fatigue behavior under in-phase and out-of-phase loading in the temperature range between 750°C and 950°C. The standard specimens’ results particularly served as reference data as well as for the verification of a recently developed lifetime prediction model for thermo-mechanical fatigue loading. The small scale specimens’ results were in good agreement with standardized specimens. The comparison of fatigue lifetimes of uniaxial and biaxial-planar tests showed that the equivalent strain hypothesis according to von Mises is applicable to correlate the fatigue life of the equibiaxial loading case within a scatter band of factor two, whereas the shear loading case was predicted conservatively. Furthermore, the recently developed lifetime prediction model correlated the fatigue lives of the isothermal and thermo-mechanical tests under uniaxial and biaxial-planar loading as well as literature data. Finally, the deformation and crack growth mechanism were studied.

Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading

Rocks in underground engineering such as coal mining and tunnel excavating applications are usually loaded and unloaded repeatedly. The relationship between the strength and deformation of rocks under cyclic loading is the foundation for design and assessment of such scenarios. A new damage constitutive model based on energy dissipation was developed to describe the behaviour of rocks under cyclic loading in this article. First, the damage variable based on energy dissipation was introduced and the damage evolution equations of two typical rock types were calculated from the results of uniaxial cyclic loading tests. Second, the concept of compaction coefficient was proposed to describe the compaction degree and being used to amend the damage constitutive model obtained by Lemaitre strain equivalence hypothesis. Finally, the damage constitutive model under cyclic loading was established using a recursive method based on the amended damage constitutive model, and the fitted results of the models were compared to experimental data. Results showed that the values of damage variables increase exponentially with strains. The amended damage constitutive model can describe the degree of compactness of rocks accurately, and the damage constitutive model under cyclic loading has reasonable error in describing the behaviour of rocks under cyclic loading.

Biaxial fatigue behavior of a powder metallurgical TRIP steel

Multiaxial fatigue behavior is an important topic in critical structural components. In the present study the biaxial-planar fatigue behavior of a powder metallurgical TRIP steel (Transformation Induced Plasticity) was studied by taking into account martensitic phase transformation and crack growth behavior. Biaxial cyclic deformation tests were carried out on a servo hydraulic biaxial tension-compression test rig using cruciform specimens. Different states of strain were studied by varying the strain ratio between the axial strain amplitudes in the range of -1 (shear loading) to 1 (equibiaxial loading). The investigated loading conditions were proportional due to fixed directions of principal strains. The studied TRIP steel exhibits martensitic phase transformation from ?-austenite via ?-martensite into ?‘- martensite which causes pronounced cyclic hardening. The ?‘-martensite formation increased with increasing plastic strain amplitude. Shear loading promoted martensite formation and caused the highest ?‘-martensite volume fractions at fatigue failure in comparison to uniaxial and other biaxial states of strain. Moreover, the fatigue lives of shear tests were higher than those of uniaxial and other biaxial tests. The von Mises equivalent strain hypothesis was found to be appropriate for uniaxial and biaxial fatigue, but too conservative for shear fatigue, according to literature for torsional fatigue. The COD strain amplitude which is based on crack opening displacement gave a better correlation of the investigated fatigue lives, especially those for shear loading. Different types of major cracks were observed on the sample surfaces after biaxial cyclic deformation by using electron monitoring in an electron beam universal system and scanning electron microscopy (SEM). Specimens with strain ratios of 1, 0.5, -0.1 and -0.5 showed mode I major cracks (perpendicular to the axis of maximum principal strain). Major cracks after shear fatigue had partially mode II orientation (tilted 45° to the loading axes) and afterwards bifurcated into two pairs of mode I cracks. Another shear test revealed a major crack of mode I orientation (parallel to the loading axes). These results are in good agreement to the literature. Micro cracks after shear fatigue were longer than those after biaxial fatigue with strain ratios of 1 and 0.5. Major and minor cracks after equibiaxial and shear loading showed crack branching and crack coalescence. The results on fatigue crack behavior support the assumption that the period of stage I (mode II) crack propagation is much longer under shear loading than under other biaxial conditions due to absence of tensile stress normal to the planes of maximum shear strain under shear loading.

A damage constitutive model for rock mass with persistent joints considering joint shear strength

Microcracks and joints, two types of flaws that appear in a rock mass, affect both the rock mass strength and deformability. A model that can simultaneously reflect the effect of these two types of flaws on the mechanical behavior of a rock mass with persistent joints is not yet available. This study focusses on a microcracked rock mass with persistent joints and establishes a mechanical model, accounting for the anisotropy in the rock mass strength and deformability induced by the existence of the joints. Firstly, the compound damage variable from the coupling macroscopic and mesoscopic flaws is deduced based on the Lemaitre strain equivalence hypothesis. Secondly, the corresponding damage constitutive model for a jointed rock mass is set up. Thirdly, the joint shear failure criterion is incorporated into the constitutive model to extend the model. Finally, the results of the calculation examples show that the existence of the joint will reduce the strength, enlarge the deformability, and lead to anisotropy of the rock mass. A series of calculation examples and comparisons validate that the proposed model is capable of presenting the joint-induced anisotropy in rock mass strength and deformability, determining its possible failure modes, and reasonably simulating its complete stress–strain relationship.

A Damage Constitutive Model for Rock Mass with Nonpersistently Closed Joints Under Uniaxial Compression

As part of the rock mass, both the macroscopic flaws such as joints and the mesoscopic flaws such as microcracks affect the strength and the deformational behavior of rock mass. Existing models can either handle any one of them alone, and a model which can consider the co-effect of these two kinds of flaws on rock mass mechanical behavior is not yet available. This study focusses on rock mass with nonpersistently closed joints and establishes a new damage constitutive model for it. Firstly, the damage model for the intact rock which contains only the mesoscopic flaws is introduced. Second, the expression of the macroscopic damage variable (tensor) which can consider the joint geometrical and mechanical properties at the same time is obtained based on the energy principle and fracture theory. Third, the damage variable based on coupling the macroscopic and mesoscopic flaws is deduced based on Lemaitre strain equivalence hypothesis, and then the corresponding damage constitutive model for rock mass with nonpersistently closed joints under uniaxial compression is set up. Finally, the test data for the intact rock under uniaxial compression are adopted to validate the proposed model. A series of calculation examples verify that the proposed model is capable of presenting the effect of joint geometrical and mechanical properties on the rock mass mechanical behavior.