Statistical Damage Constitutive Model Research Articles

Research on the statistical damage constitutive model for composite solid propellant

The study of constitutive model of composite solid propellant is an important basis for analyzing the structural integrity of propellant grains of the solid rocket motor. From the view of microscopic, composite solid propellant is composed of a large number of solid particles with various sizes embedded in the matrix. In this paper, based on the distribution of solid particles with different sizes and the failure strength of the particle-matrix interfaces, the damage evolution was assumed to obey the Weibull distribution function and power law distribution function, and the two statistical damage constitutive models were first established. Then, the model parameters were identified and validated through the uniaxial tensile tests data of HTPB propellant. Finally, the prediction abilities of the developed two models were compared. The results show that both of the two statistical damage models can describe the stress-strain curves of HTPB propellant well.

Hydraulic Fracturing Mechanism of Rock Mass under Stress-Damage-Seepage Coupling Effect

According to the damage evolution model of rock mass under stress-seepage coupling effect, the representative element theory is employed to describe the change law of rock mesostructure. Based on the theory of elasticity and Weibull distribution, the statistical damage constitutive model of rock mass and the finite element numerical algorithm are established, by adopting the COMSOL Multiphysics numerical software and MATLAB program. Besides, the validity of the statistical damage constitutive model of rock mass is verified by the triaxial compression test. Besides, the hydraulic fracturing processes of rock mass under equal and unequal in situ stresses are numerically simulated, and the mechanical behavior of rock mass during hydraulic fracturing in complex underground environment is also studied. Under the condition of equal in situ stress, the stress distribution of surrounding rock of circular hole is annular, which is similar to the elastic stress distribution of surrounding rock. Under the condition of unequal in situ stress, the stress distribution tends to be circular with the increase of lateral pressure coefficient, and the stress distribution along the diagonal decreases. The simulation results are in good agreement with the theoretical results, which indicates that the damage mechanical model and the numerical model have correlation and certain accuracy. By analyzing the size and direction of horizontal in situ stress, the shape and extension direction of cracks are judged, which provides an important theoretical basis for water inrush prediction and engineering protection.

Compressive mechanical properties of self-expanding grouting materials with different densities

The compressive mechanical properties of self-expanding grouting materials with different densities are essential in evaluating the ultimate conditions of the repaired underground infrastructure. In this study, digital imaging correlation (DIC) and acoustic emission (AE) techniques were applied to monitor the compressive damage evolution process of self- expanding materials with different densities. It was found that the varied density exhibits great effect on the compressive response of self-expanding grouting materials, and that the length of the horizontal yield plateau decreases with the density. As the density increases to 0.399 g/cm3, the horizontal yield plateau diminishes and the materials present from plastic to brittle characteristics. Moreover, a statistical damage constitutive model of the ascending branch was developed and validated by experimental results.

Nonlinear statistical damage constitutive model of granite based on the energy dissipation ratio

The stress–strain curves and mechanical properties of Shuangjiangkou granite were obtained using five groups of conventional triaxial tests under various confining pressures using MTS815 rock test equipment. From the microscale, mesoscale, and macroscale perspectives, four types of mechanisms that contribute to energy dissipation during granite deformation were investigated. Based on the energy dissipation ratio, a new approach for estimating crack closure stress and damage stress is proposed. The energy dissipation ratio was substituted into the Weibull distribution function, and then a new nonlinear statistical damage constitutive model of granite based on the energy dissipation ratio was constructed after Biot’s theory was modified per the Lemaitre strain equivalence principle. By comparing experimental data with theoretical values estimated by the model, the model’s rationality and correctness were confirmed.

Study on compressive mechanical properties of recycled aggregate concrete with silica fume at different strain rates

Treating waste concrete to produce recycled aggregate concrete (RAC) is an important measure to save resources and protect environment. Studies have shown that adding silica fume to RAC can improve the mechanical properties of RAC. Based on the experiment, the uniaxial compressive mechanical properties of RAC specimens with silica fume content (S) for 0%, 5% and 9% at strain rates of 10−5/s, 10−4/s, 10−3/s and 10−2/s were studied. From the mesoscopic point of view, the damage and failure mechanisms of RAC were analyzed based on the statistical damage constitutive model. The results showed that with the increase of strain rate, the peak stress, elastic modulus and brittleness of RAC were on the rise. In addition, the peak stress and elastic modulus of RAC with high silica fume content were higher than those of RAC with low silica fume content. Considering two damage evolution modes of mesoscopic fracture and yield, the variation characteristics of mesoscopic damage parameters were obtained. From the perspective of effective stress, the whole process of damage evolution and accumulation induced catastrophe of concrete was expounded. The critical state and peak nominal stress state were distinguished, and it is considered that the critical state should be the limit state of the stress process of concrete material. These results were evaluated and analyzed by acoustic emission (AE), scanning electron microscope (SEM) and nuclear magnetic resonance (NMR) tests.

Mechanical properties, crack evolution and damage characteristics of prefabricated fractured cemented paste backfill under uniaxial compression

The existence of joints and fractures will inevitably affect the mechanical behavior and crack propagation law of the backfill, and then degrade the stability and accelerate the damage evolution of the backfill. Thus, in this study, the uniaxial compressive strength (UCS) tests and acoustic emission (AE) monitoring were carried out for prefabricated fractured (PF) cemented paste backfill (CPB or FCPB) with different dip angles (0, 30, 45, 60, 90°) respectively. The results showed that: 1) The existence of PF collapsed the mechanical properties of the backfill. The UCS and elastic modulus of FCPB samples first decreased and then increased with the increase of PF dip angle, and the deterioration of the 30° FCPB sample was the most serious scenario. 2) Apart from the stress–strain curve of the traditional CPB sample, FCPB sample (except 90°) was a bimodal curve. The self-strengthening characteristics caused by the compression closure of PF led to the continuous upward trend of stress after reaching the first peak and then the second peak. 3) The crack of the FCPB sample usually originated at the tip of PF, and the far-field crack was easy to expand to PF. The PF was conducive to crack development propagation, resulting in macro failure. The failure modes of CPB and FCPB samples were shear failures and tensile failure respectively (shear crack and tensile crack were significantly affected by PF dip angle). 4) The AE ringing count rate and energy rate of FCPB samples (except 90°) usually surged twice, which corresponded to the vicinity of the two peak points of the stress–strain curve of FCPB samples. 5) A piecewise statistical damage constitutive model considering initial damage was established, which could fully reflect the bimodal stress–strain curve characteristics of FCPB samples. The damage evolution law of the FCPB samples obtained from this was significantly affected by PF dip angle. The damage curves of CPB and FCPB (60, 90°) increased approximately in S-shape, while the damage curves of other FCPB increased continuously in the first peak stage and then entered the stable development- accelerated damage-failure stage of the second peak stage. The findings of the study can serve as a theoretical foundation for analyzing the stability of backfill with geological defects such as joints and fractures.

Study on mechanical properties and statistical damage constitutive model of red sandstone after heating and water-cooling cycles

The repeated action of high temperature and water cooling will have a strong deteriorating effect on the mechanical properties of the rock, which will eventually lead to the damage and cracking of the rock. In order to study the influence of heating and water-cooling cycles on rocks, the P-wave velocity and mechanical properties of red sandstone after heating and water-cooling cycles were tested. Meanwhile, based on the Weibull distribution theory, a statistical damage constitutive model based on Mohr-Coulomb strength criterion considering the effects of heating and water-cooling cycles was established, and verified based on the results of triaxial tests. The results show that the P-wave velocity and peak intensity decrease with the temperature under the same number of cycles. The elastic modulus will decrease with the temperature and the number of cycles, indicating that the red sandstone will gradually soften and the ductility will increase under repeated high temperature and water-cooling cycles. And the model can well reflect the stress-strain curves of different high temperature and water-cooling cycles. The research results can provide analytical theories and methods for geothermal development projects.

Investigating high-temperature deformation evolution of concrete under sustained loading using DIC technology and a temperature-mechanical coupled damage constitutive model

Based on digital image correlation (DIC) technology and uniaxial compression tests, the deformation evolution characteristics of concrete were analyzed in the heating process under a sustained load and in the failure process under uniaxial compression. The effect of the sustained load on the mechanical properties of concrete at high temperatures was explored. A damage constitutive model of concrete under the combined action of high temperature and the sustained load was established. The research results show that a sustained load can effectively restrain the vertical thermal expansion of concrete and compact loose and weak zones of concrete. However, when the load level or temperature is too high, excessive lateral deformation of concrete will cause local strain concentration and cracking failure. In the failure process under uniaxial compression, both high temperature and sustained load can make the macroscopic cracks more smeared and branched. When the temperature is 200 °C and 400 °C, the sustained load has only a little enhancement effect on the high-temperature mechanical properties of concrete. When the temperature is 600 °C and 800 °C, the sustained load can significantly enhance the mechanical properties of concrete at high temperatures. However, at higher temperatures, excessive sustained loads can cause premature failure of the specimen. Based on the Weibull distribution, a statistical damage constitutive model of concrete under the combined action of sustained load and high temperature is established, which is in good agreement with the test curve. The curve of the degree of damage of concrete Dm shows that the sustained load causes the damage Dm to start earlier, the damage rate to increase, and the degree of damage at the peak stress to increase in the failure stage under uniaxial compression.

Statistical Damage Constitutive Model of Gas-Bearing Coal with Consideration to Crack Deformation

Statistical Damage Constitutive Model of Gas-Bearing Coal with Consideration to Crack Deformation

Experimental Investigation and Statistical Damage Constitutive Model on Layered Slate Under Thermal–Mechanical Condition

Experimental Investigation and Statistical Damage Constitutive Model on Layered Slate Under Thermal–Mechanical Condition

Experimental investigation of damage evolution and failure criterion on hollow cylindrical rock samples with different bore diameters

The roadway direction is often parallel to the direction of the maximum principal stress for the structure arrangement of underground roadway. To study the instability mechanism of roadway under the maximum principal stress, a series of uniaxial compression acoustic emission (AE) experiments were carried out on hollow red sandstone and granite rock samples with different bore diameters. The test results suggest that the oblique shear or X-shaped shear failure occurs in hollow rock samples, and the failure process is accompanied by a sudden jump in accumulative energy of AE signals, at the same time, the ringing count arrived at peak value. The increase in bore diameter haves contributed to the decline of ringing count and accumulative energy. A statistical damage constitutive model of Weibull distribution was established for hollow rock samples. On the basis of optimizing the damage variable, a damage constitutive model based on AE ringing count was obtained, which can better describe the damage state and stress state of rock samples. The AE accumulative energy was selected as the state variable, and the failure criterion model was finished based on the cusp catastrophe theory to estimate the rock sample failure. The judgment results show that the failure moment of rock sample is accurately included in the judgment time interval. This research can provide reference and technical support for the stability control and monitoring of underground engineering roadways.

Mechanical properties of ultra-high strength cement-based materials (UHSC) incorporating metal powders and steel fibers

In this work, the mechanical properties of ultra-high strength cement-based materials (UHSC) incorporating metal powders and steel fibers under steam curing and autoclave curing were studied, with the special attention devoted to the flexural load-deflection response and compressive stress-strain behavior. Additionally, the hydration degree, pore structure characteristics and micro interface morphology were investigated to provide a thorough insight into the enhancement mechanism of metal powders and steel fibers on UHSC. The results show that the incorporation of Fe and Cu powders could enhance the flexural performance of UHSC, including the increased flexural strength and energy absorption capacity. Under uniaxial compression, improved peak stress, secant modulus, and energy absorption capacity of UHSC could be observed after the addition of Fe powders, but this improvement was negligible after the addition of Cu powders. Moreover, the statistical damage constitutive model based on strain equivalence hypothesis and improved statistical damage theory could reasonably describe the stress-strain behavior of UHSC under uniaxial compression. Furthermore, incorporating Fe and Cu powders could ameliorate the pore structure of UHSC, in which the harmful pores was converted into less harmful pores. Micro-interface morphology demonstrated that metal powders were closely bonded with cement paste, and no cracks or micro pores could be detected around the interface.

Study on Dynamic Mechanical Properties and Failure Mechanism of Sandstones under Real-Time High Temperature

The research on dynamic mechanical properties of rocks under high temperature is the basis for safe and efficient implementation of deep coal mining and underground coal gasification engineering. In this paper, the split Hopkinson bar (SHPB) with real-time high-temperature function was adopted to systematically study dynamic mechanical properties of sandstones. The research showed that under the condition of a fixed temperature, with the increase of strain rate, the dynamic compressive strength and dynamic peak strain of sandstone increased gradually, and the variation of dynamic elastic modulus with strain rate was not obvious. With the increase of temperature, the dynamic compressive strength of sandstone increased first and then decreased, the dynamic peak strain increased gradually, and the dynamic elastic modulus decreased overall. The variation law of macroscopic failure mode and energy dissipation density with temperature was revealed, and the change mechanism was explained considering the influence of high temperature on the internal structure of sandstone. Based on the principle of component combination and the theory of micro-element strength distribution, the dynamic statistical damage constitutive model was established, and its parameters had certain physical significance. Compared with the experimental results, the established model can well describe the dynamic stress-strain relationship of sandstone under real-time high temperature.

A statistical damage constitutive model for rock based on modified Mohr–Coulomb strength criterion

A statistical damage constitutive model for rock based on modified Mohr–Coulomb strength criterion

Study on Energy Evolution and Damage Constitutive Model of Siltstone

In order to study the energy evolution characteristics and damage constitutive relationship of siltstone, the conventional triaxial compression tests of siltstone under different confining pressures are performed, and the evolution laws of input energy, elastic strain energy and dissipative energy of siltstone with axial strain and confining pressure are analyzed. According to the test results, the judgment criterion of the rock damage threshold is improved, and an improved three-shear energy yield criterion is proposed., The damage constitutive equation of siltstone is established based on the damage mechanics theory through the principle of minimum energy consumption and by considering the residual strength of rock, and lastly, the rationality of the model is verified by experimental data. The results reveal that (1) both the input energy and dissipative energy gradually increase with the increase of axial strain, and the elastic strain energy first increases and then decreases with the increase of axial strain, and reaches its maximum at the peak. (2) The input energy and dissipation energy increase exponentially with the increase of the confining pressure, and the elastic strain energy increases linearly with the increase of confining pressure. (3) According to the linear relationship between the sum of shear strain energy and hydrostatic pressure, an improved three-shear energy yield criterion is established. (4) The model curve can better describe the strain softening stage and the residual strength characteristics of siltstone. The relative standard deviation between the model results and the test results is only 4.35%, which verifies the rationality and feasibility of the statistical damage constitutive model that is established in this paper.

Statistical damage constitutive model based on self‐consistent Eshelby method for natural gas hydrate sediments

AbstractNatural gas hydrate (NGH) is widely distributed in marine sediments and continental permafrost, which is a promising energy resource. The sustainable and safe exploration and production of NGH requires fully understanding of its mechanical behaviors, which is still a challenge to our community. In this paper, a statistical damage constitutive model named SC‐SDCM is developed for NGH sediments. The NGH sediments are regarded as two phases: the matrix phase of solid mineral grains, pore fluid, and gas, and the inclusion phase of hydrate crystal. The effective elastic parameters of such two‐phase composite are estimated by self‐consistent method (SC) according to the equivalent inclusion principle of micromechanics. The mesoscopic element strength of the NGH sediments is described by the Weibull statistical distribution and the damage theory of composite materials. And then combined with the Drucker‐Prager failure criterion of microelement, the damage constitutive model of NGH sediments is established. The new SC‐SDCM is tested to be reliable and robust by triaxial experimental observations on artificial cores and naturally occurring samples under different confining pressures and hydrate saturations. The SC‐SDCM could properly describe the stiffness, peak strength, and strain softening properties of the NGH sediments. Moreover, the predictions of SC‐SDCM are closest to the experiment observations compared to several published constitutive models, especially for the near‐ and after‐damage stages with relatively high hydrate saturation.

Experimental Study on Mechanical Properties of Gas Storage Sandstone under Water Content

In order to investigate the influence of water content on the damage and degradation characteristics of Hutubi sandstone, different saturation experiments and laboratory mechanical experiments were carried out on Hutubi sandstone. The experimental results show that under uniaxial and triaxial conditions, with the increase in water content, the axial, lateral, and volume deformations gradually increase, and the deformation shows obvious dilatancy characteristics. The deviator stress and elasticity modulus of the sandstone decreased exponentially with the increasing water content. Confining pressure has a significant effect on the strength improvement of sandstone under the constant water content. Based on lognormal distribution, the damage constitutive model of sandstone which can reflect both uniaxial and triaxial condition with different water contents was proposed. The theoretical curves were compared with the experimental curves, and it was found that the theoretical curves and the experimental curves have similar changing trends. It shows the rationality of the statistical damage constitutive model.

Damage mechanism and constitutive model of surface paste disposal of a coal mine collapsed pit in a complicated environment

The surface paste disposal (SPD) method can effectively stabilize active coal mine collapsed pits. The degradation mechanism of the mechanical properties of SPD materials in complicated environments has not yet been explored. To investigate the deterioration mechanism of SPD in complicated environments, SPD specimens prepared from coal gangue and a small amount of cement and water as raw materials were tested by freezing-thawing (FT) cycle tests, wetting-drying (WD) cycle tests and freeze-thaw corrosion (FC) tests. The damage evolution law was obtained by the macro- and microscale methods. Studies have shown that the unconfined compressive strength (UCS) of SPD decreases exponentially under FT and FC cycles and decreases linearly after 5 WD cycles. FT, FC and WD all resulted in cracks and holes in SPD. Ettringite (Aft) produced by sulphate corrosion, calcium chloroaluminate hydrate (Friedel's salt) produced by chloride corrosion, magnesium silicate hydrate (M-S-H) produced by magnesium salt corrosion, and thaumasite produced by low temperatures and bicarbonate corrosion are important reasons for SPD strength deterioration. A segmented statistical damage constitutive model with the compaction point as the critical point is established. The damage constitutive model can completely describe the SPD stress-strain curve after corrosion in a complicated environment. The research results can provide guidance for the paste disposal of coal mine collapsed pits.

A Statistical Damage Constitutive Model of Anisotropic Rock: Development and Validation

The damage constitutive model is of great significance to research the stress-strain relationship and damage evolution of rock under loading in engineering. In order to investigate the effect of anisotropic characteristic on the stress-strain relationship and damage evolution, a statistical damage constitutive model of anisotropic rock under true triaxial condition was developed. In this study, the plane which existed perpendicular to the coordinate axis was extracted from representative volume element (RVE) of rock. The extracted plane was assumed to be composed of abundant mesoscopic elements whose failure strength satisfied the Weibull distribution. According to the number of failure elements on the plane in each direction under loading, the anisotropic damage variable was established based on the proposed concept of areal damage. A statistical damage constitutive model of anisotropic rock was developed by using strain equivalent hypothesis and generalized Hooke constitutive model. Subsequently, the parameters in the anisotropic damage constitutive model were determined by the method of total differential. Thus, the damage evolution of anisotropic rock under various stress conditions can be conveniently evaluated by the anisotropic damage model. The model was validated based on the tests of rocks under the stress conditions of conventional triaxial and true triaxial, respectively. Moreover, for the purpose of studying the influence of parameters on the model, sensitivity analyses of mechanical parameters and model parameters were carried out. The results of statistical damage constitutive clearly demonstrate the stress-strain and damage evolution of anisotropic rock under various stress conditions.

Statistical damage constitutive model based on the Hoek–Brown criterion

Statistical damage constitutive model based on the Hoek–Brown criterion