Novel damage constitutive models and new quantitative identification method for stress thresholds of rocks under uniaxial compression

Four key stress thresholds exist in the compression process of rocks,i.e.,crack closure stress(σ_(cc)),crack initiation stress(σ_(ci)),crack damage stress(σ_(cd))and compressive strength(σ_(c)).The quantitative identifications of the first three stress thresholds are of great significance for characterizing the microcrack growth and damage evolution of rocks under compression.In this paper,a new method based on damage constitutive model is proposed to quantitatively measure the stress thresholds of rocks.Firstly,two different damage constitutive models were constructed based on acoustic emission(AE)counts and Weibull distribution function considering the compaction stages of the rock and the bearing capacity of the damage element.Then,the accumulative AE counts method(ACLM),AE count rate method(CRM)and constitutive model method(CMM)were introduced to determine the stress thresholds of rocks.Finally,the stress thresholds of 9 different rocks were identified by ACLM,CRM,and CMM.The results show that the theoretical stress−strain curves obtained from the two damage constitutive models are in good agreement with that of the experimental data,and the differences between the two damage constitutive models mainly come from the evolutionary differences of the damage variables.The results of the stress thresholds identified by the CMM are in good agreement with those identified by the AE methods,i.e.,ACLM and CRM.Therefore,the proposed CMM can be used to determine the stress thresholds of rocks.

Parameter calibration of the tensile-shear interactive damage constitutive model for sandstone failure

The tensile-shear interactive damage(TSID)model is a novel and powerful constitutive model for rock-like materials.This study proposes a methodology to calibrate the TSID model parameters to simulate sandstone.The basic parameters of sandstone are determined through a series of static and dynamic tests,including uniaxial compression,Brazilian disc,triaxial compression under varying confining pressures,hydrostatic compression,and dynamic compression and tensile tests with a split Hopkinson pressure bar.Based on the sandstone test results from this study and previous research,a step-by-step procedure for parameter calibration is outlined,which accounts for the categories of the strength surface,equation of state(EOS),strain rate effect,and damage.The calibrated parameters are verified through numerical tests that correspond to the experimental loading conditions.Consistency between numerical results and experimental data indicates the precision and reliability of the calibrated parameters.The methodology presented in this study is scientifically sound,straightforward,and essential for improving the TSID model.Furthermore,it has the potential to contribute to other rock constitutive models,particularly new user-defined models.

Predicting the electromechanical properties of small caliber projectile impact igniter using PZT dynamic damage constitutive model considering crack propagation

Block piezoelectric ceramics(PZTs)are often used in impact igniters to provide activation energy for electric initiators.Under the action of strong impact stress,PZTs release electric energy accompanied by crack initiation,propagation and crushing.At present,the electrical output performance of PZTs in projectile is usually calculated by quasi-static piezoelectric equation without considering the dynamic effect caused by strong impact and the influence of crack propagation on material properties.So the ignition parameters are always not accurately predicted.To tackle this,a PZT dynamic damage constitutive model considering crack propagation is established based on the dynamic impact test and the crack propagation theory of brittle materials.The model is then embedded into the ABAQUS subroutine and used to simulate the electromechanical response of the impact igniter during the impact of a small caliber projectile on the target.Meanwhile,the experiments of projectile with impact igniter impact on the target are carried out.The comparison between experimental and numerical simulation results show that the established dynamic damage model can effectively predict the dynamic electromechanical response of PZTs in the missile service environment.

A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression

To describe the deformation and strength characteristics of the corroded rock-like specimens containing a single crack under uniaxial compression,a damage constitutive model combining hydro-chemical damage with coupling damage of micro-flaws and macro-cracks is proposed.Firstly,based on phenomenological theory,the damage variable of the rock-like specimens subjected to water environment erosion and chemical corrosion is obtained.Secondly,a coupled damage variable for cracked rock-like specimens 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 a macro single crack.Then,considering the residual strength characteristics of the rock-like materials,the damage variable is modified by introducing the correction coefficient,and the damage constitutive model of the corroded rock-like specimens with a single crack under uniaxial compression is established.The model is verified by comparing the experimental stress−strain curves,and the results are in good agreement with those provided in the literature.Finally,the correction coefficient of the damage variable proposed in this paper is discussed.The damage constitutive model developed in this paper provides an effective method to describe the stress−strain relationship and residual strength characteristics of the corroded rock-like specimens with a single crack under uniaxial compression.

Acoustic emission activity in directly tensile test on marble specimens and its tensile damage constitutive model

For understanding acoustic emission （AE） activity and accumulation of micro-damage inside rock under pure tensile state, the AE signals has been monitored on the test of directly tension on two kinds of marble specimens. A tensile constitutive model was proposed with the damage factor calculated by AE energy rate. The tensile strength of marble was discrete obviously and was sensitive to the inside microdefects and grain composition. With increasing of loading, the tensile stress-strain curve obviously showed nonlinear with the tensile tangent modulus decreasing. In repeated loading cycle, the tensile elastic modulus was less than that in the previous loading cycle because of the generation of micro damage during the prior loading. It means the linear weakening occurring in the specimens. The AE activity was corresponding with occurrence of nonlinear deformation. In the initial loading stage which only elastic deformation happened on the specimens, there were few AE events occurred; while when the nonlinear deformation happened with increasing of loading, lots of AE events were generated. The quantity and energy of AE events were proportionally related to the variation of tensile tangent modulus. The Kaiser effect of AE activity could be clearly observed in tensile cycle loading. Based on the theory of damage mechanics, the damage factor was defined by AE energy rate and the tensile damage constitutive model was proposed which only needed two property constants. The theoretical stress-strain curve was well fitted with the curve plotted with tested datum and the two property constants were easily gotten by the laboratory testing.

An elasto-plastic and viscoplastic damage constitutive model for dilatancy and fracturing behavior of soft rock squeezing deformation

Soft rock squeezing deformation mainly consists of pre-peak damage-dilatancy and post-peak fracture-bulking at the excavation unloading instant,and creep-dilatancy caused by time-dependent damage and fracturing.Based on the classic elastoplastic and Perzyna over-stress viscoplastic theories,as well as triaxial unloading confining pressure test and triaxial unloading creep test results,an elastoplastic and viscoplastic damage constitutive model is established for the short-and long-term dilatancy and fracturing behavior of soft rock squeezing deformation.Firstly,the criteria for each deformation and failure stage are expressed as a linear function of confining pressure.Secondly,the total damage evolution equation considering time-dependent damage is proposed,including the initial damage produced at the excavation instant,in which the damage variable increases exponentially with the lateral strain,and creep damage.Thirdly,a transient five-stages elasto-plastic constitutive equation for the short-term deformation after excavation that comprised of elasticity,pre-peak damage-dilatancy,post-peak brittle-drop,linear strain-softening,and residual perfectly-plastic regimes is developed based on incremental elasto-plastic theory and the nonassociated flow rule.Fourthly,regarding the timedependent properties of soft rock,based on the Perzyna viscoplastic over-stress theory,a viscoplastic damage model is set up to capture creep damage and dilatancy behavior.Viscoplastic strain is produced when the stress exceeds the initial static yield surface fs;the distance between the static yield surface fs and the dynamic yield surface fd determines the viscoplastic strain rate.Finally,the established constitutive model is numerically implemented and field applied to the-848 m belt conveyer haulage roadway of Huainan Panyidong Coal Mine.Laboratory test results and in-situ monitoring results validate the rationality of the established constitutive model.The presented model takes both the transient and time-dependent damage and fracturing into consideration.

Coupled elasto-plasticity damage constitutive models for concrete

The paper is to design and construct a coupled elasto-plasticity damage constitutive model for concrete.Based on the energy dissipation principle,the Hsieh-Ting-Chen four-parameter yield function is used.The model can reflect different strength characteristics of concrete in tension and compression,and reduce the limitation and lacuna of the traditional damage constitutive models for concrete.Furthermore,numerical test for concrete stress-strain relation under uniaxial tension and compression is given.Moreover,the damage process of concrete gravity dam is calculated and analyzed in seismic load.Compared with other damage constitutive models,the proposed model contains only one unknown parameter and the other parameters can be found in the Hsieh-Ting-Chen four-parameter yield function.The same damage evolution law,which is used for tension and compression,is good for determining stress-strain constitutive and damage characteristics in complex stress state.This coupled damage constitutive models can be applied in analyzing damage of concrete gravity dam and arch dam.

STRUCTURAL DAMAGE MODEL OF UNSATURATED EXPANSIVE SOIL AND ITS APPLICATION IN MULTI-FIELD COUPLE ANALYSIS ON EXPANSIVE SOIL SLOPE

Focused on the sensitivity to climate change and the special mechanical characteristics of undisturbed expansive soil, an elasto-plastic damage constitutive model was proposed based on the mechanics of unsaturated soil and the mechanics of damage. Undisturbed expansive soil was considered as a compound of non-damaged part and damaged part. The behavior of the non-damaged part was described using non-linear constitutive model of unsaturated soil. The property of the damaged part was described using a damage evolution equation and two yield surfaces, i.e., loading yield （LY） and shear yield （SY）. Furthermore, a consolidation model for unsaturated undisturbed expansive soil was established and a FEM program named UESEPDC was designed. Numerical analysis on solid-liquid-gas tri-phases and multi-field couple problem was conducted for four stages and fields of stress, displacement, pore water pressure, pore air pressure, water content, suction, and the damage region as well as plastic region in an expansive soil slope were obtained.

Numerical simulations on cutting of frozen soil using HJC Model

Numerical simulation is known as an effective method for mechanical properties during frozen soil excavation.In order to reveal the development of cutting force,effective stress and cutting fragments in frozen silt during the cutting process,we introduce an explicit finite element program LS-DYNA to establish a two-dimensional numerical model of the frozen soil cut.We also use the Holmquist-Johnson-Cook(HJC)damage constitutive model for simulating the variation of soil mechanical properties according to the strong dependence between the cutting tool and frozen silt during the process with different cutting depths,angles and velocities.Meanwhile,a series of experimental results are acquired of frozen silt cutting to prove the application of the HJC model during simulation of cutting force variations.The result shows that the cutting force and fragment size are strongly influenced by cutting depths and cutting velocities increased,and the maximum effective stress at points where the tool contacts frozen soil during the cutting process.In addition,when the cutting angle is 52°,the cutting force is the smallest,and the cutting angle is optimum.Thus,the prediction of frozen soil mechanical properties on the cutting process by this model is conducive to selecting machinery equipment in the field.

Numerical simulations on rock damage and fragmentation by blasting

a damage constitutive model comprising two dynamite sticks is established and handled with the transient dynamics finite element computer program PRONTO-3D to study rock damage and fragmentation during blasting. Simulation tests find that tensile stress by detonation gives rise to tensile bulk strain and consequently damage in the material. Maximum bulk strain is observed in simultaneous detonations of the two dynamite sticks. It is demonstrated that the proposed method is applicable to studying the process of rock damage by blasting as well as its affecting factors.

Numerical simulation of dynamic fracture properties of rocks under different static stress conditions

When underground cavities are subjected to explosive stress waves,a uniquely damaged zone may appear due to the combined effect of dynamic loading and static pre-load stress.In this study,a rate-dependent two-dimensional rock dynamic constitutive model was established to investigate the dynamic fractures of rocks under different static stress conditions.The effects of the loading rate and peak amplitude of the blasting wave under different confining pressures and the vertical compressive coefficient(K_(0))were considered.The numerical simulated results reproduced the initiation and further propagation of primary radial crack fractures,which were in agreement with the experimental results.The dynamic loading rate,peak amplitude,static vertical compressive coefficient(K_(0))and confining pressure affected the evolution of fractures around the borehole.The heterogeneity parameter(m)plays an important role in the evolution of fractures around the borehole.The crack propagation path became more discontinuous and rougher in a smallerheterogeneity parameter case.

Damage evolution and dynamic response of cement asphalt mortar layer of slab track under vehicle dynamic load

The damage evolution and dynamic performance of a cement asphalt(CA)mortar layer of slab track subjected to vehicle dynamic load is investigated in this paper.Initially,a statistical damage constitutive model for the CA mortar layer is developed using continuous damage mechanics and probability theory.In this model,the strength of the CA mortar elements is treated as a random variable,which follows the Weibull distribution.The inclusion of strain rate dependence affords considering its influence on the damage development and the transition between viscosity and elasticity.Comparisons with experimental data support the reliability of the model.A three-dimensional finite element(FE)model of a slab track is then created with the commercial software ABAQUS,where the devised model for the CA mortar is implemented as a user-defined material subroutine.Finally,a vertical vehicle model is coupled with the FE model of the slab track,through the wheel-rail contact forces,based on the nonlinear Hertzian contact theory.The evolution of the damage and of the dynamic performance of the CA mortar layer with various initial damage is investigated under the train and track interaction.The analysis indicates that the proposed model is capable of predicting the damage evolution of the CA mortar layer exposed to vehicle dynamic load.The dynamic compressive strain,the strain rate,and the induced damage increase significantly with an increase in the initial damage,whereas the dynamic compressive stress exhibits a sharp decrease with the increasing initial damage.Also,it is found that the strain rate dependence significantly influences the damage evolution and the dynamic behavior of the CA mortar layer.

APPLICATION AND THEORETICAL ANALYSIS OF C/SiC COMPOSITES BASED ON CONTINUUM DAMAGE MECHANICS

Based on the thermodynamic theory, an orthotropic damage constitutive model was developed to describe the nonlinear mechanical behavior of C/SiC composites. The different nonlinear kinematic and isotropic hardening functions were adopted to describe accurately the damage evolution processes. The damage variables were defined with the damaged modulus and the initial undamaged modulus on energy equivalence principle. The initial orthotropy and damage coupling were presented in the damage yield function. Tensile and in-plane shear loading and unloading tests were performed, and a good agreement between the model and the experimental results was achieved.

Research on the effects of heating and cooling processes on the mechanical properties of yellow rust granite

Geological hazards caused by high-temperature rocks cooling down after encountering water are closely related to underground mining and tunneling projects.To fully understand the impact of temperature changes on the mechanical properties of rocks,yellow rust granite samples were subjected to heating-natural cooling and heating-water cooling cycles to experimentally study the effects of these processes on the mechanical properties of the samples.The mechanism of the heating-cooling process on the macromechanical properties of the rock was discussed.Based on the Drucker-Prager criterion and Weibull distribution function,a damage variable correction factor was introduced to reflect the post-peak strain softening characteristics,and a thermo-mechanical coupled damage constitutive model of the granite was established.The results showed that in the natural cooling mode,the mechanical properties deteriorate significantly when the temperature exceeded 600C,and the failure mode changed from brittle failure to ductile failure.In the water cooling mode,the peak strength and deformation modulus increased at temperatures below 400C with an increase in the cycle number,while at 600C,the peak strength and elastic modulus notably decreased.The peak strain increased with the increase of the cycle number and temperature at all temperatures,and the failure mode of the granite tended to change from tensile failure mode to shear failure mode.The experimental results were used to validate the damage constitutive model.The shape parameter r and scale parameter S in the Weibull distribution function of the model were used as indicators to reflect the brittleness degree and peak strength.This study helps to understand the behavior of rocks in hightemperature environments,in order to prevent and mitigate potential geological hazards.