Theoretical analysis of characteristics of acoustic emission in rock failure based on statistical damage mechanics

Based on statistical damage mechanics,the constitutive model of a rock underthree-dimensional stress was established by the law that the statistical strength of rockmicro-element obeys Weibull distribution.The acoustic emission (AE) evolution model ofrock failure was put forward according to the view that rock damage and AE were consistent.Moreover,in the failure process of rock under three-dimensional stress,the change inrelationship between stress condition parameter and the characteristic parameters of AE,such as the event number and its change rate,were studied.Also,the rock AE characteristicunder uniaxial compression was analyzed in theory and verified with examples.Theresults indicate that the cumulative event number and change rate of AE in rock failure aredetermined by stress state parameter F.Along with the gradual increase of F,first the cumulativeevent number increases gradually,then rapidly,and then slowly after the stresspeak.The form of change rate of an event by increasing F is consistent with the distributionform of rock micro-element strength.The model explained the phenomenon that a relativelyquiet period of AE appears before rock rupture that is observed by many researchersin experiments.Verification examples indicate that the AE evolution model is consistentwith the test results,so the model is reasonable and correct.

A thermo-mechanical damage constitutive model for deep rock considering brittleness-ductility transition characteristics

This paper developed a statistical damage constitutive model for deep rock by considering the effects of external load and thermal treatment temperature based on the distortion energy.The model parameters were determined through the extremum features of stress−strain curve.Subsequently,the model predictions were compared with experimental results of marble samples.It is found that when the treatment temperature rises,the coupling damage evolution curve shows an S-shape and the slope of ascending branch gradually decreases during the coupling damage evolution process.At a constant temperature,confining pressure can suppress the expansion of micro-fractures.As the confining pressure increases the rock exhibits ductility characteristics,and the shape of coupling damage curve changes from an S-shape into a quasi-parabolic shape.This model can well characterize the influence of high temperature on the mechanical properties of deep rock and its brittleness-ductility transition characteristics under confining pressure.Also,it is suitable for sandstone and granite,especially in predicting the pre-peak stage and peak stress of stress−strain curve under the coupling action of confining pressure and high temperature.The relevant results can provide a reference for further research on the constitutive relationship of rock-like materials and their engineering applications.

A Modified Model for Soil–Structure Interface Considering Random Damage of Mesoscopic Contact Elements

The interaction between soil and marine structures like submarine pipeline/pipe pile/suction caisson is a complicated geotechnical mechanism process.In this study,the interface is discretized into multiple mesoscopic contact elements that are damaged randomly throughout the shearing process due to the natural heterogeneity.The evolution equation of damage variable is developed based on the Weibull function,which is able to cover a rather wide range of distribution shapes by only two parameters,making it applicable for varying scenarios.Accordingly,a statistical damage model is established by incorporating Mohr–Coulomb strength criterion,in which the interfacial residual strength is considered whereby the strain softening behavior can be described.A concept of“semi-softening”characteristic point on shear stress–displacement curve is proposed for effectively modeling the evolution of strain softening.Finally,a series of ring shear tests of the interfaces between fine sea sand and smooth/rough steel surfaces are conducted.The predicted results using the proposed model are compared with experimental data of this study as well as some results from existing literature,indicating that the model has a good performance in modeling the progressive failure and strain softening behavior for various types of soil–structure interfaces.

A damage-based constitutive model for rock under impacting load

Using the Splitting Hopkinson Pressure Bar （SHPB） experimental system, investigations were made into the dynamic mechanical performances of underground soft rocks. The experiments proved that the measured stress-strain curves display the characteristics of plastic deformation. By making use of a revised overstress constitutive formula for the stress model and by taking into account that the strain rate and strain are a function of I - E（t）/Eo, a revised overstress constitutive formula for the stress model was simplified by applying dimensional analysis and consequently, a simplified overstress formula was obtained for the stress model. Then, by taking into consideration the effects of damage under a dynamic load on the dynamic loading strength of the rock, the continuous damage theory and the statistical strength theory were introduced into the development of the simplified overstress constitutive formula for the stress model. Hence, a damage-based constitutive formula for an overstress model, which can be appropriately applied to the analysis of full dynamic stress-strain curves, was developed. By using the simplified damage-based constitutive formula for an overstress model, the actually measured curves are fitted, indicating that the fitting curves and those actually measured are in good agreement.

Effect of volume changes on complete deformation behavior of rocks

For the purpose of describing the deformation characteristics of rocks,the effect of volume changes on mechanical properties of rocks should be taken into account with relation to the development of constitutive model.Firstly,rocks are divided into three parts,i.e.,voids,a damaged part and an undamaged part in the course of loading.The void ratio was applied to describing the changes of voids or pores during the deformation process.Then,using statistical damage theory,a constitutive model was developed for rocks to describe their strain softening and hardening on the basis of investigating the relationship between the net stress and apparent stress,in which the influence of volume changes on rock behavior was correctly taken into account,such as the initial phase of compaction and the latter stage of dilation.Thirdly,a method of determining model parameters was also presented.Finally,this model was used to compare the theoretical results with those observed from experiments under conventional triaxial loading conditions.

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.