Stress-corrosion coupled damage localization induced by secondary phases in bio-degradable Mg alloys:phase-field modeling

In this study,a phase-field scheme that rigorously obeys conservation laws and irreversible thermodynamics is developed for modeling stress-corrosion coupled damage(SCCD).The coupling constitutive relationships of the deformation,phase-field damage,mass transfer,and electrostatic field are derived from the entropy inequality.The SCCD localization induced by secondary phases in Mg is numerically simulated using the implicit iterative algorithm of the self-defined finite elements.The quantitative evaluation of the SCCD of a C-ring is in good agreement with the experimental results.To capture the damage localization,a micro-galvanic corrosion domain is defined,and the buffering effect on charge migration is explored.Three cases are investigated to reveal the effect of localization on corrosion acceleration and provide guidance for the design for resistance to SCCD at the crystal scale.

Fluid solid coupling model based on endochronic damage for roller compacted concrete dam

According to the characteristics of thin-layer rolling and pouting construction technology and the complicated mechanical behavior of the roller compacted concrete dam （RCCD） construction interface, a constitutive model of endochronic damage was established based on the endochronic theory and damage mechanics. The proposed model abandons the traditional concept of elastic-plastic yield surface and can better reflect the real behavior of rolled control concrete. Basic equations were proposed for the fluid-solid coupling analysis, and the relationships among the corresponding key physical parameters were also put forward. One three-dimensional finite element method （FEM） program was obtained by studying the FEM type of the seepage-stress coupling intersection of the RCCD. The method was applied to an actual project, and the results show that the fluid-solid interaction influences dam deformation and dam abutment stability, which is in accordance with practice. Therefore, this model provides a new method for revealing the mechanical behavior of RCCD under the coupling field.

A 3D microseismic data-driven damage model for jointed rock mass under hydro-mechanical coupling conditions and its application

Rock mass is a fractured porous medium usually subjected to complex geostress and fluid pressure simultaneously.Moreover,the properties of rock mass change in time and space due to mining-induced fractures.Therefore,it is always challenging to accurately measure rock mass properties.In this study,a three-dimensional(3D)microseismic(MS)data-driven damage model for jointed rock mass under hydro-mechanical coupling conditions is proposed.It is a 3D finite element model that takes seepage,damage and stress field effects into account jointly.Multiple factors(i.e.joints,water and microseismicity)are used to optimize the rock mass mechanical parameters at different scales.The model is applied in Shirengou iron mine to study the damage evolution of rock mass and assess the crown pillar stability during the transition from open-pit to underground mining.It is found that the damage pattern is mostly controlled by the structure,water and rock mass parameters.The damage pattern is evidently different from the two-dimensional result and is more consistent with the field observations.This difference is caused by the MS-derived damage acting on the rock mass.MS data are responsible for gradually correcting the damage zone,changing the direction in which it expands,and promoting it to evolve close to reality.For the crown pillar,the proposed model yields a more trustworthy safety factor.In order to guarantee the stability of the pillar,it is suggested to take waterproof and reinforcement measures in areas with a high degree of damage.

Thermal-hydro-mechanical coupling damage model of brittle rock

Based on fluid mechanics, thermodynamics and damage mechanics, thermal-hydro-mechanical （THM） coupling damage model of brittle rock is established by analyzing THM coupling mechanism, where THM coupling damage variable DTHM is dominated by TH coupling damage variable DTH, TM coupling damage variable DTM and HM coupling damage variable DHM, and DTH is firstly expressed in term of dimensionless total thermal conductivity of the water Nu. Permeability test, uni-axial compression test and THM coupling test are conducted to measure the permeability, elastic modulus and THM coupling stress-strain curves of brittle rock. The tested values of THM coupling elastic modulus E＇HM are in good agreement with the predicted values of THM coupling elastic modulus ETHM, which can verify the newly established THM coupling damage model.

Experimental study of structural damage identification based on WPT and coupling NN

Too many sensors and data information in structural health monitoring system raise the problem of how to realize multi-sensor information fusion. An experiment on a three-story frame structure was conducted to obtain vibration test data in 36damage cases. A coupling neural network (NN) based on multi-sensor information fusion is proposed to achieve identification of damage occurrence, damage localization and damage quantification, respectively. First, wavelet packet transform (WPT) is used to extract features of vibration test data from structure with different damage extent. Then, data fusion is conducted by assembling feature vectors of different type sensors. Finally, three sets of coupling NN are constructed to implement decision fusion and damage identification. The results of experimental study proved the validity and feasibility of the proposed methodology.

An Analytical Method to Detect the Coupling Damage Relationship of Concrete Subjected to Bending Fatigue and Temperature Actions

Based on the assumptions validated by the experiments,an analytical method to detect the coupling actions of bending fatigue and temperature on concrete was proposed.To this purpose,a coefficient denoted by f D （T）with the strain distributions caused by these two actions was defined.In terms of the known parameters and the fitted functions of strain,the explicit expression for f D （T）which develops in the way same as the law of temperature change in the body of specimens was obtained.Our experimental results indicate that the weigh fraction of temperature stress decreases in the coupling damage field with the fading temperature gradient,and consequently disclose the mutual influence between these two types of actions in the loading history.

Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking

In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compaction-induced damage and the cracking-induced damage.The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage,and the cracking-induced damage variable was established based on the statistical damage theory.Secondly,based on the total damage variable,a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions,whereafter,the application of this model is extended to cyclic loading and unloading conditions.To validate the proposed monotonic and cyclic constitutive equations,a series of mechanical tests for marble specimens were carried out,which contained the monotonic uniaxial compression(MUC)experiment,cyclic uniaxial compression experiments under the variable amplitude(CUC-VA)and constant amplitude(CUC-CA)conditions.The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic,i.e.,the damage variable firstly decreases,then increases no matter under the conditions of MUC,CUC-VA or CUC-CA.Then a reasonable consistency is observed between the experimental and theoretical curves.The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors,such as the initial compaction,the strain hardening and the strain softening.Furthermore,the shapes of the theoretical curves are controlled by the modified coefficient,compaction sensitivity coefficient and two Weibull distributed parameters.

CONSTITUTIVE THEORY OF PLASTICITY COUPLED WITH ORTHOTROPIC DAMAGE FOR GEOMATERIALS

Constitutive theory of plasticity coupled with orthotropic damage for geomaterials was established in the framework of irreversible thermodynamics. Prime results include I evolution laws are presented for coupled evolution of plasticity and orthotropic damage 2) the orthotropic damage tensor is introduced into the Mohr-Coulomb criterion through homogenization. Both the degradation of shear strength and degradation of friction angle caused by damage are included in this model. The dilatancy is calculated with the so-called damage strain.

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.

Calibration of coupled hydro-mechanical properties of grain-based model for simulating fracture process and associated pore pressure evolution in excavation damage zone around deep tunnels

The objective of this paper is to develop a methodology for calibration of a discrete element grain-based model(GBM)to replicate the hydro-mechanical properties of a brittle rock measured in the laboratory,and to apply the calibrated model to simulating the formation of excavation damage zone(EDZ)around underground excavations.Firstly,a new cohesive crack model is implemented into the universal distinct element code(UDEC)to control the fracturing behaviour of materials under various loading modes.Next,a methodology for calibration of the components of the UDEC-Voronoi model is discussed.The role of connectivity of induced microcracks on increasing the permeability of laboratory-scale samples is investigated.The calibrated samples are used to investigate the influence of pore fluid pressure on weakening the drained strength of the laboratory-scale rock.The validity of the Terzaghi’s effective stress law for the drained peak strength of low-porosity rock is tested by performing a series of biaxial compression test simulations.Finally,the evolution of damage and pore pressure around two unsupported circular tunnels in crystalline granitic rock is studied.

Seepage-Stress-Damage Coupled Model of Coal Under Geo-Stress Influence

In the seepage-stress-damage coupled process,the mechanical properties and seepage characteristics of coal are distinctly different between pre-peak stage and post-peak stage.This difference is mainly caused by damage of coal.Therefore,in the process of seepage and stress analysis of coal under the influence of excavation or mining,we need to consider the weakening of mechanical properties and the development of fractures of damaged coal.Based on this understanding,this paper analyzes the influence of damage on mechanics and seepage behavior of coal.A coupled model is established to analyze the seepage-stress-damage coupled process of coal.This model implemented into COMSOL and MATLAB software to realize the numerical solving.Two examples are adopted to verify the correctness of the model and some useful conclusions are obtained.The numerical model establishes the relationship between microcosmic damage evolution and macroscopical fracture and simulates the whole process of coal from microcosmic damage to macroscopical fracture,and the dynamic simulation of fluid flow in this process.It provides a numerical tool for further research on the seepage-stress-damage analysis.

Isotropic Elastoplasticity Fully Coupled with Non-Local Damage

This paper presents a simple damage-gradient based elastoplastic model with non linear isotropic hardening in order to regularize the associated initial and boundary value problem (IBVP). Using the total energy equivalence hypothesis, fully coupled constitutive equations are used to describe the non local damage induced softening leading to a mesh independent solution. An additional partial differential equation governing the evolution of the non local isotropic damage is added to the classical equilibrium equations and associated weak forms derived. This leads to discretized IBVP governed by two algebric systems. The first one, associated with equilibrium equations, is highly non linear and can be solved by an iterative Newton Raphson method. The second one, related to the non local damage, is a linear algebric system and can be solved directly to compute the non local damage variable at each load increment. Two fields, linear interpolation triangular element with additional degree of freedom is terms of the non local damage variable is constructed. The non local damage variable is then transferred from mesh nodes to the quadrature (or Gauss) points to affect strongly the elastoplastic behavior. Two simple 2D examples are worked out in order to investigate the ability of proposed approach to deliver a mesh independent solution in the softening stage.

Application of 1D/3D finite elements coupling for structural nonlinear analysis

An element coupling model (ECM) method was proposed to simulate the global behavior and local damage of a structure.In order to reflect the local damage and improve the computational efficiency,three-dimensional (3D) solid elements and one-dimensional (1D) beam element were coupled by the multi-point constraint equations.A reduced scale 1?8 model test was simulated by the ECM and a full three dimensional model (3DM) contrastively.The results show that the global behavior and local damages of ECM agree well with the test and 3DM.It is indicated that the proposed method can be used in the structural nonlinear analysis accurately and efficiently.

Experimental and numerical investigations on the tensile mechanical behavior of marbles containing dynamic damage

To investigate the degradation mechanism of static tensile mechanical behaviors of marble containing dynamic damage,multiple impact loading tests were performed on the disc marble samples,and then static Brazilian tests were conducted for the damaged samples.Besides,coupling modeling technology of finite difference method(FDM)—discrete element method(DEM)was used to carry out the numerical investigation.The results show that after multiple impacts,more white patches appear on the surface,and some microcracks,macro-fractures as well as pulverized grains are found by optical microscopic.The static tensile strength decreases with the increase of the dynamic damage variable characterized by the ultrasonic wave velocity of sample.The interaction between grains in the damaged sample becomes intense in the subsequent static loading process,causing a relatively large strain.The volume of the fragments falling off around the loading points becomes larger as impact number increases.As the dynamic damage increases,the absorbed energy of sample during the static loading first decreases and then tends to be stable.Both the stress concentration and the breakage of the force chains are the root causes of the degradation of the static tensile strength.

NMR-based damage characterisation of backfill material in host rock under dynamic loading

It is not uncommon that backfill material used in underground mining being exposed to repetitive dynamic stresses induced by blasting operations or rockburst events. Understanding the strength and fracture evolution of backfilled stopes is critical to maintain the long-term stope stability and ensure safe mining activities. This paper aims to study the damage evolution of the backfill material and its host rock behaviour under three-dimensional(3D) dynamic loading. Using a true-triaxial testing machine, multiple samples of backfill material enclosed by country rock were fabricated and tested under various dynamic loadings with different true-triaxial confining stress conditions. In addition, the nuclear magnetic resonance(NMR) measurement was conducted on the samples before and after exerting static and dynamic loading to obtain their porosity distribution changes. The experiment results suggested that with the increase of the dynamic loading, the porosity of the backfill sample goes through a two-stage process,which shows a slightly linear decrease and then followed by an exponential increase. The research findings can help understand the damage mechanism and fracture development of backfilled stopes and its host rock in deep underground mines, which are constantly subject to the combination of 3D static confining stress and dynamic loading.

Elimination mechanism of coal and gas outburst based on geo‑dynamic system with stress–damage–seepage interactions

Coal and gas outburst is a complex dynamic disaster during coal underground mining.Revealing the disaster mechanism is of great signifcance for accurate prediction and prevention of coal and gas outburst.The geo-dynamic system of coal and gas outburst is proposed.The framework of geo-dynamic system is composed of gassy coal mass,geological dynamic environment and mining disturbance.Equations of stress–damage–seepage interaction for gassy coal mass is constructed to resolve the outburst elimination process by gas extraction with boreholes through layer in foor roadway.The results show the occurrence of outburst is divided into the evolution process of gestation,formation,development and termination of geo-dynamic system.The scale range of outburst occurrence is determined,which provides a spatial basis for the prevention and control of outburst.The formation criterion and instability criterion of coal and gas outburst are established.The formation criterion F1 is defned as the scale of the geo-dynamic system,and the instability criterion F2 is defned as the scale of the outburst geo-body.According to the geo-dynamic system,the elimination mechanism of coal and gas outburst—‘unloading+depressurization’is established,and the gas extraction by boreholes through layer in foor roadway for outburst elimination is given.For the research case,when the gas extraction is 120 days,the gas pressure of the coal seam is reduced to below 0.4 MPa,and the outburst danger is eliminated efectively.

Interface bond degradation and damage characteristics of full-length grouted rock bolt in tunnels with high temperature

Full-length grouted bolts play a crucial role in geotechnical engineering thanks to their excellent stability.However,few studies have been concerned with the degrading performance of grouted rock bolts caused by extensive and continuous heat conduction from surrounding rocks in high-geothermal tunnels buried more than 100 m(temperature from 28C to 100C).To investigate the damage mechanism,we examined the time-varying behaviors of grouted rock bolts in both constant and variable temperature curing environments and their damage due to the coupling effects of high temperature and humidity through mechanical and micro-feature tests,including uniaxial compression test,pull-out test,computed tomography(CT)scans,X-ray diffraction(XRD)test,thermogravimetric analysis(TGA),etc.,and further analyzed the relationship between grout properties and anchorage capability.In order to facilitate a rapid assessment and control of the anchorage performance of anchors in different conditions,results of the interface bond degradation tests were correlated to environment parameters based on the damage model of interfacial bond stress proposed.Accordingly,a thermal hazard classification criterion for anchorage design in high-geothermal tunnels was suggested.Based on the reported results,although high temperature accelerated the early-stage hydration reaction of grouting materials,it affected the distribution and quantity of hydration products by inhibiting hydration degree,thus causing mechanical damage to the anchorage system.There was a significant positive correlation between the strength of the grouting material and the anchoring force.Influenced by the changes in grout properties,three failure patterns of rock bolts typically existed.Applying a hot-wet curing regime results in less reduction in anchorage force compared to the hot-dry curing conditions.The findings of this study would contribute to the design and investigations of grouted rock bolts in high-geothermal tunnels.

Micromechanics of rock damage: Advances in the quasi-brittle field

Constitutive models play an essential role in numerical modeling and simulation of nonlinear deformation, progressive damage and failure of rock-like materials and structures. Recent advances in the quasi-brittle field show that upscaling methods by homogenization have provided a new efficient way to derive macroscopic formulations of rocks from their microstructure information and local properties and then to model nonlinear mechanical behaviors identified at laboratory. This paper aims first at relating the mechanical phenomena on sample scale to their respective mechanisms on microscale. Main focus is put on unilateral effects due to crack’s opening/closure transition, material anisotropy induced by crack growth in some preferred directions and multiphysical coupling at microcracks. After a brief introduction to the linear homogenization method and its application to crack problems, we present some recent advances achieved in the combined homogenization/thermodynamics framework, including anisotropic unilateral damage-friction coupling, theoretical failure prediction in conjunction with deformation analyses, poromechanical coupling, analytical solutions and numerical implementation with application to typical brittle rocks.

Constitutive model of rock under static-dynamic coupling loading and experimental investigation

The importance of study on constitutive model of statically loaded rock experiencing dynamic load is set forth, and the studying methods on dynamic constitutive model are classified according to the current studying status. By way of combining statistic damage model and viscoelastic model, uni-axial and multi-axial constitutive models of statically loaded rock experiencing dynamic load (static-dynamic coupling constitutive model) under intermediate strain rate are established. The verification experiment on 2D constitutive model under different static stress and dynamic stress with different frequencies is designed and performed. It is found that there is a good agreement between the experimental stress-strain curves and the theoretical stress-strain curves.