A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

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.

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.

An extended micromechanical-based plastic damage model for understanding water effects on quasi-brittle rocks

Water effects on the mechanical properties of rocks have been extensively investigated through experiments and numerical models.However,few studies have established a comprehensive link between the microscopic mechanisms of water-related micro-crack and the constitutive behaviors of rocks.In this work,we shall propose an extended micromechanical-based plastic damage model for understanding weakening effect induced by the presence of water between micro-crack’s surfaces on quasi-brittle rocks,based on the Mori-Tanaka homogenization and irreversible thermodynamics framework.Regarding the physical mechanism,water strengthens micro-crack propagation,which induces damage evolution during the pre-and post-stage,and weakens the elastic effective properties of rock matrix.After proposing a special calibration procedure for the determination of model parameters based on the laboratory compression tests,the proposed micromechanical-based model is verified by comparing the model predictions to the experimental results.The model effectively captures the mechanical behaviors of quasibrittle rocks subjected to the weakening effects of water.

Finite element model updating for structural damage detection using transmissibility data

This paper presents a new finite element model updating method for estimating structural parameters and detecting structural damage location and severity based on the structural responses(output-only data).The method uses the sensitivity relation of transmissibility data through a least-squares algorithm and appropriate normalization of the extracted equations.The proposed transmissibility-based sensitivity equation produces a more significant number of equations than the sensitivity equations based on the frequency response function(FRF),which can estimate the structural parameters with higher accuracy.The abilities of the proposed method are assessed by using numerical data of a two-story two-bay frame model and a plate structure model.In evaluating different damage cases,the number,location,and stiffness reduction of the damaged elements and the severity of the simulated damage have been accurately identified.The reliability and stability of the presented method against measurement and modeling errors are examined using error-contaminated data.The parameter estimation results prove the method’s capabilities as an accurate model updating algorithm.

Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry.To study the mechanical behavior of a typical ductile cast iron(GJS-450)with nodular graphite,uni-axial quasi-static and dynamic tensile tests at strain rates of 10^(-4),1,10,100,and 250 s^(-1)were carried out.In order to investigate the influence of stress state on the deformation and fracture parameters,specimens with various geometries were used in the experiments.Stress strain curves and fracture strains of the GJS-450 alloy in the strain rate range of 10^(-4)to 250 s^(-1)were obtained.A strain rate-dependent plastic flow model was proposed to describe the mechanical behavior in the corresponding strain-rate range.The available damage model was extended to take the strain rate into account and calibrated based on the analysis of local fracture strains.Simulations with the proposed plastic flow model and the damage model were conducted to observe the deformation and fracture process.The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys.The predictions with the proposed plastic flow and damage models at various strain rates agree well with the experimental results,which illustrates that the rate-dependent plastic flow and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.The proposed plastic flow and damage models can be used to describe the deformation and fracture analysis of materials with similar properties.

A whole process damage constitutive model for layered sandstone under uniaxial compression based on Logistic function

Bedding structural planes significantly influence the mechanical properties and stability of engineering rock masses.This study conducts uniaxial compression tests on layered sandstone with various bedding angles(0°,15°,30°,45°,60°,75°and 90°)to explore the impact of bedding angle on the deformational mechanical response,failure mode,and damage evolution processes of rocks.It develops a damage model based on the Logistic equation derived from the modulus’s degradation considering the combined effect of the sandstone bedding dip angle and load.This model is employed to study the damage accumulation state and its evolution within the layered rock mass.This research also introduces a piecewise constitutive model that considers the initial compaction characteristics to simulate the whole deformation process of layered sandstone under uniaxial compression.The results revealed that as the bedding angle increases from 0°to 90°,the uniaxial compressive strength and elastic modulus of layered sandstone significantly decrease,slightly increase,and then decline again.The corresponding failure modes transition from splitting tensile failure to slipping shear failure and back to splitting tensile failure.As indicated by the modulus’s degradation,the damage characteristics can be categorized into four stages:initial no damage,damage initiation,damage acceleration,and damage deceleration termination.The theoretical damage model based on the Logistic equation effectively simulates and predicts the entire damage evolution process.Moreover,the theoretical constitutive model curves closely align with the actual stress−strain curves of layered sandstone under uniaxial compression.The introduced constitutive model is concise,with fewer parameters,a straightforward parameter determination process,and a clear physical interpretation.This study offers valuable insights into the theory of layered rock mechanics and holds implications for ensuring the safety of rock engineering.

Constitutive model of viscoelastic dynamic damage for the material of gas obturator in modular-charge howitzer

In order to investigate the mechanical response behavior of the gas obturator of the breech mechanism,made of polychloroprene rubber(PCR), uniaxial compression experiments were carried out by using a universal testing machine and a split Hopkinson pressure bar(SHPB), obtaining stress-strain responses at different temperatures and strain rates. The results revealed that, in comparison to other polymers, the gas obturator material exhibited inconspicuous strain softening and hardening effects;meanwhile, the mechanical response was more affected by the strain rate than by temperature. Subsequently, a succinct viscoelastic damage constitutive model was developed based on the ZWT model, including ten undetermined parameters, formulated with incorporating three parallel components to capture the viscoelastic response at high strain rate and further enhanced by integrating a three-parameter Weibull function to describe the damage. Compared to the ZWT model, the modified model could effectively describe the mechanical response behavior of the gas obturator material at high strain rates. This research laid a theoretical foundation for further investigation into the influence of chamber sealing issues on artillery firing.

A creep model for ultra-deep salt rock considering thermal-mechanical damage under triaxial stress conditions

To investigate the specific creep behavior of ultra-deep buried salt during oil and gas exploitation,a set of triaxial creep experiments was conducted at elevated temperatures with constant axial pressure and unloading confining pressure conditions.Experimental results show that the salt sample deforms more significantly with the increase of applied temperature and deviatoric loading.The accelerated creep phase is not occurring until the applied temperature reaches 130℃,and higher temperature is beneficial to the occurrence of accelerated creep.To describe the specific creep behavior,a novel three-dimensional(3D)creep constitutive model is developed that incorporates the thermal and mechanical variables into mechanical elements.Subsequently,the standard particle swarm optimization(SPSO)method is adopted to fit the experimental data,and the sensibility of key model parameters is analyzed to further illustrate the model function.As a result,the model can accurately predict the creep behavior of salt under the coupled thermo-mechanical effect in deep-buried condition.Based on the research results,the creep mechanical behavior of wellbore shrinkage is predicted in deep drilling projects crossing salt layer,which has practical implications for deep rock mechanics problems.

Regional Climate Damage Quantification and Its Impacts on Future Emission Pathways Using the RICE Model

This study quantified the regional damages resulting from temperature and sea level changes using the Regional Integrated of Climate and Economy(RICE)model,as well as the effects of enabling and disabling the climate impact module on future emission pathways.Results highlight varied damages depending on regional economic development and locations.Specifically,China and Africa could suffer the most serious comprehensive damages caused by temperature change and sea level rise,followed by India,other developing Asian countries(OthAsia),and other high-income countries(OHI).The comprehensive damage fractions for China and Africa are projected to be 15.1%and 12.5%of gross domestic product(GDP)in 2195,with corresponding cumulative damages of 124.0 trillion and 87.3 trillion United States dollars(USD)from 2005 to 2195,respectively.Meanwhile,the comprehensive damage fractions in Japan,Eurasia,and Russia are smaller and projected to be lower than 5.6%of GDP in 2195,with cumulative damages of 6.8 trillion,4.2 trillion,and 3.3 trillion USD,respectively.Additionally,coastal regions like Africa,the European Union(EU),and OHI show comparable damages for sea level rise and temperature change.In China,however,sea level-induced damages are projected to exceed those from temperature changes.Moreover,this study indicates that switching the damage modules on or off affects the regional and global emission trajectories,but the magnitude is relatively small.By 2195,global emissions under the experiments with all of the damage modules switched off,only the sea level damage module switched on,and only the temperature damage module switched on,were 3.5%,2.3%and 1.2%higher than those with all of the damage modules switched on,respectively.

Modelling the viscoplastic behaviour of Callovo-Oxfordian claystone with consideration of damage effect

In order to evaluate the performance of deep geological disposal of radioactive waste,an underground research laboratory(URL)was constructed by Andra in the Callovo-Oxfordian(COx)claystone formation at the Meuse/Haute-Marne(MHM).The construction of URL induced the excavation damage of host formations,and the ventilation in the galleries desaturated the host formation close to the gallery wall.Moreover,it is expected that the mechanical behaviour of COx claystone is time-dependent.This study presents a constitutive model developed to describe the viscoplastic behaviour of unsaturated and damaged COx claystone.In this model,the unsaturation effect is considered by adopting the Bishop effective stress and the van Genuchten(VG)water retention model.In terms of the viscoplastic behaviour,the nonstationary flow surface(NSFS)theory for unsaturated soils is used with consideration of the coupled effects of strain rate and suction on the yield stress.A progressive hardening law is adopted.Meanwhile,a non-associated flow rule is used,which is similar to that in Barcelona basic model(BBM).In addition,to describe the damage effect induced by suction change and viscoplastic loading,a damage function is defined based on the crack volume proportion.This damage function contains two variables:unsaturated effective stress and viscoplastic volumetric strain,with the related parameters determined based on the mercury intrusion porosimetry(MIP)tests.For the model validation,different tests on COx claystone under different loading paths are simulated.Comparisons between experimental and simulated results indicated that the present model is able to well describe the viscoplastic behaviour of damaged COx claystone,including swelling/shrinkage,triaxial extension and compression,and triaxial creep.

Discrete Element Modelling of Damage Evolution of Concrete Considering Meso-Structure of ITZ

The mechanical properties of interfacial transition zones(ITZs)have traditionally been simplified by reducing the stiffness of cement in previous simulation methods.A novel approach based on the discrete element method(DEM)has been developed for modeling concrete.This new approach efficiently simulates the meso-structure of ITZs,accurately capturing their heterogeneous properties.Validation against established uniaxial compression experiments confirms the precision of thismodel.The proposedmodel canmodel the process of damage evolution containing cracks initiation,propagation and penetration.Under increasing loads,cracks within ITZs progressively accumulate,culminating in macroscopic fractures that traverse themortarmatrix,forming the complex,serpentine path of cracks.This study reveals four distinct displacement patterns:tensile compliant,tensile opposite,mixed tensile-shear,and shear opposite patterns,each indicative of different stages in concrete’s damage evolution.The widening angle of these patterns delineates the progression of cracks,with the tensile compliant pattern signaling the initial crack appearance and the shear opposite pattern indicating the concrete model’s ultimate failure.

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 cloud model target damage effectiveness assessment algorithm based on spatio-temporal sequence finite multilayer fragments dispersion

To solve the problem of target damage assessment when fragments attack target under uncertain projectile and target intersection in an air defense intercept,this paper proposes a method for calculating target damage probability leveraging spatio-temporal finite multilayer fragments distribution and the target damage assessment algorithm based on cloud model theory.Drawing on the spatial dispersion characteristics of fragments of projectile proximity explosion,we divide into a finite number of fragments distribution planes based on the time series in space,set up a fragment layer dispersion model grounded in the time series and intersection criterion for determining the effective penetration of each layer of fragments into the target.Building on the precondition that the multilayer fragments of the time series effectively assail the target,we also establish the damage criterion of the perforation and penetration damage and deduce the damage probability calculation model.Taking the damage probability of the fragment layer in the spatio-temporal sequence to the target as the input state variable,we introduce cloud model theory to research the target damage assessment method.Combining the equivalent simulation experiment,the scientific and rational nature of the proposed method were validated through quantitative calculations and comparative analysis.

Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

Experimental study of the damage characteristics of rocks containing non-penetrating cracks under cyclic loading

The damage evolution process of non-penetrating cracks often causes some unexpected engineering disasters.Gypsum specimens containing non-penetrating crack(s)are used to study the damage evolution and characteristics under cyclic loading.The results show that under cyclic loading,the relationship between the number of non-penetrating crack(s)and the characteristic parameters(cyclic number,peak stress,peak strain,failure stress,and failure strain)of the pre-cracked specimens can be represented by a decreasing linear function.The damage evolution equation is fitted by calibrating the accumulative plastic strain for each cycle,and the damage constitutive equation is proposed by the concept of effective stress.Additionally,non-penetrating cracks are more likely to cause uneven stress distribution,damage accumulation,and local failure of specimen.The local failure can change the stress distribution and relieve the inhibition of non-penetrating crack extension and eventually cause a dramatic destruction of the specimen.Therefore,the evolution process caused by non-penetrating cracks can be regarded as one of the important reasons for inducing rockburst.These results are expected to improve the understanding of the process of spalling formation and rockburst and can be used to analyze the stability of rocks or rock structures.

Effect of neutral polymeric bonding agent on tensile mechanical properties and damage evolution of NEPE propellant

Introducing Neutral Polymeric bonding agents(NPBA) into the Nitrate Ester Plasticized Polyether(NEPE)propellant could improve the adhesion between filler/matrix interface, thereby contributing to the development of new generations of the NEPE propellant with better mechanical properties. Therefore,understanding the effects of NPBA on the deformation and damage evolution of the NEPE propellant is fundamental to material design and applications. This paper studies the uniaxial tensile and stress relaxation responses of the NEPE propellant with different amounts of NPBA. The damage evolution in terms of interface debonding is further investigated using a cohesive-zone model(CZM). Experimental results show that the initial modulus and strength of the NEPE propellant increase with the increasing amount of NPBA while the elongation decreases. Meanwhile, the relaxation rate slows down and a higher long-term equilibrium modulus is reached. Experimental and numerical analyses indicate that interface debonding and crack propagation along filler-matrix interface are the dominant damage mechanism for the samples with a low amount of NPBA, while damage localization and crack advancement through the matrix are predominant for the ones with a high amount of NPBA. Finally, crosslinking density tests and simulation results also show that the effect of the bonding agent is interfacial rather than due to the overall crosslinking density change of the binder.

Predicting the Thickness of an Excavation Damaged Zone around the Roadway Using the DA-RF Hybrid Model

After the excavation of the roadway,the original stress balance is destroyed,resulting in the redistribution of stress and the formation of an excavation damaged zone(EDZ)around the roadway.The thickness of EDZ is the key basis for roadway stability discrimination and support structure design,and it is of great engineering significance to accurately predict the thickness of EDZ.Considering the advantages of machine learning(ML)in dealing with high-dimensional,nonlinear problems,a hybrid prediction model based on the random forest(RF)algorithm is developed in this paper.The model used the dragonfly algorithm(DA)to optimize two hyperparameters in RF,namely mtry and ntree,and used mean absolute error(MAE),rootmean square error(RMSE),determination coefficient(R^(2)),and variance accounted for(VAF)to evaluatemodel prediction performance.A database containing 217 sets of data was collected,with embedding depth(ED),drift span(DS),surrounding rock mass strength(RMS),joint index(JI)as input variables,and the excavation damaged zone thickness(EDZT)as output variable.In addition,four classic models,back propagation neural network(BPNN),extreme learning machine(ELM),radial basis function network(RBF),and RF were compared with the DA-RF model.The results showed that the DARF mold had the best prediction performance(training set:MAE=0.1036,RMSE=0.1514,R^(2)=0.9577,VAF=94.2645;test set:MAE=0.1115,RMSE=0.1417,R^(2)=0.9423,VAF=94.0836).The results of the sensitivity analysis showed that the relative importance of each input variable was DS,ED,RMS,and JI from low to high.

Deformation characteristics and damage ontologies of soft and hard composite rock masses under impact loading

As one of the most common occurring geological landforms in deep rock formations, the dynamic mechanical properties of layered composite rock bodies under impact loading have been widely studied by scholars. To study the dynamic properties of soft and hard composite rocks with different thickness ratios, this paper utilizes cement, quartz sand and gypsum powder to construct soft and hard composite rock specimens and utilizes a combination of indoor tests, numerical calculations, and theoretical analyses to investigate the mechanical properties of soft and hard composite rock bodies. The test results reveal that:(1) When the proportion of hard rock increases from 20% to 50%, the strength of the combined rock body increases by 69.14 MPa and 87 MPa when the hard rock face and soft rock face are loaded, respectively;however, when the proportion of hard rock is the same, the compressive strength of the hard rock face impact is 9%-17% greater than that of the soft rock face impact;(2) When a specimen of soft and hard combined rock body is subjected to impact loading, the damage mode involves mixed tension and shear damage, and the cracks generally first appear at the ends of the specimen, then develop on the laminar surface from the impact surface, and finally end in the overall damage of the soft rock part. The development rate and the total number of cracks in the same specimen when the hard rock face is impacted are significantly greater than those when the soft rock face is impacted;(3) By introducing Weibull’s statistical strength theory to establish the damage variables of soft-hard combined rock bodies, combined with the DP strength criterion, the damage model and the Kelvin body are concatenated to obtain a statistical damage constitutive model, which can better fit the full stress-strain curve of soft-hard combined rock body specimens under a single impact load.

Triaxial elastoplastic damage constitutive model of unreinforced clay brick masonry wall

Due to differences in the properties of composition materials and construction techniques,unreinforced masonry is characterized by low strength,anisotropy,nonuniformity,and low ductility.In order to accurately simulate the mechanical behavior of unreinforced brick masonry walls under static and dynamic loads,a new elastoplastic damage constitutive model was proposed and the corresponding subroutine was developed based on the concrete material constitutive model.In the proposed constitutive model,the Rankine strength theory and the Drucker-Prager strength theory were used to define the tensile and compressive yield surface function of materials,respectively.Moreover,the stress updating algorithm was modified to consider the tensile plastic permanent deformation of masonry materials.To verify the accuracy of the proposed constitutive model,numerical simulations of the brick masonry under monotonic and cyclic uniaxial tension and compression loads were carried out.Comparisons among the numerical and theoretical and experimental results show that the proposed model can properly reflect the masonry material mechanical properties.Furthermore,the numerical models of four pieces of masonry walls with different mortar strengths were established.Low cyclic loadings were applied and the results show that the proposed constitutive model can properly simulate the wall shear failure characteristics,and the force-displacement hysteretic curves obtained by numerical simulation are in good agreement with the tests.Overall,the proposed elastic-plastic damage constitutive model can simulate the nonlinear behavior of unreinforced brick masonry walls very well,and can be used to predict the structural response of masonry walls.