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.

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.

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.

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.

Research on Fatigue Damage Behavior of Main Beam Sub-Structure of Composite Wind Turbine Blade

Given the difficulty in accurately evaluating the fatigue performance of large composite wind turbine blades(referred to as blades),this paper takes the main beam structure of the blade with a rectangular cross-sectionas the simulation object and establishes a composite laminate rectangular beam structure that simultaneouslyincludes the flange,web,and adhesive layer,referred to as the blade main beam sub-structure specimen,throughthe definition of blade sub-structures.This paper examines the progressive damage evolution law of the compositelaminate rectangular beam utilizing an improved 3D Hashin failure criterion,cohesive zone model,B-K failurecriterion,and computer simulation technology.Under static loading,the layup angle of the anti-shear web hasa close relationship with the static load-carrying capacity of the composite laminate rectangular beam;under fatigueloading,the fatigue damage will first occur in the lower flange adhesive area of the whole composite laminaterectangular beam and ultimately result in the fracture failure of the entire structure.These results provide a theoreticalreference and foundation for evaluating and predicting the fatigue performance of the blade main beamstructure and even the full-size blade.

Impact Damage Testing Study of Shanxi-Beijing Natural Gas Pipeline Based on Decision Tree Rotary Tiller Operation

The North China Plain and the agricultural region are crossed by the Shanxi-Beijing natural gas pipeline.Resi-dents in the area use rototillers for planting and harvesting;however,the depth of the rototillers into the ground is greater than the depth of the pipeline,posing a significant threat to the safe operation of the pipeline.Therefore,it is of great significance to study the dynamic response of rotary tillers impacting pipelines to ensure the safe opera-tion of pipelines.This article focuses on the Shanxi-Beijing natural gas pipeline,utilizingfinite element simulation software to establish afinite element model for the interaction among the machinery,pipeline,and soil,and ana-lyzing the dynamic response of the pipeline.At the same time,a decision tree model is introduced to classify the damage of pipelines under different working conditions,and the boundary value and importance of each influen-cing factor on pipeline damage are derived.Considering the actual conditions in the hemp yam planting area,targeted management measures have been proposed to ensure the operational safety of the Shanxi-Beijing natural gas pipeline in this region.

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.

Mechanical properties and damage constitutive model of sandstone after acid corrosion and high temperature treatments

Aiming at the problem of temperature-mechanics-chemical(T-M-C)action encountered by rocks in underground engineering,sandstone was selected as the sample for acid corrosion treatment at pH 1,3,5 and 7,the acid corrosion treated samples were then subjected to high-temperature experiments at 25,300,600,and 900℃,and triaxial compression experiments were conducted in the laboratory.The experimental results show that the superposition of chemical damage and thermal damage has a significant impact on the quality,wave velocity,porosity and compression failure characteristics of the rock.Based on the Lemaitre strain equivalent hypothesis theory,the damage degree of rock material was described by introducing damage variables,and the spatial mobilized plane(SMP)criterion was adopted.The damage constitutive model can well reflect the stress-strain characteristics of the rock triaxial compression process,which verified the rationality and reliability of the model parameters.The experiment and constitutive model analyzed the change law of mechanical properties of rock after chemical corrosion and high temperature thermal damage,which had certain practical significance for rock engineering construction.

The dynamic response and damage models of rebar reinforced polymer slabs subjected to contact and near-field explosions

Non aqueous reactive polymer materials produced by the reaction of isocyanate and polyol have been widely used in infrastructure construction,which may be subjected to explosion loads during complex service conditions.The blast response of composite materials is a crucial aspect for applications in engineering structures potentially subjected to extreme loadings.In this work,damage caused to rebar reinforced polymer slabs by surface explosive charges was studied experimentally and numerically.A total of 6 field tests were carried out to investigate the performances of the failure modes of rebar reinforced polymer slabs under contact and near-field explosions.The influence of explosive quantity(10-40 g)and stand-off distances(0-20 cm)at the damage modes were studied.The results show that the failure modes of rebar reinforced polymer slabs under near-field explosion mainly were bending and surface spalling,while under the impact of contact explosion,the failure modes were craters of the top surface,spalling of the bottom surface,and middle perforation.Furthermore,a detailed fully coupled model was developed and validated with the test data.The influences of explosive quantity and slab thickness on rebar reinforced polymer slabs under contact explosion were studied.Based on this,the calculation formula between breach diameter,explosive quantity,and slab thickness is fitted.

The damage to model concrete gravity dams subjected to water explosions

Over the past century,the safety of dams has gradually attracted attention from all parties.Research on the dynamic response and damage evolution of dams under extreme loads is the basis of dam safety issues.In recent decades,scholars have studied the responses of dams under earthquake loads,but there is still much room for improvement in experimental and theoretical research on small probability loads such as explosions.In this paper,a 50-m-high concrete gravity dam is used as a prototype dam,and a water explosion model test of a 2.5-m-high concrete gravity dam is designed.The water pressure and the acceleration response of the dam body in the test are analysed.The pressure characteristics and dynamic response of the dam body are assessed.Taking the dam damage test as an example,a numerical model of concrete gravity dam damage is established,and the damage evolution of the dam body is analysed.By combining experiments and numerical simulations,the damage characteristics of the dam body under the action of different charge water explosions are clarified.The integrity of the dam body is well maintained under the action of a small-quantity water explosion,and the dynamic response of the dam body is mainly caused by the shock wave.Both the shock wave and the bubble pulsation cause the dam body to accelerate,and the peak acceleration of the dam body under the action of the bubble pulsation is only one percent of the peak acceleration of the dam body under the action of the shock wave.When subjected to explosions in large quantities of water,the dam body is seriously damaged.Under the action of a shock wave,the dam body produces a secondary acceleration response,which is generated by an internal interaction after the dam body is damaged.The damage evolution process of the dam body under the action of a large-scale water explosion is analysed,and it is found that the shock wave pressure of the water explosion causes local damage to the dam body facing the explosion.After the peak value of the shock wave,the impulse continues to act on the dam body,causing cumulative damage and damage inside the dam body.

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.