Energy evolution mechanism and failure criteria of jointed surrounding rock under uniaxial compression

The object of this article is to investigate the energy evolution mechanism and failure criteria of cross-jointed samples containing an opening during deformation and failure based on the uniaxial compression test and rock energy principle.The results show that the energy evolution characteristics of the samples correspond to a typical progressive damage mode.The peak total energy,peak elastic energy,and total input energy of the samples all first decrease and then increase with an increase of half of the included angle,reaching their minimum values when this angle is 45°,while the dissipated energy generally increases with this angle.The existence of the opening and cross joints can obviously weaken the energy storage capacity of the rock,and the change in the included angle of the cross joint has a great influence on the elastic energy ratio of the sample before the peak stress,which leads to some differences in the distribution laws of the input energy.The continuous change and the subsequent sharp change in the rate of change in the energy consumption ratio can be used as the criteria of the crack initiation and propagation and the unstable failure of the sample,respectively.

Initial support distance of a non-circular tunnel based on convergence constraint method and integral failure criteria of rock

For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initial support distance was proposed.First,based on the convergence-confinement method,a three-dimensional analytical model was constructed by combining an analytical solution of a non-circular tunnel with the Tecplot software.Then,according to the integral failure criteria of rock,the failure tendency coefficients of hard surrounding rock were computed and the spatial distribution plots of that were constructed.On this basis,the tunnel’s key failure positions were identified,and the relationship between the failure tendency coefficient at key failure positions and their distances from the working face was established.Finally,the distance from the working face that corresponds to the critical failure tendency coefficient was taken as the optimal support distance.A practical project was used as an example,and a reasonable initial support distance was successfully determined by applying the developed method.Moreover,it is found that the stability of hard surrounding rock decreases rapidly within the range of 1.0D(D is the tunnel diameter)from the working face,and tends to be stable outside the range of 1.0D.

Failure criteria of unreinforced masonry walls of rural buildings under the impact of flash floods in mountainous regions

Damage to rural buildings in mountainous regions caused by flash floods accounts for a significant proportion of economic losses from disasters.The unreinforced masonry(URM)wall is the most vulnerable structural element of rural buildings exposed to flash floods.The failure of a URM wall indicates damage to rural buildings in flash floods.Based on the yield line theory of out-of-plane damage of URM walls and the virtual work method,brittle failure criteria for URM walls under the impact of flash floods were established.According to the field investigation data of the 26 June 2020 flash flood event in Damawu Gully and the corresponding simulation results of FLO-2D,the disaster-causing process was analysed,and the failure criteria were validated.Three building parameters were identified to influence the flood-resistance of URM walls,including the mortar grade,the span-to-height ratio of the wall,and the number of floors of the rural building.The results showed that the cause of the 26June disaster was the diversion of a 50-year flash flood into the residential community on the alluvial fan.The affected buildings were constructed with hollow blocks and lacked flood-resistance reinforcement.The critical failure depth of a URM wall restrained at the top by ring beams(RBs)under hydrostatic load conditions is 1.17 to 1.20 times greater than that of a URM wall without RBs,and the difference is even more pronounced when lowerstrength mortar is used.The flood-resistance of a URM wall constructed with Mb 7.5 mortar and restrained by RBs is almost as strong as that of a URM wall constructed with Mb 20 mortar and without RBs.The span-to-height ratio of a URM wall should not be greater than 1.875 in this case.However,the flood-resistance of a URM wall with RB restraint is almost independent of the span-to-height ratio.The brittle fracture energy of masonry mortar is more crucial to the flood-resistance of 4-edge restrained URM walls if L/Z>1.875.The flood-resistance of the URM wall of the first storey increases linearly with the number of floors.Single-storey rural buildings should be given priority to the use of high-grade masonry mortar and high-density blocks to improve flood-resistance.The failure criteria and the influence laws of building parameters on the flood-resistance of URM walls can provide references for flash flood mitigation and flood-resistance reinforcement of rural buildings in mountainous regions of Southwest China.

Diagnosis and treatment of heart failure with preserved left ventricular ejection fraction

Nearly six million people in United States have heart failure.Fifty percent of these people have normal left ventricular(LV)systolic heart function but abnormal diastolic function due to increased LV myocardial stiffness.Most commonly,these patients are elderly women with hypertension,ischemic heart disease,atrial fibrillation,obesity,diabetes mellitus,renal disease,or obstructive lung disease.The annual mortality rate of these patients is 8%-12%per year.The diagnosis is based on the history,physical examination,laboratory data,echocardiography,and,when necessary,by cardiac catheterization.Patients with obesity,hypertension,atrial fibrillation,and volume overload require weight reduction,an exercise program,aggressive control of blood pressure and heart rate,and diuretics.Miniature devices inserted into patients for pulmonary artery pressure monitoring provide early warning of increased pulmonary pressure and congestion.If significant coronary heart disease is present,coronary revascularization should be considered.

Basic characteristics and development of yield criteria for geomaterials

The yield criteria of geomaterials play a crucial role in studying and designing the strength of materials and structures.The basic characteristics of yield criteria for geomaterials need to be studied under the framework of continuum mechanics.These characteristics include the effects of strength difference（SD） of materials in tension and compression,normal stress,intermediate principal stress,intermediate principal shear stress,hydrostatic stress,twin-shear stresses,and the convexity of yield surface.Most of the proposed yield criteria possess only one or some of these basic characteristics.For example,the Tresca yield criterion considers only single-shear stress effect,and ignores the effect of SD,normal stress,intermediate principal stress,intermediate principal shear stress,hydrostatic stress,and twin-shear stresses.The Mohr-Coulomb yield criterion accounts for the effect of SD,normal stress,single-shear stress and hydrostatic stress,but disregards the effect of intermediate principal stress,intermediate principal shear stress,and twin-shear stresses.The basic characteristics remain to be fully addressed in the development of yield criterion.In this paper,we propose a new yield criterion with three features,that is,newly developed,better than existing criteria and ready for application.It is shown that the proposed criterion performs better than the existing ones and is ready for application.The development of mechanical models for various yield criteria and the applications of the unified strength theory to engineering are also summarized.According to a new tetragonal mechanical model,a tension-cut condition is added to the unified strength theory.The unified strength theory is extended to the tension-tension region.

Peridynamic modeling and simulation of thermo-mechanical de-icing process with modified ice failure criterion

De-icing technology has become an increasingly important subject in numerous applications in recent years.However,the direct numerical modeling and simulation the physical process of thermomechanical deicing is limited.This work is focusing on developing a numerical model and tool to direct simulate the de-icing process in the framework of the coupled thermo-mechanical peridynamics theory.Here,we adopted the fully coupled thermo-mechanical bond-based peridynamics(TM-BB-PD)method for modeling and simulation of de-icing.Within the framework of TM-BB-PD,the ice constitutive model is established by considering the influence of the temperature difference between two material points,and a modified failure criteria is proposed,which takes into account temperature effect to predict the damage of quasi-brittle ice material.Moreover,thermal boundary condition is used to simulate the thermal load in the de-icing process.By comparing with the experimental results and the previous reported finite element modeling,our numerical model shows good agreement with the previous predictions.Based on the numerical results,we find that the developed method can not only predict crack initiation and propagation in the ice,but also predict the temperature distribution and heat conduction during the de-icing process.Furthermore,the influence of the temperature for the ice crack growth pattern is discussed accordingly.In conclusion,the coupled thermal-mechanical peridynamics formulation with modified failure criterion is capable of providing a modeling tool for engineering applications of de-icing technology.

Progressive failure analysis of composite structure based on micro- and macro-mechanics models

Based on parameter design language, a program of progressive failure analysis in composite structures is proposed. In this program, the relationship between macro- and micro-mechanics is established and the macro stress distribution of the composite structure is calculated by commercial finite element software. According to the macro-stress, the damaged point is found and the micro-stress distribution of representative volume element is calculated by finite-volume direct averaging micromechanics(FVDAM). Compared with the results calculated by failure criterion based on macro-stress field(the maximum stress criteria and Hashin criteria) and micro-stress field(Huang model), it is proven that the failure analysis based on macro- and micro-mechanics model is feasible and efficient.

Prediction of the Biaxial Failure Strength of Composite Laminates with Unit Cell Analytic Model

A new method to predict the ultimate strength of fiber reinforced composites under arbitrary load condition is introduced. The micromechanics strength theory is used to perform the final failure prediction of composite laminates. The theory is based on unit cell analytic model which can provide the ply composite material properties by only using the constituent fiber and matrix properties and the laminate geometric parameters without knowing any experimental information of the laminates. To show that this method is suitable for predicting the strength of composite laminates, the micromechanics strength theory is ranked by comparing it with all the micro-level and the best two macro-level theories chosen from the World Wide Failure Exercise. The results show that this method can be used for predicting strength of any composite laminates and provide a direct reference for composite optimum design.

Failure Pressure Analysis of Corroded Moderate-to-High Strength Pipelines

Based on the elastic-plastic, large-deformation finite element method, burst capacity of steel pipeline with longitudinal corrosion defect subjected to internal pressure is studied. The appropriate stress-based criterion is used to predict the failure pressure of finite element model of corroded pipeline under internal pressure. By considering the pipe steel grades and geometries of corrosion defects, a series of finite element analyses is conducted. The effects of corrosion depth, length and width on burst capacity are also discussed. A specific failure pressure solution for the assessment of corrosion defects in moderate-to-high strength pipeline is proposed on the base of numerical results. The failure pressures predicted by the proposed method are in better agreement with the experimental results than the results by the other methods.

A true triaxial strength criterion for rocks by gene expression programming

Rock strength is a crucial factor to consider when designing and constructing underground projects.This study utilizes a gene expression programming(GEP)algorithm-based model to predict the true triaxial strength of rocks,taking into account the influence of rock genesis on their mechanical behavior during the model building process.A true triaxial strength criterion based on the GEP model for igneous,metamorphic and magmatic rocks was obtained by training the model using collected data.Compared to the modified Weibols-Cook criterion,the modified Mohr-Coulomb criterion,and the modified Lade criterion,the strength criterion based on the GEP model exhibits superior prediction accuracy performance.The strength criterion based on the GEP model has better performance in R2,RMSE and MAPE for the data set used in this study.Furthermore,the strength criterion based on the GEP model shows greater stability in predicting the true triaxial strength of rocks across different types.Compared to the existing strength criterion based on the genetic programming(GP)model,the proposed criterion based on GEP model achieves more accurate predictions of the variation of true triaxial strength(s1)with intermediate principal stress(s2).Finally,based on the Sobol sensitivity analysis technique,the effects of the parameters of the three obtained strength criteria on the true triaxial strength of the rock are analysed.In general,the proposed strength criterion exhibits superior performance in terms of both accuracy and stability of prediction results.

Mechanical Behavior of a Glass-fiber Reinforced Composite to Steel Joint for Ships

The use of a glass-fiber reinforced composite in marine structures is becoming more common, particularly due to the potential weight savings. The mechanical response of the joint between a glass-fiber reinforced polymer （GRP） superstructure and a steel hull formed is examined and subsequently modified to improve performance through a combined program of modeling and testing. A finite-element model is developed to predict the response of the joint. The model takes into account the contact at the interface between different materials, progressive damage, large deformation theory, and a non-linear stress-strain relationship. To predict the progressive failure, the analysis combines Hashin failure criteria and maximum stress failure criteria. The results show stress response has a great influence on the strength and bearing of the joint. The Balsawood-steel interface is proved to be critical to the mechanical behavior of the joint. Good agreement between experimental results and numerical predictions is observed.

STABILITY OF BOREHOLES IN A GEOLOGIC MEDIUM INCLUDING THE EFFECTS OF ANISOTROPY

An analytical formulation is developed to investigate the stability of a deep, inclined borehole drilled in a geologic medium and subjected to an internal pressure and a non_hydrostatic stress field. The formulation consists of a three_dimensional (3_D) analysis of stresses around a borehole, combined with internal pressurization of the borehole to obtain an approximate solution of the overall stress distribution. The orientation of the borehole, the in_situ stresses and bedding plane can all be arbitrarily related to each other to represent the actual field situations. Both tensile failure and shear failure potentials of a borehole are investigated. The failure criteria applied assume that when the least principal stress exceeds the strength of the formation in tension, a tensile failure occurs. Shear failure is represented using the modified Drucker_Prager failure criterion for anisotropic materials. A parametric study is carried out to assess the effect of material anisotropy, bedding plane inclination and in_situ stress conditions on borehole stability. Results of the parametric study indicate that wellbore stability is significantly influenced by a high borehole inclination, high degree of material anisotropy, in_situ stress conditions and high formation bedding plane inclination. The stability of a borehole in an elasto_plastic medium is also investigated. In order to evaluate the extent of the plastic zone around a borehole and the effect of anisotropy of the material on this plastic zone, a mathematical formulation is developed using theories of elasticity and plasticity. The borehole is assumed to be vertical, subjected to hydrostatic stresses, and drilled in a transversely isotropic geologic medium. A parametric study is carried out to investigate the effect of material anisotropy on the plastic behavior of the geologic medium. Results indicate that the stress distribution around a borehole, the extent of the plastic zone, and the failure pressure are influenced by the degree of material anisotropy and value of in_situ overburden stresses. It was observed that the borehole becomes less stable as the degree of anisotropy of the geologic medium increases.

Discrete element modeling of acoustic emission in rock fracture

The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a result of the heterogeneity in rock specimen, the failure criterion of bonded particle is coupled by the shear and tensile strengths, which follow a normal probability distribution. The Kaiser effect is simulated in the fracture process, for a cubic rock specimen under uniaxial compression with a constant rate. The AE number is estimated with breakages of bonded particles using a pair of parameters, in the temporal and spatial scale, respectively. It is found that the AE numbers and the elastic energy release curves coincide. The range for the Kaiser effect from the AE number and the elastic energy release are the same. Furthermore, the frequency-magnitude relation of the AE number shows that the value of B determined with DEM is consistent with the experimental data.

Numerical evaluation of strength and deformability of fractured rocks

Knowledge of the strength and deformability of fractured rocks is important for design, construction and stability evaluation of slopes, foundations and underground excavations in civil and mining engineering. However, laboratory tests of intact rock samples cannot provide information about the strength and deformation behaviors of fractured rock masses that include many fractures of varying sizes, orientations and locations. On the other hand, large-scale in situ tests of fractured rock masses are economically costly and often not practical in reality at present. Therefore, numerical modeling becomes necessary. Numerical predicting using discrete element methods(DEM) is a suitable approach for such modeling because of their advantages of explicit representations of both fractures system geometry and their constitutive behaviors of fractures, besides that of intact rock matrix. In this study, to generically determine the compressive strength of fractured rock masses, a series of numerical experiments were performed on two-dimensional discrete fracture network models based on the realistic geometrical and mechanical data of fracture systems from feld mapping. We used the UDEC code and a numerical servo-controlled program for controlling the progressive compressive loading process to avoid sudden violent failure of the models. The two loading conditions applied are similar to the standard laboratory testing for intact rock samples in order to check possible differences caused by such loading conditions. Numerical results show that the strength of fractured rocks increases with the increasing confning pressure, and that deformation behavior of fractured rocks follows elasto-plastic model with a trend of strain hardening. The stresses and strains obtained from these numerical experiments were used to ft the well-known Mohr-Coulomb(MC) and Hoek-Brown(H-B) failure criteria, represented by equivalent material properties defning these two criteria. The results show that both criteria can provide fair estimates of the compressive strengths for all tested numerical models. Parameters of the elastic deformability of fractured models during elastic deformation stages were also evaluated, and represented as equivalent Young’s modulus and Poisson’s ratio as functions of lateral confning pressure. It is the frst time that such systematic numerical predicting for strength of fractured rocks was performed considering different loading conditions, with important fndings for different behaviors of fractured rock masses, compared with testing intact rock samples under similar loading conditions.

Prediction of rock brittleness using nondestructive methods for hard rock tunneling

Sand production is an undesired phenomenon occurring in unconsolidated formations due to shear failure and hydrodynamic forces. There have been many approaches developed to predict sand production and prevent it by changing drilling or production strategies. However, assumptions involved in these approaches have limited their applications to very specific scenarios. In this paper, an elliptical model based on the borehole shape is presented to predict the volume of sand produced during the drilling and depletion stages of oil and gas reservoirs. A shape factor parameter is introduced to estimate the changes in the geometry of the borehole as a result of shear failure. A carbonate reservoir from the south of Iran with a solid production history is used to show the application of the developed methodology. Deriving mathematical equations for determination of the shape factor based on different failure criteria indicate that the effect of the intermediate principal stress should be taken into account to achieve an accurate result. However, it should be noticed that the methodology presented can only be used when geomechanical parameters are accurately estimated prior to the production stage when using wells and field data.

New artificial neural networks for true triaxial stress state analysis and demonstration of intermediate principal stress effects on intact rock strength

Simulations are conducted using five new artificial neural networks developed herein to demonstrate and investigate the behavior of rock material under polyaxial loading. The effects of the intermediate principal stress on the intact rock strength are investigated and compared with laboratory results from the literature. To normalize differences in laboratory testing conditions, the stress state is used as the objective parameter in the artificial neural network model predictions. The variations of major principal stress of rock material with intermediate principal stress, minor principal stress and stress state are investigated. The artificial neural network simulations show that for the rock types examined, none were independent of intermediate principal stress effects. In addition, the results of the artificial neural network models, in general agreement with observations made by others, show （a） a general trend of strength increasing and reaching a peak at some intermediate stress state factor, followed by a decline in strength for most rock types; （b） a post-peak strength behavior dependent on the minor principal stress, with respect to rock type; （c） sensitivity to the stress state, and to the interaction between the stress state and uniaxial compressive strength of the test data by the artificial neural networks models （two-way analysis of variance; 95% confidence interval）. Artificial neural network modeling, a self-learning approach to polyaxial stress simulation, can thus complement the commonly observed difficult task of conducting true triaxial laboratory tests, and/or other methods that attempt to improve two-dimensional （2D） failure criteria by incorporating intermediate principal stress effects.

Failure behavior and criteria of metallic glasses

Metallic glasses(MGs)constitute an emerging class of advanced structural materials due to their excellent mechanical properties.However,brittle failure at room temperature and the resultant complicated fracture behavior greatly limit their wide engineering applications.Over the past decades,the deformation and fracture in ductile or brittle mode referring to material compositions,load conditions,sample size,etc.,have been widely studied,and significant progress has been made in understanding the failure behavior of MGs.Micromechanisms of fracture have been revealed involving shear banding,cavitation and the nature of the crack tip field.The ductile-to-brittle transition and inherent governing parameters have been found.To well describe and predict the failure behavior of MGs,failure criteria for ductile and brittle MGs have been established empirically or based on atomic interactions.In this paper,we provide a detailed review of the above advances and identify outstanding issues in the failure of MGs that need to be further clarified.

An Elastic-Plastic Iceberg Material Model Considering Temperature Gradient Effects and its Application to Numerical Study

To simulate the FPSO-iceberg collision process more accurately, an elastic-plastic iceberg material model considering temperature gradient effects is proposed and applied. The model behaves linearly elastic until it reaches the ‘Tsai-Wu’ yield surfaces, which are a series of concentric elliptical curves of different sizes. Decreasing temperature results in a large yield surface. Failure criteria, based on the influence of accumulated plastic strain and hydrostatic pressure, are built into the model. Based on published experimental data on the relationship between depth and temperature in icebergs, three typical iceberg temperature profiles are proposed. According to these, ice elements located at different depths have different temperatures. The model is incorporated into LS-DYNA using a user-defined subroutine and applied to a simulation of FPSO collisions with different types of icebergs. Simulated area-pressure curves are compared with design codes to validate the iceberg model. The influence of iceberg shape and temperature on the collision process is analyzed. It is indicated that FPSO structural damage not only depends on the relative strength between the iceberg and the structure, but also depends on the local shape of the iceberg.

Feasibility evaluation of failure models for predicting forming limit of metal foils

Forming limit of metal foil is an important index to evaluate its formability,and is of considerable significance to improve the quality of products.The ductile fracture(DF)behavior in microscale plastic deformation is remarkably affected by the geometry and grain size.To explore the size-dependent forming limit curve(FLC),the Holmberg and Marciniak tests of SUS304 foils with the thicknesses of less than 0.1 mm and diverse grain sizes were performed.In addition,the validity and feasibility of three types of existing failure models including Swift/Hill,MarciniakKuczynski(M-K)and DF criteria for predicting the micro-scaled FLCs were discussed.It is found that the Swift/Hill model possesses the worst accuracy with predicting deviation above 50%.Four classical DF criteria including Freudenthal,Ayada,Brozzo and Oh show great difference,and Oh model considering plastic anisotropy presents the best precision.The predicted deviation of M-K model is aggravated with increasing grain size and decreasing foil thickness,which is attributed to the intensified free surface roughening and transformation of fracture mechanism with miniaturization.This research thus provides a deeper understanding and valuable reference for the widespread application of FLC in microforming.

Safety evaluation of Dagangshan arch dam resisting strong earthquakes with a rate-dependency anisotropic damage model

This paper presents a model to simulate the safe behavior of Dagangshan arch dam with a rate-dependency anisotropic damage model. This model considers the damage of asymmetry and anisotropy under cyclic loading of tension and compression, and it is used in the compiled finite element code. The material parameters used in the model can be identified from uniaxial static and dynamic experiments. Thereafter, it is used for analyzing damage and failure patterns of the dam subjected to water pressure and strong earthquakes. The numerical results show that it is necessary to consider both asymmetry between tension and compression and anisotropy of damage. Severe damage regions of the dam reveal brittle and risky positions clearly. Meanwhile damage patterns show the failure trend and safety behaviors of the dam. These results match well with that of the experiments carried out in DUT. The proposed model may be used to predict the damage patterns and potential failure modes of concrete structures like the dam. And the aseismic performance of the dam can be figured out.