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.

International study of the Complex Stress Reaction Syndrome:Implications for transdiagnostic clinical practice

BACKGROUND The debate regarding diagnostic classification systems in psychiatry(categorial vs dimensional systems)has essential implications for the diagnosis,prevention and treatment of stress reactions.We previously found a unique pattern of stress reaction in a study executed during the coronavirus disease 2019 pandemic using large representative samples in two countries,and termed it the Complex Stress Reaction Syndrome(CSRS).AIM To investigate CSRS,Type A(psychiatric symptoms,spanning anxiety,depression,stress symptoms,and posttraumatic stress disorder(PTSD)),with or without long-coronavirus disease(COVID)residuals(CSRS,Type B,neuropsychiatric symptoms spanning cognitive deficits and fatigue,excluding systemic symptoms).Our two-tailed hypothesis was that CSRS is a condition related to an unrecognized type of stress reaction in daily life in the general population(Type A)or that it is related to the severe acute respiratory syndrome coronavirus 2 infection and its long-COVID residuals(Type B).METHODS 977 individuals in four continents(North America,Europe,Australia and the Middle East)completed the online study questionnaire in six languages using the Qualtrics platform.The study was managed by six teams in six countries that promoted the study on social media.The questionnaire assessed anxiety,depression,stress symptoms and PTSD(CSRS,Type A),cognitive deficits and fatigue(CSRS,Type B).The data were analyzed using Proportion Analyses,Multivariate Analysis of Co-Variance(MANCOVA),linear regression analyses and validated clinical cutoff points.RESULTS The results of the Proportion Analyses showed that the prevalence of 4 symptoms spanning anxiety,depression,stress symptoms,and PTSD was significantly higher than the most prevalent combinations of fewer symptoms across 4 continents,age groups,and gender.This supports the transdiagnostic argument embedded in the CSRS(Type A).The same pattern of results was found in infected/recovered individuals.The prevalence of the 4 psychiatric symptoms combination was significantly greater than that of 5 and 6 symptoms,when adding cognitive deficits and fatigue,respectively.MANCOVA showed a significant three-way interaction(age×gender×continent).Further analyses showed that the sources of this three-way interaction were threefold relating to two sub-populations at-risk:(1)Individuals that self-identified as non-binary gender scored significantly higher on all 4 psychiatric symptoms of the CSRS,Type A at young age groups(<50 years old)in North America compared to(self-identified)women and men located in the 4 continents studied,and to other ages across the adult life span;and(2)This pattern of results(CSRS,Type A)was found also in women at young ages(<40 years old)in North America who scored higher compared to men and women in other continents and other ages.Linear regression analyses confirmed the MANCOVA results.CONCLUSION These results show a combined mental health risk factor related to stress reactivity,suggesting that the CSRS is sensitive to populations at risk and may be applied to future identification of other vulnerable sub-populations.It also supports the transdiagnostic approach for more accurate prevention and treatment.Time will tell if such transdiagnostic syndromes will be part of the discussions on the next revisions of the traditional classification systems or whether the crisis in psychiatry further evolves.

Development and applications of the quasi‐dynamic triaxial apparatus for deep rocks

The mechanical behaviors of deep rocks have always posed a challenge for the implementation and safe operation of major underground engineering projects.To this end,this study modified the existing mainstream rock mechanics instruments equipped with a dynamic disturbance loading system and developed a second‐generation TFD‐2000/D triaxial instrument.The first‐generation device is equipped with an independent disturbance system and an advanced EDC‐580 all‐digital servo controller,which can apply disturbing load independently,implement the function of cyclic disturbance,and combine dynamic and static disturbances.The instrument was found to be reliable for use in analyzing the damage process of rocks in the disturbance test of marbles.The second‐generation instrument tackles three limitations of the first‐generation instrument:(i)it upgrades the strain measurement system and uses extensometers with linear variable differential transformers to accurately measure deformation;(ii)it uses the self‐balanced chamber to replace the Hoek–Franklin triaxial cell and auto‐balancing triaxial pressure chamber;and(iii)the loading rod is independently equipped with an EDC‐580 all‐digital servo controller,which measures precise loads.The experimental findings confirmed that the second‐generation instrument can be used for rock mechanics testing under cyclic disturbance loading,the disturbance–stress relaxation cycle,and the creep–fatigue cycle.In this sense,the second‐generation instrument can be a useful addition to deep rock mechanical instruments and provide a valuable reference.

Stiffness Degradation of Undisturbed Saturated Soft Clay in the Yangtze Estuary Under Complex Stress Conditions

Stiffness degradation will occur due to the generation of accumulated pore pressure in saturated soft clays under cyclic loading. The soil static-dynamic multi-purpose triaxial and torsional shear apparatus in Dalian University of Technology was employed to perform different types of test on the saturated soft marine clay in the Yangtze Estuary. Undisturbed samples of the clay were subjected to undrained cyclic vertical and torsional coupling shear and cyclic torsional shear after three-directional anisotropic consolidation with different initial consolidation parameters. Investigated were the effects of the initial orientation angle of the major principal stress, initial ratio of deviatoric stress, initial coefficient of intermediate principal stress and continuous rotation of principal stress axes on the stiffness degradation. It is found that the degradation index decreases （or degradation degree increases） significantly with increasing initial orientation angle of the major principal stress and initial ratio of deviatoric stress. Compared with the effects of the initial orientation angle of the major principal stress and initial ratio of deviatoric stress, the effect of initial coefficient of intermediate principal stress is less evident and this trend is more clearly reflected by the results of the cyclic torsional shear tests than those of the cyclic coupling shear tests. At the same cycle number, the degradation index obtained from the cyclic torsional shear test is higher than that from the cyclic coupling shear test. The main reason is that the continuous rotation in principal stress directions during cyclic coupling shear damages the original structure of the soil more than the cyclic torsional shear does.Based on a series of experiments, a mathematical model for stiffness degradation is proposed and the relevant parameters are determined.

Effect of intermediate principal stress on strength of soft rock under complex stress states

A series of numerical simulations of conventional and true triaxial tests for soft rock materials using the three-dimensional finite difference code FLAC3D were presented. A hexahedral element and a strain hardening/softening constitutive model based on the unified strength theory(UST) were used to simulate both the consolidated-undrained(CU) triaxial and the consolidated-drained(CD) true triaxial tests. Based on the results of the true triaxial tests simulation, the effect of the intermediate principal stress on the strength of soft rock was investigated. Finally, an example of an axial compression test for a hard rock pillar with a soft rock interlayer was analyzed using the two-dimensional finite difference code FLAC. The CD true triaxial test simulations for diatomaceous soft rock suggest the peak and residual strengths increase by 30% when the effect of the intermediate principal stress is taken into account. The axial compression for a rock pillar indicated the peak and residual strengths increase six-fold when the soft rock interlayer approached the vertical and the effect of the intermediate principal stress is taken into account.

Critical Cyclic Stress Ratio of Undisturbed Saturated Soft Clay in the Yangtze Estuary under Complex Stress Conditions

There exists a critical cyclic stress ratio when sand or clay is subjected to cyclic loading. It is an index dis-tinguishing stable state or failure state. The soil static and dynamic universal triaxial and torsional shear apparatus de-veloped by Dalian University of Technology in China was employed to perform different types of tests on saturated soft marine clay in the Yangtze estuary. Undisturbed samples were subjected to undrained cyclic vertical and torsional coupling shear and cyclic torsional shear after three-directional anisotropic consolidation with different initial consoli-dation parameters. The effects of initial orientation angle of major principal stress, initial ratio of deviatoric stress,initial coefficient of intermediate principal stress and stress mode of cyclic shear on the critical cyclic stress ratio wereinvestigated. It is found that the critical cyclic stress ratio decreases significantly with increasing initial orientation angle of major principal stress and initial ratio of deviatoric stress. Compared with the effects of the initial orientationangle of major principal stress and initial ratio of deviatoric stress, the effect of initial coefficient of intermediate prin-cipal stress is less evident. Under the same consolidation condition, the critical cyclic stress ratio from the cyclic cou-pling shear test is lower than that from the cyclic torsional shear test, indicating that the stress mode of cyclic shear has an obvious effect on the critical cyclic stress ratio. The main reason is that the continuous rotation in principal stressdirections during cyclic coupling shear damages the original structure of soil more than the cyclic torsional shear does.

Analysis of the stress intensity factor of welded joints under prior corrosion and complex stress fields

Taking cruciform welded joints under different corrosion degrees, together with 45° inclined angle and full penetration load-carrying fillet, as the research object, the stress intensity factor of a quarter-circular comer crack of welded joints is calculated based on FRANC3D with ABAQUS. Effects of different corrosion pit sizes, crack aspect ratios, and crack depths on stress intensity factor are analyzed. The results show that pit depth plays a major role in stress intensity factor, while the effect of pit radius is relatively small. The cracking modes of the surface and the deepest point are mode I, and mixed modes I and II, respectively. Effects of pit depths, crack aspect ratios, and crack depths on the stress intensity factor at the surface point are greater than at the deepest point.

ANALYSIS OF COMPLEX STRESS INTENSITIES FOR CRACKED LAMINATES

Classical plate theory has been used to find out interfacial stress intensity factors in composite laminates. By using a well-known relation between the crack-tip energy release rate and the complex stress intensity factor. a closed-form solution for complex. Stress intensity in terms of external loading and a mode mix parameter for fairly. general composite laminates is given. Then a procedure for determining this mode mix. parameter is presented. followed by numerical results for some laminates. Small scale contact condition is expressed in terms of external loading In particular, a symmetric property of interfacial toughness curye is proven. Finally. the accuracy of failure load predicled by elininating oscllation index is discussed. and an example is presented to show the validity and limitation of β=0 approximation.

Simulation of temperature and stress in 6061 aluminum alloy during online quenching process

The cooling curves of 6061 aluminum alloy were acquired through water quenching experiment. The heat transfer coefficient was accurately calculated based on the cooling curves and the law of cooling. The online quenching process of complex cross-section profile was dynamically simulated by the ABAQUS software. The results suggest that the heat transfer coefficient changes during online quenching process. Different parts of the profile have different cooling velocity, and it was verified by water quenching experiment. The maximum residual stress of the profile was predicted using FEM simulation based on ABAQUS software The relations between the temperature and stress were presented by analyzing the data of key points.

Reliability Based Design Optimization of Aero-Engine Spindle Ball Bearings

Aero-engine spindle ball bearings work in harsh conditions which are affected by relatively complex stresses. One of the key factors which affects bearing performance is its structure. In this paper,we used reliability based design optimization method to solve the structure design problem of aero-engine spindle ball bearings.Compared with the optimization design method, the value of equivalent dynamic load using reliability optimization design method was the least by MATLAB simulation. Also the design solutions show that the optimized structure possesses higher reliability than the original solution.

Influence of principal stress rotation of unequal tensile and compressive stress amplitudes on characteristics of soft clay

Soil behavior can reflect the characteristics of principal stress rotation under dynamic wave and traffic loads. Unequal amplitudes of tensile and compressive stresses applied to soils have complex effects on foundation soils in comparison with the pure principal stress rotation path. A series of undrained cyclic hollow torsional shear tests were performed on typical remolded soft clay from the Hexi area of Nanjing, China. The main control parameters were the tensile and compressive stress amplitude ratio(α) and the cyclic dynamic stress ratio(η). It was found that the critical η tended to remain constant at 0.13, when the value of the compressive stress amplitude was higher than the tensile stress amplitude. However, the influence of the tensile stress was limited by the dynamic stress level when α= 1.For obvious structural change in the soil, the corresponding numbers of cyclic vibration cycles were found to be independent of α at low stress levels and were only related to η. Finally, a new method for evaluating the failure of remolded soft clay was presented. It considers the influence of the tensile and compressive stresses which caused by complex stress paths of the principal stress rotation. This criterion can distinguish stable, critical, and destructive states based on the pore-water-pressure-strain coupling curve while also providing a range of failure strain and vibration cycles. These results provide the theoretical support for systematic studies of principal stress rotation using constitutive models.

Cyclic Shearing Deformation Behavior of Saturated Clays

The apparatus for static and dynamic universal triaxial and torsional shear soil testing is employed to perform stress-controlled cyclic single-direction torsional shear tests and two-direction coupled shear tests under unconsolidated-undrained conditions. Through a series of tests on saturated clay, the effects of initial shear stress and stress reversal on the clay’s strain-stress behavior are examined, and the behavior of pore water pressure is studied. The experimental results indicate that the patterns of stress-strain relations are distinctly influenced by the initial shear stress in the cyclic single-direction shear tests. When the initial shear stress is large and no stress reversal occurs, the predominant deformation behavior is characterized by an accumulative effect. When the initial shear stress is zero and symmetrical cyclic stress occurs, the predominant deformation behavior is characterized by a cyclic effect. The pore water pressure fluctuates around the confining pressure with the increase of cycle number. It seems that the fluctuating amplitude increases with the increase of the cyclic stress. But a buildup of pore water pressure does not occur. The de- formations of clay samples under the complex initial and the cyclic coupled stress conditions include the normal deviatoric deforma- tion and horizontal shear deformation, the average deformation and cyclic deformation. A general strain failure criterion taking into account these deformations is recommended and is proved more stable and suitable compared to the strain failure criteria currently used.

CONSERVATION LAW AND APPLICATION OF J- INTEGRAL IN MULTI-MATERIALS

The conservation law of J-integral in two-media with a crack paralleling to the interface of the two media was firstly proved by analytical and numerical finite element method. Then a schedule model was established that an interface crack is inserted in four media. According to the J-integral conservation law on multi-media, the energy release ratio of Ⅰ-type crack was considered to be conservation when the middle medium layers are very thin. And the conservation law was also convinced by numerical method. By means of the dimension analysis on the model, the asymptotic results and formula calculating the energy release ratio and complex stress intensity factor are presented.

INTEGRAL EQUATION METHOD'S APPLICATION IN HOLE-EDGE STRESS OF COMPOSITE MATERIAL PLATE WITH DIFFERENT SHAPED HOLES

The strength of composite plate with different hole-shapes is always one of the most important but complicated issues in the application of the composite material. The holes will lead to mutations and discontinuity to the structure. So the hole-edge stress concentration is always a serious phenomenon. And the phenomenon makes the structure strength decrease very quickly to form dangerous weak points. Most partial damage begins from these weak points. According to the complex variable functions theory, the accurate boundary condition of composite plate with different hole-shapes is founded by conformal mapping method to settle the boundary condition problem of complex hole-shapes. Composite plate with commonly hole-shapes in engineering is studied by several complex variable stress fimction. The boundary integral equations are founded based on exact boundary conditions. Then the exact hole-edge stress analytic solution of composite plate with rectangle holes and wing manholes is resolved. Both of offset axis loadings and its influences on the stress concentration coefficient of the hole-edge are discussed. And comparisons of different loads along various offset axis on the hole-edge stress distribution of orthotropic plate with rectangle hole or wing manhole are made. It can be concluded that hole-edge with continuous variable curvatures might help to decrease the stress concentration coefficient; and smaller angle of outer load and fiber can decrease the stress peak value.

STUDY OF THE STRESS INTENSITY FACTOR OF PREFORMED V SHAPE FRACTURE TIP

In order to make the fracture cross-section of rock smooth in controlled cutting-blast, generally, two V-shape-notches on the inner wall of a shot hole are notched in symmetry along the design direction. A V-shape notch approximately be considered as V-shape-fracture under certain condition. This paper gave the complex stress function of preformed V-shape-fracture under a blasting load. The stress field and displacement field at the tip of a preformed V-shape-fracture were derived with Westergaard's method, hence its stressintensity factor was obtained. To verify the derived results, blasting tests were made with concrete samples of 400mm×400mm×300mm, and all having, in the center, a drilled hole of 25mm in diameter and 200mm in height. The test result showed that the formulas derived are correct and effective.

Dynamic constitutive model for soils considering asymmetry of skeleton curve

Based on the asymmetric characteristic of skeleton curve obtained from dynamic tests on soils,a function with double asymptotes is proposed for describing the dynamic constitutive relations of soils.The hysteresis loops observed during unloading and reloading show the same form as the skeleton curve and are constructed by taking the ultimate stress as the corresponding asymptote.The coeffcient of initial unloading modulus is used to ensure that the constructed hysteresis loop fts well with the experimental data.Then,a new dynamic constitutive model considering the asymmetry of skeleton curve is elaborated.The verifcation tests on saturated Nanjing fne sand are performed using a hollow cylinder apparatus to verify the applicability of the UD model.It is found that the predicted curves by the UD model agree well with the test data.

Application of ultrasonic fatigue technology in very-high-cycle fatigue testing of aviation gas turbine engine blade materials:A review

The need for very-high-cycle fatigue(VHCF)testing up to 1010cycles of aviation gas turbine engine blade materials under combined mechanical loads and complex environments has encouraged the development of VHCF testing instrumentation and technology.This article begins with a comprehensive review of the existing available techniques that enable VHCF testing.Recent advances in ultrasonic fatigue testing(UFT)techniques are highlighted,containing their new capabilities and methods for single load,multiaxial load,variable amplitude fatigue,and combined cycle fatigue.New techniques for conducting UFT in high-temperature,humid environments,and corrosive environments are summarized.These developments in mechanical loading and environmental building techniques provide the possibility of laboratory construction for real service conditions of blade materials.New techniques that can be used for in situ monitoring of VHCF damage are summarized.Key issues in the UFT field are presented,and countermeasures are collated.Finally,the existing problems and future trends in the field are briefly described.

On the formation of shear bands in a metallic glass under tailored complex stress fields

The formation of shear bands in metallic glasses(MGs)was examined by tailoring localized complex stress fields(LCSFs).The findings have shown that the LCSFs in MGs can increase the localization of strained atoms and accelerate the release of accumulated deformation energy for initiating a shear band in confined and thin-layered regions.The findings not only add more knowledge to the formation mechanisms of shear bands in MGs,but also provide possible rationale for the discrepancies in the mechanical properties of different-sized MGs.As compared with the bulk samples,the higher strength and larger elastic limits in nanoscaled MGs could be attributed to the elimination of stress-concentrators,which can serve as LCSFs.

Stochastic fatigue damage model for concrete under complex stress states

This paper presents a stochastic fatigue damage model for concrete subjected to complex stress states.A constitutive framework considering the tensile and shear damage mechanisms and elastic and plastic energy dissipations is employed.The damage law is established through a multiscale analysis of the damage evolution mechanism.Validation results against test data show that the model can effectively predict the static strength,stress-strain curve,fatigue life,and scattering range of concrete under various multidimensional loading scenarios.

Modified Cam-Clay model incorporating unified nonlinear strength criterion

A unified nonlinear strength criterion(i.e UNS criterion) is proposed,for the sake of versatility,to capture the complex strength behaviors of frictional materials in geotechnical field.It covers wide ranges on the meridian and octahedral planes to describe nonlinear strength behaviors of soils.The Modified Cam-Clay model,incorporating the unified nonlinear strength criterion,is employed as an example to derive working mathematical equations and to illustrate yielding surfaces in three-dimensional stress space for improving the model's predictive capability.The unified nonlinear strength criterion,demonstrated here,is capable of capturing the experimental results of different types of soils on the meridian and octahedral planes.In addition,the revised model,based on this unified nonlinear strength criterion,though very simple,is versatile to predict the true triaxial test results from literature when considering the influences of the intermediate principal stress on strength and deformation under complex stress conditions.