THE GENERAL STRESS STRAIN RELATION OF SOILS INVOLVING THE ROTATION OF PRINCIPAL STRESS AXES

In the light of matrix theory, the character of stress increment which causes the rotation of principal stress axes is analysed and the general stress increment is decomposed into two parts: coaxial part and rotational part. Based on these, the complex three dimensional (3-D) problem involving the rotation of principal stress axes is simplified to the combination of the 3-D coaxial model and the theory about pure rotation of principal stress axes that is only around one principal stress axes. The difficulty of analysis is reduced significantly. The concrete calculating method of general 3-D problem is provided and other applications are also presented.

On the Consistency of Large Earthquake Moment and Strain Rate Inferred from GPS Data in North China

The new GPS data can map crustal strain rates over large areas with a useful degree of precision. Stable strain measurement results open the door for improved estimates of earthquake occurrence. The Kostrov’s formula (1974) translates the smoothed strain rates in North China into geodetic moment rates. In North China, the ratio of seismic moment released to moment accumulated from GPS measurement is 60.6% in NS direction, 68.9% in EW direction, and 104.1% in NE shear direction. The near unit ratio points to the reliability of GPS measurements there. The combination of historical seismicity and GPS measurement offers a powerful attack on earthquake hazard.

3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

A novel method for chemistry tabulation of strained premixed/stratified flames based on principal component analysis

The principal component analysis （PCA） is used to analyze the high dimen- sional chemistry data of laminar premixed/stratified flames under strain effects. The first few principal components （PCs） with larger contribution ratios axe chosen as the tabu- lated scalars to build the look-up chemistry table. Prior tests show that strained premixed flame structure can be well reconstructed. To highlight the physical meanings of the tabu- lated scalars in stratified flames, a modified PCA method is developed, where the mixture fraction is used to replace one of the PCs with the highest correlation coefficient. The other two tabulated scalars are then modified with the Schmidt orthogonalization. The modified tabulated scalars not only have clear physical meanings, but also contain passive scalars. The PCA method has good commonality, and can be extended for building the thermo-chemistry table including strain rate effects when different fuels are used.

Characteristics of evolution of mining-induced stress field in the longwall panel:insights from physical modeling

The evolution of mining-induced stress field in longwall panel is closely related to the fracture field and the breaking characteristics of strata.Few laboratory experiments have been conducted to investigate the stress field.This study investigated its evolution by constructing a large-scale physical model according to the in situ conditions of the longwall panel.Theoretical analysis was used to reveal the mechanism of stress distribution in the overburden.The modelling results showed that:(1)The major principal stress field is arch-shaped,and the strata overlying both the solid zones and gob constitute a series of coordinated load-bearing structures.The stress increasing zone is like a macro stress arch.High stress is especially concentrated on both shoulders of the arch-shaped structure.The stress concentration of the solid zone in front of the gob is higher than the rear solid zone.(2)The characteristics of the vertical stress field in different regions are significantly different.Stress decreases in the zone above the gob and increases in solid zones on both sides of it.The mechanical analysis show that for a given stratum,the trajectories of principal stress are arch-shaped or inverselyarched,referred to as the‘‘principal stress arch’’,irrespective of its initial breaking or periodic breaking,and determines the fracture morphology.That is,the trajectories of tensile principal stress are inversely arched before the first breaking of the strata,and cause the breaking lines to resemble an inverted funnel.In case of periodic breaking,the breaking line forms an obtuse angle with the advancing direction of the panel.Good agreement was obtained between the results of physical modeling and the theoretical analysis.

Strain data recorded in Xinjiang and their bearing on Tianshan’s uplift/shortening and Tarim basin’s rotation

Based on the continuous strain data recorded in Xinjiang since 1985, we discuss the mechanisms of Tianshan＇ s uplift and Tarim basin＇ s clockwise rotation. The results indicate ： 1 ） The principal - compression directions in Tianshan are nearly NS, and their intersection angles with regional structures and mountains are nearly perpendicular, which is in accordance with Tianshan＇ s uplift and crustal shortening. 2）The principal compressions around Tarim basin tend to facilitate the regional faults＇ left-lateral strike-slip movements and the basin＇ s clockwise rotation. These phenomena of uplift/shortening and rotation are fundamentally the re- suits of India plate＇ s northward push on Euro-Asia plate, and the associated Pamir arc ＇ s rapid northward movement and regional blocks＇ interaction.

Intact soft clay’s critical response to dynamic stress paths on different combinations of principal stress orientation

Comprehensive tests on Hangzhou intact soft clay were performed, which were used to obtain the soils' critical response to undrained dynamic stress paths under different combinations of principal stress orientation. The different combinations included cyclic principal stress rotation (CPSR for short), cyclic shear with abrupt change of principal stress orientation (CAPSO for short) and cyclic shear with fixed principal stress orientation (CFPSO for short). On one side, under all these stress paths, samples have obvious strain inflection points and shear bands, and the excess pore water pressure is far from the level of initial effective confining pressure at failure. Stress paths of major principal stress orientation (α) alternating from negative and positive have quite different influence on soil's properties with those in which α is kept negative or positive. On the other side, due to the soil's strongly initial anisotropy, samples under double-amplitudes CPSR and CAPSO (or single-amplitude CPSR and CFPSO) have similar properties on dynamic shear strength and pore water pressure development tendency when α is kept within ±45°, while have quite different properties when α oversteps ±45°.

Cyclic behavior of reinforced sand under principal stress rotation

Although the cyclic rotation of the principal stress direction is important,its effect on the deformation behavior and dynamic properties of the reinforced soil has not been reported to date.Tests carried out on large-scale hollow cylinder samples reveal that the cyclic rotation of the principal stress direction results in significant variations of strain components(ε,ε,εand γ) with periodic characteristics despite the deviatoric stress being constant during tests.This oscillation can be related to the corresponding variations in the stress components and the anisotropic fabric that rotate continuously along the principal stress direction.Sand under rotation appears to develop a plastic strain.Similar trends are observed for reinforced sand,but the shear interaction,the interlocking between particles and reinforcement layer,and the confinement result in significant reductions in the induced strains and associated irrecoverable plastic strains.Most of the strains occur in the first cycle,and as the number of cycles increases,the presence of strains becomes very small,which is almost insignificant.This indicates that the soil has reached anisotropic critical state(ACS),where a stable structure is formed after continuous orientation,realignment and rearrangement of the particles accompanied with increasing cyclic rotation.Rotation in the range of 60°-135° produces more induced strains even in the presence of the reinforcement,when compared with other ranges.This relates to the extension mode of the test in this range in which σ>σand to the relative approach between the mobilized plane and the weakest horizontal plane.Reinforcement results in an increase in shear modulus while it appears to have no effect on the damping ratio.Continuous cycles of rotation result in an increase in shear modulus and lower damping ratio due to the densification that causes a decrease in shear strain and less dissipation of energy.

Pore Water Pressure Buildup Under Cyclic Rotation of Principal Stress and Stability Evaluation of Seabed Deposit

The cyclic rotation of principal stress direction with a constant amplitude is the characteristics of cyclic stress in seabed deposit induced by travelling waves. Presented in the paper are the results obtained from tests simulating the cyclic stress characteristics, with emphasis laid on the buildup of pore water pressure in soil samples. Regression analysis of test data shows that the pore water pressure can be expressed as the function of the number of cycles of cyclic loading, or as the function of generalized shear strain. Using the results thus obtained, the possibility of failure of seabed deposit under cyclic loading induced by travelling waves can be evaluated. The comparison with the results of conventional cyclic torsional shear tests shows that neglect of the effect of the cyclic rotation of the principal stress direction will result in considerable over-estimation of the stability of seabed deposit.

Theoretical Analysis of Crack Propagation Measurement for Brittle Materials Based on Virtual Principal Strain Field

The measurement of crack propagation is crucial for revealing the fracture mechanical properties of materials and structures.Based on the virtual principal strain field and Steger’s algorithm,an accurate and automatic method has been proposed for measuring the geometric parameters of crack propagation.The measured geometric parameters of crack propagation include the width,length,and tip location of each crack.The mechanism of the crack-induced virtual principal strain field and the effects of subset,step,and strain window size are analyzed and discussed theoretically.The effectiveness of the derived theoretical equations is verified by the simulation experiments.According to the theoretical equations,it is determined that the distribution of the virtual principal strain field near the crack is similar to the grayscale distribution of the laser fringe image with optimized calculation parameters.Experiments are further conducted to validate the effectiveness of the derived equations.With the optimized calculation parameters,the minimum crack that can be measured is approximately 0.0362 pixel in the laboratory environment,while the measurement error of the crack width is less than 0.025 pixel for two-dimensional digital image correlation(DIC)and 0.020 pixel for three-dimensional DIC.

Friction coefficient in rubber forming process of Ti-15-3 alloy

The forming limit diagram of Ti-15-3 alloy sheet was constituted at room temperature. The effects of different punch and rubber hardness on the limit principal strain distributions were investigated experimentally. Finite element analysis models of the samples with dimensions of 180 mm×180 mm were established to analyze the friction coefficients of different interfaces. Effects of various friction coefficients on the strain distributions were studied in detail. Finally, the friction coefficients in the cold forming were determined by contrasting the strain results between the experimental data and the simulated ones.

低水灰比水泥基材料早期塑性收缩研究

为研究混凝土早期塑性收缩发展机制,探究不同的减缩抑制剂对混凝土收缩及裂缝发展的控制效果,分析水泥净浆的裂缝发展状态及主应变变化规律,分别选用再生混凝土微粉、碳化再生混凝土微粉、氧化镁基膨胀剂、聚乙烯纤维作为掺入材料,按照相应配合比拌合水泥净浆;通过二维非接触数字图像方法(2D-DIC)研究了不同净浆的收缩裂缝发展历程,定量评价了不同工况下试件中线位置最大主应变的变化趋势;最后通过扫描电镜对不同掺料作用下的裂缝开展状态进行评估。结果表明:不同材料对混凝土早期塑性收缩的裂缝发展影响不同;掺入再生混凝土微粉与碳化再生混凝土微粉均能有效抑制水泥净浆的早期塑性收缩,碳化后的再生混凝土微粉较普通再生混凝土微粉能够进一步提升水泥净浆的收缩控制效果,裂缝出现时间延迟了10 min;加入聚乙烯纤维可有效提高塑性开裂的发展时间并减少裂缝的开展宽度;随着浇筑时间的增加,最大主应变逐渐增大,在4.5 h后达到0.03380;不同掺加剂对主应变的发展趋势影响各不相同,掺入碳化再生混凝土微粉工况下最大主应变在4.5 h时为0.02795,能够使塑性最大主应变降低17.30%;无掺加剂的水泥净浆中裂缝往往呈现主裂缝贯通、其余裂缝分散分布的特征;掺入碳化再生混凝土微粉的情况下,裂缝之间的连接性增强,表明碳化再生混凝土微粉的掺入有效降低了水泥基材料的早期塑性开裂程度。

鄂尔多斯块体及其周缘现今地壳水平形变特征及应力应变耦合关系

针对鄂尔多斯块体地壳变形性质量化研究不足和应力应变耦合关系尚不明确的问题,采用球坐标最小二乘配置模型解算研究区域地壳的特征应变场,利用震源机制解数据反演区域地壳的主应力分布。结果显示,地壳变形主要集中在板块边界带和断陷盆地内,鄂尔多斯块体内部的地壳形变较小。其中,青藏高原东北缘与阿拉善块体的交界处地壳变形尤其剧烈,表现为沿板块边界的强压缩变形,主要变形机制为NW-SE向压缩与NE-SW向弱拉张共存,最大主压应变率超过0.05μstrain。研究区域地壳处于较为统一的张应力环境,最大主应力方向接近水平并指向SEE向,与对应区域的主张应变方向吻合,最小主应力方向更接近主压应变方向。

Strain and kinematic vorticity analysis of the Louzidian low-angle ductile shear detachment zone in Chifeng,Inner Mongolia,China

The Louzidian low-angle ductile shear detachment zone at the south of Chifeng is a SE-dipping, low-angle normal fault system. It is composed mainly of ductile shear zone, ductile-brittle shear zone and brittle fault zone. The ductile shear zone consists of, from bottom to top, mylonitic rocks, protomylonites and mylonites. Finite strain measurement of feldspar strain markers from those rocks using the Rf /φ method shows that strain intensities (Es) of the mylonite at core of the ductile shear zone (Es=0.65-0.96) are higher than those of the mylonitic rocks close to the granite intrusions (Es=0.59-0.62) and of the protomylonites at top of the ductile shear zone (Es= 0.47-0.70), and the strain types of the protomylonites and mylonties are elongate strain and plane-flattening strain, respectively. The kinematic vorticity values (Wk) estimated by the Polar Mohr diagram and the Rigid Grain Net range from 0.81 to 0.90 with an average of 0.85 for the protomylonites, and from 0.53 to 0.80 with 0.66 on average for the mylonites; Wk values of the extensional crenulation cleavage, i.e., C′, estimated by C′ method range from 0.63 to 0.37 with an average of 0.50. The angles between the maximum principal stress and shearing direction determined using the Maximum effective moment criterion evolved from 61° to 69° and to 75°, and finally normal to shearing direction. The results of strain and kinematic vorticity measurements suggest that high strain corresponds to low kinematic vorticity. Kinematic vorticity measurements show that the Louzidian low-angle ductile shear detachment zone is a result of a combination of simple-dominated general shearing at the early stage and pure-dominated general shearing at the late stage. All these, together with isotope geochronology and regional tectonic background, suggest that the Louzidian ductile shear detachment zone resulted from a combination of crust extension and magma intrusion. The model of simple shear at the early stage and pure shear at the late stage in the formation of metamorphic core complex has probably general significance.

Macro-micro investigation of granular materials in torsional shear test

A three-dimensional numerical torsion shear test is presented on hollow cylinder specimen which is performed on a spherical assemblage with fixed principal stress axes using the discrete element code PFC3D.Stack wall technique boundary conditions are employed and optimized to reasonably capture the microstructure evolution.Parametric studies are conducted in terms of the ratio κ,normal and shear stiffness of particles,wall stiffness and friction coefficients.Afterwards,in comparison with physical test,numerical results for a fixed principal stress angle(α=45°) are presented.The results show that the numerical test could capture the macro-micro mechanical behavior of the spherical particle assembly.The evolution of the coordination number demonstrates that particles in shear banding undergo remarkable decrease.The effects of localization on specimens illustrate that global stress and strain recorded from a hollow cylinder apparatus could not represent the localized response.The shearing band initiation and evolution from porosity and shear rate are visualized by contour lines in different shear strains.

Analytical solutions for deep tunnels in strain-softening rocks modeled by different elastic strain definitions with the unified strength theory

This paper presents the analytical solutions for the responses of tunnels excavated in rock masses exhibiting strain-softening behavior. Since previous analyses give little consideration to the effect of the intermediate principal stress on the strain-softening rock behavior, the unified strength theory was introduced to analyze the tunnel response. Four cases of different definitions of the elastic strain in the softening and residual regions, used in the existing solutions, were considered. The tunnel displacements,stresses, radii of the softening and residual zones and critical stresses were deduced. The proposed solutions were verified by comparing with numerical simulations, model tests and existing solutions. Furthermore, the solutions of the four cases were compared with each other to investigate the influence of the elastic strain expressions on the tunnel responses. The results showed that the intermediate principal stress coefficient b has a significant effect on the tunnel displacements, stress fields, and plastic radii. Parametric studies were performed to analyze the influences of the softening and residual dilatancy coefficients,softening modulus and residual strength on the tunnel responses. The parametric analysis indicated that the existing models should be carefully evaluated in the analysis of tunnels constructed through average-quality rocks;the proposed solutions outperformed the existing models in solving the mentioned problem.

Fatigue Life Estimation of an Elastomeric Pad by ε-N Curve and FEA

Failure analysis and fatigue life prediction are very important in the design procedure to assure the safety and reliability of rubber components. The fatigue life of a railway elastomeric pad is predicted by combining the test of material properties and finite element analysis (FEA). The specially developed chloroprene rubber material’s fatigue life equation is acquired based on uniaxial tensile test and fatigue life tests performed on the dumbbell specimens of the chloroprene rubber. The same chloroprene rubber was developed at Indian Rubber Manufacturer’s Research Association, Thane. The strain distribution contours and the maximum total principal strains of the elastomeric pad at different compressive loads are obtained using finite element analysis method. The software used for the FEA was ANSYS. The three parameter nonlinear hyperelastic Mooney-Rivlin Model and plane 182 elements were used for finite element analysis. The critical region cracks prone to arise are obtained and analysed. Then the maximum first principal elastic strain was used as the fatigue damage parameter, which is substituted in the chloroprene rubber’s fatigue life equation, to predict the fatigue life of an elastomeric pad in the number of cycles at different compressive loads. The results were compared with the technical requirements given by Indian Railway’s Research Designs and Standards Organization. These requirements were achieved up to certain extents. The results were also compared with the data available in the literature and a similarity was observed between the results acquired and literature data. In short, the proposed fatigue life prediction method can shorten the product design cycle, decrease the design and product cost remarkably and improve the quality of an elastomeric pad.

Numerical Simulation on Interfacial Creep Failure of Dissimilar Metal Welded Joint between HR3C and T91 Heat-Resistant Steel

The maximum principal stress, von Mises equivalent stress, equivalent creep strain, stress triaxiality in dissimilar metal welded joints between austenitic（HR3C） and martensitic heat-resistant steel（T91） are simulated by FEM at 873 K and under inner pressure of 42.26 MPa. The results show that the maximum principal stress and von Mises equivalent stress are quite high in the vicinity of weld/T91 interface, creep cavities are easy to form and expand in the weld/T91 interface. There are two peaks of equivalent creep strains in welded joint, and the maximum equivalent creep strain is in the place 27-32 mm away from the weld/T91 interface, and there exists creep constrain region in the vicinity of weld/T91 interface. The high stress triaxiality peak is located exactly at the weld/T91 interface. Accordingly, the weld/T91 interface is the weakest site of welded joint. Therefore, using stress triaxiality to describe creep cavity nucleation and expansion and crack development is reasonable for the dissimilar metal welded joint between austenitic and martensitic steel.

ANALYSIS OF INHOMOGENEOUS FINITE STRAIN FIELDS IN THE EARTH'S CRUST

This paper proposes the approximate methods of calculation for research on inhomogeneous finite strain fields in geologic bodies by means of the 'Principal Axis' theory of continuum mechanics. The methods are to obtain the principal strain orientations at finite points in the earth's crust based on the information and data provided by the actual strain measurements of deformation marked objects in the field, or by the research on crystalline fabrics in rocks, and then to obtain two sets of smooth orthogonal principal strain trajectories through mathematical treatments. A network composed of two sets of orthogonal curves shows the deformation character of the rock, and correspondent strain components satisfy compatibility conditions. The curvatures of curves are used to describe the compatibility conditions in this paper. An analytic solution of a strain field is obtained when the two sets of lines can be simulated by analytic function; the magnitudes of principal strains at every point may be obtained by means of the discrete method when the simulation by analytic functions fails.

Study on dynamic response of high speed train window glass under tunnel aerodynamic effects

Purpose-This paper aims to analyze the bearing characteristics of the high speed train window glass under aerodynamic load effects.Design/methodology/approach-In order to obtain the dynamic strain response of passenger compartment window glass during high-speed train crossing the tunnel,taking the passenger compartment window glass of the CRH3 high speed train onWuhan-Guangzhou High Speed Railway as the research object,this study tests the strain dynamic response and maximum principal stress of the high speed train passing through the tunnel entrance and exit,the tunnel and tunnel groups as well as trains meeting in the tunnel at an average speed of 300 km$h-1.Findings-The results show that while crossing the tunnel,the passenger compartment window glass of high speed train is subjected to the alternating action of positive and negative air pressures,which shows the typical mechanic characteristics of the alternating fatigue stress of positive-negative transient strain.The maximum principal stress of passenger compartment window glass for high speed train caused by tunnel aerodynamic effects does not exceed 5 MPa,and the maximum value occurs at the corresponding time of crossing the tunnel groups.The high speed train window glass bears medium and low strain rates under the action of tunnel aerodynamic effects,while the maximum strain rate occurs at the meeting moment when the window glass meets the train head approaching from the opposite side in the tunnel.The shear modulus of laminated glass PVB film that makes up high speed train window glass is sensitive to the temperature and action time.The dynamically equivalent thickness and stiffness of the laminated glass and the dynamic bearing capacity of the window glass decrease with the increase of the action time under tunnel aerodynamic pressure.Thus,the influence of the loading action time and fatigue under tunnel aerodynamic effects on the glass strength should be considered in the design for the bearing performance of high speed train window glass.Originality/value-The research results provide data support for the analysis of mechanical characteristics,damage mechanism,strength design and structural optimization of high speed train glass.