Crack initiation stress and strain of jointed rock containing multi-cracks under uniaxial compressive loading: A particle flow code approach

The ratio of crack initiation stress to the uniaxial compressive strength(SCI,B/SUC,B) and the ratio of axial strain at the crack initiation stress to the axial strain at the uniaxial compressive strength(B,UCB,CI,A,A/SSSS) were studied by performing numerical stress analysis on blocks having multi flaws at close spacing's under uniaxial loading using PFC3 D. The following findings are obtained: SCI,B/SUC,B has an average value of about 0.5 with a variability of ± 0.1. This range agrees quite well with the values obtained by former research. For joint inclination angle, β=90°,B,UCB,CI,A,A/SSSS is found to be around 0.48 irrespective of the value of joint continuity factor, k. No particular relation is found betweenB,UCB,CI,A,A/SSSS and β; however, the average B,UCB,CI,A,A/SSSS seems to slightly decrease with increasing k. The variability ofB,UCB,CI,A,A/SSSS is found to increase with k.Based on the cases studied in this work,B,UCB,CI,A,A/SSSS ranges between 0.3 and 0.5. This range is quite close to the range of 0.4to 0.6 obtained for SCI,B/SUC,B. The highest variability of ± 0.12 forB,UCB,CI,A,A/SSSS is obtained for k=0.8. For the remaining k values the variability ofB,UCB,CI,A,A/SSSS can be expressed within ± 0.05. This finding is very similar to the finding obtained for the variability of SCI,B/SUC,B.

Identifying crack initiation stress threshold in brittle rocks using axial strain stiffness characteristics

As an estimate for the in-situ spalling strength around massive underground excavations to moderately jointed brittle rocks, crack initiation stress marks the initiation of rock micro fracturing. It is crucial to accurately identify crack initiation stress level by proper method. In this study, confined compression tests of sandstone samples are used to examine the validity/applicability of proposed axial strain stiffness method. The results show that by highlighting the minuscule changes in stress-strain curve, the axial strain stiffness curve provided further insight into rock failure process and revealed five stages:(a) irregular fluctuation,(b) nearly horizontal regular fluctuation,(c) irregular fluctuation gradually decreasing to zero,(d) extreme fluctuation, and(e) near zero, which mainly correspond to five stages of stress–strain curve. The ratio of crack-initiation stress to peak strength determined using this approach is 0.44–0.51, similar to the ranges previously reported by other researchers. In this method, the key is to accurately detect the end point of the stage(b), "nearly horizontal regular fluctuation" characterized by a sudden change in axial strain stiffness curve, and the sudden change signifies crack initiation in rock sample. Finally, the research indicates that the axial strain stiffness curve can provide a mean to identify the crack-initiation stress thresholds in brittle rocks.

Antiplane shear crack in a prestressed elastic medium based on the couple stress theory

A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value problem is established.The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method.To determine their intensity,a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial.The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor(CSIF)and the force stress intensity factor(FSIF)around the crack tips.The symmetric part of the shear stress has no singularity,and the skew-symmetric part related to the couple stress exhibits an r^(-3/2)singularity,in which r is the distance from the crack tip.The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.

Effect of welding sequence on residual stress in thin-walled octagonal pipe-plate structure

A three-dimensional finite element approach based on ABAQUS code was developed to investigate the effect of welding sequence on welding residual stress distribution in a thin-walled 6061 aluminum alloy structure. To obtain sound numerical results, the therrno-mechanical behaviour was simulated using a direct-coupled formulation. Nine different simulation sequences were carried out by single-pass TIG welding of an octagonal pipe-plate joint, and the distributions of longitudinal and transverse residual stresses both on the outer and inner surfaces of the pipe were analyzed. The results suggest that the final residual stresses in the weld and its vicinity are not affected by the initial residual stresses of the structure. Selecting a suitable welding sequence can reduce the final residual stress in an octagonal pipe-plate joint.

Experimental investigation of stress unloading effects on rock damage and confining pressure-dependent crack initiation stress of porous sandstone under true triaxial stress environments

This study investigates the impact of intermediate(σ_(2))and minimum(σ_(3))principal stress unloading on damage behavior and the confining pressure influence on crack initiation stress(σci)in true triaxial stress conditions,utilizing large-scale cubic samples.Two distinct true triaxial tests were executed,examining the effects of confining stress(σ_(2)andσ_(3))unloading on porous sandstone damage and the correlation between confining stress andσci.Acoustic emission(AE)parameters,signal characteristics,and wave velocity variations were utilized to elucidate cracking mechanisms and damage development in the samples.Unloading tests reveal consistent ve-locities in three orthogonal directions(V_(11),V_(22),and V_(33))during the initial two unloading stages.In the subse-quent three stages,confining stress unloading leads to a decrease in wave velocity in the corresponding direction,while velocities in the other two directions remain nearly constant.Notably,σ_(2)unloading generates higher amplitude AE signals compared toσ_(3)unloading,with over 70%of the micro-cracks categorized as tensile.In the incremental loading tests,σ_(ci) is found to be contingent on confining pressure,withσ_(2)playing a crucial role.Duringσ_(1) loading,V_(33) decreases,indicating additional crack formation;conversely,σ_(3)loading results in V33 increase,signifying the continuous closure of existing cracks.Limitations of the experiments are summarized and prospects in this domain are outlined.

Stress initialization methods for dynamic numerical simulation of rock mass with high in-situ stress

In the context of deep rock engineering,the in-situ stress state is of major importance as it plays an important role in rock dynamic response behavior.Thus,stress initialization becomes crucial and is the first step for the dynamic response simulation of rock mass in a high in-situ stress field.In this paper,stress initialization methods,including their principles and operating procedures for reproducing steady in-situ stress state in LS-DYNA,are first introduced.Then the most popular four methods,i.e.,explicit dynamic relaxation(DR)method,implicit-explicit sequence method,Dynain file method and quasi-static method,are exemplified through a case analysis by using the RHT and plastic hardening rock material models to simulate rock blasting under in-situ stress condition.Based on the simulations,it is concluded that the stress initialization results obtained by implicit-explicit sequence method and dynain file method are closely related to the rock material model,and the explicit DR method has an obvious advantage in solution time when compared to other methods.Besides that,it is recommended to adopt two separate analyses for the whole numerical simulation of rock mass under the combined action of in-situ stress and dynamic disturbance.

PROPAGATION OF LOVE WAVES IN PRESTRESSED PIEZOELECTRIC LAYERED STRUCTURES LOADED WITH VISCOUS LIQUID

We investigate analytically the effect of initial stress in piezoelectric layered structures loaded with viscous liquid on the dispersive and attenuated characteristics of Love waves, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of initial stress in the piezoelectric layer and the viscous coefficient of the liquid on the phase velocity of Love waves are analyzed. Numerical results are presented and discussed. The analytical method and the results can be useful for the design of chemical and biosensing liquid sensors.

WAVE LOCALIZATION IN RANDOMLY DISORDERED PERIODIC PIEZOELECTRIC RODS WITH INITIAL STRESS

The elastic wave localization in disordered periodic piezoelectric rods with initial stress is studied using the transfer matrix and Lyapunov exponent method. The electric field is approximated as quasi-static. The effects of the initial stress on the band gap characteristics are investigated. The numerical calculations of localization factors and localization lengths are performed. It can be observed from the results that the band structures can be tuned by exerting the suitable initial stress. For different values of the piezoelectric rod length and the elastic constant, the band structures and the localization phenomena are very different. Larger disorder degree can lead to more obvious localization phenomenon.

Strain-rate effect on initial crush stress of irregular honeycomb under dynamic loading and its deformation mechanism

The seemingly contradictory understandings of the initial crush stress of cellular materials under dynamic loadings exist in the literature, and a comprehensive analysis of this issue is carried out with using direct information of local stress and strain. Local stress/strain calculation methods are applied to determine the initial crush stresses and the strain rates at initial crush from a cell-based finite element model of irregular honeycomb under dynamic loadings. The initial crush stress under constant-velocity compression is identical to the quasi-static one, but less than the one under direct impact, i.e. the initial crush stresses under different dynamic loadings could be very different even though there is no strain-rate effect of matrix material. A power-law relation between the initial crush stress and the strain rate is explored to describe the strain-rate effect on the initial crush stress of irregular honeycomb when the local strain rate exceeds a critical value, below which there is no strain-rate effect of irregular honeycomb. Deformation mechanisms of the initial crush behavior under dynamic loadings are also explored.The deformation modes of the initial crush region in the front of plastic compaction wave are different under different dynamic loadings.

Propagation of a Thermoelastic Wave in a Half-Space of a Homogeneous Isotropic Material Subjected to the Effect of Rotation and Initial Stress

The propagation of thermoelastic waves in a homogeneous,isotropic elastic semi-infinite space is subjected to rotation and initial stress,which is at temperature T_(0)-initially,and whose boundary surface is subjected to heat source and load moving with finite velocity.Temperature and stress distribution occurring due to heating or cooling and have been determined using certain boundary conditions.Numerical results have been given and illustrated graphically in each case considered.Comparison is made with the results predicted by the theory of thermoelasticity in the absence of rotation and initial stress.The results indicate that the effect of the rotation and initial stress is very pronounced.

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

Non-complete relief method for measuring surface stresses in surrounding rocks

The measurement of surface stresses in surrounding rocks with the use of a relief method of annular hole-drilling was studied by numerical analysis. The stress relief process by hole-drilling was then simulated with the use of finite element method. The influences of the borehole diameter(d), the initial stresses and the ratio of the initial principle stresses on the variations of the remained stress and the released stress in function of the relief depth(h) were discussed. The relation between the non-dimensional ratio of the released principle strains and that of the initial principle stresses, and the effect of the elastic modulus and the Poisson ratio of the rock mass on the stress relief curves were studied. The results show that the stress relief behavior formulated with the non-dimensional ratio of the released stress and the ratio of h/d is only sensitive to the ratio of the initial principle stresses and the Poisson ratio. The stresses are completely released when h equals 1.6d, and the tensile stresses take place on the bore core surface in the relief measurement process. Finally, a non-complete relief method of annular hole-drilling for measuring surface stress in surrounding rocks is proposed and the procedure is presented.

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introducing an improved model in this context.In this work,we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity.The MCS theory is used to investigate the material length scale effects.Using the Laplace transform,the temperature,deflection,displacement,flexure moment,and stress field variables of the micro-beam are derived.The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced.The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.

Crack initiation of granite under uniaxial compression tests:A comparison study

In this study,a combination of acoustic emission(AE)method(AEM)and wave transmission method(WTM)is used to investigate the behaviors of AE and ultrasonic properties corresponding to initial fracturing in granitic rocks.The relationships of AE characteristics,frequency spectra,and spatial locations with crack initiation(CI)are studied.The anisotropic ultrasonic characteristics,velocity distributions in different ray paths,wave amplitudes,and spectral characters of transmitted waves are investigated.To identify CI stress,damage initiations characterized by strain-based method(SBM),AEM and WTM are compared.For granite samples,it shows that the ratio of CI stress to peak strength estimated by SBM ranges from 0.4 to 0.55,and 0.49-0.6 by WTM,which are higher than that of AEM(0.38-0.46).The CI stress identified by AEM indicates the onset of microcracking,and the combination of AEM and WTM provides an insight into the detection of rock damage initiation and anisotropy.

Mathematical Modelling and 3D FEM Analysis of the Influence of Initial Stresses on the ERR in a Band Crack’s Front in the Rectangular Orthotropic Thick Plate

This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.

The Discrete-Analytical Solution Method for Investigation Dynamics of the Sphere with Inhomogeneous Initial Stresses

The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure.The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics.It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies.For the solution of these equations,which have variable coefficients,the discrete analytical solution method is developed and applied.In particular,it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems.Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.

Lateral resonances in initial stressed 1-3 piezocomposites

A theoretical analysis of the lateral resonances in 1-3 piezocomposites with poling initial stress is conducted using the Bloch wave theory. Based on the linear piezoelectricity theory, theoretical formulations that include initial stress for the propagation of acoustic plane waves are made. Numerical calculations are performed to study the effects of the initial stress on the lateral mode frequencies and the stop band. It is found that lateral mode frequencies increase with the piezoelectricity of the piezocomposites, but decrease with the poling initial stress. The influence of the initial shear stress on the lateral mode frequencies is minimal, and can thus be neglected.

Constitutive relation of weakly anisotropic polycrystal with microstructure and initial stress

Man （Nondestr Test Eval 15：191-214, 1999） derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a computational expression on the integration ∫SO（3） Q^× D^1m0dg is given. Then, by means of the computational expression, the general constitutive relation of a weakly-textured anisotropic polycrystal with the consideration of microstructure and initial stress is derived. As special cases of our general constitutive relation, two constitutive relations are given for an isotropic polycrystal and a weakly-textured anisotropic aggregate of cubic crystallites. The acoustoelastic tensor of the reference cubic crystal is derived to determine the material constants of the polycrystal. Two examples are given for understanding the physical meaning of the texture coefficients and the constitutive relations.

Bi-stable states of initially stressed elastic cylindrical shell structures with two piezoelectric surface layers

A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers.The condition for existence of bi-stability of the shell structural system is presented and analytical expressions for corresponding rolled-up radii of the stable shell are given based on the principle of minimum strain energy.The resulting solution indicates that the shell system may have two stable configurations besides its initial state under a combined action of the actuating electric field and initial stresses characterized by the bending moment.If the piezoelectric layer materials act as only sensor materials without the actuating electric field,initial stresses may produce the bi-stable states,but one corresponding to its initial state.For the shell without initial stresses,the magnitude in the actuating electric field determines the number of the stable states,one or two stable configurations besides the initial state.The theoretical prediction for the bi-stable states is verified by finite element method（FEM） simulation by using the ABAQUS code.

Effect of Initial Stress Conditions on the Threshold Shear Strain of Nanjing's Saturated Fine Sand

By using GDS dynamic hollow cylinder torsional apparatus, a series of cyclic torsional triaxial tests under complex initial consolidation condition are performed on Nanjing saturated fine sand. The effects of the initial principal stress direction αo, the initial ratio of deviatoric stress η0, the initial average effective principal stress Po and the initial intermediate principal stress parameter b0 on the threshold shear strain γt of Nanjing saturated fine sand are then systematically investigated. The results show that γt increases as η0,p0 and b0 increase respectively, while the other three parameters remain constant. ao has a great influence on γt, which is reduced when ao increases from 0° to 45°and increased when α0 increases from 45° to 90°. The effect of α0 on γt, plays a leading role and the effect of η0 will weaken when ao is approximately 45°.