Blasting induced dynamic stress concentration and failure characteristics of deep-buried rock tunnel

In this study,the dynamic stress concentration factors(DSCF)around a straight-wall arch tunnel(SWAT)were solved analytically utilizing the complex variable function methods and Duhamel’s integral.The effects of wavelength,incident angle,and blasting rising time on the DSCF distribution were analyzed.Theoretical results pointed out dynamic disturbances resulting in compressive stress concentration in the vertical direction and tensile stress in the incident direction.As the wavelength and rising time increased,there was a tendency for the amplitude of stress concentration to initially rise and then converge.Moreover,a series of 3D FEM models were established to evaluate the effect of different initial stress states on the dynamic failure of the tunnel surrounding rock.The results indicated that the failure of the surrounding rock was significantly influenced by the direction of the static maximum principal stress and the direction of the dynamic disturbance.Under the coupling of static and blasting loading,damage around the tunnel was more prone to occur in the dynamic and static stress concentration coincidence zone.Finally,the damage modes of rock tunnel under static stress and blasting disturbance from different directions were summarized and a proposed support system was presented.The results reveal the mechanisms of deep-buried rock tunnel destruction and dynamically triggered rockburst.

Exploring the Limits of a Deflection-Based Method for the Estimation of Dynamic Stress in Beams

Estimation of the dynamic stress in structures,such as beams and plates,has previously been made using the relationship between stress and velocity spatial maxima based on far-field assumptions.This paper presents a method for the estimation of dynamic stress in a beam using Euler–Bernoulli beam theory,where deflection data from a grid of measurement points on the surface of the beam is used to estimate the dynamic bending stress in the structure.The limitations of the method are investigated via response data provided by a numerical model of a freefree beam.A nondimensional wavenumber analysis is used to determine the number of points required for an accurate estimate of stress.Beams with a range of material and geometric parameters are modeled in order to explore the limits of the estimation method,and parameters representative of several real-world materials are used to assess the suitability of the method for practical applications.

Dynamic Stress Intensity Factor and Scattering of SH Wave by Circle Canyon and Crack

The dynamic stress intensity factor (DSIF) and the scattering of SH wave by circle canyon and crack are studied with Green's function. In order to solve the problem, a suitable Green's function is constructed first, which is the solution of displacement fields for elastic half space with circle canyon under output plane harmonic line loading at horizontal surface. Then the integral equation for determining the unknown forces in the problem can be changed into the algebraic one and solved numerically so that crack DSIF can be determined. Last when the medium parameters are altered, the influence on the crack DSIF is discussed partially with the displacement between circle canyon and crack.

Fault-Induced Coal Burst Mechanism under Mining-Induced Static and Dynamic Stresses

Fault is a common geological structure that has been revealed in the process of underground coal excavation and mining.The nature of its discontinuous structure controls the deformation,damage,and mechanics of the coal or rock mass.The interaction between this discontinuous structure and mining activities is a key factor that dominates fault reactivation and the coal burst it can induce.This paper first summarizes investigations into the relationships between coal mining layouts and fault occurrences,along with relevant conceptual models for fault reactivation.Subsequently,it proposes mechanisms of fault reactivation and its induced coal burst based on the superposition of static and dynamic stresses,which include two kinds of fault reactivations from:mining-induced quasi-static stress(FRMSS)-dominated and seismic-based dynamic stress(FRSDS)-dominated.These two kinds of fault reactivations are then validated by the results of experimental investigations,numerical modeling,and in situ microseismic monitoring.On this basis,monitoring methods and prevention strategies for fault-induced coal burst are discussed and recommended.The results show that fault-induced coal burst is triggered by the superposition of high static stress in the fault pillar and dynamic stress from fault reactivation.High static stress comes from the interaction of the fault and the roof structure,and dynamic stress can be ascribed to FRMSS and FRSDS.The results in this paper could be of great significance in guiding the monitoring and prevention of fault-induced coal bursts.

SCATTERING OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN MINDLIN'S THICK PLATES WITH A CUTOUT

Using the complex variable method and conformal mapping,scat- tering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied.The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique,the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations.As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular,elliptic cutout are graphically presented in sequence.

Dynamic Stress Analysis of Sewage Centrifugal Pump Impeller Based on Two-way Coupling Method

Current research on the operational reliability of centrifugal pumps has mainly focused on hydrodynamic instability. However, the interaction between the fluid and structure has not been sufficiently considered; this interaction can cause vibration and dynamic stress, which can affect the reliability. In this study, the dynamic stresses in a single-blade centrifugal pump impeller are analysed under different operating conditions; the two-way coupling method is used to calculate the fluid-structure interaction. Three-dimensional unsteady Reynolds-averaged Navier-Stokes equations are solved with the SST k-o9 turbulence model for the fluid in the whole flow passage, while transient structure dynamic analysis is used with the finite element method for the structure side. The dynamic stresses in the rotor system are computed according to the fourth strength theory. The stress results show that the highest stress is near the loose bearing and that the equivalent stress increases with the flow rate because the dynamic stresses are closely related to the pressure load. The stress distributions on the blade pressure side, suction side, leading edge, and trailing edge are each analysed for different flow rates; the highest stress distribution is found on the pressure side. On the blade pressure side, a relatively large stress is found near the trailing edge and hub side. Based on these results, a stress distribution prediction method is proposed for centrifugal pumps, which considers the interaction between the fluid and structuxe. The method can be used to check the dynamic stress at different flow rates when optimising the pump design to increase the pump reliability.

Tomography of the dynamic stress coefficient for stress wave prediction in sedimentary rock layer under the mining additional stress

In this study,the tomography of dynamic stress coefficient(TDSC)was established based on a mechanical model of stress wave propagation in bedding planes and a mathematical model of the stress wave attenuation in rock masses.The reliability of the TDSC was verified by a linear bedding plane model and field monitoring.Generally,the TDSC in the dynamic stress propagation of bedding planes increases with the following conditions:(1)the increase of the normal stiffness of the bedding plane,(2)the increase of the incident angle of the stress wave,(3)the decrease of the incident frequency of the stress wave,or(4)the growth of three ratios(the ratios of rock densities,elastic moduli,and the Poisson’s ratios)of rocks on either side of bedding planes.The additional stress weakens TDSC linearly and slowly during the stress wave propagation in bedding planes,and the weakening effect increases with the growth of the three ratios.Besides,the TDSC decreases exponentially in the rock mass as propagation distance increases.In a field case,the TDSC decreases significantly as vertical and horizontal distances increase and its wave range increases as vertical distance increases in the sedimentary rock layers.

Dynamic stress concentration and scattering of SH-wave by interface elliptic cylindrical cavity

In this paper,the dynamic stress concentration and scattering of SH-waves by bi-material structures that possess an interface elliptic cavity are investigated.First,by using the complex function method,the Green's function is constructed.This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface.Then,the problem is divided into an upper and lower half space along the horizontal interface,regarded as a harmony model.In order to satisfy the integral continuity condition, the unknown anti-plane forces are applied to the interface.The integral equations with unknown forces can be established through the continuity condition,and after transformation,the algebraic equations are solved numerically.Finally,the distribution of the dynamic stress concentration factor(DSCF)around the elliptic cavity is given and the effect of different parameters on DSCF is discussed.

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.

The dynamic stress intensity factor analysis of adhesively bonded material interface crack with damage under shear loading

This paper studies the dynamic stress intensity factor （DSIF） at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.

Dynamic Stress Analysis of the Leg Joints of Self-Elevating Platform

Since a self-elevating platform often works in water for a long time, the lattice leg is largely influenced by wave and current. The amplitude of leg joint stresses is a very important factor for the fatigue life of the platform. However, there are not many researches having been done on the mechanism and dynamic stress analysis of these leg joints. This paper focuses on the dynamic stress analysis and suppression methods of the leg joints of self-elevating platforms. Firstly, the dynamic stresses of the lattice leg joints are analyzed for a self-elevating platform by use of the 5th-order Stokes wave theory. Secondly, the axial and bending stresses are studied due to their large contributions to total stresses. And then, different joint types are considered and the leg-hull interface stiffness is analyzed for the improvement of the joint dynamic stress amplitude. Finally, some useful conclusions are drawn for the optimization design of the self-elevating platform.

AN ANALYSIS FOR DIFFRACTION OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN THICK PLATES WITH A CAVITY

By using the complex variable method and conformal mapping, the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied. A general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of an arbitrary cavity is obtained. By employing the orthogonal function expansion technique, the dynamic stress problem can be reduced to the solution of an infinite algebraic equation series. As an example, the numerical results for the dynamic stress concentration factor in thick plates with a circular, elliptic cavity are graphically presented. The numerical results are discussed.

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

STUDY ON DYNAMIC STRESS INTENSITY FACTORS OF DISK WITH A RADIAL EDGE CRACK SUBJECTED TO EXTERNAL IMPULSIVE PRESSURE

A dynamic weight function method is presented for dynamic stress intensity factors of circular disk with a radial edge crack under external impulsive pressure. The dynamic stresses in a circular disk are solved under abrupt step external pressure using the eigenfunction method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions. By making use of Fourier- Bessel series expansion, the history and distribution of dynamic stresses in the circular disk are derived. Furthermore, the equation for stress intensity factors under uniform pressure is used as the reference case, the weight function equation for the circular disk containing an edge crack is worked out, and the dynamic stress intensity factor equation for the circular disk containing a radial edge crack can be given. The results indicate that the stress intensity factors under sudden step external pressure vary periodically with time, and the ratio of the maximum value of dynamic stress intensity factors to the corresponding static value is about 2.0.

THE ANALYSIS OF DYNAMIC STRESS INTENSITY FACTOR FOR SEMI-CIRCULAR SURFACE CRACK USING TIME-DOMAIN BEM FORMULATION

The time-domain BEM was developed to analyze the dynamic stress intensity factor ( DSIF) of 3-D elastodynamic crack problems. To simulate the stress singularity along the front of a crack, eight-node isoparametric singular elements were used, and the DSIF for a semi-circular surface crack was firstly calculated based on displacement equation using the time-domain BEM formulation. The new scheme to determine the time step was brought forward. By the dynamic analysis program of time-domain BEM compiled by its, several numerical examples are presented, which demonstrate the unconditional stability and high accuracy of time-domain BEM applied to 3-D elastodynamic crack problems.

Dynamic stress accumulation model of granite residual soil under cyclic loading based on small-size creep tests

The creep behaviors of granite residual soil with pre-stress of 100 kPa was investigated by a series of small size creep tests. Three different types of strain curves were obtained at different stress levels. Based on creep characteristics of the granite residual soil under different stress levels, a creep model of the granite residual soil was established by rheological theory, and related parameters of the model were determined according to the experimental data at the same time. Further on, based on the established creep model, a theoretical model of dynamic stress accumulation in the granite residual soil under cyclic loading was deduced. It is found that there is a threshold of dynamic stress accumulation in this theoretical model. The dynamic stress accumulation laws of the granite residual soil are different under different cyclic loading stress. Finally, with the dynamic stress accumulation laws in the small-size samples of granite residual soil under different cycle loading studied and the experimental results comparing with the theoretical results, it verifies the validity of the theoretical model.

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.

DYNAMIC STRESS CONCENTRATIONS IN AMBARTSUMIAN'S PLATE WITH A CUTOUT

Based on the motion equations of flexural wave in Ambartsumian' s plates including the effects of transverse shear deformations,by using perturbation method of small parameter,the scatter- ing of flexural waves and dynamic stress concentrations in the plate with a cutout have been studied. The asypmtotic solution of the dynamic stress problem is obtained.Numerical results for the dynamic stress concentration factor in Ambartsumian's plates with a circular cutout are graphically presented and discussed.

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally~ the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method （FEM）. Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.

A METHOD FOR TOPOLOGICAL OPTIMIZATION OF STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS AND DISPLACEMENT CONSTRAINTS

A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasistatic method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.