Reflection and refraction of plane stress waves at dissipative interfaces

Upon stress wave interaction with joints, incident energy is reflected and refracted. To gain insight into the mechanisms associated with dynamic processes such as blasting, percussion drilling and seismicity, knowledge of the amplitudes of the reflected and refracted waves is of importance. This paper compiles stress, energy, displacement and velocity amplitudes of stress waves, which are reflected and refracted by a variety of interface types. In addition to covering the well-known wave interactions with standard discontinuities, such as a free boundary and welded interface, some new interface conditions are analysed, e.g. interfaces with friction and shear strength, and interfaces with normal and shear stiffness related to measurable rock properties. The aim of this tutorial paper is to act as an educational guide and reference for the blasting engineer, seismologist, geophysicist and rock engineer, and to assist in further understanding stress wave interactions with rock mass discontinuities.

Stress wave micro–macro attenuation in ceramic plates made of tiles during ballistic impact

The initial stresses have a strong effect on the mechanical behavior of underground rock masses, and the initial stressed rock masses are usually under strong dynamic disturbances such as blasting and earthquakes. The influence mechanism of a blasting excavation on underground rock masses can be revealed by studying the propagation of stress waves in them. In this paper, the improved Mohr-Coulomb elasto-plastic constitutive model of the intact rock considering the initial damage was first established and numerically implemented in Universal Distinct Element Code (UDEC) based on the variation of the experimental stress wave velocity in the initial stressed intact rock, and the feasibility of combining the established rock constitutive model and the BB (Bandis-Barton) model which characterizes the nonlinear deformation of the joints to simulate stress waves across jointed rock masses under initial stress was validated by comparing the numerical and model test results subsequently. Finally, further parameter studies were carried out through the UDEC to investigate the effect of the initial stress, angle, and number of joints on the transmission of the blasting stress wave in the jointed rock mass. The results showed that the initial stress significantly changed the propagation of the stress waves in the jointed rock mass. When the initial stress was small, the transmission coefficients of the stress waves in the jointed rock were vulnerable to be influenced by the variation of the angle and the number of joints, while the effect of the angle and the number of joints on the stress wave propagation gradually weakened as the initial stress increased.

An extended displacement discontinuity method for analysis of stress wave propagation in viscoelastic rock mass

The passage of stress waves of large amplitude through solid specimens often produces fractures which differ in several respects from those which can occur under any other conditions. Many of the observed phenomena can be accounted for in terms of the acoustical treatment of reflection and refraction of stress waves at the boundaries of the specimen and of diffraction effects in regions where the dimensions of the specimen become comparable with the wavelength of the disturbance. When a fracture occurs it results in a sudden release of stress, and consequently, secondary stress waves travel out from the fracture surfaces. The experimental investigation of these effects by means of high-speed photography, by electrical measurements of stress and strain, and by subsequent examination of the geometry and appearance of the fractured surfaces will be described, and the type of information which such investigations may give about the nature of the phenomenon of brittle fracture will be discussed.

This paper establishes the effect of auxeticity on stress wave transmission and reflection. Specifically, investigation was made on wave transmission across two perfectly bonded isotropic solids in which the Poisson’s ratios ranged between −1 and 0.5. The results show that the combined use of auxetic and conventional solids at extreme Poisson’s ratio is helpful to multiply or even to eliminate stress waves, under the prescribed density and modulus relations. These results suggest the usefulness of auxetic solids as smart materials and in smart structures for effective control of stress wave transmission.

This paper reports the second part of the study carried out by the authors on the underground explosion-induced stress wave propagation and damage in a rock mass. In the accompanying paper reporting the first part of the study, equivalent material properties were used to model the effects of existing cracks and joints in the rock mass. The rock mass and its properties were treated as deterministic. In this paper, existing random cracks and joints are modeled as statistical initial damage of the rock mass. In numerical calculation, an anisotropic continuum damage model including both the statistical anisotropic initial damage and cumulative damage dependent on principal tensile strain and stochastic critical tensile strain is suggested to model rock mass behavior under explosion loads. The statistical estimation of stress wave propagation in the rock mass due to underground explosion is evaluated by Rosenblueth's point estimate method. The suggested models and statistical solution process are also programmed and linked to Autodyn3D as its user's subroutines. Numerical results are compared with the field test data and those presented in the accompanying paper obtained with equivalent material property approach.

The stress wave reflection method is widely used in the detection of structure size and integrity due to its advantages of low environmental impact and convenience. The detection accuracy depends on the accurate extraction of the stress wave reflection period. The traditional peak–peak method (PPM) measures the time interval between the first two peaks of the reflected waves to extract the reflection period. However, human interpretation is not avoidable for identifying the weak peak due to signal energy leaks into the surrounding environment. This paper proposes an algorithm for automatic extraction of the stress wave reflection period based on image processing to avoid human interference. The image is the short-time Fourier transform (STFT) spectrogram of the reflected wave signal after applying wavelet denoising and quadratic self-correlation operations. The edge detection method of image processing is used to extract the periodically occurring trough in the image. Graying and filtering are performed to eliminate interference. The frequency of the trough distribution is calculated by using the fast Fourier transform (FFT), and then the reflection period of the stress wave is obtained. The effectiveness and accuracy of the proposed method are validated by measuring the different lengths of two buried metal piles in soil. Comparing with the existing method of extracting the stress wave reflection period, this new algorithm comprehensively utilizes the time–frequency domain information of the stress wave reflection signal.

The stress at the structural plane of bedding rock slope will change under dynamic load, which may lead to sliding failure risk of the slope. Based on the time-domain recursive method (TDRM), the propagation process of stress waves in viscoelastic rock slope with a nonlinear bedding plane is analyzed, and the propagation equation of multiple reflected waves between the plane and the slope surface is obtained. According to the superposition principle and the relation between the particle vibration velocity caused by stress waves and stress, the expressions of normal and tangential stress of any particle at the structural plane are obtained. Furthermore, in light of the gravitational impact on the rock mass, we formulate the slip criterion equation for the structural plane. The results indicate that the stress field at the structural plane is influenced by several factors, including the slope angle, horizontal positioning of monitoring points, vertical distance to the slope foot, and the initial stiffness of the structural plane. The influence of multiple reflected waves on stress field obviously increases the possibility of rock mass sliding on structural plane. This paper theoretically elucidates the slippage mechanism of a rock slope featuring a bedding structural plane subjected to the effects of stress wave. The research findings furnish a theoretical foundation for comprehending the dynamic response of rock slopes, conducting dynamic stability analyses, and ensuring the safety measures for rock mass engineering projects.

Quantitative visualization methods for continuous evolution of three-dimensional discontinuous structures and stress field in subsurface rock mass induced by excavation and construction - An overview

Once an opening is created in deep underground, the stresses surrounding the opening will be redistributed, inducing a gradient stress field. To understand how the ground rock in such a gradient stress field responses to dynamic stress loading, the gradient stress distribution at a circular opening was first analyzed and the propagation of 1D stress wave in rock mass under gradient stress field was theoretically derived. By using an implicit to explicit solution method in LS-DNA code, the dynamic mechanical behaviors of rock in gradient stress field were numerically investigated. The results indicate that the damage is mainly produced at or near the free face, partly due to the straight action of compressive stress wave and the tensile stress wave generated at the free face. The range of the induced damage zone is narrowed under the conditions of higher gradient stress rate and lower dynamic stress amplitude. However, under lower gradient stress field and higher dynamic stress, the damage becomes severer and wider with discontinuous failure regions.

Study of stress waves in geomedia and effect of a soil cover layer on wave attenuation using a 1-D finite-difference method

In structures excavated in rock mass, load progressively increases to a level and remains constant during the construction. Rocks display different elastic properties such as Ei and v under different loading conditions and this requires to use the true values of elastic properties for the design of safe structures in rock. Also, rocks will undergo horizontal and vertical deformations depending on the amount of load applied. However, under constant loads, values of Ei and v will vary in time and induce variations in the behavior of the rock mass. In some empirical equations in which deformation modulus of the rock mass is taken into consideration, elastic parameters of intact rock become functions in the equation. Hence, the use of time dependent elastic properties determined under constant loading will yield more reliable results than when only constant elastic properties are used. As well known, rock material will play an important role in the deformation mechanism since the discontinuities will be closed due to the load. In this study, Ei and v values of intact rocks were investigated under different constant loads for certain rocks with high deformation capabilities. The results indicated significant time dependent variations in elastic properties under constant loading conditions. Ei value obtained from deformability test was found to be higher than the Ei value obtained from the constant loading test. This implies that when static values of elastic properties are used, the material is defined as more elastic than the rock material itself. In fact, Ei and v values embedded in empirical equations are not static. Hence, this workattempts to emerge a new understanding in designing of safer structures in rock mass by numerical methods. The use of time-dependent values of Ei and v under different constant loads will yield more accurate results in numerical modeling analysis.

Purpose.The paper focuses on the study of the stress distribution patterns in fractured rock masses during rock breaking on high benches using blasthole explosive charges. The research aims to optimize the parameters of drilling-blasting operations through detailed analysis of stress distribution and formation of failure zones on high benches. This will significantly improve the handling equipment operating efficiency, as well as develop economically feasible blasting patterns tailored to quarry geometry. Methods. The research is based on theoretical modeling of stress propagation caused by detonating the blasthole explosive charges in fractured rock masses. The stress distribution around the charge is calculated using equations derived from elastic deformation and surface wave theory, taking into account the particular characteristics of fractured high benches. The model includes stress propagation, wave transformation, and rock fracture behavior to identify rock crushing zones. Findings. The results have revealed that the main factor of rock failure is tensile stress waves resulting from the reflection of compression waves. The degree of rock crushing and the volume of failure zones depend on the length and diameter of the blasthole explosive charge, the properties of the explosive agent, as well as the network of pre-existing fractures. Originality. A new approach to studying the stress distribution in fractured rock masses during blasting operations is presented. This paper takes into account the influence of existing fractures and the interaction of stress waves with natural disturbances in the rock, thus allowing more accurate prediction of rock crushing. For the mining conditions of the Pustynnoye Deposit, the ratios between the radii of failure zones and the value of breaking stresses have been found, and a function for determining the failure radius has been proposed. Practical implications. The results of this research can be used to optimize the parameters of blasting operations in quarries with fractured high benches. By determining the optimal sizes and placement of charges, it is possible to achieve more efficient rock crushing, reduce equipment wear and improve overall production efficiency.

This chapter explores the stress wave transmission and reflection from an incident stress wave , between isotropic solids of different Poisson’s ratio, with special emphasis on systems in which at least one of the solids is auxetic. The dimensionless transmitted stress, in terms of the ratio of transmitted to incident stresses, were investigated for longitudinal stresses in prismatic bars (1D stress), longitudinal stresses in width-constrained plates (2D stress or 2D strain), plane waves of dilatation (1D strain), torsional waves (shear waves), and Rayleigh (surface) waves. Each of these wave transmission study was performed under three special cases, i.e. when the (i) product of density and Young’s modulus for both solids are equal, (ii) product of density and shear modulus for both solids are equal, and (iii) product of density and bulk modulus for both solids are equal. Under these special conditions, results show that the stress transmission is effectively doubled or eliminated when the Poisson’s ratio for the isotropic solids are at their limits.