Stress Wave Frequency Research Articles

Instability mechanism and control technology of soft rock roadways affected by mining in karst mountain area

The deformation and damage of soft rock roadways in karst mountainous area is serious, which greatly restricts the safe and efficient mining of coal resources. To explore the instability mechanism of soft rock roadway under the influence of mining, the 226 rail cross-cut of Shanjiaoshu Coal Mine in China was taken as an engineering background. The methods of field monitoring and drilling imaging were adopted to analyze the roadway failure characteristics. In addition, the distributions of the plastic zone, surface displacement, and fracture fractal evolution characteristics of the surrounding rock for different stress wave peak and stress wave frequency are compared and analyzed using UDEC software. Then, the combined support scheme of “secondary strong bolting and grouting” is proposed to control the severe deformation of the roadway. The primary support mainly adopts short hollow grouting anchor cable to strengthen the shallow broken surrounding rock within 0–3 m. The secondary reinforced support adopts long hollow grouting anchor cable or constant resistance large deformation anchor cable to fully mobilize the bearing capacity of deep surrounding rock and to ensure the long-term stability of the roadway. On-site monitoring showed that the scheme could effectively control the severe deformation of the roadway, which also provided a reference for other similar roadway support.

Investigation on the influence of the frequency of pulsed water jet on the rock-breaking effect

Frequency plays a pivotal role in determining the rock-breaking effect of self-excited oscillating pulsed water jet. Experiments were conducted to investigate the relationship between frequency and rock-breaking effectiveness. A relationship between frequency and chamber length was established. An explanation was provided for the varying rock-breaking effects resulting from changes in frequency using the resonance effect theory, thereby revealing the mechanism through which frequency characteristics impact rock-breaking. Our findings demonstrate that the resonance effect significantly influences the rock-breaking effectiveness of the pulsed water jet. The closer the frequency ratio is to 1, the better the rock-breaking results. Notably, the pulse frequency of Helmholtz nozzles closely approximates the frequency of stress waves generated in the rock mass, and both decrease as the chamber length increases.

Experiment study and numerical simulation on the dynamic rock-breaking process of rotary percussive drilling with different cyclic and stress-wave frequencies

The rotary percussive drilling tool was designed to improve rock-breaking efficiency, and the tool’s cyclic frequency and stress-wave frequency are the key influencing factors on the rate of penetration, but the correlative research reports are few. In view of this situation, the cyclic frequency of the rotary percussion drilling tool and the frequency of stress waves generated during impact were measured. A numerical model of polycrystalline diamond compact (PDC) cutter cutting hard rock was established, and the measured frequency parameters were imported into the numerical model. The effects of cyclic frequency and stress-wave frequency on the penetration depth, rock breaking volume, and rock debris size were studied. The finding demonstrated that the average penetration depth increased with the increase of cyclic frequency, and decreased with the rise in stress wave frequency. When the two parameters were simultaneously high, it was conducive to generating smaller rock cuttings and wellbore cleaning. When the cyclic frequency was high and the stress wave frequency was low, the effect on the drilling tooth penetration was the best. The research results can provide a practical reference for optimizing the structure of rotary impact drilling tools and improving the penetration rate.

Experimental study of frequency-temperature coupling effects on wave propagation through granite

The present study investigates the frequency-temperature coupling effects on wave propagation through granite. The pendulum impact test was conducted on the thermally treated long granite bars. The wave propagation coefficients, such as attenuation ratio and wave velocity, were determined for the granite under five groups of high-temperature and six groups of incident waves with different frequencies. A relationship between the dynamic modulus of granite, frequency of stress wave and the high temperature was revealed. The frequency-temperature coupling effects on the dynamic modulus were discussed. The results show that the attenuation ratio, wave velocity and dynamic elastic modulus increase with the increase of frequency. The attenuation ratio increases with the increase of temperature, while the wave velocity and dynamic elastic modulus decrease with the increase of temperature. The proposed relationship between the dynamic modulus, frequency and temperature can efficiently describe the frequency-temperature coupling effects on the granite with acceptable error. The present study has potential in the application of wave propagation through granite in the high-temperature environment.

Effect of Nonlinear Deformational Macrojoint on Stress Wave Propagation Through a Double-Scale Discontinuous Rock Mass

The overall dynamic mechanical behavior of a double-scale discontinuous rock mass with a nonlinear deformational macrojoint was investigated. A method of combining the split three characteristic lines with the piecewise linear displacement discontinuity model (DDM) was proposed. The method was applied to investigate the transmission coefficient of P-wave propagation normally through a double-scale discontinuous rock mass with a nonlinear deformational macrojoint. The results were verified by comparison with the results of P-wave propagation normally through a double-scale discontinuous rock mass with a linear deformational macrojoint. The results showed that for a small amplitude stress wave, the nonlinear deformational macrojoint can be simplified as a linear deformational form to study the stress wave propagation, whereas for a large amplitude stress wave, the effects of the nonlinear deformational behavior of the macrojoint must be considered. The difference of the effects of nonlinear and linear deformational macrojoints on large amplitude stress wave propagation can be overlooked in the low-frequency or high-frequency regions. In addition, when the incident stress wave amplitude and initial macrojoint stiffness are sufficiently large, the effects of the nonlinear deformational macrojoint on stress wave propagation can be overlooked, and the effects of microdefects must be considered. The influence degree of microdefects on the stress wave propagation increases with the increase of incident stress wave frequency.

Numerical analysis on the mechanism of hydraulic fracture behavior in heterogeneous reservoir under the stress perturbation

Hydraulic fracturing is the key technology employed to alter the permeability of tight reservoirs. In this article, the discrete element fluid–solid coupling method is improved, and sinusoidal stress waves are applied at the boundary of a heterogeneous reservoir to simulate perturbation. The influence of stress wave frequency on the mode of crack propagation in the hydraulic fracturing process and the internal stress changes in specimens under different in situ stress ratios are investigated. The simulation results suggest that (1) under a constant injection rate, an increased frequency is associated with a gradual increase in the breakdown pressures, an increase in the time required for cracking breakdown, and faster propagation of cracks propagating; and (2) the hydraulic fracture propagation direction obviously deflects towards the stress wave propagation direction, and the failure mode becomes more complicated under the combined action of the ground stress and the stress wave; and (3) the maximum principal stress inside the specimen is compressive stress, and the curves of the maximum principal stress and maximum shear stress are periodic vibration, with the characteristics of a large amplitude at a low frequency and a small amplitude at a high frequency. The initiation of cracks near the injection hole results from a reduction in the maximum principal stress and an increase in the maximum shear stress. The analysis indicates that the stress wave has a non-negligible influence on hydraulic fracturing and provides a better guideline for understanding the mechanical nature of hydraulic fracturing under the influence of stress perturbation.

Modeling of the attenuation of stress waves in concrete based on the Rayleigh damping model using time-reversal and PZT transducers

Wave-based concrete structural health monitoring has attracted much attention. A stress wave experiences significant attenuation in concrete, however there is a lack of a unified method for predicting the attenuation coefficient of the stress wave. In this paper, a simple and effective absorption attenuation model of stress waves in concrete is developed based on the Rayleigh damping model, which indicates that the absorption attenuation coefficient of stress waves in concrete is directly proportional to the square of the stress wave frequency when the damping ratio is small. In order to verify the theoretical model, related experiments were carried out. During the experiments, a concrete beam was designed in which the d33-model piezoelectric smart aggregates were embedded to detect the propagation of stress waves. It is difficult to distinguish direct stress waves due to the complex propagation paths and the reflection and scattering of stress waves in concrete. Hence, as another innovation of this paper, a new method for computing the absorption attenuation coefficient based on the time-reversal method is developed. Due to the self-adaptive focusing properties of the time-reversal method, the time-reversed stress wave focuses and generates a peak value. The time-reversal method eliminates the adverse effects of multipaths, reflection, and scattering. The absorption attenuation coefficient is computed by analyzing the peak value changes of the time-reversal focused signal. Finally, the experimental results are found to be in good agreement with the theoretical model.

Numerical analysis of the stability of abandoned cavities in bench blasting

When open-pit bench blasting approaches a site with underground cavities, concerns arise regarding the safe blasting distance to prevent collapse of the cavities because such collapses may induce other secondary problems related to the safety and workability of the site. It is therefore necessary to estimate the stability of underground cavities in the proximity of bench blasting. In this paper, blasting tests of small scale were carried out in a site with cavities and field blasting test data were measured to obtain the site-specific attenuation relations of PPV and principal frequency of stress waves. A numerical model is then developed based on these relations to calculate bench blasting induced stress wave propagation. The accuracy of the numerical prediction is verified by the field measured data. The verified numerical model is used to perform a series of simulations. The results are then used to assess the roof stability of cavities adjacent to upper bench blasting. Based on the numerical results, the response characteristics of cavity roof with respect to different explosive charge mass are also studied.

Evaluation of stress wave propagation through rock mass using a modified dominate frequency method

This paper presents an evaluation of stress wave propagation through rock mass using a modified dominate frequency method. The effective velocity and transmission coefficient of stress wave propagation through rock mass with different joint stiffnesses are investigated. The results are validated by the theoretical method and the effects of incident frequency on the calculation accuracy are discussed. The results show that the modified dominate frequency method can be used to predict the effective velocity when the frequency of stress waves is within the low frequency range or high frequency range. However, the error cannot be ignored when the frequency is in the transitional frequency range. On the other hand, the modified dominate frequency method can be used to predict the transmission coefficient when the frequency of stress wave is within the low frequency range or optimal frequency range. However, the error cannot be ignored when the wave is within the high frequency range, which approaches 40% when the frequency is sufficiently large. Finally, the optimal stiffness–frequency relationship for the maximum calculation errors of effective velocity and the minimum calculation errors of transmission coefficient are proposed.

Development of an artificial neural network for source localization using a fiber optic acoustic emission sensor array

An intelligent algorithm was developed based on backpropagation artificial neural network for the acoustic emission source localization. The established and trained methods of the algorithm were stated with the time difference of arrival detected by a fiber optic acoustic emission sensor array and the coordinates of acoustic emission source. The response characteristic of fiber optic acoustic emission sensor was calibrated with the commercial piezoelectric ceramic transducer (PZT) acoustic emission sensor, which provided that the fiber optic acoustic emission sensor was better suited to detect the low frequency of stress wave than the PZT sensor. Four fiber optic acoustic emission sensors were deployed in a square array in an aluminum plate for comparisons between different algorithms of source localization. Comparison results of acoustic emission source location provided that the intelligent algorithm improved the accuracy by reducing the nonlinear errors. For the anisotropic materials, a sensor array deployed in a diamond pattern was adopted. The velocities of stress waves in orthogonal directions were measured as the basic performance for both algorithms of source localization. Four sensors were integrated into a carbon fiber–reinforced polymer plate as a perfect structure for locating the acoustic emission source impacting on its surface. The experiment results provide that the maximum error is only 6.3 mm using the intelligent algorithm.

Effect Analysis of Vehicle System Parameters on Dynamic Response of Pavement

In order to study the damage of a semirigid pavement under vehicle loads with varied parameters, the random dynamic loads applied on the pavement by a running vehicle were computed with two degrees of freedom, quarter-vehicle model, and then a three-dimensional finite element analysis model of semirigid asphalt pavement was established. With the peak stress index of each pavement layer, the effect of varied vehicle parameters on pavement response was studied. The results indicated that the stress wave frequency of each pavement layer was similar to that of the dynamic random load, and, with increased pavement depth, the wave effect decreased. The pavement response increased with increased suspension stiffness and tire stiffness and decreased with increased suspension damping and tire damping. Furthermore, compared to the stiffness, the response variation induced by the damping was orders of magnitude lower. Compared with the traditional time response analysis method, the peak response analysis of the pavement structure was more scientific, rational, and intuitive, which could be useful for the study of vehicle-pavement interaction and road damage.

Experimental study on wire breakage detection by acoustic emission

This paper experimentally investigated wire breakage detection in a steel cable by acoustic emission (AE) waveform. In the experiments, the attenuation laws of waveform amplitudes were discussed based on stress wave propagation in the wire, which was generated by kNocking and wire breakage. Then the wave velocity was calculated based on the reach time of the stress wave from each sensor. Finally, based on the waveform attenuation laws and the linear position method, the amplitude and energy of the source were confirmed through the measured waveform to identify the source category. The experimental results illustrated that the stress wave from different sources has a different frequency spectrum, and the amplitude attenuation factor varied with the stress wave frequency; high frequency waves had a greater attenuation factor. Compared with the other source, the wire breakage source contained a much higher energy, and thus, the wire breakage signal can be distinguished from the other source by comparing the non-attenuation energy at the source position.

Time-harmonic P-waves engulfing a rectangular limited-permeable crack in piezoelectric medium: Energy density and energy release

The dynamic behavior of a limited-permeable rectangular crack in a transversely isotropic piezoelectric material is impinged by to a P-wave. The generalized Almansi theorem and the Schmidt method are used to determine the stress intensity factor and energy density factor as the primary fracture criterion of failure. The mixed boundary value problem entails the evaluation of the appropriate crack edge stress singularities that are characteristics of the fundamental functions. The stress and electric displacement intensity factors are also used to find the energy release rate that can be computed numerically and compared with the results corresponding to those of the stress intensity factor, and energy density factor. Graphical presentation shows that the energy release rate is always negative for the boundary conditions considered while the energy density factors always remain positive. Under certain conditions, the stress and electric displacement intensity factors can be negative and subject to physical limitations. Piezoelectric material boundary value problem solutions should therefore be qualified by the application of failure criteria by fracture of otherwise, particularly when the mechanical and electrical energy can release by creating free surface at the macroscopic and microscopic scales. Negative energy release rate found for the piezoelectric medium in this work can be a case in point. Positive definiteness of the energy density factor can be applied to mutliscale fracture. This is not true for the stress intensity factor nor the energy release rate. Hence, crack initiation behavior for the permittivity of a rectangular crack due to the wave propagation effects may be studied. In particular, the initiation of micro-cracks may be identified with certain critical stress wave frequency band. Negative stress intensity factor may not enhance macrocracking but it does not exclude microcrack initiation.

Simulation of viscoelastic behavior of defected rock by using numerical manifold method

Numerical simulations of longitudinal wave propagation in a rock bar with microcracks are conducted by using the numerical manifold method which has great advantages in the simulation of discontinuities. Firstly, validation of the numerical manifold method is carried out by simulations of a longitudinal stress wave propagating through intact and cracked rock bars. The behavior of the stress wave traveling in a one-dimensional rock bar with randomly distributed microcracks is subsequently studied. It is revealed that the highly defected rock bar has significant viscoelasticity to the stress wave propagation. Wave attenuation as well as time delay is affected by the length, quantity, specific stiffness of the distributed microcracks as well as the incident stress wave frequency. The storage and loss moduli of the defected rock are also affected by the microcrack properties; however, they are independent of incident stress wave frequency.

Detection of Induced Damage in Medium-Density Fiberboard Panels Using a Neural Network Method

This research assessed the feasibility of using a neural network to detect induced and interior damage to small samples of medium-density fiberboard (MDF). The neural network was a 3-layer back-propagation network. The undamaged stress wave frequency spectrum patterns were used to train the neural network. In a previous study, we successfully used the trained patterns to evaluate low levels of damage in samples of MDF onto which various percentages of their estimated failure loads were applied. In this experiment, after introduction of grooves on the surface or a hole through the center of the samples, a small change in the wave patterns occurred. The neural network has the unique ability to train itself using data to recognize spectral patterns and was successfully used to detect structural damage.

Detection of Structural Damage in Medium Density Fiberboard Panels using Neural Network Method

This research assessed the feasibility of using a neural network to detect low levels of damage in small samples of medium density fiberboard (MDF). The neural network was a three-layer back-propagation network. The undamaged stress wave frequency spectrum patterns were trained by the neural network. The trained patterns were then compared to stress waves patterns taken from MDF samples loaded to various percentages of their estimated failure load. In this experiment, if an application load is below the proportional limit, a small change in wave patterns occurs. The neural network has the unique ability to train data to recognize spectral patterns and has been used with success for the detection of structural damage.

The Predominant Frequency of Stress Waves in Non-elastic Zone near an Explosive Source

Summary An investigation of stress waves near an explosive source in a gravelsandy medium has been carried out. Records of these waves obtained by the piezoelectric method were Fourier analysed. The amplitude spectra were discussed from the point of the predominant frequency of the stress waves. The relation between the predominant frequency and the weight of the explosive charge is defined, that frequency is indirectly proportional to the fifth root of the weight of the charge. By comparing that experimentally obtained relation with the formula of the source frequency, given by F. G. Blake, the expression for calculating the predominant frequency of the stress waves generated by the explosive sources was determined.

The Predominant Frequency of Stress Waves in Non-elastic Zone Near an Explosive Source

The Predominant Frequency of Stress Waves in Non-elastic Zone Near an Explosive Source