Multiple Parallel Joints Research Articles

The effects of joint spacing on transmission characteristics of stress waves through layered composite rock masses

AbstractThe effects of joint spacing on the transmission characteristics of stress waves through layered composite rock masses were investigated. First, a model of layered composite rock masses containing multiple parallel joints with different media in front of and behind the joints was introduced to study multiple reflections between joints. Second, wave transmission through layered composite rock masses was investigated and compared with wave transmission through traditional layered homogeneous rock masses. Finally, the effects of joint spacing and wave impedance ratio on particle velocity transmission coefficient were discussed. The results indicate that for wave propagation through rock masses with the same joint spacing, the onset time and amplitude of the transmitted wave in layered composite rock masses are smaller than those in layered homogeneous rock masses. For wave transmission through rock masses with the same nondimensional joint spacing, the onset time of the transmitted wave in the layered composite rock masses is similar to that in the layered homogeneous rock masses, while the amplitude of the transmitted wave in the layered composite rock masses is smaller than that in the layered homogeneous rock masses. In addition, the particle velocity transmission coefficient first increases and then decreases to be constant as the joint spacing increases, while it continues to increase as the wave impedance ratio increases for wave transmission through both layered composite rock masses and layered homogeneous rock masses.

Study on the size effect of the secant modulus of rocks containing multiple parallel joints

The secant modulus of the rock reflects the stiffness of the rock and the ability to resist deformation. There are significant differences in the secant modulus of the rock due to the different numbers of joints in the rock and the change in rock size. Therefore, it is important to obtain effectively the secant modulus of rocks with the number of parallel joints for evaluating rock deformation. In this study, the method of regression analysis is used, and 10 sets of numerical plans are set up to discuss the influence of a number of parallel joints and rock size on the secant modulus. The results show that the secant modulus decreases with the increase in a number of parallel joints, and the curve is a power function. The secant modulus decreases when the rock size increases, and the curve is an exponential function. The characteristic secant modulus and characteristic size decrease with the increase in the number of parallel joints, and their curves are an exponential function. The specific forms of these relationships are given in the article. The establishment of these relationships realizes the prediction and calculation of the rock secant modulus with the number of parallel joints, which provides a guiding significance for the rock deformation analysis.

Transmission and application of a P-wave across joints based on a modified g-λ model

Accurately predicting the location of a fault in front of a tunnel face is an essential part of deep-buried tunnel excavation . This paper proposes a modified g- λ ( 0 < λ < 1 ) model with in situ stress to investigate the propagation and attenuation of a P-wave across jointed rock masses , including a single joint or multiple parallel joints. Based on the modified g- λ model, the differential expressions of the transmitted wave’s particle velocity reflecting the interactions between the P-wave and the joints are deduced by using the characteristics method and the displacement discontinuity model. Parametric studies examining the in situ stress, the value of λ , the incident wave frequency and amplitude, and the number of joints are conducted to evaluate the application of the modified g- λ model. This provides support for predicting the location of the fault during the in situ stress tunnel construction when ignoring the shape and width of the fault. The results show that the effective wave velocity of the jointed rock masses increases with increasing in situ stress when a normally incident P-wave impinges upon a single joint. Considering multiple parallel joints, the magnitude and time of the maximum peak of the transmitted wave are decreases and delayed correspondingly with the increase in the number of joints, respectively. Moreover, multisource seismic interferometry is used to predict the location of the fault at different surrounding rock wave velocities and dip angles of the fault, which contribute to the identification of unfavorable geological bodies on the tunnel advanced geological predictions.

Study on the effects of joints orientation and strength on failure behavior in shale specimen under impact loads

As an anisotropic and jointed material, shale has been extensively investigated due to the rich unconventional gas reserved in the shale rock mass. In the process of hydraulic fracturing in jointed shale, joints may significantly affect hydraulic crack behavior under dynamic disturbance loads, such as crack propagation direction, speed and distance, which has a great effect on the efficiency of hydraulic fracturing and gas production. Therefore, it is of great significance to study crack dynamic propagation characteristics in shale with different orientation joints and dynamic strength. Impacting experiments were conducted on the single cleavage triangle (SCT) shale specimens with joint orientation 0°, 30°, 45°, 60° and 90°, respectively. A modified split Hopkinson pressure bar (SHPB) system was applied and AUTODYN code was used to simulate crack dynamic fracture behavior. For the case of a single joint and multiple parallel joints, crack propagation directions and trajectories were numerically analyzed. The experimental and numerical results indicate that joints have a great influence on crack dynamic propagation direction. In addition, the crack propagation speed of shale is positively related to the loading rate under dynamic loads. If joints are considered as thin layer material, dynamic tensile strength and elastic modulus of joints have a great effect on dynamic crack propagation behavior under impact loads.

Analytical Time-Domain Solution of Plane Wave Propagation Across a Viscoelastic Rock Joint

The effects of viscoelastic filled rock joints on wave propagation are of great significance in rock engineering. The solutions in time domain for plane longitudinal ( P-) and transverse ( S-) waves propagation across a viscoelastic rock joint are derived based on Maxwell and Kelvin models which are, respectively, applied to describe the viscoelastic deformational behaviour of the rock joint and incorporated into the displacement discontinuity model (DDM). The proposed solutions are verified by comparing with the previous studies on harmonic waves, which are simulated by sinusoidal incident P- and S-waves. Comparison between the predicted transmitted waves and the experimental data for P-wave propagation across a joint filled with clay is conducted. The Maxwell is found to be more appropriate to describe the filled joint. The parametric studies show that wave propagation is affected by many factors, such as the stiffness and the viscosity of joints, the incident angle and the duration of incident waves. Furthermore, the dependences of the transmission and reflection coefficients on the specific joint stiffness and viscosity are different for the joints with Maxwell and Kelvin behaviours. The alternation of the reflected and transmitted waveforms is discussed, and the application scope of this study is demonstrated by an illustration of the effects of the joint thickness. The solutions are also extended for multiple parallel joints with the virtual wave source method and the time-domain recursive method. For an incident wave with arbitrary waveform, it is convenient to adopt the present approach to directly calculate wave propagation across a viscoelastic rock joint without additional mathematical methods such as the Fourier and inverse Fourier transforms.

Study on the deformation and failure modes of rock mass containing concentrated parallel joints with different spacing and number based on smooth joint model in PFC

Engineering mechanical properties of rock mass are largely influenced by the characteristics of weak joints. Concentrated parallel joints are well developed in a large hydropower station in southwest China, and the deformation behavior of these joint belts is a key factor affecting slope stability. Therefore, this paper performed a simulation by particle flow code (PFC) and smooth joint model (SJM) to study the deformation and failure modes of rock mass containing concentrated parallel joints with different spacing and number. The following findings were obtained. (1) Four deformation phenomena of rock mass with concentrated joints were identified by field investigation: shearing along a single joint, shearing along multiple parallel joints, shearing across joints, and shearing through multiple joints and shaping as step-path deformation. (2) With the increase of joint number, peak strength and elastic modulus of rock mass decreased and the stair-shaped phenomenon of fracture became obvious. (3) The distance between tensile cracks, which are developed between joints during deformation process, has something to do with the joint spacing. Large spacing formed large distance, and small spacing formed small distance. (4) Although the elastic modulus decreased with the increase of smooth joint (SJ) number, no matter how big or small spacing is, for the rock mass with the same number of smooth joint, the elastic moduli are very close to each other. This may be the result of behavior of hard rock material and SJM assumption. The results of this paper illustrated that fracture developed along concentrated parallel joints should consider the interaction between joints. But how to consider and deal with the concentrated parallel joints for the slope stability calculation still needs more discussion.

Experimental Study of Ultrasonic Waves Propagating Through a Rock Mass with a Single Joint and Multiple Parallel Joints

Experiments were conducted to study the relationship between the transmission ratio (TR) and nor- mal stress, joint roughness, joint number and frequency of incident waves, respectively, when ultrasonic waves pass across a rock mass with one joint and multiple parallel joints oriented normally. The ultrasonic waves were gen- erated and received by pairs of piezoelectric transducers and recorded by an ultrasonic detector. The specimens were subjected to normal stress by a hydraulic jack and loading frame. The jointed rock mass was produced by superposing rock blocks in the study. Rough joints were produced by grooving notches on the planar joints formed by sawing directly. In the case of multiple parallel joints, the overall thickness of specimens was maintained while the joint number changed. Three pairs of P-wave trans- ducers and one pair of S-wave transducers with different frequencies were, respectively, applied and all transducers emitted signals perpendicular to the joints in the experi- ment. The results indicate that TR increases with increas- ing normal stress while the increment rate decreases

Prediction of Wave Attenuation across Multiple Joints with an Improved Elastic Nonlinear Model

The study on nonlinear displacement discontinuity model has been investigated in the researches of normal incident wave attenuation across rock joints. But the studies were limited only on the effects of joint with single type deformation behavior, without considering the influence of different extent in model nonlinearity. The improved elastic nonlinear normal deformational model can descript the extent of nonlinearity quantitatively. Based on this model, a displacement discontinuity model for normally incident wave propagation across multiple parallel joints was established in an elastic half-space. Using one-dimensional wave equation characteristics method, the time-domain numerical difference scheme of transmitted particle velocity was proposed, making computational programs to obtain semi-numerical solutions, and transmission coefficients. Parameter studies were conducted to get an insight into the effects of number of joints and the extent of nonlinearity, the incident wave maximum amplitude on transmission coefficients and transmission energy rate, waveform distortion and delay time.

Obliquely incident wave propagation across rock joints with virtual wave source method

Due to the presence of joints, waves are greatly attenuated when propagating across rock masses. Zhu et al. (2011) (Normally incident wave propagation across a joint set with virtual wave source method. J. Appl. Geophys.73, 283–288.) studied normally incident wave propagation across a joint set with the virtual wave source method (VWSM). The introduced VWSM has merits in some aspects, especially the capability of separating differently arriving transmitted waves. However, normal wave incidence is only the special case for wave incidence with arbitrary incident angles. Obliquely incident wave propagation across a joint set is more complicated than normally incident wave propagation due to wave transformation at the joints. As a continuation of the previous paper, this work is extended to analytically study obliquely incident wave propagation across joints with VWSM. Complete theoretical reflection and transmission coefficients across single joint described by displacement discontinuity model are derived through plane wave analysis. The superposition of P wave and S wave is for the first time mathematically expressed and studied. The VWSM is verified through comparison with the propagation matrix method. Through extensive parametric studies on wave transmission across single and multiple parallel joints, it is shown that transmitted wave energy is mainly constrained in the transmitted wave of the same type as the incident wave. And with increasing joint stiffness, the transmission coefficients across single joint increases except those whose wave type is different from the incident wave. The amplitude of superposed transmitted wave for P wave incidence increases with incident angle, which is coincident with field observations. Both joint spacing and number of joints have significant effects on transmission coefficients. We find that when joint spacing is sufficiently large, the transmission coefficient is no longer a constant as the normally incident wave propagation case (Zhu et al., 2011). And when joints are very closely spaced, wave attenuation depends little on the number of joints, which is different from the conclusions from equivalent medium method.

Wave propagation across rock joints filled with viscoelastic medium using modified recursive method

Rock joints have significant effects on wave propagation. When the joints are filled with saturated sand or clay, the filling materials exhibit viscoelastic behavior on wave propagation. In the present study, wave propagation across single and multiple parallel joints filled with viscoelastic medium is examined. Based on a layered medium model, the recursive method is adopted and a modification is made under some special conditions for faster calculation. In the theoretical formulation, analytical solutions of wave propagation across a single viscoelastic joint as well as elastic joint are mathematically derived. Through parametric studies, it is found that the more viscous the filled medium is, the less the wave energy transmits. Meanwhile, distinct stop-pass behavior exhibits with the change of joint thickness or wave frequency for a single elastic joint. While for the wave transmission across a single viscoelastic joint, the transmission coefficient generally decreases with increasing joint thickness or wave frequency, except when the two parameters match with the pass bands of the corresponding elastic joint. When parallel joints exist, multiple wave reflections among joints influence wave transmission. The transmission coefficient decreases with increasing joint number and, the stop-pass behavior for viscoelastic joints is less significant than that for the elastic joints.

Verification of UDEC Modeling 1-D Wave Propagation in Rocks

Three cases for 1-D wave propagation in ideal elastic rock, through single rock joint and multiple parallel rock joints are used to verify 1-D wave propagation in rocks. For the case for 1-D wave propagation through single rock joint, the magnitude of transmission coefficient obtained from UDEC results is compared with that obtained from the analytical solution. For 1-D wave propagation through multiple parallel joints, the magnitude of transmission coefficient obtained from UDEC results is compared with that obtained from the method of characteristics. For all these cases, UDEC results agree well with results from the analytical solutions and the method of characteristics. From these verification studies, it can be concluded that UDEC is capable of modeling 1-D dynamic problems in rocks.

Validation study of the distinct lattice spring model (DLSM) on P-wave propagation across multiple parallel joints

A validation study of the distinct lattice spring model (DLSM) for wave propagation problems is performed. DLSM is a microstructure-based numerical model, which is meshless and has advantages in modelling dynamic problems where stress wave propagation is important. To verify the applicability of DLSM to modelling wave propagation through a discontinuous medium, the virtual wave source (VWS) method is used to obtain analytical solutions for wave propagation across a jointed rock mass. Numerical modelling results of the commercial code UDEC are selected as the reference. The effects of particle size and lattice rotation angle on wave propagation are first studied. Then, the results of wave transmission across a single joint with a different joint stiffness and across multiple parallel joints with different joint spacings are derived with DLSM, UDEC and VWS. These results are in good agreement with each other. Therefore, the capability of DLSM to model P-wave propagation across jointed rock mass is verified, which provides confidence for the further application of DLSM to modelling more complex problems.

Numerical prediction of crater blasting and bench blasting

As an anisotropic and jointed material, shale has been extensively investigated due to the rich unconventional gas reserved in the shale rock mass. In the process of hydraulic fracturing in jointed shale, joints may significantly affect hydraulic crack behavior under dynamic disturbance loads, such as crack propagation direction, speed and distance, which has a great effect on the efficiency of hydraulic fracturing and gas production. Therefore, it is of great significance to study crack dynamic propagation characteristics in shale with different orientation joints and dynamic strength. Impacting experiments were conducted on the single cleavage triangle (SCT) shale specimens with joint orientation 0°, 30°, 45°, 60° and 90°, respectively. A modified split Hopkinson pressure bar (SHPB) system was applied and AUTODYN code was used to simulate crack dynamic fracture behavior. For the case of a single joint and multiple parallel joints, crack propagation directions and trajectories were numerically analyzed. The experimental and numerical results indicate that joints have a great influence on crack dynamic propagation direction. In addition, the crack propagation speed of shale is positively related to the loading rate under dynamic loads. If joints are considered as thin layer material, dynamic tensile strength and elastic modulus of joints have a great effect on dynamic crack propagation behavior under impact loads.

Numerical study on maximum rebound ratio in blasting wave propagation along radian direction normal to joints

In the process of 2-D compressional wave propagation in a rock mass with multiple parallel joints along the radian direction normal to the joints, the maximum possible wave amplitude corresponding to the points between the two adjacent joints in the joint set is controlled by superposition of the multiple transmitted and the reflected waves, measured by the maximum rebound ratio. Parametric studies on the maximum rebound ratio along the radian direction normal to the joints were performed in universal distinct element code. The results show that the maximum rebound ratio is influenced by three factors, i.e., the normalized normal stiffness of joints, the ratio of joint spacing to wavelength and the joint from which the wave rebounds. The relationship between the maximum rebound ratio and the influence factors is generalized into five charts. Those charts can be used as the prediction model for estimating the maximum rebound ratio.

Transmission ratio ( Tn) in the radian direction normal to joints in 2-D compressional wave propagation in rock masses

The transmission ratio along the radian direction normal to the joints was studied in the Universal Distinct Element Code (UDEC). The variation of the transmission ratio with the ratio of joint spacing to wavelength was generalized into a general curve, which was determined by two critical points. The relationship between the two critical points and the affecting factors, quantity of joints and the normalized normal stiffness of joints, were obtained. A prediction model of the transmission ratio in the radian direction normal to the joints was proposed. The proposed model was applied to a field explosion test. The estimated values of the peak particle velocity from the prediction model were compared with the field records. The comparisons showed that the prediction model of the transmission ratio in the direction normal to the joints in the process of 2-D compressional wave propagation through multiple parallel joints is reliable.