X. B. Zhao

Experimental study of ultrasonic wave attenuation across parallel fractures

Fractures and other non-welded discontinuities are important mechanical and hydraulic features of rock masses. Their effect on wave propagation can be modelled as a boundary condition by displacement discontinuity methods. For small-amplitude wave incidence, such as an ultrasonic waves, the magnitude of the stress wave is too small to mobilize non-linear fracture deformation, and so linear models are adopted in these studies to describe fracture deformational behaviour. J.G. Cai and J. Zhao (Int. J. Rock Min, Sci., 2000, 37(4), 661–682.) used the method of characteristics to examine P-wave attenuation across linear deformable fractures by considering interfracture wave reflections. In the present study, a series of laboratory tests were carried out to verify the theoretical solutions obtained by Cai and Zhao. These included ultrasonic tests across an aluminium specimen (calibration tests), intact cement mortar specimens, single-fracture specimens, and two-fracture specimens. During the tests, ultrasonic waves propagate normally across artificial fractures cast by cement mortar under different static stresses. Transmitted pulses are captured and subsequently are compared with the theoretical predictions. Generally, the experimental results agreed well with the theoretical predictions. In addition, the experimental study also provided further understanding of wave propagation across discontinuities (e.g. the applicability of displacement discontinuity methods in the dynamic problems).

A Numerical Study on Wave Transmission Across Multiple Intersecting Joint Sets in Rock Masses with UDEC

This paper presents a numerical study on wave transmission across jointed rock masses with UDEC, where multiple intersecting joint sets exist. The capability of UDEC of studying wave transmission across rock joints is validated through comparison with analytical solutions and experimental data. Through parametric studies on wave transmission across jointed rock masses, it is found that joint mechanical and spatial parameters including joint normal and shear stiffnesses, nondimensional joint spacing, joint spacing ratio, joint intersecting angle, incident angle, and number of joint sets together determine the wave transmission. And for P wave incidence, compared with other parameters, joint normal stiffness, nondimensional joint spacing, and joint intersecting angle have more significant effects on wave transmission. The physical reasons lying behind those phenomena are explained in detail. Engineering applications and indications of the modeling results are also mentioned.

Analytical Study for Stress Wave Interaction with Rock Joints Having Unequally Close–Open Behavior

Stress wave interaction with rock joints during wave propagation is usually dependent on the dynamic response of the joints. During wave propagation, joints may be closed and open under the effects of the stress wave and the in situ stress. A joint in nature can only resist load during close process. In this paper, the close and open behaviors of rock joints are considered to be different. The joints are assumed to be linearly elastic in close status but turn into free surfaces in open status. Wave propagation equation across joints with unequally close–open behavior is first derived and expressed as a time-differential form based on the displacement discontinuity method. SHPB test recording is then adopted to verify the present approach, which is also compared with the results from existing methods for joints with equally close–open behavior. Next, analysis is conduced for wave propagation across a single joint and a set of parallel joints with unequally close–open behavior, respectively. From the analysis, effects of unequally close–open behavior of a joint on wave propagation and the dynamic response of the joint are studied finally.

Development of a Unified Rock Bolt Model in Discontinuous Deformation Analysis

In this paper, a unified rock bolt model is proposed and incorporated into the two-dimensional discontinuous deformation analysis. In the model, the bolt shank is discretized into a finite number of (modified) Euler–Bernoulli beam elements with the degrees of freedom represented at the end nodes, while the face plate is treated as solid blocks. The rock mass and the bolt shank deform independently, but interact with each other through a few anchored points. The interactions between the rock mass and the face plate are handled via general contact algorithm. Different types of rock bolts (e.g., Expansion Shell, fully grouted rebar, Split Set, cone bolt, Roofex, Garford and D-bolt) can be realized by specifying the corresponding constitutive model for the tangential behavior of the anchored points. Four failure modes, namely tensile failure and shear failure of the bolt shank, debonding along the bolt/rock interface and loss of the face plate, are available in the analysis procedure. The performance of a typical conventional rock bolt (fully grouted rebar) and a typical energy-absorbing rock bolt (D-bolt) under the scenarios of suspending loosened blocks and rock dilation is investigated using the proposed model. The reliability of the proposed model is verified by comparing the simulation results with theoretical predictions and experimental observations. The proposed model could be used to reveal the mechanism of each type of rock bolt in realistic scenarios and to provide a numerical way for presenting the detailed profile about the behavior of bolts, in particular at intermediate loading stages.