ng Xia

Direct Tension Test for Rock Material Under Different Strain Rates at Quasi-Static Loads

Mechanical properties of rock material under dynamic tension are important in evaluating the damage characteristics of rock structures such as rock caverns, rock slopes as well as rock foundations following explosion or earthquake. In this arena, since the 1960s, many experimental works have been conducted. Among these works, indirect dynamic tensile test methods, such as the Brazil and the split Hopkinson pressure bar (SHPB) test methods, were mainly employed to study the strength and deformation properties of rock material under dynamic tension. For example, through dynamic Brazil tests for dolerite and limestone, Price and Knill (1966) suggested that the tensile strength of both rocks generally increases with the increase of the loading rate. For dolerite, the tensile strength at the highest loading rate is 17 % greater than that at the lowest loading rate. For limestone, the tensile strength at the highest loading rate is 44 % greater than that at the lowest loading rate. Wu and Liu (1996) conducted Brazil tests to study the variation of the tensile strength, the Young’s modulus and the failure strain for Longman limestone at loading rates from 10 to 10 MPa/s. The tensile strength, the Young’s modulus and the failure strain for the rock were reported to increase with the increase of the loading rate. The three-point bending and Brazil test methods were employed to study the dynamic tensile properties for Bukit Timah granite by Zhao and Li (2000). They found that the tensile strength of granite obtained by the two methods is conformably increased with increasing loading rate. When the loading rate rises by one order from 10 to 10 MPa/s, the increment of the tensile strength is about 10 %. In addition, the tensile strength of the rock by the three-point bending method was tested to be 2.5 times that obtained from the Brazil test method at the same loading rate. Based on SHPB tests for quartz monzonite rock, Birkimer (1971) pointed out that the dynamic tensile strength of the rock increases with a cube root of the strain rate when the strain rate ranges from 10 to 10 s. By SHPB tests, Cho et al. (2003) studied the variation of the tensile strength for Inada granite and Tage tuff at strain rates ranging from 1 to 10 s. It was indicated that the strengths of both rocks at the strain rate range are significantly higher than that under static load and increase notably with increasing strain rate. In addition, the fracture processes, the generation and interaction of microcracks, which contribute to the rate dependency properties of rock tensile strengths, were analysed by a proposed finite element method. By the split Hopkinson tension bar and a hydro-pneumatic machine, Cadoni (2010) studied the dynamic tensile strength of Onsernone Orthogneiss for loading directions 0 , 45 and 90 with respect to the schistosity at three different strain rates, i.e. 0.1, 10 and 100 s. It was observed that the dynamic tensile strength of the rock increases with increasing strain rate, and the dynamic tensile strength of the rock is up to about two H. Li J. Li (&) B. Liu J. Li X. Xia State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China e-mail: jcli@whrsm.ac.cn

Numerical Modeling of Wave Transmission Across Rock Masses with Nonlinear Joints

Rock masses usually consist of intact rocks and discontinuities such as faults, joints and bedding planes. The discontinuities not only govern the mechanical behaviors of rock masses but also influence wave propagation in rock masses (Goodman 1976; Pyrak-Nolte 1996). Studying wave propagation across joints is the basis for the analysis of dynamic responses and stability of jointed rock masses, which is of great interest to geophysics, mining and underground construction. Currently, a number of theoretical analyses or numerical simulations have been carried out on stress wave propagation across rock joints. The typical analytical method is the displacement discontinuity method (DDM) (Schoenberg 1980; Pyrak-Nolte et al. 1990). The DDM was coupled with the characteristic method (CM) to study normal wave propagation across linear and nonlinear joints (Zhao and Cai 2001; Zhao et al. 2006a, b). Based on DDM, the interaction between blast waves and a single rock joint with arbitrary incident angle was effectively analyzed by Li and Ma (2010) and Li et al. (2011). In addition, Zhao et al. (2012), Li et al. (2012), Zhu and Zhao (2013) proposed the propagator matrix method, the time-domain recursive method and the virtual wave source method, respectively, and applied them to study wave propagation obliquely across a set of parallel joints. Later, Li (2013) adopted and extended the time-domain recursive method to analyze the effect of nonlinear joints on wave propagation. As an alternative, numerical methods have been more popularly applied with the development of computer technology nowadays. Cai and Zhao (2000), Fan et al. (2004), Zhao et al. (2006a), Barla et al. (2010) and Sun et al. (2013) conducted a series of numerical studies on normally incident wave propagation across a single or a set of parallel rock joints. Lei et al. (2007), Deng et al. (2012), Zhu et al. (2013) and Deng et al. (2014a, b) studied oblique incidence across a set of parallel joints and intersecting rock joints with linearly elastic behavior. In addition, Lemos (1987), Brady et al. (1990), Zhao and Cai (2001), Zhao et al. (2006b), and Zhao et al. (2008) carried out numerical studies on wave transmission across a single joint or a set of parallel joints with nonlinear deformation behavior. & Haibo Li hbli@whrsm.ac.cn

Shear Wave Propagation Across Filled Joints with the Effect of Interfacial Shear Strength

The thin-layer interface model for filled joints is extended to analyze shear wave propagation across filled rock joints when the interfacial shear strength between the filling material and the rocks is taken into account. During the wave propagation process, the two sides of the filled joint are welded with the adjacent rocks first and slide on each other when the shear stress on the joint is greater than the interfacial shear strength. By back analysis, the relation between the shear stress and the relative tangential deformation of the filled joints is obtained from the present approach, which is shown as a cycle parallelogram. Comparison between the present approach and the existing method based on the zero-thickness interface model indicates that the present approach is efficient to analyze shear wave propagation across rock joints with slippery behavior. The calculation results show that the slippery behavior of joints is related to the interfacial failure. In addition, the interaction between the shear stress wave and the two sides of the filling joint influences not only the wave propagation process but also the dynamic response of the filled joint.

Study on the Mechanical Properties of Soft Rock under Dynamic Uniaxial Compression

The present paper introduces the experimental study on soft rock (analogized with mortar)under dynamic uniaxial compression at the strain rates from 10 -5 to 101s-1. It is indicated that thecompressive strength of the soft rock increase with the increasing strain rate and the rising rates are higher than that of hard rock. The Youngs moduli and Poissons ratio of the soft rock increase with the increasing strain rate, but the rising rates are less than that of compressive strength. In addition, the mechanism of the strain rate effect of the soft rock is primarily analyzed based on the SEM results.

Experimental Study on the Seismic Efficiency of Rock Blasting and Its Influencing Factors

The seismic efficiency of a blast is the percentage of seismic energy in the total energy delivered by the explosives. It is a key indicator of the blast effects in civil engineering and seismic exploration. A method to determine seismic efficiency has been proposed based on the assumption of spherical wave radiation in an indefinite elastic medium and has been used in a series of blast tests performed at the construction site of a nuclear power plant. Analysis of the influencing factors of seismic efficiency shows that seismic efficiency increases with an increasing explosive charge and stemming length of the blastholes, while it decreases with an increasing decoupling coefficient. Generally, seismic efficiency is markedly lower in bench blasts than in paddock blasts due to free surface effects. Under any circumstances, the seismic energy only accounts for a few percent of the explosive energy. A comparison with theoretical solutions proves that the errors in the present method are low and acceptable in engineering. Therefore, some practical measures have been proposed to improve or lower the seismic efficiency according to the specific requirements of the blast operations.

Numerical evaluation of topographic effects on seismic response of single-faced rock slopes

This paper investigates the seismic responses of homogenous single-faced rock slopes subjected to vertically propagating shear waves by numerical simulations in order to explore the topographic amplification of ground motion. The horizontal and vertical topographic amplification factors both on the free surface and in the slope are evaluated using parametric studies focusing on slope geometry, rock material, and input motion with the two-dimensional finite element code LS-DYNA. Comparison of the results obtained in this study with those of previous numerical analyses available in the literature and with the provisions of the existing seismic codes shows good agreement. Both qualitative and quantitative insights into the topographic amplification effects on the seismic responses of single-faced slopes are presented in this study. The results show that both slope geometry and rock material have great influences on the horizontal and vertical amplification factors. As for input motion, the magnitude and duration have negligible effects on the amplification factors when rock materials are homogeneous and elastic. However, the frequency extent of input motions has great impact on the amplification factors. It is also indicated that the modern seismic codes may underestimate the amplification effects of ground motion. Nevertheless, modification of the provisions of the codes may require more convincing evidence from reliable field experiments.

Application of coupled analysis methods for prediction of blast-induced dominant vibration frequency

Blast-induced dominant vibration frequency (DVF) involves a complex, nonlinear and small sample system considering rock properties, blasting parameters and topography. In this study, a combination of grey relational analysis and dimensional analysis procedures for prediction of dominant vibration frequency are presented. Six factors are selected from extensive effect factor sequences based on grey relational analysis, and then a novel blast-induced dominant vibration frequency prediction is obtained by dimensional analysis. In addition, the prediction is simplified by sensitivity analysis with 195 experimental blast records. Validation is carried out for the proposed formula based on the site test database of the firstperiod blasting excavation in the Guangdong Lufeng Nuclear Power Plant (GLNPP). The results show the proposed approach has a higher fitting degree and smaller mean error when compared with traditional predictions.

Numerical study on oblique incidence across rock masses with linear and nonlinear joints

The two-dimensional discrete element program Universal Distinct Element Code (UDEC) is applied to simulate stress wave propagation across linear and nonlinear rock joints with arbitrary incident angles. The numerical study for stress wave obliquely impinging upon a single linearly elastic joint is firstly conducted. For this case, the wave-type transformation is analyzed and the variations of transmission and reflection coefficients with joint stiffness and incident angle are investigated numerically. It is found that numerical results agree well with those from existing theoretical methods, which demonstrates the feasibility of using UDEC to simulate the propagation of obliquely incident stress wave across a single joint. Furthermore, the transmission of obliquely incident waves across a set of parallel joints is investigated and compared with analytical solutions when the joints are linearly and nonlinearly elastic, respectively. The numerical results indicate that the parameters, such as the joint number, the joint spacing and the mechanical property of joints, have great influence on wave propagation through joints. The results in the present study may provide a reference for revealing stress wave propagation across jointed rock masses and the responses of rock masses subjected to dynamic loads.

Failure Mechanism of an Idealized Layered Rock Slope Subjected to Seismic Loads

The dynamic response of an idealized layered rock slope with a single joint subjected to seismic loads is investigated using the three dimensional distinct element code in the present study. Based on the numerical modeling, the variations of the stresses of the blocks close to the joint and the deformation of the joint are discussed, and the progressive failure mechanism of the slope is analyzed. It is found that, with the increasing excitations, the tensile stresses and the areas of tension zones in the upper part of the slope near the joint have increased gradually. In addition, the normal displacement at the upper part of the joint also becomes larger and larger, which leads to the gradual split of the upper part of joint. Hence the contact area for blocks at both sides of the joint has decreased, which gradually results in the decrease of the cohesion of the joint. When the induced shear stress for the joint under the applied excitations exceeds its shear strength, the potential sliding blocks will slip along the joint. The results in this paper may provide references for the study on failure mechanism of complicated layered rock slopes subjected to dynamic loads.

Numerical Study on Effects of Rock Bridge Angle in Uniaxial Compression Test

Numerical specimens with two pre-existing flaws is established by using particle flow code PFC2D and by changing the relative position of the pre-existing flaws different rock bridge angle is obtained. Though the uniaxial compression test of specimens with different rock bridge angle , it can be found that rock bridge angle have a great impact on the mode of crack propagation of specimen. The different relative position between the two pre-existing flaws led to different levels of stress shielding effect under the axial force, and it is most likely to damage when the two pre-existing flaws are about overlap.