Jianchun Li

Simplified Damage Assessment Method for Buried Structures against External Blast Load

Decoupling of soil-structure interaction is applied to analyze buried structure damage due to external blast load. The structural element under analysis is assumed to deform as a simply supported rigid-plastic beam. Shear failure, bending failure, and combined failure modes are considered based on five transverse velocity profiles. With proper failure criteria, the critical equations for structural shear and bending failures are derived respectively. Pressure-impulse diagrams are then developed to assess damage of the buried structures. Comparison has been made to show the influences of the soil-structure interaction and the shear-to-bending strength ratio of the buried structure. A case study has been conducted to a buried reinforced concrete box-type structure which shows that the proposed analysis method can be effectively applied.

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

Damage Assessment of Reinforced Concrete Structural Elements Subjected to Blast Load

An analytical approach of damage assessment for reinforced concrete structural elements subjected to blast loads is proposed. The nonlinear deformational behavior of the reinforced concrete structural element is considered and the pressure-impulse diagrams with respect to combined bending and shear failure are derived. The theoretical derivation is divided into elastic and post-elastic stages. A single degree of freedom system is adopted in the elastic stage to calculate the structural response due to shear and/or bending failure, respectively. The final displacement, velocity, and acceleration of the elastic stage are used as the initial conditions of the subsequent stages. In the post-elastic stages, the structural element is assumed to behave as a multi-linear model, and the softening property of the reinforced concrete is taken into account. The present method can be applied to various reinforced concrete structures with different elastic and post-elastic behaviors. The results are compared to show the effect of the different behavior of reinforced concrete.

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

Wave Propagation in the Vicinities of Rock Fractures Under Obliquely Incident Wave

AbstractThough obliquely incident plane wave across rock fractures has been extensively investigated by theoretical analysis, the quantitative identification of each wave emerged from fractures has not been achieved either in numerical simulation or laboratory experiment. On the other hand, there are no theoretical results describing the stress/velocity state of the rocks beside a fracture. The superposition of the multiple waves propagating in the media results in the variation of the stress/velocity state. To understand the superposition of the wave components in the adjacent rocks of a facture, based on the geometrical analysis of the wave paths, the lag times among passing waves at an arbitrary point are determined. The normalised critical distances from the fracture to the measuring locations where the corresponding harmonic waves depart from other waves for a certain duration are then derived. Discussion on the correction for an arbitrary incident wave is then carried out considering the changes of the duration of the reflected and transmitted waves. Under the guidance of the analysis, wave superposition is performed for theoretical results and separated waves are obtained from numerical model. They are demonstrated to be consistent with each other. The measurement and the data processing provide an approach for wave separation in a relatively unbounded media. In addition, based on the mechanical analysis on the wave front, an indirect wave separation method is proposed which provides a possibility for laboratory experiments of wave propagation with an arbitrary incident angle.

Stress Wave Propagation Across a Rock Mass with Two Non-parallel Joints

A rock mass includes a number of joints, which govern the mechanical behavior of the rock mass and greatly affect stress wave propagation. Generally, joints do not parallel with each other, resulting in multiple wave reflections between joints and complex wave propagation process in rock masses. The present study presents an approach to analyze stress wave propagation through a rock mass with two non-parallel joints when the angle between the two joints is <10°. For incident P-wave impinging on this kind of rock mass, multiple reflections take place between the two joints. Meanwhile, transmitted waves are generated and propagate successively away from the joints. The mathematical expressions for P-wave propagation across the two joints are established in time domain by analyzing the wave field in the rock mass. By comparing with the result from numerical simulation, the new approach is proved to be effective to analyze wave propagation across two non-parallel joints, where the influence of joint tips on wave propagation is neglected. Parametric studies show that the joint stiffness, joint angle and frequency of incident wave have different effects on transmission and reflection coefficients.

Experimental Study of S-wave Propagation Through a Filled Rock Joint

This experimental study proposes a Split Shear Plates model to investigate the effects of a filled joint on S-wave attenuation. A dynamic impact is used to create frictional slip and generate an incident S-wave. The filled joint is simulated using a sand layer between two rock plates. Normal stress is applied to the filled joint, and semiconductor strain gauges are arranged on the two plates to measure the strain. Verification tests are conducted to validate the reliability of the experimental results. A series of tests is performed to investigate the influence of the normal stress, filled thickness and particle size of the filling materials on the S-wave propagation. The transmission coefficients of the filled joints are smaller than those of the non-filled joints because of the attenuation associated with the filling materials. Additionally, the transmission coefficients exhibit a stronger correlation with the normal stress than with the filled thickness or particle size. The transmission coefficients increase at a decreasing rate as normal pressure increases.

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.

Numerical study on S-wave transmission across a rough, filled discontinuity

This paper presents a numerical simulation of S-wave propagation across a rough, filled discontinuity using the universal distinct element code (UDEC). The ability of UDEC to simulate a stress wave across a smooth and planar discontinuity filled with an elastic material is validated through comparisons with analytical solutions. Next, the effect of the plastic deformation of the fill on the wave propagation is investigated. The model is extended to further study S-wave propagation across a filled discontinuity with rough interfaces, which is described using a sawtooth. The transmission coefficient defined by the energy is used to measure the wave attenuation. Finally, a parametric study is conducted to investigate the influences of the filled thickness, asperity angle, and incident amplitude on the transmission waves and transmission coefficients. The asperity angle and filled thickness together determine the transmitted waveform and transmission coefficient. The transmitted wave may be cut off when the incident wave amplitude exceeds a threshold value. The transmission coefficient decreases with a different trend with the incident wave amplitude increasing when the asperity angle varies. Compared with planar discontinuity, a filled discontinuity with rough interfaces is more sensitive to the amplitude of the incident wave. The causes of these phenomena are analyzed in detail. In addition, the deformation of the fill material is strongly related to the wave attenuation.

Special Issue: Including Papers on “Rock Dynamics and Applications”

Rock dynamics studies the response of rock materials and rock masses under dynamic loading conditions, it has wide applications in geological, civil and mining engineering and deals with some of the latest and most challenging research topics such as the dynamic load distribution and propagation, dynamic responses and failure of rock materials and rock masses in the underground environments featuring high temperature, high in situ stress and other special physicochemical conditions. With increasing engineering activities related to rock dynamics worldwide, the International Society for Rock Mechanics (ISRM) established the Commission on Rock Dynamics (CRD) in 2008. ISRM-CRD was renewed in 2011 and then in 2015, as a result of continued interests in the dynamic response of rock materials and rock masses. Remarkable advancements on challenging topics in rock dynamics have recently been made in physical testing, numerical modelling and theoretical studies, as well as in engineering applications. Rock Mechanics and Rock Engineering has promoted this Special Issue with the intention of providing a consented summary of the current state of knowledge, in accordance to the reference of ISRM-CRD to report developments and produce guidelines on the study and engineering applications of rock dynamics. This issue includes papers that represent some of the most recent works on rock dynamics and underground engineering. New laboratory dynamic testing equipment for rocks subjected to static loading, studies on dynamic fracturing and failure of rock under in situ stress or thermal treatment, dynamic fracture process of rocks, acoustic emission, and stress wave propagation through rock masses are presented. Topics such as the interaction of rock structures and ground motion due to blasting vibration or dynamic disturbance, dynamic response of rock masses in deep mines, rock bursting in discontinuous deep rock masses, numerical testing and dynamic fracture modelling are also discussed. The Editor of Rock Mechanics and Rock Engineering would welcome the setting up of an Open Forum on the above topics. Readers are kindly requested to send discussions on the papers published in this issue to RM&RE.