Shock and Vibration

Volume 2017 (2017), Article ID 5387459, 13 pages

https://doi.org/10.1155/2017/5387459

## Acoustic Emission Characteristics and Failure Mechanism of Fractured Rock under Different Loading Rates

^{1}Shandong Provincial Key Laboratory of Civil Engineering Disaster Prevention and Mitigation, Shandong University of Science and Technology, Qingdao 266590, China^{2}State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China^{3}Research Center of Geotechnical and Structural Engineering, Shandong University, Jinan 250061, China^{4}State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China^{5}College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao 266555, China

Correspondence should be addressed to Gang Wang

Received 13 June 2017; Revised 21 August 2017; Accepted 12 September 2017; Published 15 October 2017

Academic Editor: M. I. Herreros

Copyright © 2017 Yongzheng Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

To study the loading rate dependence of acoustic emissions and the failure mechanism of fractured rock, biaxial compression tests performed on granite were numerically simulated using the bonded particle model in Particle Flow Code (PFC). Uniaxial tests on a sample containing a single open fracture were simulated under different loading rates ranging from 0.005 to 0.5 m/s. Our results demonstrate the following. (1) The overall trends of stress and strain changes are not affected by the loading rate; the loading rate only affects the strain required to reach each stage. (2) The strain energy rate and acoustic emission (AE) events are affected by the loading rate in fractured rock. With an increase in the loading rate, AE events and the strain energy rate initially increase and then decrease, forming a fluctuating trend. (3) Under an external load, the particles within a specimen are constantly squeezed, rotated, and displaced. This process is accompanied by energy dissipation via the production of internal tensile and shear cracks; their propagation and coalescence result in the formation of a macroscopic rupture zone.

#### 1. Introduction

Fractured rock is commonly encountered in engineering projects in various fields, including transportation, national defense, water conservation, hydropower engineering, and mine exploitation. In recent years, the failure of engineering projects because of the weakness of rock joints has been frequently observed. Various geological disasters, landslides, and debris flow have created serious threats to human life and property and significant economic losses. These geological hazards are often macroscopic manifestations of rock mass instability. The instability of jointed rock mass has attracted the attention of experts and scholars worldwide. The existence of joints and fractures often leads to a reduction in rock strength and an increase in deformation, resulting in distinct inhomogeneity and anisotropy in the rock mass. In addition, the existence of cracks increases the likelihood of block cracking and sliding, which is likely to further cause rock instability. From the 1960s through the 1990s, significant advances in understanding the role of rock joints and rupture mechanisms of fracturing rock were achieved [1–6]. In the twenty-first century, many new technologies have been developed and used in scientific research, such as computed tomography (CT) scanning and acoustic emission. Simultaneously, numerical simulation techniques (e.g., rock failure process analysis (RFPA) and Particle Flow Code (PFC)) have been vastly improved and have enabled significant progress in modeling rock failure processes.

Vásárhelyi and Bobet [7] conducted uniaxial compression tests on prefabricated double-slit rectangular specimens and used the displacement discontinuity method to simulate the failure process. The authors were able to determine the crack initiation stress, the propagation direction of new cracks, and crack coalescence characteristics. Wong et al. [8] performed an experimental study of the crack propagation process and the peak intensity of three parallel prefabricated friction cracks in analog materials. Sahouryeh et al. [9] conducted biaxial compression tests on specimens with a built-in circular crack composed of transparent resin material and found that the crack extended along the loading direction. Lee and Jeon [10] used two types of materials with different built-in single and multigroup geometric distributions of cracks in compression tests and studied the results of these tests. Wang et al. [11] studied the failure mode of internal macrocracks using and evaluated the uniaxial compressive strength and fracture evolution processes. Ren and Hui [12] studied microdamage and failure mechanisms using CT scanning during uniaxial compression tests on sandstone with a single crack. Li et al. [13] analyzed the crack propagation process associated with damage evolution using CT real-time scanning tests on a rock-like material with a built-in single penny-shaped crack. Yang et al. [14] monitored the acoustic emission characteristics of the loading process using uniaxial compression tests on sandstone with cracks and discussed the effect of pore size distribution on the strength and fracture process.

Previous studies have applied advanced techniques to explore the crack propagation and evolution process in fractured rock specimens and have revealed the failure mechanisms of fractured rocks to a certain extent. However, little is known about the effect of the loading rate on acoustic emission and failure mechanisms. Therefore, in this work, PFC is used to study the impact of the loading rate on the fracture mechanisms of prefabricated rock with cracks under uniaxial compression tests.

#### 2. Basic Principles of Fracture Evolution in Rock Mass

Griffith [15] found that the actual tensile strength of materials was usually significantly smaller than the theoretical value and that brittle materials typically contain a large number of randomly distributed small defects and cracks. These defects and cracks change the stress propagation direction, causing energy to accumulate around the crack, thereby leading to stress concentration and a reduction in the fracture strength of the material. Based on the theory of energy balance, a relationship between the critical stress of crack initiation and crack size was established by Griffith. It is believed that crack propagation that generates a new crack surface will consume the energy expended by external forces. This process will lead to an increase in the amount of strain stored in the material and will promote further expansion of the crack until failure of the material. Under the action of pure tensile and/or compressive stress, the total energy of an infinite plate with a crack contains an energy component specified by the following equation [16]:where is the total energy stored in the infinite plate, represents the initial total elastic strain energy, is the total elastic strain energy released by the crack on the upper and lower surfaces of the crack length of , is the work performed by the external force, and is the free surface energy.

According to the theory of elastic mechanics, the energy components can be expressed aswhere is the total energy stored in the infinite plate; is the external load; is the half length of the crack; is the effective Young’s modulus, ; is Poisson’s ratio; is the area of the infinitely thin plate; is the average axial strain; and is the surface energy required to increase the surface area because of crack length expansion.

Griffith defined the critical equilibrium condition of the material damage as

Substituting (2) into (3) yields

This formula indicates that the ideal conditions for brittle material breakage are mainly related to the external force, crack length, Young’s modulus, Poisson’s ratio, and surface energy. Equation (4) can be rewritten as

The left part of (5) is the rate of elastic strain energy release of the crack, which is the energy source for crack growth and is denoted by , such that . Griffith’s theory states that is the critical condition for crack initiation, where is the critical elastic strain energy release rate.

#### 3. Introduction of PFC and Determination of Microparameters

##### 3.1. Introduction of PFC

PFC [17, 18] is an implementation of a simulation technique developed by Cundall based on the discrete-element method. This technique uses disk-like particles or spherical particles to simulate and analyze the mechanics of materials and deformation problems; it has been widely used in the field of geotechnical engineering. Researchers have used this technique to simulate continuous and discontinuous macro/mesomechanical behavioral characteristics [19–21]. In the simulation, the interaction models of two contact particles include the contact stiffness model, the sliding model, and the bond model. In the calculation process, particle motion always obeys Newton’s laws of motion and the force displacement law. The contact stiffness model is largely based on the contact forces between the particles. The sliding model is based on the inherent characteristics of the contact sphere, namely, that it has no normal tensile strength and that the particles are allowed to slide across a range of shear strengths. The cohesive model is related to the mesodamage of particle aggregates; it is used to represent the strength properties of a specimen by setting the normal tensile strength and tangential shear strength. When the external stress acting on a bond exceeds the ultimate tensile strength and ultimate shear strength, the bond breaks. Microcracks are then generated at the bonding position. With the help of the FISH language in PFC, we can monitor the entire process of microscopic damage.

##### 3.2. Determination of Microparameters

Biaxial compression tests on granite in the underground caverns of the Huangdao State Oil Reserves were virtually simulated using the bonded particle model in PFC. The numerical model is illustrated in Figure 1. The dimensions of the numerical model were 100 mm × 50 mm. The numerical model dimensions are consistent with the laboratory test dimensions. In the simulation model, the minimum particle radius was 0.3 mm, and the particle size ratio was 1.66 [22].