Experimental and analytical investigation on the coupled elastoplastic damage model of coal-rock

Y.D. Shou et alii, Frattura ed Integrità Strutturale, 53 (2020) 434-445; DOI: 10.3221/IGF-ESIS.53.34 Experimental and analytical investigation elastoplastic damage model of coal-rock on the coupled Yundong Shou* School of Civil Engineering, Wuhan University, China , https://orcid.org/0000-0001-7424-4006 Jianwei Zhang School of Civil Engineering, Chongqing University, China Filippo Berto Norwegian University of Science and Technology, Norway ABSTRACT. In this paper, a novel coupled elastoplastic damage model for coal-rock is proposed to predict the deformation and potential disaster in coal mining. The conditions of small deformation and thermodynamic potential are considered, as well as the coupling of damage evolution process with the plastic deformation and the plastic hardening of coal-rock. Based on the theory of damage mechanics, the formulas of damage evolution, plastic yield and plastic potential of coal-rock are deduced theoretically. In addition, triaxial compression tests of coal-rock under the different confining stresses are conducted to reveal the law of deviatoric stress and strain. Based on the experimental data, the control parameters of the coupled elastoplastic damage model of coal-rock are determined. The theoretical results obtained from the coupled elastoplastic damage model for coal-rock agree well with those from the experiment. The proposed model is reasonable to predict the deformation of coal-rock. Citation: Shou, Y.D., Zhang, J.W., Berto, F., Experimental and analytical investigation on the coupled elastoplastic damage model of coal-rock, Frattura ed Integrità Strutturale, 53 (2020) 434-445. Received: 23.04.2020 Accepted: 05.06.2020 Published: 01.07.2020 Copyright: © 2020 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. KEYWORDS. Coal-rock; Coupled elastoplastic damage model; Damage mechanics; Triaxial compression tests; The deformation prediction of coalrock. INTRODUCTION T 434 wo types of inelastic behaviors generally exist in most rock materials: plastic deformation, related to sliding mechanisms inside the microstructure of rock matrix; and damage to rock materials, induced by spreading microcracks[1-2]. In the case of semi-brittle rocks, for instance, limestone and porous sandstone, plastic deformation Y.D. Shou et alii, Frattura ed Integrità Strutturale, 53 (2020) 434-445; DOI: 10.3221/IGF-ESIS.53.34 and damage are usually coupled. Therefore, it is necessary to develop a coupled elastoplastic damage model to better understand the mechanical behaviors of these semi-brittle geomaterials. Coal is a complex fractured geological medium containing numerous randomly distributed micro holes and cracks [3]. Its mechanical properties are important essential parameters for the mining design, roadway support and some other underground coal engineering [4-5]. Therefore, the constitutive relation and damage model of coal-rock is still a major issue to be solved urgently. Several elastoplastic models have been proposed for coal-rock in the past, thus providing the standard framework for contemporary models [6-9]. The last two decades of geomechanic research have led to an active discussion of damage models for geomaterials, to better address microcracks. A series of isotropic and anisotropic damage models have been proposed. These approaches can be classified into two groups: (macroscopic) phenomenological and micromechanical models. The phenomenological damage models can be easily implemented in computer codes, which then provide an efficient tool for progressive failure analysis of coal-rock mass structures under complex loading conditions. Additionally, the phenomenological damage models generally take the thermodynamics of irreversible processes into account; they make use of different orders of tensorial internal variables to represent the distribution and nucleation and growth of microcracks [10-13]. However, in these coupled models, the choice of damage variables and thermodynamic potential is somewhat arbitrary, because it is based on mathematical conveniences, rather than the physical interpretation of microcracks. Moreover, most of the previous coupled elastoplastic damage models are isotropic, rather than anisotropic, models. But in fact, the anisotropic features of geomaterials are observable in triaxial and uniaxial compressive tests. The micromechanical damage mechanics approach leads to an improved understanding of the underlying physical processes. In the micromechanical approach, researchers study the growth, nucleation, and coalescence of microcracks and their influence on the mechanical properties, which is reflected in the constitutive relation in certain ways [9, 14-17]. Among these, the most widely used models are the dilute-concentration method (DCM), the self-consistent method [18-20], the differential method (DM) [21, 22], the generalized self-consistent method (GSCM) [23], and finally, the effective selfconsistent method [24]. However, the micromechanical damage mechanics model is often difficult to implement in engineering applications, because of its proclivity to cause 3D problems. Therefore, the phenomenological approach is adapted in the new model. This article proposes a novel coupled elastoplastic damage model for coal-rock to discuss the plastic deformation and induced damage found in coal mine. In section 2, reconstituted coal samples were manufactured in size of 50 mm × 100 mm by compressing machine. Then triaxial compression tests of coal-rock under four confining stresses of 0MPa, 5 MPa, 10 MPa and 15 MPa are conducted. The complete deviatoric stress-strain curves of the coal-rock under the different confining stress conditions are obtained. Moreover, in section 3, a novel coupled elastoplastic damage model for coal-rock is proposed to predict the deformation. The conditions of small deformation and thermodynamic potential are considered, as well as the coupling of damage evolution process with the plastic deformation and the plastic hardening of coal-rock. Based on the theory of damage mechanics, the formulas of damage evolution, plastic yield and plastic potential of coal-rock are deduced theoretically. In section 4, the theoretical results obtained from the coupled elastoplastic damage model for coal-rock agree well with those from the experiment. It is demonstrated that the proposed model is reasonable to predict the deformation of coal-rock. EXPERIMENT STUDY ON AND RESULT OF THE TRIAXIAL COMPRESSION DEFORMATION OF COAL AND ROCK Sample preparation I n this paper, reconstituted coal samples were used to investigate the mechanical property of coal-rock. The pulverized coal was collected from Songzao coal mining area in Chongqing. Then in laboratory, the pulverized coal and water were mixed first and stirred evenly, as shown in Fig. 1 (a). The (...truncated)