An acoustic emission-based cluster damage model for simulating triaxial compression behaviors of granite

D.J. Xue●L. Gao●L. Lu●J. Zhou●H.W. Zhou●Z.D Wu●H.Y. Yi●J.F. Liu

Abstract

The establishment of spatial correlation among scattering acoustic emission (AE) signals has great potential applied into a deep analysis of triaxial compression behaviors by the AE monitoring technology. Taking the randomly distributed AE signal-could as the cube cluster by an introduction of covering strategy from the percolation theory, the quantitative evaluation of spatial correlation instead of spatial distribution is effectively made. It presents a cluster-based perspective to investigate the triaxial compression behaviors, especially including the dilatancy based on the volumetric strain correlated to the cube cluster evolution. Besides, considering a damage definition by the AE energy count, the cube cluster damage model is successfully established. Then by implanting the cube cluster termed AE percolation cluster (APC) into the numerical software FLAC^3D, the consistency between numerical and experimental results of four descriptors of strength, axial-, hoop and volumetric strains excellently proves the reliability of the cluster damage model. In addition, the damaged cluster shows a potential application for quantitative analysis of the shear failure. Further, a percolation analysis of the granite deformation under triaxial compression is made based on the cluster damage model. The effect of pressure-induced percolation transition (PIPT) is verified for the granite and the volume fraction shows a strong linear dependence on the covering length. Moreover, a series of discussion is made to analyze the influence of mechanical parameters on the sensibility of the cluster damage model. Finally, the influence of damage distribution of sub-clusters on the triaxial compression behaviors is quantitatively determined by the comparison between the linear and exponential distributions. The results verify the effectiveness and sensitivity of the cluster damage model in describing triaxial compression behaviors, which provides a new modelling method to extract more valuable information from the correlated AE signals.

Keywords

Spatial correlation; AE signals; Cluster damage model; Triaxial compression behaviors; Damage; PIPT

引用格式：

Xue D J, Gao L, Lu L, Zhou J, Zhou H W, Wu Z D, Yi H Y, Liu J F. An acoustic emission-based cluster damage model for simulating triaxial compression behaviors of granite [J]. Rock Mechanics and Rock Engineering.

DOI: 10.1007/s00603-020-02169-1

创新点：

1. 首次建立了声发射云团信号的空间关联逾渗团簇模型

2. 首次建立了声发射云团信号和三轴压缩力学行为的关系

3. 首次建立了声发射云团信号的损伤逾渗团簇模型

建模方法（图片版权所有，侵权必究）

损伤团簇模型（图片版权所有，侵权必究）

损伤团簇三轴压缩力学行为（图片版权所有，侵权必究）

损伤团簇三轴压缩破坏效果（图片版权所有，侵权必究）

审稿人评价：It is a very interesting investigation on the cube cluster modeling of randomly distributed acoustic emission. Such a fresh idea may greatly promote the development of AE monitoring technology in a neglected field of applying spatial correlation to solve some challenges. Indeed, it is not an easy task to build a proper correlation between the AE signals and triaxial compression behaviors. This may be the first suggestion of solving such challenge and those efforts are very impressive. The spatio-temporal evolution of AE signal-cloud is very important for investigating a real-time fracture process. However, few jobs could be suggested to make a quantitative analysis of clustering behavior. This manuscript suggests a cluster damage model by establishing the spatial correlation in a critical cube. Besides, the criticality origins from the percolation theory and is properly evaluated considering the increment-to-decrement of deviator stress, the surging accumulation of AE events after the onset of dilatancy. Moreover, the criticality estimated by the local-to-whole connection of fracture network is attractive. In brief, we have carefully evaluated the first round of modification and the authors’ reply is professional and serious. Acceptance is a very proper suggestion after revising a wrong spelling in Fig.2.