Parameter studies on the mineral boundary strength influencing the fracturing of the crystalline rock based on a novel Grain-Based Model

Highlights

• The Flat-Joint contact is incorporated into grain-based model to model the minerals.

• Effects of mineral boundary properties on the crystalline rocks are investigated.

• Mineral boundary stiffness controls the deformation process of crystalline rocks.

• Strengthening mineral boundaries is likely to promote the generation of micro cracks.

Abstract

The grain-based model (GBM) in two-dimensional Particle Flow Code (PFC2D) is widely employed to investigate the mechanical response characteristics of crystalline rocks under external load considering the realistic petrographic texture. However, due to the poor self-locking effect of the Parallel-Bond (PB) inside the minerals and unreasonable parametric assignment for the Smooth-Joint (SJ) at the mineral boundaries, the original GBM cannot reproduce the exact microcracking process of brittle rocks. To solve the problem, the novel grain-based model (nGBM) composed of the Flat-Joint (FJ) and the SJ was proposed in our previous research, which not only enhances the rotational resistance of particles, but also improves the simulation of the mineral boundaries. In this study, the nGBM was carefully established and calibrated based on the properties of Alxa porphyritic granite. A series of simulation tests of uniaxial compression, triaxial compression and direct tension under different mineral boundary parametric conditions were carried out to observe the deformation, microcracking and failure behaviors of the nGBM. Quantitative analyses of the mineral boundary properties and the mechanical behaviors of the numerical specimen revealed the extremely complicated relationships between them, which can help explain the micromechanical damage process of crystalline rocks and provide valuable reference for the model calibration.

Introduction

The crystalline rocks comprised of crystalline mineral grains generally possess highly interlocked structures and ultra-low porosities [1]. Various crystalline rocks including granite and diorite are extensively applied in high-level radioactive waste repository, enhanced geothermal system and other major geological engineering activities [2], [3], [4], [5], [6]. A profound understanding of rock mechanical behaviors will facilitate efficient engineering design and construction. A consensus has been reached that the inherent microstructures (e.g., mineral sizes, mineral shapes, pre-existing microcracks) of crystalline rocks determine the strength and deformation characteristics, and control the process of microcrack closure, initiation, propagation and coalescence [7], [8], [9], [10], [11].

Various observation and analysis techniques such as petrographic investigation of thin sections, acoustic emission, X-ray computerized tomography, and scanning electron microscope have been utilized to discover the physical and mechanical differences caused by the inherent microstructures of crystalline rocks [12], [13], [14], [15]. According to the results of petrographic analyses and mechanical experiments on different granite specimens, Tuǧrul and Zarif [16] found that the strengths of granite are related to the mineral contents, especially the content difference between quartz and feldspar has a significant impact. Přikryl [17] conducted a list of image analyses to evaluate the relationship between the strength anisotropy and microstructures, and presented that the strength anisotropy increases with the degree of mineral shape-preferred orientation. Ge and Sun [18] studied the acoustic emission and crack propagation characteristics of granite after cooling and heating cycles. They believed that the thermal expansion of mineral grains induces the mineral boundaries to preferentially crack. Zuo et al. [19] used the high temperature scanning electron microscope testing system to capture the microcracking behaviors of granite under loading, and demonstrated that mineral shapes and thermal cracks dominate the initiation and propagation of microcracks.

In addition to these laboratory techniques, multifarious numerical simulation methods, such as the finite-element method (FEM), the finite-difference method (FDM), the discrete element method (DEM) and the hybrid finite-discrete element method (FDEM), are also successful in revealing the macro-mechanical response characteristics and microcracking process of rocks under complex loading conditions [20]. As one of the most robust DEM codes, PFC has great advantages in simulating the deformation and failure of rocks at both the laboratory and the field scales [21], [22], [23], [24].

In the PFC modeling framework, a set of rigid circular particles in contact with each other are bonded by giving contact models to form the solid materials [25]. Once the calculation is started, the displacements, contact forces and moments of particles will be updated in real time based on Newton's second law and force-displacement law [26]. If the contact force exceeds the strength limit allowed by the contact bond, the pairwise connecting particles will rupture and produce a microcrack. Furthermore, the micro tensile and shear failure of the contact bond generate the tensile crack and the shear crack, respectively. Therefore, the contact models reflecting the mechanical interaction of particles will ultimately decide the macroscopic behaviors of entire solid materials. Abundant basic contact models have been built into PFC, including PB, FJ, and FJ [27]. The direct applications of the basic contact models are sufficient to emulate the relatively homogeneous rocks (e.g., sandstone, coal), but they cannot match the mineral heterogeneity of crystalline rocks [28], [29], [30]. In order to overcome the drawback, the original GBM combining the PB and the SJ was first proposed by Potyondy [31], which can not only create the realistic petrographic texture in terms of mineral contents and sizes, but also monitor the information of both intragrain and intergrain cracks.

The advent of the original GBM promotes the quantitative researches of the interaction between the microstructure characteristics and mechanical behaviors of crystalline rocks. Bahrani and Kaiser [32] indicated the strength distinction between the intact marble and damaged marble containing initial cracks, and developed the strength semi-empirical relations under different confining pressures. Peng et al. [33] stated that the peak strength and the elastic modulus increase with the decrease of mineral grain heterogeneity, and quartz is more prone to cracking than other minerals. Wong et al. [34] affirmed that the increase of quartz content in granite results in the increase of strength, elastic modulus and cracks, and the decrease of Poisson's ratio and maximum volumetric strain. Taking Aue granite as an example, Hofmann et al. [35], [36] systematically explored the effects of micro-parameters on the microcracking behaviors in the original GBM, and concluded that the parameters considerably affect the number, type and spatial distribution of cracks.

Although the original GBM creatively provides a feasible method for the simulation of crystalline rock microstructures, it still has an obvious defect. Too many cracks are distributed at the mineral boundaries, and few cracks appear inside the minerals of brittle crystalline rocks under uniaxial compression, which cannot conform to the experimental observation [33], [34], [35], [36], [37], [38]. The reason for the defect may be that the contact model PB inside the minerals cannot render enough grain interlocking and rotational resistance [39], [40]. Consequently, to achieve the actual compressive strengths of rocks in the original GBM, the strength parameters of the PB have to be much larger than those of the SJ at the mineral boundaries, causing it difficult for the mineral interiors to crack.

To solve the problem, the nGBM, in which the contact model FJ replaces the PB to bond the particles inside the minerals,was proposed in our previous research [41]. Moreover, we modified the method on assigning the mineral boundary parameters to make the properties of the boundaries inherit from those of the mineral interiors, instead of simplifying them to constants. The preliminary application of the nGBM reproduced a more realistic crack propagation process of granite under uniaxial compression condition, in which the mineral grains were cut by numerous tensile cracks [41].

Considering that the current research on the GBM mainly focuses on the effects of mineral sizes, contents and pre-existing microcracks, and ignores the effects of mineral boundary properties, the detailed parametric studies on the mineral boundaries of the nGBM are carried out in this study. First, the methods of the nGBM establishment and the mineral boundary parameter assignments are introduced. Second, according to the physical and mechanical properties of Alxa porphyritic granite, the numerical granite specimen is generated and the micromechanical parameters are carefully calibrated. Third, the uniaxial compression, triaxial compression and direct tension tests under the conditions of different mineral boundary parameters are conducted in order to analyze the development trends of the strength, Young's modulus, Poisson's ratio and microcrack propagation. Finally, the influence degrees of various properties of mineral boundaries are summarized and evaluated to provide some guidance for the calibration of the nGBM.