Gao-Feng Zhao

A Preliminary Study of 3D Printing on Rock Mechanics

Abstract3D printing is an innovative manufacturing technology that enables the printing of objects through the accumulation of successive layers. This study explores the potential application of this 3D printing technology for rock mechanics. Polylactic acid (PLA) was used as the printing material, and the specimens were constructed with a “3D Touch” printer that employs fused deposition modelling (FDM) technology. Unconfined compressive strength (UCS) tests and direct tensile strength (DTS) tests were performed to determine the Young’s modulus (E) and Poisson’s ratio (υ) for these specimens. The experimental results revealed that the PLA specimens exhibited elastic to brittle behaviour in the DTS tests and exhibited elastic to plastic behaviour in the UCS tests. The influence of structural changes in the mechanical response of the printed specimen was investigated; the results indicated that the mechanical response is highly influenced by the input structures, e.g., granular structure, and lattice structure. Unfortunately, our study has demonstrated that the FDM 3D printing with PLA is unsuitable for the direct simulation of rock. However, the ability for 3D printing on manufactured rock remains appealing for researchers of rock mechanics. Additional studies should focus on the development of an appropriate substitution for the printing material (brittle and stiff) and modification of the printing technology (to print 3D grains with arbitrary shapes).

On the Truly Meshless Solution of Heat Conduction Problems in Heterogeneous Media

A truly meshless method based on the weighted least-squares (WLS) approximation and the method of point collocation is proposed to solve heat conduction problems in heterogeneous media. It is shown that, in the case of strong heterogeneity, accurate and smooth solutions for temperature and heat flux can be obtained by applying the WLS approximation in each homogeneous domain and using a double-stage WLS approximation technique together with a proper neighbor selection criterion at each interface.

Dynamic Indirect Tensile Strength of Sandstone Under Different Loading Rates

Rock failure generally refers to the process of damaging rock material to the point at which it partially or completely loses its load-carrying capacity. For rock materials, the fracture pattern and mechanical properties, including compressive strength, tensile strength, shear strength, and fracture toughness, under dynamic loads are affected by the loading rate/strain rate. This rate effect has been studied experimentally by many researchers, e.g., Grady et al. (1977), Chong et al. (1980), Blanton (1981), Masuda et al. (1987), Chong and Boresi (1990), Zhao et al. (1999), Zhao and Li (2000), Li et al. (2005), Wang et al. (2006), and Dai et al. (2010a, b). Tensile failure is the simplest and most common failure mode found in nature. A good understanding of the dynamic tensile failure of the rock material is important for rock structures subjected to dynamic loads. A comprehensive review on the dynamic testing of rock material has been provided by Zhao (2011). To quantify the dynamic tensile strength of rock material, researchers typically use the Brazilian disc (BD) specimen or semicircular bend (SCB) specimen in the split Hopkinson pressure bar (SHPB) system. Different types of rocks have been tested, e.g., Bukit Timah granite (Zhao and Li 2000), marbles (Wang et al. 2006), Laurentian granite (LG) (Dai et al. 2010a, b), and argillites (Cai et al. 2007). In this study, a series of dynamic indirect tensile tests was conducted on sandstone from Changsha, China. The tests were performed at loading rates of 10, 10, 10, 10, and 10 MPa/s to cover both the quasi-static and dynamic loading conditions. The experimental data show an apparent dynamic effect of the indirect tensile strength of the Changsha sandstone, which can be used in dynamic constitutive models and for the validation of existing or novel numerical models. Based on the experimental data, a new empirical equation is developed to describe the dynamic increase factor (DIF) of the indirect tensile strength of the Changsha sandstone. Moreover, the recently developed distinct lattice spring model (DLSM) (Zhao 2010; Zhao et al. 2011) is validated using the experimental data.

A Lattice Spring Model for Coupled Fluid Flow and Deformation Problems in Geomechanics

A lattice spring model is developed for coupled fluid flow and deformation problems. The model has an underlying structure consisting of particles connected by springs for the solid and fluid bubbles, connected by fluid pipelines for fluid flow. Formulations of the model to describe the coupled fluid flow and deformation behavior of a solid are derived. A few examples of consolidation problems are presented and compared with analytical solutions with good agreement being obtained, which means that the lattice model developed in this study can correctly simulate the coupled fluid flow and deformation response of a solid.

A MLS-based lattice spring model for simulating elasticity of materials

A MLS-based lattice spring model is presented for numerical modeling of elasticity of materials. In the model, shear springs between particles are introduced in addition to normal springs. However, the unknowns contain only particle displacements but no particle rotations. The novelty of the model lies in that the deformations of shear springs are computed by using the local strain obtained by the moving least squares (MLS) approximation rather than using the particle displacements directly. By doing so, the proposed lattice spring model can represent the diversity of Poissons ratio without violating the requirement of rotational invariance. Relationships between micro spring parameters and macro material constants are derived from the Cauchy-born rules and the hyperelastic theory. Numerical examples show that the proposed model is able to reproduce elastic solutions obtained by finite element methods for problems without fractures. Therefore, it is capable of simulating solid materials which are initially continuous, but eventually fracture when critical stress and/or displacement levels are reached. A demonstrating example is presented.

Strain localization in unsaturated elastic-plastic materials subjected to plane strain compression

AbstractAnalytical solutions have been derived for the onset of strain localization in a broad class of unsaturated elastic-plastic porous materials based on Bishop’s definition of effective stress. Critical hardening moduli for constant water content and drained loadings were found to be further gradual simplifications of the critical hardening modulus for an undrained loading. In addition, the solutions were found to reduce to the previously found solutions for fully saturated and monophasic porous materials by adequately adjusting bulk moduli of the pore fluids. This finding demonstrates that the mechanics of fully saturated and monophasic soils is the special simpler case of the mechanics of unsaturated soils. A diagnostic tool for detection of the inception of strain localization was developed by implementing the aforementioned solutions into a constitutive driver for a bounding surface plasticity model. The tool was used to further illustrate the strain localization behavior of unsaturated Bourke si...

A multiscale manifold method using particle representations of the physical domain

Multiscale modelling has great advantages by simulating material behaviours on one level using information from another level. The popular multiscale methodology couples the atomistic/meso particle model with the continuum model (e.g., multiscale model by coupling molecular dynamics and finite element analysis). In this paper, a new multiscale method is proposed using the numerical manifold method (NMM) and its micro extension particle manifold method (PMM). Due to the same mathematical and mechanical scheme NMM and PMM adopt, their multiscale coupling has a uniform framework and does not need special treatment at the multiscale boundary. The proposed method has an advantage over PMM in presenting the material’s micro structure and failure description. It also saves the computational resource by using NMM to present the macro part. In the paper, the multiscale methodology is presented with some numerical demonstrations. It is proven that this novel multiscale manifold method is a good tool for analysis of geomaterials.

Onset of Strain Localization in Unsaturated Soils Subjected to Constant Water Content Loading

Analytical solutions for the inception of strain localization in unsaturated soils were implemented into the constitutive driver for a bounding surface plasticity model. Effects of the initial net mean stress and initial suction on the inception of strain localization in a porous material subjected to constant water content plane strain compression (PSC) were investigated. It was found that decreases in both, the initial suction and the initial net mean stress decreased the axial strain at onset, thus effectively increasing the susceptibility to strain localization. The corresponding deformation bands were largely contractant shear bands. Dilatant shear bands occurred only for the initial over consolidation ratios (OCR) larger than 3.25.

An Experimental Study of Fatigue Behavior of Granite Under Low-Cycle Repetitive Compressive Impacts

In nature, rock structures such as tunnel walls, rock pillars, excavation roofs, and bridge abutments are often subjected to repetitive/cyclic loads. Cyclic loading could result in accumulated fatigue damage which may prematurely destruct rock structures at a stress level lower than its characterized strength under monotonic conditions (Bagde and Petroš 2005a). Therefore, study on fatigue damage evolution and deformation characteristics of rocks under cyclic loading could facilitate understanding of the failure mechanism of rock, and hence contribute to better evaluate the safety and long-term stability of engineering structures such as underground mines and excavations and nuclear waste repositories (Xu et al. 2012). In the past decades, numerous efforts have been devoted to investigate fatigue damage of rocks under static or quasistatic cyclic loading. After performing a great number of cyclic loading tests on a variety of rock samples, e.g., granite, sandstone, limestone, and salt rock, under confined or unconfined pressure conditions, it is now recognized that the fatigue properties of rock material are dependent on the maximum stress, loading amplitude, and frequency (Bagde and Petros 2005a, b; Cerfontaine and Collin 2018; Tao and Mo 1990; Xiao et al. 2009, 2010). To be more specific, with increasing maximum stress and amplitude, the fatigue life, i.e., the number of cycles before failure, decreases (Fuenkajorn and Phueakphum 2010; Haimson and Kim 1972; Momeni et al. 2015; Singh 1989); the fatigue strength, i.e., the maximum stress a rock material can endure for a given number of loading cycles without failure, and fatigue life slightly increase with increasing strain and stressing rate at the same applied stress level (Lajtai et al. 1991; Momeni et al. 2015; Ray et al. 1999); higher confining pressure results in larger axial strain at failure (Ma et al. 2013; Liu and He 2012). In addition, it was found that there is a threestage, i.e., transient, steady, and accelerated, deformation law of axial strain of rock under cyclic loading with an applied maximum stress level higher than the threshold value (Momeni et al. 2015; Xiao et al. 2010; Zhang et al. 2008). In addition to static or quasi-static cyclic loads, rock structures may also bear low-cycle repetitive dynamic loads such as blasting and earthquakes. For example, during blasting excavation of tunnels, adjacent rock structures and completed tunnel sections are subject to repetitive dynamic loadings from sequential blasting. In enhanced geothermal systems, rock structures such as boreholes are subjected to not only cycles of high pressure during fluid injection process but also repetitive injection-induced seismicity (Giardini 2009; Li et al. 2018a). Moreover, progressive damage accumulation of the underground excavation was also observed under repeated seismic loadings (Ma and Brady 1999). Although the mechanical and fracture properties of rock under dynamic loading have been extensively studied (Li et al. 1999, 2008; Zhang and Zhao 2013; Zhao et al. 1999), dynamic fatigue behaviors of rocks have been rarely * J. B. Zhu jbzhu@tju.edu.cn http://jgxy.tju.edu.cn/teachers.asp?id=180

Three-Dimensional DDA and DLSM Coupled Approach for Rock Cutting and Rock Penetration

AbstractRock cutting and rock penetration are typical problems in civil, mining, petroleum, and geothermal engineering disciplines. They involve dynamic fracturing and fragmentation of rock, high-speed movements of a cutter/impactor, and complex dynamic contacts between the cutter/impactor and the rock. In this study a new three-dimensional (3D) coupled approach is developed to address these problems. The distinct lattice spring model (DLSM) is used to simulate the dynamic fracturing process of the rock, and the discontinuous deformation analysis (DDA) is adopted to model the high-speed motion of the cutter/impactor. An explicit-implicit coupling scheme is developed to bridge DLSM and DDA. Moreover, to take account of interaction between DLSM and DDA, a 3D simplex sphere-to-block contact method is introduced. Finally, a number of numerical examples are conducted to verify the implementation of the coupled approach and its ability to model rock cutting and rock penetration problems.