Study on fracture of coal samples with different fracture angles under microbial environment

ABSTRACT: Rock cracks tend to grow in the form of tensile and shear failure, i.e., mixed mode I-II crack. Size effect of fracture process zone (FPZ) should be highlighted due to it may alter the fracture growth. To study the size effects of FPZ on the development characteristics of mixed mode cracks, three-point bending experiments with off-center initial crack were carried out on sandstone with ratio of length and height of 3. Combined with digital image correlation (DIC) method, the variation of deflection angle and displacement field around the crack tip were analyzed. The results show that the FPZ length increases with the specimen size while the normalized length of the FPZ decreases. The FPZ begins to develop at 60-70% pre-peak and is fully developed at 90% post-peak. The cracks of different sizes begin to deflect when the FPZ is fully developed, and the deflection is completed at 60% post-peak. The deflection angle of FPZ decreases with the sample size. To ensure that the local tensile stress is the maximum, the cracks will deflect and cause the local shear stress to decrease and disappear, which is more obvious in small-size specimens. This study further revealed the fracture mechanism of mixed mode I-II crack under different sizes. 1. INTRODUCTION Cracks are common internal structure in rock materials, due to different external forces, there will be different forms of expansion, generally can be divided into three modes: mode I (open) cracks, mode II (slip) cracks and mode III (tear) cracks (Surberg and Tschegg, 2001). In view of different shapes of prefabricated cracks, Lin and Labuz, (2013) et al. studied mode I fractures of sandstone. The results show that the critical crack opening displacement does not change with the prefabricated crack shape. The FPZ length is about 10 times the maximum particle size of the sample. The critical crack opening displacement and FPZ length in mode II cracks are larger than those in mode I cracks (Lin et al., 2014; Moazzami et al., 2020). Because cracks in actual rock structure often do not exist in a single fracture mode, such cracks are called mixed mode cracks. In practical engineering, mixed mode I-II cracks (hereinafter referred to as mixed mode cracks) are the most common (Aliha and Ayatollahi, 2013). In the mode I fracture, the fracture receives only tensile stress (Meirong. et al., 2024). Compared with mode I cracks, mixed mode cracks are not only subjected to tensile stress, but also to shear stress (de Moura et al., 2016). Since the shear resistance of rock materials is stronger than the tensile resistance, cracks generally start and expand in the direction perpendicular to the maximum tensile stress, that is, tensile failure is still the main type of mixed mode cracks (Song et al., 2018). Due to the existence of shear stress, there is a deflection Angle in the initiation of mixed mode cracks compared with mode I cracks.

Effect of loading rate on mode I fracture behavior of red sandstone: Insights from AE and DIC techniques

Owing to its importance in evaluating the fracture behavior of concrete, the crack extension resistance curve of concrete has been widely studied, both experimentally and theoretically. In this paper, a numerical approach is developed for the crack extension resistance curve of concrete by considering the variation of the fracture process zone (FPZ) length during the whole fracture process. In this approach, the FPZ length is determined by using the linear asymptotic superposition assumption. Dividing the whole fracture process into three different stages of the cohesive stress distribution within the FPZ, the crack extension resistance curve is formulated by superposition of the intrinsic fracture toughness of concrete and the fracture toughness caused by the cohesive stress within the FPZ. The developed numerical approach is applied to the tested and simulated standard three-point bending notched concrete beams. The effect of the variation of the FPZ length on the crack extension resistance curve is evaluated on the basis of the numerical results. The crack extension resistance first increases with an increase in ratio of the effective crack length to the beam depth and then reaches a plateau value when the FPZ is fully developed. When the effective crack length is normalized to the beam depth, the crack extension resistance is basically independent of the beam depth within the beam size range studied.

This paper addresses the size effect of inplane bending strength as well as Mode I fracture toughness and process zone length of wood fiber-reinforced gypsum panels. Wood fiber gypsum panels represent an incombustible short fiber composite material composed of recycled paper fibers embedded in a gypsum matrix. The material, which is used for sheathing and bracing of timber frame constructions, exhibits marked fracture softening supposedly resulting in a considerable size effect. In the paper presented, in a first step Bažant’s size effect law for quasi-brittle materials is derived. The parameters of this size effect law are then determined by means of nonlinear regression analysis applied to a test series with scaled single edge notched beam specimens. Detailed consideration is given to the adequacy of linear confidence intervals of the model parameters in comparison to nonlinear inferential results. Finally, the probability densities of fracture toughness and fracture process zone length are determined f...

In the present study, to reveal the loading rate effect on fracture process in Beishan granite, a series of Brazilian splitting tests under conventionally monotonic loading and stepwise loading conditions were performed to observe the crack propagation process of granites, with the aid of a digital image correlation (DIC) technique. The fracture process zone (FPZ) length and opening displacement ahead of notch tips, and so on were measured, and the loading-rate dependence was acquired correspondingly. The experimental results show that the peak load, axial and lateral deformation of granite gradually increased with the increasing loading rate. With the increase in the loading rate, the stress level for fracture initiation decreased, while the critical opening displacement and FPZ length gradually increased. The granite underwent insignificant deformation during the constant stress loading period when a lower stress was applied. When a larger stress was applied, obvious three-stage creep deformation was observed. The opening displacement ahead of notch tips increased slowly at a constant rate during the primary and secondary creep stages, then exhibited an approximately exponential increase with increasing time during the tertiary creep. Moreover, the FPZ length of granite at the critical state under conventional loading was higher than that under stepwise loading. The inner mechanism is analyzed to explain the rate-dependent fracturing behavior.

Mixed-mode (I-II) fracturing is a prominent mechanical characteristic of hydraulic fracture (HF) deflecting propagation. At present, understanding the effect of injection rates on HF deflecting propagation remains challenging and restricts the control of HF deflecting propagation bearing tensile and shear stresses with fluid injection rates. Our recently published experimental results show that the fracture process zone (FPZ) length of mixed-mode (I-II) fractures in rock-like materials increases with the rising quasistatic loading rate. Both the deformation in FPZ and the generation of real fracture surfaces are tensile. On this basis, the rate-dependent mixed-mode (I-II) cohesive fracture model was proposed under quasistatic loading, and a couple of theoretical outcomes were obtained. Under different injection rates, the deflecting HF propagates step-by-step under mixed-mode (I-II) fracturing, and the HF extension path is supposed to be straight in each step. With the increment of injection rate, the increased (tensile) FPZ length is the stable propagation distance of deflecting HF in each step and besides deteriorates the fracture resistance discontinuity of FPZ developing to be a real tensile fracture. Thus, the mixed-mode (I-II) fracture tends to propagate unstably driven by kinetic energy once FPZ develops completely under fast loading. Moreover, two injection rate-dependent (IRD) HF deflecting propagation modes were determined, i.e., the step-by-step stable-propagation and step-by-step unstable propagation modes. HF deflection occurs in the step alternation of fracture propagation. With the increasing fluid injection rate, the increased FPZ length and kinetic energy (from fracture resistance discontinuity) extend the stable and unstable HF propagation distance along the initial direction in an extension step, respectively. Therefore, fast fluid injection improves the HF deflecting propagation radius; i.e., it inhibits the HF deflecting propagation or promotes HF extension along the initially designed direction. The injection rate-dependent HF deflecting propagation modes (based on the proposed model) were validated by further processing of published true triaxial physical simulation tests of hydraulic fracturing. The ordinal response of Fiber Bragg grating sensors embedded along the fracture propagation path, and the continuous fluctuant injecting pressures validate the step-by-step propagation of the hydraulic fracture. The test-measured deflecting HF trajectory indicates that high fluid injection rates remarkably increase the HF deflecting radius, which is consistent with the theoretical analysis in this work. The above findings can provide theoretical bases for controlling the HF deflecting propagation in the surrounding rock of mines and oil-gas reservoirs.

Fracture process zone development and length assessment under the mixed-mode I/II load analysed by digital image correlation technique

This paper deals with a mesomechanical modeling of fracture in concrete like quasi-brittle materials. The paper seeks to provide insight regarding the variation of the fracture process zone (FPZ) length during the cracking process. The correlation between the FPZ length and the crack extension is also investigated. The FPZ variation is investigated through the evolution of cohesive tangential stresses along the crack path of different notched beams under three-point bending tests. The concept of equivalent linear elastic fracture mechanics is then employed to compute the crack extensions. The mesoscale investigation shows that the relationship between the FPZ length and the crack length is non linear. Furthermore, the numerical crack extensions are used to investigate the R-curve. It is shown that the R-curve is size-dependent and notch-sensitive.

This paper presents an experimental research on the length and shape of the fracture process zone of rocks under mode I, mixed mode (I + II) and mode II loading conditions for different geometries of cracked specimens made of two types of rocks, using the digital image correlation approach. Single edge notch bending (SENB) and semi-circular bend specimens are the two geometries considered. In order to investigate the effect of the specimen size on the fracture process zone length, rocks with three different sizes are produced and tested. To investigate the effect of the mode mixity on the fracture process zone length of marble and sandstone, the specimens are tested under different modes of loading. According to the experimental results, it is found that the fracture process zone length changes with mode ratio, specimen size, geometry and the material properties. The fracture process zone length increases when the mode of loading moves from mode I to mode II. Experimental results also show that fracture process zone becomes longer for specimens with larger sizes. The fracture process zone is also affected by the specimen geometry.

Fracture mechanics of concrete play an important role in describing fracture process in concrete members. Fracture energy is a key parameter in employing the fracture mechanics in concrete structures. To determine the fracture energy of concrete, the formation and progress of fracture process zone in front of crack tip have to be identified appropriately. Therefore, the development of fracture process zone was modeled in this study based on the concept of fractured volume. The fractured volume was defined in terms of the length and width of the fracture process zone. The length of fracture process zone was modeled based on the data of cohesive stress analyses. The continuous change of length and width of fracture process zone was modeled as a crack propagates along the ligament. The present model may allow more realistic evaluation and interpretation for the fracture energy of concrete in that it gives the fracture energy per unit volume of concrete in addition to the fracture energy per unit area of concrete. However, further study is necessary to clarify the patterns of change of FPZ size along the ligament according to various member sizes because the decreasing pattern of FPZ size according to crack-to-depth ratio may be different for different sizes of members. This task must be also implemented for the variation of width of FPZ for different member sizes. This will enable us to describe reasonably the fracture energy of concrete per unit volume for any sizes of members.

A new test method for determining fracture energy and process zone length, defined by the size effect law and its generalized theory, has been proposed. It allows the use of specimens of the same size and shape but with different notch lengths. This paper proposes test and data analysis procedures for using this variable-notch one-size method. By filling in a programmed spreadsheet, the measured maximum loads of the specimens, fracture energy and process zone length are output instantly. Tests have been conducted to verify the proposed method. It is shown that either eccentric compression prisms or split-tension cylinders can be applied to obtain accurate results. Since the method requires the maximum loads of several specimens of the same size and shape, it makes specimen preparation and testing very simple.

An analytical method for predicting mode-I crack propagation process and resistance curve of rock and concrete materials

The wetting and nonwetting fluid saturations in porous reservoirs always change during long-term injection and production. The fracture process zone (FPZ) is a prominent feature in the rock fracture process. If the FPZ properties are influenced by pore fluids, the process of hydraulic fracturing will change greatly. The existing models do not consider the role of pore fluid when characterizing the FPZ. In this paper, a modified Dugdale–Barenblatt (D–B) model with capillary pressure is proposed. The model reflects the fact that the FPZ length decreases nonlinearly with the increase in capillary pressure, and it reveals the mechanism of capillary pressure on the equivalent fracture cohesion in the FPZ, which affects the FPZ length. Three-point bending tests were carried out on sandstone under various fluid saturations through digital image correlation (DIC), acoustic emission (AE), and scanning electron microscope (SEM). It was found that the FPZ length of the water–oil-saturated samples was 30–50% smaller than that of water-saturated/oil-saturated samples due to the capillary pressure effect, and the modified D–B model was well consistent with the experiments. The AE behaviors of different saturated samples were not the same: The cumulative AE signals changed abruptly at 90% of the peak load for the water–oil-saturated samples and at 50% of the peak load for water-saturated samples. This demonstrated that the effect of capillary pressure was more obvious than the weakening effect of microstructural damages. The significant influence of capillary pressure on FPZ requires continuous recognition in hydraulic fracturing design.

Strain rate effect on the fracture parameters of concrete three-point bending beam with a small span-to-height ratio

Gastroentérologie