Experimental Study of Crack Growth in Rock-Like Materials Containing Multiple Parallel Pre-existing Flaws Under Biaxial Compression

Cracks and joints are common in rock masses and play a crucial role in rock mass stability. This study prepared specimens with multiple parallel pre-existing flaws by embedding iron sheets in rock-like materials and used the samples to investigate the crack growth characteristics of these materials. Biaxial compression experiments were performed on sixty specimens, and the influences of the number of pre-existing flaws, their angles and the lateral stress on crack growth were investigated based on video recordings of the crack growth. The results demonstrate that structural failure will occur due to crack growth when the sample contains a small number of pre-existing flaws and that as the number of cracks increases, the specimens will fail due to local failures. In addition, the types of rock bridge failures are summarized, including wing cracks, secondary shear cracks between horizontally-separated pre-existing flaws and secondary shear cracks between vertically-separated pre-existing flaws. Wing cracks play a significant role in the failure of the specimens. The results increase the understanding of crack growth in brittle materials that contain multiple parallel pre-existing flaws under biaxial compression.     

An Experimental Study of Crack Coalescence Behaviour in Rock-Like Materials Containing Multiple Flaws Under Uniaxial Compression

Experiments on man-made flawed rock-like materials are applied extensively to study the mechanical behaviour of rock masses as well as crack initiation modes and crack coalescence types. A large number of experiments on specimens containing two or three pre-existing flaws were previously conducted. In the present work, experiments on rock-like materials (formed from a mixture of sand, plaster, limestone and water at mass ratio of 126:9:9:16) containing multiple flaws subjected to uniaxial compression were conducted to further research the effects of the layout of pre-existing flaws on mechanical properties, crack initiation modes and crack coalescence types. Compared with previous experiments in which only three types of cracks were found, the present experiments on specimens containing multiple flaws under uniaxial compression revealed five types of cracks, including wing cracks, quasi-coplanar secondary cracks, oblique secondary cracks, out-of-plane tensile cracks and out-of-plane shear cracks. Ten types of crack coalescence occurred through linkage among wing cracks, quasi-coplanar secondary cracks, oblique secondary cracks, out-of-plane shear cracks and out-of-plane tensile cracks. Moreover, the effects of the non-overlapping length and flaw angle on the complete stress–strain curves, the stress of crack initiation, the peak strength, the peak strain and the elastic modulus were also investigated in detail.     

Crack Initiation, Propagation and Coalescence in Rock-Like Material Containing Two Flaws: a Numerical Study Based on Bonded-Particle Model Approach

Cracking and coalescence behavior in a rectangular rock-like specimen containing two parallel (stepped and coplanar) pre-existing open flaws under uniaxial compression load has been numerically studied by a parallel bonded-particle model, which is a type of bonded-particle model. Crack initiation and propagation from two flaws replicate most of the phenomena observed in prior physical experiments, such as the type (tensile/shear) and the initiation stress of the first crack, as well as the coalescence pattern. Eight crack coalescence categories representing different crack types and trajectories are identified. New coalescence categories namely “New 1” and “New 2”, which are first observed in the present simulation, are incorporated into categories 3 and 4, and category 5 previously proposed by the MIT Rock Mechanics Research Group, respectively. The flaw inclination angle (β), the ligament length (L) (spacing between two flaws) and the bridging angle (α) (inclination of a line linking up the inner flaw tips, between two flaws) have different effects on the coalescence patterns, coalescence stresses (before, at or post the peak stress) as well as peak strength of specimens. Some insights on the coalescence processes, such as the initiation of cracks in the intact part of specimens at a distance away from the flaw tips, and coalescence due to the development and linkage of a number of steeply inclined to vertical macro-tensile cracks are revealed by the present numerical study.     

Crack Initiation and Coalescence Behavior of Two Non-parallel Flaws

Crack initiation and coalescence behavior of rock or rock-like specimens containing artificial flaws under uniaxial compression have been subjects of intensive investigation in the past. Most of these investigations however focused on crack initiation and coalescence between two or more parallel flaws. Although there have been few experimental studies on non-parallel flaws, these studies did not address the influence of geometrical factors such as ligament length and ligament angle on the crack initiation and coalescence behavior of non-parallel flaws. To investigate whether the individual geometrical factors have similar effects on the crack initiation and coalescence behavior of both parallel and non-parallel flaws, we conducted uniaxial compression tests to investigate crack cracking and coalescence processes in rock like material containing two non-parallel flaws. The paper presents the influence of individual geometrical factors on the crack initiation process and coalescence pattern of non-parallel flaws. Initiation of primary first cracks from all the tips of the two flaws did not occur simultaneously in all the flaw configurations. The flaw configuration of the non-parallel flaws influences the crack initiation, crack trajectories and coalescence behavior. The crack coalescence pattern changes with an increasing ligament angle from indirect to shear crack or mixed tensile-shear crack to tensile crack coalescence. The chance of direct coalescence is reduced with an increase in ligament length. In conclusion, the crack initiation and coalescence behavior of prismatic rock-like specimens with non-parallel flaws, as influenced by the geometrical factors, are analogous to the cracking and coalescence pattern observed in specimens with parallel flaws.     

Numerical Study on Coalescence of Pre-Existing Flaw Pairs in Rock-Like Material

The present numerical study, which is an extension of our previous numerical analysis on cracking processes of a single pre-existing flaw, focuses on the coalescence of two pre-existing parallel open flaws in rock subjected to a uniaxial compressive loading. To facilitate a systematic investigation, the arrangements of the flaw pair are classified into 11 categories. Simulations engaging AUTODYN are conducted on each category. The numerical results are compared with some published physical experimental test results. Eleven typical coalescence patterns are obtained, which are in good agreement with the experimental results, which include two coalescence patterns obtained in flaw pair arrangements (II) and (VIII″) not being reported in previous studies. The information gathered in the simulations helps identify the type (tensile/shear) of each crack segment involved in the coalescence. Most of the coalescence cracks initiate at or around the flaw tips, except those in flaw pair arrangements (II) and (IX′) with a very short ligament length, in which the coalescence cracks initiate on the flaw surfaces away from the flaw tip regions. Based on the numerical simulation results, the properties of the 11 coalescence patterns are obtained. Except those in flaw pair arrangements (II) and (IX′), the other coalescence patterns can be interpreted with respect to the basic crack types—tensile wing crack, horsetail crack and anti-wing crack. In addition, based on the type of crack segments involved in coalescence, namely tensile and shear, the coalescence can be classified into T mode (tensile mode), S mode (shear mode) and TS mode (mixed tensile–shear mode).     

Modeling of Crack Initiation, Propagation and Coalescence in Uniaxial Compression

Summary ?Cracks that initiate from pre-existing discontinuities can link with other cracks or with other discontinuities and produce failure in a rock mass. The Displacement Discontinuity Method (DDM), FROCK, is used in this investigation to model experimental observations on pre-cracked specimens of gypsum. In these experiments two fractures, which were either both open or closed, were placed through the thickness of the specimens, and detailed observations of the cracking process were performed as the specimens were loaded in uniaxial compression. The following aspects are studied for both open and closed fractures: 1) crack initiation stress; 2) direction and propagation of the new cracks; 3) type of coalescence and stress at which it occurs. Modeling is done considering the actual size of the specimens. Relations between the direction of initiation for each type of crack, the orientation of the initial fractures, and the type and coalescence are established. In addition, comparisons between results from experiments and predictions from the model are presented. The numerical results are in agreement with the experiments.     

Cracking Processes in Rock-Like Material Containing a Single Flaw Under Uniaxial Compression: A Numerical Study Based on Parallel Bonded-Particle Model Approach

Cracking processes have been extensively studied in brittle rock and rock-like materials. Due to the experimental limitations and the complexity of rock texture, details of the cracking processes could not always be observed and assessed comprehensively. To contribute to this field of research, a numerical approach based on the particle element model was used in present study. It would give us insights into what is happening to crack initiation, propagation and coalescence. Parallel bond model, a type of bonded-particle model, was used to numerically simulate the cracking process in rock-like material containing a single flaw under uniaxial vertical compression. The single flaw’s inclinations varied from 0° to 75° measured from the horizontal. As the uniaxial compression load was increased, multiple new microcracks initiated in the rock, which later propagated and eventually coalesced into longer macrocracks. The inclination of the pre-existing flaw was found to have a strong influence on the crack initiation and propagation patterns. The simulations replicated most of the phenomena observed in the physical experiments, such as the type, the initiation location and the initiate angle of the first cracks, as well as the development of hair-line cracks, which later evolved to macrocracks. Analyses of the parallel bond forces and displacement fields revealed some important mechanisms of the cracking processes. The first cracks typically initiated from the tensile stress concentration regions, in which the tensile stress was partially released after their initiation. The tensile stress concentration regions subsequently shifted outwards close to the propagating tips of the first cracks. The initiation and propagation of the first cracks would not significantly influence the compressive stress singularity at the flaw tips, which was the driving force of the initiation of secondary cracks. The initiation of microcracking zone consisting almost exclusively of micro-tensile cracks, and that of microcracking zone consisting of micro-tensile cracks and mixed micro-tensile and shear cracks, were found to be correlated with two distinct types of displacement fields, namely type I (DF_I) and type II (DF_II), respectively.     

Crack Coalescence in Molded Gypsum and Carrara Marble: Part 1. Macroscopic Observations and Interpretation

Cracking and coalescence behavior has been studied experimentally with prismatic laboratory-molded gypsum and Carrara marble specimens containing two parallel pre-existing open flaws. This was done at both the macroscopic and the microscopic scales, and the results are presented in two separate papers. This paper (the first of two) summarizes the macroscopic experimental results and investigates the influence of the different flaw geometries and material, on the cracking processes. In the companion paper (also in this issue), most of the macroscopic deformation and cracking processes shown in this present paper will be related to the underlying microscopic changes. In the present study, a high speed video system was used, which allowed us to precisely observe the cracking mechanisms. Nine crack coalescence categories with different crack types and trajectories were identified. The flaw inclination angle (β), the ligament length (L), that is, intact rock length between the flaws, and the bridging angle (α), that is, the inclination of a line linking up the inner flaw tips, between two flaws, had different effects on the coalescence patterns. One of the pronounced differences observed between marble and gypsum during the compression loading test was the development of macroscopic white patches prior to the initiation of macroscopic cracks in marble, but not in gypsum. Comparing the cracking and coalescence behaviors in the two tested materials, tensile cracking generally occurred more often in marble than in gypsum for the same flaw pair geometries.

The Effect of Specimen Size on Strength and Other Properties in Laboratory Testing of Rock and Rock-Like Cementitious Brittle Materials

The effect of specimen size on the measured unconfined compressive strength and other mechanical properties has been studied by numerous researchers in the past, although much of this work has been based on specimens of non-standard dimensions and shapes, and over a limited size range. A review of the published literature was completed concentrating on the presentation of research pertaining to right cylindrical specimens with height:diameter ratios of 2:1. Additionally, new data has been presented considering high strength (70 MPa) cement mortar specimens of various diameters ranging from 63 to 300 mm which were tested to failure. Currently, several models exist in the published literature that seek to predict the strength–size relationship in rock or cementitious materials. Modelling the reviewed datasets, statistical analysis was used to help establish which of these models best represents the empirical evidence. The findings presented here suggest that over the range of specimen sizes explored, the MFSL (Carpinteri et al. in Mater Struct 28:311–317, 1995) model most closely predicts the strength–size relationship in rock and cementitious materials, and that a majority of the empirical evidence supports an asymptotic value in strength at large specimen diameters. Furthermore, the MFSL relationship is not only able to model monotonically decreasing strength–size relationships but is also equally applicable to monotonically increasing relationships, which although shown to be rare do for example exist in rocks with fractal distributions of hard particles.     

Numerical Simulation of Crack Evolution Mechanism and Subsidence Characteristics Effected by Rock Mass Structure in Block Caving Mining

Geotechnical and Geological Engineering - In the block caving mining, the significant rock mass deformation and surface subsidence will be formed with the continuous extraction of ore. However, the...     

Numerical Simulation Study on Crack Evolution Characteristics of Coal Specimen Subjected to Conventional Compression Loading

Geotechnical and Geological Engineering - The paper represents a simulation investigation about the crack evolution and acoustic emission characteristics of coal specimen subjected to conventional...     

不同围压下岩石抗压强度与变形参数尺寸效应的数值模拟

岩石抗压强度和变形参数是岩石工程设计的重要指标。由于岩石是典型的非均质材料,其强度和变形特性随样品尺 寸的变化而不同。本文采用PFC2D程序模拟了不同围压下不同尺寸岩样的压缩试验。结果表明（1） 岩样具有明显的尺寸效 应。同一围压下,尺寸越大,岩石强度、峰值应变和压缩模量越小,尺寸的变化对岩样的破坏模式影响较小;（2） 岩样具 有明显的围压效应。同一尺寸的岩样,随着围压的增大,岩石强度、峰值应变和压缩模量均增加,其中强度和峰值应变随 围压的增加呈线性增加。同时,随着围压的增大,岩石破裂模式由轴向劈裂破坏向剪切破坏变化;（3） 围压的存在会影响 岩样的尺寸效应。不同尺寸岩样的强度和峰值应变在相同围压区间内的增量基本相同,同时随着围压的增大,其强度和峰 值应变增加,进而使岩石强度和峰值应变的尺寸效应弱化;而不同尺寸岩样的压缩模量在相同围压区间内的增长率大致相 同,因而造成围压对压缩模量尺寸效应的影响较小     

岩溶水数值模拟研究进展

本文从岩溶水赋存介质及特性出发,介绍了岩溶地下水数值模拟模型研究的国内外研究发展状况,几种常用软件特点及其应用情况,提出了岩溶水模拟研究存在的不足,并就开展进一步研究提出了相应的建议。     

Numerical Simulation of Explosion in Twin Tunnel System

Rapid growth of urban population in Indian cities have led traffic congestion leading to demand for scientific utilization of underground space. Immediate underground level and deep level underground below the major arterial roads are the sustainable spaces available for meeting the demand of the future traffic/transport. Due to recent increased transit activities it has become one of the soft targets by terrorists or prone to catastrophic accidents in recent years which have increased the importance of rock structures study under explosive loading. In this paper, the response of a underground metro tunnel subjected dynamic loads have been investigated including explosive capacity (30 kg TNT), ground characteristics, liner thickness and blast pressure characteristics. Blast pressure representing CONWEP air blast loading model with positive over pressure phase was applied to lining of tunnel. A three dimensional explicit finite element method was used to analyze dynamic response and damage in twin tunnels of underground metro. It is found that liner of thickness 28 cm will start deforming at the explosive loading of more than 65 kg TNT.