Application of Cracked Triangular Specimen Subjected to Three-Point Bending for Investigating Fracture Behavior of Rock Materials

Numerical and experimental studies were performed on a new fracture test configuration called the edge cracked triangular (ECT) specimen. Using several finite-element analyses, the fracture parameters (i.e., K _I, K _II, and T-stress) were obtained for different combinations of modes I and II. The finite-element results show that the ECT specimen is able to provide pure mode I, pure mode II, and any mixed-mode loading conditions in between. Also, a series of mixed-mode fracture experiments were conducted on Neiriz marble rock using the proposed specimen. Furthermore, the generalized maximum tangential stress (GMTS) criterion was used to predict the experimental results. The GMTS criterion makes use of a three-parameter model (based on K _I, K _II, and T) for describing the crack tip stresses. Due to the significant positive T-stresses that exist in the ECT specimen, typical minimum fracture toughness values were expected to be obtained when the ECT specimen is used. The direction of fracture initiation and the path of fracture growth were also obtained theoretically using the GMTS criterion, and good agreement was observed between the experimental fracture path and theoretical simulations. The fracture study of this specimen reveals that the ECT specimen can be also used in mixed-mode fracture studies of rock materials in addition to the conventional circular or rectangular beam test samples.     

Rock interface strength influences fluid-filled fracture propagation pathways in the crust

Rock interface strengths have often been assumed to be zero in numerical and analogue models of fracture propagation and magma intrusion in the crust. Rock strength tests were performed to explore the role that rock interfaces have on the geometry and propagation dynamics of fluid-filled fractures in the crust. We used a 1 kN test machine to study 5 mm thick cuboidal specimens cut from a sandstone-siltstone rock core, where the strata were known to host magma intrusions and the rock interface between the units was intact. By measuring the load required to grow a crack running along the lithological contact between the layers we calculate its fracture toughness K_c. The siltstone had an average K_c of 0.56 ± 0.03 MPa m^1/2 compared to the sandstone at 0.42 ± 0.02 MPa m^1/2. The rock interface had intermediate average fracture toughness to the parent units at 0.45 ± 0.03 MPa m^1/2. These results have important implications on fracture propagation pathways through rocks, as well as for the geometry and propagation dynamics of magma intrusions in the crust.     

Typical Upper Bound–Lower Bound Mixed Mode Fracture Resistance Envelopes for Rock Material

Mixed mode fracture experiments were conducted on Harsin marble using two disc-shape samples namely the Brazilian disc (BD) and the semi-circular bend (SCB) specimens. For each specimen, a complete fracture toughness envelope ranging from pure mode I to pure mode II was obtained. The experimental results indicate that the mixed mode fracture toughness depends on the geometry and loading conditions such that for any similar mode mixture, the BD test data were significantly greater than the SCB fracture toughness results. Therefore, the conventional fracture criteria which present a unique mixed mode fracture curve, fail to predict the test results. It is shown that a generalized criterion, which takes into account the effects of geometry and loading conditions, is able to provide individual fracture curves for theses specimens with very good estimates for the test results obtained from both BD and SCB specimens. The BD and SCB specimens can be suggested as appropriate specimens for obtaining typical upper bound and lower bound envelopes for mixed mode fracture toughness of rocks.     

Fracture toughness analysis on cracked ring disks of anisotropic rock

Summary  This paper presents a combination of the Boundary Element Method (BEM) and the cracked ring test to determine the mixed-mode (I–II) fracture toughness of anisotropic rocks. The proposed BEM is used to accurately calculate the Stress Intensity Factors (SIFs) of a cracked anisotropic plate. An anisotropic Hualien marble of Taiwan with a distinct foliation was selected to conduct the cracked ring tests. Based on the measurement of the failure load during the test, the mixed-mode (I–II) fracture toughness can be determined. Experimental results show that the radius ratio, inclination and crack angle significantly affect the fracture toughness. The mode-I fracture toughness (K _IC ) is shown to decrease with the increase in hole diameter, whereas the mode-II fracture toughness (K _IIC ) increases with the increase in hole diameter when the crack angle β is equal to 0°. The experimental methods proposed have the advantage that the material is easily prepared, the test procedure is simple, and the cost is low. Correspondence: Chia-Hau Chen, Chao-Shi Chen, Department of Resources Engineering, National Cheng Kung University, 701 Tainan, Taiwan     

Determination of Fracture Toughness of Anisotropic Rocks by Boundary Element Method

Summary  This paper presents a systematic procedure for determining fracture toughness of an anisotropic marble using the diametral compression test (Brazilian test) with a central crack on the discs. Additionally, a novel formulation to increase the accuracy in Stress Intensity Factor (SIF) calculations using Boundary Element Method (BEM) is applied to determine the stress intensity factors and the fracture toughness of anisotropic rocks under mixed-mode loading. The numerical results show that the SIFs for both isotropic and anisotropic problems are in good agreement with those reported by previous authors. The marble with clear white-black foliation from Hualien (in eastern Taiwan), was selected for the Brazilian tests. Diametral loading was conducted on the Cracked Straight Through Brazilian Disc (CSTBD) specimens to evaluate their fracture toughness. In addition, a new fracture criterion was developed to predict pure mode I, pure mode II or mixed mode (I–II) fracture toughness of the anisotropic marble. The new fracture criterion is based on the examination of mode I, mode II and mixed mode (I–II) fracture toughness for different crack angles and anisotropic orientation. Authors’ address: Associate Professor Chao-Shi Chen, Department of Resources Engineering, National Cheng Kung University, No. 1 Dasyue Rd., East District, Tainan 701, Taiwan     

Comparing Reservoir and Outcrop Specimens for Mixed Mode I–II Fracture Toughness of a Limestone Rock Formation at Various Conditions

Summary A fracture toughness study was conducted on a limestone rock formation from a petroleum reservoir in Saudi Arabia, and results were compared with those for outcrop specimens from the same geological formation. The objective was to investigate the possibility of using outcrop specimens to estimate the fracture toughness behavior of reservoir rock at in-situ conditions of temperature and confining pressure. The study was made on reservoir specimens from a depth of about 3.5 km, at both ambient and reservoir conditions. Mixed mode I–II fracture toughness at reservoir conditions of high temperature and confining pressure was studied using straight notched Brazilian disk (SNBD) specimens under diametrical compression. Tests were conducted at ambient conditions, at an effective confining pressure (σ₃) of 28 MPa (4000 psi), and at a temperature of 116^°C. The results showed a substantial increase in fracture toughness under confining pressure. Under σ₃=28 MPa, the pure mode-I fracture toughness (K _IC), increased by a factor of about 3.2, and the pure mode-II fracture toughness (K _IIC) increased by a factor of 4.4, compared to those under ambient conditions. On the other hand, K _IC at 116^°C was only 25% more than that at ambient conditions. These results were compared with recent results for outcrop specimens from the same geological formation. The results reveal that outcrop specimens can be successfully used to predict the fracture behavior of reservoir specimens at in-situ conditions, in spite of some differences at ambient conditions. Additionally, fracture toughness envelopes were obtained for reservoir specimens at ambient and high pressure conditions, in both positive and negative regions. Received September 14, 2000; accepted February 22, 2002 Published online September 2, 2002     

Effect of Specimen Geometry and Testing Method on Mixed Mode I–II Fracture Toughness of a Limestone Rock from Saudi Arabia

Summary The effect of testing method and specimen geometry such as diameter, thickness, and crack length and type on measured fracture toughness was investigated using specimens collected from a limestone rock formation outcropping in the Central Province of Saudi Arabia. Straight Edge Cracked Round Bar Bend (SECRBB), semicircular disk specimens under three point bending, and Brazilian disk specimens under diametrical compression were used in this investigation. SECRBB specimens were used for the Mode-I study, and notched Brazilian disk and semicircular specimens were used for the mixed Mode I–II study. The results show that specimen diameter and crack type have a substantial influence on the measured fracture toughness; however, loading rate, crack size, and specimen thickness seem to have a negligible effect on the fracture toughness. Mode-I fracture toughness is significantly influenced by specimen diameter and crack type, while their effects on Mode-II fracture toughness are generally negligible. The different specimens (SECRBB, Brazilian disk, and semicircular) can give comparable results only when the proper span to diameter ratio is used. The Brazilian disk with a straight notch was found to be the most convenient geometry to use for fracture toughness determination. A simple method of making a precise notch inside the disk is presented, using the combination of a drilling machine and a wire saw.     

ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular Bend Specimen

The International Society for Rock Mechanics has so far developed two standard methods for the determination of static fracture toughness of rock. They used three different core-based specimens and tests were to be performed on a typical laboratory compression or tension load frame. Another method to determine the mode I fracture toughness of rock using semi-circular bend specimen is herein presented. The specimen is semi-circular in shape and made from typical cores taken from the rock with any relative material directions noted. The specimens are tested in three-point bending using a laboratory compression test instrument. The failure load along with its dimensions is used to determine the fracture toughness. Most sedimentary rocks which are layered in structure may exhibit fracture properties that depend on the orientation and therefore measurements in more than one material direction may be necessary. The fracture toughness measurements are expected to yield a size-independent material property if certain minimum specimen size requirements are satisfied.     

Fracture toughness of geomaterials

An understanding of the fracture mechanics of geomaterials is important for the solution of many problems in geomechanics. One of the most important material properties involved in fracture mechanics is the fracture toughness, K_Ic. The short-rod test configuration proposed by Barker¹ has significant potential for becoming a standard test for fracture toughness determination in geomechanics. The purpose of this brief is to examine the application potential of the short-rod test for geomechanics problems.     

Tensile Fracture Strength of Brisbane Tuff by Static and Cyclic Loading Tests

This research presents the results of laboratory experiments during the investigation of tensile strength–strain characteristics of Brisbane tuff disc specimens under static and diametral cyclic loading. Three different cyclic loading methods were used; namely, sinusoidal cyclic loading, type I and II increasing cyclic loading with various amplitude values. The first method applied the stress amplitude?cycle number (s–n) curve approach to the measurement of the indirect tensile strength (ITS) and fracture toughness (K _IC) values of rocks for the first time in the literature. The type I and II methods investigated the effect of increasing cyclic loading on the ITS and K _IC of rocks. For Brisbane tuff, the reduction in ITS was found to be 30 % under sinusoidal loading, whereas type I and II increasing cyclic loading caused a maximum reduction in ITS of 36 %. The maximum reduction of the static K _IC of 46 % was obtained for the highest amplitude type I cyclic loading tested. For sinusoidal cyclic loading, a maximum reduction of the static K _IC of 30 % was obtained. A continuous irreversible accumulation of damage was observed in dynamic cyclic tests conducted at different amplitudes and mean stress levels. Scanning electron microscope images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both inter-granular fracturing and trans-granular fracturing. The main characteristic was grain breakage under cyclic loading, which probably starts at points of contact between grains and is accompanied by the production of very small fragments, probably due to frictional sliding within the weak matrix.     

岩石非理想裂纹圆盘试件动态断裂韧性测试的有限元分析及试验研究

采用中心裂纹圆盘-霍普金森压杆(CCCD-SHPB)试验系统对大理岩中心裂纹圆盘试件进行不同加载速率下的纯Ⅰ型加载试验,研究岩石材料动态断裂韧性的加载速率相关性。考虑到试验中所使用的圆盘试件是带有中心切口的非理想裂纹,结合试件的实际加工情况,提出采用切口尖端形状为小圆弧形的预制裂纹,介绍了试件的制作方法,并利用有限元计算论证了采用这种形状非理想裂纹试件的试验可行性。结果表明,采用圆弧形裂尖、裂纹宽度为1 mm的中心切口非理想裂纹圆盘试件来代替理想裂纹圆盘试件是可行的,误差不超过2.13%。分析试验数据得出：非理想裂纹圆盘试件在纯Ⅰ型加载条件下,其断裂韧度表现出明显的速率相关性,且随着加载速率的增大而增大。     

复合型加载条件下锈岩断裂韧度试验研究

岩石断裂韧度表征其抵抗裂纹起裂和扩展的能力,作为其力学性能的一个重要指标,在岩石力学理论研究与岩体工程应用中有着不可替代的作用。由于岩石结构的复杂性,其破坏形式大多呈现为复合型断裂破坏,研究复合型加载条件下岩石断裂韧度具有重要的意义。为了研究锈岩的断裂力学性能,以便其在建筑工业中得到更为广泛的应用,通过18个中心裂纹圆盘（CSTBD）试件径向受压试验,进行了复合型加载条件下锈岩断裂韧度的试验研究。测得了锈岩在纯I型,纯II型以及复合型加载时的断裂韧度,并将试验结果与基于广义最大周向应力（GMTS）准则的理论值进行了对比分析,结果表明：锈岩的纯I型断裂韧度为1.01 MPa?m0.5,而纯II型断裂韧度为1.51 MPa?m0.5,是纯I型断裂韧度的1.49倍,这与基于GMTS准则的理论值1.34非常接近,而比基于最大周向应力（MTS）准则的理论值0.87大很多。裂纹尖端附近的T应力及断裂过程区裂纹尖端的临界距离rc对岩石类材料的开裂路径以及复合型断裂韧度都有较大的影响。考虑了T应力的广义最大周向应力（GMTS）准则能很好的预测试验结果。     

Physicomechanical properties of cryptocrystalline fluorite from the Suran deposit, southern Urals

Microhardness (H) and fracture toughness (K _1C) have been studied for the main varieties of shock-resistant cryptocrystalline fluorite, a natural ceramic widespread at the Suran deposit. Suran cryptocrystalline fluorite (SCF) is characterized by high fracture toughness (K _1C), which is 2–5 times higher than K _1C of common fluorite monocrystals. The relationship between K _1C and microhardness H is complex and nonlinear. The SCF varieties from the sellaite-fluorite orebody are distinguished by the highest K _1C = 1.9–2.3 MPa m^1/2, which exceeds K _1C = 0.84 MPa m^1/2 of porcelain-like fluorite from the main fluorite orebody. Qualitative and quantitative variations of structural point defects in the studied samples exert a much stronger effect on microhardness than on fracture toughness, which mainly depends on the size of crystallites, their mutual crystallographic orientation, and the structure of intergranular boundaries, i.e., on the parameters seemingly related to recrystallization and/or twinning of fluorite. In general, the nature of the Suran deposit of fluorite ceramic with unusual physicomechanical properties remains a geological puzzle in many respects.     

Experimental Calibration of ISRM Suggested Fracture Toughness Measurement Techniques in Selected Brittle Rocks

Summary A wide variety of specimen types and methods are employed in fracture toughness measurement of rocks, which result in scattered values for the same rock type. In order to provide some consistency to the values, the International Society for Rock Mechanics (ISRM) recommended three suggested methods using core based specimens, the Chevron Bend (CB) test, the Short Rod (SR) test and the Cracked Chevron Notch Brazilian Disc (CCNBD) test. This standardization helped obtain more consistent values but still a variation of 20–30% was observed in the values of fracture toughness obtained with the CB and SR methods. The values obtained with the CCNBD method were found to be consistently lower (30–50%) than those of the other two methods (CB and SR). Many reasons have been offered to explain this deviation. These include size of the specimen, anisotropy of rock, a dimensionless parameter in the fracture toughness calculation equation for the CCNBD test, etc. A comprehensive test program was initiated to identify the cause of these discrepancies between the CB and CCNBD methods. Three brittle rock types were selected for the study and more than 200 tests were conducted to measure the values of fracture toughness. A rigorous statistical analysis was carried out to determine the confidence level and find the significance of the test results. It was found that the CB and CCNBD methods were very comparable provided the correct equation for fracture toughness calculation was used for the CCNBD method and the size of the specimens was selected carefully. The error in the ISRM 1995 formula of fracture toughness for the CCNBD method could be the major factor responsible for the consistently lower values obtained with the method.     

基于数字图像相关法的两类岩石断裂特征研究

岩石破坏时的临界断裂特征,如过程区长度,裂缝口张开位移是运用断裂力学解决岩石断裂问题的关键所在。传统测量方法,如应变片、直线位移传感器无法获得岩石破坏时的全场变形,因此,也无法准确地获得上述断裂特征。数字图像相关法是一种光学的变形测量方法,其通过试样表面的数字图像采集及相关计算,能够获得岩石破裂过程各个阶段的高精度全场变形特征。利用该试验手段,对两类岩石,即相对较硬的大理岩和相对较软的黄砂岩开展了一系列半圆盘三点弯曲断裂试验并获得了岩石断裂时的临界变形场,对变形场进行分析,从而确定了两类岩石破坏时临界特征、过程区长度及裂缝口张开位移。结果表明,大理岩的断裂过程区长度明显小于黄砂岩的断裂过程区长度,峰值时黄砂岩COD的值均大于相同裂纹长度的大理岩,而较软岩的力学行为更容易受边界效应的影响。上述研究有助于进一步了解不同类型岩石的断裂发展过程并采用相应的方法来解决岩石破裂问题。     

Fracture Toughness and Fracture Roughness in Anisotropic Granitic Rocks

In this paper we present an experimental approach aimed at assessing the correlation between fracture toughness (K _IC) and fracture roughness of two granitic rocks (Barre and Stanstead granites) exhibiting significant fracture toughness anisotropy. Roughness values have been estimated for fractured surfaces obtained from Chevron Cracked Notch Brazilian Disc samples failed under mode I along three orthogonal planes with respect to their microstructural fabrics. There exists a clear correlation between roughness and toughness within each rock examined along the three planes. Specific orientation of micro-crack alignment could result in preferred out-of-plane propagation of the test-crack irrespective of grain-size distribution. These experimental observations reinforce the hypothesis of the existence of a link among pre-existing petrofabric anisotropy, fracture toughness, fracture roughness, and the evolution and extent of the associated induced fractures within the process zone of granitic rocks along specific directions. This study also highlights the need for employment of pre-failure and advanced post-failure diagnostic techniques in quantifying these inter-relationships.     

An Experimental Study of the Fracture Coalescence Behaviour of Brittle Sandstone Specimens Containing Three Fissures

To analyse the fracture coalescence behaviour of rock, rectangular prismatic sandstone specimens (80?×?160?×?30?mm in size) containing three fissures were tested under uniaxial compression. The strength and deformation behaviours of the specimens are first analysed by investigating the effects of the ligament angle β₂ on the peak strength, peak strain and crack initiation stress of the specimens. To confirm the sequence of crack coalescence, a photographic monitoring technique is used throughout the entire period of deformation. Based on the results, the relationship between the real-time crack coalescence process and the axial stress–strain curve of brittle sandstone specimens is also developed, and this relationship can be used to evaluate the macroscopic deformation characteristics of pre-cracked rock. The equivalent strain evolution fields of the specimen, with α?=?β₁?=?45° and β₂?=?90°, are obtained using the digital image correlation technique and show good agreement with the experimental results of pre-cracked brittle sandstone. These experimental results are expected to improve the understanding of fracture mechanisms and be used in rock engineering with intermittent structures, such as deep underground excavated tunnels.     

Microcracking in calcite and dolomite marble: microstructural influences and effects on properties

Microstructure‐based finite-element analysis with a microcracking algorithm was used to simulate an actual degradation phenomenon of marble structures, i.e., microcracking. Both microcrack initiation and crack propagation were characterized, as were their dependence on lattice preferred orientation (LPO), grain shape preferred orientation (SPO), grain size, marble composition (calcite and dolomite) and grain‐boundary fracture toughness. Two LPOs were analyzed: a random orientation distribution function and an orientation distribution function with strong directional crystalline texture generated from a March–Dollase distribution. Three SPOs were considered: equiaxed grains; elongated grains and a mixture of equiaxed and elongated grains. Three different grain sizes were considered: fine grains of order 200 μm (only calcitic marble); medium size grains of order 1 mm (calcitic and dolomitic marbles); and large grains of order 2 mm (only dolomitic marble). The fracture surface energy for the grain boundaries, γ_ig, was chosen to be 20 and 40 % of the fracture surface energy of a grain, γ_xtal, so that both intergranular and transgranular fracture were possible. Studies were performed on these idealized marble microstructures to elucidate the range of microcracking responses. Simulations were performed for both heating and cooling by 50 °C in steps of 1 °C. Microcracking results were correlated with the thermoelastic responses, which are indicators related to degradation. The results indicate that certain combinations of LPO, SPO, grain size, grain‐boundary fracture toughness and marble composition have a significant influence on the thermal-elastic response of marble. Microstructure with the smallest grain size and the highest degree of SPO and LPO had less of a tendency to microcrack. Additionally, with increasing SPO and LPO microcracking becomes more spatially anisotropic. A significant observation for all microstructures was an asymmetry in microcracking upon heating and cooling: more microcracking was observed upon cooling than upon heating. Given an identical microstructure and crystallographic texture, calcite showed larger thermal stresses than dolomite, had an earlier onset of microcracking upon heating and cooling, and a greater microcracked area at a given temperature differential. Thermal expansion coefficients with and without microcracking were also determined.     

A comparison of seismic and structural measurements of scaling exponents during tensile subcritical crack growth

The observed fractal nature of both fault length distributions and earthquake magnitude-frequency distributions suggests that there may be a relationship between the structure of active fault systems and the resulting seismicity. In previous theoretical work, a positive correlation between the exponent D from the fracture length distribution, and the seismic or acoustic emission (AE) b-value has been inferred from a simple dislocation model of the seismic source. Here, we present the first experimental evidence for a correlation between D and b from a series of tensile fracture mechanics tests on crystalline rock, carried out in different environmental conditions, both air-dry and water-saturated, and at ambient temperature and pressure. The microseismic acoustic emissions were monitored during subcritical crack growth under controlled conditions of constant stress intensity, K_I, and quantitative analyses of the resulting fracture patterns were carried out on the same specimens. It is found that AE b-values, ranging from 1.0 to 2.3, correlate negatively with the normalized stress intensity K_I/KIC, where K_IC is the fracture toughness of the specimen. The microcrack length distribution exponent D, ranges from 1.0 to 1.7. Fluid presence has a first-order influence on both the AE and structure produced in these experiments. For experiments at low stress intensity or high fluid content, the activation of the stress corrosion mechanism for K_I < K_IC leads to a greater relative proportion both of small cracks and of low amplitude acoustic emissions, reflected in higher values of D and b. The exponent D is found to correlate positively with the AE b-value.     

A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily over-consolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as half of the critical distance. This fracture criterion is known as the point method, and is part of the theory of critical distances, which is utilised in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, σ ₀, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, σ _c and σ _t. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (σ _c/σ _t = 3–50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low-confining stresses.