Experimental and theoretical study of static-dynamic mixed mode brittle fracture of rock

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Effect of specimen thickness on Mode II fracture toughness of rock

Anti-symmetric four-point bending specimens with different thickness, without and with guiding grooves, were used to conduct Mode II fracture test and study the effect of specimen thickness on Mode II fracture toughness of rock. Numerical calculations show that the occurrence of Mode II fracture in the specimens without guiding grooves (when the inner and outer loading points are moved close to the notch plane) and with guiding grooves is attributed to a favorable stress condition created for Mode II fracture, i.e. tensile stress at the notch tip is depressed to be lower than the tensile strength or to be compressive stress, and the ratio of shear stress to tensile stress at notch tip is very high. The measured value of Mode II fracture toughness K _{II C} decreases with the increase of the specimen thickness or the net thickness of specimen. This is because a thick specimen promotes a plane strain state and thus results in a relatively small fracture toughness. Foundation item: The National Natural Science Foundation of China (No: 49672164) Biography of the first author: RAO Qiu-hua, doctor of engineering, born in 1965, majoring in rock fracture mechanics.     

Analysis of fracture process zone in brittle rock subjected to shear-compressive loading

1　INTRODUCTIONFracture process zone (FPZ) is very importantto study some physical phenomena, such as nonlin ear behavior of brittle rock and initial angle ofcrack extension which has to be taken into accountin order to predict the initial angle of crack exten sion and the fracture locus. Besides, the structureand size of FPZ ahead of crack tip are crucial forthe application of conventional fracture criteria,since the stress or energy in these criteria shouldbe ca…     

Mode II fracture analysis of double edge cracked circular disk subjected to different diametral compression

A detailed analysis of modeⅡstress intensity factors(SIFs) for the double edge cracked Brazilian disk subjected to different diametral compression is presented using a weight function method. The mode Ⅱ SIFs at crack tips can be obtained by simply calculating an integral of the product of mode Ⅱ weight function and the shear stress on the prospective crack faces of uncracked disk loaded by a diametral compression. A semi-analytical formula for the calculation of normalized mode Ⅱ SIF, fⅡ , is derived for different crack lengths (from 0.1 to 0.7) and inclination angles (from 10^。 to 75^。) with respect to loading direction. Comparison between the obtained results and finite element method solutions shows that the weight function method is of high precision. Combined with the authors‘ previous work on modeⅠfracture analysis, the new specimen geometry can be used to study fracture through any combination of mode Ⅰ and mode Ⅱ loading by a simple alignment of the crack relative to the diameter of compression loading, and to obtain pure mode Ⅱ crack extension. Another advantage of this specimen geometry is that it is available directly from rock core and is also easy to fabricate.     

Effect of loading rate on fracture characteristics of rock

The three-point bending experiments were applied to investigating effects of loading rates on fracture toughness of Huanglong limestone. The fracture toughness of Huanglong limestone was measured over a wide range of loading rates from 9×10⁻⁴ to 1.537 MPa·m^1/2/s. According to the approximate relationship between static and dynamic fracture toughness of Huanglong limestone, relationship between the growth velocity of crack and dynamic fracture toughness was obtained. The main conclusions are summarized as follows. (1) When the loading rate is higher than 0.027 MPa·m^1/2/s, the fracture toughness of Huanglong limestone increases markedly with increasing loading rate. However, when loading rate is lower than 0.027 MPa·m^1/2/s, fracture toughness slightly increases with an increase in loading rate. (2) It is found from experimental results that fracture toughness is linearly proportional to the logarithmic expression of loading rate. (3) For Huanglong limestone, when the growth velocity of crack is lower than 100 m/s, the energy release rate slightly decreases with increasing the growth velocity of crack. However, when the growth velocity of crack is higher than 1 000 m/s, the energy release rate dramatically decreases with an increase in the crack growth velocity.     

Rock fracture under anti-plane shear (Mode III) loading

Anti-plane punch-through shear test and anti-plane four-point bending test are used to study the crack initiation and propagation under anti-plane shear (Mode III) loading. The tensile and shear stresses at the crack tip are calcualted by finite element method. The results show that under Mode III loading the maximum principal stress σ₁ at crack tip is smaller or a little larger than the maximum shear stress τ_max. Since the tensile strength of brittle rock is much lower than its shear strength, σ₁ is easy to reach its critical value before τ_max reaches its critical value and thus results in Mode I fracture. The fracture trajectory is helicoid and the normal direction of tangential plane with the fractured helicoid is along the predicted direction of the maximum principal stress at the notch tip. It is further proved that Mode I instead of Mode III fracture occurs in brittle rock under Mode III loading. The fracture mode depending on the fracture mechanism must be distinguished from the loading form. Foundation item: Project (50374073) supported by the National Natural Science Foundation of China; project (2002032256) supported by the Postdoctor Science Foundation of China     

岩石裂隙的法向蠕变及渗流的影响

法向蠕变是岩石裂隙的重要力学性质之一．通过分析岩石裂隙法向蠕变机理、进行干燥及渗流情况下岩石裂隙法向蠕变试验,探讨了岩石裂隙的法向蠕变及渗流的影响．研究表明,对于粗糙岩石裂隙来说,瞬时有效应力总等于裂隙凸起的压缩强度,因而初始法向蠕变明显,而后随接触面增加,蠕变速率逐渐降低;渗流过程中,岩石裂隙法向蠕变更加明显,且初次加栽应力水平下岩石裂隙法向蠕变远大于后续加载应力水平;岩石裂隙法向蠕变不能决定岩石裂隙渗流能力的降低,水力冲蚀作用明显时,可能产生裂隙渗流能力随裂隙法向压缩而增大的情况;岩石裂隙的蠕变闭合与岩石裂隙面粗糙度有关,粗糙度越大,岩石裂隙蠕变闭合量越大．研究结果对岩石裂隙法向蠕变的数值模拟及工程实践有一定参考价值．     

Particle simulation of the failure process of brittle rock under triaxial compression

In order to investigate the failure process of brittle rock under triaxial compression through both experimental and numerical approaches, the particle simulation method was used in numerical simulations and the simulated results were compared with those of the experiment. The numerical simulation results, such as fracture propagation, microcrack distribution, stress-strain response, and damage patterns, were discussed in detail. The simulated results under various confining pressures (0-60 MPa) are in good...     

A composite material model for investigation of micro-fracture mechanism of brittle rock subjected to uniaxial compression

Ｓｔｕｄｙｏｎｔｈｅｒｏｃｋｆａｉｌｕｒｅｐｒｏｃｅｓｓｆｒｏｍｃｒａｃｋｉｎｉｔｉａｔｉｏｎ ,ｐｒｏｐａｇａｔｉｏｎｔｏｃｏａｌｅｓｃｅｎｃｅｉｓｖｅｒｙｉｍ ｐｏｒｔａｎｔｔｏｕｎｄｅｒｓｔａｎｄｔｈｅｆｒａｃｔｕｒｅｍｅｃｈａｎｉｓｍｏｆｂｒｉｔｔｌｅｒｏｃｋｕｎｄｅｒｕｎｉａｘｉａｌｃｏｍｐｒｅｓｓｉｏｎ .Ｍａｎｙｒｅ ｓｅａｒｃｈｅｒｓｔａｃｋｌｅｄｔｈｉｓｐｒｏｂｌｅｍａｔｔｈｅｍａｃｒｏｓｔｒｕ ｃｔｕｒｅｌｅｖｅｌ.ＨｏｒｉｉａｎｄＮｅｍａｔ Ｎａｓｓｅｒ[1,2 ] ｉｎｖｅｓｔｉｇａ ｔ…     

Rheological characteristics of soft rock structural surface

There are two mechanisms of the coarse surface asperity resistance effect and rubbing resistance effect in the course of the soft rock structural surface creep,of which the former plays a dominant role in hindering the deformation in the starting creep phase,so that the structural surface creep usually displays the strong surface roughness effect,and so does the latter when the asperities in the coarse surface were fractured by shearing.Under the low stress condition,there are only two phases of the decelerating creep and the constant creep for the soft rock structural surface,and as the stress increases and overcomes the rubbing resistance,the accelerating creep failure of the structural surface will happen suddenly.Therefore,a multiple rheological model,which combines the nonlinear NEWTON body(NN) of a certain mass and the empirical plastic body(EM) with the classical SAINT VENANT body,NEWTON body,KELVIN body and HOOKE body,could be used to comprehensively describe the creep characteristics of the soft rock structural surface.Its mechanical parameter values will vary owing to the different surface roughness of the structural surface.The parameters of GH,GK and ηL are positively linearly correlative to the surface roughness.The surface roughness and m are negative exponential function correlation.The long-term strength τS is positively correlative to the surface roughness.     

基于三维裂隙网络的岩体剪切特性尺寸效应分析

为研究复杂裂隙岩体剪切特性的尺寸效应,以西藏怒江松塔水电站PDC3平硐为例,在现场采集裂隙信息的基础上,基于颗粒流PFC^3D软件通过统计学方法及蒙特卡洛原理生成三维裂隙网络,构建等效岩体,进行大尺度直剪模拟试验得到裂隙岩体的抗剪强度、内摩擦系数及内聚力,分别研究其尺寸效应并确定不同参数下的REV尺寸,继而对相关参数和试样尺寸分别进行非线性回归拟合,探究其函数关系。结果表明：抗剪强度、内聚力及内摩擦系数随着试样尺寸的变化而趋于稳定,且不同参数得到的REV大小不同;综合分析不同参数的REV尺寸,得出研究区裂隙岩体的剪切特性REV尺寸为11 m×11 m×11 m;通过函数关系拟合,抗剪强度、内聚力和内摩擦系数与试样尺寸之间均存在指数函数关系。该成果为研究复杂裂隙岩体的力学REV以及合理确定力学参数提供了依据。     

A model to determine hole spacing in the rock fracture process by non-explosive expansion material

The application of the non-explosive expansion material(NEEM)is widely used as the controlled fiactrre method in quarry mining,especially in hard rocks.The pressure of NEEM is an important parameter in causing rock fracture.An empirical model based on hole spacing was developed to determine the pressure of NEEM in the rock fracture process.Primarily,the empirical model was developed by the mathematical method,utilizing dimensional analysis.Then,the Phase2 code,which is based on the finite element method,was utilized to predict crack growth in rocks.The results of numerical analysis show slight deviations fiom the empirical model.Hence,the polynomial regression analysis was used to modify the model.Finally,the modified model shows a good agreement with the results gained from numerical modeling.     

Failure mode and strength anisotropic characteristic of stratified rock mass under uniaxial compressive situation

A stratified rock mass model was founded by FLAC^3D. The failure mode and anisotropic characteristic of strength for stratified rock mass were analyzed. The analysis results show that the numerical simulation can visually reflect the failure modes of rock samples under different inclination angles β of structural plane. The stiffness of rock sample before peak strength changes in the compressive procedure. With the increase of β, the compressive strength σ _c of rock sample decreases firstly and then increases; when β is in the range of 20°–30° and 80°–90°, σ _c has the largest sensitivity to β; while β falls in the range of 30°–70°, σ _c varies little. When ϕ _j <β<90° (β _j is friction angle of structure plane), the results obtained from numerical simulation and theoretical analysis are in almost the same values; while β⩽ ϕ _j or β=90°, they are in great different values. The results obtained from theoretical analysis are obvious larger than those from numerical simulation; and the results from numerical simulation can reflect the difference of compressive strength of rock samples for the two situations of β⩾ ϕ _j and β=90°, which is in more accordance with the real situation. Foundation item: Project (50099620) supported by the National Natural Science Foundation of China     

Numerical study on rock fracture and vibration due to blasting

Fracture and ground vibration of rock subjected to different decoupling decked charges are investigated based on the numerical simulation.The dynamic pressure value is studied,which demonstrates that simulation of fracture zone is feasible.Attenuation index of dynamic pressure is 2.06,2.05 and 1.93 for air,water and sand intervals respectively.The small attenuation of sand interval results in the large ground vibration.The predicted vertical vibration waveform and peak particle velocities(PPV) in far-field are in agreement with the monitoring results.The results show that the air and water decked charges can improve the effect of rock fracture in near-field and reduce ground vibration in far-field.     

Measuring dynamic fracture toughness of cement rock using a short rod specimen

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Thermal-hydro-mechanical coupling damage model of brittle rock简

Based on fluid mechanics, thermodynamics and damage mechanics, thermal-hydro-mechanical （THM） coupling damage model of brittle rock is established by analyzing THM coupling mechanism, where THM coupling damage variable DTHM is dominated by TH coupling damage variable DTH, TM coupling damage variable DTM and HM coupling damage variable DHM, and DTH is firstly expressed in term of dimensionless total thermal conductivity of the water Nu. Permeability test, uni-axial compression test and THM coupling test are conducted to measure the permeability, elastic modulus and THM coupling stress-strain curves of brittle rock. The tested values of THM coupling elastic modulus E＇HM are in good agreement with the predicted values of THM coupling elastic modulus ETHM, which can verify the newly established THM coupling damage model.     

Fatigue properties analysis of cracked rock based on fracture evolution process

Fracture evolution process (initiation, propagation and coalescence) of cracked rock was observed and the force- displacement curves of cracked rock were measured under uniaxial cyclic loading. The tested specimens made of sandstone-like modeling material contained three pre-existing intermittent cracks with different geometrical distributions. The experimental results indicate that the fatigue deformation limit corresponding to the maximal cyclic load is equal to that of post-peak locus of static complete force?displacement curve; the fatigue deformation process can be divided into three stages: initial deformation, constant deformation rate and accelerative deformation; the time of fracture initiation, propagation and coalescence corresponds to the change of irreversible deformation.     

大理岩剪切裂隙渗流特性

针对高水头抽水蓄能电站、高坝枢纽工程和深埋隧洞工程的建设和运行中,由于高水压造成的突涌水及岩体失稳问题,以大理岩为例,研究了大理岩剪切裂隙渗流规律.试验结果表明:径向渗流试验中,渗流过程符合达西定律,水头压力与流量呈线性关系;裂隙面中局部张拉破坏的特征对渗流起到了阻碍作用;法向力对裂隙渗流的影响显著,在法向应力从14 MPa升至19 MPa过程中,渗流通道随法向力的增加出现了闭合现象,裂隙中形成了大面积死水区,渗流特性表现出突变.     

Use of double edge-cracked Brazilian disk geometry for compression-shear fracture investigation of rock

A new specimen geometry-the double edge-cracked Brazilian disk and a relevant fracture analysis by weight function method are proposed for the investigation of rock fracture caused by compression-shear loading. Not only can the mixed mode fracture with any ratio of KI /KII be achieved, but also the pure mode n crack extension can be obtained. The combined mode fracture analysis for this geometry shows that diametral compression in the far-field can induce a compression-shear stress state in the singular stress field ahead of crack tips. Experimental investigations conducted on marble specimens show that the pure mode [I crack extension can be obtained when the dimen-sionless crack length a>0. 7 and the inclined crack angle 5°≤ψ≤40°. Normalized mode I and mode II stress intensity factors decrease from -0. 45 and 2. 47 at ψ= 5° to - 1. 65 and 1. 52 at ψ=40°, respectively. The strains at three points of specimen are also measured in order to investigate the influence of stress singularity on initi     

超显微金矿物的电子显微分析

本文应用EPMA、SEM/EDX,TEM/EDX等分析技术对卡林型金矿中超微金的赋存状态进行了研究,并对这些分析技术及其对金矿的测量方法的特点进行了讨论。通过对金赋存状态的电子显微分析,揭示出所谓“不可见金”是由一系列超微金颗粒(大约3mm至几μm)所组成,它们被包裹于黄铁矿、含砷黄铁矿中,并首次观察到3nm的超微金矿物,这为人们正确评价超微金的赋存状态提供了重要依据。