Numerical analysis of the failure process around a circular opening in rock

Damage and fracture propagation around underground excavations are important issues in rock engineering. The analysis of quasi-brittle materials can be performed using constitutive laws based upon damage mechanics. The finite element code RFPA2D (Rock Failure Process Analysis) based on damage mechanics was used to simulate a loading-type failure process around an underground excavation (model tunnel) in brittle rock. One of the features of RFPA2D is the capability of modeling heterogeneous materials. In the current model, the effect of the homogeneous index (m) of rock on the failure modes of a model tunnel in rock was studied. In addition, by recording the number of damaged elements and the associated amount of energy released, RFPA2D is able to simulate acoustic activities around circular openings in rock. The results of a numerical simulation of a model tunnel were in very good agreement with the experimental test using the acoustic emission technique. Finally, the influence of the lateral confining pressure on the failure mechanism of the rock around the model tunnel was also investigated by numerical simulations.     

圆环试样内径对抗拉强度的影响

运用RFPA2D软件对岩石的单轴拉伸强度试验、不同内径的圆环试样的劈裂试验进行了模拟。比较模拟结果 ,重点研究了圆环试样内径对试件抗拉强度的影响 ,确定了最接近单轴拉伸试验结果内径的范围 ,利用回归分析确定了内径与试样抗拉强度之间的关系。     

孔隙压力作用下煤岩破裂及声发射特性的数值模拟

运用嵌入孔隙压力的岩石破裂过程分析RFPA2D系统,对孔隙压力作用下煤岩的变形强度特性进行了数值试验研究。数值试验结果表明,在孔隙压力一定时,随着围压的增加,煤岩的杨氏模量、抗压强度都随之增高;而当围压一定时,随着孔隙压力的增加,煤岩的杨氏模量、抗压强度则稍有降低,而且峰值强度后的应力-应变曲线有呈现脆性的趋势。此外数值模拟还研究了不同围压及孔隙压力作用下煤岩的声发射特性     

巴西劈裂法在层状岩体抗拉强度测试中的分析与讨论

为分析巴西圆盘劈裂法在层状岩体抗拉强度试验中的适用性,在以往层状岩体巴西圆盘劈裂试验成果分析基础上,选取层理砂岩为试验对象,设计并进行了考虑不同层理角度的砂岩巴西圆盘劈裂试验。分析结果表明,（1）层状岩体抗拉强度的各向异性特点非常明显,层理角度对各种层状岩体的劈裂抗拉强度的影响规律是基本类似的,只是影响程度不一样;（2）不同层理角度圆盘试样的破裂面形状差别较大,其破坏模式可以归纳为直线型、折线型和弧形型;（3）当层理角度0°＜β＜90°时,破裂面的发展规律不能严格满足巴西圆盘劈裂试验力学理论模型的假定,采用式（1）计算得到的劈裂抗拉强度只能是一个近似的值;（4）当圆盘试样加载线两侧的岩石材料、层理结构对称分布时,加载时圆盘内的应力分布可以较好地满足其理论计算模型,其试验结果比较准确。研究成果可为层状岩体抗拉强度的准确测定提供较好的参考。     

脆性基多孔材料孔洞的尺寸效应及其破坏模式研究

运用材料真实破坏过程分析系统RFPA2D,对含多孔的脆性材料进行单轴加载情况下的破坏机制以及孔洞的尺寸效应研究。其中的数值模型具有同样的尺寸（高 宽= 65 mm 100 mm）、同样的孔洞分布类型、同样的孔隙率（20 %）、不同的孔洞直径。数值计算的结果显示,各种孔径的模型具有近似的抗压强度,并且可以观察到没有裂纹局部化的拉破坏模式。结果表明,含孔脆性材料的近似脆性行为并没有引起材料的尺寸效应。     

Investigating the Effect of Cyclic Loading on the Indirect Tensile Strength of Rocks

This paper presents the results of laboratory experiments during the investigation of the stress–strain characteristics of Brisbane tuff disc specimens under diametral compressive cyclic loading. Two different cyclic loading methods were used: namely, sinusoidal cyclic loading and cyclic loading with increasing mean level. The first method applied the S–N curve approach to the indirect tensile strength (ITS) of rock specimens for the first time in the literature, and the second method investigated the effect of increasing cyclic loading on the ITS of rock specimens. The ITS of Brisbane tuff disc specimens was measured using the Brazilian tensile strength test. The reduction in ITS was found to be 33% with sinusoidal loading tests, whereas increasing cyclic loading caused a maximum reduction of 37%. It is believed that the fracturing under cyclic loading starts at contact points between strong grains and weak matrices, and that contact points at grain boundaries are the regions of stress concentration (i.e., indenters). Transgranular cracks emanate from these regions and intergranular cracks sometimes pass through the contact points. Once cracking begins, there is a steady progression of damage and a general ‘loosening’ of the rock, which is a precursor to the formation of intergranular cracks.     

Experimental Study on the Validity and Rationality of Four Brazilian Disc Tests

The validity and rationality of the Brazilian disc test have attracted much attention since it was proposed. To verify the validity of four Brazilian disc tests, red sandstone and yellow rust granite were employed. In these experiments, uniaxial tensile tests and four Brazilian disc tests were performed. Meanwhile, the typical location of the Brazilian discs was arranged with gages to detect the crack initiation location. By analyzing the rationality of the four Brazilian disc tests from two aspects, the crack initiation location and the difference between indirect tensile strength and direct tensile strength, it was found that the Brazilian disc tests without cushion and the Brazilian disc tests with two small-diameter steer rods are suitable for determining the indirect tensile strength of rock materials. However, the Brazilian disc tests with arc loading jaws should be carefully adopted to measure the indirect tensile strength due to their overestimation of the indirect tensile strength. Additionally, flattened Brazilian disc tests were found to be not suitable for measuring the indirect tensile strength of rock materials.     

The Brazilian Disc Test for Rock Mechanics Applications: Review and New Insights

The development of the Brazilian disc test for determining indirect tensile strength and its applications in rock mechanics are reviewed herein. Based on the history of research on the Brazilian test by analytical, experimental, and numerical approaches, three research stages can be identified. Most of the early studies focused on the tensile stress distribution in Brazilian disc specimens, while ignoring the tensile strain distribution. The observation of different crack initiation positions in the Brazilian disc has drawn a lot of research interest from the rock mechanics community. A simple extension strain criterion was put forward by Stacey (Int J Rock Mech Min Sci Geomech Abstr 18(6):469–474, 1981) to account for extension crack initiation and propagation in rocks, although this is not widely used. In the present study, a linear elastic numerical model is constructed to study crack initiation in a 50-mm-diameter Brazilian disc using FLAC^3D. The maximum tensile stress and the maximum tensile strain are both found to occur about 5 mm away from the two loading points along the compressed diameter of the disc, instead of at the center of the disc surface. Therefore, the crack initiation point of the Brazilian test for rocks may be located near the loading point when the tensile strain meets the maximum extension strain criterion, but at the surface center when the tensile stress meets the maximum tensile strength criterion.     

Experimental and Numerical Studies on Determination of Indirect Tensile Strength of Rocks

Indirect tension tests using Brisbane tuff Brazilian disc specimens under standard Brazilian jaws and various loading arcs were performed. The standard Brazilian indirect tensile tests caused catastrophic, crushing failure of the disc specimens, rather than the expected tensile splitting failure initiated by a central crack. This led to an investigation of the fracturing of Brazilian disc specimens and the existing indirect tensile Brazilian test using steel loading arcs with different angles. The results showed that the ultimate failure load increased with increasing loading arc angles. With no international standard for determining indirect tensile strength of rocks under diametral load, numerical modelling and analytical solutions were undertaken. Numerical simulations using RFPA^2D software were conducted with a heterogeneous material model. The results predicted tensile stress in the discs and visually reproduced the progressive fracture process. It was concluded that standard Brazilian jaws cause catastrophic, crushing failure of the disc specimens instead of producing a central splitting crack. The experimental and numerical results showed that 20° and 30° loading arcs result in diametral splitting fractures starting at the disc centre. Moreover, intrinsic material properties (e.g. fracture toughness) may be used to propose the best loading configuration to determine the indirect tensile strength of rocks. Here, by using numerical outcomes and empirical relationships between fracture toughness and tensile strength, the best loading geometry to obtain the most accurate indirect tensile strength of rocks was the 2α?=?30° loading arc.     

Anchorage behaviour of reinforced specimens containing a single fissure under uniaxial loading: a particle mechanics approach

Particle flow code (PFC^2D) software was adopted to investigate the anchorage behaviour and the characteristics of crack initiation, propagation and coalescence of reinforced specimens containing a single fissure (RSCSF). The microscopic parameters of the specimens in the numerical simulation were first validated by experimental outcomes of intact specimens, while the microscopic parameters of the rock bolts were validated based on the results of the RSCSF tests. Then, the mechanical parameters as well as the failure modes in the physical experiments were compared with those derived by the numerical simulation; the results showed good agreement between the simulated macroscopic mechanical properties and failure modes and those obtained in the laboratory experiments. The peak strength, number of cracks and the failure mode varied considerably as the anchorage angle α and fissure angle β increased. Three types of stress–strain curves, types I to III, were obtained from the RSCSF. Shear cracks were observed for all three categories of curves, but the tensile cracks were dominant. The number of cracks and the rate of bond failures decreased as the curve changed from type II to type I to type III. RSCSF failure can be classified into three failure modes: (1) tip crack propagation mode, (2) midpoint crack propagation mode and (3) rock bolt crack propagation mode. These failure modes are primarily differentiated by relations between α and β, and the ratio UCS_S/UCS_I between the uniaxial compressive strength (UCS, σ _max) of the RSCSF (UCS_S) and the uniaxial compressive strength of the intact specimen (UCS_I).     

Indirect tensile test assessments for rock materials using 3-D disc-type specimens

Indirect test methods are usually the preferred approach for determining the tensile strength of brittle and quasi-brittle materials such as ceramics, rocks, and concrete. In this paper, the tensile strength of a rock material (Iranian Harsin marble) was obtained indirectly by means of two disc type samples. The test samples were the well-known Brazilian disc and semi-disc specimen under three-point bend loading. Since the existing formula for determining the indirect tensile strength is based on 2-D stress assumption which ignores the effects of specimen thickness, a general 3-D tensile strength formulation was derived for each sample by employing finite element analysis. A series of tensile strength tests were conducted on Harsin white marble using disc and semi-disc specimens with different thicknesses in parallel to finite element analysis. The test results using 3-D formulation showed that the tensile strength of the tested marble depends on the thickness/diameter ratio of the specimen and generally decreases from 11.5 to 7 MPa on increasing the thickness of test samples. The average values of tensile strength were about 8.8 MPa for the Brazilian disc specimen and 9.8 MPa for the semi-disc specimen. The good agreement existing between the results of the two specimens suggests that the semi-disc specimen can also be used for determining the rock tensile strength in addition to using the conventional Brazilian test.     

Tensile strength and its anisotropy measured by point and line-loading of sandstone

Tensile fracture is an ubiquitous feature of rock failure ranging in size from microfracture around Griffith cracks to the large-scale explosive failure accompanying rock bursts in underground cavities. Hence the resistance of rock to failure in tension, the tensile strength, is one of the fundamental parameters of rock strength. The tensile strength of rock is, however, a most elusive parameter which is difficult to measure and to define.

The tensile strength, and its variation with direction, was determined by the pointloading and the line-loading (Brazilian test) methods for nine rocks from five sandstone formations in New Brunswick, Canada. Altogether 319 double point-load and 357 line-load tests were conducted on discs having a diameter of 22.9 mm and thickness of 7.9 mm.

The tensile strength determined by the point-load test and as calculated by the Frocht formula was found to be consistently lower than that obtained by the line-loading technique. To some extent, the difference is due to the fact that most of the sandstones are anisotropic with respect to tensile strength and that the constraints in the point-load test are such that fracture occurs along the plane of minimum tensile strength; the computed tensile strength therefore represents a minimum value. To a greater extent, the lower tensile strength calculated from the point-load test is due to the difference in the states of stress induced by the two techniques. When correction is made for the anisotropy, the tensile strength from the Brazilian test is still 3.76 times larger than the one obtained from the point-load test.

The Brazilian test seems to yield a more accurate definition of both the tensile strength and its variation with direction. The point-load test is more suitable for the determination of the minimum value of tensile strength and the direction of the preferred fracture plane.     

裂隙充填影响巴西圆盘抗拉力学特性试验研究

裂隙是影响岩石力学特性和破裂模式最重要的因素之一,通过试验、数字照相技术和声发射监测对完整和含不同裂隙倾角 单裂隙、不同岩桥与裂隙夹角 双裂隙充填与非充填类岩石材料巴西圆盘的抗拉强度和破裂模式进行研究,探讨了随着 、 的不断变化和裂隙充填与否对试样最终破坏机制的影响。试验结果表明：（1）随着裂隙倾角 不断增大,单裂隙试样的抗拉强度先减小后增大,然后又减小;预制裂隙尖端萌生的翼裂纹贯通造成试样破坏;（2）双裂隙试样的抗拉强度随着 的增大先减小后增大;预制裂隙尖端萌生的翼裂纹和远场裂纹的扩展导致试样破坏;（3）在 、 相同的情况下,充填试样抗拉强度明显要高于非充填试样;预制裂隙充填与否对试样裂纹扩展的时间和裂纹数目影响较大;（4）加载初期,声发射较为平稳;宏观裂纹出现或者抗拉强度跌落时声发射将会变的异常活跃;在 、 相同的情况下充填试样声发射的起伏变化更为剧烈。     

A three-dimensional numerical investigation of the fracture of rock specimens containing a pre-existing surface flaw

Three-dimensional surface crack initiation and propagation in two kinds of heterogeneous rocks were numerically investigated via parallel finite element analysis using a supercomputer. Numerically simulated rock specimens containing a pre-existing flaw were subjected to uniaxial compression until failure. The initiation and propagation of wing cracks, anti-wing cracks, and shell-like cracks were reproduced by numerical simulations. The numerically simulated results demonstrate that the further propagation of wing cracks and shell-like cracks stop due to their wrapping (curving) behavior in three-dimensional spaces, even if the applied loads continue to increase. Furthermore, rock heterogeneity could significantly influence crack propagation patterns and the peak uniaxial compressive strengths of rock specimens. Moreover, anti-wing cracks only appeared in relatively heterogeneous rocks, and the peak uniaxial compressive strengths of the specimens were observed to depend on the inclination of the pre-existing flaw. Finally, the mechanism of surface crack propagation is discussed in the context of numerically simulated anti-plane loading tests, wherein it was identified that Mode III loading (anti-plane loading) does not lead to Mode III fracture in rocks due to their high ratio of uniaxial compressive strength to tensile strength. This finding could explain the lateral growth of an existing flaw in its own plane, which is a phenomenon that has not been observed in laboratory experiments.     

The effect of specimen size and stress rate for the Brazilian test—A statistical analysis

Summary The Brazilian test is a widely accepted method for the determination of the tensile strength of intact rock. Specifications for the Brazilian tensile strength test have been established by the American Society for Testing and Materials (ASTM), ASTM D 3967-86 and a suggested approach is provided by the International Society for Rock Mechanics (ISRM). The ASTM and ISRM allow a relatively wide range of values for specimen geometry defined in terms of length to diameter ratio and loading rates defined as either time to failure or stress rate.A statistical study was carried out on a coal measure sandstone to determine whether the tensile strength determined by the Brazilian test is independent of the specimen geometry and the stress rate.     

延脆性变化对隧道掘进机刀具破岩过程及其破坏模式影响的颗粒元模拟分析

在全断面岩石掘进机（TBM）刀具破岩的颗粒元模拟中颗粒参数的选取至关重要,其中颗粒间平行黏结切向、法向强度是关键控制性参数之一,它们之间的比值关系直接决定所模拟试样的延脆性质,影响刀具破岩过程及其破岩效果。为探讨延脆性对刀具破岩模式的影响,（1）建立9种采用不同平行黏结强度比值的数值模型,分别进行单轴压缩及巴西劈裂模拟,研究不同延脆性试样的力学行为及破坏模式的变化。（2）对9种模型进行双刀破岩,并监控其裂缝的发展情况及刀具的受力状况。（3）为减小随机性对模拟结果的影响,通过改变随机数,每种模型重复模拟5次,综合分析5次的计算结果。模拟分析发现,随着切向和法向黏结强度比值( )的增大,试样的脆性增加,破坏模式逐渐从剪切破坏转变为脆性张拉破坏,刀具破岩压碎区范围减小,张拉裂缝更容易在刀具间贯通延伸从而切割出块体更大的岩渣;随着试样脆性的增加,归一化比能减小,刀具破岩的效率增加;平行黏结强度比值相同的条件下采用不同随机数种子生成的模型中,试样的具体破坏情况有一定的差别,但总体破坏模式相似。     

岩爆及采矿诱发岩体失稳破坏过程数值模拟新方法

岩石介质的宏观非线性主要是由非均质性和各向异性造成的,应用新的数值计算软件RFPA(2D)——基于岩石宏观非线性行为可能是由具弹脆性特征的细观微元体不断破裂造成的,造成微元体不断破裂(并非某一时刻同时破裂)的原因是微元体材料性质(微元体强度、弹性模量和泊松比等参数)的非均匀性,是一个数学上相对简单但能充分考虑岩石介质复杂性的方法,对采动引起岩体失稳破坏的全过程进行了数值模拟研究,表明应用RFPA(2D)是切实可行的。      

动静组合作用下刀具破岩机制数值分析

基于细观损伤有限元方法,模拟分析了刀具在单一动载、动静联合荷载、静态围压条件下动静联合荷载3种情况下岩体破碎的全过程。模型采用黏弹性人工边界剔除了边界应力波反射对模拟结果准确性的影响。数值模拟结果表明：在弹性情况下,静压的存在对岩体内部最小主应力值影响不大,却显著提高了材料内部最大主应力水平,增大了剪应力的大小,导致剪切破坏可能性增加;当有围压存在时,岩体内部受拉区域减少,岩体强度有所提高。单一动载和动静联合荷载破岩时,岩体内部除刀头附近呈现少量压破坏外,破坏均以拉破坏为主;而围压条件下,岩体破碎面积相对减小,裂纹在围压的作用下向两侧自由面延伸,岩体内部破坏形式则趋于多样化,压破坏比重明显增大,整体表现为拉压复合作用。模拟结果还表明,刀头侵入量主要受动载力大小影响,在相同幅值增量下,动载力增加导致的刀头侵入量远大于静压增加所导致的侵入量。相对单一动载和静压作用下的岩石破碎机制来说,动静组合加载破岩的研究还需更为深入的探讨。研究结果可望对岩体破坏机制以及地下工程作业等实际应用提供一定的参考。     

The Effect of High Temperature on Tensile Strength and Damage Characteristics of Limestone

In this paper, the limestone specimens are heated from room temperature 25 to 800 °C in a high temperature furnace and then are subjected to Brazilian test with the AG-I250 electronic precision material testing machine. The physical properties, mechanical properties, disc failure pattern, energy absorbed per unit area and damage characteristics of disc are comprehensively investigated. The results show that: with the increase of temperature, the changing trends of tensile strength, peak strain, tensile modulus and accumulated energy absorbed per unit area of disc are similar, they are first increases, then decrease, the energy consumption index is consistent with the macroscopic damage characteristics; the value of ε_s increase first and then reduce, reaches the maximum at 600 °C. The value of n is increasing and fluctuating, but the change trend of D_c is opposite, which is decreasing and fluctuating. The slope of the damage variable-strain curves decreases first and then increases, the minimum value at 600 °C. This study is of significance to the prediction and evaluation of the stability and safety of rock mass post-high temperature.