Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

大陆岩石圈在张裂和分离时的变形模式

通过对南海南北共轭边缘地壳剖面的对比研究,发现大陆岩石圈的物理性质是分层的：上、中地壳呈脆性,下地壳表现出塑性,而岩石圈上地幔则仍呈脆性。因此,在它受张性应力场作用时,其变形和破裂分离方式也是分层进行的：上、中地壳能发生犁式断裂,产生的断块沿断面转动在地表产生一系列半地堑,并使地壳厚度减薄;如拉张应力继续作用时,上、中地壳将沿犁式断裂被拉开,从而形成上、下板块边缘,并彼此分开。下地壳则发生塑性变形,使地壳厚度减薄,并最终将其拉断。岩石圈上地幔亦可产生陡倾断裂,形成的断块沿断面转动亦使其厚度减薄,并最终沿陡倾断裂被拉断。这就是我们称之为岩石圈变形和破裂分 离时的分层变形及分层破裂分离模式。     

The Glarus thrust: excursion guide and report of a field trip of the Swiss Tectonic Studies Group (Swiss Geological Society, 14.–16. 09. 2006)

This excursion guide results form a field trip to the Glarus nappe complex organized by the Swiss Tectonic Studies Group in 2006. The aim of the excursion was to discuss old and recent concepts related to the evolution of the Glarus thrust. The major aspects were (i) the interplay between deformation, fluid flow and geochemical alteration, (ii) episodic versus continuous deformation and fluid flow, and (iii) the link between large-scale structures, microstructures, and geochemical aspects. Despite 150 years of research in the Glarus nappe complex and the new results discussed during the excursion, there exist controversies that still are unsolved.     

甘肃小西弓金矿地质地球化学特征及成因探讨

小西弓金矿产于敦煌岩群的低绿片岩相变质岩层中，受NWW向脆韧性剪切带控制。二云母征岩不仅是矿源层，而且还是赋矿围岩。成矿流体主要是印支期岩浆期后含金热液，还包括少量变质水和大气降水，淋滤韧性剪切带内岩石中的Au元素并在有利的部位成矿。     

河南省文峪金矿床构造控矿规律研究

峪金矿床是小秦岭金矿带内一大型金矿床，属韧—脆性叠加剪切带石英脉型金矿，构造是其首要控矿因素。早期韧性剪切带只对矿脉起宏观控制作用。晚期的脆性断裂为含金石英脉的直接控矿构造。成矿期脆性断裂的多次继承性活动分别控制了热液期4个成矿阶段。脆性断裂形成的空间形态对矿体形态产状具控制作用。有利的矿化富集部位为：①显示压扭性质的近东西向断裂沿走向产状变化处，沿倾向由陡变缓处，断裂面的凹凸转变处；②断裂分支复合部位；③成矿期断裂多次脉动的启张部位；④成矿期断裂构造继承性活动强的部位等。在构造控矿研究的基础上，结合前人部分研究成果。构建了该矿床构造控矿模式。     

湘中雪家坡脆韧性剪切构造岩地球化学特征

在１∶５万黄材幅区调中，对脆韧性剪切构造岩进行的岩石化学、微量元素、稀土元素研究表明，由中细粒含斑二云母二长花岗岩改造为糜棱岩化花岗岩、初糜棱岩、绢云母糜棱岩、硅化糜棱岩、千糜岩、糜棱片岩等，其化学成分发生了不同程度的改变。化学元素的分散、聚集或不变，既受原岩控制（继承性），又受变形强度和流体的成分、性质、活动性等控制（变化性）。     

Analysis of crack movements observed in an alpine bedrock cliff

Crack widths and rock temperatures were monitored on an andestic bedrock cliff in the summit area of the Daisetsu Mountains, Hokkaido, northern Japan. Sequential data recorded the gradual widening of a crack to the point of critical crack extension, which resulted in catastrophic rock breakage. The data indicate that a combination of liquid water in?ltration into crack tip and subsequent freezing is the most signi?cant factor contributing to critical crack extension. The recorded sub‐critical crack movements involved a number of minor crack extensions and contractions, the timing of which correlates well with the magnitude of the reconstructed thermal stresses at the crack tip derived from thermal deformation of the plate‐shaped rock fragment. Larger crack extensions occurred when stress at the crack tip exceeded a threshold value, possibly re?ecting the control of rock fracture mechanics by which cracks are thought to propagate when the stress intensity factor at the crack tip exceeds the threshold values for stress corrosion cracking and the fracture toughness of the material. Copyright © 2004 John Wiley & Sons, Ltd.     

Discrete element model for crack propagation in brittle materials

We propose a discrete element model for brittle rupture. The material consists of a bidimensional set of closed‐packed particles in contact. We explore the isotropic elastic behavior of this regular structure to derive a rupture criterion compatible to continuum mechanics. We introduce a classical criterion of mixed mode crack propagation based on the value of the stress intensity factors, obtained by the analysis of two adjacent contacts near a crack tip. Hence, the toughness becomes a direct parameter of the model, without any calibration procedure. We verify the consistency of the formulation as well as its convergence by comparison with theoretical solutions of tensile cracks, a pre‐cracked beam, and an inclined crack under biaxial stress. Copyright © 2015 John Wiley & Sons, Ltd.     

Polygonal grain‐based distinct element modeling for mechanical behavior of brittle rock

The microstructure of rock was numerically reproduced by a polygonal grain‐based model, and its mechanical behavior was examined by performing the uniaxial compression test and Brazilian tests via the Universal Distinct Element Code. The numerical results of the model demonstrated good agreement with the experimental results obtained with rock specimens in terms of the stress–strain behavior, strength characteristics, and brittle fracture phenomenon. An encouraging result is that the grain‐based model‐Universal Distinct Element Code model can reproduce a low ratio of tensile to compressive strength of 1/20 to 1/10 without the need for an additional process. This finding is ascribed to the fact that the geometrical features of polygons can effectively capture the effects of angularity, finite rotation, and interlocking of grains that exist in reality. A numerical methodology to monitor the evolution of micro‐cracks was developed, which enabled us to examine the progressive process of the failure and distinguish the contribution of tensile cracking to the process from that of shear cracking. From the observations of the micro‐cracking process in reference to the stress–strain relation, crack initiation stress, and crack damage stress, it can be concluded that the failure process of the model closely resembles the microscopic observations of rock. We also carried out a parametric study to examine the relationships between the microscopic properties and the macroscopic behavior of the model. Depending on the micro‐properties, the model exhibited a variety of responses to the external load in terms of the strength and deformation characteristics, the evolution of micro‐cracks, and the post‐peak behavior. Copyright © 2016 John Wiley & Sons, Ltd.