A new fracture criterion for brittle rocks

A general form of a “fracture function” for isotropic brittle materials is expressed in terms of the three invariants of the stress tensor. The coefficients in the function are determined by use of the small number of experimental data under specific conditions. This function is applicable to an estimate of the fracture condition of brittle rocks under a general stress state i.e., σ₁ ≠ σ₂ ≠ σ₃. The application of this function is attempted for the data of three brittle rocks i.e., Dunham dolomite, Mizuho trachyte, and Westerly granite, reported by previous workers. For the first two, this criterion gives a good estimation of the effect of the intermediate principal stress σ₂ on failure. For the last, the fracture strength at high confining pressure is estimated by use of the several data obtained under very low confining pressures, and the agreement with experimental data is also satisfactory.     

一种模拟岩石蠕变的数值流形方法

为了保障岩土工程结构能长期正常使用,需要对其蠕变变形进行分析。“时步-初应变”法是一种常用的计算岩石蠕变的方法。数值流形方法是一种新兴的数值计算方法,常用于计算节理岩体的变形,但尚未被试用于计算蠕变变形。在原数值流形方法的程序中增加了基于“时步-初应变”法的计算模块,通过对广义开尔文模型进行的模拟,显示新程序可以正确反映岩石的黏弹性蠕变趋势,并能够计算包含节理的岩体的蠕变变形,改进后的数值流形方法不但能够模拟岩石的线弹性变形,而且可以模拟岩石的黏弹性蠕变,比原流形方法更能全面地模拟岩石的变形,扩展了数值流形方法在岩土工程中的使用范围。     

脆性岩石破裂演化过程的三维细胞自动机模拟

在三维条件下定义了实体细胞自动机的基本组件,综合运用弹塑性理论、细胞自动机自组织演化理论、统计原理以及岩石力学理论等,建立了模拟岩石三维破裂过程的张量型细胞自动机模型,并开发了相应的数值模拟软件EPCA3D。利用EPCA3D对脆性岩石进行单轴压缩破裂过程模拟,通过破裂模式、岩样内部破裂情况、全应力-应变曲线和声发射曲线等的分析,揭示岩石破裂的机制。结果表明,EPCA3D能够较好地模拟非均质岩石在载荷作用下微裂纹的萌生、扩展和贯通的全过程。利用该模拟系统,采用应力-应变线性组合的加载控制方式,研究了不同围压对岩石全应力-应变曲线的影响。研究结果表明：对于脆性非均质岩石,低围压下容易表现为II类行为,且强度较低;高围压下容易表现为I类变形行为,且强度较高。     

水气二相流方程的一种离散数值解法

提出了水气二相流方程的一种数值解法.在利用有限元方法求解水气二相流方程时,引入了离散Newton迭代方法,用于非线性有限元方程组的线性化处理,将这一步计算的收敛阶由原有研究的线性收敛提高到平方收敛,并避免了直接应用Newton迭代方法给编程带来的不便.同时在求解两相的有限元方程组时,采用两相方程组并行迭代的方法,与联立计算相比节省了大量的内存空间.     

颗粒破碎的三维离散元模拟研究

采用PFC等离散元方法研究岩土材料的颗粒破碎已经成为热点。采用考虑局部应力集中的点荷载破碎准则,利用阿波罗填充和膨胀法保证破碎前、后颗粒之间的种群平衡,并引入尺寸因子来表征不同粒径的颗粒强度。在此基础上,开展了石英砂、钙质砂和萨克拉门托河砂3种不同破碎难易程度材料的数值试验,并与室内试验结果进行对比。结果表明:建立的三维颗粒破碎模型能够很好地描述破碎难易程度不同的颗粒材料的压缩特性;考虑应力集中效应的点荷载破碎准则比基于平均应力Mohr-Coulomb理论的颗粒破碎准则更能真实地反应颗粒材料的破碎现象。同时,所建立的模型能够揭示破碎对颗粒材料各向异性消散和级配曲线演化的影响规律。     

螺旋挤土桩下旋成孔过程的颗粒流数值模拟

卵砾石地层可压缩性低、抗剪强度大,水泥土搅拌桩工法在应用于卵砾石地层时存钻进困难、钻具磨损大等问题。为确定卵砾石地层条件下钻头形式的最优布置,基于离散元法(DEM),对不同切削叶片数量、切削叶片角度、截齿布置形式、钻头中心底部布置形式、机械压力工况下,搅拌桩机钻头钻进卵砾石地层的物理过程进行三维动态仿真模拟,并分析研究了不同钻头布置形式对钻进效果的影响。计算结果表明：钻头切削叶片数量的增加会提高钻进阻转矩,但是会增强钻头的定心能力。设置截齿的钻头钻进阻力矩并无明显提高,但钻进速度有一定程度的提高。钻头切削叶片角度的提高会增加钻进阻力矩,但过低或者过高的切削叶片角度均会降低钻进速度。适当提高钻进压力可提高钻进速度,但须考虑动力装置的功率及扭矩输出能力。三切削叶片、高切削叶片角度、设置三截齿的高效率钻头在应用于北京市某项目卵砾石地层时效果良好,文章提出的方法可以为其他工程的施工机械选型提供参照依据。

     

A numerical method for the study of shear band propagation in soft rocks

This paper investigates the possibility of interpreting progressive shear failure in hard soils and soft rocks as the result of shear propagation of a pre‐existing natural defect. This is done through the application of the principles of fracture mechanics, a slip‐weakening model (SWM) being used to simulate the non‐linear zone at the tips of the discontinuity. A numerical implementation of the SWM in a computation method based on the boundary element technique of the displacement discontinuity method (DDM) is presented. The crack and the non‐linear zone at the advancing tip are represented through a set of elements, where the displacement discontinuity (DD) in the tangential direction is determined on the basis of a friction law. A residual friction angle is assumed on the crack elements. Shear resistance decreases on elements in the non‐linear zone from a peak value at the tip, which is characteristic of intact material, to the residual value. The simulation of a uniaxial compressive test in plane strain conditions is carried out to exemplify the numerical methodology. The results emphasize the role played by the critical DD on the mechanical behaviour of the specimen. A validation of the model is shown through the back analysis of some experimental observations. The results of this back analysis show that a non‐linear fracture mechanics approach seems very promising to simulate experimental results, in particular with regards to the shear band evolution pattern. Copyright © 2009 John Wiley & Sons, Ltd.     

A conceptual modeling on the behavior of strain localization for brittle rocks

Acta Geotechnica - This paper captures the frequently encountered strain localization of brittle rocks in laboratory compression experiments under moderate confining pressures generally ranging...     

A mathematical and numerical model for reactive fluid flow systems

We formulate mathematical and numerical models for multispecies, multi-phase and non-isothermal reactive fluid flow in porous media focusing on the chemical reactions and the transport of solutes. Mass conservation and stability in the time integration are emphasized. We use cell-centered finite volume differencing in space and an implicit Runge-Kutta method in time. Assuming two space dimensions, we introduce flux approximation for arbitrarily shaped convex quadrilaterals. On equidistant and variable sized rectangular grids we choose limited κ= related schemes to approximate the advective flux and the central difference scheme for the diffusive flux. On non-rectangular grids we recommend the VF9 scheme for the estimation of the diffusive flux. Our model exists as a code. This revised version was published online in July 2006 with corrections to the Cover Date.     

A discrete approach for anisotropic plasticity and damage in semi-brittle rocks

In this paper, we propose an anisotropic plastic damage model for semi-brittle geomaterials based on a discrete thermodynamic approach. The macroscopic plastic deformation is generated by frictional sliding of weakness planes. The evolution of damage is related to growth of such weakness planes. The local frictional sliding in each family of weakness planes is described by a non-associated plastic model taking into account material softening and volumetric dilatancy. The damage evolution is coupled with plastic deformation and modelled by an isotropic damage criterion. The proposed model is applied to modelling mechanical responses of typical sandstone under different loading paths. There is good agreement between numerical predictions and experimental data. Further, the anisotropic distributions of plastic deformation and induced damage are analysed and discussed.     

Experimental and numerical study of failure characteristics of brittle rocks with single internal 3D open-type flaw

Open flaws without any filling material are common fracture structures in real rock. To study the failure characteristics of this fracture structure, small-scale rock-like samples with single internal 3D open flaws are prepared, and uniaxial compression tests are conducted. Digital image correlation (for surface strain and failures) and acoustic emission (for internal microfracture behaviors) monitoring technologies are also employed to analyze the flaws. The test results are verified through numerical simulations. Different inclination angles of the internal preset flaws are found to have little influence on the strength of the samples, and the surface and internal secondary failures of the samples exhibit very different development processes and distributions. The particle displacement trend method is applied to explain the initiation mechanism of secondary cracks, but the corresponding analyses are only reasonable if particle information along the y-axis is considered. Therefore, the particle information in the y-axis is incorporated by defining new 2D sections (with y-axis) or partial 3D models. Based on these research methods, the initiation mechanism of secondary cracks is reasonably explained, and the influence of the preset flaw thickness on the particle displacement trend fields and secondary failures in surrounding rocks can be discussed. Finally, the simulation results prove that the Mode II and III failures are usually coupled, and direct Mode III failures (displacement of two parts of rock parallel to each other and in opposite directions) only occur in the front and rear surrounding rocks of the preset flaw.

     

Time-dependent cracking and brittle creep in crustal rocks: A review

Rock fracture under upper crustal conditions is driven not only by applied stresses, but also by time-dependent, chemically activated subcritical cracking processes. These subcritical processes are of great importance for the understanding of the mechanical behaviour of rocks over geological timescales. A macroscopic manifestation of time-dependency in the brittle field is the observation that rocks can deform and fail at constant applied stresses, a phenomenon known as brittle creep. Here, we review the available experimental evidence for brittle creep in crustal rocks, and the various models developed to explain the observations. Laboratory experiments have shown that brittle creep occurs in all major rock types, and that creep strain rates are extremely sensitive to the environmental conditions: differential stress, confining pressure, temperature and pore fluid composition. Even small changes in any of these parameters produce order of magnitude changes in creep strain rates (and times-to-failure). Three main classes of brittle creep model have been proposed to explain these observations: phenomenological, statistical, and micromechanical. Statistical and micromechanical models explain qualitatively how the increasing influence of microcrack interactions and/or the increasing accumulated damage produces the observed evolution of macroscopic deformation during brittle creep. However, no current model can predict quantitatively all of the observed features of brittle creep. Experimental data are limited by the timescale over which experiments are realistically feasible. Clearly, an extension of the range of available laboratory data to lower strain rates, and the development of new modelling approaches are needed to further improve our current understanding of time-dependent brittle deformation in rocks.     

基于离散裂隙网络法和水流数值模拟技术的地下水封洞库水封性研究

水封性是保证地下水封洞库安全运营的关键,目前研究地下水封洞库水封性的主要难点在于裂隙岩体含水层强烈的非均质性和各向异性.以某地下水封洞库工程为背景,通过实测裂隙几何参数分析裂隙发育特征,建立了研究区离散裂隙网络模型.之后对研究区进行网格化划分计算了各单元体渗透系数张量,基于对裂隙渗流基本规律的理解和假设建立了研究区高精...     

Micromechanics modelling for stress–strain behaviour of brittle rocks

A micromechanics model for stress–strain behaviour of brittle rocks has been developed. Microcracking is the mechanism of the non-linear deformation behaviour for brittle rocks in the pre-peak stage. The non-linear behaviour in this stage is simulated by considering the local axial splitting of microcracks. The relationships between the compressive stresses, the growth of microcracks, and the fracture-induced deformation are analytically established. In the post-peak stage the shear faulting predominates the process of deformation, which is simulated by a damage model. This micromechanics model is helpful in understanding the failure process in brittle rocks. The model can be used to simulate the complete stress–strain behaviour of rock. The model simulations are consistent with experimental results.     

岩土工程数值计算中的无网格方法及其全自动布点技术

自然单元法采用无网格的思想全域构造插值函数,它的求解精度高,计算时间少,可准确地施加边界条件,兼具有无网格法和有限单元法的优点和特点,是一种理想的用于岩土及地下工程分析计算的数值方法。文中简要地介绍了自然单元法的基本理论,并针对岩土及地下工程问题特点,给出了一种无网格离散点的全自动布置方法。     

A mathematical programming approach for scheduling equipment in a surface coal mining operation

Summary A mathematical programming model for scheduling open pit mining was developed and validated using data from a surface mining operation. A two-phase solution procedure was used involving repeated evaluations of an integer scheduling model and a simple transportation model.     

一种新的岩浆岩分类定量方法

目前,岩浆岩的超基性、基性、中性、酸性的分类均根据SiO2的含量,但这种单一含量判别标准并不严谨,含量经常与分类不完全对应。使用TraceElem 1.0软件对各种岩浆岩进行逐步判别分析、聚类分析和对应分析研究,据此认为超基性岩由MgO和FeO组成的因子确定,基性岩则由P2O5、Fe2O3、TiO2、CaO、MnO组成的因子确定,中性岩由Na2O和Al2O3组成的因子确定,酸性岩由K2O和SiO2组成的因子确定。岩浆岩的分类宜以SiO2为主、以MgO和CaO为辅,尤其要引入MgO。在SiO2含量相同的情况下,MgO、CaO含量越高,基性程度越强。基于这一分析结果,提出一种新的酸度指数（ADI)计算方法,即ADI=w(SiO2)-0.75w(MgO)-0.23w(CaO),ADI<38.0%为超基性岩,在38.0%～52.0%之间为基性岩,在52.0%～62.5%之间为中性岩,>62.5%为酸性岩。     

A numerical method for laterally loaded piles

A numerical model for a laterally loaded pile in an elastic continuum is presented. The governing differential equations for vertical piles in a homogeneous and a layered soil are obtained by using variational calculus. Two parameters, k and t, are used in this approach to represent the elastic foundation, and an iterative technique is adopted to obtain a consistent energy solution. Both free and fixed headed piles have been considered. Two kinds of boundary conditions of practical interest at the pile tip, floating tip and clamped tip, are also considered. The proposed method has been validated by comparison of the results with those obtained by other available methods. Typical solutions are presented and recommendations are given for their use in design problems.