A new phase field model for mixed-mode brittle fractures in rocks modified from triple shear energy criterion

Acta Geotechnica - Fracture initiation, propagation, merging and branching in rocks are considerably complicated and commonly exhibit a great variety of patterns. How to characterize and capture...     

A phenomenological failure criterion for brittle rock

Summary A phenomenological model is developed to represent failure in intact media as a consequence of shear-band formation. A stepped arrangement of connected flaws is assumed to be distributed within a planar shear-band inclined with respect to the applied deviatoric stresses. The flaws within the shear-band isolate a series of wedges that transmit tractions across the pre-failure zone. Gross stress transmission is controlled by static equilibrium with spatial stress inhomogeneity modulated through the distribution of flaws in the continuum adjacent to the shear-band. Under increased confinement, flaw closure beyond the shear-band results in a more homogeneous transmission of normal tractions across the failure plane. This stress dependent transition is based on physical arguments, related to mean flaw closure, to yield a distribution coefficient,W, that is controlled by macroscopic flaw rigidity,B. The model is able to replicate the power law dependency of ultimate strength with confining stress that is commonly observed. The model is specifically calibrated against experimental data for Daye marble. The phenomenological coefficients describing the failure process appear as material constants.     

A discrete numerical method for brittle rocks using mathematical programming

A computational formulation of discrete simulations of damage and failure in brittle rocks using mathematical programming methods is proposed. The variational formulations are developed in two and three dimensions. These formulations naturally lead to second-order cone programs and can conveniently be solved using off-the-shelf mathematical programming solvers. Pure static formulations are derived so that no artificial damping parameters are required. The rock is represented by rigid blocks, with interfaces between blocks modelled by zero-thickness springs based on the rigid-body–spring network method. A modified Mohr–Coulomb failure criterion is proposed to model the failure of the interfaces. When the interface’ strength limits are reached, a microscopic crack forms and its strength is irreversibly lost. The microscopic elastic properties of the springs are related to the observed elastic behaviour of rocks with the developed empirical equations. The program is first validated with three simple tests. Then, numerical uniaxial and biaxial compression tests and the Brazilian tests are conducted. Furthermore, the proposed approach is employed to study the rock crack propagation and coalescence using cracked Brazilian disc test. The results are in good agreements with reported experimental data, which shows its potential in modelling mechanical behaviour of brittle rocks.     

A simple criterion for the machinability of hard rocks

Conclusions The application of mechanical methods for rapid excavation requires more detailed and precise knowledge of the site, but there is no single parameter which can provide a comprehensive measure for the selection and performance of a tunnel boring machine.The machinability index proposed in this paper is based on four different parameters which influence the performance of a tunnelling machine and are widely accepted by the engineers and geologists. In order to develop a comprehensive measure regarding the borability of rocks,in situ conditions must be evaluated. The machinability index coupled with thein situ information would facilitate judicious decisions regarding the application and selection of tunnel boring machines.The geological conditions and rock characteristics cannot be controlled but their knowledge can prevent costly mistakes in equipment selection and assist in identifying alternative excavation systems, therefore a thorough site investigation can substantially reduce the economic and technical risks associated with tunnelling and mine development.     

A dual-mechanism tensile failure criterion for transversely isotropic rocks

Acta Geotechnica - We propose a tensile failure criterion for transversely isotropic rocks that distinguishes tensile fracturing mechanisms either through the anisotropic rock matrix or along the...     

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...     

裂隙蠕变的稳定性准则

介绍了最小耗能原理及其建立材料强度准则的一般步骤,在强度准则通常为能量蓄积程度表达式这一前提下,从最小耗能原理出发,利用线粘弹性断裂理论推导了裂纹蠕变的稳定性准则。为对比起见,将线弹性断裂理论的应变能密度因子断裂判据直接推广到粘弹性状态,得到了与最小耗能原理相同的稳定性准则表达式,并分析了几种流变材料中裂纹蠕变的长期稳定性。     

Prediction of fracture trajectory in anisotropic rocks using modified maximum tangential stress criterion

A new criterion to predict crack propagation trajectory in anisotropic rocks with incorporating the concept of T-stress in formulating stress field near the crack tip was developed. The developed criterion along with enrichment functions and interaction integral in the extended finite element method (XFEM) framework made a sophisticated tool in modeling fracturing process in anisotropic media. Numerical results indicated that stress intensity factors considerably depend on orientation of anisotropy axes and ratio of the elastic modulus. The proposed formulation for anisotropic media provides a more accurate prediction of crack propagation trajectory compared with conventional methods, especially in mixed mode conditions.     

On the pressure dependence of strength of rocks and the coulomb fracture criterion

The observed microfracturing before faulting in rocks provides a basis for a physical model for the internal friction and the cohesive stress of the Coulomb criterion. Based on recent experimental results in the literature, the applicability of the Coulomb criterion is reexamined. The pressure dependence of strength of brittle rocks can be predicted approximately by the Coulomb criterion using measured values of sliding friction, except for a low-pressure region for certain rocks and near the brittle-ductile transition pressure. Deviation at low pressure seems to be explained either by the effect of cracked state or by different fracture mechanisms at low confining pressures, and deviation near the transition pressure is attributed to the increase of local yielding or fracturing before faulting.     

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.     

一个与弹性应变能相协调的脆性横观各向同性材料破坏准则

岩土材料广泛存在于自然界中,在重力沉积作用下表现出明显的横观各向同性。为了更好地研究横观各向同性材料的破坏机制,基于Christensen提出的破坏准则应与弹性应变能函数相协调的思想,推导了横观各向同性材料的弹性应变能,通过应变能的分解和整理,分析了应变能中各项所表示的物理意义,确定了级数展开的基,从而使得应变能函数和材料破坏准则在形式上具有一致性,最终提出了一个适用于脆性横观各向同性材料的破坏准则。该准则由5项能够与弹性应变能相协调的部分组成,仅包含5个独立且物理力学意义清晰的参数。基于常规试验给出了5个独立参数的确定方案。通过与Tsai-Wu准则及已发表的多组试验数据的对比,验证了准则的正确性。     

孔隙水压力对岩石裂纹扩展影响的数值模拟

应用岩石破坏过程渗流-应力-损伤(FSD)耦合分析软件F-RFPA2D,通过对孔隙水压作用下岩石试件加载破坏过程的数值模拟,对孔隙水压力大小和梯度对岩石试样中裂纹的萌生和扩展进行了数值模拟研究。模拟结果再现了孔隙水压力作用下裂纹萌生扩展的全过程,表明孔隙水压力大小和梯度对岩石中裂纹的萌生和扩展模式都有很大的影响。     

闭合裂纹断裂的有效剪应力准则

将闭合裂纹表面的有效剪应力引入裂尖应力强度因子的计算,获得了无限大板和有限宽板含中心闭合裂纹在不同裂纹长度、倾角以及摩擦系数下裂纹尖端的应力强度因子值。引入等径向剪应力线 这一概念,建立了闭合裂纹断裂的有效剪应力准则：（1）岩板内闭合裂纹将沿着等 线上双剪应力的和最小的方向扩展;（2）裂纹尖端的应力强度因子KⅡ达到材料的临界值KⅡC,裂纹将开始扩展。该准则成功预测了闭合裂纹的临界起裂角 ,与各种经典复合型断裂准则计算Ⅱ型裂纹起裂角比较,结果较为接近。将其应用于闭合裂纹的断裂判定是安全的。     

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.     

Stochastic dynamics of damage evolution in brittle rocks

Development of defects in brittle rocks is analysed in terms of continuous damage mechanics with an emphasis on a shear damage evolution. Necessity to account for an effect of stochastic action leads to an introduction of kinetic relations for damage accumlation in a form of stochastic differential equations. Numerical algorithms for their solution for three types of noise are proposed. Results of simulation are compared with analytical solutions for a determiistic case (absence of stochastic action). Effect of various types of noise on damage accumulation and on time-to-fracture distributions is investigated. The study is limited to the case of temporal stochasticity; ways for unification of approach and schemes with spatial randomness are discussed.     

一种新的岩石非线性黏弹塑性流变模型

借鉴经典元件组合模型的建模思路,将含分数阶微积分的软体元件与弹簧元件串联,结合一个幂函数黏塑性体,提出一种新的四元件非线性黏弹塑性流变模型,并给出该模型的本构方程和蠕变方程,得到在不同应力条件下的蠕变曲线。可以发现,岩石稳定蠕变阶段的非线性渐变过程和加速蠕变阶段蠕变速率的快慢程度可通过调整蠕变参数进行有效地模拟。在较低应力水平时,模型能够有效地刻画岩石的初始蠕变和稳定蠕变;当应力水平超过岩石的长期强度时,能够反映加速蠕变特性。利用该模型对试验数据拟合的结果表明,含有软体元件和幂函数黏塑性体的非线性流变模型能够有效地描述岩石的蠕变特性,减少组合模型中的元件个数和参数数量。     

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。