Implementation of a coupled plastic damage distinct lattice spring model for dynamic crack propagation in geomaterials

This paper studies dynamic crack propagation by employing the distinct lattice spring model (DLSM) and 3‐dimensional (3D) printing technique. A damage‐plasticity model was developed and implemented in a 2D DLSM. Applicability of the damage‐plasticity DLSM was verified against analytical elastic solutions and experimental results for crack propagation. As a physical analogy, dynamic fracturing tests were conducted on 3D printed specimens using the split Hopkinson pressure bar. The dynamic stress intensity factors were recorded, and crack paths were captured by a high‐speed camera. A parametric study was conducted to find the influences of the parameters on cracking behaviors, including initial and peak fracture toughness, crack speed, and crack patterns. Finally, selection of parameters for the damage‐plasticity model was determined through the comparison of numerical predictions and the experimentally observed cracking features.     

含裂隙组岩体的稳定问题

借鉴单晶体塑性理论,构建了岩体的多屈服面模型,用以模拟岩体中初始存在的多组裂隙。通过重构屈服函数,及简单的两种情况表明,可以采用常用的屈服准则作为屈服函数。随后,使用该多屈服面模型,分析了包含初始裂隙组岩体的稳定问题。在算例中研究了硬化模量随局部化条带方向的变化规律,并分析了不同破坏模式对临界硬化模量和临界局部化条带方向的影响。分析表明,该模型用于分析裂隙岩体的稳定问题是可行的。     

Continuum large cracking in a rate‐dependent plastic–damage model for cyclic‐loaded concrete structures

Formulation and algorithmic treatment of a rate‐dependent plastic–damage model modified to capture large tensile cracking in cyclic‐loaded concrete structures are presented in detail for a three‐dimensional implementation. The plastic–damage model proposed by Lee and Fenves in 1998 was founded based on isotropic damaged elasticity in combination with isotropic multi‐hardening plasticity to simulate cracking and crushing of concrete under cyclic or dynamic loadings. In order that the model can capture large crack opening displacements, which are inevitable in plain concrete structures, the excessive increase in plastic strain causing unrealistic results in cyclic behaviors is prevented when the tensile plastic–damage variable controlling the evolution of tensile damage is larger than a critical value. In such a condition, the crack opening/closing mechanism becomes similar to discrete cracking. The consistent tangent operator required to accelerate convergence rate is also formulated for the large cracking state including viscoplasticity. The validation and performance of the modified algorithm implemented in a special finite element program is exemplified through several single‐element tests as well as three structural applications. The last example examines the model in the seismic fracture analysis of Koyna dam as a benchmark problem and the resulting crack profile is compared with the available experiment. The numerical experimentations well demonstrate that the developed model whose modification is necessary to properly simulate the cyclic behavior of plain concrete subjected to large tensile strains is robust and reasonably accurate. Copyright © 2012 John Wiley & Sons, Ltd.     

Modeling of dynamic cohesive fracture propagation in porous saturated media

In this paper, a mathematical model is presented for the analysis of dynamic fracture propagation in the saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double‐nodded zero‐thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The crack is automatically detected and propagated perpendicular to the maximum effective stress. The spatial discretization is continuously updated during the crack propagation. Numerical examples from the hydraulic fracturing test and the concrete gravity dam show the capability of the model to simulate dynamic fracture propagation. The comparison is performed between the quasi‐static and fully dynamic solutions, and the performance of two analyses is investigated on the values of crack length and crack mouth opening. Copyright © 2010 John Wiley & Sons, Ltd.     

高渗透压脆性岩石蠕变宏−细观力学模型研究

高渗透压对深部地下工程脆性岩石蠕变力学特性有着重要影响。然而,能够解释高渗透压作用脆性岩石完整减速、稳态及加速三级蠕变过程中,细观裂纹扩展与宏观变形关系的宏细观力学模型研究很少。基于考虑含有初始裂纹与新生成翼型裂纹影响的裂纹尖端应力强度模型,引入渗透水压与初始裂纹及新生成翼型裂纹之间的力学关系,建立了考虑渗透水压作用的裂纹尖端应力强度模型;然后结合亚临界裂纹扩展法则,与裂纹及应变损伤关系模型,推出了考虑渗透水压影响的脆性岩石蠕变裂纹扩展与宏观变形关系的宏细观力学模型。当施加轴向应力小于岩石裂纹启裂应力时,岩石近似表现为线弹性变形;当施加轴向应力大于裂纹启裂应力且小于岩石峰值强度,岩石表现为塑性蠕变变形。研究了不同渗透压作用下,分级轴向应力加载岩石蠕变应变时间演化曲线,并通过试验结果验证了模型的合理性。分别讨论了恒定渗透压与分级渗透压,对脆性岩石蠕变过程中裂纹长度、裂纹扩展速率、轴向应变及轴向应变率的影响。该模型为高渗透压深部地下工程围岩稳定性评价提供了重要理论依据。     

A numerical study of the influence from pre‐existing cracks on granite rock fragmentation at percussive drilling

The aim of this study is to investigate the effect of pre‐existing, or structural, cracks on dynamic fragmentation of granite. Because of the complex behavior of rock materials, a continuum approach is employed relying upon a plasticity model with yield surface locus as a quadratic function of the mean pressure in the principal stress space coupled with an anisotropic damage model. In particular, Bohus granite rock is investigated, and the material parameters are chosen based on previous experiments. The equation of motion is discretized using a finite element approach, and the explicit time integration method is employed. The pre‐existing cracks are introduced in the model by considering sets of elements with negligible tensile strength that leads to their immediate failure when loaded in tension even though they still carry compressive loads as crack closure occurs because of compressive stresses. Previously performed edge‐on impact tests are reconsidered here to validate the numerical model. Percussive drilling is simulated, and the influence of the presence of pre‐existing cracks is studied. The results from the analysis with different crack lengths and orientations are compared in terms of penetration stiffness and fracture pattern. It is shown that pre‐existing cracks in all investigated cases facilitate the drilling process. Copyright © 2014 John Wiley & Sons, Ltd.     

A multi‐asperity plastic‐contact crack plane model for geomaterials

A mechanistic constitutive model for fully formed cracks in geomaterials, such as concrete and rock, is presented. A three‐dimensional characterisation of the crack morphology is employed in which the crack surface is idealised as a series of conical teeth and corresponding recesses of variable height and slope. Based on this geometrical characterisation, an effective contact function is derived to relate the contact stresses that develop on the sides of the teeth to the net stresses on a crack plane. Plastic embedment and frictional sliding are simulated using a local plasticity model in which the plastic surfaces are expressed in terms of the contact surface function in cylindrical relative displacement space. Finally, the performance of the model is assessed against several sets of experimental data from direct shear tests, and it is concluded that the model is able to capture key characteristics of the behaviour of fully formed cracks in geomaterials. Copyright © 2012 John Wiley & Sons, Ltd.     

Analytical simulation of the dynamic compressive strength of a granite using the sliding crack model

A sliding crack model is employed to simulate rock strength under dynamic compression. It is assumed that the growth and nucleation of a sliding crack array presented results in the shear fault failure and dominate the mechanical properties of rock material. The pseudo‐tractions method is used to calculate the stress intensity factor of the sliding crack array under compression. With the utilization of a dynamic crack growth criterion, the growth of the sliding crack array is studied and the simulated strengths of a granite under dynamic compression are correspondingly obtained. It is concluded that the simulated rock strengths increase with increasing strain rates at different confining pressures, and the rising rates have a trend to decrease with increasing confining pressures. It is also indicated that the simulated rock strengths increase with increment of confining pressure at different strain rates, and the rising rates are almost identical at different strain rates. The simulation results are validated by the experimental data for the granite. Copyright © 2001 John Wiley & Sons, Ltd.     

砂土液化大变形模型在FLAC3D中的开发与应用

通过FLAC3D二次开发平台,在VC++环境下实现了基于砂土液化大变形机制的变动映射中心边界面弹塑性模型的二次开发。基于饱和砂土液化大变形本构理论,该模型符合三维应力空间边界面映射规则,并引入临界状态变量,可实现对不同密度和围压状态下砂土液化大变形分析。针对FLAC3D程序混合离散技术与数据调用模式和模型的体积相容性条件,测试分析了将模型采用不同植入方案的计算稳定性,开发了在FLAC3D混合离散技术下不同子区共享映射中心,进入与离开液化状态保持同步的开发方案,并给出模型开发的关键技术与实施方法。利用开发的模型,对饱和砂土开展了不排水/排水/循环三轴试验与不排水循环扭剪试验模拟,及三维地基的动力反应分析。计算结果表明,模型及所开发程序具有很好的模拟与分析砂土液化后大变形的能力。     

Constitutive modelling of aggregate interlock in concrete

A model for formed cracks in concrete is presented. The model can be used in isolation for existing cracks or linked with other damage or plasticity models and applied once a crack has fully formed. It can be applied directly to interface finite elements or used to control the behaviour of crack planes in more general constitutive models that are applied to 2D and 3D continuum elements. The focus of the present development is on aggregate interlock and crack closing behaviour, which is examined from available experimental data. A contact function is derived and is used to differentiate between three contact states. These states are named open, where there is no contact, interlock, for which the stresses depend upon the nearest distance to the contact surface and closed, for which the stresses depend upon the relative displacements directly. The model is developed within an elasto‐plastic framework using effective stresses, which are related to the total stresses via a contact proportion function. The relationship between the effective normal and shear yield stresses is found to be parabolic and the yield shear stress to be dependent upon the opening and embedment displacements. The performance of the model is assessed against experimental data from shear‐normal tests and it is concluded that the model is able to represent the key characteristics of the behaviour of formed cracks in concrete. Copyright © 2002 John Wiley & Sons, Ltd.     

花岗岩动三轴抗压强度的裂纹模型研究（I）：理论基础

简要地介绍了岩石材料在压应力作用下的裂纹模型。应用虚拟力方法(Pseudo-tractionmethod)考虑2阶虚拟力情形,求解裂纹组应力强度因子表达式,为岩石动三轴抗压强度的裂纹模型研究提供理论基础。     

锦屏水电站左坝肩岩体深卸荷带成因分析

平洞探坑揭露了锦屏水电站普斯罗沟坝址左坝肩岩体内部存在深卸荷带,该卸荷带生成原因及分布范围将严重影响未来水电站坝肩的稳定及工程处理费用。在充分考虑断层、裂隙带、岩性特点基础上,应用ANSYS软件分析了不同荷载组合情况下普斯罗沟坝址左坝肩高陡边坡岩体深卸荷带的力学特点,建立了解释深卸荷带形成的简单力学模型,确定出深卸荷带应力场异常范围。     

基于损伤塑性模型的地下洞室结构地震作用分析

基于损伤力学原理,通过引入损伤变量的方法,详细推导了ABAQUS中的损伤塑性本构模型,描述混凝土后继屈服阶段及其卸荷后的损伤机制和力学行为。此本构模型可考虑循环荷载条件下材料刚度退化和应变率的影响,适用于类似混凝土材料的脆性材料,如岩石等。以某水电站地下厂房洞室结构为例,进行二维动力时程非线性分析,考虑不同的刚度恢复权重因子和应变率相关性对结构损伤的影响。多个数值算例表明：洞室混凝土结构和其周围一定深度的围岩的损伤是一个渐进积累的过程;材料的率相关性效应并不是在地震动作用开始时就立即产生,而是在一段时间后,结构经历一定程度的损伤后才慢慢体现出来;此损伤塑性模型适合地震荷载等循环荷载作用下地下洞室结构的动力时程非线性分析,尤其是强震下采用此损伤塑性模型是合理和必要的。     

压裂过程中地面和井下倾斜场的主控因素研究

水力压裂技术改造储层已经成为非常规油气开发的重要技术手段,以井下测斜仪为代表的远场测量技术进行裂缝形态监测已经逐步应用于压后裂缝效果评价。采用不同的裂缝分析模型对压裂过程中地面和井下倾斜场进行了正演研究,验证了模型的正确性,并采用矩形张裂缝模型对影响压裂倾斜场的地层和裂缝参数进行了定量分析。研究表明,（1）地面倾斜场对于裂缝的方位角和倾角变化较为敏感,对于裂缝的尺寸及裂缝中心深度变化不敏感;（2）井下倾斜场值对于裂缝的尺寸、裂缝中心深度变化较为敏感,对于裂缝的方位角及倾角变化不敏感。研究结果可应用于储层水力压裂优化设计中。     

Numerical modelling of bit–rock fracture mechanisms in percussive drilling with a continuum approach

This paper presents a numerical method for continuum modelling of the dynamic bit–rock interaction process in percussive drilling. The method includes a constitutive model based on a combination of the recent viscoplastic consistency model, the isotropic damage concept and a parabolic compression cap. The interaction between the drill bit and rock is modelled using contact mechanics by treating the bit as a rigid body. As the bit–rock interaction in percussive drilling is a transient event, the method is implemented in explicit dynamics FEM. The rock strength heterogeneity is characterized at the mesoscopic level statistically using the Weibull distribution. The bit–rock interaction is simulated under axisymmetric conditions using cylindrical and hemispherical buttons. The choice of the quite complex constitutive model accounting, e.g. for plastic compaction, viscoplastic shear and tensile failure along with induced damage and rate dependency is justified by numerical simulations. Moreover, the quasi‐static and dynamic cases are compared in plane strain simulations. Finally, some results clarifying the discrepancy of opinions found in the literature concerning the side (lateral) crack formation are obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

花岗岩动三轴抗压强度的裂纹模型研究(Ⅱ):应用

根据压缩载荷作用下的滑移型裂纹模型，结合裂纹的动态断裂准则，模拟了花岗岩在应变速度从10^-4-10^0s^-1以及围压力20，50，80MPa时的强度特性。结果表明，模拟结果与实验结果基本一致。还探讨了地从裂纹扩展和聚合特性入手揭示岩石材料强度随应变速率以及围压变化的机理。     

Significance of localized pore pressures to the genesis of septarian concretions

The burial-stress and hydrologic conditions existing during concretion formation in mudrocks are evaluated and integrated into a model for the genesis of septarian cracks. Initial concretion cement formation will lower concretion permeability through the filling of pre-existing pore space. During progressive burial, this may lead to increased excess pore pressure, localized within the concretion body causing a reduction of the effective stress. Analysis of the stress conditions and crack morphology suggests that cracks in septarian concretions result from tensional failure (sub-critical crack growth), as a consequence of this localized excess pore pressure. Conditions suitable for crack formation will depend upon the magnitude of the excess pore pressure and the stress corrosion limit of the concretion body. A review of the likely strength of such concretions indicates that cracking could be initiated at depths less than 10 m. A variety of observed crack morphologies can be explained with this model, depending upon the spatial distribution of strength and effective stress in the concretion. Crack orientations mostly reflect stress anisotropy, but are also influenced by directional anisotropy in the crack growth rates. Locally increased pore pressure also likely occurs in non-septarian concretions, but is not sufficient to cause cracking. This enhanced local pressure may assist the crystal surface growth reactions of the carbonate cement. Through this enhancement process, the shape of concretions may be a response to the local anisotropic pore-pressure contours, which reflect the permeability anisotropy of the concretion and surrounding mudrock.     

页岩水力压裂过程的态型近场动力学模拟研究

水力压裂技术广泛使用于页岩气开采工程中。为了分析压裂过程中多裂缝扩展形成复杂裂缝网的机制,尝试将态型近场动力学理论引入页岩水平井水力压裂过程的力学建模与数值仿真,在物质点间相互作用力模型中加入等效水压力项以实现在新生裂缝面上跟踪施加水压力,建立了水力压裂过程的近场动力学分析模型。通过模拟页岩储层的水力压裂过程,可得到复杂的裂缝扩展路径、裂缝网络的形成过程以及裂缝扩展受射孔间距及页岩天然裂缝和层理的影响。研究结果表明:射孔间距过小会造成起裂干扰,使中心射孔的裂缝扩展受到抑制;在压裂压力一定的情况下适当增大射孔间距,可以显著增强页岩压裂形成裂缝网的能力;压裂过程中水平层理面可能张开形成水平裂缝,且天然裂缝会诱导形成更复杂的垂直裂缝。模型和方法可为页岩水力压裂过程和机制研究及工程实践提供参考。     

Testing and modeling of the mechanical behavior of dolomite in the Wudongde hydropower plant

In order to understand the mechanical behaviours of the surrounding rocks in the underground caverns of the Wudongde hydropower plant, triaxial tests are performed on a type of dolomite. It is revealed that damage induced by crack development is the main factor controlling the nonlinear plastic deformation and failure behaviour of the dolomite in both pre- and post-peak regimes. Based on this understanding, a coupled elastoplastic damage model is developed for capturing the dolomite’s mechanical behaviours. In the model, the effects of plasticity and damage on rocks is described by introducing plastic hardening and damage softening commonly in the plastic yield surface. Which are both derived from a suitable Helmholtz free energy function. The model is used to simulate the triaxial tests. Comparisons between test results and the numerical modelling show that the developed model is capable of describing the macro mechanical behaviours of the Wudongde dolomite.     

爆炸应力波作用下缺陷介质裂纹扩展的动态分析

采用透射式焦散线测试系统,进行爆炸应力波作用下缺陷介质裂纹扩展试验,研究了含与炮孔共线的预制裂隙介质裂纹扩展速度、加速度、裂纹尖端动态应力强度因子和动态能量释放率的变化规律以及它们之间的变化关系。试验结果表明,在爆炸应力波作用下裂隙两端产生了两条翼裂纹A、B,翼裂纹A的长度较翼裂纹B长,两条翼裂纹向相反的方向扩展;在翼裂纹扩展过程中,存在着加速与减速的过程,扩展速度瞬间达到峰值,其后逐渐振荡下降;动态应力强度因子也呈现瞬间达最大值到逐渐减小连续振荡变化的趋势,动态应力强度因子 > ;翼裂纹尖端的动态能量释放率对裂纹扩展具有驱动作用。