动力水力压裂的相场模拟方法

 水力压裂计算对页岩气开采至关重要,将岩体等效为均匀多孔介质,以动力达西–毕奥流描述岩体内的渗流过程,以相场方法追踪裂缝扩展,将压裂裂缝内流体近似为泊肃叶流,并通过修正渗流方程予以实现,从而提出了动力水力压裂的相场模拟方法,并基于显式有限元框架进行数值求解。通过与一维解析解对比说明所提方法计算位移和动水压的准确性。一系列数值算例表明,提出的压裂相场模拟方法能够模拟动力水力压裂作用下裂缝动态扩展的典型特征,且能够计算水力压裂裂缝的相交、分叉和三维扩展等复杂裂缝扩展形态,为动力水力压裂设计提供了强有力的数值计算工具。     

层理页岩水力裂缝扩展规律的相场法研究

准确预测层理页岩水力裂缝扩展路径对于页岩压裂方案优化与压裂效果评价至关重要.基于多孔弹性理论和能量最小化原理建立水力耦合的相场模型,采用交错策略的分离式耦合方法进行求解.通过压裂试验数据对比验证模型的可靠性,同时基于页岩三维水力压裂模拟分析,验证该方法对于模拟不同地应力条件下的水力裂纹扩展问题的适用性.基于该模型,利用...     

钢结构的脆性断裂分析

通过简述钢结构的脆性断裂事故,应用断裂力学的原理对结构发生断裂的因素进行分析,指出其主要影响因素。最后,分别从焊接钢结构的设计,施工工艺、质量控制以及维修监控等方面对钢结构的脆性断裂提出防治措施,以期为实际工程提供参考。     

A FEniCS implementation of the phase field method for quasi-static brittle fracture

In the recent years, the phase field method for simulating fracture problems has received considerable attention. This is due to the salient features of the method: 1) it can be incorporated into any conventional finite element software; 2) has a scalar damage variable is used to represent the discontinuous surface implicitly and 3) the crack initiation and subsequent propagation and branching are treated with less complexity. Within this framework, the linear momentum equations are coupled with the diffusion type equation, which describes the evolution of the damage variable. The coupled nonlinear system of partial differential equations are solved in a ‘staggered’ approach. The present work discusses the implementation of the phase field method for brittle fracture within the open-source finite element software, FEniCS. The FEniCS provides a framework for the automated solutions of the partial differential equations. The details of the implementation which forms the core of the analysis are presented. The implementation is validated by solving a few benchmark problems and comparing the results with the open literature.     

Shear fracture (Mode II) of brittle rock

Mode II fracture initiation and propagation plays an important role under certain loading conditions in rock fracture mechanics. Under pure tensile, pure shear, tension- and compression-shear loading, the maximum Mode I stress intensity factor, K_Imax, is always larger than the maximum Mode II stress intensity factor, K_IImax. For brittle materials, Mode I fracture toughness, K_IC, is usually smaller than Mode II fracture toughness, K_IIC. Therefore, K_Imax reaches K_IC before K_IImax reaches K_IIC, which inevitably leads to Mode I fracture. Due to inexistence of Mode II fracture under pure shear, tension- and compression-shear loading, classical mixed mode fracture criteria can only predict Mode I fracture but not Mode II fracture. A new mixed mode fracture criterion has been established for predicting Mode I or Mode II fracture of brittle materials. It is based on the examination of Mode I and Mode II stress intensity factors on the arbitrary plane θ,K_I(θ) and K_II(θ), varying with θ(−180°θ+180°), no matter what kind of loading condition is applied. Mode I fracture occurs when (K_IImax/K_Imax)<1 or 1<(K_IImax/K_Imax)<(K_IIC/K_IC) and K_Imax=K_IC at θ_IC. Mode II fracture occurs when (K_IImax/K_Imax)>(K_IIC/K_IC) and K_IImax=K_IIC at θ_IIC. The validity of the new criterion is demonstrated by experimental results of shear-box testing.Shear-box test of cubic specimen is a potential method for determining Mode II fracture toughness K_IIC of rock since it can create a favorable condition for Mode II fracture, i.e. K_IImax is always 2–3 times larger than K_Imax and reaches K_IIC before K_Imax reaches K_IC. The size effect on K_IIC for single- and double-notched specimens has been studied for different specimen thickness B, dimensionless notch length a/W (or 2a/W) and notch inclination angle α. The test results show that K_IIC decreases as B increases and becomes a constant when B is equal to or larger than W for both the single- and double-notched specimens. When a/W (or 2a/W) increases, K_IIC decreases and approaches a limit. The α has a minor effect on K_IIC when α is within 65–75°. Specimen dimensions for obtaining a reliable and reproducible value of K_IIC under shear-box testing are presented. Numerical results demonstrate that under the shear-box loading condition, tensile stress around the notch tip can be effectively restrained by the compressive loading. At peak load, the maximum normal stress is smaller than the tensile strength of rock, while the maximum shear stress is larger than the shear strength in the presence of compressive stress, which results in shear failure.     

A concise review about fracture assessments of brittle solids with V-notches

A concise review of recent studies about the fracture assessments of elastic brittle solid materials containing V-notches is presented. In this preliminary and brief survey, elastic stress distributions in V-notched solids are discussed first. The concept of notch stress intensity factor is introduced. Combine the digital image correlation method with numerical computation techniques to analyze the stress distribution near the notches. Fracture criteria such as strain energy density, J-integral, theory of critical distance are used.However, various new materials are developed in different engineering fields, thus, the establishment of reliable and accurate material strength theory or failure criterion is imperative. Therefore, predicting fracture for various modern materials would require more experiments to infer material dependent parameters in the local fracture model.     

类岩石脆性材料非闭合裂纹的Ⅰ-Ⅱ压剪复合型断裂准则研究

实际工程中,结构体裂纹常处于拉剪和压剪复合受力状态,研究适合于复合型裂纹的断裂准则和裂纹扩展机理具有重要的理论意义和实用价值。以Ⅰ-Ⅱ复合型裂纹为研究对象,基于线弹性理论,在考虑裂纹几何特征及受力形式的基础上,系统介绍了裂纹应力强度因子（SIF）的理论解。提出了适用于Ⅱ型断裂的径向剪应力准则和双剪应力准则。对于Ⅰ-Ⅱ复合型裂纹,提出用等效Ⅰ、Ⅱ型SIF比值与Ⅰ、Ⅱ型断裂韧度比值的关系判定裂纹断裂类型,并分别选择适合于Ⅰ、Ⅱ型断裂的断裂准则,计算了裂纹断裂扩展理论角度。理论断裂角与预制非闭合裂纹类岩石脆性材料压剪断裂试验结果符合得较好。     

钢框架梁柱节点脆性断裂原因及新型节点形式

针对节点受力机理的复杂性,分析了地震中钢框架梁柱节点脆性断裂的原因,并提出了新型的节点形式,如加强型节点和削弱型节点,以防止节点发生脆性破坏,改善节点的抗震性能。     

Development of a local degradation approach to the modelling of brittle fracture in heterogeneous rocks

At the microscopic scale (say, of the order of grain size), rock is a heterogeneous material whose brittle fracture is a complicated progressive process caused by isolated microstructural changes, known also as dissipative processes. These processes are particularly difficult to predict and model in the compressive field. This paper develops a novel numerical methodology for the simulation of these isolated processes, particularly in compressive fields, such that the resulting non-linear macroscopic behaviour can be predicted.The core of the model is elemental degradation. As suggested by laboratory investigations, the microscopic processes involved in rock fracture can be classified into a combination of brittle and ductile processes. The former cause degradation in both local material elasticity and strength, with the extent of degradation being determined by the degree of bond breakage in forming crack surfaces or the like. The latter, however, lead only to plastic deformation. Thus, when brittle processes dominate the deformation of a material, more degradation occurs than if ductile processes dominate.Elemental degradation is represented by a new parameter termed the degradation index, which is introduced in this research and defined as the ratio of the degradation occurring at a certain confining stress level to the corresponding degradation occurring under uniaxial conditions. In combination with an elasto-plastic constitutive relation, the degradation model yields an elastic–brittle–plastic elemental constitutive behaviour. In the model, failure of an element causes disturbance of the local stress field, which may lead to progressive failure of surrounding elements. An explicit finite difference scheme is used to implement the degradation model.An engineering application of the degradation model to the plane strain analysis of mine pillar behaviour is presented. In terms of isolated fracture processes and the corresponding macroscopic mechanical behaviour, the degradation model produces simulation results that are similar to field observations. That is, the fracture process of a squat pillar begins with the initiation of local failure at random sites, and progresses through extension of these failed sites, coalescence of the extended sites, and slabbing or spalling of the ribsides, until development of large shear fractures ultimately occurs.The results suggest that the degradation model is a powerful approach to the study of macroscopic brittle behaviour encountered in rock mechanics and rock engineering. The application of the degradation model to the simulation of brittle fracture of rock specimens in laboratory compression tests is the subject of a companion paper.     

Prediction of brittle fracture initiating at ends of CJP groove welded joints with defects: study into applicability of failure assessment diagram approach

A series of tests, which reproduced brittle fracture starting from the region around the terminations of complete joint penetration groove welded joints, was conducted. The joint models under study represented a portion of welded beam flange-to-through diaphragm joints in beam-to-column connections. Various artificial weld defects were installed in the welded joints prior to testing. Test results were evaluated based on the failure assessment diagram approach specified in BS 7910. The conventional failure assessment diagrams predicted occurrences of brittle fracture erring on the very conservative side as expected, especially when applied to surface defects. The failure assessment diagram approach was modified by considering the effect of enhanced apparent toughness of material due to the loss of crack tip constraint. The modified failure assessment approach was found to predict the test results well.     

相场断裂模型分步算法在ABAQUS中的实现

 首次基于ABAQUS平台实现相场断裂模型的分步算法,利用UMAT/VUMAT子程序接口对非线性平衡方程进行隐式/显式求解,提出位移场和相场的分步求解算法。准静态加载下的I和II型裂缝扩展问题、冲击荷载作用下的I型动态裂缝分叉和II型动态裂缝扩展问题,计算所得结果与已有文献和试验成果基本一致,说明了方法的可靠性;同时,对岩石力学领域中的双平行翼型裂缝相交和动态裂缝三维曲面扩展等问题,也利用该方法进行模拟。计算实例表明,结构储存的较高弹性应变能是脆性材料动态裂缝分叉的主要原因,而相场断裂模型是一种能够计算包括裂缝起裂、相交、分叉和三维曲面扩展的有效断裂计算方法,借助通用有限元平台可以方便地实现其分步算法。     

混凝土断裂能尺寸效应的修正分形方法

提出了混凝土断裂能尺寸效应的修正分形方法。首先，根据混凝土的断裂特性，认为小尺寸混凝土构件的主宏观裂缝是一条分形曲线，而大尺寸混凝土构件的主宏观裂缝由分形曲线和直线两部分组成。然后，根据能量等价原理，导出了混凝土名义断裂能的计算公式。该公式反映了混凝土实验中所观测到的宏观物理现象，即混凝土名义断裂能随着构件尺寸的增大而增大，而且当构件尺寸趋向无穷大时，名义断裂能趋近于常数。最后，将理论预测与6组混凝土实验进行了比较，从而证实了本文方法的有效性。     

脆性岩石渐进及蠕变失效特性宏细观力学模型研究

压应力作用脆性岩石渐进及蠕变失效特性是其力学性质研究的两个主要研究方向。其对于深部地下开挖围岩稳定性的判断有着重要的指导意义。岩石内部微裂纹扩展对脆性岩石的渐进及蠕变特性有着重要的影响。因此,基于岩石的应力与裂纹扩展关系及裂纹扩张演化法则,并结合宏细观损伤定义之间的关系,提出了一个新的宏细观力学模型,推出了岩石完整的应力–应变关系与蠕变理论表达式。分析了围压对岩石的应力–应变关系的影响。研究了岩石内部初始微裂纹尺寸及裂纹间摩擦系数对应力应变关系及岩石强度的影响。并给出了不同围压下岩石裂纹初始应力与峰值应力,其对蠕变实验中的施加应力初始值选取提供了一定参考。然后,研究了恒定围压、轴压分级加载应力路径下的岩石蠕变应变及应变率变化趋势。通过试验结果验证了理论模型的合理性。进而,对压应力作用下细观裂纹扩展对岩石力学特性影响的理解提供了一定的理论参考。     

Phenomena and theoretical analysis for the failure of brittle rocks

Rockburst, an unstable failure of brittle rocks, has been greatly concerned in rock mechanics and rock engineering for more than 100 years. The current understanding on the mechanical mechanism of rockburst is based on the Coulomb theory, i.e. compressive-shear failure theory. This paper illustrates a series of tensile and tensile-shear fracture phenomena of rockburst, and proposes a methodology for the analysis of fracture mode and its energy dissipation process based on Griffith theory. It is believed that: (1) the fracture modes of rockburst should include compressive-shear, tensile-shear and pure tensile failures; (2) the rupture angle of rock mass decreases with the occurrence of tensile stress; (3) the proportion of kinetic energy in the released strain energy from a rockburst may be much larger than that transferred into surface energy; and (4) the understanding on the tensile and tensile-shear failure modes of rockburst may change the basic thinking of rockburst control, i.e. from keeping the reduction in initial compressive stress σ3 to restricting the creation of secondary tensile stress.     

Estimation of REV size and three-dimensional hydraulic conductivity tensor for a fractured rock mass through a single well packer test and discrete fracture fluid flow modeling

A new methodology is presented to determine the representative elementary volume (REV) size and three-dimensional (3-D) hydraulic conductivity tensor for a fractured rock mass. First, a 3-D stochastic fracture network model was built and validated for a gneissic rock mass based on the fracture data mapped from scanline surveys at the site. This validated fracture network model was combined with the fracture data observed on a borehole to generate a stochastic-deterministic fracture network system in a cubic block around each packer test conducted at a different depth region in the same borehole. Each packer test was simulated numerically applying a developed discrete fracture fluid flow model to estimate the influenced region or effective range for the packer test. A cubic block of size 18 m, with the packer test interval of length about 6.5 m located at the centre of this block, was found to be suitable to represent the influenced region. Using this block size, the average flow rate per unit hydraulic gradient (defined as the transmissivity multiplied by mean width of flow paths) field for fractures was calibrated at different depth regions around the borehole by numerically simulating the packer tests conducted at different depth regions. The average flow rate per unit hydraulic gradient of the fractures that intersect the borehole was considered to be quite different to the average flow rate per unit hydraulic gradient of the fractures that do not intersect the borehole. A relation was developed to quantify the ratio between these two parameters. By studying the directional hydraulic conductivity behaviour of different cubic block sizes having the validated stochastic fracture network and calibrated hydraulic parameters, a REV for the hydraulic behaviour of the rock mass was estimated to be a block size of 15 m. The hydraulic conductivity tensor in 3-D computed through regression analysis using the calculated directional hydraulic conductivity values in many directions was found to be significantly anisotropic. The principal directions of the hydraulic conductivity tensor were found to be agreeable with the existing fracture system of the site. Further, the geometric hydraulic conductivity calculated was found to be comparable to the hydraulic conductivity estimated through the radial flow assumption in continuum porous media.     

Stability assessment of landslide-prone road cut rock slopes in Himalayan terrain:A finite element method based approach

Large-scale slope destabilization could be aggravated due to swift urbanization and ever-rising demands of geoengineering projects such as dams,tunnels,bridges and widening roads.National Highway-58 connects Delhi to Badrinath in India,which passes through complex geomorphological and geological terrain and often encounters cut slopes susceptible to slope failures.In the present investigation,a detailed geotechnical appraisal is conducted along the road cut slopes from Rishikesh to Devprayag in the Himalayas.Twenty vulnerable road cut slopes were demarcated for detailed slope stability analysis using Phase2D finite element modeling simulator.Nonlinear generalized Hoek-Brown(GHB) criterion was adopted for stability analyses.Out of 20 slopes,five slopes(S6,S7,S18,S19 and S20) are unstable with factor of safety(FoS) less than or equal to 1,and thus needs immediate attention.The FoS values of four slopes(S2,S9,S13 and S17) lie between 1 and 1.3,i.e.marginally stable,and slopes S1,S3,S4,S5,S8,S10,Sll,S12,S14,S15 and S16 are stable.Mohr-Coulomb(MC) criterion was also adopted to compare the slope stability analysis with GHB criterion.The FoS calculated from GHB criterion is close to that using MC criterion for lower values of FoS whereas for higher values,the difference is marked.For the jointed rock in the Himalayan region,the nonlinear GHB criterion gives better results as compared to MC criterion and matches with the prevailing field conditions.Accordingly,some suggestions are proposed to strengthen the stability of cut slopes.     

低周反复荷载作用下交错桁架钢结构抗震性能试验研究与分析

进行了1∶8缩尺比例钢结构交错桁架的低周反复荷载试验,深入研究了钢结构交错桁架结构的屈服荷载、最大荷载、极限荷载、滞回曲线、骨架曲线及位移延性和耗能能力等抗震性能。通过建立考虑材料非线性和几何非线性影响的有限元模型对试验模型进行模拟分析,规律方面基本吻合。采用有限元方法分析了不同结构高度、桁架形式、底层桁架落地布置、结构空腹节间距、结构高宽比以及桁架跨高比对钢结构交错桁架结构抗震性能的影响。研究表明:桁架落地混合式交错桁架结构的位移延性系数和能量耗散系数比桁架不落地式的分别高9%和17%;随着结构高度增大,空腹节间距增大、高宽比增大和跨高比的减小,钢结构交错桁架结构的抗震性能均有所降低。最后给出了交错桁架结构相应参数的合理取值范围和设计建议,可供工程设计参考。     

西岙隧道上穿排污隧道设计浅析

紧密结合隧道工程地质和支护设计特点,应用有限元数值分析,并根据爆破安全性评价,为沿海通道甬台温铁路西岙隧道上穿排污隧道的设计方案提供依据。     

Post-failure fracture angle of brittle pipes subjected to differential ground movements

Centrifuge testing of four glass pipe models has been used to measure the kinematics associated with cast iron pipe fracture and the relative rotation of the pipeline on either side of the fracture when fracture is induced by a normal ground fault. The model pipelines were fabricated at 1/30th scale using solid glass rod of semi-circular cross-section. After placing each model against the transparent sidewall of a test box, the pipe was buried and the tested at 30 g. Movements of the soil and the model pipe were monitored using particle image velocimetry, and analysis was used to examine both the curvature distributions before fracture, the fracture pattern (i.e. the fracture locations) expected for cast iron pipes passing across a normal ground fault, and the post-test rotations across the fractures. The depth of soil cover was observed not to make a significant difference to the amount of initial fracture angle for the range of covers investigated in this study (1.125–2.25 m in prototype scale). The fracture angle was shown to be well represented by the slope of the pipe displacements at the inflection point. The use of normalized peak curvature to estimate the fracture angle (rotation across the fracture) was demonstrated. The estimated magnitude of rotation after the pipe breaks can then be used to estimate the local stresses and strains that would develop in a polymer liner inserted within the cast iron pipeline before fracture initiates and which is therefore subjected to longitudinal bending stresses after the cast iron pipe fractures, values of ‘demand‘ that can then be evaluated against measurements of liner strength (i.e. its stress and/or strain limits). The initial angle of rotation directly across the fractures after they form is approximately the same regardless of when the pipe initially breaks, and regardless of the soil cover depth and soil density. However, the magnitude of the vertical ground displacement across the normal fault needed to induce fracture varies considerably for the different burial conditions that were considered, and the rotation angle increases steadily after fracture if the amount of vertical ground displacement continues to grow.