Modeling three‐dimensional hydraulic fracture propagation using virtual multidimensional internal bonds

Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.     

The role of eddies in solute transport and recovery in rock fractures: Implication for groundwater remediation

A better understanding of solute transport and retention mechanism in rock fractures has been challenging due to difficulty in their direct observations in microscale rough‐walled fractures. Six representative troughs in a rough‐walled fracture were selected for microscale observations of eddy formation with increasing flow velocity and its effect on spatiotemporal changes of solute concentration. This experimental study was enabled by a microscale visualization technique of micro particle image velocimetry. With increasing flow velocity (Re ≤ 2.86), no eddies were generated, and solutes along the main streamlines transported rapidly, whereas those near the wall moved slowly. A larger amount of solutes remained trapped at all troughs at Re = 2.86 than Re < 1. For Re = 8.57, weak eddies started to be developed at the troughs on the lee side, which little contributed to overall solute flushing in the fracture. Accordingly, a large of amount of water was needed for solute flushing. The flow condition of 1 < Re < 10, before a full development of eddies, was least favourable in terms of time and amount of remediation fluid required to reach a target concentration. After large eddies were fully developed at troughs on the lee side for Re = 17.13, solutes were substantially reduced by eddies with less amount of water. Fully developed eddies were found to enhance solute transport and recovery, as opposed to a general consensus that eddies trap and delay solutes. Direct inflow into troughs on the stoss side also made a great contribution to solute flushing out of the troughs. This study indicates that fully developed eddies or strong inflows at troughs are highly possible to form for Re > 10 and this flow range could be favourable for efficient remediation.     

上海及其邻区潜在地质灾害的构造背景与成因机理

本文基于上海及其邻区活动断裂构造及有关地区潜在地质灾害特点的研究,论证了上海及其邻区潜在地质灾害的三种基本类型及其构造背景与成因机理;指出:上海及其邻区楔形断裂系统的存在与活动是诱发有关地区潜在地质灾害的主导因素。文中明确指出了上海及其邻区楔形断裂系统的研究在相关地区进行潜在地质灾害评价与预测方面的应用前景与发展方向。     

An empirical approach to estimating population parameters from censored fracture-length distributions

Most fracture data sets are length-censored because of incomplete exposure at the surface, so estimating values of parameters of the sampled populations is difficult. Unless the form of the distribution function of the population is known, or one which is analytically tractable is assumed, length-censoring presents formidable problems in determining population parameters. Tests conducted on experimental fracture patterns developed in clay samples subjected to simple shear loading are the basis of a distribution-free way to estimate population parameters. Comparison of random samples of censored and uncensored fracture lengths shows that a useful, homogeneous data set consists of those cracks which lie entirely within the sampling area (two-ended cracks). The properties of this data set can be used to estimate the mean and variance of uncensored data. Estimates of the maximum fracture length of uncensored data, using the variance and maximum length of these two-ended cracks, show good agreement with measured values. Knowledge of the mean, variance, and maximum value of fracture-length populations are of interest in engineering and hydraulic studies, as well as in remote sensing studies of the Earth and other planets. Application of these results to data on rock masses are subject to the caveat that different crack-growth mechanisms in clay and rock may affect the accuracy of the calculations.     

渤海陆缘地震的力学特征和成因

渤海陆缘是华北强震活动区,如1966年的邢台震群,1967年的河间地震,1969年的渤海地震,1975年的海城地震,1976年的唐山震群和1983年的菏泽地震,都是在该区发生的。显然,深入研究该地区的构造运动和地震成因是有重要科学意义的。本文拟从应力场角度进行研究。     

Fractal reconstruction of sea-floor topography

Sea-floor bathymetric profiles exhibit features at many different scales of length; this suggests that they could be described as fractals. An algorithm interpolating a fractal line between points has been used to reconstruct bathymetric profiles from a few data points. In general, this fractal line has the same Fourier amplitude spectrum as real bathymetry, and, if the parameters of the interpolation are suitably chosen, it has a very similar appearance. The success of this fractal reconstruction algorithm for the sea-floor raises the possibility that it could be used to extrapolate, from data collected at one scale, the properties of the sea-floor at finer scales, and that similar techniques could be used to interpolate a surface between bathymetric profiles. The fractal character is a sign that the processes that shape the sea-floor are scale invariant and suggests that the renormalization group technique could be used to model these processes.     

岩石压剪性断裂特性及Ⅰ—Ⅱ型复合断裂判据

本文系统阐述了岩石压剪性断裂的特性,认为金属断裂力学复合断裂判据基本上不适用于压剪状态下的岩石斯裂;在此基础上,提出了新的岩石压剪性断裂判据:2COSθ_0/2(cosθ_0-1)[(1+1/f~2)~(1/2)-1]K_Ⅰ+[(sin θ_0/2-3sin 3θ_0/2)(1+1/f~2)~1/2+4sin θ_0/2]K_Ⅱ=4K_(Ⅰc),推导了起始断裂角ψ_0,说明了实验验证结果,指出了该判据在工程地质领域中的应用途径。     

破裂系分形研究进展

介绍了破裂系从宏观到微观破裂均具有分形结构，在此基础上，利用破裂系分维定量表征破裂系发育的各种向异性；研究了影响破裂系数分维的结构参娄，对破裂系进行了解析，并且将分维用于地壳稳定性和地震活动性研究，取得了很好的效果；分析了目前破裂系分开研究中存在的一些问题，展望一其研究趋势。     

福建省推覆构造研究及其意义

本文主要是根据“闽西南地区推覆构造与隐伏煤田预测研究”的主要成果来写的。在概述两次研究课题取得主要成果的同时，对福建省重大基础地质有关的问题提出了新的认识。文中重点是总结了福建省推覆构造发育的特征，将推覆构造划分为两大类（逆冲推覆构造，拆离构造）和五种类型（中深层次逆冲推覆构造、浅层次逆冲推覆构造、褶皱逆冲推覆构造和拆离（滑脱）构造、褶皱拆离构造），对各类型的主要特征、分布规律、组合特征和推覆构造的发生和发展进行系统的总结，明确指出了燕山早期中深层次边冲推覆构造是福建省规模最大、对今后寻找隐伏矿产关系最密切和最重要的推覆构造，对研究我省的推覆构造具有重要意义。并结合福建省的实际，从基础地质和找矿两方面进行论述。     

Dynamic faulting under rate-dependent friction

We discuss the effects of rate-dependent friction on the propagation of seismic rupture on active faults. Several physicists using Burridge and Knopoff's box and spring model of faulting have proposed that fault complexity may arise from the spontaneous development of a self-similar stress distribution on the fault plane. If this model proves to be correct, it has important consequences for the origin of the complexity of seismic sources. In order to test these ideas on a more realistic earthquake model, we developed a new boundary integral equation method for studying rupture propagation along an antiplane fault in the presence of nonlinear rate-dependent friction. We study rupture dynamics of models with single and twin asperities. In our models, asperities are places on the fault with a higher value of prestress. Othewise all fault parameters are homogeneous. We show that for models with such asperities, a slip velocity weakening friction leads to the propagation of supersonic healing phases and to the spontaneous arrest of fracture if the prestress outside the asperities is low enough. For models with asperities, we can also observe narrow slip velocity pulses, qualitatively similar to the so-called Heaton pulses observed in some earthquake accelerograms. We also observe a complex distribution of stress after the rupture that depends on details of the initial distribution of asperities and on the details of the friction law.