Evolution of fluid pressure and fracture propagation during contact metamorphism

Abstract Rock fracture enhances permeability and provides pathways through which fluids migrate. During contact metamorphism, fluids contained in isolated pores and fractures expand in response to temperature increases caused by the dissipation of heat from magmas. Heat transport calculations and thermomechanical properties of water-rich fluids demonstrate (1) that thermal energy is a viable mechanism to produce and maintain pore fluid pressure (P_f) in a contact metamorphic aureole; (2) that the magnitude of P_f generated is sufficient to propagate fractures during the prograde thermal history (cause hydrofracture) and enhance permeability; and (3) that P_f-driven fracture propagation is episodic with time-scales ranging from years to thousands of years. Because P_f dissipation is orders of magnitude faster than P, _f buildup, P_f oscillations and cyclical behaviour are generated as thermal heating continues. The P_f cycle amplitude depends on the initial fracture length, geometry and the rock's resistance to failure whereas the frequency of fracture depends on the rate of heating. Consequently, oscillation frequency also varies spatially with distance from the heat source. Time series of fluid pressures caused by this process suggest that cyclical fracture events are restricted to an early time period of the prograde thermal event near the intrusive contact. In the far field, however, individual fracture events have a lower frequency but continue to occur over a longer time interval. Numerous fracture cycles are possible within a single thermal event. This provides a provisional explanation for multiple generations of veins observed in outcrop. P _f cycling and oscillations may explain several petrological features. If pore fluids are trapped at various positions along a pressure cycle, the large amplitude of P_f variations for small fractures may account for different pressures recorded by fluid inclusions analysed from a single sample. P_f oscillations, during a single thermal episode, also drive chemical reactions which can produce complex mineral textures and assemblages for discontinuous reactions and/or zoning patterns for continuous reactions. These can mimic polymetamorphic or disequilibrium features. Temporal aspects of fracture propagation and permeability enhancement also constrain the likely timing of fluid flow and fluid-mineral interactions. These data suggest that fluid flow and fluid-mineral reactions are likely to be restricted to an early period in the prograde thermal history, characterized by high P_f coincident with relatively high temperatures, fracture propagation and consequent increases in permeability. This early prograde hydration event is followed by diffusional peak metamorphic reactions. This relationship is evident in the complex mineralogical textures common in some metamorphosed rocks.     

Effect of rock discontinuities on certain rock strength and fracture energy parameters under uniaxial compression

Summary Five series of test blocks of Pendeli marble with artificially created discontinuities of different crack densities (simulating three mutually orthogonal joint sets) were tested in uniaxial compression in order to study the effect of discontinuities on: (a) the compressive strength and the modulus of elasticity, and (b) certain fracture energy parameters expressed by the ratio W _A/W _V, where W _A is the surface energy and W _V the volume elastic strain energy. Mathematical relationships are derived similar to those suggested by other authors relating strength parameters to crack densities. Such relationships clearly show a reduction in strength with increased crack density. The experimental results obtained permit the extension of Persson's relation (which refers to ideal intact rock) to the more realistic case of discontinuous rock mass by introducing the appropriate term that takes into consideration the effect of rock mass discontinuities on the energy ratio W _A/W _V. A comparison between laboratory results and field observations was subsequently carried out assuming the rock mass to behave as a linearly elastic material, obeying the Hoek and Brown failure criterion. This comparison showed that laboratory results can be extended to larger scale. Furthermore, in order to predict the in situ strength and stability of a rock mass in uniaxial compression (which is of major importance in underground excavations) certain concepts are proposed based on laboratory tests, in situ investigations and first principles of linear elastic fracture mechanics.     

地下空间逾渗与裂缝属性的关系分析

裂缝连通性评价是地下空间研究的重要内容。逾渗分析是研究裂缝网络连通性的一种有效手段。裂缝网络逾渗临界值多使用裂缝间接表征参数(如分形维数)来确定,但存在裂缝网络连通性不同却有相同间接表征参数的情况,这降低了预测的可靠性。为避免此类问题并更加准确快速地表征裂缝网络的连通性,文章在构建逾渗临界值方程时,摒弃了间接参数简化的方式,使用裂缝直接表征参数(如裂缝数量、长度等)进行非线性拟合。通过二维数值模拟建立不同参数的离散裂缝网络模型,分析逾渗低、中、高概率临界条件与裂缝直接表征参数的关系,建立逾渗临界条件预测方程,并对方程在不同尺度研究区的应用进行了讨论和验证。结果表明：预测方程可有效地预测不同概率的逾渗临界值。同时文章在预测方程的基础上,建立了裂缝网络连通性评价标准,这对于裂缝发育地区的地下空间评价工作具有一定的指导和借鉴意义。     

3D numerical modelling of bit–rock fracture mechanisms in percussive drilling with a multiple‐button bit

This paper considers numerical modelling of rock fracture induced by dynamic bit–rock interaction in percussive drilling. The work presented here extends the author's earlier research on the topic from the axisymmetric case to 3D case. The numerical method for modelling rock fracture includes a constitutive model for rock and a contact mechanics‐based technique to simulate the bit–rock interaction. The constitutive model is based on a combination of the recent viscoplastic consistency model, the isotropic damage concept and a parabolic compression cap. This model is improved here from its earlier state by calibrating the softening laws using fracture energies G_Ic and G_IIc in tension and compression, respectively. Moreover, the viscosity modulus in tension is calibrated based on the dynamic Brazilian disc test. With these enhancements, the developed method is applied to 3D case of the bit–rock interaction problem assuming one symmetry plane. Single impact with single and multiple‐button bits is simulated. In the latter case, an initial borehole is modelled in order to simulate the usual in‐situ drilling conditions. The different failure types observed in the experiments as well as the interaction between the buttons resulting in chipping are realistically captured in the simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

裂隙岩体渗流概念模型研究

裂隙岩体中的渗流和传统的多孔介质渗流在机理上存在本质的差别,这种差别主要表现为裂隙岩体在各种尺度上存在的非均质性。模拟裂隙岩体渗流的主要困难在于描述这种非均质性。目前的概念模型,包括等效连续体模型、离散裂隙网络模型和混合模型使用了不同的技术来预测裂隙岩体中的渗流。这些模型基于不同的假设和概念框架,有着各自不同的优缺点。在实际应用时,应当根据研究域的具体特点和所要解决的问题的要求对其选择,此外,还讨论了单裂隙的概念模型。     

A model for crack connectivity in rocks, a discussion

We reanalyzed a model introduced by T. R. Madden for the evaluation of the state of connectivity among the microcrack population existing inside crystalline rocks. The model assumes that cracks are distributed randomly in a cubic lattice with a basic occupation probability, p.Depending on the value of p, the stale of connectivity can give rise to macroscopic paths, which allow electrical conduction of the sample, or to extended crack surfaces, which would be responsible for rock failure. The position of the phase boundaries, that is, the threshold values of pfor the onset of conductivity or macroscopic fracture, are estimated by a real-space renormalizalion-group (RG) technique. By identifying all the relevant configurations of the lattice model, we have been able to provide explicit analytic formulae for the critical lines. The criterion used by Madden to accept the existence of microscopic linear connectivity is modified and the new consequences discussed. We analyze the limitations of simple versions of the RG technique, in particular when concerned with anisotropic spatial distributions of cracks. Finally, we emphasize the interest of acquiring experimental data, especially to test the position of the conduction thresholds.     

基于离散裂隙网络模型的节理岩体渗透张量及特性分析

节理岩体几何结构非常复杂,研究其渗流特性对于指导含水岩层稳定性分析具有重要价值。应用离散裂隙网络模型DFN方法,基于VC++6.0软件平台,建立了平面渗流分析方法,分析了节理岩体不同几何分布情况下的渗透率张量特征,通过定义渗流定向性系数对岩体渗流的定向性特征进行了定量分析。结果表明：单组节理岩体渗流具有明显的各向异性特征,渗流定向性随着节理角度变化显著;节理随着节理贯通性增加,节理渗透率呈现对数增加趋势;两组节理情况下,各向异性特征随着节理组间夹角变化;两组节理岩体渗流特征研究中,正交分布下,岩体仍存在各向异性,但渗流定向性系数较低;当节理倾角服从正态分布时,随着节理倾角标准差增大,渗透率增加;两组节理夹角不同时,节理渗透主方向倾角随着夹角增大而相应增大,基本沿两组节理夹角方向的角平分线方向。     

Quantification of Aperture and Relations Between Aperture,Normal Stress and Fluid Flow for Natural Single Rock Fractures

Accurate quantification of rock fracture aperture is important in investigating hydro-mechanical properties of rock fractures. Liquefied wood’s metal was used successfully to determine the spatial distribution of aperture with normal stress for natural single rock fractures. A modified 3D box counting method is developed and applied to quantify the spatial variation of rock fracture aperture with normal stress. New functional relations are developed for the following list: (a) Aperture fractal dimension versus effective normal stress; (b) Aperture fractal dimension versus mean aperture; (c) Fluid flow rate per unit hydraulic gradient per unit width versus mean aperture; (d) Fluid flow rate per unit hydraulic gradient per unit width versus aperture fractal dimension. The aperture fractal dimension was found to be a better parameter than mean aperture to correlate to fluid flow rate of natural single rock fractures. A highly refined variogram technique is used to investigate possible existence of aperture anisotropy. It was observed that the scale dependent fractal parameter, K _v, plays a more prominent role than the fractal dimension, D _a1d, on determining the anisotropy pattern of aperture data. A combined factor that represents both D _a1d and K _v, D _a1d × K _v, is suggested to capture the aperture anisotropy.     

离散裂隙渗流方法与裂隙化渗透介质建模

流体渗流模拟的连续介质方法通常适用于多孔地质体，并不一定适用于裂隙岩体，由于裂隙分布及其特征与孔隙差异较大。若流体渗流主要受裂隙的控制，对于一定尺寸的裂隙岩体，多孔介质假设则较难刻划裂隙岩体的渗流特征。离散裂隙渗流方法不但可直接用于模拟裂隙岩体非均质性和各向异性等渗流特征，而且可用其确定所研究的裂隙岩体典型单元体及其水力传导（渗透）张量大小。主要讨论了以下问题：（1）饱和裂隙介质中一般的离散流体渗流模拟；（2）裂隙岩体中的REV（典型单元体）及其水力传导（渗透）张量的确定；（3）利用离散裂隙网络流体渗流模型研究裂隙方向几何参数对水力传导系数和REV的影响；（4）在二维和三维离散裂隙流体渗流模型中对区域大裂隙和局部小裂隙的处理方法。调查结果显示离散裂隙流体渗流数学模型可用来评价不同尺度上的裂隙岩体的水力特征，以及裂隙方向对裂隙化岩体的水力特征有着不可忽视的影响。同时，局部小裂隙、区域大裂隙应当区别对待，以便据其所起的作用及水力特征，建立裂隙化岩体相应的流体渗流模型。     

基于离散裂隙网络模型的裂隙水渗流计算

离散裂隙网络模型(Discrete Fracture Network（DFN）)是研究裂隙水渗流最为有效的手段之一。文章根据裂隙几何参数和水力参数的统计分布,利用Monte Carlo随机模拟技术生成二维裂隙网络,基于图论无向图的邻接矩阵判断裂隙网络的连通,利用递归算法提取出裂隙网络的主干网或优势流路径。基于立方定律和渗流连续性方程,利用数值解析法建立了二维裂隙网络渗流模型,分析不同边界条件下裂隙网络中的流体流动。结果表明,该方法可以模拟区域宏观水力梯度和边界条件下,裂隙网络水力梯度方向总的流量,以及节点的水位、节点间的流量和流动方向的变化特征,为区域岩溶裂隙水渗流计算提供了一种实用、可行的方法。      

Three-dimensional discrete element simulation of indirect tensile behaviour of a transversely isotropic rock

This paper presents the development of a three-dimensional discrete element model using flat-joint and smooth-joint contact models to investigate the effect of anisotropy on the tensile behaviour of slate, a transversely isotropic rock, under Brazilian testing from both macro and microscales. The effect of anisotropy is further realised by exploring the influence of foliation orientations (β and ψ) on the tensile strength, fracture pattern, microcracking and stress distribution of the transversely isotropic rock. The variation of tensile strength with foliation orientation is presented. The cross-weak-plane fracture growth observed in laboratory is reproduced, and the criterion for which to form is also given from the aspect of foliation orientation. Furthermore, the proportional variations of microcracks well account for the effects of foliation orientation on the tensile strength and failure pattern. Finally, it is found that the existence of weak planes increases both the heterogeneity and the anisotropy of stress distributions within the transversely isotropic rock, with the degree of influence varying with the foliation orientation.     

Discrete element modeling of tool‐rock interaction I: rock cutting

Tool‐rock interaction processes can be classified as indentation or cutting depending on the direction of motion of the tool with respect to the rock surface. The modes of failure induced in the rock by an indenting or a cutting tool can be ductile and/or brittle. The ductile mode is associated with the development of a damage zone, whereas the brittle mode involves the growth of macrocracks. This is the first part of a series of two papers concerned with an analysis of the cutting and the indentation processes based on using the discrete element method. In this paper, numerical simulations of the cutting process are conducted to reproduce the transition from a ductile to a brittle failure mode with increasing depth of cut, which is observed in experiments. The numerical results provide evidence that the critical depth of cut d _* controlling the failure mode transition is related to the characteristic length ? = (K_Ic ∕ σ_c)² with K_Ic denoting the material toughness and σ_c its unconfined compressive strength. The nature of frictional contact between the cutter face and the rock in the ductile failure mode is also examined. It is shown that the inclination of the total cutting force is controlled by a multi‐directional flow mechanism ahead of the cutter that is related to the formation of a wedge of failed material, intermittently adhering to the cutter. As a result, the inclination of the total cutting force varies with the rake angle of the cutter and cannot be considered an intrinsic measure of the interfacial friction between the cutter and the rock. Copyright © 2012 John Wiley & Sons, Ltd.     

Stochastic continuum modeling of flow and transport in a crystalline rock mass: Fanay-Augères,France, revisited

A stochastic discrete-fracture model was used by Cacas et al.^a,b to interpret flow measurements and transport experiments in a fractured crystalline rock mass at Fanay-Augères. They considered continuum models to be incapable of properly interpreting small-scale measurements or tracer tests in fractured systems, which, in their view, require three-dimensional modeling of numerous discrete channels; in their opinion, continuum modeling applies only to average flow on a relatively large scale. Cacas et al. considered their discrete fracture model to have been validated by its demonstrated ability to reproduce selected experimental results. In this paper, flow and transport at Fanay-Augères are modeled by viewing the fractured rock as a stochastic continuum in a manner originally proposed by Neuman^c,d. The stochastic continuum approach obviates the need for detailed information about fracture geometry or assumptions about how individual fractures control flow and transport. All it requires is the delineation of a few dominant features, which can be embedded into the stochastic continuum model as heterogeneous porous slabs. Though a fault zone has been identified at the Fanay-Augères experimental site, it has been modeled neither by Cacas et al. nor in this paper. In fact, in this paper, a larger selection of experimental results than those considered by Cacas et al. are reproduced merely by modeling the rock as a statistically homogeneous continuum in two dimensions. These results demonstrate that a continuum approach may be well suited for the analysis of flow and transport in fractured rock. This does not constitute a validation of the continuum approach, just as the results of Cacas et al. fall short of validating the discrete fracture approach. Instead, the two sets of results illustrate jointly the well-established principle that an open system, especially one as complex as fractured hydrogeologic environments tend to be, cannot be described uniquely on the basis of sparse data and need not be described in great detail to capture its salient behavior by a model.^a Cacas MC, Ledoux E, de Marsily G, Barbreau A, Calmels P, Gaillard B, Margritta R (1990a) Modelling fracture flow with a stochastic discrete fracture network: calibration and validation. 1. The flow model. Water Resour Res 26(3):479–489^b Cacas MC, Ledoux E, de Marsily G, Barbreau A, Calmels P, Gaillard B, Margritta R (1990b) Modelling fracture flow with a stochastic discrete fracture network: calibration and validation. 2. The transport model. Water Resour Res 26(3):491–500^c Neuman SP (1987) Stochastic continuum representation of fractured rock permeability as an alternative to the REV and fracture network concepts, in Rock Mechanics. In: Farmer IW, Daemen JJK, Desai CS, Glass CE, Neuman SP (eds) Proceedings of the 28th U.S. Symposium, Tucson, Arizona. Balkema, Rotterdam, pp 533–561^d Neuman SP (1988) A proposed conceptual framework and methodology for investigating flow and transport in Swedish crystalline rocks. SKB Swedish Nuclear Fuel and Waste Management Co., Stockholm, September, Arbetsrapport 88–37, 39 pp     

川西顺层斜坡破坏模式及层间弱面连通率对斜坡稳定性的影响

顺层岩质斜坡是沉积岩地区常见的一种斜坡类型,也是各种工程建设重点关注的一类斜坡。以川西雅安地区典型的顺层岩质斜坡为例,采用现场调查、无人机测绘、钻探、物探和稳定性计算等技术方法,归纳总结目前斜坡存在的变形破坏模式。分析计算斜坡在不同工况条件下,层间破碎带连通率与斜坡稳定性之间的关系。研究结果表明:层间破碎带对斜坡稳定性具有重要的影响或控制作用,当斜坡浅表部强风化岩体内层间破碎带连通率小于86%时,斜坡稳定性与现状调查结果吻合。研究结果对川西地区基础设施规划建设和防灾减灾具有重要的工程意义。     

The stability of merwinite in the system CaO-MgO-SiO2-H2O-CO2 with CO2-poor fluids

The stability of merwinite (Mw) and its equivalent assemblages, akermanite (Ak)+calcite (Cc), diopside (Di)+calcite, and wollastonite (Wo)+monticellite (Mc)+calcite was determined at T=500–900° C and P _f=0.5–2.0 kbar under H₂O–CO₂ fluid conditions with X _{CO 2}=0.5, 0.1, 0.05, and 0.02. Merwinite is stable at P _f=0.5 kbar with T>700° C and X _{CO 2}<0.1. At P _f=2.0 kbar, the assemblage Di+Cc replaces merwinite at all T and X _{CO 2} conditions. At intermediate P _f=1 kbar, the assemblage Ak+Cc is stable above 707° C and Wo+Mc+Cc is stable below 707° C. The univariant curve for the reaction Di+Cc=Wo+Mc+CO₂ is almost parallel to the T axis and shifts to low P _f with increasing X _{CO 2}, with the assemblage Di+Cc on the high-P _f side. The implications of the experimental results in regard to contact metamorphism of limestone are discussed using the aureole at Crestmore, California as an example.     

Coupled Hydro-mechanical Processes Associated with Multiphase Flow in a Dual-continuum System: Formulations and an Application

Fractured rock has often been conceptualized as a dual-continuum system for many practical applications. This study proposes a systematic approach to deal with multiphase flow in a dual-continuum system. Considering that fluid flow occurs in pore volumes (including fracture apertures), we first develop a so-called pore-space conservation equation for deformed fractured rock and then combine this equation with fluid mass balance to derive governing equations for multiphase flow associated with rock deformation. Constitutive relationships are also presented for describing stress dependence of hydraulic properties and effective mechanical parameters for bulk rock body (as a function of the corresponding parameters for fracture and matrix continua). Finally, we applied the developed approach to a CO₂ geological sequestration problem to demonstrate the usefulness of the approach.     

Fracture corridors as seal-bypass systems in siliciclastic reservoir-cap rock successions: Field-based insights from the Jurassic Entrada Formation (SE Utah,USA)

Closely spaced, sub-parallel fracture networks contained within localized tabular zones that are fracture corridors may compromise top seal integrity and form pathways for vertical fluid flow between reservoirs at different stratigraphic levels. This geometry is exemplified by fracture corridors found in outcrops of the Jurassic Entrada Formation in Utah (USA). These fracture corridors exhibit discolored (bleached) zones, interpreted as evidence of ancient fracture-enhanced circulation of reducing fluids within an exhumed siliciclastic reservoir-cap rock succession. Extensive structural and stratigraphic mapping and logging provided fracture data for analysis with respect to their occurrence and relationships to larger faults and folds. Three types of fracture corridors, representing end-members of a continuum of possibly interrelated structures were identified: 1) fault damage zone including segment relays; 2) fault-tip process zone; and 3) fold-related crestal-zone fracture corridors. The three types exhibit intrinsic orientations and patterns, which in sum define a local- to regional network of inferred vertical and lateral, high-permeability conduits. The results from our analysis may provide improved basis for the evaluation of trap integrity and flow paths across the reservoir-cap rock interface, applicable to both CO₂ storage operations and the hydrocarbon industry.     

Calculated stabilities of sodic phases in the Sambagawa metapelites and their implications

Pressure (P)–temperature (T) pseudosection analyses were carried out on metapelites from Sambagawa belt by using Perple_X 07 so as to determine mineral equilibria and the stability of sodic phases, in the model system MnO–Na₂O–K₂O–CaO–FeO–MgO–Al₂O₃–SiO₂–H₂O–(CO₂) under high‐pressure (HP) conditions (0.5–2.5 GPa/400–600 °C). A pressure–X_NA [=Na/(Na+Al–2K–1.5Ca)] pseudosection at 500 °C is also calculated to examine the effect of Na/Al value of the bulk‐rock composition on the stabilities of sodic minerals. The bulk‐rock compositions of Sambagawa metapelite are variable in X_NA values. The calculation results of stable assemblages in metapelites under the blueschist and eclogite facies conditions indicate that: (i) paragonite and glaucophane are stable throughout the wide X_NA range of bulk‐rock compositions of host rocks; (ii) stable P–T conditions of sodic pyroxene enlarge with increasing X_NA value; and (iii) the stability field of paragonite enlarges with the presence of CO₂ in the metamorphic fluid. The suggested wide stability of paragonite in metapelites and the relationships between the stability of sodic pyroxene and the bulk‐rock compositions explain the reasons why (i) the occurrence of omphacite in metapelites from several subduction‐related terranes is rare; and (ii) paragonite commonly occurs as inclusions in garnet of metapelites from the Besshi region of the Sambagawa belt. Paragonite is an important sodic phase of HP metapelites, and a combination of paragonite and quartz with high residual pressure included in garnet may be a useful indicator to verify the evidence for the eclogite facies metamorphism recorded in metapelites.     

裂隙岩体等效力学参数结构效应的计算机模拟试验研究

为研究裂隙岩体结构效应对其等效力学参数的影响,引入基于离散元的合成岩体技术,通过可控的改变三维岩体结构网络中的结构参数,制作相应的合成岩体试件,开展计算机模拟试验研究。结果表明：随岩体中裂隙体积密度增大,裂隙的变形参数和强度参数随裂隙密度增加而减少,其中等效弹性模量对结构面密度变化最为敏感;随岩体中裂隙倾角增加,岩体等效弹性模量随之单调增加,且等效弹性模量的离散程度（标准差）随倾角增加而减小,而各强度参数指标则先减少而后增加,形成一个U形变化规律;岩体等效力学参数均随结构面尺寸增加而减小,同时等效力学参数的离散程度（标准差）随结构面直径增加而增加,其中单轴抗压强度指标变化最为敏感;岩体等效力学参数对裂隙尺寸和产状的离散程度不敏感。该研究结论可为其他结构效应研究提供一种新思路。