Description:

_Journal of Structural Geology 32 (2010) 1257–1270_ Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com/locate/jsg Why Joints Are More Abundant Than Faults: A Conceptual Model to Estimate Their Ratio in Layered Carbonate Rocks Riccardo Caputo Department of Earth Sciences, University of Ferrara, via Saragat 1, 44100 Ferrara, Italy Article info Article history: Received 29 January 2008 Received in revised form 5 May 2009 Accepted 20 May 2009 Available online 6 June 2009 Keywords: Fractures Brittle deformation Rock mechanics Stress variability Abstract It is a commonplace field observation that extension fractures are more abundant than shear fractures. The questions of how much more abundant, and why, are posed in this paper and qualitative estimates of their ratio within a rock volume are made on the basis of field observations and mechanical considerations. A conceptual model is also proposed to explain the common range of ratios between extension and shear fractures, here called the j f ratio. The model considers three major genetic stress components originated from overburden, pore-fluid pressure, and tectonics and assumes that some of the remote genetic stress components vary with time (i.e., stress-rates are included). Other important assumptions of the numerical model are that: i) the strength of the sub-volumes is randomly attributed following a Weibull probabilistic distribution, ii) all fractures heal after a given time, thus simulating the cementation process, and therefore iii) both extensional jointing and shear fracturing could be recurrent events within the same sub-volume. As a direct consequence of these assumptions, the stress tensor at any point varies continuously in time and these variations are caused by both remote stresses and local stress drops associated with in-situ and neighboring fracturing events. The conceptual model is implemented in a computer program to simulate layered carbonate rock bodies undergoing brittle deformation. The numerical results are obtained by varying the principal parameters, like depth (viz., confining pressure), tensile strength, pore-fluid pressure, and shape of the Weibull distribution function, in a wide range of values, therefore simulating a broad spectrum of possible mechanical and lithological conditions. The quantitative estimates of the j f ratio confirm the general predominance of extensional failure events during brittle deformation in shallow crustal rocks and provide useful insights for better understanding the role played by the different parameters. For example, as a general trend it is observed that the j f ratio is inversely proportional to depth (viz., confining pressure) and directly proportional to pore-fluid pressure, while the stronger is the rock, the wider is the range of depths showing a finite value of the j f ratio and in general the deeper are the conditions where extension fractures can form. Moreover, the wider is the strength variability of rocks (i.e., the lower is the m parameter of the Weibull probabilistic distribution function), the wider is the depth range where both fractures can form providing a finite value of the j f ratio. Natural case studies from different geological and tectonic settings are also used to test the conceptual model and the numerical results showing a good agreement between measured and predicted j f ratios. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction Extension fractures, represented by joints and veins (the latter being mineral-filled joints), appear to be much more abundant than faults. The proportion between the two brittle deformational features mainly depends on the tectonic setting, but in weakly deformed sedimentary terrains, the ratio between the number of extension fractures and the number of faults (here called the j f ratio) is always very high. Why is this? Since this note will focus on brittle tectonic structures as commonly observed by a geologist in the field at the meso-scale, an introduction is provided to the terminology used in this paper. From a mechanical point of view, any interruption of the otherwise continuous properties of a rock mass is a discontinuity. Any discontinuity caused by any stress field is a fracture irrespective of its scale. This distinction is necessary in order to separate, for example, bedding planes from fractures. Any stress field potentially generating a fracture can be visualised by a unique stress tensor. 1258 R. Caputo Journal of Structural Geology 32 (2010) 1257–1270 virtually composed of different genetic components (Caputo, 2005) as discussed in a later section. At the grain scale all fractures involve displacement, either dilation or shear or a combination of the two, though at the scale of observation possible in the field it may not be straightforward to measure the magnitude of the displacement if it is much less than about 1 mm (see discussions in Hancock, 1985; Pollard and Aydin, 1988; Dunne and Hancock, 1994). In this paper, fractures are classified according to the displacement vector, which connects two points contiguous before failure. This vector is partitioned into a component tangential to the fracture plane and a normal one. The ratio between the two or the angle between the displacement vector and the normal to the fracture plane can be a simple and objective parameter to express the type of displacement that occurred and therefore to classify a fracture. Accordingly, if the former component is predominant, we refer to a fault; if the opposite is true, an extension joint; while the intermediate cases are commonly referred to as hybrid fractures (Hancock, 1985; Price and Cosgrove, 1990). In principle, fractures can show all possible values between ‘ideal’ extension joints (a ≈ 0°) and ‘ideal’ faults (a ≈ 90°), but based on more than 20 years of field observations, fractures with an oblique displacement (10° < a < 85°) are the rarest. Also on a theoretical ground, based on a critical review of i) the theoretical aspects of mixed mode ruptures (Lawn, 1993), ii) the results of laboratory experiments and iii) field case studies, Engelder (1999) argued that the transitional-tensile rupture process, which produces planar hybrid fractures, is unlikely to occur in homogeneous isotropic rocks, though it is possible in particular cases of inhomogeneous anisotropic materials. Accordingly, as far as the competition between extensional and shearing fracturing events is here considered from a statistical point of view by analysing large numbers of fractures, hybrid features will be neglected in the following discussion and the associated conceptual model. A mineral-filled fracture is commonly referred to as a vein. For the sake of simplicity, in the following we will simply refer to joints and faults, respectively as extensional and shear fractures, irrespective of the occurrence of healing material whose role is further discussed in a later section. The principal aims of this note are i) to suggest possible causes that facilitate the formation of joints instead of faults, ii) to propose a conceptual model to investigate the evolution of a carbonate rock mass, which frequently represents important reservoirs for water and hydrocarbons, during a distinctive brittle deformational event, considering both extension and shear fractures to be geologically coeval and iii) to understand the role played by the most important mechanical and geological parameters. For the latter aim, numerous computer simulations are performed based on a wide range of values of the input parameters. Although the proposed conceptual and numerical models have been specifically applied to, and tested with, carbonate rocks, showing a good fit between the j f ratio measured in several natural case studies and the numerically predicted values, the general results can be certainly exported to other layered lithologies provided that the proper mechanical parameters are considered. Ключевые слова: laboratory, sedimentary, stress ?eld, laboratory test, tectonophysics, north america, brace, set, diagenetic process, tectonic, cell, soc, rev, curve represent, oxford, pore-?uid pressure, numerical procedure, site condition, shear fracturing, burton, natural material, carbonate, parameter, rock volume, based, conning pressure, subsequent burial, bin size, case study, rock strength, general trend, geological setting, brittle structure, remote stress, component, geologically coeval, eds, deformational event, layered rock, geological, gray symbol, extension fracture, geological aspect, hydrostatic, genetic component, hancock, jointing, pore ?uid, commonly, compressive strength, rupture process, rock mechanic, mech, models cell, fracturing, pore-uid pressure, struct, america, tectonic setting, fracture, peacock, principal parameter, university, study, geological condition, size, figs, extension joint, nal number, pet, carbonate rock, represented, pollard, event, jaeger, role played, host rock, rupture plane, geol, rock, mechanical condition, commonly referred, note, local, earth, york, tensile strength, numerical result, sparry calcite, quantitative estimate, structural, simulation, tectonic component, shaded area, variability, fracture mechanics, stress variability, failure condition, pore ?uid pressure, principal, greece, shear plane, physical property, ratio, failure, stratigraphic setting, le, geology, conceptual, fracture porosity, process, fracture plane, mechanism, bull, ann, range, mass, conceptual model, bed thickness, mechanical, numerical model, numerical, volume, wide range, basin, outcrop, deformation, stress, maximum overburden, extensional, mpa, press, struct geol, appl, joint, geological parameter, engelder, weibull distribution, mechanics, setting, depth, wa, fracturing event, atkinson, price, burial, mechanical property, result, upper threshold, rock mech, ha, brittle fracture, rock mass, function, mechanical consideration, formation, rst approximation, exposed area, weibull, crack-jump mechanism, pressure, numerical simulation, cementation process, brittle, layer, nova, shallow condition, tensile, pore-?uid, scale, failure event, eng, ?uid, high, layered, zoback, journal structural, differential stress, material, london, fracture pattern, laboratory experiment, number, cosgrove, order, young modulus, point, caputo, healing material, large variability, pore, fracture spacing, displacement vector, ?uid pressure, abnormal, sci, assoc, model, case, bosellini, crack-seal mechanism, stress tensor, gross, genetic, structural geology, randomly assigned, engineering, considered, mechanical parameter, strength, local stress, elsevier, brittle behaviour, depth interval, time, brittle deformation, plane, fault, journal, uid pressure, shear fracture, ii, agreement, condition, tectonicae, extension, initiation propagation, approach, deformational, sedimentary rock, ?eld, distribution, overlying rock