JF3 (v. 2.0): a programme for quantitative estimates of the joints to faults ratio.

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-ates 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 neighbouring 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.