Abstract - Opening-mode fractures in mechanically layered materials, such as sedimentary rock sequences or laminates, are often best, or exclusively, developed in the more brittle layers. Fieldwork on joints in layered rocks and physical experiments on laminates have revealed that the fracture spacing scales with layer thickness. A wide variety of mechanisms for the origin of layer-confined opening-mode fractures and their scaling relation have been suggested. In the present study we exclusively focus on one of the most common mechanisms, namely fracturing due to an applied layer-parallel extension under constant layer normal stress. Experimental work has revealed that under these circumstances fracture spacing decreases approximately as the inverse of the applied layer-parallel extension by fractures forming in-between existing fractures, a process referred to as sequential infilling. Eventually no further infill fractures form, irrespective of any further increase in applied extension, a condition called fracture saturation.
The evolution of fracturing in single layers with welded and/or frictional interfaces under extension is often predicted using 1-D approximations which are centred on the transfer of tensile stress from the matrix to the layer by means of interfacial shear stresses, commonly referred to as shear lag models. If interfacial slip is allowed then in the limit, i.e. when the entire interface is sliding, these 1-D approximations predict that the maximum fracture spacing to layer thickness ratio at saturation is equal to the ratio of layer tensile strength to interface shear strength.
The above-described 1-D approximations, however, were criticised in the past: First, for welded interfaces they predict zero joint spacing at large strain, i.e. the joint spacing decreases with increasing strain ad infinitum. Second they cannot predict the details of the 2-D stress distribution within the fracture bound blocks because they are 1-D approximations for which certain assumptions in terms of stress variations have to be made. 2-D continuum models (e.g. FEM) consisting of fractured layers embedded in an elastic matrix, however, have revealed that at a fracture spacing to layer thickness ratio of ~1.0 a through-going central belt of layer-parallel compressive normal stress develops in-between the fractures. This compressive stress is interpreted to inhibit further fracture growth and is hence used as an explanation for joint saturation.
In order to test these contrasting theories for joint spacing and saturation in single layers we performed a suite of discontinuum numerical models which permit simulation of the growth of fractures and associated interfacial, or bedding parallel, slip. The models demonstrate that the validity and consequent applicability of the 1-D shear-lag models depends on the ratio of layer tensile strength to interface shear strength. High ratios (ca. >3.0 in our models) promote interfacial slip and yield results that, in terms of fracturing and interfacial slip evolution, provide an excellent fit to a 1-D shear lag model. At lower strength ratios, however, interfacial slip is suppressed and the heterogeneous 2-D stress distribution within fracture-bound blocks controls further fracture nucleation. Two mechanisms are identified that lead to fracture spacing not predicted by 1-D models: (i) Curved fractures adjacent to exiting straight fractures and (ii) infill fractures which propagate through fracture bound blocks even though the layer-parallel normal stress in the centre is compressive. Our models provide a rationale for the wide range of joint spacing observed in nature and clearly demonstrate that joint spacing is not an indicator of joint system maturity, e.g. saturation, as has been previously suggested.
Abstract of talk presented at:
Tectonomechanics Colloquium: Mechanics of Faulting and Fault-Zone Processes, Salzburg, Austria, May 2010.