Evidence for a critically stressed upper crust
David J Sanderson, Department of Earth Science and Engineering, Imperial College London, Exhibition Road, London SW7 2AZ.
david.sanderson@ic.ac.uk.
Recent work by Barton et al (1995) has demonstrated that, in fractured crystalline rocks that typify much of the upper crust, fluid flow is largely controlled by fractures that are optimally oriented in relation to the in situ stress state (critically stressed fractures). A critically stressed crust accounts for the widespread occurrence of earthquakes and their repetition on the same fault segments. It also explains the ease of inducing earthquakes by small increases in fluid pressure (from fluid injection, filling of surface reservoirs, etc.) or through perturbation of stresses by engineering activities (such as sub-surface excavation and hydrocarbon production).
This paper will examine the role of critically stressed fractures using numerical (discrete element) models of fractured rock, and discuss the main controls of the critical stress state (including fracture geometry, density, frictional properties and rock rheology). A common feature of a critically stressed fracture network is the localized nature of the fluid flow, often with enhanced overall permeability of the rock mass (Sanderson & Zhang 1999). Localized flow is common in the upper crust and can be regarded as evidence for it being critically stressed.
The critical stress state has been evaluated for different loading paths and is found to be largely controlled by a simple parameter, the driving stress ratio (R), where
R = 2 (fluid pressure – mean stress) / (differential stress)
In most cases the critical driving stress ratio (RC) is between -2 and –1.5.
In numerical models of highly fractured rock and in analytical solutions for infinitely long fractures, RC can be demonstrated to depend mainly on the frictional properties of the rock fractures, with other parameters controlling the form of the resulting deformation and localization of fluid flow (Zhang & Sanderson 2001). Fracture orientation, as in the model of Barton et al (1995), is important, but is not the only significant parameter.
In situ stress measurements, especially those from deep boreholes, will be reviewed. These commonly show an approximately linear increase in principal stresses and differential stress with depth. In most cases the driving stress ratios, R, are -2 or higher, which agrees well with estimates from numerical models with typical frictional parameters.
Barton, C.A., Zoback, M.D. and Moos, D. 1995. Fluid flow along potentially active faults in crystalline rock, Geology, 23, 683-686.
Sanderson, D.J. and Zhang, X. 1999. Critical stress localization of flow associated with deformation of well-fractured rock masses, with implications for mineral deposits. Geological Society of London Special Publication 155, 69-81.
Zhang X. and Sanderson D.J. 2001. Evaluation of instability in fractured rock masses using numerical analysis methods: effects of fracture geometry and loading direction. Journal of Geophysical Research. 106, 26671-26687.