FINITE-ELEMENT MODELING OF THE PROPAGATION OF A PRESSURE SOLUTION CLEAVAGE SEAM

The propagation of a cleavage scam is modelled by a two-dimensional finite element technique, which extends Fletcher and Pollard's elastic 'anticrack' theory to a composition-dependent viscous rheology. The viscous solution is obtained by repeated solutions of the force equilibrium equations at successive time steps, with the viscosity of each element varying as a function of its strain history. The rheology assumed follows previous modelling by Robin: the rock is modelled as a 'quartz'-'mica' mixture in which deformation proceeds by diffusion of 'silica'. The viscosity of an element depends on its proportion of 'quartz', varying from a minimum for intermediate 'quartz'-'mica' mixtures to higher values for either pure 'quartz' or pure 'micas'. As a result of its incremental strain, an element either loses OT gains 'quartz' (i.e. volume), and therefore changes its viscosity for the next strain increment. The system can be either open ('silica'escapes the system; all individual elements lose volume) or closed (individual elements may gain or lose volume but the total volume of the system is preserved). At the start of a run, a nucleus of a cleavage seam is introduced as a thin layer of elements with a lower viscosity (corresponding to a higher 'mica' content) than the rest of the rock. The stress concentration at the tip of the seam leads to a weakening of the elements in front of it through loss of 'quartz'; this results in crack propagation, for both open and closed systems. All other parameters being equal, the 'speed' of propagation is greater for open systems than for closed ones.