Finite Element Study On the Closure of Thermal Microcracks In Feldspar/Quartz-Rocks-I. Grain-Boundary Cracks

Abstract

SUMMARY The formation of microcracks is simulated in 2-D composites using the finite element method. the rock is modelled by a planar, periodic array of angular-cornered grains embedded in a matrix with different thermoelastic moduli. During cooling or unloading stress-concentration points arise at sharp corners inside the grain aggregate. Microcracking is simulated in a system containing quartz (QTZ) grains surrounded by feldspar (FSP). By investigating stress-intensity factors for different crack paths one can conclude that grain-boundary cracking (GBC) is most likely. Seismic velocities of the fractured composite are calculated from effective moduli. In a rock containing an array of parallel aligned GBC (1 mm length), the anisotropy turned out to be 29 per cent for P waves and 20 per cent for S waves. Crack-closure modelled by repressurizing the rock is substantially different for an aggregate with parallel oriented cracks (GBC I) than for a composite where most of the grain boundaries are broken (matrix containing totally separated grains, GBC II). the closing pressure of GBC I is finite and lies between 31 MPa (QTZ grains) and 41 MPa (FSP grains) after a temperature change of 400°C. the closing pressure of thermal cracks is largest in composites with very small inclusions and decreases for composites with larger grains. In case of small inclusions a collapse closure of GBC is evident, whereas in systems with larger grains a more gradual crack-closure dominates. the closure of GBC II is characterized by the occurrence of residual pores. the pores originate in the final stage of crack closure near sharp corners of the grains, where the former stress-concentration points after cooling were located. the phenomenon of residual pores may be a hint for interpreting fluid inclusions in rocks as a relic of the incomplete closure of cracks. From the results obtained in this study it can be concluded that significant in situ porosity of QTZ/FSP-rich rocks may be found at pressures as high as 300 MPa corresponding to a depth of about 10 km in the crust of the earth.