Relationship between fracture spacing and bed thickness in sedimentary rocks: Approach by means of Michaelis–Menten equation

Fractures occur in nearly all rocks at the Earth's surface and exert essential control on the mechanical strengths of rock masses and permeability. The fractures strongly impact the stability of geological or man-made structures and flow of water and hydrocarbons, CO2 and storing waste. For this, the dependence of opening mode fracture spacing (s) on bed thickness (t) in sedimentary basins (reservoirs) is studied in this context. This paper shows that the Michaelis–Menten equation can provide an algebraic expression for the nonlinear s-t relationship. The two parameters have clear geological meanings: a is the maximum fracture spacing which can no longer increase with increasing t, and b is the characteristic bed thickness when s = 0.5a. The tensile fracture strength (C) of the brittle beds during the formation of tensile fractures can be estimated from the two parameters. For sandstones of 16 areas reported in the literature, C ranges from 2.7 MPa to 15.7 MPa with a mean value of 8 MPa, which lies reasonably within the range of tensile strengths determined experimentally. This field-based approach by means of Michaelis–Menten equation provides a new method for estimating the tensile fracture strength of rock layers under natural conditions.