Differential thermal stresses in the Earth

Abstract

Summary. Rocks have a significant thermal expansion coefficient and a high modulus of elasticity. Small thermal changes can therefore generate very substantial stresses. A convenient idealized example is the mechanically free, cooling thermal boundary layer in a material that suddenly turns from plastic to rigid in cooling through a ‘rigidus’ temperature. This simplified case can be solved analytically for both a linear and an error function temperature profile. A compressed layer develops near the surface, with a logarithmic singularity of stress at the boundary. At a depth of 0.2 of the elastic thickness, the stress changes to tensile, and peaks at 15 per cent of the confined shrinkage stress in the middle of the rigid layer. The situation is similar to the stresses in one half of a piece of tempered glass. Like the tempered glass, both the cooling lithosphere and a plated boundary to a magma chamber are subject to breakage when cracks are induced in the tensile layer. Positive pore (magma) pressure is required to overcome confining pressure at depth in the lithosphere, but cracking could become catastrophic in the plated boundary to a near‐surface magma chamber. Copyright © 1986, Wiley Blackwell. All rights reserved