Stress and temperature in the bending lithosphere as constrained by experimental rock mechanics

TLDR

Previous studies of stress in the bending lithosphere near consuming plate margins have relied on bathymetry and assumed constitutive relations, but these simplifications fail to capture brittle failure, temperature‑dependent elasticity, and strain‑rate effects. The authors aim to formulate a more realistic constitutive relation by constructing a temperature‑dependent limiting yield strength curve from brittle failure and ductile flow experiments. They compare the moments supported by plates using this constitutive behavior to moments derived from bathymetric profiles. The comparison shows that experimentally derived constitutive laws produce moments consistent with bathymetry, requiring stresses above 100 MPa at 25–45 km, with geotherms matching heat‑flow data for most trenches except Kuril, and suggests that bending moment is better treated as independent of plate curvature.

Abstract

Previous attempts to deduce the stress distribution in the bending lithosphere near a consuming plate margin have relied on the observed bathymetry and an assumed constitutive relation for lithospheric behaviour, e.g. perfectly elastic, viscous/perfectly plastic, or elastic perfectly plastic. From the point of view of rock mechanics, each of these approximations fails to describe one or more of several basic phenomena, including brittle failure of rock, temperature dependence of elasticity, and temperature and/or strain rate dependence of ductile behaviour. In order to formulate a more realistic constitutive relation, a limiting yield strength curve, which is primarily a function of temperature, is constructed from data from brittle failure and ductile flow experiments. The moments which can be supported by plates with this constitutive behaviour are compared to the moments calculated from bathymetric profiles. The comparison indicates that moments required by the bathymetric data are consistent with moments supported by plates with experimentally determined constitutive laws as extrapolated to geologically reasonable temperatures and strain rates. The stresses developed in such models are required to reach values greater than 100 MPa† in the depth range 25–45 km. Geotherms necessary for strength curves consistent with moments calculated from the bathymetric data match those derived from heat flow data for the Aleutian, Bonin, Mariana and Tonga trenches. Of the trenches studied, only the geotherm inferred from the Kuril trench data is significantly different, perhaps implying that the Kuril plate is weaker than the others. The strength curves show that as a first approximation it is better to assume that bending moment is independent of curvature of the plate than to assume that bending moment and curvature are linearly related.