The trench pull force: constraints from elasto-plastic bending models

Dan Sandiford 

The negative buoyancy of subducting slabs is generally regarded as a principal source of plate-driving force, but its mechanical coupling to trailing plates remains uncertain. The conventional slab-pull model represents slab pull as a tension-like stress resultant transmitted through the subduction hinge, where it acts as an edge force on the trailing plate. A distinct contribution arises from non-isostatic trench topography: downbending creates a near-surface pressure deficit relative to an isostatic column in the trailing plate. Because the trench relief is non-isostatic, the column falls outside the standard gravitational potential energy (GPE) framework. Extending that framework requires only retaining the full vertical normal stress that satisfies equilibrium. The trench-pull force is defined here as the change in vertically integrated vertical normal stress between the trench and the first isostatic column. Equilibrium requires the trench-pull force to be balanced jointly by basal shear and a change in the normal-stress-difference resultant. The basal term is negligible over the short flexural region, so the changes in the two stress resultants are approximately equal. Horizontal gradients of vertical shear stress equilibrate the pressure deficit with depth. Expressing these gradients as an equivalent density recasts the trench-pull force in the familiar density-moment form, with the force determined by the first moment of the combined true and equivalent density difference. Uniform elastic bending predicts an effective moment arm near half the plate thickness. Finite-element models show that this scaling persists across elastic and elasto-plastic plates and variations in loading, background stress and strength distribution. At fixed thickness, trench-pull forces lie within approximately 10% of a common pull-deflection relation; across different thicknesses, they increase nearly in proportion to plate thickness. Applying the scaling to the mechanical thickness of old oceanic lithosphere gives approximately 2.5 TN/m for a representative trench depth, comparable to ridge push. The combined ridge-to-trench driving force arising from the topographic pressure gradient is approximately 5 TN/m, sufficient to balance basal drag across an entire oceanic plate for plausible magnitudes of basal shear stress.