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

Stresses transmitted through slabs are thought to provide an important component of the driving force on the trailing plates. This “net slab pull” is usually conceptualized in terms of in-plane differential stress, acting in the sense of deviatoric tension. However, an additional component of the net slab pull arises due to the pressure deficit created by plate downbending. The purpose of this paper is to investigate the mechanics and typical magnitude of this mechanism, which is termed “trench pull.” The challenge is that because trench topography is non-isostatic, the pressure distribution cannot be treated with the lithostatic approximation that has been exploited, with much insight, in other settings. Here, the relative pressure reduction depends on the vertical distribution of horizontal gradients of the vertical shear stress. These stress gradients are denoted Q(z), and Q(z)/g can be interpreted as a pseudo-density denoted here as ρ*. The concept of the force due to gravitational potential energy differences (ΔGPE) is extended to include the effect of ρ*(z). In terms of the contribution to the ΔGPE, the distribution of ρ*(z) functions exactly like the real density – notably, there is the same dependence on the vertical center of mass. In this study, elastic and elasto-plastic models are used to investigate this problem, specifically the distribution of the vertical shear stress and its partial derivatives. A key conclusion is that the length scale over which the trench pressure deficit acts is half the mechanical thickness of the lithosphere. Based on this model, a typical trench pull force is estimated to be about 2.5 TN/m. The total topography that exists between ridges and trenches is associated with a net driving force of about 5 TN/m, enough to balance basal drag of 1 MPa, over a plate length of 5000 kilometers (km).