The present results, however, have some limitations which have to be further investigated in future studies. First, some parameters in transformation kinetics are not well constrained. In particular, parameters related to nucleation processes are poorly constrained [10][39]. This leads to large uncertainties in grain size in the low temperature regime (see Eq. 19 ), although it will not affect the results in the high temperature regime (Eq. 17 ). In addition, changes in the nucleation and growth rates due to the accompanying pressure drop are neglected. Second, the flow laws for spinel in the grain-size sensitive regime are poorly constrained, which leads to large uncertainties in estimated strength from grain size and temperature (and pressure), Fig. 6 Fig. 7 . Third, the temperatures in slabs are also only poorly constrained, the main uncertainties include the effects of shear heating and of latent heat. Thus, the details of the present results must be taken with caution. However, the notion of large rheological weakening due to grain-size reduction in cold slabs seems robust and should be taken into account in any models of slab dynamics.