Tortuosity figures prominently in geochemical, hydrological, and geophysical calculations concerned with sediments, but it is a difficult parameter to measure. Past theoretical models for predicting the tortuosity from porosity data do not work with marine muds, and scientists and engineers have had to resort to entirely empirical models, without a mechanistic explanation and with unknown predictive power. We offer the first geometric model for the dependence of tortuosity on porosity in marine muds; the model is based on the tortuosity of separated layers of nonoverlapping disks. The fitted geometric constant in this model indicates that natural marine sediments act as if their fabric were made of disks with thickness:diameter ratios very close to 1:2, which indicates a blocklike fabric with respect to diffusion. The model was also applied to predict the tortuosity of a variety of sediments and soils not in the original database, and it provides a satisfactory prediction of the mean trend in these data.