Pore geometrical models are widely used to study transport in porous media, permeability, internal stability, and filter compatibility. Transport of fine grains through the voids between the skeleton of the coarser fraction is mainly controlled by the pore throats or constriction sizes. This study compares various constriction size distribution criteria and capillary tube models, which elucidate the limitations of the Kovacs capillary tube model, and this model is explained and developed. The new proposed threshold boundaries (d(0) = 2.3d(85)(f) and d(0) = 2.8d(85)(f)) categorized soil samples as internally stable, transient zone, or unstable. The model also incorporates the precise shape coefficient of particles. This improved model was validated based on a database from the literature, as well as performing 10 new experimental tests on two ideal gradation curves that identified the threshold boundary of Kenney and Lau criteria. This proposed model, which is dependent on grading, porosity, and grain shape, provides accurate predictions using a precise shape factor. This finding may enhance our knowledge about transport in porous media and contribute toward internal stability assessing for practical applications.