Distribution of reaction underneath a heap of dry sand indicates one of the interesting characteristics of granular media. It has been found that a nonhomogeneous second-order differential equation of hyperbolic type governs the stress distributions. Sand heaps stabilize own their weight in a state of equilibrium, where the compressive forces hold the configuration of arches together in both major and minor directions. According to the author's recent work, the closure of polarized principal axes for planar sand heaps has been proposed. This is where a whole heap does not mobilize static friction except along the slope surface. The resulting stress field was entirely admissible under Coulomb friction inequality and found agreeable with many pieces of experimental evidences that has already been published. The present research aims to investigate the arch shape function based on continuum mechanical approach. Unlike straight arches obtained from the closure of fixed principal axes, it was found that under the closure of polarized principal axes, trajectories of principal compression consist of smooth networks of parabolic arches. As stacks of assembled arches transfer outward and downward pressure to a rigid and rough base supporting the heaps, the resultant forces obtained by integrating forces along arch shapes regularize a non-linear distribution of basal pressure.