To fall or not to fall: the physics of sandcastles

Abstract

Understanding how porous structures become rigid and retain their strength or fail over variable saturation rates is crucial for designing materials with targeted performances under different processing conditions. This is especially true for the development of materials with time-dependent viscosities (i.e., thixotropic or rheopectic materials) and the emerging science behind manipulatable advanced geometamaterials. Nowhere are these issues more ubiquitous than in the physics of sandcastles. Modeling unconstrained granular columns traversing the microscale (granular temperature) to the mesoscale (internal granular force chains and interactions with pore fluid) and defining the macroscale properties, characteristics and behaviors are key to the development of a universal picture. Herein, we experimentally investigate how an unconstrained granular column can retain structure over a range of saturations. Analyzing a suite of 487 macroscale tests, sigmoid saturation models were developed that define state variable interactions within the mesoscale mechanical domain. This led to the formulation of an energy balance model based on microscale interactions via a 1D thermostatistical picture applied to the granular temperature. The difference between strength and stability can thus be independently observed simultaneously. The two domains are not necessarily synonymous (i.e., strong may not be stable), and the energy cost to change the stability state on the microscopic scale becomes a quantifiable physical property that manifests in macroscopic granular behavior.