Peridynamics for mechanism analysis of soil desiccation cracking: Coupled hygro-mechanical model, staggered and monolithic solution

Soil shrinkage cracking is a hygro-mechanical coupled phenomenon and it can significantly weaken the mechanical properties of soil and cause various potential natural disasters. This study proposes an improved bond-based peridynamics (PD) formulation, based on a comprehensive review of the hygro-mechanical peridynamic models. The proposed model with a certain influence function can be recast as an existing bond-based PD diffusion model. Also, an attenuation kernel function and discretized micro-modulus are adopted to revise the bond force density in the prototype micro-elastic brittle (PMB) model. For the numerical implementation, both monolithic and staggered schemes are adopted for the coupled hygro-mechanical problem. Specifically, the coupled stiffness matrix in the discretized equilibrium equation is constructed by using the Lagrange multiplier method for the monolithic scheme. While the direct integration method of explicit dynamics with an artificial damping term is adopted for the staggered scheme. For modeling of soil drying and cracking, two-dimensional soil rings, and two- and three-dimensional soil strips are simulated and demonstrated. The soil ring model verifies the accuracy of the coupled moisture-soil bond-based PD model through an explicit staggered scheme, and explores the effect of the relative thickness of rings on the number of cracks. The implicit monolithic solution is adopted to analyze the mechanisms of soil strip cracking. A detailed discussion on the scheme for controlling the maximum number of bond breakage is provided to guarantee convergency and accuracy with optimal efficiency. The soil strip cracking pattern and upward curling deformation agree well with experimental observations. The results show that the hygro-mechanical coupled peridynamic model has great advantages in solving soil drying and cracking. The present work shows a potential way in soil desiccation cracking investigation for real-scale simulation and fine mechanism exploration.