# SHPB Experiment and MPM Simulation on Dynamic Properties of Unsaturated Clay Under Impact Loading
## 1 Introduction
Up until now, the research object of the soil SHPB test has been mainly concentrated in cohesionless soil and saturated clay; meanwhile, there has been little SHPB experimental research conducted on unsaturated clay, thereby causing an imperfect knowledge of the dynamic properties of unsaturated clay subjected to impact loading. To overcome the imperfection of SHPB experimental evaluations regarding certain complicated and unstable problems of material dynamic mechanical behavior, various numerical methods have been applied to carry out in-depth analyses. The classical Finite Element Method (FEM) has been used for reproducing the SHPB test and extensively studying the friction and inertial effect [26; 27], as well as the optimization of specimen height [28] through the commercial software ABAQUS ([https://www.3 ds.com/products/simulia/abaqus](https://www.3 ds.com/products/simulia/abaqus) (accessed on 6 March 2025)) or LS-DYNA ([[https://lsdyna.ansys.com/](https://lsdyna.ansys.com/)]([https://lsdyna.ansys.com/](https://lsdyna.ansys.com/)) (accessed on 6 March 2025)). However, the above-mentioned Finite Element Methods (FEMs) have been proven to be more applicable for simulating the mechanical behavior of solid material due to the native defect of continuum mechanical theory. Especially for dealing with granular matter, some problems stand out, such as modeling the fracture and examining the particle breakage. Thus, some meshless methods have been put forward. For example,Prabhu et al. [29] and [PERSON] et al. [30] studied the breakage of cohesionless soil particles using the 3D discrete element method. [PERSON] et al. [31] simulated the interaction between the copper shaper and SHPB bar using the smoothed particle hydrodynamics method. By combining the benefits of Lagrangian and Eulerian descriptions, the Material Point Method (MPM) was recently employed to solve a problem involving extensive deformation and dynamics. [PERSON] et al. [32] successfully reported the performance of MPM on the steel SHPB test and verified its efficiency. However, there have been no reports on MPM simulations for the dynamic behavior of unsaturated clay under impact loading due to lack of experimental research and effective dynamic constitutive models. In this paper, the objective of this paper is to clarify some of the previously outlined controversial issues on unsaturated clay through SHPB experiment and MPM simulation. Firstly, the SHPB test on unsaturated clay is elaborately designed to ensure the validity of testing data. The dynamic stress-strain response of unsaturated clay is systematically examined and the Cowper Symonds (CS) model is adopted to represent the strain rate dependency behavior. Accordingly, a modified elastic-plastic constitutive model combining the Van Genuchten (VG) retention curve and the Drucker-Prager (DP) yield function considering strain rate effect is proposed and employed to interpret the dynamic behavior of unsaturated clay. Lastly, the above SHPB test is reproduced and numerically simulated by MPM, and the simulated and testing results are compared to verify the accuracy of the improved MPM computation program.