# SHPB Experiment and MPM Simulation on Dynamic Properties of Unsaturated Clay Under Impact Loading
## 4 Conclusions  
This study examined the dynamic stress-strain response of unsaturated clay with a saturation of 85% using a modified SHPB device. Based on the experimental results, the rate dependency of the dynamic strength of the specimen was evaluated for strain rates ranging from 204 s\({}^{-1}\) to 590 s\({}^{-1}\). Subsequently, a modified dynamic elastic-plastic model for unsaturated soil was proposed and embedded the MPM program to reproduce the SHPB test. The main conclusions are summarized as follows:  
1. Under passive confinement, the stress-strain curve of unsaturated clay experienced three typical stages, which are elastic compression, plastic flow and failure. As the strain rate increases up to approximately 500 s\({}^{-1}\), much more soil particles or aggregates may break up at high stress state and the pores were occupied by finer gains and water. Eventually, an even denser arrangement of particles formed, leading to a lock-up behavior observed in the plastic flow stage. 2. The dynamic response of unsaturated clay exhibited a significant strain rate effect. The strain rate dependency of dynamic strength can be quantitatively characterized using the CS model. When the strain rate was in the range of 204-590 s\({}^{-1}\), the appropriate CS parameters were calibrated to be an intercept \(C\) of 55 and a slope \(P\) of 0.8 in the double logarithmic scale of dynamic increase factor and strain rate space. 3. An improved dynamic constitutive model for unsaturated soil was proposed, incorporating a VG model to represent the hydraulic behavior and a modified D-P model considering strain rate effect to characterize the mechanical behavior. Additionally, a modified MPM program was employed to perform numerical simulations of theSHPB test. The simulated stress-strain curves basically agree with the experimental results, indicating the feasibility of the proposed dynamic constitutive model for unsaturated clay under impact loading. Conceptualization, Y.Y., F.Z., J.L. ([PERSON]) and J.L. ([PERSON]); Data curation, F.Z., Z.L., R.Z., L.L., Y.Z. and Z.X. ; Formal analysis, F.Z., Z.L., Y.W., R.Z., L.L., Y.Z. and Z.X. ; Investigation, F.Z., Z.L., Y.W., R.Z., L.L., Y.Z. and Z.X. ; Methodology, Y.Y., F.Z., J.L. ([PERSON]) and J.L. ([PERSON]); Resources, Y.Y., F.Z., J.L. ([PERSON]) and J.L. ([PERSON]); Software, F.Z., Z.L. and Y.W. ; Validation, F.Z., J.L. ([PERSON]) and Y.W. ; Visualization, F.Z. ; Writing--original draft, F.Z. ; Writing--review and editing, F.Z. All authors have read and agreed to the published version of the manuscript. The authors are grateful for the financial support provided by National Natural Science Foundation of China (No. 51874118; No. 52478525), Jiangsu Funding Program for Excellent Postdoctoral Talent (No. 2023 ZB583), and State Key Laboratory of Precision Blasting and Hubei Key Laboratory of Blasting Engineering, Jianghan University (No. PBSKL2022A03; No. PBSKL2023B5). Not applicable. Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request. The authors declare no potential conflicts of interest concerning the research, authorship, and/or publication of this article. References  
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