# SHPB Experiment and MPM Simulation on Dynamic Properties of Unsaturated Clay Under Impact Loading
## 2 SHPB Test on Unsaturated Clay
### Results and Discussion  
Figure 3 shows the stress-strain curves of unsaturated clay at strain rates ranging from 204 s\({}^{-1}\) to 590 s\({}^{-1}\). Since soil is a non-homogeneous material and the applied gas pressure cannot be precisely controlled by the air compressor and pneumatic value, impact tests at each gas pressure were repeated at least 3 times for self-calibration. Error bars were added in Figure 3 to indicate the data scatter extent for repeated tests. Although there is some discrepancy for repeated tests, the stress-strain curves obtained at the same gas pressure exhibit good consistency. According to Figure 3, the dynamic stress-strain curve of unsaturated clay under passive confinement demonstrates three distinct stages:  
1. Elastic compression: The stress increases linearly with strain in this stage. Under high loading rate conditions, the closure speed of cracks or pores inside the soil becomes rapid. Consequently, unsaturated clay typically reaches its yield limit at a tiny strain. \begin{table}
\begin{tabular}{c c c c c c c} \hline \(E\) **(GPa)** & \(v\) **(m/s)** & _I\({}_{s}\) **(mm)** & _d\({}_{s}\) **(mm)** & \(L\) **(mm)** & \(k\) **(\%)** & \(U\) **(V)** \\ \hline
75 & 2700 & 50 & 20 & 400 & 2.0 & 10.0 \\ \hline \end{tabular} \(E\)–elastic modulus of SHPB bar, \(v\)—elastic wave velocity of SHPB bar, \(l_{s}\)—length of specimen, \(d_{s}\)—diameter of specimen, \(L\)—length of bullet, \(k\)—strain sensitivity coefficient of strain gauge, \(U\)—testing voltage.  
\end{table} 
Table 2: Calculation parameters used for data processing. Figure 2: Data processing: (**a**) original waveforms and (**b**) dynamic stress equilibrium. 2. Plastic flow: Following elastic compression, a distinct plastic flow stage occurs, during which the breakage and rearrangement of soil gains may take place. Since soil particles move into a dense arrangement, the relative motion between particles becomes increasingly difficult. Due to the rising strain rate and passive confinement, the soil sample experiences a high-stress condition, causing soil particles to break and the soil skeleton to contract more tightly, thereby enhancing compression resistance. Eventually, an even denser state of particles or aggregates forms, shifting the response of the soil sample to a lock-up behavior [20; 21]. As can been seen from Figure 3, at a strain rate of approximately 500 s\({}^{-1}\), a lock-up behavior can be observed in this stage. 3. Failure: A significant downward trend in the stress-strain curve is observed after the stress reaches its peak value. As plastic strain increases, soil fracture or damage occurs, eventually leading to a fully damaged state. Considering whether a lock-up behavior can be observed during the plastic flow stage, the stress-strain curves of unsaturated soil under high loading rate condition were classified into two types: (**a**) Type-I, composed of elastic compression, yielding of the soil skeleton, and failure stages; (**b**) Type-II, composed of elastic compression, yielding of the soil skeleton, lock-up, hardening, and failure stages. As the strain rate increases, the energy of soil particles or aggregates under passive confinement increases with the axial pressure, promoting the breakage and arrangement of particles or aggregates. When the pores inside the soil are fully occupied by finer particles or water, a lock-up behavior emerges, indicating that the soil sample transforms from an unsaturated state to a saturated state. Based on the above analysis, the lock-up behavior depends on the applied and confining pressures, breakage and arrangement of soil particles or aggregates, and closure of pores. Notably, these factors are all related to the strain rate.