## 1 Introduction  
To estimate the service performance of subgrade materials under vehicle loads and provide a reference for the design of road and railway subgrades, increasingly more researchers in recent years have focused on the study of the dynamic characteristics of compacted subgrades. The same is true for the research on various new modified subgrade materials. The dynamic modulus of resilience (\(\mathrm{M_{R}}\)) of the subgrade is an important parameter reflecting the deformation characteristics and impact strength of the subgrade, and it is often used as a criterion for evaluating the compaction quality of the subgrade. The modulus is affected by many factors, such as the self-consolidation state, soil particle characteristics, water content, and stress level. When subgrade is considered as a whole in a layered-resilience system, researchers often express the \(\mathrm{M_{R}}\) of the subgrade under dynamic load as mathematical models related to stress, including the K-\(\theta\) model [1], composite prediction model [2], etc. These models express the nonlinear stress-strain properties of the subgrade by combining the soil physical properties (such as water content and dry density) and stress state variables (such as deviatoric, confining, volumetric, and shear stresses). The AASHTO Pavement Design Guide (NCHRP1-37A) [3] proposes a prediction model to improve the characteristics of model uncertainty and dimensional disagreement:  
\[M_{R}=k_{1}p_{a}\bigg{(}\frac{\theta}{p_{a}}\bigg{)}^{k2}\bigg{(}\frac{\tau_{ oct}}{p_{a}}+1\bigg{)}^{k3} \tag{1}\]  
where \(k1\), \(k2\), and \(k3\) are regression parameters dependent on the material types and soil physical properties; \(\theta\) is the bulk stress, i.e., \(\sigma 1+\sigma 2+\sigma 3\) (\(\sigma 1\), \(\sigma 2\), and \(\sigma 3\) are the three principal stresses); \(\tau_{\rm oct}\) is the octahedral shear stress, i.e., \(1/3\sqrt{\left(\sigma_{1}-\sigma_{2}\right)^{2}+\left(\sigma_{2}-\sigma_{3} \right)^{2}+\left(\sigma_{1}-\sigma_{3}\right)^{2}}\); \(Pa\) is the atmospheric pressure. In the method of determining the modulus of resilience by the triaxial test under dynamic load, \(\sigma_{1}\) represents the applied vertical stress, \(\sigma_{2}=\sigma_{3}=\) confining compressive stress. The subgrade surface clay in arid or semi-arid areas is always unsaturated, and its mechanical properties are very different from those in the saturated state. The subgrade strength and deformation will be affected obviously when climate change or groundwater migration causes the subgrade moisture fluctuation [4; 5]. It relates to the problems in the field of unsaturated soil mechanics. With the development of unsaturated soil research, it is widely believed that matric suction is an important variable affecting the structural mechanical behavior of unsaturated soil. Matric suction is related to the capillary effect [6; 7; 8], which is different from the external stress effect caused by an external load. Its response in soil mechanics can be seen as the surface tension at the water-air interface strengthens the links and bonds between soil particles, which in turn reduces the possibility of sliding between particles and hinders the plastic deformation of the soil [9; 10]. Matric suction depends on many factors, such as the soil saturation state, initial dry density, particle composition, etc., [11; 12], and many studies have shown a strong correlation between the \(\rm M_{R}\) and suction. [PERSON], [PERSON] et al. demonstrated using a modified triaxial test device that matric suction can increase the soil elasticity and that all stress variables also increased the angle of internal friction between the soil particles [13]. The \(\rm M_{R}\) has shown a nonlinear increasing trend with a decrease in matric suction in the referenced review literature [14; 15]. [PERSON] et al. found that when the acyclic stress was 30 kPa, the increase in the suction from 0 to 250 kPa increased the \(\rm M_{R}\) by up to one order of magnitude [16].