# The Application of Fine Sand in Subgrades: A Review
## 2 Materials
### Dynamic Characteristics of Fine Sand  
Dynamic resilient modulus and permanent deformation are two main indicators for evaluating the dynamic performance of fine sand fillers, and the dynamic characteristics of fine sand under traffic loads are the primary factors affecting the performance of subgrade structures over their service life. Currently, there are several laboratory test methods for evaluating dynamic performance including dynamic modulus tests, static creep tests, and repeated load triaxial tests. Figure 1: Sampling gradation of sand subgrade. Figure 2: MTS-810. Laboratory tests were conducted on windblown sand (SP, A-3), which is used in the subgrade of Interstate 1-94 in northern Indiana, to simulate the effects of impact and vibratory compaction [6]. The assessment employed an MTS-810 soil testing system (Figure 2). A comprehensive test for granular soil encompasses six preparatory stages and twenty-seven distinct testing phases, each involving various combinations of confining stress and repeated deviator stress magnitudes. To administer the repeated loading, a haversine stress pulse was employed, characterized by a 0.1 s load duration within a 1 s cycle. During the resilient modulus assessment, it was noted that at a confining stress level of 6.9 kPa (equivalent to 1 psi), the cumulative deformation consistently surpassed the displacement gauge's measurement capacity, which was set at 4 mm. The resilient modulus of a granular material is generally approximated by Equation (1):  
\[M_{R}=k_{1}\theta^{k_{2}} \tag{1}\]  
where \(M_{R}\) is the resilient modulus, \(\theta\) is the first invariant of stress (\(\sigma_{1}+\sigma_{2}+\sigma_{3}\)), and \(k_{1}\) and \(k_{2}\) are experimentally determined constants. This equation, supported by repeated load triaxial test data, summarizes the key resilient factors of granular materials: stress state, saturation, initial density, and gradation. Parameters \(k_{1}\) and \(k_{2}\) are plotted against relative compaction in Figure 3. It is observed that parameter \(k_{1}\) increases almost linearly as relative compaction increases, while parameter \(k_{2}\) is almost constant. Therefore, when the relative compaction degree is between 95% and 103%, the resilient modulus demonstrates a linear increase with dry density, and a regression equation for the resilient modulus was established using Equation (2) as follows:  
\[M_{R}=(-20,\!163+232.886\mathrm{R_{C}})\theta^{0.595} \tag{2}\]  
where \(\mathrm{R_{C}}\) is relative compaction degree in %, the ratio of dry density is obtained from 5 min of vibration per layer to the dry density, and \(\theta\) is the first invariant of stress in psi. The results revealed that at a lower moisture content, the compaction curves for both impact and vibratory compaction were comparable. However, at higher moisture levels, vibratory compaction was found to produce a higher dry density. When comparing specimens compacted under the same moisture content and dry density, it was observed that those compacted using the vibratory method exhibited significantly less permanent deformation than those compacted by impact. Furthermore, the elastic modulus of the vibratory compacted specimens was approximately 40% higher, indicating that vibratory compaction is more effective in enhancing the resilient modulus response of sand dune sands. It is noteworthy that the compaction moisture content had a minimal impact on the resilient properties of the sand. [PERSON] [11] proposed a simple method for estimating the in situ resilient modulus of sandy subgrade soils while obtaining the particle size distribution of core samples and  
Figure 3: Effect of relative compaction on parameters \(k_{1}\) and \(k_{2}\). non-destructive testing at various locations within the subgrade soil. Non-destructive testing was conducted using a falling weight deflectometer at different load levels, and the subgrade resilient modulus was calculated based on the data collected from various pavement areas.