*3.3. Effect of Moisture Content on Dynamic Mechanical Properties of Coral Sand*

The test results of different moisture contents at strain rates of 460 s−1, 650 s−1, and 800 s−<sup>1</sup> are shown in Figure 14. The highest strength of the sample is observed at moisture contents between 6% and 8% and the lowest strength occurs at 20%. The moisture content has little influence on the strength of the coral sand under unsaturated conditions, but some observations regarding the mechanical properties can be made. Generally, the water has a softening effect on the strength of coral sand. Research has shown that water significantly reduces the strength of terrestrial soil, such as quartz sand and clay before reaching a high saturation state [10,16]. However, in this experiment, the influence of the water on the entire strength of the ECS is smaller than that of LCS [29]. Water reduces the friction of particles [10,16,29], and the difference between the responses of the two samples is related to the difference in the frictional dissipation of the particle motion during compression. The frictional dissipation results from the movement of the unbroken particles and the movement of the small sub-particles when the particles are crushed. The ECS has superior grading than the LCS; therefore, there is less particle breakage and the friction dissipation is lower in the ECS than the LCS during compression. As a result, the moist ECS does not decrease significantly due to the lower lubrication efficiency.

**Figure 14.** Stress–strain curves of the samples with different moisture contents at different strain rates: (**a**) 460 s<sup>−</sup>1, (**b**) 650 s<sup>−</sup>1, (**c**) 800 s<sup>−</sup>1.

The strength of water-bearing sand is higher than that of dry sand during the initial compression process but it is slightly lower than that of dry sand with increasing deformation. This yielding phenomenon is observed at the strain rate of 460 s−<sup>1</sup> and 650 s−<sup>1</sup> (Figure 14a,b). These properties are related to the high porosity of coral sand. In this study, the increase in the initial modulus occurs because water is present in the cavities of the particles, resulting in an increase in the strength of the skeleton. However, the water in the supporting pores lubricates the secondary particles as the particles are crushed, causing a decrease in the modulus after yielding.

This effect is also related to the strain rate. It was interesting that when the strain rate increased, the position of the intersection point (where the stress is equal to that of dry sand) moves towards the origin of the coordinates on the abscissa. As shown in Figure 14, the intersection points are located between 0.04 and 0.08 for the strain rate of 460 s−1, between 0.02 and 0.07 for 650 s−1, and near 0.01 for 800 s−1. That is, as the loading rate increases, the initial stiffening response for moist sand occurs at a different location on the curve. This phenomenon is also closely related to the strain rate effect of coral sand. The results in Section 3.2 and those of Huang provide the explanation [18]. As the loading speed increases, the friction dissipation ratio increases, and the water lubrication becomes more effective.

The stress increases sharply at the strain rate of 800 s−<sup>1</sup> for the initial moisture content of 30%, indicating that the coral sand exhibits a hardening response in the compaction state. The saturation is about 77% upon reaching the compaction point. This demonstrates that coral sand reaches the compaction state earlier than quartz sand or clay, whose saturation is more than 90% [16]. Although there are few inter-particle pores in the hardened section, some unbroken coral sand still has a high internal porosity and does not reach a high saturation state. The strain still increases in the sample due to the release and compression of internal pores caused by particle breakage. However, the compression mechanism in the hardening response is different from that of the non-compaction stage due to the disappearance of the inter-particle pores. In the compaction state, the specimen cannot be easily compressed due to the absence of inter-particle movement. Therefore, the stress increases rapidly with a higher modulus.

The research on the mechanical properties of dry coral sand is relatively comprehensive. In order to quantitatively analyze the impact of water content on coral sand, the obtained regular conclusions are applied to previous studies. Based on the dimensionless stress ratio, the relationship between the stress ratio of water containing coral sand and dry sand at different strain rates is established, as shown in Figure 15. It can be more clearly seen that as the strain rate increases, the softening effect of water on coral sand becomes more pronounced.

**Figure 15.** Normalized stress of moist coral sand to dry coral sand: (**a**) 460 s<sup>−</sup>1, (**b**) 650 s<sup>−</sup>1, (**c**) 800 s<sup>−</sup>1.

#### *3.4. Effect of Lateral Pressure and Equation of State*

The circumferential strain of the sleeve at strain rates of 460 s<sup>−</sup>1, 650 s−1, 800 s−<sup>1</sup> and 900 s−<sup>1</sup> was obtained from the pulses recorded at the outer face of the sleeve. The signals were converted into the confining pressure of the sample using Equation (3). As shown in Figure 16, the duration of the pressure increases from zero to the peak value in about 290 μs, which is consistent with the axial loading duration of the sample. The confining pressure increases with the increase in the compaction level at the same strain rate.

**Figure 16.** The confining pressure of the coral sand samples at different strain rates: (**a**) 460 s−<sup>1</sup> (**b**) 650 s−<sup>1</sup> (**c**) 800 s−<sup>1</sup> (**d**) 900 s<sup>−</sup>1.

The relationship between the average pressure and volumetric strain (*P* − εv) of the coral sand at different strain rates is calculated using Equation (4), as shown in Figure 17. However, in this study, in the initial compression stage of the coral sand, the slope of these curves of the coral sand decreases or even remains constant. Therefore, it is necessary to establish the constitutive model and fit the EOS for the solid-like response of the coral sand using exponential form.

The EOS is using the form of *P* = *a* × ε<sup>v</sup> *<sup>b</sup>*. The fitting results of the EOS for the three relative densities at different strain rates are shown in Table 4. The value of the goodness of fit *R*<sup>2</sup> > 0.95 indicates that the power exponent form is suitable to describe the solid-like response of coral sand.

**Figure 17.** Relationship of average pressure and volumetric strain at different strain rates: (**a**) 460 s−<sup>1</sup> (**b**) 650 s−<sup>1</sup> (**c**) 800 s−<sup>1</sup> (**d**) 900 s<sup>−</sup>1.


**Table 4.** Fitting parameters of the EOS.

#### **4. Conclusions**

Coral sand has high porosity, irregularly shaped particles, and strain-rate dependency, and exhibits complex mechanical properties. An understanding of the essential mechanical properties allows us to determine the influence of the relative density and the water content on the dynamic mechanical behavior of coral sand, thus providing scientific guidance for practical engineering design and applications. The following conclusions were determined based on the HRS impact experiments of coral sand:

(1) A significant correlation was observed between the strain rate and the stiffness with increasing relative density of coral sand. The breakage-energy efficiency decreases with an increase in the relative density, and the strain rate becomes more insensitive to the stiffness of the coral sand.


**Author Contributions:** Conceptualization, K.D.; methodology, K.D. and K.J.; validation, K.D. and K.J.; formal analysis, K.D. and K.J.; investigation, K.D.; resources, K.J. and W.R.; data curation, K.D. and W.R.; writing—original draft preparation, K.D.; writing—review and editing, K.J.; project administration, K.J. and W.R.; funding acquisition, K.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


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