## 3 The Trend of Change in Dynamic Characteristics
### Variation in the Dynamic Elastic Modulus of EPS-Sisal-Modified Lightweight Soils  
Figure 5 shows the post-test EPS-sisal lightweight soils with different sisal admixtures at 5% EPS volume fraction (from left to right: the sisal fibre admixtures are 0.6%, 0.8%, 1.0%, 1.2% and 1.4%). Figures 6 and 7 show the \(\varepsilon_{d}-\sigma_{d}\) and \(\varepsilon_{d}-E_{d}\) curves for the EPS lightweight soils modified with different sisal admixtures at 5% EPS volume fraction, respectively. In the soil mixed with sisal fibres, the fibres in the soil body have an irregular staggered arrangement by means of a random distribution, forming a \"network\" structure. When the specimen is ruptured under a large load, the contact between the fibres and the soil particles and the skeleton structure formed at this time make the dislocation and deformation of the soil particles be subjected to a certain restriction and better inhibit the development of cracks in the soil, thus enhancing the integrity and toughness of the specimen. As shown in Figure 6, the stress-strain curves for the EPS-sisal-modified lightweight soils changed considerably at the beginning. With increasing amounts of sisal, the dynamic stresses first increased and then stabilised. This was because the increase in sisal fibres led to a rougher surface and an increase in inter-surface forces, and a greater dynamic stress was required to achieve the same strain [21]. This was because the increase in sisal incorporation under dynamic loading caused the difference between the maximum and minimum dynamic strains of the composite soil to decrease and then increase, changing the stiffness of the soil [14]. In Figure 7, the trend of each specimen was basically the same, between 0% and 0.5% of the strain, while the trend gradually diverged between 0.5% and 1%. When the strain was greater than 1%, the trend of each specimen was more divergent with different trends. This was because, when the soil deformation was \(0<\varepsilon_{d}<0.5\%\), the soil sample was in the elastic deformation stage, the plastic deformation was small, and the soil was prone to rebound. When the deformation was \(\varepsilon_{d}>0.5\%\), some of the specimens underwent plastic deformation, the resistance of the soil to deformation was reduced, and the difference in the dynamic modulus of elasticity of the soil with different sisal admixtures was significantly reflected at this time. To further analyse the trend of the maximum value of the dynamic modulus of elasticity of the specimen [22] and the maximum value of \(E_{dmax}\), the inverse of the dynamic modulus of elasticity and \(E_{dmax}\) curves were established, as shown in Figures 8 and 9. The modulus of dynamic elasticity did not consistently increase or decrease with an increasing amount of sisal but increased when the amount of sisal was less than 1.2% and decreased when it was greater than 1.2%, i.e., the maximum was reached when the amount of sisal was 1.2% and the improvement effect was the best. According to the [PERSON] [23] model, the maximum dynamic modulus of elasticity is expressed as the following:  
\[\frac{1}{E_{\text{dmax}}}=\text{a}+\text{b}\times\epsilon_{\text{d}} \tag{3}\]  
where a and b are fitted parameters. Figure 8: Reciprocal of the strain–kinetic elastic modulus of soil–5% EPS mixtures with different sisal dosages. Figure 6: Stress–strain curve of soil–5% EPS mixtures with different sisal dosages. Figure 7: Strain–kinetic elastic modulus curve of soil–5% EPS mixtures with different sisal dosages. To study the relationship between the dynamic modulus ratio decay and dynamic strain for the EPS-sisal-modified lightweight soil, the \(E_{d}/E_{dmax}-\epsilon_{d}\) relationship was plotted for different sisal fibre admixtures, as shown in Figure 10. Figure 10 shows that \(E_{d}/E_{dmax}-\epsilon_{d}\) continued to increase with increasing sisal admixture and then tended to be stable.