## 3 Results and Discussion
### Nonlinear Crep Behavior Modeling of EPS  
As shown in Figure 8, with increasing applied stress for each EPS density scenario, the instantaneous elastic strain in the 12-h-long creep test increased, and the creep amount and rate also increased in the subsequent transient and steady-state creep steps. In particular, the difference in these characteristics between the lower two levels (32.7-54.5% of \(\sigma_{10}\)  
Figure 6: SEM images for several conditions: EPS20. (**a**) Intact specimen. (**b**) Compression up to \(\epsilon=0.5\). (**c**) an applied load (0.0791 MPa) for 12 h.  
Figure 7: [PERSON]’s ratio, for different EPS densities. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Density (kg/m\({}^{3}\))**} & **Initial Tangent** & **Secant Modulus** & **Tangent Modulus** \\  & **Modulus (MPa)** & **(MPa)** & **(MPa)** \\ \hline
16 & 2.47 (\(\pm 0.77\)) \({}^{\text{a}}\) & 0.86 (\(\pm 0.06\)) \({}^{\text{a}}\) & 0.21 (\(\pm\) 0.04) \({}^{\text{a}}\) \\
20 & 3.71 (\(\pm 0.68\)) \({}^{\text{b}}\) & 1.35 (\(\pm 0.09\)) \({}^{\text{b}}\) & 0.24 (\(\pm 0.03\)) \({}^{\text{b}}\) \\
25 & 4.43 (\(\pm 0.67\)) \({}^{\text{c}}\) & 1.58 (\(\pm 0.06\)) \({}^{\text{c}}\) & 0.26 (\(\pm 0.02\)) \({}^{\text{b}}\) \\
30 & 5.48 (\(\pm 0.76\)) \({}^{\text{d}}\) & 2.08 (\(\pm 0.09\)) \({}^{\text{d}}\) & 0.29 (\(\pm 0.03\)) \({}^{\text{c}}\) \\ \hline \hline \end{tabular} Note: Mean comparison by [PERSON]’s multiple range tests. \({}^{\text{a}\text{b},\text{cd}}\) letters indicate the statistical difference in columns (significance level at 5%).  
\end{table} 
Table 3: Various elastic moduli of EPS, for different density levels. under \(\sigma_{\rm EL}\)) and the upper three levels (60.2-84.5% of \(\sigma_{\rm EL}\), over \(\sigma_{\rm EL}\)) among the five levels of applied stress for each EPS density was large. The nonlinear creep behavior of EPS, varying with the applied stress level and time (Figure 8) was captured well by the mathematical model in Table 4.  
When the measured creep data were modeled using the Burgers model (Equation (1)), the creep behavior for each applied stress was qualitatively analyzed by comparing the constant values in the model. As an example, the 12 h-long creep data measured after applying a stress of 0.0791 MPa to the EPS specimen with the density of 20 kg/m\({}^{3}\) were expressed using the Burgers model and nonlinear regression analysis; the analysis process of the constant value and retardation time of the model are shown in Figure 9. Table 5 summarizes the modeling of the 12-h-long creep test results for each applied stress at the different EPS density levels, using the Burgers model. Coefficient '\(a\)' represents the instantaneous elastic strain after loading the applied stress, while coefficient '\(b\)' represents the extent of the transient creep, and coefficient '\(d\)' represents the creep rate of the steady-state creep stage; all of these increased with increasing applied stress. In addition, the difference between these values for the lower two levels and the upper three levels among the five levels of applied stress for each density was large. Therefore, the EPS creep strain was large, depending on whether the applied stress level was below or above the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Density** **(kg/m\({}^{3}\))**} & \multicolumn{4}{c}{\(\varepsilon(\sigma_{o}\)**,_t_) = _ac\({}^{b}_{o}\)(\(c+d\) \(t-exp(-e\) \(t\))**)**} \\  & \(\varepsilon\) **= Strain**, \(\sigma_{o}\) **= Applied Stress (MPa)**, \(t\) **= Elapsed Time (min)** & \(\mathbf{r^{2}}\) \\ \cline{2-6}  & \(a\) & \(b\) & \(c\) & \(d\) & \(e\) \\ \hline
16 & 9302.7755 & 4.0384 & 1.4975 & 1.3301 \(\times\) 10\({}^{-3}\) & 0.0189 & 0.9856 \\ \hline
20 & 24,220.0535 & 5.0773 & 1.3275 & 8.4345 \(\times\) 10\({}^{-4}\) & 0.0174 & 0.9816 \\ \hline
25 & 143,392.3430 & 6.1685 & 1.2528 & 7.7452 \(\times\) 10\({}^{-4}\) & 0.0152 & 0.9912 \\ \hline
30 & 393.4906 & 4.1404 & 1.3821 & 1.0923 \(\times\) 10\({}^{-3}\) & 0.0254 & 0.9666 \\ \hline \hline \end{tabular}
\end{table}