## Materials and Methods
### Physical Parameters of Ramsar Sand  
The relative density \(\mathrm{D_{r}}\) is a critical parameter that can control the stress-strain behavior or change the liquefaction susceptibility. In this study, three values of relative density (2%, 30%, and 45%) were considered to include very loose, loose, and medium dense sand, respectively. Ramsar sand is poorly graded clean sand which is extensively found in the southern coast of the Caspian Sea and classified as SP according to Unified Soil Classification System (USCS). The \(\mathrm{e_{max}}\) and \(\mathrm{e_{min}}\) values of Ramsar sand, measured according to ASTM D-4253 [45], and ASTM D-4254 [46], are 0.88 and 0.54, respectively. The mass of sand needed to prepare specimens with known relative densities was calculated and then it was gradually poured into the mold for each sample. The grain size distribution curve of Ramsar sand is depicted in Figure 4 and its basic properties are summarized in Table 1.  
Figure 3: Geological and structural map of the sampling area (taken from 1:100,000 maps of Chalous, Shokran, Marzanabad, Baladeh and Ramsar, Geological Survey of Iran). The grain size distribution of the specimens after triaxial testing was investigated and plotted against sand specimens obtained at 2 m depth from a borrow pit. Figure 4 shows that sand particles around 0.6-0.8 mm are further broken because there is a reduction in this particle percentage, whereas adversely, there is an increase in the particle percentage in the 0.1-0.2 mm particle size range. This observation reveals that after shearing, Ramsar sand particles are brittle. To identify the observed behavior in quantitative terms, the Hardin equation for relative breakage index (B\({}_{\text{r}}\)) was adopted [47]. [PERSON] [47] defined breakage potential, B\({}_{\text{P}}\), as the area above the initial grading curve (which is the sand specimen before shearing in this case) up to the 100% passing line, confined between the lower-bound 74 \(\upmu\)m minimum grain diameter and upper-bound 2 mm as the maximum grain diameter. Furthermore, total breakage, B\({}_{\text{t}}\), was calculated as the area between the particle size distribution curve of the initial grading curve and post crushed state (after shearing) grading curve. The breakage index is defined as the ratio of B\({}_{\text{t}}\) over B\({}_{\text{p}}\). For the grading curves seen in Figure 4, breakage potential (B\({}_{\text{p}}\)) and total breakage (B\({}_{\text{t}}\)) were found to be 60.3 and 0.74, respectively. As a result, the relative breakage \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Maximum void ratio, \(e_{max}\) & 0.88 \\ Minimum void ratio, \(e_{min}\) & 0.54 \\ Specific gravity, \(G_{s}\) & 2.67 \\ \(D_{50}\)(mm) \({}^{*}\) & 0.22 \\ \(D_{10}\)(mm) \({}^{*}\) & 0.147 \\ \(D_{30}\)(mm) \({}^{*}\) & 0.187 \\ \(D_{60}\)(mm) \({}^{*}\) & 0.246 \\ Coefficient of curvature, \(C_{c}\) & 0.96 \\ Coefficient of uniformity, \(C_{u}\) & 1.67 \\ \hline \hline \end{tabular} \({}^{*}\)\(D_{50}\), \(D_{10}\), \(D_{30}\), and \(D_{60}\): the particle size diameters for which 50%, 10%, 30% and 60% of the sample is finer, respectively.  
\end{table} 
Table 1: Basic properties of intact Ramsar sand. Figure 4: Grain size distribution before (unbroken) and after (broken) the performance of the triaxial test on Ramsar sand. index (B\({}_{r}\)) was found to be 0.012 and quantitatively confirmed the observed breakage of the Ramsar sand particles. In order to further investigate this observation, sand particles before and after the test were examined using an optical microscope. The grains of the sand in Figure 5a are rounded with certain sharp ends, whereas in Figure 5b, the edges of the parent particle appear broken. Due to extensive shearing, more rounded particles are generated with very tiny spots related to broken bits of sand grains, clearly demonstrating the inherent brittleness.