## 2 Materials and Methods
### One-Dimensional Ground Response Analysis  
One-dimensional non-linear ground response analyses (NL-GRAs) were carried out at six distinct locations in the Gwadar region to assess the dynamic behavior of the soil. Generally, empirical correlations for backbone curves, such as those in [55], are typically based on fitting experimental data at small to medium shear strain levels using the hyperbolic model. At large strains, the shear resistance is often estimated through extrapolation, which can result in either underestimation or overestimation. Additionally, some hyperbolic models may inaccurately capture the shear resistance at larger strains (>1-3%) and fail to represent the shear-stress behavior accurately at small strain levels [19].  
To overcome these challenges, the authors of [19] introduced the Generalized Quadratic/Hyperbolic (GQ/H) constitutive soil model, a non-linear stress-strain (\(\tau\)-\(\gamma\)) approach designed to address inaccuracies at both small and large strains. This model incorporates modifications to better align with laboratory-measured initial or monotonic stress-strain (backbone) curves across all strain levels, including the actual shear strength or failure shear stress observed at larger strains (e.g., \(\gamma_{\mathrm{f}}\) = 10%).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Site Profile** & **Vs Soil, m/s** & **Vs 30, m/s** & **Site Natural Period, s** & **Site Classification** \\ \hline S-1 & 178 & 267 & 0.238 & S\({}_{\mathrm{D}}\) \\ S-2 & 155 & 283 & 0.141 & S\({}_{\mathrm{D}}\) \\ S-3 & 220 & 292 & 0.210 & S\({}_{\mathrm{D}}\) \\ S-4 & 208 & 252 & 0.350 & S\({}_{\mathrm{D}}\) \\ S-5 & 157 & 153 & 0.864 & S\({}_{\mathrm{E}}\)The GQ/H constitutive soil model, developed by [19], was employed alongside the DEEPSOIL v7.0 software [18] to evaluate the dynamic response of soils. This model is widely used in site response analyses and is advantageous because it can capture both the initial shear modulus at zero shear strain and the limiting shear strength at high strains [56; 57; 58]. The accuracy of the model is well established, and it is recommended for use in site-specific ground response analyses by many researchers [59; 60; 61].  
The NL dynamic response was assessed by examining key dynamic soil properties such as the maximum shear modulus (G\({}_{\text{max}}\)), the ratio of the shear modulus to the maximum shear modulus (G/G\({}_{\text{max}}\)), and the damping ratio (D) over a wide strain range. The Darendeli model [55] was applied to each layer within the site profile to evaluate the modulus reduction and damping curves. Based on the recommendations of [55], the values for the over-consolidation ratio, number of cycles, and frequency were set to 1.0, 10, and 1.0, respectively, whereas the value of K\({}_{0}\) for each layer was evaluated using [PERSON]'s equation [62]. The frictional angle (d) for the investigated profiles ranged from 29\({}^{\circ}\) to 35\({}^{\circ}\) and the plasticity index (PI) values ranged from 0 to 11, inclusive.  
The modulus reduction factor (MRDF) was applied to match the NL empirical curves. The initial modulus reduction curve (G/G\({}_{\text{max}}\)) for each soil layer, calculated using [55], was manually adjusted by modifying the data points to align with the desired shear strength levels at larger strains. The rationale behind fitting the real data was twofold: to achieve an effective hyperbolic depiction, and to offer a more precise depiction at high strains. The target shear strength of the soil was evaluated using the Mohr-Coulomb  
Figure 4: Site profiles used in this study.  
failure criterion [18]. The layers were meshed to ensure that each layer could support wave propagation with frequencies exceeding 30 Hz, as suggested by [18].