# Seismic Study of An Isolated Cable-Stayed Bridge under Near-Fault Ground Motions
## 5 Influence of Various Factors
### Influence of Soil Type  
The SSI effect is a crucial factor influencing the seismic response of cable-stayed bridges [34]. In this section, four different soil types are considered, and their material parameters are provided in Table 2. In the table, \(\mu\) represents the soil mass density, \(\
u\) is the Poisson's ratio, G is the shear modulus of the soil, and Vs is the shear wave velocity of the soil. To assess the impact of soil types on the dynamic response of cable-stayed bridges, five computational models are established, including a fixed-base model at the tower base and SSI effect models considering the influence of the four different soil types.  
Figure 11 presents the average values of bounding forces under five different conditions. As the soil stiffness decreases, the bounding force slightly increases, but the difference is not significant. For example, when the foundation is fixed and the soil type is D, the bounding forces at expansion joint 1 are 6.11 \(\times\) 10\({}^{4}\) kN and 6.65 \(\times\) 10\({}^{4}\) kN, and at expansion joint 2, the bounding forces are 2.74 \(\times\) 10\({}^{4}\) kN and 3.12 \(\times\) 10\({}^{4}\) kN, respectively.  
Figure 11b displays the deformations of the bearings under five different constraints. Due to the decreasing soil stiffness, the lower structure experiences less constraint, making it more prone to vibrate in the same direction as the main beam, resulting in smaller bearing deformations.  
Figure 11c illustrates the distribution of bending moments at the bridge towers under five different constraints. It is observed that, considering the SSI effect, lower soil stiffness  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Soil Type** & \(\mathbf{v}\) & \(\mathbf{\mu}\) & \(\mathbf{G}\) & \(\mathbf{V_{s}}\) \\ \hline A (Hard rock soil) & 0.25 & 2300 & 5184 & 1608 \\ B (Rock soil) & 0.26 & 2200 & 3160 & 1156 \\ C (Dense soil-Flexible rock) & 0.32 & 2000 & 1082 & 698 \\ D (Hard soil) & 0.44 & 1800 & 264 & 302 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Soil material properties.  
Figure 11: Average maximum responses considering different soil type: (**a**) bounding force at each expansion joint; (**b**) longitudinal bearing displacement; (**c**) longitudinal bending moment of tower.  
significantly reduces the internal forces in the main tower. This phenomenon can be explained by the seismic spectrum characteristics: the SSI effect makes the structural system more flexible, leading to increased deformation. Compared to the fixed-base model at the tower base, the SSI model exhibits a lower spectral acceleration value corresponding to the first natural frequency, causing a decrease in internal forces in the main tower. Additionally, considering the damping effect of the soil, a certain amount of seismic input energy is dissipated during the earthquake excitation, further reducing the internal forces in the main tower. When the soil type is A, the seismic response results of the two bridge types are close, suggesting that a fixed-base model can be used for dynamic analysis when the foundation consists of hard rock. However, as the soil stiffness decreases, differences between the SSI effect model and the fixed-base model emerge. Therefore, in the dynamic time-history analysis of large-span cable-stayed bridges, the influence of the SSI effect should be considered when the foundation soil is relatively soft.  
The above study indicates that, although the influence of SSI on bounding forces is not pronounced, relatively soft soil can extend the natural period of vibration for large-span cable-stayed bridges, reduce the overall system stiffness, and consequently decrease bearing deformations and bending moments in the bridge towers.