# Influence of Deep Foundation Pit Excavation on Adjacent Pipelines: A Case Study in Nanjing, China
## 4 Numerical Simulations  
### Meshes and Boundary Conditions  
Figure 5 demonstrates the use of the PIAXIS (Exton, PA, USA) finite element simulation program for studying the foundation pit excavation process [20]. The soil was modeled using the hardening soil small strain (HSS) model [21], with parameters established through laboratory tests (refer to Tables 1 and 2). For the rock mass, the Mohr-Coulomb model was applied, and its material parameters are detailed in Table 3. The enclosure structure of the foundation pit was represented by a plate element structure. To simulate the interaction between the enclosure structure and the adjacent soil, positive and negative interfaces were created on both sides of the plate. The stiffness of the building's upper floors and basement was simulated using single plates, with parameters derived based on the equivalent stiffness principle. Concrete supports were simulated using beam elements, with parameters defined based on actual dimensions and concrete grades, considering the effects of temperature, creep, and construction on the deformation of reinforced concrete structures, which could lead to cracking. The building's superstructure was simplified into a three-dimensional frame structure. This structure comprised linear elastic beams and columns, simulated using beam elements with dimensions of 300 \(\times\) 400 mm\({}^{2}\) for beams and 350 \(\times\) 350 mm\({}^{2}\) for columns. The column pile in the foundation pit and the building's pile foundation were modeled using embedded-pile elements. Figure 4: Final settlement of pipelines after completion of pit excavation. Figure 5: Plan of the site and layout of the instruments (unit: m). In the numerical model, certain assumptions differed from the actual project conditions. The underground pipeline was assumed to have a density similar to that of the soil, regardless of the pressure within the pipeline and the effect of the fluid on it. It was treated as a line unit, without considering the cross-sectional size of the pipeline. The model adopted the actual parameters of the gas pipeline (diameter \(d\) = 1200 mm, wall thickness \(t\) = 5 mm) and the water supply line (\(d\) = 1000 mm, \(t\) = 5.5 mm). The distances between the pipeline and the foundation pit were set at 8 m and 10 m, respectively, with a burial depth of 5 m. The overall material parameters are presented in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Definition** & **Unit** \\ \hline \(\text{E}_{50}^{ref}\) & Reference secant modulus & MPa \\ \(\text{E}_{ood}^{ref}\) & Reference tangent modulus & MPa \\ \(\text{E}_{ur}^{ref}\) & Reference loading and unloading modulus & MPa \\ \(m\) & Stiffness stress level related power exponent & / \\ \(c^{\prime}\) & Effective cohesion & kPa \\ \(\varphi^{\prime}\) & Effective internal friction angle & \(\circ\) \\ \(\psi\) & Dilatancy angle & \(\circ\) \\ \(R_{f}\) & damage ratio & / \\ \(v_{ur}\) & Load–unload Poisson’s ratio & / \\ \(C_{0}^{ref}\) & Initial shear modulus under reference confining pressure & MPa \\ \(K_{0}\) & Static side pressure coefficient & \\ \(70.7\) & Shear strain threshold & / \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Constitutive parameters of HSS model.