PSI - Issue 78

Stefano Ercolessi et al. / Procedia Structural Integrity 78 (2026) 1497–1504

1502

Fig. 2. Gmsh soil and foundation model.

with Gmsh is shown in Figure 2. The soil domain is modelled with a base width of 112 m and a height of 50 m (excluding the foundation). Two free-field columns, each which a base of 20 m, are added on the lateral sides of the soil domain. The soil domain and the free-field columns are connected using zero-length elements to implement Lysmer-Kuhlemeyer dashpot (Lysmer and Kuhlemeyer (1969)) in both horizontal and vertical directions. To ensure consistent boundary behaviour, the nodes along the lateral edges of the free-field column are separately tied using equalDof constraints in both horizontal and vertical directions. The bottom boundary of the model is constrained in the vertical direction. Additionally, a zero-length dashpot element is introduced in correspondence of the leftmost node to apply the input excitation using the Joyner and Chen methodology (Joyner and Chen (1975)). This is achieved imposing an equalDof condition along the horizontal direction along the base nodes, with the leftmost node defined as primary node. Two coincident nodes share the primary node’s coordinates, one of which is fixed in all directions, forming the dashpot connection. A structured mesh is used to ensure that nodes along the lateral boundaries of both the soil domain and the free-field columns share the same vertical coordinates. A single elastic isotropic material model is adopted for both the soil and the free-field columns (c.f. Tab. 4).

Table 4. Soil domain and free-field columns mechanical parameters. Description Parameter

Unit

Shear waves velocity

V s ν s ρ s

800.00

m / s

0.48 2.16

Poisson’s ratio Mass density

−

3

t / m

Proportional damping is introduced in the model by defining two regions; the first corresponds to the frame struc ture, while the second include the soil domain and the foundation. Damping is calibrated considering a damping ratio ζ = 2% for both the regions, using the first and the third modal frequencies as reference. Soil domain and foundation, body forces are defined into the SSPquad elements defining appropriate sets of body forces. The seismic excitation is applied in form of velocity time history in agreement with the Joyner and Chen procedure. The input motion is depicted in Figure 3. Results are evaluated in terms of stress for the gravity analysis and acceleration responses for the dynamic analysis. Indeed, stress output is important in the gravity analysis to verify that the load application produces the expected geostatic stress distribution. However, since they are recorded at correspondence of the element Gauss points and then averaged over their number, the PVD recorder export them as cell-centered data. As a result, transition between adjacent elements may appear discontinuous. To address this, the Cell Data to Point Data filter in ParaView is applied during post-processing. This filter interpolates the cell-centered values from surrounding elements and assigns a representative value to each mesh node (point). Typically, the point value is computed as the average of all adjacent cell values that share that node, producing a smoother and more interpretable stress field visualization (c.f. Figure 4).