# Visualization of Distributed Plasticity in Concrete Piles Using OpenSeesPy
## 2 Modeling Methodology
### Pile Geometry, Material Properties, and Loading  
Gravity loads are applied first to the pile model, followed by monotonic lateral load at the pile head. The modeled pile has an overall length of 16.75 m and diameter of 60 cm, precast concrete as shown in Figure 1.  
The pile is prestressed using twelve 15 mm diameter strands with a characteristic tensile strength \(f_{pk}\) = 1860 MPa. Confinement is provided by a W20 spiral (Grade 420 MPa yielding strength) at 64 mm pitch with a clear cover of 76 mm. The pile connection consists of eight 32 mm dowel bars, which project into a pile cap. Figure 2 illustrates the cross-sectional details of the precast concrete pile at its connection to the cap beam.  
The selected concrete compressive strength is 48 MPa, while the yield strength of the connection reinforcement dowels was taken as 420 MPa, which are representative values used in the design of RC piles in wharf structures. For modeling of concrete materials, the stress-strain proposed by [PERSON] et al. [57] is utilized for both confined and unconfined conditions. Dowel steel bars are modeled using methodology outlined by [PERSON] [58]. Prestressing strands are not modeled under the premise that inground hinging is undesirable in practice. However, for simplicity and for the sole purpose of comparing results of the two modeling platforms (SAP2000 vs. OpenseesPy), the section in Figure 2 was also used in-ground. Figure 3 illustrates the stress-strain relationships of the pile section materials.  
Figure 1: Pile–soil overall geometry configuration: (**a**) elevation view; (**b**) isometric view.  
Soil consists of loose sand. The effective unit weight and friction angle are 32 kN/m\({}^{3}\) and 33 degrees, respectively. Soil spring spacing for both SAP2000 and OpenseesPy models follows the recommendations of ASCE61-14 [1] for a 60 cm prestressed pile. Parameters to define PySimple1, TzSimple1, and QzSimple1 springs for the OpenseesPy model are computed at each depth below the mudline. For the SAP2000 model, the p-y curves are generated using the same PySimple1 parameters as those used in the OpenseesPy model at four depths. For the upper five pile diameters below the mudline, three p-y curves corresponding to depths 1 m to 3 m are utilized with a spring spacing of 30.5 cm, designated as K1-1, K1-2, and K1-3. Beyond this depth, one additional p-y curve at a 6 m depth is employed with a spring spacing of 61 cm and 1.2 m, referred to as K2 and K3, respectively. T-z and Q-z springs are not considered in the SAP2000 model. Figure 4 illustrates the force-deformation relationships for each soil spring and their distribution along the pile length.  
Figure 2: Cross-section modeling approaches for nonlinear analysis of prestressed piles: (**a**) Fiber-section model developed in OpenSeesPy, representing the location of confined and unconfined concrete fibers along with longitudinal reinforcement. (**b**) Representation in SAP2000 section modeler. (**c**) Reinforcement detailing.  
Figure 4: _Cont._  
Figure 3: Stress–strain curves for section materials: (**a**) Unconfined concrete. (**b**) Confined concrete. (**c**) Dowel reinforcement.