PSI - Issue 78

Marco Gaetani d’Aragona et al. / Procedia Structural Integrity 78 (2026) 968–975

970

In this framework, flexural behavior is modeled using a distributed fiber-based approach, whereas shear and axial failures are incorporated through concentrated nonlinear springs. The modeling scheme adopted in OpenSees ® is illustrated in Fig. 1. The flexural response is captured using a distributed fiber-based method via force-based beam-column elements with fiber-defined cross-sections (Fig. 1(a)). To account for potential brittle failure in RC columns, a lumped plasticity approach is adopted (Elwood & Moehle, 2005b, 2005a). This involves adding axial and shear springs in series with the fiber element, governed by limitCurve materials. These springs activate when the element exceeds predefined limit states, concentrating flexural deformation in the fiber element (Fig. 1(b)) and axial/shear deformation in the springs (Fig. 1(c) and (d)). The limitCurve materials influence the global response of the element. The backbone curve results to be redefined to include strength deterioration once the global response of the beam-column element exceeds a predefined limit state surface (Fig. 1(d)). The shear strength can degrade up to a preselected residual value. The same procedure is used to incorporate the axial response into the column model (Fig. 1(e)). In the case of axial springs, if column drift surpasses a critical threshold, axial capacity drops sharply, risking convergence issues. To mitigate this, a soft elastic axial spring is added between spring nodes to facilitate smoother load redistribution (Fig. 1(a)) (Gaetani d’Aragona et al., 2017) . 3. Degradation of materials in RC members due to corrosion The structural performance of RC elements, particularly those exposed to aggressive environments like bridge piers, can deteriorate significantly due to corrosion. This degradation in strength and ductility arises from several interrelated mechanisms: reduction in the yield strength of corroded stirrups, which weakens confinement; loss of mechanical properties in longitudinal reinforcement; reduction of concrete compressive strength near the corroded steel often accompanied by cracking and cover spalling; bond deterioration at the steel – concrete interface; and the formation of gaps between longitudinal and transverse rebars, which exacerbates bar buckling. One of the most relevant effect of corrosion is the steel cross-section loss, that can be quantified via the average mass loss:

m m −

(1)

m  =

0

m

0

where m o and m denote the mass of uncorroded and corroded bar, respectively. For uniform corrosion, the corrosion attack penetration can be quantified through a reinforcement diameter decrease as follow:

*   = −  2

ave x

(2)

where ϕ and ϕ * represent the uncorroded and the equivalent corroded diameter. The average attack penetration x ave can be linked to the average mass loss of Eq. (1) via (Vidal et al., 2004): ( ) 1 1 ave x m For bars subjected to uniform corrosion, the average mass loss Δm mainly governs the degradation of mechanical properties of steel rebars. In the scientific literature, a linear decay of yield and ultimate strength degradation of corroded rebars (Zeng et al., 2020): ( ) * 1 y Fy y F m F  = −  (4)   = − − (3)

(

) m F

*

1  = − 

F

(5)

u

Fu

u