PSI - Issue 84

Giovanni Stasi et al. / Procedia Structural Integrity 84 (2026) 789–796

794

6. Structural design description To increase pier stiffness and optimize the deck isolation system, considering that the tallest pier currently exhibits a longitudinal period of 3.5s, the existing walls of piers 2 through 5 were reinforced into 50cm-thick box-shaped structures for heights ranging from 6 to 12m from the base. Deck continuity was ensured by eliminating transverse joints and connecting the slabs using Dywidag bars. Two constraint solutions were hypothesized. Solution 1 uses Lead Rubber Bearings (LRB) acting in both directions, integrated with longitudinal sliders on the abutments. Solution 2 utilizes LRB devices with longitudinal sliders on all supports except Pier 6, which acts as a longitudinal fixed constraint, and four fluid-viscous dampers with a damping coefficient of C=1350kN(s/m)  located on Abutment 2. The main characteristics of the devices are reported in the following table.

Table 1. Main characteristic of LRB devices.

Combination

F2 ( kN )

F1 ( kN )

d1 ( mm )

d2 ( mm )

ke=F2/d2 (kN/m)

k1=F1/d1 (kN/m)

k2 (kN/m)

k2/k1 (-)

ξe

SP_01 + P01 A P05 new 190

86 13.5 200 55 13.5 200

950 680

6370 4074

558 0.087537 24.5% 434 0.106605 21.4%

P_06 + SP02 new

136

7. Structural model and analysis Three finite element models were used to evaluate the effects of the actions. The first model models the existing structure with an isostatic carriage-hinge scheme and decks constrained to the piers and abutment 2. The effects of hammering have been neglected. In the longitudinal direction, the existing structure can be considered as many individual elementary oscillators, the piers, with the mass of the deck and 30% of the pier mass concentrated at the head. The following table shows the stiffnesses, masses, and periods of the first longitudinal mode of all the piers of the existing structure, evaluated according to the formulation T=2  √(M/k), similar to those obtained from the calculation model.

Table 2. Stiffnesses, masses, and periods of the first longitudinal mode of all the piers of the existing structure. Element k1=kx=F/DX ( kN/m ) Wpila ( kN ) WT pila=Wimp+0.3Wpila ( kN ) T=2p √ (M/k) ( s ) Pier 01 18182 3210 11773 1.61 Pier 02 9524 4346 12114 2.26 Pier 03 4708 5760 12538 3.27 Pier 04 4363 5871 12571 3.41 Pier 05 5018 5604 12491 3.17 Pier 06 33784 1995 9123 1.04

The second and third finite element models are characterized by the axial connection of the deck slabs with a total mass of approximately M imp total = 7240 kNs 2 /m and the inclusion of nonlinear n-link elements with the characteristics of the isolation devices described previously. Seismic performance was assessed by comparing nonlinear dynamic analyses (using seven pairs of bi-directional time histories) with linear response spectrum analyses. The evaluation focused on averaged peak responses, specifically support reactions and displacements at the deck and pier tops. Structurally, foundations were modeled as rigid links fixed at the base, while abutments were treated as fixed constraints.