## 4 Case Study  
A RC bridge with an irregular configuration, typical of many highway bridges around the world (Figure 7a), was designed according to Chinese codes [64; 65; 66] using the spectrum in [PERSON] et al. [24], and a horizontal elastic spectrum reduction factor equal to three for ductile design and deck vertical loads of 200 kN/m. The design materials included Chinese strength grade C30 concrete (cylindrical characteristic compressive strength f\({}_{\rm ck}\) = 20.1 MPa), Chinese steel mark HRB335E (characteristics yield strength f\({}_{\rm y}\) = 335 MPa) for the longitudinal rebar, and Chinese steel mark Q235A for the transversal steel reinforcement. The transversal steel spacing was not designed using the capacity design criteria because many existing bridges have insufficient shear reinforcement, so seismic retrofitting is often needed. For example, 50% of bridges constructed between 1989 and 2008, and 40% before 1989 in China before the introduction of the actual seismic code JTG/T-B02/01/2008 [66] present this deficiency. The present study focuses on the seven-meter pier of the bridge, the most stressed and damaged one after a strong seismic event. Two RC circular columns, P16A and P16B--the as-built columns (ASB)--were designed to represent the seven-meter pier of the bridge, and were selected as the case study. Proper scale factors [36] were applied to the pier concrete and steel reinforcement geometries. These scale factors ensure global similarity (flexural and shear strength) between the pier and scaled column using the same design materials without scaling the concrete aggregates and steel rebar geometries. This permitted us to inexpensively test scaled RC columns to obtain results that could be extended to the corresponding seven-meter pier. The geometries and the steel reinforcement details of the scaled RC columns are provided in Figure 7c. Pieces of HRB335E steel rebar, used to realize the longitudinal reinforcement of the RC columns, were tested at the laboratory of Fuzhou University. The stress strain curves for two rebar specimens (NSR1 and NSR2 in Figure 8) showed a mean yield stress f\({}_{\rm sy}\) of 450 MPa and a mean maximum stress f\({}_{\rm su}\) of 600 MPa. The C30 concrete, used to build the columns, was tested by compression tests on a 100 \(\times\) 100 \(\times\) 100 mm\({}^{3}\) cube after 28 days of standards curing in the Fuzhou University laboratory. The resulting mean compressive strength R\({}_{\rm cm}\) was 31 MPa. This concrete is a self-compacting concrete (SCC), which simplifies the concrete casting and mix design, consisting of two types of coarse aggregates, sand, cement, mineral admixture, polycarboxylic acid superplasticizer, and a water/cement ratio of 0.56. The as-built (ASB) columns, P16A and P16B, were severely damaged by the cyclic tests described in Section 5, and were then repaired using the proposed repair strategy. The axial load at the top of the column was not applied during the repair operations to simulate the unloading of the RC component during repair by props to ensure safe repair operations. The 100 mm thick external concrete part of the column was removed along the column, up to a height from the base of the column about 500 mm; this height is higher than the theoretical plastic  
Figure 8: New rebar segments tested in tension: Not turned (NSR) and turned (TSR) segments; skeleton curve (Skel) to calibrate the steel material model in OpenSees. Figure 7: (a) Bridge geometries, (b) applied displacement history to test the scaled pier, (c) geometries and reinforcement of the 1:6 scale pier (mm), and (d) proposed repair strategy: Rebar substitution and concrete jacket building. hinge length (Figure 7d). The removal was performed around the whole column surface to expose the transverse steel and the longitudinal rebar. In the plastic hinge region, the transverse steel and each longitudinal rebar were cut.