## 1. Introduction

In recent years, enhancing the seismic resilience of structures, communities, and even nations has received extensive attention in the field of earthquake engineering [

1,

2]. In 2015, the importance of promoting the resilience of new and existing critical infrastructure (water, transportation, telecommunications infrastructure, etc.) was emphasized at the Third United Nations World Conference on Disaster Risk Reduction [

3]. These critical infrastructures play a crucial role in post-earthquake relief and reconstruction. However, previous post-earthquake surveys have shown that conventional reinforced concrete piers dissipate seismic energy through plastic hinge zones, which results in residual drifts and irreparable damage. For instance, after the 1995 Japan Kobe earthquake, approximately 100 reinforced concrete piers, with residual drift ratios exceeding 1%, were demolished [

4].

Based on the lessons learned from previous earthquakes, several pier systems have been proposed to satisfy the requirements of seismic resilient structures [

5,

6]. Pioneering research on rocking bridge columns incorporating unbonded posttensioning was conducted by Mander and Cheng [

7]. Later, Hewes and Priestley experimentally investigated the response of segmental bridge piers with unbonded prestress tendons [

8]. Subsequently, experimental and analytical studies were performed by many researchers to demonstrate the potential advantages of self-centering piers [

9,

10,

11,

12,

13]. Corresponding results confirmed that unbonded posttensioning could effectively mitigate residual deformation. However, despite the desirable self-centering capacity, the energy dissipating capacity is less than satisfactory. Therefore, a hybrid system, a posttensioned structure assembled with additional energy dissipation, is proposed [

14]. This system results in a flag-shaped hysteretic relationship. Many studies have been conducted for further validation of the superiority of the hybrid pier system and the development of various solutions for energy dissipation. In previous studies, the energy dissipating capability of the hybrid system was enhanced in two ways: (1) Embedding internal energy dissipation (ED) devices consisting of mild steel bars or shape-memory-alloy bars with unbonded length at the critical joint [

15,

16,

17,

18,

19,

20,

21,

22]. Obviously, such internal ED devices are not readily replaceable if damaged after a major earthquake, which increases the difficulty of post-earthquake restoration. (2) Installing external ED devices (viscous energy dissipation, steel dissipater, aluminum bars, etc.) around the bottom of the piers [

20,

23,

24,

25,

26,

27,

28]. However, the limited installation space for external ED devices restricts the development of energy dissipation performance. Moreover, the external ED devices located at the bottom of the piers are more vulnerable to other natural and artificial factors, such as corrosion from water, impacts from vehicles, or floating debris.

Replaceable shear links have been successfully applied in buildings [

29,

30,

31,

32] and bridges [

33,

34,

35,

36,

37,

38] as sacrificial elements to dissipate seismic energy. Inspired by previous research, this work proposes a novel pier system, which combines the advantages of both self-centering piers and replaceable shear links. As shown in

Figure 1, the pier system relies on unbonded prestress steel strands to provide self-centering forces and adopts shear links between the columns to act as reformative external ED devices. The shear link consists of two parts, i.e., the replaceable part and the pre-embedded part, which are connected by high strength grade 12.9 bolts. During a severe earthquake (E2 level earthquake defined in Chinese Code [

39], the largest acceleration in the lateral acceleration response spectrum is 0.34 g), inelastic deformation is concentrated in the replaceable part of the shear link, while the damage of key components (bent cap, columns, footing, unbonded prestress steel strands, and the pre-embedded parts of the shear links) can be prevented. In addition, the bolted connection ensures that the damaged parts can be easily and quickly replaced, which will accelerate post-earthquake restoration. Furthermore, the interval between the columns provides adequate space for the shear links. Therefore, sufficient energy dissipation of the proposed pier system can be guaranteed.

Although the double-column self-centering pier with shear links has outstanding seismic performance theoretically, the nonlinear behavior and design method of the pier have not been systematically studied. An experimental study of the entire pier system is costly and difficult. Consequently, in this work, a finite element (FE) model of the proposed pier is developed, and the mechanical behavior of the proposed double-column self-centering pier fused with shear links is investigated. The investigation is mainly focused on the application of the innovated pier in urban viaducts, the piers of which are not slender. To calculate the lateral force-displacement skeleton curve, a theoretical model based on the matrix displacement method and the virtual work principle is established. The outcomes of this study can benefit the further development of the design method of the innovated pier.

## 3. Performance of Double-Column Self-Centering Piers with Shear Links under Quasi-Static Cyclic Loading

An FE model of the double-column self-centering piers with shear links was built based on the modeling method presented in

Section 2. Each column has a height of 3.00 m with a 2.00 m × 2.00 m cross section, and the clear distance between the columns is 3.00 m. The steel strand in each column has a total area of 15424 mm

^{2} and an initial stress of 1395 MPa. Further, a vertical concentrated load of 3.08 × 10

^{4} kN is applied at the bent cap to simulate the superstructure gravity. Grade C60 concrete (Chinese concrete grade, standard uniaxial unconfined compressive strength

f_{c} = 38.5 MPa, standard elastic modulus

E_{c} = 3.6 × 10

^{4} MPa) is adopted, while 15.2 mm diameter strands (ultimate strength

f_{PT} = 1860 MPa, elastic modulus

E_{s} = 195 GPa) are used for unbonded prestress steel strands. The initial stiffness and yield strength of the adopted shear link are 6.0×105 kN/m and 1.4 × 106 kN, respectively. The responses of the piers under quasi-static cyclic loading are discussed in this section.

#### 3.1. Rocking Process

Figure 8 illustrates the rocking process of the pier. The column-footing interface remains closed until the lateral force has increased to the force at the imminent gap opening. Then, the columns begin to rotate about the compression toe. Large nonlinear rotations can be sustained at the column-footing and column-cap beam joints with minimal structural damage. However, high stress may develop in the contact area during joint gap opening; the maximum stress is 179 MPa, at the edge of the contact area. Therefore, the joints should be strengthened (e.g., by installing steel jacketing) to avoid local failure and corresponding posttensioning losses.

Figure 9 shows the coordinates of the column axis while the pier rocks at the maximum lateral displacement (the centroid of the bottom column section is the coordinate origin). As shown, the column axis is approximately a straight line. The rigid-body motion significantly affects the displacement. Consequently, the deformation of each column under the action of lateral loads can be neglected.

#### 3.2. Influence of Shear Link Arrangement

As shown in

Figure 10, a uniformly distributed spring model (

Figure 10a) and an integrated spring model (

Figure 10b) were built to compare the influence of the shear link arrangement. Note that the spring in the integrated spring model is a superposition of the springs in the uniformly distributed spring model, i.e.,

${k}_{\mathrm{ISM}}={\displaystyle \sum _{i=1}^{n}{k}_{\mathrm{UDSM}i}}$ and

${F}_{\mathrm{yISM}}={\displaystyle \sum _{i=1}^{n}{F}_{\mathrm{yUDSM}i}}$, where

k_{ISM} and

F_{yISM} represent the initial stiffness and yield strength of the spring in the integrated spring model, respectively, while

k_{UDSMi} and

F_{yUDSMi} represent the initial stiffness and yield strength of each spring in the uniformly distributed spring model, respectively;

n is the number of springs.

Comparing the results of the two models (

Figure 11), it can be concluded that the shear link arrangement has little impact on the hysteretic performance of the hybrid bridge pier. The reason for this phenomenon is that the relative shear displacement of each shear link is subjected to the identical rigid-body motions of the columns. Therefore, the analysis and discussion of this study are based on the integrated spring model. Note that the integrated spring model is more convenient for computing, while uniformly distributed shear links will be adopted in reality to significantly reduce the difficulties in construction.