Hybrid Sliding-Rocking Bridges

A major portion of Dr. Mohammad Salehi’s doctoral research was devoted to the computational modeling, design, and experimental testing of the so-called Hybrid Sliding-Rocking (HSR) bridge columns. The HSR columns, which are suitable for Accelerated Bridge Construction (ABC) in highly seismic areas, consist of precast concrete segments connected through unbonded posttensioning tendons, end rocking joints, and intermediate sliding joints. These components provide the HSR columns with significant energy dissipation and self-centering capabilities and the sliding joints act as controlled-amplitude multi-level isolation system.

HSR substructure

HSR bridge column components

Computational Modeling and Design

Although the proof-of-concept tests conducted at the University at Buffalo had shown the effectiveness of the HSR columns in mitigating seismic damages, simplified computational modeling of these columns to further the understanding of their dynamic behavior and enable their optimal design was a major challenge, particularly because of the complex sliding-rocking interactions between their precast concrete segments and the interactions between the unbonded posttensioning tendons and their ducts. In order to address these modeling challenges, Dr. Salehi developed multiple element formulations, such as the so-called HSR element formulation and the so-called co-rotational continuous multi-node truss element formulation. The former element formulation, which represents a sliding joint and its close vicinity, combines a gradient inelastic beam-column element formulation (to simulate material- and rocking-induced deformations) with a hysteretic friction model at sliding-dominant joint location (to simulate friction-sliding response). The latter element formulation is capable of simulating an unbonded tendon of intermediate contacts with its duct, while enforcing a uniform axial strain along its entire length in spite of its potential transverse deviations.


Modeling of HSR columns

By implementing the 2D and 3D versions of these element formulations in the structural analysis framework of OpenSees, Dr. Salehi could build robust simplified simulation models able to reproduce the experimental data available for HSR columns with acceptable accuracy. Furthermore, in order to investigate the effects of various variables associated with the design of HSR columns (e.g. their joint distribution and joint sliding amplitude) and different earthquake excitation characteristics (e.g. source-to-site distance and excitation direction) on the seismic performance of HSR columns, Dr. Salehi used the above models to perform hundreds of time-history analyses on these columns. The results of this study showed the versatility of HSR columns subjected to different base excitations and led to the development of the second generation of HSR columns, which provides an optimal seismic performance compared to the original system. Two of Dr. Salehi’s publications on the modeling and design of HSR columns are found here and here.


Validation of displacement time-history obtained from the developed model against shake table test data

Experimental Testing

After completion of the computational part of this research project, Dr. Salehi designed an experimental testing program to further validate the created computational models and investigate the quasi-static and dynamic responses of the second generation of HSR columns under a variety of loading conditions. For this purpose, four identical half-scale hollow HSR column specimens were built and tested in the Structural and Materials Testing Laboratory at Texas A&M University. The tests were conducted under both quasi-static and dynamic uniaxial lateral loading (considering both free and fixed top ends), biaxial lateral loading, and torsional loading. Video clips from some of the performed tests in each phase of testing are found below. The most important results of this experimental testing program have been published here and here.


Experimental test setups