# Nonlinear Stiffness of Semi-Fixed Dowel Joints in Semi-Integral Bridges
## 1 Introduction  
Most small and medium span bridges are simply supported beam-type structures. In order to accommodate the variation of ambient temperature, expansion joints are usually arranged between beams and abutments, and between adjacent spans for multi-span bridges. Expansion joints often become the weakest parts of bridges, bringing adverse effects to traffic and bridge structure. Their maintenance and replacement consume a lot of manpower, material resources and costs. An effective solution is to retrofit them into integral abutment bridges (IABs), in which the expansion gaps, expansion joints and bearings can be eliminated by integrating the superstructure and the abutments [1,2]. An IAB is a statically indeterminate structure in longitudinal direction due to these rigid connections, and the substructure stiffness has a significant effect on the stress level induced by thermal loads in the structure [3, 4, 5, 6]. For new IABs, flexible piles like H-shaped steel piles or concrete piles with an enclosure of the top part by a rubber sleeve or filled with loose sand can be used as the foundation [7,8]. However, for most of the existing bridges with expansion joints (jointed bridges), the stiffness of the substructures are generally highand integral design is not feasible; thus, the semi-integral abutment bridges (SIABs) are used to be an alternative of jointless bridges [3,9,10]. In a SIAB, the superstructure may rest on conventional bearings at abutments, and moves longitudinally independent of the abutments. In order to reduce the detrimental effects of temperature-induced displacements, the Virginia Department of Transportation (VDOT) in the USA developed the dowel joints for semi-integral abutment bridges, in which the dowels protruded into the superstructure were loosely wrapped with three layers of roofing felt. Tests on the two types of joints were carried out; one was the original type with a shear key but without a pad, while the other was the revised type without a shear key, instead it used a pad as bearing. Test results showed that the dowel joints could significantly reduce the moments transferred from the superstructure to the foundation piles. The original joints experienced the shear key failure, while the revised ones did not exhibit this behavior and showed no sign of damage during the tests [11]. In the rehabilitation of the Jingpu Bridge transformed from a simply supported structure into a SIAB, dowel joints wrapped by rubber sleeves were used [12]. The rubber sleeve can provide space for the daily small thermal movements with small restraint, while the steel dowel can control the extra movements induced by seasonal temperature by transmitting shear forces from superstructure to substructure, the steel dowel can prevent fatigue failure caused by daily thermal movements. In addition, a rubber (neoprene) pad is used for the proper sitting of the superstructure on the substructure, to ensure the even distribution of the stresses at the bearing face and allow small thermal movements. The rubber sleeve and rubber pad will make the dowel joint behave nonlinearly, and the joint becomes a semi-fixed one. The nonlinear stiffness of the semi-fixed dowel joint has an impact on the performance of SIABs, and is the key parameter in the design calculation. Dowel joints are used widely in buildings because they can play an important role in seismic energy dissipation of a structure and an unseating prevention system. Research studies up to now have mainly focused on their seismic energy dissipation capacity [13, 14, 15]. The studs used in the rehabilitation of the Isola Della Scala bridge transformed from a simply supported structure into an IAB can be considered as novels, in which the push-out test of the stud was carried out [16]. However, the studs had no rubber sleeve and were used together with expansive concrete mortar incorporated with the existing bearings; accordingly, the connection between the superstructure and substructure is rigid.