Prediction of bond–slip behaviour of embedded steel reinforcement through control field equations

In reinforced concrete design, bond-slip behavior at the reinforcement-concrete interface is critical to determine development length and the force-slip relationship of steel bars in concrete. The former ensures composite action between concrete and rebars while the latter governs rotation of structural joints. However, current bond-slip models are based on simplified assumptions or complicated computation resulting in either low accuracy or limited applications. In this paper, analytical models derived from control field equations are proposed and they have the advantages of low computing cost, high accuracy, and wide applicability. The control field equations describe stress state of embedded rebars in the form of second-order differential equations and give accurate predictions by incorporating local bond stress-slip relationship. The evolution of bond-slip distribution along the embedded rebar can be obtained by solving the control field equations. At perfect anchorage condition, a closed-form solution can be obtained and avoid iterative nested computations. However, when the embedment length is inadequate, a mathematical function in Matlab is involved to solve nonlinear control field equations and obviate complicated nested iteration. Finally, the proposed models agree well with published test results.