Analytical Models for the Force-Displacement Response of a Corroded Seven-Wire Strand

Reliable analytical models are needed for the estimation of the maximum strength and ductility of corroded cables, in order to assess the safety level of existing structures exposed to corrosion (especially bridges in which post-tension technology with following mortar injection is used). This paper proposes a simplified analytical approach for the estimation of the axial force-displacement response of corroded seven-wire strands, assuming an elastoplastic constitutive model for the steel material. The analytical approach is grounded on the two key-parameters governing the behaviour of a corroded wire: the normalized corroded length and the normalized corroded cross-section area. The model allows to obtain analytical expressions of the mechanical parameters (initial stiffness, yielding strength and ductility) governing the behaviour of the basic unit, namely the wire portion. Two different force-displacement models (based on the concepts of series and parallel systems) are then derived for the seven-wire strand. The first model ignores the frictional actions exchanged between the seven wires, since the seven-wire strand is modelled as a parallel system of seven “equivalent wires”. The second model, instead, accounts for the friction by introducing discrete internal constraints between selected nodes of the seven wires, thus considering the specific location of each corroded part of the individual wires. In this way the seven-wire strand is modelled as a series system of “equivalent stripes”. Each stripe of the strand is modelled by connecting in parallel the corresponding wire portions (that could be either intact or corroded) of the seven wires.