Multiscale damage evaluation of broken wires in semi-parallel stay cables

The wires in stay cables inevitably fracture due to fatigue and corrosion, impacting the stiffness contribution of the cable-stayed bridge. A damage assessment method for stay cables, which consider the redistribution of adjacent wire tension around the fractured wire and central wire tension in semi-parallel configurations, is proposed to calculate recovery length and damage coefficient. The method involves establishing compatibility equations, broken equilibrium equations, friction and contact force equations, and accounting for the pinch effect of polyethylene sheaths. Nonlinear least squares are used to solve the unknown variables according to the governing equations. Based on the equivalent strain principle, the damage coefficient of the stay cable along the axial direction is calculated from the recovery length, and the cable area is adjusted in the finite element model (FEM). The strain in the stay cable is iteratively fed back into the analytical model until convergence conditions are met. This study compares the damage coefficient and recovery length under different wire breakage conditions and live loads. The results show that broken wires have a relatively small impact on the axial stiffness of semi-parallel stay cables. However, increased friction around the broken wire raises the stress amplitude and sliding length, exacerbating fatigue and wear.