A simplified procedure to track the tension force: numerical validation

Recently, bridge collapses due to brittle fracture of grouted post-tensioning external tendons have been reported, highlighting the importance of structural health monitoring to prevent and predict these situations that strongly compromise safety. Non-destructive testing techniques based on the vibration response have proven their reliability in this aspect, as they allow continuous monitoring of the tendon modal parameters and the estimation of tension force. The tension force can be indirectly estimated from the modal properties of the tendon. A simplified method to track the tension force is proposed, which consists of calibrating the tendon model by obtaining the equivalent modal lengths for each natural frequency in such a way that general boundary conditions are considered for each mode. This study proposes a first numerical validation of this method through a detailed finite element model of a tendon. The finite element tendon model is subjected to a given stressing force; the bending stiffness and all other relevant parameters of the tendon are also known, subsequently, a modal analysis is performed to obtain the natural frequencies. The first twenty natural frequencies numerically calculated are then used to estimate the tension force based on the simplified method presented previously, the modal length calibration and optimization for each natural frequency is carried out for this example, and the estimated tension force and bending stiffness can be obtained. These results are compared with the finite element model of the tendon and then, the proposed tension force estimation procedure can be validated