# Research on the Tie Cable Replacement Method of Half-through Tied-Arch Bridge
## 3 Replacement Scheme and Finite Element Simulation Method
### Finite Element Simulation Method  
The tie cable replacement analysis model of the third Lingjiang bridge was established by using the Midas/Civil 2021 finite element analysis software, as shown in Figure 3. The main arch rib, side arch rib, cross beam, pier, and pile were simulated by the beam element, and the suspender and tie cable were simulated by the truss element.  
The concrete of the arch ribs on the side arch was C50, and the elastic modulus was 34,500 MPa. Q345 steel is used for the steel pipe of the main arch rib, with an elastic modulus of 210,000 MPa. The steel pipe is filled with micro-expans  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Tie Cable** & **Non-Substitution** & **Temporary Substitution** \\ \hline one by one & 1\# & Scheme 1 & Scheme 5 \\ pair by pair & 1\#, 2\# & Scheme 2 & Scheme 6 \\ one by one symmetrically on & 1\#, 8\# & Scheme 3 & Scheme 7 \\ both sides & 1\#, 2\#, 7\#, & & \\ pair by pair symmetrically & 1\#, 2\#, 7\#, & & \\ on both sides & 8\# & Scheme 4 & Scheme 8 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Design of the cable replacement schemes.  
Figure 3: FE model of the third Lingjiang bridge.  
cable is made of a steel strand with a design strength of 1860 MPa and an elastic modulus of 195,000 MPa. The suspended adopts a parallel steel wire with a design strength of 1760 MPa and an elastic modulus of 195,000 MPa. The hanger beam and column beam were made of Q345 steel. C30 concrete was adopted for the arch seat, and C25 concrete was adopted for the pile foundation.  
The boundary condition was that the main arch and side arch were fixed at the top of the arch seat. The suspender was hinged to the arch rib and cross beam, and the tie cable was hinged to the side arch rib. The bridge deck and the beam were connected by common nodes. The boundary condition of the pile included the pile-bottom constraint and pile-side soil friction. The vertical fixed constraint was imposed on the pile bottom, and the constraint of the pile-side soil was simulated by soil spring. First, starting from the local scouring line, the pile was divided into a section of 2 m, and then according to the pile length, calculated width, and foundation horizontal resistance coefficient, the soil stiffness at the corresponding node was calculated, and finally, the stiffness value was given to the plane direction of the pile nodes.  
The removal and installation of the tie cable in the non-substitution method scheme were realized by using the unit \"passivation\" function, and the tensioning and unloading of the temporary tie cable in the temporary substitution method scheme was realized by using the \"initial tension replacement\" function. Since the replacement of tie bars needs to interrupt the traffic, only the dead load was considered in the replacement process.  
To verify the accuracy of the finite-element model, the suspender cable force was selected as the verification index. The calculated suspender force of the model was compared with the field-measured suspender cable force. The DH5906W cable-force sensor was used to measure the cable force of the suspender based on the frequency method, as shown in Figure 4.  
The comparison of the designed cable force, calculated cable force, and measured cable force are shown in Table 2.  
Figure 4: Field test of suspender cable force.  
It can be seen from Table 2 that the maximum deviation between the calculated cable force and the design cable force was 3.1% (R6, R15), and the total cable force deviation was 0.4%. The maximum deviation between the calculated cable force and the measured cable force was less than 15%, and the total cable-force deviation was 1%, which shows that the calculated model was in good agreement with the field test and verifies the effectiveness of the finite element model.