# Research on the Tie Cable Replacement Method of Half-through Tied-Arch Bridge
## 4 Results  
### Results of the Impact of Each Replacement Scheme on the Substructure  
The arch rib and arch seat of the half-through tied-arch bridge were consolidated, and the horizontal forces of the main arch, side arch, and tie cable were balanced at the arch seat, so the arch seat and pile foundation were sensitive to the cable force changes in the tie cable. Therefore, the impact of each replacement scheme on the safety of the substructure needs to be considered first.  
The type of bridge pile is the friction pile. The pile adopts a circular section with a diameter of 1.5 m. The longitudinal reinforcement is arranged as 32 HRB335 reinforceents with a diameter of 28. The pile length is 44 m, and the depth below the local scouring line is 30 m. The pile foundation layout and soil layer distribution are shown in Figure 5.  
To ensure the safety of the pile during the replacement of tie cables, the construction process was controlled according to the principle that there is no tensile stress during the replacement process. According to the model, the axial force of each pile under the dead load is 6438.3 kN, and the bending moment of the pile when tensile stress is about to appear is 1207.5 kN, which is the control bending-moment value during replacement.  
The most unfavorable state of pile stress is the state after cutting off the old tie cable in the non-substitution method schemes and the state after tensioning the temporary tie cable in the temporary substitution method schemes. The bending moment of the pile under each scheme is shown in Figure 6:  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Suspender** & **Design** & **Measured** & **Calculated** & **Difference between** & **Difference between** \\  & **kN** & **kN** & **kN** & **Calculation and Design** & **Calculated and Measured** \\ \hline R2 & 745 & 686 & 756 & 1.5\% & \(-9.3\%\) \\ R3 & 745 & 806 & 745 & 0.0\% & 8.2\% \\ R4 & 745 & 754 & 750 & 0.7\% & 0.5\% \\ R5 & 745 & 740 & 728 & \(-2.3\  
Figure 5: Bridge foundation and soil layer: (**a**) arrangement of the pile-group foundation; (**b**) geological conditions around the pile.  
Figure 6: File bending moment under each scheme (Unit: kN\(\cdot\)m): (**a**) initial state; (**b**) pile-bending moment of scheme 1; (**c**) pile-bending moment of scheme 2; (**d**) pile-bending moment of scheme 3; (**e**) pile-bending moment of scheme 4; (**f**) pile-bending moment of scheme 5; (**g**) pile-bending moment of scheme 6; (**h**) pile-bending moment of scheme 7; (**i**) pile-bending moment of scheme 8.  
It can be seen from Figure 6a that the bending moment at the pile top is negative under the dead load, indicating that the total horizontal thrust of the arch seat is toward the middle of the main span. In Figure 6b of scheme 1, due to tie cable 1# being removed, the direction of the horizontal force changes. With the increase in the number of tie cables removed, the bending moment at the pile top gradually increases, as shown in Figure 6c-e. In the temporary substitution schemes, the direction of the pile-top bending moment is the same as that under the dead load, and the pile-top bending moment increases with the increase in the number of tie cable replacements, as shown in Figure 6f-i. It can also be seen from Figure 6 that  
1. The bending moments of the pile caused by schemes 2, 4, and 8 are 1454.2 kN, 2351.7 kN, and \(-1141.0\) kN, respectively, of which the bending moment value of scheme 2 and scheme 4 exceeds the limit value.
2. In the non-substitution-method schemes, only one-sided single-tied cable replacement (scheme 1) and two-sided single-tie cable replacement (scheme 3) meet the need for the principle of no tensile stress in the piles.
3. In the temporary-substitution-method schemes, the bending moment of the pile changes slightly, and the bending moment value caused by scheme 8 is the largest.