## 6 Study on Two-Parameter Control of Synchronization in Incremental Launching Construction  
According to [PERSON]'s research [31], the probability of the normal operation of jacking equipment in incremental launching construction obeys a normal distribution; as a result, it is highly likely that two unfavorable states, unsynchronized vertical jacking and lateral offset, will occur simultaneously. If the influence of only a single factor is considered, it is easy to set the safety control thresholds to a large extent, which is not conducive to structural safety. To address this problem, based on the above single-parameter-influenced model of steel box girders, a correlation study of two parameters (unsynchronized vertical jacking and lateral offset) for the control of jacking synchronization is carried out. While changing the relative position of the pads to the base of the beam, a forced displacement in the Z-direction is applied to the base of pad on one side to simulate the simultaneous occurrence of the two unfavorable states. The results obtained from the analysis of the variation in the stresses of each main stress member with the vertical jacking height difference and lateral offset distance are shown in Figure 12.  
From the figure, it can be seen that the magnitude of the stress increase in each major stress member under the influence of a single parameter is smaller than the magnitude of the stress increase under the combined effect of two parameters. Observing the variation in  
Figure 12: Stress contour plots of major components under two-parameter action. the maximum equivalent force of the base plate, it can be found that, under the influence of a single parameter, the maximum equivalent force is 229.85 MPa at a lateral offset of 20 mm, and when the vertical jacking height difference is 15 mm, the maximum equivalent stress is 209.97 MPa, none of which exceeds the permissible stress of steel and meets the requirement of single-parameter control. However, under the joint influence of the two parameters, the maximum equivalent stress of the base plate reaches 256.31 MPa, which exceeds the allowable stress of steel. When the lateral offset reaches 50 mm and the vertical jacking height difference reaches 20 mm, the maximum equivalent stress of the base plate reaches 391 MPa, even exceeding the yield stress of steel, and the structure is very easy to be unstable. Therefore, when the two parameters act together, it will exacerbate the stress changes in each stressed member, and setting the control threshold only from the perspective of a single parameter is not enough to ensure the safety of the structure in incremental launching construction; it is necessary to synthesize the effects of the two to set the control threshold. In order to calculate the two-parameter control threshold, a nonlinear surface is fitted to the maximum equivalent stress value of the beam under the influence of the two parameters. For ease of computation, \(Z=Z_{0}+ax+by\) is chosen as the fitted equation, where \(x\) represents the vertical jacking height difference and \(y\) the lateral offset distance. The fitting results are shown in Figure 13. Solve for \(Z_{0}\) = 182.71, \(a\) = 2.97, \(b\) = 2.50. Then, the nonlinear surface fitting equation is:  
\[Z=182.71+2.97x+2.50y \tag{1}\]  
\(R^{2}=0.99762\), which is very close to 1, suggesting that the fit is valid. The allowable stress of Q345 Qd steel is 233 MPa, when \(Z\leq 233\) MPa:  
\[y\leq-1.19x+20.06 \tag{2}\]  
At this point, the structure is in a safe state and the image of the function is plotted, as shown in Figure 14. The green area in the figure shows the safety range under the two-parameter control of the synchronization of incremental launching construction, and the intersections of the function with the coordinate axes are (16.86, 0), (0, 20.06). In practice, the vertical jacking height difference value can be read directly from the vertical jack controller, while the lateral offset value needs to be further measured manually.