# Cause Analysis of Pier Inclination of An Expressway Interchange Bridge: Case Study
## 5 Numerical Analysis
### Pier Deformation under Dead Load and Displacement of Girder End  
5.1.1. Pier Deformation under Dead Load  
A 3D model was developed using Midas Civil to analyze pier inclination during construction, girder-end displacement under temperature, and the creep of concrete, as shown in Figure 12.  
There is a difference between the measured and design values of the support eccentricities for Piers P30 and P33 (see in Figure 9). Two models were established in the numerical analysis, the design model, considering the design values of support eccentricities, and the as-built model, considering the measured values. The analysis results show that Piers P30 and P33 are obviously inclined in both the design and as-built models (see in Figure 13).  
The original design was changed; a steel box girder was adopted between Piers P30 and P33, resulting in the reaction force of the concrete side being much greater than that of the steel girder side on Piers P30 and P33. However, the design values of support eccentricities on Piers P30 and P33 are not reasonable, leading to a large eccentric compression occurring on the piers during construction and operation. Significantly, due to the difference between the measured and design values of support eccentricities, in the as-built model, the effect of the eccentricities of Pier P30 decreases and the same effect of Pier P33 increases, different to the design model.  
Figure 12: Three-dimensional Midas model.  
Considering the actual construction process and eccentricities of the support on the cap, the Midas as-built model was used to analyze the deformation of the bridge after the design was changed. The analysis results show that Piers P30, P33, and P35 incline obviously while the other piers are almost vertical.  
Using Pier P30 as an example, the longitudinal inclination change during construction is shown in Figure 14, and the deformation process is described as follows:  
1. Step 1: After the substructure was completed, there was a small longitudinal inclination of \(-9\) mm since the cap is equivalent to the eccentricity of the pier.
2. Step 2: The displacement increased to \(-12\) mm due to concrete shrinkage and creep in one year.
3. Step 3: After the superstructure between Piers P27 and P30 was constructed, the displacement increased abruptly to \(-78\) mm since only the concrete bridge was erected on the pier.
4. Step 4: Over half a year, the displacement reached \(-121\) mm.
5. Step 5: After the erection of the steel box girder between Piers P30 and P33, the displacement decreases to \(-95\) mm since the eccentricity on the pier reduces.
6. Step 6: When the bridge construction was completed, the displacement was \(-108\) mm.
7. Step 7: After 3 years of shrinkage and creep, the displacement reached \(-134\) mm.  
It is shown that after the design change, the reaction force of the concrete side is much greater than that of the steel girder side on Piers P30 and P33, as is the eccentricities of the support, and the concrete and steel girder were constructed asynchronously. All of the above data show that a large eccentric compression occurs on the piers during construction and operation, resulting in a larger inclined deformation of Piers P30 and P33.  
Figure 13: Pier inclination in the design model and as-built model.