The layout plane of Bridge SE is shown in Fig. (1). As shown in the figure, a prestressed concrete continuous girder with a single box was used as the superstructure of Bridge SE. The construction of this bridge was completed in May of 2010. It was found by inspection and monitoring that all indexes of this bridge were compliant with code specifications until September 20, 2010 [8]. However, several tons of soil have been stacked besides bridge piers for further planting construction since September 21, 2010. Fig. (2) shows the location of the tons of stacked soil. As shown in the figure, the stacked soil was located between two piers, i.e., SE 9# and SE 10#. The mound of soil was as tall as 7.0 m.

The width of expansion joints is measured after finishing the construction of the bridge structure. It was found that the measured widths of several expansion joints, i.e., SE #5, #6, #7, #8, #9, #10, and #11, have exceeded the design value of 120 mm. The detailed measurement results are shown in Table 1, among which the greatest sliding displacement was found for SE #9. The location of Points A-E is shown in Fig. (3). The horizontal displacement of the box girder is presented in Fig. (2) after the tons of soil were piled up. The box girders from SE #7 to #11 moved with different displacements to the left, where SE #9 exhibited the highest displacement of approximately 129 mm.

Fig. (1). Layout plane of Bridge SE.

Fig. (2). Measured horizontal shift of box girder.

Significant sliding displacements occurred at the bridge bearings of the abovementioned piers. Fig. (3) presents the sliding displacement of the bridge bearing at SE #9 as an example. As shown in the figure, the sliding displacement was as great as 142.5 mm, more than 1/3 of the width of the upper steel plate (440 mm).

Table 2 presents the horizontal displacement and slope rate of all slanted piers at two orthogonal direactions. Noting that the limits of inclination indexes for the bridge piers were 3‰ (slope rate) and 20 mm (top displacement) [9, 10], the inclination of SE #6, #7, #8 and #9 exceeded the limits.

To simulate the mechanical behavior of hidden bridge piles, an FD model, using the commercial software FLAC 3D shown in Fig. (4a), was established by integrating the bridge bearings, pier columns, pile cap, piles, and multiple soil layers. Pile elements were used to simulate the actual bridge piles with a length of 65.0 m. The bridge bearings, pier columns, and pile caps were simulated by solid elements. Concrete C30 and C50 were, respectively, applied for the bridge piles and other bridge members according to the design scheme. The elastic moduli of concrete C30 and C50 were, respectively, 3.00×10¹⁰ MPa and 3.45×10¹⁰ MPa with a uniform Poisson's ratio of 0.20. Goodman's joint element was used to simulate contact behavior between the pile and soil, in which the contact surfaces between the pile cap and soil were defined as sliding contact. The Mohr-Coulomb model was used to simulate the mechanical behavior of soils, whose parameters are shown in Table 3. To improve computation efficiency, the geometrical dimensions of the whole model were selected as 40 m × 40 m × 90 m, as shown in Fig. (5).

Fig. (3). Sliding displacement of bridge bearing at SE #9.

Fig. (4). Finite difference calculation model.

Fig. (5). Calculation results of four piles.

A regional distributed load, whose plane-view dimension was 15.0 m × 8.0 m, was applied on the ground to simulate the action of ground loading. The distribution load was as great as 93.3 kPa, calculated by multiplying the gravity of soil with the average height of 5.3 m. Two-directional horizontal forces of 320 kN and 231 kN were applied on the top of the bridge pier to simulate the action of temperature and creep of concrete, respectively. In addition, four vertical concentrated forces were applied on four bridge bearings to simulate the gravity load of the box girders, as shown in Fig. (4b).

The FD model was calibrated and confirmed by the measurement results of pier displacements. The ultimate calculation results are shown in Table 4, along with the measurement results. As shown in the table, the calculation results fit well with the measurement results.

Fig. (5a, b) show the calculated deformation of four piles under the ground loading. As shown in the figure, the maximum deformation of these piles in the X and Y directions was 19.4 mm and 15.2 mm, respectively. The maximum bending moments in the X and Y directions were 1432 kN·m and 1548 kN·m, respectively. As the designed bending capacity of these four piles was as great as 1851.2 kN·m, the bending performances of these four piles were within the safe state. Fig. (5c) shows calculated results of axial force distribution of these four piles along the pile length. As shown in the figure, the maximum axial forces among these four piles were 3110 kN, much smaller than the designed capacity of 6481 kN.

The calculation results indicate that the ground loading was the major reason inducing the inclination of the bridge. Under the unbalanced ground loading, four bridge piles sustained different axial forces and two-direction bending moments, inducing uneven deformation of the bridge piles. Connected rigidly to the bridge piles, the bridge piers deformed in coordination with the bridge piles, inducing an abnormal situation for the bridge bearings and expansion joints. In addition, the piles and connected bridge piers were within the elastic state and did not have to be strengthened.

Fig. (6) presents a construction flow chart of the general strengthening scheme. The main construction programs were executed according to the following steps.

1. Sensors were first installed at specific positions to monitor strains and displacements of the box girders and piers, sliding displacement of the bridge bearings, the width of the expansion joints, and ground displacements.

2. Limiting devices were installed at the bridge bearings to prevent the movement of girders during the rectification of bridge piers. A hydraulic power system was simultaneously installed at the bridge bearings to reset the bridge piers, girders, and bearings.

3. Initial values of the installed sensors were measured as a reference for subsequent monitoring.

4. Slanted piers were rectified in three steps: 1) construction of a reverse ground loading; 2) construction of stress release holes; and 3) construction of a foundation reinforcement.

5. Recovery of the abovementioned members was conducted in two steps: 1) the bridge piers, girders, and expansion joints were reset, and 2) the damaged bridge bearings were replaced.

a) Entire model. b) Model of the bridge pier.

The stacked soils were removed immediately once the bridge abnormalities were detected. Then, reverse ground loading was conducted by stacking soil at the opposite side of SE #6, SE #7, SE #8, and SE #9 to produce a reverse incline of bridge piers. Fig. (7) shows schematic and actual views of the reverse ground loading. As shown in the figure, the distance between the toe of the mound and the edge of the piers was 4.0 m. The mound was 10.0 m wide with 13 layers. The first soil layer was 4.0 m high. Soil layers were subsequently added, each of which was 0.5 m high. A new layer was only added when the speed of deep displacement was no more than 2.0 mm/d. The total final soil weight was 38200 kN.

Several rows of stress release holes were constructed on the opposite side of the reverse ground loading to shorten the procedure of the reverse incline of bridge piers. Stress release holes with diameters of 120-150 mm were dug using spiral drilling machines. As shown in Fig. (7), these holes were arranged in three or four sector-shaped rows with a spacing of 0.5-1.0 m. The design distance between the edge of the piers and the nearest hole was 2.0 m. The stress release holes in different rows had different depths. The stress release holes with the largest depth (20.0 m) were in the nearest row to the pier. The depth of the stress release holes was reduced by 5.0 m for each subsequent row. Pipes were embedded in the holes as a preparation for grouting with cement paste to prevent excessive ground deformation. After the pier rectification, all holes were filled with cement paste to prevent ground instability.

Fig. (1) shows that the bridge is close to the Houyuan River. Two types of piles were constructed around the bridge piers as ground reinforcements to stabilize the foundation and prevent riverbank landslides. The first type was a deep-mixed pile, and the second type was a high-pressure jet grouting pile. Fig. (8a, b) show the plane and section for the two types of piles. The high-pressure jet grouting piles were used because the height of the machinery used to construct low-cost deep-mixed piles exceeded that of the girder-covered area. With the longitudinal axles of bridge piers as the axis of symmetry, the total width of the ground reinforcement area was 30.0 m. The ground adjacent to SE #10 and SE #5 was also reinforced to prevent potential soil deformation induced by the reverse ground loading.

As shown in Fig. (8b), the side profile of deep-mixed piles was applied as a nail shape. Arranged in rectangular arrays of 1.5-m spacing, the total length of these piles was 15.0m with an expanded 3.0-m-long top. The diameters of the expanded and other segments were 1000 mm and 500 mm, respectively. The piles were 15% cement, and the design's unconfined compressive strength on the 28th day was no less than 750 kPa. The high-pressure jet grouting piles had similar lengths with a diameter of 600 mm. The piles were arranged in rectangular arrays with a 1.8-m spacing. The edge area of the high-pressure jet grouting pile was placed 2.0 m away from the edge of the pile cape to prevent damage to the bridge piles against the high injection pressure of 20 MPa.

A hydraulic power system using jacks was introduced to rectify two of the most slanted bridge piers, SE #9 and #10. Fig. (9) shows the structure of the hydraulic power system using jacks. As shown in Fig. (9a), two 300-kN jacks were installed at SE 9# and SE10#, and a pair of pushing forces was acted on top of these two bridge piers by reaction forces from the girder structure. The reaction forces were transmitted by the limiting structure and the side retainer of the bridge girder. The limiting structure was preassembled on top of the bridge piers and composed of three members: 1) a reaction member; 2) a limiting steel plate; and 3) a connection steel plate.

A similar hydraulic power system was used to push the shifted girder back to its original position, restoring the expansion joints to their original width. Taking the expansion joint of SE #12 as an example, two 300-kN jacks were simultaneously installed at the expansion joint of SE #12 with a 400 mm spacing. Supported by the girder between SE #12 and #15, a horizontal pushing force was applied to the girder between SE #9 and #12. Real-time monitoring results were used to adjust the pushing force and switch the next pushing case. The target displacement of each pushing case was applied as 5.0 mm, and the design interval of the construction period was 5 days.

Some bridge bearings required being replaced because of the non-code-compliant deformation of the bolts and the upper steel plates. To provide essential space for replacement of damaged bridge bearing, a hydraulic system was used to lift the girder temporarily. Lifting forces were calculated by a simplified calculation model, which is shown in Fig. (10). As shown in the figure, the dead loads (line load, Qk), the flexural rigidity (EI) of the girders, and the stiffness of bridge bearings (ki,j, where i indicates the number of piers, and j indicates the transverse location, with 1=left and 2=right) were taken into account in the calculation model. In the calculation model, fourd bridge piers were simulated by articulated hinged supports. The calculated lifting force of bridge bearings is shown in Table 5.

Fig. (6). Construction flow chart of the general program.

Fig. (7). Schematic and actual view of ground loading.

Fig. (8). Ground reinforcement.

Fig. (9). Structure of hydraulic power system.

Fig. (11a) shows the lifting system using jacks along with the added members and dial indicators. A bottom steel plate supported by sand was used as a platform. Round steel pipes were used to eliminate the difference between the maximum stroke of the jacks and the headroom under the girder. Steel plates with a 20-mm thickness were inserted between the jacks and the steel pipes to improve the stability of the lifting system. Wedge blocks were placed on top of the jacks with a slope rate of 5% to accommodate the bottom surface of the girder. Steel plates were inserted between the jacks and the girder to prevent local compression failure of concrete.

The damaged upper steel plate and bolts were removed after lifting bridge girders by 3-5 mm, as shown in Fig. (11b, c). A new upper steel plate was added to replace the damaged upper steel plate and welded to the embedded steel plates. Limiting devices were installed in advance to prevent longitudinal girder motion. Fig. (12) shows the detailed structure of the limiting devices. The limiting devices were placed in front of the side retainer and bolted to the bars plated into the girder in advance.

The damaged upper steel plate and bolts were removed after lifting the bridge girders by 3-5 mm, as shown in Fig. (11b, c). A new upper steel plate was added to replace the damaged upper steel plate and welded to the embedded steel plates. Limiting devices were installed in advance to prevent longitudinal girder motion. Fig. (12) shows the detailed structure of the limiting devices. The limiting devices were placed in front of the side retainer and bolted to the bars plated into the girder in advance.