Research on disturbance influence of goaf residual deformation on simply

Considering that the upper part of the simply-supported beam bridge is a hinged link^37,38, the shear force and bending moment of the simply-supported beam bridge remain unchanged within the range of abutment support^39,40. Therefore, this article focuses on the co-deformation of the bridge construction site, pile, and bridge floor when discussing the impact of goaf residual deformation on the disturbance of the simply-supported beam bridge.

Disturbance influence caused by residual subsidence

The subsidence of the ground, piles, and bridge floor are obtained during the simulation experiments, as shown in Fig. 7. As illustrated in Fig. 7, With the increase of ground residual subsidence, the residual subsidence of pile and bridge floor also increase gradually. The overall subsidence characteristics of ground, piles, and bridge floor are similar, showing a non-linear change process of rapid subsidence first and then slowing down. However, the ground subsidence is significantly greater than that of pile and bridge floor. When the ground residual subsidence reaches its maximum of 230 mm, the maximum subsidence of pile is 24.4 mm, while the maximum subsidence of bridge floor is only 12 mm. As the bridge in the study area is located above the goaf center, the subsidence of ground, pile and bridge floor are all gentle. However, considering that the relative positions of each pile and the goaf are not strictly the same, the subsidence values of different piles are also different. For example, the ground subsidence of B3 pile location is 230 mm, while the subsidence of B3 pile is 24.0 mm. The ground subsidence of B4 pile location is 224.1 mm, while the subsidence of B4 pile is 22.1 mm. Thus, the subsidence of ground and pile decrease with the distance increasing from the ground to the goaf center. The final subsidence distribution of the model, as shown in Fig. 8, the figure results are consistent with the above analysis. To analyze the collaborative subsidence of ground, pile and bridge floor in the same vertical direction, k₁ is employed to represent the ratio of ground subsidence to pile subsidence, and k₂ is employed to represent the ratio of pile subsidence to bridge floor subsidence. It can be calculated that at the final residual subsidence state, the pile subsidence is about 1/10 of the ground subsidence at any position, and the bridge floor subsidence is about 1/2 of the pile subsidence at any position.

Residual subsidence curves of ground, pile and bridge floor.

Final subsidence distribution of the model.

It should be noted that k₁ and k₂ are not constant values, but exhibit a nonlinear evolution process with the occurrence of residual subsidence, and the change process of k₁ and k₂ is opposite. k₁ is about 12 at the initial stage, and then gradually decreases to 10, which can be fitted by a power function. While k₂ is about 1.9 at the initial stage, and then gradually increases to 2.0, which can be fitted by an exponential function.

Based on the above analysis, uneven ground subsidence can lead to uneven pile subsidence, resulting in bridge tilting and instability. Uneven tilting deformation of pile can result in curvature deformation, which can be obtained by laying an observation line on the bridge floor. As illustrated in Fig. 9, Due to the bridge in the study area being located above the goaf center, the bridge floor subsidence is gentle, resulting in less tile and curvature deformation, and the bridge floor is always in the positive curvature influence zone. Based on the analysis of the pile position, it is found the bridge floor curvature reaches its maximum between the pile locations and its minimum at the pile location, indicating that the pile has an inhibitory effect on the curvature deformation of the bridge floor when the bridge is above the goaf center.

Curvature curve of bridge floor.

Disturbance influence caused by residual horizontal movement

The horizontal movement of the ground, piles, and bridge floor is obtained during the simulation experiments, as shown in Fig. 10. The horizontal movement of the simply-supported beam bridge can be divided into along the bridge direction and perpendicular to the bridge direction. As the horizontal movement perpendicular to the bridge direction is small, this paper only analyzes the horizontal movement along the bridge direction. As illustrated in Fig. 10, With the increase of ground horizontal movement, the horizontal movement of pile and bridge floor also increases gradually. The overall horizontal movement characteristics of ground, piles, and bridge floor are similar, showing a non-linear change process of rapid movement first and then slowing down. However, the ground horizontal movement is significantly greater than that…