Spatial Seismic Response Analysis of Large-Span Steel-Concrete Composite Arch Bridges

Overview and Background

The paper by Zheng Jiashu and Jin Bangyuan (2003), published in the Journal of Southwest Jiaotong University (Vol. 38, No. 1, pp. 53–56), presents a spatial seismic response analysis of the Longtanhe Bridge, a large-span steel-concrete composite arch bridge. The authors, affiliated with Southwest Jiaotong University and China Railway Second Engineering Bureau (Qinghai-Tibet Railway Highway Command), developed a three-dimensional dynamic finite element model to evaluate the seismic performance of this significant infrastructure project.

The Longtanhe Bridge is a notable example of steel-concrete composite arch bridge technology applied to large-span crossings in geologically active regions. The seismic design of such bridges requires careful consideration of geometric nonlinearity, foundation-structure interaction, and the complex dynamic behavior of composite structural systems.

Modeling Approach

Finite Element Model Development

The authors developed a spatial (three-dimensional) dynamic finite element model of the Longtanhe Bridge. The model incorporates the following elements:

1. Steel-concrete composite arch ribs: Modeled using beam elements that account for the composite action between the steel tube and the core concrete.
2. Hangers and suspenders: Modeled as tension-only elements to represent the cable system.
3. Deck: Modeled using plate or shell elements to capture the in-plane and out-of-plane behavior of the bridge deck.
4. Foundations: Modeled using spring elements to represent the foundation-structure interaction.

The use of spring elements for the foundation is a practical approximation that captures the essential dynamic interaction between the bridge structure and the supporting soil or rock mass. The spring stiffness values are derived from geotechnical site investigation data.

Geometric Nonlinearity

A key feature of the analysis is the inclusion of geometric nonlinearity, which accounts for the effects of large displacements and rotations on the structural stiffness. For large-span arch bridges, geometric nonlinearity is particularly important because:

• The arch ribs undergo significant axial deformation under seismic loading.
• The change in geometry alters the load path and stiffness distribution.
• The P-Δ effect (second-order effect) can be significant under lateral loading.

The authors employed a spatial iterative algorithm to solve the nonlinear equilibrium equations. This algorithm iteratively adjusts the stiffness matrix to account for the changing geometry as the structure deforms.

Dynamic Analysis Method

The seismic response was calculated using the Wilson θ method, a time-history integration procedure that is well-suited for nonlinear dynamic analysis. The Wilson θ method offers the following advantages:

• Unconditional stability: For θ ≥ 1.375, the method is unconditionally stable, allowing larger time steps without loss of stability.
• Accuracy control: The parameter θ can be adjusted to control the accuracy of the solution.
• Efficiency: The method is computationally efficient for large-scale models.

Key Findings

Foundation-Structure Interaction Effects

The most significant finding of the study is the influence of foundation-structure interaction on the seismic response of the bridge. The analysis revealed that:

1. Natural frequencies: The inclusion of foundation flexibility reduces the natural frequencies of the bridge compared to a fixed-base model. The reduction is most pronounced for the lower modes, which are most relevant to seismic response.
2. Axial forces: The foundation-structure interaction significantly affects the axial forces in the arch ribs. The flexible foundation allows for additional deformation that alters the axial force distribution.
3. Bending moments: The bending moments in the arch ribs and deck are also affected by the foundation flexibility. The interaction can either increase or decrease the moments depending on the mode shape and the phase of the seismic input.
4. Mid-span displacement: The mid-span displacement of the deck is influenced by the foundation flexibility. A flexible foundation can increase the displacement by allowing additional rotation at the supports.

Modal Characteristics

The spatial iterative algorithm identified the following modal characteristics of the bridge:

The pattern of foundation effects is consistent with theoretical expectations: lower modes, which involve more global deformation, are more sensitive to foundation flexibility.

Seismic Response Characteristics

The time-history analysis revealed several important characteristics of the seismic response:

• Peak response: The peak displacement, axial force, and bending moment occur at different times during the seismic event, reflecting the complex dynamic interaction between the structural components.
• Nonlinear behavior: The geometric nonlinearity becomes significant for large seismic inputs, with the effective stiffness of the structure decreasing as displacements increase.
• Arch rib behavior: The arch ribs experience the most significant seismic demands, with high axial forces and bending moments concentrated at the crown and springing regions.
• Deck behavior: The deck experiences significant transverse displacement and torsional response, particularly in the mid-span region.

Design Implications

Foundation Design

The findings of this study have important implications for the foundation design of steel-concrete composite arch bridges in seismic regions:

1. Foundation stiffness must be characterized accurately: The dynamic properties of the foundation significantly affect the seismic response of the bridge. Simplistic assumptions about foundation stiffness can lead to inaccurate predictions.
2. Foundation-structure interaction should be included in seismic design: Fixed-base models may not capture the true seismic response of the bridge. The inclusion of foundation flexibility can lead to more accurate and potentially more economical designs.
3. Geotechnical investigation is essential: The quality of the seismic analysis is directly dependent on the quality of the geotechnical data used to characterize the foundation.

Structural Design

The seismic analysis results inform several structural design decisions:

1. Arch rib reinforcement: The regions of highest seismic demand (crown and springing) require additional reinforcement or detailing to ensure adequate ductility and energy dissipation.
2. Deck connection design: The connections between the deck and the arch ribs must be designed to accommodate the significant relative displacements predicted by the analysis.
3. Hanger design: The hangers must be designed to remain elastic under seismic loading, as they are typically not designed for inelastic deformation.

Construction Considerations

The construction of steel-concrete composite arch bridges in seismic regions requires special attention to:

1. Temporary works design: Temporary supports and cable stays used during construction must be designed for seismic events that may occur during the construction period.
2. Erection sequence: The sequence of erection affects the final structural configuration and must be carefully planned to ensure that the completed structure has the intended seismic performance.
3. Quality control: The quality of the steel-concrete composite action is critical to the seismic performance. Welding quality, concrete fill quality, and bond quality must be rigorously controlled.

Methodological Insights

The approach taken in this study represents a mature methodology for the seismic analysis of complex bridge structures. Several methodological aspects are noteworthy:

1. Spatial modeling: The use of a three-dimensional model is essential for capturing the complex spatial behavior of arch bridges, particularly the torsional and lateral response that cannot be captured by planar models.
2. Geometric nonlinearity: The inclusion of geometric nonlinearity is critical for large-span structures where displacements are significant relative to structural dimensions.
3. Foundation-structure interaction: The spring-based foundation model is a practical and effective approach that captures the essential dynamics without requiring a full geotechnical model.
4. Wilson θ method: The choice of integration method is appropriate for the nonlinear dynamic analysis of this type of structure, offering a good balance between accuracy and computational efficiency.

Summary

This paper presents a comprehensive spatial seismic response analysis of a large-span steel-concrete composite arch bridge, incorporating geometric nonlinearity and foundation-structure interaction. The findings demonstrate that foundation flexibility has a significant influence on the seismic response of the bridge, affecting natural frequencies, internal forces, and displacements. The methodological approach, combining a three-dimensional finite element model, spatial iterative algorithms, and the Wilson θ time-history integration method, represents a rigorous and practical framework for the seismic analysis of complex bridge structures. For engineers involved in the design and assessment of steel-concrete composite arch bridges in seismic regions, this paper provides valuable insights into the importance of foundation-structure interaction and the need for nonlinear spatial analysis in seismic design. The study underscores that the seismic performance of these structures is a system-level phenomenon that requires integrated analysis of structural, geotechnical, and dynamic aspects.