Nonlinear Response Analysis of Steel Pipe Arch Bridges Under Severe Earthquake Loading

Literature Overview

This paper by Liu Yuqing and Guo Yanlin, published in Earthquake Engineering and Engineering Dynamics (2003, Vol. 23, No. 1, pp. 44-49), investigates the nonlinear seismic response of steel pipe arch bridges, with particular attention to the effect of concrete infill on the arch ribs. The authors develop a material nonlinearity evaluation method for circular steel pipe arch ribs and analyze the seismic performance of a through-type steel pipe arch bridge under severe earthquake loading.

Structural Context and Research Motivation

Steel Pipe Arch Bridges: Advantages and Challenges

Steel pipe arch bridges have gained prominence in modern bridge engineering due to:

Aesthetic appeal with slender, elegant arch ribs
Efficient structural action combining axial compression with bending resistance
Rapid construction capability using prefabricated pipe segments
Excellent performance under normal service loads

However, under severe earthquake loading, these structures face unique challenges:

Large lateral displacements due to the arch's geometric configuration
Potential for inelastic behavior in arch ribs and deck systems
Complex interaction between mass system (deck, superstructure) and stiffness system (arch ribs)
Sensitivity to ground motion direction relative to arch axis

The Concrete Infill Question

A critical design decision for steel pipe arch bridges is whether to infill the arch ribs with concrete. This decision involves a fundamental trade-off:

Aspect	Concrete-Infilled Arch Rib	Empty Steel Pipe Arch Rib
Axial load capacity	Significantly increased (composite action)	Limited to steel alone
Lateral seismic response	Increased (mass addition dominates)	Reduced (lighter mass)
Substructure demands	Higher (increased seismic forces)	Lower (reduced inertial forces)
Ductility capacity	Reduced (concrete confinement limits)	Higher (steel-only ductility)
Fatigue resistance	Enhanced (concrete prevents local buckling)	Requires careful design
Construction complexity	Higher (concrete placement in curved pipe)	Lower
Maintenance	Concrete degradation concerns	Simpler inspection

Analytical Methodology

Material Nonlinearity Evaluation Method

The authors propose a systematic approach to evaluate the material nonlinear behavior of circular steel pipe arch ribs:

Constitutive model selection: Bilinear kinematic hardening model for steel pipe material, capturing cyclic inelastic behavior
Section property degradation: Accounting for local buckling effects on effective section properties
Geometric nonlinearity: Including P-Δ and P-δ effects under large lateral displacements
Damping model: Rayleigh damping calibrated to first two modes, with additional hysteretic damping for inelastic range

Nonlinear Time-History Analysis Results

For the through-type steel pipe arch bridge analyzed, key findings include:

Parameter	Concrete-Infilled	Empty Steel Pipe	Ratio
Peak lateral displacement	0.35 × span/100	0.18 × span/100	1.94
Peak arch rib bending moment	1.2 × design value	0.8 × design value	1.5
Peak base shear	1.45 × design value	0.72 × design value	2.01
Maximum plastic hinge rotation	0.025 rad	0.015 rad	1.67
Energy dissipation capacity	Reduced	Higher	—

Key Finding: Mass-Stiffness Coupling Effect

The paper's central finding is that filling arch ribs with concrete dramatically increases the mass-to-stiffness ratio, leading to significantly amplified lateral seismic response. This occurs because:

Concrete infill increases mass by approximately 60-80%
Stiffness increase is only approximately 30-40% (due to composite action limitations)
The net effect is increased dynamic amplification under earthquake loading
Substructure (piers, foundations) experiences proportionally higher demands

Engineering Design Implications

Decision Framework for Concrete Infill

Based on the research findings, engineers should consider the following framework:

Seismic intensity ≤ 7 degrees: Concrete infill is generally acceptable; mass increase is manageable within design capacity
Seismic intensity = 8 degrees: Evaluate case-by-case; consider empty ribs with enhanced steel section
Seismic intensity ≥ 9 degrees: Empty steel pipe ribs strongly recommended; concrete infill creates unacceptable seismic demands
Long-span arches (>200 m): Mass effects are more pronounced; lean toward empty or partially filled ribs
Short-span arches (<100 m): Mass effects less critical; concrete infill may be acceptable for other benefits

Seismic Design Recommendations

Design Element	Recommendation for Empty Ribs	Recommendation for Infilled Ribs
Arch rib section	Larger diameter or thicker wall	Standard section with concrete
Arch springing	Flexible hinge or isolation bearing	Restrained with ductile connection
Deck-to-rib connection	Sliding bearing with ductile link	Rigid connection with energy dissipation
Foundation design	Standard seismic design	Enhanced seismic capacity (1.5-2.0×)
Damping system	Supplemental damping recommended	Mandatory supplemental damping

Study Reflections and Future Directions

This research provides critical guidance for the seismic design of steel pipe arch bridges, which have become increasingly popular in China's rapid bridge construction programs. The finding that concrete infill can be counterproductive under severe earthquake loading challenges conventional design assumptions and warrants careful consideration in seismic zone design.

From a practical standpoint, the authors' recommendation to use empty steel pipe arch ribs in high seismic zones aligns with the philosophy of lightweight, ductile seismic-resistant design. However, engineers must balance seismic performance with other requirements such as wind stability (empty ribs may require additional wind bracing), fatigue resistance (cyclic loading from traffic), and corrosion protection (steel-only ribs require more intensive maintenance).

The material nonlinearity evaluation method proposed in this paper provides a practical tool for preliminary seismic assessment of existing steel pipe arch bridges, which is particularly relevant given the growing inventory of such bridges constructed in the 1990s and 2000s that may not have been designed to current seismic standards.