Thermal Stress Analysis During Concrete Hardening in Large-Diameter Steel Tube Arch Bridges Using Equivalent Age Method

Literature Overview

Sun Jianyuan and Xie Jinbao from the College of Civil Engineering, Tongji University, present a rigorous theoretical and numerical study on the thermal stress development within large-diameter steel tube concrete (STC) arch bridges during the concrete hardening phase. Published in the Journal of Tongji University (Natural Science) in 2019, Volume 47, Issue 6, this paper addresses a critical construction-phase engineering challenge: the thermal-mechanical coupling effects arising from hydration heat generation in massive concrete sections confined within steel tube arch ribs. The research was funded by the National Natural Science Foundation of China (Grant No. 51778468).

Theoretical Framework and Methodology

The study employs a multi-stage analytical approach that integrates heat transfer analysis, concrete maturity theory, and thermoelastic mechanics. The methodology proceeds through three sequential phases:

The equivalent age method serves as the central analytical tool, accounting for the temperature-dependent acceleration of concrete hardening. This approach recognizes that hydration heat elevates the internal concrete temperature, which in turn accelerates the chemical reactions governing concrete strength and stiffness development. The resulting accelerated elastic modulus growth creates differential thermal strains between the concrete core and the steel tube, generating significant internal stresses.

Core Findings: Temperature-Dependent Elastic Modulus Effects

The principal finding is that the hydration heat temperature field significantly accelerates the elastic modulus growth of the concrete during hardening, leading to substantially amplified thermal stresses. The quantitative results are striking:

The longitudinal stress amplification of 1.4x is particularly concerning for arch bridge applications, where longitudinal thermal stresses directly affect the structural integrity of the arch rib and can influence the overall stability of the bridge system. The fact that steel tube stresses remain largely unaffected indicates that the steel tube functions primarily as a boundary constraint and formwork rather than sharing the thermal stress burden proportionally.

Thermal-Mechanical Coupling Mechanism

The underlying mechanism can be understood through the following sequence: hydration heat generation raises the internal concrete temperature; elevated temperature accelerates cement hydration reactions; accelerated hydration increases the concrete elastic modulus at a faster rate than would occur under ambient temperature conditions; the rapidly stiffening concrete experiences greater thermal restraint from the relatively cooler steel tube shell; this restraint generates amplified thermal stresses. This positive feedback loop between temperature, stiffness development, and thermal stress is the core insight of the study.

The equivalent age method provides a practical framework for capturing this feedback mechanism. By defining an equivalent age that accounts for temperature history through a maturity function, engineers can predict the time-varying elastic modulus of the concrete at any point within the section. The maturity function typically takes the form of the Nurse-Saul equation or the Arrhenius equation, both of which relate the degree of hydration to the accumulated temperature-time product.

Engineering Practice Implications

For large-diameter STC arch bridges, this study has direct implications for construction sequence planning and thermal management strategies. The key engineering recommendations include:

1. Concrete mixture design should incorporate thermal control measures such as low-heat cement types, supplementary cementitious materials (fly ash, slag), and thermal admixtures to moderate hydration heat generation.
2. Construction sequencing should allow adequate time for temperature stabilization before proceeding with subsequent segments, particularly in cold-weather construction where the temperature differential between the hydration zone and the ambient environment is maximized.
3. Thermal stress verification should be included in the construction-phase structural analysis, using the equivalent age method to capture the temperature-dependent stiffness evolution.
4. Monitoring instrumentation should include embedded thermocouples at multiple depths within the concrete section to validate the predicted temperature field and enable real-time adjustment of construction procedures.

FMEA Analysis of Thermal Stress Risks

Applying the Failure Mode and Effects Analysis (FMEA) framework to the thermal stress problem identified in this study:

The highest risk priority number corresponds to radial cracking, underscoring the need for careful thermal management during concrete placement in large-diameter STC arch ribs.

Key Questions and Reflections

One question that arises from this study is the applicability of the equivalent age method to very large sections where temperature gradients are significant. In extremely large diameter tubes, the temperature difference between the core and the shell can exceed 50 degrees Celsius, creating a complex three-dimensional temperature field that may challenge the assumptions of the equivalent age approach. The study's finite element validation against measured temperature data provides some confidence, but engineers should exercise caution when extrapolating results to sections significantly larger than those studied.

Another consideration is the time-dependence of thermal stress. The study focuses on the hardening phase, but thermal stresses evolve over the entire service life as the structure experiences seasonal temperature variations, solar radiation, and environmental cycling. The construction-phase thermal stresses identified here become residual stresses that interact with service-phase thermal loads, and their combined effect on fatigue performance warrants further investigation.

Summary and Concluding Remarks

This study makes a significant contribution to the understanding of thermal-mechanical coupling in large-diameter STC arch bridges during the construction phase. The demonstration that hydration heat temperature fields can amplify thermal stresses by up to 1.4 times provides compelling evidence that conventional thermal stress analyses, which assume temperature-independent material properties, are inadequate for these structures. Engineers designing and constructing large-diameter STC arch bridges must incorporate temperature-dependent elastic modulus evolution into their construction-phase analyses. The equivalent age method offers a practical and theoretically sound framework for this purpose, and the study's quantitative results provide valuable benchmarks for validating analytical and numerical models. The negligible effect on steel tube stresses is a reassuring finding that simplifies the design verification process for the steel tube component, allowing engineers to focus their attention on the concrete core's thermal stress state.