Study Note on Hydration-Induced Temperature Field in Composite Cementitious Steel Tube Concrete Arch Ribs

Literature Overview

This paper by Sun Guofu, Li Shucai, Lu Wei, and Chen Lei, published in Journal of Shandong University (Engineering Science) (2011, Vol. 41, No. 3, pp. 106-111), investigates the cross-section temperature field during the concrete hydration process in steel tube concrete (CFT) arch ribs using composite cementitious materials. Funded by the National Science Fund for Distinguished Young Scholars (Grant No. 50625927), the research combines continuous experimental observation with finite element numerical simulation to understand and predict the thermal behavior during the critical early-age hardening period of CFT arch ribs used in bridge and tunnel structures.

Technical Significance

Steel tube concrete (CFT) arch ribs are widely used in large-span bridges and tunnel structures, where the steel tube acts as both a formwork during concrete placement and a structural component after hardening. The hydration heat generated during concrete curing creates significant temperature gradients within the arch rib cross-section, which can induce thermal stresses, cracking, and long-term durability issues. Understanding the temperature field evolution is essential for:

• Preventing early-age thermal cracking in the concrete core
• Assessing the development of interfacial bond between steel and concrete
• Predicting residual thermal stresses that affect structural capacity
• Optimizing concrete mix design and placement procedures

Experimental Methodology

Test Configuration

The research employed continuous temperature monitoring during the hydration process of CFT arch rib specimens. Thermocouples were embedded at multiple locations within the cross-section to capture the spatial and temporal evolution of the temperature field. The use of composite cementitious materials (likely incorporating supplementary cementitious materials such as fly ash, slag, or silica fume) is significant because these materials alter the hydration kinetics compared to ordinary Portland cement, producing delayed but potentially higher peak temperatures.

Key Experimental Parameters

Numerical Modeling

Heat Conduction Model

The numerical model is based on the heat conduction equation combined with the finite element method. The governing equation for transient heat conduction in the CFT arch rib cross-section is:

ρc(∂T/∂t) = ∇·(k∇T) + Q(t)

Where:

• ρ = density of the material
• c = specific heat capacity
• T = temperature
• k = thermal conductivity
• Q(t) = hydration heat generation rate

Hydration Heat Model

The authors evaluated different mathematical models for describing the hydration heat generation rate and concluded that a hyperbolic function provides the most reasonable representation for composite cementitious materials. This is a significant finding because the commonly used exponential or double-exponential models may not accurately capture the delayed and prolonged heat generation characteristic of blended cement systems.

The hyperbolic model captures the characteristic hydration behavior of composite cements, where the heat generation rate rises gradually, reaches a broad peak at later ages, and then declines slowly. This is in contrast to ordinary Portland cement, which produces a sharp early peak followed by rapid decline.

Key Results and Analysis

Effect of Steel Tube Wall Thickness

The research found that steel tube wall thickness has a relatively small influence on the cross-section temperature field, with a maximum temperature difference of only 2-3°C between different wall thicknesses. This is because the steel tube, while having high thermal conductivity (approximately 50 W/m·K compared to 1.5-2.5 W/m·K for concrete), represents a small volume fraction of the total cross-section. The heat generated within the concrete core dominates the temperature field, and the steel tube primarily acts as a heat sink at the boundary rather than a significant heat source or insulator.

Effect of Steel Tube Diameter

In contrast, the steel tube diameter (OD) has a substantial influence on the cross-section temperature field, with a maximum temperature difference reaching 20°C. This is because larger diameter tubes result in larger concrete core volumes, which generate more total hydration heat while having a relatively smaller surface area for heat dissipation. The heat dissipation rate is proportional to the surface area (2πr·h for a cylindrical tube), while the heat generation is proportional to the volume (πr²). As the diameter increases, the volume-to-surface-area ratio increases, leading to higher internal temperatures.

Temperature Field Distribution

The cross-section temperature field during hydration exhibits a characteristic pattern:

• Core region: Highest temperature, with the peak occurring at the geometric center of the concrete core.
• Transition zone: Temperature decreases radially outward from the core.
• Steel tube region: Lowest temperature, acting as a heat sink due to high thermal conductivity.
• Interface: A steep temperature gradient exists at the steel-concrete interface, which can induce interfacial thermal stresses.

Engineering Practice Implications

Thermal Stress Assessment

The temperature gradients identified in this study have direct implications for structural design:

1. Self-equilibrated thermal stresses: The temperature difference between the core and the steel tube creates self-equilibrated stresses within the cross-section. These stresses are compressive in the cooler outer regions and tensile in the hotter inner regions.
2. Interfacial shear stress: The differential thermal expansion between the steel tube and concrete core generates interfacial shear stresses that can affect bond strength development.
3. Residual stresses: As the concrete cools after the hydration peak, residual stresses develop that can either be beneficial (compressive in the concrete) or detrimental (tensile cracking) depending on the cooling rate and constraint conditions.

Design Recommendations

Based on the research findings, the following practical recommendations can be made:

• For large-diameter CFT arch ribs (OD > 800 mm), consider using low-heat composite cementitious materials or incorporating cooling tubes within the concrete core to control peak temperatures.
• The steel tube wall thickness can be selected primarily based on structural requirements rather than thermal considerations, as its influence on the temperature field is minimal.
• Numerical models using the hyperbolic hydration heat function should be employed for predicting temperature fields in CFT structures with composite cementitious materials, rather than relying on conventional exponential models.
• Early-age thermal cracking risk should be assessed using the predicted temperature gradients, with particular attention to the concrete core region where peak temperatures and temperature gradients are highest.

Critical Reflections

The study provides valuable quantitative data on the thermal behavior of CFT arch ribs during the hydration process. However, several aspects warrant further consideration. The experimental study focuses on cross-section temperature fields, but the three-dimensional temperature distribution in actual arch ribs, which are curved and have varying section properties along their length, may differ significantly from the idealized cross-sectional behavior studied here. The interaction between the arch rib geometry and the temperature field, particularly in regions of high curvature or section transitions, is not addressed.

Additionally, the study does not explicitly discuss the effect of concrete placement rate on the temperature field. In practice, the rate of concrete placement significantly affects the hydration heat accumulation, with rapid placement leading to higher peak temperatures due to reduced heat dissipation time between layers. The numerical model should incorporate placement rate as a variable parameter to better represent actual construction conditions.

The hyperbolic hydration heat model, while identified as the best fit for composite cementitious materials, should be validated against a wider range of material compositions and curing conditions. The model parameters (Q₀, a, b) may vary significantly depending on the specific blend of cement and supplementary materials, the water-cement ratio, and the curing temperature. A parametric study to establish model parameter ranges for different composite cement systems would enhance the practical applicability of the findings.

Summary

This research establishes that the steel tube diameter is the dominant geometric parameter affecting the cross-section temperature field during hydration in CFT arch ribs, while wall thickness has minimal influence. The hyperbolic function provides the most accurate representation of hydration heat generation for composite cementitious materials. Engineers designing CFT arch ribs should use these findings to predict and control early-age thermal effects, particularly for large-diameter applications where peak temperature differences can reach 20°C. The integration of experimental data with finite element modeling using appropriate hydration heat functions provides a reliable tool for thermal analysis and design optimization in CFT structural applications.