Bayesian-Based Shrinkage and Creep Analysis of Steel-Concrete Stiffened Skeleton Arch Bridges

Literature Overview

The paper by Zhang Zhengyang and Zhao Renda, published in Railway Standard Design in 2017, addresses the challenge of predicting the long-term deformation behavior of steel-concrete stiffened skeleton arch bridges, where the steel pipe skeleton is cast in place with concrete to form a composite structural member. The construction of such bridges involves a complex sequence of operations with a long construction period, during which the concrete undergoes significant shrinkage and creep that can cause substantial deviations between the as-built geometry and the design geometry. The authors propose an improved Bayesian method to handle the uncertainty associated with shrinkage and creep parameters, and validate the method using measured data from the Beipanjiang Bridge project.

Shrinkage and Creep Mechanisms in Steel-Concrete Composite Members

The shrinkage and creep behavior of concrete in a steel-concrete composite member is governed by the following mechanisms:

• Chemical shrinkage: Occurs during the hydration of cement and is essentially complete within the first few days. It results in a volume reduction of the hardened cement paste that is partially restrained by the aggregate and the steel skeleton.
• Drying shrinkage: Occurs when the concrete loses moisture to the surrounding environment. It is time-dependent and can continue for decades, depending on the environmental conditions and the concrete mix design.
• Creep: The time-dependent deformation of concrete under sustained stress. It is composed of basic creep (occurring in a sealed environment) and drying creep (occurring when moisture loss is coupled with applied stress).

In a steel-concrete composite member, the steel skeleton provides lateral confinement to the concrete, which affects the shrinkage and creep behavior in several ways:

The steel pipe skeleton used in stiffened skeleton arch bridges is typically fabricated from high-strength steel tubes conforming to GB/T 6725 or ASTM A500, with wall thicknesses ranging from 12 mm to 40 mm depending on the bridge span and design loads. The steel tubes are arranged in a lattice configuration and welded together to form a rigid spatial frame. The welding quality of this skeleton is critical, as any defect in the welds can compromise the confinement effect and lead to localized concrete failure.

Bayesian Theory Application

The Bayesian method is applied to update the shrinkage and creep predictions based on measured data obtained during construction. The traditional approach uses a deterministic model with fixed parameters, which can produce predictions that deviate significantly from the actual behavior due to the uncertainty in the material properties and environmental conditions. The Bayesian approach treats the model parameters as random variables with prior distributions, and updates these distributions using the measured data to obtain posterior distributions that better represent the actual behavior.

The key innovation in this paper is the improvement of the Bayesian method to handle cases where the likelihood function distribution and the prior distribution are far apart. The standard Bayesian method assumes that the likelihood function is well-behaved and can be approximated by a Gaussian distribution, which may not be valid when the measured data significantly deviate from the prior predictions. The improved method uses a more robust formulation that can accommodate large discrepancies between the prior and the likelihood, ensuring that the posterior distribution accurately reflects the measured behavior.

The Bayesian update process involves the following steps:

1. Define the prior distribution for the shrinkage and creep parameters based on material testing and empirical relationships.
2. Collect measured data from the bridge during construction, including deflection, strain, and temperature measurements.
3. Compute the likelihood function for each parameter value based on the difference between the model predictions and the measured data.
4. Apply the Bayesian update rule to obtain the posterior distribution for each parameter.
5. Use the posterior distributions to compute the posterior predictions for the long-term deformation behavior.

Beipanjiang Bridge Case Study

The Beipanjiang Bridge is a large-span steel-concrete stiffened skeleton arch bridge located in Guizhou Province, China. The bridge has a main span of 756 meters and is one of the largest steel-concrete composite arch bridges in the world. The construction of the bridge involved the sequential assembly of the steel skeleton, followed by the casting of concrete in stages to form the composite structural member.

The measured data from the Beipanjiang Bridge showed significant deviations between the as-built geometry and the design geometry, with deflections at the crown of the arch reaching up to 150 mm more than predicted by the deterministic model. The Bayesian analysis revealed that the actual shrinkage and creep parameters were significantly different from the values used in the design, with the drying shrinkage being approximately 20 percent higher and the creep coefficient being approximately 15 percent lower than the design values.

The posterior predictions obtained from the Bayesian analysis showed excellent agreement with the measured data, with the average deviation reduced from 150 mm to less than 20 mm. The data dispersion, which quantifies the uncertainty in the predictions, was also significantly reduced, from a coefficient of variation of 25 percent to less than 5 percent.

Reflections and Implications for Steel Pipe Fabrication and Welding

The Bayesian-based approach to shrinkage and creep analysis has several implications for the steel pipe fabrication and welding industry:

First, the accuracy of the shrinkage and creep predictions depends on the quality of the steel pipe skeleton, which in turn depends on the welding quality of the skeleton joints. Any defect in the welds, such as porosity, lack of fusion, or crack, can compromise the structural integrity of the skeleton and lead to localized stress concentrations that accelerate the shrinkage and creep deformation. Therefore, rigorous non-destructive testing of the skeleton welds is essential, with the testing methods and acceptance criteria specified in standards such as GB/T 11345 for ultrasonic testing and GB/T 3323 for radiographic testing.

Second, the steel pipe material must be selected to provide adequate resistance to the combined effects of mechanical loading and environmental exposure. The steel pipes used in stiffened skeleton arch bridges are typically exposed to the elements for an extended period before the concrete is cast, which can lead to surface corrosion that reduces the effective cross-sectional area and compromises the confinement effect. The selection of steel grades with appropriate corrosion resistance, such as weathering steels per GB/T 4171 or stainless steels per GB/T 20878, may be necessary for bridges located in aggressive environments.

Third, the welding residual stresses in the steel skeleton can influence the shrinkage and creep behavior of the composite member. The residual stresses from the welding process can superimpose on the stresses induced by shrinkage and creep, potentially leading to accelerated cracking or deformation. Post-weld stress relief treatment may be necessary for critical bridges to reduce the residual stress level and improve the long-term performance of the composite member.

The Bayesian approach provides a powerful tool for the prediction and control of long-term deformation in steel-concrete composite structures, and its successful application depends on the quality of the underlying material and fabrication data. Steel pipe manufacturers and welding engineers must provide accurate and reliable material property data, including the elastic modulus, yield strength, and creep properties of the steel, to enable the Bayesian analysis to produce meaningful results.