Efficient Approximation Method for Concrete Creep Compliance Function

Abstract

For concrete, the strain tends to grow when the stress is kept at a constant level. This phenomenon is usually referred to as creep. Creep is an important physical property of concrete. For a prestressed concrete containment, creep could lead to prestress losses, stress redistribution, additional displacements, and even cracking. In general, the stress-strain relation of creep is nonlinear, but the principal stresses of concrete remain within the service stress range which is below 40% to 50% of the uniaxial strength. Therefore, the superposition principle can be utilized in linear elasticity, which works with the current values of stress and strain. Based on the theory of linear viscoelasticity, the principle of superposition can be used to characterize creep at a constant stress and the compliance function is used to describe the concrete creep mathematically, which facilitates numerical calculations. However, when the exponential algorithm is used to solve the creep effect of concrete, it is necessary to express the concrete creep compliance function by Dirichlet series and the calculation of the Dirichlet series corresponding to the compliance function is the key to implementing the exponential algorithm. The Weeks method for the inverse Laplace transform was used to approximate the Dirichlet series based on the continuous retardation spectrum method. The problem of approximating the concrete creep compliance function by the Weeks method was examined. First, the process of using the Weeks method to solve the continuous retardation spectrum was introduced. By taking the CEB MC90 creep model commonly used in engineering as an example, the equations for solving the concrete creep compliance function were derived by the Weeks method. The idea for improving the performance of the Weeks method was proposed. Based on this idea, the ranges of the various parameters that play a role in this solution were proposed. The numerical integration formula for the time-dependent term in the compliance function was derived. The results show that the calculation relative error with this method is no larger than ±1% when the duration is larger than 10 days. The validity of the algorithm was checked by comparing the numerical algorithm with the exact solution. This method is well suited for calculating the concrete creep compliance function for a long-term duration. The solution based on the Weeks method only requires the first-order derivative of the concrete creep compliance function to obtain the explicit function in the time domain, avoiding the complex computations of high-order derivatives and the low computational efficiency. Finally, the efficient Weeks method developed for the concrete creep model of CEB MC90 can also be extended and applied to other concrete creep models such as ACI 209R-92, JSCE, and GL2000.

Keywords

• concrete containment
• concrete creep
• compliance function
• dirichlet series
• continuous retardation spectrum
• weeks method