Advances in Materials Science and Engineering

Volume 2018, Article ID 1058170, 16 pages

https://doi.org/10.1155/2018/1058170

## Numerical Modelling of Field Test for Crack Risk Assessment of Early Age Concrete Containing Fly Ash

^{1}SINTEF Ocean, 7450 Trondheim, Norway^{2}The Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway^{3}Norwegian Public Roads Administration, Tunnel and Concrete Section, Norway

Correspondence should be addressed to T. Kanstad; on.untn@datsnak.ejret

Received 20 March 2018; Accepted 7 June 2018; Published 9 September 2018

Academic Editor: Candido Fabrizio Pirri

Copyright © 2018 G. M. Ji et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The high-strength/high-performance concretes are prone to cracking at early age due to low water/binder ratio. The replacement of cement with mineral additives such as fly ash and blast-furnace slag reduces the hydration heat during the hardening phase, but at the same time, it has significant influence on the development of mechanic and viscoelastic properties of early age concrete. Its potential benefit to minimize the cracking risk was investigated through a filed experiment carried out by the Norwegian Directorate of Roads. The temperature development and strain development of the early age concrete with/without the fly ash were measured for a “double-wall” structure. Based on experimental data and well-documented material models which were verified by calibration of restraint stress development in TSTM test, thermal-structural analysis was performed by finite element program DIANA to assess the cracking risk for concrete structures during hardening. The calculated and measured temperature and strain in the structure had good agreement, and the analysis results showed that mineral additives such as flay ash are beneficial in reducing cracking risk for young concrete. Furthermore, parameter studies were performed to investigate the influence of the two major factors: creep and volume change (autogenous shrinkage and thermal dilation) during hardening, on the stress development in the structure.

#### 1. Introduction

Prediction of early age cracking is traditionally based on temperature criteria. The temperature development in the young concrete is then calculated and cracking tendency is deduced from the maximal temperature difference in a structure. To avoid cracking, limitations were applied to maximum temperature, temperature difference between the surface and the center of the structure, and between the new and the older adjoining structures. These limitations were based on practical experience and experience from the laboratory [1].

The main drawback of the temperature-based crack risk estimation is that the other involving factors are not considered: restraint conditions and several other material properties. Many researchers [2–4] have shown that there is no general correlation between stress and temperature. Whether young concrete will crack or not, it depends very much on restraint conditions and material properties.

For reliable crack prediction at early ages, strain criteria must be applied, and this calls for well-documented material models. In recent years, an increased interest in cracking of hardening concrete has led to extensive research on this subject. Making reliable cracking risk assessments involves experimental testing and advanced modelling of the time and temperature-dependent behavior of the properties, the restraint conditions of the structure, and the external environmental conditions. A large number of material models for young concrete have been presented and implemented in computer programs for the simulation of stress development [5–9]. Based on extensive experimental test, the well-documented material models were proposed, and verification of the development of the restraint stress in the TSTM test showed that the combination of the material models is capable to describe the total behavior of hardening concrete [10, 11].

Mineral additives such as silica fume (SF), blast-furnace slag (BFS), and fly ash (FA) have been used extensively in production of high-performance concrete in the last decades, and the influences of fly ash on various properties of early age concrete were investigated extensively in [11]. The potential benefit to minimize the cracking risk by replacement of cement with FA was investigated through a field experiment in the current study. Temperature and strain developments in 26 different positions were measured in two different sections of the “double-wall” structure with one wall of SV40 concrete and another of low-heat concrete. Advanced thermal and structural analyses were then performed by finite element program DIANA [12], and the simulation results were compared with the test results.

#### 2. Methodology of Thermal and Structural Analysis

The thermal and structure problems are solved in sequence. Concrete is treated as a homogeneous material in simulation; therefore, the calculated stresses are not representative for, e.g., the boundary zones around aggregate but represent only regions with a size larger than some characteristic dimensions, e.g., the maximum aggregate size. The procedures to solve the thermal and structural problems are described in following section.

##### 2.1. Solution of the Thermal Problem

Transient thermal analysis is used to calculate the temperature field. The general theory to solve the thermal problem is well established and described in many researches [3, 6, 13–16]. The finite element equations of the thermal problem are formulated using the Galerkin weighting procedure, and the procedure extends the equilibrium to a finite volume. In the finite element method, the structure is divided into discrete element, and the temperature field and the temperature gradient are approximated as the linear function of the nodal temperature. The temperature gradient depends on the total quantity of hydration heat, boundary conditions, thermal properties, and discontinuity in geometry and material properties [14].

##### 2.2. Solution of the Mechanical Problem

The nonlinear finite element analysis is used to calculate the stress development, and the theory is described in [14]. The starting point for numerical analysis of the development of stresses in time is the incremental formulation of the principle of virtual work. The displacements are approximated by interpolation of the nodal displacement. The constitutive relation for aging viscoelastic material is given via creep compliance or relaxation compliance and can be solved by integral or differential formulation [14]:where and are the dimensionless matrix that relate the three-dimensional deformation state to the one-dimensional creep or relaxation function by using Poisson’s ratio :

The stress gradient depends on temperature distribution, mechanical properties, restraint conditions, discontinuity in geometry, and material properties. In the thermal stress analysis, the element model must permit the same level of complexity for the strain field as that for the temperature field. Since the stresses are less accurate than displacements and temperatures, stress calculations need finer mesh than temperature calculations, and the order of the element in stress analysis has to be of higher order than the element in temperature analysis. If the same element model is used in both analyses, the requirements of stress analysis are usually decisive [14].

#### 3. Field Test

Within the NOR-CRACK project, a great deal of R&D work was carried out by the Norwegian Public Roads Administration to develop a low-heat concrete with a minimal risk of early age cracking. In order to evaluate the crack risk of the low-heat concrete, a field investigation on a specially designed structure with relevant dimensions was carried out in Norway. It was essential to compare the cracking risk of low-heat concrete with that of SV40 concrete which is commonly used in Norway. The composition of SV40 and low-heat concretes is shown in Table 1.