Analytical model predicting the concrete tensile stress development in the restrained shrinkage ring test

doi:10.1016/j.conbuildmat.2021.124930

Construction and Building Materials

Volume 307, 8 November 2021, 124930

https://doi.org/10.1016/j.conbuildmat.2021.124930 Get rights and content

Highlights

•
A new analytical model of the restrained ring test is proposed.
•
The analytical model is based on the age-adjusted effective modulus theory.
•
Free shrinkage and tensile creep were measured on prism and dog-bone specimens.
•
The model was validated by 21 concrete mixes with SCMs and various strength grades.
•
A numerical finite element simulation was used to validate new analytical model.

Abstract

Concrete structures may experience unexpected cracking at an early age. Early age cracking can be induced by restrained deformations where tensile stress generated in concrete exceeds its tensile strength. The restrained concrete ring test is often used to evaluate the ability of concrete to resist early age cracking induced by shrinkage. This paper proposed an analytical model of the restrained ring test by capturing the effect of both restrained shrinkage and tensile creep based on the age-adjusted effective modulus theory. The analytical model allows for accurately predicting the tensile stress of the restrained concrete ring based on the experimental measurements of the time-dependent development of elastic modulus, total free shrinkage, and tensile creep of concrete. A numerical finite element simulation was also successfully carried out to validate the new analytical model. Importantly, the model was validated considering a total of 21 concretes consisting of 6 strength grades ranging from 25 MPa to 100 MPa. For each grade, one fly ash blend (30%), two GGBFS blends (40% and 60%) and a reference mix without supplementary cementitious materials were tested.

Introduction

The risk of early-age cracking is a critical indicator of the performance of concrete structures [1], [2], [3], [4]. Concrete structures may experience unexpected cracking at an early age when the tensile strength of concrete becomes lower than the tensile stress induced by restraint [5], [6]. The tensile stress induced by restraint in concrete is governed by restrained shrinkage and tensile creep [7]. To increase the safety and serviceability of concrete structures, it is essential to understand their performance over time, and to develop suitable and reliable theoretical models for their analysis and safety assessment.

Numerous researchers have been investigating restrained shrinkage induced cracking of concrete [8], [9], [10], [11], [12]. Traditionally, three types of approaches have been used to investigate early age cracking of concrete caused by restrained shrinkage, such as one-dimensional restrained shrinkage analysis [13], [14], two-dimensional restrained shrinkage analysis [15], [16] and restrained ring test [17], [18]. The restrained ring test is the most popular experimental method to determine the cracking potential of concrete subjected to restrained shrinkage because it is simple to implement compared to the one-dimensional and the two-dimensional restrained shrinkage tests [8], [19], [20].

Hossain and Weiss [8] proposed a method allowing to assess both residual stress development and stress relaxation using the restrained ring test. They also provided quantitative information to estimate the theoretical elastic stress and actual residual stress in a restrained ring specimen. Khan et al. [9] conducted an experimental study using both restrained ring tests and tensile creep tests to examine the effect of early age tensile creep on early-age cracking. Results showed that the tensile creep coefficients measured using tensile creep tests could be used to assess the stress relaxation induced by tensile creep in the restrained ring test. In another study, Khan et al. [5], carried out internally restrained shrinkage tests using reinforced concrete specimens including the effect of tensile creep. The degree of restraint and ageing coefficient were calibrated [5].

As mentioned above, the restrained ring test is the most popular method to investigate the risk of early-age cracking and evaluate tensile stress development. The tensile stress development in concrete can be computed by measuring the strain of the steel ring [8]. As such, this approach is not suitable for predicting the tensile stress development in concrete but only for the analysis of ring test results. Meanwhile, the theoretical elastic stress model proposed by Hossain and Weiss [8] allows for calculating the tensile stress in concrete from free shrinkage, elastic modulus, and degree of restraint. The effect of tensile creep is not considered. Thus, this model needs to be improved to account for the effect of tensile creep and correctly predict the tensile stress development in concrete.

Supplementary cementitious materials (SCMs) and new construction materials have been widely used in concrete due to numerous beneficial effects, including i) improving the sustainability of concrete by reducing the usage of Portland cement, ii) lowering the heat of hydration by decreasing the content of cement, and iii) improving the durability of concrete [21], [22], [23], [24], [25], [26]. However, it is still difficult to accurately predict the performance of these blended cement-based concretes because of the inconsistent physical and chemical properties of SCMs used in concrete [27], [28]. There are also controversial results on their shrinkage and early-age cracking behaviour [29], [30], [31]. Several experimental studies can be found in the literature regarding the effects of fly ash and slag on the risk of early-age cracking. Khan et al. [32] concluded that the strength development of fly ash-blended concrete is lower than OPC concrete and the cracking time is reduced. Nguyen et al. [33] summarized that ferronickel slag decreases the risk of early-age cracking because of a significantly higher tensile creep.

In this paper, an analytical model is proposed to accurately predict the tensile stress in the restrained concrete ring test and capture the effect of both restrained shrinkage and tensile creep. The risk of early-age cracking of concrete is significantly influenced by the compressive strength and the incorporation of either fly ash or GGBFS. As a result, the analytical model presented in this paper is validated considering a total of 21 concretes consisting of 6 strength grades (25 MPa to 100 MPa), one fly ash blend (30%), and 2 different GGBFS blends (40% and 60%). However, the purpose of this paper is not to discuss the influence of the concrete mix design parameters such as fly ash or GGBFS content on early-age cracking.

Section snippets

Prediction of concrete tensile stress in the restrained ring test

The shrinkage of the concrete ring in the radial direction can induce a uniform external pressure to the steel ring. The schematic diagram of the pressure and stress obtained in the ring specimen is shown in Fig. 1. The steel ring is pressurised at the outer surface, and the strain developing in the steel ring is equivalent to the measured strain at the corresponding time [8]. The tensile stress of concrete specimens ( $σ_{act}$ ) can be expressed as a function of the measured steel strain, steel

Materials and mixture proportions

General Purpose (GP) cement was used to prepare all concrete mixtures, complying with Australian Standard AS3972 type GP [41]. The compressive strength of GP cement is higher than 45 MPa at 28 days. It contains up to 7.5% of mineral additions such as limestone to reduce the clinker content and up to 5% of additional mineral constituents such as cement kiln dust [41]. Two typical SCMs, such as fly ash and GGBFS, were used in this study, complying with Australian Standard AS3582.1 [42] and

Finite element modelling

Finite element modelling of restrained ring specimens was performed using the commercial finite element (FE) code ABAQUS, to simulate the time-dependent tensile stress development. For the FE modelling, due to the symmetry of the restrained ring specimens and the uniform free shrinkage, a two-dimensional (2-D) axisymmetric model was used for simulating the steel and concrete ring. An axisymmetric quadrilateral element with eight nodes and quadratic shape functions (CAX8) was used. The generated

Test results

The time-dependent mechanical properties including compressive strength, indirect tensile strength, and elastic modulus are provided in Table 3. As shown in Table 3, the mechanical properties test failed for N25-G40 and N25-G60 at the age of 1 day due to their very low compressive and tensile strength at that time. It can be seen that the incorporation of SCMs delays the development of compressive strength, indirect tensile strength, and elastic modulus. For the concrete mixes with 30% fly ash,

Conclusions

In this paper, an analytical model of the restrained ring test is proposed by capturing the effect of both restrained shrinkage and tensile creep based on the age-adjusted effective modulus theory. The main conclusions can be drawn as follows:

1.
Free shrinkage and tensile creep, measured on prismatic and dog-bone-shaped concrete specimens, were successfully used to determine the age-adjusted effective modulus.
2.
Importantly, the model was validated considering a total of 21 concretes consisting of 6

CRediT authorship contribution statement

Yingda Zhang: Writing – original draft, Conceptualization, Methodology, Software, Validation, Formal analysis. Sumaiya Afroz: Data curation, Validation, Writing – review & editing. Quang Dieu Nguyen: Data curation, Validation, Writing – review & editing. Taehwan Kim: Supervision, Resources, Writing – review & editing. Johanna Eisenträger: Methodology, Software, Writing – review & editing. Arnaud Castel: Supervision, Resources, Validation, Writing – review & editing, Project administration,

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The financial support of Cement Concrete & Aggregates Australia and the Australian Research Council (Linkage Project LP170100912) is gratefully acknowledged.

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Analytical model predicting the concrete tensile stress development in the restrained shrinkage ring test

Highlights

Abstract

Introduction

Section snippets

Prediction of concrete tensile stress in the restrained ring test

Materials and mixture proportions

Finite element modelling

Test results

Conclusions

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgements

Cem. Concr. Compos.

Proc. Eng.

Constr. Build. Mater.

Cem. Concr. Compos.

Constr. Build. Mater.

Constr. Build. Mater.

Cem. Concr. Res.

Constr. Build. Mater.

Constr. Build. Mater.

Cem. Concr. Compos.

Cem. Concr. Res.

Cem. Concr. Compos.

Constr. Build. Mater.

Cem. Concr. Compos.

Constr. Build. Mater.

Constr. Build. Mater.

Cem. Concr. Compos.

Cem. Concr. Compos.

Theor. Appl. Fract. Mech.

Constr. Build. Mater.

Cem. Concr. Res.

Comput. Struct.

Eng. Struct.

Constr. Build. Mater.

Insight into thermal stress distribution and required reinforcement reducing early-age cracking in mass foundation slabs

Materials

Early-age tensile creep and shrinkage-induced cracking in internally restrained concrete members

Mag. Concr. Res.

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Mater. Struct.

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J. Mater.

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A new look at tensile creep of fiber reinforced concrete

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