Ground granulated blast furnace slag, which is a byproduct obtained during steel manufacture, has been widely used for concrete structures in order to reduce carbon dioxide emissions and improve durability. This paper presents a numerical model to evaluate compressive strength development of slag blended concrete at isothermal curing temperatures and time varying curing temperatures. First, the numerical model starts with a cement-slag blended hydration model which simulates both cement hydration and slag reaction. The accelerations of cement hydration and slag reaction at elevated temperatures are modeled by Arrhenius law. Second, the gel-space ratios of hardening concrete are calculated using reaction degrees of cement and slag. Using a modified Powers’ gel-space ratio strength theory, the strength of slag blended concrete is evaluated considering both strengthening factors and weakening factors involved in strength development process. The proposed model is verified using experimental results of strength development of slag blended concrete with different slag contents and different curing temperatures.
Granulated slag from metal industries is a steel industrial byproduct and can be used as a mineral admixture to produce normal and high strength concrete. It is broadly recognized that slag blended concrete has many advantages, including lower permeability, better chloride resistance, and higher strength at later ages. In addition, economics (lower cement requirement), energy, and environmental considerations can be achieved by using slag blended concrete [
Compressive strength is the most important property of hardened concrete; other properties such as tensile strength, flexural strength, elasticity modulus, water tightness, and durability all are related to compressive strength closely. The compressive strength of slag blended concrete generally relates to materials properties, such as water to binder ratios and slag replacement ratios, and curing conditions, such as curing temperatures. Many experimental investigations have been done about strength development of slag blended concrete. Ramezanianpour and Malhotra [
Compared with abundant experimental study on strength development of slag blended concrete [
The development of mechanical properties of slag blended concrete relates to cement hydration and slag reaction. To overcome the weak points of current models [
The development of concrete properties closely relates to hydration process. For hardening concrete, heat properties, mechanical properties, and chemical properties develop accompanied with cement hydration. For hardened concrete, compositions of hydration reaction products and capillary pore structures closely relate to degree of hydration. Hence modeling of hydration process is important for evaluating concrete properties. For cement-slag blends, cement hydration and slag reaction will occur simultaneously. To model hydration of cement-slag blends, we propose cement hydration model, slag reaction model, and interaction model between cement hydration and slag reaction.
Tomosawa [
As shown in (
During initial dormant period, the formation of initial impermeable layer will lower rate of hydration, and the destruction of this impermeable layer will increase the rate of hydration. The reaction coefficient
The effective diffusion coefficient of water
The amount of water in the capillary pores
The influence of curing temperatures on reaction coefficients is described using Arrhenius’s law as shown in
Using degree of reactions of mineral compounds of cement [
Coefficients of cement hydration model.
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8.1 × 10−9 | 0.02 | 9.0 × 10−6 | 2.7 × 10−7 | 1.4 × 10−6 | 6.8 × 10−8 | 8.6 × 10−10 | 1000 | 1000 | 7500 | 5400 |
Maekawa et al. [
The influence of temperature on slag reaction is described by the Arrhenius law as follows:
In addition, besides chemical reaction, the addition of slag also presents dilution effect [
Maekawa et al. [
Considering the production of calcium hydroxide from cement hydration and the consumption of calcium hydroxide from slag reaction, the amounts of calcium hydroxide in cement-slag can be determined as follows:
Chemically bound water relates to both cement hydration and slag reaction. The chemically bound water contents can be determined as follows:
In cement-slag blends, capillary water will be consumed from cement hydration and slag reaction. The capillary water contents can be calculated as follows:
Summarily, the proposed blended cement hydration model considers both cement hydration and slag reaction. The influences of water to binder ratios, slag replacement ratios, and curing temperatures on hydration are taken into account. The interactions between cement hydration and slag reaction are considered through calcium hydroxide content and capillary water contents. The reaction coefficients in hydration model are not changed with concrete mixing proportions. When water to binder ratio or slag replacement alters, these parameters of slag do not change.
Iyoda et al. [
Coefficients of slag reaction model.
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8.9 × 10−9 | 0.1 | 1.0 × 10−5 | 1.9 × 10−9 | 1000 | 1000 | 5000 | 7000 |
As shown in Figure
Reaction degree of slag with different slag replacement ratios and curing temperatures: (a) cement-slag paste with 42% slag; (b) cement-slag paste with 67% slag.
Parameter study of reaction degree of slag: (a) slag replacement ratios; (b) water to binder ratios; (c) curing temperatures; and (d) fineness of slag (Blaine surface).
Slag replacement ratios
Water to binder ratios
Curing temperatures
Fineness of slag
Zheng et al. [
Evaluation of calcium hydroxide contents in cement-slag blends (water to binder ratio 0.5).
The flowchart of modeling is summarized in Figure
Flowchart of modeling.
Wang [
Wang [
The development of compressive strength of Portland cement concrete can be calculated using Powers’ strength theory as follows [
Powers’ strength theory (see (
To improve Powers’ strength theory (see (
Wang [
For hardening concrete, the development of compressive strength relates to some competing factors: with the increasing of curing temperature, the rate of cement hydration and slag reaction will increase (see (
Brooks and Al-Kaisi [
Properties of binders.
Material | Oxide, percent | Specific surface area (m2/kg) | |||||||||
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CaO | SiO2 | Al2O3 | Fe2O3 | MgO | SO3 | K2O | Na2O | MnO | TiO2 | ||
OPC | 65.8 | 20.5 | 5.8 | 2.5 | 1.2 | 2.3 | 0.6 | 0.3 | 0.1 | 0.2 | 391 |
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Slag | 40.4 | 36.1 | 10.8 | 0.4 | 9.5 | 0.3 | 0.5 | 0.3 | 0.6 | 0.7 | 412 |
For each concrete, cubes were cast at 20°C cured in water tanks under two conditions: isothermal curing, where cubes were subjected to temperatures of 20, 40, and 47°C; and heat-cycled curing, where the cubes were subjected to a controlled ascending temperature rise, and on reaching the peak temperature, the control system was switched off, and the cubes were allowed to cool to the ambient temperature. The amount of inhibitions of capillary water from surrounding moist curing related to the chemical shrinkage of hardening paste [
Using experimental results of compressive strength of concrete cured as 20°C, the intrinsic strength coefficients in (
Evaluation of compressive strength development of slag blended concrete at 20°C curing temperature.
The phase volume fractions of hardening slag-cement paste are shown in Figure
Phase volume fractions of hardening slag-cement paste (water to binder ratio 0.5, slag replacement ratio 0.5).
Figure
Effects of slag additions on strength development of concrete.
Using experimental results of strength development of slag blended concrete at different isothermal curing temperatures, we can calibrate the strength reduction coefficient
As shown in Figure
Strength development of concrete at different curing temperatures.
OPC concrete at different curing temperatures
Slag 50% concrete at different curing temperatures
Slag 70% concrete at different curing temperatures
In addition, as shown in Figure
Figure
Comparsion between analysis results and experimental results.
For hardening concrete with time varying curing temperature, by using the differential expression of (
Temperature history of hardening concrete.
Temperature histroy of OPC concrete
Temperature histroy of slag 70% concrete
Strength development of concrete at time varying curing temperature.
Strength development of OPC concrete at time varying curing temperature
Strength development of slag 70% concrete at time varying curing temperature
In addition, it should be noticed that the proposed model is generally valid for normal strength concrete. For ultrahigh strength concrete, aggregate will contribute to compressive strength. To accurately evaluate strength development of hardening concrete, composite model which simulates interactions between cement paste and aggregate is necessary [
This paper presents a numerical procedure to simulate cement hydration, slag reaction, microstructure development, and strength development of slag blended concrete. Cement hydration model and slag reaction model are simulated separately. The interactions between cement hydration and slag reaction are considered through available capillary water contents and calcium hydroxide contents in cement-slag blends system. Furthermore, using reaction degrees of cement and slag, volumetric stoichiometries of cement hydration and slag reaction and mixing proportions of slag blended concrete, the gel-space ratio and strength development of hardening concrete are determined.
The proposed model considers both strengthening factors and weakening factors involved in strength development process of slag blended concrete: due to the increase of curing temperature, cement hydration and slag reaction are accelerated, the ratios between the volume of reaction products and that of reacted binders decrease, and the ultimate strength of concrete is reduced. The proposed procedure can reproduce strength crossover phenomenon of hardening concrete with low curing temperatures and high curing temperatures. The proposed model is valid for concrete with different slag contents, different curing temperatures, and time varying temperature history.
The authors declare that they have no competing interests.
This research was supported by a grant (13SCIPA02) from Smart Civil Infrastructure Research Program funded by Ministry of Land, Infrastructure and Transport (MOLIT) of Korea Government and Korea Agency for Infrastructure Technology Advancement (KAIA).