Optimised mix design and elastic modulus prediction of ultra-high strength concrete
Introduction
Normal strength concrete (NSC) and high strength concrete (HSC) with the compressive strength up to 100 MPa have been widely used in practical constructions for many years. UHSC, on the other hand, has been mostly studied in recent decades but increasingly gained much attention as well as achievements from researchers. For instance, UHSC could be filled into steel columns to create an excellent composite column that took advantage of the two constituting materials [1], [2], [3], [4], [5], [6], [7]. In term of concrete mix design, previous studies proposed various mix designs for UHSC. The ratio of cement to supplementary cementitious materials (C:SCM) by mass was studied in the range from 1:0.17 [8] to 1:0.50 [9]. Another important factor in manufacturing UHSC is aggregate content which also varies in the previous studies. It could be from very low as 1:0.62 (the cement to aggregate ratio) as in the study of Ragalwar el at. [10] to very high up to 1:3.16 as in the study of Baduge el at. [11] for similar UHSC with compressive strength of 140 MPa. It is also well-documented that UHSC has been applied a very low content of water. The maximum water to binder (w/b) ratio recorded in the report of Graybeal [9] was 30%. In the case of UHSC with the compressive strength exceeding 150 MPa, Shin el at. [12] suggested the w/b of 12.5%. Under low water content, water-reducing agents have been applied to concrete batching to make UHSC workable. The superplasticizer to binder (sp/b) ratios, on other hand, is related to the w/b since water-reducing agents or superplasticizers allowed less water using in concrete [13].
In the literature, many papers can be found related to optimized UHSC mix designs. While most of them focused on the effect of concrete components such as cement, substitute cementitious materials [14], [15], [16], aggregate [17], [18] or water-reducing admixture [19], other researchers studied the improvement of concrete performance under different curing conditions [20], or the mechanic and chemical performance of concrete [10], [21], [22]. Only a few studies discussed the economic aspect of the UHSC mix design [23], [24], [25]. In this contribution, several UHSC mixes were compared to investigate the influence of constituent materials on the manufacturing cost of UHSC. The adjustments on the raw components, w/b and sp/b ratios obtained from the comparison were then suggested to create a new economical UHSC mix design.
Regarding the manufacture of USHC, there are many methods to improve the compressive strength of concrete. Ipek et al. [26] applied the curing approach of 90 °C steam cure, 90 °C hot-water cure or 300 °C dry air and the pressure up to 125 MPa to produce concrete with compressive strength up to 475 MPa. Shaheen and Shrive’s concrete [14] achieved 288 MPa with heat treatment of 300 °C and pressure of 55 MPa. It is noted that these studies have been done with special concrete treatments. These manufacturing processes seemed to be extremely difficult and complicated so that they were only able to carry out in laboratory as small-scale experiments. Other studies proposed less intensive manufacturing processes including heat curing [12], [27], [28] or applying specially graded aggregates for their mix design [4], [29], [30], [31] to create UHSC with compressive strength up to 200 MPa. Specially graded aggregates such as ground quartz, silica sand or very-fine aggregate are too expensive as well as difficult to find their supplier. As a result, the wide application of these mix designs to practical civil engineering structures is limited due to the difficulty of curing methods and high manufacturing cost. Therefore, it is critically important to develop an economic mix design of UHSC based on traditional constituent materials and the conventional curing process.
Moreover, the elastic modulus has been considered as an important concern for the analysis and design of concrete structures. Hence, many current standards such as Eurocode 2 (EC 2) 2004 [32], American Concrete Institute (ACI 318) 2009 [33], Canadian Standards (CSA A23.3) 2004 [34], British Standard (BS 8110) 1997 [35], Australia Standards Association (AS 3600) 2009 [36] and Federal Highway Administration (FHWA) 2000 [37] have proposed the various equations to calculate the elastic modulus of concrete. These design equations seemed to be suitable for predicting the elastic modulus of NSC and HSC, but their application to UHSC is restricted due to the fact that the behaviour of UHSC is different from that of NSC and HSC. In addition, most of the equations for predicting elastic modulus proposed in the literature are based on the information of the mix design such as concrete density (w) [33], [34], [36], [38], type of aggregate [39], [40], [41], [42] or its Poisson's ratio and curing time [43]. For example, in the equation of Noguchi et al. [42], the elastic modulus was related to w, k1 and k2 represented by density, type of coarse aggregates and mineral admixtures, respectively, for concrete ranged from 40 MPa to 160 MPa. Baduge et al. [41] proposed another equation based on the density of aggregates and concrete. This restricts the practical application of the existing equations due to the involvement of too many parameters. Therefore, there is a need to develop a simple equation (as a function of compressive strength only) for predicting the elastic modulus of UHSC.
In order to fill the current research gap, this paper presents an experimental study to investigate different UHSC mixes using the conventional curing process and traditional constituent materials such as cement, aggregate, fly ash, slag and silica fume. An optimised mix for UHSC based on minimising the material costs was then proposed for promoting the practical applications of UHSC in civil and building constructions. A comprehensive test database composed of about 300 specimens with compressive strength ranging from 100 to 200 MPa was also newly collected to develop an empirical equation for predicting the elastic modulus of UHSC. The proposed equation was then compared with existing equations and the equations from the current designs to demonstrate its accuracy and merits.
Section snippets
Constituent materials
The raw materials including cement, fly ash, silica fume, sand, basalt aggregate and superplasticizer was presented in Fig. 1. In this study, general-purpose or type GP cement conforming to AS 3972 [44] was provided by Independent Cement and Lime Pty Ltd. It has up to 50% particle size below 10 μm and a fineness index of 370–430 m2/kg, as described in the datasheet of the supplier. Fly ash, supplied by Cement Australia Pty Ltd, is an ultrafine material meeting the requirements of AS 3582.1 [45]
Compressive strength
Table 2 summarises the compressive strength of two UHSC mixes obtained after 3, 7, 28 and 90 curing days. The mixes with only sand are indicated by S1-3 which have various combinations of w/b (from 14 to 15%) and sp/b (from 1.7 to 1.8%) ratios. The highest compressive strength archived at 28 days were 144.2 MPa with the elastic modulus of 34.3 GPa for specimen S1. Mix B with basalt aggregate also includes three different batches but utilize the same water (w/b = 14%) and superplasticizer (sp/b
Evaluation of materials
Table 3 showed the unit price of constituent materials in the Australian dollar (AUD). In this study, it is assumed that all examined mix designs were evaluated based on the raw material costs given by Isa et al. [56] and several Australian suppliers. It means that they were considered under an identical scale which may not comprehensively assess the manufacturing cost because the value of materials may be different depending on the supplier and availability. However, this comparison could
Evaluation of existing equations
A large number of equations from design codes and existing studies have been proposed to predict the elastic modulus of concrete. Table 5 summarised a list of current equations used in design codes for concrete such as EC 2, ACI 318, CSA A23.3, BS 8110, AS 3600 and FHWA as well as those proposed by Rashid et al. [39], Kheder and Al-Windawi [60], Gardner and Zhao [61] and Mendis et al. [38]. A comprehensive databased on UHSC tests with the cylinder compressive strength from 100 MPa to 200 MPa
Conclusions
Based on the investigation of several previous mix designs, the study denoted some improvements that should be applied to the UHSC mix design to arrive at a solution for manufacturing cost-reduction. Firstly, the use of common materials such as natural sand and coarse aggregate, instead of specially graded aggregates, could cut the total price of raw materials. Secondly, the cost of aggregates has been much cheaper than other constitute materials so more use of aggregates would be seemingly a
CRediT authorship contribution statement
Tan-Trac Nguyen: Data curation, Investigation, Writing - original draft. Huu-Tai Thai: Conceptualization, Supervision, Writing - review & editing. Tuan Ngo: Conceptualization, Supervision, Writing - review & editing.
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
This research work was supported by the Australian Research Council (ARC) under its Future Fellowship awarded to the second author (Project No: FT200100024). This financial support is gratefully acknowledged. The authors would like to thank Dr. Mark Betar, Dr. Jinghan Lu, Mr. Ray Furmston and other laboratory technicians at the University of Melbourne for their assistance. The authors are also grateful to Independent Cement and Lime Pty. Ltd., BASF Australia Ltd. and Hi-Quality Group for
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