Mixture design methods for ultra-high-performance concrete - a review

Abstract

A highly efficient mixture design should have a good balance among workability, strength, durability, economic efficiency, and sustainability. Ultra-high-performance concrete (UHPC) is a relatively novel composite material with ultra-high strength, high toughness, and superior durability, although new solutions are constantly being developed. Previous mixture design methods for normal concrete and high-performance concrete involve a series of trial tests and empirical analyses, which cannot be directly applied to UHPC without modification. This paper reviews four commonly used mixture design methods, including close packing methods based on dry and wet packing densities, rheology-based method, statistical analysis method, and artificial neural network (ANN) model, according to design principles. The design procedures of these methods and the effect of mixture proportioning on the key performance of UHPC are presented and discussed. The advantages and disadvantages of these methods are finally compared. Depending on the actual production situation and performance requirements, an appropriate method should be chosen to develop UHPC with specified requirements. Integration of two or more methods can serve as a good approach to deal with the complexities of UHPC mixture design by exerting each method's advantages.

Introduction

Ultra-high-performance concrete (UHPC) is a relatively novel composite material characterized by ultra-high strength, great toughness, and excellent durability due to low water-to-binder (w/b) ratio of around 0.2 and the use of superplasticizer and steel fibers [1,2], although new solutions are constantly being developed. France, China, the United States (USA), Japan, and South Korea, etc., have formulated relevant standards and specifications on design, testing, and applications of UHPC [[3], [4], [5], [6], [7]]. Due to the different materials and sample sizes used in each country or region, the definition of UHPC regarding compressive, flexural, and tensile strengths of UHPC are inconsistent with each other. For example, the compressive and flexural strengths of UHPC should be greater than 100 and 12 MPa, respectively, according to GB/T 31387 from China [3]. Asian Concrete Federation (ACF) defines UHPC a cementitious composite containing discrete fibers for tensile post-cracking ductility with a minimum specified compressive strength of 120 MPa and a flexural strength of 14 MPa or direct tensile strength of 5 MPa [7]. JSCE (Japan) [5] and France [6] agree that the compressive strength of UHPC is 150 MPa, and the minimum tensile strengths are 5 and 8 MPa, respectively. ASTM (United States) [4] and KCI (South Korea) [8] recommend a minimum compressive strength of 120 and 180 MPa, respectively, for UHPC. However, in practice and laboratory conditions, the compressive strength of UHPC can reach up to 250 MPa [9], and even 400 MPa [10] due to heat and autoclave curing. UHPC is widely applied in bridges, explosion-resistant structures, thin-walled structures, architectural ornaments, marine structures, and rehabilitated and strengthening members [[11], [12], [13]]. However, the use of high contents of superfine particles and superplasticizer can lead to high viscosity and autogenous shrinkage of UHPC [[14], [15], [16]]. These eventually cause difficulty in castability and impair hardened performance of UHPC due to entrapped air bubbles, non-uniform dispersion, and orientation of steel fibers [17]. Considering the conflicting requirements of these performances, conventional mixture design methods for normal concrete and high-performance concrete based on empirical parameters cannot directly deal with these complexities without appropriate modification [18,19]. It requires extensive trial tests due to the lack of theoretical basis [20]. The mixture design of normal concrete is mainly based on the water-cement ratio (W/C) law [21], and adjusts the workability of concrete by changing the water consumption [19]. Traditional ACI mixture design method gives priority to the workability of concrete, followed by strength, durability, and economy [22,23]. Although it has been successfully applied in many engineering applications, it often leads to high cement consumption if applied to UHPC [24]. Unlike normal concrete, the key to the UHPC mixture design is to produce a tightly packed structure through optimizing particle size distribution [25]. This requires strictly selected materials to fill the pores to achieve a possible maximum packing density. The mixture design for UHPC is more complicated and can be considered a multi-objective optimization process [26]. Therefore, it is essential to develop scientific and efficient mixture design methods to produce UHPC meeting requirements of workability, strength, durability, and economy.

The properties of UHPC are governed by mixture proportion and curing methods, etc. [[27], [28], [29]]. The binder content in UHPC is high of 800–1000 kg/m³ [1,30,31], And only 30%–40% of cement content participates in hydration due to the low w/b ratio of UHPC. Thus, a large amount of unhydrated cement is acted as inactive filler [32]. Supplementary cementitious materials (SCMs), such as fly ash (FA), ground granulated blast-furnace slag (GGBS) [33], silica fume (SF), metakaolin [34], limestone powder [35], steel slag powder [36], and rice husk ash [37] are used to reduce cement consumption, carbon emission, and enhance flowability without sacrificing mechanical properties [[38], [39], [40], [41]]. UHPC with a binder content of 500 kg/m³ hardly flows, while mixture with a binder content of 700 kg/m³ has a slump of 130 mm [35]. The compressive strength of UHPC is lower than 100 MPa and sharply reduced when the amount of cement replacement increased from 50% to 73%, which is only 280 kg/m³ [42]. UHPC incorporated 20%–30% FA content showed the highest compressive strength and static elastic modulus [43]. Yalçınkaya et al. [44] produced UHPC with compressive strength over 145 MPa by replacing cement with 30% FA or 50% GGBS. Wu et al. [45] pointed out that the addition of 20% GGBS or 3.2% nano-CaCO3 can densify the microstructure of UHPC and increase fiber-matrix bond strength by 30%–48%. Besides, the addition of SCMs in UHPC effectively improves the mechanical strength and durability of UHPC through the filler and pozzolanic effects [44,45]. Superplasticizer is the core that renders UHPC with a low w/b ratio. Although 0.5% superplasticizer can significantly increase the flowability of cement paste more than 3 times [46], the addition of 0.2% superplasticizer delays the initial setting time of concrete for nearly 30 minutes [47]. Besides, the superplasticizer molecules interfere with the growth of hydration products in pore solution and weaken the positive effects of SCMs, which is unfavorable to early strength development of UHPC [48,49]. In the research of Li et al. [50], 3% of nano-silica, by mass of cement, is the optimal content to reduce the retardation of UHPC induced by superplasticizer.

In traditional UHPC mixtures, fine aggregate is used to increase homogeneity and eliminate inherent weakness, such as defects of interfacial transition zone (ITZ) between matrix and coarse aggregate. Nowadays, some researchers attempt to introduce coarse aggregates into UHPC to further reduce cost and achieve better workability [51], mitigate autogenous shrinkage, and improve projectile impact resistance [52,53]. The total volume of coarse and fine aggregate accounts for more than 75% of the total volume of concrete [54,55], and the coarse aggregate incorporated is usually 20%–50% [56]. The optimal coarse aggregate content for UHPC is affected by its maximum particle size, fiber type, and volume [57,58]. When the maximum aggregate size changed from 3 to 16 mm, the 28-d compressive strength of UHPC decreased by 12 MPa [52]. Although the addition of coarse aggregate can increase workability and reduce the drying shrinkage of UHPC, excessive coarse aggregate content can introduce more ITZs, thus resulting in lower compressive strength, higher permeability, and even impair structural quality [59]. As the essential component of UHPC, fiber can enhance tensile properties and restrain shrinkage of UHPC through inhibiting crack propagation [60]. The efficiency of fibers depends on volume, aspect ratio, shape, distribution, type, strength and elastic modulus, and other characteristics [61]. Yoo et al. [62] investigated the influence of fiber volume, shape, and aspect ratio on the flexural properties of UHPC. It was found that the optimal volumes of long twisted fiber and medium-length straight fiber to effectively improve the flexural strength of UHPC are less than 1% and 1.5%, respectively. Wu et al. [63] compared the effects of three shaped steel fibers with same length and diameter, including straight, corrugated, and hooked-end, on the performance of UHPC made with volumes of 0, 1%, 2%, and 3%. It is showed that the 28-d compressive strengths of UHPC using corrugated and hooked-end fibers were increased by 48% and 59%, respectively, while the flowability values were decreased by 45.1% and 51.2%. Another investigation by Wu et al. [60] that the optimal steel fiber volume for enhancing strength and toughness and restraining shrinkage of UHPC was 2%, regardless of fiber shape with a length of 13 mm and a diameter of 0.2 mm. It should be noted that the increase in steel fiber content can inevitably increase the UHPC cost. Steel fiber of 2% volume take up to approximately 50% of the total cost of UHPC.

Hybrid fibers with different sizes [64,65], shapes [63], and types [66], such as steel, carbon, wollastonite, basalt, PVA, PP-PE, biochip fiber, are employed to minimize fiber content and exert their combined strengthening effects. The use of PVA within 0.5% did not significantly affect the elastic modulus of UHPC [67]. The 28-d compressive strength of UHPC with 1.2% PVA was 37.5% higher than that without PVA [68]. The tensile strain capacity of UHPC with 33% steel fibers replaced by PE fiber was increased by 29.7% [69]. UHPC mixed with 1.5% long and 0.5% short fibers exhibited the best static and dynamic mechanical properties [65]. The increase of fiber aspect ratio can promote the possibility of non-uniform fiber dispersion and flocculation in UHPC, and the fiber volume significantly affects the workability of UHPC [70]. However, uniform fiber dispersion and orientation issues and reduction in rheology properties are still main difficulties in the production of UHPC [71,72]. Besides, increases in aggregate size and content, especially the use of coarse aggregate in UHPC, can further intervene with fiber dispersion and distribution. This is mainly due to the interlocking between the coarse aggregate and fibers, and the insufficient fiber length to completely wrap the coarser aggregate, thus eventually affecting the flowability and mechanical properties of UHPC [73]. Liu et al. [74] found that when the coarse aggregate content reached 35%, the slump of the fresh UHPC was only 130 mm. Therefore, selecting the type and quantity of individual constituents to yield UHPC that meets specifiable characteristics for a particular application should be discussed.

The development of mixture design methods for UHPC has become a research hotspot, especially in recent years. In light of the concept that smaller particles fill voids between larger particles, thus reducing void volume and increasing packing density of solid constituents, several close packing models have been proposed [1,75,76]. After Furnas model for the binary mixture was put forward in 1931 [75], Toufar model, Linear packing density model (LPDM), and Compressible packing model (CPM) were developed. Despite the most significant error occurred at the maximum packing density, the linear packing density model (LPDM) for multi-component mixtures can be applied for concrete, as was pointed out by Stovall et al. [77]. The improved compressible packing model (CPM) introduces compaction index and virtual packing concepts and successfully develops UHPC with compressive strength over 200 MPa [78]. Using a compressible packing model and considering the rheological properties of paste, a suitable binder type was selected to design UHPC [55,79]. However, these particle packing models are established on the packing density of dry particles. The effects of water and superplasticizer on wet packing density are not taken into account, which results in an inaccurate prediction of UHPC properties. Considering the effect of liquid in concrete, Larrard et al. [80] used concepts of wet packing density and maximum paste thickness to design UHPC with satisfactory performance. Hoang et al. [81] proposed an iterative optimization method to optimize the mixture design of UHPC. Fan et al. [82] and Yu et al. [83] designed an environmentally friendly UHPC by achieving the maximum wet packing density using novel approaches, including statistical methods of D-optimal design and response surface method (RSM). RSM and D-optimal design methods were found to have the potential to predict the influence of aggregate proportion, admixture, and fibers on UHPC performance [[84], [85], [86]]. Ghafari et al. [87] proposed an artificial neural network (ANN) model derived from biological systems to predict UHPC performance. They found that it is more efficient and accurate than traditional statistical methods. Such as backpropagation (BP) algorithm in ANN, can accurately obtain output value by varying the weight of input value [88,89].

Although different mixture design methods have been developed, most of the proposed mixture design methods involve a series of trial tests and empirical reference values. Due to different principles, the design methods exhibit varying characteristics and applicability. To design UHPC with target performance, it is indispensable to comprehensively review and compare the principles, procedures, and advantages and disadvantages of these commonly used mixture design methods. Table 1 summarizes the design principles and features of these methods. This review focuses on four categories of mixture design methods based on design principles, which include close packing methods divided into dry or wet packing, method developed from rheological properties of paste, statistical design method, and ANN-based method. The basic design principle, procedures, features, and advantages and disadvantages of each method are described and compared. The influences of key raw materials and interaction among superplasticizer, aggregate, fibers, and other components on the design efficiency and performance of UHPC are discussed. This paper can provide a reasonable scientific basis for the production of UHPC with meeting requirements of workability, mechanical properties, durability, and economy.