**1. Introduction**

Self-compacting concrete (SCC) is a kind of high fresh-performance concrete that fills and compacts in a given framework by its own weight without other assistance [1]. As opposed to other conventional vibrated concretes, the defining feature of SCC is its superior workability. Besides the typical requirements of setting time, cohesiveness and water retention, fresh SCC should also satisfy stricter requirements of filling ability, passing ability and segregation resistance. Furthermore, there is a closed relationship between the workability of fresh SCC and the basic mechanical properties of hardened SCC [2,3]. The correct proportioning of self-compacting concrete mixes based on the target fresh and hardened performances is a hot research point.

The mix proportion requires the segregation and settlement of fresh SCC, a large number of binder materials, a higher sand ratio and a smaller maximum particle size of coarse aggregate in order to maintain a sufficient yield value, ensure the viscosity of the fresh mixes and, ultimately, to reduce bleeding [4–7]. A traditional method to ensure the equal performance of SCC is to add mineral materials. The presence of fly ash in SCC reduces its water demand and improves its desired workability but also decreases its compressive strength [7–9]. The presence of granulated ground blast furnace slag (GGBS) in SCC improves its fresh properties as well as its continuing strength development [10,11]. A

**Citation:** Ding, X.; Zhao, M.; Qiu, X.; Wang, Y.; Ru, Y. The Optimization of Mix Proportion Design for SCC: Experimental Study and Grey Relational Analysis. *Materials* **2022**, *15*, 1305. https://doi.org/10.3390/ ma15041305

Academic Editor: Dario De Domenico

Received: 20 December 2021 Accepted: 3 February 2022 Published: 10 February 2022

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positive effect can be observed in SCC with both GGBS and fly ash added in an appropriate proportion and dosage [12]. The passing ability and the segregation resistance of fresh SCC reduce with increasing coarse aggregate size from 9.5 mm to 19 mm, while the compressive strength of hardened SCC increases [13]. A greater amount of binder material content is required to obtain self-compacting workability for an SCC mixed with manufactured sand compared with an SCC mixed with river sand. This is due to the special morphology features of manufactured sand, such as its rough surfaces, irregular shapes, angular edges and inevitable stone powder [14–16]. The workability of fresh SCC could change with hybrid sand mixed with different contents of river sand and manufactured sand due to the changes of particle grading of the hybrid sand [17].

Numerous methods have been used to study the properties of concrete, such as laboratory tests [2,18], field monitoring [19], mathematical statistics [20], numerical analysis [21] and software simulation [22]. As the workability and strength of SCC are affected by multiple factors, it is unclear which one is the major factor. Therefore, the optimal mix proportion of SCC is difficult to obtain from original tests. This encourages research that takes concrete as a system with random, gray and fuzzy uncertain messages and tries to predict and evaluate its properties by grey relational analysis [23–25]. The grey relational analysis theory was founded in 1982 by Deng in China; it is an uncertain systematic theory dealing with a "small sample" and "poor information" [26]. As a type of system analytical technology, the basic principle of grey relational analysis is to evaluate the relationships of connections between sequences according to the geometric shape of a sequence curve. The closer the geometric shapes, the greater the correlation between the corresponding sequences and vice versa.

Based on the above statement, the optimization of the mix proportion of SCC is important to ensure its transition from laboratory research to industrial production. In this paper, an experimental verification was conducted for the mix proportion design of SCC with multiple factors, including the type and content of mineral admixtures, the type and content of sand and the maximum particle size of the coarse aggregate. The test results were evaluated by grey relational analysis to clarify the main influencing factors for both the workability and strength of SCC.

## **2. Mix Proportion Design of SCC**
