## 1 Introduction  
With the high speed of economic development and the increased investment in infrastructure in countries around the world, the amount of concrete used has increased dramatically [1, 2]. Natural sand is a fundamental component of concrete, and with the increase in concrete consumption, more and more river sand is being mined. The widespread mining of river sand can have a negative impact on the surrounding environment; therefore, some rivers have now banned the mining of river sand. Manufactured sand is gradually replacing natural sand in building materials [3]. As shown in Figure 1, the consumption of aggregates and the proportion of manufactured sand used in China has increased from year to year over the last decade. Manufactured sand is made from the crushing of sedimentary rocks and has some unique components not found in natural sand [4, 5]. Manufactured sand is able to avoid the reactions between the active silica components of natural sand and the alkali metal hydroxides of cement. Numerous publications have shown that some of the properties of manufactured sand concrete are better than those of natural sand concrete [6, 7, 8]. Various mineral admixtures are an essential component to improve the performance of the manufactured sand concrete [9]. SP may induce hydride precipitation, which increases the strength of concrete by increasing the content of effective crystallization products [10]. PFA promotes deflecculation in the hydration of cement clinker to reduce water consumption and fills pores to prevent agglomeration between cement particles. The addition of SF to concrete markedly improves the adhesion and cohesion of shotcrete and increases the sequential forming thickness. In addition, some publications have shown that the addition of SP, PFA, and SF to manufactured sand concrete can have a \"superimposed effect\" on each other, reducing the heat of hydration of the concrete while improving its mechanical properties [11; 12; 13]. [PERSON] [14], [PERSON] [15] et al. investigated the effect of SP content in manufactured sand on the mechanical properties of concrete. [PERSON] [16], [PERSON] [17] et al. showed that the SP content of manufactured sand has an important influence on the durability of concrete. [PERSON] et al. [18] investigated the effects of PFA alone, SP alone, and a combination of PFA and SP on the workability and strength of manufactured sand concrete. [PERSON] et al. [19] modified the concrete by incorporating PFA into the manufactured sand. His design for shotcrete, with a PFA admixture of 40% and a water-cement ratio of 0.37, reduced the water consumption while reducing the rebound rate of the shotcrete. [PERSON] [20] found that the addition of marble powder reduced the strength of ordinary Portland cement. After curing the concrete with 20% marble powder for 28 days, a maximum compressive strength of 54.5 MPa was achieved. Currently, most publications report the effect of a single admixture of SP, PFA, and SF or both on the strength of manufactured sand concrete. However, no investigation of the combined effect of the three on compressive strength has been reported. Response surface methodology (RSM) is a statistical method for solving multivariate problems that enables experiments to be conducted using rational experimental design methods with multivariate quadratic equations to be fitted as a function of the relationship between factors and response values. The Box-Behnken experimental design in RSM has been widely used in engineering applications since it was proposed [21], and research on admixtures and concrete has recently become a hot topic. [PERSON] et al. [22] applied RSM to the design of a recycled aggregate permeable concrete mix and found a suitable combination of aggregate gradation and admixture mix. [PERSON] et al. [23] used the two-level central composite design in RSM to optimize the ratio of water-to-binder, PFA-to-binder and iron oxide nanoparticles-to-binder for Portland cement permeable concrete.