Optimization of UHPC Mix Design Using Polyacrylonitrile Fibers and Coarse Aggregates for Cost Reduction

Abstract

To reduce the production cost of ultra-high performance concrete (UHPC), this study incorporated polyacrylonitrile (PAN) fibers and coarse aggregates (CA) to develop a novel UHPC with both excellent performance and reduced cost. A two-stage mortar-concrete design approach was employed to optimize the UHPC mix proportion. First, the mortar matrix was preliminarily optimized based on particle packing theory, and its strength development mechanism was analyzed. Subsequently, response surface methodology was applied to systematically investigate the effects of PAN fiber content, CA content, and superplasticizer (SP) dosage on the slump flow, compressive strength, flexural strength, indirect tensile strength, freeze–thaw resistance, and dynamic mechanical properties of UHPC. The entropy weight method was then adopted to determine the optimal mix proportion, followed by cost estimation. The results indicate that the optimal mortar matrix composition consists of 61.4% cement, 15% silica fume, and 23.6% fly ash, achieving a flow spread of 246 mm, a compressive strength of 117.2 MPa, and a flexural strength of 24.9 MPa. When the PAN fiber content, CA content, and SP dosage were 0.5%, 20%, and 3.8%, respectively, the prepared PAN-CA UHPC(PCUHPC) exhibited the best overall performance. Compared with conventional UHPC, the material cost was reduced by 81.7%, and the compressive strength-normalized cost decreased by 75.4%. The UHPC developed in this study, characterized by outstanding performance and significant cost advantages, provides a feasible solution and theoretical support for broader engineering applications.

1. Introduction

Ultra-high performance concrete (UHPC) is a revolutionary cement-based composite material that has emerged in recent years. Owing to its high compressive strength, low permeability, and excellent durability, it has become an ideal material for long-span bridges, super high-rise buildings, marine engineering, and special protective structures [1,2,3]. The superior performance of UHPC primarily stems from its low porosity and high compactness. By optimizing the composition of cementitious materials and aggregate gradation to reduce weak interfacial transition zones [4,5,6,7,8] and incorporating various types of fibers to enhance toughness [9,10], its overall performance is significantly improved. However, the high cost of UHPC limits its large-scale application, making cost reduction a major research focus.

In conventional UHPC design, the cement content is generally two to three times that of ordinary concrete, and cement together with silica fume accounts for approximately 20% of the total UHPC cost [11,12,13]. Therefore, reducing the amount of cementitious materials is an effective approach to lowering UHPC costs. Reference [14] reported the use of supplementary cementitious materials such as fly ash, blast furnace slag, glass powder, rice husk ash, and limestone powder to partially replace cement and silica fume, resulting in reductions in normalized UHPC cost by 56%, 4.9%, 61%, 55%, and 52%, respectively. Replacing steel fibers is another rapid and effective strategy for reducing UHPC costs. In classical UHPC mixtures, the steel fiber content is typically 2% by volume, accounting for about 40% of the total cost [11]. Steel fibers significantly enhance ductility, tensile strength, and energy absorption capacity, thereby improving the flexural performance of UHPC [15]. However, issues such as corrosion, high cost, and increased self-weight have prompted researchers to explore alternatives. Fibers such as polypropylene, polyvinyl alcohol (PVA), and basalt fibers have been reported for use in UHPC [15,16,17,18,19,20,21], but their corresponding performance generally remains inferior to that of conventional steel-fiber-reinforced UHPC. Incorporating coarse aggregates (CA) into UHPC is another cost-reduction strategy. The addition of CA reduces the content of cementitious materials and superplasticizer, thereby controlling overall cost [22]. The reported cost reduction in CA-containing UHPC ranges from approximately 8.6% to 54% [12,22,23,24].

Polyacrylonitrile (PAN) fiber is a synthetic fiber characterized by high tensile modulus, strong chemical resistance, excellent thermal stability, and low density. It can reduce the initiation and propagation of cracks under freeze–thaw cycles and improve concrete durability [25,26]. Compared with conventional steel fibers, PAN fibers have lower density, better corrosion resistance, and lower cost. In particular, under corrosive environments such as chloride exposure, high humidity, and salt-freezing conditions, PAN fibers do not suffer from the rusting problems that may occur with steel fibers. Therefore, PAN fibers show promising application prospects in low-cost UHPC designed for long-term service environments. Manuel et al. [27] investigated the effects of PAN fibers on mortar properties and found that PAN fibers mitigated microcrack propagation within the mortar matrix, enhanced durability, and significantly reduced drying shrinkage. Similar findings were reported by Wang et al. [28], who further observed that PAN fibers significantly improved the strength, compressive toughness, and abrasion resistance of mortar, particularly at early ages. Zhou et al. [29] compared polypropylene (PP), polyvinyl alcohol (PVA), and polyacrylonitrile (PAN) fibers in concrete and reported that shrinkage resistance and crack resistance ranked as PVA > PAN > PP, while impermeability ranked as PAN > PVA > PP. They also found that the improvement in impermeability due to PAN fibers was mainly attributed to reductions in porosity, the proportion of large capillary pores, and hardened air content. The enhancement of compressive and flexural strength by PAN fibers depends on matrix strength and fiber dosage, whereas excessive fiber content may adversely affect these strengths. Duan et al. [25,30,31] demonstrated that PAN fibers significantly improve freeze–thaw and salt-freeze resistance of concrete, recommending a PAN dosage of 1.5–1.8 kg/m³.

Coarse aggregates can reduce UHPC costs without significantly compromising mechanical properties. References [32,33,34] investigated the workability and mechanical properties of CA-containing UHPC and reported that although the addition of CA significantly affects workability, it does not reduce compressive strength and may even enhance it within an appropriate dosage range. In addition, the elastic modulus increases markedly. The incorporation of CA reduces the post-peak flexural performance of UHPC; however, the overall performance remains satisfactory. Flexural strength primarily depends on the bridging effect and dispersion of steel fibers. The addition of CA also influences fatigue performance, including tensile and compressive fatigue, due to the introduction of weaker interfacial transition zones and interference with fiber distribution, as confirmed by Li et al. [35,36]. Notably, CA incorporation can mitigate autogenous shrinkage, enhance high-temperature performance, and improve abrasion and impact resistance [35,37,38,39], thereby facilitating broader engineering applications.

In summary, PAN fibers and CA can reduce the cost of UHPC while maintaining its favorable mechanical performance and durability. Compared with steel-fiber-reinforced UHPC, this type of UHPC can satisfy a wider range of application scenarios and therefore shows broad prospects. However, the existing studies still have the following limitations: (1) PAN fibers have so far been mainly used to enhance and toughen ordinary cement concrete, and reports on their application in UHPC remain scarce; (2) most existing studies reduce the cost of UHPC by regulating a single variable, focusing primarily on the influence of one material parameter on cost, while insufficient attention has been paid to the synergistic relationship between material performance and cost under the combined effects of multiple factors; (3) current research has mainly focused on introducing a single low-cost material into the UHPC system, but most of these studies remain at the level of material substitution or single-factor modification, lacking a systematic analysis of the relationships among mechanical properties, durability, and economic cost. In particular, during the mix design process, a multi-objective optimization framework that simultaneously considers multiple performance indicators and cost constraints has not yet been fully established. Based on this, the present study first designed UHPC mortar using particle packing theory and analyzed its strength formation mechanism. Subsequently, Polyacrylonitrile fiber-CA UHPC was prepared through response surface methodology, and its workability, mechanical properties, and durability were systematically evaluated. Then, entropy weight theory was employed for multi-objective optimization to determine the optimal PCUHPC mixture proportion in terms of workability, mechanical performance, durability, and cost. Finally, the price of the optimal mixture was compared with that of currently mainstream UHPC. The UHPC developed in this study exhibits a clear cost advantage while maintaining good mechanical performance and durability, providing an economically feasible new material solution for expanding the application of UHPC in a wider range of engineering scenarios. The experimental design workflow is illustrated in Figure 1.

2. Materials and Methods

2.1. Materials

The chemical compositions and technical properties of PO 52.5 Portland cement (Zhongsha Cement Co., Ltd.; Shannxi, China), Grade I fly ash (Sunward Building Materials Co., Ltd., Shannxi, China), and silica fume (Silicon Materials Co., Ltd., Shannxi, China) are presented in

Table 1. Parameters of Gel-Phase Materials.

Item	—	Unit	Cement	Silica Fume	Fly Ash
Chemical composition	CaO	%	64.06	—	4.87
	SiO2	%	21.32	94.33	54.01
	Al2O3	%	4.97	—	28.01
	Fe2O3	%	3.96	0.28	5.49
	K2O	%	0.71	—	3.06
	SO3	%	4.15	—	1.05
	TiO2	%	0.37	—	1.69
	ZrO2	%	—	2.69	—
	Others	%	0.46	2.7	1.82
Physical properties	LOI	%	3.79	1.48	2.62
	Specific surface area	m2/kg	381	22,100	299
	Apparent density	g/cm3	3.12	2.20	2.1

. All performance indicators of the cement complied with the relevant requirements of GB 175-2007 [40], those of the silica fume complied with GB/T 27690-2011 [41], and those of the fly ash complied with the requirements of GB/T 1596-2017 [42]. The technical specifications of quartz sand with particle sizes of 40–70 mesh, 70–110 mesh, and 110–160 mesh used in this study are shown in

Table 2. Technical Properties of Quartz Sand.

Item	Indicator	Unit	Test Value
Chemical properties	Refractoriness	°C	1700
	SiO2 content	%	99.6
	Clay content	%	≤1
	Coefficient of uniformity	—	≤1.8
Physical properties	Abrasion loss	%	0.35
	Porosity	%	43
	Density	g/cm3	2.65
	Crushing rate	%	0.51
	Hardness	%	7.5

. All performance indicators of the quartz sand complied with the relevant provisions for aggregates used in UHPC preparation specified in GB/T 31387-2015 [43]. Their particle size distribution is illustrated in Figure 2. Their particle size distribution is illustrated in Figure 2.

Limestone coarse aggregate (CA) (Guangshan Stone Processing Factory Co., Ltd.; Laiyang, Shannxi, China) with a particle size of 5–10 mm was used in this study, and its technical properties are presented in

Table 3. Technical Properties of CA.

Item	Unit	Test Value
Crushing value	%	13.2
Los Angeles abrasion value	%	11.8
Firmness	%	3.8
Adhesion	—	5
Sand equivalent	%	64.6
Soft stone content	%	2.0

. The technical properties of the limestone coarse aggregates used complied with the requirements of GB/T 14685-2022 [44]. The properties of the PAN fibers (Yuanwang Group, Shandong, China) are listed in

Table 4. Technical Properties of PAN Fibers.

Item	Unit	Test Value
Tensile strength	MPa	537
Elongation at break	%	22
Elastic modulus	GPa	7.2
Density	g/cm3	1.18
Diameter	µm	12
Melting point	℃	240

. Their performance should comply with the requirements of GB/T 21120-2018 [45], and the basic fiber specifications may refer to GB/T 16602-2008 [46].

The properties of the PAN fibers are listed in Table 4. The polycarboxylate superplasticizer (Xingzhenghe Chemical Co., Ltd.; Liaoning, China) exhibited a water-reducing efficiency greater than 30%, and its detailed technical specifications are provided in

Table 5. Technical Properties of the SP.

Item	Unit	Test Value
Water-reducing ratio	%	31
Air content	%	2.8
Bleeding ratio	%	17
PH value	—	6.5
Solid content	%	19.5
Alkali content	%	1.13
Density	g/cm3	1.054

. All performance indicators of the superplasticizer complied with the relevant provisions for superplasticizers used in UHPC preparation specified in GB/T 31387-2015.

2.2. Test Methods for UHPC Mortar Properties

The preparation procedure of UHPC mortar was as follows: ① Before formal mixing, the inner wall and blades of the planetary mortar mixer (Jitong technology, Shen Zhen, China) were pre-wetted to reduce fluctuations in the water-to-binder ratio caused by water adsorption on the equipment surface during mixing. ② Cement, silica fume, fly ash, and quartz sand were then accurately weighed according to the designed mix proportion. After weighing, these components were sequentially added into the mixer and dry-mixed for 1 min to ensure thorough blending of the cementitious materials and fine aggregate. ③ After dry mixing, the pre-prepared superplasticizer solution was mixed uniformly with 90% of the total mixing water and then slowly poured into the mixer. The mixture was stirred at low speed for 3 min to avoid local agglomeration or lump formation caused by adding the liquid all at once. Subsequently, the remaining 10% of the mixed liquid was added into the mixer, followed by low-speed mixing for 30 s to further regulate the flow state of the paste and promote the uniform dispersion of incompletely wetted particles. The mixer was then switched to high speed for 5 min until the paste reached a uniform, dense, and highly workable state. ④ Once the mixture surface appeared uniformly glossy, free of visible dry powder and agglomerates, and exhibited stable flowability, it was immediately cast into molds. During casting, the freshly mixed UHPC mortar was poured continuously or in layers into pre-cleaned molds and compacted on a vibrating table to avoid void defects. Finally, the specimen surface was leveled with a scraper to ensure a dense and smooth finish and then covered with plastic film or protected by other moisture-retaining measures to prevent early moisture loss.

The flowability test was conducted in accordance with GB/T 2419-2005 [47] Test Method for Fluidity of Cement Mortar. Compressive strength and flexural strength were measured following GB/T 17671-2021 [48] Method of Testing Cements-Determination of Strength (ISO Method), with loading rates of 2.4 kN/s and 50 N/s for compressive and flexural tests, respectively.

X-ray diffraction (XRD) analysis was performed using a Bruker D8 Advance diffractometer (Bruker, Karlsruhe, Germany). The operating voltage and current were 40 kV and 35 mA, respectively. The scanning range was 5–60°, with a step size of 0.02 °and a scanning speed of 0.3 s per step.

Thermogravimetric-differential scanning calorimetry (TG-DSC) tests were carried out using an STA449F3 synchronous thermal analyzer (Netzsch, Selb, Germany) to determine the Ca(OH)₂ content and chemically bound water content of hardened composite cementitious samples. The calculation methods are provided in Equations (1) and (2). Tests were conducted under a nitrogen (N₂) atmosphere over a temperature range of 30–800 °C at a heating rate of 10 °C/min, with both purge and protective gas flow rates set at 20 mL/min. Prior to testing, all samples were ground, passed through a 200-mesh sieve, and dried in a vacuum oven at 50 °C for 24 h.

$$m(H_{2}O)=m_B+m_C+m_D\times {\displaystyle \frac{M_{H_{2}O}}{M_{C{O}_2}}}$$

(1)

$$m(Ca{(OH)}_2)=m_c\times {\displaystyle \frac{M_{Ca{(OH)}_2}}{M_{H_{2}O}}}+m_D\times {\displaystyle \frac{M_{Ca{(OH)}_2}}{M_{C{O}_2}}}$$

(2)

where $m\left(H_{2}O\right)$ represents the chemically bound water content (%); $m\left(Ca{\left(OH\right)}_2\right)$ represents the calcium hydroxide content (%); $m_B$, $m_C$, $m_D$ denote the mass losses (%) in the three corresponding stages; $M\left(H_{2}O\right)$, $M\left(Ca{\left(OH\right)}_2\right)$, $M\left({CO}_2\right)$ are the relative molecular masses of the respective chemical compounds.

The porosity and pore size distribution of the specimens were determined using a Micromeritics Autopore V 9505 high-performance automatic mercury intrusion porosimeter (Micromeritics Instrument Corporation, GA, USA). For each measurement, approximately 1 g of sample was placed into a dilatometer. Prior to mercury intrusion, the chamber was evacuated to remove air from the pores, and mercury was then injected under an absolute pressure of 60,000 psia.

Scanning electron microscopy (SEM) analysis was conducted using a Zeiss Gemini 300 microscope (Carl Zeiss, Oberkochen, Germany) operating in secondary electron mode under high vacuum with an accelerating voltage of 2 kV. The SEM samples were dried at 55 °C for 12 h prior to testing. Multiple regions were examined to ensure that the observed microstructures were representative of the samples.

A detailed illustration of the experimental images of UHPC mortar has been provided in Figure 1.

2.3. Test Methods for PCUHPC Properties

In this study, following the method proposed by Wang [49], coarse aggregates were incorporated by replacing UHPC mortar with an equal volume proportion. The slump test was conducted in accordance with GB/T 50080-2016 [50] to evaluate the workability of each concrete mixture. The compressive strength, flexural strength, and splitting tensile strength tests were carried out according to JTG 3420-2020 [51].

Freeze–thaw resistance was evaluated using the rapid freezing method specified in GB/T 50082-2009 [52], with 300 freeze–thaw cycles applied within a temperature range of −18 °C to 5 °C. The freeze–thaw resistance of UHPC was evaluated based on the mass loss rate of the specimens before and after freeze–thaw cycling.

The impact test was performed based on the method provided by Chi [53]. A split Hopkinson pressure bar (SHPB) apparatus was used to investigate the dynamic impact performance of the concrete. The specimen dimensions were 50 mm in diameter and 25 mm in height. The test was conducted under an air pressure of 0.26 MPa, corresponding to an approximate strain rate of 150 s⁻¹. According to the one-dimensional stress wave theory, the instantaneous strain rate of the specimen can be calculated from the incident, reflected, and transmitted wave signals. Under the condition of dynamic stress equilibrium at both ends of the specimen, the strain rate can be expressed by Equation (3) [54]. It should be noted that the strain rate of the specimen is usually not strictly constant, which is related to the characteristics of the testing apparatus used.

$$\epsilon \dot{}(t)=-{\displaystyle \frac{2C_0}{l_s}}{\epsilon }_F(t)$$

(3)

where $\epsilon \dot{}(t)$ is the strain rate; $C_0$ is the wave velocity in the pressure bar, in m/s; $l_s$ is the specimen thickness, in m; ${\epsilon }_F(t)$ is the reflected tensile wave.

A detailed explanation of all the experimental images for the above PCUHPC tests has been provided in Figure 1.

3. Experimental Program

3.1. Optimization of UHPC Mortar Mix Proportion Based on Dense Packing Theory

The Modified Andreasen and Andersen (MAA) model was employed to design the optimal mortar mix proportion, and the model parameters are presented in Equation (4).

$$U_t\left(x_i\right)=100{\displaystyle \frac{x_i^q-x_{\min }^q}{x_{\max }^q-x_{\min }^q}}$$

(4)

where x is the particle size; $Uₜ\left(x\right)$ is the cumulative fraction of particles smaller than $x$; $x_{\min }$ represents the minimum particle size; and $x_{\max }$ represents the maximum particle size. $q$ is the distribution modulus, and a smaller q value indicates a higher proportion of fine particles in UHPC. In this study, the $q$ value was set to 0.23, which is considered appropriate for UHPC [1,55]. Equations (5)–(7) were used to determine the volume fractions of each material under the optimal particle packing condition.

$$U_m\left(x_i\right)=A{y}_{Cement}+B{y}_{SF}+C{y}_{FA}+D{y}_{QS110-160}+E{y}_{QS70-110}+F{y}_{QS40-70}$$

(5)

$$\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}=1$$

(6)

$$RSS={\displaystyle \sum _1^n{\left[U_t\left(x_i\right)-U_m\left(x_i\right)\right]}^2}\to \min$$

(7)

where $Uₘ\left(xᵢ\right)$ represents the cumulative fraction of constituent particles smaller than $x$; A is the volume fraction of cement; B is the volume fraction of silica fume (SF); C is the volume fraction of fly ash (FA); D–F represent the volume fractions of quartz sand (QS); and RSS denotes the residual sum of squares.

The MAA model can only determine the densest packing of different particles under dry conditions and cannot guarantee optimal performance after hardening. Therefore, based on particle packing theory, different constraint conditions were introduced to obtain five UHPC mix designs. In general, the silica fume content should not exceed 20%, and the fly ash content should not exceed 30% [56,57,58], otherwise the mechanical performance and workability of UHPC may be adversely affected. The applied constraints are listed in

Table 6. Constraints Applied to UHPC Mortar.

Types	Constraint Conditions
UHPC1	$0.8\le m_{QS}/(m_{Cement}+m_{SF}+m_{FA})\le 1.2$; $0.5\le m_{\mathrm{c}ement}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})\le 1$; $0.1\le m_{SF}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})\le 0.2$; $0.1\le m_{FA}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})\le 0.3$
UHPC2	$0.8\le m_{QS}/(m_{Cement}+m_{SF}+m_{FA})\le 1.2$; $0.5\le m_{\mathrm{c}ement}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})\le 1$; $0.1\le m_{SF}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})\le 0.2$; $m_{FA}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})=0.3$
UHPC3	$0.8\le m_{QS}/(m_{Cement}+m_{SF}+m_{FA})\le 1.2$; $0.5\le m_{\mathrm{c}ement}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})\le 1$; $m_{SF}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})=0.15$; $m_{FA}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})=0.236$
UHPC4	$0.8\le m_{QS}/(m_{Cement}+m_{SF}+m_{FA})\le 1.2$; $0.5\le m_{\mathrm{c}ement}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})\le 1$; $m_{SF}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})=0.2$; $m_{FA}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})=0.236$
UHPC5	$0.8\le m_{QS}/(m_{Cement}+m_{SF}+m_{FA})\le 1.2$; $0.5\le m_{\mathrm{c}ement}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})\le 1$; $m_{SF}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})\le 0.2$; $m_{FA}/(m_{\mathrm{c}ement}+m_{SF}+m_{FA})\le 0.3$

. Based on these constraints, the volume fractions and mass proportions of each component were further determined. The sand-to-binder ratio was theoretically derived as 1.2, while the water-to-binder ratio and superplasticizer dosage were obtained from preliminary tests as 0.18 and 1.7%, respectively. The mix proportions of the five UHPC formulations are presented in

Table 7. Mix Design of UHPC Mortar.

Types	Total Mass of Binder Materials (kg/m3)	Cement Proportion (%)	Silica Fume Proportion (%)	Fly Ash Proportion (%)	Quartz Sand Proportion (%)
					110–170	70–110	110–160
UHPC1	1214	66.4	10.0	23.6	35.0	20.0	45.0
UHPC2	1200	60.0	10.0	30.0	34.0	21.0	45.0
UHPC3	1205	61.4	15.0	23.6	34.0	20.0	46.0
UHPC4	1195	56.4	20.0	23.6	33.0	21.0	46.0
UHPC5	1219	70.0	0	30.0	35.0	20.0	45.0

Note: The proportions of cement, silica fume, and fly ash are expressed relative to the total binder materials, while the quartz sand proportions represent the weight of each grade of quartz sand relative to the total quartz sand.

.

(In the equation, $m_{QS}$ denotes the mass of quartz sand, $m_{Cement}$ the mass of cement, $m_{SF}$ the mass of silica fume, and $m_{FA}$ the mass of fly ash).

3.2. Experimental Program for Evaluating PCUHPC Performance Based on Response Surface Methodology

A Box–Behnken design (BBD) was employed to develop the experimental program. The PAN fiber content, coarse aggregate (CA) content, and superplasticizer dosage were selected as input factors, and their ranges were determined based on preliminary experiments and the literature [2,3,4]. The slump, compressive strength, flexural strength, indirect tensile strength, mass loss rate, and dynamic compressive strength were chosen as response outputs. A response surface methodology (RSM) model was established using Design-Expert software, and the optimal solutions for different response indices were obtained through numerical optimization. The factor levels are listed in

Table 8. Levels of Factors.

Impact Factor	Unit	Level
		−1	0	1
Dosage of PAN	%	0.2%	0.5%	0.8%
Dosage of CA	%	10%	20%	30%
Dosage of SP	%	3.3%	3.8%	4.3%

. The experimental design is presented in

Table 9. Response Surface Experimental Design.

Test Combination	Dosage of PAN (%)	Dosage of CA (%)	Dosage of SP (%)
1	0.2	10	3.8
2	0.8	10	3.8
3	0.2	30	3.8
4	0.8	30	3.8
5	0.2	20	3.3
6	0.8	20	3.3
7	0.2	20	4.3
8	0.8	20	4.3
9	0.5	10	3.3
10	0.5	30	3.3
11	0.5	10	4.3
12	0.5	30	4.3
13	0.5	20	3.8
14	0.5	20	3.8
15	0.5	20	3.8
16	0.5	20	3.8
17	0.5	20	3.8

, comprising a total of 17 runs, including five replicate tests. In the response surface design, five replicated center-point runs (Runs 13–17) were included to evaluate the repeatability of the experiments and to provide an estimate of pure error for the subsequent analysis of variance (ANOVA). The variation among the replicated center-point results under identical factor levels reflects the unavoidable random experimental error, thereby providing a statistical basis for model significance analysis and lack-of-fit testing.

4. Results and Discussion

4.1. Workability and Mechanical Properties of UHPC Mortar

4.1.1. Flowability

The Flowability results of the five UHPC mixtures are shown in Figure 3. The Flowability ranking is as follows: UHPC3 > UHPC4 > UHPC1 > UHPC2 > UHPC5, with UHPC3 exhibiting the highest flowability and UHPC5 the lowest. Notably, UHPC5 showed significant difficulty in mixing during the actual preparation process, requiring a considerably longer mixing time than the other four mixtures. By comparing specimens with varying silica fume contents, it can be observed that when the silica fume content increased from 10% (UHPC1, UHPC2) to 15% (UHPC3), the flowability improved. However, when further increased to 20% (UHPC4), the flowability showed a decreasing trend. This indicates a nonlinear relationship between silica fume content and UHPC workability, with an optimal dosage range identified as 15% in this study. When the silica fume content was 0% (UHPC5), the cement content reached 70%, which increased the paste viscosity and consequently reduced the flowability.

4.1.2. Mechanical Properties

Figure 4 presents the mechanical properties of the five UHPC mixtures. The compressive strength ranking is: UHPC3 > UHPC4 > UHPC2 > UHPC1 > UHPC5, while the flexural strength ranking is: UHPC3 > UHPC2 > UHPC4 > UHPC1 > UHPC5. UHPC5 exhibited the poorest mechanical performance, indicating that the densest packing under dry conditions does not necessarily correspond to optimal mechanical properties. UHPC3 achieved the highest strength with 15% silica fume and 61.4% cement content. This is mainly attributed to the filling effect, pozzolanic reaction, and improvement of the interfacial transition zone provided by silica fume within the matrix [5,6]. In comparison, when the silica fume content increased to 20% (UHPC4), the compressive strength decreased relative to UHPC3. This is because excessive silica fumes increase water demand and reduces hydration efficiency. Overall, UHPC3 exhibited the best combination of mechanical performance and workability and can therefore be selected as the reference mortar for subsequent concrete mix design.

4.2. Hydration Characteristics and Microstructural Features of UHPC Mortar

4.2.1. Phase Composition and Hydration Reactions

The five XRD patterns shown in Figure 5 collectively confirm that all UHPC samples produced a standard phase assemblage under normal hydration conditions, with stable formation of SiO₂, calcium hydroxide, calcite, and silicate phases. The silicate phases in cement hydrate to generate calcium hydroxide and C-S-H gel. Subsequently, the reactive silica in fly ash and silica fume consumes part of the calcium hydroxide through pozzolanic reactions, producing additional C-S-H gel [5]. The remaining calcium hydroxide partially carbonates into calcite under the influence of environmental carbon dioxide, while the quartz sand remains chemically inert and does not participate in the reaction. XRD analysis also revealed the formation of a certain amount of ettringite during hydration. This is attributed to the presence of Al₂O₃ in fly ash and aluminates in cement, which react with water to form ettringite. Ultimately, a consistent phase assemblage composed of quartz, calcium hydroxide, calcite, ettringite, and partially unhydrated silicate phases was obtained, which corresponds well with the composition of the raw materials used in this study.

Figure 6 presents the TG-DTG test results of the five UHPC mixtures. All samples exhibited similar curve trends, accompanied by varying degrees of mass loss. Three distinct endothermic peaks were observed in the TG curves. As shown in Figure 6f, the total mass loss of the five UHPC samples ranked as UHPC4 > UHPC3 > UHPC5 > UHPC1 > UHPC2. Based on the calculated results (Figure 6g,h), the relatively high mass loss of UHPC5 is directly associated with its 70% cement content, which enhances the degree of hydration. However, the absence of pozzolanic reactions results in calcium hydroxide accumulation, potentially leading to increased microporosity (further discussed in Section 4.2.2). Although UHPC3 exhibited a moderate degree of hydration, the presence of 15% silica fume promoted the conversion of calcium hydroxide into high-density C-S-H, resulting in the lowest mass loss and the most compact microstructure.

4.2.2. Pore Structure Characteristics and Micro-Morphology

Figure 7 presents the mercury intrusion porosimetry (MIP) results of the five UHPC samples. The results indicate clear differences in pore size distribution among the mixtures. UHPC1 contains a higher proportion of pores within the 100–10,000 nm range, whereas UHPC5 exhibits a significantly greater number of pores smaller than 100 nm. As shown in Figure 7b, the cumulative pore volume of UHPC1 and UHPC5 is higher than that of the other three mixtures. In Figure 7c, the average pore diameter of all samples exceeds the median pore diameter, suggesting that the overall pore structure is influenced by the presence of larger pores. The porosity results in Figure 7d reveal that UHPC3 has the lowest porosity (1.61%), while UHPC5 has the highest (8.95%). According to the pore volume fraction analysis across different pore size ranges in Figure 7f, UHPC5 has the lowest proportion of large pores (13%), yet its overall porosity remains high, indicating a greater number of small pores within the matrix, resulting in the lowest compactness. In contrast, UHPC3 possesses the highest proportion of harmless pores (<10 nm) and the lowest overall porosity, which contributes to its superior mechanical performance. Wang et al. [7] reported that pores larger than 20 nm significantly deteriorate concrete performance, which also explains the weakest mechanical behavior observed in UHPC5. Comparatively, UHPC3 exhibits the highest fraction of harmless pores below 10 nm and the lowest porosity, enabling it to achieve the best mechanical performance.

Figure 8 presents the SEM images of the five UHPC samples after 28 days of curing. The results show that all samples exhibit similar microstructural characteristics, with evident hydration products (C-S-H and Ca(OH)₂) and pores. Some samples also contain microcracks, which are commonly observed in cement-based materials. Among them, UHPC5 displays a greater number of pore structures, consistent with the pore structure analysis indicating that UHPC5 possesses the highest microporosity. As shown in Figure 8a,c,d, distinct hydration clusters can be observed. This is attributed to the nucleation effect of materials such as silica fume, which promotes the aggregation of hydration products [8].

4.3. Response Surface Methodology Analysis of PCUHPC

4.3.1. Results of Response Outputs

The PCUHPC mixtures designed based on the response surface methodology were experimentally tested under different factor combinations, and the results are presented in

Table 10. RSM Results.

Test Combination	Dosage of PAN (%)	Dosage of CA (%)	Dosage of SP (%)	Slump (mm)	Compressive Strength (MPa)	Flexural Strength (MPa)	Splitting Tensile Strength (MPa)	Weight Loss Ratio (%)	Dynamic Compressive Strength (MPa)
1	0.20%	10%	3.80%	267.3	77.42	11.23	5.92	1.85	91.3
2	0.80%	10%	3.80%	150.4	90.28	10.45	6.18	1.8	110
3	0.20%	30%	3.80%	121.8	91.45	9.03	6.85	2.9	100.32
4	0.80%	30%	3.80%	21.6	71.35	6.51	6.55	2.87	82.74
5	0.20%	20%	3.30%	182.3	105.6	10.72	6.25	2.7	118.6
6	0.80%	20%	3.30%	51.4	104.36	10.01	6.11	2.71	110.3
7	0.20%	20%	4.30%	280.4	96.51	10.87	6.95	2.65	108.9
8	0.80%	20%	4.30%	89.3	89.53	9.13	6.41	2.71	110.6
9	0.50%	10%	3.30%	158.4	97.9	11.42	6.34	1.59	110.9
10	0.50%	30%	3.30%	79.7	84.57	9.56	7.23	2.69	105.96
11	0.50%	10%	4.30%	269.4	98.2	10.54	6.45	1.62	120
12	0.50%	30%	4.30%	77.9	112.19	8.43	7.15	2.65	135.89
13	0.50%	20%	3.80%	115.26	110.06	12.24	7.01	1.67	130.6
14	0.50%	20%	3.80%	133.56	105.23	11.89	6.95	1.74	135.6
15	0.50%	20%	3.80%	126.21	109.27	12.73	7.12	1.7	129.63
16	0.50%	20%	3.80%	111.45	115.26	12.16	7.09	1.76	123.69
17	0.50%	20%	3.80%	119.23	116.26	12.23	6.83	1.7	134.8

.

Taking the indirect tensile strength as an example, the variations across the 17 experimental runs were analyzed under the single-factor effects of PAN fiber content, CA content, and SP dosage, as shown in Figure 9. The indirect tensile strength changed progressively with variations in PAN content, CA content, and SP dosage; however, these trends could not be accurately characterized using single-factor analysis alone. Similarly, changes in each of the three individual factors also influenced other performance indices in a comparable manner. This indicates that traditional single-variable control is insufficient to fully capture the interactions among multiple factors. Therefore, a multifactor analysis approach was adopted to investigate the combined effects of PAN content, CA content, and SP dosage on the various response outputs.

4.3.2. Regression Model and Factor Significance Analysis

Table 11. ANOVA results for the models and parameters (α = 0.05).

Source	${\mathit{Y}}_1$		${\mathit{Y}}_2$		${\mathit{Y}}_3$		${\mathit{Y}}_4$		${\mathit{Y}}_5$		${\mathit{Y}}_6$
	p	R	p	R	p	R	p	R	p	R	p	R
Model	<0.0001	S.	0.0344	S.	0.0001	S.	0.005	S.	<0.0001	S.	0.0202	S.
A	<0.0001	S.	0.5045		0.0020	S.	0.2059		0.9204		0.8249
B	<0.0001	S.	0.8525		<0.0001	S.	0.0008		<0.0001	S.	0.7688
C	0.0010	S.	0.8607		0.0558		0.0863		0.5537		0.2543
AB	0.6166		0.0716		0.0787		0.1690		0.7779		0.0686
AC	0.1010		0.7228		0.2628		0.3096		0.4874		0.5720
BC	0.0095	S.	0.1222		0.7762		0.6189		0.3390		0.2568
A2	0.1721		0.0079	S.	0.0003	S.	0.0009	S.	0.0001	S.	0.0016	S.
B2	0.3777		0.0061	S.	0.0001	S.	0.1837		0.0361	S.	0.0101	S.
C2	0.0548		0.6694		0.0121	S.	0.4198		0.0001	S.	0.6973
Lack of Fit	0.0542		0.0670		0.1455		0.0923		0.5603		0.0586

Note: p: probability of error; S.: statistically significant (p less than 0.05), $Y_1$, $Y_2$, $Y_3$, $Y_4$, $Y_5$ and $Y_6$ represent slump, compressive strength, flexural strength, indirect tensile strength, mass loss rate, and dynamic compressive strength, respectively.

presents the ANOVA results, where smaller p-values indicate greater model significance. The data obtained from the replicated center-point runs were incorporated into the ANOVA. The variability among these replicates was used to estimate the pure error and further applied in the lack-of-fit test to determine whether the developed quadratic regression model could adequately describe the relationship between the factors and responses. Meanwhile, the replicated center points also improved the reliability of parameter estimation and significance testing. At a significance level of 5%, the p-values of all regression models are less than 0.05, demonstrating that each model is statistically significant. In contrast, the p-values for lack of fit are all greater than 0.05, indicating that the lack-of-fit terms are not significant. This suggests a good agreement between the predicted values and the experimental measurements.

4.3.3. Interaction Effects Among Factors

To better understand the interactions among the factors, contour plots of $Y_1$, $Y_2$, $Y_3$, $Y_4$, $Y_5$ and $Y_6$ are presented in Figure 10, Figure 11, Figure 12, Figure 13, Figure 14 and Figure 15.

As shown in Figure 10, increasing the PAN fiber content and CA content negatively affects the slump, and their adverse effects tend to accumulate. This is mainly because PAN fibers exhibit a certain degree of water absorption, which removes part of the free water within the concrete during hardening. Meanwhile, the larger particle size of coarse aggregates increases internal friction. The incorporation of coarse aggregates reduces the proportion of cementitious materials in the UHPC system, while these materials are also required to coat the aggregate surfaces, resulting in reduced overall fluidity of the paste. In contrast, increasing the dosage of superplasticizer can significantly improve the flowability of the concrete.

Figure 11 presents the contour plots of compressive strength. The effects of PAN content and CA content on compressive strength are more pronounced than that of the superplasticizer dosage. At moderate levels, both PAN and CA contribute most effectively to enhancing the compressive strength of PCUHPC. An appropriate amount of PAN fibers can provide fiber-bridging effects and suppress the propagation of microcracks, while a suitable CA content helps form a stable load-bearing skeleton, thereby jointly improving strength. However, excessive PAN or CA introduces more interfacial defects into the PCUHPC system and may lead to poorer workability, resulting in a reduction in compressive strength. Conversely, insufficient dosages fail to provide adequate reinforcement. The influence of the superplasticizer on compressive strength is relatively limited, mainly improving it indirectly by enhancing the workability of the concrete.

The contour plots of flexural strength in Figure 12 exhibit an overall quadratic nonlinear pattern, characterized by higher values at intermediate levels and lower values at both extremes. The flexural strength reaches its maximum when the PAN content ranges between 0.45% and 0.6%. Excessive CA content leads to a reduction in strength due to the weakening of the interfacial transition zone (ITZ) and increased internal friction. An appropriate dosage of superplasticizer promotes particle dispersion and uniform fiber distribution, thereby enhancing the bridging and toughening effect of PAN fibers. Overall, the optimal combination for flexural strength is 0.5% PAN, 20% CA, and 3.8% SP.

Figure 13 presents the response surface results of indirect tensile strength, which ranges from 6.2 to 7.2 MPa. An appropriate PAN fiber content is required, with the optimal range between 0.4% and 0.5%. In contrast, increasing CA content and SP dosage both contribute to enhancing the indirect tensile strength, and they exhibit a certain synergistic effect. When both are at higher levels, the indirect tensile strength reaches its maximum value of 7.2 MPa.

The mass loss rate results are shown in Figure 14. The incorporation of coarse aggregates has a noticeably adverse effect on the freeze–thaw resistance of PCUHPC, mainly because it introduces additional weak interfacial zones between the matrix and aggregates. In contrast, both PAN fibers and the superplasticizer exhibit a trend of first reducing and then increasing the mass loss rate. An appropriate amount of PAN fibers helps inhibit crack development, while the superplasticizer acts as a lubricant within the mixture.

The dynamic compressive strength results are shown in Figure 15. Its variation trend is similar to that of compressive strength. Coarse aggregate and PAN fiber content have a more pronounced influence on dynamic compressive strength, while the effect of the superplasticizer is relatively minor. The synergistic effect between PAN fibers and coarse aggregates is most significant when the PAN content is 0.5% and the CA content is around 20%, under which the dynamic compressive strength of PCUHPC reaches its maximum.

4.4. Microstructural Analysis of PCUHPC

Figure 16 illustrates the micro-morphology of fibers and coarse aggregates in PCUHPC. As shown in Figure 16, PAN fibers were firmly anchored within the PCUHPC matrix, and a distinct layer of hardened cementitious material was observed on the fiber surface. The fiber morphology changed from the originally soft and flocculent state to a hard, elongated block-like form. This indicates that after being wetted during mixing, the fibers came into sufficient contact with the fresh paste, allowing an initial paste coating to form on their surfaces. A magnified view of the fiber-matrix interfacial transition zone (ITZ) in Figure 16a shows that the entire interface was densely filled with C-S-H gel. Hydration products deposited continuously along the fiber surface and filled interfacial pores, gradually densifying the fiber-paste interface. This dense interfacial structure provides the fundamental basis for the development of anchorage force and pull-out resistance at later stages.

Figure 16b presents the morphology of coarse aggregates in PCUHPC. A distinct layered feature can be clearly observed. The aggregate surface exhibits irregular fractured or flaky textures, with a rough and uneven morphology, which is favorable for the penetration of the surrounding paste into the surface micropores and depressions of the aggregate. In contrast, the matrix surface, mainly formed by the accumulation of hydration products, appears more fragmented. A magnified view of the aggregate-matrix ITZ reveals that hydration products formed an interlocking structure with the aggregate edges and grew along the aggregate boundary, indicating that the aggregate could influence the growth direction of hydration products to some extent. However, local interfacial voids were also observed in certain regions between the coarse aggregate and the matrix. In these areas, hydration products were unable to completely bond the coarse aggregate to the PCUHPC matrix, and a continuous dense structure was not formed. Consequently, the ITZ exhibited lower mechanical strength than both the aggregate and the surrounding matrix, making it a relatively weak region in the overall concrete structure.

4.5. Application-Oriented Optimization of PCUHPC Mix Proportion

The entropy weight method was employed to conduct a comprehensive evaluation and selection of concrete performance, where the weights of each evaluation index were determined based on the magnitude of information entropy. A smaller entropy value indicates a greater degree of variation in the index, implying a larger contribution to the overall evaluation and therefore a higher assigned weight. The specific calculation procedure of the entropy weight method follows Equations (8)–(16).

$$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}& x_{m2}& \dots & x_{mn}\end{array}\right]$$

(8)

where $x_{ij}$ represents the original value of the i-th evaluation object under the j-th indicator.

To eliminate the influence of dimensional differences, the original data were standardized. Benefit-type indicators (where larger values are preferable) were calculated using Equation (14), while cost-type indicators (where smaller values are preferable) were calculated using Equation (15).

$$r_{ij}={\displaystyle \frac{x_{ij}-\min (x_j)}{\max (x_j)-\min (x_j)}}$$

(9)

$$r_{ij}={\displaystyle \frac{\max (x_j)-x_{ij}}{\max (x_j)-\min (x_j)}}$$

(10)

The normalized matrix is expressed as $R=[r_{ij}]$. $r_{ij}\in [0,1]$

$$p_{ij}={\displaystyle \frac{r_{ij}}{{\displaystyle \sum _{i=1}^m}{r}_{ij}}}$$

(11)

The entropy value measures the degree of uncertainty associated with an indicator, and is calculated as follows:

$$\begin{array}{l}{e}_j=-k{\displaystyle \sum _{i=1}^m}{p}_{ij}\ln (p_{ij})\end{array}$$

(12)

Here, $k={\displaystyle \frac{1}{\ln m}}$, if $p_{ij}=0$, than $p_{ij}\ln p_{ij}=0$

$$d_j=1-e_j$$

(13)

$$w_j^{(obj)}={\displaystyle \frac{d_j}{{\displaystyle \sum _{j=1}^n}{d}_j}}$$

(14)

$$w_j^{(final)}=\alpha \cdot w_j^{(sub)}+(1-\alpha )\cdot w_j^{(obj)}$$

(15)

$$S_i=\sum _{j=1}^m{w}_j^{\mathrm{final}}{r}_{ij}$$

(16)

$e_j$, $d_j$, $w_j^{(obj)}$, $\alpha \cdot w_j^{(sub)}$ and $w_j^{(final)}$ represent the entropy value, redundancy, objective weight, subjective weight, and final weight, respectively. In this study, subjective weighting was not applied; instead, a fully objective entropy weight method was used to determine the weights of slump, compressive strength, flexural strength, splitting tensile strength, mass loss rate, dynamic compressive strength, and unit cost. The unit cost and entropy weight scores of the 17 mix designs are shown in Figure 17. The weighted scores, ranked from highest to lowest, are: $S_{15}$ > $S_{17}$ > $S_{13}$ > $S_{16}$ > $S_{14}$ > $S_{11}$ > $S_{12}$ > $S_9$ > $S_7$ > $S_{10}$ > $S_5$ > $S_2$ > $S_1$ > $S_3$ > $S_8$ > $S_6$ > $S_4$, Therefore, the PCUHPC designed under Scheme 15 exhibits the best overall performance.

4.6. Cost Analysis

To quantify the cost of PCUHPC, Scheme 15, which exhibited the best overall performance, was selected as the reference for comparison with conventional UHPC containing 2% steel fibers, low-cost UHPC without fibers achieved by reducing cementitious material content, and the UHPC3 mortar developed in this study. Taking compressive strength as an example, their performance and cost were compared. The mix proportions of the different UHPCs are presented in

Table 12. UHPC mix proportions and compressive strength.

References	Cementitious Materials (kg/m3)	W/B	Cement (kg/m3)	Silica Fume (kg/m3)	Fly Ash (kg/m3)	Fiber (kg/m3)	SP (kg/m3)	Fine Aggregate (kg/m3)	Coarse Aggregate (kg/m3)	Compressive Strength (MPa)
[60]	1543	0.2	1234.4	308.6	0	156	49.4	607	0	147.15
[59]	945	0.18	810	135	0	0	9.45	1203	0	108
UHPC3	1205	0.18	739.87	180.75	284.38	0	29.7776	1446	0	117.19
PCUHPC	964	0.18	591.896	144.6	227.504	5.9	36.532	1156.8	540	109.27

, while

Table 13. Unit prices and total cost of UHPC materials.

References	Cement (CNY/t)	Silica Fume (CNY/t)	Fly Ash (CNY/t)	Fiber (CNY/t)	SP (CNY/t)	Fine Aggregate (CNY/t)	Coarse Aggregate (CNY/t)	Cost(CNY/m3)	Normalized Cost (CNY/m3/MPa)
[60]	574	5600	280	35,000	23,800	280	0	14,511	98.61366
[59]	4004	4599	—	—	5110	665	—	4711	43.62037
UHPC3	595	9464	560	—	2924.6	490	—	3105	26.49543
PCUHPC	595	9464	560	13,843.9	2924.6	490	97.3	2656	24.30676

provides the cost of each material, unit cost, and normalized cost [9]. The results indicate that the incorporation of coarse aggregates significantly reduces the consumption of cementitious materials, allowing the total binder content of PCUHPC to be controlled within 1000 kg/m³. The addition of steel fibers markedly improves compressive strength; consequently, the compressive strength of PCUHPC is 25.7% lower than that of conventional UHPC. However, compared with the low-cost UHPC designed by Liu et al. [59], PCUHPC achieves a 1.2% increase in compressive strength. A comparative cost analysis shows that PCUHPC has a clear cost advantage. Compared with conventional UHPC designed by Ali et al. [60], the cost is reduced by 81.7%; compared with the low-cost UHPC designed by Liu et al., the cost is reduced by 43.7%; and compared with the UHPC mortar, the cost is reduced by 14.6%. Analysis of compressive strength-normalized cost further reveals that PCUHPC achieves reductions of 75.4% and 44.3% compared with the UHPC designed by Ali et al. and Liu et al., respectively, and an 8.3% reduction compared with the mortar. It should be noted that the raw material cost of UHPC varies significantly by region; nevertheless, the PCUHPC developed in this study effectively reduces overall cost by incorporating coarse aggregates and lowering binder content while maintaining adequate mechanical performance.

5. Conclusions

This study addresses the high cost of UHPC, which limits its engineering application, by developing a low-cost PCUHPC suitable for practical use through a two-stage design approach. The main conclusions are as follows:

① Mix proportions derived solely from dense particle packing theory do not necessarily correspond to optimal workability and mechanical performance of UHPC. Therefore, further concrete-scale mix design based on an optimized mortar matrix is required to achieve coordinated multi-performance optimization.

② In this study, the mortar containing 15% silica fume and 61.4% cement exhibited the best flowability, compressive strength, and flexural strength. The incorporation of silica fume reduced the porosity of the matrix, promoted the formation of C-S-H gel, and improved the structural integrity of the interfacial transition zone.

③ When the PAN fiber content was 0.5%, the coarse aggregate content was 20%, and the superplasticizer dosage was 3.8%, the prepared PCUHPC exhibited the best overall performance. At around 0.5%, PAN fibers effectively bridged microcracks, mitigated damage propagation under freeze–thaw cycles, and significantly improved tensile strength, impact resistance, and durability. A CA content of approximately 20% enabled the formation of a stable skeletal structure, enhancing compressive and splitting tensile strength, while also demonstrating a synergistic strengthening effect in systems with low fiber content.

④ Excessive PAN fiber content or an overly high CA dosage can introduce interfacial defects and fiber agglomeration, thereby weakening the overall performance. The incorporation of coarse aggregates has a noticeably adverse effect on the freeze–thaw resistance of PCUHPC. Meanwhile, a superplasticizer dosage of around 3.8% significantly improves paste dispersion and fiber distribution uniformity, alleviating the workability deterioration caused by high PAN and CA contents; however, excessive usage may result in bleeding, segregation, and localized defects.

⑤ The unit cost of PCUHPC was reduced by 81.7% compared with conventional UHPC and by 14.6% compared with the matrix, while the normalized cost decreased by 75.4% relative to conventional UHPC and by 8.3% relative to the matrix.