Uniaxial Compressive Behavior and Constitutive Modeling of Fiber-Reinforced Self-Compacting Concrete with Granite Powder and Expansive Agent: An Experimental Study with Acoustic Emission Monitoring

Abstract

Fiber-reinforced self-compacting concrete (FR-SCC) incorporating granite powder (GP), an expansive agent (EA), steel fibers (SFs), and polypropylene fibers (PPFs) was investigated for potential pre-cast tunnel-segment applications. Sixteen mixtures, covering GP replacement ratios of 0–18%, EA dosages of 0–8% by binder mass, and SF and PPF volume fractions of 0–0.75% and 0–0.15%, were tested in uniaxial compression on 100 mm × 100 mm × 300 mm prisms with acoustic emission (AE) monitoring. Within the tested range, 12% GP and 8% EA gave the most favorable binder composition. XRD and SEM analyses indicated that GP acted predominantly as an inert filler with no detectable portlandite consumption, while the expansive agent was associated with additional ettringite formation. At this composition, hybrid SF/PPFs increased the post-peak energy by a factor of 7.66 relative to the fiber-free mixture, mainly improving the post-peak rather than the pre-peak behavior. Among the Carreira–Chu, GB 50010, and modified Weibull formulations, the GB 50010 piecewise model best reproduced the full stress–strain curves and was used as the primary constitutive model. Two-variable regressions were established to separate the apparent effects of the SF and PPF volume fractions on the ascending- and descending-branch shape parameters, and a ductility-calibrated expression was developed for the descending-branch parameter. The Pearson coefficient between the descending-branch parameter and the AE characteristic strain was −0.904, while that between the AE characteristic strain and the macroscopic residual strain was +0.983. These results link constitutive modeling, AE damage evolution, and macroscopic post-peak ductility for FR-SCC within the tested range of mix proportions.

1. Introduction

Self-compacting concrete (SCC) is a highly flowable, non-segregating concrete that fills the formwork and encapsulates the reinforcement under its own weight without mechanical consolidation. SCC is therefore suitable for pre-cast tunnel segments and structural lining applications [1]. With river sand becoming increasingly scarce, manufactured sand (MS) is widely used as fine aggregate in SCC. Its angular particles and the stone powder finer than 75 μm generated during crushing affect the packing state and deformation behavior of the matrix. For pre-cast segments, the uniaxial post-peak compressive response is a critical indicator, as it reflects the deformation capacity and damage resistance of the material under compression [2].

Granite powder (GP) in this study refers to the <75 μm stone-powder fraction separated during the production of granite manufactured sand and derived from the same crushed granite as the fine aggregate. This fraction is commonly controlled or removed to meet the fines-content requirement of manufactured sand, and its reuse in cementitious systems has attracted increasing attention, where, depending on the mixture design, such granite-derived powder has been investigated as a supplementary fine material, cement replacement, or sand replacement. At a suitable replacement ratio, GP can fill inter-particle voids, improve packing density, and reduce matrix porosity [3,4,5]. The resulting strength changes reflect the combined effect of filler action, packing modification, and cement dilution [5,6]. GP can partially replace fine aggregate without obvious strength reduction and can improve durability when blended with fly ash [7,8]. However, the combined performance of GP, expansive agent, and hybrid steel/polypropylene fibers (SF/PPFs) in SCC has not been systematically investigated, and it remains unclear whether the packing benefits of GP are retained in such a coupled fiber-reinforced self-compacting concrete (FR-SCC) system.

Incorporating an expansive agent (EA) is another common approach to reduce the shrinkage of SCC. EA forms expansive hydration products, primarily ettringite, portlandite, and brucite, which under restrained conditions produce a controlled volume expansion that compensates for shrinkage and induces internal self-stress in the hardened matrix. Previous studies on EA-modified SCC and fiber-reinforced SCC indicate that a suitable EA dosage can mitigate shrinkage while maintaining or improving the hardened-state mechanical performance, with the optimum dosage depending on EA chemistry, restraint condition, fiber volume fraction, and matrix composition [9,10,11]. When EA is combined with fibers, the fibers restrain part of the expansive deformation; this restrained expansion has been reported to introduce an internal confinement, or self-stress, in the hardened matrix that may enhance fiber–matrix load transfer and densify the interfacial transition zone in both single-fiber [12,13] and hybrid-fiber [14,15] systems. However, the dosage-dependent effect of EA on the uniaxial compressive response of FR-SCC has not been conclusively established, particularly when GP is also incorporated into the binder phase.

Hybrid fiber systems combining SF and PPF have been widely used to enhance the post-peak compressive response of SCC. SFs bridge macrocracks and improve ductility, energy absorption, and residual strength, whereas PPFs inhibit microcrack propagation and contribute to energy dissipation [16,17]. The uniaxial compressive stress–strain response of SCC reinforced with hybrid SF/PPF or steel–polyvinyl alcohol fibers is sensitive to fiber type, volume fraction, and combination [17,18,19,20]. For constitutive modeling, the Carreira–Chu equation [21], the GB 50010 piecewise formula [22], and Weibull-type damage formulations [23] have been used to describe full compressive stress–strain curves. Residual-strength correction and elastoplastic-damage extensions have also been proposed for hybrid-fiber concrete [24,25].

Although considerable progress has been made, three problems remain unresolved for SCC containing GP, EA, and hybrid SF/PPF. First, the combined effects of GP replacement ratio and EA dosage on the full uniaxial compressive stress–strain response of FR-SCC, especially the post-peak branch, remain insufficiently characterized. Second, limited attention has been paid to the dosage-dependent effect of EA on the compressive ductility of FR-SCC, particularly in GP-containing binder systems. Third, existing studies [17,24] generally evaluate the post-peak softening behavior of hybrid SF/PPF-reinforced SCC using total fiber volume fraction, hybrid ratio, or fiber factor, rather than quantifying the individual contributions of V_SF and V_PP through regression. In addition, the consistency between constitutive descending-branch parameters and AE-based damage descriptors has rarely been examined for this material system.

To address these problems, the uniaxial compressive behavior and constitutive modeling of FR-SCC with GP and EA were experimentally investigated. Sixteen mixtures, including 15 FR-SCC mixtures and one fiber-free reference, were prepared as 100 mm × 100 mm × 300 mm prismatic specimens. The experimental design covered systematic variations in GP replacement ratio, EA dosage, and hybrid SF/PPF volume fractions. Uniaxial compression tests with acoustic emission (AE) monitoring were then performed. The objectives were threefold: (i) to characterize the full compressive stress–strain response and quantify the effects of GP, EA, and hybrid SF/PPF on the peak and post-peak parameters; (ii) to compare the fitting accuracy of the Carreira–Chu, GB 50010, and modified Weibull models, to establish two-variable regressions separating the SF and PPF contributions to the ascending- and descending-branch shape parameters, and to develop a ductility-calibrated expression for the descending-branch parameter a_d; and (iii) to fit the AE-based damage variable D_AE with a two-parameter Weibull cumulative function and to examine the consistency among a_d, the AE scale parameter λ_AE, and the post-peak strain measure ε_0.20.

2. Materials and Methods

2.1. Materials

The powder materials included P.O 42.5 ordinary Portland cement (Henan Tianrui Group Zhengzhou Cement Co., Ltd., Zhengzhou, China) complying with GB 175-2023 [26], Grade I fly ash (FA) (Henan China Resources Power Xingye Fly Ash Co., Ltd., Zhengzhou, China) with low CaO content complying with GB/T 1596-2017 [27], a CaO-based expansive agent (EA) (Tuoda, Foshan, China) complying with GB/T 23439-2017 [28], and granite powder (GP), the <75 μm stone-powder fraction separated from the granite manufactured sand and reintroduced into the mixtures at prescribed replacement ratios (Figure 1). Their properties are summarized in

Table 1. Chemical composition of cement, FA, EA and GP (% by mass).

Component	Cement	FA	EA	GP
SiO2	20.71	51.92	6.39	72.47
Al2O3	6.99	16.21	2.54	12.7
Fe2O3	3.21	4.91	1.26	4.45
CaO	62.12	8.59	80.87	1.28
MgO	2.03	3.82	2.16	— 1
SO3	2.03	1.73	3.71	—
Na2O	0.11	0.58	0.28	2.23
K2O	0.56	1.86	0.42	4.89
f-CaO 2	0.76	0.66	0.96	—
LOI 3	3.66	2.53	4.61	—

¹ —: not reported. ² f-CaO refers to free calcium oxide. ³ LOI refers to loss on ignition.

,

Table 2. Properties of cement, FA, EA and GP.

Material	Blaine Specific Surface Area (m2/kg)	Apparent Density (g/cm3)
Cement	356	3.10
FA	400	2.49
EA	643	2.70
GP	609	2.69

and

Table 3. Properties and activity indices of GP.

Property	Value
45 μm sieve residue (%)	28
Methylene blue value (g/kg)	0.5
Moisture content (%)	0.1
7-day activity index 1 (%)	73.3
28-day activity index 1 (%)	76.7

¹ The 7- and 28-day activity indices of GP were evaluated according to GB/T 18736-2017 [29].

.

Manufactured sand (MS) of fineness modulus 2.9 produced from crushed granite obtained as tunnel spoil from the Shangyoufang Tunnel of the Xixia–Xichuan Expressway, Henan, China, was used as the fine aggregate, complying with GB/T 14684-2022 [30]. The coarse aggregate (CA), supplied by Nanjing Huiju Stone Co., Ltd. (Nanjing, China), consisted of crushed granite blended from three size fractions (4.75–9.50 mm, 9.5–13.2 mm, and 13.2–16.0 mm). Their properties are summarized in

Table 4. Properties of aggregates.

Aggregate Type	Fineness Modulus	Apparent Density (kg/m3)	Loose Bulk Density (kg/m3)	Compacted Bulk Density (kg/m3)	Water Absorption (%)	Fines Content (%)
CA	— 1	2720	1550	1630	1.1	0.2
MS	2.9	2690	1580	1725	2.2	9.0

¹ —: not applicable.

, in which the loose and compacted bulk densities were determined according to ASTM C29/C29M-23 [31].

Hooked-end steel fibers (SFs; Dramix 3D 65/35BG, Bekaert, Shanghai, China) and polypropylene fibers (PPFs; Lingshou County Jiashuo Building Materials Processing Co., Ltd., Shijiazhuang, China), as shown in Figure 2, were employed as reinforcement and their properties are listed in

Table 5. Properties of fibers.

Fiber	Length (mm)	Diameter (mm)	Aspect Ratio	Density (g/cm3)	Tensile Strength (MPa)	Elastic Modulus (GPa)	Volume Fraction (%)
SF (hooked-end) 1	35	0.55	65	7.85	1345	210	0–0.75
PPF	12	0.031	387	0.91	>450	8	0–0.15

¹ Hooked-end SF was supplied by Bekaert (Shanghai) as the Dramix 3D 65/35BG series; the nominal aspect ratio of 65 follows the manufacturer’s product specification.

. A polycarboxylate-based superplasticizer (SP; Jiangsu Sobute New Materials Co., Ltd., Nanjing, China) with a water-reduction rate of 21% and a solid content of 17.3% was used to adjust the workability of the fresh mixtures.

2.2. Mixture Proportions

The mix design followed the standard SCC procedure with a target strength grade of C50. A constant water-to-binder ratio (w/b) of 0.32 was adopted, with the total binder content and water content fixed at 596 kg/m³ and 191 kg/m³, respectively. The reference SCC without fibers used a CA volumetric proportion of 0.31, obtained by blending the three CA fractions at a mass ratio of 5:2.5:2.5. Prior to mixing, MS was dry-sieved to remove particles below 75 μm, and GP was introduced separately as a controlled fine-powder component. The GP replacement ratio and EA dosage are expressed as percentages of the total binder mass, whereas V_SF and V_PP denote the volume fractions of SF and PPF in the concrete. The SP dosage was fixed at 1.3% of the total binder mass based on preliminary trial mixes.

To ensure that the introduction of fibers did not alter the mortar film thickness (t_cm) of the reference SCC, the constant-t_cm approach of Khayat et al. [32] was adopted with t_cm = 0.442 mm. The CA and MS volumes were adjusted accordingly whenever SF or PPF was incorporated. At the highest fiber volume fractions (V_SF = 0.75%, V_PP = 0.15%), the CA content was reduced from 843.2 kg/m³ (M12) to 780.6 kg/m³ (M16), with the MS volume increased accordingly.

The 16 mixtures were organized into two series. Series I (M1–M11) covered GP replacement ratios of 0, 9, 12, 15, and 18% and EA dosages of 0, 4, and 8% by total binder mass at fixed fiber volume fractions (V_SF = 0.50% and V_PP = 0.10%); the GP–EA matrix was simplified by testing the EA = 0% condition only for the GP-free mixture. Series II (M12–M16) fixed the binder composition at GP = 12% and EA = 8% and varied V_SF over 0–0.75% and V_PP over 0–0.15%. M9 from Series I served as the baseline mixture for comparison with Series II. Detailed proportions are listed in

Table 6. Mix proportions of the 16 mixtures (kg/m³).

Mix ID	Mix Code	Cement	FA	GP	EA	Water	MS	CA	SP
M1	GP00EA00S50P10	476.8	119	0	0	191	776.0	801.0	7.7
M2	GP00EA04S50P10	453.0	119	0	24	191	776.0	801.0	7.7
M3	GP09EA04S50P10	399.3	119	53.6	24	191	776.0	801.0	7.7
M4	GP12EA04S50P10	381.4	119	71.5	24	191	776.0	801.0	7.7
M5	GP15EA04S50P10	363.6	119	89.4	24	191	776.0	801.0	7.7
M6	GP18EA04S50P10	345.7	119	107.3	24	191	776.0	801.0	7.7
M7	GP00EA08S50P10	429.1	119	0	48	191	776.0	801.0	7.7
M8	GP09EA08S50P10	375.5	119	53.6	48	191	776.0	801.0	7.7
M9	GP12EA08S50P10	357.6	119	71.5	48	191	776.0	801.0	7.7
M10	GP15EA08S50P10	339.7	119	89.4	48	191	776.0	801.0	7.7
M11	GP18EA08S50P10	321.8	119	107.3	48	191	776.0	801.0	7.7
M12	GP12EA08S00P00	357.6	119	71.5	48	191	747.7	843.2	7.7
M13	GP12EA08S25P05	357.6	119	71.5	48	191	762.5	821.4	7.7
M14	GP12EA08S25P15	357.6	119	71.5	48	191	762.5	821.4	7.7
M15	GP12EA08S75P05	357.6	119	71.5	48	191	789.5	780.6	7.7
M16	GP12EA08S75P15	357.6	119	71.5	48	191	789.5	780.6	7.7

, and the compositional variables and fiber reinforcement index RI_v of each mixture are given in

Table 7. Compositional variables and fiber reinforcement indices of mixtures.

Mix ID	GP (%)	EA (%)	VSF (vol.%)	VPP (vol.%)	SF Dosage (kg/m3) 1	PPF Dosage (kg/m3) 1	RIv 2
M1	0	0	0.50	0.10	39.25	0.91	71.2
M2	0	4	0.50	0.10	39.25	0.91	71.2
M3	9	4	0.50	0.10	39.25	0.91	71.2
M4	12	4	0.50	0.10	39.25	0.91	71.2
M5	15	4	0.50	0.10	39.25	0.91	71.2
M6	18	4	0.50	0.10	39.25	0.91	71.2
M7	0	8	0.50	0.10	39.25	0.91	71.2
M8	9	8	0.50	0.10	39.25	0.91	71.2
M9	12	8	0.50	0.10	39.25	0.91	71.2
M10	15	8	0.50	0.10	39.25	0.91	71.2
M11	18	8	0.50	0.10	39.25	0.91	71.2
M12	12	8	0	0	0	0	0
M13	12	8	0.25	0.05	19.63	0.46	35.6
M14	12	8	0.25	0.15	19.63	1.37	74.3
M15	12	8	0.75	0.05	58.88	0.46	68.1
M16	12	8	0.75	0.15	58.88	1.37	106.8

¹ The mass concentrations of SF and PPF (kg/m³) are obtained by multiplying the volume fractions V_SF and V_PP (vol.%) by the fiber densities of 7.85 g/cm³ (SF) and 0.91 g/cm³ (PPF) given in Table 5, providing the actual fiber mass concentrations used in batching. ² The fiber reinforcement index RI_v is calculated from Equation (1) using V_SF and V_PP in vol.% and aspect ratios of 65 (SF) and 387 (PPF).

. The fiber reinforcement index is defined as

RI_v = V_SF · (l/d)_SF + V_PP · (l/d)_PP

(1)

where the aspect ratios (l/d)_SF = 65 and (l/d)_PP = 387 are taken from Table 5.

2.3. Specimen Preparation and Curing

The mixing protocol followed the fiber dispersion procedures reported by Khayat et al. [32] and Abdelrazik and Khayat [33]. All mixtures were prepared using a 60 L drum mixer. MS was first dry-mixed for 1 min. Subsequently, CA and fibers were incorporated and mixed for another 1 min until no visible fiber agglomeration occurred. Half of the mixing water and SP were then added, followed by 1.5 min of mixing. Thereafter, cement, FA, GP, and EA were introduced and mixed for 30 s. A 2 min mixing pause was applied to facilitate full powder wetting. The remaining water and SP were finally added, and the mixture was continuously mixed for 2 min to achieve a visually homogeneous state. For the fiber-free reference mixture, the fiber-addition step was omitted.

The fresh mixtures were cast into 100 mm × 100 mm × 300 mm prismatic steel molds in a single layer without external vibration or compaction. The specimen geometry follows the prismatic provisions of GB/T 50081-2019 [34]. The molded specimens were leveled, covered with a polyethylene sheet, and stored at 20 ± 2 °C for 24 h before demolding. Three replicate specimens were prepared for each mixture, giving 48 specimens in total. After demolding, the specimens were cured for 28 days in a standard curing room maintained at 20 ± 2 °C and a relative humidity of not less than 95% in accordance with GB/T 50081-2019 [34].

2.4. Fresh-State Properties

The fresh-state properties of the 16 mixtures were measured immediately after mixing. As listed in

Table 8. Fresh-state properties of mixtures.

Mix ID	Slump-Flow (mm)	T500 (s)	V-Funnel Time (s)
M1	710	4.4	9.1
M2	705	4.9	11.3
M3	715	4.3	10.0
M4	720	4.2	9.1
M5	715	4.4	9.9
M6	690	4.6	11.0
M7	685	6.1	13.0
M8	710	4.3	8.5
M9	715	4.1	7.9
M10	690	5.5	8.9
M11	680	7.1	10.5
M12	750	2.1	3.6
M13	735	2.9	5.4
M14	685	3.8	8.1
M15	690	3.1	6.9
M16	630	7.2	11.9

, the slump-flow diameter, the T₅₀₀ flow time, and the V-funnel discharge time were determined according to JGJ/T 283-2012 [35]. All mixtures satisfied the measured slump-flow and flow-time criteria specified in JGJ/T 283-2012 [35]. For the highest fiber-volume-fraction combination (M16: V_SF = 0.75%, V_PP = 0.15%), the fiber-induced lattice effect reduced the slump-flow to 630 mm and increased the V-funnel time to 11.9 s. All mixtures were cast successfully without external vibration, and no visible segregation or fiber blocking was observed during casting.

2.5. Uniaxial Compression Test

After 28 d curing, the uniaxial compression tests were performed in accordance with GB/T 50081-2019 [34] and CECS 13-2009 [36]. The 100 mm × 100 mm × 300 mm prismatic specimens adopted in this study differ from the standard 150 mm × 150 mm × 300 mm prismatic specimens specified in GB/T 50081-2019 [34]. Because all 16 mixtures adopted the same specimen size, the results were used for internal comparisons and constitutive fitting without applying size-conversion coefficients. The test setup is presented in Figure 3a. A 5000 kN electro-hydraulic servo testing machine (Jinan Docer Testing Machine Technology Co., Ltd., Jinan, China) equipped with a stiffness-compensating spring assembly (four high-stiffness springs between the upper and lower platens) was used to capture the descending branch of FR-SCC by compensating for the elastic strain energy stored in the loading frame.

The loading procedure consisted of two stages. A pre-loading stage was conducted under force control at 0.5 MPa/s up to approximately 40% of the expected peak load and then unloaded to seat the specimen. The formal loading stage was applied under displacement control at a constant rate of 0.06 mm/min until either the post-peak stress decreased to approximately 0.20f_c, where f_c denotes the peak compressive stress of the specimen, or the test was terminated automatically by unstable specimen disintegration (applicable mainly to the fiber-free reference). The load was measured by the built-in load cell of the testing machine, and the axial deformation was measured by two linear variable differential transformers (LVDTs), as shown in Figure 3b. Load and displacement signals were synchronously sampled at 10 Hz. The compressive stress was calculated by dividing the recorded load by the nominal cross-sectional area of 100 × 100 mm², while the compressive strain was determined as the average axial deformation measured by two LVDTs divided by a 100 mm gauge length located at the mid-height of the specimen.

Three replicate specimens were tested for each mixture. The characteristic parameters reported in

Table 9. Characteristic results of uniaxial compression.

Mix ID	fc (MPa)	εp (×10−3)	Ec (GPa)	Esec (GPa)
M1	47.62 ± 2.09	2.39 ± 0.20	30.38 ± 1.41	19.92 ± 1.03
M2	42.07 ± 1.83	2.44 ± 0.20	28.82 ± 1.45	17.24 ± 0.63
M3	41.01 ± 1.59	2.31 ± 0.16	28.59 ± 1.47	17.75 ± 1.09
M4	39.52 ± 2.01	2.23 ± 0.19	27.63 ± 1.23	17.72 ± 0.57
M5	35.90 ± 1.80	2.26 ± 0.22	26.22 ± 1.44	15.88 ± 0.75
M6	34.52 ± 1.55	2.14 ± 0.22	26.05 ± 1.07	16.13 ± 0.91
M7	36.25 ± 2.02	2.26 ± 0.22	26.37 ± 1.53	16.04 ± 0.68
M8	38.54 ± 1.92	2.28 ± 0.22	27.25 ± 1.53	16.90 ± 0.76
M9	39.52 ± 2.16	2.58 ± 0.25	27.87 ± 1.21	15.32 ± 0.67
M10	36.68 ± 2.51	2.21 ± 0.22	27.20 ± 1.10	16.60 ± 0.48
M11	33.72 ± 2.35	2.17 ± 0.24	25.82 ± 1.06	15.54 ± 0.60
M12	36.02 ± 1.73	1.84 ± 0.14	26.86 ± 1.07	19.58 ± 0.55
M13	38.27 ± 1.80	1.96 ± 0.15	27.82 ± 1.11	19.53 ± 0.53
M14	39.76 ± 1.79	2.32 ± 0.20	27.65 ± 1.17	17.14 ± 0.71
M15	35.97 ± 2.33	3.16 ± 0.43	25.05 ± 1.62	11.38 ± 0.80
M16	37.33 ± 2.21	3.25 ± 0.43	25.43 ± 1.63	11.49 ± 0.83

Note: f_c = peak compressive stress; ε_p = strain at peak stress; E_c = elastic modulus, taken as the secant modulus at 40% of peak stress (0.40f_c divided by the corresponding strain); E_sec = secant modulus at peak stress, defined as E_sec = f_c/ε_p. All values are reported as the mean ± standard deviation of three replicate specimens.

are the arithmetic means of three replicate specimens, including peak stress f_c, peak strain ε_p, elastic modulus E_c, and peak secant modulus E_sec. The full stress–strain curve plotted for each mixture was taken from the replicate with the median peak stress.

2.6. Acoustic Emission Monitoring

Acoustic emission (AE) monitoring was performed in parallel with the uniaxial compression tests. AE activity is closely associated with the progressive cracking and fiber–matrix interfacial evolution throughout the loading process. The acquisition system is an Express-8 multichannel AE system (MISTRAS Group, Princeton Junction, NJ, USA), and the AE setup follows the general recommendations of RILEM TC 212-ACD [37]. Four piezoelectric AE sensors were mounted on two opposite lateral faces of each prismatic specimen, with two sensors arranged diagonally on each face: one near the upper corner and one near the opposite lower corner (Figure 3a). All sensors were placed 30–50 mm from the upper and lower loading faces and were vertically offset from the LVDT clamping fixtures.

The sensors were R3α-type piezoelectric AE sensors (MISTRAS Group, Princeton Junction, NJ, USA) with a nominal center frequency of 30 kHz. At each sensor location, a spring-loaded magnetic holder bonded to the specimen surface pressed the sensor against the concrete, and a thin layer of petroleum jelly was used as the acoustic couplant. Each channel was connected to a pre-amplifier with a fixed gain of 40 dB. The detection threshold was determined from the background noise: with the testing machine powered but unloaded, the background and electrical-instrumentation noise on all four channels remained below 40 dB, so the threshold was set to 40 dB to exclude mechanical-system and electronic noise while retaining genuine cracking signals; this value lies within the 30–50 dB range recommended by RILEM TC 212-ACD [37]. Sensor coupling and channel sensitivity were verified before each test using the Hsu–Nielsen source (pencil-lead break), and a test proceeded only when the four channels gave comparable responses, otherwise the couplant and holder were reseated. The cumulative AE ring-down count N(t), defined as the cumulative number of threshold crossings, was exported throughout each test and subsequently used to derive the AE damage variable.

3. Results

3.1. Failure Modes and Stress–Strain Response

The 16 mixtures exhibited distinct compressive failure modes (Figure 4 and Figure 5, Table 9).

The fiber-free reference M12 failed by brittle vertical splitting, with a single dominant longitudinal crack parallel to the loading direction propagating through the matrix–aggregate skeleton (Figure 4a). Its stress–strain curve (Figure 5d) shows a nearly linear ascending branch followed by a sharp post-peak drop, and only a short descending segment was captured. M12 also has the lowest peak strain among the 16 mixtures (1.84 × 10⁻³, Table 9).

At the same V_SF and V_PP levels, M1 (without GP and EA) and M9 (12% GP and 8% EA) developed multiple inclined surface cracks with slight corner spalling and no structural disintegration (Figure 4b,c). M1 reached a higher peak stress, whereas M9 showed a higher peak strain, a lower secant modulus, and a milder post-peak descent (Table 9). Because the two mixtures had the same V_SF and V_PP levels, these differences are consistent with the influence of GP–EA binder modification on strain capacity and post-peak softening.

The highest-fiber mixture M16 formed a dense network of fine vertical, inclined, and secondary cracks and retained its integrity after loading (Figure 4d). Its stress–strain curve shows the highest peak strain and a gentler descending branch than M12, M1, and M9, with a wider post-peak strain range. This response is consistent with multiscale crack bridging: PPF can restrain microcrack propagation, whereas SF can bridge macrocracks [17,18,38]. The detailed mechanism is discussed in Section 4.2.

Figure 5 groups the 16 stress–strain curves by mixture variable. Without GP, increasing the EA dosage from 0% (M1) to 8% (M7) monotonically reduced the peak stress, with little change in the peak strain (Figure 5a). At an EA dosage of 4%, increasing GP from 0% (M2) to 18% (M6) also reduced the peak stress monotonically (Figure 5b). At an EA dosage of 8%, the peak stress no longer decreased monotonically and reached a maximum at a 12% GP replacement ratio (M9) (Figure 5c, Table 9). With this composition, all fiber-reinforced mixtures (M9 and M13–M16) showed longer descending branches and higher peak strains than the fiber-free reference M12 (Figure 5d). The post-peak softening varied mainly with V_SF, with the descending branch becoming gentler as V_SF increased from 0.25% to 0.75%, whereas increasing V_PP from 0.05% to 0.15% produced a smaller change in the descending branch. Compared with the changes in peak strain and post-peak softening, the elastic-stage stiffness varied less.

3.2. Effects of Mixture Variables on Compressive Characteristic Parameters

Without GP incorporation, increasing EA from 0% to 8% reduced f_c by 23.9% (from 47.62 MPa for M1 to 36.25 MPa for M7) and decreased E_c from 30.38 to 26.37 GPa, while ε_p remained within 2.26–2.44 × 10⁻³. The decrease in E_sec from 19.92 to 16.04 GPa within this EA range was mainly induced by the reduced f_c; and the variations in post-peak performance were directly reflected by the curve profiles in Figure 5a.

At a constant EA dosage of 4%, increasing the GP replacement ratio from 0% (M2) to 18% (M6) monotonically reduced f_c by 17.9% (from 42.07 MPa to 34.52 MPa) and decreased E_c from 28.82 to 26.05 GPa, whereas ε_p remained within 2.14–2.44 × 10⁻³. In contrast, at a fixed 8% EA dosage, f_c no longer declined monotonically and reached its maximum at 12% GP (M9: 39.52 MPa). Similarly, ε_p peaked at the same GP replacement ratio (M9: 2.58 × 10⁻³), which was higher than the values of 2.17–2.28 × 10⁻³ obtained at the other four GP replacement ratios. These results indicate that the GP–EA combination in M9 gave the most favorable binder composition for the uniaxial compression tests in this study. The intrinsic interaction mechanism between GP and EA in modifying matrix performance is discussed in Section 4.

With the favorable binder composition (12% GP and 8% EA), the hybrid SF/PPF system exerted a more prominent effect on peak strain and post-peak softening than on peak stress. Compared with the fiber-free M12, the M16 mixture with the highest fiber volume fractions increased ε_p by 76.6% (from 1.84 × 10⁻³ to 3.25 × 10⁻³) and reduced E_sec by 41.3% (from 19.58 GPa to 11.49 GPa), while f_c slightly fluctuated within 35.97–39.76 MPa. Within the tested range, increasing V_SF produced a greater increase in ε_p than increasing V_PP. At a fixed V_PP, increasing V_SF from 0.25% to 0.75% increased ε_p by 61.2% (M13 to M15) and 40.1% (M14 to M16). In contrast, increasing V_PP from 0.05% to 0.15% at a fixed V_SF only increased ε_p by 18.4% (M13 to M14) and 2.8% (M15 to M16).

Across the five Series II mixtures, the ε_p and E_sec were expressed as linear functions of RI_v, as given in Equations (2) and (3).

ε_p = 1.72 + 0.0137RI_v  (R² = 0.71)

(2)

E_sec = 20.44 − 0.0811RI_v (R² = 0.64)

(3)

The moderate R² values indicate that one aspect-ratio-weighted descriptor does not separate the differing effect magnitudes of V_SF and V_PP; this limitation is revisited in Section 3.5.2.

Across the 16 mixtures, E_c ranged from 25.05 to 30.38 GPa (average 27.2 GPa). The mixture variables had a smaller effect on the elastic-regime stiffness than on the peak and post-peak parameters. The quantitative ductility and energy-dissipation indices are analyzed in Section 3.3.

3.3. Post-Peak Ductility and Energy Dissipation

The post-peak energy and ductility of the 16 mixtures were quantified using the parameters summarized in

Table 10. Post-peak energy dissipation and ductility parameters of the 16 mixtures.

Mix ID	RIv	Wpre (MPa)	Wpost (MPa)	Wtotal (MPa)	μ85	ε0.20 (×10−3)	ε0.20/εp	TI
M1	71.2	0.077	0.182	0.259	1.28	8.27	3.46	3.35
M2	71.2	0.072	0.158	0.229	1.25	8.37	3.43	3.20
M3	71.2	0.069	0.146	0.214	1.23	7.95	3.44	3.12
M4	71.2	0.059	0.142	0.200	1.31	7.79	3.50	3.42
M5	71.2	0.057	0.119	0.175	1.25	6.76	2.99	3.09
M6	71.2	0.046	0.103	0.149	1.29	6.07	2.84	3.21
M7	71.2	0.057	0.122	0.180	1.26	7.41	3.28	3.14
M8	71.2	0.055	0.141	0.196	1.36	7.93	3.48	3.56
M9	71.2	0.067	0.172	0.238	1.38	10.31	3.99	3.58
M10	71.2	0.050	0.119	0.169	1.32	6.55	2.96	3.36
M11	71.2	0.049	0.101	0.150	1.30	5.96	2.75	3.07
M12	0	0.038	0.029	0.067 1	1.14	2.93	1.59	1.75 1
M13	35.6	0.045	0.072	0.117 1	1.24	4.82	2.46	2.60 1
M14	74.3	0.058	0.098	0.156 1	1.27	6.21	2.68	2.70 1
M15	68.1	0.079	0.204	0.283	1.39	12.75	4.03	3.58
M16	106.8	0.090	0.222	0.312	1.48	14.40	4.43	3.48

¹ Recorded strain terminated below ε_u = 0.015; W_total and TI for these mixtures were integrated only up to the measured terminal strain, without extrapolation.

.

The energy and ductility parameters are defined as follows. The pre-peak and post-peak energy densities W_pre and W_post are the areas under the stress–strain curve from the origin to ε_p and from ε_p to a fixed ultimate strain ε_u, with W_total = W_pre + W_post. The post-peak ductility ratio μ₈₅ is defined by Equation (5), where ε_0.85 is the strain at which the stress descends to 0.85f_c on the post-peak branch. Following Cui et al. [24], the residual strain ε_0.20 is the strain at which the stress descends to 0.20f_c. Following the energy-ratio toughness-index approach for fiber-reinforced concrete [39], the toughness index TI is defined as the ratio of total to pre-peak energy density. The numerical integration was performed using the trapezoidal rule on the raw stress–strain data with a (0, 0) origin, taking ε_u = 0.015 for curves that reached this strain; for curves terminating earlier, the integration was carried out up to the measured terminal strain without extrapolation.

$$W_{\mathrm{p}\mathrm{r}\mathrm{e}}={\int }_0^{{\epsilon }_{\mathrm{p}}}\sigma \hspace{0.17em}\mathrm{d}\epsilon ,\hspace{1em}{W}_{\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{t}}={\int }_{{\epsilon }_{\mathrm{p}}}^{{\epsilon }_{\mathrm{u}}}\sigma \hspace{0.17em}\mathrm{d}\epsilon$$

(4)

μ₈₅ = (ε_0.85)/(ε_p)

(5)

σ(ε_0.20) = 0.20f_c

(6)

TI = (W_total)/(W_pre)

(7)

From the fiber-free reference M12 to the highest-fiber mixture M16 with the same binder composition, W_post rose from 0.029 to 0.222 MPa, by a factor of 7.66; ε_0.20 increased from 2.93 × 10⁻³ to 14.40 × 10⁻³, by a factor of 4.92; and TI increased from 1.75 to 3.48. Meanwhile, W_pre increased by a factor of 2.37, ε_0.20/ε_p from 1.59 to 4.43, and μ₈₅ from 1.14 to 1.48 (Table 10). The larger increase in W_post than in W_pre indicates that hybrid SF/PPFs mainly improved the post-peak response rather than the pre-peak regime.

Within the M12–M16 series with the favorable binder composition, the absolute energy and strain measures (W_post, W_total, ε_0.20, and μ₈₅) reached their maxima at M16, whereas TI peaked at M15 (3.58) and decreased slightly at M16 (3.48). This decrease occurs because the larger ε_p of M16 raised W_pre and thus lowered the post-peak weighting in TI, although its absolute W_post was the largest. TI therefore reflects the relative post-peak contribution rather than its absolute value.

Within Series I, the 11 mixtures M1–M11 had the same fiber volume fractions (V_SF = 0.50% and V_PP = 0.10%; RI_v = 71.2) but differed in GP replacement ratio and EA dosage. The coefficients of variation of μ₈₅ and TI across these mixtures were only 3.5% and 5.3%, respectively, indicating limited variation in the pre-/post-peak energy partitioning under fixed fiber volume fractions. In contrast, the absolute energy parameters W_pre, W_post, and W_total showed coefficients of variation of 16–19% and correlated with f_c (r = 0.932 between f_c and W_total). The influence of binder composition was therefore mainly reflected in the magnitude of energy absorption through its association with f_c, whereas the pre-/post-peak partitioning varied less under the fixed hybrid-fiber system.

The dependence of TI and ε_0.20/ε_p on RI_v is presented in Figure 6. Linear regressions on the 16 mixtures give Equations (8) and (9), with RI_v entered as percentage values via Equation (1).

TI = 1.974 + 0.017RI_v   (R² = 0.677)

(8)

ε_0.20/ε_p = 1.554 + 0.025RI_v (R² = 0.637)

(9)

The positive slopes indicate that higher RI_v was associated with higher TI and higher ε_0.20/ε_p. The moderate R² values reflect the clustered RI_v design and the fact that RI_v does not distinguish the mechanical roles of SF and PPF; for example, M14 has a relatively high RI_v (74.3) owing to the high PPF aspect ratio, yet its ε_0.20/ε_p (2.68) is lower than those of M15 and M16. Therefore, RI_v should be treated only as a first-order descriptor.

These macroscopic ductility and energy indices provide the basis for the subsequent AE damage analysis.

3.4. Acoustic Emission Characteristics and Damage Evolution

The AE signals recorded during loading were used to characterize the evolution of internal cracking. AE monitoring has been widely used to track damage development in fiber-reinforced concrete under axial loading [40,41]. The AE response is first divided into loading stages and then used to define an AE-based damage variable, which is fitted with a two-parameter Weibull distribution.

3.4.1. Stage-Wise Division of the Acoustic Emission Response

In Figure 7, the dashed lines mark the times at which the axial stress first reaches 0.30f_c and 0.80f_c, used here as operational thresholds rather than universal damage limits. They define three stages: Stage I (0–0.30f_c), a low-activity stage associated with seating, defect closure, and possible early microcracking; Stage II (0.30–0.80f_c), stable microcrack propagation; and Stage III (0.80f_c through the descending branch), accelerated crack coalescence, peak formation, and post-peak softening. This division follows the AE framework of RILEM TC 212-ACD [37] and earlier AE studies of concrete under compression [42].

Stage I accounted for about 1% or less of ΣC_AE in all four specimens, indicating that low-stress microcracking contributed little to the total recorded activity. Stage II contributed 3.0–15.1%, and Stage III accounted for 83.9–96.5% (Figure 7). The Stage III dominance suggests that the recorded AE activity was concentrated near the peak and during post-peak softening rather than at low stress.

The peak per-second ring count C_AE increased from 110 for the fiber-free M12 to 1059 for M16, about ten times higher. The total ring count N_u for M12 (4072) was far below those of the fiber-reinforced mixtures (63,000–181,000), consistent with its shorter post-peak history and brittle, localized failure. Therefore, the absolute AE count of M12 should be interpreted separately from those of the fiber-reinforced mixtures, for the reasons discussed in Section 3.4.2.

3.4.2. AE Damage Variable and Weibull Evolution

An empirical AE-based damage variable is defined as the normalized cumulative ring count:

D_AE(ε) = (N(ε))/N_u

(10)

where N(ε) is the cumulative ring count at axial strain ε and N_u is the cumulative ring count at the end of loading. The ring-count record (1 s sampling) and the stress–strain record were mapped onto a common strain axis by linear interpolation, with the ascending and descending branches treated separately.

Following the statistical damage treatment used for concrete under compression [24], the AE damage evolution was fitted with a two-parameter Weibull cumulative distribution:

$$D_{\mathrm{A}\mathrm{E}}\left(\epsilon \right)=1-\exp \left[-{\left({\displaystyle \frac{\epsilon }{{\lambda }_{\mathrm{A}\mathrm{E}}}}\right)}^{m_{\mathrm{A}\mathrm{E}}}\right]$$

(11)

where m_AE is the shape parameter, controlling the concentration of damage accumulation in strain, and λ_AE is the scale parameter, the characteristic strain at which the fitted D_AE reaches 1 − e⁻¹ ≈ 0.632 rather than a failure strain. Equation (11) was fitted to the 16 normalized AE–strain curves by non-linear least squares; the fitted m_AE, λ_AE, and R²_AE are listed in

Table 11. Fitted parameters of the AE damage evolution model for the 16 mixtures.

Mix ID	mAE	λAE (×10−3)	R2AE
M1	1.509	5.978	0.973
M2	1.426	6.013	0.966
M3	1.396	5.737	0.958
M4	1.452	5.781	0.959
M5	1.349	5.380	0.961
M6	1.348	4.856	0.967
M7	1.400	5.574	0.961
M8	1.375	5.664	0.961
M9	1.135	7.187	0.983
M10	1.359	4.921	0.977
M11	1.252	5.152	0.949
M12	5.628	1.748	0.979
M13	1.193	3.472	0.971
M14	1.464	4.148	0.984
M15	1.152	10.199	0.982
M16	1.164	11.531	0.972

, and Figure 8 shows the measured and fitted D_AE–ε curves for the four representative specimens.

All 16 fits gave R²_AE above 0.94 (mean 0.969). For the 15 fiber-reinforced mixtures, m_AE fell within a narrow range of 1.135–1.509, indicating that the AE damage accumulated progressively over a broad strain range, consistent with their distributed cracking. The fiber-free M12 had m_AE = 5.628, about 3.7 times the largest fiber-reinforced value, consistent with its more concentrated damage accumulation and brittle failure.

The scale parameter λ_AE ranged from 1.748 × 10⁻³ (M12) to 11.531 × 10⁻³ (M16), spanning nearly a factor of seven, and varied consistently with the post-peak deformation capacity of the mixtures. M12 gave the lowest value, whereas the high-V_SF mixtures M15 and M16 gave the two highest values. Within Series I, M9 gave the highest λ_AE (7.187 × 10⁻³), consistent with its higher ε_p and flatter post-peak slope noted above. This suggests a contribution of the favorable GP–EA binder composition to deformation capacity at the same V_SF and V_PP levels.

Across the 16 mixtures, λ_AE was linearly associated with the macroscopic residual strain ε_0.20 (r = 0.987). The corresponding correlation restricted to the 15 FR-SCC mixtures is examined in the cross-method consistency check in Section 3.5.3. This association indicates that D_AE(ε) can serve as an empirical AE-based counterpart to the macroscopic post-peak descriptors used in the constitutive analysis. For each mixture, three replicate specimens were tested, and the AE results reported here (Figure 7 and Figure 8, Table 11) were taken from the same representative specimen (the median-peak-stress replicate) defined in Section 2.5. Because the absolute AE counts depend on the recorded post-peak duration, the degree of crack localization, and signal attenuation along the propagation path, the cumulative and per-second ring counts are expected to show larger specimen-to-specimen scatter than the normalized damage variable. Expressing the AE response through the normalized damage variable D_AE reduces the sensitivity to the absolute count level and yields the more reproducible shape descriptors m_AE and λ_AE, which is why the subsequent analysis is based on D_AE rather than on absolute counts. Given the limited number of replicates (three per mixture), the AE parameters and the AE-based correlations in Section 3.5.3 are regarded as consistency trends within the present dataset rather than as population estimates.

3.5. Constitutive Modeling

The post-peak stress–strain response analyzed above is next described using parametric constitutive models, and the AE-based descriptor is then used for a cross-method consistency check with the constitutive and macroscopic post-peak parameters. This section proceeds in three steps: parameter calibration on the 16 representative curves, regression of the model parameters against fiber volume fractions and post-peak ductility, and a cross-method consistency check among the constitutive, AE-based, and macroscopic post-peak descriptors.

3.5.1. Comparison of Three Constitutive Models

Three constitutive forms with different theoretical bases were fitted to the 16 normalized stress–strain curves: the single-shape-parameter Carreira–Chu rational model [21], the piecewise GB 50010 model [22], and a modified Weibull damage model with residual correction [24]. Comparable frameworks for hybrid-fiber UHPC [43] and hybrid-fiber cementitious composites [44] provide related constitutive-modeling references. Each model was fitted independently for every mixture by non-linear least squares on ξ = ε/ε_p and η = σ/f_c, using the three-replicate mean f_c and ε_p from Table 9 for normalization.

The Carreira–Chu form is

η = (β·ξ)/(β − 1 + ξ^β)

(12)

where β is the shape parameter controlling both the ascending and descending branches. The GB 50010 form is piecewise:

$$\eta =\left\{\begin{array}{c}{a}_{\mathrm{a}} \xi +(3-2a_{\mathrm{a}}) {\xi }^2+(a_{\mathrm{a}}-2) {\xi }^3, \xi \le 1\\ \xi /(a_{\mathrm{d}} {(\xi -1)}^2+\xi ), \xi >1\end{array}\right.$$

(13)

with two parameters a_a and a_d controlling the ascending and descending branches separately. The modified Weibull form, in its normalized version, is

$$\eta =c \xi \left\{a\exp \left[-{\left({\displaystyle \frac{\xi }{v_{\mathrm{w}}}}\right)}^{m_{\mathsf{\sigma }}}\right]+\left(1-a\right)\right\}$$

(14)

where a is the damage correction coefficient, m_σ is the Weibull shape parameter, and v_w = u₀/ε_p is the normalized Weibull characteristic strain. The normalizing constant c enforces η(1) = 1.

The fitted parameters and coefficients of determination are listed in

Table 12. Fitted parameters and coefficients of determination for the three constitutive models on the 16 mixtures.

Mix ID	β	R2CC	aa	ad	R2GB	a	mσ	vw	R2MW
M1 1	3.322	0.987	1.659	2.048	0.998	0.968	1.832	1.317	0.983
M2	3.345	0.976	1.780	2.114	0.993	0.968	1.801	1.280	0.981
M3	3.395	0.977	1.838	2.200	0.999	0.969	1.822	1.277	0.985
M4	3.356	0.985	1.676	2.107	0.997	0.968	1.854	1.315	0.984
M5	3.567	0.971	1.907	2.506	0.998	0.971	1.866	1.265	0.985
M6	3.785	0.973	1.827	2.888	0.996	0.974	1.961	1.283	0.983
M7	3.512	0.973	1.895	2.406	0.999	0.970	1.847	1.267	0.985
M8	3.409	0.977	1.801	2.220	0.997	0.969	1.837	1.283	0.984
M9	3.027	0.977	1.870	1.801	0.993	0.988	1.362	1.158	0.966
M10	3.694	0.978	1.740	2.696	0.993	0.973	1.944	1.301	0.984
M11	3.876	0.971	1.917	3.064	0.997	0.975	1.970	1.273	0.987
M12 2	9.958	0.938	1.341	18.078	1.000	0.963	5.495	1.231	0.982
M13	4.111	0.985	1.079	3.416	0.994	0.975	2.492	1.428	0.972
M14	4.090	0.964	1.716	3.500	0.996	0.974	2.161	1.291	0.978
M15	2.650	0.979	2.137	1.224	0.985	0.988	1.148	1.061	0.969
M16	2.527	0.965	2.656	1.085	0.990	0.988	1.017	0.894	0.978
Mean	— 3	0.976	—	—	0.995	—	—	—	0.980

¹ M1: recorded post-peak range terminates at ε = 9.55 × 10⁻³, shorter than that of the other 14 FR-SCC mixtures; the modified Weibull residual coefficient a for M1 reflects this limited post-peak coverage. ² M12: fiber-free reference; fitted parameters fall outside the FR-SCC range and are excluded from the regression below. ³ —: not calculated.

. On the 15 FR-SCC mixtures, all three forms gave high fitting precision, with mean R² of 0.976, 0.995, and 0.980 for the Carreira–Chu, GB 50010, and modified Weibull forms, respectively. The fiber-free reference M12 was fitted with R² of 0.938, 1.000, and 0.982, but its β = 9.96 and a_d = 18.08 fall well outside the FR-SCC parameter window (β = 2.5–4.1, a_d = 1.09–3.50), reflecting its brittle response (Table 12, footnote ¹). The post-peak range of M1 terminated earlier at ε = 9.55 × 10⁻³ (footnote ²), which affects its modified Weibull residual coefficient.

GB 50010 was adopted as the primary FR-SCC constitutive model for three reasons: its mean R² = 0.995 (minimum 0.985 among the 15 FR-SCC mixtures) was the highest of the three forms; its piecewise parameters a_a and a_d describe the ascending and descending branches separately, making them suitable regression targets in the next subsection; and it is widely used in Chinese engineering practice. The Carreira–Chu and modified Weibull fits are retained as reference benchmarks in Table 12. The measured stress–strain curves and the three constitutive fits for four representative FR-SCC specimens are compared in Figure 9. The modified Weibull form was not adopted as the primary model: beyond its lower mean R², the residual-stiffness term cξ(1 − a) in Equation (14) becomes dominant at strains far beyond the measured range, which restricts extrapolation but did not govern the fitted response within the measured strain range.

3.5.2. Fiber-Volume-Fraction-Based and Ductility-Calibrated Regression of GB 50010 Parameters

The two GB 50010 shape parameters a_a and a_d were used as regression targets to examine the apparent contributions of V_SF and V_PP within the present mixture design, fitted on the 15 FR-SCC mixtures (M12 excluded as the fiber-free reference). An auxiliary regression of a_d on ε_0.20/ε_p is also reported for use when post-peak test data are available.

A two-variable linear regression of a_a on V_SF and V_PP gives:

a_a = 0.256 + 1.998V_SF + 5.780V_PP

(15)

with V_SF and V_PP in vol.%, R² = 0.927 and adjusted R² = 0.915. On a per-vol.% basis, the fitted PPF coefficient is about 2.9 times the SF coefficient; however, over the tested ranges (V_SF 0.25–0.75 vol.%, V_PP 0.05–0.15 vol.%), the predicted contribution of SF to a_a is comparable to that of PPF because the SF range is wider. The PPF coefficient is therefore interpreted as a per-unit-volume sensitivity of a_a to fine fibers, qualitatively consistent with the smaller diameter and larger specific surface area of PPF, rather than as evidence that PPF governs a_a. Since the binder variables (GP and EA) are not included in Equation (15), this coefficient reflects an apparent sensitivity rather than a mechanistic SF–PPF separation. A single-variable regression of a_a on RI_v gives R² = 0.819, indicating that RI_v retains most of the variance but does not resolve the separate V_SF and V_PP contributions.

A two-variable linear regression of a_d on V_SF and V_PP gives:

a_d = 4.683 − 4.607V_SF − 0.275V_PP

(16)

with R² = 0.778 and adjusted R² = 0.741. The V_SF coefficient is the larger in magnitude and is negative, indicating that increasing V_SF flattens the descending branch, consistent with the post-peak crack-bridging contribution of hooked steel fibers. The V_PP coefficient is small, suggesting a limited apparent contribution of PPF to the descending-branch shape over the tested range. When the measured ductility ratio ε_0.20/ε_p is available, the alternative regression

a_d = 6.431 − 1.230(ε_0.20/ε_p)

(17)

reaches a higher R² = 0.943 (adjusted R² = 0.939), because ε_0.20/ε_p directly samples the measured descending branch that Equation (16) only approximates from composition. Equation (16) requires only the fiber volume fractions and is retained as the fiber-volume-fraction-based predictor, whereas Equation (17) is the ductility-calibrated form usable once post-peak test data are obtained.

The in-sample reconstruction accuracy of Equations (15)–(17) was evaluated at the curve level by substituting them into Equation (13) and comparing with each measured trace (Figure 10). Across the 15 FR-SCC mixtures, the fiber-volume-fraction-based form (Equations (15) and (16)) gave a mean curve-level R² of 0.955 (all specimens above 0.84), and the ductility-calibrated form (Equations (15) and (17)) gave a mean of 0.972 (all above 0.912). The minimum occurred at M15 for the fiber-volume-fraction-based form and at M13 for the ductility-calibrated form. The fiber-volume-fraction-based form is suitable for preliminary in-sample curve screening within the tested calibration window, whereas the ductility-calibrated form gives more reliable reconstructed curves.

Because Equations (15)–(17) were calibrated and assessed on the same 15 FR-SCC mixtures, leave-one-out cross-validation (LOOCV) was carried out to check their robustness against overfitting. In each fold the regression was refitted on 14 mixtures and used to predict the parameter of the single mixture left out, and the predictive coefficient of determination (Q²) and the root-mean-square error (RMSE) were computed from the held-out predictions. For the ascending-branch regression (Equation (15)) the in-sample R² of 0.927 decreased only to Q² = 0.859 (RMSE from 0.084 to 0.116); for the fiber-volume-fraction-based descending-branch regression (Equation (16)) R² = 0.778 decreased to Q² = 0.733 (RMSE from 0.318 to 0.349); and for the ductility-calibrated regression (Equation (17)) R² = 0.943 decreased to Q² = 0.919 (RMSE from 0.161 to 0.191). The small reductions, with the cross-validated error concentrated in the corner mixtures M13–M16 of the clustered fiber design, indicate that the regressions did not show severe overfitting and support interpolation within the calibrated composition window, the ductility-calibrated Equation (17) being the most robust. This LOOCV is an internal robustness check rather than independent external validation; validation on independent specimens, as noted in Section 4.4, remains future work.

The validity of Equations (15)–(17) is restricted to the experimental window of this study: V_SF 0.25–0.75 vol.%, V_PP 0.05–0.15 vol.%, ε_0.20/ε_p 2.46–4.43, and RI_v 35.6–106.8. Equation (16) is intended for in-sample composition screening before specimens are prepared and Equation (17) for refined prediction after benchmark mixtures are tested.

3.5.3. Cross-Method Consistency Among Constitutive, Acoustic Emission and Ductility Descriptors

The GB 50010 descending-branch parameter a_d, the AE characteristic strain λ_AE, and the macroscopic residual strain ε_0.20 describe related but non-identical aspects of the post-peak response. Two pairwise checks were performed on the same 15 FR-SCC mixtures, with M12 excluded as the fiber-free reference.

The first check pairs a_d with λ_AE. A larger a_d corresponds to a steeper descending branch, whereas a larger λ_AE indicates a larger characteristic strain scale for cumulative AE damage, so a negative correlation is expected. The linear regression gives

a_d = 4.164 − 0.297λ_AE

(18)

with λ_AE in 10⁻³, a negative Pearson correlation coefficient of −0.904 (n = 15, 95% CI [−0.968, −0.730], p < 0.001), and R² = 0.817. The negative sign is consistent with a steeper descending branch corresponding to a smaller AE characteristic strain scale, and the magnitude indicates a close cross-method relationship between the constitutive descending-branch shape and the AE characteristic strain scale. This relation is therefore interpreted as a cross-method consistency check.

The second check pairs λ_AE with the macroscopic residual strain ε_0.20. Both quantities locate damage development on the strain axis, so a positive relation is expected. The linear regression on the 15 FR-SCC mixtures gives

λ_AE = −0.425 + 0.806ε_0.20

(19)

with both λ_AE and ε_0.20 in 10⁻³, r = +0.983 (n = 15, 95% CI [+0.949, +0.995], p < 0.001) and R² = 0.967, indicating a close linear association between the AE and macroscopic strain scales. This represents a strain-scale consistency check that complements the shape-based check in Equation (18).

The two checks examine different facets of the same post-peak loading history. These checks are not independent validation, because the descriptors share the same loading history; their simultaneous agreement indicates that a_d tracks post-peak behavior that is also captured by the AE and ductility measures.

For completeness, the modified Weibull shape parameter m_σ (Table 12) correlates with m_AE (Table 11) at r = +0.471 (n = 15, p = 0.076) across the same 15 mixtures, and the characteristic strain u₀ = v_wε_p correlates with λ_AE at r = +0.497 (n = 15, p = 0.059). These weaker correlations are not statistically significant at the 0.05 level and are reported only as supplementary benchmarks, consistent with the choice of GB 50010 as the primary constitutive form. To the authors’ knowledge, this specific constitutive–AE consistency check has rarely been reported for FR-SCC incorporating GP, EA, and hybrid SF/PPF.

3.6. Microstructural Evidence for the Role of GP and EA

To clarify the respective roles of GP and EA, the hardened FR-SCC was characterized by X-ray diffraction (XRD; X’Pert3, PANalytical B.V., Almelo, The Netherlands; Cu Kα, 5–90° 2θ) on bulk powders and by scanning electron microscopy (SEM; MIRA, TESCAN, Brno, Czech Republic) on the fracture surfaces of the post-test prisms, using the GP0, GP12 and GP18 mixtures (M7, M9 and M11, all at 8% EA) as a representative series in which only the GP content varies. No energy-dispersive X-ray spectroscopy was performed, so all phase and fiber assignments below are inferred from morphology and the XRD peak positions and are not confirmed by elemental microanalysis. Figure 11 compares the XRD patterns; the main reflections were assigned from their characteristic 2θ positions to ettringite (AFt, ~9.1°), portlandite (CH, ~18.0°), quartz (~26.6°) and calcite (~29.4°). The portlandite peak did not decrease with increasing GP content and was strongest for the GP18 mixture; since a pozzolanic reaction would consume portlandite, this absence of any reduction indicates that, under the present materials, age and detection conditions, the GP behaved predominantly as a filler rather than as a pozzolanic addition, consistent with its limited reactivity (28-day activity index of 76.7%). Any residual pozzolanic contribution is therefore more likely dominated by the fly ash than by the GP. At a fixed GP content the ettringite peak increased with EA dosage (from 22.4 to 28.2 at GP0 and from 19.2 to 27.4 at GP12 in semi-quantitative peak-area units), consistent with additional ettringite formation associated with the EA and in line with the restrained-expansion mechanism discussed in Section 4.1. The quartz reflection originates mainly from the manufactured-sand and GP grains and is not used as a tracer of GP content, whereas the calcite peak is attributed to secondary carbonation during sample exposure and preparation rather than to primary hydration.

The filling action of GP is shown in Figure 12. In the GP0 mixture only the coarse manufactured-sand grains are present and the matrix appears comparatively loose and porous, whereas with 12% GP the inter-particle voids are densely occupied by fine angular powder grains and the matrix becomes markedly denser and more compact; at 18% GP the matrix is still filled but spherical entrapped-air voids and air-void imprints become more frequent, indicating that the filling benefit is subject to an optimum dosage. In all cases the GP grains show angular, brittle fracture surfaces (locally conchoidal) and clean particle–matrix boundaries; no reaction rim was resolved at the SEM scale examined, consistent with a predominantly physical filling and packing action that refines the pore structure and increases the packing density, while any low-level chemical contribution was below the resolution of the present SEM/XRD observations.

The fiber–matrix and aggregate–matrix interfaces are shown in Figure 13. The polypropylene fibers (nominal diameter 31 µm) are partly coated with hydration products but exhibit longitudinal fibrillation and debonding near the fiber root, and the steel fibers (nominal diameter ≈ 0.55 mm) present a smooth surface and a clean debonding gap with smooth pull-out channel walls; in neither case was a reaction layer observed at the fiber surface, and the spherical fly-ash particles and the GP and sand grains likewise debonded cleanly. The post-fracture morphology indicates that load transfer at these interfaces was dominated by mechanical interlock and friction, whereas chemical adhesion was not directly evidenced by the present SEM images; the interfacial behavior was also spatially variable, ranging from debonding gaps (indicating a weaker interface) to crack propagation through the matrix (indicating a locally stronger interface).

4. Discussion

4.1. Interaction Between Granite Powder and Expansive Agent in the FR-SCC Matrix

The non-monotonic f_c–GP trend at 8% EA can be attributed to two competing effects. At a moderate GP replacement ratio, fine GP can improve matrix packing, consistent with previous granite-powder filler studies [4]; this helps explain the higher f_c and ε_p of M9 relative to M7. Beyond 12% GP, dilution of the cement by a weakly reactive powder becomes dominant, consistent with the strength reduction reported by Sadek et al. [3] at high replacement levels. The measured 28-day activity index of 76.7% (Table 3) indicates limited reactivity. The 12% GP peak therefore reflects a balance between matrix densification and binder dilution.

The role of EA can be interpreted as shrinkage compensation and matrix modification under fiber restraint. EA alone reduced f_c approximately linearly with dosage, consistent with the cement-replacement effect of CaO-based expansive agents at a fixed binder mass. Combined with GP, the restrained volume expansion may impose a limited internal confinement, or self-stress, and improve fiber–matrix load transfer mainly through matrix densification rather than through any chemical modification of the fiber surface [12,13,45], consistent with the favorable response of M9. This interpretation is supported by the SEM observations in Section 3.6, where the fiber surfaces showed no resolvable reaction layer and the interfaces were dominated by mechanical interlock and friction. The 12% GP and 8% EA combination is therefore regarded as the favorable balance within the tested composition window, and extension to other cementitious systems requires composition-specific calibration.

4.2. Differentiated Roles of SF and PPF in Pre-Peak and Post-Peak Response

The regressions based on V_SF and V_PP identify SF as the larger contributor to the descending-branch parameter a_d, whereas PPF has the larger coefficient per unit volume fraction for the ascending-branch parameter a_a within the tested range. This apparent separation is supported by the geometric contrast between the two fibers (Table 5). Hooked-end SF carries tensile force across macrocracks through mechanical anchorage and frictional pull-out, becoming effective in the post-peak softening regime where a_d governs the curve shape; this is consistent with the steel-fiber-controlled trend reported for fiber-reinforced concrete [17,18,46] and with the negative SF coefficient in Equation (16).

The fine geometry of PPF may increase the number of microcrack interception sites per unit volume, as suggested by the microscale fracture model of polypropylene-fiber concrete proposed by Wang et al. [16]. The higher PPF coefficient in Equation (15) is therefore interpreted as an empirical correlate of this geometric inference rather than as direct micromechanical evidence. Within the tested V_PP range of 0.05–0.15%, PPF appeared to have a limited direct influence on the descending-branch shape, whereas SF was the larger contributor. Whether the PPF contribution remains monotonic beyond this range is not constrained by the present dataset.

4.3. Residual-Stiffness Limitation of the Modified Weibull Form

The residual-stiffness term of Equation (14) gives a far-field cξ(1 − a) component that becomes dominant at very large strain. This limitation is specific to the present residual-stiffness variant and does not extend to the Weibull-based statistical damage formulation of Cui et al. [24] or to the stochastic damage evolution law of Xu et al. [47]. Within the measured strain range, this far-field limitation did not govern the fitted response reported in Table 12.

4.4. Engineering Implications and Limitations

The two consistency checks carry two engineering implications. First, the link between a_d and λ_AE (Equation (18)) suggests a possible route for estimating a_d from AE monitoring when the full descending branch is difficult to capture with routine compression equipment. Second, the link between λ_AE and ε_0.20 (Equation (19)) supports the use of AE as a damage-evolution counterpart to the macroscopic damage variable in FR-SCC components where direct post-peak testing is impractical. These implications complement the AE/NDE recommendations of RILEM TC 212-ACD [37] by adding a direct link to the GB 50010 constitutive parameter.

Several limitations should be noted. The 100 mm × 100 mm × 300 mm prism is a non-standard size relative to the 150 mm × 150 mm × 300 mm reference prism of GB/T 50081-2019 [34], so size-conversion verification is still required. In addition, the experimental design did not include a GP-bearing mixture without expansive agent: in Series I the EA = 0% condition was examined only for the GP-free mixture (M1), so that every GP-containing mixture also contained at least 4% EA. The independent effect of GP at zero EA dosage therefore cannot be fully separated from that of the coupled GP–EA binder, and the GP-related trends should be interpreted within this coupled system. The tests were conducted at 28 days under uniaxial compression; multiaxial confinement, sustained loading, and long-term aging are outside the present scope. Equations (16) and (17) are valid within the calibration window defined above. Future work should extend the FR-SCC system to confined compression, widen the V_PP calibration range, and verify the a_d–λ_AE link on independent specimens.

5. Conclusions

Sixteen SCC mixtures, comprising 15 FR-SCC mixtures and one fiber-free reference, were tested in uniaxial compression with concurrent AE monitoring. The main conclusions are as follows.

(1)

At an EA dosage of 8%, the peak stress reached its maximum at a 12% GP replacement ratio (M9), where the peak strain was also the highest within the GP–EA series (Table 9). The 12% GP and 8% EA combination is therefore identified as the favorable binder balance within the tested composition window, consistent with a balance between matrix densification and binder dilution. At this binder composition, increasing the hybrid-fiber volume fraction from 0 in M12 to the highest level in M16 raised the peak strain by 76.6%, the post-peak energy by a factor of 7.66, the residual strain ε_0.20 by a factor of 4.92, and the toughness index from 1.75 to 3.48 (Table 10), indicating that hybrid SF/PPF fibers mainly improved the post-peak response rather than the pre-peak regime.

(2)

Among the three constitutive forms compared on the 15 FR-SCC mixtures, the GB 50010 piecewise model achieved the highest mean fitting precision (R² = 0.995, Table 12) and was adopted as the primary constitutive form, with its ascending and descending shape parameters used as the main descriptors. Two regression equations relating V_SF and V_PP to the ascending- and descending-branch parameters were established (Equations (15) and (16)), with R² of 0.927 and 0.778. A ductility-calibrated descending-branch regression (Equation (17)) reached a higher R² of 0.943.

(3)

Across the 15 FR-SCC mixtures, the descending-branch parameter a_d showed a Pearson correlation of r = −0.904 (95% CI [−0.968, −0.730], p < 0.001) with the AE characteristic strain λ_AE, and λ_AE showed r = +0.983 (95% CI [+0.949, +0.995], p < 0.001) with the macroscopic residual strain ε_0.20 (Equations (18) and (19)). These correlations indicate that the constitutive descending-branch shape, the AE characteristic strain, and the macroscopic post-peak descriptor track related facets of the same post-peak loading history. This agreement should be regarded as a consistency check rather than independent validation. It should be emphasized that all findings and the regression relationships above are valid only within the material and loading ranges of this study—GP of 0–18%, EA of 0–8% by binder mass, steel- and polypropylene-fiber volume fractions of 0–0.75% and 0–0.15%, tested at 28 days in uniaxial compression on 100 mm × 100 mm × 300 mm prisms—and should be recalibrated before extrapolation to other binder systems, fiber types, specimen sizes, or loading regimes.