The utilization of alkali-free accelerators, primarily based on aluminum sulfate, in shotcrete often leads to significant shrinkage and cracking, jeopardizing long-term durability. This study aims to mitigate this issue by investigating the efficacy of silica fume (SF) and fly ash (FA), individually and combined, in controlling the shrinkage deformation of shotcrete.
Shotcrete mixtures were prepared with cement partially replaced by SF, FA, or their combination (SF-FA). Aluminum sulfate was used as an accelerator. The shrinkage behavior under sealed and dry conditions was monitored. The underlying mechanisms were elucidated through hardened air-void analysis, mercury intrusion porosimetry (MIP), and internal humidity tracking.
Contrary to some previous studies, both individual and combined incorporation of mineral admixtures reduced the 28-day shrinkage. The SF-FA composite exhibited the most substantial reduction (23.72% sealed, 17.76% dry), followed by SF alone (18.11% sealed) and FA alone (11.35% sealed). Mechanism analysis revealed that the admixtures refined the pore structure, reduced the volume of harmful pores, and, crucially, optimized the air-void system by increasing the population of fine bubbles. This created an internal buffering effect that alleviates capillary stress. The synergistic effect in the SF-FA group is attributed to complementary pore-filling at dual scales.
This work demonstrates that, within an aluminum sulfate-accelerated shotcrete system, silica fume can effectively reduce shrinkage when its pore-refining effect is counterbalanced by a well-optimized micro-bubble network. It provides the first comprehensive evidence of the synergistic shrinkage-reducing mechanism of SF and FA in such systems, offering a practical strategy for mix design optimization to enhance the volume stability of shotcrete.
1. Introduction
Shotcrete, a specialized form of concrete applied by spraying, is a crucial material in the construction industry, particularly in infrastructure projects like highways, railways, and water management systems (Li, Zhang, Niu, & Song, 2020). Its unique application method, which eliminates the need for formwork, makes it a preferred choice for various construction scenarios. In tunnel construction for transportation networks, shotcrete plays a pivotal role in providing initial structural support. This is essential for managing rock deformation after blasting, preventing collapses, and ensuring the safety of both workers and equipment within the tunnel environment. Accelerators are often added to shotcrete mixtures to expedite the setting process and enhance early strength development (Tang, Xu, Lian, & Qu, 2016; Garba et al., 2024; Yang, He, & Xu, 2022). However, the use of accelerators has caused a series of durability problems in shotcrete, among which the cracking phenomenon caused by shrinkage deformation is particularly prominent.
Accelerators are generally classified into alkaline accelerators and alkali-free accelerators based on their alkali content. The alkali content of alkali-free accelerators is less than 1%, while that of alkaline accelerators is higher than 1% (British Standards Institution, 2005). Currently, alkali-free accelerators with aluminum sulfate as the main component are gradually replacing alkaline accelerators due to their low alkali content, safety, environmental friendliness, rapid setting, and minimal impact on concrete strength (Prudencio, 1998). However, the use of alkali-free accelerators significantly impairs the durability of shotcrete, particularly manifested as cracking caused by shrinkage deformation. Austin and Robins (E&FN Spon, 1995) compared the shrinkage behavior of shotcrete and traditional concrete and found that the total shrinkage rate of shotcrete was significantly higher. Wang, Li, and Tan (2023) observed that both the autogenous shrinkage and drying shrinkage of shotcrete increased significantly under the action of alkali-free accelerators. Sheng, Xue, and Li (2017) developed an alkali-free liquid accelerator based on aluminum sulfate and conducted studies on three dosage levels (5%, 7%, and 9%). The results showed that the dosage of the accelerator was directly related to the shrinkage strain of shotcrete - the higher the dosage, the greater the shrinkage rate. Huang (2021) pointed out that the alkali-free accelerator composed of aluminum sulfate and fluoroaluminate complex accelerated the early shrinkage rate of cement paste; however, the shrinkage rate slowed down over time, and at the same age, the paste shrinkage rate decreased with the increase in accelerator dosage. Given that aluminum sulfate is the core active component for accelerating setting and early strength development of alkali-free accelerators and its composition system is relatively complex, aluminum sulfate was used to replace the alkali-free accelerator in this study.
In the past shrinkage inhibition research, silica fume (SF), fly ash (FA) and other mineral admixtures have been widely used in ordinary concrete. When it is used in shotcrete, it can not only improve the utilization rate of solid waste, reduce carbon emission, but also improve workability and durability. However, research on controlling the shrinkage of sprayed concrete with admixtures is still limited. Bruce, Alexandre, and Marc (2022) found that FA reduces rebound, increases porosity, and reduces total shrinkage in dry-mix shotcrete. Wan, He, and Zheng (2024). studied the effect of SF/FA on alkali-free accelerator modified mortar, pointing out that SF can improve early strength and durability, but will significantly increase shrinkage; FA can improve volume stability, but high content will accelerate the internal humidity decline. Li (2013) obtained through the test, the results show that: FA admixture can significantly reduce the early self-shrinkage of high performance concrete, while SF will increase its early self-shrinkage; at the same time, the impact of ground slag on self-shrinkage is related to its fineness and content. However, some scholars have found different experimental phenomena. Wang, Zeng, and Qiao (2022a) found that FA and slag powder single or compound admixture in low content conditions will cause further deterioration of the drying shrinkage performance of shotcrete, in which the deterioration caused by FA is greater than slag powder. Currently, the shrinkage deformation of cement-based materials is often described as a two-stage process: rapid chemical shrinkage during the early humidity-saturated stage, and subsequent shrinkage deformation induced by self-desiccation or drying during the humidity-declining stage (Zhang, Hou, & Wei, 2010; Wang et al., 2023). The shrinkage deformation of cement-based materials is closely related to the evolution of internal relative humidity (Zhang, Hou, & Han, 2012). This pattern provides a foundation for analyzing the shrinkage mechanisms of cement-based materials. However, in the complex system of shotcrete containing aluminum sulfate-based accelerators, how mineral admixtures affect the progression and magnitude of these two stages, and their underlying micro-mechanisms, have not yet been systematically elucidated.
While most of the aforementioned studies have focused on the drying shrinkage or autogenous shrinkage of shotcrete, with limited research addressing the simultaneous control of both shrinkage types. Moreover, the majority of existing studies employ a single addition of mineral admixtures and have not systematically compared the effects of single versus combined additions on the shrinkage deformation of shotcrete. This paper selects SF and FA as the primary research materials. By partially replacing cement using both single and compound blending methods, it investigates the synergistic regulatory effects of SF and FA on the autogenous shrinkage and drying shrinkage of shotcrete, elucidating their influence on shrinkage deformation. Additionally, through an analysis of pore structure parameters in hardened concrete and mercury intrusion porosimetry tests, the internal mechanisms by which mineral admixtures affect the shrinkage deformation of shotcrete are clarified at the microscopic level. Finally, an optimized application scheme for mineral admixtures that effectively controls the shrinkage deformation of shotcrete is proposed.
2. Experiments and materials
2.1 Raw materials
The raw materials used in the shotcrete test in this study are as follows: The cement was Ordinary Portland Cement (P.O 42.5) produced by Beijing Jinyu Group Co., Ltd. Its chemical composition and mineral constituents are provided in Table 1, with its particle size distribution shown in Figure 1. The fine aggregate was medium sand with a fineness modulus of 2.94 and an apparent density of 2,423 kg/m3. The coarse aggregate was crushed stone with a particle size range of 5–10 mm and an apparent density of 2,783 kg/m3. The mineral admixtures included Grade I low-calcium fly ash and SF-90 grade silica fume produced by Gansu Sanyuan Silicon Materials Co., Ltd. To ensure adequate workability of the concrete, a polycarboxylate superplasticizer was incorporated. The accelerator used was analytically pure aluminum sulfate octadecahydrate (Al2(SO4)3·18H2O) supplied by Sinopharm Chemical Reagent Co., Ltd.
Chemical composition and main mineral composition of cement
| Chemical composition | Main mineral composition | ||
|---|---|---|---|
| Component | Content (%) | Component | Content (%) |
| SiO2 | 18.89 | C3S | 50.57 |
| Al2O3 | 6.41 | C2S | 16.01 |
| Fe2O3 | 3.19 | C4AF | 9.71 |
| CaO | 62.80 | C3A | 12.97 |
| Na2O | 0.36 | CaSO4 | 6.17 |
| K2O | 0.86 | ||
| MgO | 2.62 | ||
| SO3 | 3.63 | ||
| LOI | / | ||
| Chemical composition | Main mineral composition | ||
|---|---|---|---|
| Component | Content (%) | Component | Content (%) |
| SiO2 | 18.89 | C3S | 50.57 |
| Al2O3 | 6.41 | C2S | 16.01 |
| Fe2O3 | 3.19 | C4AF | 9.71 |
| CaO | 62.80 | C3A | 12.97 |
| Na2O | 0.36 | CaSO4 | 6.17 |
| K2O | 0.86 | ||
| MgO | 2.62 | ||
| SO3 | 3.63 | ||
| LOI | / | ||
The horizontal axis is labeled “Particle size distribution (micrometers)” and ranges from 0.1 to 1000 in a logarithmic scale, and the values are the multiples of 10. The vertical axis is labeled “Volume (percent)” and ranges from 0 to 6 in increments of 1 unit. A curve begins at approximately (0.4, 0) and rises to reach a first peak at approximately (0.8, 2.3). The curve descends to a local minimum at approximately (1.4, 1.4), then rises again to reach a second and higher peak at approximately (20.9, 4.7). The curve then descends continuously, reaching approximately (88.8, 0). Note: All numerical data values are approximated.Cement particle size distribution. Source: Authors’ own work
The horizontal axis is labeled “Particle size distribution (micrometers)” and ranges from 0.1 to 1000 in a logarithmic scale, and the values are the multiples of 10. The vertical axis is labeled “Volume (percent)” and ranges from 0 to 6 in increments of 1 unit. A curve begins at approximately (0.4, 0) and rises to reach a first peak at approximately (0.8, 2.3). The curve descends to a local minimum at approximately (1.4, 1.4), then rises again to reach a second and higher peak at approximately (20.9, 4.7). The curve then descends continuously, reaching approximately (88.8, 0). Note: All numerical data values are approximated.Cement particle size distribution. Source: Authors’ own work
2.2 Experimental mix proportions
To investigate the impact of different admixtures on shotcrete shrinkage, four shotcrete series were analyzed: a control group, FA only, SF only, and a combination of SF and FA, labeled JZ, FA, SF, and SF-FA, respectively. The mixture ratios are detailed in Table 2.
Mix proportion of shotcrete test
| Num | Materials (kg/m3) | Aluminum sulfate | Superplasticizer | |||||
|---|---|---|---|---|---|---|---|---|
| Cement | Sand | Stone | Water | FA | SF | |||
| JZ | 470 | 850 | 850 | 175 | 4% | 0.9% | ||
| FA | 399.5 | 850 | 850 | 175 | 70.5 | 4% | 0.9% | |
| SF | 446.5 | 850 | 850 | 175 | 23.5 | 4% | 0.9% | |
| SF-FA | 376 | 850 | 850 | 175 | 70.5 | 23.5 | 4% | 0.9% |
| Num | Materials (kg/m3) | Aluminum sulfate | Superplasticizer | |||||
|---|---|---|---|---|---|---|---|---|
| Cement | Sand | Stone | Water | FA | SF | |||
| JZ | 470 | 850 | 850 | 175 | 4% | 0.9% | ||
| FA | 399.5 | 850 | 850 | 175 | 70.5 | 4% | 0.9% | |
| SF | 446.5 | 850 | 850 | 175 | 23.5 | 4% | 0.9% | |
| SF-FA | 376 | 850 | 850 | 175 | 70.5 | 23.5 | 4% | 0.9% |
The experiment utilized the mixing ratios specified in Table 2. The blank control group was denoted as JZ. FA comprised 15% of the total cementitious material by mass, while SF made up 5% of the cementitious material by mass. A combination of FA and SF, denoted as SF-FA, accounted for 15% of the cementitious material by mass. The aluminum sulfate was applied at a rate of 4% of the gelling material by mass, and the superplasticizer at 0.9% of the gelling material by mass.
2.3 Method
2.3.1 Performance evaluation
The mechanical strength of shotcrete will be evaluated according to the “Standard for test methods of physical and mechanical properties of concrete” (GB/T 50,081–2019). To test the influence law of mineral admixtures on the compressive strength of shotcrete, 12 cube specimens with dimensions of 100 × 100 × 100 mm will be prepared for each test mix proportion. After molding, the specimens will be cured in a standard curing chamber. The compressive strength will be measured using a WAW-600Q pressure testing machine at the corresponding ages (3, 7, 14, and 28 d) to monitor the strength development law.
2.3.2 Shrinkage and humidity integration test of shotcrete
A linear variable differential transformer (LVDT) was employed to measure the shrinkage deformation of shotcrete, with a measuring range of 2 mm and an accuracy of 1μm. The LVDT was coaxially positioned to accurately capture the deformation of the shotcrete material over time. The shrinkage specimens were molded in a special plexiglass mold with an inner diameter of 400 × 100 × 100 mm, and extractable thin plates were arranged around the mold (Hou, 2010). Before the initial setting of the specimens, the thin plates around the mold were pulled out to allow the specimens to deform freely, and each specimen was sealed with butter and plastic film. Finally, a magnetic device was used to fix the LVDT at both ends of the specimens to determine the free shrinkage deformation law of the specimens. In addition to the LVDT, a capacitive sensor was also installed in the experimental device to monitor the temperature and humidity changes at a depth of 5 cm below the sample interface. This depth corresponds to the geometric center of the specimen, effectively minimizing direct interference from rapid surface drying and boundary effects, thereby allowing it to sensitively reflect the overall trend and rate of moisture migration from the interior outward. The sensor was placed in a PVC pipe for auxiliary positioning, and two rectangular holes with a width of 2 mm were opened on both sides of the bottom of the PVC pipe to ensure the moisture exchange between the sensor and the shotcrete around the holes. The humidity measuring range of the sensor was 0% to 100%, with an accuracy of 1%. Before conducting the experiment, the capacitive sensor underwent a calibration procedure using distilled water and standard saturated salt solutions under controlled temperature conditions. Then, the obtained calibration curve (see Figure 2) was applied to adjust the humidity data obtained from the shotcrete specimens to ensure the accuracy and reliability of the collected data. Table 3 presents the theoretical humidity values of distilled water and various standard saturated salt solutions, which serve as reference points for calibrating and verifying the humidity sensor readings during the experimental measurement.
The horizontal axis is labeled “Theoretical Value (percent)” and ranges from 50 to 100 in increments of 5 units. The vertical axis is labeled “Measured Value (percent)” and ranges from 50 to 100 in increments of 5 units. A legend in the upper left identifies eight lines: “S F-F A-Seal” marked with circles, “S F-F A-Dry” marked with triangles, “S F-Seal” marked with diamonds, “S F-Dry” marked with crosses, “F A-Seal” marked with plus signs, “F A-Dry” marked with right-pointing arrows, “J Z-Seal” marked with squares, and “J Z-Dry” marked with downward-pointing triangles. All eight lines follow a similar upward trend and remain closely grouped throughout the graph. At a theoretical value of 57, the measured values range from approximately 57 to 59. At 75, the measured values range from approximately 69 to 72. At 85, the measured values range from approximately 79 to 81. At 90, the measured values range from approximately 84 to 89. At 97, the measured values range from approximately 88 to 91. At 100, the measured values range from approximately 90 to 93. Note: All numerical data values are approximated.Humidity sensor calibration curve. Source: Authors’ own work
The horizontal axis is labeled “Theoretical Value (percent)” and ranges from 50 to 100 in increments of 5 units. The vertical axis is labeled “Measured Value (percent)” and ranges from 50 to 100 in increments of 5 units. A legend in the upper left identifies eight lines: “S F-F A-Seal” marked with circles, “S F-F A-Dry” marked with triangles, “S F-Seal” marked with diamonds, “S F-Dry” marked with crosses, “F A-Seal” marked with plus signs, “F A-Dry” marked with right-pointing arrows, “J Z-Seal” marked with squares, and “J Z-Dry” marked with downward-pointing triangles. All eight lines follow a similar upward trend and remain closely grouped throughout the graph. At a theoretical value of 57, the measured values range from approximately 57 to 59. At 75, the measured values range from approximately 69 to 72. At 85, the measured values range from approximately 79 to 81. At 90, the measured values range from approximately 84 to 89. At 97, the measured values range from approximately 88 to 91. At 100, the measured values range from approximately 90 to 93. Note: All numerical data values are approximated.Humidity sensor calibration curve. Source: Authors’ own work
Theoretical humidity values of distilled water and saturated salt solution
| Saturated salt solution | NaBr | NaCl | KCl | BaCl2 | K2SO4 | Distilled water |
|---|---|---|---|---|---|---|
| Theoretical humidity/% | 58.4 | 75.4 | 84.6 | 90.5 | 97.5 | 100 |
| Saturated salt solution | NaBr | NaCl | KCl | BaCl2 | K2SO4 | Distilled water |
|---|---|---|---|---|---|---|
| Theoretical humidity/% | 58.4 | 75.4 | 84.6 | 90.5 | 97.5 | 100 |
For the shrinkage and humidity tests of shotcrete, two parallel specimens are formed for each mix ratio, namely the dry specimen and the sealed specimen. After sealing, all specimens and data acquisition equipment were placed in a laboratory maintained at 16 ± 1°C and 60 ± 5% RH. The shrinkage deformation and internal humidity development of the specimens under sealed drying conditions were continuously measured to ensure comparability of the results. In the first 3 days of the test, both the sealed and dry specimens are kept sealed with plastic film. After 3 days, remove the plastic sealing film on the top and around the dry specimen to allow it to fully contact the external environment, while the sealed specimen remains unchanged until the end of the test, as shown in Figure 3.
The photograph shows two light-colored rectangular test specimens horizontally mounted in a laboratory testing frame. The upper specimen represents the sealed condition, while the lower specimen is in the dried condition. Both ends of each specimen are secured with black mechanical clamps and connected to shrinkage sensors. Transparent acrylic plates are positioned beneath and surrounding the specimens. A humidity sensor is centrally placed on top of each specimen. The setup is viewed from above, clearly illustrating the arrangement of the two specimens and the placement of their respective sensors.Shrinkage and humidity test specimens. Source(s): Authors’ own work
The photograph shows two light-colored rectangular test specimens horizontally mounted in a laboratory testing frame. The upper specimen represents the sealed condition, while the lower specimen is in the dried condition. Both ends of each specimen are secured with black mechanical clamps and connected to shrinkage sensors. Transparent acrylic plates are positioned beneath and surrounding the specimens. A humidity sensor is centrally placed on top of each specimen. The setup is viewed from above, clearly illustrating the arrangement of the two specimens and the placement of their respective sensors.Shrinkage and humidity test specimens. Source(s): Authors’ own work
2.3.3 Concrete bubble parameter analysis
The research utilizes a digital bubble spacing coefficient tester to analyze the bubble properties in shotcrete. The test samples consist of 100 mm cubic specimens that undergo a 28 d curing process before being sliced into 100 mm × 100 mm × 10 mm sections. These sections are meticulously polished to attain a surface roughness not exceeding . Subsequently, an optical microscope is employed to examine the polished sections, enabling the measurement of bubble chord length and spacing along a specified scan line. For each mixture ratio, three slices are meticulously prepared, and the average measurements from these slices are aggregated to determine the final outcomes for each test cohort.
2.3.4 Pore structure analysis
The mercury intrusion test, a common method for evaluating pore structures, was employed to analyze the specimen. To provide a detailed representation of the internal pore structure of shotcrete, cement paste obtained from the 28d strength test was utilized for sample preparation. Subsequently, these samples underwent a 24-h immersion in absolute ethanol followed by drying in a vacuum oven until reaching a consistent weight. The pore size distribution analysis was carried out using the Micromeritics AutoPore IV 962, which covered a broad range from 0.003 to 450 μm.
3. Results and discussion
3.1 Compressive strength
Figure 4 illustrates the compressive strength test outcomes for four distinct mixtures at varying ages. A comparison between the JZ group and the FA group shows that the FA group showed a notable increase of 1.4% and 5.6% in compressive strength at 14 and 28 days, respectively. Similarly, the SF group exhibited enhancements of 5.7% and 8.8% in compressive strength at 14 and 28 days, while the SF-FA group displayed improvements of 3.6% and 9.7% at the same time points. It is important to note that the ranking of 3-day compressive strength across the groups was SF > JZ > SF-FA > FA. The effectiveness of mineral admixtures, such as SF and FA, in improving shotcrete strength can be attributed to their fine particle sizes. These admixtures utilize a micro-aggregate effect to penetrate the pores of the cement paste, leading to the densification of the concrete structure. Silica fume, with its SiO2 content, and FA, containing Al2O3, engage in a pozzolanic reaction with calcium hydroxide (CH) produced during cement hydration. This reaction results in the formation of a significant amount of Calcium Silicate Hydrate gel (C-S-H), which fills the voids in the cement paste and enhances the strength of the concrete. Partially replacing cement with FA affects the early hydration process of cement. The active Al2O3 in fly ash gradually dissolves, increasing the concentration of Al3+ in the solution, breaking the hydration equilibrium of C3A, and leading to the massive formation of expansive ettringite, which in turn causes a decrease in the strength of shotcrete (Wang, He, Shu, Wei, & Wang, 2022b). In addition, the difference in reactivity between fly ash and silica fume leads to a delayed reaction of fly ash, resulting in slow strength development of specimens in the FA group. Therefore, although the 3d compressive strength of the JZ group is higher than that of the SF-FA composite admixture group and the pure fly ash group, its strength improvement effect is inferior to that of the pure silica fume group (Qu, Yu, Ji, Gauvin, & Voets, 2020).
The vertical axis is labeled “Compressive Strength (megapascals)” and ranges from 0 to 60 in increments of 20 units. The horizontal axis is labeled “Time (day)” and shows four categories: 3 d, 7 d, 14 d, and 28 d. A legend at the top shows four categories: J Z, F A, S F, and S F hyphen F A. Each time category displays four grouped bars with error bars. The data for the bars are as follows: 3 d: J Z: 39; F A: 34; S F: 36; S F hyphen F A: 34. 7 d: J Z: 49; F A: 44; S F: 45; S F hyphen F A: 45. 14 d: J Z: 53; F A: 51; S F: 55; S F hyphen F A: 53. 28 d: J Z: 57; F A: 53; S F: 60; S F hyphen F A: 57. Note: All numerical data values are approximated.Compressive strength curves of shotcrete at different age. Source(s): Authors’ own work
The vertical axis is labeled “Compressive Strength (megapascals)” and ranges from 0 to 60 in increments of 20 units. The horizontal axis is labeled “Time (day)” and shows four categories: 3 d, 7 d, 14 d, and 28 d. A legend at the top shows four categories: J Z, F A, S F, and S F hyphen F A. Each time category displays four grouped bars with error bars. The data for the bars are as follows: 3 d: J Z: 39; F A: 34; S F: 36; S F hyphen F A: 34. 7 d: J Z: 49; F A: 44; S F: 45; S F hyphen F A: 45. 14 d: J Z: 53; F A: 51; S F: 55; S F hyphen F A: 53. 28 d: J Z: 57; F A: 53; S F: 60; S F hyphen F A: 57. Note: All numerical data values are approximated.Compressive strength curves of shotcrete at different age. Source(s): Authors’ own work
3.2 Shrinkage and internal humidity development analysis
This research conducted a comprehensive analysis of shrinkage deformation and internal humidity variations in specimens with four different mix proportions. The specimens were subjected to two distinct environmental conditions: sealed and dry. Two specimens were prepared for each mix proportion, allowing for comparative analysis between the sealed and dry environments. Detailed results and data are depicted in Figures 5–8.
The graph is titled “J Z”. The horizontal axis is labeled “Time (days)” and ranges from 0 to 28 in increments of 4 units. The left vertical axis is labeled “Shrinkage Strain (times 10 to the negative 6 power)” and ranges from 0 to 1000 in increments of 200 units. The right vertical axis is labeled “Relative Humidity (percent)” and ranges from 0 to 100 in increments of 10 units. A legend in the lower right identifies four lines: “J Z-Seal Autogenous Shrinkage” marked with diamonds, “J Z-Dry Total Shrinkage” marked with circles, “J Z-Seal Relative Humidity” marked with squares, and “J Z-Dry Relative Humidity” marked with right-pointing triangles. The “J Z-Seal Autogenous Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 270 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 490 shrinkage strain by day 16 and leveling off to end at approximately 537 shrinkage strain by day 28. The “J Z-Dry Total Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 323 shrinkage strain. The curve continues to rise but at a decreasing rate, reaching approximately 635 shrinkage strain by day 16 and leveling off to end at approximately 665 shrinkage strain by day 28. The “J Z-Seal Relative Humidity” line begins at (0, 100) and shows a slight gradual decrease to end at 91.5 percent by day 28. The “J Z-Dry Relative Humidity” line begins at (0, 100) and decreases steadily throughout the time period, reaching approximately 88 percent by day 8, approximately 85 percent by day 16, and ending at approximately 83 percent by day 28. Note: All numerical data values are approximated.JZ shrinkage and humidity development curves. Source(s): Authors’ own work
The graph is titled “J Z”. The horizontal axis is labeled “Time (days)” and ranges from 0 to 28 in increments of 4 units. The left vertical axis is labeled “Shrinkage Strain (times 10 to the negative 6 power)” and ranges from 0 to 1000 in increments of 200 units. The right vertical axis is labeled “Relative Humidity (percent)” and ranges from 0 to 100 in increments of 10 units. A legend in the lower right identifies four lines: “J Z-Seal Autogenous Shrinkage” marked with diamonds, “J Z-Dry Total Shrinkage” marked with circles, “J Z-Seal Relative Humidity” marked with squares, and “J Z-Dry Relative Humidity” marked with right-pointing triangles. The “J Z-Seal Autogenous Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 270 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 490 shrinkage strain by day 16 and leveling off to end at approximately 537 shrinkage strain by day 28. The “J Z-Dry Total Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 323 shrinkage strain. The curve continues to rise but at a decreasing rate, reaching approximately 635 shrinkage strain by day 16 and leveling off to end at approximately 665 shrinkage strain by day 28. The “J Z-Seal Relative Humidity” line begins at (0, 100) and shows a slight gradual decrease to end at 91.5 percent by day 28. The “J Z-Dry Relative Humidity” line begins at (0, 100) and decreases steadily throughout the time period, reaching approximately 88 percent by day 8, approximately 85 percent by day 16, and ending at approximately 83 percent by day 28. Note: All numerical data values are approximated.JZ shrinkage and humidity development curves. Source(s): Authors’ own work
The graph is titled “F A”. The horizontal axis is labeled “Time (days)” and ranges from 0 to 28 in increments of 4 units. The left vertical axis is labeled “Shrinkage Strain (times 10 to the negative 6 power)” and ranges from 0 to 1000 in increments of 200 units. The right vertical axis is labeled “Relative Humidity (percent)” and ranges from 0 to 100 in increments of 10 units. A legend in the lower right identifies four lines: “F A-Seal Autogenous Shrinkage” marked with diamonds, “F A-Seal Relative Humidity” marked with squares, “F A-Dry Total Shrinkage” marked with circles, and “F A-Dry Relative Humidity” marked with right-pointing triangles. The “F A-Seal Autogenous Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 218 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 445 shrinkage strain by day 16 and leveling off to end at approximately 490 shrinkage strain by day 28. The “F A-Dry Total Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 260 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 560 shrinkage strain by day 16 and leveling off to end at approximately 615 shrinkage strain by day 28. The “F A-Seal Relative Humidity” line begins at (0, 100) and shows a slight gradual decrease to end at 91 percent by day 28. The “F A-Dry Relative Humidity” line begins at (0, 100) and decreases steadily throughout the time period, reaching approximately 88 percent by day 8, approximately 84 percent by day 16, and ending at approximately 80 percent by day 28. Note: All numerical data values are approximated.FA shrinkage and humidity development curves. Source(s): Authors’ own work
The graph is titled “F A”. The horizontal axis is labeled “Time (days)” and ranges from 0 to 28 in increments of 4 units. The left vertical axis is labeled “Shrinkage Strain (times 10 to the negative 6 power)” and ranges from 0 to 1000 in increments of 200 units. The right vertical axis is labeled “Relative Humidity (percent)” and ranges from 0 to 100 in increments of 10 units. A legend in the lower right identifies four lines: “F A-Seal Autogenous Shrinkage” marked with diamonds, “F A-Seal Relative Humidity” marked with squares, “F A-Dry Total Shrinkage” marked with circles, and “F A-Dry Relative Humidity” marked with right-pointing triangles. The “F A-Seal Autogenous Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 218 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 445 shrinkage strain by day 16 and leveling off to end at approximately 490 shrinkage strain by day 28. The “F A-Dry Total Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 260 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 560 shrinkage strain by day 16 and leveling off to end at approximately 615 shrinkage strain by day 28. The “F A-Seal Relative Humidity” line begins at (0, 100) and shows a slight gradual decrease to end at 91 percent by day 28. The “F A-Dry Relative Humidity” line begins at (0, 100) and decreases steadily throughout the time period, reaching approximately 88 percent by day 8, approximately 84 percent by day 16, and ending at approximately 80 percent by day 28. Note: All numerical data values are approximated.FA shrinkage and humidity development curves. Source(s): Authors’ own work
The graph is titled “S F”. The horizontal axis is labeled “Time (days)” and ranges from 0 to 28 in increments of 4 units. The left vertical axis is labeled “Shrinkage Strain (times 10 to the negative 6 power)” and ranges from 0 to 1000 in increments of 200 units. The right vertical axis is labeled “Relative Humidity (percent)” and ranges from 0 to 100 in increments of 10 units. A legend in the lower right identifies four lines: “S F-Seal Autogenous Shrinkage” marked with diamonds, “S F-Dry Total Shrinkage” marked with circles, “S F-Seal Relative Humidity” marked with squares, and “S F-Dry Relative Humidity” marked with right-pointing triangles. The “S F-Seal Autogenous Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 230 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 435 shrinkage strain by day 16 and leveling off to end at approximately 465 shrinkage strain by day 28. The “S F-Dry Total Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 295 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 570 shrinkage strain by day 16 and leveling off to end at approximately 610 shrinkage strain by day 28. The “S F-Seal Relative Humidity” line begins at (0, 100) and shows a slight gradual decrease to end at 91 percent by day 28. The “S F-Dry Relative Humidity” line begins at (0, 100) and decreases steadily throughout the time period, reaching approximately 88 percent by day 8, approximately 85 percent by day 16, and ending at approximately 83 percent by day 28. Note: All numerical data values are approximated.SF shrinkage and humidity development curves. Source(s): Authors’ own work
The graph is titled “S F”. The horizontal axis is labeled “Time (days)” and ranges from 0 to 28 in increments of 4 units. The left vertical axis is labeled “Shrinkage Strain (times 10 to the negative 6 power)” and ranges from 0 to 1000 in increments of 200 units. The right vertical axis is labeled “Relative Humidity (percent)” and ranges from 0 to 100 in increments of 10 units. A legend in the lower right identifies four lines: “S F-Seal Autogenous Shrinkage” marked with diamonds, “S F-Dry Total Shrinkage” marked with circles, “S F-Seal Relative Humidity” marked with squares, and “S F-Dry Relative Humidity” marked with right-pointing triangles. The “S F-Seal Autogenous Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 230 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 435 shrinkage strain by day 16 and leveling off to end at approximately 465 shrinkage strain by day 28. The “S F-Dry Total Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 295 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 570 shrinkage strain by day 16 and leveling off to end at approximately 610 shrinkage strain by day 28. The “S F-Seal Relative Humidity” line begins at (0, 100) and shows a slight gradual decrease to end at 91 percent by day 28. The “S F-Dry Relative Humidity” line begins at (0, 100) and decreases steadily throughout the time period, reaching approximately 88 percent by day 8, approximately 85 percent by day 16, and ending at approximately 83 percent by day 28. Note: All numerical data values are approximated.SF shrinkage and humidity development curves. Source(s): Authors’ own work
The graph is titled “S F-F A”. The horizontal axis is labeled “Time (days)” and ranges from 0 to 28 in increments of 4 units. The left vertical axis is labeled “Shrinkage Strain (times 10 to the negative 6 power)” and ranges from 0 to 1000 in increments of 200 units. The right vertical axis is labeled “Relative Humidity (percent)” and ranges from 0 to 100 in increments of 10 units. A legend in the lower right identifies four lines: “S F-F A-Seal Autogenous Shrinkage” marked with diamonds, “S F-F A-Seal Relative Humidity” marked with squares, “F A-Dry Total Shrinkage” marked with circles, and “S F-F A-Dry Relative Humidity” marked with right-pointing triangles. The “S F-F A-Seal Autogenous Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 215 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 410 shrinkage strain by day 16 and leveling off to end at approximately 442 shrinkage strain by day 28. The “F A-Dry Total Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 215 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 523 shrinkage strain by day 16 and leveling off to end at approximately 556 shrinkage strain by day 28. The “S F-F A-Seal Relative Humidity” line begins at (0, 100) and shows a slight gradual decrease to end at 91 percent by day 28. The “S F-F A-Dry Relative Humidity” line begins at (0, 100) and decreases steadily throughout the time period, reaching approximately 88 percent by day 8, approximately 85 percent by day 16, and ending at approximately 81 percent by day 28. Note: All numerical data values are approximated.SF-FA shrinkage and humidity development curves. Source(s): Authors’ own work
The graph is titled “S F-F A”. The horizontal axis is labeled “Time (days)” and ranges from 0 to 28 in increments of 4 units. The left vertical axis is labeled “Shrinkage Strain (times 10 to the negative 6 power)” and ranges from 0 to 1000 in increments of 200 units. The right vertical axis is labeled “Relative Humidity (percent)” and ranges from 0 to 100 in increments of 10 units. A legend in the lower right identifies four lines: “S F-F A-Seal Autogenous Shrinkage” marked with diamonds, “S F-F A-Seal Relative Humidity” marked with squares, “F A-Dry Total Shrinkage” marked with circles, and “S F-F A-Dry Relative Humidity” marked with right-pointing triangles. The “S F-F A-Seal Autogenous Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 215 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 410 shrinkage strain by day 16 and leveling off to end at approximately 442 shrinkage strain by day 28. The “F A-Dry Total Shrinkage” line begins at (0, 0) and rises steeply until approximately day 4, reaching around 215 shrinkage strain. The curve continues to rise at a decreasing rate, reaching approximately 523 shrinkage strain by day 16 and leveling off to end at approximately 556 shrinkage strain by day 28. The “S F-F A-Seal Relative Humidity” line begins at (0, 100) and shows a slight gradual decrease to end at 91 percent by day 28. The “S F-F A-Dry Relative Humidity” line begins at (0, 100) and decreases steadily throughout the time period, reaching approximately 88 percent by day 8, approximately 85 percent by day 16, and ending at approximately 81 percent by day 28. Note: All numerical data values are approximated.SF-FA shrinkage and humidity development curves. Source(s): Authors’ own work
According to the analysis of experimental results, regardless of being in a sealed or dry environment, the relative humidity (RH) of specimens in each group shows typical two-stage change characteristics with age (Han, Zhang, Wang, & Hao, 2017; Wang, Xie, Zhong, & Qu, 2022c). The first stage is the humidity saturation and stabilization period (RH ˜ 100%). The reason for the stable humidity in this stage is that the hydration products (such as AFt and C-S-H) generated in the early stage of cement hydration adsorb a large amount of bound water, and the free water in the pores has not been significantly consumed; moreover, the dry specimens have not exchanged moisture with the environment. The second stage is the non-linear humidity attenuation period (after 3d). The humidity change in this stage is the result of the dynamic coupling effect of water consumption and migration. On the one hand, the continuous hydration of cement and the pozzolanic reaction of mineral admixtures will continuously consume free water. On the other hand, under the action of the micro-aggregate of mineral admixtures, the pore structure inside the shotcrete will evolve, affecting the water migration path, and then the humidity decline rate fluctuates non-linearly.
In a sealed environment, humidity attenuation is entirely dominated by water consumption during the hydration process. The JZ group, without mineral admixtures, has a relatively higher cement content, leading to faster early hydration. This generates abundant hydration products such as ettringite and C-S-H, which rapidly consume free water within the system, resulting in a relatively high relative humidity attenuation rate in the specimen (Wang, Xie, Zhong, & Li, 2020). FA particles, with their spherical shape and smooth surface, exhibit a smaller specific surface area and lower pozzolanic reactivity (Wu, Farzadnia, Shi, Zhang, & Wang, 2017). Consequently, early water consumption in the specimen primarily derives from the sole hydration of cement. Meanwhile, as FA partially replaces cement, the absolute cement content in the system is lower than in the JZ group, significantly slowing the rate of free water consumption by cement hydration. Thus, the relative humidity attenuation rate in the FA group is slower than that of the JZ group. In the SF group, SF—characterized by its ultra-high specific surface area and submicron particle size (<0.1 μm)—exhibits an intense early pozzolanic reaction that accelerates cement hydration (Liu, Sun, Miao, 2009). This not only rapidly consumes a large amount of free water but also induces higher early hydration temperatures, making the humidity attenuation rate in the specimen the fastest. In a dry environment, humidity attenuation is driven by a combination of “hydration consumption + surface evaporation,” accelerating humidity reduction across all groups. Compared with the control group, the fine particles in the SF group fill pores, forming more developed evaporation channels within the specimen and causing humidity to decline more rapidly. FA particles, being spherical, retain free water more effectively than cement or SF particles, thereby delaying humidity attenuation. For the composite admixture group, building on the improved matrix compactness from pozzolanic reactions, SF fills gel pores (10–100 nm) while FA fills capillary pores (>100 nm). This “dual-scale filling” effect optimizes particle size grading, weakens pore connectivity, and further slows internal humidity decline, resulting in the lowest humidity attenuation rate.
The influence of mineral admixtures on the shrinkage deformation of shotcrete also shows two-stage characteristics: at the early age (0–4 d), the shrinkage deformation of each mix proportion increases rapidly at an approximately linear rate. Then, after the shrinkage reaches a certain value, the rate of shrinkage deformation increase begins to decelerate with the development of age. Among them, the rapid growth stage corresponds to the humidity saturation period, and the shrinkage in this stage is mainly related to the chemical shrinkage caused by cement hydration; the decelerating development stage corresponds to the humidity decline period, and the shrinkage deformation in this stage is mainly related to the self - drying caused by water migration and evaporation (Wang et al., 2023). At 28d, the shrinkage values of the mineral admixture groups are all lower than those of the control group. Among them, the shrinkage of the sealed and dried specimens in the FA group is reduced by 11.35% and 8.53% respectively compared with the JZ group, that of the SF group is reduced by 18.11% and 6.76% respectively compared with the JZ group, and the SF - FA group shows the largest reduction, with the shrinkage of the sealed specimens decreased and that of the dried specimens decreased by 17.76%.
The above experimental results indicate that mineral admixtures can effectively inhibit the shrinkage of shotcrete, and the composite system of SF and FA exhibits a synergistic enhancement effect. The reason for the above differences lies in the synergistic regulation of the hydration process and microstructure by mineral admixtures: Firstly, the approximately spherical particles and low specific surface structure of FA can reduce the “squeezing effect” of water in the particle gaps, making it easier for free water to be retained in the pores of the paste, retaining more free water and delaying the formation of the internal humidity gradient, thereby improving the shrinkage deformation. In addition, the pozzolanic reaction of FA and SF undergoes a secondary reaction with CH, generating a large amount of C-S-H gel, which enhances the early stiffness and compactness of the matrix and inhibits the volume deformation of the specimen (Zhang, Zhang, & Yan, 2016). Secondly, the micro-aggregate effect of SF and FA synergistically optimizes the pore structure. They fill the internal pores, reducing the porosity and the proportion of connected pores, slowing down the water migration and evaporation rate (Li, Tan, & Zhang, 2000), and inhibiting the shrinkage deformation of the specimen. Finally, the composite system achieves shrinkage inhibition through hydration regulation: SF and FA replace part of the cement, weakening the intensity of the hydration reaction. Moreover, the hydration retardation of FA increases the effective water - binder ratio through the dilution effect, which is beneficial to reducing the early autogenous shrinkage of shotcrete.
3.3 Shotcrete bubble characteristics
Figures 9–14 depict the experimental results of the distribution of bubble diameter, average bubble diameter, and bubble spacing coefficient in hardened shotcrete. It can be observed from the figures that the bubble distribution in the JZ group exhibits the characteristics of “low frequency for small sizes and high sparsity for large sizes”, and the proportion of small bubbles (d < 50 μm) is relatively insufficient. After the incorporation of mineral admixtures, the size gradation of the bubble population is significantly improved: compared with the control group, the proportion of small bubbles in the FA group increases by 17.4%, that in the SF group increases by 14.3%, and the highest increase in the compound SF - FA group reaches 24.3%, indicating that mineral admixtures promote the formation of tiny bubbles and increase the number of “buffer units” in the matrix. The proportion of bubbles with a diameter of 50–100 μm shows a gradient decline trend with the addition of admixtures. Specifically, the FA group decreases by 54.3%, the SF group decreases by 44.7%, and the SF - FA group decreases by 35.9%. The number of large bubbles with a diameter >100 μm also decreases, with a 16.6% reduction in the SF group and an 11.2% reduction in the SF - FA group. In addition, mineral admixtures shorten the bubble spacing coefficient, increase the density between bubbles, make the bubble distribution in the matrix more compact, and form an elastic buffer zone inside the specimen. As the relative humidity inside the specimen decreases, it can alleviate the shrinkage deformation of cement and other cementitious material particles caused by the increase in surface tension, and reduce the deformation driving force of the matrix (Hang, Sun, & Guo, 2020).
The vertical axis is labeled “Chord Length Frequency (percent)” and ranges from 0 to 40 in increments of 5 units. The horizontal axis is labeled “Chord Size (millimeters)” and shows multiple size intervals progressing from left to right, starting at “0.00 to 0.01” and extending through larger ranges up to “3.00 to 4.00”. The data for the bars are as follows: 0.00 to 0.01: 24.5 0.01 to 0.02: 24 0.02 to 0.03: 7.5 0.03 to 0.04: 9 0.04 to 0.05: 6 0.05 to 0.06: 4.5 0.06 to 0.08: 4 0.08 to 0.10: 6.5 0.10 to 0.12: 2 0.12 to 0.14: 0.5 0.14 to 0.16: 0 0.16 to 0.18: 0.5 0.18 to 0.20: 0.5 0.20 to 0.22: 0.5 0.22 to 0.24: 0.5 0.24 to 0.26: 0 0.26 to 0.28: 0.5 0.28 to 0.30: 1 0.30 to 0.35: 1 0.35 to 0.40: 0 0.40 to 0.45: 0.5 0.45 to 0.50: 1.5 0.50 to 1.00: 2 1.00 to 1.50: 0 1.50 to 2.50: 0 2.50 to 3.00: 0 3.00 to 4.00: 0 Note: All numerical data values are approximated.Hardened bubble pore size distribution of JZ. Source(s): Authors’ own work
The vertical axis is labeled “Chord Length Frequency (percent)” and ranges from 0 to 40 in increments of 5 units. The horizontal axis is labeled “Chord Size (millimeters)” and shows multiple size intervals progressing from left to right, starting at “0.00 to 0.01” and extending through larger ranges up to “3.00 to 4.00”. The data for the bars are as follows: 0.00 to 0.01: 24.5 0.01 to 0.02: 24 0.02 to 0.03: 7.5 0.03 to 0.04: 9 0.04 to 0.05: 6 0.05 to 0.06: 4.5 0.06 to 0.08: 4 0.08 to 0.10: 6.5 0.10 to 0.12: 2 0.12 to 0.14: 0.5 0.14 to 0.16: 0 0.16 to 0.18: 0.5 0.18 to 0.20: 0.5 0.20 to 0.22: 0.5 0.22 to 0.24: 0.5 0.24 to 0.26: 0 0.26 to 0.28: 0.5 0.28 to 0.30: 1 0.30 to 0.35: 1 0.35 to 0.40: 0 0.40 to 0.45: 0.5 0.45 to 0.50: 1.5 0.50 to 1.00: 2 1.00 to 1.50: 0 1.50 to 2.50: 0 2.50 to 3.00: 0 3.00 to 4.00: 0 Note: All numerical data values are approximated.Hardened bubble pore size distribution of JZ. Source(s): Authors’ own work
The vertical axis is labeled “Chord Length Frequency (percent)” and ranges from 0 to 40 in increments of 5 units. The horizontal axis is labeled “Chord Size (millimeters)” and shows multiple size intervals progressing from left to right, starting at “0.00 to 0.01” and extending through larger ranges up to “3.00 to 4.00”. The data for the bars are as follows: 0.00 to 0.01: 35.5 0.01 to 0.02: 29.5 0.02 to 0.03: 10 0.03 to 0.04: 2.5 0.04 to 0.05: 5.5 0.05 to 0.06: 2 0.06 to 0.08: 4 0.08 to 0.10: 0.5 0.10 to 0.12: 0 0.12 to 0.14: 1 0.14 to 0.16: 1 0.16 to 0.18: 2 0.18 to 0.20: 0.5 0.20 to 0.22: 0 0.22 to 0.24: 0 0.24 to 0.26: 0 0.26 to 0.28: 0.5 0.28 to 0.30: 0.5 0.30 to 0.35: 0 0.35 to 0.40: 0.5 0.40 to 0.45: 0 0.45 to 0.50: 0 0.50 to 1.00: 0 1.00 to 1.50: 0 1.50 to 2.00: 0 2.00 to 2.50: 0 2.50 to 3.00: 0 3.00 to 4.00: 0 Note: All numerical data values are approximated.Hardened bubble pore size distribution of FA. Source(s): Authors’ own work
The vertical axis is labeled “Chord Length Frequency (percent)” and ranges from 0 to 40 in increments of 5 units. The horizontal axis is labeled “Chord Size (millimeters)” and shows multiple size intervals progressing from left to right, starting at “0.00 to 0.01” and extending through larger ranges up to “3.00 to 4.00”. The data for the bars are as follows: 0.00 to 0.01: 35.5 0.01 to 0.02: 29.5 0.02 to 0.03: 10 0.03 to 0.04: 2.5 0.04 to 0.05: 5.5 0.05 to 0.06: 2 0.06 to 0.08: 4 0.08 to 0.10: 0.5 0.10 to 0.12: 0 0.12 to 0.14: 1 0.14 to 0.16: 1 0.16 to 0.18: 2 0.18 to 0.20: 0.5 0.20 to 0.22: 0 0.22 to 0.24: 0 0.24 to 0.26: 0 0.26 to 0.28: 0.5 0.28 to 0.30: 0.5 0.30 to 0.35: 0 0.35 to 0.40: 0.5 0.40 to 0.45: 0 0.45 to 0.50: 0 0.50 to 1.00: 0 1.00 to 1.50: 0 1.50 to 2.00: 0 2.00 to 2.50: 0 2.50 to 3.00: 0 3.00 to 4.00: 0 Note: All numerical data values are approximated.Hardened bubble pore size distribution of FA. Source(s): Authors’ own work
The vertical axis is labeled “Chord Length Frequency (percent)” and ranges from 0 to 40 in increments of 5 units. The horizontal axis is labeled “Chord Size (millimeters)” and shows multiple size intervals progressing from left to right, starting at “0.00 to 0.01” and extending through larger ranges up to “3.00 to 4.00”. The data for the bars are as follows: 0.00 to 0.01: 24.5 0.01 to 0.02: 24.5 0.02 to 0.03: 13 0.03 to 0.04: 8.5 0.04 to 0.05: 5 0.05 to 0.06: 5.5 0.06 to 0.08: 5 0.08 to 0.10: 0.5 0.10 to 0.12: 2.5 0.12 to 0.14: 0.5 0.14 to 0.16: 0.5 0.16 to 0.18: 1 0.18 to 0.20: 2 0.20 to 0.22: 1.5 0.22 to 0.24: 0 0.24 to 0.26: 1.5 0.26 to 0.28: 0 0.28 to 0.30: 0 0.30 to 0.35: 0.5 0.35 to 0.40: 0.5 0.40 to 0.45: 0 0.45 to 0.50: 0 0.50 to 1.00: 0 1.00 to 1.50: 0 1.50 to 2.00: 0 2.00 to 2.50: 0 2.50 to 3.00: 0 3.00 to 4.00: 0 Note: All numerical data values are approximated.Hardened bubble pore size distribution of SF. Source(s): Authors’ own work
The vertical axis is labeled “Chord Length Frequency (percent)” and ranges from 0 to 40 in increments of 5 units. The horizontal axis is labeled “Chord Size (millimeters)” and shows multiple size intervals progressing from left to right, starting at “0.00 to 0.01” and extending through larger ranges up to “3.00 to 4.00”. The data for the bars are as follows: 0.00 to 0.01: 24.5 0.01 to 0.02: 24.5 0.02 to 0.03: 13 0.03 to 0.04: 8.5 0.04 to 0.05: 5 0.05 to 0.06: 5.5 0.06 to 0.08: 5 0.08 to 0.10: 0.5 0.10 to 0.12: 2.5 0.12 to 0.14: 0.5 0.14 to 0.16: 0.5 0.16 to 0.18: 1 0.18 to 0.20: 2 0.20 to 0.22: 1.5 0.22 to 0.24: 0 0.24 to 0.26: 1.5 0.26 to 0.28: 0 0.28 to 0.30: 0 0.30 to 0.35: 0.5 0.35 to 0.40: 0.5 0.40 to 0.45: 0 0.45 to 0.50: 0 0.50 to 1.00: 0 1.00 to 1.50: 0 1.50 to 2.00: 0 2.00 to 2.50: 0 2.50 to 3.00: 0 3.00 to 4.00: 0 Note: All numerical data values are approximated.Hardened bubble pore size distribution of SF. Source(s): Authors’ own work
The vertical axis is labeled “Chord Length Frequency (percent)” and ranges from 0 to 40 in increments of 5 units. The horizontal axis is labeled “Chord Size (millimeters)” and shows multiple size intervals progressing from left to right, starting at “0.00 to 0.01” and extending through larger ranges up to “3.00 to 4.00”. The data for the bars are as follows: 0.00 to 0.01: 33 0.01 to 0.02: 38 0.02 to 0.03: 12.5 0.03 to 0.04: 3 0.04 to 0.05: 1.5 0.05 to 0.06: 4 0.06 to 0.08: 5 0.08 to 0.10: 0.5 0.10 to 0.12: 0 0.12 to 0.14: 0.5 0.14 to 0.16: 0 0.16 to 0.18: 0 0.18 to 0.20: 0 0.20 to 0.22: 0 0.22 to 0.24: 0 0.24 to 0.26: 0 0.26 to 0.28: 0 0.28 to 0.30: 0 0.30 to 0.35: 0 0.35 to 0.40: 0 0.40 to 0.45: 0 0.45 to 0.50: 0 0.50 to 1.00: 0 1.00 to 1.50: 0 1.50 to 2.00: 0 2.00 to 2.50: 0 2.50 to 3.00: 0 3.00 to 4.00: 0 Note: All numerical data values are approximated.Hardened bubble pore size distribution of SF-FA. Source(s): Authors’ own work
The vertical axis is labeled “Chord Length Frequency (percent)” and ranges from 0 to 40 in increments of 5 units. The horizontal axis is labeled “Chord Size (millimeters)” and shows multiple size intervals progressing from left to right, starting at “0.00 to 0.01” and extending through larger ranges up to “3.00 to 4.00”. The data for the bars are as follows: 0.00 to 0.01: 33 0.01 to 0.02: 38 0.02 to 0.03: 12.5 0.03 to 0.04: 3 0.04 to 0.05: 1.5 0.05 to 0.06: 4 0.06 to 0.08: 5 0.08 to 0.10: 0.5 0.10 to 0.12: 0 0.12 to 0.14: 0.5 0.14 to 0.16: 0 0.16 to 0.18: 0 0.18 to 0.20: 0 0.20 to 0.22: 0 0.22 to 0.24: 0 0.24 to 0.26: 0 0.26 to 0.28: 0 0.28 to 0.30: 0 0.30 to 0.35: 0 0.35 to 0.40: 0 0.40 to 0.45: 0 0.45 to 0.50: 0 0.50 to 1.00: 0 1.00 to 1.50: 0 1.50 to 2.00: 0 2.00 to 2.50: 0 2.50 to 3.00: 0 3.00 to 4.00: 0 Note: All numerical data values are approximated.Hardened bubble pore size distribution of SF-FA. Source(s): Authors’ own work
The vertical axis is labeled “Average Chord Length (micrometers)” and ranges from 0 to 200 in increments of 50 units. The horizontal axis is labeled “Sample Number” and shows four categories: J Z, F A, S F, and S F-F A. A legend at the top shows four categories: J Z, F A, S F, and S F-F A. Each bar displays a value labeled at the top. The data for the bars are as follows: J Z: 138 F A: 102 S F: 95 S F-F A: 70Average bubble diameter of shotcrete. Source(s): Authors’ own work
The vertical axis is labeled “Average Chord Length (micrometers)” and ranges from 0 to 200 in increments of 50 units. The horizontal axis is labeled “Sample Number” and shows four categories: J Z, F A, S F, and S F-F A. A legend at the top shows four categories: J Z, F A, S F, and S F-F A. Each bar displays a value labeled at the top. The data for the bars are as follows: J Z: 138 F A: 102 S F: 95 S F-F A: 70Average bubble diameter of shotcrete. Source(s): Authors’ own work
The vertical axis is labeled “Spacing Factor (millimeters)” and ranges from 0 to 0.3 in increments of 0.1 units. The horizontal axis is labeled “Sample No.” and shows four categories: J Z, F A, S F, and S F-F A. A legend at the top shows four categories: J Z, F A, S F, and S F-F A. Each bar displays a value labeled at the top. The data for the bars are as follows: J Z: 0.232 F A: 0.174 S F: 0.186 S F-F A: 0.136Shotcrete bubble spacing factor. Source(s): Authors’ own work
The vertical axis is labeled “Spacing Factor (millimeters)” and ranges from 0 to 0.3 in increments of 0.1 units. The horizontal axis is labeled “Sample No.” and shows four categories: J Z, F A, S F, and S F-F A. A legend at the top shows four categories: J Z, F A, S F, and S F-F A. Each bar displays a value labeled at the top. The data for the bars are as follows: J Z: 0.232 F A: 0.174 S F: 0.186 S F-F A: 0.136Shotcrete bubble spacing factor. Source(s): Authors’ own work
3.4 Pore structure
The Mercury Intrusion Porosimetry (MIP) test is widely recognized as a fundamental technique for evaluating the pore characteristics of cementitious materials. These pores play a crucial role in determining capillary action, as well as the speed at which free water is absorbed and removed within the material. The pores present in cement paste are typically classified based on their size into four main categories: gel pores (d ≤ 10 nm), medium capillary pores (10 nm < d < 100 nm), large capillary pores (100 nm ≤ d ≤ 1,000 nm), and air pores ((d ≥ 1,000) (Deng, He, Lu, Wang, & Hu, 2023; Singh, Kumar, & Goyal, 2019; Yuan, Peng, & Li, 2021).
Figures 15–17 present the results of the MIP test, which indicate that mineral admixtures can quantitatively optimize the pore structure parameters. On the one hand, mineral admixtures significantly reduce the total porosity and total pore volume of shotcrete, and the effect of composite admixture is more remarkable. The total porosity of the control group at 28d is 15.23%, while that of the FA group decreases to 12.05%, the SF group to 9.85%, and the composite admixture group has the lowest porosity, which is 9.49%. On the other hand, it can be seen from Figure 16 that mineral admixtures change the internal pore size distribution of shotcrete. Under the action of admixtures, the overall volume fractions of gel pores and capillary pores inside the specimens of each group from large to small are as follows: JZ > SF > FA > SF-FA, which are 59.16%, 57.47%, 56.19%, and 53.08% respectively. The results of the SF and FA groups are similar, and the difference between the SF-FA group and the JZ group is the most significant.
The illustration contains two side-by-side multi-line graphs. In both graphs, the horizontal axis is labeled “Pore Diameter (nanometers)” and ranges from 1 to 1000000 in a logarithmic scale, and the values are the multiples of 10. A legend in the upper right identifies four lines in both graphs: “J Z” marked with black circles, “F A” marked with blue diamonds, “S F” marked with green crosses, and “S F-F A” marked with purple squares. In the left graph, the vertical axis is labeled “d V over d log D (milliliters per gram)” and ranges from 0 to 0.15 in increments of 0.03 units. All four lines follow almost the same path and are almost close to one another. The lines begin at about 1 nanometer with values ranging from 0.03 to 0.05. The lines show a general decrease to a minimum around 10 nanometers with values near 0.01. They then rise to peaks between 40 and 100 nanometers, with peak values ranging from 0.05 to 0.06. After the peaks, all lines decrease, reaching as low as 0.005 around 10000 nanometers. After 100000 nanometers, the lines show a slight upturn, with values rising to approximately 0.01 to 0.03. In the right graph, the vertical axis is labeled “Cumulative Pore Volume (milliliters per gram)” and ranges from 0 to 0.15 in increments of 0.03 units. The “J Z” line begins at 0.08 at 3.5 nanometers and decreases steadily to 0.07 at 10 nanometers. The line continues to decrease, reaching 0.04 at 100 nanometers, then shows a gradual decline to 0.02 at 10000 nanometers, finally approaching 0 by 1000000 nanometers. The “F A” line begins at 0.07 at 3.5 nanometers and decreases to 0.06 at 10 nanometers. It continues declining to 0.03 at 100 nanometers, then shows a gradual decrease, reaching 0.01 at 10000 nanometers and approaching 0 by 1000000 nanometers. The “S F” line begins at 0.07 at 3.5 nanometers and decreases to 0.06 at 10 nanometers. The line continues to decline, reaching 0.03 at 100 nanometers, then gradually decreases to 0.01 at 10000 nanometers, finally approaching 0 by 1000000 nanometers. The “S F-F A” line begins at 0.06 at 3.5 nanometers and decreases to 0.05 at 10 nanometers. It shows a steady decrease to 0.02 at 100 nanometers, then continues declining gradually to 0.01 at 10000 nanometers, ending at 0 at 1000000 nanometers. Note: All numerical data values are approximated.Differential curve and integral curve of shotcrete. Source(s): Authors’ own work
The illustration contains two side-by-side multi-line graphs. In both graphs, the horizontal axis is labeled “Pore Diameter (nanometers)” and ranges from 1 to 1000000 in a logarithmic scale, and the values are the multiples of 10. A legend in the upper right identifies four lines in both graphs: “J Z” marked with black circles, “F A” marked with blue diamonds, “S F” marked with green crosses, and “S F-F A” marked with purple squares. In the left graph, the vertical axis is labeled “d V over d log D (milliliters per gram)” and ranges from 0 to 0.15 in increments of 0.03 units. All four lines follow almost the same path and are almost close to one another. The lines begin at about 1 nanometer with values ranging from 0.03 to 0.05. The lines show a general decrease to a minimum around 10 nanometers with values near 0.01. They then rise to peaks between 40 and 100 nanometers, with peak values ranging from 0.05 to 0.06. After the peaks, all lines decrease, reaching as low as 0.005 around 10000 nanometers. After 100000 nanometers, the lines show a slight upturn, with values rising to approximately 0.01 to 0.03. In the right graph, the vertical axis is labeled “Cumulative Pore Volume (milliliters per gram)” and ranges from 0 to 0.15 in increments of 0.03 units. The “J Z” line begins at 0.08 at 3.5 nanometers and decreases steadily to 0.07 at 10 nanometers. The line continues to decrease, reaching 0.04 at 100 nanometers, then shows a gradual decline to 0.02 at 10000 nanometers, finally approaching 0 by 1000000 nanometers. The “F A” line begins at 0.07 at 3.5 nanometers and decreases to 0.06 at 10 nanometers. It continues declining to 0.03 at 100 nanometers, then shows a gradual decrease, reaching 0.01 at 10000 nanometers and approaching 0 by 1000000 nanometers. The “S F” line begins at 0.07 at 3.5 nanometers and decreases to 0.06 at 10 nanometers. The line continues to decline, reaching 0.03 at 100 nanometers, then gradually decreases to 0.01 at 10000 nanometers, finally approaching 0 by 1000000 nanometers. The “S F-F A” line begins at 0.06 at 3.5 nanometers and decreases to 0.05 at 10 nanometers. It shows a steady decrease to 0.02 at 100 nanometers, then continues declining gradually to 0.01 at 10000 nanometers, ending at 0 at 1000000 nanometers. Note: All numerical data values are approximated.Differential curve and integral curve of shotcrete. Source(s): Authors’ own work
The vertical axis is labeled “Porosity (percent)” and ranges from 0 to 20 in increments of 2 units. The horizontal axis is labeled “Sample No.” and shows four categories: J Z, F A, S F, and S F-F A. Each bar displays a value labeled at the top. The data for the bars are as follows: J Z: 15.23 F A: 12.05 S F: 9.85 S F-F A: 9.49Specimen porosity. Source(s): Authors’ own work
The vertical axis is labeled “Porosity (percent)” and ranges from 0 to 20 in increments of 2 units. The horizontal axis is labeled “Sample No.” and shows four categories: J Z, F A, S F, and S F-F A. Each bar displays a value labeled at the top. The data for the bars are as follows: J Z: 15.23 F A: 12.05 S F: 9.85 S F-F A: 9.49Specimen porosity. Source(s): Authors’ own work
The vertical axis is labeled “Volume Percentage (%)” and ranges from 0 to 100 in increments of 20 units. The horizontal axis is labeled “Specimen No.” and shows four categories: J Z, S F, F A, and S F - F A. A legend at the top indicates three pore size ranges: 0–10 nm, 10–100 nm, and 100–1000 nm. Each specimen category is represented by a stacked bar divided into three segments, with lines connecting the corresponding segments across all four bars. The data for the stacked bars are as follows: J Z: 0–10 nm: 0–12; 10–100 nm: 12–59; 100–1000 nm: 59–80.S F: 0–10 nm: 0–12; 10–100 nm: 12–57; 100–1000 nm: 57–78.F A: 0–10 nm: 0–12; 10–100 nm: 12–56; 100–1000 nm: 56–76.S F - F A: 0–10 nm: 0–14; 10–100 nm: 14–55; 100–1000 nm: 55–76. Note: All numerical values are approximate.Pore volume fraction. Source(s): Authors’ own work
The vertical axis is labeled “Volume Percentage (%)” and ranges from 0 to 100 in increments of 20 units. The horizontal axis is labeled “Specimen No.” and shows four categories: J Z, S F, F A, and S F - F A. A legend at the top indicates three pore size ranges: 0–10 nm, 10–100 nm, and 100–1000 nm. Each specimen category is represented by a stacked bar divided into three segments, with lines connecting the corresponding segments across all four bars. The data for the stacked bars are as follows: J Z: 0–10 nm: 0–12; 10–100 nm: 12–59; 100–1000 nm: 59–80.S F: 0–10 nm: 0–12; 10–100 nm: 12–57; 100–1000 nm: 57–78.F A: 0–10 nm: 0–12; 10–100 nm: 12–56; 100–1000 nm: 56–76.S F - F A: 0–10 nm: 0–14; 10–100 nm: 14–55; 100–1000 nm: 55–76. Note: All numerical values are approximate.Pore volume fraction. Source(s): Authors’ own work
The MIP test results reveal the microscopic mechanism by which mineral admixtures inhibit shrinkage through pore structure refinement. As shown in Figures 15–17, the incorporation of SF and FA, particularly in combination, significantly optimizes the pore structure parameters of shotcrete. On the one hand, mineral admixtures notably reduce the total porosity and total pore volume, with the group SF-FA exhibiting the most pronounced effect. The total porosity of the group JZ at 28 days was 15.23%, while that of the FA group, SF group, and SF-FA group decreased to 12.05%, 9.85%, and 9.49%, respectively. On the other hand, mineral admixtures alter the internal pore size distribution, leading to a reduction in the overall volume fractions of both gel pores and capillary pores.
According to the model proposed by Zhang et al. (2012), the shrinkage strain (εw) of cement-based materials depends simultaneously on its internal relative humidity (Ln(RH)) and pore structure characteristics (vp), and can be expressed as the following functional relationship (Eq. 1). In the equation (1), the vp is pore structure influence factor, whose physical meaning is the volume fraction of interconnected pores capable of forming menisci and generating effective capillary tension under a given RH. This model reveals that shrinkage is regulated by two factors: the rate of RH decrease and the amount of effective pores that can participate in forming the capillary stress network (vp).
Experimental data indicate that the combined incorporation of SF and FA achieves efficient shrinkage suppression through the synergistic optimization of the aforementioned two factors. First, in terms of humidity regulation, as shown in Figures 5–8, under drying conditions, the SF-FA composite group exhibits the slowest initial rate of RH decline. This is because SF fills gel pores at the nanoscale, while FA fills capillary pores at the micron scale. This “dual-scale filling” effect not only reduces porosity but, more importantly, significantly refines the pore size gradation and reduces pore connectivity, thereby increasing transport resistance and creating a “throttling effect.” This effectively retards the decline in internal humidity, i.e. it reduces the decay rate of ln(RH) in Equation (1). Second, in terms of pore structure regulation, MIP results show that the microstructure formed by the SF-FA composite system exhibits a more uniform pore size distribution, along with a reduced proportion of gel pores and capillary pores. This implies that the composite system overall decreases the volume fraction of “effective pores” capable of generating capillary stress under a given RH. Consequently, the total net capillary stress generated per unit change in internal humidity is reduced, thereby achieving a “stress-relief effect”.
4. Conclusion
This study delved into the impact of mineral admixtures on the shrinkage deformation of shotcrete and delved into the underlying reasons for this influence from a microscopic viewpoint. The findings of this research lead to the following conclusions:
When utilized independently or in conjunction, SF and FA demonstrate the ability to significantly improve the 28d compressive strength of shotcrete. This enhancement is primarily attributed to the micro-aggregate effect and pozzolanic reaction facilitated by these additives. Nevertheless, the sluggish hydration kinetics of FA render its standalone application less favorable for the early strength development of shotcrete.
Mineral admixtures significantly inhibit the shrinkage deformation of shotcrete by reconstructing the microporous structure and regulating the hydration process. In the experiment, the development of the shrinkage deformation of shotcrete with age shows a two-stage pattern of “rapid growth stage in the early stage and decelerated development stage in the later stage”. The rapid growth stage of shrinkage corresponds to the humidity saturation period, during which the shrinkage is mainly due to the chemical shrinkage of cement hydration. The decelerated development stage corresponds to the humidity attenuation period, and the shrinkage is mainly caused by self-drying. At the age of 28 days, the shrinkage rate of the group containing admixtures is lower than that of the control group. Among them, the SF-FA composite admixture group shows the best inhibitory effect - the shrinkage rate of the sealed specimens is 23.72% lower than that of the JZ group, and the shrinkage rate of the dry specimens is 17.76% lower. This reduction in shrinkage deformation is beneficial as it mitigates the negative impact on the durability and reliability of shotcrete.
The shrinkage deformation of shotcrete is significantly influenced by its bubble characteristics and pore structure. Supplementary materials like SF and FA play a crucial role in enhancing the distribution of bubbles of varying sizes within the shotcrete matrix. The increased presence of numerous small bubbles helps mitigate the impact of capillary tension and surface tension on the solid-phase particles of shotcrete, providing a buffering effect within the material. Simultaneously, mineral admixtures synergistically regulate both the humidity field and the stress field. On one hand, the “dual-scale filling” by SF and FA optimizes the pore size distribution and connectivity, creating a “throttling effect” that significantly retards the rate of internal humidity decline. On the other hand, SF and FA also reduce the number of gel pores and capillary pores in shotcrete, decreasing the volume fraction of effective pores (vp) which lowers the driving stress for shrinkage and produces a “stress-relief effect.” The SF-FA composite system demonstrates the most pronounced synergistic optimization of the aforementioned two parameters, thus exhibiting the best performance in shrinkage inhibition.

