Experimental Study on Flexural Fatigue Resistance of Recycled Fine Aggregate Concrete Incorporating Calcium Sulfate Whiskers

Abstract

In order to study the flexural fatigue resistance of calcium sulfate whisker-modified recycled fine aggregate concrete (RFAC), flexural fatigue cyclic loading tests at different stress levels (0.6, 0.7, and 0.9) considering a calcium sulfate whisker (CSW) admixture as the main influencing factor were designed. Furthermore, the fatigue life was analyzed, and fatigue equations were established using the three-parameter Weibull distribution function theory. In addition, the micro-morphology of CSW-modified recycled fine aggregate concrete was observed and analyzed through Scanning Electron Microscopy (SEM), and the strengthening and toughening mechanisms of CSW on recycled fine aggregate concrete were further explored. The test results demonstrate that the inclusion of recycled fine aggregate reduces the fatigue life of concrete, while the incorporation of CSW can effectively improve the fatigue life of the recycled fine aggregate concrete, where 1% of CSW modification can extend the fatigue life of recycled fine aggregate concrete by 56.5%. Furthermore, the fatigue life of concrete under cyclic loading decreases rapidly as the maximum stress level increases. Fatigue life equations were established with double logarithmic curves, and P-S-N curves considering different survival probabilities (p = 0.5, 0.95) were derived. Microscopic analyses demonstrate that the CSW has a “bridging” effect at micro-seams in the concrete matrix, delaying the generation and enlargement of micro-cracks in the concrete matrix, thus resulting in improved mechanical properties and flexural fatigue resistance of the recycled fine aggregate concrete.

1. Introduction

Concrete is a traditional material in the construction industry, which presents several resource and ecological issues, such as increased carbon emissions, shortages of sand and stone resources, and large amounts of waste during construction and demolition [1,2]. To achieve low-carbon and sustainable development, waste concrete can be crushed and sifted into recycled materials to prepare new concrete, called recycled concrete. This approach can not only help to solve the waste concrete disposal problem but also alleviate short-term natural resource and environmental pollution issues, which is in alignment with the goal of “green and sustainable development of the construction industry” [3,4,5,6]. Previous research on recycled aggregates has mainly focused on the mechanical properties and durability of recycled coarse aggregates in concrete, and substantial progress has been made [7,8]. As natural river sand has become increasingly scarce and its overexploitation has led to economic depletion and environmental degradation, the use of recycled fine aggregate (RFA) to replace natural fine aggregate (NFA) in the preparation of concrete is becoming increasingly important for the green and sustainable development of the construction industry [9,10,11,12].

In reality, static load failure rarely occurs in concrete structures, while fatigue failure under cyclic loads more often occurs [13,14]. To date, researchers have studied the compression and fatigue behavior of recycled concrete. For example, Xiao J. et al. [15] have found no significant difference between the compressive fatigue behavior of 100% recycled concrete and natural concrete under uniaxial compressive loading; however, at the same stress level, the fatigue life of recycled concrete was lower than that of natural concrete. Peng Q. et al. [16] have investigated the effect of a different recycled aggregate replacement rate on the fatigue behavior of recycled concrete through compressive fatigue residual strength tests. It was observed that the compressive fatigue life and residual strength decreased gradually with an increase in the level of recycled aggregate. Thomas C. et al. [17] have studied the fatigue properties of recycled concrete under repetitive compressive loading with different recycled aggregate substitution rates. They revealed that the incorporation of recycled aggregate increased the loss of concrete stiffness and shortened the fatigue life. Saini B. S. et al. [18], by investigating the flexural fatigue properties of self-compacting concrete with 100% recycled aggregate replacement, showed that the shape parameters obtained for 100% recycled aggregate self-compacting concrete were significantly lower and the variation in fatigue life distribution was greater when compared to natural aggregate self-compacting concrete.

Researchers have found that the mechanical and durability properties of recycled concrete can be significantly improved by strengthening the recycled aggregates through chemical solution immersion [19], adding reactive minerals [20,21], and externally mixing various types of fibers. Among them, adding fibers to recycled concrete is a common method to compensate for its brittle damage [22]. Bawa S. et al. [23] have studied the flexural fatigue characteristics of self-compacting concrete with a blend of steel fibers and polypropylene fibers. They noted that a blend of steel and polypropylene fibers in a ratio of 1:3 exhibited a higher fatigue life when the fiber volume fraction was 1%. Tan Y et al. [24] added steel fibers to RCA, and the fatigue flexural strength of steel fiber recycled concrete was even better than that of natural concrete when steel fibers were incorporated at 1%. Moreover, at the same stress level, the fatigue strain development rate of recycled concrete with steel fibers was slower than that of recycled concrete, and the flexural fatigue performance was improved. Yao Y et al. [25] have carried out an investigation of the synergistic action of recycled steel fibers and silica fume on the mechanical and fatigue properties of recycled concrete. The combined use of recycled steel fibers and silica fume greatly improved the impact life of recycled concrete. Surong L. et al. [26] have researched the effect of nano-SiO₂ on the single-week fatigue performance of recycled concrete. They found that nano-SiO₂ can effectively fill the pores of concrete and make the structure denser, and the fatigue life was improved by 73% compared with that of recycled concrete.

The above results indicate that the incorporation of certain fibers or nanomaterials can improve the fatigue performance of recycled concrete by inhibiting the expansion of cracks within the matrix, filling the internal pores of the concrete to make the structure more dense, and so on. As a new, inexpensive inorganic microfiber, CSW has the advantages of high strength and modulus and is considered a low-cost, non-toxic, and green material [27,28]. It is now widely used in the development of rubber, paper, plastics, and construction materials, as well as in other areas [29]. Pan Q. et al. [30] and Li X. et al. [31] have investigated the mechanical properties of CSW-reinforced cement-based composite materials. Their results indicated that adding CSW can effectively enhance the compressive and flexural strengths of cementitious composites. Cao K. et al. [32] compared CSW and nano-SiO₂ when incorporated into cement-based composite materials and showed that CSW exhibited better tensile and flexural properties than nano-SiO₂, with bending and splitting tensile strengths increasing by 79.9% and 34.8%, respectively, at 1% CSW. Sheng Z et al. [33] found that, when 1% CSW was added to phosphogypsum, CSW was closely combined with the gypsum crystals, and the flexural strength increased by 80% when compared to the ceramic tile without CSW. Ma F. et al. [34] have explored the effect of CSW content on the mechanical properties of paraffin (PA)/gypsum composites. It was observed that the introduction of CSW significantly improved the strength of the composites. The best mechanical properties of the composites were obtained when the CSW content was 3.5%. M. Liu. et al. [35] have observed that the carbonation resistance significantly increased in concrete mixed with CSW, with the increase in carbonation resistance performance first increasing with CSW content, then decreasing when the CSW was combined at a rate greater than 5 kg/m³. Zhang J. et al. [36] have noted that the chloride migration coefficient of concrete mixed with CSW showed a decrease followed by an increase with increasing admixture, reaching a minimum at 3 kg/m³ and a reduction of 23.08% compared to NFA, with the addition of CSW reducing the concrete macropore ratio and increasing the chloride resistance. Furthermore, through microscopic tests, it was found that the improvement effect of CSW on cement-based composite materials and concrete is not only due to the microfiber effect of CSW but also to the filling effect of CSW as an inorganic filler [32,35] and the nucleation effect [36]. Therefore, using CSW as a mineral microfiber to enhance the properties of RFAC is a relatively new line of research.

For this paper, mechanical and flexural fatigue tests were carried out to study the specimens of recycled fine aggregate concrete, including CSW. Based on the flexure fatigue test results, three-parameter Weibull distribution function theory was selected to analyze the fatigue life of the calcium sulfate whisker recycled fine aggregate concrete (CSWRF), and fatigue life equations were established to investigate the fatigue performance of RFAC with a replacement rate of 20% at different CSW mass percentages (0.5%, 1%, 2%, 3%), considering the P-S-N curves under different survival probabilities (p = 0.5, 0.95), allowing for the development of a double logarithmic fatigue equation to predict the fatigue life at different stress levels. In addition, SEM was used to observe the microstructure of CSWRF in order to investigate the mechanisms by which CSW can improve the performance of RFAC.

2. Materials and Methods

2.1. Experimental Materials

The cementitious materials used were P.O42.5 ordinary Portland cement produced by Wuhan Huaxin Co., Ltd. and Grade I fly ash produced by a company in Zhengzhou, Henan Province. The coarse aggregate was 5–20 mm of continuously graded limestone gravel and river sand with grain sizes not larger than 5 mm was used for NFA. The RFA was obtained by crushing discarded blocks. In order to avoid the influence of the modulus of fineness of the aggregate on the test results, an aggregate sieving machine was used to separate the RFA with different particle sizes so that it matched the NFA grading. After soaking in water for 24 h, the aggregate was taken out and put in a cool place indoors to dry, such that it reached a saturated surface drying state (24 h mass loss rate < 1%). The primary performance indicators of fine aggregates can be seen in

Table 1. Fine aggregate performance indicators.

Aggregate Types	Apparent Density (kg/m3)	Stack Density (kg/m3)	Water Absorption (%)	Crushing Indicator
NFA	2536	1368	2.2%	12.6%
RFA	2312	1226	13.1%	19.22%

. The RFA preparation process is shown in Figure 1. The macroscopic appearance and particle gradation of the fine aggregates are shown in Figure 2 and Figure 3. To ensure sufficient workability in the fresh concrete, a polycarboxylic acid high-efficiency water reducer was used with a water reduction rate of 20%. CSW refers to anhydrous CSW produced by a company in Guangdong, China which appears as a white, fluffy powder. The CSW performance indices, as well as its macroscopic and microscopic morphology, are shown in

Table 2. CSW performance indices.

Chemical Formula	Average Diameter (μm)	Average Length (μm)	Density (g/cm3)	Water Soluble (ppm)	Tensile Strength (GPa)	Elastic Modulus (GPa)	PH
CaSO4	1–8	30–200	2.69	<1200	20.5	178	7

and Figure 4, respectively.

2.2. Mixing Ratio and Test Programme

According to the design specification requirements of JGJ 55-2011 [37], the design strength of concrete in this test was C40, and the water-cement ratio was 0.45. The fixed substitution rate of RFA was 20%, and the mixing amount of CSW (in terms of the mass percentage of the total cementitious material) was 0%, 0.5%, 1%, 2%, or 3%. The detailed mixing ratios are given in

Table 3. CSWRF Matching Ratios (kg/m³).

Project	Cement	Fly Ash	Coarse Aggregates	Fine Aggregates		CSW	Water
				NFA	RFA
NC	328.00	82.00	1173.00	632.00	0.00	0.00	185.00
RF	328.00	82.00	1173.00	506.00	126.00	0.00	185.00
C0.5RF	328.00	82.00	1173.00	506.00	126.00	2.05	185.00
C1RF	328.00	82.00	1173.00	506.00	126.00	4.10	185.00
C2RF	328.00	82.00	1173.00	506.00	126.00	8.20	185.00
C3RF	328.00	82.00	1173.00	506.00	126.00	12.30	185.00

.

To avoid the problems of uneven distribution and agglomeration of CSW, the CSW was first added to water to prepare a dispersion liquid. The dispersion liquid was added to a mixer in which the homogeneous cementitious materials and aggregates had already been mixed. The specimens were cured in modls for 1 day and then de-molded, put into a standard curing room (average temperature of 20 ± 2 °C, relative humidity of 95%), and cured for 28 days. The process of specimen preparation is shown in Figure 5.

For each group, three 100 mm × 100 mm × 100 mm cubic specimens and three 100 mm × 100 mm × 400 mm prismatic specimens were utilized for mechanical property testing. The mechanical property tests were carried out in accordance with GB/T 50081-2002 [38]. The compressive test was loaded at 0.5 MPa/s, the flexural test was loaded at 0.05 MPa/s, and the load was increased uniformly until the specimen was destroyed. The data for each group of tests was recorded, and the average value was calculated.

For each group, twelve prismatic specimens were utilized for the flexure fatigue test. A vertical MTS Labdmark electro-hydraulic servo fatigue tester was used prior to the flexure fatigue test, and the maximum and minimum loading values for the flexure fatigue test were first set according to the flexural strength obtained in a four-point bending test. Equal-amplitude sine wave fatigue loading was applied to the specimens in equal stress control mode, and the fatigue test frequency was controlled at 10 Hz (i.e., 600 sine wave string loading cycles per minute). Stress levels (S) of 0.6, 0.7, and 0.8 were selected for this test, and the flexural fatigue test loading process is shown in Figure 6. Before the test was formally started, the specimens were first pre-compressed to avoid test errors caused by poor contact and stress concentration in the specimens. The test was stopped when the specimen could not continue to withstand the load damage, and the fatigue life was recorded for each group of specimens at different stress levels.

SEM testing of the CSWRF was carried out to analyze the toughening mechanisms of recycled fine aggregate concrete by CSW.

3. Results and Discussion

3.1. Mechanical Characteristics of CSWRF

Figure 7 demonstrates the average compressive strength and flexural strength of RFAC at 28 days under varying CSW content.

From Figure 7, it can be seen that the mechanical strength of the RF group was reduced compared to the NC group, and the compressive and flexural strengths of the RFAC were enhanced after doping with CSW. When the CSW doping rate was less than 1%, the mechanical strength of RFAC increased with an increase in CSW doping. The overall growth rate of compressive and flexural strength of CSWRF was the highest when 1% CSW was added, and the growth rate of compressive and flexural strength of C1RF was 6.58% and 11.63% higher than those of RF, respectively, and even exceeded the compressive and flexural strength of NC by 1.7% and 5.1%. This is due to the microfiber and filling effects of CSW [31,32,33,34]: on the one hand, as CSW acts as microfiber, when the specimen is loaded, CSW plays a “bridging” role inside the concrete, which will form a reverse stress at the crack tip and consume the energy required for crack generation [30], thus delaying the expansion of cracks within the matrix. On the other hand, as an inorganic microaggregate, CSW has a smaller size to play a filling role inside the concrete, allowing it to fill into the smaller pores inside the recycled concrete and improve the internal structure. However, it is not the case that more CSW provides better results; instead, an optimal mixing amount was observed. When the CSW mixing amount was higher than 1%, the compressive strength and flexural strength of RFAC with an increase in CSW were reduced. In particular, when the CSW dosage reached 3%, the mechanical strength of C3RF was even lower than that of RF. This is due to the fact that when the CSW dosage is too high, the CSW cannot be evenly dispersed inside the concrete, and the internal pores of the concrete not only cannot become well-filled, but also the whisker agglomeration phenomenon also occurs, resulting in a reduction in the strength of the concrete [34].

3.2. Analysis of Specimen Fatigue Damage Pattern

From the point of view of the whole fatigue damage process, after the cyclic loading on the specimen began, the first place where the micro-cracks appeared was in the specimen between the two loading points of the lower tensile zone defective region. With an increase in the number of cyclic loadings, the micro-cracks gradually expanded and connected to the macroscopic cracks until the end of the fatigue loading, at which point the cracks had expanded throughout the entire specimen, with specimen fatigue damage breaking into two parts, showing the obvious characteristics of brittle damage [39]. The bonding surface of sand and cement mortar is a weak surface, which often produces bonding joints, and the admixture of RFA can increase the weak surface between cement mortar, making the crack development of RFAC more rapid than that in ordinary concrete under the action of cyclic loading. While the destruction process of CSW-added recycled fine aggregate concrete was basically the same as that of unadulterated recycled fine aggregate concrete, which also showed brittle destruction characteristics, CSW played the role of a microfiber inside the concrete, absorbing the energy released from crack expansion [40] and thus retarding the crack expansion rate. As such, the flexural fatigue destruction process of CSWRF specimens was longer and smoother.

3.3. Fatigue Test Results and Analysis

Fatigue loading tests were conducted at three different stress levels (S = 0.6, 0.7, and 0.8), and the flexural fatigue life of each RFAC specimen with different CSW doping was measured, as shown in

Table 4. Specimen fatigue life test results.

Project	S	N1/Second	N2/Second	N3/Second	N4/Second	Ñ/Second
NC	0.6	190,243	259,072	306,251	451,789	301,839
	0.7	12,900	24,156	42,637	59,982	34,919
	0.8	1728	3327	6139	9125	5080
RF	0.6	80,874	149,003	211,725	335,672	194,319
	0.7	8692	16,725	29,028	43,485	24,483
	0.8	1331	2142	3890	4482	2961
C0.5RF	0.6	126,926	213,786	228,903	351,003	230,155
	0.7	10,307	20,394	33,187	51,326	28,804
	0.8	1604	3067	4192	7089	3988
C1RF	0.6	151,908	245,596	348,007	470,789	304,075
	0.7	19,820	27,089	52,707	68,311	41,982
	0.8	2468	4132	6655	8908	5541
C2RF	0.6	126,344	199,872	320,984	399,189	261,597
	0.7	13,720	25,519	39,819	60,181	34,810
	0.8	1805	2795	55641	7932	4543
C3RF	0.6	81,722	159,871	241,772	373,259	214,156
	0.7	16,510	21,078	30,862	53,972	30,581
	0.8	941	2012	4181	6673	3452

. In the table, N₁~N₄ denote the fatigue life under the same stress level in the same group in descending order. In the flexure fatigue test, due to the non-homogeneity of the concrete material itself [41,42], there was a certain degree of variability even when the same batch of raw materials was used to prepare the specimens. As such, the cyclic load situation compared to the static load situation was more complex, leading to difficulties in accurately predicting the fatigue life of concrete. The average fatigue life Ñ for each group of specimens at different stress levels was obtained from the overall fatigue data, as detailed in Table 4 and shown three-dimensionally in Figure 8.

From Figure 8, it can be observed that the fatigue life of CSWRF with different ratios varied greatly with the stress level, and the fatigue life was mainly controlled by the magnitude of S and decreased with increasing S. This is due to the fact that a higher stress level accelerates the rate of crack propagation, which leads to the appearance of more cumulative cracks within the concrete, ultimately accelerating the failure damage of the concrete [24]. At the concrete proportioning level, the incorporation of RFA at the same stress level reduced the flexural fatigue life of the concrete, with RF fatigue life decreasing by 35.62% compared to NC at a stress level of 0.6. The reason for the decreased fatigue life in RF is two-fold [12]: First, the RFA mainly includes sand particles, cement stone particles, and a small amount of broken stones with cement mortar attached to the surface formed after the mortar body is broken, leading to high pore space, loose internal structure, and the overall performance being inferior to that of NFA. Second, as the incorporation of RFA leads to more initial defects within the recycled fine aggregate concrete, the junctions between RFA and other materials are relatively more fragile, and these interfaces are prone to cracking under fatigue loading, thus affecting the fatigue life of the concrete specimens. However, with the incorporation of CSW, the RFAC fatigue life was enhanced. In particular, the fatigue life reached a maximum value of 304,075 times when the CSW dosage was 1%, which was 1.565 times higher than that of the RF group at a stress level of 0.6. At this time, CSW was uniformly dispersed in the concrete and formed micro-units within the concrete [32,33,34,35], which resulted in better bending deformation capacity and increased fatigue life of the specimens after being subjected to cyclic loading. In addition, with an increase in CSW dosage, the fatigue life of RFAC under the same stress level presented a trend of increasing and then decreasing, consistent with the trend observed in the static loading test. This is because when the amount of CSW is too large, the excessive microfiber cannot be uniformly distributed and may even cause agglomeration [43], leading to insufficient densification of the specimen and the formation of more pore spaces, thus decreasing the concrete’s ability to withstand cyclic loading.

4. Flexure Fatigue Life Estimation

4.1. Life Distribution Function of Three-Parameter Weibull Distribution

As the three-parameter Weibull distribution yields a fatigue life when the reliability is 100%, it can ensure superior processing of the test data and allow for a more accurate description of the fatigue life of concrete [39]. In the fatigue life assessment characterized by loss, the three-parameter Weibull distribution model showed higher fitting accuracy; furthermore, its physical meaning and calculation results are more reasonable. Therefore, in this experiment, the three-parameter Weibull distribution was used as the theoretical basis to study and analyze the CSWRF fatigue life data. The three-parameter Weibull distribution function is calculated as follows:

$$F(N)=1-\exp \left[-{(\frac{N-\gamma }{\beta })}^n\right],N\ge \gamma .$$

(1)

$$P=1-F(N).$$

(2)

where F (N) is the failure probability; N is the fatigue life of the specimen, N ≥ γ; n is the shape parameter, n > 0; β is the scale parameter, β > 0; and γ is the position parameter. In the fatigue life analysis of a specimen, γ₀ is the minimum life value of the specimen, indicating that the service life of the specimen will not fail before reaching this γ value, and p is the survival probability.

After taking two natural logarithms on both sides of Equation (1), we obtain

$$\frac{1}{P}=\exp {(\frac{N-\gamma }{\beta })}^n.$$

(3)

$$\ln \ln \left(\frac{1}{p}\right)=n[\ln (N-\gamma )-\ln \beta ].$$

(4)

Let Y = lnln(1/p), X = ln (N − γ), and B = −nlnβ. Then, a linear equation can be obtained from Equation (4):

$$Y=n\cdot X-B.$$

(5)

In the analysis of the test data, the cumulative failure probability (F(N_i)) is calculated by using the median rank algorithm:

$$F(N_i)=\frac{i-0.3}{m+0.4}.$$

(6)

where F (N_i) is the cumulative failure probability, i is the serial number of the fatigue test data (i = 1,2,3,4), and m is the sample size under a certain stress level (m = 4).

Taking X as the abscissa and Y as the ordinate, the data in Table 4 were processed using Equations (1)–(6). By fitting the linear relationship between Y = $\mathrm{l}\mathrm{n}\mathrm{l}\mathrm{n}\frac{1}{1-F\left(N\right) }$ and X = ln (N − γ) for the 6 groups of concrete specimens under different stress levels, the corresponding parameter values were obtained. As the three-parameter Weibull distribution is more complicated than the two-parameter Weibull distribution, the position parameter γ needs to be obtained first. In this paper, γ was analyzed and solved using MS EXCEL, in order to obtain the distribution parameters under different stress levels. The calculation results are given in

Table 5. Distribution parameters under different stress levels.

Project	S	n	β	γ	R2
NC	0.6	2.721	339,280	2597	0.9642
	0.7	1.402	395,07.8	1481	0.9938
	0.8	0.9535	5601	82	0.9557
RF	0.6	1.477	207,997.8	17,603	0.9985
	0.7	1.316	27,147.6	1483	0.9974
	0.8	1.338	2884.3	543	0.9657
C0.5RF	0.6	1.955	228,966.8	33,926	0.9572
	0.7	1.404	32,980	822	0.9997
	0.8	1.373	4172	447	0.9945
C1RF	0.6	1.981	340,238	11,183	0.9995
	0.7	0.759	285,49.3	16,948	0.9736
	0.8	1.079	4521.3	1564	0.9831
C2RF	0.6	1.732	279,271	23,706	0.9864
	0.7	1.47	38,692.6	1956	0.9998
	0.8	1.334	4742.4	420	0.9765
C3RF	0.6	1.557	251,501.4	222	0.9999
	0.7	0.71	16,589.2	15,104	0.9999
	0.8	1.018	3719.3	269	0.9946

.

From Table 5, it can be seen that the correlation coefficient R² was higher than 0.95 and tended to 1, and the fitting accuracy is high, indicating that there exists a good linear correlation between the parameters X and Y. Thus, the three-parameter Weibull distribution can be used to characterize the fatigue life of CSWRF.

Figure 9 shows the shape parameter n for NC, RF, and CSWRF under different stress levels. The shape parameter can reflect the discreteness of fatigue life; the larger the shape parameter value, the lower the discreteness [18]. It can be seen from Figure 9 that the shape parameters of NC decreased with an increase in the stress level. While the shape parameters of RF decreased first and then increased with increasing stress levels, with the incorporation of CSW, the shape parameters of CSWRF did not show a significant trend with a change in stress level. However, for NC, RF, and CSWRF, when the stress level was 0.6, the shape parameters of the concrete were the largest, indicating that the distribution of fatigue life of concrete under low stress levels is more uniform, the discreteness is smaller, and the fatigue performance is better.

4.2. Fatigue Life Equation

4.2.1. Selection of S-N Curve

By establishing a functional relationship between the stress level S in the fatigue test and the measured average fatigue life N, the stress level-fatigue life curve (S-N curve) was fitted to estimate and evaluate the fatigue life, which can accurately characterize the fatigue characteristics of a material. The boundary conditions for the fatigue equation of concrete are as follows:

$$\{\begin{array}{c}N=1,S=1\\ N\to \infty ,S\to 0\end{array}.$$

(7)

Note that the single logarithmic equation cannot meet the extended boundary condition of S → 0 in the concrete fatigue equation. Thus, the two parameters can be better satisfied when the double logarithmic fatigue equation is used to fit the stress level-fatigue life curve:

$$\lg (S)=\lg (a)-b\lg (N).$$

(8)

The test results are shown in Figure 10. Under the same stress level (i.e., the same longitudinal coordinate value), the smaller the value of the horizontal coordinate of the function, the smaller the fatigue life and the poorer the fatigue performance. Thus, the test group corresponding to the function image in the upper right of the figure had better fatigue performance. The anti-fatigue performance gradually decreases from the upper right to the lower left. and the anti-fatigue performance of concrete with different mixture proportions was ranked as follows: C1RF > NC > C2RF > C0.5RF > C3RF > RF.

4.2.2. Fatigue life P-S-N Curves and Analysis of Results

As the double logarithmic fatigue S-N curve is a median fatigue equation based on the average fatigue life of four tests corresponding to each stress level without considering the probability of failure, the guarantee rate was only 50% [44]. At the same time, the discrete nature of concrete itself leads to large differences in the test data; therefore, in order to endow the obtained test data with practical engineering value, the P-S-N curves under different survival probabilities were also explored.

The equivalent fatigue life NP of concrete under different survival probabilities is calculated by Equation (9):

$$N_P=\gamma +\beta {(-\ln P)}^{\frac{1}{n}}.$$

(9)

Based on the equivalent fatigue life N_P under the different survival probabilities obtained, the fatigue life and stress level under different survival probabilities were fitted using double logarithmic fatigue equations, and the P-S-N curves of CSWRF specimens with different fitting ratios under different survival probabilities (0.5, 0.95) could be obtained, as shown in Figure 11, and the corresponding fatigue equations are provided in

Table 6. P-S-N fatigue equations with different survival probabilities.

Project	Survival Probability	a	b	Fatigue Equation	R2
NC	0.5	1.4430	0.06906	lg(S) = 0.15624 − 0.06906lg(N)	0.9999
RF		1.3828	0.06873	lg(S) = 0.14076 − 0.06873lg(N)	0.9969
C0.5RF		1.4212	0.06968	lg(S) = 0.15264 − 0.06968lg(N)	0.9994
C1RF		1.4485	0.06988	lg(S) = 0.16093 − 0.06988lg(N)	0.9993
C2RF		1.4318	0.06906	lg(S) = 0.15587 − 0.06906lg(N)	0.9959
C3RF		1.3782	0.06779	lg(S) = 0.13932 − 0.06779lg(N)	0.9942
NC	0.95	1.2077	0.0605	lg(S) = 0.08196 − 0.0605lg(N)	0.9791
RF		1.2919	0.07191	lg(S) = 0.11122 − 0.07191lg(N)	0.9916
C0.5RF		1.2132	0.06269	lg(S) = 0.08394 − 0.06269lg(N)	0.9743
C1RF		1.4060	0.07369l	lg(S) = 0.148 − 0.07369lg(N)	0.9626
C2RF		1.2539	0.06574	lg(S) = 0.09828 − 0.06574lg(N)	1
C3RF		1.1562	0.05796	lg(S) = 0.06304 − 0.05796lg(N)	0.869

.

As can be seen from Table 6, the correlation coefficients were all above 0.85, so the linear fitting correlation was good. Among them, the parameter a reflects the height of the fatigue curve (the larger the value of a, the higher the curve and the better the flexural fatigue resistance of concrete), while the parameter b reflects the degree of inclination of the fatigue curve (the larger the value of b, the steeper the curve and the more insensitive the fatigue life of concrete is to a change in stress).

From Figure 11, it can be seen that the higher the survival probability, the smaller the concrete flexural fatigue life at the same stress level. Under different survival probabilities, the predicted life of CSWRF was generally higher than that of RF, and the predicted fatigue life of C1RF was the highest, consistent with the previous conclusions and further verifying that doping with CSW can increase the fatigue life of RFAC. However, a higher doping level is not necessarily better; when the survival probability was 0.95, the fatigue life of specimens in the C3RF group was predicted to be lower than that in RF at high stress levels.

The stress level of concrete when it reaches 2 million cycles is usually called the fatigue limit (Sc) of concrete. The Sc values for NC, RF, C0.5RF, C1RF, C2RF, and C3RF at p = 0.5 were 0.526, 0.510, 0.517, 0.526, 0.525, and 0.516, respectively. The Sc of RF group specimens was 3.14% lower than that of the NC group. The decrease was small, consistent with the conclusion of Deng Y. S [45]. When the replacement rate of recycled aggregate is lower, the effect on Sc is small, which remains basically equivalent to that of concrete. Compared with the RF group, the Sc of the CSWRF group was improved, indicating that the addition of CSW can make up for the adverse effect of RFA on the fatigue performance of concrete and effectively improve the fatigue strength of RFAC.

5. The Action Mechanism of CSW in RFAC

In order to further explore the effect of CSW on the fatigue performance of recycled fine aggregate concrete, two groups of recycled fine aggregate concrete specimens (RF and C1RF) were selected for SEM microstructure observation. The results are shown in Figure 12. In Figure 12a, the existence of micro-cracks and holes can be clearly seen inside the recycled fine aggregate concrete; meanwhile, in Figure 12b, the recycled fine aggregate concrete mixed with CSW presents needle-like crystals with a large aspect ratio, and its integrity remains high. The CSW appears to interact well with the cement matrix and is evenly distributed in the recycled concrete.

CSW, as a kind of microfiber, presents toughening mechanisms (e.g., crack “bridging” and whisker filling [32,33,34,35]) in concrete, thus preventing and slowing down the failure process of concrete. According to the research of Becher et al. [46], micro-cracks will connect with the whisker crack tip area. CSW efficiently mitigates stress concentration at the tip of the crack by exerting closing pressure at both ends of the fracture, thus preventing the continuous propagation of micro-cracks.

According to the Roumualdi fiber spacing theory [47], when the whiskers are randomly and uniformly distributed in the concrete specimen, with an increase in the whisker admixture, the average center distance between whiskers decreases, and the cracks will be limited to a smaller size range when they extend to the whisker-cement mortar interface with a relatively small size. Therefore, when CSW is well-dispersed in the RFAC specimen, the increase in CSW per unit volume allows more whiskers to participate in the crack arresting effect. However, when the dosage of CSW is too high, due to the increased interactions between whiskers, the resistance of whiskers in the dispersion process increases [34,43], resulting in insufficient dispersion of whiskers and the whisker aggregation phenomenon occurring inside the test block. This loose accumulation of whiskers leads to a decrease in the densification of concrete, accelerating the expansion of the cracks under the action of cyclic loading and negatively affecting the fatigue performance of the CSWRF. These results indicate the existence of an optimum value for the enhancement effects when incorporating CSW into RFAC.

6. Conclusions

In this study, the influence of CSW content on the basic mechanical properties and flexure fatigue properties of RFAC was studied. The three-parameter Weibull distribution function theory was selected to analyze and predict the fatigue life of CSWRF, and the microstructure of CSW-modified RFAC was observed via SEM. The following conclusions were drawn:

(1)

The admixture of RFA reduces the mechanical properties of concrete; however, after adding CSW into RFAC, the mechanical properties of the RFAC were significantly improved, where the improvement effect of CSW on the flexural strength of RFAC was more obvious than that on the compressive strength, the brittleness of RFAC was reduced, and its toughness was enhanced by the admixture of CSW. However, when the CSW dosage is higher than 2%, the mechanical properties are instead reduced.

(2)

The fatigue life of concrete decreases rapidly with an increase in the maximum stress level, and the fatigue life in the RFAC group shrinks more than that of the NC group under the same stress level; meanwhile, 1% CSW modification can extend the fatigue life of the RF group by 56.5% overall.

(3)

The fatigue life of recycled concrete obeys the three-parameter Weibull distribution theory. The P-S-N fatigue equation, considering the fatigue probability, was derived by double logarithm, and the fitting correlation was good. Under the condition of 2 × 10⁶ cycles, the Sc for six kinds of concrete with a survival rate of 0.5 was estimated. The results indicate that the incorporation of RFA reduces the Sc level of concrete, while CSW modification can reduce the fatigue life dispersion caused by recycled aggregate and increase the Sc.

(4)

According to the analysis of SEM images, the whiskers have a high aspect ratio and act as microfibers to play a “bridging” role. The cement paste encapsulates CSW to form a spatial skeleton structure, delaying the propagation of cracks and exerting a toughening mechanism, thereby improving the mechanical properties and fatigue properties of recycled concrete.