Study on Fatigue Characteristics of Cement-Emulsified Asphalt Mortar Under Coupled Effects of Humidity and Freeze–Thaw

Abstract

Cement-emulsified asphalt mortar (CA mortar) is an organic–inorganic composite material composed of cement, emulsified asphalt, fine sand, water, and various admixtures. It is mainly used as the cushion layer for high-speed railway ballastless tracks. CA mortar cushion layers in North China often have to withstand the coupling effects of humidity and freeze–thaw, which has a very important impact on the fatigue performance of CA mortar. Based on the big data statistical results, the temperature conditions and cycle times of the CA mortar layer Freeze–Thaw cycle in North China were determined. Also, a fatigue performance test under humidity–freeze–thaw coupling conditions was designed and carried out. The fitting curve equations of fatigue stress and fatigue life under different humidity conditions and freeze–thaw coupling were established. The relationship between fatigue performance parameters K and n and humidity conditions was analyzed. This study shows that with the increase in humidity, the fatigue life of CA mortar under different humidity conditions shows an overall downward trend. The fatigue performance and fatigue life stress level sensitivity of CA mortar decrease with increasing humidity. The proportion of water damage and freeze–thaw damage to total damage increases with increasing humidity, which means that the humidity and freeze–thaw have a more significant impact on the fatigue properties of CA mortar. When the humidity is low, the fatigue cracks of CA mortar are mostly generated across the cement paste, and the macroscopic damage presents as longitudinal cracking. When the humidity is high, the fatigue cracks of CA mortar are mostly generated at the interface between aggregate and paste, and the macroscopic damage presents as oblique cracking. Based on the analysis of the damage mechanism, it is suggested that the humidity of CA mortar should be controlled below 25% in the actual project to ensure its durability.

1. Introduction

Cement emulsion asphalt mortar (CA mortar) is an important layer material in the slab ballastless track structure of high-speed railway CRTS-I and CRTS-II types [1]. CA mortar is an organic–inorganic composite material composed of cement, emulsified asphalt, fine sand, water, and various admixtures [2,3]. The slab ballastless track is composed of four parts: the concrete base under the slab, the CA mortar cushion layer, the track slab, the long rails and fasteners. CA mortar is an important component of the slab track as the elastic adjustment layer between the concrete base and the track slab [4,5,6]. It plays the role of filling and adjusting, bearing loads, and absorbing and reducing vibration in the high-speed rail track structure [7].

In recent years, with the rapid development of high-speed rail, the study of mechanical properties of CA mortar has attracted extensive attention. Relevant studies show that the ratio of asphalt to cement (A/C ratio) is the most important factor affecting the mechanical properties of CA mortar [8,9,10,11]. The elastic modulus, compressive strength, and damage energy of CA mortar all decrease with the increase in the A/C ratio [12,13,14,15]. These studies indicate that the presence of excessive asphalt has a certain inhibitory effect on the hydration reaction of cement [16].

The service life of CA mortar cushion layer is related to the life of the entire high-speed rail track, so it is necessary to study its fatigue life. Studies have shown that increasing the amount of cement can improve the stability of the fatigue properties of CA mortar repair materials but will reduce the fatigue life of CA mortar repair materials [17]. Furthermore, increasing asphalt content amplifies the sensitivity of fatigue properties to stress levels [18]. Relevant scholars have established a numerical simulation equation for the correlation between the fatigue number (N) and stress level (S) of CA mortar. From the fatigue equation, it can be seen that CA mortar has good fatigue resistance under different temperature conditions due to its viscoelastic characteristics. In addition, there is a good linear correlation between the logarithm of fatigue life and stress level [19].

In order to facilitate pouring construction, the freshly mixed cement emulsion asphalt mortar must have sufficient fluidity [20]. When designing the mix ratio, it is often necessary to add a large amount of mixing water. In the later stage of hardening, the hydration reaction of cement consumes some water, but there is still a lot of free water inside the CA mortar, which is trapped inside of mortar. In addition, during the service of the high-speed rail track, rainwater can easily enter the CA mortar cushion layer through the cracks [21]. These phenomena cause the CA mortar cushion layer to be in a water-carrying working state for a long time. Relevant studies indicate that the peak strain of CA mortar increases with higher strain rates and prolonged water immersion periods. The water immersion time has a greater impact on the peak strain of CA mortar [22]. Long-term soaking will significantly reduce the compressive strength of CA mortar, and the higher the asphalt content, the greater the reduction [23].

The North China region is located in a seasonally frozen zone. Every winter, under alternating high and low temperatures, water entering the pavement structure can cause freeze–thaw effects [24,25,26]. The Freeze–Thaw cycles will affect the mechanical properties of CA mortar under static and dynamic loads. Studies have found that Freeze–Thaw cycles can lead to the destruction of the mechanical properties of CA mortar, which father affects the structural stability of high-speed railway ballastless track. The Freeze–Thaw cycles weaken the deformation resistance of CA mortar and increase the hysteresis of mechanical response [27]. Freeze–thaw cycling progressively increases the mass loss rate of CA mortar while reducing its relative dynamic modulus [28].

In order to simulate the actual situation, some scholars began to study the performance decay of CA mortar under multi-condition coupling, such as fatigue and freeze–thaw coupling, humidity, and freeze–thaw coupling. Related studies have shown that fatigue has a significant effect on the freeze–thaw damage of CA mortar. A small amount of fatigue can compact the structure of CA mortar, thereby improving the freeze resistance of CA mortar. When fatigue damage accumulates to a certain extent, cracks and microcracks will appear inside the CA mortar. At this time, fatigue will aggravate the freeze–thaw damage of CA mortar [29]. When A/C is 0 to 0.45, the freeze–thaw resistance of mortar decreases with the increase in emulsified asphalt content [30]. When A/C is 0.8 to 1.2, as the asphalt content increases, the freeze–thaw damage decreases. Therefore, the freeze resistance of CA mortar is improved. As the number of Freeze–Thaw cycles increases, the fatigue life of CA mortar decreases, and the sensitivity of fatigue life to stress level decreases. As the number of Freeze–Thaw cycles increases, both freeze–thaw damage and total fatigue damage increase [31].

Relevant scholars have studied the effect of moisture on the frost resistance of CA mortar. Under water immersion, the amount of spalling per unit area of CA mortar continues to increase with the increase in Freeze–Thaw cycles. However, the amount of spalling per unit area is very small. Therefore, CA mortar has excellent frost resistance under both surface immersion and absolute humidity conditions. In actual engineering, the possibility of CA mortar being damaged by Freeze–Thaw cycles due to the freezing of free water is very small [32].

In most practical situations, CA mortar is subjected to the coupling effect of fatigue, humidity, and freeze–thaw, so the fatigue failure of CA mortar under the condition of humidity and Freeze–Thaw cycles is more realistic. However, no relevant scholars have conducted relevant research on this. Therefore, the purpose of this paper is to establish a model to characterize the fatigue damage of CA mortar under the humidity–freeze–thaw coupling. In this way, the evolution law of fatigue failure of CA mortar under various humidity conditions after Freeze–Thaw cycles can be analyzed. This provides a basic reference for improving the fatigue resistance of CA mortar under the coupling effect of humidity and freeze–thaw.

2. Materials and Methods

2.1. Raw Materials and Mix Proportions

2.1.1. Raw Materials

The emulsified asphalt used in this study was an anionic slow-cracking type, formulated with 70# base asphalt and JY-AFF1 anionic emulsifier supplied by China Zhejiang Jinyang Company. The solid content of the emulsified asphalt is 60%. Its physical and mechanical properties are shown in

Table 1. Properties of asphalt.

Needle Penetration 25 °C (0.1 mm)	Elongation 15 °C (cm)	Softening Point (°C)	Flash Point (°C)	Solubility (%)	Residual Penetration Ratio (%)	Residual Ductility (cm)
68	105	46	300	107	68	10

. The cement is ordinary Portland cement of P·O 42.5 grade, and its physical and mechanical properties are shown in

Table 2. Properties of cement.

Density (g/cm3)	Standard Consistency Water Consumption (%)	Initial Condensation Time (min)	End Coagulation Time (min)	Fineness  (%)	28d Compressive Strength (MPa)	28d Flexural Strength (MPa)
3.08	27.8	40	450	2.8	45	6.7

. The sand used in the test is machine-made sand. The density is 2.64g/cm³. The fineness modulus is 2.58. The maximum particle size is 2.50mm. The sand gradation is shown in

Table 3. Gradation of sand.

Screen Size/mm	4.75	2.36	1.18	0.6	0.3	0.15
Count the residue/%	0	0.02	36.2	26.16	3.64	27.28
Cumulative residue/%	0	0.02	36.22	62.38	66.02	93.3

and Figure 1. The water reducer is a kind of polycarboxylic acid high-efficiency water reducer produced by China Shanxi Feike New Material Technology Co., Ltd. with a water reduction rate of 25%. The expansion agent is a UEA expansion agent produced by China Laiyang Hongxiang Building Admixture Factory. The defoamer is a type of silicone defoamer.

2.1.2. Mix Proportions

This study mainly investigates the influence of humidity–freeze–thaw coupling conditions on the fatigue performance of CA mortar. Therefore, according to the requirements of the standard of Interim Technical Specifications for Cement Emulsion Asphalt Mortar for CRTS II Type Slab Ballastless Track on Passenger Dedicated Line Railways, only one mix ratio was designed for fatigue tests under different conditions. The ratio of emulsified asphalt to cement (abbreviate to A/C) is 0.4. The amount of superplasticizer is 1%. The dosage of the defoamer is 0.00246 kg/m³. The ratio of other materials is shown in

Table 4. CA mortar mix ratios.

Cement/(kg/m3)	Emulsified Asphalt/(kg/m3)	Sand/(kg/m3)	Water/(kg/m3)	UEA/(kg/m3)
563	225	867	185	28

.

2.1.3. Specimen Preparation

The JJ-5 mortar mixer produced by China Wuxi Jianyi Instrument Machinery Co., Ltd. was used to prepare CA mortar. The mixing procedure comprised the following steps. Firstly, pour the emulsified asphalt into the mixer. Stir the water reducer, defoamer, and water evenly. Then, add to the mixer. Stir at the speed of 140 r/min for 1 min. Then, slowly add dry powders such as cement and sand. This process should be completed within 1 min. Then, increase the speed to 285 r/min and stir for 1 min. Finally, stir at the speed of 140 r/min for 1 min. Pour the stirred CA mortar into the mold with the size of ϕ 50 mm × 50 mm. A total of 30 CA mortar specimens were prepared. The CA mortar shall be cured in accordance with the conditions specified in the standard of Interim Technical Specifications for Cement Emulsion Asphalt Mortar for CRTS II Type Slab Ballastless Track on Passenger Dedicated Line Railways. Firstly, the cast CA mortar specimens were placed in an environment with a temperature of 20–25 °C and a humidity of 95 ± 5% for 24 h and then demolded. After that, they were cured in an environment with a temperature of 25 ± 2 °C and a humidity of 65 ± 5% for 28 days.

2.2. Compressive Strength

The compressive strength was measured using an electronic universal testing machine, as shown in Figure 2. According to the method specified in the standard of Interim Technical Specifications for Cement Emulsion Asphalt Mortar for CRTS II Type Slab Ballastless Track on Passenger Dedicated Line Railways, the uniaxial compression test was performed on the specimens.

The 28d compressive strength were tested on three parallel specimens, and the maximum pressure P was recorded, respectively. The compressive strength σ was calculated according to Equation (1). The average value of the compressive strengths from three parallel specimens was taken as the representative compressive strength at 28d.

$$\sigma ={\displaystyle \frac{P}{S}}$$

(1)

where $\sigma$ is the compressive strength (MPa), P is the maximum pressure (N), S is the bottom area of the specimen (mm²). Since the specimen size is ϕ 50 mm × 50 mm, S = 1962.5 mm².

2.3. Humidity–Freeze–Thaw Coupling Condition Design

2.3.1. Humidity Conditions

In order to simulate the working state of CA mortar under different humidity conditions, this study designed five moisture contents of 0%, 25%, 50%, 75%, and 100%. The preparation process is as follows.

First, place the prepared CA mortar specimen in an oven for drying. Then, measure the mass of the CA mortar specimen and record it. The humidity condition at this time is considered to be 0% moisture content. After the CA mortar is saturated with vacuum water, take out the specimen. Wipe the water on the surface of the specimen with a towel before weighing. Weigh and record the data. The humidity condition at this time is considered to be 100% moisture content. Calculate the water absorption rate by mass and water absorption rate by volume of the specimen after vacuum saturation according to Equations (2) and (3).

$$W_m={\displaystyle \frac{m-m_0}{m_0}}\times 100\%$$

(2)

$$W_v={\displaystyle \frac{V_v}{V}}={\displaystyle \frac{m-m_0}{{\rho }_w}}·{\displaystyle \frac{1}{V}}\times 100\%$$

(3)

where $W_m$ is the water absorption rate by mass (%), $W_v$ is the water absorption rate by volume (%), m is the mass of the specimen after water absorption (g), m₀ is the mass of the specimen before water absorption (g), V_v is the volume of water absorbed by the specimen (cm³), V is the volume of the specimen (cm³), ${\rho }_w$ is the water density (g/cm³).

The water absorption rate by mass and water absorption rate by volume of the specimen after vacuum saturation are taken as the maximum moisture content that can be achieved under natural conditions; it is regarded as 100% moisture content. Accordingly, the mass of the specimen at 75%, 50%, and 25% moisture content was calculated, respectively. The saturated specimen was placed in an environment with a temperature of 20 °C and a relative humidity of 50% to lose water naturally and weighed regularly. When the mass reached the mass corresponding to the moisture content, the CA mortar was wrapped with plastic film to prevent moisture exchange with the outside world. For the subsequent progress of the test, six samples were prepared for each moisture content. In order to make the moisture distribution on the surface and inside of the CA mortar uniform, the wrapped CA mortar specimens were stored in a cool place for 24 h before testing.

2.3.2. Temperature Conditions

The temperature of the ballastless track structure shows periodic changes. The changing patterns of the ambient temperature, track plate surface temperature, support layer temperature and CA mortar cushion layer temperature are basically the same. The temperature of each layer of the track structure can be fitted by a fourth-order polynomial [33], and the coefficient of determination of the fit is 90.74%. The polynomial expression is shown in Equation (4).

$$Y=-6.47\times {10}^3+1.288x-0.043x^2+0.002x^3-2.34\times {10}^{-5}{x}^4$$

(4)

where $Y$ is the temperature of the CA mortar cushion layer (°C), $x$ is the atmospheric temperature (°C).

The meteorological data of Beijing Station with the area station number of 54,511 was obtained from the China Meteorological Data Network platform. Using daily temperature data, the highest and lowest daily temperatures in Beijing from November 2011 to February 2023 were screened out. Substitute the atmospheric temperature of Beijing into Equation (4). The daily maximum temperature T_max and minimum temperature T_min corresponding to the temperature of CA mortar cushion layer can be calculated. Some data are shown in Figure 3. If the maximum temperature T_max on a certain day is greater than zero and the minimum temperature T_min is less than zero, it is considered that a Freeze–Thaw cycle has occurred. According to these statistics, the number of Freeze–Thaw cycles of the CA mortar cushion layer in Beijing from 2011 to 2023 is shown in Figure 4, which indicates that the average annual Freeze–Thaw cycle number from 2011 to 2023 is 82 times. Taking five years as an example, the number of Freeze–Thaw cycles is set to 410 times as the number of Freeze–Thaw cycles of the CA mortar cushion layer.

In order to determine the temperature of the Freeze–Thaw cycle, the temperature distribution range of the CA mortar cushion layer was calculated by the cumulative frequency method. All dates that meet the Freeze–Thaw cycle in the 12 years from 2011 to 2023 were extracted. The daily minimum temperature and daily maximum temperature were sorted from low to high according to the temperature. The temperature threshold range with a confidence level of more than 95% for Freeze–Thaw alternation within 12 years was clarified. As can be seen from Figure 5, the main temperature range for Freeze–Thaw cycles between 2011 and 2023 was between −20 °C and 10 °C. The Freeze–Thaw cycle temperature range was set to −20~10 °C.

2.3.3. Freeze–Thaw Cycle Process

The Freeze–Thaw cycle is carried out on CA mortar by the DR-01concrete Freeze–Thaw test machine produced by China Beijing Aerospace Test Equipment Technology Co., Ltd. The specific process is shown in Figure 6.

1. The specimens were cured to a curing age of 28 days.

2. The moisture content of the CA mortar was set to specified value, including 0%, 25%, 50%, 75%, and 100%, as previously mentioned. There are three CA mortar specimens with each moisture content.

3. After treatment, they were packaged with plastic film to ensure that there was no water exchange between the CA mortar specimen and the outside world.

4. Placing the CA mortar specimens into the rubber sleeves in the tank of Freeze–Thaw machine. One temperature sensor was placed in the slot reserved at the center of a specimen which was placed in the middle of tank to monitor the temperature inside the specimen. The other temperature sensors were placed in the antifreeze around the rubber sleeves to monitor the environment temperature inside the tank.

5. Setting the parameters of the testing machine. According to the previous statistical result, the freezing temperature was set to −20 °C. The melting temperature was set to 10 °C. The temperature change rate was set to 10 °C/h.

6. The heating condition was that the temperature at the center of the specimen reached the specified temperature 2 h later, or when the freezing time reached 8 h, the temperature started to rise. The cooling condition was that the temperature at the center of the specimen reached the specified temperature 2 h later, or when the melting time reached 4 h, the temperature started to fall. Temperature profile of Freeze–Thaw cycles is shown in Figure 7.

7. The Freeze–Thaw cycle continues until the numbers reach the specified Freeze–Thaw cycles, and then the instrument was turned off. The CA mortar specimen was taken out for use.

2.4. Design of Fatigue Test Under Humidity–Freeze–Thaw Coupling

2.4.1. Fatigue Test Steps

The fatigue test was conducted using an MTS universal testing machine. The fatigue loading form of CA mortar is axial compression. The loading frequency is 10 Hz. The sine wave was adopted as the test loading waveform. The loading process is shown in Figure 8 and Figure 9. Before formal loading, the upper and lower surfaces of the specimen were polished to keep the upper and lower surfaces of the specimen flat and free of obvious defects. This will reduce the data error caused by the uneven surface of the specimen. In addition, CA mortar was always packaged with plastic film to prevent moisture exchange between the CA mortar specimen and the atmosphere. During the test, fatigue loading peaks loads, fatigue loading trough loads and displacements were gathered, and the full-cycle stress and strain data were collected once every 100 cycles. In order to reduce the test error, 3 parallel specimens were measured under the same fatigue stress.

2.4.2. Fatigue Stress Level

Before carrying out fatigue tests, the stress level must be determined. At present, many scholars conduct fatigue tests under the condition of controlling stress levels. Although this mode is simple and easy to control, in actual engineering, this mode may not be able to fully simulate the actual situation. Because the strength of CA mortars with different moisture contents is quite different. If different stress levels are used for loading tests, the fatigue stress varies greatly, which is not consistent with the actual conditions. In order to more intuitively compare the fatigue properties of CA mortar under the different humidity conditions, the same stress is used to load on the CA mortar with different moisture conditions. The fatigue stress and corresponding stress level are shown in

Table 5. Fatigue stress of CA mortar under humidity–freeze–thaw coupling.

Moisture Content (%)	Fatigue Stress (Stress Level)
0	8.92 (0.70)	7.64 (0.60)	6.37 (0.50)	5.35 (0.42)
25	8.92 (0.78)	7.64 (0.67)	6.37 (0.56)	5.35 (0.47)
50	7.39 (0.73)	6.37 (0.63)	5.35 (0.53)	4.33 (0.43)
75	7.39 (0.85)	6.37 (0.74)	5.35 (0.62)	4.33 (0.50)
100	7.39 (0.92)	6.37 (0.79)	5.35 (0.67)	4.33 (0.54)

.

2.5. SEM Test Method

The specimen is cut into a cube with a side length of 1 cm and pasted on a conductive adhesive. To improve the conductivity of the test section, a 45-s gold spray was performed using the Quorum SC7620 sputter coater produced by United Kingdom Quorum Technologies Limited. The gold spray current is set to 10mA. The sample topography was then captured using a ZEISS Gemini 300 SEM scanning electron microscope produced by Germany Carl Zeiss AG. The acceleration voltage is 3kV when the topography is taken. The detector is a SE2 secondary electron detector. The observation fold is between 50× and 5000×. The microscopic topography of different phase transition zones, needle-like/fibrous, plate-like, granular, and block-like objects, as well as pore structures and fractures were selected.

3. Results and Discussion

3.1. Mechanical Properties Under Humidity–Freeze–Thaw Coupling

According to the test method, the compressive strength tests were carried out on CA mortar specimens with different moisture contents before and after the condition of Freeze–Thaw. The test results are summarized in

Table 6. CA mortar strength test results.

Condition	Moisture Content (%)	Maximum Load (kN)	Strength (MPa)
Before Freeze–Thaw	0	24.98	12.73
	25	22.33	11.38
	50	19.76	10.07
	75	16.99	8.66
	100	15.73	8.02
After Freeze–Thaw	0	24.57	12.52
	25	21.33	10.87
	50	17.78	9.06
	75	15.95	8.13
	100	13.79	7.03

.

For convenience, the compressive strength before and after Freeze–Thaw and the strength ratio of the compressive strength after Freeze–Thaw to the compressive strength before Freeze–Thaw are plotted in Figure 10. As can be seen from Figure 10, the compressive strength of CA mortar decreases with the increase in moisture content. After the 410 Freeze–Thaw cycles, the compressive strength significantly reduced compared with that before the Freeze–Thaw cycles. With the increase in moisture content, the strength decline of CA mortar after Freeze–Thaw cycles also increases. After the Freeze–Thaw cycles, the strength reduction in CA mortar with more than 50% moisture content is greater than that of CA mortar with less than 50% moisture content. This indicates that the more moisture in the CA mortar, the greater the damage of Freeze–Thaw cycle to the strength of the CA mortar. Moreover, the influence of moisture on the strength of CA mortar is greater than that of temperature. The strength of CA mortar comes from the hydration of cement and the demulsification of asphalt emulsions. If there is free water in the CA mortar that is not easily discharged, the water can invade the interface between the asphalt and cement or between the asphalt and sand. This destabilizes the interface and weakens the interfacial cohesion. Therefore, the greater the moisture content of CA mortar, the lower the strength of CA mortar [34]. Moreover, there are open pores in the CA mortar, and the moisture entering the pores and the moisture inside the CA mortar will produce frost heave reaction under the action of Freeze–Thaw cycles. Frost heave cracks occur inside the CA mortar, which further reduces the strength of the CA mortar [35].

3.2. Fatigue Life of CA Mortar Under Humidity–Freeze–Thaw Coupling

3.2.1. Fatigue Life Under the Same Fatigue Stress

The fatigue life of 5 moisture content gradient CA mortars after 410 Freeze–Thaw cycles was tested by fatigue loading test. The average test results are shown in

Table 7. Fatigue life of CA mortar with different moisture contents under humidity–freeze–thaw coupling.

Moisture Content (%)	Fatigue Life N Under Different Fatigue Stresses (Stress Levels) (Times)
0	8.92 (0.70)	7.64 (0.60)	6.37 (0.50)	5.35 (0.42)
	461	6222	105,963	1,586,673
25	8.92 (0.78)	7.64 (0.67)	6.37 (0.56)	5.35 (0.47)
	421	3676	30,578	428,448
50	7.39 (0.73)	6.37 (0.63)	5.35 (0.53)	4.33 (0.43)
	233	4516	69,238	484,630
75	7.39 (0.85)	6.37 (0.74)	5.35 (0.62)	4.33 (0.50)
	269	1834	9242	79,417
100	7.39 (0.92)	6.37 (0.79)	5.35 (0.67)	4.33 (0.54)
	18	624	2796	18,997

.

It can be seen from Table 7 that as the moisture content increases, the fatigue life of CA mortars with different moisture contents shows an overall downward trend. This shows that the fatigue performance of CA mortar deteriorates under the action of humidity–Freeze–Thaw coupling. Under the same loading stress, the fatigue life of CA mortar with different moisture content gradients is quite different. As shown in Figure 11, taking the loading stress of 6.37 kN as an example, the fatigue life of CA mortar with moisture content of 25%, 50%, 75%, and 100% is 71.14%, 95.74%, 98.27%, and 99.41% lower than that of 0% moisture content, respectively. It can be seen that the influence of moisture content on the fatigue life of CA mortar is very significant. The fatigue life of CA mortar with identical moisture content varies significantly across different stress levels. As shown in Figure 12, taking the moisture content of 0% as an example, the fatigue life of CA mortar with stress levels of 0.5, 0.6, and 0.7 is 93.32%, 99.61%, and 99.97% lower than that of the stress level of 0.42, respectively. It can be seen that the influence of stress level on the fatigue life of CA mortar is also very significant.

The ε–N curves of various CA mortars under the same fatigue stress of 6.37 MPa are shown in Figure 13. The ε–N curve reflects the relationship between the strain of CA mortar under the fatigue loading and the number of fatigue loadings. ε is the strain in the vertical direction of the specimen in the axial compressive fatigue test. The strain at the crest is the maximum strain, corresponding to the black line in Figure 13. The strain at the trough is the minimum strain, corresponding to the red line in Figure 13. The blue point in Figure 13 is the difference between the maximum strain and the minimum strain under the same fatigue life.

As can be seen from Figure 13, Each ε–N curve can be roughly divided into three stages, which correspond to the three loading stages acting on CA mortar from initial loading to fatigue failure. Stage 1: fatigue compression stage. In this stage, the vertical relative displacement of the specimen expands rapidly. The CA mortar pores are compressed which causes microcracks in CA mortar. Stage 2: fatigue damage accumulation stage. In this stage, the vertical relative displacement of the specimen develops extremely slowly, and this state lasts the longest, which corresponds to the stable propagation of microcracks in CA mortar. Stage 3: fatigue failure stage. At this stage, the vertical relative displacement of the specimen increases rapidly, and the final specimen fails, which corresponds to the instability propagation of the micro-cracks of the CA mortar. Under the same fatigue loading times, the higher the moisture content, the faster the damage develops. Moreover, by observing the difference changes under various moisture contents, it is found that the difference curve as a whole shows a pattern of first decreasing, then flattening, and finally increasing. This corresponds to the above three stages.

Compared with the fatigue failure curve of CA mortar with the moisture content of 0%, the fatigue compression stage of CA mortar under the action of humidity–Freeze–Thaw coupling is shorter. The fatigue compression stage ends when the number of loading time is less than 5% of the fatigue life and enters the fatigue damage accumulation stage. The higher the moisture content, the shorter the fatigue compression stage. As shown in Figure 13e, the CA mortar with a moisture content of 100% almost entered the damage accumulation stage directly at the beginning of loading. The reason is that the internal pores of the CA mortar with a moisture content of 100% are full of water. When subjected to fatigue load, the compression should be achieved by draining the water in the pores, which is a difficult process. The other part of the water in the pores generates dynamic water pressure, which also prevents the compression of the CA mortar. This shortens the compression process of the CA mortar under humidity–Freeze–Thaw coupling.

3.2.2. Influence of Moisture Content on Fatigue Life Under Humidity–Freeze–Thaw Coupling

For fatigue testing, the relationship between fatigue life and fatigue stress generally satisfies the power function, as shown in Equation (5).

$$N=K{\sigma }^{-n}$$

(5)

where $N$ is the fatigue life (times), $\sigma$ the fatigue stress (MPa), $K$ and $n$ are fitted parameters.

Regression analysis was performed on the fatigue stress and fatigue life listed in Table 7 according to Equation (5). The fatigue life fitting equations under various moisture contents are obtained as shown in Figure 14. The fitting parameters K and n in the equations are exhibited in

Table 8. Fatigue equation fitting parameters.

Parameter	Moisture Content (%)
	0	25	50	75	100
K	$3.1391\times {10}^{17}$	$4.1644\times {10}^{16}$	$4.8559\times {10}^{11}$	$2.2375\times {10}^{11}$	$1.1064\times {10}^{10}$
n	$15.5094$	$15.0856$	$9.4278$	$10.1335$	$9.0579$
R2	1.0000	1.0000	0.9995	1.0000	0.9999

. The parameters K and n reflect the fatigue properties of CA mortar. The K value reflects the fatigue resistance of CA mortar. The larger the K value is, the larger the intercept of fatigue curve is, and the better the fatigue resistance is. The value of n reflects the sensitivity of fatigue life to stress level. The larger the n value is, the steeper the fatigue curve is, the more sensitive the fatigue life is to the stress level.

The parameters K and n are fitted with the moisture content. The fitting results all satisfy the Boltzmann equation. The fitting equations are shown in Equations (6) and (7). The fitting curves are shown in Figure 15.

$$K=1.1740 \ast {10}^{11}+{\displaystyle \frac{3.1392 \ast {10}^{17}}{1+e^{\frac{w-0.2102}{0.0212}}}}$$

(6)

$$n=9.5397+{\displaystyle \frac{5.9721}{1+e^{\frac{w-0.2734}{0.0091}}}}$$

(7)

where $w$ is the moisture content, $K$ and $n$ are fitted parameters.

As shown in Figure 15, parameters K and n decrease with increasing moisture content, which indicates that the fatigue performance and fatigue life sensitivity of CA mortar to stress level decrease with the increasing of moisture content. The parameter K value decreases steeply as the moisture content from 0% to 25% and decreases gently as the moisture content from 25% to 100%. The variation in parameter n value decreases slowly as the moisture content from 0% to 25%, decreases rapidly as the moisture content from 25% to 50%, and decreases slowly again as the moisture content from 50% to 100%. The actual value fluctuates slightly above and below the fitting curve. The determination coefficients of the regression equation of parameters K and n are both greater than 0.98, which is very high. This shows that parameters K and n are affected by moisture content greatly. In summary, in order to ensure the fatigue resistance of CA mortar, it is recommended that the moisture content of CA mortar in construction and working stage should not be higher than 25%.

3.2.3. Influence of Moisture Content on Performance Damage Under Humidity–Freeze–Thaw Coupling

The total performance damage produced by the fatigue test of CA mortar after Freeze–Thaw cycles at different moisture contents consists of three parts. The first part is the water damage caused by moisture changes. The second part is the Freeze–Thaw damage caused by Freeze–Thaw cycles. The third part is the fatigue damage caused by the generation and extension of cracks in the fatigue test. In the fatigue test under the effect of humidity–Freeze–Thaw coupling designed in this study, these three types of damage exist simultaneously.

The compressive strength of CA mortar decreases with increasing moisture content. Thus, water damage caused by moisture can be characterized by a change in compressive strength ${\sigma }_0\left(w\right)$ before Freeze–Thaw. According to the basic theory of damage mechanics [36], the degree of water damage under the action of water can be calculated $D_0\left(w\right)$is

$$D_0\left(w\right)=1-{\displaystyle \frac{{\sigma }_0\left(w\right)}{{\sigma }_0\left(0\right)}}$$

(8)

where $D_0\left(w\right)$ is the water damage degree, ${\sigma }_0\left(w\right)$ is the compressive strength of CA mortar at different moisture contents before Freeze–Thaw (MPa), ${\sigma }_0(0$) is the compressive strength of CA mortar at 0% moisture content before Freeze–Thaw (MPa).

The compressive strength of CA mortar after Freeze–Thaw cycles decreases with the increase in moisture content. Therefore, Freeze–Thaw damage caused by Freeze–Thaw cycles is characterized by the ratio of the compressive strength ${\sigma }_1\left(w\right)$ after Freeze–Thaw to the compressive strength ${\sigma }_0\left(w\right)$ before Freeze–Thaw. According to the basic theory of damage mechanics, the degree of Freeze–Thaw damage $D_d\left(w\right)$ under the effect of Freeze–Thaw cycles can be obtained as

$$D_d\left(w\right)=1-{\displaystyle \frac{{\sigma }_1\left(w\right)}{{\sigma }_0\left(w\right)}}$$

(9)

where $D_d\left(w\right)$ is the Freeze–Thaw damage degree, ${\sigma }_1\left(w\right)$ is the compressive strength of CA mortar at different moisture contents after Freeze–Thaw (MPa), ${\sigma }_0\left(w\right)$ is the compressive strength of CA mortar at different moisture contents before Freeze–Thaw (MPa).

In fatigue tests, in addition to water damage and Freeze–Thaw damage, fatigue damage will also occur. After fatigue tests, the fatigue performance parameter K of CA mortar decreases with the increase in moisture content. Therefore, the total damage generated by the fatigue test of CA mortar can be characterized by the change in fatigue performance parameter K. According to the basic theory of damage mechanics, the total damage degree $D_Z\left(w\right)$ under the combined action of moisture, Freeze–Thaw and fatigue can be calculated as Equation (10).

$$D_Z\left(w\right)=1-{\displaystyle \frac{K\left(w\right)}{K\left(0\right)}}$$

(10)

where $D_Z\left(w\right)$ is the total damage degree, K(w) is the fatigue performance parameter K of CA mortar at different moisture contents, K(0) is the fatigue performance parameter K of CA mortar at 0% moisture content.

The water damage degree $D_0\left(w\right)$, Freeze–Thaw damage degree $D_d\left(w\right)$ and total damage degree $D_Z\left(w\right)$ were calculated by Equation (8), Equation (9) and Equation (10), respectively. The calculated values are shown in

Table 9. Calculated values of damage degree.

Damage Degree	Moisture Content (%)
	0	25	50	75	100
$D_0\left(w\right)$	0.0000	0.1060	0.2090	0.3197	0.3700
$D_d\left(w\right)$	0.0165	0.0448	0.1003	0.0612	0.1234
$D_Z\left(w\right)$	0.0000	0.8673	0.9999	0.9999	0.9999

. A line chart of the damage degree variation with moisture content is shown in Figure 16.

As shown in Table 9 and Figure 16, with the increase in moisture content, each damage degree gradually increases. The water damage degree $D_0\left(w\right)$ and Freeze–Thaw damage degree $D_d\left(w\right)$ increase almost linearly, but the increase in total damage degree $D_Z\left(w\right)$ is not linear. The increase rate of the total damage degree $D_Z\left(w\right)$ gradually decreases, which is very high in the initial stage with moisture content lower than 25%, then slows down in the stage with moisture content from 25% to 50%, and finally, almost turns to zero in the stage with moisture content higher than 50%.

In order to analyze the contribution of water damage and Freeze–Thaw damage to total damage, the variation trend of $D_0\left(w\right)/D_Z\left(w\right)$ and $D_d\left(w\right)/D_Z\left(w\right)$ with moisture content can be further obtained, as shown in

Table 10. The ratio of the damage degree.

Ratio (%)	Moisture Content (%)
	0	25	50	75	100
$D_0\left(w\right)/D_Z\left(w\right)$	0.00	12.23	20.90	31.97	37.00
$D_d\left(w\right)/D_Z\left(w\right)$	0.00	5.17	10.03	6.12	12.34

and Figure 17. It can be seen that as the moisture content increases, the $D_0\left(w\right)/D_Z\left(w\right)$ value and $D_d\left(w\right)/D_Z\left(w\right)$ value increase linearly as a whole. The values of $D_0\left(w\right)/D_Z\left(w\right)$ from 25% to 100% are 12.23%, 20.90%, 31.97%, 37.00%, respectively. The values of $D_d\left(w\right)/D_Z\left(w\right)$ from 25% to 100% are 5.17%, 10.03%, 6.12%, 12.34%, respectively. This indicates that the contribution of humidity damage to total damage and Freeze–Thaw damage to total damage increased both, but the contribution of humidity damage to total damage increases more. In addition, the contribution of humidity damage to total damage is more significant than that of Freeze–Thaw damage to total damage.

When the moisture content is small, water damage and Freeze–Thaw damage account for a smaller proportion of the total damage, and fatigue damage accounts for a larger proportion. Fatigue damage has a greater impact on the fatigue performance of CA mortar. At the same time, the fatigue life of CA mortar under different stress levels varies greatly. It shows that the fatigue performance is more sensitive to the stress level, that is, the fatigue parameter n is larger. When the moisture content is large, the proportion of water damage and Freeze–Thaw damage in the total damage increased, and the proportion of fatigue damage decreased. Freeze–Thaw damage significantly reduces the fatigue life of CA mortar. At this time, the fatigue life of CA mortar varies with stress levels slightly. Therefore, when the moisture content is larger, the effect of stress level on the fatigue life of CA mortar becomes smaller. It shows that the sensitivity of fatigue performance to stress level is low, that is, the fatigue parameter n is small.

3.3. Fatigue Damage Mechanism of CA Mortar Under Humidity–Freeze–Thaw Coupling

In order to better explore the influence mechanism of humidity–Freeze–Thaw coupling on the fatigue damage of CA mortar, the damage behavior of CA mortar was analyzed from macroscopic and microscopic aspects.

3.3.1. Macroscopic Damage

After the fatigue test, the damaged CA mortar specimens were photographed and analyzed. Figure 18 shows the crack morphology of specimens with different moisture contents after fatigue test.

As shown in Figure 18, the fatigue failure form of CA mortar under compression load is mainly axial cracking. When the moisture content is 0%, the surface of the specimen shows obvious longitudinal cracks. As the moisture content increases, the failure of CA mortar gradually changes from longitudinal cracking to oblique cracking. When the moisture content is 100%, the surface of the specimen shows obvious oblique cracks. And as the moisture content increases, the crack width also gradually increases. CA mortar is a typical porous structure, and its macroscopic performance depends on the microstructure, so it is necessary to observe and analyze microscopic damage.

3.3.2. SEM Microstructure

In order to reveal the fatigue failure mechanism of CA mortar under the coupling of humidity and Freeze–Thaw, the effect of humidity on the micromorphology of CA mortar was investigated. The micromorphology of CA mortar with different moisture contents after fatigue load was studied by SEM electron microscopy. The observation results are shown in Figure 19 and Figure 20. Unlike Zhao et al. [16], which analyzed the structure of CA mortar, this section studies the microscopic mechanism of CA mortar failure. The microscopic failure of the CA mortar is shown in Figure 21.

As can be seen from Figure 19, after fatigue load, obvious compression deformation occurs in the internal pore structure of CA mortar with 0% moisture content. Most of the cracks penetrate the pores and distribute in the cement phase in Figure 21. This shows that under the action of fatigue load, microcracks first occur around the pores. Under the action of fatigue load, they continue to expand along the cement hydration products. Eventually, through-break failure is formed. In addition, its destructive cracks are mostly vertical cracks, and there are fewer transverse cracks. This is because under the action of longitudinal compression fatigue load, the principal compressive stress is much greater than the stress in the other two directions. Therefore, longitudinal compression will inevitably lead to transverse expansion, that is, tensile strain is generated in the transverse direction. When the tensile strain exceeds the limit value, cracks will occur along the longitudinal direction. Finally, longitudinal cracking is formed on a macro scale.

As can be seen from Figure 20, the smooth sand surface can be clearly seen, and the paste peeling is serious on the sand surface. Fatigue failure cracks of CA mortar with 100% moisture content mostly occur at the interface between aggregate and paste in Figure 21. The reason is that in CA mortar, the interfacial adhesion between cement hydration products and asphalt is weak. Under the combined effects of humidity and Freeze–Thaw cycles, external moisture penetrates the interface between hydration products and asphalt in CA mortar, thereby reducing interfacial adhesion. The mechanism analysis here is roughly the same as that of Xu et al. [34]. Unlike CA mortar with 0% moisture content, the cracks of CA mortar with 100% moisture content are mostly inclined cracks. The reason is that CA mortar with 100% moisture content is full of water inside the pores. Under the action of Freeze–Thaw cycles and high-frequency fatigue loads, the pore pressure increases sharply, which generates dynamic water pressure distributed throughout the specimen. Under the action of vertical load, the maximum shear stress is formed on the inclined surface, which is approximately 45 degrees to the longitudinal direction. The shearing action is generated on the interface between aggregate and paste of CA mortar. Therefore, its fatigue failure cracks are mostly inclined, and the macroscopic appearance is oblique cracking.

4. Conclusions

In this study, CA mortars with five moisture contents were prepared. A systematic study was conducted on the fatigue performance of CA mortar under the effect of humidity–Freeze–Thaw coupling. The fatigue failure mechanism of CA mortar was analyzed in combination with macroscopic and microscopic failure morphologies. The following main conclusions were obtained.

(1) With the increase in moisture content, the fatigue life of CA mortar with different moisture contents shows an overall downward trend. This indicates that the fatigue performance of CA mortar deteriorates obviously under the coupling effect of humidity and Freeze–Thaw cycles. Under the same loading stress, the fatigue life gradually decreases with the increase in moisture content. Under the loading stress of 6.37 kN, the fatigue life of CA mortar with moisture content of 25%, 50%, 75%, and 100% is 71.14%, 95.74%, 98.27%, and 99.41% lower than that of 0% moisture content, respectively. For CA mortar with the same moisture content, the fatigue life gradually decreases with the increase in stress level.

(2) The ε–N curve can be divided into three stages, namely fatigue compression stage, fatigue damage accumulation stage and fatigue failure stage. The fatigue compression stage of CA mortar under the action of humidity–Freeze–Thaw coupling is shorter than that of CA mortar with the moisture content of 0%. The higher the moisture content, the shorter the fatigue compression stage.

(3) A fatigue equation considering fatigue stress was established. Parameters K and n decrease with the increase in moisture content. It shows that the fatigue performance and fatigue life stress level sensitivity of CA mortar both decrease with the increase in moisture content. It is recommended that the moisture content of CA mortar during both construction and operational phases should be controlled below 25%.

(4) The total performance damage produced by the fatigue test of CA mortar after Freeze–Thaw cycles at different moisture contents consists of three parts. They are water damage, Freeze–Thaw damage, and fatigue damage. The damage caused by the humidity–Freeze–Thaw coupling is much greater than that caused by the action of a single factor. As the moisture content increases, the proportion of water damage and Freeze–Thaw damage to the total damage increases. However, the contribution of humidity damage to the total damage is greater, with a ratio of 37.00% when the moisture content is 100%. The effect of stress level on the fatigue life of CA mortar becomes smaller with the increasing of the moisture content.

(5) When the moisture content is 0%, the failure of CA mortar is the maximum tensile strain failure. The destruction occurs inside the hydration products. Macroscopic manifestations are vertically cracking. When the moisture content is 100%, the failure of CA mortar is the maximum shear stress failure. The failure occurs at the aggregate–slurry interface junction. The macroscopic manifestation is oblique cracking.

(6) In this study, the fatigue characteristics of cement-emulsified asphalt mortar under the coupling effect of humidity–Freeze–Thaw cycle were studied. Due to the time limitation of the test, the effect of different Freeze–Thaw cycles on the fatigue properties of cement-emulsified asphalt mortar was not studied. Moreover, the selection of temperature range is limited to the Beijing area. Subsequently, the fatigue performance of cement-emulsified asphalt mortar in different regional ambient temperature ranges under the action of different Freeze–Thaw cycles can be studied.