# Fatigue Performance of Rubber Concrete in Hygrothermal Environment

Authors: Yushan Liu; Jianyong Pang; Weijing Yao
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

It is widely accepted that the rubber concrete (RC) originating from waste is a promising material that can contribute to the conservation and rational use of natural resources and the protection of the environment. However, the fatigue performance in a hygrothermal environment is a major concern because little pertinent information is available in the relevant literature. In this study, a cyclic loading test was carried out on RC subjected to different wet-dry cycles at different temperatures. The loading strain, plastic strain, and elastic strain of the concrete were compared and analyzed. The results revealed that the loading strain and plastic strain of the RC were obvious after the 1st loading cycle. As the number of loading cycles increased, the stress-strain curve became denser and the RC exhibited good elasticity. As the wet-dry cycles increased, the average plastic strain in the 10th–60th loading cycle increased while the elastic strain decreased. After 28 wet-dry cycles, the average plastic strain at 60°C increased by 42.31% compared with 20°C. In fact, as the temperature became higher, the plastic damage incurred by the RC became more severe. Finally, the damage variable was defined based on the elastic modulus and plastic strain to evaluate the fatigue performance of the RC in a hygrothermal environment. The findings of this study can provide a useful reference for RC applications.


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## Body

## 1. Introduction

With the rapid development of the automobile industry and the rapid increase in automobile demand, tire rubber waste, which is toxic and hazardous, has increased, and the recycling and disposal of end-of-life tires are considered as “black pollution” [1–3]. Most waste tires are piled up in landfills without any particular treatment, which poses a risk to the wellbeing of the ecological environment and creates fire hazards [4, 5]. With regard to the recycling of rubber tires and reduction of environmental pollution, studies have attempted to introduce processed rubber aggregates as elastic materials into concrete to prepare rubber concrete (RC) [6, 7]. Notably, RC can not only make use of waste tires with high added value but also improve the ductility, toughness, wear resistance, and skid resistance of concrete. Moreover, RC exhibits excellent performance in vibration reduction and noise reduction [8–10]. Although the addition of rubber reduces the compressive strength of concrete, its plastic deformation ability and fatigue performance are significantly improved [11, 12].Nowadays, RC is widely used in bridges, tunnels, railways, airport runways, nuclear structures, and so on [7, 12]. These structures are subjected to fatigue loading over long time periods while in service, and the antifatigue performance of the structure plays a vital role in its effective use in engineering applications [13, 14]. Therefore, many studies have investigated the mechanical properties and damage of RC under cyclic loading [15–21]. Pang et al. [18] found that the total strain, elastic strain, and plastic strain of RC are significantly higher compared with those of ordinary concrete in the process of cyclic loading, while the relative strain is extremely small, which indicates good ductility and stability. Lv et al. [20] investigated the effect of rubber particles on the fatigue performance of self-compacting lightweight rubber aggregate concrete. Their results revealed that the fatigue life and strain increased as the replacement of rubber particles increased. Pacheco-Torres et al. [21] investigated the suitability of using discarded waste tire rubber particles in concrete rigid road pavements and presented an optimal combination of the size and proportion of rubber particles that improves the performance of the material subjected to cyclic loading stresses, which makes the material suitable for use in the construction of rigid concrete pavements.However, in practical applications, tunnels, railways, and bridges are often subjected to two main groups of actions: traffic loadings and hygrothermal actions [22–24]. Multiple studies indicate that the strength, durability, and fatigue performance of the material rapidly decline in a hygrothermal environment [24–28]. Morshed et al. [26] found out the hygrothermal environments are deleterious to the durability of the interfacial bonding between concrete and CFRP. Tuakta and Büyüköztürk [27] observed a significant degradation of the bond strength when exposed to prolonged moisture condition, which can be up to 70% when specimens are conditioned for 8 weeks. Tang et al. [28] concluded that the higher the temperature, the lower the cohesive strength of the surrounding rock supporting structure under hygrothermal environments. Additionally, in areas with high temperature and humidity, a considerable proportion of highways suffer fatigue damage soon after being put into use, and this phenomenon develops rapidly [29–31]. Hence, it is understood that the fatigue performance of concrete in a hot and humid environment is somewhat different from that under normal conditions. Thus, it is necessary to investigate the fatigue performance of RC in a hygrothermal environment.The objective of this study was to investigate the fatigue performance of RC in a hygrothermal environment. To this end, a cyclic loading test was carried out on the RC after different wet-dry cycles at different temperatures. Moreover, to quantify the fatigue damage of RC under the coupled action of the hygrothermal environment and loading, the damage variable was defined based on the elastic modulus and plastic strain. This has important practical significance for the promotion of RC engineering applications, natural resource preservation, and environmental protection.


## 2. Materials and Methods

### 2.1. Raw Materials

The cement used in this study was Chinese standard Portland cement; the chemical composition is presented in Table1. The coarse aggregate was crushed limestone with continuous grading, particle size of 5–15 mm, and an apparent density of 2780 kg/m3. The fine aggregate was river sand with a fineness modulus of 2.6. A high-performance water reducer (HPWR) with a water-reducing rate of 30% was employed to ensure fluidity and water retention. The rubber particles had a size of 0.85 mm and density of 1030 kg/m3. Table 2 represents the technical indexes of rubber particle, used for preparing the concrete. The appearance and microstructure of the rubber particle are presented in Figure 1.Table 1
Chemical composition of cement.
CompositionSiO2Al2O3Fe2O3CaOMgOSO3Ignition lossContent (%)22.605.034.3863.111.462.241.18Table 2
Technical indexes of rubber particle.
Moisture content (%)Ash content (%)Acetone extract (%)Metal content (%)Fiber content (%)Sieve residue content (%)Tensile strength (MPa)Elongation at break (%)0.628.755.120.020.000.01416.8564Figure 1
The (a) appearance and (b) microstructure of the rubber particles.
(a)(b)


### 2.2. Preparation of Specimens

The mix proportions of RC are presented in Table3. The dimensions of the cylindrical specimens were Φ50 × 100 mm.Table 3
Mix proportions of RC (kg/m3).
CementLimestoneSandRubberWaterWater reducerWater cement ratio32212256892751613.210.5The materials were measured using an electronic balance and mixed in a double-horizontal-shaft forced-type concrete mixer. First, preweighted aggregate and rubber were mixed for 1 min; then, binder material was added and mixed for 1 min. Subsequently, the already measured water and water reducer were poured into the properly mixed dry materials and stirred for 3 min to ensure a mix with uniform plastic consistency. The mold was filled in three layers and consolidated using a vibratory table. Additionally, the top surface was smoothed with a trowel. The specimens were subjected to the laboratory conditions of 20 ± 2°C and 70% relative humidity. After hardening, the specimens were released from the molds and were cured in a saturated Ca(OH)2 solution at 20 ± 2°C for 90 d.


### 2.3. Test and Characterization

To prevent the moisture content from affecting the result of wet-dry cycles, all specimens were placed in an oven at the temperature of 105 ± 5°C for 24 h before testing. After cooling, the specimens were divided into two groups and placed into thermostatic water bath box at the temperatures of 20°C and 60°C, respectively. In order to investigate the influence of hygrothermal environment on the fatigue performance of RC accurately, a wet-dry cycle test (soaking 16 h + drying 6 h + cooling 2 h) was used in lab conditions to simulate the humid and hot environment. The number of wet-dry cycles was 7, 14, and 28, respectively. Subsequently, the treated specimens were preserved in sealed polyethylene bags until the day of testing. The details of the test process are illustrated in Figure2.Figure 2
Details of test process.Using the RDL-200 electronic creep machine, uniaxial compression and cyclic loading tests were carried out on the RC specimens subjected to different wet-dry cycles. The uniaxial compression test was carried out at a rate of 1 mm/min until the specimen failed, so as to obtain the compressive strength, which is denoted asfc. In the cyclic loading test, a small preload of 500 N was applied to the specimen before the test to ensure that the specimen and test device were properly aligned and centred. The equal amplitude cyclic loading method was used; the upper load was 30 kN and the lower unloading limit was 0 kN. The rate of loading and unloading was set to 30 kN/min. One loading and unloading process was considered as one cycle, and 60 cycles were carried out in total. The residual compressive strength was obtained at the rate of 1 mm/min after cyclic loading and is denoted as fc′. The cyclic loading path of the test is shown in Figure 3.Figure 3
Cyclic loading path.


## 2.1. Raw Materials

The cement used in this study was Chinese standard Portland cement; the chemical composition is presented in Table1. The coarse aggregate was crushed limestone with continuous grading, particle size of 5–15 mm, and an apparent density of 2780 kg/m3. The fine aggregate was river sand with a fineness modulus of 2.6. A high-performance water reducer (HPWR) with a water-reducing rate of 30% was employed to ensure fluidity and water retention. The rubber particles had a size of 0.85 mm and density of 1030 kg/m3. Table 2 represents the technical indexes of rubber particle, used for preparing the concrete. The appearance and microstructure of the rubber particle are presented in Figure 1.Table 1
Chemical composition of cement.
CompositionSiO2Al2O3Fe2O3CaOMgOSO3Ignition lossContent (%)22.605.034.3863.111.462.241.18Table 2
Technical indexes of rubber particle.
Moisture content (%)Ash content (%)Acetone extract (%)Metal content (%)Fiber content (%)Sieve residue content (%)Tensile strength (MPa)Elongation at break (%)0.628.755.120.020.000.01416.8564Figure 1
The (a) appearance and (b) microstructure of the rubber particles.
(a)(b)


## 2.2. Preparation of Specimens

The mix proportions of RC are presented in Table3. The dimensions of the cylindrical specimens were Φ50 × 100 mm.Table 3
Mix proportions of RC (kg/m3).
CementLimestoneSandRubberWaterWater reducerWater cement ratio32212256892751613.210.5The materials were measured using an electronic balance and mixed in a double-horizontal-shaft forced-type concrete mixer. First, preweighted aggregate and rubber were mixed for 1 min; then, binder material was added and mixed for 1 min. Subsequently, the already measured water and water reducer were poured into the properly mixed dry materials and stirred for 3 min to ensure a mix with uniform plastic consistency. The mold was filled in three layers and consolidated using a vibratory table. Additionally, the top surface was smoothed with a trowel. The specimens were subjected to the laboratory conditions of 20 ± 2°C and 70% relative humidity. After hardening, the specimens were released from the molds and were cured in a saturated Ca(OH)2 solution at 20 ± 2°C for 90 d.


## 2.3. Test and Characterization

To prevent the moisture content from affecting the result of wet-dry cycles, all specimens were placed in an oven at the temperature of 105 ± 5°C for 24 h before testing. After cooling, the specimens were divided into two groups and placed into thermostatic water bath box at the temperatures of 20°C and 60°C, respectively. In order to investigate the influence of hygrothermal environment on the fatigue performance of RC accurately, a wet-dry cycle test (soaking 16 h + drying 6 h + cooling 2 h) was used in lab conditions to simulate the humid and hot environment. The number of wet-dry cycles was 7, 14, and 28, respectively. Subsequently, the treated specimens were preserved in sealed polyethylene bags until the day of testing. The details of the test process are illustrated in Figure2.Figure 2
Details of test process.Using the RDL-200 electronic creep machine, uniaxial compression and cyclic loading tests were carried out on the RC specimens subjected to different wet-dry cycles. The uniaxial compression test was carried out at a rate of 1 mm/min until the specimen failed, so as to obtain the compressive strength, which is denoted asfc. In the cyclic loading test, a small preload of 500 N was applied to the specimen before the test to ensure that the specimen and test device were properly aligned and centred. The equal amplitude cyclic loading method was used; the upper load was 30 kN and the lower unloading limit was 0 kN. The rate of loading and unloading was set to 30 kN/min. One loading and unloading process was considered as one cycle, and 60 cycles were carried out in total. The residual compressive strength was obtained at the rate of 1 mm/min after cyclic loading and is denoted as fc′. The cyclic loading path of the test is shown in Figure 3.Figure 3
Cyclic loading path.


## 3. Results and Discussion

### 3.1. Compressive Strength Analysis

The influence of wet-dry cycles and cyclic loading on the compressive strength of RC is demonstrated in Figure4. The compressive strength of RC decreases and the pace of decline is prone to be faster with increasing wet-dry cycles. When the temperature was 20°C, the compressive strength of RC after 7, 14, 21, and 28 wet-dry cycles decreased by 5.63%, 16.90%, 30.99%, and 38.03%, while that of RC after cyclic loading declined by 10.28%, 23.00%, 37.87%, and 45.99%, respectively. After the same wet-dry cycles, the higher the temperature, the poorer the residual compressive strength.Figure 4
Compressive strength under different wet-dry cycles.


### 3.2. Typical Cyclic Loading Curves

The typical curve of RC under cyclic loading is shown in Figure5(a). As can be seen, the stress-strain curve of RC is first sparse and then becomes dense. The deformation of RC under cyclic loading mainly occurs in the first cycle and is observed as a large opening at the bottom of the curve. The hydrophobicity of the rubber particles resulted in a weak interface between the rubber particles and the cement matrix, which led to many initial pores in the specimen. Once the specimen was loaded, the internal pores of RC were compressed and microcracks quickly appeared, mainly with plastic deformation. Because rubber particles have better elasticity and toughness, the addition of rubber particles into concrete is equivalent to the introduction of an elastomer to some extent [32, 33]. Hence, the deformation of RC is mainly elastic deformation after the primary pores have been gradually compacted, which indicates that there exists a reduced hysteretic loop area and a denser curve.Figure 5
Typical RC curves under cyclic loading: (a) full strain curve under cyclic loading; (b) single-cycle curve.
(a)(b)As can be seen from the single-cycle curve in Figure5(b), the loading period is mainly divided into three stages: the compaction stage, approximate elastic stage, and crack evolution stage [34]. In Figure 5(b), εl represents the loading strain, εp represents the plastic strain (also called plastic strain), and εe represents the elastic strain during each loading-unloading cycle. The curve in the compaction stage is concave, which indicates that the stress is kept at a low value and grows very slowly as the strain increases. This stage corresponds to the process of compacting and closing the internal pores. As the pores are gradually compacted, the specimen is uniformly compressed and the stress-strain curve increases approximately linearly, which indicates the approximate elastic stage. As the load and strain increase, the stress slowly increases and the curve exhibits a convex shape, which indicates the stage of microcrack evolution. As the load continues to increase, the curve exhibits a convex shape and the strain continues to increase, which indicates the stage of crack evolution. This is attributed to the breaking of the internal pores as the load increases, and the generation and expansion of microcracks with the breaking of the pores. The brittleness of concrete was weakened while its ductility is enhanced, and ductile deformation becomes the main deformation type.


### 3.3. Loading Strain Analysis

The relationships between the loading strain and the number of loading cycles are shown in Figure6. As can be seen, the variation trend of the loading strain of the RC specimen with the number of loading cycles is essentially the same, although the number of wet-dry cycles is different. The loading strain increased with the number of cyclic loading, and the loading strain rate in the 0th–10th loading was obvious. After 10 loading cycles, the strain slowly increased and the curve tended to be flat. When the number of wet-dry cycles of the RC at 20°C was 0, 7, 14, 21, and 28, the loading strain in the 0th–10th cycle accounted for 97.22%, 96.36%, 96.86%, 91.2%, and 89.93% of the total strain, respectively.Figure 6
Relationships between loading strain and number of loading cycles: (a) 20°C; (b) 60°C.
(a)(b)Additionally, the loading strain increased with the wet-dry cycles under the same number of loading cycles. At 20°C, compared with the RC specimens without soaking, the loading strain in the 0th–10th loading cycle of the specimens, which had been subjected to 7, 14, 21, and 28 wet-dry cycles, increased by 7.14%, 17.62%, 25.95%, and 46.67%, respectively, and the loading strain in the 0th–60th loading cycle increased by 8.10%, 18.06%, 34.26%, and 58.56%. The influence of the wet-dry cycles on the loading strain was more significant as the number of loading cycles increased.


### 3.4. Plastic Strain Analysis

Figure7 presents the average plastic strain within the 10th–60th loading cycle under different wet-dry cycles. As can be seen, the average plastic strain increased with the wet-dry cycles. When the temperature was 20°C, compared with the untreated RC specimens, the average plastic strain increased by 31.82% after 7 wet-dry cycles. As the wet-dry cycles increased, the average plastic strain increased by 40.91%, 77.27%, and 254.55%.Figure 7
Average plastic strain in 10th–60th loading cycle under different wet-dry cycles.When the number of wet-dry cycles was the same, the average plastic strain at 60°C was larger compared with that at 20°C. This suggests the growth rate of the irreversible plastic strain was greater under higher temperature. Because rubber particles have good elasticity, the plastic deformation was mainly caused by the pores and cracks in the cement matrix. In a humid and hot environment, high temperature accelerates the wet-dry erosion, which further weakens the bonding of the rubber particles and cement matrix. Therefore, under cyclic loading, the accumulation of plastic deformation occurs owing to the internal crack propagation and damage evolution.


### 3.5. Elastic Strain Analysis

The deformation of concrete under loading, which can be recovered after unloading, is called elastic deformation. The difference between the loading strainεl at the maximum axial stress of 30 kN and the plastic strain εp when the specimen is unloaded to 0 kN is defined as the elastic strain εe. The average elastic strain within the 10th–60th loading cycle under different wet-dry cycles is shown in Figure 8.Figure 8
Average elastic strain in 10th–60th loading cycle under different wet-dry cycles.It can be deduced from Figure8 that the average elastic strain shows a fluctuating reduction. Obviously, the average elastic strain after the first seven wet-dry cycles is dropped at most, which is up to 3.79% at 20°C, and 5.96% at 60°C. As wet-dry cycles increased, the pace of the decline tended to be slow. It is attributed to the fact that the deterioration of RC is a continuing process induced by the wet-dry cycles. During the initial wet-dry cycles, the rearrangement of aggregates and cement matrix promotes the development of crack quickly.As can be seen, the average elastic strains at 20°C were higher than those at 60°C, which confirms that the coupled corrosion of the hygrothermal environment and loading makes the process of durability performance deterioration easier, resulting in partial elastic strain transformed into plastic strain.


### 3.6. Damage Evolution

Damage refers to the microdefects or microcracks that exist inside the material as a result of manufacturing or external factors and results in the attenuation of mechanical properties and increase of deformation [35, 36]. A damage variable is a reference physical quantity, such as the stress, strain, elastic modulus, density, and energy density, and can be used to describe the internal damage of the material [37]. The damage variable can be selected according to the research object.


#### 3.6.1. Damage Variable of Elastic Modulus

The elastic modulusE0 reflects the deformation resistance of concrete and is essential for evaluating the material performance. The elastic modulus E0 is calculated using the elastic stage of the unloading curve, which can be expressed as follows:(1)E0=σεe.The elastic modulusE0 of the RC subjected to various wet-dry cycles after 10, 20, 30, 40, 50, and 60 loading cycles is shown in Figure 9. As can be seen, E0 of the RC specimen after 10, 20, 30, 40, 50, and 60 loading cycles fluctuated within a certain range. Therefore, the average E¯0 value was used to investigate the influence of the wet-dry cycles on the elastic modulus of RC [38]. According to Ma et al. [39], the increase of E¯0 after different wet-dry cycles was defined as the total damage variable DEn, and the average increase of E¯0 after each adjacent wet-dry cycle was defined the phase damage variable ΔDE, as follows:(2)DEn=E¯0n−E¯00E¯00,(3)ΔDE=DEn−DEmn−m,where E¯00 is the average elastic modulus of RC without soaking and E¯0n is the average elastic modulus of RC when the wet-dry cycle is n. When the number of the wet-dry cycle n is 7, 14, 21, and 28, the corresponding m value is 0, 7, 14, and 21.Figure 9
Elastic modulus of RC after being subjected to different wet-dry cycles.According to the definition in (2) and (3), the trend of the total damage variable DEn and the phase damage variable ΔDE of the RC specimen subjected to various wet-dry cycles are shown in Figure 8.As shown in Figures9 and 10, as the wet-dry cycles increased, the elastic modulus increased, and its total deterioration gradually increased. This is attributed to the fact that the amount of damage and energy dissipation increased, which accelerated the fatigue process. When the temperature was 20°C, the total damage variable of RC was 16.28% after seven wet-dry cycles. As the wet-dry cycles increased, the total degradation variables were 19.73%, 21.18%, and 22.60%.Figure 10
Total damage variable and phase damage variable of RC after being subjected to different wet-dry cycles.However, during this process, the phase deterioration gradually decreased: the 0–7 phase of damage decreased up to 2.33%, and the 21–28 phase of damage decreased by the minimum amount of only 1.41%, which indicates that the wet-dry cycles result in the gradual deterioration of RC.


#### 3.6.2. Damage Variable of Plastic Strain

Considering that the concrete is brittle and ductile, and its failure is mainly caused by excessive deformation, strain is one of the important indices for controlling the structural deformation and investigating the safety of concrete. The failure strain, which is also known as peak strain, is the strain that indicates structural failure and is denoted asεf. The plastic strain εp refers to the deformation that cannot be recovered, which is known as residual deformation. To measure the fatigue plastic damage of RC specimens under cyclic loading, the ratio of the plastic strain εp to the peak strain εf in 0–60 loading cycles is defined as the damage variable Dε and is expressed as follows [19]:(4)Dε=εpεf.Figure11 shows the variation of Dε under different wet-dry cycles. Under the coupling action of wet-dry cycles and cyclic loading, the damage variable of the RC specimen increased with the number of wet-dry cycles. When the temperature was 20°C, the Dε values of RC after 0, 7, 14, 21, and 28 wet-dry cycles were 0.457, 0.617, 0.626, 0.651, and 0.679, respectively. Comparing the specimen without wet-dry cycle, the Dε values of RC at 20°C after 7, 14, 21, and 28 wet-dry cycles increased by 35.01%, 36.98%, 42.45%, and 48.58%, while those of 60°C increased by 35.89%, 45.73%, 61.27%, and 88.40%, respectively. After the same wet-dry cycles, the Dε values increased with the temperature. After 7, 14, 21, and 28 wet-dry cycles, compared with 20°C, the Dε value increased by 0.32%, 3.19%, 6.61%, and 11.76%, respectively.Figure 11
Damage variableDε of RC subjected to different wet-dry cycles.


#### 3.6.3. Damage Mechanism Analysis

From the results we have obtained, one can conclude that the damage caused by the wet-dry cycles to the concrete is not negligible. Figure12 shows the schematic diagram of internal structure, and Figure 13 displays the microstructure of the interfacial zone in the hygrothermal environment. The repeated soaking and high temperature drying precipitated the internal microcracks through. The soluble particles in the specimen were lost through the leftover pores, while the remaining particles expanded during the drying process and formed new internal voids and cracks. With the increase of wet-dry cycles, the pores left by the loss of soluble components accumulate (Figures 13(g) and 13(h)). Under repeated loading, the slip distance between the particles increased, and the cracks had sufficient time to develop and expand, which led to a loose internal structure and increased deformation. After 21 wet-dry cycles, wider fractures can be observed at the interface zone compared to the microstructure without wet-dry cycles (Figures 13(e) and 13(f)), illustrating the fact that the formation of fractures and pores significantly aggravates the deformation.Figure 12
The internal structure schematic diagram of RC subjected to different wet-dry cycles.Figure 13
Microstructures of the interfacial transition zone, subjected to (a) 0 wet-dry cycles, (b) 0 wet-dry cycles, (c) 14 wet-dry cycles at 20°C, (d) 14 wet-dry cycles at 60°C, (e) 21 wet-dry cycles at 20°C, (f) 21 wet-dry cycles at 60°C, (g) 28 wet-dry cycles at 20°C, and (h) 28 wet-dry cycles at 60°C.
(a)(b)(c)(d)(e)(f)(g)(h)Comparing the specimens subjected to the same wet-dry cycles, it can be seen that the higher the temperature, the looser the cement matrix and the longer the fracture length. The interaction effect caused by the negative influence of the temperature and wet-dry cycles resulted in the differential deformation and internal stress of the rubber particles and cement paste, and the internal structure was not as dense as before. This resulted in the more severe fatigue plastic damage of RC in the hygrothermal environment.


## 3.1. Compressive Strength Analysis

The influence of wet-dry cycles and cyclic loading on the compressive strength of RC is demonstrated in Figure4. The compressive strength of RC decreases and the pace of decline is prone to be faster with increasing wet-dry cycles. When the temperature was 20°C, the compressive strength of RC after 7, 14, 21, and 28 wet-dry cycles decreased by 5.63%, 16.90%, 30.99%, and 38.03%, while that of RC after cyclic loading declined by 10.28%, 23.00%, 37.87%, and 45.99%, respectively. After the same wet-dry cycles, the higher the temperature, the poorer the residual compressive strength.Figure 4
Compressive strength under different wet-dry cycles.


## 3.2. Typical Cyclic Loading Curves

The typical curve of RC under cyclic loading is shown in Figure5(a). As can be seen, the stress-strain curve of RC is first sparse and then becomes dense. The deformation of RC under cyclic loading mainly occurs in the first cycle and is observed as a large opening at the bottom of the curve. The hydrophobicity of the rubber particles resulted in a weak interface between the rubber particles and the cement matrix, which led to many initial pores in the specimen. Once the specimen was loaded, the internal pores of RC were compressed and microcracks quickly appeared, mainly with plastic deformation. Because rubber particles have better elasticity and toughness, the addition of rubber particles into concrete is equivalent to the introduction of an elastomer to some extent [32, 33]. Hence, the deformation of RC is mainly elastic deformation after the primary pores have been gradually compacted, which indicates that there exists a reduced hysteretic loop area and a denser curve.Figure 5
Typical RC curves under cyclic loading: (a) full strain curve under cyclic loading; (b) single-cycle curve.
(a)(b)As can be seen from the single-cycle curve in Figure5(b), the loading period is mainly divided into three stages: the compaction stage, approximate elastic stage, and crack evolution stage [34]. In Figure 5(b), εl represents the loading strain, εp represents the plastic strain (also called plastic strain), and εe represents the elastic strain during each loading-unloading cycle. The curve in the compaction stage is concave, which indicates that the stress is kept at a low value and grows very slowly as the strain increases. This stage corresponds to the process of compacting and closing the internal pores. As the pores are gradually compacted, the specimen is uniformly compressed and the stress-strain curve increases approximately linearly, which indicates the approximate elastic stage. As the load and strain increase, the stress slowly increases and the curve exhibits a convex shape, which indicates the stage of microcrack evolution. As the load continues to increase, the curve exhibits a convex shape and the strain continues to increase, which indicates the stage of crack evolution. This is attributed to the breaking of the internal pores as the load increases, and the generation and expansion of microcracks with the breaking of the pores. The brittleness of concrete was weakened while its ductility is enhanced, and ductile deformation becomes the main deformation type.


## 3.3. Loading Strain Analysis

The relationships between the loading strain and the number of loading cycles are shown in Figure6. As can be seen, the variation trend of the loading strain of the RC specimen with the number of loading cycles is essentially the same, although the number of wet-dry cycles is different. The loading strain increased with the number of cyclic loading, and the loading strain rate in the 0th–10th loading was obvious. After 10 loading cycles, the strain slowly increased and the curve tended to be flat. When the number of wet-dry cycles of the RC at 20°C was 0, 7, 14, 21, and 28, the loading strain in the 0th–10th cycle accounted for 97.22%, 96.36%, 96.86%, 91.2%, and 89.93% of the total strain, respectively.Figure 6
Relationships between loading strain and number of loading cycles: (a) 20°C; (b) 60°C.
(a)(b)Additionally, the loading strain increased with the wet-dry cycles under the same number of loading cycles. At 20°C, compared with the RC specimens without soaking, the loading strain in the 0th–10th loading cycle of the specimens, which had been subjected to 7, 14, 21, and 28 wet-dry cycles, increased by 7.14%, 17.62%, 25.95%, and 46.67%, respectively, and the loading strain in the 0th–60th loading cycle increased by 8.10%, 18.06%, 34.26%, and 58.56%. The influence of the wet-dry cycles on the loading strain was more significant as the number of loading cycles increased.


## 3.4. Plastic Strain Analysis

Figure7 presents the average plastic strain within the 10th–60th loading cycle under different wet-dry cycles. As can be seen, the average plastic strain increased with the wet-dry cycles. When the temperature was 20°C, compared with the untreated RC specimens, the average plastic strain increased by 31.82% after 7 wet-dry cycles. As the wet-dry cycles increased, the average plastic strain increased by 40.91%, 77.27%, and 254.55%.Figure 7
Average plastic strain in 10th–60th loading cycle under different wet-dry cycles.When the number of wet-dry cycles was the same, the average plastic strain at 60°C was larger compared with that at 20°C. This suggests the growth rate of the irreversible plastic strain was greater under higher temperature. Because rubber particles have good elasticity, the plastic deformation was mainly caused by the pores and cracks in the cement matrix. In a humid and hot environment, high temperature accelerates the wet-dry erosion, which further weakens the bonding of the rubber particles and cement matrix. Therefore, under cyclic loading, the accumulation of plastic deformation occurs owing to the internal crack propagation and damage evolution.


## 3.5. Elastic Strain Analysis

The deformation of concrete under loading, which can be recovered after unloading, is called elastic deformation. The difference between the loading strainεl at the maximum axial stress of 30 kN and the plastic strain εp when the specimen is unloaded to 0 kN is defined as the elastic strain εe. The average elastic strain within the 10th–60th loading cycle under different wet-dry cycles is shown in Figure 8.Figure 8
Average elastic strain in 10th–60th loading cycle under different wet-dry cycles.It can be deduced from Figure8 that the average elastic strain shows a fluctuating reduction. Obviously, the average elastic strain after the first seven wet-dry cycles is dropped at most, which is up to 3.79% at 20°C, and 5.96% at 60°C. As wet-dry cycles increased, the pace of the decline tended to be slow. It is attributed to the fact that the deterioration of RC is a continuing process induced by the wet-dry cycles. During the initial wet-dry cycles, the rearrangement of aggregates and cement matrix promotes the development of crack quickly.As can be seen, the average elastic strains at 20°C were higher than those at 60°C, which confirms that the coupled corrosion of the hygrothermal environment and loading makes the process of durability performance deterioration easier, resulting in partial elastic strain transformed into plastic strain.


## 3.6. Damage Evolution

Damage refers to the microdefects or microcracks that exist inside the material as a result of manufacturing or external factors and results in the attenuation of mechanical properties and increase of deformation [35, 36]. A damage variable is a reference physical quantity, such as the stress, strain, elastic modulus, density, and energy density, and can be used to describe the internal damage of the material [37]. The damage variable can be selected according to the research object.


### 3.6.1. Damage Variable of Elastic Modulus

The elastic modulusE0 reflects the deformation resistance of concrete and is essential for evaluating the material performance. The elastic modulus E0 is calculated using the elastic stage of the unloading curve, which can be expressed as follows:(1)E0=σεe.The elastic modulusE0 of the RC subjected to various wet-dry cycles after 10, 20, 30, 40, 50, and 60 loading cycles is shown in Figure 9. As can be seen, E0 of the RC specimen after 10, 20, 30, 40, 50, and 60 loading cycles fluctuated within a certain range. Therefore, the average E¯0 value was used to investigate the influence of the wet-dry cycles on the elastic modulus of RC [38]. According to Ma et al. [39], the increase of E¯0 after different wet-dry cycles was defined as the total damage variable DEn, and the average increase of E¯0 after each adjacent wet-dry cycle was defined the phase damage variable ΔDE, as follows:(2)DEn=E¯0n−E¯00E¯00,(3)ΔDE=DEn−DEmn−m,where E¯00 is the average elastic modulus of RC without soaking and E¯0n is the average elastic modulus of RC when the wet-dry cycle is n. When the number of the wet-dry cycle n is 7, 14, 21, and 28, the corresponding m value is 0, 7, 14, and 21.Figure 9
Elastic modulus of RC after being subjected to different wet-dry cycles.According to the definition in (2) and (3), the trend of the total damage variable DEn and the phase damage variable ΔDE of the RC specimen subjected to various wet-dry cycles are shown in Figure 8.As shown in Figures9 and 10, as the wet-dry cycles increased, the elastic modulus increased, and its total deterioration gradually increased. This is attributed to the fact that the amount of damage and energy dissipation increased, which accelerated the fatigue process. When the temperature was 20°C, the total damage variable of RC was 16.28% after seven wet-dry cycles. As the wet-dry cycles increased, the total degradation variables were 19.73%, 21.18%, and 22.60%.Figure 10
Total damage variable and phase damage variable of RC after being subjected to different wet-dry cycles.However, during this process, the phase deterioration gradually decreased: the 0–7 phase of damage decreased up to 2.33%, and the 21–28 phase of damage decreased by the minimum amount of only 1.41%, which indicates that the wet-dry cycles result in the gradual deterioration of RC.


### 3.6.2. Damage Variable of Plastic Strain

Considering that the concrete is brittle and ductile, and its failure is mainly caused by excessive deformation, strain is one of the important indices for controlling the structural deformation and investigating the safety of concrete. The failure strain, which is also known as peak strain, is the strain that indicates structural failure and is denoted asεf. The plastic strain εp refers to the deformation that cannot be recovered, which is known as residual deformation. To measure the fatigue plastic damage of RC specimens under cyclic loading, the ratio of the plastic strain εp to the peak strain εf in 0–60 loading cycles is defined as the damage variable Dε and is expressed as follows [19]:(4)Dε=εpεf.Figure11 shows the variation of Dε under different wet-dry cycles. Under the coupling action of wet-dry cycles and cyclic loading, the damage variable of the RC specimen increased with the number of wet-dry cycles. When the temperature was 20°C, the Dε values of RC after 0, 7, 14, 21, and 28 wet-dry cycles were 0.457, 0.617, 0.626, 0.651, and 0.679, respectively. Comparing the specimen without wet-dry cycle, the Dε values of RC at 20°C after 7, 14, 21, and 28 wet-dry cycles increased by 35.01%, 36.98%, 42.45%, and 48.58%, while those of 60°C increased by 35.89%, 45.73%, 61.27%, and 88.40%, respectively. After the same wet-dry cycles, the Dε values increased with the temperature. After 7, 14, 21, and 28 wet-dry cycles, compared with 20°C, the Dε value increased by 0.32%, 3.19%, 6.61%, and 11.76%, respectively.Figure 11
Damage variableDε of RC subjected to different wet-dry cycles.


### 3.6.3. Damage Mechanism Analysis

From the results we have obtained, one can conclude that the damage caused by the wet-dry cycles to the concrete is not negligible. Figure12 shows the schematic diagram of internal structure, and Figure 13 displays the microstructure of the interfacial zone in the hygrothermal environment. The repeated soaking and high temperature drying precipitated the internal microcracks through. The soluble particles in the specimen were lost through the leftover pores, while the remaining particles expanded during the drying process and formed new internal voids and cracks. With the increase of wet-dry cycles, the pores left by the loss of soluble components accumulate (Figures 13(g) and 13(h)). Under repeated loading, the slip distance between the particles increased, and the cracks had sufficient time to develop and expand, which led to a loose internal structure and increased deformation. After 21 wet-dry cycles, wider fractures can be observed at the interface zone compared to the microstructure without wet-dry cycles (Figures 13(e) and 13(f)), illustrating the fact that the formation of fractures and pores significantly aggravates the deformation.Figure 12
The internal structure schematic diagram of RC subjected to different wet-dry cycles.Figure 13
Microstructures of the interfacial transition zone, subjected to (a) 0 wet-dry cycles, (b) 0 wet-dry cycles, (c) 14 wet-dry cycles at 20°C, (d) 14 wet-dry cycles at 60°C, (e) 21 wet-dry cycles at 20°C, (f) 21 wet-dry cycles at 60°C, (g) 28 wet-dry cycles at 20°C, and (h) 28 wet-dry cycles at 60°C.
(a)(b)(c)(d)(e)(f)(g)(h)Comparing the specimens subjected to the same wet-dry cycles, it can be seen that the higher the temperature, the looser the cement matrix and the longer the fracture length. The interaction effect caused by the negative influence of the temperature and wet-dry cycles resulted in the differential deformation and internal stress of the rubber particles and cement paste, and the internal structure was not as dense as before. This resulted in the more severe fatigue plastic damage of RC in the hygrothermal environment.


## 3.6.1. Damage Variable of Elastic Modulus

The elastic modulusE0 reflects the deformation resistance of concrete and is essential for evaluating the material performance. The elastic modulus E0 is calculated using the elastic stage of the unloading curve, which can be expressed as follows:(1)E0=σεe.The elastic modulusE0 of the RC subjected to various wet-dry cycles after 10, 20, 30, 40, 50, and 60 loading cycles is shown in Figure 9. As can be seen, E0 of the RC specimen after 10, 20, 30, 40, 50, and 60 loading cycles fluctuated within a certain range. Therefore, the average E¯0 value was used to investigate the influence of the wet-dry cycles on the elastic modulus of RC [38]. According to Ma et al. [39], the increase of E¯0 after different wet-dry cycles was defined as the total damage variable DEn, and the average increase of E¯0 after each adjacent wet-dry cycle was defined the phase damage variable ΔDE, as follows:(2)DEn=E¯0n−E¯00E¯00,(3)ΔDE=DEn−DEmn−m,where E¯00 is the average elastic modulus of RC without soaking and E¯0n is the average elastic modulus of RC when the wet-dry cycle is n. When the number of the wet-dry cycle n is 7, 14, 21, and 28, the corresponding m value is 0, 7, 14, and 21.Figure 9
Elastic modulus of RC after being subjected to different wet-dry cycles.According to the definition in (2) and (3), the trend of the total damage variable DEn and the phase damage variable ΔDE of the RC specimen subjected to various wet-dry cycles are shown in Figure 8.As shown in Figures9 and 10, as the wet-dry cycles increased, the elastic modulus increased, and its total deterioration gradually increased. This is attributed to the fact that the amount of damage and energy dissipation increased, which accelerated the fatigue process. When the temperature was 20°C, the total damage variable of RC was 16.28% after seven wet-dry cycles. As the wet-dry cycles increased, the total degradation variables were 19.73%, 21.18%, and 22.60%.Figure 10
Total damage variable and phase damage variable of RC after being subjected to different wet-dry cycles.However, during this process, the phase deterioration gradually decreased: the 0–7 phase of damage decreased up to 2.33%, and the 21–28 phase of damage decreased by the minimum amount of only 1.41%, which indicates that the wet-dry cycles result in the gradual deterioration of RC.


## 3.6.2. Damage Variable of Plastic Strain

Considering that the concrete is brittle and ductile, and its failure is mainly caused by excessive deformation, strain is one of the important indices for controlling the structural deformation and investigating the safety of concrete. The failure strain, which is also known as peak strain, is the strain that indicates structural failure and is denoted asεf. The plastic strain εp refers to the deformation that cannot be recovered, which is known as residual deformation. To measure the fatigue plastic damage of RC specimens under cyclic loading, the ratio of the plastic strain εp to the peak strain εf in 0–60 loading cycles is defined as the damage variable Dε and is expressed as follows [19]:(4)Dε=εpεf.Figure11 shows the variation of Dε under different wet-dry cycles. Under the coupling action of wet-dry cycles and cyclic loading, the damage variable of the RC specimen increased with the number of wet-dry cycles. When the temperature was 20°C, the Dε values of RC after 0, 7, 14, 21, and 28 wet-dry cycles were 0.457, 0.617, 0.626, 0.651, and 0.679, respectively. Comparing the specimen without wet-dry cycle, the Dε values of RC at 20°C after 7, 14, 21, and 28 wet-dry cycles increased by 35.01%, 36.98%, 42.45%, and 48.58%, while those of 60°C increased by 35.89%, 45.73%, 61.27%, and 88.40%, respectively. After the same wet-dry cycles, the Dε values increased with the temperature. After 7, 14, 21, and 28 wet-dry cycles, compared with 20°C, the Dε value increased by 0.32%, 3.19%, 6.61%, and 11.76%, respectively.Figure 11
Damage variableDε of RC subjected to different wet-dry cycles.


## 3.6.3. Damage Mechanism Analysis

From the results we have obtained, one can conclude that the damage caused by the wet-dry cycles to the concrete is not negligible. Figure12 shows the schematic diagram of internal structure, and Figure 13 displays the microstructure of the interfacial zone in the hygrothermal environment. The repeated soaking and high temperature drying precipitated the internal microcracks through. The soluble particles in the specimen were lost through the leftover pores, while the remaining particles expanded during the drying process and formed new internal voids and cracks. With the increase of wet-dry cycles, the pores left by the loss of soluble components accumulate (Figures 13(g) and 13(h)). Under repeated loading, the slip distance between the particles increased, and the cracks had sufficient time to develop and expand, which led to a loose internal structure and increased deformation. After 21 wet-dry cycles, wider fractures can be observed at the interface zone compared to the microstructure without wet-dry cycles (Figures 13(e) and 13(f)), illustrating the fact that the formation of fractures and pores significantly aggravates the deformation.Figure 12
The internal structure schematic diagram of RC subjected to different wet-dry cycles.Figure 13
Microstructures of the interfacial transition zone, subjected to (a) 0 wet-dry cycles, (b) 0 wet-dry cycles, (c) 14 wet-dry cycles at 20°C, (d) 14 wet-dry cycles at 60°C, (e) 21 wet-dry cycles at 20°C, (f) 21 wet-dry cycles at 60°C, (g) 28 wet-dry cycles at 20°C, and (h) 28 wet-dry cycles at 60°C.
(a)(b)(c)(d)(e)(f)(g)(h)Comparing the specimens subjected to the same wet-dry cycles, it can be seen that the higher the temperature, the looser the cement matrix and the longer the fracture length. The interaction effect caused by the negative influence of the temperature and wet-dry cycles resulted in the differential deformation and internal stress of the rubber particles and cement paste, and the internal structure was not as dense as before. This resulted in the more severe fatigue plastic damage of RC in the hygrothermal environment.


## 4. Conclusions

In this study, a cyclic loading test was carried out on RC subjected to different wet-dry cycles at different temperatures. The loading strain, plastic strain, and elastic strain of the specimens were compared and analyzed. Additionally, the damage variable was defined based on the elastic modulus and plastic strain. The main findings of this study are as follows:(1)
There existed primary pores and microcracks in the RC owing to the addition of hydrophobic rubber particles. The loading strain and plastic strain of the RC were obvious after the 1st loading cycle. As the number of loading cycles increased, the stress-strain curve became denser and the RC exhibited good elasticity.(2)
As the number of wet-dry cycles increased, the average plastic strain in the 10th–60th increased while the average elastic strain declined. Compared with the RC specimens without soaking, the average plastic strain in the 0th–60th loading cycle of the specimens, which were subjected to 7, 14, 21, and 28 wet-dry cycles at 20°C, increased by 31.82%, 40.91%, 77.27%, and 254.55%, respectively.(3)
The elastic modulus of RC increased logarithmically with the number of wet-dry cycles. The total damage variable gradually increased, which indicates that the deterioration of RC is a continuing process induced by the wet-dry cycles. The damage variable of the elastic modulus was maximum during the 0th–7th wet-dry cycles, that is, 16.27% at 20°C and 17.01% at 60°C, respectively.(4)
The comparison of the damage variable, which was defined based on the elastic modulus and plastic strain, revealed that the coupled corrosion of the hygrothermal environment and cyclic loading made the deterioration of durability performance easier, and fatigue damage accumulated faster.



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*Source: 9913297-2021-07-16.xml*