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Uniaxial compression stress–strain relationship of fully aeolian sand concrete at low temperatures

  • Wei Dong , Zhiqiang Ren EMAIL logo and Menghu Zhou
Published/Copyright: September 9, 2024
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Science and Engineering of Composite Materials
From the journal Science and Engineering of Composite Materials Volume 31 Issue 1

Abstract

The aim of this study is to investigate the impact of various ambient temperatures on the mechanical properties of full aeolian sand concrete (ASC100). Using ordinary concrete (ASC0) as the control group, we analyzed the effects of different ambient temperatures (−20, −15, −10, −5, 0, and 20°C) on the mechanical properties of both ASC0 and ASC100 through cube compression, splitting tensile, and uniaxial compression tests. The results demonstrate that the compressive strength and splitting tensile strength of concrete cubes increased with decreasing temperature. At −20°C, the compressive strength of ASC100 increased by 30.1% and that of ASC0 increased by 27.31% compared to that at 20°C. Additionally, compared to normal temperatures, the elastic modulus of ASC0 and ASC100 at subzero temperatures increased by 28.2–61.4% and 6.8–65.7%, respectively, while the peak stress increased by 7–35% and 6.8–38%, respectively. The stress–strain curve of ASC100 showed three stages: elastic, elastic-plastic, and yield failure, serving as the reference group. Finally, based on the classical constitutive model, we modified the constitutive parameters by axial compressive strength and temperature, proposing a constitutive model of concrete suitable for different low-temperature environments, which is in good agreement with experimental data.

Keywords: aeolian sand concrete; low temperature; mechanical properties; stress–strain curve; constitutive model

1 Introduction

With the robust development of the construction industry, there has been an escalating demand and exploitation of natural river sand, causing significant ecological damage [1]. Therefore, it is highly essential to find alternatives to construction sand. Simultaneously, the exacerbation of desertification in Northwest China has not only caused a severe decline in the land production capacity but also increased the probability of natural disasters such as sandstorms [2,3]. Aeolian sand, also referred to as desert sand, is a specific type of fine sand widely distributed in deserts and the Gobi region [4]. Utilizing aeolian sand as a substitute for river sand in concrete fine aggregate to produce aeolian sand concrete (ASC) not only addresses the scarcity of building materials but also aligns with the principles of environmentally sustainable development [5]. The mechanical qualities of concrete are put to the test when it comes to engineering applications where concrete buildings may be placed in challenging and complicated settings, including severe climates, earthquakes, and construction impacts during construction or service [6]. Therefore, in order to ensure the normal usage of ASC at low temperatures, it has important engineering significance to study the mechanical properties of ASC at different temperatures.

In recent years, the incorporation of aeolian sand in concrete production has garnered significant attention, attributed to its potential to enhance the mechanical and durability properties of concrete. For instance, the processability and mechanical properties of ASC have been markedly enhanced through the optimization of aggregate grading and the augmentation of concrete density [7]. Additionally, Dong et al. [8] investigated the frost resistance of ASC across varying aeolian sand replacement rates and identified the optimal replacement rate to be 20–30%, considering the extent of freeze–thaw damage. Subsequent research by Li et al. [9] demonstrated that a 100% aeolian sand replacement maximized the frost resistance of ASC, with a 19.49% increase in freeze–thaw fatigue life compared to that of conventional concrete. Furthermore, Dong and Wang [10] examined the degradation mechanism of ASC under sulfate freeze–thaw conditions, revealing that a 100% aeolian sand replacement rate significantly mitigated the damage and deterioration induced by salt freeze erosion. Jiang et al. [11] explored the use of aeolian sand in creating ultra-high performance concrete (UHPC); the results show that aeolian sand can improve the workability and mechanical properties of UHPC and reduce the porosity under the new process of enhanced stirring. However, the increase in cement hydration degree remains relatively modest. Li et al. [12] used nuclear magnetic resonance (NMR), nanoindentation, and SEM to explore the micropore, mechanical, and morphological properties of ASC after carbonization. The results showed that the corrosion resistance of ASC surface was intact, while ordinary concrete was damaged to varying degrees. Bai et al. [13,14] performed freeze–thaw cycle tests on ASC with the aeolian sand content as a variable. The results show that the introduction of aeolian sand can inhibit and delay the damage and deterioration of concrete, thus enhancing its frost resistance. The frost resistance of ASC is significantly improved when the aeolian sand content is above 80%. Although research on ASC is abundant, studies on its low-temperature mechanical properties are limited. Given that the mechanical properties of concrete change significantly in low-temperature environments, it is crucial to investigate the impact of low temperatures on ASC. This research is significant for ensuring the safety and durability of ASC structures in civil engineering projects in Northwest China and other cold regions worldwide.

The low-temperature performance of concrete is pivotal for its durability and structural integrity in cold climates. Guo et al. [15] investigated the low-temperature performance of asphalt mixtures reinforced with glass fibers, basalt fibers, and steel fibers. Their findings indicated that basalt fibers demonstrated superior low-temperature performance and crack resistance compared to glass and steel fibers in cold environments. Additionally, it has been well documented that the mechanical properties of concrete, including compressive strength and elastic modulus, undergo significant changes with variations in temperature [16]. Li et al. [17] utilized low-field NMR (LF-NMR) to examine the microstructural properties of concrete subjected to subzero temperatures. This technique proved effective in monitoring the liquid water content and assessing the efficacy of antifreeze additives, which are crucial for mitigating frost heave stress and enhancing the early performance of concrete in negative temperature conditions. Yu et al. [18] studied the variation of axial compressive mechanical properties of concrete at 20 ∼ −60°C. The results show that the peak load and the degree of damage increase as the temperature decreases. Hu and Fan [19] conducted a three-point flexural fracture test to examine the fracture mode and parameters of concrete at different temperature levels (−40, −20, 0, and 20°C). The results reveal significant changes in the shape of the softening curve and in the fracture parameters as the temperature decreases. Xie et al. [20] observed enhancements in the crack resistance and ultimate bearing capacity of concrete beams subjected to three-point bending as temperatures decreased. Notably, the transition from 20 to −80°C resulted in marked improvements in fracture toughness and energy absorption capacity for concrete specimens. Jin [21] performed studies investigating the static uniaxial compression and splitting tensile performance of concretes with varying sizes (100, 150, and 300 mm) at four distinct temperature levels (+20, −30, −60, and −90°C), indicating that lower temperatures led to increased brittleness but improved strength properties. In summary, the mechanical properties of concrete undergo significant changes in low-temperature environments, and there is a paucity of research on the properties of ASC under such conditions. Therefore, investigating the mechanical properties of ASC at low temperatures is of substantial importance.

The stress–strain relationship serves as a mathematical model to characterize the macroscopic properties of materials. It is instrumental in analyzing material failure causes, mechanisms, and failure modes under various stresses, thereby significantly contributing to the enhancement of material properties and nonlinear analysis [22]. Tang et al. [23] investigated the mechanical properties and stress–strain behavior of fully recycled aggregate concrete (FRAC). Their findings indicated that incorporating recycled materials generally reduces the strength and elastic modulus, and there are notable differences in the impact of recycled aggregate and recycled cementitious materials on the stress–strain curve. Additionally, Liao et al. [24] examined the stress–strain relationship of FRP-confined UHPC and proposed a novel design-oriented stress–strain model. This new model accurately predicts characteristic stress and strain. However, studies on the constitutive relationship of concrete in low-temperature environments are scarce, with limited focus on the changes in stress–strain behavior of ASC under such conditions.

In summary, the current research on ASC is fairly comprehensive, but there are still deficiencies. In this article, ASC100 is prepared by replacing the river sand with 100% aeolian sand. The variation of mechanical properties and the mechanism of low temperature action under low temperature environments (0, −5, −10, −15, and −20°C) were studied. Finally, based on the classical constitutive model, we modified the parameters of the constitutive model based on key parameters such as the axial compressive strength and temperature and established the ASC constitutive model in different low-temperature environments. It provides a theoretical reference for the application of ASC in cryogenic environments.

2 Experimental program

2.1 Raw materials of the ASC

2.1.1 Cement

P.O. 42.5R ordinary Portland cement produced by the Inner Mongolia Mengxi Cement Company was used in the study. Table 1 shows the performance metrics of the cement.

Table 1

Main physical indicators of cement

Indexes Density (g/cm3) SWSC (%) Setting time (min) Compressive strength (MPa) Flexural strength (MPa)
Initial Final 3 days 28 days 3 days 28 days
Test results 3.1 26.4 132 228 24.7 53.6 5.3 8.4

SCWC: standard consistency water consumption.

2.1.2 Fly ash (FA)

Grade II FA produced by the Daqi Power Plant in Inner Mongolia was used. The water requirement was 95%, the loss on ignition was 2.8% and the apparent density was 2,200 kg/m3.

2.1.3 Coarse aggregate

Continuous graded ordinary gravel used was of 5–25 mm size with an apparent density of 2,550 kg/m3 and a mud content of 2.1%.

2.1.4 Fine aggregate

Natural river sand with good particle gradation and aeolian sand from Ordos, China, were used in the study. The grain size distribution of fine aggregates is illustrated in Figure 1. Essential physical property indices and chemical compositions of fine aggregates are outlined in Table 2 and Table 3, as determined by the experimental method outlined in “Standards for quality and inspection methods of sand and stone for ordinary concrete” (JGJ 52-2006) [25].

Figure 1 Grading curves of various fine aggregates.
Figure 1

Grading curves of various fine aggregates.

Table 2

Physical properties of fine aggregates

Type Apparent density (kg/m3) Bulk density (kg/m3) Water content (%) Mud content (%) Fineness modulus Chloride ion content (%)
River sand 2,610 1,550 2.0 0.9 2.6 0.29
Aeolian sand 2,660 1,560 0.2 0.4 0.8 0.02
Table 3

Chemical composition of aeolian sand and natural river sand (in %)

Material SiO2 Al2O3 CaO Fe2O3 K2O Na2O C MgO Other
River sand 76.3 6.9 5.1 2.4 1.3 2.4 2.2 1.3 1.8
Aeolian sand 74.4 9.0 4.1 3.0 1.7 2.0 1.6 1.4 2.8

2.1.5 Water

Water used in the study was ordinary tap water.

2.1.6 Water-reducing agent

Polycarboxylic acid was utilized as a high-efficiency water-reducing agent with a reduction rate of 23%.

2.2 Mix proportion of ASC

Table 4 presents the detailed mixing proportion of ASC. The mix design followed the guidelines outlined in ref. [26]. The test design employed ASC0 (ordinary concrete) with a water–cement ratio of 0.55 and a sand ratio of 38%. Based on this, aeolian sand of equivalent quality was substituted for ordinary river sand to produce ASC100, a full aeolian sand concrete. Specimen preparation followed the ref. [27]. Prism specimens measuring 150 mm × 150 mm × 300 mm were employed for uniaxial compression tests, while specimens of dimensions 100 mm × 100 mm × 100 mm were utilized for cube compression and splitting tensile tests.

Table 4

Concrete mix proportion and basic performance index (in (kg/m3))

Group Cement FA River sand Aeolian sand Coarse aggregate Water Water reducing agent 28d cube compressive strength (MPa) Slump (mm)
ASC0 330 35 697 0 1,138 200 3.65 41.7 200
ASC100 330 35 0 697 1,138 200 3.65 40.3 135

2.3 Test setup and loading

The specimen preparation process is shown in Figure 2. The test method and data processing were in accordance with the ref. [28]. First, the specimens were removed after 28 days of standard curing and divided into six groups. The test temperature for the first group was set at 20°C (room temperature), requiring no special treatment. The other five groups underwent low-temperature treatment prior to testing to simulate the environmental conditions of concrete in cold climates. Specifically, the low-temperature test chamber was set to 0, −5, −10, −15, and −20°C, respectively. Once the chamber reached the target temperatures, the remaining five groups of specimens were placed inside and exposed to these conditions. After 24 h, the specimens were removed for testing.

Figure 2 Schematic diagram of the specimen preparation process.
Figure 2

Schematic diagram of the specimen preparation process.

The axial compression apparatus used in this paper is illustrated in Figure 3. A microcomputer-controlled electro-hydraulic servo press was employed for the compression test on the prism. Test data were automatically collected using a DTS-530 high-speed static data acquisition instrument. Because it is challenging to obtain the descent profile of the stress–strain curve, this test used an additional rigid element on the hydraulic test machine to enhance the rigidity of the test machine. Two displacement meters were positioned on either side of the specimen to measure the vertical displacement, and concrete strain gauges were affixed to the vertical and horizontal centerlines of the remaining two sides to measure concrete strain in the ascending section of the stress–strain curve. To efficiently capture the ascending section of the stress–strain curve, an initial loading rate of 0.010 mm/s was used until the stress reached approximately 75% of the peak stress. Subsequently, the loading rate was reduced to 0.003 mm/s to fully capture the descending curve.

Figure 3 Axial compressive test apparatus.
Figure 3

Axial compressive test apparatus.

3 Results and discussion

3.1 Compressive strength and split tensile strength analysis

Figures 4 and 5 show the variation trend of compressive strength and splitting tensile strength of ASC0 and ASC100 at different temperatures, respectively. With the decrease of temperature, the compressive strength and splitting tensile strength of the two groups of concrete show a gradual increasing trend. This is due to the freezing of pore water at low temperatures, which fills the internal voids and increases the compactness of concrete. At the same time, the appearance of ice crystals enhances the stress level near the pores and improves the bonding force between the aggregate and the mortar, thus delaying the development of microcracks [29]. Specifically, according to the data in Figure 4, at 0, −5, −10, −15, and −20°C, the compressive strength of the ASC0 group increased by 5.28, 10.07, 15.11, 20.62, and 27.31%, respectively, compared with that at 20°C, while that of the ASC100 group increased by 6.37, 12.08, 16.51, 22.38, and 30.1%, respectively. In each low temperature environment, the increase of compressive strength values of the ASC100 group was lower than those of the ASC0 group. This is because the specific surface area of aeolian sand is larger than that of river sand. The incorporation of aeolian sand destroys the particle gradation of aggregate, and the quantitative cementitious material is not enough to fully cover the concrete aggregate particles, thereby increasing the porosity and macropore proportion in concrete. According to the data in Figure 5, at 20°C, the splitting tensile strength of the ASC0 group increased by 6.84, 17.09, 53.84, 79.06, and 86.32%, respectively, compared with that at the subzero temperature environment, while that of the ASC100 group increased by 1.34, 16.96, 36.16, 42.86, and 48.21%, respectively. This shows that the decrease of temperature reduces the tensile strength difference between the cement mortar and coarse aggregate [30], followed by an improvement of the tensile strength of the interfacial transition zone.

Figure 4 Curve of compressive strength at different temperatures.
Figure 4

Curve of compressive strength at different temperatures.

Figure 5 Curve of tensile strength at different temperatures.
Figure 5

Curve of tensile strength at different temperatures.

3.2 Specimen failure process and damage mechanism

Figure 6 shows the uniaxial compressive damage morphology of ASC0 and ASC100 at different temperatures. It is observed that the collapse modes at low temperatures are similar for both ASC0 and ASC100 specimens. The failure behavior encompasses three stages: crack initiation, crack propagation, and specimen rupture. At the initial stage of low applied load, the propagation of microcracks in the interfacial transition zone of concrete is offset by the compaction action. As the applied load increases, the concrete begins to suffer visible damage upon entering the second stage, which manifests itself as minute vertical cracks along the periphery of the specimen in the longitudinal axis. In the third stage, when the load is close to the peak stress, the vertical compressive strain increases rapidly, resulting in lateral expansion of the specimen and increasing and traversing the vertical crack. The specimen undergoes instantaneous failure, accompanied by a clear cracking sound. It can be seen from Figure 6 that as the temperature is lowered, the integrity of the specimen after failure first deteriorates and then becomes better, and the phenomenon of missing corners is more pronounced. As shown in Figure 7, the reason for this phenomenon is as follows: when the pore water freezes, ice fills the voids, reducing the stress levels and stress concentration near voids, retarding micro-crack development, and strengthening the bond between the aggregate and the cementitious material [31]. Therefore, the strength is increased and the brittleness is increased correspondingly.

Figure 6 Failure mode of concrete under uniaxial compression at different temperatures. (a) −20°C, (b) −15°C, (c) −10°C, (d) −5°C, (e) 0°C, and (f) 20°C.
Figure 6

Failure mode of concrete under uniaxial compression at different temperatures. (a) −20°C, (b) −15°C, (c) −10°C, (d) −5°C, (e) 0°C, and (f) 20°C.

Figure 7 Phase transition diagram of pore water.
Figure 7

Phase transition diagram of pore water.

3.3 Uniaxial compressive stress–strain full curve characterization

A comprehensive reflection of a material’s constitutive relation structure or macroscopic mechanical properties under different deformation conditions is provided by different constitutive models [32]. Figure 8 displays the stress–strain curves in various low-temperature environments.

Figure 8 Stress–strain curves: (a) ASC0 and (b) ASC100.
Figure 8

Stress–strain curves: (a) ASC0 and (b) ASC100.

1. The rise of the stress–strain curve includes three different stages: linear elasticity (σ < 0.4 f c), elastic plasticity (0.4 f c < σ < 0.9 f c), and strain hardening (0.9 f c < σ < f c). Figure 8 illustrates that with decreasing temperature, the slope of the curve in the linear elastic stage and the peak stress both increase. This phenomenon is attributed to the ongoing freezing of pore water, resulting in ice filling the pores, thereby improving the original microcracks and additional initial defects in the concrete.

2. After the peak stress, the stress–strain curve enters a decreasing profile. A comparison of the stress–strain curves of ASC0 and ASC100 at different temperatures reveals that the curves become steeper with decreasing temperature. In low-temperature conditions, water within the concrete freezes, forming ice crystals that induce volume expansion and internal stress. This phenomenon leads to the propagation of microcracks within the concrete, consequently increasing its brittleness. Consequently, the ductility of the specimen is lessened, and the damage is more rapid.

3.4 Evaluation of the toughness index and brittleness index

Failure modes can be classified as either brittle or ductile based on the ultimate strength and deformation of different materials, which are obviously different. It is important to research the toughness and brittleness of concrete because brittle failure in practical engineering should be minimized as much as feasible. The energy ratio approach is used to solve the toughness index and brittleness index based on the toughness assessment techniques of ASTM-C1080 and JSCE-SF4. As shown in Figure 9, with 1.0 and 3.0 times of the peak strain chosen as the typical reference points, or ε p and 3ε p. The toughness index and brittleness index calculation formulae are shown in Equations (1) and (2).

(1) I = A 1 + A 2 A 1 = ∫ 0 3 ε P σ d ε ∫ 0 ε P σ d ε ,

(2) C = A 1 A 2 = ∫ 0 ε P σ d ε ∫ ε P 3 ε P σ d ε = 1 I − 1 .

Figure 9 Characteristic points and calculation area of the toughness index.
Figure 9

Characteristic points and calculation area of the toughness index.

The brittleness index is indicated by C in the formula, and the toughness index is indicated by I. The region between the peak point and the equivalent point of three times the peak strain is represented by A 2, while the area contained by the stress–strain curve before the peak point is represented by A 1.

Figure 10 displays the toughness index and brittleness index computation results. The toughness index I and the brittleness index C exhibit opposite changing tendencies, as can be seen in the diagram. The toughness index falls as the temperature drops, but the brittleness index rises. This is due to the fact that when strain increases, stress rapidly drops, exhibiting clear strain softening, and the specimen exhibits brittle failure characteristics. The strain softening is more noticeable at lower temperatures. At 20°C, the ASC0 and ASC100 brittleness indices increased by 151.4 and 36.2%, respectively, and toughness indices dropped by 44.1 and 18.7%, respectively, as compared to the room temperature environment. Consequently, the addition of aeolian sand improves concrete’s resistance to low temperatures and lessens the temperature sensitivity of ASC.

Figure 10 Toughness index I and brittleness index C.
Figure 10

Toughness index I and brittleness index C.

3.5 Energy dissipation analysis

The process of energy dissipation is fundamental to the damage that a specimen experiences under load, and it can provide insight into the extent of the specimen’s damage. In general, the greater the energy dissipation capacity of a specimen, the bigger its energy dissipation coefficient. Therefore, the more the energy is dissipated, the less likely the structural damage would occur. With reference to the theory of seismic resistance in buildings, the following formula represents the energy dissipation coefficient E:

(3) E = S OABC / S OEDC .

In the formula, S OABC stands for the area contained by the abscissa axis, the load–displacement curve, and the limit load σ u point abscissa line. The coordinate axis of S OEDC indicates the region bound by the vertical line of σ u, the ultimate load point, and the horizontal line of σ max, the maximum load point. The ultimate load σ u is 0.85 σ max. The computed area’s schematic diagram is displayed in Figure 11. Table 5 displays the ASC0 and ASC100 results that were computed using formula (3).

Figure 11 Calculation area diagram of energy dissipation coefficient.
Figure 11

Calculation area diagram of energy dissipation coefficient.

Table 5

Coefficient of energy dissipation

No. 20°C 0°C −5°C −10°C −15°C −20°C
AC0 0.779 0.794 0.816 0.875 0.909 0.959
ASC100 0.743 0.776 0.779 0.876 0.884 0.973

Table 5 demonstrates that when temperature drops, the energy dissipation coefficient rises. This is due to the fact that when the temperature drops, ice crystals fill the pores and make the concrete interface transition zone more compact, which increases the specimen’s bearing capacity and total energy consumption. Second, some energy is lost during the ice crystal disintegration. At −20°C, the energy dissipation coefficient of ASC0 and ASC100 increased by 23.1 and 31.0%, respectively, compared with the normal temperature environment (20°C). This suggests that the ability of ASC to absorb energy is enhanced by a drop in the temperature.

3.6 Typical features of the stress–strain curve

The main features reflecting the stress–strain behavior include the peak stress (f c), peak strain (ε c), elastic modulus (E c), and Poisson’s ratio (μ).

3.6.1 Peak stress

The peak stress of ASC0 and ASC100 increases with the decrease of temperature, as shown in Figure 12. Furthermore, when the specimens were exposed to temperatures of 20, 0, −5, −10, −15, and −20°C, respectively, the peak stress of ASC0 was found to be 1.09, 1.08, 1.06, 1.12, and 1.07 times that of ASC100. The reduction in temperature from room temperature to −20°C resulted in an increase in peak stresses for ASC0 and ASC100 by approximately 34.5 and 38.1%, respectively. This transition can be attributed to the transformation of pore water from a liquid to a solid phase when the temperature falls below the freezing point of pore water. Moreover, the lower the temperature, the more pronounced the effect of the ice-bearing pressure skeleton, leading to an increase in concrete stiffness. Additionally, the effect of temperature reduction on the improvement of the structural performance of the interface transition zone (ITZ) cannot be ignored. When the temperature drops below the freezing point, ice crystals formed at the bonding interface can increase the mechanical interlocking force between materials, thereby improving the bonding strength of the ITZ [33]. Meanwhile, hydrophilic silicate materials can attract and retain water molecules. As the temperature drops, the water molecules in the silicate material freeze, further enhancing the bonding force between materials. In a low-temperature environment, molecular movement is weakened, making the material less likely to deform and helping to maintain high bonding strength [34]. Therefore, the combined effect of ice and hydrophilic silicate materials in a low-temperature environment causes the bonding strength to increase as the temperature decreases, thereby increasing the peak stress of the ASC (Figure 13).

Figure 12 Relationship between the peak stress and temperature.
Figure 12

Relationship between the peak stress and temperature.

Figure 13 Mechanism of axial compression failure.
Figure 13

Mechanism of axial compression failure.

3.6.2 Peak strain

Figure 14 illustrates the correlation between the temperature and peak strain for ASC0 and ASC100. As depicted in Figure 14, the peak strain of ASC0 and ASC100 decreases with decreasing temperature. This reduction is attributed to the freezing of water in the pores at low temperatures, which increases the brittleness of concrete [35]. Compared to room temperature conditions, ASC100 exhibited a reduction in the peak strain of 4.9, 7.8, 9.5, 14.1, and 16.7% at temperatures of 0, −5, −10, −15, and −20°C, respectively, and the peak strain of ASC0 decreased by 6.7, 8.3, 16.7, 19, and 23.3%, respectively.

Figure 14 Relationship between the peak strain and temperature.
Figure 14

Relationship between the peak strain and temperature.

Figure 15 shows the relationship between the axial compression strength and peak strain for ASC0 and ASC100 at different temperatures, where the peak strain is inversely proportional to the axial compression strength. Specifically, the strength of the specimen increases, while its deformation capacity decreases. In general, as the temperature increases, the damage resistance of the ASC0 and ASC100 structures weakens; in other words, the stiffness of the concrete decreases, and the safety factor of the structure decreases. According to the linear fitting formula, the fitting degree of ASC100 (0.8927) is better than that of ASC0 (0.8094), indicating that the ASC100 fitting formula can predict more accurately.

Figure 15 Relationship between the peak stress and peak strain.
Figure 15

Relationship between the peak stress and peak strain.

3.6.3 Elastic modulus

Figure 16 illustrates the temperature dependence of the elastic modulus for ASC0 and ASC100. The analysis shows that the modulus of elasticity increases with decreasing temperature for both concretes. Compared to 20°C, the elastic modulus of ASC0 increased by 28, 30, 32.9, 48.3, and 61.4% at temperatures of 0, −5, −10, −15, and −20°C, respectively. In contrast, the elastic modulus of ASC100 increased by 6.8, 9.4, 14.3, 45.4, and 65.7% at the same respective temperatures. This is because as the temperature decreases, more pore water freezes, generating a large number of ice crystals that fill the pores in the concrete structure, making it denser [36]. Additionally, when the temperature dropped from 0 to −10°C, the elastic modulus increments of ASC0 and ASC100 were 3.6 and 4.5%, respectively, but when the temperature decreased from −10 to −20°C, the elastic modulus increments of ASC0 and ASC100 were 21.5 and 50%, respectively. That is, the elastic modulus initially increased at a faster rate with decreasing temperature [37]. On the one hand, the ice crystals themselves have high strength and hardness, which can bear part of the load and act as a skeleton [38]. On the other hand, the bonding force between the coarse aggregate and cement stone is greatly improved under the action of ice, delaying the occurrence of microcracks in the ITZ and reducing the relative deformation between the aggregate and the cement matrix [39]. Therefore, the elastic modulus of concrete at low temperatures will be significantly improved.

Figure 16 Curve of elastic modulus versus temperature.
Figure 16

Curve of elastic modulus versus temperature.

3.6.4 Poisson’s ratio

Poisson’s ratio holds a pivotal role in the design and calculation of structural concrete members, serving as a critical parameter reflecting concrete deformation and providing insight into internal crack development [40]. Figure 17 shows the Poisson’s ratio as a function of temperature for the two concrete types. In general, the Poisson’s ratio shows a decreasing trend with increasing temperature, indicating a reduction in specific dilatonic deformation as the temperature rises. This trend is primarily attributed to the phase transition of concrete pore water at lower temperatures, leading to the generation of pore expansion stress and subsequently increasing the lateral deformation of the concrete [41].

Figure 17 Relationship between Poisson’s ratio and temperature.
Figure 17

Relationship between Poisson’s ratio and temperature.

At −20, −15, and −10°C, the Poisson’s ratio of ASC0 is 17.6, 23.7, and 4.9% larger than that of ASC100, respectively. This observation suggests that the incorporation of aeolian sand constrains the transverse expansion of the concrete and reduces its transverse strain.

4 Constitutive relationship of concrete axial compression

4.1 Comparison with existing models

Currently, there is a great deal of domestic and international research being done on the constitutive connection of concrete under compression, leading to the establishment of various kinds of constitutive models. On the whole, the research on the constitutive relationship of concrete is mostly focused on ordinary concrete at room temperature, and there are few studies on the constitutive model of ASC, especially in a low temperature environment [42,43]. It can be seen from Section 3.3 that the stress and deformation process of ASC is similar to that of ordinary concrete. The study is based on the results of research by experts from home and abroad on the constitutive relationships of concrete under uniaxial compression at room temperature. Simultaneously, the remarkable distinction between the ASC0 and ASC100 stress–strain curves in the descending and ascending regions at low temperatures is considered. The experimental data in this work were fitted using the conventional constitutive relation model of the piecewise functional Guo [44] and Mander models [45].

Among them, the Guo model [44] is a piecewise form, bound by the peak strain and divided into ascending and descending profiles. They are expressed as follows:

(4) y = a x + ( 3 − 2 a ) x 2 + ( a − 2 ) x 3 1 > x > 0 ,

(5) y = x b ( x − 1 ) 2 + x x > 1 .

The stress–strain curve in the Mander model [45] is described by the unified rational equation. In the rising part of the current “Code for Design of Concrete Structures” (GB50010-2010) [46], a term akin to Mander’s proposal is utilized.

(6) σ = σ C x r r − 1 + x r ,

Note: x = ε/ε 0; y = σ/σ c, where σ c is the peak stress, ε 0 is the peak strain; a, b, and r are the undetermined parameters of the model.

The dimensionless ASC uniaxial compression curve was fitted with two models for the ascending and descending segments and with the Mander model [45] for the entire curve. Tables 6 and 7 present the fitting findings, respectively.

Table 6

Guo model fitting coefficient of determination R 2

Type Phase Coefficient 20°C 0°C −5°C −10°C −15°C −20°C
ASC0 Ascending stage a 0.995 0.998 0.993 0.995 0.995 0.995
Declining stage b 0.979 0.973 0.896 0.997 0.949 0.955
ASC100 Ascending stage a 0.981 0.985 0.983 0.982 0.981 0.983
Declining stage b 0.902 0.996 0.991 0.995 0.992 0.991
Table 7

Mander model fitting determination coefficient R 2

Type Phase Coefficient 20°C 0°C −5°C −10°C −15°C −20°C
ASC0 Ascending stage r 0.994 0.997 0.997 0.998 0.994 0.997
Declining stage 0.995 0.973 0.996 0.979 0.972 0.977
Complete curves 0.950 0.911 0.982 0.928 0.896 0.965
ASC100 Ascending stage r 0.994 0.999 0.997 0.994 0.994 0.999
Declining stage 0.993 0.992 0.996 0.979 0.972 0.972
Complete curves 0.978 0.975 0.995 0.928 0.896 0.976

The fitting findings of Tables 6 and 7 indicate that the Mander full curve model [45] does not perform well. The primary cause is because temperature variations have a major impact on the descending segment. Consequently, for the two types of concrete, a piecewise expression must be used. In the ascending and descending segments, the Guo model’s coefficient of determination is high for ASC0. Simultaneously, this study selects the same Guo model [44] as at room temperature to depict the stress–strain complete curve of ASC0 at low temperatures, taking into account the ease of engineering computation. It is evident from the examination of the ASC100 fitting data that the Mander model’s fitting effect in the rising portion is superior to that of the Guo model’s, and the variation law of the stress–strain curve is more visibly represented. The Guo model’s fitting degree is superior to the Mander model’s when the temperature drops. As a result, in this work, the Guo model [44] was utilized to explain the ASC100’s descending segment, while the Mander model [45] was chosen to describe its ascending section at low temperatures.

At low temperatures, the constitutive model of ASC100 is as follows:

(7) y = σ C x r r − 1 + x r , ( 0 ≤ x ≤ 1 ) y = x b ( x − 1 ) 2 + x , ( x ≥ 1 ) .

The constitutive model of ASC0 at low temperatures is as follows:

(8) y = A x + ( 3 − 2 A ) x 2 + ( A − 2 ) x 3 ( 0 ≤ x ≤ 1 ) y = x b ( x − 1 ) 2 + x ( x ≥ 1 ) .

4.2 Comparison of fitting curves and test curves

The model curve and the test curve may be created using the fitting model parameters found in Tables 6 and 7, in conjunction with the relevant uniaxial compression constitutive model, as seen in Figures 18 and 19. Simultaneously, the models (Equations (7) and (8)) suggested in this study are used to do the nonlinear fitting of the experimental data. Figures 18 and 19 also display the results.

Figure 18 ASC0 curve and model curve comparison fitting. (a) −20°C, (b) −15°C, (c) −10°C, (d) −5°C, (e) 0°C, and (f) 20°C.
Figure 18

ASC0 curve and model curve comparison fitting. (a) −20°C, (b) −15°C, (c) −10°C, (d) −5°C, (e) 0°C, and (f) 20°C.

Figure 19 ASC100 curve and model curve comparison fitting. (a) −20°C, (b) −15°C, (c) −10°C, (d) −5°C, (e) 0°C, and (f) 20°C.
Figure 19

ASC100 curve and model curve comparison fitting. (a) −20°C, (b) −15°C, (c) −10°C, (d) −5°C, (e) 0°C, and (f) 20°C.

In a detailed comparison, the Guo model [44] fits the experimental data better for ASC0 at low temperatures. In the case of ASC100 at low temperatures, the Guo model [44] can suit the falling part effectively, while the Mander model [45] clearly has a greater fitting impact in the ascending section. The comparison findings of Figures 18 and 19 show that the model developed in this work fits the stress–strain test curve to a sufficient degree throughout. The determination coefficient and value interval for the model fitting findings mentioned previously are displayed in Figure 20. It is evident that compared to previous models, the model developed in this work is better suited to represent the constitutive connection of ASC. This study’s constitutive model for predicting ASC at low temperatures offers valuable insights into its mechanical property changes. Nonetheless, extending this model to ASC with varying aeolian sand content requires future research to incorporate the aeolian sand content as a variable, enhancing the model’s reliability and applicability.

Figure 20 Determination coefficient and value range of two kinds of concrete.
Figure 20

Determination coefficient and value range of two kinds of concrete.

4.3 Determination of the parameters of the model

4.3.1 Parameter a of the ASC0 ascending stage

As depicted in Equation (4), the parameter a = E 0/E c signifies the ascending section of the concrete stress–strain curve, where E 0 is the initial tangential elastic modulus and E c is the peak secant modulus. The slope of the ascending phase is inversely proportional to the value of a. The value of a is the same as the deformation trend of the elastic modulus. A smaller a implies a more brittle material, resulting in a reduced area below the curve, indicating greater elastic deformation of the concrete, a lower residual strength, and a faster failure process.

Figure 21 shows the relationship between the elastic modulus and axial compressive strength obtained from ASC0, ASC100, and other literature sources [47]. The results from this study and MacLean and Lloyd [16] indicate that the axial compressive strength and elastic modulus increase with decreasing temperature. The law presented by Tu et al. [48], based on different carbonization concentrations, is similar to the observed law in the low-temperature environment of this study. Referring to the regression formula of E c and f cu in GB50010-2010, a regression analysis of E c and f c in this article yields the following regression formula:

(9) E c = 10 1.34 − 0.25 + 46.9 f c ,

(10) E c = 10 1.25 − 0.62 + 56.1 f c ,

where E c is the elastic modulus (GPa); f c is the axial compressive strength (MPa).

Figure 21 Relationship of the elastic modulus and axial compressive strength.
Figure 21

Relationship of the elastic modulus and axial compressive strength.

The parameters of the ascending segment a and the descending segment b have been extensively studied in the literature, but the corresponding factors differ. For example, Xiao et al. [47] propose that parameters a and b are related to the substitution rate of recycled aggregate, while Yan et al. [22] suggested that the water absorption of mixed recycled aggregate is closely linked to parameters a and b. However, Rao et al. [40] argued that polyvinyl alcohol content is a key factor in determining parameters a and b. It is evident that different research directions in concrete lead to different related factors for parameters a and b, making generalization challenging.

This article focuses on the constitutive relationship under different low-temperature environments, demonstrating that temperature plays a crucial role in determining the concrete behavior, and axial compressive strength is a key parameter of the stress–strain curve. Thus, this study establishes a relationship between temperature, axial compression strength, and coefficients a and b. Then, the present constitutive parameter a is fitted with the data of temperature T and concrete axial compressive strength f c, yielding the following fitted relationship:

(11) a = ( 23.04 T 2 − 0.096 ƒ c T 2 − 18.72 T + 0.078 ƒ c T + 0.01058 ƒ c − 2.5392 × 10 − 3 − 6 ( R 2 = 0.917 ) .

4.3.2 ASC100 parameter r

Mander et al. [45], in 1983, proposed a uniaxial compressive principal structure model for concrete, referred to as the Mander model. The model was fitted to the dimensionless ASC100 stress–strain test results at different temperatures to determine the corresponding fitting parameter r. The parameter r was further fitted to the axial compressive strength f c with temperature T, yielding the results presented in Equation (12).

(12) r = ( − 0.00124 T 2 − 2.6798 T ƒ c + 0.3109 T + 0.07808 ƒ c − 0.476992 ) × 10 − 3 ( R 2 = 0.907 ) .

4.3.3 Parameter b of the declining stage

The expression for the descending section of the stress–strain curve for both concrete types at low temperatures is shown in Equation (4). The decline section b to some extent indicates the steepness of the falling section, positively correlating with the absolute value of the falling section stiffness [44]. This model was separately fitted to the falling section of the stress–strain curve for both concrete types to determine parameter b. Subsequently, b was established as a function of temperature T and axial compressive strength f c, and the results are presented in Equations (13) and (14).

(13) b 0 = ( 0.132796 ƒ c T 2 − 0.000155 ƒ c T + 0.1325 ƒ c − 0.911 T 2 + 0.001067 T + 3 , 896 ) × 10 − 3 ( R 2 = 0.896 ) ,

(14) b 100 = ( 1.087 ƒ c T 2 + 0.00015 ƒ c T + 0.04327 ƒ c + 7.416 T 2 − 0.00103 T − 0.295 ) × 10 − 4 ( R 2 = 0.894 ) .

Using the Origin software developed by Origin Lab Company and based on the experimental data of Equations (7) and (8), a nonlinear least squares fitting approach employing the Levernberg–Marquardt algorithm (LMA) was utilized to determine the optimal parameters for both the rising and falling parts. Table 8 shows the correlation coefficients for parameters a and b. Additionally, under the same low-temperature conditions, the correlation coefficient of ASC0 is higher than that of ASC100, possibly attributed to the filling effect of aeolian sand [18].

Table 8

Fitting parameters and determination coefficients of the constitutive model

Type Coefficient 20°C 0°C −5°C −10°C −15°C −20°C
ASC0 a 2.389 2.405 2.098 2.354 2.515 1.782
b 3.357 3.579 1.648 3.114 5.937 5.177
ASC100 r 1.936 1.925 2.261 1.886 1.736 2.064
b 1.243 1.345 1.009 0.546 1.143 1.553

4.3.4 Proposed stress–strain model and model verification

The stress–strain model for ASC0 and ASC100 under uniaxial compression at low temperatures is proposed, as shown in Equations (7) and (8). A comparison with the results in Tables 7 and 8 shows that the experimental values align excellently with the model chosen in this article, with a correlation coefficient exceeding 0.97. Thus, the proposed model effectively predicts the stress–strain relationship of ASC100 and ASC0 in cryogenic environments.

To verify the adaptability of the proposed model, it is compared with the experimental curves of Wu et al. [49] at −20°C and Ning et al. [50] at −10°C. Figure 22 shows the comparison of results. Wu et al. [49] used natural river sand and a cyclic loading test method. Although the low temperature test method of Ning et al. [50] differs from the approach in this article (direct placement of the test block in a low-temperature environment for maintenance), Figure 22(c) suggests that the low-temperature test method has a minor effect on the test results. The ASC0 constitutive model presented in this article corresponds better to the experimental data in the literature at low temperatures due to the particularity of ASC itself. Overall, the stress–strain model presented here accurately predicts the trend of longitudinal deformation throughout the process with relatively minor errors. Further experimental testing is needed to determine the applicability of the proposed model to a wider range of parameters.

Figure 22 Comparison between the test curve and the model curve. (a) ASC0/−20°C, (b) ASC100/−20°C, (c) ASC0/−10°C, and (d) ASC100/−10°C.
Figure 22

Comparison between the test curve and the model curve. (a) ASC0/−20°C, (b) ASC100/−20°C, (c) ASC0/−10°C, and (d) ASC100/−10°C.

5 Conclusions

The uniaxial compression stress–strain constitutive relationship of ASC0 and ASC100 under different low-temperature environments was studied. The conclusions are summarized as follows:

  1. The axial compression process of ASC100 and ASC0 at cryogenic and room temperatures involved three phases: elastic, elastoplastic, and yield failure. However, the failure of concrete specimens at cryogenic temperatures was more severe than at room temperature, suggesting an increase in the brittleness of concrete at cryogenic temperatures.

  2. In the full stress–strain curves of ASC0 and ASC100, the rising and falling profiles showed similar variations, but the ASC100 curve was gentler compared to the ASC0 curve. As the temperature decreased, the ascending curve became steeper, indicating an increase in concrete stiffness. Moreover, the descending profile became steeper, signifying an increase in concrete brittleness.

  3. The modulus, peak stress, and Poisson’s ratio showed an approximately linear increase with decreasing temperature. Compared to the normal temperature, the elastic modulus increased by 28.2–61.4% for ASC0 and by 6.8–65.7% for ASC100. The range of peak stress increase for ASC0 at temperatures below normal was estimated to be between 7 and 35%. The peak stress of ASC100 increased by 6.8–38%.

  4. With decreasing temperature, the peak strain of concrete decreased, with a more pronounced decrease below 0°C. When the temperature decreased from 20 to −20°C, the peak strain of ASC0 and ASC100 decreased by 6.7–14.5% and 4.9–16.7%, respectively. Experimental results indicate that decreasing temperatures lead to reduced ductility and increased brittleness in concrete.

  5. A principal constitutive model for the uniaxial compression stress–strain relationship of ASC0 and ASC100 in the cryogenic environment was developed through multivariate nonlinear analysis. The expressions for parameters, considering both the axial compression strength and temperature at low temperatures, were established. Upon comparison, it was found that the model developed in this study aligns excellently with the experimental data, exhibiting a coefficient of determination R 2 greater than 0.97.

  1. Funding information: We are very grateful to the National Natural Science Foundation of China (52268044), the Natural Science Foundation of Inner Mongolia (2021LHMS05019), the Fundamental Research Funds for Inner Mongolia University of Science and Technology (2023QNJS161, 2024YXXS008) for supporting this research.

  2. Author contributions: All authors accepted the responsibility for the content of the manuscript and consented to its submission, reviewed all the results, and approved the final version of the manuscript. WD: writing – review and editing, funding acquisition, supervision, resources, conceptualization, project administration, and methodology. ZR: writing – original draft, data curation, formal analysis, validation, and visualization. MZ: writing – review and editing, and validation.

  3. Conflict of interest: Authors state no conflict of interest.

  4. Data availability statement: Data will be made available on request.

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Received: 2024-05-13
Revised: 2024-07-28
Accepted: 2024-08-10
Published Online: 2024-09-09

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/secm-2024-0033
Keywords for this article
aeolian sand concrete; low temperature; mechanical properties; stress–strain curve; constitutive model
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