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Article

Optimization of All-Desert Sand Concrete Aggregate Based on Dinger–Funk Equation

by
Yong Huang
1,2,
Rui Yu
1,
Jian Sun
2,3,4,*,
Yubin Liu
1,
Siyu Luo
5 and
Sining Li
2
1
School of Architecture and Engineering, Xinjiang University, Urumqi 830017, China
2
State Key Laboratory of Chemistry and Utilization of Carbon Based Energy Resources, College of Chemistry, Xinjiang University, Urumqi 830017, China
3
Department of Automobile Road Construction and Maintenance, Kharkiv National Automobile and Highway University, Yaroslava Mudrovo Str., 25, 61002 Kharkiv, Ukraine
4
Faculty of Architect and Civil Engineering, Pavement Construction and Maintenance, University of Wuppertal, 42119 Wuppertal, Germany
5
School of Chemical Engineering, Xinjiang University, Urumqi 830017, China
*
Author to whom correspondence should be addressed.
Buildings 2024, 14(8), 2332; https://doi.org/10.3390/buildings14082332
Submission received: 5 June 2024 / Revised: 22 July 2024 / Accepted: 25 July 2024 / Published: 27 July 2024
(This article belongs to the Section Building Materials, and Repair & Renovation)
Browse Figures
Versions Notes

Abstract

In recent years, with the development of the construction industry and the wide application of concrete materials, the demand for natural resources such as sand and gravel in China has continued to grow. The Xinjiang region is rich in natural desert sand resources due to its large desert area, which are inexpensive and easy to obtain, providing new possibilities for the production of concrete materials. The use of natural desert sand as concrete aggregate not only reduces the cost of construction but also contributes to the protection of the environment and the rational development and utilization of natural resources. However, poor particle gradation in natural desert sand leads to poor concrete properties. In this study, the Dinger–Funk equation was used to optimize the aggregate gradation of natural desert sand from Toksun, Xinjiang, and concrete specimens were prepared for mechanical properties and sulfate erosion resistance tests. The test results show that the four groups of aggregates optimized by the Dinger–Funk equation are better than the single gradation and natural gradation in terms of apparent density, bulk density, void ratio, mechanical properties, and durability of concrete. Where the distribution modulus n = 0.3 was the best, the compressive strength, splitting strength, and flexural strength were increased by 13.14%, 15.71%, and 11.08%, respectively, as compared to the natural gradation. After 90 sulfate erosion and dry–wet cycles, the mass change rate and relative dynamic elastic modulus of concrete specimens first increased and then decreased, and at the distribution modulus n = 0.3, the aggregate particles of 0.3–0.6 mm, 0.6–1.18 mm, and 1.18–2.36 mm accounted for 26.98%, 32.33%, and 40.69%, respectively, and the smallest of the mass change rates of durability was the best.

1. Introduction

Concrete is a basic material for modern construction; its performance directly affects the quality and durability of the project [1]. The aggregate, as the main component of concrete, has a decisive influence on the workability, mechanical properties, and durability of concrete with its particle gradation [2,3,4]. With the continuous progress of concrete technology, the optimization of aggregate particle gradation has gradually become the focus of the concrete research field to continuously improve engineering quality standards [5].
Desert sand concrete prepared using traditional methods suffers from defects of workability and a small slump, thus limiting its application in practical engineering to a certain extent [6]. To improve the performance deficiencies of desert sand concrete, researchers have proposed various solutions. Among them, most of the scholars are mixing the coarser-grained mechanism sand into the desert sand in a certain proportion [7] in order to optimize its gradation and obtain the mixed sand with a moderate fineness modulus. The Zhou Zepei et al. study [8] demonstrated the effectiveness of the double-mixing method in the preparation of high-performance desert sand concrete. By preparing desert sand concrete with good workability and mechanical properties and comparing its properties with medium sand concrete. The results showed that desert sand concrete prepared by the double mixing method had a good slump and compressive strength.
The Dinger–Funk [9,10,11,12,13] formula is a common theoretical calculation method for optimizing aggregate particle gradation and is widely used in concrete design. This equation was proposed by Dinger and Funk et al. and was obtained by correcting the Anderson [14] distribution equation by introducing finite minimal particles into it. Brouwers et al. [15] found that fine-grained self-compacting concretes with excellent flowability can be formulated when n is taken between 0.25 and 0.3, especially at the lower value of 0.25. Qian Wang [16] successfully investigated the optimum mix ratio for self-compacting concrete using n = 0.33 to 0.41. He Yebang et al. [17] used the Dinger–Funk equation to optimize the mix ratio of various materials in concrete by adjusting the particle distribution modulus. The experimental results showed that the concrete with an optimized mix ratio had better-working properties, such as compactness and impermeability. Peng Yanzhou [18] successfully prepared powder concrete with excellent stability and durability properties by utilizing the dense stacking theory of the Dinger–Funk equation, selecting fine-grained materials such as steel slag and pulverized activated powder, and choosing a theoretical distribution modulus of 0.25. Cui Gong et al. [19] used the densest pile theory for ratio design to improve the densification of activated powder concrete. Theoretical calculations of concrete composites were carried out using Matlab and Excel Solver Tool programming tools, and the accuracy of the theoretical calculations was verified experimentally. Qin Lian et al. [20] carried out theoretical calculations of cementitious material particle gradation and aggregate gradation based on the Dinger–Funk dense grading model, systematically verified and optimized the proportion of C100 concrete, and successfully determined the proportion of C100 concrete that meets the performance of use. Ronghua Zhang et al. [21] researchers conducted an in-depth study of concrete mix ratios through orthogonal experimental design and Dinger–Funk continuous distribution theory to comprehensively evaluate the role of different mix ratio design schemes on the mechanical properties of concrete. Yang Songsen et al. [22] established a strength assessment model for non-destructive testing of concrete based on a fuzzy system approach by using a single-valued fuzzy, product inference machine, and center-averaged defuzzifier. Chen Yang et al. [23] studied the effect of the molar ratio of carbonate to sulfate on the compressive strength of cementitious under the erosion of carbon–sulfur silica–calcite-type sulfate, summarized the law of change in compressive strength with erosion time, and constructed a prediction model of compressive strength and erosion time.
At present, the main research of a large number of scholars is to use desert sand to partially replace river sand for the optimization of aggregate gradation of concrete, and there is no research on the optimization of aggregate gradation of concrete using full desert sand. This paper investigates the optimal grading scheme for aggregate particle gradation in all desert sand through systematic theoretical analysis and experimental research. The Dinger–Funk equation was used to optimize the aggregate gradation of natural desert sand in the Xinjiang Torkon region, and the optimal aggregate gradation composition of desert sand in the Xinjiang Torkon region was derived based on the mechanical properties of concrete and the resistance to sulfate erosion. It not only turns desert sand into treasure and protects the environment but also has important guiding significance for practical engineering applications.

2. Materials

2.1. Aggregate

All-natural, untreated Toksun desert sand was used. Its bulk density was 1602.5 kg/m3, its apparent density was 2604.5 kg/m3, its gradation composition was shown in Table 1, its fineness modulus was 2.89, it belonged to medium sand, and its chemical composition was shown in Table 2.

2.2. Cement

In this study, Qingsong P.O 42.5 ordinary silicate cement was used from Xinjiang Uygur Autonomous Region, China, and its properties are shown in Table 3.

2.3. Fly Ash

In this paper, class II fly ash from a power plant in Xinjiang was used, and its SEM is shown in Figure 1. The main elements contained were detected by ICP as Al, Ca, S, K, Mg, Na, Fe, etc., and their main compositions were measured by XRF, as shown in Table 4.

2.4. Admixture

This paper used powder polycarboxylic acid high-efficiency water reducer from Shanghai Chenqi Chemical Technology Co., Ltd. (Shanghai, China) and its main properties, as shown in Table 5.

3. Experimental Methods

The gradation of natural desert sand aggregate was optimized according to the theory of the Dinger–Funk equation and tested for apparent density, bulk weight, and porosity. Then, four sets of optimized values of the fineness modulus of natural desert sand with different distribution moduli were calculated according to the theory of the Dinger-Funk equation. One group is the natural grade (NG). Through sieving, it was found that the particle size range of natural sand was mainly concentrated in 0.6–1.18 mm, which accounted for 70.3% of the total amount, so the desert sand in the range of 0.6–1.18 mm was also studied as a separate group of single gradation (SG) in this experiment. Then, the concrete mixes with the strength of C35 were obtained through precast tests, which are shown in Table 6, and a total of 6 sets of grades were designed. Concrete mechanical properties and sulfate attack dry and wet cycle tests were carried out in accordance with JTG 3420-2020 [24] “Test Procedures for Cement and Cement Concrete for Highway Engineering”. The compressive strength and splitting strength tests used 100 mm × 100 mm × 100 mm cubic specimens, and the flexural strength and sulfate attack dry and wet cycle tests used 100 mm × 100 mm × 400 mm prismatic specimens. According to JGJ 52-2006, “Standard for Quality and Inspection Methods of Sand and Stone for Ordinary Concrete” [25] the physical properties of aggregates are tested. In the process of concrete preparation, the first natural desert sand, cement, and fly ash were put into the mixer dry mixing for 2 min, followed by the addition of a water-reducing agent and water mixture mixing for 4 min, and then loaded into the mold to the vibration table vibration for 30 s, covered with plastic wrap static 24 h after demolding, and put into the standard steam curing room to age.

4. Results and Discussion

4.1. Optimization Analysis of Aggregate Particle Gradation

The particle size range of the desert sand used in this study was 2.36–0.3 mm. Therefore, the maximum aggregate size DL is 2.36 mm, and the minimum size DS is 0.3 mm. Since the distribution modulus was selected too small, the variability of each particle range of aggregate was small, which was not conducive to the experimental study, so 0.1–0.4 was selected. Since the range of aggregate particle size varies less when selecting the distribution modulus, four distribution moduli, n = 0.1, n = 0.2, n = 0.3, and n = 0.4, are selected in this paper, which are brought into the Dinger–Funk Equation (1) for calculating the theoretical percentage of each particle size of the aggregate under different distribution modulus, as shown in Figure 2. It can be seen from Figure 2 that the theoretical percentage of aggregate particles in the range of 0.3–0.6 mm decreases as the value of the modulus of distribution of equation n increases. On the contrary, the theoretical percentage of particles in the range of 1.18–2.36 mm increases gradually.
Dinger–Funk equation:
U ( D ) 100 = D n − D S n D L n − D S n
D: particle size dimension;
n: modulus of distribution of particles;
DL: particle size of the largest particle;
DS: size of the smallest particle;
U(D): percentage of particles smaller than the particle size (wt%).

4.2. Apparent Density

The apparent density of aggregates is a key indicator of the density of concrete. The higher the apparent density of the aggregate, the denser the concrete, and the better the strength and durability [26,27,28]. The variation rule of apparent density with a gradation of natural desert sand in Toksun is shown in Figure 3.
As can be seen in Figure 3, the apparent density of the single-gradation aggregate is the smallest at 2590.50 kg/m3, which is 0.54% lower than that of the natural gradation aggregate due to the absence of fine aggregate to fill the voids. After the optimized desert sand was compacted and piled up, the proportion of fine aggregate increased, and the apparent density was greater than that of single primary and natural gradation. With the increase in distribution modulus, the apparent density shows the change law of increasing first and then decreasing. It is the largest at the distribution modulus n = 0.3, which is 2745.90 kg/m3, and the enhancement rate is 5.43%. The decrease at n = 0.4 is due to the excessive specific gravity of coarse aggregate, the gradual decrease in the specific gravity of fine aggregate, and the lack of sufficient fine aggregate to fill the voids in the fine aggregate, which leads to the decrease in apparent density.

4.3. Bulk Density and Void Ratio

Aggregate filling density is also an important indicator of concrete compactness; the greater the filling density, the smaller the porosity of the aggregate filling, and the higher the compactness of the concrete after molding. The filling density and porosity of different grades of Toksun natural desert sand are shown in Figure 4.
From Figure 4, it can be clearly seen that the stacking density and porosity of Toksun natural desert sand are greatly affected by the gradation and show the corresponding change rule. When single-grade mixing, Toksun natural desert sand is also due to the absence of fine-grained aggregates; the voids cannot be filled, so the accumulation density is the smallest, 1578.90 kg/m3, followed by the natural graded desert sand. Aggregate optimized gradation after close stacking: with the increase in distribution modulus, the accumulation density of desert sand first increases and then decreases, is higher than a single gradation and natural gradation, and in n = 0.3 time to reach the maximum, for 1643.76 kg/m3, and the apparent density of the law of change is consistent. At the same time, after calculation, it can be found that the change rule of void ratio is opposite to the change rule of accumulation density, showing a trend of decreasing and then increasing; in n = 0.3, the void ratio is the smallest, 36.89%, and the accumulation is the densest.

4.4. Concrete Design Ratio

According to the precast test, the concrete ratios to satisfy the C35 strength were obtained, according to which six sets of concrete ratios were designed, as shown in Table 6. The values were kept constant except for the different proportions of coarse and fine desert sand.

4.5. Slump Analysis

The influence of aggregate gradation on the slump of natural desert sand concrete is shown in Figure 5.
As can be seen in Figure 5, the slump of concrete is minimized in single-gradation. The slump of natural-gradation concrete is higher than that of single-graded concrete, mainly due to the fact that natural-gradation concrete contains some coarse-grained sand, the specific surface area of coarse aggregate is small, the water requirement is less, and the slump increases. Meanwhile, the slump of the gradation-optimized aggregate concrete increases continuously with the increase in distribution modulus. The slump of the grade-optimized concrete can be increased by a maximum of 36.8% compared to the natural-gradation concrete. This is due to the fact that the greater the admixture of coarse aggregate in the concrete, the smaller the specific surface area of the aggregate, the less water is required, and the slump increases. In addition, the reduction in voids increases the amount of cement paste that acts as a lubricant, thus increasing the fluidity accordingly [29].

4.6. Compressive Strength Analysis

The effect of aggregate gradation on the compressive strength of concrete at 7 d and 28 d is shown in Figure 6.
It can be seen from Figure 6 that the change law of concrete compressive strength at 7 d is similar to that at 28 d. At distribution modulus n = 0.3, the 7 d and 28 d compressive strengths of the concrete were increased by 12.89% and 13.14%, respectively, over the compressive strength of the natural-gradation concrete. The 7 d and 28 d compressive strengths of single-gradation concrete are 1.34% and 3.11% lower than the compressive strengths of natural-gradation concrete, respectively. The strength values of the optimized concrete with Dinger–Funk aggregate gradation were higher than those of the natural gradation and single gradation, and the 7 d compressive strength enhancement of the concrete was 3.76~12.89%, and the 28 d compressive strength enhancement was 2.14~13.14%. With the increase in distribution modulus, the compressive strength values showed a tendency to increase and then decrease due to the influence of concrete structural compactness. After calculation, the 7 d compressive strength value of concrete can reach 76~82% of the 28 d compressive strength value.

4.7. Splitting Strength and Flexural Strength Analysis

The effect of aggregate gradation on the 28 d splitting strength and flexural strength of concrete are shown in Figure 7.
When the distribution modulus n = 0.3, the concrete 28 d splitting strength is at its maximum at 4.05 MPa, which is 15.71% higher than the splitting strength of natural-gradation concrete. The lowest splitting strength of 2.98 MPa was recorded for single gradation, which is 14.86% lower than the splitting strength of natural-gradation concrete. The 28 d concrete splitting strength values optimized using Dinger–Funk equation gradation were all higher than the splitting strength of natural-gradation concrete, with an improvement rate of 2.29~15.71%. The splitting strength slightly decreases at distribution modulus n = 0.2 and shows a decreasing trend from n = 0.3 to n = 0.4, while the tensile–compression ratio of concrete is calculated to be between 0.07 and 0.09. When n = 0.3, the concrete has the largest tensile–compression ratio and relatively the best toughness, while the single primary distribution concrete has the smallest tensile–compression ratio and relatively the worst toughness.
When the distribution modulus n = 0.3, the maximum 28 d flexural strength of concrete is 7.12 MPa, which is 11.08% higher than the flexural strength of natural-gradation concrete. The single-gradation concrete has the lowest flexural strength of 6.29 MPa, which is 1.87% lower than the flexural strength of natural-gradation concrete. The 28 d concrete flexural strength values optimized using Dinger–Funk equation gradation are higher than the natural-gradation concrete flexural strength with an increase of 5.62~11.08%. The flexural strength of concrete showed a tendency to increase and then decrease with the increase in distribution modulus.

4.8. Dry and Wet Cycle Analysis of Sulphate Erosion

4.8.1. Apparent Characteristics

Under the long-term combined effect of sulfate erosion and dry–wet cycling, the performance of concrete will gradually degrade and deteriorate, seriously threatening durability and service life. The effects of sulfate attack and dry–wet cycling on concrete are extensive and complex, involving not only changes in physical properties [30,31]. Figure 8 shows the effect of aggregate gradation on the apparent morphology of natural desert sand concrete specimens under the action of sulfate attack and dry–wet cycling. The pictures on the left show the initial specimen, and the pictures on the right show the specimen after 90 cycles of sulfate attack and dry–wet cycling.
As can be seen in Figure 8, the surface morphology of the concrete changed significantly, and after 90 sulfate attack dry–wet cycles, the mortar on the surface of the concrete appeared to be dislodged, and the most serious dislodgment occurred at the corners. This is due to the fact that under the action of sulfate erosion and the wet–dry cycle, sulfate ions penetrate into the internal voids of concrete specimens with the solution, and the sulfate crystals expand to generate manganese nitrate (Na2SO4–10H2O) during the drying process. The crystalline material gathers and expands in the concrete voids, generating large expansion stresses and leading to internal cracking of the concrete specimen [32]. As shown in the right picture of Figure 8a, the surface of the single-gradation concrete specimen was most severely damaged by sulfate attack and wet–dry cycling, with severe missing corners and severe surface mortar detachment. As shown in the right picture of Figure 8b, the surface of the natural-graded concrete specimens had less mortar detachment and missing corners compared to the single-gradation concrete. The surface damage of the concrete specimens after optimizing the gradation using the Dinger–Funk equation is significantly less than that of the single gradation and natural-gradation concrete. As shown in the right picture of Figure 8e, the concrete specimens with a distribution modulus of n = 0.3 had the least apparent damage, fewer missing corners, less surface mortar shedding, and better integrity.

4.8.2. Rate of Mass Change

Figure 9 shows the effect of aggregate gradation on the rate of change in the mass of natural desert sand concrete specimens under dry–wet cycling conditions.
As can be seen in Figure 9, the mass of the concrete specimens continued to increase after 1~30 cycles of sulfate erosion. On the one hand, this is due to the further hydration of the cement at the initial stage, where sulfate is involved in the reaction to produce gypsum and calomel (AFt) [33]. On the other hand, during the immersion process, the sodium sulfate solution continuously penetrates into the internal voids in the concrete specimens. Water evaporation during the drying process leads to the precipitation of sulfate crystals, and some of the sulfate crystals are retained in the internal voids of the concrete specimen, which plays a role in filling the voids and increasing the density of the concrete [34]. When the concrete specimens were subjected to 31~90 sulfate attack cycles, the rate of increase in the rate of mass change slowed down, followed by a decreasing rate of increase. This is due to the fact that the internal pores of the concrete specimens continued to fill up as the number of sulfate erosions increased. At the same time, the concrete surface mortar started to peel off, with more severe peeling at the corners and more severe peeling as the number of erosions increased. It can also be seen from Figure 9 that the rate of change in mass of single-gradation concrete specimens reaches its maximum value after 60 cycles of sulfate attack with an increase in mass of 0.74%, followed by a decreasing trend in the rate of change in mass. For concrete with a distribution modulus of n = 0.1, n = 0.2, n = 0.3, and n = 0.4, the rate of mass change reaches its maximum value after 70 cycles of sulfate attack, with an increase in mass of 0.68, 0.56, 0.54, 0.47, and 0.57%, respectively, after which there is a decreasing trend in the rate of mass change. The range of variation in the rate of change in the mass of concrete specimens using single gradation and natural gradation is relatively large, while the range of variation in the rate of change in the mass of concrete specimens after optimizing the gradation using the Dinger–Funk equation is relatively small, with the smallest range of variation at the distribution modulus n = 0.3.

4.8.3. Relative Dynamic Elastic Modulus

The effect of the dynamic modulus of elasticity of natural desert sand concrete specimens with different gradations under the effects of sulfate erosion and wet and dry cycles is shown in Figure 10.
The relative dynamic modulus of elasticity of the six groups of concrete specimens after sulfate attack and wet–dry cycling were similar and showed a tendency to increase and then decrease. This is because the sulfate ions in the early solution will continue to hydrate with the concrete, producing more calcium, alumina, gypsum, etc., to fill the voids inside the concrete, thus increasing the density of the specimen to some extent [35]. At a later stage, with the increase in the number of cycles, the volume of the erosion products inside the concrete increases, and the resulting expansion stress leads to cracks in the microporous and interfacial transition zones, which gradually enlarge the initial pores, leading to the loosening of the internal structure of the concrete, resulting in the dislodging of the concrete paste [36]. As can be seen in Figure 10, the relative dynamic elastic modulus of the single-gradation concrete specimens reaches its maximum value after 60 cycles of wet–dry cycling, which is 0.16% lower than that of the natural-gradation concrete specimens. The relative dynamic elastic modulus of the remaining gradation concrete specimens reached its maximum value after 70 wet–dry cycles, while the relative dynamic modulus of elasticity of the single-gradation concrete specimens was the lowest, which was 2.31% lower than that of the natural-gradation concrete specimens. The relative dynamic modulus of elasticity of concrete specimens with optimized gradation using the Dinger–Funk equation was higher than that of single gradation and natural gradation concrete specimens, and the relative dynamic modulus of elasticity of concrete specimens with distribution modulus n = 0.1, n = 0.2, n = 0.3, and n = 0.4 were higher than that of the natural-gradation concrete specimens by 0.8, 1.16, 1.78, and 0.44%, respectively.

4.9. X-ray Diffraction (XRD)

Figure 11 shows the X-ray diffraction (XRD) patterns of the natural gradation of desert sand concrete with an age of 28 d.
The diffraction peaks prominently present in the pattern correspond to quartz (SiO2), C–S–H gel, calcite (CaCO3), calcium hydroxide [Ca(OH)2], and alunite (AFt). These components dominate the microstructure of concrete and have a significant influence on its macroscopic properties [37]. After 90 wet–dry cycles of sulfate attack, the XRD patterns of natural gradation desert sand concrete are shown in Figure 12, in which the diffraction peaks of quartz (SiO2), calcite (CaCO3), C–S–H gel, and calcite alumina (Aft) are still present, whereas the diffraction peaks of calcium hydroxide have disappeared. This is due to the chemical reaction between calcium ions (Ca2+) and sulfate ions (SO42−) in calcium hydroxide during sulfate erosion to produce gypsum [38]. This reaction mechanism leads to the depletion of calcium hydroxide and, consequently, the formation of pores in the concrete matrix. In addition, the generated gypsum further reacts with the hydration products to produce calcite with solubility properties. However, it is worth noting that the diffraction peaks of gypsum are not directly observed in the plots in Figure 12. This is attributed to the fact that gypsum-type erosion dominates at higher concentrations of sulfate ions (SO42−). In addition, there is some error due to the randomness in the selection of the specimens, which resulted in the failure to directly observe gypsum during the analysis [34].

4.10. Scanning Electron Microscope (SEM) Analysis

Figure 13 shows the scanning electron microscope (SEM) images of different grades of concrete magnified 5000 times at a resolution of 1109 × 890.
Figure 13a shows a single grade of concrete, Ca(OH)2, fibrous C–S–H gel, needle AFt, and laminated AFm can be seen; the C–S–H gel crosses to form a spatial network structure connecting the cement particles and their hydration products, while some areas are relatively sparse with a large number of voids, which may have some influence on the performance of the concrete. Figure 13b shows a natural-gradation concrete where C–S–H gel is mixed with other hydration products to form a spatial network of pristine pores but with a more varied particle size distribution than in a single-gradation concrete, which achieves better filling and reduces voids. The concretes optimized for gradation using the Dinger–Funk equation all have a denser internal structure compared to the other two groups. Figure 13c shows the concrete with a distribution modulus of n = 0.1, from which a large amount of C–S–H gel, a small amount of Ca(OH)2, Aft, and a smaller number of voids can be seen. Figure 13d shows the concrete with a distribution modulus of n = 0.2; the main hydration products are Ca(OH)2 and C–S–H, and there are only a few voids with relatively good internal structural compactness. Figure 13e shows that the concrete with a distribution modulus of n = 0.3 has the best concrete hydration; the pores between the cement particles are filled with various hydration products; and the gel, such as C–S–H, is sufficient and connects the hydration products, such as Ca(OH)2 crystals and needle AFt, to form a dense cement stone with the best densification. Figure 13f shows that the concrete with a distribution modulus of n = 0.4 has a relatively poor structure of hydration products with obvious internal pores and a relatively loose structure. It can be seen that the appropriate proportion of aggregate particle size can effectively reduce the voids in the cement paste, forming a dense structure and improving the performance of concrete.

5. Conclusions

In this paper, the effect of optimized aggregate particle gradation on engineering parameters and the performance of natural desert sand concrete are investigated. The particle gradation of aggregates was optimized by using the Dinger–Funk close-packing theory, and the improvement effect of optimized gradation on concrete properties was verified by mechanical properties and durability tests. The optimal particle gradation of Xinjiang Tokxon Desert sand and the optimal distribution modulus of Dinger–Funk were obtained, and the main conclusions are as follows:
(1)
In the optimization analysis of aggregate particle gradation, as the value of distribution modulus n increases, the content of coarse particles increases and the content of fine particles decreases, which makes the fineness modulus of desert sand increase. The apparent density and bulk density of the desert sand optimized by compact stacking were greater than those of single gradation and natural gradation and reached the maximum at the distribution modulus n = 0.3 when the void ratio was the smallest and the stacking was the denser, and the ratio of aggregate particles 0.3~0.6 mm, 0.6~1.18 mm, and 1.18~2.36 mm were 26.98%, 32.33%, and 40.69%, respectively.
(2)
The gradation-optimized concrete showed better performance than single-gradation and natural-gradation concrete in terms of slump and mechanical properties. At the distribution modulus n = 0.3, the properties of natural desert sand concrete reached the optimum, and the compressive, splitting, and flexural strengths were improved by 13.14%, 15.71%, and 11.08%, respectively, compared with the natural gradation.
(3)
During the sulfate erosion and dry–wet cycling processes, the concrete specimens optimized by gradation had less apparent damage, a smaller fluctuation of mass change rate, and a relatively larger relative dynamic elastic modulus compared to the concrete specimens with single gradation and natural gradation. The concrete specimens with a distribution modulus of n = 0.3 had the best integrity, showed better stability, and showed the best resistance to sulfate attack.
In future research work, it will be further combined with different regional climatic characteristics of the Xinjiang region to carry out comprehensive tests on the durability of desert sand aggregate gradation-optimized concrete, such as frost resistance, alkali-aggregate reaction, seepage resistance, etc., to study its coupled physicochemical characteristics in complex, harsh environmental conditions.

Author Contributions

Methodology, Y.H. and S.L. (Sining Li); Software, R.Y. and S.L. (Sining Li); Investigation, Y.H., R.Y., J.S., Y.L. and S.L. (Siyu Luo); Writing—original draft, R.Y.; Writing—review & editing, Y.H. and J.S.; Supervision, J.S. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Scientific and Technological Research Programs in key Areas of Xinjiang Production and Construction Corps Science and technology Bureau (Grant 2023AB013), Natural science foundation of Xinjiang Uygur Autonomous Region (general project, No. 2021D01A68), Sino-Ukrainian Science and Technology Exchange Project (CU03-32), Project of Xinjiang Science and Technology Department Project (2018E02075).

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflict of interest.

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Buildings 14 02332 g001
Figure 1. SEM image of fly ash.
Figure 1. SEM image of fly ash.
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Figure 2. Gradation optimization curve.
Figure 2. Gradation optimization curve.
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Figure 3. Apparent density of natural desert sand.
Figure 3. Apparent density of natural desert sand.
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Figure 4. Natural desert sand accumulation density and porosity.
Figure 4. Natural desert sand accumulation density and porosity.
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Figure 5. Concrete slump.
Figure 5. Concrete slump.
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Figure 6. The compressive strength of concrete.
Figure 6. The compressive strength of concrete.
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Figure 7. 28 d splitting strength and flexural strength of concrete.
Figure 7. 28 d splitting strength and flexural strength of concrete.
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Figure 8. Apparent morphology of concrete specimens. (The Chinese characters in the figure represent respectively: (a) single gradation; (b) natural gradation).
Figure 8. Apparent morphology of concrete specimens. (The Chinese characters in the figure represent respectively: (a) single gradation; (b) natural gradation).
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Buildings 14 02332 g009
Figure 9. Rate of change in concrete specimen quality.
Figure 9. Rate of change in concrete specimen quality.
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Figure 10. Relative dynamic modulus of elasticity of concrete specimens.
Figure 10. Relative dynamic modulus of elasticity of concrete specimens.
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Figure 11. XRD pattern of 28 d natural desert sand concrete.
Figure 11. XRD pattern of 28 d natural desert sand concrete.
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Buildings 14 02332 g012
Figure 12. XRD pattern of natural desert sand concrete with 90 cycles of wet–dry cycles of sulfate erosion.
Figure 12. XRD pattern of natural desert sand concrete with 90 cycles of wet–dry cycles of sulfate erosion.
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Buildings 14 02332 g013
Figure 13. SEM images of concrete.
Figure 13. SEM images of concrete.
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Table 1. Desert sand gradation.
Table 1. Desert sand gradation.
Sieve size (mm)00.0750.150.30.61.182.364.75
Percentage sieved (%)00.61.22.819.189.499.0100
Table 2. Chemical composition of desert sand.
Table 2. Chemical composition of desert sand.
IngredientSiO2Al2O3MgONa2OCaOK2OFe2O3Others
Content (%)73.1014.631.372.702.692.962.130.49
Table 3. Properties of P.O 42.5 cement.
Table 3. Properties of P.O 42.5 cement.
Properties28 d Compressive
Strength (MPa)		3 d Flexural
Strength (MPa)		Initial Setting
Time (min)		Final Setting
Time (min)		Soundness
Measured value53.35.9170230qualified
Table 4. Main chemical composition of fly ash.
Table 4. Main chemical composition of fly ash.
Chemical CompositionSiO2Al2O3MgOCaOSO3Fe2O3Others
Content (%)37.3117.385.9513.145.2315.075.92
Table 5. Main properties of water reducer.
Table 5. Main properties of water reducer.
PropertiesWater Content (%)PHCement Net Slurry Fluidity (mm)Water Reduction Rate (%)Air Content of Concrete (%)Soundness
Measured value1.817.128026.21.7qualified
Table 6. Concrete mix ratio of natural desert sand in Toksun.
Table 6. Concrete mix ratio of natural desert sand in Toksun.
No.Desert Sand (kg/m3)Water (kg/m3)Fly Ash (kg/m3)W/CWater Reducing Agent (%)
SG14006001500.391
NG14006001500.391
n = 0.114006001500.391
n = 0.214006001500.391
n = 0.314006001500.391
n = 0.414006001500.391
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MDPI and ACS Style

Huang, Y.; Yu, R.; Sun, J.; Liu, Y.; Luo, S.; Li, S. Optimization of All-Desert Sand Concrete Aggregate Based on Dinger–Funk Equation. Buildings 2024, 14, 2332. https://doi.org/10.3390/buildings14082332

AMA Style

Huang Y, Yu R, Sun J, Liu Y, Luo S, Li S. Optimization of All-Desert Sand Concrete Aggregate Based on Dinger–Funk Equation. Buildings. 2024; 14(8):2332. https://doi.org/10.3390/buildings14082332

Chicago/Turabian Style

Huang, Yong, Rui Yu, Jian Sun, Yubin Liu, Siyu Luo, and Sining Li. 2024. "Optimization of All-Desert Sand Concrete Aggregate Based on Dinger–Funk Equation" Buildings 14, no. 8: 2332. https://doi.org/10.3390/buildings14082332

APA Style

Huang, Y., Yu, R., Sun, J., Liu, Y., Luo, S., & Li, S. (2024). Optimization of All-Desert Sand Concrete Aggregate Based on Dinger–Funk Equation. Buildings, 14(8), 2332. https://doi.org/10.3390/buildings14082332

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