Prediction method and system for elasticity modulus of coal gangue aggregate concrete

Abstract

The invention provides a method and system for predicting the elasticity modulus of coal gangue aggregate concrete, and belongs to the field of coal gangue aggregate concrete. The invention aims to solve the problem that the prediction precision and the universality are influenced when the elastic modulus of the existing coal gangue aggregate concrete is predicted by taking the compressive strength of the coal gangue aggregate concrete as a basic parameter. The method comprises the following steps: establishing a coal gangue aggregate concrete elastic modulus prediction model by using a Russ model based on a two-phase composite material theory, and establishing a corresponding prediction model by using the two-phase composite material theory and taking aggregate rigidity and aggregate volume content as basic parameters; wherein the rigidity of the coal gangue and the natural aggregate is simulated by adopting a Counto model. The prediction model can obtain more accurate gangue aggregate concrete elasticity modulus, the test result verifies the accuracy of the prediction model, the gangue aggregate concrete elasticity modulus prediction model based on the two-phase composite material is proposed for the first time, and the prediction model can be better applied to actual engineering.

Description

Technical Field

[0001] This invention relates to the field of coal gangue aggregate concrete technology, and more specifically, to a method and system for predicting the elastic modulus of coal gangue aggregate concrete. Background Technology

[0002] my country's fossil energy distribution is characterized by abundant coal reserves. This fundamentally establishes coal's strategic pillar status in my country's energy supply system. As the world's largest producer of raw coal, my country's coal production capacity continues to rank first globally. During coal development and utilization, a large amount of coal gangue is generated as a byproduct—a low-calorific-value mineral byproduct separated during mining and washing, typically accounting for 10%-25% of raw coal production, and has become a key target in my country's industrial solid waste management.

[0003] Compared to ordinary concrete, the mechanical properties of coal gangue aggregate concrete are reduced in all aspects. A reasonable and reliable predictive model for the mechanical properties of coal gangue aggregate concrete is fundamental for its application in practical engineering. However, most existing models are derived by directly establishing the relationship between a certain mechanical property and compressive strength, using limited experimental data for regression analysis. The influence mechanism of coal gangue aggregate on the elastic modulus of coal gangue aggregate concrete differs fundamentally from its influence mechanism on strength. Using compressive strength as the basic parameter will affect the accuracy and universality of model predictions. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] To address the issue that the existing method of predicting the elastic modulus of coal gangue aggregate concrete using the compressive strength of coal gangue aggregate concrete as the basic parameter affects its prediction accuracy and universality.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a method for predicting the elastic modulus of coal gangue aggregate concrete, comprising the following steps:

[0008] Based on the Reuss model of two-phase composite material theory, an expression for the elastic modulus of ordinary concrete is constructed, and then an expression for the elastic modulus of coal gangue aggregate concrete is constructed. Based on the Counto model of two-phase composite material theory, the equivalent stiffness of aggregates in coal gangue aggregate concrete is calculated by the volume fraction of natural aggregates in the total aggregates, and the volume fraction of natural aggregates in coal gangue aggregate concrete is obtained.

[0009] Based on the constant value of the elastic modulus of coal gangue aggregate, a simplified prediction model for the final elastic modulus of coal gangue aggregate concrete is obtained.

[0010] Furthermore, a predictive model for the elastic modulus of coal gangue aggregate concrete is established by setting the relationship between the elastic modulus of coal gangue aggregate concrete and the elastic modulus of ordinary concrete with the same mix proportion:

[0011]

[0012] Among them, E CGAC E represents the elastic modulus of coal gangue aggregate concrete. NAC This refers to the elastic modulus of ordinary concrete. It is the elastic modulus coefficient between the elastic modulus of coal gangue aggregate concrete and the elastic modulus of ordinary concrete with the same mix proportion.

[0013] Furthermore, in ordinary concrete, the relationship between the volume fraction of aggregate and the volume fraction of cement paste is shown in equation (2). Substituting equation (3) into equation (2) simplifies to equation (4):

[0014]

[0015] Among them, E NAC E represents the elastic modulus of ordinary concrete. NA E CP V represents the elastic modulus of natural aggregate and cement paste, respectively. NA V CP These represent the volume fractions of natural aggregates and cement paste in ordinary concrete, respectively.

[0016] Based on the elastic modulus of ordinary concrete, the expression for the elastic modulus of coal gangue aggregate concrete is obtained as follows:

[0017]

[0018] in, This represents the elastic modulus of the total aggregate in coal gangue aggregate concrete. This represents the volume fraction of total aggregate in coal gangue aggregate concrete.

[0019] Furthermore, the elastic modulus of coal gangue aggregate concrete depends on the elastic modulus of the total aggregate and cement paste in the concrete, as well as the volume ratio of the total aggregate. The total aggregate volume in coal gangue aggregate concrete includes both coal gangue aggregate and natural aggregate, and their relationship is shown in equation (6):

[0020]

[0021] Among them, V CGA This represents the volume percentage of coal gangue aggregate in coal gangue aggregate concrete. This represents the volume fraction of natural aggregates in coal gangue aggregate concrete.

[0022] Furthermore, based on the Counto model of two-phase composite material theory, the elastic modulus of the total aggregate in coal gangue aggregate concrete is obtained as follows:

[0023]

[0024] Among them, E CGA The elastic modulus of coal gangue aggregate. The volume fraction of natural aggregate in coal gangue aggregate concrete.

[0025] The volume fraction of natural aggregate in coal gangue aggregate concrete is calculated from the replacement rates of coarse and fine coal gangue aggregate and the volume fraction of each aggregate in the total aggregate.

[0026]

[0027] Where, r CGCA r represents the replacement rate of coarse aggregate from coal gangue. CGFA The replacement rate of fine aggregate from coal gangue, This refers to the volume fraction of coarse aggregate from coal gangue in the total aggregate. This refers to the volume fraction of fine aggregate from coal gangue in the total aggregate.

[0028] Furthermore, the elastic modulus of coal gangue aggregate is taken as 15.3 GPa, and the elastic modulus of natural aggregate is taken as 73.5 GPa. After substituting into equations (7) and (8), the elastic modulus of the total aggregate in coal gangue aggregate concrete is simplified to obtain:

[0029]

[0030] Substituting equation (9) into equation (5), we obtain the expression for the elastic modulus of coal gangue aggregate concrete:

[0031]

[0032] Since coal gangue aggregate concrete and ordinary concrete use the same mix proportion, and the coal gangue aggregate replaces natural aggregate by volume substitution, the aggregate volume and cement paste volume of both are equal.

[0033]

[0034] in, This refers to the volume fraction of total aggregate in concrete. This refers to the volume fraction of cement paste in the concrete.

[0035] The ratio between the volume percentage of aggregate in concrete and the volume percentage of cement paste is expressed as α. p / a replace:

[0036]

[0037] After simplification, the final prediction model for the elastic modulus of coal gangue aggregate concrete is obtained:

[0038]

[0039] A system for predicting the elastic modulus of coal gangue aggregate concrete is provided. The system has program modules corresponding to the above steps and executes the steps in the above-described method for predicting the elastic modulus of coal gangue aggregate concrete when running.

[0040] A computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps of a method for predicting the elastic modulus of coal gangue aggregate concrete.

[0041] Compared with the prior art, the beneficial effects of the present invention are:

[0042] This invention proposes a method and system for predicting the elastic modulus of coal gangue aggregate concrete. Considering that coal gangue aggregate has a looser, more porous structure and more internal defects compared to natural aggregate, and that the apparent density of both coarse and fine aggregates is lower than that of natural aggregate, while its water absorption rate is significantly higher, the correlation between elastic modulus and compressive strength differs significantly from that of ordinary concrete. Therefore, this invention uses stiffness as the basic parameter instead of compressive strength when calculating the elastic modulus. Based on this, this invention proposes for the first time to construct an expression for the elastic modulus of coal gangue aggregate concrete using the Reuss model of two-phase composite material theory, and uses the Counto model to calculate its stiffness, ultimately obtaining a predictive model for the elastic modulus of coal gangue aggregate concrete. Experiments show that the predictive model of this invention can obtain a more accurate elastic modulus of coal gangue aggregate concrete, verifying the accuracy of the predictive model and enabling its better application in practical engineering. Attached Figure Description

[0043] Figure 1 The images shown are actual pictures of natural aggregate and coal gangue aggregate in the embodiments of the present invention, wherein (a) is an actual picture of coarse coal gangue aggregate, (b) is an actual picture of fine coal gangue aggregate, (c) is an actual picture of natural coarse aggregate, and (d) is an actual picture of natural fine aggregate.

[0044] Figure 2 This is a gradation curve of the aggregate in an embodiment of the present invention;

[0045] Figure 3 This is a diagram of the elastic modulus testing apparatus in an embodiment of the present invention;

[0046] Figure 4This is a comparison diagram of the effects of coarse and fine aggregates of coal gangue on the elastic modulus of concrete under different water-cement ratios in embodiments of the present invention.

[0047] Figure 5 This is a graph showing the relationship between the compressive strength and elastic modulus of coal gangue aggregate concrete in an embodiment of the present invention.

[0048] Figure 6 This is a graph showing the relationship between the normalized elastic modulus of coal gangue aggregate concrete and the replacement rate of coal gangue coarse aggregate in an embodiment of the present invention.

[0049] Figure 7 This is a diagram of the Reuss model in the theory of two-phase composite materials in this embodiment of the invention;

[0050] Figure 8 This is a diagram of the Counto model in the theory of two-phase composite materials in this embodiment of the invention;

[0051] Figure 9 This is a comparison chart of the elastic modulus predicted by the model of the present invention and the experimental value in an embodiment of the present invention. Detailed Implementation

[0052] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0053] To investigate the method for predicting the elastic modulus of coal gangue aggregate concrete, the following experiment was conducted.

[0054] The experimental parameters and specimen names are shown in the figure. The experimental parameters include: replacement rate of coarse aggregate of coal gangue, replacement rate of fine aggregate of coal gangue, and water-cement ratio. A total of 30 150mm×150mm×300mm prism elastic modulus specimens were prepared.

[0055] The specimen number contains four elements: 1) NAC represents ordinary concrete, and CGAC represents coal gangue aggregate concrete; 2) coarse aggregate is represented by C, and fine aggregate by F; 3) the numerical suffixes C and F indicate the replacement rate of coal gangue aggregate; 4) the last number indicates the water-cement ratio. Taking the typical specimen CGAC-C50-F50-0.35 as an example, the replacement rate of both coarse and fine coal gangue aggregate in this coal gangue aggregate concrete specimen is 50%, and the water-cement ratio is 0.35.

[0056] surface Concrete mix proportion per unit volume

[0057]

[0058] Where, r CGCA r represents the replacement rate of coarse aggregate from coal gangue. CGFACGCA represents the replacement rate of fine aggregate from coal gangue; NCA represents natural coarse aggregate; NFA represents natural fine aggregate; CGCA represents coarse aggregate from coal gangue; CGFA represents fine aggregate from coal gangue.

[0059] Test materials

[0060] The cement used in this experiment was ordinary Portland cement PO42.5 grade. The natural coarse aggregate (NCA) was limestone with a particle size of 5mm~25mm, and the natural fine aggregate (NFA) was river sand with a particle size of less than 5mm. To ensure similar workability of the concrete and control its slump between 200mm±20mm, HWR-S naphthalene-based high-efficiency water-reducing agent with a water-reducing efficiency of 16% was used, with its admixture weight being 1%~1.5% of the total cement content.

[0061] The production of coal gangue aggregate includes two parts: crushing and screening. First, the coal gangue raw material is fed into a jaw crusher and crushed into fragments with a particle size of less than 30 mm. Then, the fragments are screened, with those less than 5 mm used as fine coal gangue aggregate (CGFA), and those between 5 mm and 25 mm used as coarse coal gangue aggregate (CGCA). The four types of aggregates used in the experiment are as follows: As shown.

[0062] To avoid interference from aggregate gradation differences in the test results, the gradation of all aggregates was adjusted. The aggregate gradation is as follows: As shown in the figure. All coarse aggregates use a continuous gradation of 5mm to 20mm, and all fine aggregates are controlled as zone II sand. The adjusted aggregate gradation meets the requirements of the "Standard for Quality and Testing Methods of Sand and Stone for Ordinary Concrete" (JGJ 52-2006).

[0063] Depend on It can be seen that, due to its loose and porous structure and numerous internal defects, the apparent density of both the coarse and fine coal gangue aggregates is lower than that of natural coarse and fine aggregates, while its water absorption rate is significantly higher. For example, the water absorption rate of the coal gangue aggregate used in this invention is 4.6 to 4.7 times that of natural aggregates, and its apparent density is 0.92 to 0.94 times that of natural aggregates.

[0064] surface Physical properties of natural aggregates and coal gangue aggregates

[0065]

[0066] Concrete preparation

[0067] For concrete mix proportions, please refer to [link / reference]. This invention employs a three-factor, multi-level experiment, constructing an orthogonal experiment with water-cement ratios (0.35 and 0.55), coarse aggregate replacement rates of coal gangue (0%, 50%, and 100%), and fine aggregate replacement rates of coal gangue (0%, 50%, and 100%) as parameters. Ten mix proportions were designed to study the influence of coal gangue aggregate on the mechanical properties of concrete under different water-cement ratios. The replacement method for coal gangue aggregate was volume replacement, ensuring that the total volume fraction of coarse and fine aggregate remained consistent across different mix proportions at the same water-cement ratio. Considering the high water absorption rate of coal gangue aggregate, and to ensure similar workability of the concrete, an 80% additional water method was adopted when using coal gangue aggregate, taking into account practical engineering applications. The specific method is as follows: The saturated surface-dry water absorption rate and moisture content of the coal gangue aggregate are measured. The moisture content of the coal gangue aggregate (i.e., the saturated surface-dry water absorption rate multiplied by the mass of the coal gangue aggregate) is subtracted from the saturated surface-dry water absorption capacity of the coal gangue aggregate (i.e., the saturated surface-dry water absorption rate multiplied by the mass of the coal gangue aggregate). 80% of the difference is taken as the additional water content W. add Add to fresh concrete as shown in formula (1). The water consumption listed is the sum of the baseline water consumption (refer to the ordinary concrete mix proportion) and the additional water consumption.

[0068]

[0069] Among them, w a-CGCA The saturated surface-dry water absorption rate of coal gangue coarse aggregate, w m-CGCA The moisture content of the coarse aggregate of coal gangue, in m CGCA For the quality of coal gangue coarse aggregate, w a-CGFA The saturated surface-dry water absorption rate of fine aggregate from coal gangue, w m-CGFA The moisture content of fine aggregate from coal gangue, in m CGFA For the quality of fine aggregate from coal gangue;

[0070] Specimen preparation and curing process

[0071] based on Concrete specimens were prepared according to the listed mix proportions. During the aggregate pretreatment stage, all coarse aggregate, all fine aggregate, and the first batch of mixing water (1 / 3 of the total water volume) were added to the mixer for pre-mixing (30 seconds). Mixing was then paused, and all cement was added for secondary mixing (30 seconds). Next, the remaining mixing water (approximately 2 / 3 of the total water volume) and water-reducing agent were added to the mixer for final mixing (180 seconds). After mixing, the fresh concrete was poured into concrete molds and thoroughly compacted in layers using an immersion vibrator. Three parallel specimens were prepared for each mix proportion and each test, including a standard 150mm × 150mm × 300mm elastic modulus specimen. After pouring, the specimens were sealed with plastic film to prevent moisture loss. After 24 hours of settling, the specimens were demolded and transferred to a standard curing room at a temperature of 20.0 ± 2.0℃ and a relative humidity greater than 95% until the day of the test.

[0072] Test methods

[0073] The flowability of concrete was tested according to the "Standard for Test Methods of Performance of Ordinary Concrete Mixtures" GB / T 50080-2002, with the slump test completed within 150 seconds after concrete mixing. The mechanical properties of concrete were tested according to the "Standard for Test Methods of Mechanical Properties of Ordinary Concrete" GB / T 50081-2002, with the test apparatus and specimens as specified. As shown (the test setup is an existing device). The loading rate for the elastic modulus test is 5 kN / s. In the elastic modulus test, the concrete specimen must first be pre-loaded and physically centered to ensure that it is in a state of axial compression. Then, three cycles of loading are performed, with the peak value of the load in each cycle causing the axial compressive stress of the concrete to reach 1 / 3 of the axial compressive strength.

[0074] Analysis of Experimental Results

[0075] The average value of the elastic modulus of each group of concrete specimens is as follows: As shown in the figure. The effect of coal gangue aggregate replacement rate on the elastic modulus of concrete under different water-cement ratios is as follows. As shown. Where r is the replacement rate of coal gangue aggregate, that is, r represents... c Also for r f r c r represents the coarse aggregate replacement rate. f This represents the fine aggregate replacement rate. From... As shown in (a), the elastic modulus of concrete decreases significantly with increasing coal gangue aggregate replacement rate, but the decrease in elastic modulus also decreases with decreasing water-cement ratio. For example, with both coarse and fine coal gangue aggregates, compared to ordinary concrete, a 50% volume replacement rate reduces the elastic modulus of concrete with a water-cement ratio (w / c) of 0.55 by 39.6%, while a 100% volume replacement rate reduces it by 55.9%. However, when the water-cement ratio is reduced to 0.35, a 50% volume replacement rate reduces the elastic modulus by 25%, while a 100% volume replacement rate reduces it by 51.2%. This is because the stiffness of coal gangue aggregate is significantly lower than that of natural aggregate, and the decrease in the elastic modulus of concrete is more significant with increasing coal gangue aggregate content. Reducing the water-cement ratio increases the stiffness of the cement paste, and its encapsulation effect on the aggregate is also stronger, which to some extent compensates for the deficiencies of coal gangue aggregate. Therefore, the decrease in the elastic modulus of concrete is smaller after the water-cement ratio is reduced.

[0076] surface Basic mechanical properties of coal gangue aggregate concrete

[0077]

[0078] in, Represents the compressive strength of concrete; Represents splitting tensile strength; Represents flexural strength; Represents the elastic modulus;

[0079] contrast In (b) and (c), the effect of coarse coal gangue aggregate on the elastic modulus of concrete is greater than that of fine coal gangue aggregate. For example, compared to ordinary concrete, when only coarse coal gangue aggregate is present, the elastic modulus of concrete decreases by 38% to 43%; while when only fine coal gangue aggregate is present, the elastic modulus of concrete decreases by 22% to 24% compared to ordinary concrete. The reason for this difference is that the elastic modulus of concrete depends on the stiffness and volume fraction of each component in the concrete, and under normal circumstances, the volume fraction of total fine aggregate in concrete is less than the volume fraction of total coarse aggregate. Therefore, the influence of the incorporation of fine coal gangue aggregate on the elastic modulus of concrete is smaller than that of coarse coal gangue aggregate. However, the stiffness of both coarse and fine coal gangue aggregate is significantly lower than that of the corresponding natural aggregate (in this study, the stiffness of natural aggregate is 4.8 times that of coal gangue aggregate), and the influence of both on the elastic modulus of concrete cannot be ignored. In existing experimental studies on the elastic modulus of concrete with coal gangue aggregate, the addition of 100% coal gangue coarse aggregate reduces the elastic modulus of concrete by 23.1% to 57.6%.

[0080] For ordinary concrete, its modulus of elasticity is typically significantly correlated with the corresponding cubic compressive strength, and current standards generally use an empirical function based on concrete compressive strength to characterize the modulus of elasticity. However, for coal gangue aggregate concrete, the mechanism by which coal gangue aggregate affects the modulus of elasticity and compressive strength differs, leading to a significantly different correlation between the two compared to ordinary concrete. Specifically, coal gangue aggregate is loose and porous, with numerous internal defects, resulting in low inherent strength. Furthermore, its high water absorption alters the local effective water-cement ratio of the concrete, thus affecting its compressive strength. However, the influence of coal gangue aggregate on the modulus of elasticity is primarily due to its low aggregate stiffness.

[0081] To clearly demonstrate the degree of dispersion in the relationship between compressive strength and elastic modulus of coal gangue aggregate concrete, This paper presents the elastic modulus of concrete with only coal gangue coarse aggregate replacing natural coarse aggregate, collected from multiple existing literatures. Under a given compressive strength, the elastic modulus of coal gangue aggregate concrete varies significantly. For example, for concrete with a compressive strength of 36 MPa, its elastic modulus varies between 11.8 GPa and 31.2 GPa, a difference of 132%.

[0082] Taking the replacement rate of coarse aggregate from coal gangue as an example, this paper demonstrates the relationship between the normalized modulus of elasticity of concrete with coal gangue aggregate and the replacement rate of coarse aggregate from coal gangue. (Comparison) And 6, we can see The dispersion of the scatter points is significantly smaller than that of the scatter points. The largest difference decreased from 132% to 45%.

[0083] Considering the mechanism by which coal gangue aggregate affects the elastic modulus of concrete, this invention establishes the elastic modulus (E) of coal gangue aggregate concrete. CGAC The elastic modulus (E) of ordinary concrete with the same mix proportion is compared with that of ordinary concrete. NAC The relationship between the two is used to establish a predictive model for the elastic modulus of coal gangue aggregate concrete, as shown in equation (2).

[0084]

[0085] in, The elastic modulus coefficient represents the relationship between the elastic modulus of coal gangue aggregate concrete and the elastic modulus of ordinary concrete with the same mix proportion.

[0086] Concrete can be considered a composite material consisting of two phases: aggregate and cement paste. The elastic modulus of concrete mainly depends on the elastic modulus E of the aggregate. NA and volume fraction V NA and the elastic modulus E of cement paste CPand volume fraction V CP The Reuss model based on the theory of two-phase composite materials, such as... As shown, the expression for the elastic modulus of ordinary concrete can be obtained, as shown in equation (3).

[0087] In ordinary concrete, the relationship between the volume fraction of aggregate and the volume fraction of cement paste is shown in equation (4). Substituting equation (4) into equation (3) simplifies to equation (5).

[0088]

[0089] Among them, E NAC E represents the elastic modulus of ordinary concrete. NA E CP V represents the elastic modulus of natural aggregate and cement paste, respectively. NA V CP These represent the volume fractions of natural aggregates and cement paste in ordinary concrete, respectively.

[0090] For coal gangue aggregate concrete, it can also be considered as a composite material of aggregate and cement paste. Similar to formula (5), the expression for the elastic modulus of coal gangue aggregate concrete can be obtained as shown in formula (6).

[0091]

[0092] in, This represents the elastic modulus of the total aggregate in coal gangue aggregate concrete. This refers to the volume fraction of total aggregate in coal gangue aggregate concrete.

[0093] As shown in equation (6), the elastic modulus of coal gangue aggregate concrete depends on the elastic modulus of the total aggregate and cement paste in the coal gangue aggregate concrete, as well as the volume ratio of the total aggregate. The total aggregate volume in coal gangue aggregate concrete includes both coal gangue aggregate and natural aggregate, and their relationship is shown in equation (7):

[0094]

[0095] Among them, V CGA This represents the volume percentage of coal gangue aggregate in coal gangue aggregate concrete. This refers to the volume fraction of natural aggregates in coal gangue aggregate concrete.

[0096] Existing research indicates that the elastic modulus of cement paste ranges from 12.0 GPa to 23.8 GPa, with an average value of 17.0 GPa. Therefore, it is only necessary to determine the stiffness of the aggregate in coal gangue aggregate concrete. The aggregate in coal gangue aggregate concrete can be regarded as a two-phase composite material composed of coal gangue aggregate and natural aggregate. Based on the theory of two-phase composite materials, this invention uses the Counto model to calculate its stiffness (through trial calculations, this model has high accuracy and is also well-suited for use in other deformation-related prediction models), such as... As shown, the calculation formula is shown in formula (8).

[0097]

[0098] Among them, E CGA The elastic modulus of coal gangue aggregate. The volume fraction of natural aggregate in coal gangue aggregate concrete.

[0099] The volume fraction of natural aggregate in coal gangue aggregate concrete can be calculated from the replacement rate of coal gangue coarse aggregate and coal gangue fine aggregate and the volume fraction of coal gangue coarse aggregate and coal gangue fine aggregate in the total aggregate, as shown in equation (9).

[0100]

[0101] Where, r CGCA r represents the replacement rate of coarse aggregate from coal gangue. CGFA The replacement rate of fine aggregate from coal gangue, This refers to the volume fraction of coarse aggregate from coal gangue in the total aggregate. This refers to the volume fraction of fine aggregate from coal gangue in the total aggregate.

[0102] Based on existing research, the elastic modulus of coal gangue aggregate can be taken as 15.3 GPa. The elastic modulus of natural aggregate can be taken as 73.5 GPa. Substituting the two values ​​above into equations (8) and (9), the elastic modulus of the total aggregate in coal gangue aggregate concrete can be simplified and obtained as shown in equation (10).

[0103]

[0104] Substituting equation (10) into equation (6), we can obtain the expression for the elastic modulus of coal gangue aggregate concrete, as shown in equation (12).

[0105]

[0106] Since coal gangue aggregate concrete and ordinary concrete use the same mix proportion, and the coal gangue aggregate replaces the natural aggregate by volume substitution, the aggregate volume and cement paste volume of the two are equal, i.e., formula (13) and formula (14).

[0107]

[0108] in, This refers to the volume fraction of total aggregate in concrete. This refers to the volume fraction of cement paste in the concrete.

[0109] The ratio of the volume percentage of total aggregate in concrete to the volume percentage of cement paste is expressed as α. p / a The alternative is equation (15).

[0110]

[0111] After simplification, the final prediction model of the elastic modulus of coal gangue aggregate concrete is obtained, as shown in Equation (16).

[0112]

[0113] Using 10 articles The experimental data of 55 sets of elastic modulus of coal gangue aggregate concrete collected in the present invention and the experimental results of the present invention were used to verify the proposed model (Equation (16)), and the results are as follows. As shown. From As can be seen, the model proposed in this invention can predict the elastic modulus of coal gangue aggregate concrete quite well. The linear regression coefficient of the ratio of the experimental value to the predicted value is 0.972, and the coefficient of determination (R²) is [missing value]. 2 The value was 0.993, which verifies the reliability of the model proposed in this invention.

[0114] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

[0115] References

[0116] [1] Yang Shangyu, Zhou Mei, Zhang Yuzhuo, et al. Effect of replacement rate of self-igniting coal gangue coarse aggregate on fracture toughness of concrete [J]. Journal of Building Materials, 2020, 23(04): 858-864.

[0117] [2]GAO S, ZHAO G, GUO L, et al. Utilization of coal gangue as coarse aggregates in structural concrete [J]. Construction and Building Materials, 2021, 268.

[0118] [3]ZHOU M, DOU Y, ZHANG Y, et al. Effects of the variety and content of coal gangue coarse aggregate on the mechanical properties of concrete [J]. Construction and Building Materials, 2019, 220: 386-395.

[0119] [4]ZHANG T, WEN Q, GAO S, et al. Comparative study on mechanical and environmental properties of coal gangue sand concrete [J]. Construction andBuilding Materials, 2023, 400.

[0120] [5]WANG Q, LI Z, ZHANG Y, et al. Influence of coarse coal gangueaggregates on elastic modulus and drying shrinkage behavior of concrete [J]. Journal of Building Engineering, 2020, 32.

[0121] [6] Li Shaowei, Zhou Mei, Zhang Limin. Characteristics of self-igniting coal gangue coarse aggregate and its influence on concrete performance [J]. Journal of Building Materials, 2020, 23(02): 334-340+80.

[0122] [7]ZHOU M, BAI J, LI S, et al. Mechanical Properties and UniaxialFailure Behavior of Concrete with Different Solid Waste Coarse Aggregates[J]. Materials (Basel), 2022, 15(18).

[0123] [8]ZHANG Y, WANG Q, ZHOU M, et al. Mechanical properties of concrete with coarse spontaneous combustion gangue aggregate (SCGA): Experimental investigation and prediction methodology [J]. Construction and Building Materials, 2020, 255.

[0124] [9]ZHANG Y, XU Q, WANG Q, et al. Axial compressive behavior of circular concrete-filled steel tube stub columns prepared with spontaneous-combustion coal gangue aggregate [J]. Journal of Building Engineering, 2022, 48.

[0125]

[10] WANG Y, ZHANG H, GENG Y, et al. Prediction of the elastic modulus and the splitting tensile strength of concrete incorporating both fine and coarse recycled aggregate [J]. Construction and Building Materials, 2019, 215: 332-346.

[0126]

[11] Zhou Haoran. Research on the axial compressive mechanical properties of concrete-filled steel tube stub columns with coal gangue aggregate [D], 2023.

Claims

1. A method for predicting the elastic modulus of coal gangue aggregate concrete, characterized in that, Includes the following steps: Based on the Reuss model of two-phase composite material theory, an expression for the elastic modulus of ordinary concrete is constructed, and then an expression for the elastic modulus of coal gangue aggregate concrete is constructed. Based on the Counto model of two-phase composite material theory, the equivalent stiffness of aggregates in coal gangue aggregate concrete is calculated by the volume fraction of natural aggregates in the total aggregates, and the volume fraction of natural aggregates in coal gangue aggregate concrete is obtained. Based on the constant value of the elastic modulus of coal gangue aggregate, a simplified prediction model for the final elastic modulus of coal gangue aggregate concrete is obtained.

2. The method for predicting the elastic modulus of coal gangue aggregate concrete according to claim 1, characterized in that: To establish a predictive model for the elastic modulus of coal gangue aggregate concrete, the relationship between the elastic modulus of coal gangue aggregate concrete and that of ordinary concrete with the same mix proportion is established. ； Among them, E CGAC E represents the elastic modulus of coal gangue aggregate concrete. NAC This refers to the elastic modulus of ordinary concrete. It is the elastic modulus coefficient between the elastic modulus of coal gangue aggregate concrete and the elastic modulus of ordinary concrete with the same mix proportion.

3. The method for predicting the elastic modulus of coal gangue aggregate concrete according to claim 2, characterized in that: In ordinary concrete, the relationship between the volume fraction of aggregate and the volume fraction of cement paste is shown in equation (2). Substituting equation (3) into equation (2) simplifies to equation (4): ； ； ； Among them, E NAC E represents the elastic modulus of ordinary concrete. NA E CP V represents the elastic modulus of natural aggregate and cement paste, respectively. NA V CP These represent the volume fractions of natural aggregates and cement paste in ordinary concrete, respectively. Based on the elastic modulus of ordinary concrete, the expression for the elastic modulus of coal gangue aggregate concrete is obtained as follows: ； in, This represents the elastic modulus of the total aggregate in coal gangue aggregate concrete. This represents the volume fraction of total aggregate in coal gangue aggregate concrete.

4. The method for predicting the elastic modulus of coal gangue aggregate concrete according to claim 3, characterized in that: The elastic modulus of coal gangue aggregate concrete depends on the elastic modulus of the total aggregate and cement paste in the concrete, as well as the volume ratio of the total aggregate. The total aggregate volume in coal gangue aggregate concrete includes coal gangue aggregate and natural aggregate, and their relationship is shown in equation (6): ； Among them, V CGA This represents the volume percentage of coal gangue aggregate in coal gangue aggregate concrete. This represents the volume fraction of natural aggregates in coal gangue aggregate concrete.

5. The method for predicting the elastic modulus of coal gangue aggregate concrete according to claim 4, characterized in that: Based on the Counto model of two-phase composite material theory, the elastic modulus of total aggregate in coal gangue aggregate concrete is obtained as follows: ； Among them, E CGA The elastic modulus of coal gangue aggregate. The volume fraction of natural aggregate in coal gangue aggregate concrete. The volume fraction of natural aggregate in coal gangue aggregate concrete is calculated from the replacement rates of coarse and fine coal gangue aggregate and the volume fraction of each aggregate in the total aggregate. ； Where, r CGCA r represents the replacement rate of coarse aggregate from coal gangue. CGFA The replacement rate of fine aggregate from coal gangue, This refers to the volume fraction of coarse aggregate from coal gangue in the total aggregate. This refers to the volume fraction of fine aggregate from coal gangue in the total aggregate.

6. The method for predicting the elastic modulus of coal gangue aggregate concrete according to claim 5, characterized in that: The elastic modulus of coal gangue aggregate is taken as 15.3 GPa, and the elastic modulus of natural aggregate is taken as 73.5 GPa. After substituting into equations (7) and (8), the elastic modulus of the total aggregate in coal gangue aggregate concrete is simplified to obtain: ； Substituting equation (9) into equation (5), we obtain the expression for the elastic modulus of coal gangue aggregate concrete: ； Since coal gangue aggregate concrete and ordinary concrete use the same mix proportion, and the coal gangue aggregate replaces natural aggregate by volume substitution, the aggregate volume and cement paste volume of both are equal. ； in, This refers to the volume fraction of total aggregate in concrete. This refers to the volume fraction of cement paste in the concrete. The ratio between the volume percentage of aggregate in concrete and the volume percentage of cement paste is expressed as α. p / a replace: ； After simplification, the final prediction model for the elastic modulus of coal gangue aggregate concrete is obtained: （15）。 7. A system for predicting the elastic modulus of coal gangue aggregate concrete, characterized in that: The system has a program module corresponding to the steps described in any one of claims 1-6 above, and executes the steps in the above-described method for predicting the elastic modulus of coal gangue aggregate concrete when it is run.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the method for predicting the elastic modulus of coal gangue aggregate concrete according to any one of claims 1-6.

Images