A method for determining the minimum air-entraining agent dosage of early frozen concrete based on air hole absorption of frost heaving

Abstract

The method for determining the minimum air entraining agent dosage of early frozen concrete based on the air hole absorption of frost heaving belongs to the field of concrete winter construction, in order to effectively evaluate the frozen damage risk of concrete, optimize the air entraining agent dosage, reduce the construction cost, and improve the frost resistance of concrete, the capillary index, the initial air content and the deformation index of concrete under the negative temperature environment of the concrete under the specified pre-curing age are obtained respectively, the water-air ratio and the air hole absorption efficiency value are calculated by combining the capillary index, the initial air content and the deformation index, and the minimum air entraining agent dosage required for the concrete to reach the frost resistance state is obtained by the quantitative relationship between the water-air ratio and the air hole absorption efficiency.

Description

Technical fields:

[0001] This invention belongs to the field of winter construction of concrete, and specifically relates to a method for determining the minimum air-entraining agent dosage of early-stage frozen concrete based on the absorption of frost heave by air bubbles. Background technology:

[0002] Because early-age concrete has a high water content and a fragile structure, it is exposed to freezing conditions before it has fully hardened during winter construction. This results in lower strength and makes it highly susceptible to frost damage, severely impacting the safety and durability of the project. In sub-zero temperatures, the water in the concrete pores expands by up to 9% when it freezes, squeezing unfrozen water and causing it to migrate into the surrounding pores, releasing significant frost heave stress. However, when the pores cannot fully absorb the squeezed unfrozen water, hydrostatic pressure forms within the pores. Once this hydrostatic pressure exceeds the tensile strength of the pore walls, cracks will form. Therefore, frost damage to concrete is the result of both water expansion upon freezing and the pores' ability to absorb frost heave.

[0003] To mitigate frost damage to concrete, air-entraining agents can be added to optimize the concrete's pore structure, shorten moisture migration paths, and enhance the pores' ability to absorb frost heave. However, excessive air-entraining agents increase costs and reduce concrete strength. Because current techniques do not quantify the pores' ability to absorb frost heave, the dosage of air-entraining agents relies on strength retention tests after concrete freeze-thaw cycles. This method is not only time-consuming, costly in terms of curing and labor, but also fails to adequately consider the influence of concrete mix design and pre-curing time, making it difficult to apply widely. Therefore, there is an urgent need to establish a scientific method for determining the minimum dosage of air-entraining agents. Summary of the Invention:

[0004] To address the problems mentioned in the background section, the present invention aims to provide a method for determining the minimum air-entraining agent dosage for early-stage frozen concrete based on the absorption of frost heave by air bubbles.

[0005] The method for determining the minimum air-entraining agent dosage for early-stage frozen concrete based on pore absorption of frost heave involves obtaining the capillary index, initial air content, and deformation index of the concrete under negative temperature conditions at a specified pre-curing age. The water-air ratio and pore absorption efficiency are then calculated based on these parameters. The minimum air-entraining agent dosage required for the concrete to reach its frost-resistant state is determined through the quantitative relationship between the water-air ratio and the pore absorption efficiency.

[0006] Preferably, obtaining the capillary parameters in concrete at a specified pre-curing age includes obtaining the capillary water volume W. c The process for obtaining the capillary pore volume ΔV includes the following steps:

[0007] A1. Calculate the overall hydration degree ξ(t) of cement paste using the Parrot & Killoh model:

[0008] ξ(t)=ξ t,i m i , i=C3S, C2S, C3A, C4AF,

[0009] In the above formula, ξ(t) represents the overall hydration degree of the cement paste at time t, and i represents the mineral composition of the cement clinker as C3S, C2S, C3A, and C4AF. t,i m represents the degree of hydration of phase i at time t. i The mass fraction of phase i in the cement;

[0010]

[0011] In the above formula, S and S0 are the actual specific surface area and reference specific surface area of ​​cement, respectively, and S0 = 385m². 2 / kg, R 1,i R 2,i and R 3,i β represents the reaction rate of the i-phase clinker hydration reaction controlled by the nucleation and growth stage, the diffusion process, and the ion dissolution and transport process, respectively. w / c,i β RH and β T,i The effects of water-cement ratio, relative humidity, and temperature on the hydration rate of phase i are represented respectively.

[0012]

[0013] R 2,i =K 2,i (1-ξ t,i ) 2 / 3 / [1-(1-ξ t,i ) 1 / 3 ];

[0014]

[0015] β w / c,i =[1+3.333(H)] i ·w / c-ξ t,i )] 4 ;

[0016] β RH =[(RH-0.55) / 0.45] 4 ;

[0017] β T,i =exp[-E a,i / R(1 / T-1 / T0)];

[0018] In the above formula, w / c represents the water-cement ratio, RH represents the relative humidity, R represents the universal gas constant, T and T0 are the actual ambient temperature and the reference temperature, and T0 = 293K;

[0019] A2. After obtaining the overall hydration degree ξ(t) of the cement paste, the capillary water content W inside the concrete is further calculated using the Powers hydration model. c And capillary pore content ΔV:

[0020]

[0021] f air,cp (t)=1-f clin,cp (t)-f hyd,cp (t)-f w,cp (t);

[0022]

[0023] W c =f w,cp (t)×f cp ;

[0024] ΔV=f air,cp (t)×f cp ;

[0025] In the above formula, f clin,cp (t), f hyd,cp (t), f w,cp (t) and f air,cp (t) represents the volume fraction of unhydrated clinker, hydration products, capillary water, and capillary pores caused by chemical shrinkage in the cement paste at time t, respectively; ρ clin , ρ w and ρ hyd These represent the densities of cement clinker, capillary water, and hydration products, respectively; f cp Represents the volume fraction of cement paste in concrete; m w m c m ca and m fa ρ represents the mass of water, cement, coarse aggregate, and fine aggregate in 1 cubic meter of concrete. w ρ c ρ ca and ρ fa V represents the density of water, cement, coarse aggregate, and fine aggregate, respectively. A VA represents the initial air content of the concrete; when VA = 0, the capillary water and capillary porosity content of the concrete at the specified pre-curing age is denoted as W. C_VA0 and ΔV VA0 .

[0026] Preferably, obtaining the initial air content in concrete includes: pre-setting multiple low air-entraining agent dosages and testing the initial air content V of fresh concrete at these dosages. A The term "low air-entraining agent" refers to an amount not exceeding the commonly used dosage range of the selected air-entraining agent.

[0027] The initial gas content can be tested using the pressure method in standard GB / T50080.

[0028] Preferably, obtaining the deformation index of concrete under negative temperature conditions includes: testing the apparent deformation V of concrete under negative temperature conditions. C_T and temperature deformation V T The apparent deformation V of the tested concrete under negative temperature conditions is... C_T The acquisition process involves conducting tests using a negative-temperature concrete apparent deformation testing device and obtaining data. The apparent deformation is then calculated using the following formula:

[0029] V C_T =(HD) f ) 3 / (H-D0) 3 -1

[0030] In the above formula, V C_T The apparent deformation of the concrete after cooling to temperature T is represented by H, where H represents the height from the laser sensor to the apex of the cone; D represents the distance from the laser sensor to the concrete surface; HD represents the height of the concrete; and the subscripts 0 and f correspond to the concrete before and after freezing, respectively.

[0031] Preferably, the calculation process for the water-to-air ratio and the pore absorption efficiency values, which are calculated by combining capillary index, initial gas content, and deformation index, is as follows:

[0032] B1. Calculate the frost heave deformation V absorbed by the pores. ab_air ,

[0033] V ab_air =V E -V T -V C_Tf ;

[0034] In the above formula, V E The volume representing the capillary water freeze-swell deformation is 0.09W. C V C_Tf This indicates that the preset negative temperature T has been reached. f The apparent deformation value at time; V T Represents temperature deformation, where V T =α C ΔT, α C =V C_5℃ / 15, in the above formula, α CΔT and ΔT represent the volumetric thermal expansion coefficient and temperature difference of the cement-based material, respectively. ΔT is determined by the difference between 20℃ and the preset negative temperature T. f The temperature difference was calculated, and the volumetric thermal expansion coefficient of concrete within the temperature range of 20–5℃ was used to approximate the temperature difference between 20℃ and the preset negative temperature T. f The average volumetric thermal expansion coefficient α between C ;

[0035] B2. Calculate the water-air ratio W of the concrete before freezing. C / A,

[0036] W C / A=W C / (V A +ΔV);

[0037] B3, and the pore absorption efficiency coefficient γ of concrete after freezing.

[0038] γ=V ab_air / (V A +ΔV);

[0039] Wherein, the water-to-air ratio W C / A refers to the capillary water volume W in the concrete. c The ratio of the initial gas content to the total volume of all pores, A, where A is the sum of the initial gas content and the capillary pore volume.

[0040] Preferably, the process of determining the minimum air-entraining agent dosage required for concrete to reach its frost-resistant state through the quantitative relationship between the water-air ratio and the pore absorption efficiency includes:

[0041] Plotting γ-W c / A relationship diagram, fitting γ-W c / A Damaged Area;

[0042] According to the γ-W c The intersection of the data points in the / A relationship diagram and the non-damage line determines the critical water-gas ratio (W). c / A) cr ;

[0043] According to the critical water-gas ratio (W c / A) cr The capillary water volume fraction W of concrete at a specified pre-curing age under conditions of 0 initial air content. C_VA0 and capillary pore volume fraction ΔV VA0 Calculate the initial air content required for concrete to reach the critical frost resistance state, and select the corresponding air-entraining agent dosage according to the type of air-entraining agent.

[0044] Preferably, the reasoning process for the non-damaging line includes:

[0045] When the concrete reaches a non-damaged state, V ab_air =V E =0.09W C Stomatal absorption efficiency coefficient γ and water-to-air ratio W C / A satisfies γ = 0.09W C / A.

[0046] Preferably, the process of determining the minimum air-entraining agent dosage required for concrete to reach its frost-resistant state through the quantitative relationship between the water-air ratio and the pore absorption efficiency further includes: based on γ-W c The / A relationship determines the risk of frost damage to concrete, when γ-W c If the data point A is located on the non-damage line, it is determined that the concrete has not suffered frost damage. When γ-W c If data point A is located below the non-damage line, it indicates that the concrete is at risk of frost damage. The moisture migration process after the concrete freezes is divided into three stages:

[0047] S1, when the water-to-air ratio is W C When / A is high, the pores absorb frost heave deformation V ab_air Both the pore absorption efficiency coefficient γ and W C If / A decreases and increases, then the water migration of concrete after freezing is in the stage controlled by the pore spacing coefficient.

[0048] S2, when the water-to-air ratio is W C When / A decreases to a certain value, the pores absorb the frost heave deformation V ab_air With W C / A decreases and increases, the pore absorption efficiency coefficient γ increases with W C If / A decreases and shows a decreasing trend, then the water migration of concrete after freezing is in a transitional stage.

[0049] S3, when the water-to-air ratio is W C When / A is below the critical value, the pores absorb frost heave deformation V ab_air The volume V of capillary water freeze-swell deformation reaches E If the pore absorption efficiency coefficient γ is in a state of sharp decrease, then the water migration of concrete after freezing is in the air content controlled stage.

[0050] Preferably, the step according to the γ-W c The intersection of the data points in the / A relationship diagram and the non-damage line determines the critical water-gas ratio (W). c / A) cr include:

[0051] C1, when the γ-W of cement-based materials c The / A relationship graph shows obvious transition stages, and the data in the transition stages are fitted.

[0052] C2, when γ-W c If no obvious transition stage is shown in the / A relationship diagram, then according to the required accuracy or workload, you can choose to add data points in the damaged area or directly fit the data in the pore spacing coefficient control stage. The amount of air-entraining agent corresponding to the data points in the added damaged area should not be less than the maximum value in the pore spacing coefficient control stage, but less than the minimum value in the gas content control stage.

[0053] C3. Based on the increase in data points in the damaged area, determine again whether a transition phase exists. If it exists, proceed to step C1; otherwise, proceed to step C2 again.

[0054] C4. The water-to-air ratio corresponding to the intersection of the fitted curve and the non-damage line is the critical water-to-air ratio (W). c / A) cr The critical water-gas ratio (W) c / A) cr This corresponds to the critical freeze-thaw resistance state of cement-based materials.

[0055] Preferably, the step of basing the water-air ratio (W) on the critical water-air ratio (W) c / A) cr The capillary water volume fraction W of concrete at a specified pre-curing age under conditions of 0 initial air content. C_VA0 and capillary pore volume fraction ΔV VA0 The process of calculating the initial air content required for concrete to reach its critical frost resistance state is as follows:

[0056]

[0057] Among them, W C_VA0 and ΔV VA0 W represents the capillary water volume and capillary pore volume content when the initial air content of concrete is 0. C_VA0 =W C / (1-V A ), ΔV VA0 =ΔV / (1-V) A Compared with the prior art, the beneficial effects of the present invention are as follows:

[0058] I. This invention can assess the moisture migration state of cement paste and further assess the risk of concrete freezing damage.

[0059] Second, the method proposed in this invention is applicable to mortars and concretes with different air-entraining agent dosages, and has universality.

[0060] Third, compared with traditional methods that rely on strength testing, the method provided by this invention not only improves the accuracy of predicting the minimum air-entraining agent dosage, but also reduces the amount of testing and saves the time required for strength curing.

[0061] IV. After extensive testing, a range of critical water-air ratios for concrete can be obtained. Based on this, a universally applicable minimum critical water-air ratio can be determined. From this critical water-air ratio, the dosage of air-entraining agents for universally applicable antifreeze cementitious materials can be further determined. Attached image description:

[0062] For ease of explanation, the present invention will be described in detail below with reference to specific embodiments and accompanying drawings.

[0063] Figure 1 This is a schematic diagram of the deformation testing device used in this invention;

[0064] Figure 2 This is a diagram illustrating the mechanism by which increasing the amount of air-entraining agent affects γ evolution.

[0065] Figure 3 Typical γ-W C / A Relationship Diagram;

[0066] Figure 4 The curves showing the changes in capillary water and capillary porosity of the cement paste with the curing age are shown in the examples.

[0067] Figure 5 This is a diagram showing the determination of the critical water-air ratio of concrete in the embodiments;

[0068] Figure 6 This is a diagram showing the verification of the minimum air-entraining agent dosage in concrete in the examples.

[0069] In the diagram, 1-horizontal base; 2-vertical column; 3-horizontal support; 4-base box; 5-top cover; 6-laser sensor; 7-computer; 8-temperature recorder. Detailed implementation method:

[0070] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0071] It should also be noted that, in order to avoid obscuring the invention with unnecessary details, only the structures and / or processing steps closely related to the solution according to the invention are shown in the accompanying drawings, while other details that are not closely related to the invention are omitted.

[0072] Example 1: As Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6As shown, this specific embodiment adopts the following technical solution: a method for determining the minimum air-entraining agent dosage of early-frozen concrete based on pore absorption of frost heave, characterized in that: the method for determining the minimum air-entraining agent dosage of early-frozen concrete involves obtaining the capillary index, initial air content, and deformation index of concrete under negative temperature conditions at a specified pre-curing age, and then calculating the water-air ratio and pore absorption efficiency values ​​by combining the capillary index, initial air content, and deformation index. The minimum air-entraining agent dosage required for the concrete to reach the frost-resistant state is obtained through the quantitative relationship between the water-air ratio and the pore absorption efficiency.

[0073] In determining the minimum air-entraining agent dosage for early-stage frozen concrete, obtaining capillary parameters in the concrete at a specified pre-curing age can include, but is not limited to, obtaining capillary water volume and capillary pore volume. For the initial air content, it can be tested by pre-setting multiple low air-entraining agent dosages at different dosages. The type of air-entraining agent is not limited and can include, but is not limited to, rosin-based, synthetic, saponin-based, and nitrate-based agents. The deformation parameters can include, but are not limited to, the apparent deformation, temperature deformation, and volumetric deformation of the concrete at different temperatures. This embodiment does not limit the method of obtaining deformation parameters. Based on the above data, the water-air ratio and pore absorption efficiency can be calculated. The minimum air-entraining agent dosage required for the concrete to reach its frost-resistant state can be determined through the quantitative relationship between the water-air ratio and pore absorption efficiency. The quantitative relationship between the water-air ratio and pore absorption efficiency can be expressed by drawing a relationship diagram or forming a relationship table.

[0074] Example 2: This example further limits the above examples. This example only provides a preferred implementation method. Obtaining the capillary index in concrete at a specified pre-curing age includes obtaining the capillary water volume W. c The process for obtaining the capillary pore volume ΔV includes the following steps:

[0075] A1. Calculate the overall hydration degree ξ(t) of cement paste using the Parrot & Killoh model:

[0076] ξ(t)=ξ t,i m i , i=C3S, C2S, C3A, C4AF,

[0077] In the above formula, ξ(t) represents the overall hydration degree of the cement paste at time t, and i represents the mineral composition of the cement clinker as C3S, C2S, C3A, and C4AF. t,i m represents the degree of hydration of phase i at time t. i The mass fraction of phase i in the cement;

[0078]

[0079] In the above formula, S and S0 are the actual specific surface area and reference specific surface area of ​​cement, respectively, and S0 = 385m². 2 / kg, R 1,i R 2,i and R 3,i β represents the reaction rate of the i-phase clinker hydration reaction controlled by the nucleation and growth stage, the diffusion process, and the ion dissolution and transport process, respectively. w / c,i β RH and β T,i The effects of water-cement ratio, relative humidity, and temperature on the hydration rate of phase i are represented respectively.

[0080]

[0081] R 2,i =K 2,i (1-ξ t,i ) 2 / 3 / [1-(1-ξ t,i ) 1 / 3 ];

[0082]

[0083] β w / c,i =[1+3.333(H)] i ·w / c-ξ t,i )] 4 ;

[0084] β RH =[(RH-0.55) / 0.45] 4 ;

[0085] β T,i =exp[-E a,i / R(1 / T-1 / T0)];

[0086] In the above formula, w / c represents the water-cement ratio, RH represents the relative humidity, R represents the universal gas constant, T and T0 are the actual ambient temperature and the reference temperature, and T0 = 293K;

[0087] A2. After obtaining the overall hydration degree ξ(t) of the cement paste, the capillary water content W inside the concrete is further calculated using the Powers hydration model. c And capillary pore content ΔV:

[0088]

[0089] f air,cp (t)=1-f clin,cp (t)-f hyd,cp (t)-f w,cp (t);

[0090]

[0091] W c =f w,cp (t)×f cp ;

[0092] ΔV=f air,cp (t)×f cp ;

[0093] In the above formula, f clin,cp (t), f hyd,cp (t), f w,cp (t) and f air,cp (t) represents the volume fraction of unhydrated clinker, hydration products, capillary water, and capillary pores caused by chemical shrinkage in the cement paste at time t, respectively; ρ clin , ρ w and ρ hyd These represent the densities of cement clinker, capillary water, and hydration products, respectively; f cp Represents the volume fraction of cement paste in concrete; m w m c m ca and m fa ρ represents the mass of water, cement, coarse aggregate, and fine aggregate in 1 cubic meter of concrete. w ρ c ρ ca and ρ fa V represents the density of water, cement, coarse aggregate, and fine aggregate, respectively. A VA represents the initial air content of the concrete; when VA = 0, the capillary water and capillary porosity content of the concrete at the specified pre-curing age is denoted as W. C_VA0 and ΔV VA0 The parameters related to i used in the above formula are shown in Table 1:

[0094] Table 1. Parameters required for Parrot & Killoh model calculation

[0095]

[0096]

[0097] Example 3: This example further limits the above examples. This example only provides a preferred implementation method. Obtaining the initial air content of concrete includes: presetting multiple low air-entraining agent dosages and testing the initial air content V of fresh concrete at these dosages. A Wherein, the low air-entraining agent refers to a dosage not exceeding the commonly used dosage range of the selected air-entraining agent, and the initial gas content V AThe tests can be conducted, but are not limited to, those in accordance with the GB / T50080 standard.

[0098] Example 4: This example further limits the above examples. This example only provides a preferred implementation method. Obtaining the deformation index of concrete under negative temperature conditions includes: testing the apparent deformation V of concrete under negative temperature conditions. C_T and temperature deformation V T .

[0099] Specifically, this embodiment provides a preferred implementation, wherein the apparent deformation is the deformation value directly observed in the experiment. During the testing of the apparent deformation and temperature deformation of concrete under negative temperature conditions, an apparent deformation testing device is used to acquire relevant data. The apparent deformation testing device consists of a deformation testing system and a temperature testing system. The deformation testing system comprises a horizontal base 1, a vertical column 2, a horizontal support 3, a bottom box 4, a top cover 5, a laser sensor 6, and a computer 7. The vertical column 2 is mounted on the horizontal base 1, and the bottom box 4 is placed on the horizontal base 1. The bottom box 4 has a double-layered hollow structure; the outer layer is a cylinder, and the inner layer is an inverted cone with a 60° apex angle. Freshly mixed concrete can be poured into the conical shell of the bottom box 4. The top cover 5 is located on the upper part of the bottom box 4. The top cover 5 has an annular double-layered hollow structure. To achieve concrete temperature control, two interfaces are provided on the sides of both the bottom box 4 and the top cover 5, both connected to hollow pipes, serving as the inlet and outlet for circulating liquid. The circulating fluid can be, but is not limited to, liquids with a freezing point below the freezing temperature and a boiling point above 40°C, such as ethylene glycol. The temperature of the concrete is controlled by regulating the temperature of the bottom chamber 4 and the top cover 5 through the circulating fluid. A laser sensor 6 is fixed to the vertical column 2 via a horizontal bracket 3, allowing the laser to reach the top surface of the concrete through a hole in the center of the top cover 5. The laser sensor 6 is connected to a computer 7, which records the laser transmission distance and calculates the apparent deformation according to the following formula. The temperature testing system consists of a thermocouple and a temperature recorder 8. When pouring concrete into the bottom chamber 4, one end of the thermocouple is pre-embedded in the center of the concrete, and the other end is connected to the temperature recorder 8.

[0100] V C_T =(HD) f ) 3 / (H-D0) 3 -1

[0101] In the above formula, V C-T The apparent deformation of the concrete after cooling to temperature T is represented by H, which represents the height from the laser sensor 6 to the apex of the cone; D represents the distance from the laser sensor 6 to the concrete surface; HD represents the height of the concrete; and the subscripts 0 and f correspond to the concrete before and after freezing, respectively.

[0102] In this embodiment, when conducting an apparent deformation test on the concrete, the temperature of the circulating fluid can first be adjusted to 20°C, and the circulating fluid is circulated in the bottom tank 4 and the top cover 5 until the temperature inside the conical shell stabilizes at 20°C. Subsequently, freshly mixed concrete is poured into the conical shell of the bottom tank 4, a thermocouple is pre-embedded in the center of the concrete, and after the concrete has cured for the specified time, the temperature of the circulating fluid is immediately adjusted to a preset negative temperature. Simultaneously, the laser sensor 6 and the temperature recorder 8 are activated to record the apparent deformation and temperature deformation of the concrete. Throughout the above process, except during the pouring of cement-based materials, the bottom tank 4 should always be covered with the top cover 5 to maintain the internal temperature of the conical shell.

[0103] In this embodiment, since the water in concrete mainly consists of capillary water and gel water, and the freezing temperature of gel water is below -50℃, considering that the temperature in China during winter is generally not lower than -50℃, this invention only considers the case of capillary water freezing. For safety, the amount of air-entraining agent in this invention can ensure that the concrete resists frost heave damage caused by the complete freezing of all capillary water. Because early-age concrete has relatively coarse pores and is extremely susceptible to freezing, for energy conservation, a maximum negative temperature of -15℃ can be preset as the temperature at which all capillary water in the concrete freezes. Therefore, a negative temperature between -15℃ and -50℃ can be preset to test the apparent deformation and temperature change of concrete after freezing at a specified pre-curing time and negative temperature. The concrete is cooled to 5℃ and reaches the preset negative temperature T. f The apparent deformation value at time is denoted as V. C_5℃ and V C_Tf .

[0104] Example 5: This example further limits the above examples. This example only provides a preferred implementation. Considering that the apparent deformation is composed of temperature deformation, capillary water frost heave deformation, and pore absorption frost heave deformation, the calculation process for the water-air ratio and pore absorption efficiency values ​​is as follows, combining capillary indices, initial gas content, and deformation indices:

[0105] B1. Calculate the frost heave deformation V absorbed by the pores. ab_air ,

[0106] V ab_air =V E -V T -V C_Tf ;

[0107] In the above formula, V E The volume representing the capillary water freeze-swell deformation is 0.09W. C V C_Tf This indicates that the preset negative temperature T has been reached. f The apparent deformation value at time; V TRepresents temperature deformation, where V T =α C ΔT, α C =V C_5℃ / 15, in the above formula, α C ΔT and ΔT represent the volumetric thermal expansion coefficient and temperature difference of the cement-based material, respectively. ΔT is determined by the difference between 20℃ and the preset negative temperature T. f The temperature difference was calculated, and the volumetric thermal expansion coefficient of concrete within the temperature range of 20–5℃ was used to approximate the temperature difference between 20℃ and the preset negative temperature T. f The average volumetric thermal expansion coefficient α between C ;

[0108] B2. Calculate the water-air ratio W of the concrete before freezing. C / A,

[0109] W C / A=W C / (V A +ΔV);

[0110] B3, and the pore absorption efficiency coefficient γ of concrete after freezing.

[0111] γ=V ab_air / (V A +ΔV);

[0112] Wherein, the water-to-air ratio W C / A refers to the capillary water volume W in the concrete. c The ratio of the total volume of all pores, A, to the initial gas content and the total volume of capillary pores. The pore absorption efficiency coefficient refers to the ratio of the volume of squeezed water that freezes after entering the pores to the total volume of the pores.

[0113] Example 6: This example further limits the above examples. This example only provides a preferred embodiment. The process of determining the minimum air-entraining agent dosage required for concrete to reach its frost-resistant state through the quantitative relationship between the water-air ratio and the pore absorption efficiency includes:

[0114] Plotting γ-W c / A relationship diagram, fitting γ-W c / A Damaged Area;

[0115] According to the γ-W c The intersection of the data points in the / A relationship diagram and the non-damage line determines the critical water-gas ratio (W). c / A) cr ;

[0116] According to the critical water-gas ratio (W c / A) crThe capillary water volume W of concrete at a specified pre-curing age under conditions of 0 initial air content. C_VA0 and capillary pore volume ΔV VA0 Calculate the initial air content required for concrete to reach the critical frost resistance state, and select the corresponding air-entraining agent dosage according to the type of air-entraining agent.

[0117] Example 7: This example further limits the above examples. This example only provides a preferred implementation. The reasoning process of the non-damaging line includes:

[0118] When the concrete reaches a non-damaged state, V ab_air =V E =0.09W C Stomatal absorption efficiency coefficient γ and water-to-air ratio W C / A satisfies γ = 0.09W C / A.

[0119] Example 8: This example further limits the above examples. This example only provides a preferred embodiment. The process of determining the minimum air-entraining agent dosage required for concrete to reach the frost-resistant state through the quantitative relationship between the water-air ratio and the pore absorption efficiency further includes: based on γ-W c The / A relationship determines the risk of frost damage to concrete, when γ-W c If the A data point is located on the non-damage line, it indicates that the concrete has not suffered frost damage. In this case, the moisture migration of the concrete after freezing is controlled by the air content. When γ-W c If the A data point is below the non-damage line, the concrete is at risk of frost damage. As the air-entraining agent dosage increases, the initial air content V of the concrete... A Increase, leading to W C / A decreases accordingly, and the pores absorb the frost heave deformation V ab_air Both the stomatal absorption efficiency coefficient γ and V are affected. ab_air Based on the development trend of γ, the development process of γ and its corresponding moisture migration process after freezing of cement-based materials can be divided into three stages, see... Figure 2 and Figure 3 , Figure 2 In this context, 'a' represents the maximum value of the stomatal absorption efficiency coefficient γ, and 'b' represents the critical antifreeze state. Figure 3 The P-line represents the non-damage line, the L-line is the critical water-to-air ratio line, the M region represents the safe water-to-air ratio, and the N region represents the water-to-air ratio with damage risk.

[0120] In the following steps, stage S1 is the stomatal spacing coefficient control stage, and the control factor is the stomatal spacing coefficient; stage S2 is the transition stage, and the control factors are the stomatal spacing coefficient and gas content; stage S3 is the gas content control stage, and the control factor in this stage is the gas content.

[0121] S1, when the water-to-air ratio is W C When / A is high, the pores absorb frost heave deformation V ab_air Both the pore absorption efficiency coefficient γ and W C When / A decreases and increases, the water migration of concrete after freezing is in the stage controlled by the pore spacing coefficient. This corresponds to concrete with poor pore structure, where the large pore spacing coefficient is the main obstacle to the migration of squeezed water from frozen pores to pores. In this case, increasing the amount of air-entraining agent will lead to a significant decrease in the pore spacing coefficient, increasing the volume of frost heave absorbed by the pores, and correspondingly, γ will also increase. Concrete in this stage faces a high risk of freezing damage.

[0122] S2, when the water-to-air ratio is W C When / A decreases to a certain value, the pores absorb the frost heave deformation V ab_air With W C / A decreases and increases, the pore absorption efficiency coefficient γ increases with W C If the air content V decreases as A decreases, the water migration of concrete after freezing is in a transitional stage. With further increases in the air-entraining agent dosage, the number of pores gradually approaches saturation, and the decreasing trend of the pore spacing coefficient slows down, limiting its promoting effect on water migration. At this point, the air content V... A The contribution to the increased volume of frost heave absorption is already significant. However, due to the gas content V... A The increase in γ exceeds the increase in absorbed frost heave deformation, and γ begins to decrease. Therefore, the moisture migration process in frozen concrete during this stage is jointly controlled by the pore spacing coefficient and air content, and the concrete still faces the risk of frost damage.

[0123] S3, when the water-to-air ratio is W C When / A is below the critical value, the volume of frost heave caused by capillary freezing can be completely absorbed by nearby pores, and the pores absorb the frost heave deformation V. ab_air The volume V of capillary water freeze-swell deformation reaches E The value indicates that the moisture migration of concrete after freezing is in the air content-controlled stage; as the dosage of air-entraining agent continues to increase, the pores absorb the frost heave deformation V. ab_air Volume V of capillary water freeze-swell deformation E The total gas content increases at the same time as the total gas content decreases, and the combined effect of the two makes the decreasing trend of γ more significant. During this stage, cement-based materials will not be at risk of freezing damage.

[0124] For concrete with a specific mix proportion and pre-curing time, stages S1 and S2 do not always coexist with increasing air-entraining agent dosage. Stage S1 may not exist because the blank concrete may exhibit a better pore structure due to its dense filling and longer pre-curing time. In this case, increasing the air-entraining agent dosage does not significantly reduce the pore spacing coefficient, and the moisture migration in the blank concrete has already entered the transition stage upon freezing. Stage S2 may not exist because the pore structure of the blank concrete is poor upon freezing, requiring a large number of pores to reduce its pore spacing coefficient. When the pore spacing coefficient decreases to a level that is no longer a major obstacle to moisture migration, its air content is already sufficient to accommodate all the moisture expansion volume upon freezing. Therefore, there is no transition stage.

[0125] Example 9: This example further limits the above examples. This example only provides a preferred implementation method, wherein the γ-W c The intersection of the data points in the / A relationship diagram and the non-damage line determines the critical water-gas ratio (W). c / A) cr include:

[0126] C1, when the γ-W of cement-based materials c The / A relationship graph shows obvious transition stages, and the data in the transition stages are fitted.

[0127] C2, when γ-W c If no obvious transition stage is shown in the / A relationship diagram, then according to the required accuracy or workload, you can choose to add data points in the damaged area or directly fit the data in the pore spacing coefficient control stage. The amount of air-entraining agent corresponding to the data points in the added damaged area should not be less than the maximum value in the pore spacing coefficient control stage, but less than the minimum value in the gas content control stage.

[0128] C3. Based on the increase in data points in the damaged area, determine again whether a transition phase exists. If it exists, proceed to step C1; otherwise, proceed to step C2 again.

[0129] C4. The water-to-air ratio corresponding to the intersection of the fitted curve and the non-damage line is the critical water-to-air ratio (W). c / A) cr The critical water-gas ratio (W) c / A) cr Corresponding to the critical freeze-thaw resistance state of cement-based materials;

[0130] C5. The critical water-gas ratio (W) c / A) crThe following formula can be used to convert it into critical saturation, where critical saturation is a more commonly used indicator. Converting it into critical saturation as an indicator provides a more intuitive physical meaning, facilitating comparisons between different studies and engineering applications:

[0131]

[0132] Example 10: This example further limits the above examples. This example only provides a preferred implementation method, wherein the critical water-gas ratio (W) is used. c / A) cr The capillary water volume fraction W of concrete at a specified pre-curing age under conditions of 0 initial air content. C_VA0 and capillary pore volume fraction ΔV VA0 The process of calculating the initial air content required for concrete to reach its critical frost resistance state is as follows:

[0133]

[0134] Example 11: This example provides the required dosage of air-entraining agent to reach the critical frost resistance state when concrete is pre-cured at 20°C for 24 hours. This example only provides a specific implementation method, and the method provided by this invention is not limited to the situation described in this example. In this example, the main component of the selected air-entraining agent is triterpenoid saponin. The mix proportions and phase densities of the blank group concrete are shown in Table 2, and the cement composition is shown in Tables 3 and 4.

[0135] Table 2 Concrete mix proportions and phase densities of the blank group (kg / m³) 3 )

[0136]

[0137] Table 3 Chemical composition of cement

[0138]

[0139]

[0140] Table 4 Cement mineral composition

[0141]

[0142] The curves showing the changes in capillary water volume content and capillary pore volume content of cement paste with the pre-curing age are shown below. Figure 4 After 24 hours, the cement paste had a water content of 42.5% and a capillary porosity of 2.34%. When the initial air content was 0, the capillary water content W of the concrete was... C_VA0 and capillary pore content ΔV VA0 They were 15.28% and 0.84%, respectively.

[0143] The preset air-entraining agent dosage is Test the initial air content V of concrete A The capillary water content (Wc) of the pre-cured concrete after 24 hours was calculated to be 14.88%, 14.71%, 14.50%, and 14.31%, respectively, based on the aggregate volume fraction and initial air content. The capillary pore volume (ΔV) was also calculated to be 0.82%, 0.81%, 0.80%, and 0.79%, respectively. The preset temperature at which the capillary water in the concrete completely freezes was -17.5℃. The apparent deformation and temperature curve of the concrete during the cooling process were tested. After the concrete cooled to -17.5℃, the apparent deformation value (V) of the concrete at the preset negative temperature under the four air-entraining agent dosages was measured. c_-17.5℃ The percentages of the concrete were stabilized at 0.132%, 0.014%, 0.012%, and -0.039%, respectively; the deformation of the concrete in the temperature range of 20–5℃ was 13.72 × 10⁻⁶. -6 15.32×10 -6 18.52×10 -6 and 19.21×10 -6 The corresponding temperature deformations at ℃ were 0.0514%, 0.0575%, 0.0695%, and 0.0720%, respectively. The expansion volume V of capillary water after complete freezing... E The percentages are 1.34%, 1.32%, 1.31%, and 1.29%; therefore, the pore absorption of frost heave deformation V... ab_air The percentages were 1.157%, 1.249%, 1.229%, and 1.257%.

[0144] Next, we calculate the water-to-air ratio W. C / A Stomatal absorption efficiency coefficient γ, and plot γ-W c / A relationship diagram, see Figure 5 The dosage of air-entraining agent is: The γ value of the concrete is lower than The concrete at these two dosages, and below the non-damage line, indicates that the concrete is in a transitional stage and is at risk of frost damage; the air-entraining agent dosage is... and The data points corresponding to the concrete are located on the non-damage line, indicating that the concrete at this dosage has no risk of frost damage; the air-entraining agent dosage is... and The x-coordinate of the intersection point of the fitted data line and the undamaged line is 2.77. According to the formula... The initial porosity required for concrete to reach its critical freeze-thaw resistance state is 4.47%; based on the properties of the air-entraining agent selected in this embodiment, the required AEA dosage to achieve this initial air content is...

[0145] To verify the selected air-entraining agent dosage in this embodiment, a strength test was conducted. The molding air-entraining agent dosage was... Positive temperature strength specimens, negative temperature strength specimens, and temperature specimens, all with the selected optimal air-entraining agent dosage, were prepared, each measuring 100mm × 100mm × 100mm. Thermocouples were embedded inside the temperature specimens to record the concrete temperature. Positive temperature strength specimens were cured under standard curing conditions for 28 days. Negative temperature strength specimens and temperature specimens were cured under standard curing conditions for 24 hours and then placed in an environment at -17.5℃. Temperature monitoring of the specimens showed that the concrete temperature dropped to ambient temperature after 3 hours. The negative temperature strength specimens were then transferred to an environment at 20℃ and cured for another 28 days. The strength of the positive and negative temperature strength specimens was tested after 28 days. The obtained strength data are shown in [link to data]. Figure 6 When the amount of air-entraining agent is lower than At that time, the strength retention rate of the frozen concrete was less than 95%. However, when the air-entraining agent dosage reached... Subsequently, the strength retention rate exceeded 95%, proving the accuracy of the present invention in predicting the amount of air-entraining agent.

[0146] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for determining the minimum air-entraining agent dosage for early-stage frozen concrete based on pore absorption of frost heave, characterized in that: The method for determining the minimum air-entraining agent dosage for early-stage frozen concrete involves obtaining the capillary index, initial air content, and deformation index of the concrete under negative temperature conditions at a specified pre-curing age. Then, the water-air ratio and pore absorption efficiency are calculated based on these parameters. The process is as follows: B1. Calculate the deformation caused by frost heave due to pore absorption. , ； In the above formula, Represents the volume of capillary water heave deformation; This indicates that the preset negative temperature has been reached. Apparent deformation value at time; Represents temperature deformation, in which In the above formula, and These represent the volumetric thermal expansion coefficient and temperature difference of cement-based materials, respectively. The temperature difference between 20℃ and the preset negative temperature Calculations show that the volumetric thermal expansion coefficient of concrete within the temperature range of 20~5℃ is used to approximate the temperature range of concrete from 20℃ to the preset negative temperature. Average volumetric thermal expansion coefficient within the range ; B2. Calculate the water-air ratio of the concrete before freezing. , ； B3, and the pore absorption efficiency coefficient of concrete after freezing. , ； Wherein, the water-to-air ratio This refers to the capillary water volume in concrete. A is the sum of the initial gas content and the capillary pore volume; The minimum air-entraining agent dosage required for concrete to reach its frost-resistant state was determined by quantitatively analyzing the relationship between the water-air ratio and the pore absorption efficiency. The process is as follows: [Drawing...] Relationship diagram, fitting Damaged area; According to the above The critical water-to-air ratio is determined by the intersection of the data points in the relationship diagram and the non-damage line. ; Based on the critical water-gas ratio The volume fraction of capillary water in concrete at a specified pre-curing age under conditions of zero initial air content. and capillary pore volume fraction Calculate the initial air content required for concrete to reach the critical frost resistance state, and select the corresponding air-entraining agent dosage according to the type of air-entraining agent.

2. The method for determining the minimum air-entraining agent dosage for early-stage frozen concrete based on pore absorption of frost heave, as described in claim 1, is characterized in that: Obtaining capillary parameters in concrete at a specified pre-curing age includes obtaining capillary water volume. and capillary pore volume The acquisition process includes the following steps: A1. Calculate the overall hydration degree of cement paste using the Parrot & Killoh model. : ， In the above formula, The value of i represents the overall hydration degree of the cement paste at time t, and i represents the mineral composition of the cement clinker. , This represents the degree of hydration of phase i at time t. The mass fraction of phase i in the cement; ， In the above formula, S and These are the actual specific surface area and the reference specific surface area of ​​cement, respectively. , , and These represent the reaction rates of the i-phase clinker hydration reaction, controlled by the nucleation and growth stage, the diffusion process, and the ion dissolution and transport process, respectively. and The effects of water-cement ratio, relative humidity, and temperature on the hydration rate of phase i are represented respectively. ； ； ； ； ； ； In the above formula, Represents the water-cement ratio, RH represents relative humidity, R represents the universal gas constant, and T and For actual ambient temperature and reference temperature, =293K; A2. Obtaining the overall hydration degree of cement paste Then, the capillary water volume inside the concrete was further calculated using the Powers hydration model. and capillary pore volume : ； ； ； ； ； ； ； In the above formula, and These represent the volume fractions of unhydrated clinker, hydration products, capillary water, and capillary pores caused by chemical shrinkage in the cement paste at time t, respectively. and These represent the densities of cement clinker, capillary water, and hydration products, respectively. This represents the volume fraction of cement paste in the concrete. and These represent the masses of water, cement, coarse aggregate, and fine aggregate in 1 cubic meter of concrete. and These are the densities of water, cement, coarse aggregate, and fine aggregate, respectively. The initial air content of concrete is denoted as VA. When VA=0, the capillary water and capillary porosity content of concrete at a specified pre-curing age are recorded as VA. and .

3. The method for determining the minimum air-entraining agent dosage for early-stage frozen concrete based on pore absorption of frost heave, as described in claim 2, is characterized in that: Obtaining the initial air content in concrete includes: pre-setting multiple low air-entraining agent dosages and testing the initial air content of fresh concrete at these dosages. The term "low air-entraining agent" refers to an amount not exceeding the commonly used dosage range of the selected air-entraining agent. The initial gas content can be tested using the pressure method in standard GB / T50080.

4. The method for determining the minimum air-entraining agent dosage for early-stage frozen concrete based on pore absorption of frost heave according to any one of claims 1 to 3, characterized in that: Obtaining the deformation parameters of concrete under negative temperature conditions includes: testing the apparent deformation of concrete under negative temperature conditions. and temperature deformation The apparent deformation of the tested concrete under negative temperature conditions. The acquisition process involves conducting tests using a negative-temperature concrete apparent deformation testing device and obtaining data. The apparent deformation is then calculated using the following formula: ； In the above formula, The apparent deformation of the concrete after cooling to temperature T is represented by H; the height of the sensor from the top of the cone is represented by D; the distance of the sensor from the concrete surface is represented by HD; the subscripts 0 and f correspond to the concrete before and after freezing, respectively.

5. The method for determining the minimum air-entraining agent dosage of early-stage frozen concrete based on pore absorption of frost heave, as described in claim 4, is characterized in that: The reasoning process for the non-damaged line includes: When the concrete reaches a non-damaged state Stomatal absorption efficiency coefficient γ and water-to-air ratio satisfy .

6. The method for determining the minimum air-entraining agent dosage of early-frozen concrete based on pore absorption of frost heave, as described in claim 5, is characterized in that: The process of determining the minimum air-entraining agent dosage required for concrete to reach its frost-resistant state through the quantitative relationship between the water-air ratio and the pore absorption efficiency also includes: based on The relationship determines the risk of concrete freezing damage, when If the data point is located on the non-damage line, it indicates that the concrete has not suffered frost damage. If the data point is below the non-damage line, it indicates that the concrete is at risk of frost damage. The moisture migration process after the concrete freezes is divided into three stages: S1, when the water-to-air ratio At high temperatures, the pores absorb frost heave and deformation. And the pore absorption efficiency coefficient All follow If the value decreases and increases, then the water migration of concrete after freezing is in the stage controlled by the pore spacing coefficient. S2, when the water-to-air ratio When the temperature drops to a certain level, the pores absorb frost heave deformation. along with The pore absorption efficiency coefficient increases as the pore size decreases. along with If the value decreases and shows a decreasing trend, then the water migration of concrete after freezing is in a transitional stage. S3, when the water-to-air ratio Below the critical value, the pores absorb frost heave deformation. To achieve the volume of capillary water freezing and swelling deformation Value, pore absorption efficiency coefficient If the water content is in a state of sharp decrease, then the water migration of concrete after freezing is in the air content control stage.

7. The method for determining the minimum air-entraining agent dosage for early-stage frozen concrete based on pore absorption of frost heave as described in claim 6, characterized in that: According to the The critical water-to-air ratio is determined by the intersection of the data points in the relationship diagram and the non-damage line. include: C1. When cement-based materials The relationship diagram has obvious transition stages, and the data in the transition stages are fitted. C2, when If the relationship diagram does not show a clear transition stage, then according to the required accuracy or workload, you can choose to add data points to the damaged area or directly fit the data of the pore spacing coefficient control stage. The amount of air-entraining agent corresponding to the data points of the added damaged area should not be less than the maximum value in the pore spacing coefficient control stage, but less than the minimum value in the gas content control stage. C3. Based on the increase in data points in the damaged area, determine again whether a transition phase exists. If it exists, proceed to step C1; otherwise, proceed to step C2 again. C4. The water-to-air ratio corresponding to the intersection of the fitted curve and the non-damage line is the critical water-to-air ratio. The critical water-air ratio This corresponds to the critical freeze-thaw resistance state of cement-based materials.

8. The method for determining the minimum air-entraining agent dosage for early-stage frozen concrete based on pore absorption of frost heave, as described in claim 7, is characterized in that: The critical water-gas ratio The volume fraction of capillary water in concrete at a specified pre-curing age under conditions of zero initial air content. and capillary pore volume fraction The process of calculating the initial air content required for concrete to reach its critical frost resistance state is as follows: ； in, and This represents the capillary water volume and capillary pore volume content when the initial air content of concrete is 0. .

Images