A fast and efficient method for predicting chloride ion diffusion coefficient of hydrated calcium silicate gel

Abstract

A rapid and efficient method for predicting the chloride ion diffusion coefficient of hydrated calcium silicate gel belongs to the field of concrete construction technology. The present invention predicts the effective chloride ion diffusion coefficient in hydrated calcium silicate gel through a steady-state electromigration test and a differential effective medium method. First, a steady-state electromigration test is performed on a hardened tricalcium silicate slurry to obtain its chloride ion diffusion coefficient. Then, the tricalcium silicate slurry is assumed to have a two-phase material structure, and the chloride ion diffusion coefficient in the hydrated calcium silicate gel is predicted using the differential effective medium method and scanning electron microscopy technology. The method described in the present invention can directly infer the chloride ion diffusion coefficient in the hydrated calcium silicate based on the chloride ion diffusion coefficient in the tricalcium silicate slurry, without changing the chloride ion diffusion path and humidity balance, and thus can quickly and efficiently obtain the diffusion coefficient in the hydrated calcium silicate gel.

Description

Technical Field

[0001] The invention relates to the technical field of concrete construction, and in particular to a method for quickly and efficiently predicting the chloride ion diffusion coefficient of calcium silicate hydrate gel. Background Art

[0002] Reinforced concrete is widely used in civil engineering (such as buildings, roads, bridges and ports) because of its superior mechanical properties and moldability. In coastal areas, reinforced concrete structures are often subject to chloride erosion, causing steel bar corrosion, and ultimately causing concrete structure failure. Therefore, the chloride ion diffusion performance of concrete has become one of the important indicators for evaluating concrete durability. The chloride ion diffusion performance of concrete under low water-cement ratio conditions is mainly determined by the diffusion performance in the calcium silicate hydrate in the material. In the prior art, when measuring the chloride ion diffusion coefficient in calcium silicate hydrate gel, it is necessary to first adopt epoxy resin to seal the capillary pores in the cement paste to realize diffusion path conversion, and then the specimen is subjected to humidity balance for at least two weeks. This technology needs to consume a large amount of time cost and can not quickly predict the chloride ion diffusion coefficient in calcium silicate hydrate. Summary of the Invention

[0003] Technical problem to be solved: In view of the technical problem that in the prior art, when measuring the chloride ion diffusion coefficient in calcium silicate hydrate gel, it is necessary to first use epoxy resin to seal the capillaries in the slurry to achieve diffusion path transformation, and then subject the specimen to humidity equilibrium for at least half a month, which makes it impossible to quickly and effectively measure the chloride ion diffusion coefficient in calcium silicate hydrate gel. The present invention provides a fast and efficient method for predicting the chloride ion diffusion coefficient of calcium silicate hydrate gel, which can quickly and effectively predict the chloride ion diffusion coefficient in calcium silicate hydrate.

[0004] Technical solution: A fast and efficient method for predicting the chloride ion diffusion coefficient of hydrated calcium silicate gel. The method uses steady-state electromigration tests and the differential effective medium method to predict the effective chloride ion diffusion coefficient in hydrated calcium silicate gel. The steps are as follows:

[0005] Step 1. The stirred tricalcium silicate slurry is placed into a disc-shaped rubber mold to obtain a tricalcium silicate hydrated slurry, and then the slurry is cured. After the curing is completed, two disc-shaped hardened slurries are taken out, one for the chloride ion steady-state electromigration test, and the other for scanning electron microscopy to take microscopic images;

[0006] Step 2. In the steady-state electromigration test, the chloride ion concentration in the anode test tank was measured using silver nitrate titration. The slope of the concentration change over time under steady-state chloride ion diffusion was then obtained using linear fitting. Finally, the effective diffusion coefficient of chloride ions in the tricalcium silicate hardened slurry was calculated using the simplified Nernst-Planck equation:

[0007]

[0008] In the formula represents the effective diffusion coefficient of chloride ions in tricalcium silicate hardening paste, m 2 ·s -1 ; L represents the thickness of the disk-shaped hardened slurry, m; V AT represents the volume of the anode solution, m 3 ; ΔC1 represents the change in chloride ion concentration in the anode test tank, mol·L -1 ; ΔE represents the potential difference, V; C s represents the initial concentration of chloride ions in the cathode test tank, mol·L -1 ; A represents the surface area of ​​the diffusion surface of the specimen, m 2 ; Δt represents the time variable, s; Z represents the absolute value of the chloride ion charge, which is 1; F represents the Faraday constant, which is 9.65×10000 C·mol -1 ; E represents the electric potential, V; R represents the ideal gas constant, which is 8.314 J·mol -1 ·K -1 ; T represents the ambient temperature, K;

[0009] Step 3. When taking a scanning electron microscope image, cut and polish the disk-shaped hardened slurry into a small cube of 5 mm × 5 mm × 5 mm, and randomly select one surface for scanning;

[0010] Step 4. Process the obtained scanning electron microscope image. First, grayscale processing is performed on the scanning electron microscope. The grayscale distribution histogram of the image is obtained using MATLAB software. Then, grayscale thresholds of different phases are divided according to the peak value of the grayscale histogram. Then, the phases in the image are divided according to the grayscale thresholds to obtain the distribution of four phases: unhydrated tricalcium silicate, hydrated calcium silicate gel, calcium hydroxide, and capillary pores. Finally, the number of pixels corresponding to each object in the image is counted to calculate the area fraction of each phase. Assuming that the area fraction is equal to the volume fraction, the volume fraction of unhydrated tricalcium silicate, hydrated calcium silicate gel, calcium hydroxide, and capillary pores is obtained.

[0011] Step 5. Simplify the tricalcium silicate hardened paste into a two-phase structure, assume the unhydrated tricalcium silicate and calcium hydroxide as the inclusion phase, and the hydrated calcium silicate gel and capillary pores as the matrix phase. According to the differential effective medium approximation method, the relationship between the effective diffusion coefficients of the inclusion phase, matrix phase and composite material is obtained as follows. According to this formula, D ph1 :

[0012]

[0013] Where D ph1 It represents the effective diffusion coefficient of chloride ions after the calcium silicate hydrate gel and capillary pores are combined, m 2 ·s-1 ;D ph2 It represents the effective diffusion coefficient of chloride ions in the complex of unhydrated tricalcium silicate and calcium hydroxide, m 2 ·s -1 ; represents the effective diffusion coefficient of chloride ions in tricalcium silicate hardening paste, m 2 ·s -1 ; V ph2 It represents the sum of the volume fractions of unhydrated tricalcium silicate and calcium hydroxide;

[0014] The composite material composed of hydrated calcium silicate gel and capillary pores is simplified into a two-phase structure, in which the hydrated calcium silicate gel is assumed to be the matrix phase and the capillary pores are assumed to be the inclusion phase. The differential effective medium approximation method is used again to obtain the relationship between the effective diffusion coefficient of chloride ions in the capillary pores, the effective diffusion coefficient in the hydrated calcium silicate gel, and the total effective diffusion coefficient of the composite material as follows. According to this formula, D C-S-H :

[0015]

[0016] Where D pore represents the effective diffusion coefficient of chloride ions in the capillary pores, m 2 ·s -1 ;D C-S-H represents the effective diffusion coefficient of chloride ions in hydrated calcium silicate gel, m 2 ·s -1 ; V pore It represents the volume fraction of capillary pores, which is defined as the ratio of the volume of capillary pores to the sum of the volume of capillary pores and calcium silicate hydrate.

[0017] Preferably, the water-cement ratio of the tricalcium silicate slurry in step 1 is 0.4.

[0018] Preferably, the inner diameter of the disc-shaped rubber mold in step 1 is 26 mm and the thickness is 4 mm.

[0019] Preferably, the curing condition in step 1 is sealed curing at 20°C.

[0020] As a preference, in step 2, F is 9.65×10000 C·mol -1 ; R is 8.314 J·mol -1 ·K -1 .

[0021] Preferably, in the step 2, the chloride ion concentration in the anode test tank is measured by silver nitrate titration in the steady-state electromigration test, and the specific steps are as follows: first, 1 mL of liquid is drawn from the anode test tank into a conical flask, and then deionized water is added to the conical flask to dilute it to 100 mL; then 1 mL of potassium chromate solution is added to the water sample using a pipette; then, the solution is titrated with a standard silver nitrate solution until a brick-red precipitate just appears; finally, the titration test in the blank control group is repeated using the same volume of deionized water.

[0022] Beneficial effects: Compared with the existing technology, the method for predicting the chloride ion diffusion coefficient of hydrated calcium silicate gel described in the present invention does not require the use of epoxy resin to seal the capillaries in the cement slurry, nor does it require the specimen to be subjected to humidity balancing for at least half a month, thereby saving a lot of time and personnel costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is the linear fitting diagram of the chloride ion concentration in the anode test tank when the hydration time is 3 days and the water-to-solid ratio is 0.4;

[0024] Figure 2 This is a microstructure picture of the hardened tricalcium silicate paste with a hydration time of 3 days and a water-to-solid ratio of 0.4;

[0025] Figure 3 The grayscale histogram of the scanning electron microscope of tricalcium silicate hardened paste;

[0026] Figure 4 is the distribution diagram of unhydrated tricalcium silicate;

[0027] Figure 5 is the distribution diagram of hydrated calcium silicate gel;

[0028] Figure 6 is the distribution diagram of calcium hydroxide;

[0029] Figure 7 is the distribution map of capillary pores;

[0030] Figure 8 This is a flow chart of the method for predicting the chloride ion diffusion coefficient of the rapid and efficient calcium silicate hydrate gel of the present invention;

[0031] Figure 9 Figure 2 is a diagram of the electromigration experimental setup. DETAILED DESCRIPTION

[0032] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0033] Example 1

[0034] A fast and efficient method for predicting chloride ion diffusion coefficient of hydrated calcium silicate gel, see Figure 8 , the specific steps are as follows:

[0035] Step 001: Place a stirred tricalcium silicate slurry with a water-cement ratio of 0.4 into two rubber molds with an inner diameter of 26 mm and a thickness of 4 mm to obtain a disc-shaped tricalcium silicate hydrated slurry. The slurry is then cured at 20°C for 3 days in a sealed container. After the curing is complete, two disc-shaped hardened slurries are removed, one for a steady-state electromigration test of chloride ions, and the other for microscopic imaging using a scanning electron microscope.

[0036] Step 002: In the steady-state electromigration test, the chloride ion concentration in the anode test tank is measured by silver nitrate titration. The device used for electromigration is as follows: Figure 9 As shown, the position of the anode solution (0.3mol / LNaOH solution) on the left is the anode test tank, and the position of the cathode solution (0.3mol / LNaOH and 1mol / LNaCl) on the right is the cathode test tank. The disc-shaped specimen is placed in the middle and sealed with epoxy resin. During the steady-state electromigration test, the positive pole of the 12V DC power supply is first connected to the anode test tank, and the negative pole is connected to the cathode test tank. After power is turned on, the chloride ions in the cathode test tank on the right will pass through the disc specimen under the action of the electric field and reach the anode test tank on the left. The chloride ion concentration in the anode test tank is then measured by silver nitrate titration. The slope of the concentration change with time under the steady-state diffusion of chloride ions is then obtained by linear fitting. Finally, the effective diffusion coefficient of chloride ions in tricalcium silicate slurry is calculated based on the simplified Nernst-Planck equation. The specific steps are as follows: First, draw 1 mL of liquid from the anode test tank into a conical flask, then add deionized water to dilute it to 100 mL; then use a pipette to add 1 mL of potassium chromate solution to the water sample; then titrate with silver nitrate standard solution until a brick-red precipitate just appears, and the amount of silver nitrate standard solution consumed is V 消耗 Then, the same volume of deionized water was taken to repeat the titration test in the blank control group, and the amount of silver nitrate standard solution consumed was V 空 Finally, according to the chloride ion concentration calculation formula specified in the standard "GB 11896-89",

[0037] Where C represents the chloride ion concentration, mg·L -1 ; V 空 V represents the amount of silver nitrate standard solution consumed by deionized water in the blank control group, mL; 消耗 Indicates the amount of silver nitrate standard solution consumed by the sample, mL; M silver nitrate standard solution concentration, mol·L -1 ; V 试 represents the sample volume, mL, and the calculated chloride ion concentration is (V 消耗 -V 空 )×M×35.45×1000 / V试 (mg·L -1 ), where the concentration of the silver nitrate standard solution is 0.0141 mol·L -1 ,V 试 Indicates the sample volume, taking 100mL. The slope of the concentration change with time under the steady-state diffusion of chloride ions is obtained by linear fitting, see Figure 1 The thickness of the specimen L is 0.0036m; the volume of the anode solution V AT Take 0.0001m 3 ; The potential difference ΔE is 12V; The initial chloride ion concentration in the cathode test tank is C s Take 1 mol·L -1 The surface area A of the diffusion surface of the specimen is 0.0008m 2 Under steady-state conditions, the change in chloride ion concentration per unit time in the anode test tank, namely ΔC1 / Δt, can be obtained based on the linear relationship between ion concentration and time. The ΔC1 / Δt value obtained by fitting after hydration for 3 days and a water-to-solid ratio of 0.4 is 2.6×10 -6 mol·L -1 s -1 ; Then according to the formula Calculation of the effective chloride ion diffusion coefficient of tricalcium silicate hardening paste Where T is 273K, Faraday constant F is 9.65×10000C / mol, and ideal gas constant R is 8.314J / (mol·K), we get The value is 2.27×10 -12 m 2 ·s -1 .

[0038] Step 003: Cut and polish the disk-shaped hardened slurry obtained in step 001 into a small cube of 5mm×5mm×5mm, and then use a scanning electron microscope to take a microscopic image of the slurry. When taking the image, select any surface for scanning. The obtained microstructure image is shown in FIG. Figure 2 .

[0039] Step 004: grayscale processing is performed on the obtained SEM image to obtain the grayscale distribution histogram of the image, see Figure 3 Then, the grayscale thresholds of different phases are divided according to the grayscale histogram peaks. Then, the phases in the image are divided according to the grayscale thresholds, and the distributions of unhydrated tricalcium silicate (C3S), hydrated calcium silicate gel (CSH), calcium hydroxide (CH) and capillary pores are obtained as shown below. Figure 4 — Figure 7As shown, the number of pixels corresponding to each object in the image is finally counted to calculate the area fraction of each phase. Assuming that the area fraction is equal to the volume fraction (this assumption is made based on the principle of stereology. See reference [1] Xie Deqing. Numerical simulation of the hydration process and transmission performance of cement-based materials based on irregular particles [D]. Southeast University, 2015.), the volume fractions of unhydrated tricalcium silicate, hydrated calcium silicate gel, calcium hydroxide and capillary pores are 20.2%, 31.9%, 16.4% and 31.5% respectively.

[0040] Step 005: The tricalcium silicate hardened slurry is simplified into a two-phase structure. According to the homogenization method (see the literature Salvatore T, Springer. Random heterogeneous materials [J]. Interdisciplinary Applied Mathematics, 2002, 55 (4): B62.), the unhydrated tricalcium silicate and calcium hydroxide are assumed to be inclusion phases. Since the unhydrated tricalcium silicate and calcium hydroxide are crystalline minerals with almost no pores, the diffusion coefficient D ph2 The value is 0m 2 ·s -1 The effective diffusion coefficient of chloride ions in the tricalcium silicate hardened paste is obtained from the steady-state electromigration test in step 002, and its value is 2.27×10 -12 m 2 ·s -1 ; The sum of the volume fractions of unhydrated tricalcium silicate and calcium hydroxide V ph2 =20.2%+16.4%=36.6%. Substituting these values ​​into the formula Solve D ph1 The value is 4.50×10 -12 m 2 ·s -1 Then according to the reference Ma L., Zhang Y.Microstructure-based prediction model for chloride ion diffusivity in hydrated cement paste[J].Ceramics Silikaty,2017,61(2):1-9., it is assumed that the diffusion coefficient of chloride ions in the pores is the same as that in free water, so D pore The value is 2.032×10 -9 m 2 ·s -1(See reference Haynes WMCCRCHandbook of chemistry and physics[M].95ed.Boca Raton:CRC Press,2014.); the volume fraction of capillary pores and the volume fraction of calcium silicate hydrate are obtained by the method in step 004, and their values ​​are 31.5% and 16.4% respectively, so V pore =31.5% / (31.5%+16.4%)=0.658. ph1 、D pore and V pore Substitute the value into the formula (D pore -D ph1 ) / (D p ore-D C-S-H )·(D C-S-H / D ph1 ) 1 / 3 =1-V pore Solve for the chloride ion diffusion coefficient D of hydrated calcium silicate gel C-S-H 1.8×10 -13 m 2 ·s -1 .

[0041] In the existing literature (see Kurumisawa K, Nawa T, Owada H. Prediction of the diffusivity of cement-based materials using a three-dimensional spatial distribution model [J]. Cement and Concrete Composites, 2012, 34 (3): 408-418.), a prediction method based on gel porosity was used to obtain that when the water-cement ratio was 0.4-1.0, the effective diffusion coefficient range was approximately 1.8×10 -13 m 2 ·s -1 to 2.5×10 -11 m 2 ·s -1 The effective diffusion coefficient of calcium silicate hydrate gel measured by this method is just at the lower limit of this range, so it basically meets the requirements.

Claims

1. A fast and efficient method for predicting the chloride ion diffusion coefficient of calcium silicate hydrate gel, characterized in that: The effective diffusion coefficient of chloride ions in calcium silicate hydrate gel was predicted by steady-state electromigration test and differential effective medium method. The steps are as follows: Step 1. The stirred tricalcium silicate slurry is placed into a disc-shaped rubber mold to obtain a tricalcium silicate hydrated slurry, and then the slurry is cured. After the curing is completed, two disc-shaped hardened slurries are taken out, one for the chloride ion steady-state electromigration test, and the other for scanning electron microscopy to take microscopic images; Step 2. In the steady-state electromigration test, the chloride ion concentration in the anode test tank was measured using silver nitrate titration. The slope of the concentration change over time under steady-state chloride ion diffusion was then obtained using linear fitting. Finally, the effective diffusion coefficient of chloride ions in the tricalcium silicate hardened slurry was calculated using the simplified Nernst-Planck equation: ； In the formula represents the effective diffusion coefficient of chloride ions in tricalcium silicate hardening paste, m 2 ·s -1 ; L represents the thickness of the disk-shaped hardened slurry, m; V AT represents the volume of the anode solution, m 3 ; ΔC1 represents the change in chloride ion concentration in the anode test tank, mol·L -1 ; ΔE represents the potential difference, V; C s represents the initial concentration of chloride ions in the cathode test tank, mol·L -1 ; A represents the surface area of ​​the diffusion surface of the specimen, m 2 ; Δt represents the time variable, s; Z represents the absolute value of the chloride ion charge, which is 1; F represents the Faraday constant, which is 9.65×10000 C·mol -1 ; E represents the electric potential, V; R represents the ideal gas constant, which is 8.314 J·mol -1 ·K -1 ; T represents the ambient temperature, K; Step 3. When taking a scanning electron microscope image, cut and polish the disk-shaped hardened slurry into a small cube of 5 mm × 5 mm × 5 mm, and randomly select one surface for scanning; Step 4. Process the obtained scanning electron microscope image. First, grayscale processing is performed on the scanning electron microscope. The grayscale distribution histogram of the image is obtained using MATLAB software. Then, grayscale thresholds of different phases are divided according to the peak value of the grayscale histogram. Then, the phases in the image are divided according to the grayscale thresholds to obtain the distribution of four phases: unhydrated tricalcium silicate, hydrated calcium silicate gel, calcium hydroxide, and capillary pores. Finally, the number of pixels corresponding to each object in the image is counted to calculate the area fraction of each phase. Assuming that the area fraction is equal to the volume fraction, the volume fraction of unhydrated tricalcium silicate, hydrated calcium silicate gel, calcium hydroxide, and capillary pores is obtained. Step 5. Simplify the tricalcium silicate hardened slurry into a two-phase structure, assume the unhydrated tricalcium silicate and calcium hydroxide as the inclusion phase, and the hydrated calcium silicate gel and capillary pores as the matrix phase. According to the differential effective medium approximation method, the relationship between the effective diffusion coefficients of the inclusion phase, matrix phase and composite material is obtained as follows. According to this formula, : ； In the formula It represents the effective diffusion coefficient of chloride ions after the calcium silicate hydrate gel and capillary pores are combined, m 2 ·s -1 ; It represents the effective diffusion coefficient of chloride ions in the complex of unhydrated tricalcium silicate and calcium hydroxide, m 2 ·s -1 ; represents the effective diffusion coefficient of chloride ions in tricalcium silicate hardening paste, m 2 ·s -1 ; It represents the sum of the volume fractions of unhydrated tricalcium silicate and calcium hydroxide; The composite material composed of hydrated calcium silicate gel and capillary pores is simplified into a two-phase structure, in which the hydrated calcium silicate gel is assumed to be the matrix phase and the capillary pores are assumed to be the inclusion phase. The differential effective medium approximation method is used again to obtain the relationship between the effective diffusion coefficient of chloride ions in the capillary pores, the effective diffusion coefficient in the hydrated calcium silicate gel, and the total effective diffusion coefficient of the composite material as follows. According to this formula, we can solve : ； In the formula represents the effective diffusion coefficient of chloride ions in the capillary pores, m 2 ·s -1 ; represents the effective diffusion coefficient of chloride ions in hydrated calcium silicate gel, m 2 ·s -1 ; It represents the volume fraction of capillary pores, which is defined as the ratio of the volume of capillary pores to the sum of the volume of capillary pores and calcium silicate hydrate.

2. A fast and efficient method for predicting chloride ion diffusion coefficient of calcium silicate hydrate gel according to claim 1, characterized in that: The water-cement ratio of the tricalcium silicate slurry in step 1 is 0.

4.

3. A fast and efficient method for predicting chloride ion diffusion coefficient of calcium silicate hydrate gel according to claim 1, characterized in that: The inner diameter of the disc-shaped rubber mold in step 1 is 26 mm and the thickness is 4 mm.

4. A fast and efficient method for predicting chloride ion diffusion coefficient of calcium silicate hydrate gel according to claim 1, characterized in that: The curing condition in the step 1 is sealed curing at 20°C.

5. A fast and efficient method for predicting chloride ion diffusion coefficient of calcium silicate hydrate gel according to claim 1, characterized in that: In step 2, the chloride ion concentration in the anode test tank is measured by silver nitrate titration in the steady-state electromigration test. The specific steps are as follows: first, 1 mL of liquid is drawn from the anode test tank into a conical flask, and then deionized water is added to the conical flask to dilute it to 100 mL; then, 1 mL of potassium chromate solution is added to the water sample using a pipette; then, the solution is titrated with a standard silver nitrate solution until a brick-red precipitate just appears; finally, the titration test in the blank control group is repeated using the same method with the same volume of deionized water.

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