A method for ion transport in hydraulic concrete based on real pore structure and solution composition

Abstract

The application discloses a kind of water concrete ion transport methods based on real pore structure and solution composition, it is related to ion transport technical field. Including: based on the construction of multiscale diffusion model of fractal dimension;Pore network is obtained based on multiscale diffusion model, and local micro-region is formed through pore network electrochemical potential gradient;Based on electrochemical potential gradient, capillary action parameter and convection parameter, ion transport model is constructed;Based on ion transport model, ion transport result is evaluated.The ion transport model constructed by considering electrochemical potential gradient, capillary action parameter and convection parameter established by the application can well reproduce the distribution of ions in the test, and the ion distribution in the concrete at different stages can be accurately predicted.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ion transport, in particular to a hydraulic concrete ion transport method based on real pore structure and solution composition. BACKGROUND

[0002] In recent years, in addition to the strength and mechanical properties of concrete structures, durability has gradually attracted widespread attention from academia and engineering. Especially for long-term exposure to humid, underwater hydraulic concrete structures, moisture migration and harmful substance erosion are common forms of environmental degradation, which often seriously threaten structural safety and cause significant economic losses. The erosion of harmful substances such as chlorides and sulfates seriously endangers the durability of concrete, and chlorides mainly reduce the load-bearing capacity of the structure by eroding embedded steel bars, posing a risk. Sulfates are widely distributed in rainwater and industrial wastewater externally, and under the combined influence of physical and chemical effects, they generate expansive products, produce expansive stress, and cause concrete to expand, crack, and spall, eventually leading to complete degradation.

[0003] At present, a large number of numerical studies have been conducted to simulate multi-scale diffusion behavior and sulfate erosion under dry-wet cycles. Sukrit Kumar De et al. proposed a multi-scale diffusion model including pore structure, aggregate, and interface transition zone, and explained the correlation between pores and diffusion at the microscale. Jian Gong et al. combined damage mechanics with the B3 model of creep and introduced a dry-wet cycle influence factor to predict creep under dry-wet cycles and sulfate erosion. Suining Zheng et al. reconstructed the three-dimensional structure of cement aggregates and ITZ using CEMHYD3D and cellular automata to study the differences in diffusion performance of sulfate ions in cement matrix and ITZ under dry-wet cycles. Samson attempted to describe the degradation of unsaturated concrete under sulfate erosion by establishing a multi-ion transport model, but it cannot represent the drying process. Although a large number of experiments and theoretical studies have been conducted, the macroscopic diffusion behavior of sulfates under dry-wet cycles has not been fully determined, and few studies have considered the influence of pore structure on diffusion.

[0004] Therefore, a hydraulic concrete ion transport method based on real pore structure and solution composition is proposed to solve the difficulties existing in the prior art, which is a problem that needs to be solved by those skilled in the art. SUMMARY

[0005] Therefore, a hydraulic concrete ion transport method based on real pore structure and solution composition is proposed to solve the difficulties existing in the prior art, which is a problem that needs to be solved by those skilled in the art.

[0006] To achieve the above purpose, the present application adopts the following technical solutions: Therefore, a hydraulic concrete ion transport method based on real pore structure and solution composition is proposed to solve the difficulties existing in the prior art, which is a problem that needs to be solved by those skilled in the art.

[0007] A water conservancy concrete ion transport method based on real pore structure and solution composition, comprising the following steps:

[0008] Constructing a multi-scale diffusion model based on a fractal dimension;

[0009] Obtaining a pore network based on the multi-scale diffusion model, and forming an electrochemical potential gradient through a local micro-region of the pore network;

[0010] Based on the electrochemical potential gradient, capillary action parameters and convection parameters, an ion transport model is constructed;

[0011] Based on the ion transport model, the ion transport result is evaluated.

[0012] Optionally, the specific content of constructing a multi-scale diffusion model based on a fractal dimension is:

[0013] A square with a size of 2000nm is selected as a representative volume unit, and a circular pore is selected for two-dimensional modeling, and the pore size distribution is 10-300nm;

[0014] According to the porosity of each pore size, the number of each type of pore in the RE range is calculated, and the corresponding circular pore is generated;

[0015] The generated circular pore is put into the RE range and the intrusion judgment of pore and boundary, pore and pore is carried out, if the circular pore put in each time meets the condition that it is in the boundary range and does not intrude with other circular pores, a two-dimensional model is generated, otherwise the pore put information is regenerated, and the intrusion judgment is carried out again until the non-intrusion condition is met;

[0016] The generated two-dimensional model is divided into a grid by using a direct division method to obtain two-dimensional model image data;

[0017] The generated two-dimensional model image data is binarized, the fractal dimension of the two-dimensional model is calculated by a box-counting method, and the fractal dimension is obtained;

[0018] The diffusion equation based on the second law of Fick is described as:

[0019]

[0020] In the formula, w is the water content, unit kg / m 3 , c is the sulfate concentration, unit mol / m 3 , D i is the diffusion coefficient, unit m 2 / s, V is the average velocity of liquid flowing through the pore system under the action of capillary suction, unit m / s.

[0021] Optionally, the specific content of forming an electrochemical potential gradient by local micro-regions of the pore network is:

[0022] Adopting the Nernst-Planck equation to describe the diffusion of charged ions in the porous medium while moving relative to the medium due to the electric coupling effect, the electric migration flux of the ions is:

[0023]

[0024] where s i is the charge number of the i-th ion, F is the Faraday constant, 9.649×104C / mol, T is the absolute temperature, 298K, and Φ is the electrostatic potential.

[0025] Optionally, the Poisson equation based on the Gaussian electrostatic theory is introduced to represent the relationship between the charge imbalance and the potential gradient of the liquid pore solution system. Considering the unsaturated state of hydraulic concrete, the saturation parameter correction formula (3) is adopted to obtain:

[0026]

[0027] where ε0 is the vacuum permittivity, 8.854×10-12C / (V·m), ε r is the relative permittivity of liquid water, and 80.

[0028] Optionally, the specific content of constructing an ion transport model based on the electrochemical potential gradient, capillary action parameter, and convection parameter is:

[0029] According to the second Fick's law and the mass conservation law, the spatiotemporal distribution of ions is:

[0030]

[0031] where c bi is the concentration of ions solidified in the pore wall structure due to reaction or adsorption, with the unit of mol / m 3 , c fi is the concentration of free ions in the pore solution, with the unit of mol / m 3 , J i is the transport flux of the i-th ion, with the unit of mol / (m 2 ·s);

[0032] The migration of ions under unsaturated conditions is driven by diffusion and convection. Adopting the Nernst-Planck equation to extend Fick's law, the flux of ions under the action of these two driving forces can be represented as:

[0033]

[0034] where, For the porosity of concrete;

[0035]

[0036] The Langmuir isotherm is used to describe the relationship between the solidified ions and free ions, and the saturation parameter is introduced to modify formula (8) as follows:

[0037]

[0038] Wherein, alpha, beta are modified Langmuir adsorption constants, omega is a dimensionless constant, and is 0.3;

[0039] The formula (8) and formula (9) are combined to obtain

[0040]

[0041] Compared with the prior art, the technical scheme has the following beneficial effects:

[0042] (1) The ion transport model established by the present application considering the electrochemical potential gradient, capillary action parameter and convection parameter can well reproduce the ion distribution in the test and accurately predict the ion distribution in the concrete at different stages;

[0043] (2) The concrete pore structure not only has the characteristics of bending and interlacing, but also has the characteristics of multiple scales, and the pore size distribution observed in different scales is also different, but according to the fractal theory, the concrete pore structure can be regarded as a fractal, so according to the self-similarity of the fractal, it can be proved that the pore structure of the concrete at different scales has similarity;

[0044] (3) The method provided by the present application has certain significance for the study of the ion transport and diffusion of hydraulic concrete with real pore structure and solution composition, simplifies the model to a certain extent, and can predict the test trend to a certain extent. BRIEF DESCRIPTION OF DRAWINGS

[0045] In order to more clearly illustrate the technical scheme in the embodiments of the present application or the prior art, the drawings needed in the embodiment or prior art description will be briefly introduced below, and obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings according to the provided drawings without creative labor.

[0046] Figure 1 A flowchart of a method for transporting ions in hydraulic concrete based on real pore structure and solution composition is provided.

[0047] Figure 2 The ion transport model and the boundary layer grid structure diagram under the dry-wet cycle system provided by the present application are shown in the following table. DETAILED DESCRIPTION

[0048] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0049] Referring to Figure 1 The present application discloses a water concrete ion transport method based on real pore structure and solution composition, including the following steps:

[0050] A multi-scale diffusion model is constructed based on a fractal dimension;

[0051] A pore network is obtained based on the multi-scale diffusion model, and an electrochemical potential gradient is formed by local micro-regions of the pore network;

[0052] An ion transport model is constructed based on the electrochemical potential gradient, capillary action parameters and convection parameters;

[0053] The ion transport result is evaluated based on the ion transport model.

[0054] Further, the specific content of constructing the multi-scale diffusion model based on the fractal dimension is as follows:

[0055] A square with a size of 2000 nm is selected as a representative volume unit, and circular pores are selected for two-dimensional modeling, with a pore size distribution of 10-300 nm;

[0056] The number of each type of pore in the RE range is calculated according to the porosity occupied by each pore size, and the corresponding circular pores are generated;

[0057] The generated circular pores are placed within the RE range and the intrusion judgment of pores and boundaries and pores and pores is performed. If the circular pores placed each time are within the boundary range and do not intrude each other with other circular pores, a two-dimensional model is generated, otherwise the pore placement information is regenerated, and the intrusion judgment is performed again until the non-intrusion condition is met;

[0058] A direct division method is used to divide the generated two-dimensional model into grids to obtain two-dimensional model image data;

[0059] The generated two-dimensional model image data is binarized, the fractal dimension of the two-dimensional model is calculated by a box-counting method, and the fractal dimension is obtained;

[0060] The diffusion equation based on Fick's second law is described as:

[0061]

[0062] where w is the water content, unit kg / m 3 , c is the sulfate concentration, unit mol / m 3 , D i is the diffusion coefficient, unit m 2 / s, and V is the average velocity of liquid flowing through the pore system under the action of capillary force, unit m / s.

[0063] Specifically, the representative volume element (RVE) is a representative element range.

[0064] Fractal geometry is a new method that takes irregular geometric shapes as the research object, and can describe the morphological characteristics of non-integer dimensional space filling. Its basic characteristic is the self-similarity of the described matter, that is, there is a certain similarity between the local and the whole of the fractal. Many studies have found that fractal geometry can better represent the pore characteristics of cement-based materials through fractal dimension, thereby linking microstructure and macroscopic properties of materials. Box counting method is used to check whether the object has fractal characteristics, that is, the geometry is placed on a uniformly divided grid, the number of grids required to cover the fractal is calculated, and the number of boxes used to cover the object is recorded by changing the grid precision. Through fitting analysis of the entire fractal set, the relationship between the number of boxes required for covering and the size is obtained.

[0065] Further, the specific content of forming an electrochemical potential gradient in the local micro area of the pore network is:

[0066] The Nernst-Planck equation is used to describe the diffusion of charged ions in porous media while moving relative to the medium due to the electric coupling effect. The electric migration flux of ions is:

[0067]

[0068] where s i is the charge number of the i-th ion, F is the Faraday constant, 9.649×104C / mol, T is the absolute temperature, 298K, and Φ is the electrostatic potential.

[0069] Specifically, under the condition of saturation and no pressure gradient, the migration of ions is mainly driven by the electrochemical potential gradient of the solution, where the chemical potential gradient is also known as diffusion, which can make the charged solute transfer from the area with high concentration to the area with low concentration; another driving force is controlled by the electric potential gradient, which is formed due to the different moving speeds of different charged ions in the solution. Generally, the charged solute moving faster carries excess charges to form an electric field in the micro area of the solution, in which process, the existence of the electric potential gradient accelerates the migration rate of the ions moving slower and reduces the migration rate of the ions moving faster. Since the dry-wet process of hydraulic concrete is in contact with the water medium environment rich in multiple ions, the pore solution of the concrete is actually an environment coexisting with multiple ions, and therefore, the electric coupling effect formed by multiple ions will inevitably have an important influence on the transmission of the ions inside.

[0070] Further, the Poisson equation based on the Gaussian electrostatic theory is introduced to characterize the relationship between the charge imbalance and the electric potential gradient of the liquid phase pore solution system, and considering the unsaturated state of the hydraulic concrete, the saturation parameter correction formula (3) is adopted to obtain:

[0071]

[0072] wherein ε0 is the vacuum permittivity, 8.854×10-12 C / (V·m), εr is the relative permittivity of liquid water, and 80. r

[0073] Further, as shown in Figure 2 , based on the electrochemical potential gradient, the capillary action parameter and the convection parameter, the specific content of the ion transmission model is constructed as follows:

[0074] According to the second Fick's law and the mass conservation law, the space-time distribution of the ions is:

[0075]

[0076] wherein c bi is the concentration of the ions solidified in the pore wall structure due to the reaction or adsorption, with the unit of mol / m 3 , c fi is the concentration of the ions free in the pore solution, with the unit of mol / m 3 , J i is the transport flow of the i-th ion, with the unit of mol / (m 2 ·s);

[0077] The migration of the ions under the unsaturated condition is driven by the diffusion and convection, and the Nernst-Planck equation is used to expand the Fick's law, so that the flux of the ions under the action of the two driving forces can be expressed as: ​

[0078]

[0079] wherein, is the porosity of the concrete;

[0080]

[0081] The Langmuir isotherm is used to describe the relationship between the solidified ions and the free ions, and the saturation parameter is introduced to modify the formula (8) as follows:

[0082]

[0083] wherein, a, b are the modified Langmuir adsorption constants, and w is a dimensionless constant, and w = 0.3;

[0084] The formula (8) and the formula (9) are combined to obtain

[0085]

[0086] Specifically, according to capillary dynamics, when the external environment water invades the pores of the concrete matrix, an adsorption layer (water and pore wall have wettability) is formed, and capillary negative pressure is generated under the action of surface tension. Therefore, the water transmission of unsaturated concrete is dominated by capillary action caused by the surface tension of adsorbate in the liquid phase pore structure. When the water level rises, the water of the hydraulic structure concrete contacts with the environment water source, and the diffusion of water vapor in the pore structure of the concrete is more difficult than in the atmospheric environment. Based on the classic theory of soil science Darcy's law, the relationship between the liquid phase transmission flow of water in the saturated porous medium and the hydraulic gradient can be expressed as:

[0087]

[0088] wherein, q is the vector flow rate, V is the capillary potential energy, K (0) is the hydraulic conductivity, and 0 is the relative water content.

[0089] In 1931, Richards proposed an extended Darcy equation to describe the liquid phase transmission of water in unsaturated porous media:

[0090]

[0091] The standard form thereof with the capillary potential energy as the independent variable can be expressed by the formula (14):

[0092]

[0093] wherein, C (V) = d0 / dV, and K (V) is the hydraulic conductivity, which can be expressed as:

[0094]

[0095]

[0096] Among them, K s K is the saturated permeability coefficient, Θ is the degree of saturation, and K is the saturated permeability coefficient. r (Ψ) and K r (Θ) are the relative permeability coefficients that vary with ψ and Θ, respectively, and can be expressed by equation (17):

[0097] K r (Θ)=Θ 1 / 2 [1-(1-Θ 1 / m ) m ] 2 (17)

[0098] The saturated permeability coefficient reflects the ease of water transport in a porous medium. It is defined as the amount of water that flows vertically through a unit area of ​​saturated concrete per unit time under a unit hydraulic gradient. Formally, the saturated permeability coefficient is expressed as the proportionality coefficient between the water velocity and the hydraulic gradient in Darcy's law, as shown in the following formula:

[0099]

[0100] The saturated permeability coefficient is taken as 3 × 10⁻⁶. -11 m 2 / s.

[0101] In reality, during the migration of liquid water under dry-wet conditions, the entire system is in a non-equilibrium state. Here, we borrow the local equilibrium assumption of irreversible processes in classical non-equilibrium thermodynamics to approximate that the system is in equilibrium within its local volume element. Therefore, the balance relationship between liquid water content and energy in hydraulic concrete (i.e., the moisture characteristic curve) can be applied to this non-equilibrium system.

[0102] The master curve of the isothermal adsorption curve (or moisture characteristic curve) is described by the calculation formula proposed by Van Genuchten, as follows:

[0103]

[0104] Where m = 1 - 1 / n, and n and α are empirical parameters.

[0105] The convection parameter, namely the convection peak, is a special aggregation mechanism of ions formed in a specific environment of dry-wet alternation. The ion concentration taken in by the concrete increases first and then decreases with the increase of the penetration depth, and the peak ion concentration appears in the range of 1mm to 3mm from the surface of the concrete. This is because the convection effect of sulfate ions is generated in the surface layer of the concrete under the condition of dry-wet alternation, and the ion diffusion rate is accelerated by considering the convection peak. For different conditions of dry-wet alternation, the greater the dry-wet ratio, the more it can promote the ion penetration, and the peak ion concentration under the T1_R7 system is selected in the application.

[0106] The various embodiments are described in the present specification in a progressive manner, and each embodiment focuses on the difference from other embodiments, and the same or similar parts between various embodiments can be referred to each other. For the device disclosed by the embodiments, since it corresponds to the method disclosed by the embodiments, the description is relatively simple, and the related parts can be referred to the method part.

[0107] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for ion transport in hydraulic concrete based on real pore structure and solution composition, characterized in that, Includes the following steps: Constructing a multi-scale diffusion model based on fractal dimension; A porous network is obtained based on a multi-scale diffusion model, and an electrochemical potential gradient is formed through the local micro-regions of the porous network. An ion transport model is constructed based on the electrochemical potential gradient, capillary action parameters, and convection parameters. The ion transport results were evaluated based on the ion transport model. The specific content of constructing a multi-scale diffusion model based on fractal dimension is as follows: A square with a size of 2000nm was selected as the representative volume unit, and circular pores were selected for two-dimensional modeling with a pore size distribution of 10-300nm. Based on the porosity occupied by each pore size, calculate the number of pores of each type within the representative unit area and generate the corresponding circular pores; The generated circular holes are placed within the representative unit range, and intrusion judgments are made between holes and boundaries, and between holes. If each placed circular hole is within the boundary range and does not intrude into other circular holes, a two-dimensional model is generated. Otherwise, the hole placement information is regenerated, and intrusion judgment is made again until the non-intrusion condition is met. The generated two-dimensional model is meshed using the direct partitioning method to obtain two-dimensional model image data. The generated two-dimensional model image data is binarized, and the fractal dimension of the two-dimensional model is calculated using the box-counting dimension method to obtain the fractal dimension. The diffusion equation based on Fick's second law can be described as follows: In the formula, It is the water content, measured in kg / m³. 3 , This refers to sulfate concentration, expressed in mol / m³. 3 , It is the diffusion coefficient of the i-th ion, in units of m. 2 / s, It is the average velocity of a liquid flowing through a porous system under the action of capillary suction, and its unit is m / s; The specific content of constructing the ion transport model based on the electrochemical potential gradient, capillary action parameters, and convection parameters is as follows: According to Fick's second law and the law of conservation of mass, the spatiotemporal distribution of ions is as follows: in, The concentration of ions solidified in the pore wall structure due to reaction or adsorption, expressed in mol / m³. 3 , The concentration of ions in the pore solution, in mol / m 3 , The transport flux of the i-th ion is expressed in mol / (m³). 2 ·s), Saturation; The migration of ions under unsaturated conditions is driven by diffusion and convection. Using the extended Fick theorem from the Nernst-Planck equation, the ion flux under these two driving forces can be expressed as: in, The porosity of concrete; in, Let be the charge number of the i-th ion. F For Faraday's constant, it is 9.649 × 10⁻⁶. 4 C / mol, T The absolute temperature is 298 K. Φ It is the electrostatic potential; The relationship between solidified ions and free ions is described using Langmuir isotherms, and a correction formula for the saturation parameter (8) is introduced as follows: in, , To correct the Langmuir adsorption constant, It is a dimensionless constant, and its value is 0.3; By combining equations (8) and (9), we obtain 。 2. The ion transport method for hydraulic concrete based on real pore structure and solution composition according to claim 1, characterized in that, The specific details of forming an electrochemical potential gradient through local micro-regions of a porous network are as follows: Using the Nernst-Planck equation to describe the diffusion of charged ions in a porous medium and their movement relative to the medium due to electrocoupling, the electromigration flux of the ions is: in, Let be the charge number of the i-th ion. F For Faraday's constant, it is 9.649 × 10⁻⁶. 4 C / mol, T The absolute temperature is 298 K. Φ It represents the electrostatic potential.

3. The ion transport method for hydraulic concrete based on real pore structure and solution composition according to claim 2, characterized in that, The Poisson equation based on Gaussian electrostatic theory is introduced to characterize the relationship between charge imbalance and potential gradient in the liquid phase porous solution system. Considering the unsaturated state of hydraulic concrete, the saturation parameter correction formula (3) is adopted to obtain: in, The vacuum permittivity is 8.854 × 10⁻⁶. -12 C / (V·m), is the relative permittivity of liquid water, which is 80.

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