Numerical simulation method, system, equipment and medium for calcium dissolution process of concrete water pipe

Abstract

The present application provides a numerical simulation method, system, equipment and medium for the calcium dissolution process of concrete water pipes, which belongs to the field of computer-aided design optimization technology. According to the calcium dissolution mechanism under water erosion, the law of conservation of mass and Fick's second law, combined with the solid-liquid equilibrium relationship of calcium in concrete, a variable coefficient transmission model of the calcium ion dissolution process in water-conveying concrete pipes is established. The model not only considers the influence of the porosity and pore tortuosity changes caused by dissolution on the calcium ion diffusion coefficient in concrete, but also considers the influence of the movement of the inner wall boundary of the pipe caused by the damage of concrete calcium dissolution at different water flow rates on the calcium ion transmission process; the finite difference method is used to numerically solve the established variable coefficient calcium ion dissolution transmission equation. It has been verified that the prediction results of the variable coefficient transmission model are consistent with the test results and the test results of the existing literature, and can accurately evaluate the evolution law of calcium dissolution and service life of the concrete water pipes buried underground.

Description

Technical Field

[0001] The present application relates to the technical field of computer-aided design optimization, and in particular to a numerical simulation method, system, equipment and medium for a calcium dissolution process of a concrete water pipe. Background Art

[0002] Reinforced concrete and prestressed concrete pipes are commonly used water pipes and are widely used in underground water supply and drainage projects. The durability of water pipes directly affects the service life of the water supply system. As water pipes are exposed to soft water or flowing water for a long time, calcium hydroxide (CH) and calcium silicate hydrate (CSH) in the concrete gradually dissolve. At the same time, under the action of concentration gradient, calcium ions in the concrete pore fluid diffuse into the external environmental water. This process is called calcium dissolution. Calcium dissolution will increase the porosity of concrete pipes and accelerate the degradation of durability and bearing capacity of water concrete pipes. Therefore, studying the evolution law of calcium dissolution of underground water concrete pipes under the action of flowing water and establishing a calcium dissolution model for water concrete pipes are the basis for predicting the service life of water concrete pipes.

[0003] In some existing technologies, a large amount of data on the solid calcium concentration of cement paste and the calcium ion concentration in the pore solution during groundwater dissolution was obtained through experiments, and the solid-liquid equilibrium curve during calcium dissolution was established. Other technologies have established a one-dimensional constant coefficient calcium dissolution model for cement-based materials in deionized water based on the two stages of calcium hydroxide and CSH gel decomposition, taking into account the effect of porosity changes on calcium dissolution. Still other technologies have established a constant coefficient calcium dissolution model under external sulfate erosion by considering the calcium leaching process and temperature changes in the transmission damage model. However, the above calcium dissolution model is difficult to accurately describe the physical dissolution process of calcium ions in concrete water pipes, and it is difficult to obtain reliable prediction results for the service life of concrete water pipes.

[0004] Therefore, it is necessary to provide an improved technical solution to address the above-mentioned deficiencies in the prior art. Summary of the invention

[0005] The purpose of the present application is to provide a numerical simulation method, system, equipment and medium for the calcium dissolution process of a concrete water pipe, so as to solve or alleviate the problems existing in the above-mentioned prior art.

[0006] In order to achieve the above objectives, this application provides the following technical solutions:

[0007] In a first aspect, the present application provides a numerical simulation method for the calcium dissolution process of a concrete water pipe, comprising:

[0008] According to the calcium dissolution mechanism under water erosion, the law of conservation of mass and Fick's second law, combined with the solid-liquid equilibrium relationship of calcium in concrete, a variable coefficient transmission model of calcium ion dissolution process in water delivery concrete pipe is established.

[0009] The variable coefficient transmission model of calcium ion dissolution process in water delivery concrete pipe is numerically solved by finite difference method.

[0010] The expression of the variable coefficient transmission model is as follows:

[0011] ,

[0012] In the formula, is the coordinate of the concrete cross section, i.e. the thickness of the concrete wall in the diameter direction of the concrete water pipe; for Moment concrete section The calcium ion concentration in the pore fluid at for Moment concrete section Solid phase calcium content at Abbreviated as , is the water-cement ratio Concrete Time Section The porosity at Abbreviated as ,yes Moment concrete section The effective diffusion coefficient of calcium ions at Porosity , tortuosity and temperature Related; , are the initial calcium ion concentration and the initial solid phase calcium content, respectively; and are the inner and outer diameters of the concrete water pipe respectively; is the initial calcium ion saturation concentration in the concrete pore fluid; and are the initial molar volume contents of calcium hydroxide CH and calcium silicate hydrate CSH in the concrete skeleton, respectively; , They are The calcium ion concentration in the pore fluid and the solid calcium content at the starting position at time t; is the diffusion coefficient of calcium ions in the ambient water in the tube; is the concentration of calcium ions in the ambient water in the tube; It is the calcium ion exchange rate at the contact surface between the inner wall of the concrete pipe and water, that is, the speed at which calcium ions in the pore fluid flow into the water; The critical content of solid calcium for the inner wall boundary of the concrete pipe to move; is the water flow velocity in the pipe.

[0013] In one possible implementation, Moment concrete section Solid phase calcium content It is expressed by the solid-liquid equilibrium curve of calcium dissolved from the solid phase skeleton that plays a gelling role in concrete and the calcium ion concentration in the pore fluid.

[0014] In one possible embodiment, the porosity , is the initial porosity , porosity change caused by calcium dissolution and porosity in the interface transition zone sum;

[0015] The initial porosity , which is the sum of the initial capillary porosity and the initial gel porosity.

[0016] In a possible embodiment, the initial capillary porosity and the initial gel porosity are both related to the water-cement ratio. and hydration level Related.

[0017] In one possible embodiment, based on the distance between the interface transition zone and the aggregate surface The porosity , capillary porosity of cement paste , and the thickness of the interface transition zone, and the porosity of the interface transition zone is calculated. .

[0018] In one possible implementation, according to the Nernst-Einstein equation, Moment concrete section The effective diffusion coefficient of calcium ions at is calculated as follows: Moment concrete section The porosity Divide by the tortuosity , and then multiplied by the calcium ion diffusion coefficient in the concrete pore fluid.

[0019] In one possible implementation, a finite difference method is used to numerically solve a variable coefficient transmission model of calcium ion dissolution process in a water delivery concrete pipe, including:

[0020] The wall of the concrete water pipe is used as the solution area, time is used as the vertical coordinate, and the thickness of the concrete pipe wall in the pipe diameter direction is used as the horizontal coordinate. The solution area is evenly divided into multiple grids.

[0021] For the variable coefficient transmission model, three layers of implicit difference are performed at any time step, thereby obtaining an iterative solution form of the variable coefficient transmission model;

[0022] Using the chasing method, the calcium ion concentration at any time and any position in the concrete water pipe is obtained through programming. , and then calculate the solid calcium content at any time and any position in the concrete water pipe , porosity , tortuosity , diffusion coefficient ;

[0023] in, are the coordinates of the grid.

[0024] In a second aspect, this embodiment provides a numerical simulation system for the calcium dissolution process of a concrete water pipe, comprising:

[0025] The construction unit is used to establish a variable coefficient transmission model of the calcium ion dissolution process in the water delivery concrete pipe according to the calcium dissolution mechanism under water erosion, the law of conservation of mass and Fick's second law, combined with the solid-liquid equilibrium relationship of calcium in concrete;

[0026] A solution unit is used to numerically solve the variable coefficient transmission model of calcium ion dissolution process in water delivery concrete pipe by using finite difference method;

[0027] The expression of the variable coefficient transmission model is as follows:

[0028] ,

[0029] In the formula, is the coordinate of the concrete cross section, i.e. the thickness of the concrete wall in the diameter direction of the concrete water pipe; for Moment concrete section The calcium ion concentration in the pore fluid at for Moment concrete section Solid phase calcium content at Abbreviated as , is the water-cement ratio Concrete Time Section The porosity at Abbreviated as ,yes Moment concrete section The effective diffusion coefficient of calcium ions at Porosity , tortuosity and temperature Related; , are the initial calcium ion concentration and the initial solid phase calcium content, respectively; and are the inner and outer diameters of the concrete water pipe respectively; is the initial calcium ion saturation concentration in the concrete pore fluid; and are the initial molar volume contents of calcium hydroxide CH and calcium silicate hydrate CSH in the concrete skeleton, respectively; , They are The calcium ion concentration in the pore fluid and the solid calcium content at the starting position at time t; is the diffusion coefficient of calcium ions in the ambient water in the tube; is the concentration of calcium ions in the ambient water in the tube; It is the calcium ion exchange rate at the contact surface between the inner wall of the concrete pipe and water, that is, the speed at which calcium ions in the pore fluid flow into the water; The critical content of solid calcium for the inner wall boundary of the concrete pipe to move; is the water flow velocity in the pipe.

[0030] In a third aspect, this embodiment provides an electronic device, comprising: a memory for storing instructions executed by one or more processors of the electronic device; a processor, which, when the processor executes the instructions in the memory, enables the electronic device to implement the steps of the numerical simulation method for the calcium dissolution process of a concrete water pipe as provided in any of the above embodiments.

[0031] In a fourth aspect, the present embodiment provides a computer-readable storage medium having instructions stored thereon, which, when executed on a computer, implement the steps of a numerical simulation method for the calcium dissolution process of a concrete water pipe as provided in any of the above embodiments.

[0032] The technical solution of the embodiment of the present application has the following beneficial effects:

[0033] According to the calcium dissolution mechanism under water erosion, the law of conservation of mass and Fick's second law, combined with the solid-liquid equilibrium relationship of calcium in concrete, a variable coefficient transmission model of calcium ion dissolution process in water delivery concrete pipes is established; the finite difference method is used to numerically solve the variable coefficient transmission model of calcium ion dissolution process in water delivery concrete pipes. Among them, the variable coefficient transmission model of calcium ion dissolution process established not only considers the influence of porosity and pore tortuosity changes caused by dissolution on the calcium ion diffusion coefficient in concrete, but also considers the influence of the inner wall boundary movement caused by concrete calcium dissolution damage under different water flow velocities on the calcium ion transmission process, which improves the accuracy of the service life prediction of concrete water delivery pipes. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A schematic flow chart of a numerical simulation method for the calcium dissolution process of a concrete water pipe provided according to some embodiments of the present application.

[0035] Figure 2 A schematic diagram of an electronic device provided according to some embodiments of the present application.

[0036] Figure 3 Schematic diagram of the physical dissolution evolution process, where (a) is a schematic diagram of a concrete water pipe, (b) is a microscopic pore diagram, (c) is a schematic diagram of calcium ion diffusion, (d) is a schematic diagram of the pore enlargement after dissolution, (e) is a schematic diagram of the pores connecting with each other after enlargement, and (f) is a schematic diagram of surface peeling.

[0037] Figure 4 Schematic diagram of the cross section of a concrete water pipe.

[0038] Figure 5 Schematic diagram of the solid-liquid equilibrium curve.

[0039] Figure 6 Diagram of the meshing of the solution area for a concrete water pipe.

[0040] Figure 7 An example of numerical solution of a variable coefficient transport model.

[0041] Figure 8 Schematic diagram of cement mortar specimen.

[0042] Fig. 9 For the specimen at 6 mol / m 3 Schematic diagram comparing the simulation results and experimental test results of the depth of the calcium dissolution front during 90 days of immersion in NH4NO3 solution.

[0043] Fig.10 Schematic diagram for comparison between simulation results and experimental results of Wan et al.

[0044] 31-concrete pipe wall, 32-water flowing in the pipe, 33-flow direction, 34-pores, 35-diffusion direction, 36-calcium ions, 52-inner boundary of the pipe, 53-inner diameter, 54-outer diameter. DETAILED DESCRIPTION

[0045] The embodiments of the present application are described below in conjunction with the accompanying drawings.

[0046] The embodiments of the present application can be applied to Figure 2Among the electronic devices shown, the electronic device can be but is not limited to mobile terminals such as mobile phones, tablet computers, handheld computers, personal digital assistants (PDAs), smart home devices such as smart TVs and smart cameras, wearable devices such as smart bracelets, smart watches, smart glasses, or other computer devices such as desktops, laptops, notebook computers, ultra-mobile personal computers (UMPCs), netbooks, smart screens, etc.

[0047] like Figure 2 As shown, the electronic device 200 may include one or more of the following components: a processor 201, a memory 203, a communication interface 202, and a communication bus 204. The memory 203 may be connected to the processor 201 via the bus 204. The bus may transmit data between the processor 201 and the memory 203. The bus may be divided into an address bus, a data bus, a control bus, and the like.

[0048] The processor 201 may include one or more processing cores, and the processor 201 may use various interfaces and lines to connect various parts of the entire electronic device 200, and execute various functions and process data of the electronic device 200 by running or executing instructions, programs, code sets or instruction sets stored in the memory 203, and calling data stored in the memory 203. Exemplarily, the processor 201 may include an application processor (application processor, AP), a modem processor, a CPU, a graphics processor (graphics processing unit, GPU), an image signal processor (image signal processor, ISP), a controller, a video codec, a digital signal processor (digital signal processor, DSP), a field programmable gate array (field-programmable gate array, FPGA), a programmable logic array (programmable logic array, PLA) and / or a neural network processor (neural-network processing unit, NPU), etc. Among them, the CPU mainly processes the operating system, user interface and application programs, etc.; the GPU is responsible for rendering and drawing the content to be displayed; the NPU is used to implement artificial intelligence (artificial intelligence, AI) functions; and the modem is used to process wireless communications. Different processing units may be independent devices or integrated into one or more processors. For example, the multiple processing units shown above are integrated into one SoC, or the AP is a separate semiconductor chip and other processing units are integrated into one SoC, which is not limited in this application.

[0049] The memory 203 may include a random access memory (RAM), a read-only memory (ROM), or a non-transitory computer-readable storage medium. The memory 203 may be used to store instructions, programs, codes, code sets, or instruction sets. The memory 203 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function, such as a numerical simulation method for calcium dissolution process of a concrete water pipe, etc.; the data storage area may store data created according to the use of the electronic device 200, such as input data for numerical solutions, etc.

[0050] In addition, those skilled in the art can understand that the structure of the electronic device 200 shown in the above drawings does not constitute a limitation on the electronic device 200, and the electronic device may include more or fewer components than shown in the drawings, or combine certain components, or arrange the components differently. For example, the electronic device 200 also includes components such as a microphone, a speaker, a radio frequency circuit, a sensor, an audio circuit, a power supply, and a Bluetooth module, which will not be described in detail here.

[0051] This embodiment provides a numerical simulation method for the calcium dissolution process of a concrete water pipe. Figure 1 As shown, the method includes:

[0052] Step S101, based on the calcium dissolution mechanism under water erosion, the law of conservation of mass and Fick's second law, combined with the solid-liquid equilibrium relationship of calcium in concrete, a variable coefficient transmission model of the calcium ion dissolution process in the water delivery concrete pipe is established;

[0053] Step S102: using the finite difference method to numerically solve the variable coefficient transmission model of the calcium ion dissolution process in the water delivery concrete pipe.

[0054] Below, refer to Figure 3 The calcium dissolution mechanism under water erosion in step S101 is described as follows:

[0055] The inner wall of the concrete water pipe is in a soft water or flowing water environment for a long time, and its calcium dissolution mechanism can be mainly divided into physical dissolution and chemical dissolution.

[0056] Figure 3 Figure 1 is a schematic diagram of the physical dissolution evolution process, where: (a) is a schematic diagram of a concrete water pipe, which consists of a concrete pipe wall 31 and water 32 in the pipe, where the water 32 in the pipe flows along a flow direction 33; (b) is a microscopic pore diagram; (c) is a schematic diagram of calcium ion diffusion, where calcium ions 36 move along pores 34 in a diffusion direction 35; (d) is a schematic diagram of the enlargement of pores 34 after being dissolved; (e) is a schematic diagram of the interconnection of pores 34 after enlargement; and (f) is a schematic diagram of surface peeling.

[0057] Physical dissolution refers to the diffusion of calcium ions 36 in the pore solution of concrete into the soft water under the action of soft water or flowing water under the action of its concentration gradient through the pores 34 of the concrete, such as Figure 3 As shown in (b) to (c), with the continuous diffusion of calcium ions 36 in the pore solution, the easily soluble calcium hydroxide (Ca(OH)2) and hydrated calcium silicate gel (CSH) solid phase skeleton in the cement hydration product dissolve, and the dissolution reaction can be simply expressed as:

[0058] (1a)

[0059] (1b)

[0060] After the solid skeleton of calcium hydroxide (Ca(OH)2) and calcium silicate hydrate gel (CSH) dissolves, it diffuses into the flowing water, causing the pores 34 inside the concrete pipe wall 31 to continue to increase (e.g. Figure 3 As calcium dissolution proceeds, the pores 34 are interconnected (as shown in (d)); Figure 3 As shown in (e), the surface of the concrete pipe wall 31 peels off and the boundary of the dissolution moves (as shown in Figure 3 As shown in (f) in the figure). The damage of the concrete pipe wall 31 caused by physical erosion is a process from the outside to the inside. On a macro scale, it is manifested as the surface of the concrete pipe wall 31 peeling off, and the strength and durability are reduced.

[0061] Chemical dissolution refers to the chemical reaction between chemical substances in flowing water and soluble calcium in cement hydration products, which causes the solid phase calcium in the hydration products to decompose and precipitate into the pore fluid. Chemical corrosion can be divided into acid corrosion and salt corrosion according to the different corrosion media, and there are many related research results.

[0062] It should be noted that this application focuses on the physical dissolution of calcium, rather than chemical dissolution. It should also be noted that the calcium dissolution process and speed of concrete are different at different temperatures, different flow rates and different environments.

[0063] According to the calcium dissolution process and mechanism in concrete under the action of soft water or flowing water, the calcium ions 36 in the pore fluid of the concrete pipe wall 31 diffuse into the external soft water environment under the action of the concentration difference between the inside and the outside, causing the calcium ion concentration in the pore fluid to decrease. In order to maintain the solid-liquid balance, the soluble solid phase calcium (CH and CSH) in the concrete skeleton is dissolved.

[0064] Figure 4 It is a schematic diagram of the cross section of a concrete water pipe. Figure 4 As shown, the concrete water pipe comprises: a concrete pipe wall 31, water flowing in the pipe 32, a pipe inner boundary 52, and an inner diameter 53 of the pipe. r 1 Indicates that the outer diameter is 54 r 2 express.

[0065] Taking the calcium ion concentration in the concrete pore solution as the dissolution variable, the calcification content in the solid phase skeleton of concrete gel and the calcium ion concentration in the pore solution satisfy the thermodynamic equilibrium relationship, that is, the solid-liquid equilibrium relationship. Combined with Fick's law and the law of conservation of mass, a variable coefficient transmission model of the calcium ion dissolution process in water-transport concrete pipes is established.

[0066] The variable coefficient transmission model is also called the one-dimensional variable coefficient dissolution model of calcium ions. At the initial moment, the calcium ion concentration in the concrete pore solution is the saturated concentration, the calcium ion concentration at the boundary position of the tube is the calcium ion concentration in the water environment in the tube, and the calcium ion exchange condition at the boundary position is the Newtonian boundary condition, which is expressed as follows:

[0067] (2)

[0068] In the formula, is the coordinate of the concrete cross section, i.e. the thickness of the concrete wall in the diameter direction of the concrete water pipe; for Moment concrete section Calcium ion concentration in pore fluid, mmol / m 3 ; for Moment concrete section Solid phase calcium content at 3 ; For simplicity of expression, Abbreviated as , The water-cement ratio is Concrete Time Section For simplicity of expression, Abbreviated as , yes Moment concrete section The effective diffusion coefficient of calcium ions at Porosity , tortuosity and temperature Related, m 2 / s; , are the initial calcium ion concentration and the initial solid phase calcium content, respectively; and are the inner and outer diameters of the concrete water pipe, m; is the initial calcium ion saturation concentration in the concrete pore fluid, mmol / m 3 ; and are the initial molar volume contents of calcium hydroxide CH and calcium silicate hydrate CSH in the concrete skeleton, mmol / m 3 ; , They are The calcium ion concentration in the pore fluid and the solid calcium content at the starting position at time t; is the diffusion coefficient of calcium ions in the ambient water inside the tube, m 2 / s; is the concentration of calcium ions in the ambient water in the tube; is the calcium ion exchange rate at the contact surface between the inner wall of the concrete pipe and water, that is, the speed at which calcium ions in the pore fluid flow into the water, m / s; Critical content of solid calcium for the movement of the inner wall boundary of the concrete pipe, mmol / m 3 ; is the water flow velocity in the pipe, m / s.

[0069] The calculation methods of various parameters in the variable coefficient transmission model (i.e., Formula 2) are described below.

[0070] In this embodiment, the initial solid phase calcium content The calculation is as follows:

[0071] The calcium-containing solid phase skeleton in concrete is mainly calcium hydroxide CH and hydrated calcium silicate CSH gel. These two products are formed by the hydration of tricalcium silicate and dicalcium silicate. The reaction equation can be expressed as shown in formula (3):

[0072] (3)

[0073] According to the stoichiometric reaction equation, the mineral composition, water-cement ratio and hydration degree of cement clinker can be used to calculate the concentration of hydration products CH and CSH in unit volume of concrete, thereby calculating the initial solid phase calcium content in formula (2): , the expression is as follows:

[0074] (4a)

[0075] (4b)

[0076] In the formula, and are the initial molar volume contents of calcium hydroxide CH and calcium silicate hydrate CSH in the concrete skeleton, mmol / m 3 ; and are the percentages of tricalcium silicate and dicalcium silicate, respectively; and is the molar mass of tricalcium silicate and dicalcium silicate, , ; is the cement hydration degree; is the density of cement paste, g / m 3 ; is the density of cement, ; is the density of water, ; is the water-cement ratio.

[0077] The degree of cement hydration depends mainly on the water-cement ratio ( ), curing conditions and curing time, hydration degree It can be expressed as:

[0078] (4c)

[0079] In the formula, is the cement hydration degree; is the cement hydration time.

[0080] Calculate the initial solid calcium content after, Solid phase calcium content at the concrete cross section at the moment The calculation method is as follows: it is expressed by the solid-liquid equilibrium curve of the calcium dissolved from the solid phase skeleton that plays a gelling role in the concrete and the calcium ion concentration in the pore fluid.

[0081] Specifically, in the variable coefficient transmission model, The concentration of available calcium in the solid skeleton (CH and CSH) that plays a role in cementing concrete is related to the calcium ion concentration in the pore solution (i.e. Moment concrete section The calcium ion concentration in the pore fluid ) is represented by the solid-liquid equilibrium curve. Figure 5 shown.

[0082] according to Figure 5 , Moment concrete section Solid phase calcium content The calculation expression is as follows:

[0083] (5)

[0084] In the formula, is the calcium ion concentration in the pore fluid when the CSH gel in concrete rapidly dissolves into silica gel (SiO2), mmol / m 3 ; is the calcium ion concentration in the pore fluid when CSH begins to dissolve after CH in concrete is completely dissolved, mmol / m 3 ; is the initial calcium ion saturation concentration in the concrete pore fluid, mmol / m 3 .

[0085] In the variable coefficient transmission model of this embodiment, the pore structure parameters include porosity and tortuosity , porosity and tortuosity Average over time It changes with the change of porosity, so it is also called time-varying porosity and time-varying tortuosity Among them, the time-varying porosity The calculation steps are as follows:

[0086] In soft water or flowing water environment, calcium ions in the concrete pore fluid are transported outward under the action of internal and external gradients. In order to meet the solid-liquid equilibrium relationship, the soluble solid phase calcium (mainly CH and CSH) in the concrete skeleton begins to dissolve, resulting in an increase in the porosity of the concrete, which further accelerates the calcium dissolution process of the concrete. Therefore, the porosity is the initial porosity , porosity change caused by calcium dissolution and porosity in the interface transition zone The sum of is as follows:

[0087] (6a)

[0088] In the formula, is the porosity of the interface transition zone; is the volume of the interface transition zone; is the total volume of concrete material; is the molar mass of calcium hydroxide, ; is the density of calcium hydroxide, .

[0089] Initial porosity (i.e. initial porosity of concrete) is the sum of initial capillary porosity and initial gel porosity.

[0090] Furthermore, the initial capillary porosity and the initial gel porosity are both related to the water-cement ratio. and hydration level Related, the expression is as follows:

[0091] (6b)

[0092] (6c)

[0093] In the formula, is the initial capillary porosity; is the initial gel porosity.

[0094] It should be noted that the interfacial transition zone (ITZ) usually refers to the area between aggregate and cement paste in concrete. The structure of this area is different from that of the cement paste itself. It is usually looser and has a higher porosity. Crystal structures such as CH may have different distributions here. This structural difference causes the mechanical properties and transmission properties of the ITZ to be different from those of the surrounding matrix.

[0095] Based on the distance between the interface transition zone and the aggregate surface The porosity , capillary porosity of cement paste , and the thickness of the interface transition zone, the porosity of the interface transition zone is calculated , the expression is as follows:

[0096] (6d)

[0097] (6e)

[0098] In the formula, is the distance between the interface transition zone and the aggregate surface The porosity at is the capillary porosity of cement paste; is the thickness of the interface transition zone and is the unknown coefficient, among which .

[0099] The value can be determined by the water-cement ratio, the maximum cement particle size and the thickness of the interface transition zone, and its calculation equation is:

[0100] (6g)

[0101] (6h)

[0102] In the formula, is the volume distribution density of cement; is the maximum diameter of cement particles in concrete, is the water-cement ratio.

[0103] The above is the time-varying porosity The calculation process of time-varying tortuosity is introduced below. The calculation steps are as follows:

[0104] Concrete is a porous medium material. The transmission path and transmission rate of calcium ions in concrete are affected by the geometric tortuosity of the pores in concrete. According to the research of existing scholars, the geometric tortuosity of the pores in concrete can be expressed as:

[0105] (7a)

[0106] (7b)

[0107] (7c)

[0108] In the formula, and are the upper and lower limits of the geometric tortuosity of concrete pores, respectively; is the volume fraction of stone particles; is the geometric tortuosity of the mortar pores, , , , are the densities of gravel, cement, sand and water respectively. , , , They are the quality of gravel, cement, sand and water. Among them, the geometric tortuosity of the mortar pores The calculation formula is as follows:

[0109] (7d)

[0110] (7e)

[0111] (7f)

[0112] (7g)

[0113] In the formula, and are the upper and lower limits of the geometric tortuosity of the mortar pores, is the average diameter of sand particles; is the average gap between sand particles; is the geometric tortuosity of hardened cement paste at any age; is the volume fraction of sand particles. Calculated according to the following formula:

[0114] (7h)

[0115] (7i)

[0116] (7j)

[0117] (7k)

[0118] (7l)

[0119] In the formula, is the hydration degree of Portland cement, obtained by formula (4c); and are the geometric tortuosity of unhydrated and fully hydrated cement particles, respectively; , are the upper and lower limits of the geometric tortuosity of unhydrated cement particles, respectively; , are the upper and lower limits of the geometric tortuosity of fully hydrated cement particles, respectively; It is the porosity of unhydrated cement, which is generally 58%.

[0120] is the porosity of fully hydrated cement, which is similar to the porosity of concrete , Hydration degree , Porosity of unhydrated cement The relationship is:

[0121] (7m)

[0122] The above is the calculation process of pore structure parameters. Moment concrete section The effective diffusion coefficient of calcium ions at The calculation steps.

[0123] Moment concrete section The effective diffusion coefficient of calcium ions at , also known as the calcium ion diffusion coefficient The diffusion coefficient of calcium ions in concrete is mainly related to the pore structure of concrete, such as porosity and tortuosity, and the diffusion coefficient of calcium ions in the pore fluid of concrete. During the calcium dissolution process, the soluble solid phase calcium (CH and CSH) in the concrete skeleton gradually dissolves, causing the pore structure of concrete to change, and the porosity and tortuosity to change. Therefore, the diffusion coefficient also changes. Changes in temperature will also cause changes in the calcium ion diffusion coefficient.

[0124] According to the Nernst-Einstein equation, Moment concrete section The effective diffusion coefficient of calcium ions at is calculated as follows: Moment concrete section The porosity Divide by the tortuosity , and then multiplied by the calcium ion diffusion coefficient in the concrete pore fluid, the expression is as follows:

[0125] (8a)

[0126] In the formula, for Diffusion coefficient of calcium ions in concrete at time t, m 2 / s; is the time-varying porosity of concrete, obtained by equations (6a) to (6h); is the time-varying tortuosity of concrete, obtained by equations (7a) to (7m); is the calcium ion diffusion coefficient in the concrete pore fluid, which is related to temperature T Related, m 2 / s.

[0127] Further, The expression is as follows:

[0128] (8b)

[0129] (8c)

[0130] (8d)

[0131] In the formula, is the ideal gas constant, ; is Kelvin temperature, K; is the Faraday constant, ; is the valence state of calcium ions, ; is the radius of the calcium ion, ; is the conductivity of calcium ions in the pore fluid, ; is the calcium ion strength, which is related to the valence and concentration of calcium ions; and is a temperature-related parameter; is the basic charge, ; is the dielectric constant of vacuum, ; is the relative dielectric constant of the aqueous solution, , M The total number of divisions for the pipe wall thickness.

[0132] In step S102, a finite difference method is used to numerically solve a variable coefficient transmission model of calcium ion dissolution process in a water delivery concrete pipe, including the following steps:

[0133] Step S112, taking the wall of the concrete water pipe as the solution area, using time as the ordinate and the thickness of the concrete pipe wall in the pipe diameter direction as the abscissa, and evenly dividing the solution area into a plurality of grids;

[0134] Step S122, discretizing the variable coefficient transmission model, performing three-layer implicit difference at any time step, and then obtaining an iterative solution form of the variable coefficient transmission model;

[0135] Step S132: Using the chasing method, the calcium ion concentration at any time and any position in the concrete water pipe is obtained by programming. , and then calculate the solid calcium content at any time and any position in the concrete water pipe , porosity , tortuosity , diffusion coefficient ;

[0136] in, are the coordinates of the grid.

[0137] The purpose of step S112 is to perform discretization processing:

[0138] Specifically, the Crank-Nicolson finite difference scheme is used to numerically solve the variable coefficient transmission model of calcium ion dissolution process in the water delivery concrete pipe established in equation (2). The wall of the water delivery concrete pipe is taken as the solution area, and the solution area is divided into grids for discretization processing.

[0139] Figure 6 The mesh division diagram for the concrete water pipe solution area. Figure 6 As shown in the figure, in the grid division and calculation process, the horizontal axis is the thickness of the concrete pipe wall in the pipe diameter direction, and the vertical axis is time. The pipe wall thickness L is divided into M equal parts, and the time field T is divided into K equal parts, then the position step length mm, time step s.

[0140] exist Figure 6 In the solution area shown, the horizontal axis includes M+1 nodes, the vertical axis includes K+1 nodes, and the coordinates of each node can be expressed as :

[0141] (9)

[0142] For ease of expression, the nodes in the calcium dissolution process The calcium ion concentration at , the solid phase calcium content is expressed as , the porosity is expressed as , the diffusion coefficient is expressed as During the calcium dissolution process, the boundary of the concrete water pipe continuously moves inwards with a spatial step length of The fraction M of the divided concrete pipe wall thickness keeps getting smaller, but it will not affect the solution of the diffusion equation. The parameters of the moment are given by and The parameters at the moment are calculated.

[0143] Based on the results of the above discretization processing, the variable coefficient transmission model, that is, the solution process of equation (2) is as follows:

[0144] In order to numerically solve the model, let:

[0145] (10)

[0146] Substituting equation (10) and equation (6a) into equation (2), after derivation, transformation, and simplification, the chasing method can be used to solve equation (2) through MATLAB programming to obtain the calcium ion concentration at any time and any position in the concrete water pipe: On this basis, according to equations (5), (6a)~(6h), (7a)~(7l), (8a)~(8d), the solid phase calcium content in the concrete water pipe during the dissolution process can be further obtained. , porosity , tortuosity and the diffusion coefficient , in order to perform iterative calculations.

[0147] In order to obtain the discrete numerical iterative solution of formula (2), the coefficients in formula (2) are discretized, that is, according to the division of the pipe wall grid, the discretized form of the coefficients in formula (2) is written:

[0148] (11).

[0149] In the formula, , , , , is the ratio of the molar mass of calcium hydroxide to its density.

[0150] It should be noted that the numerical solution of the variable coefficient transmission model can be obtained by explicit or implicit difference method.

[0151] In order to improve the accuracy and stability of the calculation, the implicit difference method is used in this embodiment. Specifically, Perform three levels of implicit differencing at any time step:

[0152] (12a)

[0153] make:

[0154] (12b)

[0155] (12c)

[0156] (12d)

[0157] (12e)

[0158] (12f)

[0159] (12g)

[0160] Combining equations (12a)-(12g), the final iterative solution form of the variable coefficient transmission model of concrete water pipe can be written as:

[0161] (12h)

[0162] (12i) (12j) (12k)

[0163] (12l)

[0164] As an example, the following combines Figure 7 , the numerical solution process of the variable coefficient transmission model is further explained. After the numerical solution starts, the process can be performed as follows:

[0165] Step S701: input the initial parameters of the variable coefficient transmission model of the concrete calcium dissolution process, including: the initial calcium ion saturation concentration in the concrete pore solution and initial soluble solid calcium content , initial porosity , initial tortuosity , the initial diffusion coefficient .in, It is calculated according to formula (4a)~(4c), the initial porosity It is calculated according to formula (6a)~(6h), the initial tortuosity It is calculated according to formula (7a)~(7m), the initial diffusion coefficient It is calculated according to formula (8a)~(8d);

[0166] Step S702: t=t+1 ; i.e. time step , iterative calculation is performed with a time step of +1;

[0167] Step S703: Solve the next moment by implicit difference method t Any location x Calcium ion concentration in the pore fluid of water pipe concrete at , calculated according to formula (9)~(12l);

[0168] Step S704: Calculate based on the solid-liquid equilibrium relationship t Any time, any location x Solid phase calcium content , calculated according to formula (5);

[0169] Step S705: Calculate the pore structure parameters of the concrete, that is, calculate the time-varying porosity of the water pipe concrete using formulas (6a) to (6h): , the time-varying tortuosity is calculated by formulas (7a) to (7m): ;

[0170] Step S706: Calculate the time-varying diffusion coefficient of calcium ions in the water pipe concrete according to the porosity, tortuosity and temperature of the concrete. , calculated according to formula (8a)~(8d);

[0171] Step S707: Determine t<T Is it established? If so, return to step S702 to continue iterative solution. If not, output the distribution results of various coefficients in the process of calcium dissolution of water pipe concrete and end the iteration.

[0172] Furthermore, in order to illustrate the reliability of the method proposed in this application, a model verification step is also included. The specific implementation is as follows:

[0173] Calcium dissolution of concrete is a slow process. In order to study the degradation law of concrete durability under the action of calcium dissolution, an ammonium nitrate solution accelerated calcium dissolution test was carried out in accordance with the standard "Test Method for Long-term Performance and Durability of Concrete" (GBT50082-2024) to verify the reliability of the calcium dissolution model (variable coefficient transfer model) proposed in the application.

[0174] The raw materials of the cement mortar specimens used in the test are silicate P∙I42.5 standard cement (in accordance with GB8076-2008), the main chemical composition and mineral composition are shown in Table 1 and Table 2, ISO standard sand (meets the technical requirements of GB / T17671-1999), and its basic properties are shown in Table 3. Table 1, Table 2, Table 3 are as follows:

[0175] Table 1 Chemical composition of cement (%)

[0176]

[0177] Table 2 Mineral composition of cement (%)

[0178]

[0179] Table 3 Basic performance parameters of sand

[0180]

[0181] Cement mortar specimens with water-cement ratios of 0.35 and 0.5 were prepared, and their mix ratios are shown in Table 4:

[0182] Table 4 Mixing ratio

[0183]

[0184] The cement mortar specimen is a cubic structure with a molding size of 40 mm × 40 mm × 40 mm. Under the condition of ambient temperature of 20 °C, after 28 days of standard curing, one set of faces of the cubic specimen is wax-sealed to form a closed boundary, and the other faces are dissolution boundaries, such as Figure 8 As shown in the figure, the arrows indicate the direction of calcium ion transmission. 3 In the NH4NO3 solution, the immersion times were 10d, 30d, 50d, 70d and 90d respectively.

[0185] After the immersion reaches the specified erosion time, calcium dissolution detection is carried out in accordance with the "Technical Standard for Building Structure Inspection" GB / T 50344-2019. The brief process is as follows: (1) Take out the immersed specimen, use a cutting machine to cut the specimen into two 40 mm × 40 mm × 20 mm rectangular specimens along the vertical direction of the wax cover, and soak them in anhydrous ethanol to terminate their hydration process; (2) Prepare phenolphthalein indicator solution, spray phenolphthalein solution along the erosion surface, and then the dissolution part will turn pink. Measure the distance from the edge of the sample to the red part, that is, the dissolution depth, and take the average value of multiple measurements.

[0186] According to the water-cement ratio, mix design and curing age, the parameters in the variable coefficient transmission equation (2) are calculated as follows: Saturated calcium ion concentration in concrete pore fluid , the ion exchange rate at the contact surface between the inner wall of the concrete pipe and water (Experimental value), diffusion coefficient of calcium ions in solution , the calcium ion concentration in the solution , 6 mol / m 3 The acceleration ratio of calcium dissolution in NH4NO3 solution is 121 compared with that in pure water. , time step When the water-cement ratio is 0.35, the hydration degree α =0.67, initial solid phase calcium content , initial porosity , initial calcium ion diffusion coefficient When the water-cement ratio is 0.5, the hydration degree α =0.74, initial solid phase calcium content , initial porosity , initial calcium ion diffusion coefficient Substitute the above parameters into the variable coefficient transmission model, that is, formula (2), and follow Figure 7 The steps shown are numerically solved.

[0187] Fig. 9 For cement mortar specimens at 6 mol / m 3 Comparison of simulation results and experimental test results of the depth of calcium dissolution front during 90 days of immersion in NH4NO3 solution. As can be seen from the figure, the distribution trend of the simulation value and the experimental test value of the depth of dissolution front is basically consistent. According to verification, the error between the simulation value and the experimental test value of the depth of dissolution front is basically within 15%, and the maximum error is 17%. According to relevant research, since concrete is a non-homogeneous material, the model prediction accuracy is relatively reasonable within 30%. Therefore, the prediction results of the variable coefficient transmission model for the calcium ion dissolution process in the water delivery concrete pipe established in this application are reasonable.

[0188] In order to further verify the reliability of the model, the test results of scholars Wan et al. were used. The test used type I silicate cement and cement pastes with water-cement ratios of 0.53, 0.35 and 0.23, respectively, with a size of 40 mm×40 mm×20 mm. After 300 days of standard curing, 6 mol / L ammonium nitrate solution was used for accelerated dissolution experiments. The model proposed in this application was verified based on the test results of water-cement ratios of 0.35 and 0.53, and the relevant parameters: the diffusion coefficient of calcium ions in the solution

[0189] , the hydration degrees are 0.77 and 0.89 respectively, ,

[0190] Substituting the model proposed in this application, the simulation results are compared with the experimental results in the literature. Fig.10 As shown in the figure, it can be seen that the simulation value is basically consistent with the experimental results, with the maximum error being 18.3%.

[0191] In summary, the technical solution proposed in this embodiment, based on the calcium dissolution mechanism of concrete, Fick's law and the law of conservation of mass, establishes a one-dimensional variable coefficient transmission model of calcium ions in concrete water pipes, and uses MATLAB software for numerical solution. The established calcium ion transmission model in concrete water pipes (i.e., variable coefficient transmission model) not only considers the influence of changes in porosity and pore tortuosity caused by dissolution on the calcium ion diffusion coefficient in concrete, but also considers the influence of the movement of the inner wall boundary of the pipe caused by concrete calcium dissolution damage at different water flow rates on the calcium ion transmission process. The three-layer implicit difference Crank-Nicolson (CN) format in the finite difference method is used for discretization processing, and numerical simulation is performed using MATLAB software. The solution results of the model are basically consistent with the experimental and literature results, and the error is basically controlled at about 15%, which verifies the reliability of the model and shows that the model can accurately evaluate the evolution law of calcium dissolution and service life of concrete water pipes buried underground.

[0192] Based on the same inventive concept, this embodiment provides a numerical simulation system for the calcium dissolution process of a concrete water pipe, comprising:

[0193] The construction unit is used to establish a variable coefficient transmission model of the calcium ion dissolution process in the water delivery concrete pipe according to the calcium dissolution mechanism under water erosion, the law of conservation of mass and Fick's second law, combined with the solid-liquid equilibrium relationship of calcium in concrete;

[0194] A solution unit is used to numerically solve the variable coefficient transmission model of calcium ion dissolution process in water delivery concrete pipe by using finite difference method;

[0195] The expression of the variable coefficient transmission model is as follows:

[0196] ,

[0197] In the formula, is the coordinate of the concrete cross section, i.e. the thickness of the concrete wall in the diameter direction of the concrete water pipe; for Moment concrete section The calcium ion concentration in the pore fluid at for Moment concrete section Solid phase calcium content at Abbreviated as , is the water-cement ratio Concrete Time Section The porosity at Abbreviated as ,yes Moment concrete section The effective diffusion coefficient of calcium ions at Porosity , tortuosity and temperature , related; , are the initial calcium ion concentration and the initial solid phase calcium content, respectively; and are the inner and outer diameters of the concrete water pipe respectively; is the initial calcium ion saturation concentration in the concrete pore fluid; and are the initial molar volume contents of calcium hydroxide CH and calcium silicate hydrate CSH in the concrete skeleton, respectively; , They are The calcium ion concentration in the pore fluid and the solid calcium content at the starting position at time t; is the diffusion coefficient of calcium ions in the ambient water in the tube; is the concentration of calcium ions in the ambient water in the tube; It is the calcium ion exchange rate at the contact surface between the inner wall of the concrete pipe and water, that is, the speed at which calcium ions in the pore fluid flow into the water; The critical content of solid calcium for the inner wall boundary of the concrete pipe to move; is the water flow velocity in the pipe.

[0198] The numerical simulation system for the calcium dissolution process of concrete water pipes provided in this embodiment can implement the process and steps of the numerical simulation method for the calcium dissolution process of concrete water pipes provided in any of the above embodiments and achieve the same technical effects, which will not be described in detail here.

[0199] The present application also provides a computer program product, which includes computer executable instructions. In one embodiment, the computer executable instructions are used to enable a computer to execute the functions of the above method embodiment.

[0200] The computer executable instructions may be stored in a computer readable storage medium. The present application also provides a computer readable storage medium, wherein the computer readable storage medium stores the executable instructions. In one embodiment, the computer executable instructions are used to enable a computer to execute the functions in the above method embodiment.

Claims

1. A numerical simulation method for the calcium dissolution process of a concrete water pipe, characterized in that: include: According to the calcium dissolution mechanism under flowing water erosion, the law of conservation of mass and Fick's second law, combined with the solid-liquid equilibrium relationship of calcium in concrete, a variable coefficient transmission model of calcium ion dissolution process in water delivery concrete pipe is established. The variable coefficient transmission model of calcium ion dissolution process in water delivery concrete pipe is numerically solved by finite difference method. The expression of the variable coefficient transmission model is as follows: ， In the formula, is the coordinate of the concrete cross section, i.e. the thickness of the concrete wall in the diameter direction of the concrete water pipe; for Moment concrete section The calcium ion concentration in the pore fluid at for Moment concrete section Solid phase calcium content at Abbreviated as , is the water-cement ratio Concrete Time Section The porosity at Abbreviated as ,yes Moment concrete section The effective diffusion coefficient of calcium ions at Porosity , tortuosity and temperature Related; , are the initial calcium ion concentration and the initial solid phase calcium content, respectively; and are the inner and outer diameters of the concrete water pipe respectively; is the initial calcium ion saturation concentration in the concrete pore fluid; and are the initial molar volume contents of calcium hydroxide CH and calcium silicate hydrate CSH in the concrete skeleton, respectively; , They are The calcium ion concentration in the pore fluid and the solid calcium content at the starting position at time t; is the diffusion coefficient of calcium ions in the ambient water in the tube; is the concentration of calcium ions in the ambient water in the tube; It is the calcium ion exchange rate at the contact surface between the inner wall of the concrete pipe and water, that is, the speed at which calcium ions in the pore fluid flow into the water; The critical content of solid calcium for the inner wall boundary of the concrete pipe to move; is the water flow velocity in the pipe.

2. The method according to claim 1, characterized in that Moment concrete section Solid phase calcium content It is expressed by the solid-liquid equilibrium curve of calcium dissolved from the solid phase skeleton that plays a gelling role in concrete and the calcium ion concentration in the pore fluid.

3. The method according to claim 1, characterized in that The porosity , is the initial porosity , porosity change caused by calcium dissolution and porosity in the interface transition zone sum; The initial porosity , which is the sum of the initial capillary porosity and the initial gel porosity.

4. The method according to claim 3, characterized in that The initial capillary porosity and the initial gel porosity are both related to the water-cement ratio. and hydration level Related.

5. The method according to claim 3, characterized in that: Based on the distance between the interface transition zone and the aggregate surface The porosity , capillary porosity of cement paste , and the thickness of the interface transition zone, and the porosity of the interface transition zone is calculated. .

6. The method according to claim 1, characterized in that According to the Nernst-Einstein equation, Moment concrete section The effective diffusion coefficient of calcium ions at is calculated as follows: Moment concrete section The porosity Divide by the tortuosity , and then multiplied by the calcium ion diffusion coefficient in the concrete pore fluid.

7. The method according to claim 1, characterized in that The finite difference method is used to numerically solve the variable coefficient transmission model of calcium ion dissolution process in water delivery concrete pipe, including: The wall of the concrete water pipe is used as the solution area, time is used as the vertical coordinate, and the thickness of the concrete pipe wall in the pipe diameter direction is used as the horizontal coordinate. The solution area is evenly divided into multiple grids. For the variable coefficient transmission model, three layers of implicit difference are performed at any time step, thereby obtaining an iterative solution form of the variable coefficient transmission model; Using the chasing method, the calcium ion concentration at any time and any position in the concrete water pipe is obtained through programming. , and then calculate the solid calcium content at any time and any position in the concrete water pipe , porosity , tortuosity , diffusion coefficient ; in, are the coordinates of the grid.

8. A numerical simulation system for the calcium dissolution process of a concrete water pipe, characterized in that: include: The construction unit is used to establish a variable coefficient transmission model for the calcium ion dissolution process in the water delivery concrete pipe according to the calcium dissolution mechanism under water erosion, the law of conservation of mass and Fick's second law, combined with the solid-liquid equilibrium relationship of calcium in concrete; A solution unit is used to numerically solve the variable coefficient transmission model of calcium ion dissolution process in water delivery concrete pipe by using finite difference method; The expression of the variable coefficient transmission model is as follows: ， In the formula, is the coordinate of the concrete cross section, i.e. the thickness of the concrete wall in the diameter direction of the concrete water pipe; for Moment concrete section The calcium ion concentration in the pore fluid at for Moment concrete section Solid phase calcium content at Abbreviated as , is the water-cement ratio Concrete Time Section The porosity at Abbreviated as ,yes Moment concrete section The effective diffusion coefficient of calcium ions at Porosity , tortuosity and temperature Related; , are the initial calcium ion concentration and the initial solid phase calcium content, respectively; and are the inner and outer diameters of the concrete water pipe respectively; is the initial calcium ion saturation concentration in the concrete pore fluid; and are the initial molar volume contents of calcium hydroxide CH and calcium silicate hydrate CSH in the concrete skeleton, respectively; , They are The calcium ion concentration in the pore fluid and the solid calcium content at the starting position at time t; is the diffusion coefficient of calcium ions in the ambient water in the tube; is the concentration of calcium ions in the ambient water in the tube; It is the calcium ion exchange rate at the contact surface between the inner wall of the concrete pipe and water, that is, the speed at which calcium ions in the pore fluid flow into the water; The critical content of solid calcium for the inner wall boundary of the concrete pipe to move; is the water flow velocity in the pipe.

9. An electronic device, characterized in that: include: a memory for storing instructions executed by one or more processors of the electronic device; The processor, when the processor executes the instructions in the memory, can enable the electronic device to implement the steps of any one of the methods described in claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores instructions, which implement the steps of the method according to any one of claims 1 to 7 when executed on a computer.

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