Inverse method for moisture diffusion coefficient of unsaturated hydraulic concrete based on measured swelling strain

Abstract

The present invention provides a method for inverting the water diffusion coefficient of unsaturated hydraulic concrete based on measured swelling strain, comprising the following steps: Step 1, establishing a mathematical optimization model; Step 2, constructing a basic parameter combination; Step 3, establishing a finite element model, inputting the orthogonally designed parameter combination into the water diffusion finite element model, and calculating the swelling strain of the concrete at different immersion times; Step 4, calculating the difference between the measured swelling strain and the calculated swelling strain at different immersion times, and constructing a neural network training sample; Step 5, establishing a neural network for inverting unsaturated hydraulic concrete, training the neural network, and testing the neural network; Step 6, inputting the optimal value of the difference between the measured swelling strain and the calculated swelling strain into the trained and tested neural network model for inversion. This method can accurately obtain the water diffusion coefficient of unsaturated concrete under the condition of non-destructive monitoring of concrete hydraulic structures, and is more suitable for actual engineering.

Description

Technical Field

[0001] The present invention relates to the field of numerical inversion analysis of concrete hydraulic structures, and in particular to an inversion method for moisture diffusion coefficient of unsaturated hydraulic concrete based on measured swelling strain. Background Art

[0002] The natural environment directly impacts the durability and safety of concrete structures. Hydraulic concrete, due to its chronic or periodic exposure to water, can be significantly affected by the transport of water within the concrete, including carbonization, structural stress and strain, freeze-thaw cycles, salt attack, and steel corrosion. The water diffusion coefficient is a key parameter for studying the transport of water within concrete.

[0003] Many scholars have conducted research on the acquisition of concrete moisture diffusion coefficient. In general, there are currently two main methods for the moisture diffusion coefficient of unsaturated concrete: one method is to use the traditional weighing method to obtain the saturation or water content of concrete at different times, and then obtain the moisture diffusion coefficient of concrete. The other method is to assume that the moisture inside the concrete specimen migrates in one dimension, and by monitoring the relative humidity inside the concrete under external moist conditions, the relative humidity at different positions inside the concrete is obtained (generally obtained by drilling holes and burying humidity sensors at different positions), and the moisture diffusion coefficient of concrete is obtained by combining numerical model inversion. For example, CN114895009A discloses a method for testing the moisture diffusion coefficient of concrete under surface negative pressure. The humidity sensor is cast at a specified position inside the concrete through a PVC pipe with a hole at the bottom, and the moisture diffusion coefficient is calculated based on the tested humidity data.

[0004] Because it is difficult to measure the concrete saturation or moisture content of actual concrete hydraulic structures at different times, the former method is difficult to apply to the acquisition of the moisture diffusion coefficient of actual concrete hydraulic structures. Although the inversion method based on the combination of measured relative humidity and numerical calculation to obtain the concrete moisture diffusion coefficient is an effective method, the current research focuses on the inversion analysis of the concrete moisture diffusion coefficient in a non-water-related state affected by ambient humidity. Moreover, the method of obtaining relative humidity destroys the original structure of the concrete. In actual concrete hydraulic structures, they are generally submerged in water and are essentially unsaturated water absorption. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an inversion method for the moisture diffusion coefficient of unsaturated hydraulic concrete based on the measured swelling strain, which realizes the accurate acquisition of the moisture diffusion coefficient of unsaturated concrete under the condition of non-destructive monitoring of concrete hydraulic structures, and is more suitable for actual engineering.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is: a method for inverting the moisture diffusion coefficient of unsaturated hydraulic concrete based on measured swelling strain, comprising the following steps:

[0007] Step 1: Establish a mathematical optimization model for the inversion of water diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete;

[0008] Step 2: Construct a basic parameter combination based on the orthogonal test and the range of the parameters to be inverted;

[0009] Step 3: Establish an unsaturated concrete finite element model based on step 1, input the orthogonal design parameter combination into the unsaturated concrete water diffusion finite element model one by one, and calculate the Gaussian point saturation of each unit of the concrete specimen. i , the change of concrete water content Δ is obtained from the porosity of concrete specimens w Then, the parameter combination of the orthogonal design is input into the finite element model for calculating the swelling stress and strain, and the swelling strain of the concrete at different immersion times is calculated;

[0010] Step 4: Measure the swelling strain of unsaturated hydraulic concrete at different immersion times, combine it with the swelling strain calculated in step 3, and calculate the difference between the measured swelling strain and the calculated swelling strain at different immersion times. Combine the difference with the corresponding parameters to construct a neural network training sample.

[0011] Step 5: Establish a neural network for inversion of the water diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete, train and test the neural network based on the neural network training samples in step 4, and obtain a reasonable neural network model;

[0012] Step 6. Input the appropriate value of the difference between the measured swelling strain and the calculated swelling strain at different immersion times into the trained and tested neural network model, optimize the inversion to obtain the moisture diffusion coefficient and swelling coefficient of unsaturated concrete, substitute the obtained parameters into the finite element model, calculate the swelling strain of concrete and compare it with the measured swelling strain to verify the rationality of the inversion analysis and calculated values.

[0013] In a preferred solution, in step 1, without considering the gravitational potential, the water diffusion of unsaturated concrete is described by the Richards equation, and then the Galerkin weighted residual method is used to obtain the saturation finite element calculation control equation:

[0014] (1);

[0015] in, , ,

[0016] ;

[0017] Where, i is the saturation, %; t is the time, the unit is s; x is the spatial position in the transmission direction, in m; D ij ( i ) is the water diffusion coefficient as a function of saturation; for isotropic water diffusion, D ij ( i ) degenerates into D ( i ); K i3 is the permeability coefficient related only to the third coordinate axis, that is, hydraulic conductivity. i ≠3, K i3 =0, when i =3, K i3 =K i3 ( i ); n i is the cosine of the normal to the boundary surface; q n is the single width flow of Γ2 on the flow boundary; NE is the total number of units; N m 、 N n is the unit shape function; Ω is the computational space domain; S is the calculation area;

[0018] use e Exponential function to describe the water diffusion coefficient D ( i ) and saturation relationship:

[0019] (2);

[0020] Where, D 0 is the concrete moisture diffusion coefficient, which is D ( i ) in m 2 / s; n The parameter that characterizes the shape of the water diffusion coefficient curve, namely the shape coefficient, is 6 to 9;

[0021] The nonlinear iteration of equation (1) is solved by the difference format to obtain the Gaussian point saturation of each unit of the concrete specimen i After that, the change of concrete water content Δ can be obtained from the porosity of concrete specimens w, and then by the expansion coefficient or w Get the swelling strain increment Δ e w :

[0022] (3);

[0023] Where, or w is the coefficient of expansion; w is the water content, %;

[0024] For complex stress states, the Poisson's ratio matrix is ​​introduced, and then the finite element governing equation for expansion stress and strain calculation can be obtained by the initial strain method:

[0025] (4);

[0026] in, ;

[0027] In the formula, [ K ] is the overall stiffness matrix; {Δ d n} is the node displacement increment; {Δ P n} w is the node load increment caused by the swelling strain increment; [ B ],[ D n ] are the geometric matrix and elastic matrix respectively; It is the swelling increment;

[0028] From the above formulas (1) and (4), the mathematical optimization model for the inversion of the moisture diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete can be obtained as follows:

[0029] (5);

[0030] Where, e w,C To calculate the swelling strain, 10 -6 ; e w,M is the measured swelling strain, 10 -6 ; Subscript l is the lower limit of the parameter, subscript u The upper limit of the parameter.

[0031] In the preferred solution, in step 2, the parameters to be inverted include the concrete moisture diffusion coefficient D 0. Shape coefficient n and coefficient of expansion or w .

[0032] In the preferred embodiment, in the step three, when establishing the unsaturated concrete finite element model, a finite element model for calculating moisture diffusion of unsaturated hydraulic concrete under immersion conditions is first established, the finite element model is meshed, the boundary conditions of the model under immersion conditions are set to the first type of boundary conditions, the surface saturation is 1, and a finite element model for calculating the expansion stress and strain of unsaturated hydraulic concrete is established based on the same finite element mesh as the finite element model for calculating moisture diffusion. The boundary conditions are determined to apply a vertical connecting rod constraint at the bottom of the model and a horizontal constraint at the horizontal middle section.

[0033] The present invention provides a method for inverting the moisture diffusion coefficient of unsaturated hydraulic concrete based on measured swelling strain. By establishing the relationship between the concrete moisture diffusion coefficient, swelling coefficient, and swelling strain, and employing a combination of "orthogonal design, neural network, and numerical calculation," a method for inverting the moisture diffusion coefficient of unsaturated hydraulic concrete based on measured swelling strain is proposed. The concrete swelling coefficient serves as a bridge between the moisture diffusion coefficient and swelling strain, indirectly obtaining the moisture diffusion coefficient of actual concrete hydraulic structures. Simultaneously, the measured swelling strain can be obtained by pre-embedded strain gauges to obtain the strain values ​​of the concrete at different times, thereby separating the measured swelling strain of the concrete. This method achieves real-time nondestructive monitoring of the hydraulic structure without damaging the original structure. The method accurately obtains the moisture diffusion coefficient of unsaturated concrete under nondestructive monitoring conditions, making it more suitable for practical engineering. Preferably, the moisture diffusion equation for unsaturated hydraulic concrete established based on the Richards equation is more suitable for describing the moisture diffusion process of concrete hydraulic structures under actual immersion conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The present invention will be further described below with reference to the accompanying drawings and examples:

[0035] Figure 1 This is the flow chart for inversion of moisture diffusion coefficient and expansion coefficient of unsaturated concrete;

[0036] Figure 2 is the concrete finite element mesh;

[0037] Figure 3 This is a comparison chart of the measured and calculated values ​​of the longitudinal expansion strain of concrete; DETAILED DESCRIPTION

[0038] A method for inverting the water diffusion coefficient of unsaturated hydraulic concrete based on measured swelling strain, combined with Figure 1 The following steps are included:

[0039] Step 1: Establish a mathematical optimization model for the inverse analysis of the water diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete. The saturation finite element calculation control equation is: , the finite element governing equation for swelling stress and strain calculation is: .

[0040] Without considering the gravity potential, the moisture diffusion of unsaturated concrete is described by the Richards equation, and then the Galerkin weighted residual method is used to obtain the governing equation for the finite element calculation of saturation:

[0041] (1);

[0042] in, , ,

[0043] ;

[0044] Where, i is the saturation, %; t is the time, the unit is s; x is the spatial position in the transmission direction, in m; D ij ( i ) is the water diffusion coefficient as a function of saturation; for isotropic water diffusion, D ij ( i ) degenerates into D ( i ); K i3 is the permeability coefficient related only to the third coordinate axis, that is, hydraulic conductivity. i ≠3, K i3 =0, when i =3, K i3 =K i3 ( i ); n i is the cosine of the normal to the boundary surface; q n is the single width flow of Γ2 on the flow boundary; NE is the total number of units; N m 、 N n is the unit shape function; Ω is the computational space domain; S is the calculation area;

[0045] use e Exponential function to describe the water diffusion coefficient D ( i ) and saturation relationship:

[0046] (2);

[0047] Where, D 0 is the concrete moisture diffusion coefficient, which is D ( i ) in m 2 / s; n The parameter that characterizes the shape of the water diffusion coefficient curve, namely the shape coefficient, is 6 to 9;

[0048] The nonlinear iteration of equation (1) is solved by the difference format to obtain the Gaussian point saturation of each unit of the concrete specimen i After that, the change of concrete water content Δ can be obtained from the porosity of concrete specimens w , and then by the expansion coefficient or w Get the swelling strain increment Δ e w :

[0049] (3);

[0050] Where, or w is the coefficient of expansion; w is the water content, %;

[0051] For complex stress states, the Poisson's ratio matrix is ​​introduced, and then the finite element governing equation for expansion stress and strain calculation can be obtained by the initial strain method:

[0052] (4);

[0053] in, ;

[0054] In the formula, [ K ] is the overall stiffness matrix; {Δ d n} is the node displacement increment; {Δ P n} w is the node load increment caused by the swelling strain increment; [ B ],[ D n ] are the geometric matrix and elastic matrix respectively; It is the swelling increment;

[0055] From the above formulas (1) and (4), the mathematical optimization model for the inversion of the moisture diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete can be obtained as follows:

[0056] (5);

[0057] Where, e w,C To calculate the swelling strain, 10 -6 ; e w,M is the measured swelling strain, 10 -6 ; Subscript l is the lower limit of the parameter, subscript u is the upper limit of the parameter, and the other symbols have the same meanings as before.

[0058] Step 2: Construct basic parameter combinations based on orthogonal test and the range of parameters to be inverted. Concrete moisture diffusion coefficient D 0. Shape coefficient n and coefficient of expansion or w These are the three key parameters for calculating swelling strain, and all of them have uncertainties, so they are taken as parameters to be inverted. D 0. n and or w The benchmark value and its value range are combined with the orthogonal design table to formulate different parameter combinations.

[0059] Step 3. Establish an unsaturated concrete finite element model according to step 1, perform finite element model mesh division, set the model boundary conditions under immersion conditions to the first type of boundary conditions, and the surface saturation to 1. Then, based on the same finite element mesh as the water diffusion calculation finite element model, establish an unsaturated hydraulic concrete expansion stress and strain calculation finite element model, and determine the boundary conditions to apply a vertical connecting rod constraint at the bottom of the model and a horizontal constraint at the horizontal middle section. Use a numerical calculation program to calculate the water diffusion of unsaturated concrete, and then solve the saturation of each unit Gauss point of the concrete specimen. i .

[0060] Perform finite element calculation of concrete expansion stress and strain, input the orthogonal design parameter combination into the unsaturated concrete moisture diffusion finite element model one by one, and calculate the longitudinal expansion strain of concrete at different immersion times e w .

[0061] Step 4: Measure the swelling strain of unsaturated hydraulic concrete at different immersion times. Combined with the swelling strain calculated at different immersion times in step 3, calculate the difference between the measured swelling strain and the calculated swelling strain at different immersion times. d w , which is combined with the corresponding parameters to construct the neural network training samples.

[0062] Step 5: Establish a neural network for inversion of water diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete, see Figure 1, according to the neural network training samples in step 4, the neural network is trained and tested to obtain a reasonable neural network model. The difference between the calculated value and the measured value of the longitudinal expansion strain of concrete at different times is used as input, and the corresponding D 0. n 、 or w As output. Using the neural network toolbox in MATLAB, the training samples were normalized and input into the BP neural network model for training and testing. After iteration, the mean square error was reduced to below 0.01, thus establishing the difference between the calculated value and the measured value of the longitudinal expansion strain of concrete. d w The nonlinear mapping relationship between the moisture diffusion coefficient and the expansion coefficient of unsaturated hydraulic concrete.

[0063] Step 6: Input the appropriate value of the difference between the measured swelling strain and the calculated swelling strain under different immersion times into the trained and tested neural network model, so that the difference between the calculated swelling strain and the measured swelling strain in the longitudinal direction of concrete at different immersion times is d w The purpose is to obtain the optimal water diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete, so that the water content of the concrete can be reduced to 0. d w The values ​​are all minimum, which are input into the trained and tested neural network model to optimize the inversion and obtain the water diffusion coefficient of unsaturated hydraulic concrete. D 0. Shape coefficient n , expansion coefficient or w .

[0064] The parameters obtained by the inversion analysis were sequentially input into the unsaturated concrete moisture diffusion finite element model and the expansion stress and strain calculation finite element model for forward analysis. The calculated expansion strain values ​​for different immersion times were obtained. The calculated expansion strains for different immersion times were compared with the measured expansion strains at the corresponding times to verify the accuracy of the inversion results.

[0065] Now let’s explain it in detail through experimental data. The specific operations are as follows:

[0066] (1) Determination of inversion parameters and their value ranges

[0067] The size of the concrete specimen after immersion is 150mm×150mm×500mm. The three parameters are inverted based on the measured swelling strain of the concrete specimen. According to the trial analysis, the D 0. n and or w The benchmark values ​​and their ranges are shown in Appendix 1.

[0068]

[0069] (2) Orthogonal design combination of inversion parameters

[0070] According to the parameter reference values ​​and their ranges determined in Appendix 1, combined with the three-factor four-level orthogonal design table L 16 (3 4 ) 16 different parameter combinations were proposed, as shown in Appendix 2.

[0071]

[0072] (3) Establishment of finite element model of unsaturated hydraulic concrete

[0073] The 150mm×150mm×500mm prism specimen after immersion in water is simplified to a 150mm×500mm plane. The model is meshed using isoparametric quadrilateral elements, with a total of 1988 isoparametric quadrilateral elements and 1890 nodes. Figure 2 Since the specimen is completely immersed in water, the boundary condition is the first type of boundary condition, that is, the saturation of the specimen surface is 1.

[0074] Based on the same finite element mesh as the water diffusion model, a finite element model for calculating the expansion stress and strain of unsaturated hydraulic concrete was established. The boundary condition was a vertical link constraint applied to the bottom. Considering the symmetry of the expansion strain, a horizontal constraint was applied to the horizontal middle section of the specimen. Referring to the elastic modulus experimental research of concrete with the same raw materials and mix ratio, the Poisson's ratio of concrete was set to 0.168, and the variation of the elastic modulus of concrete with age is as follows:

[0075] (6)

[0076] Where, E is the elastic modulus, GPa; is the age, in d.

[0077] A numerical calculation program was used to calculate the water diffusion of unsaturated concrete, thereby solving the saturation of each Gaussian point of the concrete specimen, and then performing finite element calculation of concrete expansion stress and strain. During the numerical calculation, the initial saturation of the cubic specimen formed and cured under the same conditions was measured to be 86.3%, the porosity was 0.1, and the dry density of the concrete was 2380kg / m 3 .

[0078] (4) Establishment of inversion neural network model

[0079] Input the parameters in Appendix 2 one by one into the above-established unsaturated hydraulic concrete water diffusion finite element model and expansion stress and strain calculation finite element model, and calculate the longitudinal expansion strain of concrete under different immersion days (3d, 7d, 14d, 21d, 28d, 30d) e w , as shown in Appendix 3.

[0080]

[0081] Combined with the measured swelling strain under different immersion days, it is easy to calculate the difference between the calculated longitudinal swelling strain of concrete under typical immersion days and the measured swelling strain. d w , as shown in Appendix 4.

[0082]

[0083] The six differences between the calculated longitudinal swelling strain values ​​of concrete for typical immersion days in Appendix 4 and the measured values ​​are used as input, and the corresponding D 0. n 、 or w As the output, a neural network for inversion of the water diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete is established, as shown in the attached figure. Figure 1 Using the neural network toolbox in MATLAB, the training samples were normalized and input into the BP neural network model for training and testing. After iteration, the mean square error was reduced to below 0.01, thus establishing the difference between the calculated value and the measured value of the longitudinal expansion strain of concrete. d w The nonlinear mapping relationship between the moisture diffusion coefficient and the expansion coefficient of unsaturated hydraulic concrete.

[0084] (5) Parameter inversion results

[0085] In order to obtain the optimal water diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete, it is theoretically necessary to make the water diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete under 6 typical immersion days d w Take the minimum value, so let d w 0 respectively, and input them into the trained and tested neural network model to obtain the water diffusion coefficient of unsaturated hydraulic concrete by inversion. D 0. Shape coefficient n , expansion coefficient or w 3.98×10 -12 m 2 / s, 6.07 and 3.08×10 -3 .

[0086] (6) Verification of inversion results

[0087] The parameters obtained by the above inversion are sequentially input into the unsaturated concrete moisture diffusion finite element model and the expansion stress and strain calculation finite element model for forward analysis calculation to obtain the expansion strain calculation value at the typical time node. The calculated expansion strain at the typical time node is compared with the measured expansion strain, as shown in the attached figure. Figure 3 shown.

[0088] By the attached Figure 3 It can be seen that the calculated swelling strain at the typical time node is in good agreement with the measured swelling strain, with the root mean square error (RMSE) of 0.541 and the determination coefficient (C R 2 It is 0.998. Therefore, it can be seen that the finite element calculation model for moisture diffusion and swelling strain calculation of unsaturated concrete established in this patent is effective.

Claims

1. A method for inverting the water diffusion coefficient of unsaturated hydraulic concrete based on measured swelling strain, characterized in that: The steps include: Step 1: Establish a mathematical optimization model for the inversion of water diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete; Step 2: Construct a basic parameter combination based on the orthogonal test and the range of the parameters to be inverted; Step 3: Establish an unsaturated concrete finite element model based on step 1, input the orthogonal design parameter combination into the unsaturated concrete water diffusion finite element model one by one, and calculate the Gaussian point saturation of each unit of the concrete specimen. θ , the change of concrete water content Δ is obtained from the porosity of concrete specimens w Then, the parameter combination of the orthogonal design is input into the finite element model for calculating the swelling stress and strain, and the swelling strain of the concrete at different immersion times is calculated; In the step 3, when establishing the unsaturated concrete finite element model, first establish a finite element model for calculating water diffusion of unsaturated hydraulic concrete under immersion conditions, perform meshing of the finite element model, set the model boundary conditions under immersion conditions to be first-class boundary conditions, the surface saturation to 1, and establish a finite element model for calculating the expansion stress and strain of unsaturated hydraulic concrete based on the same finite element mesh as the water diffusion calculation finite element model, and determine the boundary conditions as applying a vertical connecting rod constraint at the bottom of the model and applying a horizontal constraint to the horizontal middle section; Step 4: Measure the swelling strain of unsaturated hydraulic concrete at different immersion times, combine it with the swelling strain calculated in step 3, and calculate the difference between the measured swelling strain and the calculated swelling strain at different immersion times. Combine the difference with the corresponding parameters to construct a neural network training sample. Step 5: Establish a neural network for inversion of the water diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete, train and test the neural network based on the neural network training samples in step 4, and obtain a reasonable neural network model; Step 6. Input the appropriate value of the difference between the measured swelling strain and the calculated swelling strain at different immersion times into the trained and tested neural network model, optimize the inversion to obtain the moisture diffusion coefficient and swelling coefficient of unsaturated concrete, substitute the obtained parameters into the finite element model, calculate the swelling strain of concrete and compare it with the measured swelling strain to verify the rationality of the inversion analysis and calculated values.

2. The method for inverting the water diffusion coefficient of unsaturated hydraulic concrete based on measured swelling strain according to claim 1 is characterized in that: In the first step, without considering the gravity potential, the water diffusion of unsaturated concrete is described by the Richards equation, and then the Galerkin weighted residual method is used to obtain the saturation finite element calculation control equation: (1)； in, , , ； Where, θ is the saturation, %; t is the time, the unit is s; x is the spatial position in the transmission direction, in m; D ij ( θ ) is the water diffusion coefficient as a function of saturation; for isotropic water diffusion, D ij ( θ ) degenerates into D ( θ ); K i3 is the permeability coefficient related only to the third coordinate axis, that is, hydraulic conductivity. i ≠3, K i3 =0, when i =3, K i3 =K i3 ( θ ); n i is the cosine of the normal to the boundary surface; q n is the single width flow of Γ2 on the flow boundary; NE is the total number of units; N m 、 N n is the unit shape function; Ω is the computational space domain; S is the calculation area; use e Exponential function to describe the water diffusion coefficient D ( θ ) and saturation relationship: (2)； Where, D 0 is the concrete moisture diffusion coefficient, which is D ( θ ) in m 2 / s; n The parameter that characterizes the shape of the water diffusion coefficient curve, namely the shape coefficient, is 6 to 9; The nonlinear iteration of equation (1) is solved by the difference format to obtain the Gaussian point saturation of each unit of the concrete specimen θ After that, the change of concrete water content Δ can be obtained from the porosity of concrete specimens w , and then by the expansion coefficient η w Obtain the swelling strain increment Δ ε w : (3)； Where, η w is the coefficient of expansion; w is the water content, %; For complex stress states, the Poisson's ratio matrix is ​​introduced, and then the finite element governing equation for expansion stress and strain calculation can be obtained by the initial strain method: (4)； in, ; In the formula, [ K ] is the overall stiffness matrix; {Δ δ n } is the node displacement increment; {Δ P n } w is the node load increment caused by the swelling strain increment; [ B ],[ D n ] are the geometric matrix and elastic matrix respectively; It is the swelling increment; From the above formulas (1) and (4), the mathematical optimization model for the inversion of the moisture diffusion coefficient and expansion coefficient of unsaturated hydraulic concrete can be obtained as follows: (5)； Where, ε w,C To calculate the swelling strain, 10 -6 ; ε w,M is the measured swelling strain, 10 -6 ; Subscript l is the lower limit of the parameter, subscript u The upper limit of the parameter.

3. The method for inverting the water diffusion coefficient of unsaturated hydraulic concrete based on measured swelling strain according to claim 1 is characterized in that: In step 2, the parameters to be inverted include the concrete moisture diffusion coefficient D 0. Shape coefficient n and coefficient of expansion η w .

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