Calculation method and system for non-load structural design value of early temperature of wall

Abstract

The invention relates to a calculation method and system for a non-load structural design value of the early temperature of a wall, and belongs to the technical field of construction control. The calculation method comprises the steps that geometric parameters, material parameters, environmental parameters and hydration heat parameters of a concrete continuous wall are obtained; according to the material parameters, a thermal diffusion coefficient is calculated, and a heat production rate function changing along with time is generated; based on the geometric parameters, the material parameters and the environmental parameters, calculating a Pitot number, and defining dimensionless coordinates and dimensionless time; solving the characteristic equation according to the Pitot number to obtain a characteristic value sequence and a corresponding vibration mode function sequence; calculating a weight coefficient of each mode based on the initial temperature distribution and the vibration mode function sequence; and solving a time domain ordinary differential equation and applying convolution integration, generating a time-varying modal amplitude function sequence, synthesizing a dimensionless temperature field, determining a convergence solution through a truncated modal number, and converting the dimensionless temperature field into a physical temperature field for output. The early temperature gradient distribution rule of the wall can be accurately captured.

Description

Technical Field

[0001] The present application relates to the field of construction control technology, and in particular to a calculation method and system for early temperature non-load structural design values ​​of a wall. Background Art

[0002] During the construction of large-volume structures such as diaphragm concrete walls, the heat generated by cement hydration causes a sharp rise in internal temperature, while surface heat dissipation to the environment creates a temperature differential between the inside and outside. This uneven temperature field triggers thermal stresses. When the tensile stress exceeds the concrete's tensile strength, cracks form, seriously impacting the durability and safety of the structure. Therefore, accurately predicting the early-stage temperature distribution of concrete is a key prerequisite for crack prevention and control.

[0003] Currently, temperature calculation models for mass concrete are widely used in engineering practice. These models are derived based on the assumption of bidirectional symmetrical heat dissipation. Their boundary conditions assume uniform heat dissipation from both sides, and the heat transfer path is simplified to symmetrical diffusion from the center of the cross-section to the surface. However, the actual operating conditions of diaphragm walls in underground spaces differ fundamentally from these models. First, the thickness of diaphragm walls is much smaller than that of mass concrete structures. Their high specific surface area significantly improves heat dissipation efficiency, and the cooling rate increases sharply with decreasing wall thickness. Second, the thinness of the walls results in a strongly nonlinear temperature gradient through the thickness, with gradient values ​​much higher than those for mass concrete at the same temperature difference. These differences in boundary conditions and heat transfer paths lead to systematic deviations between the calculated results of existing models and the measured temperature field of diaphragm walls. In particular, the coupled effect of rapid surface cooling and delayed temperature rise in the core region prevents existing models from accurately capturing the early temperature gradient distribution of the wall, resulting in inaccurate cracking risk assessment. Summary of the Invention

[0004] In order to accurately capture the early temperature gradient distribution law of the wall, the present application provides a calculation method and system for the non-load structural design value of the early temperature of the wall.

[0005] In a first aspect, the present application provides a method for calculating the design value of the non-load structure of the early temperature of a wall, using the following technical solution: A calculation method for early-stage temperature non-load structural design values ​​of a wall, the calculation method comprising: Obtain the geometric parameters, material parameters, environmental parameters and hydration heat parameters of the concrete continuous wall; Calculating a thermal diffusivity coefficient based on the material parameters, and generating a heat generation rate function that varies with time based on the hydration heat parameters; Calculating a Biot number based on the geometric parameters, material parameters, and environmental parameters, and defining dimensionless coordinates and dimensionless time based on the geometric parameters and thermal diffusivity; Solving the characteristic equation according to the Biot number to obtain a sequence of characteristic values ​​and a corresponding sequence of vibration mode functions; Based on the initial temperature distribution and the mode function sequence, the weight coefficient of each mode is calculated by orthogonal integration; Solving a time-domain ordinary differential equation and applying convolution integral according to the heat production rate function, the eigenvalue sequence, and the weight coefficient to generate a time-varying modal amplitude function sequence; The dimensionless temperature field is synthesized by utilizing the time-varying modal amplitude function sequence and the mode shape function sequence, a converged solution is determined by truncating the modal number, and the dimensionless temperature field is converted into a physical temperature field for output.

[0006] By adopting the above technical solutions, a coupled calculation framework of an asymmetric heat dissipation boundary model for concrete continuous walls, a time-varying source term for hydration heat, and an eigenvalue expansion method is established, thus solving the boundary condition mismatch problem of the traditional large-volume concrete formula in continuous wall applications. The characteristic equation is used to accurately characterize the heat dissipation of one-sided convection, spatial discretization is achieved through orthogonal modal decomposition, and the transient effect of hydration heat release is captured in combination with Duhamel integral. Finally, the temperature field T(x,t) at any position-time is outputted with adaptive series truncation. Compared with the empirical formula, the method of the present application improves the temperature prediction accuracy to the theoretical solution level, significantly reduces the risk of cracks caused by temperature rise estimation deviations, and can provide a reliable data-driven decision-making basis for the early maintenance of underground projects.

[0007] In a second aspect, the present application provides a calculation system for determining the early temperature non-load structural design value of a wall, which adopts the following technical solution: A calculation system for obtaining early-stage temperature non-load structural design values ​​of a wall, the calculation system comprising: An acquisition module is used to obtain geometric parameters, material parameters, environmental parameters and hydration heat parameters of the concrete continuous wall; a heat generation rate function generating module, configured to calculate the thermal diffusion coefficient according to the material parameters, and generate a heat generation rate function that varies with time according to the hydration heat parameters; A Biot number calculation module, configured to calculate the Biot number based on the geometric parameters, material parameters, and environmental parameters; A dimensionless definition module, configured to define dimensionless coordinates and dimensionless time based on the geometric parameters and the thermal diffusivity; A characteristic solving module is used to solve the characteristic equation according to the Biot number to obtain a sequence of characteristic values ​​and a corresponding sequence of vibration mode functions; A weight coefficient calculation module, configured to calculate the weight coefficient of each mode by orthogonal integration based on the initial temperature distribution and the mode shape function sequence; a modal amplitude function sequence generation module, configured to solve a time-domain ordinary differential equation and apply convolution integral based on the heat production rate function, the eigenvalue sequence, and the weight coefficient, to generate a time-varying modal amplitude function sequence; A dimensionless temperature field synthesis module, used to synthesize a dimensionless temperature field using the time-varying modal amplitude function sequence and the mode shape function sequence; The physical temperature field output module is used to determine the converged solution by truncating the modal number and convert the dimensionless temperature field into a physical temperature field output. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 This is a first flow chart of a method for calculating the non-load structural design value of early-stage wall temperature in one of the embodiments of the present application.

[0009] Figure 2 This is a second flow chart of a method for calculating the non-load structural design value of early-stage wall temperature in one of the embodiments of the present application.

[0010] Figure 3 This is a third flow chart of a method for calculating the non-load structural design value of early-stage wall temperature in one of the embodiments of the present application. DETAILED DESCRIPTION

[0011] In order to make the purpose, technical solutions and advantages of this application more clear, the following Figure 1-3 It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application.

[0012] The embodiment of the present application discloses a method for calculating the non-load structural design value of the early temperature of a wall.

[0013] Reference Figure 1 , a calculation method for the non-load structural design value of the early temperature of the wall, the calculation method includes: Step S101, obtaining geometric parameters, material parameters, environmental parameters and hydration heat parameters of the concrete continuous wall; Among them, the geometric parameters include wall thickness L, material parameters include density ρ, specific heat capacity C and thermal conductivity k, environmental parameters include ambient temperature Te and surface heat exchange coefficient h, hydration heat parameters include cementitious material dosage per cubic meter W, total hydration heat Q and time coefficient z; Specifically, four types of physical essential parameters of the concrete continuous wall are systematically collected to construct a complete input domain of the temperature field. The geometric parameters (wall thickness L) define the spatial scale of heat conduction and directly affect the dimensionless process; the material parameters (ρ, C, k) jointly characterize the thermal inertia (the product of density and specific heat capacity) and thermal conductivity (thermal conductivity) of concrete, and the ratio of the two will derive the thermal diffusion coefficient α; the environmental parameters (Te, h) quantify the boundary heat dissipation intensity, where the heat exchange coefficient h is related to the surface Newton's cooling law; the hydration heat parameters (W, Q, z) are based on the chemical kinetics of cement and are calculated through an exponential decay model. Describe the time-varying characteristics of hydration heat release of cementitious materials.

[0014] It can be understood that the essence of this step is to establish a digital mapping of the physical world. For example, W (amount of adhesive used) directly determines the total heat release W×Q, while z (time coefficient) controls the heat release rate. The two together constitute the core driver of the internal heat source.

[0015] Step S102, calculating the thermal diffusion coefficient α according to the material parameters, and generating a heat generation rate function that varies with time according to the hydration heat parameters; The formula for the thermal diffusion coefficient α is α=k / (ρ·C); In the above formula, k is thermal conductivity, ρ is density, and C is specific heat capacity.

[0016] Specifically, the thermal diffusion coefficient α is the core control parameter of unsteady-state heat conduction. Its physical meaning is the propagation speed of temperature disturbance in the medium. Calculating this value can simplify the Fourier heat conduction equation into a standard diffusion form. v The generation of (t) relies on engineering modeling of hydration thermodynamics: Step S103, calculating the Biot number Bi based on the geometric parameters (wall thickness L), material parameters (thermal conductivity k), and environmental parameters (surface heat exchange coefficient h), and defining dimensionless coordinates and dimensionless time based on the geometric parameters (wall thickness L) and thermal diffusion coefficient α; Specifically, the calculation formula of the Biot number Bi is: The Biot number Bi is a competing parameter between boundary heat dissipation and internal heat conduction. Its numerical value determines the temperature distribution: when Bi→0, the surface temperature is uniform (ideal insulation); when Bi→∞, the surface temperature is equal to the ambient temperature (ideal heat dissipation). This parameter embeds the third type of boundary condition (convective heat transfer) into the eigenvalue problem and is the core feature that distinguishes it from the symmetrical heat dissipation of large-volume concrete. In addition, the dimensionless coordinate is defined as X=x / L, which compresses the spatial scale to [0,1] and eliminates the absolute size influence of the wall thickness L; the dimensionless time is defined as τ=αt / L 2 , the time required for heat diffusion to pass through the wall is α / L 2 is the benchmark scale time course.

[0017] In the above formula, h is the surface heat exchange coefficient, L is the wall thickness, k is the thermal conductivity, x is the spatial coordinate, and t is the time.

[0018] Step S104, solving the characteristic equation according to the Biot number Bi to obtain the eigenvalue sequence and the corresponding mode function sequence; Specifically, the formula for solving the characteristic equation according to the Biot number Bi is: ; in, is the nth item of the eigenvalue sequence, representing the spatial frequency of different modes, and the mode shape function describes the spatial form of the corresponding mode; the corresponding mode shape function sequence is: ; Among them, the orthogonality between the vibration modes is satisfied. , and are the vibration mode function sequences corresponding to the nth and mth terms respectively, and m and n are integers greater than or equal to 1.

[0019] Step S105, calculating the weight coefficient of each mode by orthogonal integration based on the initial temperature distribution and the mode shape function sequence; Specifically, the weight coefficient C n The calculation formula is: ; Where θ0(X) is the initial dimensionless temperature distribution, is the vibration mode function, is the norm Nn. In the above formula, the physical essence of the weight coefficient is the projection decomposition of the initial temperature field in the vibration mode space. Through the generalized Fourier series expansion in the Hilbert space, any initial distribution is expressed as a linear combination of the standard orthogonal basis. The coefficient C n This is the energy contribution weight of each mode. The integration process uses modal orthogonality to extract independent components. The numerator is the inner product of the initial temperature distribution and the mode function Xn, representing the spatial correlation between the two. The denominator is the modulus square of the mode function, which is used to normalize the contribution weights of different modes. This step is essentially a Fourier series expansion, which can transform any initial condition into the superposition initial value of the eigenmode.

[0020] Step S106 , solving the time domain ordinary differential equation and applying convolution integral according to the heat production rate function, the eigenvalue sequence and the weight coefficient, to generate a time-varying modal amplitude function sequence; Specifically, the formula of the time domain ordinary differential equation is: ; The expression for generating the time-varying modal amplitude function sequence by solving the time-domain ordinary differential equation and applying the convolution integral is: .

[0021] It should be noted that the core of this step is to establish a dynamic mapping relationship between hydration heat release and temperature evolution. Its mathematical basis is the modal amplitude ordinary differential equation derived from the separation of variables method, which reveals the dual composite response mechanism of the heat conduction system: on the one hand, the eigenvalue Characterizes the inherent thermal attenuation characteristics of each mode. The high-order mode corresponds to the high-frequency component with rapid decay, while the low-order mode dominates the long-term temperature rise behavior. On the other hand, the source term f n (τ) projects the spatially distributed heat source into the eigenmode space, quantifying the energy input of hydration exotherm to a specific mode.

[0022] The specific solution process uses the Duhamel convolution principle, whose physical essence is to characterize the thermal memory effect of the system: the modal amplitude at the current moment depends not only on the transient heat source intensity, but also on the cumulative effect of historical heat sources. The convolution kernel function As a decaying memory factor, it assigns greater weight to recent heat sources. Under this modeling approach, when the hydration heat release rate decays exponentially (controlled by the time coefficient z), the convolution integral can be solved analytically, completely avoiding numerical iteration. For complex heat release curves, efficient computation can be achieved through piecewise integration. This mechanism ultimately generates a sequence of time-varying modal amplitude functions. Its physical significance is to decouple the continuous spatiotemporal coupling problem into the time-domain evolution of independent modes, laying the foundation for temperature field reconstruction.

[0023] Step S107 , synthesizing a dimensionless temperature field using the time-varying modal amplitude function sequence and the mode shape function sequence, determining a converged solution by truncating the modal number, and converting the dimensionless temperature field into a physical temperature field for output.

[0024] Specifically, the conversion formula for converting the dimensionless temperature field into the physical temperature field output is: .

[0025] In the above formula, T e The holographic reconstruction of the temperature field is achieved by superposition of orthogonal modes. Its mathematical principle is derived from the core inference of the Sturm-Liouville theory: the complete orthogonal function system can accurately represent any physical field distribution. Modal superposition essentially involves performing a generalized inverse Fourier transform in Hilbert space. The reconstructed dimensionless temperature field strictly satisfies the governing equations and boundary conditions for heat conduction. Adaptive determination of the truncated modal number N is crucial for engineering accuracy: based on the eigenvalue spectral distribution, the contribution of higher-order modes decays exponentially with increasing n. Truncation is controlled by a relative error threshold, achieving a dynamic balance between computational efficiency and accuracy. The conversion of the physical temperature field relies on the principle of dimensional consistency. When reassigning the dimensionless solution to actual physical units, the construction of the characteristic temperature difference incorporates three key parameters: material thermal inertia, thermal conductivity, and heat generation intensity. This ensures that the output temperature T(x,t) strictly corresponds to the actual physical process. This process ultimately forms a spatially continuous, temporally evolving three-dimensional temperature field cloud map, which can be directly input into the stress calculation module to assess cracking risk.

[0026] In the above implementation, a coupled calculation framework of an asymmetric heat dissipation boundary model of a continuous concrete wall, a time-varying source term of hydration heat, and an eigenvalue expansion method is established to solve the boundary condition mismatch problem of the traditional large-volume concrete formula in the application of continuous walls. The characteristic equation is used to accurately characterize the heat dissipation of one-sided convection, spatial discretization is achieved through orthogonal modal decomposition, and the transient effect of hydration heat release is captured in combination with Duhamel integral. Finally, the temperature field T(x,t) at any position-time is output by adaptive series truncation. Compared with the empirical formula, the method of the present application improves the temperature prediction accuracy to the theoretical solution level, significantly reduces the risk of cracks caused by temperature rise estimation deviations, and can provide a reliable data-driven decision-making basis for the early maintenance of underground projects.

[0027] Reference Figure 2 As an implementation of step S102, the step of generating a heat production rate function that varies with time according to the hydration heat parameter includes: Step S201, calculating the adiabatic temperature rise function T according to the hydration heat parameter ad (t): ; In the above formula, W is the amount of cementitious material per cubic meter, Q is the total hydration heat, z is the time coefficient, and t is the time; It can be understood that the adiabatic temperature rise is calculated according to the above formula of the "Massive Concrete Construction Standard". The model uses the exponential term e -zt Approximate the self-deceleration characteristics of cement hydration; Step S202: Derivative the adiabatic temperature rise function to obtain the heat generation rate function: .

[0028] Specifically, its physical essence is the heat release power per unit volume of concrete per unit time (W / z³). This derivative relationship originates from the first law of thermodynamics: the internal energy increment under adiabatic conditions is equal to the heat release.

[0029] Reference Figure 3 As an implementation of truncating the modal number in step S107, the step of determining the truncated modal number includes: Step a: Set the initial modal number n=1 and the preset error threshold ; Among them, the fundamental mode (n=1) corresponds to the lowest-order vibration mode and occupies the dominant part of the temperature field energy. Starting from this mode ensures that the iteration path conforms to the energy attenuation priority of the physical system. Preset error threshold (Usually 10 −3 ~10 −5 ) is set based on the balance between engineering accuracy requirements and numerical stability: when the temperature field magnitude is 10 2 ℃, =10 −3 The corresponding absolute error is 0.1℃, which meets the sensitivity requirements of concrete temperature control specifications for crack control. The threshold is essentially the upper limit control parameter of the truncation remainder, and its mathematical meaning is equivalent to requiring the relative residual of the truncation series to be less than .

[0030] Step b: Calculate the modal amplitude function under the current modal number n and mode function ; Among them, the modal amplitude function is essentially the time domain energy weight of the nth-order mode, which is determined by the Duhamel convolution solution; the mode shape function is the spatial eigenfunction of the Sturm-Liouville eigenvalue problem, and its physical meaning is to describe the standing wave distribution of temperature along the wall thickness direction.

[0031] Step c, synthesize the approximate solution of the temperature field: ; In the above equation, the approximate solution to the synthetic temperature field is essentially a projection into a finite-dimensional Hilbert space. The characteristic function system {Φn} forms a complete orthogonal basis, and any temperature field that satisfies the boundary conditions can be expanded in this space. The approximate solution, truncated to order n, is equivalent to an optimal subspace approximation in the energy norm sense, and its convergence is guaranteed by the amplitude decay characteristics and mode shape orthogonality.

[0032] Step d, calculate the relative error of adjacent modal solutions as: , where θ (0) ≡0; The essence of defining relative error is the online diagnosis of series convergence. , indicating that the energy contribution of the newly added mode is negligible compared to the existing solution, satisfying the sufficient condition for numerical convergence. The underlying reason for using relative error (rather than absolute error) here is that the temperature field magnitude varies dramatically over time and space (for example, the temperature rise at the center during initial curing can reach 50°C, while the surface only rises by 10°C), and relative quantities can adaptively match local sensitivity.

[0033] Step e, if , then jump to step f; otherwise jump to step g; Step f, determining the truncated mode number N=n; In step g, set n=n+1 and return to step b.

[0034] In the above steps, as the Bi number increases (e.g., due to thick walls or weak convection), the eigenvalues ​​λn become denser, requiring more modes to capture boundary layer effects. The iterative mechanism automatically adapts to this demand. The loop structure in this step essentially establishes a greedy algorithm framework: it progressively sweeps from lower-order to higher-order modes, targeting the cutoff point with minimal computational cost while maintaining accuracy.

[0035] The above implementation utilizes a closed-loop control mechanism consisting of progressive modal expansion, incremental error diagnosis, and adaptive truncation, based on strict series convergence criteria. This reduces the computational complexity to 1 / 10 to 1 / 50 of the full modal solution while ensuring accurate temperature field calculations. As the hydration heat release rate changes, the system automatically adjusts the number of modes to capture transient details of the rapid temperature rise process. As the wall thickness L increases, the number of modes is adaptively increased by redistributing the eigenvalues ​​λn, avoiding overfitting in thin walls and underfitting in thick walls.

[0036] The embodiment of the present application also discloses a calculation system for obtaining the design value of the non-load structure of the early temperature of the wall.

[0037] A calculation system for obtaining early-stage temperature non-load structural design values ​​of a wall, the calculation system comprising: An acquisition module is used to obtain geometric parameters, material parameters, environmental parameters and hydration heat parameters of the concrete continuous wall; A heat generation rate function generation module is used to calculate the thermal diffusion coefficient based on material parameters and generate a time-varying heat generation rate function based on hydration heat parameters; Biot number calculation module, used to calculate Biot number based on geometric parameters, material parameters and environmental parameters; Dimensionless definition module, used to define dimensionless coordinates and dimensionless time based on geometric parameters and thermal diffusivity; The characteristic solving module is used to solve the characteristic equation according to the Biot number to obtain the characteristic value sequence and the corresponding vibration mode function sequence; The weight coefficient calculation module is used to calculate the weight coefficient of each mode through orthogonal integration based on the initial temperature distribution and the vibration mode function sequence; The modal amplitude function sequence generation module is used to solve the time domain ordinary differential equation and apply convolution integral based on the heat production rate function, eigenvalue sequence and weight coefficient to generate the time-varying modal amplitude function sequence; Dimensionless temperature field synthesis module, used to synthesize dimensionless temperature field using time-varying modal amplitude function sequence and vibration shape function sequence; The physical temperature field output module is used to determine the converged solution by truncating the modal number and convert the dimensionless temperature field into a physical temperature field output.

[0038] A calculation system for determining the non-load structural design value of early-stage wall temperature in an embodiment of the present application can implement any of the above-mentioned calculation methods, and the specific working processes of each module in the calculation system can refer to the corresponding processes in the above-mentioned method embodiments.

[0039] In the several embodiments provided in this application, it should be understood that the provided methods and systems can be implemented in other ways. For example, the system embodiments described above are merely illustrative; for example, the division of a module is merely a logical functional division, and in actual implementation, other division methods may be used, such as combining or integrating multiple modules into another system, or ignoring or not implementing certain features.

[0040] The above are all preferred embodiments of the present application and are not intended to limit the scope of protection of this application. Unless otherwise specified, any feature disclosed in this specification (including the abstract and drawings) may be replaced by other equivalent or similar features. In other words, unless otherwise specified, each feature is merely an example of a series of equivalent or similar features.

Claims

1. A calculation method for the design value of the non-load structure of the early temperature of the wall, characterized in that: The calculation method includes: Obtain the geometric parameters, material parameters, environmental parameters and hydration heat parameters of the concrete continuous wall; Calculating a thermal diffusivity coefficient based on the material parameters, and generating a heat generation rate function that varies with time based on the hydration heat parameters; Calculating a Biot number based on the geometric parameters, material parameters, and environmental parameters, and defining dimensionless coordinates and dimensionless time based on the geometric parameters and thermal diffusivity; Solving the characteristic equation according to the Biot number to obtain a sequence of characteristic values ​​and a corresponding sequence of vibration mode functions; Based on the initial temperature distribution and the mode function sequence, the weight coefficient of each mode is calculated by orthogonal integration; Solving a time-domain ordinary differential equation and applying convolution integral according to the heat production rate function, the eigenvalue sequence, and the weight coefficient to generate a time-varying modal amplitude function sequence; The dimensionless temperature field is synthesized by utilizing the time-varying modal amplitude function sequence and the mode shape function sequence, a converged solution is determined by truncating the modal number, and the dimensionless temperature field is converted into a physical temperature field for output.

2. The calculation method for determining the design value of the non-load structure of the early temperature of a wall according to claim 1 is characterized by: The formula of the thermal diffusion coefficient α is α=k / (ρ·C); wherein k is thermal conductivity, ρ is density, and C is specific heat capacity.

3. The calculation method for the non-load structural design value of the early temperature of a wall according to claim 1 is characterized in that: The step of generating a heat production rate function that varies with time according to the hydration heat parameter comprises: Calculate the adiabatic temperature rise function T according to the hydration heat parameter ad (t): ； In the above formula, W is the amount of cementitious material per cubic meter, Q is the total hydration heat, z is the time coefficient, and t is the time; The heat generation rate function is obtained by differentiating the adiabatic temperature rise function: 。 4. The calculation method for the non-load structural design value of the early temperature of a wall according to claim 1 is characterized in that: The calculation formula of the Biot number Bi is: ; The dimensionless coordinate is defined as X=x / L; the dimensionless time is defined as τ=α·t / L 2 ; In the above formula, h is the surface heat exchange coefficient, L is the wall thickness, k is the thermal conductivity, x is the spatial coordinate, and t is the time.

5. The calculation method for the design value of the non-load structure of the early temperature of the wall according to claim 4 is characterized in that: The formula for solving the characteristic equation according to the Biot number Bi is: ； in, is the nth item of the eigenvalue sequence, and the corresponding vibration mode function sequence is: ； Among them, the orthogonality between the vibration modes is satisfied. , and are the vibration mode function sequences corresponding to the nth and mth terms respectively, and m and n are integers greater than or equal to 1.

6. The calculation method for the non-load structural design value of the early temperature of a wall according to claim 5 is characterized in that: The weight coefficient C n The calculation formula is: ； Where θ0(X) is the initial dimensionless temperature distribution, is the vibration mode function, is the norm Nn.

7. The calculation method for the non-load structural design value of the early temperature of a wall according to claim 6 is characterized in that: The formula of the time domain ordinary differential equation is: ； Solving the time domain ordinary differential equation and applying the convolution integral, the expression for the time-varying modal amplitude function sequence is generated as follows: 。 8. The calculation method for the design value of the non-load structure of the early temperature of a wall according to claim 7 is characterized in that: The step of determining the truncated modal number comprises: Step a. Set the initial modal number n=1 and the preset error threshold ε; Step b. Calculate the modal amplitude function under the current modal number n and mode function ; Step c. Synthesize the approximate solution of the temperature field: ； Step d. Calculate the relative error of adjacent modal solutions as: , where θ (0) ≡0; Step e. If , then determine the truncated mode number N=n; otherwise, set n=n+1 and return to step b.

9. The calculation method for the non-load structural design value of early-stage wall temperature according to claim 8 is characterized in that: The conversion formula for converting the dimensionless temperature field into the physical temperature field output is: ； In the above formula, T e is the ambient temperature.

10. A calculation system for early temperature non-load structural design values ​​of walls, characterized by: The computing system includes: An acquisition module is used to obtain geometric parameters, material parameters, environmental parameters and hydration heat parameters of the concrete continuous wall; a heat generation rate function generating module, configured to calculate the thermal diffusion coefficient according to the material parameters, and generate a heat generation rate function that varies with time according to the hydration heat parameters; A Biot number calculation module, configured to calculate the Biot number based on the geometric parameters, material parameters, and environmental parameters; A dimensionless definition module, configured to define dimensionless coordinates and dimensionless time based on the geometric parameters and the thermal diffusivity; A characteristic solving module is used to solve the characteristic equation according to the Biot number to obtain a sequence of characteristic values ​​and a corresponding sequence of vibration mode functions; A weight coefficient calculation module, configured to calculate the weight coefficient of each mode by orthogonal integration based on the initial temperature distribution and the mode shape function sequence; a modal amplitude function sequence generation module, configured to solve a time-domain ordinary differential equation and apply convolution integral based on the heat production rate function, the eigenvalue sequence, and the weight coefficient, to generate a time-varying modal amplitude function sequence; A dimensionless temperature field synthesis module, used to synthesize a dimensionless temperature field using the time-varying modal amplitude function sequence and the mode shape function sequence; The physical temperature field output module is used to determine the converged solution by truncating the modal number and convert the dimensionless temperature field into a physical temperature field output.

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