Energy pile (column) multilayer heat exchange thermal-mechanical coupling calculation method

Abstract

The invention discloses an energy pile (column) multilayer heat exchange thermal-mechanical coupling calculation method, and relates to the technical field of geothermal energy utilization. The method comprises the following steps: acquiring layered thermophysical properties and mechanical parameters of an energy pile and a rock-soil body, and performing numerical simulation on the energy pile and a peripheral transient temperature field thereof by adopting a layered heat transfer model; deriving a Green function considering a non-uniform anisotropic medium, solving the transient heat conduction model, obtaining temperature field distribution at any moment in the computational domain, and calculating the temperature stress of the energy pile body; by establishing a load transfer model and a shearing model of a pile-soil contact surface, pile body axial force, displacement and pile-soil side frictional resistance are obtained, and the heat exchange performance and mechanical safety of the energy pile are comprehensively evaluated. According to the method, the defects of analysis in the aspects of layered media and complex interaction in the prior art are overcome, the precision and reliability of energy pile design are remarkably improved, and a scientific basis is provided for optimizing energy pile system design and structural safety.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of efficient utilization of geothermal energy, and particularly relates to a multi-layer heat exchange thermodynamic coupling calculation method for energy piles (columns). BACKGROUND

[0002] In urban construction, energy piles, as a new type of structure combining building foundation functions and geothermal energy utilization functions, have attracted more and more attention. Energy piles achieve building heating or cooling by embedding heat exchange pipes in the pile body and exchanging heat with the constant temperature of the stratum soil. However, the long-term service performance and safety of energy piles, especially the thermodynamic coupling response of energy piles under the combined action of thermal cyclic loads and upper structure loads, is a complex and key problem. Accurate prediction of the heat exchange performance and mechanical response of energy piles is of great significance for optimizing design and ensuring operation safety. Traditional energy pile design methods usually decouple thermal and mechanical behaviors, ignoring the influence of temperature changes on the mechanical properties of the pile body and the slight feedback of mechanical response on thermal performance. At the same time, in the multi-layer heat exchange structure, the nonlinear coupling of the thermal-mechanical coupling effect leads to significant errors in the estimation of temperature field, pressure field and thermal resistance by traditional single-layer approximation.

[0003] Chinese patent CN101408359B discloses a pile-buried spiral pipe type ground source heat pump system and a heat transfer model of its geothermal heat exchanger. The patent aims to solve the problem of heat transfer efficiency calculation of the pile foundation spiral pipe ground source heat pump system by establishing a heat transfer model. The model can simulate the heat transfer characteristics of spiral pipes with different burial depths and pipe diameters, thereby optimizing the design of the geothermal heat exchanger. This technology to some extent solves the problem of establishing a heat transfer model for the spiral pipe type ground source heat pump system, and can analyze the heat exchange performance of the geothermal heat exchanger. However, this patent mainly focuses on the heat transfer model of the geothermal heat exchanger, and does not deeply consider the complexity of actual geological conditions, such as the multi-layer structure of rock-soil mass, the non-homogeneity of thermal physical parameters, and the anisotropic difference of horizontal and vertical thermal conductivity coefficients. Although some studies have begun to try thermodynamic coupling analysis, few studies have integrated geological layered heat transfer, temperature stress calculation considering soil constraints, and nonlinear pile-soil interface model nested iterative solution into a unified calculation framework and conducted comprehensive evaluation. SUMMARY

[0004] In view of this, the present application proposes a multi-layer heat exchange thermodynamic coupling calculation method for energy piles (columns), which improves through a multi-layer coupling model and adaptive solution, effectively making up for the shortcomings of existing calculation methods in heat exchange calculation and mechanical safety evaluation of energy piles under complex layered geological conditions, thereby improving the accuracy of energy pile heat exchange calculation and the scientificity of structural mechanics design.

[0005] This invention provides a method for calculating the thermo-mechanical coupling of multi-layer heat exchange in energy piles (piles), the steps of which are as follows: S1 defines the computational domain and mesh generation for the energy pile and its surrounding soil and rock mass; S2 acquires the thermophysical and mechanical parameters of the energy pile, the pile body material, and each layer of the soil and rock mass, including the thermal conductivity in the horizontal and vertical directions of each layer of the soil and rock mass. S3 establishes a transient thermal conductivity model of the energy pile and its surrounding soil and rock mass based on the heat transfer boundary conditions of the energy pile, and considers the difference in thermal conductivity of each layer of the soil and rock mass in the horizontal and vertical directions. S4 uses the Green's function method to solve the transient heat conduction model and obtains the temperature field distribution at any time within the computational domain; S5 calculates the temperature stress of each section of the energy pile body based on the temperature field distribution; S6 establishes a load transfer model for energy piles under vertical loads and temperature stresses, and introduces a nonlinear shear model of the pile-soil interface considering the softening effect. The shear model can describe the entire process of the pile-soil interface from elasticity, peak strength to softening and finally residual strength. S7 uses an iterative calculation method to solve the load transfer model and obtain the axial force, displacement, and pile-soil friction of the energy pile. S8 comprehensively evaluates the heat exchange performance and mechanical safety of the energy pile based on the axial force, displacement, and pile-soil friction.

[0006] Furthermore, the transient heat conduction model is a non-uniform, anisotropic heat conduction equation established in cylindrical coordinates, and its calculation equation is as follows: Where T is temperature, t is time, r is the radial coordinate, and z is the axial coordinate. Let z be the density at depth z. Let z be the specific heat capacity at depth z. Let z be the horizontal thermal conductivity at depth z. Let be the vertical thermal conductivity at depth z, and Q be the internal heat source term.

[0007] Furthermore, the nonlinear shear model of the pile-soil contact surface considering the softening effect is expressed in piecewise function form, as follows: in, Shear stress at the pile-soil interface, unit: ; s represents the relative displacement between the pile and the soil, in mm; This represents the peak shear stress. Residual strength, in units of ; To achieve residual strength at the pile-soil interface The relative displacement at time t is expressed in mm; a, b, and c are fitting parameters used to describe the shape of the curve.

[0008] Furthermore, the Green's function method solves the transient heat conduction model by deriving the Green's function considering the non-uniform anisotropic medium, thereby obtaining a high-precision temperature field distribution.

[0009] Furthermore, the thermophysical parameters of each layer of the rock and soil mass include density, specific heat capacity, horizontal thermal conductivity, and vertical thermal conductivity; the mechanical parameters include elastic modulus, Poisson's ratio, initial effective stress of the formation, and initial horizontal effective stress of the formation.

[0010] Furthermore, the temperature stress at each cross-section of the energy pile is calculated using the principle of linear thermal expansion. Based on the elastic modulus of the pile concrete Coefficient of thermal expansion and temperature change Confirmed, the calculation formula is: .

[0011] Furthermore, the load transfer model divides the pile body into multiple discrete elements and considers the pile's self-weight. Within each element, the pile axial force, pile side friction, and pile displacement satisfy equilibrium and deformation compatibility conditions. The equilibrium equation and deformation compatibility equation can be expressed as follows: in, For the axial force of the pile body, Let be the shear stress at the pile-soil interface, C be the pile perimeter, W be the self-weight per unit length of the pile, E be the elastic modulus of the pile, A be the cross-sectional area of ​​the pile, w be the pile displacement, and z be the axial coordinate.

[0012] Furthermore, the iterative calculation method includes: initially assuming pile displacement, calculating pile side friction, calculating pile axial force, and then back-calculating pile displacement based on pile axial force, until the pile displacement calculated in the previous two calculations reaches the preset convergence standard.

[0013] Furthermore, when comprehensively evaluating the heat exchange performance of the energy pile, the evaluation indicators include average heat exchange power, cumulative heat exchange, and the fitting results of the thermal response test.

[0014] Furthermore, when conducting a comprehensive assessment of the mechanical safety of the energy pile, the assessment indicators include the maximum axial force of the pile, the maximum bending moment, the settlement, and the shear stress distribution at the pile-soil contact surface.

[0015] The present invention has the following advantages over the prior art: This approach fully considers the differences in thermal conductivity between different layers of soil and rock in the horizontal and vertical directions within the transient thermal conductivity model, and accurately captures the heterogeneity of the strata. By constructing and solving a thermal conductivity model that reflects these complex characteristics, this method can accurately simulate the subtle differences in heat propagation along different directions in layered soil and rock masses, significantly improving the accuracy of temperature field distribution prediction for energy piles, especially in practical engineering contexts with complex geological structures or groundwater flow. This thermal model, which better reflects the actual geological characteristics, provides a more realistic and reliable temperature load input for subsequent mechanical calculations, avoiding mechanical analysis errors caused by inaccurate temperature field predictions, thereby reducing potential safety hazards and resource waste during the design phase.

[0016] Secondly, given the complex nonlinear behavior that the pile-soil interface may undergo during the service life of energy piles, especially the strength degradation or softening phenomena that easily occur under long-term temperature cycling and vertical loads, this scheme introduces a nonlinear shear model of the pile-soil interface considering the softening effect into the load transfer model. This model, using a piecewise function form, can comprehensively and precisely describe the entire process of the pile-soil interface from elasticity and peak strength to softening and residual strength. Compared with traditional simplified models, the simulation of the frictional performance between the pile and the surrounding soil under radial deformation is closer to reality, and can more accurately reflect the interaction forces between the pile and the soil under complex loads, especially the nonlinear changes and strength degradation trends of pile side friction under large displacements or cyclic loads. This results in higher accuracy in calculating pile axial force, displacement, and pile-soil side friction, effectively filling the gaps in existing technologies for assessing the internal forces and displacements of energy piles under thermal coupling. Through precise characterization of the pile-soil interface behavior, this method can more reliably assess the settlement and stability of energy piles, providing crucial support for ensuring their long-term service safety.

[0017] By organically combining a thermal model that considers the anisotropy and stratification of the soil and rock mass with a nonlinear shear model of the pile-soil interface that incorporates softening effects, this scheme achieves deep coupling of the thermal and mechanical responses of the energy pile. This coupled calculation can not only comprehensively and accurately evaluate the heat transfer performance of the energy pile, but also accurately predict its mechanical safety under the combined action of temperature stress and vertical load.

[0018] In summary, this invention provides an accurate, reliable, and highly valuable verification calculation method for the design, evaluation, and operation of energy piles by employing advanced heat conduction simulation and nonlinear pile-soil interaction models. This method has significant technical implications and practical benefits for promoting the development and application of renewable energy ground source heat pump systems. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the multilayer heat exchange thermodynamic coupling calculation method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the energy pile structure according to an embodiment of the present invention; Figure 3 This is a heat transfer model of a layered rock and soil instantaneous annular heat source according to an embodiment of the present invention; Figure 4 This is the pile side load transfer function in an embodiment of the present invention; Figure 5 The layered heat transfer model and embodiments of the present invention Comparison chart of model results. Detailed Implementation

[0021] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0022] This invention provides a thermo-mechanical coupling calculation method for multi-layer heat exchange in energy piles (columns), aiming to address the lack of mechanical safety assessments after the implantation of heat exchange pipes in energy piles (columns) and improve the accuracy of heat exchange calculations for energy piles under complex layered geological conditions. This method provides a precise verification calculation means by deeply coupling and analyzing the thermal and mechanical responses of the energy pile.

[0023] like Figure 1 As shown, this invention provides a method for calculating the thermo-mechanical coupling of multi-layer heat exchange in energy piles (columns), including the following steps: S1: Determine the computational domain and mesh generation for the energy pile and its surrounding soil and rock mass.

[0024] This step is fundamental to numerical simulation, aiming to construct a computational model that reflects the actual engineering conditions. Specifically, based on the actual dimensions of the energy pile (pile length and diameter) and the site's geological strata distribution, a three-dimensional computational domain is established. A structured mesh is used to divide the energy pile, heat exchange pipe, and surrounding soil and rock mass into meshes, ensuring that the mesh density of the contact surface between the heat exchange pipe and the pile body concrete, and the contact surface between the pile body and the soil and rock mass, meets the computational accuracy requirements.

[0025] S2: Obtain the thermophysical and mechanical parameters of the energy pile, the pile material, and each layer of the soil and rock mass.

[0026] In one implementation, the following key parameters need to be obtained for the energy pile and its surrounding soil and rock mass: The energy pile itself and its materials: mainly including the density, specific heat capacity, thermal conductivity, elastic modulus, Poisson's ratio, and coefficient of thermal expansion of the pile concrete.

[0027] The calculation parameters include: ① thermophysical parameters, such as pile / soil density, thermal conductivity, and specific heat capacity at constant pressure, referencing in-situ monitoring data; ② mechanical parameters, such as pile elastic modulus E, cross-sectional area A, effective friction angle φ, and cohesion c of the soil; ③ pile-soil shear model parameters. These parameters can be determined through inversion fitting of indoor tests, in-situ measurements, or numerical simulation results.

[0028] S3: Based on the heat transfer boundary conditions of the energy pile, establish a transient heat conduction model of the energy pile and its surrounding soil and rock.

[0029] This step aims to construct a mathematical model that can accurately describe the heat transfer process of the pile-soil system. This invention focuses on considering the differences in thermal conductivity between different layers of the soil and rock mass in the horizontal and vertical directions to more realistically reflect actual geological conditions.

[0030] As an underground heat exchange component, the energy pile's heat exchange process mainly relies on the flow of circulating liquid in the heat exchange pipes, which sequentially exchanges heat with the heat exchange pipes, the pile body concrete, and the surrounding soil and rock. Figure 2 , Figure 3 As shown. The entire heat transfer process can be divided into the following six stages: (1) convective heat transfer between the circulating liquid and the inner wall of the heat exchange tube; (2) heat conduction along the tube wall inside the heat exchange tube; (3) contact heat conduction between the outer wall of the heat exchange tube and the pile concrete; (4) heat conduction inside the pile concrete; (5) contact heat conduction between the outer wall of the pile and the surrounding rock; (6) heat conduction and diffusion process in the surrounding rock.

[0031] In one implementation, the transient heat conduction model is established in cylindrical coordinates. First, the heat transfer control equations, based on a transient annular heat source as the basic unit, can be expressed in initial form as follows: For the heat source located in the i-th layer, the heat transfer equation is: For the j-th layer without a heat source, the heat transfer equation is: in, and These represent the soil and rock temperatures of the i-th layer where the heat source is located and the j-th layer, respectively, in units of... ; and , respectively, are the thermal diffusivity in the horizontal and vertical directions of the i-th layer where the heat source is located. and These are the thermal diffusivity coefficients in the horizontal and vertical directions for the j-th layer, respectively, in units of... ; t is the time variable, in seconds; r is the radial coordinate, the horizontal distance from the axis of symmetry to a point, in meters; z is the axial coordinate, representing the depth of the point heat source, in meters; These are the radial and axial position coordinates of the heat source, respectively, both of which are fixed values ​​in meters; It is the Dirac function; For time The function represents an instantaneous pulse heat source.

[0032] To more generally describe the transient heat conduction process across the entire computational domain, the above equations can be transformed into expressions using thermal conductivity, density, and specific heat capacity. Based on the thermal diffusivity... The definition of is given by where k is the thermal conductivity, ρ is the density, and c is the specific heat capacity. Multiplying both sides of the above equation by ρ(z)c(z) and introducing the more general internal heat source term Q, we obtain a transient heat conduction model applicable to non-uniform, anisotropic media. This transient heat conduction model is expressed in cylindrical coordinates by the following non-uniform, anisotropic heat conduction equation, as follows: Figure 2 The schematic diagram of heat conduction of the energy pile shown is governed by the following equation: Where T is temperature, t is time, r is the radial coordinate, and z is the axial coordinate. Let z be the density at depth z. Let z be the specific heat capacity at depth z. Let z be the horizontal thermal conductivity at depth z. denoted as the vertical thermal conductivity at depth z, and Q is the internal heat source term, which is usually generated when there is heat exchange inside the heat exchange tubes of the pile body.

[0033] Simultaneously, the boundary conditions and initial conditions of the model need to be determined: the initial temperature is obtained through in-situ monitoring, assuming that the initial temperature of the computational domain is uniform; the convective heat transfer between the inner wall of the heat exchange tube and the circulating liquid is simplified as follows: Boundary conditions: heat flux density is known; formula form is: The surrounding rock is subjected to Dirichlet boundary conditions, and its temperature is known, representing the initial ground temperature. Simultaneously, considering the differences in thermal conductivity between different layers of the soil and rock mass in the horizontal and vertical directions, a governing equation is established based on Fourier's law of heat conduction. In low-permeability saturated soil layers, this can be simplified to a pure heat conduction equation. .

[0034] Boundary conditions: Setting boundary conditions is crucial, as it simulates the heat exchange between the computational domain and the external environment. These can be categorized into two types: Type I boundary conditions, namely Dirichlet boundary conditions, where the temperature at the boundary is known or a function of time t, suitable for situations where the specific temperature at the boundary can be determined after running for a period of time; and Type II boundary conditions, namely... Boundary conditions: The heat flux density at the boundary is known or is a function of time t. For heat convection between the heat exchange fluid and the inner wall of the heat exchange tube, it can be simplified to the heat flux density of the inner wall of the heat exchange tube; or the third type of boundary condition, namely the Cauchy boundary condition, where the temperature and heat transfer coefficient of the fluid medium in contact with the boundary are known.

[0035] Clearly, transient temperature fields under such complex geometric boundary conditions are not suitable for analytical solutions. The finite element method (FEM) is a better approach, employing a weighted residual method. To simplify the analysis or solution of the temperature increment field, the upper and lower boundaries of the computational region (e.g., the top z=0 and the bottom z=0) are considered. ) and radial far boundary (e.g., These boundaries can be set to constant temperature boundaries. For example, the temperature increment on these boundaries can be set to zero, i.e.: Where T(r,z,t) represents the temperature field, which depends on the radial coordinate r, the axial coordinate z, and the time t. r is the radial coordinate, representing the distance from the central axis to a point, and z is the axial coordinate, representing the depth. The total height of the medium. Let be the radius of the outer boundary.

[0036] This means that at these boundaries, the temperature remains constant relative to its initial value.

[0037] More specifically, for energy pile (column) problems, boundary conditions typically include heat transfer conditions at the contact surface between the pile and the soil / rock mass, usually assuming continuous temperature and heat flow, as well as heat exchange conditions between the pile top and the atmosphere or superstructure, such as convective heat transfer or at a given temperature, and heat transfer conditions between the pile bottom and deep soil. These specific boundary conditions will be selected based on the actual engineering conditions and calculation requirements.

[0038] S4: The transient heat conduction model is solved using the Green's function method to obtain the temperature field distribution at any time within the computational domain.

[0039] In one implementation, the Green's function method is used to solve the non-homogeneous, anisotropic transient heat conduction equation established in step S3. The Green's function method has the advantage of transforming complex partial differential equations into integral equations, and is particularly suitable for problems involving non-homogeneous equations and complex boundary conditions. Its core idea is to first construct a point source solution, i.e., the Green's function, that satisfies specific boundary conditions, and then obtain the temperature field distribution under arbitrary heat sources and boundary conditions through integral superposition. For the non-homogeneous, anisotropic medium considered in this invention, the derivation and construction of the Green's function are crucial to the solution, and its specific process requires customized mathematical processing based on the governing equations and boundary conditions.

[0040] In a preferred embodiment, the analytical form of the Green's function can be obtained by solving the equivalent problem without internal heat sources and using the method of separation of variables. For example, for layered media, the Green's function can be expressed as an infinite series, and its general analytical form is as follows: in, Indicates in ( Apply an instantaneous point heat source at point ) The temperature response at time t at (r,z); It is a zero-order Bessel function; Radial eigenvalues; It is an axial characteristic function; To and Relevant parameters; These are time-related characteristic values; These are the modal coefficients.

[0041] If the instantaneous heat source is in region 1, that is... Then the modal coefficients are: If the instantaneous heat source is located in region 2, that is Then the modal coefficients are: in, The normalization factor for the radial m-th mode is... is the normalization factor for the mn-th axial mode.

[0042] like Figure 3 As shown in the diagram, the discretization of the computational domain is illustrated by dividing the computational domain into a grid and marking the interface between the pile and the soil. After solving using the Green's function method, the temperature field distribution within the computational domain (including the interior of the energy pile and the surrounding soil and rock mass) at any time t can be obtained. This temperature field distribution forms the basis for subsequent mechanical response analysis.

[0043] In a preferred embodiment, the temperature field distribution is calculated as follows: Heat transfer model selection: A transient three-dimensional or two-dimensional axisymmetric heat transfer model is adopted to consider the heat transfer process of the pile body, backfill material, surrounding soil and rock, and fluid inside the pile.

[0044] This invention employs a heat transfer model that considers the layered characteristics of soil and rock masses. Based on the geological layering information obtained in step S1, this model can precisely consider the individual thermophysical parameters (such as thermal conductivity, specific heat capacity, and density) of different soil layers (e.g., sand, clay, rock, etc.), as well as the influence of groundwater flow on heat transfer. This model reflects the actual temperature field distribution more accurately than traditional homogeneous soil models or simplified models.

[0045] For comparison or verification, heat transfer models in existing literature can also be cited, such as The proposed model is used to verify the superiority or applicability of the hierarchical model of this invention.

[0046] Numerical simulation methods: The heat transfer model is discretized and solved using numerical methods such as the finite element method (FEM), finite difference method (FDM), or boundary element method (BEM).

[0047] Consider the heat source (heat exchange between the fluid inside the pile and the pile wall), thermal boundary conditions (such as surface temperature and deep isothermal boundary), and initial conditions (geothermal gradient).

[0048] The calculation parameters include: Thermal properties: Thermal conductivity, specific heat capacity, density, etc. of different soil layers obtained in steps S1 and S2.

[0049] Pile fluid parameters: The inlet temperature, flow rate, specific heat capacity, etc. of the heat exchange fluid set in step S3 are adopted.

[0050] Geometric parameters: pile diameter, pile length, heat exchanger tube arrangement, etc.

[0051] Results Verification and Comparison: In order to verify the accuracy and superiority of the layered heat transfer model used, this invention can compare and analyze the calculation results under different models.

[0052] To verify the effectiveness and reliability of the analytical solution of the layered heat transfer model used in this invention, the method can be compared with theoretical analytical solutions or numerical simulation results in existing literature. For example, a program can be written using tools such as MATLAB to solve the temperature field, and the calculation results of the layered heat transfer model of this invention can be compared with existing accepted theoretical models (e.g., The models were compared. Figure 5 For the stratified heat transfer model and The comparison of model results (R=2.6) demonstrates that at a pile-soil thermal resistance ratio of R=2.6 and different Fourier numbers... The temperature response calculation results of the layered heat transfer model proposed in this invention and the Man homogeneous model in homogeneous rock and soil are shown in the figure. As can be seen from the figure, the results of the two models are highly consistent, indicating that the analytical process and results of the layered heat transfer model constructed in this invention are reasonable and accurate. This comparison verifies the accuracy of the proposed layered heat transfer model under basic working conditions and lays the foundation for subsequent calculations considering geological stratification and heterogeneity.

[0053] The validity and reliability of the analytical solution can be verified by comparing it with theoretical analytical solutions or numerical simulation results in existing literature, which is a common and recognized verification method. Based on the analytical solution of the above-mentioned layered heat transfer theoretical model, this invention uses a MATLAB program to solve and calculate the temperature field. The layered model and... The model comparison showed a high degree of consistency between the two results, demonstrating the rationality and accuracy of the analytical process and results of the established layered heat transfer model.

[0054] S5: Calculate the temperature stress of each section of the energy pile body based on the temperature field distribution.

[0055] Transforming thermal analysis results into mechanical input is a crucial step in thermo-mechanical coupling. Energy piles expand and contract under temperature changes, but are constrained by the surrounding soil and structure, preventing free deformation and thus generating thermal stress.

[0056] In one implementation, the temperature stress at each cross-section of the energy pile is calculated using the principle of linear thermal expansion. Since the pile is constrained and cannot deform freely, temperature stress is generated. To illustrate the axial temperature stress generated in the pile due to constraint under temperature changes, the pile temperature stress is... The calculation can usually be expressed as: in, The elastic modulus of the pile concrete. The strain is caused by constraints. When the constraints are complex, it is necessary to combine mechanical equilibrium and deformation compatibility conditions for solution.

[0057] S6 establishes a load transfer model for energy piles under vertical loads and temperature stresses, and introduces a nonlinear shear model of the pile-soil interface considering the softening effect. The shear model can describe the entire process of the pile-soil interface from elasticity, peak strength to softening and finally residual strength.

[0058] In one implementation, the load transfer model divides the energy pile body into multiple discrete elements and considers the pile's self-weight. The axial force, side friction, and displacement of the pile body within each element satisfy equilibrium and deformation compatibility conditions.

[0059] Its equilibrium equations and deformation compatibility equations can be expressed as: in, For the axial force of the pile body, Let be the shear stress at the pile-soil interface, C be the pile perimeter, W be the self-weight per unit length of the pile, E be the elastic modulus of the pile, A be the cross-sectional area of ​​the pile, w be the pile displacement, and z be the axial coordinate.

[0060] The shear model of the pile-soil interface aims to accurately describe the interaction characteristics between the pile and the surrounding soil and rock mass, especially the nonlinear relationship between pile side friction and the relative displacement of the pile and soil. Given that energy piles may experience repeated load and temperature changes during long-term operation, the pile-soil interface may soften, harden, or even yield. Therefore, it is crucial to use a model that can fully reflect the softening effect of the pile-soil interface.

[0061] This invention preferably employs a shear model that considers the softening effect at the pile-soil interface. This model can depict the entire process of the pile-soil interface from elasticity, reaching peak strength, softening, and finally residual strength. The pile-soil contact shear model adopts a piecewise softening function form, the expression of which is as follows: In a more refined implementation, a shear model that considers the softening effect at the pile-soil interface can be used, such as... Figure 4 The figure shows a shear stress-relative displacement model of the pile-soil interface considering the softening effect. This model can describe the entire process of the pile-soil interface from elasticity, peak strength, softening to residual strength. The pile-soil contact shear model adopts a piecewise softening function form, the expression of which is as follows: in, This refers to the shear stress at the contact surface, i.e., the skin friction of the pile, with units of... s represents relative displacement, in mm; This represents the peak shear stress. Residual strength, i.e., the stable value of the pile side friction when the shear displacement is large, is expressed in units of... ; To achieve residual strength The corresponding shear displacement is expressed in mm; a, b, and c are fitting parameters used to describe the shape of the curve, determined through indoor or field tests, reflecting the nonlinear characteristics of the pile-soil interface. Based on the characteristics of this piecewise softening function and the softening properties of the pile-soil interface from elasticity and peak strength to residual strength, this function needs to satisfy the following three conditions: When the shear displacement reaches the peak displacement At that time, the shear stress reaches the peak strength. : At peak point At this point, the slope of the shear stress-shear displacement curve is zero (i.e., the shear stress reaches its maximum value): When the shear displacement reaches the residual displacement When the shear stress reaches the residual strength : Substituting the above three conditions into the piecewise softening function expression, the specific expressions for the fitting parameters a, b, and c can be obtained by solving: In the formula, Shear displacement to achieve residual strength Shear displacement corresponding to peak strength The ratio, i.e. ; Residual strength With peak intensity The ratio, i.e. .

[0062] This piecewise softening function model can accurately describe the nonlinear response of the pile-soil interface under shear displacement, including the softening behavior after peak strength. When the relative displacement is large, the shear stress may decrease to the residual strength. Its relationship with the peak shear stress satisfies The relationship. This is a dimensionless parameter, typically less than or equal to 1, reflecting the degree of shear strength softening at the pile-soil interface after reaching peak strength. (Model required parameters) Based on the soil and rock parameters obtained in steps S1 and S2, the parameters can be determined through indoor geotechnical tests (such as direct shear tests and triaxial shear tests) or empirical relationships, thereby providing key pile side friction input for solving the load transfer model in step S7.

[0063] This more complex hyperbolic model can more accurately reflect the elastic properties of the pile-soil interface in the stage of small relative displacement and the plastic properties in the stage of large relative displacement, thereby improving the accuracy of mechanical coupling analysis.

[0064] S7: Using an iterative calculation method, solve the load transfer model to obtain the axial force, displacement, and pile-soil friction of the energy pile.

[0065] Due to the interaction between thermal and mechanical parameters and the nonlinear characteristics of the pile-soil interface, iterative methods are usually required to solve the problem in order to achieve convergence.

[0066] In one implementation, the thermo-coupling iterative calculation process includes the entire process of thermal field calculation, temperature stress calculation, force field calculation, and iterative convergence determination.

[0067] The iterative calculation is performed in three steps: Calculation of pile top load acting alone: ​​Assuming that the pile top load P acts alone, the pile is discretized into several linear elastic elements, and the element compression is calculated according to Hooke's law. By combining the load transfer function with iterative calculation of side friction, the convergence condition of axial force is verified. And satisfy the overall static equilibrium. .

[0068] Neutral point determination: The neutral point is defined as the position where there is no relative additional displacement between the pile and the soil under temperature load. The pile is divided into upper (1~NP-1) and lower (NP~N) elements. The displacement and axial force of the upper and lower elements are calculated separately. The overall static equilibrium condition is satisfied through iteration. Determine the cell NP where the neutral point is located.

[0069] Thermo-coupling iterative calculation: Introducing the temperature change obtained in S4 Calculate the temperature deformation of the pile body ( Using the linear expansion coefficient of the pile body, iterate through the upper (NP-1~1) and lower (NP~N) elements respectively to verify the displacement convergence condition. The final output includes the axial force of the pile, the displacement of the pile, and the distribution of pile-soil side friction.

[0070] This method has a clear computational approach and can be solved using the displacement compatibility method. Its significant advantage lies in its ability to consider the varying mechanical parameters of different soil layers, thereby improving computational accuracy and engineering adaptability. For ease of description in the subsequent detailed calculation process, the following notation conventions are used for the relevant physical quantities: These represent pile load, side skin friction, and displacement, respectively; subscripts H, S, and B represent the top, middle, and bottom positions of the element, respectively; subscripts M, T, and MT represent the individual action of mechanical load, temperature load, and thermo-coupling effect, respectively; i indicates the element number. Example: This represents the axial force at the top of element i under the action of the pile top load alone; This represents the axial force in the middle of element i under the action of temperature load alone; This represents the axial force at the bottom of unit i under the action of thermo-coupling.

[0071] This represents the side resistance of element i under the action of the pile top load alone; This represents the side resistance of element i under the sole action of temperature load; This represents the side resistance of unit i under the action of thermo-coupling.

[0072] This represents the displacement at the top of element i under the action of the pile top load alone; This represents the displacement of the middle part of element i under the action of temperature load alone; This represents the total displacement at the bottom of element i under the action of thermo-mechanical coupling.

[0073] Using the displacement compatibility method, the pile needs to be discretized into N linear elastic elements, with element numbers sequentially from pile top to pile tip: 1, ..., N. For unit consistency, the stiffness of element i can be expressed as... ,in, The unit is kN / m, and E is the elastic modulus of the pile. and Let i represent the cross-sectional area and length of element i, respectively.

[0074] The following procedure is used to calculate the stress and strain under a single load P on the pile top: Assume the axial force at the top of element i is .

[0075] According to Hooke's law of elasticity, the compression of unit i is calculated. : Calculate the top displacement of unit i and middle displacement : Calculate the side drag of element i based on the mid-displacement and load transfer function of element i. : Calculate the new top load of element i based on the static equilibrium of element i. : verify Is it valid? If true, then the calculation meets the accuracy requirements. Similarly, calculate the next element (i+1); otherwise, assume the top load of element i. Repeat the above steps until the condition is met. .

[0076] In actual calculations, starting from pile tip element 1, we assume pile tip displacement. The axial force at the pile end is obtained. Then, using the iterative method described above, the side resistance of elements N, N-1, ..., 1 is calculated one by one: , ..., .

[0077] The entire energy pile remains in static equilibrium, and its governing equations are as follows: Where P represents the external load applied to the top of the pile.

[0078] If the equilibrium equations are satisfied, the calculation ends; otherwise, it is assumed that... Repeat the above calculation process until the required accuracy of the overall equilibrium equation is met.

[0079] In a preferred embodiment, the free deformation caused by temperature changes is restricted due to the constraint of the pile body on the surrounding soil, thus generating constrained temperature stress. This invention employs an iterative calculation method to accurately determine these temperature stresses and the corresponding pile deformation. The additional axial force caused by temperature changes in the pile body is calculated by introducing the neutral point method. The neutral point (NP) is the point in the pile body where there is no relative displacement between the pile and the soil. Determining this point is crucial for accurately calculating the temperature stress in the pile body. The neutral point is the position where, under the action of a temperature load ∆T, there is no additional relative displacement between the pile and the soil in the axial direction. It is assumed that the temperature of the energy pile is uniformly distributed during heat extraction and dissipation.

[0080] (1) Pile Discretization and Initial Assumptions: The pile body is discretized into N elements, and the neutral point is assumed to be NP. The pile is divided into upper and lower parts by the neutral point. The element numbers of the upper pile are 1 to NP-1, and the element numbers of the lower pile are NP to N. In the iterative calculation, the upper and lower elements are calculated using the load transfer displacement coordination method, and the accuracy requirements are met.

[0081] First, assume that the deformation of pile element i is as follows: ,in is the coefficient of linear expansion of the pile material. The change in temperature The unit length is denoted as .

[0082] (2) Iterative calculation of pile deformation and axial force: Iterative calculations are performed for the upper and lower regions of the neutral point to coordinate the pile axial force and deformation.

[0083] For the pile subunit (NP~N): Assuming temperature deformation of unit i For free deformation, that is: in is the coefficient of linear expansion of the pile.

[0084] Calculate the displacement of element i: Top displacement: Mid-section displacement: , where + indicates Under the condition, - indicates Bottom displacement: , where + indicates Under the condition, - indicates Where element NP has the top displacement: Mid-section displacement: , where + indicates Under the condition, - indicates Bottom displacement: , where + indicates Under the condition, - indicates .

[0085] Calculate the axial force of unit i: Bottom axial force: Side resistance: Top axial force: In element N, the bottom axial force is: Transformation of computational unit i: verify Is it valid? If true, the calculation ends; if false, then assume... Repeat the above iterative process until the condition is met. .

[0086] For the pile superstructure (NP-1~1): Assuming the temperature deformation of unit i For free deformation, that is Calculate the displacement of element i: Bottom displacement: Mid-section displacement: , where + indicates Under the condition, - indicates Top displacement: , where + indicates Under the condition, - indicates For element NP-1, the bottom displacement is: Mid-section displacement: , where + indicates Under the condition, - indicates Top displacement: , where + indicates Under the condition, - indicates Calculate the axial force of unit i: Top axial force: Side resistance: Bottom axial force: In element 1, the top axial force is: Calculate the deformation of unit i.

[0087] verify Whether it is valid or not.

[0088] If true, the calculation ends; if false, then assume... Repeat the above iterative process until the condition is met. .

[0089] The upper and lower parts of the energy pile are required to maintain overall static equilibrium, that is: In calculation time NP = 1~N, can be calculated , ..., The smallest of them In the middle, NP is the cell where the neutral point is located, and the top of the cell is the location of the neutral point.

[0090] Based on the segmented calculation and coupling of the neutral point, once the neutral point is determined, the pile body will be divided into upper and lower parts. The temperature stress and the resulting additional axial force in each part of the pile body will be calculated using the displacement compatibility method, taking into account the constraint effect of the surrounding soil. The calculated temperature stress (additional axial force) will serve as an important input for the iterative solution of the load transfer model in step S7, jointly determining the final distribution of axial force, displacement, and side skin friction in the pile body, and must satisfy the overall static equilibrium condition. Through the above iterative calculation, the temperature stress and deformation distribution of each section of the energy pile body under temperature action can be obtained.

[0091] In the energy-thermal coupling calculation, the upper part of the lower pile induces upward expansion, and the lower part induces upward contraction, resulting in negative skin friction, which is an unloading process in the load transfer function. When calculating the thermal-mechanical coupling load, the upper and lower parts of the neutral point still need to be calculated separately using iterative calculations, as follows: ① For the lower pile element (NP~N), assume the temperature deformation of element i For free deformation, that is .

[0092] Calculate the displacement of element i: Top displacement: Mid-section displacement: , where + indicates Under the condition, - indicates Bottom displacement: , where + indicates Under the condition, - indicates ② For element NP, top displacement: Mid-section displacement: , where + indicates Under the condition, - indicates Bottom displacement: , where + indicates Under the condition, - indicates Calculate the axial force of unit i: Bottom axial force: Side resistance: Top axial force: Deformation of computational unit i : ③For the pile superstructure (NP-1~1): Assuming the temperature deformation of unit i For free deformation, that is .

[0093] Calculate the displacement of element i: Bottom displacement: Mid-section displacement: , where + indicates Under the condition, - indicates Top displacement: , where + indicates Under the condition, - indicates ④ For unit NP-1: Bottom displacement: Mid-section displacement: , where + indicates Under the condition, - indicates Top displacement: , where + indicates Under the condition, - indicates Calculation unit i axial force Top axial force: Side resistance: Bottom axial force: Calculate the deformation of unit i.

[0094] verify Check if it's true or false. If true, the calculation ends; otherwise, proceed. Repeat the iteration of the upper and lower units of the neutral point until the condition is met. The magnitude of the axial force in the energy pile body at different depths was obtained.

[0095] Once the entire iterative process converges, the axial force, displacement, and pile-soil skin friction distribution of the energy pile are output. Through the aforementioned nested iterative calculation method, the axial force, displacement, and pile-soil skin friction of the energy pile under vertical loads and temperature stresses can be accurately calculated, providing a reliable data foundation for subsequent performance evaluation.

[0096] S8: Based on the axial force, displacement, and soil-pile friction, a comprehensive evaluation of the heat exchange performance and mechanical safety of the energy pile is conducted.

[0097] In one implementation, the comprehensive evaluation typically includes the following two main aspects: The heat exchange performance assessment aims to quantify the heat exchange efficiency and capacity of energy piles under different operating modes and conditions.

[0098] Evaluation metrics include average heat exchange power, cumulative heat exchange, and the fitting results between the predicted thermal response test curve (TRT curve) from numerical simulation and measured data. Average heat exchange power reflects the average heat exchange volume per unit time of the energy pile and is a core indicator for measuring its cooling or heating capacity. Cumulative heat exchange reflects the total heat exchange of the energy pile over a certain operating cycle and is used to assess its long-term economic efficiency and energy effectiveness. The thermal response test curve, obtained by fitting the predicted thermal response curve (TRT curve) from numerical simulation with actual test data, is used to verify the accuracy and predictive ability of the model and to obtain key parameters such as effective thermal conductivity. These metrics reflect the cooling or heating efficiency of the energy pile during operation.

[0099] Based on the transient temperature field distribution of the energy pile and its surrounding soil and rock obtained in step S4, and combined with the heat transfer model of the fluid inside the heat exchanger tube and effective heat transfer calculation methods, such as numerical heat transfer or lumped parameter method, the instantaneous and long-term heat transfer performance of the energy pile can be obtained. Furthermore, the influence of different geological conditions, groundwater flow, and operating strategies on the heat transfer performance can also be considered.

[0100] Mechanical safety assessment aims to verify the structural integrity and stability of energy piles under the combined effects of external loads, soil constraints, and internal temperature stress.

[0101] Evaluation indicators include: maximum axial force, maximum bending moment and shear force of the pile, pile top settlement, shear stress distribution at the pile-soil contact surface, pile crack control, and foundation soil stability. The maximum axial force of the pile is calculated by comparing the maximum calculated axial force with the ultimate compressive bearing capacity of the pile material (e.g., concrete or reinforced concrete) to ensure that the pile does not suffer axial failure. Maximum bending moment and shear force are assessed when considering additional bending moments caused by eccentric loads, lateral soil deformation, uneven settlement, or thermal stress. This assessment determines whether the maximum bending moment and shear force exceed the material's bending and shear bearing capacity to prevent pile yielding or cracking. Pile top settlement is calculated by comparing the total pile top settlement with the maximum allowable settlement specified in the engineering design code or usage requirements to ensure that deformation control requirements are met and to avoid adverse effects on the superstructure. The shear stress distribution at the pile-soil interface is used to assess the magnitude and distribution of shear stress at various points on the pile-soil interface. This is compared with the ultimate shear strength of the pile-soil interface to ensure that, under normal operating conditions, the pile-soil interface does not experience excessive plastic deformation, localized damage, or overall failure. Pile crack control, when considering temperature stress, assesses whether it will cause cracks in the pile exceeding the allowable width specified in the code, affecting its durability and bearing capacity. Foundation soil stability assesses the changes in pore water pressure around the pile under thermal cycling, and the potential deterioration of the foundation soil's strength and deformation characteristics, thereby ensuring the overall stability of the foundation.

[0102] The mechanical response results obtained in step S7, such as pile axial force, pile displacement, and pile-soil side friction distribution, are compared and verified in detail with relevant design specifications and material mechanical performance indicators. For example, the maximum axial force of the pile should not exceed the compressive bearing capacity of the pile material, the settlement at the pile top should meet the deformation control requirements, and the shear stress at the pile-soil interface should be ensured to be within a safe range, without excessive plastic deformation or failure.

[0103] In one illustrative application embodiment, assume an energy pile with a radius of 0.3m and a length of 20m, traversing two soil layers: a clay layer and a sand layer. The method of this invention is applied as follows: Layered parameter acquisition: Based on steps S1-S2, obtain the geological, hydrological, and thermal properties of the clay and sand layers respectively. Based on step S3, determine the pile material and internal fluid parameters.

[0104] Temperature field calculation: Based on step S4, a layered heat transfer model is established, and the transient temperature field changes of the soil around the pile and at a distance are calculated under a given heat transfer load.

[0105] Pile-soil interface model: Based on S6, determine the pile-soil shear model parameters (parameters of the piecewise softening function) corresponding to each soil layer (clay and sand).

[0106] Thermo-coupling analysis: Input the pile top load, and use the temperature change calculated in step S4 to calculate the additional temperature stress on the pile body through step S5, as part of the load. Perform thermo-coupling load transfer analysis according to step S7. Through nested iterative calculations, the axial force distribution, side friction distribution, and displacement distribution of the energy pile body are finally obtained.

[0107] Results Analysis: The calculation results of this method can reveal complex phenomena such as neutral point shift and pile axial force redistribution caused by temperature changes and soil layer changes (heterogeneity), which are difficult to accurately capture by traditional methods.

[0108] The theoretical predictions of the method of this invention can be compared with actual engineering monitoring data or higher-precision numerical simulations to further verify its accuracy and reliability. The results show that, compared with traditional homogeneous soil models and simplified mechanical models, the method of this invention can predict the thermo-mechanical coupling behavior of energy piles more accurately and comprehensively, providing more reliable technical support for the design optimization, performance evaluation, and safe operation of energy piles.

[0109] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the energy pile (column) multilayer heat exchange thermal coupling, characterized in that, The method comprises the following steps: S1 determining a calculation domain and a grid division of an energy pile and a surrounding rock-soil body; S2 obtaining thermal physical parameters and mechanical parameters of each layer of the energy pile, the pile body material and the rock-soil body, the each layer of the rock-soil body including a horizontal thermal conductivity and a vertical thermal conductivity; S3 establishing a transient heat conduction model of the energy pile and the surrounding rock-soil body according to a heat exchange boundary condition of the energy pile, and considering differences in the horizontal thermal conductivity and the vertical thermal conductivity of each layer of the rock-soil body; S4 solving the transient heat conduction model by using a Green function method to obtain a temperature field distribution at any time in the calculation domain; S5 calculating temperature stresses of each section of the energy pile body according to the temperature field distribution; S6 establishing a load transfer model of the energy pile under the action of vertical load and temperature stress, and introducing a nonlinear shear model of a pile-soil contact surface considering softening effect, the shear model being capable of describing a whole process from elasticity, peak strength to softening and residual strength of the pile-soil interface; S7 solving the load transfer model by using an iterative calculation method to obtain a pile body axial force, a pile body displacement and a pile-soil side friction of the energy pile; S8 comprehensively evaluating heat exchange performance and mechanical safety of the energy pile according to the pile body axial force, the pile body displacement and the pile-soil side friction.

2. The energy pile multi-layer heat exchange thermodynamic coupling calculation method of claim 1, wherein, The transient heat conduction model is a non-uniform and anisotropic heat conduction equation established in a cylindrical coordinate system, and a calculation equation thereof is as follows: where T is temperature, t is time, r is radial coordinate, z is axial coordinate, is density at depth z, is specific heat capacity at depth z, is horizontal thermal conductivity at depth z, is vertical thermal conductivity at depth z, Q is internal heat source term.

3. The energy pile multi-layer heat exchange thermodynamic coupling calculation method of claim 1, wherein, The nonlinear shear model of the pile-soil contact surface considering softening effect is expressed in a segmented function form, and an expression thereof is as follows: wherein, is the peak shear stress, and is the residual strength, and is the relative displacement of the pile-soil interface at the peak shear stress, and is the relative displacement of the pile-soil interface at the residual strength, ; is the relative displacement of the pile-soil interface at the residual strength, ; a, b, c are fitting parameters to describe the shape of the curve.

4. The energy pile multi-layer heat exchange thermodynamic coupling calculation method of claim 1, wherein, The Green function method solves the transient heat conduction model by deriving a Green function considering a non-uniform and anisotropic medium to obtain a high-precision temperature field distribution.

5. The energy pile multi-layer heat exchange thermodynamic coupling calculation method of claim 1, wherein, The thermal physical parameters of each layer of the rock-soil body include density, specific heat capacity, horizontal thermal conductivity and vertical thermal conductivity; and the mechanical parameters include elastic modulus, Poisson's ratio, initial effective stress of a stratum and initial horizontal effective stress of the stratum.

6. The energy pile multi-layer heat exchange thermodynamic coupling calculation method of claim 1, wherein, The temperature stress of each section of the energy pile body is calculated by linear thermal expansion principle, and the temperature stress is determined by the elastic modulus of the pile body concrete , the thermal expansion coefficient and the temperature change amount , and the calculation formula is: .

7. The energy pile multi-layer heat exchange thermodynamic coupling calculation method of claim 1, wherein, The load transfer model divides the pile body into a plurality of discrete units and considers a self weight of the pile, and in each unit, the pile body axial force, the pile side friction and the pile body displacement satisfy a balance condition and a deformation coordination condition, and balance equations and deformation coordination equations thereof can be expressed as follows: wherein, is the shaft force of the pile body, is the shaft force of the pile body, C is the circumference of the pile body, W is the unit length weight of the pile body, E is the elastic modulus of the pile body, A is the cross-sectional area of the pile body, w is the displacement of the pile body, and z is the axial coordinate. 8.The energy pile multi-layer heat exchange thermodynamic coupling calculation method according to claim 1, wherein, The iterative calculation method comprises: initially assuming a pile body displacement, calculating a pile side friction, calculating a pile body axial force, and then recalculating the pile body displacement according to the pile body axial force until the pile body displacements calculated in two consecutive times reach a preset convergence standard.

9. The energy pile multi-layer heat exchange thermodynamic coupling calculation method of claim 1, wherein, When the heat exchange performance of the energy pile is comprehensively evaluated, evaluation indexes include average heat exchange power, cumulative heat exchange amount and fitting results of a thermal response test.

10. The energy pile multi-layer heat exchange thermodynamic coupling calculation method of claim 1, wherein, When the mechanical safety of the energy pile is comprehensively evaluated, evaluation indexes include a maximum axial force, a maximum bending moment, a settlement amount and a shear stress distribution of the pile-soil contact surface.

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