Energy pile reliability analysis and design method considering soil parameter spatial variability

Abstract

The invention provides an energy pile reliability analysis and design method considering soil parameter spatial variability. The method comprises the steps that S1, an energy pile certainty analysis model under the thermal-hydraulic-mechanical coupling effect is selected; s2, determining a failure mode of the energy pile; s3, soil uncertainty parameters and design variables are selected, and the design space of the pile length and the pile diameter is determined based on the design variables; s4, sampling is carried out to form alternative design schemes; s5, representing the spatial variability of the thermal physical mechanical parameters of the soil body, generating a random field sample, and calculating a failure probability; s6, establishing an energy pile total probability design method based on a response surface method; s7, determining a design feasible region in the design space; and S8, selecting an optimal design scheme from the design feasible region according to an economic optimal principle. According to the method, efficient reliability analysis and design of the energy pile are achieved by fusing the heat-water-force coupling model, the efficient probability analysis algorithm and the multi-failure-mode collaborative optimization strategy.

Description

Technical Field

[0001] This invention relates to the field of sustainable development and utilization technology of shallow geothermal energy, and in particular to a reliability analysis and design method for energy piles that takes into account the spatial variability of soil parameters. Background Technology

[0002] With the global energy structure transitioning towards a low-carbon model, shallow geothermal energy, as a renewable and clean energy source, has attracted widespread attention for its development and utilization. Early research (Brandl, 2006; Laloui et al., 2006) spurred the development of energy pile technology, which combines load-bearing and heat exchange functions, by integrating heat exchange tubes into pile foundation structures, enabling the efficient development and utilization of shallow geothermal energy. However, in actual operation, energy piles must simultaneously withstand the loads of the superstructure and cyclic thermal loads. The multi-field coupling effect of heat, water, and force significantly affects the mechanical properties and heat exchange efficiency of the pile foundation, posing higher requirements for design methods.

[0003] Early research primarily focused on the heat transfer characteristics and bearing capacity analysis of energy piles. In terms of heat transfer analysis, Kavanaugh (1985) et al. proposed a cylindrical heat source model to solve for the temperature variation of the soil around the pile. Ingersoll (1948) et al. established an analytical method for infinitely long linear heat sources based on linear heat source theory. Mogenson (1983) further improved the model to facilitate the analysis of heat transfer theories based on linear and cylindrical heat source models. Eskilson (1988) pioneered a temperature response G-function based on infinitely long heat sources, applicable to borehole heat exchange and capable of considering various parameters of the borehole heat exchanger. In terms of bearing capacity analysis, Seed and Reese (1957) proposed the load transfer method, studying the transmission mechanism of pile axial resistance through load transfer curves. Pasten and Santamarana (2014) improved the load transfer model and used it to predict the thermomechanical behavior of energy piles.

[0004] In the design of energy piles, traditional design typically employs a deterministic analysis framework, determining parameters such as pile diameter and length through empirical formulas or simplified models. In recent years, numerical simulation techniques based on thermo-hydraulic-mechanical coupling have been gradually applied in design practice, but they still have the following limitations: First, they ignore the variability of soil thermophysical and mechanical parameters, leading to conservative or risky design results; second, they isolate the heat transfer and bearing capacity functions of the energy pile, failing to consider the pile response under thermo-mechanical coupling to establish a unified multi-failure mode evaluation system, making it difficult to simultaneously meet the synergistic optimization requirements of bearing capacity, settlement control, and heat transfer efficiency.

[0005] To overcome the limitations of traditional design methods, energy pile design is gradually shifting from deterministic to uncertain design. A key challenge is how to quantify the impact of uncertainties on the design of energy piles under multi-field coupling effects, and how to achieve synergistic optimization of safety and economy based on reliability theory. Some scholars have attempted to introduce probabilistic methods to quantify the impact of uncertainties. For example, Barker et al. (1991) proposed a load and resistance coefficient design method, and Phoon et al. (1995) proposed a multiple resistance coefficient design method. Compared with traditional design methods, reliability design methods can reasonably consider various uncertainties encountered by energy piles during the design process, using reliability indices or failure probabilities to evaluate the reliability of various design schemes within the design space, and selecting the optimal design scheme based on the principle of economic optimization (Wang and Kulhawy, 2008). Although existing reliability design methods can effectively quantify the impact of uncertainties on the design, they focus more on single failure modes (such as load failure) and lack comprehensive evaluation of normal serviceability limits (such as settlement failure and heat transfer failure), resulting in design results that fail to fully reflect actual engineering risks. The aforementioned problems severely restrict the engineering promotion and application of energy pile technology. Therefore, it is urgent to develop an efficient and accurate reliability optimization design method to overcome the technical bottlenecks of multi-field coupling, parameter variability, and multi-failure mode synergistic optimization, and to provide theoretical support for the sustainable development of energy piles. Summary of the Invention

[0006] This invention provides a reliability analysis and design method for energy piles that considers the spatial variability of soil parameters. By integrating a thermal-hydraulic-mechanical coupling model, an efficient probabilistic analysis algorithm, and a multi-failure mode collaborative optimization strategy, it can achieve efficient reliability analysis and design of energy piles, providing theoretical and technical support for the efficient and safe design of energy piles.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: Reliability analysis and design methods for energy piles considering the spatial variability of soil parameters, including: S1. Select a deterministic analysis model for energy piles under thermal-hydraulic-mechanical coupling. This model includes a heat transfer model that simulates the heat exchange process of the pile body and a load transfer model that simulates the pile-soil interaction. S2. Determine the failure modes and corresponding limit state equations of the energy pile. The failure modes include bearing failure under the ultimate limit state, settlement failure under the serviceability limit state, and heat transfer failure. S3. Select uncertainty parameters and design variables. The uncertainty parameters are thermophysical and mechanical parameters, and the design variables are the pile length and pile diameter of the energy pile. Determine the design space for the pile length and pile diameter based on the design variables. S4. Within the design space, samples are taken of combinations of pile diameter and pile length, and the extracted design parameter samples form alternative design schemes. S5. Determine the probability distribution and spatial variability characterization parameters of soil thermophysical and mechanical parameters, and generate random field samples of soil thermophysical and mechanical parameters that conform to the characteristics of probability statistics and spatial correlation using the random field discretization method; then, in combination with Monte Carlo simulation, call the deterministic analysis model in step S1 and the limit state equation in S2 for each random field sample to calculate the failure probability of the three failure modes under the given alternative design scheme in step S4. S6. Based on the failure probability calculation results of some design parameter samples in step S4 corresponding to step S5, establish a full probability design method for energy piles based on the response surface methodology. S7. Based on the full probability design method in step S6, calculate the failure probability of all design schemes in the design space described in step S3, and determine the design feasible region in the design space according to the target failure probability of each failure mode in step S2. S8. Based on the principle of economic optimization, select the optimal design scheme from the feasible design domain described in step S7.

[0008] In this specification, S1 includes: S11. Select a heat transfer model to simulate pile heat exchange, including finite or infinite length line heat source model, solid cylindrical heat source model, heat transfer G function, and CFD model. S12. Select load transfer models for simulating pile-soil interaction, including fully elastic-plastic model, exponential model, hyperbolic model, bilinear model, trilinear model, and generalized softening model. S13. Select the load transfer algorithm for the energy pile, including the finite element method, the finite difference method, and the discrete element method; S14. Establish a deterministic analysis model for the energy pile based on the selected heat transfer model and load transfer model to calculate the bearing capacity, displacement, and outlet water temperature of the pile under thermo-coupling conditions.

[0009] In this specification, S2 includes: S21. Definition of bearing failure under ultimate bearing capacity state: When the mechanical response of the pile exceeds the ultimate bearing capacity of the pile, it is considered as bearing failure; S22. Definition of settlement failure under normal serviceability limit state: When the settlement value of the pile top unit exceeds the allowable settlement value, it is considered as settlement failure; S23. Define heat transfer failure under normal operating limits: When the outlet temperature of the heat exchange tube of the energy pile is higher or lower than the target temperature, it is considered heat transfer failure.

[0010] In this specification, S3 includes: S31. Determine the uncertain parameters, which are divided into mechanical parameters and thermodynamic parameters: For sandy soil sites, the mechanical parameters are cohesion and internal friction angle, and for clay sites, the undrained shear strength is used; Thermodynamic parameters include the thermal conductivity, thermal diffusivity and specific heat capacity of the soil. S32. Determine the design variables as the pile diameter and pile length of the energy pile, and construct the design space based on the range of selectable pile diameters and pile lengths.

[0011] In this specification, S4 includes: S41. Determine the design space for energy pile dimensions, namely the range of pile diameter and pile length; S42. Within the design space, the combination of pile diameter and pile length is sampled using the Latin hypercube sampling method to ensure that the extracted design samples cover the entire design space and are representative, forming different design sample points.

[0012] In this specification, S5 includes: S51. Soil uncertainty parameters are divided into mechanical parameters and thermodynamic parameters. The mechanical parameters are treated differently for sandy soil sites and clay soil sites. The thermodynamic parameters are selected as soil thermal conductivity, thermal diffusivity and specific heat capacity. S52. Determine the probability distribution type, mean, and standard deviation of the soil thermophysical and mechanical parameters based on site information; S53. Determine the autocorrelation function (such as exponential or Gaussian type) that characterizes the spatial variability of soil thermophysical and mechanical parameters and its correlation distance in the vertical and horizontal directions; S54. Using random field discretization technology (preferably local averaging method), the continuous random field is discretized onto the numerical analysis grid, and a large number of parameter sample fields that can accurately reflect the spatial variability of soil are generated using the Cholesky decomposition method or the fast Fourier transform method. S55. Take each generated random field sample as input and substitute it into the deterministic analysis model of the energy pile. For each alternative design scheme (pile length and pile diameter combination) in step S4, calculate the failure probability of the three modes of bearing failure, settlement failure and heat transfer failure by counting the number of times the limit state equation is triggered in the simulation results of all random field samples.

[0013] In this specification, S6 includes: S61. Select failure probability, reliability index or logarithmic failure probability as the target variable for calculation; S62. Based on the failure probability calculation results of the extracted design parameter samples, establish the response relationship between the input variables (pile diameter, pile length) and the target variables (failure probabilities under three failure modes) through proxy models such as response surface model, and form a full probability design method for energy piles.

[0014] In this specification, S7 includes: S71. Select the target reliability index corresponding to each failure mode based on the importance of the energy pile structure. S72. Predict the unsampled design sample points in the design space using the response surface model, and input the pile diameter and pile length to calculate its reliability index. S73. Based on the reliability index calculation results of each design point, draw and determine the full probability design feasible region with the target reliability index as the boundary.

[0015] In this specification, S8 includes: S81. Within the fully probabilistic design feasible region determined in step S7, calculate the comprehensive cost of different design schemes by combining the cost information corresponding to the pile diameter and pile length. S82. Taking the lowest overall cost as the economic optimal principle, select the design scheme with the lowest cost that meets the requirements of all failure modes from the feasible region as the optimal design scheme.

[0016] In this specification, in step S14, the calculation of the pile response under the thermal coupling condition requires simultaneous input of the superstructure load, periodic thermal load, and soil thermodynamic parameters. The pile temperature field distribution is calculated through the heat transfer model, and then the influence of the additional stress caused by the temperature field on the pile bearing capacity and displacement is calculated in combination with the load transfer model.

[0017] In summary, the present invention has at least the following beneficial effects: Enhancing design reliability and safety: By quantifying the variability of soil thermophysical and mechanical parameters (such as internal friction angle and thermal conductivity), and combining the thermal-hydraulic-mechanical coupling model, the risks of three modes of failure—bearing failure, settlement failure, and heat transfer failure—are accurately assessed. This avoids the conservative or risky problems caused by ignoring uncertainties in traditional deterministic design, and ensures that the reliability indicators of the energy pile structure are within a safe range.

[0018] Improve computational efficiency: The response surface methodology is introduced to establish a surrogate model, which replaces the time-consuming Monte Carlo simulation full-sample calculation. This significantly reduces the analysis time of thermal-hydraulic-mechanical coupling problems, solves the computational efficiency bottleneck of reliability analysis under multiple parameters and multiple failure modes, and makes efficient design of complex engineering scenarios possible.

[0019] Achieving multi-objective synergistic optimization: By constructing a design feasible domain that simultaneously satisfies load-bearing capacity, settlement control, and heat exchange efficiency, the limitations of isolated heat transfer and load-bearing functions in traditional design are overcome, achieving synergistic assurance of structural safety, performance, and heat exchange efficiency, and providing a comprehensive risk control solution for the project.

[0020] Enhanced economic efficiency: By selecting a scheme based on the principle of economic optimization within the design feasible domain, the overall cost of energy piles can be significantly reduced compared with traditional design methods. Under the premise of ensuring safety and performance, a balance between cost and benefit is achieved, thereby improving the economic efficiency of shallow geothermal energy development and utilization.

[0021] Provide theoretical and technical support: offer a systematic approach to the integrated design of geothermal energy and building structures, quantify the impact of thermally induced additional stress on the reliability of pile foundations, clarify the design boundaries under multi-field coupling effects, and promote the engineering application and standardized application of energy pile technology. Attached Figure Description

[0022] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. 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.

[0023] Figure 1 This is a flowchart of the algorithm for the reliability analysis and design method of energy piles involved in this invention.

[0024] Figure 2 This is a graph showing the calculated parameters in the verification case involved in this invention.

[0025] Figure 3 This is a sample diagram of design parameters in the verification cases involved in this invention.

[0026] Figure 4 Feasibility domain diagrams are designed for the three failure modes in the verification cases involved in this invention.

[0027] Figure 5 This is the final design feasibility domain diagram in the verification cases involved in this invention.

[0028] Figure 6 These are the response surface model calculation results and Monte Carlo simulation results for the verification cases involved in this invention. Detailed Implementation

[0029] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0030] The following disclosure provides many different implementations or examples for carrying out different structures of the embodiments of the present invention. To simplify the disclosure of the embodiments of the present invention, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. Furthermore, reference numerals and / or reference letters may be repeated in different examples of the embodiments of the present invention; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various implementations and / or arrangements discussed.

[0031] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0032] like Figure 1 As shown, this embodiment provides a reliability analysis and design method for energy piles that considers the spatial variability of soil parameters, including: S1. Select a deterministic analysis model for energy piles under thermal-hydraulic-mechanical coupling. This model includes a heat transfer model that simulates the heat exchange process of the pile body and a load transfer model that simulates the pile-soil interaction. S2. Determine the failure modes and corresponding limit state equations of the energy pile. The failure modes include bearing failure under the ultimate limit state, settlement failure under the serviceability limit state, and heat transfer failure. S3. Select uncertainty parameters and design variables. The uncertainty parameters are thermophysical and mechanical parameters, and the design variables are the pile length and pile diameter of the energy pile. Determine the design space for the pile length and pile diameter based on the design variables. S4. Within the design space, samples are taken of combinations of pile diameter and pile length, and the extracted design parameter samples form alternative design schemes. S5. Determine the probability distribution and spatial variability characterization parameters of soil thermophysical and mechanical parameters, and generate random field samples of soil thermophysical and mechanical parameters that conform to the above probability statistics and spatial correlation characteristics using the random field discretization method; then, in conjunction with Monte Carlo simulation, call the deterministic analysis model in step S1 and the limit state equation in S2 for each random field sample to calculate the failure probability of the three failure modes under the given alternative design scheme in step S4. S6. Based on the failure probability calculation results of some design parameter samples in step S4 corresponding to step S5, establish a full probability design method for energy piles based on the response surface methodology. S7. Based on the full probability design method in step S6, calculate the failure probability of all design schemes in the design space described in step S3, and determine the design feasible region in the design space according to the target failure probability of each failure mode in step S2. S8. Based on the principle of economic optimization, select the optimal design scheme from the feasible design domain described in step S7.

[0033] In some embodiments, S1 includes: S11. Select a heat transfer model to simulate pile heat exchange, including but not limited to finite length and infinite length line heat source models, solid cylindrical heat source models, heat transfer G function, CFD models, etc. S12. The load transfer model for simulating pile-soil interaction includes, but is not limited to, the fully elastic-plastic model, the exponential model, the hyperbolic model, the bilinear model, the trilinear model, the generalized softening model, etc. S13. The energy pile load transfer algorithm includes, but is not limited to, finite element method, finite difference method, discrete element method, etc. S14. Establish a deterministic analysis model for the energy pile based on the selected heat transfer model and load transfer model to calculate the bearing capacity, displacement, and outlet water temperature of the pile under thermo-coupling conditions. In some embodiments, S2 includes: S21. Considering the ultimate limit state (ULS), when the mechanical response of the pile exceeds the ultimate bearing capacity of the pile, it is considered as bearing failure. S22. Consider the serviceability limit state (SLS), which includes two cases: when the settlement value of the pile top unit exceeds the allowable settlement value, it is considered as settlement failure; S23. When the temperature at the outlet of the heat exchanger tube of the energy pile is higher or lower than the target temperature, it is considered a heat transfer failure.

[0034] In some embodiments, S3 includes: S31. The uncertain parameters of the soil are divided into mechanical parameters and thermodynamic parameters. The mechanical parameters are mainly considered in two cases: sandy soil site and clay soil site. For sandy soil site, the internal force and displacement response of the energy pile are calculated using cohesion and internal friction angle. For clay soil site, the internal force and displacement response of the energy pile are calculated using undrained shear strength. The thermodynamic parameters mainly consider the thermal conductivity, thermal diffusivity and specific heat capacity of the soil.

[0035] S32. The main design variables of the energy pile are pile diameter D and pile length L, and the design space is composed of the range of selectable pile diameters and pile lengths.

[0036] In some embodiments, in S3, design parameters within the design space are sampled using Latin hypercube (LHS) to form different design sample points.

[0037] In some embodiments, S4 includes: S41. Determine the design space for energy pile dimensions, namely the range of pile diameter and pile length; S42. Within the design space, the combination of pile diameter and pile length is sampled using the Latin hypercube sampling method to ensure that the extracted design samples cover the entire design space and are representative, forming different design sample points.

[0038] In some embodiments, S5 includes: S51. Considering the uncertain parameters of the soil, the uncertain parameters are divided into two categories: mechanical parameters and thermodynamic parameters. Among them, the mechanical parameters are treated differently based on the soil type. That is, the cohesion and internal friction angle are used to calculate the internal force and displacement response of the pile in sandy soil, and the undrained shear strength is used as the control parameter in clay soil. The thermodynamic parameters are selected from the soil thermal conductivity, specific heat capacity and thermal diffusivity to characterize the heat conduction and heat storage characteristics in the heat exchange process of the energy pile. S52. Determine the probability distribution type, mean, and standard deviation of the soil thermophysical and mechanical parameters based on site information; S53. Determine the autocorrelation function (such as exponential or Gaussian type) that characterizes the spatial variability of soil thermophysical and mechanical parameters and its correlation distance in the vertical and horizontal directions; S54. Using random field discretization technology (preferably local averaging method), the continuous random field is discretized onto the numerical analysis grid, and a large number of parameter sample fields that can accurately reflect the spatial variability of soil are generated using the Cholesky decomposition method or the fast Fourier transform method. S55. Take each generated random field sample as input and substitute it into the deterministic analysis model of the energy pile. For each alternative design scheme (pile length and pile diameter combination) in step S4, calculate the failure probability of the three modes of bearing failure, settlement failure and heat transfer failure by counting the number of times the limit state equation is triggered in the simulation results of all random field samples.

[0039] In some embodiments, S6 includes: S61. Select appropriate reliability indicators as the target variable for calculation, including but not limited to failure probability. Reliability indicators Logarithmic failure probability wait; S62. Based on the failure probability calculation results of the three failure modes of the extracted design sample points, establish a model describing the input variables (pile diameter, pile length) and the target variable (reliability index) using a surrogate model (including but not limited to response surface model, machine learning algorithm, etc.). The response relationship between the two is used to calculate the failure probability using a proxy model, thus forming a full probability design method for energy piles.

[0040] In some embodiments, S7 includes: S71. Select the target value of the reliability index (including but not limited to the target reliability index) based on the importance of the energy pile structure. S72. Predict other uncalculated sample points in the design space using the response surface model, input the pile diameter and pile length, and calculate the reliability index. S73. Based on the reliability index calculation results of each design point, draw the full probability design feasible region with the target reliability index as the boundary.

[0041] In some embodiments, S8 includes: S81. Within the fully probabilistic design feasible region determined in step S7, calculate the comprehensive cost of different design schemes by combining the cost information corresponding to the pile diameter and pile length. S82. Taking the lowest overall cost as the economic optimal principle, select the design scheme with the lowest cost that meets the requirements of all failure modes from the feasible region as the optimal design scheme.

[0042] In some embodiments, in step S14, the calculation of the pile response under the thermo-coupling condition requires simultaneous input of the superstructure load, periodic thermal load, and soil thermodynamic parameters. The pile temperature field distribution is calculated through a heat transfer model, and then the influence of the additional stress caused by the temperature field on the pile bearing capacity and displacement is calculated in combination with the load transfer model.

[0043] In some embodiments, in step S11, the selection of the heat transfer model needs to take into account the actual engineering scenario of the energy pile. When the pile length is large and the heat exchange time is short, the infinitely long line heat source model is preferred; when the pile length is finite and the end heat loss needs to be accurately calculated, the finitely long line heat source model or the solid cylindrical heat source model is selected.

[0044] In some embodiments, in step S53, the failure probability is calculated by counting the number of samples in the Monte Carlo simulation where the result of the limit state equation is less than 0, and using the ratio of this number to the total number of samples as the failure probability of the corresponding design scheme.

[0045] In some embodiments, in step S62, the response surface model adopts a second-order polynomial form. By performing linear regression fitting on the failure probability data of the design parameter samples, the polynomial coefficients are determined, enabling the model to accurately predict the failure probability of unsampled design points.

[0046] In some embodiments, in step S73, the feasible region of the full probability design is a set of design points that simultaneously satisfy the target reliability index under the three modes of load failure, settlement failure, and heat transfer failure. The boundary of the feasible region is presented intuitively by drawing a three-dimensional or two-dimensional coordinate graph.

[0047] In some embodiments, in step S31, the variability of the soil thermophysical and mechanical parameters is obtained through statistical analysis of field survey data. For sandy sites, the probability distribution of cohesion and internal friction angle adopts a normal distribution or a log-normal distribution; for clay sites, the probability distribution of undrained shear strength adopts a normal distribution.

[0048] In some embodiments, in step S42, the sample size of the Latin hypercube sampling is determined according to the design space dimension. When the pile diameter and pile length are the main design variables, the sample size is not less than 30 groups to ensure sampling representativeness.

[0049] The technical concept of this invention is as follows: The specific technical solution includes the following steps: S1. Select a deterministic analysis model for energy piles under thermal-hydraulic-mechanical coupling, including a heat transfer model simulating the heat exchange process of the pile body and a load transfer model simulating the pile-soil interaction. S2. Determine the failure modes of the energy pile (ultimate limit state and serviceability limit state) and the limit state equations; S3. Select uncertain parameters (such as the internal friction angle, cohesion, specific heat capacity, thermal conductivity, thermal diffusivity and other thermophysical and mechanical parameters of soil considering the spatial variability of soil) and design variables to determine the design space of energy pile length and pile diameter. S4. Sampling of pile diameter and pile length combinations within the design space to extract design parameter samples to form alternative design schemes. S5. Determine the probability distribution and spatial variability characterization parameters of soil thermophysical and mechanical parameters, and generate random field samples of soil thermophysical and mechanical parameters that conform to the above probability statistics and spatial correlation characteristics using the random field discretization method; then, in conjunction with Monte Carlo simulation, call the deterministic analysis model and limit state equation in step S1 for each random field sample, and calculate the failure probability of the three failure modes under the given alternative design scheme in step S4. S6. To solve the problem of long calculation time, a full probability design method for energy piles based on the response surface methodology is established based on the calculation results of some design parameter samples. S7. Based on the above method, calculate the failure probability of all design schemes in the design space, and determine the design feasible region in the design space according to the target failure probability of each failure mode. S8. Based on the principle of economic optimization, select the optimal design scheme from the feasible design domain.

[0050] In step S1, a deterministic analysis model for the energy pile considering the multi-physics coupling effect of hydrodynamics is selected. The heat transfer model and the load transfer model are respectively exemplified by the heat transfer G-function and the load transfer method, as shown below: S11. The temperature field change of the pile body is solved by the improved heat transfer G function as shown below: (1) In the formula: —Average fluid temperature change; —Heat exchange efficiency per unit length; —The thermal conductivity of the soil layer; —Temperature response function of the soil layer; —Temperature response function of pile concrete; —Thermal resistance of the pile body concrete; —Heat exchanger tube thermal resistance; S12. Introducing the Fourier number determined by time. The temperature response function is calculated as shown in the following equation. (2) In the formula: —Soil thermal diffusivity; —Time step; —Pile radius; (3) In the formula: —Temperature response function parameters; (4) (5) (6) In the formula: —Lower bound state stake radius; —Upper bound state stake radius; —The ratio of the thermal conductivity of concrete to that of soil in the lower bound state; —The ratio of the thermal conductivity of concrete to that of soil in the upper bound state; —These are the concrete temperature response functions for the upper and lower bound states, respectively; S13. Calculate the water temperature at the outlet of the heat exchanger tube of the energy pile using equation (2) and the following equations (8) and (9). and pile body temperature change : (7) (8) (9) (10) In the formula: —Inlet and outlet fluid temperatures; —Heat exchanger tube length; —Heat transfer fluid density; —Specific heat capacity of the heat transfer fluid; —Specific density of fluid per unit time; S14. Select a load transfer curve model that describes the pile-soil interaction. Common load transfer curve models are shown in the table below:

[0051] S15. After determining the pile-side and pile-end soil interaction load transfer models to be used, the key parameters of the load transfer model can be calculated according to empirical or theoretical formulas. Taking the hyperbolic model as an example, the key parameters are calculated as shown in the following formula (11): (11) In the formula: This represents the shear stress at depth; , These are the parameters for the load transfer curve; The specific implementation method of step S2 is as follows: S21. Determine the failure mode of the energy pile, mainly considering three aspects: bearing failure under ultimate limit state (ULS), settlement failure and heat transfer failure mode under serviceability limit state (SLS). S22. The limit state equations corresponding to the three failure modes are shown below: The limit state equation under the load failure mode is shown in equation (12): (12) In the formula: —Ultimate bearing capacity of energy piles; —Response value of internal force in the pile body under the thermal coupling effect of energy pile; The limit state equation under the settlement failure mode is shown in equation (13): (13) In the formula: —Maximum allowable settlement at the top of the pile; —Pile top settlement value; The limit state equation under the heat transfer failure mode is shown in equation (14): (14) In the formula: —Target outlet water temperature; The specific implementation method of step S3 is as follows: S31. Considering the uncertainties in soil parameters, there are two main parameters: mechanical parameters and thermodynamic parameters. Mechanical parameters are considered in two cases: sandy soil and clay soil. Taking clay soil as an example, the undrained shear strength is selected as the uncertainty parameter to calculate the internal forces and displacement response of the energy piles in the clay soil site. Thermodynamic parameters mainly consider the soil's thermal conductivity, thermal diffusivity, and specific heat capacity.

[0052] S32. The main design variables for energy piles are pile diameter D and pile length L. Based on field test data or by referring to the experience of similar projects, the selectable range of pile diameter and pile length is determined, which constitutes the design space.

[0053] The specific implementation of step S4 is as follows: S41. Determine the design space for energy pile dimensions (pile diameter range, pile length range). S42. Sampling is performed within the design space using the Latin Hypercube (LHS) method. The LHS algorithm is used to ensure that the extracted design samples cover the entire design space and are representative. Different design sample points are extracted using the LHS algorithm.

[0054] The specific implementation method of step S5 is as follows: S51. Based on site information, determine the probability distribution type, mean, and standard deviation of soil thermophysical and mechanical parameters; determine the autocorrelation function (such as exponential or Gaussian type) characterizing the spatial variability of soil thermophysical and mechanical parameters and its correlation distance in the vertical and horizontal directions; use random field discretization technology (preferably local averaging method) to discretize the continuous random field onto the numerical analysis grid, and use the Choreski decomposition method or fast Fourier transform method to generate a large number of parameter sample fields that can accurately reflect the spatial variability of soil. S52. Substitute each generated random field sample as input into the deterministic analysis model of the energy pile considering the thermo-coupling effect for Monte Carlo simulation. Statistically calculate the limit state equation results under the three failure modes, and calculate the failure probability under the three failure modes. The specific calculation of the failure probability is shown in the following formula: (15) In the formula: —Number of failed samples; —Total number of samples; The specific implementation of step S6 is as follows: S61. Determine the design parameter samples extracted by the LHS method, and calculate the Monte Carlo simulation results of the failure probabilities of the three failure modes under different design parameter samples. S62. By constructing a proxy model, taking the response surface methodology as an example, and using the design parameters (pile diameter D, pile length L) as input variables, the failure probabilities under the three failure modes are... (or reliable indicators) Logarithmic probability of failure The input variables (design parameters) and the target variables (failure probabilities under the three failure modes) are respectively used as target variables. Linear regression fitting is performed using second-order or higher-order polynomials to obtain the response relationship between the input variables (design parameters) and the target variables (failure probabilities under the three failure modes). A full probability design method for energy piles based on the response surface method is established. The response surface model is a second-order polynomial as an example, as shown in the following equation (16): (16) In the formula: —Fit parameters; The specific implementation method of step S7 is as follows: S71. Based on the response relationship between the input variables and the target variables established by the surrogate model, and by inputting the design parameters of other unextracted design sample points within the design space, calculate the three failure modes for those unextracted design sample points. (or reliable indicators) Logarithmic probability of failure ); S72. By specifying the target failure probability (or target reliability index β, logarithmic value of target failure probability) for the three failure modes respectively, draw the full probability design feasible region diagram for the three failure modes respectively. S73. Summarize the full probability design feasible region diagrams corresponding to the three failure modes, and draw the full probability design feasible region diagram that considers the three failure modes simultaneously.

[0055] The specific implementation method of step S8 is as follows: S81. In the full probability design feasible region diagram considering three failure modes simultaneously, the cost of feasible design sample points near the failure region is calculated, and the final design scheme is selected according to the principle of economic optimality.

[0056] This invention verifies the reliability and feasibility of the proposed method for designing single energy piles considering thermo-coupling effects using Monte Carlo simulation. The case study site consists of saturated clay soil, with an 800kN mechanical load acting on the pile top. The calculation parameters involved in the case study are as follows: Figure 2 As shown. Figure 3 The design parameter samples extracted using the LHS algorithm, Figure 4 The method proposed in this invention involves performing Monte Carlo simulations on sample points of design parameters, constructing a response surface based on the Monte Carlo simulation results, calculating the failure probabilities of all design points within the design space under three failure modes, and then drawing the feasible region. The feasible region and failure region are defined according to the target reliability index. Figure 5 This is a full probability design feasible region diagram drawn after comprehensively considering three failure modes in the design feasible region of the method proposed in this invention. Figure 6 Comparing the calculation results of the method proposed in this invention with the Monte Carlo simulation results, it can be found that under random simulation with a large number of samples, the calculation results and simulation results maintain good consistency. Moreover, the method proposed in this invention greatly reduces the calculation time and significantly improves the calculation efficiency, proving the effectiveness and reliability of the method in the optimization design of energy piles.

[0057] The embodiments described above are for illustrative purposes only and are not intended to limit the invention. Therefore, any changes in numerical values ​​or substitutions of equivalent elements should still fall within the scope of this invention.

[0058] The above detailed description will enable those skilled in the art to understand that the present invention can indeed achieve the aforementioned objectives and has complied with the provisions of the Patent Law.

[0059] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention. The above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

[0060] It should be noted that the above description of the process is for illustrative purposes only and does not limit the scope of this specification. Those skilled in the art can make various modifications and changes to the process under the guidance of this specification. However, these modifications and changes remain within the scope of this specification.

[0061] The basic concepts have been described above. Obviously, for those skilled in the art who have read this application, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application, and therefore, such modifications, improvements, and corrections still fall within the spirit and scope of the exemplary embodiments of this application.

[0062] Furthermore, this application uses specific terms to describe its embodiments. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different positions in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application can be appropriately combined.

[0063] Furthermore, those skilled in the art will understand that aspects of this application can be described and illustrated through several patentable types or situations, including any new and useful combination of processes, machines, products, or substances, or any new and useful improvements thereof. Therefore, aspects of this application can be implemented entirely in hardware, entirely in software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. All of the above hardware or software can be referred to as a “unit,” “module,” or “system.” Furthermore, aspects of this application can take the form of a computer program product embodied in one or more computer-readable media, wherein computer-readable program code is contained therein.

[0064] The computer program code required for the operation of each part of this application can be written in any one or more programming languages, including object-oriented programming languages ​​such as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB.NET, and Python; general programming languages ​​such as C; Visual Basic, Fortran2103, Perl, COBOL2102, PHP, and ABAP; dynamic programming languages ​​such as Python, Ruby, and Groovy; or other programming languages. This program code can run entirely on the user's computer, or as a standalone software package on the user's computer, or partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer can be connected to the user's computer via any network, such as a local area network (LAN) or wide area network (WAN), or connected to an external computer (e.g., via the Internet), or in a cloud computing environment, or used as a service such as Software as a Service (SaaS).

[0065] Furthermore, unless expressly stated in the claims, the order of processing elements and sequences, the use of numbers and letters, or other names described in this application are not intended to limit the order of the processes and methods of this application. Although some currently considered useful embodiments of the invention have been discussed in the foregoing disclosure by way of various examples, it should be understood that such details are for illustrative purposes only, and the appended claims are not limited to the disclosed embodiments; rather, the claims are intended to cover all modifications and equivalent combinations that conform to the substance and scope of the embodiments of this application. For example, although the implementation of the various components described above can be embodied in a hardware device, it can also be implemented as a purely software solution, such as an installation on an existing server or mobile device.

[0066] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments of the invention, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this approach of the present application should not be construed as reflecting an intention that the claimed subject matter requires more features than expressly recited in each claim. Rather, the subject of the invention should possess fewer features than in any single embodiment described above.

Claims

1. A reliability analysis and design method for energy piles considering the spatial variability of soil parameters, characterized in that, include: S1. Select a deterministic analysis model for energy piles under thermal-hydraulic-mechanical coupling. This model includes a heat transfer model that simulates the heat exchange process of the pile body and a load transfer model that simulates the pile-soil interaction. S2. Determine the failure modes and corresponding limit state equations of the energy pile. The failure modes include bearing failure under the ultimate limit state, settlement failure under the serviceability limit state, and heat transfer failure. S3. Select uncertainty parameters and design variables. The uncertainty parameters are soil thermophysical and mechanical parameters, and the design variables are the pile length and pile diameter of the energy pile. Determine the design space for the pile length and pile diameter based on the design variables. S4. Within the design space, samples are taken of combinations of pile diameter and pile length, and the extracted design parameter samples form alternative design schemes. S5. Determine the probability distribution and spatial variability characterization parameters of soil thermophysical and mechanical parameters. Use the random field discretization method to generate random field samples of soil thermophysical and mechanical parameters that conform to the characteristics of probability statistics and spatial correlation. Combine Monte Carlo simulation, call the deterministic analysis model and limit state equation of energy pile under thermal-hydraulic-mechanical coupling for each random field sample, and calculate the failure probability of three failure modes under alternative design schemes. S6. Based on the failure probability calculation results of some design parameter samples in step S4 corresponding to step S5, establish a full probability design method for energy piles based on the response surface methodology. S7. Based on the full probability design method in step S6, calculate the failure probability of all design schemes in the design space described in step S3, and determine the design feasible region in the design space according to the target failure probability of each failure mode in step S2. S8. Based on the principle of economic optimization, select the optimal design scheme from the feasible design domain described in step S7.

2. The reliability analysis and design method for energy piles considering the spatial variability of soil parameters according to claim 1, characterized in that, S1 includes: S11. Select a heat transfer model to simulate pile heat exchange, including finite or infinite length line heat source model, solid cylindrical heat source model, heat transfer G function, and CFD model. S12. Select load transfer models for simulating pile-soil interaction, including fully elastic-plastic model, exponential model, hyperbolic model, bilinear model, trilinear model, and generalized softening model. S13. Select the load transfer algorithm for the energy pile, including the finite element method, the finite difference method, and the discrete element method; S14. Establish a deterministic analysis model for the energy pile based on the selected heat transfer model and load transfer model to calculate the bearing capacity, displacement, and outlet water temperature of the pile under thermo-coupling conditions.

3. The reliability analysis and design method for energy piles considering the spatial variability of soil parameters according to claim 1, characterized in that, S2 include: S21. Definition of bearing failure under ultimate bearing capacity state: When the mechanical response of the pile exceeds the ultimate bearing capacity of the pile, it is considered as bearing failure; S22. Definition of settlement failure under normal serviceability limit state: When the settlement value of the pile top unit exceeds the allowable settlement value, it is considered as settlement failure; S23. Define heat transfer failure under normal operating limits: When the outlet temperature of the heat exchange tube of the energy pile is higher or lower than the target temperature, it is considered heat transfer failure.

4. The reliability analysis and design method for energy piles considering the spatial variability of soil parameters according to claim 1, characterized in that, S3 include: S31. Determine the uncertain parameters, which are divided into mechanical parameters and thermodynamic parameters: For sandy soil sites, the mechanical parameters are cohesion and internal friction angle, and for clay sites, the undrained shear strength is used; Thermodynamic parameters include the thermal conductivity, thermal diffusivity and specific heat capacity of the soil. S32. Determine the design variables as the pile diameter and pile length of the energy pile, and construct the design space based on the range of selectable pile diameters and pile lengths.

5. The reliability analysis and design method for energy piles considering the spatial variability of soil parameters according to claim 1, characterized in that, S4 include: S41. Determine the design space for energy pile dimensions, namely the range of pile diameter and pile length; S42. Within the design space, the combination of pile diameter and pile length is sampled using the Latin hypercube sampling method to ensure that the extracted design samples cover the entire design space and are representative, forming different design sample points.

6. The reliability analysis and design method for energy piles considering the spatial variability of soil parameters according to claim 1, characterized in that, S5 include: S51. Soil uncertainty parameters are divided into mechanical parameters and thermodynamic parameters. The mechanical parameters are treated differently for sandy soil sites and clay soil sites. The thermodynamic parameters are selected as soil thermal conductivity, thermal diffusivity and specific heat capacity. S52. Determine the probability distribution type, mean, and standard deviation of the soil thermophysical and mechanical parameters based on site information; S53. Determine the autocorrelation function characterizing the spatial variability of soil thermophysical and mechanical parameters and its correlation distance in the vertical and horizontal directions; S54. Using random field discretization technology, the continuous random field is discretized onto the numerical analysis grid, and the Choreski decomposition method or fast Fourier transform method is used to generate a parameter sample field that can accurately reflect the spatial variability of soil. S55. Take each generated random field sample as input and substitute it into the deterministic analysis model of the energy pile under the action of thermal-water-mechanical coupling. For each alternative design scheme in step S4, calculate the failure probability of the three modes of bearing failure, settlement failure and heat transfer failure by counting the number of times the limit state equation is triggered in the simulation results of all random field samples.

7. The reliability analysis and design method for energy piles considering the spatial variability of soil parameters according to claim 1, characterized in that, S6 include: S61. Select failure probability, reliability index or logarithmic failure probability as the target variable for calculation; S62. Based on the failure probability calculation results of the extracted design parameter samples, the response relationship between the input variables and the target variables is established through the response surface model to form the full probability design method for energy piles.

8. The reliability analysis and design method for energy piles considering the spatial variability of soil parameters according to claim 1, characterized in that, S7 includes: S71. Select the target reliability index corresponding to each failure mode based on the importance of the energy pile structure. S72. Predict the unsampled design sample points in the design space using the response surface model, and input the pile diameter and pile length to calculate its reliability index. S73. Based on the reliability index calculation results of each design point, draw and determine the full probability design feasible region with the target reliability index as the boundary.

9. The reliability analysis and design method for energy piles considering the spatial variability of soil parameters according to claim 1, characterized in that, S8 includes: S81. Within the fully probabilistic design feasible region determined in step S7, calculate the comprehensive cost of different design schemes by combining the cost information corresponding to the pile diameter and pile length. S82. Taking the lowest overall cost as the economic optimal principle, select the design scheme with the lowest cost that meets the requirements of all failure modes from the feasible region as the optimal design scheme.

10. The reliability analysis and design method for energy piles considering the spatial variability of soil parameters according to claim 2, characterized in that, In step S14, the calculation of the pile response under the thermo-coupling condition requires simultaneous input of the superstructure load, periodic thermal load, and soil thermodynamic parameters. The pile temperature field distribution is calculated through the heat transfer model, and then the influence of the additional stress caused by the temperature field on the pile bearing capacity and displacement is calculated in combination with the load transfer model.

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