Unsaturated soil energy pile heat-water-force multi-field coupling response calculation method

Abstract

The invention provides an unsaturated soil energy pile heat-water-force multi-field coupling response calculation method. The unsaturated soil energy pile heat-water-force multi-field coupling response calculation method comprises the steps that S1, a saturated soil energy pile load transfer algorithm is determined; s2, determining a soil-water characteristic curve model considering the temperature effect; s3, calculating the shearing strength of the energy pile-unsaturated soil interface considering the contribution of the matric suction; s4, calculating the ultimate resistance of the pile end considering the coupling effect of the temperature load and the unsaturated condition; s5, calculating the shear modulus of the soil body around the pile considering the coupling effect of the temperature load and the unsaturated condition; s6, the energy pile-raft plate contact rigidity is calculated; and S7, the heat-water-force multi-physics field coupling response of the unsaturated soil energy pile is calculated. The invention aims to reveal the bearing mechanism of the energy pile under the combined action of the temperature load and the unsaturated soil condition, and provides theoretical and method support for the analysis and design of the unsaturated soil energy pile.

Description

Technical Field

[0001] The present invention relates to the fields of geothermal energy technology and unsaturated soil energy pile technology, and in particular to a method for calculating the thermal-hydraulic-mechanical multi-field coupling response of an unsaturated soil energy pile. Background Art

[0002] Pile foundations are widely used in geotechnical engineering practice, as they can transfer superstructure loads to the underlying soil and effectively control differential settlement. Accurately calculating the bearing response of pile foundations is crucial for their geotechnical engineering design. Currently, the most widely used bearing response calculation method in pile foundation research focuses on saturated soil conditions. This method assumes the soil surrounding the pile is dry or saturated, and the analysis only considers the pile-dry / saturated soil interaction. With the increasing understanding of unsaturated soils, the bearing response of pile foundations in unsaturated soils has also garnered increasing attention. For example, Georgiadis et al. (2003) used finite element analysis to investigate the influence of unsaturated soil conditions on the bearing response of pile foundations. Liu and Vanapalli (2019) analyzed the load-displacement response of single pile foundations in unsaturated expansive soils using a load transfer method. Vanapalli and Taylan (2012) extended the bearing capacity method for pile foundations in saturated soils to unsaturated soils under both drained and undrained conditions. The above studies show that due to the different pore fluid states and mechanical mechanisms of the soil around the pile, the bearing response of the pile foundation is significantly different in unsaturated soil and saturated soil.

[0003] With innovations in shallow geothermal energy development technology, traditional pile foundations have evolved from a single load-bearing structure to a dual function of load bearing and heat exchange, giving rise to energy pile technology that combines both heat transfer and load-bearing functions (Brandl, 2006; Laloui et al., 2006). Energy pile technology organically combines heat exchange tubes with building pile foundations. While bearing the loads of the upper structure, it also enables the efficient development and utilization of shallow geothermal energy, making it an important green geotechnical engineering technology. As a derivative of traditional building pile foundations, the load-bearing response design of energy piles typically adheres to the dry and saturated soil assumptions and related theories of traditional building pile foundations, ignoring their applicability to unsaturated soil conditions (for example, in semi-arid regions where the groundwater level is below the pile end, resulting in a naturally unsaturated state). Furthermore, the temperature of energy piles fluctuates between 5 and 45°C during service. Research has shown that the changes in pore water viscosity and density caused by the heat exchange process within this temperature range will drive the soil surrounding the pile to transform from a saturated to an unsaturated state. This indicates that even under saturated conditions, the saturated soil around the pile may transform into an unsaturated soil due to the effects of temperature loads and long-term heat exchange within the pile, thereby affecting the pile's bearing response. In this case, continuing to use the dry / saturated soil assumption and related theories could lead to significant errors in the design results of the pile's bearing response.

[0004] In recent years, researchers have gradually focused on the bearing response of energy piles in unsaturated soils and conducted preliminary studies (Wang et al., 2012; Goode and McCartney, 2015). For example, to reasonably estimate the bearing response of energy piles in unsaturated soils, Thota et al. (2021) comprehensively considered the thermodynamic properties of unsaturated soils and the pile-soil interface and proposed an analytical framework for estimating the ultimate bearing capacity variation of energy piles in unsaturated fine-grained soils. The validity of this framework was verified using experimental data on the ultimate bearing capacity of energy piles in unsaturated Bonny silt. Based on thermodynamic theory, Pham and Sutman (2023) established a non-isothermal soil-water characteristic curve (SWCC) model that considers temperature variations. They further combined this model with bearing capacity theory to propose a simplified analysis method for the bearing capacity of energy piles in unsaturated soils. Although the above methods provide an effective means for calculating the bearing response of energy piles in unsaturated soil, there are still some limitations in related research: (1) the change in the shear strength of the pile-soil interface under the coupling of temperature load and the unsaturated state of the soil around the pile is not considered, which leads to errors in the estimation of the pile side friction resistance; (2) the contribution and influence of the matrix suction of the unsaturated soil around the pile on the bearing response of the pile body are not considered; (3) only the ultimate bearing capacity of energy piles in unsaturated soil can be estimated, and the key response characteristics such as axial strain, stress, side friction resistance and displacement of the energy pile and their distribution along the pile body cannot be calculated. The above limitations make the research on energy piles in unsaturated soil still face key challenges such as unclear interaction mechanism between pile and unsaturated soil interface and lack of calculation method for bearing response. Summary of the Invention

[0005] The present invention provides a calculation method for the thermal-hydraulic-mechanical multi-field coupled response of unsaturated soil energy piles, aiming to reveal the bearing mechanism of energy piles under the combined action of temperature load and unsaturated soil conditions, and to provide theoretical and methodological support for the analysis and design of unsaturated soil energy piles.

[0006] To achieve the above object, the present invention adopts the following technical solutions: A calculation method for the thermal-hydraulic-mechanical multi-field coupled response of an unsaturated soil energy pile includes: S1. Compare and select pile-side-soil and pile-end-soil load transfer models, simulate pile-soil nonlinear interaction, and determine the energy pile load transfer algorithm for saturated soil; S2. Compare and select soil-water characteristic curve models that consider temperature effects to simulate the relationship between matrix suction and saturation under different temperature loads; S3. Calculate the horizontal stress of the unsaturated soil on the pile side under temperature load. Combined with the soil-water characteristic curve model that considers temperature effects, matrix suction, saturation, and the effective friction angle and cohesion of the pile-soil interface, calculate the shear strength of the energy pile-unsaturated soil interface, taking into account the contribution of matrix suction. S4. Based on the calculation formula for the ultimate resistance of energy piles in saturated soil, the contribution of matrix suction is introduced to calculate the ultimate resistance of the pile tip considering the coupling effects of temperature load and unsaturated conditions. S5. Calculate the shear modulus of the soil around the pile considering the coupling of temperature load and unsaturated conditions, which is used to calculate the parameters of the energy pile load transfer model; S6. Calculate the energy pile-raft contact stiffness based on the raft dimensions, Young's modulus of the soil beneath the raft, and Poisson's ratio, and simulate the interaction between the energy pile and the superstructure. S7. Substitute the shear strength of the energy pile-unsaturated soil interface contributed by matrix suction, the ultimate resistance of the pile tip considering the coupling of temperature load and unsaturated conditions, the shear modulus of the soil around the pile considering the coupling of temperature load and unsaturated conditions, and the energy pile-raft contact stiffness into the load transfer algorithm of the saturated soil energy pile to calculate the thermal-hydraulic-mechanical multi-physics field coupling response of the unsaturated soil energy pile.

[0007] In this specification, the energy pile-soil relative displacement in the pile-soil nonlinear interaction in S1 is composed of the nonlinear displacement of the pile-soil shear disturbance zone and the elastic displacement of the soil in the undisturbed zone around the pile, where: The nonlinear displacement of the pile-soil shear disturbance zone is calculated using a fully elastic-plastic model, exponential model, hyperbolic model, double-broken-line model, triple-broken-line model, or generalized softening model; The elastic displacement of the soil in the undisturbed area around the pile is solved using elastic theory.

[0008] In this specification, the load transfer algorithm for saturated soil energy piles in S1 is as follows: Select the load transfer model and pile top contact stiffness to simulate the pile-soil nonlinear interaction; Determine the energy pile side- and pile tip-soil interaction models in saturated or dry soils. The pile side- and pile tip-soil interaction models are formulas (1) and (2), respectively. (1); (2); Where: is the ultimate shear strength; is the shear modulus of the soil at the pile side; is the pile radius; is the shear influence radius; is the shear modulus of soil at the pile tip; is the Poisson's ratio of the soil at the pile tip; It is the sum of the nonlinear displacement and elastic displacement of the soil around the pile; and are the total displacement and shear stress of the pile side at the unloading point or reloading point, respectively; is the loading and unloading status judgment factor; is the shear strength of the soil on the pile side; is the pile side-soil initial shear stiffness; is the pile side shear stress; is the sum of the nonlinear displacement and elastic displacement of the pile tip; and are the total displacement and shear stress at the pile tip at the unloading point or reloading point, respectively; Initial stiffness of pile tip-soil interaction; is the loading and unloading status judgment factor; is the ultimate end resistance; Pile tip resistance; Determine the pile-side and pile-tip-soil interaction model parameters, including pile-soil interface shear strength, pile-side-soil initial shear stiffness, pile-tip ultimate strength, pile-tip-soil initial stiffness, and pile-raft contact stiffness; The energy pile side- and pile-tip-soil interaction models in saturated or dry soil are substituted into the single energy pile load transfer algorithm to obtain the thermal-mechanical coupling response of the energy pile in saturated or dry soil.

[0009] In this specification, by introducing the temperature correction parameter into the model of the soil-water characteristic curve without considering the temperature effect in S2, the soil-water characteristic curve model considering the temperature effect can be obtained; the soil-water characteristic curve model without considering the temperature effect includes two types: empirical models and theoretical models. The theoretical models include thermodynamic models and pore network models, and the empirical models include the van Genuchten model, Fredlund-Xing model, Brooks-Corey model, and Gardner model.

[0010] In this manual, the van Genuchten model is used in S2, and the soil-water characteristic curve model and temperature correction parameters considering the temperature effect are The corresponding formulas are (3) and (4); (3); (4); Where: is saturation; is matrix suction; and are model parameters; It is the temperature; and is the model coefficient.

[0011] In this manual, the energy pile is considered as a completely elastic body in the calculation of the horizontal stress of the unsaturated soil on the pile side under the action of temperature load. is Equation (5) and (6); (5); (6); Where: is the volume of the energy pile under the effect of temperature; is the initial volume of the energy pile; is the thermal expansion coefficient of the pile; is the temperature change; It is the length of the pile; is the radius of the pile under temperature. According to equations (5) and (6), the change in the radius of the pile under temperature load is calculated. for: (7); Then the horizontal stress at the energy pile-unsaturated soil interface caused by temperature load is for: (8); is the Young's modulus of soil; The total horizontal stress at the energy pile-unsaturated soil interface is the sum of the effective horizontal stress of the soil on the pile side and the horizontal stress at the pile-soil interface caused by the temperature load. , as shown in formula (9); (9); is the effective internal friction angle of soil; is the effective weight of soil; z is the depth; The energy pile-unsaturated soil interface shear strength It consists of three parts: soil cohesion contribution, horizontal stress contribution, and matrix suction contribution, as shown in formula (10): (10); Where: is the soil Poisson's ratio; is the effective internal friction angle of the pile-soil interface; is the effective cohesion of the pile-soil interface; is the residual saturation; is the current saturation.

[0012] In this specification, the ultimate resistance of pile tip considering the coupling of temperature load and unsaturated condition in S4 is The calculation formula is: (11); Where: is the effective internal friction angle of the soil at the pile tip; is the effective vertical stress in the soil at the pile tip; is the effective cohesion of soil at the pile end; is the model coefficient, calculated according to equations (12) and (13); (12); (13); Where: is the adjustment factor; is the effective cohesion of soil at the pile tip; exp is the exponential function; is the measured data of the ultimate end resistance, and the adjustment coefficient is calculated using the empirical formula (14); (14); Where: and 1 and -0.006 respectively.

[0013] In this specification, the shear modulus of the soil around the pile considering the coupling effect of temperature load and unsaturated condition in S5 is calculated according to Equation (15) and Equation (16); (15); (16); Where: k is the model parameter; and are the Young's modulus of soil in dry and saturated states, respectively; It is the measured Young's modulus for soil states between dry and saturated; It is used to measure saturated soil.

[0014] In this specification, the energy pile-raft contact stiffness in S6 is calculated according to formula (17): (17); Where: and are the raft width and length respectively; is the calculation coefficient; for layered soil, Young's modulus and Poisson's ratio weighted average Calculate according to formula (18) and (19) respectively; (18); (19); Where: is the soil thickness; is the Young's modulus of each soil layer; is the Poisson's ratio of each soil layer.

[0015] In this specification, Young's modulus E and shear modulus The relationship between is shown in formula (20): (20).

[0016] In summary, the present invention has at least the following beneficial effects: This method considers the contribution and influence of the changes in the shear strength of the pile-soil interface under the coupled effects of temperature loads and the unsaturated state of the surrounding soil, as well as the matric suction of the unsaturated soil surrounding the pile, on the pile's bearing response (load transfer). It can calculate the numerical values ​​and distribution patterns of the thermal-hydraulic-mechanical multi-physics coupled axial strain, stress, frictional resistance, end resistance, and displacement of energy piles under the coupled effects of temperature loads and unsaturated conditions. This method is simple in principle and easy to use, providing theoretical support and computational tools for the analysis and design of energy piles in unsaturated soils. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0018] Figure 1 It is a schematic diagram of the calculation method of the thermal-hydraulic-mechanical multi-field coupled response of the unsaturated soil energy pile involved in the present invention.

[0019] Figure 2 It is a flow chart of the dry or saturated soil energy pile coupling response algorithm involved in the present invention.

[0020] Figure 3 Schematic diagram of the calculation parameters involved in the verification case involved in the present invention.

[0021] Figure 4 It is a schematic diagram of the soil-water characteristic curve at different temperatures involved in the present invention.

[0022] Figure 5 Schematic diagram comparing the simulated value and the test value of the pile bearing capacity involved in the present invention.

[0023] Figure 6 It is a schematic diagram of the soil-water characteristic curve at different temperatures involved in the present invention.

[0024] Figure 7 Schematic diagram comparing the simulated value and the test value of the pile bearing capacity involved in the present invention. DETAILED DESCRIPTION

[0025] Hereinafter, only certain exemplary embodiments are briefly described. As will be appreciated by those skilled in the art, the described embodiments may be modified in various ways without departing from the spirit or scope of the embodiments of the present invention. Therefore, the drawings and description are to be regarded as illustrative in nature and not restrictive.

[0026] The disclosure below provides many different embodiments or examples for implementing different structures of the embodiments of the present invention. In order to simplify the disclosure of the embodiments of the present invention, the components and configurations of specific examples are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. In addition, the embodiments of the present invention may repeat reference numerals and / or reference letters in different examples. Such repetition is for the purpose of simplicity and clarity and does not in itself indicate the relationship between the various embodiments and / or configurations discussed.

[0027] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0028] like Figure 1 As shown, this embodiment provides a method for calculating the thermal-hydraulic-mechanical multi-field coupled response of an unsaturated soil energy pile, including: S1. Compare and select pile-side-soil and pile-end-soil load transfer models, simulate pile-soil nonlinear interaction, and determine the energy pile load transfer algorithm for saturated soil; S2. Compare and select soil-water characteristic curve models that consider temperature effects to simulate the relationship between matrix suction and saturation under different temperature loads; S3. Calculate the horizontal stress of the unsaturated soil on the pile side under temperature load. Combined with the soil-water characteristic curve model that considers temperature effects, matrix suction, saturation, and the effective friction angle and cohesion of the pile-soil interface, calculate the shear strength of the energy pile-unsaturated soil interface, taking into account the contribution of matrix suction. S4. Based on the calculation formula for the ultimate resistance of energy piles in saturated soil, the contribution of matrix suction is introduced to calculate the ultimate resistance of the pile tip considering the coupling effects of temperature load and unsaturated conditions. S5. Calculate the shear modulus of the soil around the pile considering the coupling of temperature load and unsaturated conditions, which is used to calculate the parameters of the energy pile load transfer model; S6. Calculate the energy pile-raft contact stiffness based on the raft dimensions, Young's modulus of the soil beneath the raft, and Poisson's ratio, and simulate the interaction between the energy pile and the superstructure. S7. Substitute the shear strength of the energy pile-unsaturated soil interface contributed by matrix suction, the ultimate resistance of the pile tip considering the coupling of temperature load and unsaturated conditions, the shear modulus of the soil around the pile considering the coupling of temperature load and unsaturated conditions, and the energy pile-raft contact stiffness into the load transfer algorithm of the saturated soil energy pile to calculate the thermal-hydraulic-mechanical multi-physics field coupling response of the unsaturated soil energy pile.

[0029] The present invention is based on the following basic assumptions: (1) Existing studies have shown that the radial deformation and pile side normal stress of vertically loaded energy piles have little effect on the changes in the mechanical properties of the pile body. Therefore, the influence of the axial deformation of the pile is mainly considered in this study. (2) The stress and strain of the pile body under compression are positive, the friction resistance is positive upward, and the displacement of the pile body is positive upward; (3) The cross-sectional geometry, physical and mechanical properties, and temperature changes of the pile body are evenly distributed along the pile body.

[0030] In some embodiments, in S1, the relative displacement of the energy pile-soil is composed of the nonlinear displacement of the pile-soil shear disturbance zone and the elastic displacement of the soil in the undisturbed zone around the pile. The specific calculation method is: the nonlinear displacement of the energy pile-soil shear disturbance zone can be calculated by a commonly used load transfer model, including but not limited to a complete elastic-plastic model, an exponential model, a hyperbola model, a bilinear model, a trilinear model, a generalized softening model, etc.; the elastic displacement of the soil in the undisturbed zone around the pile can be solved by methods related to elastic theory; the thermal-hydraulic-mechanical coupling response algorithm of the unsaturated energy pile is similar to the energy pile load transfer algorithm in saturated or dry soil, the difference being that the pile side-soil and pile end-soil load transfer models that take into account the coupling of temperature load and unsaturated conditions are used; the steps of the energy pile load transfer algorithm in saturated or dry soil are as follows: Figure 2 As shown, specifically: 1) Select the load transfer model and pile top contact stiffness to simulate the nonlinear interaction between pile and soil.

[0031] 2) Determine the energy pile-side and pile-tip-soil interaction models in saturated or dry soil. Preferably, taking the exponential model as an example, the pile-side and pile-tip-soil interaction models are Equations (1) and (2), respectively.

[0032] (1); (2); Where: is the shear modulus of the soil at the pile side; is the pile diameter; is the shear influence radius; is the shear modulus of soil at the pile tip; is the Poisson's ratio of the soil at the pile tip; It is the sum of the nonlinear displacement and elastic displacement of the soil around the pile; and are the total displacement and shear stress of the pile side at the unloading point or reloading point, respectively; is the loading and unloading status judgment factor; is the shear strength of the soil on the pile side; is the pile side-soil initial shear stiffness; is the pile side shear stress; is the sum of the nonlinear displacement and elastic displacement of the pile tip; and are the total displacement and shear stress at the pile tip at the unloading point or reloading point, respectively; Initial stiffness of pile tip-soil interaction; is the loading and unloading status judgment factor; is the ultimate end resistance; Pile tip resistance.

[0033] 3) Determine the parameters of the pile-side and pile-tip-soil interaction model. These key parameters include the pile-soil interface shear strength, pile-side-soil initial shear stiffness, pile-tip ultimate strength, pile-tip-soil initial stiffness, and pile-raft contact stiffness. These parameters can be determined using field test results, unit test results, and corresponding empirical formulas.

[0034] 4) Substitute the side- and tip-soil interaction models of the energy pile in saturated or dry soil into the load transfer algorithm for a single energy pile to obtain the coupled thermal-mechanical response of the energy pile in saturated or dry soil. This load transfer (bearing response) algorithm for a single energy pile can be implemented using methods such as the finite element method, finite difference method, and matrix displacement method.

[0035] In some embodiments, S2 is specifically implemented as follows: SWCC models that do not consider temperature effects include empirical models and theoretical models. Commonly used empirical models include the van Genuchten model, the Fredlund-Xing model, the Brooks-Corey model, and the Gardner model. Commonly used theoretical models include thermodynamic models and pore network models. For coarse-grained soils, the Brooks-Corey model is recommended; for fine-grained soils, the van Genuchten model and the Fredlund-Xing model are recommended. By introducing a temperature correction parameter into the model that does not consider temperature effects, a SWCC model that considers temperature effects can be obtained. The specific expression of the temperature correction coefficient can be reasonably selected based on the specific situation.

[0036] Preferably, taking the van Genuchten model as an example, the SWCC model and temperature correction coefficient considering the temperature effect are equations (3) and (4), respectively.

[0037] (3); (4); Where: is saturation; is matrix suction; and are model parameters; It is the temperature; and is the model coefficient.

[0038] In some embodiments, the specific implementation method of S3 is as follows: the horizontal stress of the unsaturated soil on the pile side under the action of temperature load can be calculated by treating the pile body as a completely elastic body; the shear strength of the energy pile-unsaturated soil interface is composed of three parts: the soil cohesion contribution item, the horizontal stress contribution item, and the matrix suction contribution item. Among them, the soil cohesion contribution item is related to the cohesion of the unsaturated soil, the horizontal stress contribution item is related to the horizontal stress of the unsaturated soil on the pile side under the action of temperature load and the effective friction angle of the pile-soil interface, and the matrix suction contribution item is related to the SWCC model considering the temperature effect, matrix suction, saturation, and the effective friction angle of the pile-soil interface.

[0039] In the calculation process of the horizontal stress of the unsaturated soil on the pile side under the temperature load, the energy pile is regarded as a completely elastic body. Then the volume change of the energy pile under the temperature load is expressed by equations (5) and (6).

[0040] (5); (6); Where: is the thermal expansion coefficient of the pile; is the pile radius; is the temperature change; It is the length of the pile; is the radius of the pile under temperature. According to equations (5) and (6), the change in the radius of the pile under temperature load can be calculated as: (7); Then the horizontal stress at the energy pile-unsaturated soil interface caused by temperature load is: (8); The total horizontal stress at the energy pile-unsaturated soil interface is the sum of the effective horizontal stress of the soil on the pile side and the horizontal stress at the pile-soil interface caused by the temperature load, as shown in Equation (9).

[0041] (9); The shear strength of the energy pile-unsaturated soil interface is composed of three parts: soil cohesion contribution, horizontal stress contribution, and matrix suction contribution, as shown in formula (10): (10); Where: is the soil Poisson's ratio; is the effective internal friction angle of the pile-soil interface; is the effective cohesion of the pile-soil interface; is the residual saturation; is the current saturation.

[0042] In some embodiments, S4 specific implementation method: the calculation formula of the pile end ultimate resistance considering the coupling effect of temperature load and unsaturated condition is similar to the calculation formula of the pile end ultimate resistance of saturated soil energy pile, except that the contribution of matrix suction needs to be considered.

[0043] The calculation formula for the ultimate resistance of the pile tip considering the coupling effect of temperature load and unsaturated conditions is: (11); Where: is the effective internal friction angle of the soil at the pile tip; is the effective vertical stress in the soil at the pile tip; is the effective cohesion of soil at the pile end; is the model coefficient and can be calculated according to equations (12) and (13).

[0044] (12); (13); Where: is the adjustment factor; is the measured data of the ultimate end resistance. Based on a large amount of measured data, the adjustment coefficient can be calculated using the empirical formula (14).

[0045] (14); Where: and 1 and -0.006 respectively.

[0046] In some embodiments, S5 specific implementation method: considering the coupling of temperature load and unsaturated conditions, the shear modulus of the soil around the pile is related to the shear modulus in dry and wet states, the specific surface area of ​​soil particles, etc. The obtained shear modulus can be used for parameter calculation of the energy pile load transfer model.

[0047] The shear modulus of the soil around the pile considering the coupling effect of temperature load and unsaturated condition can be calculated according to equations (15) and (16).

[0048] (15); (16); Where: and are the Young's modulus of soil in dry and saturated states, respectively; It is the measured Young's modulus for soil states between dry and saturated; It is used to measure saturated soil.

[0049] In some embodiments, S6 is implemented as follows: the energy pile-raft contact stiffness is related to parameters such as the raft size, the Young's modulus of the soil beneath the raft, and the Poisson's ratio. For layered soils, a weighted average of the Young's modulus and Poisson's ratio of the unsaturated soil within the energy pile depth can be used.

[0050] The energy pile-raft contact stiffness can be calculated according to formula (17): (17); Where: and are the raft width and length, respectively; is the calculation coefficient. For layered soils, the weighted average values ​​of Young’s modulus and Poisson’s ratio are calculated according to Equations (18) and (19), respectively.

[0051] (18); (19); Where: is the soil thickness; is the Young's modulus of each soil layer; is the Poisson's ratio of each soil layer.

[0052] The relationship between the Young's modulus and the shear modulus is shown in formula (20): (20); This paper verifies the reliability and effectiveness of the proposed method in analyzing the thermal-hydraulic-mechanical multi-field coupled response of unsaturated soil energy piles through two experimental cases, of which Case 1 is a centrifuge model test and Case 2 is a scaled model test. The calculation parameters involved in the verification cases are all taken from the experimental work, such as Figure 3 As shown. Case 1 SWCC curve is shown Figure 4 , Case 2 SWCC curve see Figure 6 . Figure 5 and 7 The figure shows a comparison between the simulated and experimental values ​​of the pile bearing capacity in Cases 1 and 2. It can be found that under different temperatures and soil saturations, the simulation results and the experimental results maintain good consistency, demonstrating the effectiveness and reliability of this method in calculating the thermal-hydraulic-mechanical multi-field coupled response of energy piles in unsaturated soils.

[0053] The above embodiments are intended to illustrate the present invention, not to limit the present invention. Therefore, changes in illustrative values ​​or substitutions of equivalent components should still fall within the scope of the present invention.

[0054] From the above detailed description, it will be clear to those skilled in the art that the present invention can indeed achieve the aforementioned objectives and is in compliance with the provisions of the Patent Law.

[0055] Although preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they become aware of the basic inventive concepts. Therefore, the appended claims are intended to be interpreted as covering the preferred embodiments and all changes and modifications that fall within the scope of the invention. The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

[0056] It should be noted that the above description of the relevant processes is for illustration and purpose only and does not limit the scope of application of this specification. For those skilled in the art, various modifications and changes can be made to the processes under the guidance of this specification. However, such modifications and changes are still within the scope of this specification.

[0057] The basic concepts have been described above. It will be apparent to those skilled in the art after reading this application that the above disclosures are merely illustrative and do not constitute limitations on this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and amendments to this application. Such modifications, improvements, and amendments are suggested in this application and remain within the spirit and scope of the exemplary embodiments of this application.

[0058] At the same time, this application uses specific terms to describe the embodiments of this application. For example, "one embodiment," "an embodiment," and / or "some embodiments" refer to a certain feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "one embodiment," "an embodiment," or "an alternative embodiment" mentioned twice or more in different places in this specification does not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application may be appropriately combined.

[0059] Furthermore, those skilled in the art will appreciate that various aspects of the present application may be illustrated and described in terms of a number of patentable categories or situations, including any new and useful process, machine, product, or combination of substances, or any new and useful improvement thereof. Thus, various aspects of the present application may be implemented entirely in hardware, entirely in software (including firmware, resident software, microcode, etc.), or in a combination of hardware and software. Each of the above hardware and software may be referred to as a "unit," "module," or "system." Furthermore, various aspects of the present application may take the form of a computer program product embodied in one or more computer-readable media, with computer-readable program code embodied therein.

[0060] 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, Python, etc., conventional procedural programming languages ​​such as C programming language, Visual Basic, Fortran2103, Perl, COBOL2102, PHP, ABAP, dynamic programming languages ​​such as Python, Ruby and Groovy, or other programming languages. The program code can be run entirely on the user's computer, or as a standalone software package on the user's computer, or partly on the user's computer and partly 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 form, such as a local area network (LAN) or a 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).

[0061] In addition, unless expressly stated in the claims, the order of the processing elements and sequences described in this application, the use of alphanumeric characters, or the use of other names are not intended to limit the order of the processes and methods of this application. Although the above disclosure discusses some embodiments of the invention that are currently considered useful through various examples, it should be understood that such details are only for illustrative purposes, and the attached claims are not limited to the disclosed embodiments. On the contrary, the claims are intended to cover all modifications and equivalent combinations that are consistent with the essence 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 pure software solution, for example, installation on an existing server or mobile device.

[0062] Similarly, it should be noted that in order to simplify the presentation of this disclosure and thereby facilitate understanding of one or more of the invention's embodiments, the foregoing descriptions of the embodiments of this disclosure sometimes combine multiple features into a single embodiment, figure, or description thereof. However, this approach should not be interpreted as reflecting an intention that the claimed subject matter requires more features than expressly recited in each claim. Rather, the subject matter of the invention may possess fewer features than the single embodiment described above.

Claims

1. A method for calculating the thermal-hydraulic-mechanical multi-field coupled response of an unsaturated soil energy pile, characterized in that: include: S1. Compare and select pile-side-soil and pile-end-soil load transfer models, simulate pile-soil nonlinear interaction, and determine the energy pile load transfer algorithm for saturated soil; S2. Compare and select soil-water characteristic curve models that consider temperature effects to simulate the relationship between matrix suction and saturation under different temperature loads; S3. Calculate the horizontal stress of the unsaturated soil on the pile side under temperature load. Combined with the soil-water characteristic curve model that considers temperature effects, matrix suction, saturation, and the effective friction angle and cohesion of the pile-soil interface, calculate the shear strength of the energy pile-unsaturated soil interface, taking into account the contribution of matrix suction. S4. Based on the calculation formula for the ultimate resistance of energy piles in saturated soil, the contribution of matrix suction is introduced to calculate the ultimate resistance of the pile tip considering the coupling effects of temperature load and unsaturated conditions. S5. Calculate the shear modulus of the soil around the pile considering the coupling of temperature load and unsaturated conditions, which is used to calculate the parameters of the energy pile load transfer model; S6. Calculate the energy pile-raft contact stiffness based on the raft dimensions, Young's modulus of the soil beneath the raft, and Poisson's ratio, and simulate the interaction between the energy pile and the superstructure. S7. Substitute the shear strength of the energy pile-unsaturated soil interface contributed by matrix suction, the ultimate resistance of the pile tip considering the coupling of temperature load and unsaturated conditions, the shear modulus of the soil around the pile considering the coupling of temperature load and unsaturated conditions, and the energy pile-raft contact stiffness into the load transfer algorithm of the saturated soil energy pile to calculate the thermal-hydraulic-mechanical multi-physics field coupling response of the unsaturated soil energy pile.

2. The calculation method for thermal-hydraulic-mechanical multi-field coupled response of unsaturated soil energy piles according to claim 1 is characterized in that: The energy in the pile-soil nonlinear interaction in S1, the pile-soil relative displacement, consists of the nonlinear displacement of the pile-soil shear disturbance zone and the elastic displacement of the soil in the undisturbed zone around the pile, where: The nonlinear displacement of the pile-soil shear disturbance zone is calculated using a fully elastic-plastic model, exponential model, hyperbolic model, double-broken-line model, triple-broken-line model, or generalized softening model; The elastic displacement of the soil in the undisturbed area around the pile is solved using elastic theory.

3. The calculation method for thermal-hydraulic-mechanical multi-field coupled response of unsaturated soil energy piles according to claim 1 is characterized in that: The specific load transfer algorithm for saturated soil energy piles in S1 is: Select the load transfer model and pile top contact stiffness to simulate the pile-soil nonlinear interaction; Determine the energy pile side- and pile tip-soil interaction models in saturated or dry soils. The pile side- and pile tip-soil interaction models are formulas (1) and (2), respectively. (1)； (2)； Where: is the ultimate shear strength; is the shear modulus of the soil at the pile side; is the pile radius; is the shear influence radius; is the shear modulus of soil at the pile tip; is the Poisson's ratio of the soil at the pile tip; It is the sum of the nonlinear displacement and elastic displacement of the soil around the pile; and are the total displacement and shear stress of the pile side at the unloading point or reloading point, respectively; is the loading and unloading status judgment factor; is the shear strength of the soil on the pile side; is the pile side-soil initial shear stiffness; is the pile side shear stress; is the sum of the nonlinear displacement and elastic displacement of the pile tip; and are the total displacement and shear stress at the pile tip at the unloading point or reloading point, respectively; Initial stiffness of pile tip-soil interaction; is the loading and unloading status judgment factor; is the ultimate end resistance; Pile tip resistance; Determine the pile-side and pile-tip-soil interaction model parameters, including pile-soil interface shear strength, pile-side-soil initial shear stiffness, pile-tip ultimate strength, pile-tip-soil initial stiffness, and pile-raft contact stiffness; The energy pile side- and pile-tip-soil interaction models in saturated or dry soil are substituted into the single energy pile load transfer algorithm to obtain the thermal-mechanical coupling response of the energy pile in saturated or dry soil.

4. The method for calculating the thermal-hydraulic-mechanical multi-field coupled response of an unsaturated soil energy pile according to claim 1 is characterized in that: In S2, by introducing the temperature correction parameter into the model of the soil-water characteristic curve without considering the temperature effect, the soil-water characteristic curve model considering the temperature effect can be obtained; the soil-water characteristic curve model without considering the temperature effect includes two types: empirical models and theoretical models. Theoretical models include thermodynamic models and pore network models, and empirical models include the van Genuchten model, Fredlund-Xing model, Brooks-Corey model, and Gardner model.

5. The calculation method for thermal-hydraulic-mechanical multi-field coupled response of unsaturated soil energy piles according to claim 4 is characterized in that: The van Genuchten model is used in S2, and the soil-water characteristic curve model and temperature correction parameters considering the temperature effect are The corresponding formulas are (3) and (4); (3)； (4)； Where: is saturation; is matrix suction; and are model parameters; It is the temperature; and is the model coefficient.

6. The method for calculating the thermal-hydraulic-mechanical multi-field coupled response of an unsaturated soil energy pile according to claim 1 is characterized in that: In the calculation process of horizontal stress of unsaturated soil on the pile side under temperature load, the energy pile is regarded as a completely elastic body. The volume change of the energy pile under temperature load is is Equation (5) and (6); (5)； (6)； Where: is the volume of the energy pile when the temperature changes; is the initial volume of the energy pile is the thermal expansion coefficient of the pile; is the temperature change; It is the length of the pile; is the radius of the pile under temperature. According to equations (5) and (6), the change in the radius of the pile under temperature load is calculated. for: (7)； Then the horizontal stress at the energy pile-unsaturated soil interface caused by temperature load is for: (8)； is the Young's modulus of soil; The total horizontal stress at the energy pile-unsaturated soil interface is the sum of the effective horizontal stress of the soil on the pile side and the horizontal stress at the pile-soil interface caused by the temperature load. , as shown in formula (9); (9)； is the effective internal friction angle of soil; is the effective weight of soil; z is the depth; The energy pile-unsaturated soil interface shear strength It consists of three parts: soil cohesion contribution, horizontal stress contribution, and matrix suction contribution, as shown in formula (10): (10)； Where: is the Poisson's ratio of the soil; is the effective internal friction angle of the pile-soil interface; is the effective cohesion of the pile-soil interface; is the residual saturation; is the current saturation.

7. The method for calculating the thermal-hydraulic-mechanical multi-field coupled response of an unsaturated soil energy pile according to claim 1 is characterized in that: Ultimate resistance of pile tip considering coupling of temperature load and unsaturated condition in S4 The calculation formula is: (11)； Where: is the effective internal friction angle of the soil at the pile tip; is the effective vertical stress in the soil at the pile tip; is the effective cohesion of soil at the pile end; is the model coefficient, calculated according to equations (12) and (13); (12)； (13)； Where: is the adjustment factor; is the effective cohesion of soil at the pile tip; exp is the exponential function; is the measured data of the ultimate end resistance, and the adjustment coefficient is calculated using the empirical formula (14); (14)； Where: and 1 and -0.006 respectively.

8. The method for calculating the thermal-hydraulic-mechanical multi-field coupled response of an unsaturated soil energy pile according to claim 1 is characterized in that: In S5, the shear modulus of the soil around the pile considering the coupling effect of temperature load and unsaturated condition is calculated according to equations (15) and (16); (15)； (16)； Where: k is the model parameter; and are the Young's modulus of soil in dry and saturated states, respectively; It is the measured Young's modulus for soil states between dry and saturated; It is used to measure saturated soil.

9. The method for calculating the thermal-hydraulic-mechanical multi-field coupled response of an unsaturated soil energy pile according to claim 1 is characterized in that: The contact stiffness of the energy pile and raft in S6 is calculated according to formula (17): (17)； Where: and are the raft width and length, respectively; is the calculation coefficient; for layered soil, Young's modulus and Poisson's ratio weighted average Calculate according to formula (18) and (19) respectively; (18)； (19)； Where: is the soil thickness; is the Young's modulus of each soil layer; is the Poisson's ratio of each soil layer.

10. The method for calculating the thermal-hydraulic-mechanical multi-field coupled response of an unsaturated soil energy pile according to claim 1 is characterized in that: Young's modulus E and shear modulus The relationship between them is shown in formula (20): (20)。

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