Thermal-mechanical coupling analytical solution solving method for multilayer soil semi-floating energy pile

Abstract

The invention relates to the technical field of energy pile thermal coupling analytical solution solving, in particular to a multilayer soil semi-floating energy pile thermal coupling analytical solution solving method, which comprises the following steps of: determining basic assumption and symbol parameters, establishing an energy pile analysis model, applying strain and displacement continuity conditions and pile top boundary conditions and setting equation coefficients; all the undetermined coefficients are determined according to the pile end boundary conditions to obtain analytical solutions of displacement, strain and stress, the pile top boundary conditions are modified, the undetermined coefficients are recalculated, and new analytical solutions of displacement, strain and stress are obtained. According to the method, based on a load transfer method, a balance relation, a kinematics relation, a pile thermoelastic constitutive relation and a pile-soil interface elastic constitutive equation, simpler, correct and reasonable analytical solutions of axial displacement, strain and stress of the single semi-floating energy pile under multiple layers of soil are given; and known conditions of boundary soil are associated through two coefficient matrixes, so that an analytical solution of any layer of soil instead of an ideal end bearing pile is solved.

Description

Technical Field

[0001] The invention relates to the technical field of thermal-mechanical coupling analytical solution for energy piles, and in particular to a thermal-mechanical coupling analytical solution method for multi-layer soil semi-floating energy piles. Background Art

[0002] Energy piles are well-known for their ability to balance load-bearing and heat exchange energy saving properties. The soil temperature at a certain depth is relatively stable throughout the year. When the energy pile is at that depth, the geothermal energy at that depth can be directly used to heat or cool the superstructure, which will reduce the fossil energy required for the building and help save energy and reduce carbon emissions.

[0003] The heat exchange fluid conducts convective heat exchange through the pipes pre-buried inside the energy pile. At the same time, the energy pile is restricted by the surrounding soil. Therefore, the pile body will inevitably produce thermal stress and strain. At the same time, the additional thermal load also has a great impact on the stress and displacement of the pile body.

[0004] However, in general, the existing technical methods believe that the soil around the pile and the pile end constraints have a certain influence on the thermal-mechanical coupling response of the energy pile. On this basis, the traditional load transfer method is proposed, and different numerical analytical solutions in the axial one-dimensional direction of the energy pile are given, which further explains the pile-soil structure interaction in the energy pile. The current technical method gives the analytical solution of the axial displacement, strain and stress of a single energy pile in homogeneous soil, but does not take into account the situation of thermal load coupling.

[0005] Based on this, the present invention provides a method for solving the thermal-mechanical coupling analytical solution of a multi-layer soil semi-floating energy pile to solve the above-mentioned technical problems. Summary of the invention

[0006] The purpose of the present invention is to provide a method for solving the thermal-mechanical coupling analytical solution of a multi-layer soil semi-floating energy pile, so as to solve the problems raised by the above-mentioned background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] The method for solving the thermal-mechanical coupling analytical solution of a multi-layer soil semi-floating energy pile includes the following steps:

[0009] S1. Determine basic assumptions and symbolic parameters;

[0010] S2. Establish energy pile analysis model;

[0011] S3. Apply the strain and displacement continuity conditions and the pile top boundary conditions and set the equation coefficients, and apply the pile end boundary conditions to determine all the unknown coefficients to obtain the analytical solutions of displacement, strain, and stress;

[0012] S4. Modify the boundary conditions at the top of the pile and recalculate the unknown coefficients to obtain new analytical solutions of displacement, strain and stress;

[0013] S5. Considering two boundary conditions at the same time, the analytical solution is obtained by superposition principle;

[0014] S6. Verification and calibration: verify the correctness of the analytical solution through experiments or numerical simulations.

[0015] Preferably, the implementation steps of step S2 are:

[0016] The analytical model of a semi-floating energy pile buried in multi-layer soil is constructed. The lateral soil constraint on the pile is determined by the stiffness value k si The pile top and pile bottom constraints are represented by tangential springs (i=1,2,...,n), with stiffness k h and k b The normal spring of the pile top represents the restriction of the pile top structure on the free movement of the pile top and is only affected by the temperature load. The normal spring of the pile end represents the restriction of the pile bottom structure on the free movement of the pile body.

[0017] The entire pile is divided into n parts according to the boundary of the soil layer. The length of each section is L1(m), L2(m),…,Ln(m), and the total pile length is L(m). A local coordinate system x1, x2,…,xn is established for each part. The origin of the coordinate axis, i.e. x1=0, x2=0,…,xn=0, is the boundary between the pile end and the soil layer. It is stipulated that the x-axis and displacement are both upward as positive.

[0018] The kinematic relationship of the pile is expressed as formula (1):

[0019]

[0020] Where u = u(x) is the axial (vertical) displacement (m), dx represents the microelement along the length of the pile, and ε = ε(x) is the axial strain;

[0021] The thermoelastic constitutive relation is expressed as formula (2):

[0022] σ=E(ε-αΔΤ)(2);

[0023] Where, σ = σ(x) is the axial stress (Pa), E is the elastic modulus (MPa), α is the thermal expansion coefficient of the pile (1 / °C), and ΔΤ is the temperature difference between the pile and the soil around the pile (°C);

[0024] The pile-soil interface is represented by a continuous linear shear spring, and the shear stress at the interface is expressed as formula (3):

[0025] τ|=k si |u|(3);

[0026] In the formula, k si (i=1,2,...,n) is the stiffness of the spring (MPa / m), which is constant at a specific depth for a given soil layer;

[0027] The relationship between the stress and displacement at the pile end can be expressed by the normal spring as formula (4):

[0028] σ(0)=k b u(0)(4);

[0029] In the formula, k b is the stiffness of the normal spring (MPa / m).

[0030] Preferably, the implementation steps of step S3 are:

[0031] S3.1. Continuity conditions for application of strains and displacements

[0032] Only the temperature load (ΔΤ) is applied, and the energy pile micro-unit is taken as the object for analysis. According to the equilibrium condition, the equation (5) is as follows:

[0033] Ad i = pτ i ,i=1,2,...n(5);

[0034] Where A is the cross-sectional area of ​​the pile (m 2 ), p is the circumference of the pile (m);

[0035] The combined solution is: Equation (6), (7) and (8):

[0036]

[0037] Where c i,1 and c i,2 is the unknown coefficient, a i is a constant. To determine u(x i ), ε i (x i ) and σ i (x i ) only needs to determine c 1,1 and c 1,2 There are 2n undetermined coefficients in total;

[0038] S3.2. According to the continuity condition, the stress, strain and displacement of the pile at the interface between the two soil layers are equal. From equations (6), (7) and (8), it can be seen that the stress and strain are equivalent, so the continuity condition is obtained, see equations (9) and (10):

[0039] u i (L i )=u i+1(0),i=1,2,...,n (9);

[0040] ε i (L i )=ε i+1 (0),i=1,2,...,n (10);

[0041] After simplification, we can see formula (11):

[0042] c i+1 =c i ×γ i, (i=1,2,...n-1) (11);

[0043] where c i =(c i,1 c i,2 ),i=1,2,...n, coefficient matrix

[0044] S3.3. Apply boundary conditions at the top of the pile;

[0045] For an energy pile with no constraints on the pile top, that is, kh=0, according to the boundary conditions: σ n (L N )=0 and substitute it into equation (12):

[0046]

[0047] in

[0048] S3.4. Set the equation coefficients:

[0049] Let coefficient We can get formula (13);

[0050]

[0051] Let ω i,1 =ζ i,1 Ea n ,ω i,2 =ζ i,2 Ea n ,(i=1,2,...,n-1), when i=1, there is ω 1,1 =ζ 1,1 Ea n ,ω 1,2 =ζ 1,2 Ea n , see formula (14):

[0052] ω 1,1 c 1,1 +ω 1,2c 1,2 =EαΔΤ (14);

[0053] S3.5. Apply boundary conditions at the pile end, σ(0) = k b u(0) can be obtained as formula (15):

[0054] (Ea 1 -k b )c 1,1 -(Ea 1 +k b )c 1,2 =EαΔT (15);

[0055] S3.6. Determination coefficient c 1,1 and c 1,2 , let Ea 1 -k b =B 1 ,-(Ea 1 -k b )=B 2 B 1 c 1,1 +B 2 c 1,2 =EαΔΤ

[0056] Combining equations (16) and (17) we can get:

[0057]

[0058] At this point, all the unknown coefficients can be found.

[0059] S3.7. Substituting constants

[0060] S3.8. Obtain the analytical solutions of displacement, strain and stress. Combining the above formulas, we can get formula (18):

[0061]

[0062] Preferably, the implementation steps of step S4 are:

[0063] S4.1. When an axial load of magnitude F is applied to the top of the pile, the boundary condition at the top of the pile becomes: Taking ΔT = 0, we can get Similar to step S3, there is The required c can be obtained by combining 1,1 and c 1,2 , see equations (19) and (20):

[0064]

[0065] S4.2 Finally, the analytical solutions of displacement, strain and stress are obtained, as shown in formula (21):

[0066]

[0067] Preferably, the implementation steps of step S5 are:

[0068] S5.1. When an axial load of magnitude F is applied to the top of the pile, the boundary condition at the top of the pile becomes: Substituting into Right now The same as step S4 can be obtained The required c can be obtained by combining 1,1 and c 1,2 , see equations (22) and (23):

[0069]

[0070] By comparing the three different cases 1,1 and c 1,2 It can be seen that the response of applying temperature load and mechanical load simultaneously is equivalent to the superposition of the response of applying temperature load and mechanical load separately. 1,1 and c 1,2 Under temperature load conditions u i (x i ), ε i (x i ) and σ i (x i ) formula can be used to obtain the analytical solution of the first layer displacement, strain and stress, as shown in formula (24):

[0071]

[0072] Similarly, c 1,1 and c 1,2 Can be Determine, and the axial displacement, strain and stress of the i-th layer of soil are shown in formula (25):

[0073]

[0074] Compared with the prior art, the present invention has the following beneficial effects:

[0075] The present invention provides a simpler, more correct and reasonable analytical solution of the axial displacement, strain and stress of a single semi-floating energy pile under multi-layer soil based on the load transfer method and equilibrium, kinematic relations, pile thermoelastic constitutive relations and pile-soil interface elastic constitutive equations, and connects the known conditions of the boundary soil through two coefficient matrices, thereby solving the analytical solution of any layer of soil instead of the study on ideal end-bearing piles or ideal floating piles and limited soil layers. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is an analytical model of energy piles in multi-layer soil under the condition of thermal-mechanical coupling of the present invention;

[0077] Figure 2 This is the analysis micro unit of the thermal-mechanical coupling of the energy pile under the condition that only the temperature load is applied in the present invention. DETAILED DESCRIPTION

[0078] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0079] See also Figure 1 to Figure 2 The present invention proposes a method for solving a thermal-mechanical coupling analytical solution of a multi-layer soil semi-floating energy pile, comprising the following steps:

[0080] S1. Determine basic assumptions and symbolic parameters;

[0081] S2. Establish energy pile analysis model;

[0082] In this step, it should be noted that the implementation steps of step S2 are:

[0083] The analytical model of a semi-floating energy pile buried in multi-layer soil is constructed. The lateral soil constraint on the pile is determined by the stiffness value k si The pile top and pile bottom constraints are represented by tangential springs (i=1,2,...,n), with stiffness k h and k b The normal spring of the pile top represents the restriction of the pile top structure on the free movement of the pile top and is only affected by the temperature load. The normal spring of the pile end represents the restriction of the pile bottom structure on the free movement of the pile body.

[0084] The whole pile is divided into n parts according to the boundary of soil layer. The length of each part is L1(m), L2(m), ..., Ln(m), and the total pile length is L(m). A local coordinate system x1, x2, ..., xn is established for each part. The origin of the coordinate axis, that is, x1 = 0, x2 = 0, ..., xn = 0, is the boundary between the pile end and the soil layer. It is stipulated that the x-axis and displacement are both upward as positive.

[0085] The kinematic relationship of the pile is expressed as formula (1):

[0086]

[0087] Where u = u(x) is the axial (vertical) displacement (m), dx represents the microelement along the length of the pile, and ε = ε(x) is the axial strain;

[0088] The thermoelastic constitutive relation is expressed as formula (2):

[0089] σ=E(ε-αΔΤ) (2);

[0090] Where, σ = σ(x) is the axial stress (Pa), E is the elastic modulus (MPa), α is the thermal expansion coefficient of the pile (1 / °C), and ΔΤ is the temperature difference between the pile and the soil around the pile (°C);

[0091] The pile-soil interface is represented by a continuous linear shear spring, and the shear stress at the interface is expressed as formula (3):

[0092] |τ|=k si |u| (3);

[0093] In the formula, k si (i=1,2,...,n) is the stiffness of the spring (MPa / m), which is constant at a specific depth for a given soil layer;

[0094] The relationship between the stress and displacement at the pile end can be expressed by the normal spring as formula (4):

[0095] σ(0)=k b u(0)(4);

[0096] In the formula, k b is the stiffness of the normal spring (MPa / m);

[0097] S3. Apply the strain and displacement continuity conditions and the pile top boundary conditions and set the equation coefficients, and apply the pile end boundary conditions to determine all the unknown coefficients to obtain the analytical solutions of displacement, strain, and stress;

[0098] In this step, it should be noted that the implementation steps of step S3 are:

[0099] S3.1. Continuity conditions for application of strains and displacements

[0100] Only the temperature load (ΔΤ) is applied, and the energy pile micro-unit is taken as the object for analysis. According to the equilibrium condition, the equation (5) is as follows:

[0101] Ad i = pτ i ,i=1,2,...n (5);

[0102] Where A is the cross-sectional area of ​​the pile (m 2 ), p is the circumference of the pile (m);

[0103] The combined solution is: Equation (6), (7) and (8):

[0104]

[0105] Where c i,1 and c i,2 is the unknown coefficient, a i is a constant. To determine u(x i ), ε i (x i ) and σ i (x i ) only needs to determine c 1,1 and c 1,2 There are 2n undetermined coefficients in total;

[0106] S3.2. According to the continuity condition, the stress, strain and displacement of the pile at the interface between the two soil layers are equal. From equations (6), (7) and (8), it can be seen that the stress and strain are equivalent, so the continuity condition is obtained, see equations (9) and (10):

[0107] u i (L i )=u i+1 (0),i=1,2,...,n (9);

[0108] ε i (L i )=ε i+1 (0),i=1,2,...,n (10);

[0109] After simplification, we can see formula (11):

[0110] c i+1 =c i ×γ i, (i=1,2,...n-1) (11);

[0111] where c i =(c i,1 c i,2 ),i=1,2,...n, coefficient matrix

[0112] S3.3. Apply boundary conditions at the top of the pile;

[0113] For an energy pile with no constraints on the pile top, that is, kh=0, according to the boundary conditions: σ n (L N )=0 and substitute it into equation (12):

[0114]

[0115] in

[0116] S3.4. Set the equation coefficients:

[0117] Let coefficient We can get formula (13);

[0118]

[0119] Let ω i,1 =ζ i,1 Ea n ,ω i,2 =ζ i,2 Ea n ,(i=1,2,...,n-1), when i=1, there is ω 1,1 =ζ 1,1 Ea n ,ω 1,2 =ζ 1,2 Ea n , see formula (14):

[0120] ω 1,1 c 1,1 +ω 1,2 c 1,2 =EαΔΤ (14);

[0121] S3.5. Apply boundary conditions at the pile end, σ(0) = k b u(0) can be obtained as formula (15):

[0122] (Ea 1 -k b )c 1,1 -(Ea 1 +k b )c 1,2 =EαΔT (15);

[0123] S3.6. Determination coefficient c 1,1 and c 1,2 , let Ea 1 -k b =B1 ,-(Ea 1 -k b )=B 2 B 1 c 1,1 +B 2 c 1,2 =EαΔΤ

[0124] Combining equations (16) and (17) we can get:

[0125]

[0126]

[0127] At this point, all the unknown coefficients can be found.

[0128] S3.7. Substituting constants

[0129] S3.8. Obtain the analytical solutions of displacement, strain and stress. Combining the above formulas, we can get formula (18):

[0130]

[0131] S4. Modify the boundary conditions at the top of the pile and recalculate the unknown coefficients to obtain new analytical solutions of displacement, strain and stress;

[0132] In this step, it should be noted that the implementation steps of step S4 are:

[0133] S4.1. When an axial load of magnitude F is applied to the top of the pile, the boundary condition at the top of the pile becomes: Taking ΔT = 0, we can get Similar to step S3, there is The required c can be obtained by combining 1,1 and c 1,2 , see equations (19) and (20):

[0134]

[0135] S4.2 Finally, the analytical solutions of displacement, strain and stress are obtained, as shown in formula (21):

[0136]

[0137] S5. Considering two boundary conditions at the same time, the analytical solution is obtained by superposition principle;

[0138] In this step, it should be noted that the implementation steps of step S5 are:

[0139] S5.1. When an axial load of magnitude F is applied to the top of the pile, the boundary condition at the top of the pile becomes: Substituting into Right now The same as step S4 can be obtained The required c can be obtained by combining 1,1 and c 1,2 , see equations (22) and (23):

[0140]

[0141] By comparing the three different cases 1,1 and c 1,2 It can be seen that the response of applying temperature load and mechanical load simultaneously is equivalent to the superposition of the response of applying temperature load and mechanical load separately. 1,1 and c 1,2 Under temperature load conditions u i (x i ), ε i (x i ) and σ i (x i ) formula can be used to obtain the analytical solution of the first layer displacement, strain and stress, as shown in formula (24):

[0142]

[0143] Similarly, c 1,1 and c 1,2 Can be Determine, and the axial displacement, strain and stress of the i-th layer of soil are shown in formula (25):

[0144]

[0145] S6. Verification and calibration: verify the correctness of the analytical solution through experiments or numerical simulations.

[0146] Example

[0147] In practical applications, the above-mentioned method for solving the thermal-mechanical coupling analytical solution of the multi-layer soil semi-floating energy pile specifically includes the following steps:

[0148] See also Figure 1 , Figure 1 An analytical model for a semi-floating energy pile buried in multi-layer soil;

[0149] The lateral soil constraint on the pile is given by the stiffness value k si The pile top and pile bottom constraints are represented by tangential springs (i=1,2,...,n), with stiffness k h and k bThe normal spring representation of ;

[0150] The pile top normal spring represents the restriction of the pile top structure on the free movement of the pile top and is only affected by the temperature load; the pile end normal spring represents the restriction of the pile bottom structure on the free movement of the pile body;

[0151] Furthermore, the deadweight of the pile can be ignored in this patent;

[0152] The whole pile is divided into n parts according to the boundary of the soil layer. The length of each part is L1(m), L2(m), ..., Ln(m), and the total pile length is L(m). A local coordinate system x1, x2, ..., xn is established for each part. The origin of the coordinate axis, that is, x1 = 0, x2 = 0, ..., xn = 0, is the boundary between the pile end and the soil layer.

[0153] The basic assumptions of this method are as follows:

[0154] (1) Using a one-dimensional model to establish a vertical coordinate system;

[0155] (2) The temperature change of the entire energy pile is relatively uniform;

[0156] (3) The higher-order terms in the kinematic relationship are ignored;

[0157] (4) The energy pile follows the thermoelastic constitutive law;

[0158] (5) It is assumed that the pile-soil interface is always in the elastic range, that is, the shear stress at the interface is linearly related to the vertical displacement, and the normal stress at the pile end is linearly related to the vertical displacement at the pile end;

[0159] (6) The material properties of the pile and soil do not change with temperature;

[0160] (7) Ignore the contact thermal resistance between soil layers;

[0161] (8) The entire pile body maintains vertical balance;

[0162] In addition, the axial displacement of the energy pile is more significant than the horizontal displacement, so the axial displacement of the pile will be mainly investigated in this method;

[0163] It is stipulated that the x-axis and displacement are all upward as positive, on the contrary, pressure, compressive stress and compressive strain are all negative;

[0164] The kinematic relationship of the pile can be expressed as follows:

[0165]

[0166] Where u = u(x) is the axial (vertical) displacement (m), dx represents the microelement along the length of the pile, and ε = ε(x) is the axial strain

[0167] The thermoelastic constitutive relation can be expressed as follows:

[0168] σ=E(ε-αΔΤ);

[0169] Where σ = σ(x) is the axial stress (Pa), E is the elastic modulus (MPa), α is the thermal expansion coefficient of the pile (1 / °C), and ΔΤ is the temperature difference between the pile and the soil around the pile (°C);

[0170] The pile-soil interface is represented by a continuous linear shear spring, and the shear stress at the interface can be expressed as:

[0171] |τ|=k si |u|;

[0172] Among them, k si (i=1,2,...,n) is the stiffness of the spring (MPa / m), which is constant at a specific depth for a given soil layer;

[0173] The stress-displacement relationship at the pile end can be expressed by the normal spring:

[0174] σ(0)=k b u(0);

[0175] Where k b is the stiffness of the normal spring (MPa / m);

[0176] This formula represents the boundary conditions of energy piles in general, that is, there are certain restrictions on the pile end, and the stress and displacement at the pile end are not zero;

[0177] For an ideal end-bearing pile, the pile end displacement is 0, but the stress is not 0;

[0178] For an ideal floating pile, the pile end displacement is not 0, and the pile end stress is 0;

[0179] A cross-sectional model of a multi-layer soil is shown in Figure 1 As shown in the figure, the constraint effect of the soil around the pile on the energy pile is expressed by the shear stiffness k si (i=1,2,...,n), the constraints on the pile top and pile end are represented by k h and k b It means that the normal spring at the top of the pile represents the constraint of the superstructure on the free deformation of the pile;

[0180] This method considers that kh is activated only by temperature loads, and the deadweight of the pile is not taken into account;

[0181] The entire pile is divided into n parts according to the soil stratification, the length of each part is Li(m) (i=1,2,…,n), and the total pile length is L(m);

[0182] Each length segment has its own local coordinate system, and the origin of the coordinate axis is xi=0 (i=1,2,…,n);

[0183] 2. The process of establishing the thermal-mechanical coupling analytical solution of multi-layer soil energy pile

[0184] 2.1 The process of establishing the analytical solution with temperature load only

[0185] (1) Application of continuity conditions for strain and displacement

[0186] In this section, only the temperature load (ΔΤ) is applied, and the energy pile micro-unit ( Figure 2 ) is the object for analysis, according to the equilibrium conditions:

[0187] Ad i = pτ i ,i=1,2,...n;

[0188] Where A is the cross-sectional area of ​​the pile (m 2 ), p is the circumference of the pile (m);

[0189] The solution is

[0190]

[0191] Where c i,1 and c i,2 is the unknown coefficient, a i is a constant;

[0192] To determine u(x i ), ε i (x i ) and σ i (x i ) only needs to determine c 1,1 and c 1,2 There are 2n undetermined coefficients in total;

[0193] According to the continuity condition, the stress, strain and displacement of the pile at the interface between the two soil layers are equal. From formula (2), it can be seen that the stress and strain are equivalent, so the following continuity condition can be obtained:

[0194] u i (L i )=u i+1 (0), i = 1, 2, ..., n;

[0195] ε i (L i )=ε i+1 (0), i = 1, 2, ..., n;

[0196] After calculation, it can be simplified into the following mode:

[0197] c i+1 =c i ×γ i, (i=1,2,...n-1);

[0198] where c i =(c i,1 c i,2 ),i=1,2,...n, coefficient matrix

[0199] (2) Apply boundary conditions at the pile top

[0200] For an energy pile with no constraints on the pile top, that is, kh=0, according to the boundary conditions: σ n (L N )=0 and we can get

[0201]

[0202] in

[0203] (3) Set equation coefficients

[0204] Let coefficient We can get:

[0205]

[0206] Let ω i,1 =ζ i,1 Ea n ,ω i,2 =ζ i,2 Ea n , (i=1,2,...,n-1), (Note: when i=n, ​​ζ n,1 =ζ n , n,2 =δ n,2 is known);

[0207] When i=1, there is ω 1,1 =ζ 1,1 Ea n ,ω 1,2 =ζ 1,2 Ea n , so we have:

[0208] ω 1,1 c 1,1 +ω 1,2 c 1,2 =EαΔΤ;

[0209] (4) Apply boundary conditions at the pile end, σ(0) = k b u(0) gives:

[0210] (Ea 1 -k b )c 1,1 -(Ea 1 +k b )c 1,2 =EαΔT;

[0211] (5) Determination coefficient c 1,1 and c 1,2 ;

[0212] Let Ea 1 -k b =B 1 ,-(Ea 1 -k b )=B 2 B 1 c 1,1 +B 2 c 1,2 =EαΔΤ;

[0213] Combined to get:

[0214]

[0215] At this point, all the unknown coefficients can be found.

[0216] (6) Substitute the constant

[0217] (7) Obtain analytical solutions for displacement, strain, and stress;

[0218] Combining the above formulas, we can get:

[0219]

[0220] 2.2 Apply only mechanical load

[0221] Step (2) is different from applying only temperature load. When an axial load of magnitude F is applied to the pile top, the boundary condition at the pile top becomes: Taking ΔT = 0, we can get Similar to the previous section, we have Combined, we can get the c required in step (5) 1,1 and c 1,2 :

[0222]

[0223] Finally, the analytical solutions of displacement, strain and stress are obtained:

[0224]

[0225] 2.3 Simultaneous application of temperature and mechanical load

[0226] Step (2) is different from applying only temperature load. When an axial load of magnitude F is applied to the pile top, the boundary condition at the pile top becomes: Substituting into Right now The same as in the previous section Combined, we can get the c required in step (5) 1,1 and c 1,2 :

[0227]

[0228] By comparing the three different cases 1,1 and c 1,2 , it can be seen that the response of applying temperature load and mechanical load simultaneously is equivalent to the superposition of the response of applying temperature load and mechanical load separately;

[0229] The c under the conditions of simultaneous application of temperature and mechanical load 1,1 and c 1,2 Substitute u from step (1) under temperature load conditions i (x i ), ε i (x i ) and σ i (x i ) formula can be used to obtain the analytical solution of the displacement, strain and stress of the first layer

[0230]

[0231] Similarly, c 1,1 and c 1,2 Can be This formula is determined, and the axial displacement, strain and stress of the i-th layer of soil can also be obtained as follows:

[0232]

[0233] Through the above steps, the present invention provides a simpler, correct and reasonable analytical solution of the axial displacement, strain and stress of a single semi-floating energy pile under multi-layer soil based on the load transfer method and the equilibrium, kinematic relationship, pile thermoelastic constitutive relationship and pile-soil interface elastic constitutive equation. And through two coefficient matrices to link the known conditions of the boundary soil, the analytical solution of any layer of soil is solved instead of the study on the ideal end-bearing pile or the ideal floating pile and the limited soil layer.

[0234] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0235] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for solving the thermal-mechanical coupling analytical solution of a multi-layer soil semi-floating energy pile, characterized in that: The following steps are involved: S1. Determine basic assumptions and symbolic parameters; S2. Establish energy pile analysis model; S3. Apply the strain and displacement continuity conditions and the pile top boundary conditions and set the equation coefficients, and apply the pile end boundary conditions to determine all the unknown coefficients to obtain the analytical solutions of displacement, strain, and stress; S4. Modify the boundary conditions at the top of the pile and recalculate the unknown coefficients to obtain new analytical solutions of displacement, strain and stress; S5. Considering two boundary conditions at the same time, the analytical solution is obtained by superposition principle; S6. Verification and calibration: verify the correctness of the analytical solution through experiments or numerical simulations.

2. The method for solving the thermal-mechanical coupling analytical solution of a multi-layer soil semi-floating energy pile according to claim 1 is characterized in that: The implementation steps of step S2 are: The analytical model of a semi-floating energy pile buried in multi-layer soil is constructed. The lateral soil constraint on the pile is determined by the stiffness value k. si The pile top and pile bottom constraints are represented by tangential springs (i=1,2,...,n), with stiffness k h and k b The normal spring of the pile top represents the restriction of the pile top structure on the free movement of the pile top and is only affected by the temperature load. The normal spring of the pile end represents the restriction of the pile bottom structure on the free movement of the pile body. The entire pile is divided into n parts according to the boundary of the soil layer. The length of each section is L1(m), L2(m),…,Ln(m), and the total pile length is L(m). A local coordinate system x1, x2,…,xn is established for each part. The origin of the coordinate axis, i.e. x1=0, x2=0,…,xn=0, is the boundary between the pile end and the soil layer. It is stipulated that the x-axis and displacement are both upward as positive. The kinematic relationship of the pile is expressed as formula (1): Where u = u(x) is the axial (vertical) displacement (m), dx represents the microelement along the length of the pile, and ε = ε(x) is the axial strain; The thermoelastic constitutive relation is expressed as formula (2): σ=E(ε-αΔΤ)(2); Where, σ = σ(x) is the axial stress (Pa), E is the elastic modulus (MPa), α is the thermal expansion coefficient of the pile (1 / °C), and ΔΤ is the temperature difference between the pile and the soil around the pile (°C); The pile-soil interface is represented by a continuous linear shear spring, and the shear stress at the interface is expressed as formula (3): τ|=k si |u|(3); In the formula, k si (i=1,2,...,n) is the stiffness of the spring (MPa / m), which is constant at a specific depth for a given soil layer; The relationship between the stress and displacement at the pile end can be expressed by the normal spring as formula (4): σ(0)=k b u(0)(4); In the formula, k b is the stiffness of the normal spring (MPa / m).

3. The method for solving the thermal-mechanical coupling analytical solution of a multi-layer soil semi-floating energy pile according to claim 1 is characterized in that: The implementation steps of step S3 are: S3.

1. Continuity conditions for application of strains and displacements Only the temperature load (ΔΤ) is applied, and the energy pile micro-unit is taken as the object for analysis. According to the equilibrium condition, the equation (5) is as follows: Adσ i =pτ i ,i=1,2,...n(5); Where A is the cross-sectional area of ​​the pile (m 2 ), p is the circumference of the pile (m); The combined solution is: Equation (6), (7) and (8): Where c i,1 and c i,2 is the unknown coefficient, a i is a constant. To determine u(x i ), ε i (x i ) and σ i (x i ) only needs to determine c 1,1 and c 1,2 There are 2n undetermined coefficients in total; S3.

2. According to the continuity condition, the stress, strain and displacement of the pile at the interface between the two soil layers are equal. From equations (6), (7) and (8), it can be seen that the stress and strain are equivalent, so the continuity condition is obtained, see equations (9) and (10): u i (L i )=u i+1 (0),i=1,2,...,n(9); e i (L i )=e i+1 (0),i=1,2,...,n(10); After simplification, we can see formula (11): c i+1 =c i ×γ i, (i=1,2,...n-1)(11); where c i =(c i,1 c i,2 ),i=1,2,...n, coefficient matrix S3.

3. Apply boundary conditions at the top of the pile; For an energy pile with no constraints on the pile top, that is, kh=0, according to the boundary conditions: σ n (L N )=0 and substitute it into equation (12): in S3.

4. Set the equation coefficients: Let coefficient We can get formula (13); Let ω i,1 =ζ i,1 Ea n ,ω i,2 =ζ i,2 Ea n ,(i=1,2,...,n-1), when i=1, there is ω 1,1 =ζ 1,1 Ea n ,ω 1,2 =ζ 1,2 Ea n , see formula (14): oh 1,1 c 1,1 +oh 1,2 c 1,2 =EαΔT(14); S3.

5. Apply boundary conditions at the pile end, σ(0) = k b u(0) can be obtained as formula (15): (Ea1-k b )c 1,1 -(Ea1+k b )c 1,2 =EαΔT(15); S3.

6. Determination coefficient c 1,1 and c 1,2 , let Ea1-k b =B1,-(Ea1-k b )=B2, we get B1c 1,1 +B2c 1,2 =EαΔΤ Combining equations (16) and (17) we can get: At this point, all the unknown coefficients can be found. S3.

7. Substituting constants S3.

8. Obtain the analytical solutions of displacement, strain and stress. Combining the above formulas, we can get formula (18):

4. The method for solving the thermal-mechanical coupling analytical solution of a multi-layer soil semi-floating energy pile according to claim 1 is characterized in that: The implementation steps of step S4 are: S4.

1. When an axial load of magnitude F is applied to the top of the pile, the boundary condition at the top of the pile becomes: Taking ΔT = 0, we can get Similar to step S3, there is The required c can be obtained by combining 1,1 and c 1,2 , see equations (19) and (20): S4.2 Finally, the analytical solutions of displacement, strain and stress are obtained, as shown in formula (21):

5. The method for solving the thermal-mechanical coupling analytical solution of a multi-layer soil semi-floating energy pile according to claim 1 is characterized in that: The implementation steps of step S5 are: S5.

1. When an axial load of magnitude F is applied to the top of the pile, the boundary condition at the top of the pile becomes: Substituting into Right now The same as step S4 can be obtained The required c can be obtained by combining 1,1 and c 1,2 , see equations (22) and (23): By comparing the three different cases 1,1 and c 1,2 It can be seen that the response of applying temperature load and mechanical load simultaneously is equivalent to the superposition of the response of applying temperature load and mechanical load separately. 1,1 and c 1,2 Under temperature load conditions u i (x i ), ε i (x i ) and σ i (x i ) formula can be used to obtain the analytical solution of the first layer displacement, strain and stress, as shown in formula (24): Similarly, c 1,1 and c 1,2 Can be Determine, and the axial displacement, strain and stress of the i-th layer of soil are shown in formula (25):

Images