A method for calculating horizontal nonlinear response of large-diameter pile in layered ground considering end resistance
By using the equivalent nonlinear springs of the pile side soil and pile tip soil in layers, and combining Timoshenko beam theory and iterative calculations, the problem of inaccurate calculation of the nonlinear response of the pile tip soil of large-diameter piles in layered foundations was solved, and more accurate pile foundation design was achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- 中交第三航务工程局有限公司宁波分公司
- Filing Date
- 2026-04-03
- Publication Date
- 2026-07-03
AI Technical Summary
Existing technologies are insufficient to accurately describe the nonlinear response of large-diameter piles to the soil at the pile tip in layered foundations. In particular, the soil resistance at the pile tip exhibits significant nonlinearity as displacement increases in soft clay or sand. Traditional methods are inaccurate in their calculations and lack a universal analytical framework.
The Winkler foundation model is used to represent the pile side soil as a nonlinear horizontal soil spring in layers, and the pile tip soil is simplified as a shear and bending elastoplastic spring. Combining Timoshenko beam theory and the finite difference method, the nonlinear response of the pile side soil and the pile tip soil is reflected by iterative calculation.
It enables reliable prediction of horizontal displacement, bending moment and shear force of large-diameter piles in layered foundations, provides more accurate engineering design basis, and reflects the contribution of soil deformation on the pile side and soil resistance at the pile tip.
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Figure CN122333592A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of pile foundation engineering technology, and in particular to a method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance. Background Technology
[0002] In geotechnical and marine engineering, large-diameter piles are widely used in major engineering structures such as offshore wind power foundations, cross-sea bridges, deep-water wharves, and high-rise buildings. As engineering projects develop towards deeper water and larger scale, the diameter of pile foundations continues to increase, making their horizontal load-bearing performance a crucial factor affecting structural safety. Under the combined action of horizontal loads, vertical loads, and bending moments, the pile-soil interaction of large-diameter piles exhibits significant nonlinear characteristics, and the changes in soil properties under layered foundation conditions further increase the complexity of the analysis.
[0003] Existing pile-soil interaction analyses mostly focus on conventional diameter piles. However, for large-diameter piles, the soil deformation patterns, stress diffusion mechanisms, and end reactions in the pile tip region differ significantly from those of conventional piles. Traditional methods often neglect the contribution of the soil at the pile tip under horizontal stress, easily leading to inaccurate calculations of pile displacement, bending moment, and bearing capacity. Furthermore, existing methods often treat the pile tip as a hinged or fixed boundary, failing to accurately reflect the influence of shear and bending deformation at the pile tip on the pile's horizontal response. In engineering practice, large-diameter piles often possess high resistance reserves at the ends, especially in layered soft clay or sand foundations, where the soil resistance at the pile tip exhibits a significant nonlinear excitation phenomenon with increasing displacement. These effects lack effective characterization in existing analytical models. Simultaneously, traditional analytical methods struggle to obtain closed-form solutions when dealing with nonlinear Py curves, variations in layered foundation parameters, and pile tip boundary conditions. Numerical simulations or empirical methods are typically required, with calculations relying heavily on trial and error and lacking a universal analytical framework, hindering engineering design and parameter analysis.
[0004] Therefore, there is an urgent need for an analytical method that can simultaneously consider the nonlinear effects of the soil along the pile and the resistance effects of the soil at the pile tip, in order to accurately describe the horizontal nonlinear response of large-diameter piles in layered foundations. This method should be able to combine nonlinear Py curves, end-pile elastoplastic characteristics, and finite difference discretization techniques to achieve reliable prediction of pile displacement, bending moment, and shear force, thereby meeting the needs of engineering design for refined pile-soil analysis. Summary of the Invention
[0005] In view of this, the purpose of this invention is to provide a method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations that considers end resistance. This method comprehensively considers the nonlinear effects of the soil along the pile and the resistance of the soil at the pile tip, providing a theoretical basis for the design and construction of large-diameter pile foundations.
[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, comprising:
[0007] S1. Input the parameters and load conditions of the large-diameter pile to establish a calculation model for the horizontal nonlinear response of the large-diameter pile in the stratified foundation considering the end resistance.
[0008] S2. Based on the Winkler foundation model, the soil around the pile is divided into several layers according to the depth direction, and each layer of soil around the pile is equivalent to a nonlinear horizontal soil spring.
[0009] S3. The soil at the pile tip is simplified into an end shear elastoplastic spring describing the shear force-displacement relationship and an end bending elastoplastic spring describing the bending moment-rotation relationship.
[0010] S4. Determine the secant stiffness of the soil spring at each depth based on the nonlinear py curve of clay or sand.
[0011] S5. Based on Timoshenko beam theory, establish the differential equations governing the horizontal deflection of the pile body, and use the finite difference method to discretize the governing equations.
[0012] S6. Set virtual nodes at the pile top and pile end, and combine the discretization results of step S5 to establish the horizontal load, vertical load and bending moment constraint conditions at the pile top, as well as the boundary conditions of shear force and bending moment at the pile end.
[0013] S7. Combine the discrete equations with the boundary conditions and use iterative calculation to solve the nonlinear responses such as horizontal displacement, bending moment and shear force at each node of the pile.
[0014] In a preferred embodiment, in step S2, a micro-element of the pile body within the soil layer i on the pile side is randomly selected, and the following equation is satisfied by the statically balanced micro-element:
[0015]
[0016]
[0017] In the formula, Q is the horizontal load, z is the soil depth, p is the horizontal soil resistance per unit depth, M is the pile bending moment, N is the vertical load, and w is the pile horizontal displacement.
[0018] In a preferred embodiment, in step S3, the horizontal load Q, the pile bending moment M, and the rotation angle θ are written in differential form:
[0019]
[0020]
[0021]
[0022] In the formula, EI is the pile stiffness, N0 is the vertical load on the pile top, GA is the section shear stiffness, and κ is the shear coefficient.
[0023] In a preferred embodiment, in step S4, the py curve of the clay is determined by the following formula:
[0024]
[0025]
[0026]
[0027]
[0028] In the formula, y c This is the horizontal displacement required for the soil around the pile to exert 50% of its ultimate resistance; p u The ultimate soil resistance; ε 50 The soil strain at 50% of the maximum shear strength in a triaxial undrained test; s u γ represents the undrained shear strength. denoted as , where is the effective unit weight of the soil; J is an empirical coefficient, typically taken as 0.25 ~ 0.5, for normally consolidated clay J = 0.5; z R It is the critical depth of the inflection point of ultimate soil resistance, that is, the critical position depth of wedge flow and full flow mechanism;
[0029] For sandy soil, the py curve is:
[0030]
[0031]
[0032]
[0033]
[0034]
[0035]
[0036] In the formula, k is the initial ground reaction modulus, which is a function of the internal friction angle of the soil; ϕ β is the effective internal friction angle of the soil; C1, C2, and C3 are coefficients related to the internal friction angle of the soil; β = 45 + ϕ / 2;α= ϕ / 2; K0=0.4; K a =(1-sin ϕ ) / (1+sin ϕ ).
[0037] In a preferred embodiment, in step S5, the differential equation controlling the horizontal deflection of the pile is expressed as:
[0038]
[0039] In the formula, EI is the pile stiffness, N0 is the vertical load on the pile top, p is the soil resistance along the pile, and k is equal to the pile stiffness. py w(k) py (For the secant stiffness of the soil spring); further, the finite difference method is used to solve the nonlinear control equation. Rewriting the above equation in difference form, the finite difference equation for the deflection of the i-th pile segment is:
[0040]
[0041] In the formula, h is the differential step size, the subscript i is the pile node number, and w i-1 w represents the horizontal displacement of the first adjacent node above the current node i. i-1 w represents the horizontal displacement of the first adjacent node below the current node i; i-2 w represents the horizontal displacement of the second node above the current node i. i+2 k represents the horizontal displacement of the second node below the current node i. py,i Let be the soil reaction modulus at the i-th node.
[0042] In a preferred embodiment, in step S6, the horizontal displacement load at the pile top, the vertical load, the bending moment constraint conditions, and the boundary conditions for the shear force and bending moment at the pile end are as follows:
[0043] If the pile head is subjected to displacement loading and can rotate freely, then the difference form of the boundary conditions at the pile top is:
[0044]
[0045]
[0046] In the formula, w0 is the pile head displacement load; e c The height representing the load eccentricity; the difference form of the pile tip boundary condition is:
[0047]
[0048]
[0049] In the formula, K b With K r The secant stiffnesses of the pile bottom shear spring and bending moment spring are respectively equal to T. b / u and M b / θ.
[0050] In a preferred embodiment, the pile tip shear force T b The relationship between the pile end displacement u and the pile end displacement u satisfies an ideal elastic-plastic relationship:
[0051]
[0052] In the formula, T bu The ultimate shear force at the end is related to the cross-sectional area A of the steel casing and the maximum shear strength of the soil at the end. Related to; G s With v s These are the shear modulus and Poisson's ratio of the soil, respectively.
[0053] In a preferred embodiment, the pile end bending moment M b The pile bottom rotation angle θ is described using an ideal elastic-plastic model:
[0054]
[0055] In the formula, It is the ultimate bending moment at the pile bottom, which depends on the pile diameter D and the ultimate vertical resistance q at the pile tip. u k is the vertical ground reaction modulus of the soil; t is the wall thickness of the steel casing.
[0056] In a preferred embodiment, in step S6, if the differential equation of the pile nodal is in matrix form, then the lateral displacement {w} of the pile is expressed as:
[0057]
[0058] In the formula, [A] - {B} is the inverse of the coefficient matrix of the difference equation system; {B} is the coefficient on the right-hand side of the difference equation system.
[0059] In a preferred embodiment, in step S7, the simultaneous equations need to be solved using an iterative method to obtain the pile displacement, thereby obtaining the nonlinear response of the pile. The specific iterative process is as follows:
[0060] 1) Based on the py curve and T b -u curve, M b The -θ curves determine the initial soil spring stiffness k along the pile. py0_i Initial stiffness K of the pile bottom shear spring b0 Initial stiffness K of the pile bottom bending moment spring r0 Where the subscript i represents the i-th soil node, 0 represents the initial value, and the initial pile side displacement w is calculated in combination with the boundary conditions. 0_i
[0061] 2) Based on the displacement w of each node 0_i and the earth pressure p corresponding to this displacement 0_i Calculate the corresponding soil spring stiffness kpy1_i K b1 With K r1 ;
[0062] 3) Calculate the soil spring stiffness k py1_i K b1 With K r1 Substituting these values into the simultaneous equations derived from the difference equations and the boundary conditions, the lateral displacement k of the pile can be calculated. py2_i ;
[0063] 4) Repeat steps 2) to 3) until w is obtained in two consecutive iterations. k_i The value is less than the specified error (set to 10). -4 ),Right now .
[0064] Compared with existing technologies, this invention has the following advantages: This invention simultaneously considers the nonlinear py characteristics of the soil along the pile and the shear and flexural elasto-plastic responses of the soil at the pile tip under layered foundation conditions. By establishing the pile body control equations and introducing virtual nodes and an iterative solution mechanism, it can simultaneously reflect the deformation characteristics of the soil along the pile and the resistance contribution of the soil at the pile tip in large-diameter pile foundations. Compared with traditional analytical methods that ignore the pile tip effect or use simplified boundary conditions, this invention can obtain horizontal displacement, bending moment, and bearing characteristics of large-diameter piles that are more consistent with engineering practice, providing a more reasonable theoretical reference for the design and safety assessment of large-diameter pile foundations. Attached Figure Description
[0065] Figure 1 This is a schematic diagram of the calculation process according to one embodiment of the present invention;
[0066] Figure 2 This is a schematic diagram of the computational model proposed in this invention;
[0067] Figure 3 This is a schematic diagram of the virtual node method of the present invention;
[0068] Figure 4 This is a distribution diagram of the undrained shear strength of soil according to an embodiment of the present invention;
[0069] Figure 5 This is a load-displacement comparison diagram between the inventive calculation method and existing methods according to an embodiment of the present invention;
[0070] Figure 6 This invention illustrates how the contribution ratio of the soil resistance at the pile bottom to the bearing capacity of large-diameter piles with different pile diameters varies with the pile head displacement. Detailed Implementation
[0071] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0072] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.
[0073] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.
[0074] Reference Figure 1 and Figure 2 , Figure 1 This is a schematic diagram of the calculation process of the present invention. Figure 2 This is a schematic diagram of the calculation model proposed in this invention. The present invention provides a method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, comprising the following steps:
[0075] Step 1 Figure 2 This is a schematic diagram of the calculation model proposed in this invention, where the length of a single pile is L. p The pile has a diameter of D and is subjected to a combined horizontal displacement load Q0, a vertical load N0, and a bending moment M0 at its top. The horizontal displacement of the pile is w, and the rotation angle φ and the shear deformation of the cross section are θ. s Let p represent the horizontal soil resistance per unit depth. A coordinate system is established with the midpoint of the pile top as the origin. The horizontal coordinate w represents the horizontal displacement of any point on the pile, and the vertical coordinate z represents any length below the pile top. A single pile is considered an isotropic linear elastic material with a stiffness of EI. It is assumed that the pile has no vertical deformation and that its axial force gradient remains constant along the depth direction. The Winkler foundation model is used, and horizontal nonlinear soil springs are employed to simulate the pile-soil interaction, reflecting the relationship between the horizontal soil reaction and the horizontal displacement of the pile. The soil below the pile bottom is simplified to a base soil spring. Considering the stratification of the foundation, the soil along the pile within the pile length and depth is divided into n layers, each with a thickness of L.
[0076] Step 2: Perform a stress analysis on a micro-element of the pile within any soil layer i; based on the static equilibrium micro-element, the following equations are satisfied:
[0077]
[0078]
[0079] Step 3: Further combining Timoshenko beam theory, the differential equation governing the horizontal deflection of the pile can be expressed as:
[0080]
[0081] In the formula, EI is the pile stiffness, N0 is the vertical load on the pile top, p is the soil resistance along the pile, and k is equal to the pile stiffness. py w(k) py (for earth spring secant stiffness)
[0082] Step 4: Further rewrite the pile bending moment M, shear force Q, and rotation angle θ in differential form:
[0083]
[0084]
[0085]
[0086] In the formula, GA is the cross-sectional shear stiffness, and κ is the shear coefficient.
[0087] Step 5, Nonlinear soil spring secant stiffness k py The determination of the pile-soil interaction modulus is achieved by using a nonlinear py curve. For clay, the py curve reflecting the pile-soil interaction can be determined by the following formula:
[0088]
[0089]
[0090]
[0091]
[0092] In the formula, y c This is the horizontal displacement required for the soil around the pile to exert 50% of its ultimate resistance; p u The ultimate soil resistance; ε 50 The soil strain at 50% of the maximum shear strength in a triaxial undrained test; z represents the soil depth; s u γ represents the undrained shear strength. denoted as , where is the effective unit weight of the soil; J is an empirical coefficient, typically taken as 0.25 ~ 0.5, for normally consolidated clay J = 0.5; z R It is the critical depth of the inflection point of ultimate soil resistance, that is, the critical position depth of wedge flow and full flow mechanism.
[0093] For sandy soil, the py curve is:
[0094]
[0095]
[0096]
[0097]
[0098]
[0099]
[0100] In the formula, k is the initial ground reaction modulus, which is a function of the internal friction angle of the soil; ϕ β is the effective internal friction angle of the soil; C1, C2, and C3 are coefficients related to the internal friction angle of the soil; β = 45 + ϕ / 2;α= ϕ / 2; K0=0.4; K a =(1-sin ϕ ) / (1+sin ϕ ).
[0101] Step 6: Solve the differential equation of pile deflection; use the finite difference method to solve the nonlinear control equation. Write the differential equation of pile deflection in difference form, then the difference equation of the i-th segment of pile deflection is:
[0102]
[0103] In the formula, h is the differential step size, and the subscript i is the pile node number.
[0104] Step 7: Introduce the virtual node method; to ensure that the number of nodes in the pile body is consistent with the number of difference equations, add 2 virtual nodes at the pile top and pile end. Figure 3 The pile deflection difference equation can only yield n-4 equations. The missing 4 equations can be given by the boundary conditions of the pile head and pile tip.
[0105] The difference form of the boundary conditions at the pile top is:
[0106]
[0107]
[0108] In the formula, w0 is the pile head displacement load; e c This represents the height of load eccentricity. The difference form of the pile tip boundary condition is:
[0109]
[0110]
[0111] In the formula, K b With K r The secant stiffnesses of the pile bottom shear spring and bending moment spring are respectively equal to T.b / u and M b / θ.
[0112] Step 8, T b and M b Determination of the shear force at the pile tip; assuming the shear force T at the pile tip b The relationship between the pile bottom displacement u and the pile bottom displacement u satisfies an ideal elastic-plastic relationship, as follows:
[0113]
[0114] In the formula, T bu The ultimate shear force at the end is related to the cross-sectional area A of the large-diameter single pile and the maximum shear strength of the soil at the end. Related to; G s With v s These are the shear modulus and Poisson's ratio of the soil, respectively.
[0115] The pile end bending moment M is described using an ideal elastic-plastic model. b Relationship with pile bottom rotation angle θ:
[0116]
[0117] In the formula, It is the ultimate bending moment at the pile bottom, which depends on the pile diameter D and the ultimate vertical resistance q at the pile tip. u t represents the wall thickness of a large-diameter pile.
[0118] Step 9, Nonlinear Response of Pile Body; Rewriting the pile body nodal differential equations in matrix form, the lateral displacement {w} of the pile body can be expressed as:
[0119]
[0120] In the formula, [A] - {B} is the inverse of the coefficient matrix of the difference equation system; {B} is the coefficient on the right-hand side of the difference equation system.
[0121] Note that the above system of simultaneous equations needs to be solved using an iterative method to determine the pile displacement and thus obtain the nonlinear response of the pile. The specific iterative process is as follows:
[0122] 1) Based on the py curve and T b -u curve, M b The -θ curves determine the initial soil spring stiffness k along the pile. py0_i Initial stiffness K of the pile bottom shear spring b0 Initial stiffness K of the pile bottom bending moment spring r0 Where the subscript i represents the i-th soil node, 0 represents the initial value, and the initial pile side displacement w is calculated in combination with the boundary conditions. 0_i ;
[0123] 2) Based on the displacement w of each node0_i and the earth pressure p corresponding to this displacement 0_i Calculate the corresponding soil spring stiffness k py1_i K b1 With K r1 ;
[0124] 3) Calculate the soil spring stiffness k py1_i K b1 With K r1 Substituting these values into the simultaneous equations derived from the difference equations and the boundary conditions, the lateral displacement k of the pile can be calculated. py2_i ;
[0125] 4) Repeat steps 2) to 3) until w is obtained in two consecutive iterations. k_i The value is less than the specified error (set to 10). -4 ),Right now .
[0126] To verify the accuracy of the invention, a large-diameter monopile field test using PISA was selected as the test object. The test pile had a diameter of 2m and a length of 10.6m, with a Young's modulus of 200 GPa. The soil at the test site was Cowden moraine clay, whose undrained strength ranged from 50 to 160 kPa at a depth of 12m. (See details...) Figure 4 The load-displacement curves of large-diameter monopiles measured in PISA are compared with the results of this invention and existing methods, as shown in the figure. Figure 5 As shown in the figure, the solution presented in this paper is consistent with the trends of the field test results for CL2 piles and the API method. Compared with the traditional API method, the solution presented in this paper agrees better with the field test results, thus verifying the correctness and advancement of the solution presented in this paper.
[0127] Figure 6 The study presents the variation of the contribution ratio of the pile bottom soil resistance to the bearing capacity with pile head displacement for different pile diameters. It can be observed that when the displacement is small, the pile bottom soil resistance is not fully activated, and the load is mainly borne by the soil at the pile bottom. However, as the displacement increases, the contribution ratio of the pile bottom soil resistance to the bearing capacity gradually increases. When the pile head displacement reaches the critical displacement (0.1D), the increase in pile head displacement has almost no effect on the contribution ratio of the pile bottom soil resistance to the bearing capacity for different diameters. Furthermore, increasing the pile diameter significantly increases the contribution ratio of the pile bottom soil resistance; under the same displacement, the larger the pile diameter, the greater the contribution ratio of the pile bottom soil resistance to the bearing capacity (up to 28% at D = 4 m).
[0128] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.
Claims
1. A method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, characterized in that, include: S1. Input the parameters and load conditions of the large-diameter pile to establish a calculation model for the horizontal nonlinear response of the large-diameter pile in the stratified foundation considering the end resistance. S2. Based on the Winkler foundation model, the soil around the pile is divided into several layers according to the depth direction, and each layer of soil around the pile is equivalent to a nonlinear horizontal soil spring. S3. The soil at the pile tip is simplified into an end shear elastoplastic spring describing the shear force-displacement relationship and an end bending elastoplastic spring describing the bending moment-rotation relationship. S4. Determine the secant stiffness of the soil spring at each depth based on the nonlinear py curve of clay or sand. S5. Based on Timoshenko beam theory, establish the differential equations governing the horizontal deflection of the pile body, and use the finite difference method to discretize the governing equations. S6. Set virtual nodes at the pile top and pile end, and combine the discretization results of step S5 to establish the horizontal load, vertical load and bending moment constraint conditions at the pile top, as well as the boundary conditions of shear force and bending moment at the pile end. S7. Combine the discrete equations with the boundary conditions and use iterative calculation to solve the nonlinear responses such as horizontal displacement, bending moment and shear force at each node of the pile.
2. The method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, as described in claim 1, is characterized in that... In step S2, a micro-element of the pile body is randomly selected from the soil layer i on the side of the pile. According to the static equilibrium micro-element, the following equations are satisfied: In the formula, Q is the horizontal load, z is the soil depth, p is the horizontal soil resistance per unit depth, M is the pile bending moment, N is the vertical load, and w is the pile horizontal displacement.
3. The method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, as described in claim 1, is characterized in that... In step S3, the horizontal load Q, the pile bending moment M, and the rotation angle θ are written in differential form: In the formula, EI is the pile stiffness, N0 is the vertical load on the pile top, GA is the section shear stiffness, and κ is the shear coefficient.
4. The method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, as described in claim 1, is characterized in that... In step S4, the py curve of the clay is determined by the following formula: In the formula, y c This is the horizontal displacement required for the soil around the pile to exert 50% of its ultimate resistance; p u The ultimate soil resistance; ε 50 The soil strain at 50% of the maximum shear strength in a triaxial undrained test; s u γ represents the undrained shear strength. denoted as , where is the effective unit weight of the soil; J is an empirical coefficient, typically taken as 0.25 ~ 0.5, for normally consolidated clay J = 0.5; z R It is the critical depth of the inflection point of ultimate soil resistance, that is, the critical position depth of wedge flow and full flow mechanism; For sandy soil, the py curve is: In the formula, k is the initial ground reaction modulus, which is a function of the internal friction angle of the soil; ϕ β is the effective internal friction angle of the soil; C1, C2, and C3 are coefficients related to the internal friction angle of the soil; β = 45 + ϕ / 2;α= ϕ / 2; K0=0.4; K a =(1-sin ϕ ) / (1+sin ϕ ).
5. The method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, as described in claim 1, is characterized in that... In step S5, the differential equation governing the horizontal deflection of the pile is expressed as: In the formula, EI is the pile stiffness, N0 is the vertical load on the pile top, p is the soil resistance along the pile, and k is equal to the pile stiffness. py w, k py Let the secant stiffness of the soil spring be denoted; further, the finite difference method is used to solve the nonlinear control equation. Rewriting the above equation in difference form, the finite difference equation for the deflection of the i-th pile segment is: In the formula, h is the differential step size, the subscript i is the pile node number, and w i-1 w represents the horizontal displacement of the first adjacent node above the current node i. i-1 w represents the horizontal displacement of the first adjacent node below the current node i; i-2 w represents the horizontal displacement of the second node above the current node i. i+2 k represents the horizontal displacement of the second node below the current node i. py,i Let be the soil reaction modulus at the i-th node.
6. The method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, as described in claim 1, is characterized in that... In step S6, the boundary conditions for the horizontal displacement load at the pile top, the vertical load, and the shear force and bending moment at the pile end are as follows: If the pile head is subjected to displacement loading and can rotate freely, then the difference form of the boundary conditions at the pile top is: In the formula, w0 is the pile head displacement load; e c The height representing the load eccentricity; the difference form of the pile tip boundary condition is: In the formula, K b With K r The secant stiffnesses of the pile bottom shear spring and bending moment spring are respectively equal to T. b / u and M b / θ.
7. The method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, as described in claim 6, is characterized in that... Pile tip shear force T b The relationship between the pile end displacement u and the pile end displacement u satisfies an ideal elastic-plastic relationship: In the formula, T bu The ultimate shear force at the end is related to the cross-sectional area A of the steel casing and the maximum shear strength of the soil at the end. Related to; G s With v s These are the shear modulus and Poisson's ratio of the soil, respectively.
8. The method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, as described in claim 6, is characterized in that... Pile end bending moment M b The pile bottom rotation angle θ is described using an ideal elastic-plastic model: In the formula, It is the ultimate bending moment at the pile bottom, which depends on the pile diameter D and the ultimate vertical resistance q at the pile tip. u t represents the wall thickness of the steel casing.
9. The method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, as described in claim 1, is characterized in that... In step S6, the differential equation of the pile nodes is in matrix form, so the lateral displacement {w} of the pile is expressed as: In the formula, [A] - {B} is the inverse of the coefficient matrix of the difference equation system; {B} is the coefficient on the right-hand side of the difference equation system.
10. The method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, as described in claim 1, is characterized in that... In step S7, the simultaneous equations need to be solved using an iterative method to determine the pile displacement, thereby obtaining the nonlinear response of the pile. The specific iterative process is as follows: 1) Based on the py curve and T b -u curve, M b The -θ curves determine the initial soil spring stiffness k along the pile. py0_i Initial stiffness K of the pile bottom shear spring b0 Initial stiffness K of the pile bottom bending moment spring r0 The subscript i represents the i-th soil node, and 0 represents the initial value. Combined with the boundary conditions, the initial pile side displacement w is calculated. 0_i ; 2) Based on the displacement w of each node 0_i and the earth pressure p corresponding to this displacement 0_i Calculate the corresponding soil spring stiffness k py1_i K b1 With K r1 ; 3) Calculate the soil spring stiffness k py1_i K b1 With K r1 Substituting these values into the simultaneous equations derived from the difference equations and the boundary conditions, the lateral displacement k of the pile can be calculated. py2_i ; 4) Repeat steps 2) to 3) until w is obtained in two consecutive iterations. k_i The value is less than the specified error (set to 10). -4 ),Right now .