A tunnel excavation induced displacement calculation method for pile foundation-frame structure

Abstract

The present application relates to a kind of tunnel excavation induced pile foundation-frame structure displacement calculation method, belong to underground tunnel engineering technical field.The method includes: input soil, tunnel and pile foundation calculation parameter, establish the expression of soil displacement caused by tunnel excavation;Considering the influence of soil cohesion, introduce the equivalent internal friction angle of soil, correct soil displacement expression;Establish the pile-soil interaction model considering the correlation of soil stiffness-stress;Solve the pile-soil interaction force, represent the restraint effect of in-service pile, calculate the soil displacement of tunnel excavation;Establish the pile foundation-tunnel-soil interaction mechanical model considering the correlation of soil stiffness-stress and the restraint effect of in-service pile, obtain the pile foundation displacement control equation, calculate and output soil and pile foundation displacement;Pile foundation-tunnel-soil interaction mechanical model is coupled with upper frame structure, obtains frame-pile foundation-tunnel-soil deformation coordination equation, calculates and outputs frame structure displacement.

Description

Technical Field

[0001] This invention belongs to the field of underground tunnel engineering technology, specifically relating to a method for calculating displacement of pile foundation-frame structure induced by tunnel excavation. Background Technology

[0002] During tunnel construction, the dynamic redistribution of soil stress field induces deformation and stress redistribution in adjacent soil and pile foundation systems, leading to a significant deterioration in the bearing capacity of the pile foundation. When the deformation exceeds the design allowable range, it will seriously threaten the safe operation of the superstructure. Therefore, constructing an accurate tunnel excavation-pile foundation interaction prediction model and quantitatively assessing the influence domain and degree of construction disturbance has become a key problem that urgently needs to be solved in the field of geotechnical engineering.

[0003] Current academic research on this problem mainly presents a three-pronged approach: numerical simulation, model testing, and theoretical analytical methods are developing in tandem. Numerical simulation and model testing studies have revealed the influence mechanisms of factors such as soil stress release, ground loss, and disturbance effects on the displacement field, providing important support for the construction and verification of theoretical analytical models. Among them, the two-stage method has become the preferred theoretical tool for engineering design due to its advantages such as clear physical meaning, high parameter identification, and strong engineering applicability. This method decomposes the solution process into two stages: first, the soil displacement field is calculated under the condition of ignoring the existence of piles; then, the obtained displacement field is applied as an external load to the pile foundation for mechanical response analysis.

[0004] Based on this, this invention deeply analyzes the pile-soil interaction mechanism and constructs a matrix governing equation. This equation not only fully considers the constraint effect of in-service piles on soil displacement but also incorporates the interaction between the superstructure and the pile foundation. Within this theoretical framework, an innovative nonlinear foundation beam model combining soil stiffness-stress correlation is proposed, along with a modified two-stage calculation method for the restraining effect of in-service piles on soil displacement, providing new insights for pile foundation response analysis in complex engineering scenarios. Simultaneously, by introducing the concept of equivalent internal friction angle, the soil cohesion is effectively quantified, thereby optimizing and improving traditional formulas. Finally, a frame-pile-tunnel-soil interaction mechanical model that comprehensively considers the effects of the superstructure is established. The accuracy and reliability of the invention are verified by comparing the results obtained using the calculation method of this invention with existing research methods from multiple dimensions. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the displacement of a pile-frame structure induced by tunnel excavation, which comprehensively considers the restraining effect of in-service piles and the correlation between soil stiffness and stress, providing a theoretical basis for tunnel excavation design and construction.

[0006] To achieve the above objectives, the technical solution of the present invention is: a method for calculating displacement of a pile foundation-frame structure induced by tunnel excavation, comprising:

[0007] S1. Input the calculation parameters for soil, tunnel and pile foundation, and establish the expression for soil displacement caused by tunnel excavation;

[0008] S2. Considering the influence of soil cohesion, the equivalent internal friction angle of the soil is introduced to modify the soil displacement expression.

[0009] S3. Establish a pile-soil interaction model that considers the correlation between soil stiffness and stress.

[0010] S4. Solve for pile-soil interaction forces. Characterizes the restraining effect of in-service piles and calculates the displacement of soil during tunnel excavation;

[0011] S5. Determine the parameters of the nonlinear spring foundation beam, establish a mechanical model of pile-tunnel-soil interaction considering the correlation between soil stiffness and stress and the restraint effect of in-service piles, obtain the control equation of pile displacement, and calculate and output the soil and pile displacement.

[0012] S6. The mechanical model of the interaction between pile foundation, tunnel and soil is coupled with the upper frame structure to obtain the deformation coordination equation of frame-pile foundation-tunnel-soil, and the displacement of the frame structure is calculated and output.

[0013] Furthermore, in step S1, the expression for the soil displacement caused by tunnel excavation is as follows:

[0014]

[0015]

[0016] In the formula, This represents the vertical displacement of the soil. Let be the horizontal displacement of the soil, R be the tunnel radius, z be the vertical distance from the ground surface, H be the tunnel depth, and y be the horizontal distance from the tunnel centerline. For formation loss rate, The equivalent internal friction angle of the soil. γ is the Poisson's ratio of the soil, and γ is the natural unit weight of the soil.

[0017] Furthermore, in step S2, considering the influence of soil cohesion, the equivalent internal friction angle of the soil is... It is expressed as follows:

[0018]

[0019] In the formula, c' and These represent the effective cohesion and effective internal friction angle of the soil, respectively, and d is the calculated depth of the soil.

[0020] Furthermore, in step S3, in the pile-soil interaction model, the spring stiffness of the soil along the horizontal pile... and the soil spring stiffness of vertical piles They are represented as follows:

[0021]

[0022]

[0023] In the formula, The Young's modulus of soil. For the pile diameter, For the moment of inertia, The elastic modulus of the pile foundation. Poisson's ratio of the soil; This is an empirical parameter, and its value is:

[0024]

[0025] Depending on the soil heterogeneity, take = 2.5, The length of the pile;

[0026] Young's modulus of soil E t Considering the correlation of foundation soil stress:

[0027]

[0028] In the formula: Reference stress p at different depths ref Young's modulus of the soil below Let K0 be the effective horizontal stress at different depths, m be the stress-related power exponent, and c' be the stress at rest. These are the effective cohesion and effective internal friction angle of the soil, respectively.

[0029] Furthermore, in step S4, the pile-soil interaction force The calculation formula is as follows:

[0030]

[0031] In the formula, The pile foundation flexibility matrix, The relative displacement column vector of the soil considering the restraining effect of in-service piles is calculated by the following formula:

[0032]

[0033]

[0034] In the formula: Each of the following points ( Unit force This causes vertical and horizontal displacements of the soil at a given point (x, y, z). The distance between piles and tunnels. For the soil spring stiffness at the vertical pile tip, The flexibility at each node of the pile foundation. This represents the relative displacement of the soil at each node. The elastic modulus of the pile foundation. Let be the cross-sectional area of ​​the pile. Let be the pile length, and the pile be divided into n units, where i is the pile section number (i = 1 to n+1), j is the unit number (j = 1 to n), and the unit length is... , , , any point ( Unit force The expression for the soil displacement at a point (x, y, z) in the surrounding area is:

[0035]

[0036]

[0037] In the formula, unit force This causes vertical displacement of the soil. unit force This causes horizontal displacement of the soil. Let z be the Young's modulus of the soil, and z be the vertical distance from the ground surface. Poisson's ratio of soil Determined by the following formula:

[0038]

[0039]

[0040] In the formula, H represents the tunnel depth.

[0041] Furthermore, in step S4, the soil displacement during tunnel excavation, considering the restraining effect of in-service piles and the correlation between soil stiffness and stress, includes both vertical and horizontal soil displacement, calculated as follows:

[0042]

[0043]

[0044] In the formula, This represents the vertical displacement of the soil. This represents the horizontal displacement of the soil. The pile-soil interaction forces at each node. unit force This causes vertical displacement of the soil. unit force This causes horizontal displacement of the soil. The pile is divided into n units, where j is the unit number.

[0045] Furthermore, in step S5, the control equation for pile foundation displacement is expressed as follows:

[0046]

[0047] In the formula, and These are the vertical and horizontal displacements of a single pile, respectively. and These are the vertical and horizontal displacements of the soil around the pile, respectively. and The parameters for the vertical nonlinear spring foundation beam and the horizontal nonlinear spring foundation beam are respectively:

[0048]

[0049]

[0050] In the formula, These refer to the soil spring stiffness of horizontal piles and the soil spring stiffness of vertical piles, respectively. The elastic modulus of the pile foundation. For the moment of inertia, Let be the cross-sectional area of ​​the pile.

[0051] Furthermore, in step S5, the pile foundation displacement control equation applies to both single piles and pile groups; wherein, the single pile displacement control matrix equation is expressed as:

[0052]

[0053]

[0054] In the formula, and These are the vertical stiffness matrix and the horizontal stiffness matrix of the pile foundation, respectively. and These are the vertical load column vector and the horizontal load column vector, respectively. and These are the vertical and horizontal displacements of the pile nodes, respectively. and These are the vertical stiffness matrix and the horizontal stiffness matrix of the soil, respectively. and These represent the vertical and horizontal displacements of the soil at the pile joint, respectively.

[0055] The displacement control matrix equation for a pile group is expressed as follows:

[0056]

[0057]

[0058] In the formula, Let be the displacement decay function. This is the displacement influence coefficient matrix between two adjacent piles.

[0059] Furthermore, the displacement decay function Considering the curtain effect of pile groups, it can be expressed as:

[0060]

[0061] In the formula, Let be the pile radius, and s be the pile spacing. These are empirical values ​​that depend on the heterogeneity of the soil.

[0062] Displacement influence coefficient matrix between two adjacent piles Represented as:

[0063]

[0064] Displacement influence coefficient between two adjacent piles Represented as:

[0065]

[0066] In the formula, This represents the displacement influence coefficient between node j of pile 1 and node i of pile 2. Let G be the vertical spring modulus of the soil at node j, G be the soil shear modulus, and h be the tunnel excavation depth. Poisson's ratio of soil and The distances from the ground surface to pile node i and pile node j are respectively, and x is the distance between the pile and the tunnel centerline. (Intermediate variables) .

[0067] Furthermore, by coupling the pile-tunnel-soil interaction mechanical model with the superstructure, the deformation compatibility equations of the frame-pile-tunnel-soil are obtained:

[0068]

[0069] In the formula, Here is the vertical stiffness matrix of the soil. Here is the stiffness matrix of the superstructure. The stiffness matrix of the pile group is... This is the pile foundation displacement matrix. This represents the external force vector of the pile group caused by tunnel excavation.

[0070] The deformation compatibility equations for the frame-pile-tunnel-soil structure can be expanded as follows:

[0071]

[0072] The subscript F indicates the connection node between the pile and the superstructure, and the subscript E indicates the pre-embedded pile node at the pile head. The displacement vector of the soil caused by tunnel excavation; the stiffness of the superstructure frame is calculated by the following formula:

[0073]

[0074]

[0075] In the formula, The equivalent stiffness of the sunken area of ​​the upper frame structure. EI represents the equivalent stiffness of the protruding region of the superstructure frame, EI represents the bending stiffness of the superstructure frame, and EI represents the column stiffness coefficient. and Represented as:

[0076]

[0077]

[0078] The average stiffness of the lower column. The average stiffness of the upper column is... Let be the average stiffness of the beam. This refers to the length of the sunken area in the upper frame structure. This refers to the length of the protruding area of ​​the upper frame structure. This refers to the span of the beam in the frame structure.

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] This invention comprehensively considers the restraining effect of in-service piles and the correlation between soil stiffness and stress during tunnel excavation, takes into account the influence of soil cohesion, and introduces the equivalent internal friction angle of the soil. It can solve for the pile foundation displacement induced by tunnel excavation that is more consistent with the actual situation, and provide a more reasonable theoretical reference for existing construction design. Attached Figure Description

[0081] Figure 1 This is a schematic diagram of the calculation process according to one embodiment of the present invention;

[0082] Figure 2 This is a schematic diagram of the pile-soil interaction mechanism model and interaction forces according to an embodiment of the present invention; Figure 2 In the middle (a), the pile-soil horizontal interaction analysis is shown. Figure 2 (b) shows the vertical interaction analysis between the pile and the soil;

[0083] Figure 3 This is a schematic diagram of the vertical displacement of a frame structure according to an embodiment of the present invention;

[0084] Figure 4 This is a schematic diagram of the sunken and raised areas of the ground surface and frame structure according to an embodiment of the present invention;

[0085] Figure 5 This is a comparison diagram of the vertical displacement of the soil around a single pile using the inventive calculation method described in one embodiment of the present invention and the existing analytical solution;

[0086] Figure 6 This is a comparison diagram of the horizontal displacement of soil between the inventive calculation method and existing methods according to an embodiment of the present invention;

[0087] Figure 7 This is a comparison diagram of the vertical displacement of soil calculated by the method described in an embodiment of the present invention and existing methods.

[0088] Figure 8 This is a comparison diagram of the horizontal displacement of a single pile between the inventive calculation method and existing methods according to an embodiment of the present invention;

[0089] Figure 9 This is a comparison diagram of the lateral displacement of pile groups between the inventive calculation method and existing methods according to an embodiment of the present invention;

[0090] Figure 10 This is a comparison diagram of the lateral displacement of the soil around the pile group using the inventive calculation method described in one embodiment of the present invention and existing methods;

[0091] Figure 11 This is a comparison diagram of the vertical displacement of the soil around the pile group using the inventive calculation method described in one embodiment of the present invention and existing methods.

[0092] Figure 12 This is a displacement diagram of the framework structure of the calculation method described in one embodiment of the present invention. Detailed Implementation

[0093] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0094] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0095] Reference Figure 1 and Figure 2 , Figure 1 This is a schematic diagram of the calculation process of a preferred embodiment of the present invention. Figure 2 This is a preferred embodiment of the pile-soil interaction mechanism model and a schematic diagram of the interaction forces. Figure 2 In the middle (a), the pile-soil horizontal interaction analysis is shown. Figure 2 (b) shows the vertical interaction analysis between the pile and the soil. It should be noted that this invention is described in detail with reference to schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views showing the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples, used only to facilitate and clearly illustrate the embodiments of this invention. This invention provides a method for calculating the displacement of a pile-frame structure induced by tunnel excavation, comprising the following steps:

[0096] Step 1: Input the calculation parameters for the soil, tunnel, and pile foundation, and establish the expression for the soil displacement caused by tunnel excavation:

[0097]

[0098]

[0099] In the formula, This represents the vertical displacement of the soil. Let be the horizontal displacement of the soil, R be the tunnel radius, z be the vertical distance from the ground surface, H be the tunnel depth, and y be the horizontal distance from the tunnel centerline. For formation loss rate, The equivalent internal friction angle of the soil. γ is the Poisson's ratio of the soil, and γ is the natural unit weight of the soil.

[0100] Step 2: Considering the influence of soil cohesion, introduce the equivalent internal friction angle of the soil and modify the soil displacement expression; equivalent internal friction angle of soil. The calculation formula is as follows:

[0101]

[0102] In the formula, c' and These represent the effective cohesion and effective internal friction angle of the soil, respectively, and d is the calculated depth of the soil.

[0103] Step 3: Establish a pile-soil interaction model that considers the correlation between soil stiffness and stress; in the pile-soil interaction model, the spring stiffness of the soil along the horizontal pile is... and the soil spring stiffness of vertical piles They are represented as follows:

[0104]

[0105]

[0106] In the formula, The Young's modulus of soil. For the pile diameter, For the moment of inertia, The elastic modulus of the pile foundation. Poisson's ratio of the soil; This is an empirical parameter, and its value is:

[0107]

[0108] Depending on the soil heterogeneity, take = 2.5, The length of the pile;

[0109] Young's modulus of soil E t Considering the correlation of foundation soil stress:

[0110]

[0111] In the formula: Reference stress p at different depths ref Young's modulus of the soil below Let K0 be the effective horizontal stress at different depths, m be the stress-related power exponent, and c' be the stress at rest. These are the effective cohesion and effective internal friction angle of the soil, respectively.

[0112] Step 4: Solve for pile-soil interaction forces Characterizes the restraining effect of in-service piles and calculates soil displacement during tunnel excavation; pile-soil interaction force. The calculation formula is as follows:

[0113]

[0114] In the formula, The pile foundation flexibility matrix, The relative displacement column vector of the soil considering the restraining effect of in-service piles is calculated by the following formula:

[0115]

[0116]

[0117] In the formula: Each of the following points ( Unit force This causes vertical and horizontal displacements of the soil at a given point (x, y, z). The distance between piles and tunnels. For the soil spring stiffness at the vertical pile tip, This represents the relative displacement of the soil at each node. The flexibility at each node of the pile foundation. The elastic modulus of the pile foundation. Let be the cross-sectional area of ​​the pile. Let be the pile length, and the pile be divided into n units, where i is the pile section number (i = 1 to n+1), j is the unit number (j = 1 to n), and the unit length is... , , , any point ( Unit force The expression for the soil displacement at a point (x, y, z) in the surrounding area is:

[0118]

[0119]

[0120] In the formula, unit force This causes vertical displacement of the soil. unit force This causes horizontal displacement of the soil. Let z be the Young's modulus of the soil, and z be the vertical distance from the ground surface. Poisson's ratio of soil Determined by the following formula:

[0121]

[0122]

[0123] In the formula, H represents the tunnel depth.

[0124] The formulas for calculating the vertical and horizontal displacements of the soil are as follows:

[0125]

[0126]

[0127] In the formula, This represents the vertical displacement of the soil. This represents the horizontal displacement of the soil. The pile-soil interaction forces at each node. unit force This causes vertical displacement of the soil. unit force This causes horizontal displacement of the soil. The pile is divided into n units, where j is the unit number.

[0128] Step 5: Determine the parameters of the nonlinear spring foundation beam, establish a pile-tunnel-soil interaction mechanical model considering the soil stiffness-stress correlation and the restraining effect of in-service piles, obtain the pile foundation displacement control equation, calculate and output the soil and pile foundation displacements; the pile foundation displacement control equation is expressed as follows:

[0129]

[0130] In the formula, and These are the vertical and horizontal displacements of a single pile, respectively. and These are the vertical and horizontal displacements of the soil around the pile, respectively. and The parameters for the vertical nonlinear spring foundation beam and the horizontal nonlinear spring foundation beam are respectively:

[0131]

[0132]

[0133] In the formula, These refer to the soil spring stiffness of horizontal piles and the soil spring stiffness of vertical piles, respectively. The elastic modulus of the pile foundation. For the moment of inertia, Let be the cross-sectional area of ​​the pile.

[0134] Step 5.1: The pile foundation displacement control equations are applicable to both single piles and pile groups; the single pile displacement control matrix equation is expressed as:

[0135]

[0136]

[0137] In the formula, and These are the vertical stiffness matrix and the horizontal stiffness matrix of the pile foundation, respectively. and These are the vertical load column vector and the horizontal load column vector, respectively. and These are the vertical and horizontal displacements of the pile nodes, respectively. and These are the vertical stiffness matrix and the horizontal stiffness matrix of the soil, respectively. and These represent the vertical and horizontal displacements of the soil at the pile joint, respectively.

[0138] The displacement control matrix equation for a pile group is expressed as follows:

[0139]

[0140]

[0141] In the formula, Let be the displacement decay function. The displacement influence coefficient matrix between two adjacent piles; the displacement attenuation function Considering the curtain effect of pile groups, it can be expressed as:

[0142]

[0143] In the formula, Let be the pile radius, and s be the pile spacing. The values ​​are empirically determined based on soil heterogeneity; the displacement influence coefficient matrix between two adjacent piles. Represented as:

[0144]

[0145] Displacement influence coefficient between two adjacent piles Represented as:

[0146]

[0147] In the formula, This represents the displacement influence coefficient between node j of pile 1 and node i of pile 2. Let G be the vertical spring modulus of the soil at node j, G be the soil shear modulus, and h be the tunnel excavation depth. Poisson's ratio of soil and The distances from the ground surface to pile node i and pile node j are respectively, and x is the distance between the pile and the tunnel centerline. (Intermediate variables) .

[0148] Step 6, see Figure 3 , Figure 4 The mechanical model of the interaction between pile foundation, tunnel and soil is coupled with the superstructure to obtain the deformation coordination equation of frame-pile foundation-tunnel-soil, and the displacement of frame structure is calculated and output.

[0149] The linear deformation compatibility equation of the frame-pile foundation-tunnel-soil can be expressed as:

[0150]

[0151] In the formula, Here is the vertical stiffness matrix of the soil. Here is the stiffness matrix of the superstructure. The stiffness matrix of the pile group is... This is the pile foundation displacement matrix. This represents the external force vector of the pile group caused by tunnel excavation.

[0152] The deformation compatibility equations for the frame-pile-tunnel-soil structure can be expanded as follows:

[0153]

[0154] The subscript F indicates the connection node between the pile and the superstructure, and the subscript E indicates the pre-embedded pile node at the pile head. The displacement vector of the soil caused by tunnel excavation; the equivalent stiffness of the superstructure frame is calculated by the following formula:

[0155]

[0156]

[0157] In the formula, The equivalent stiffness of the sunken area of ​​the upper frame structure. EI represents the equivalent stiffness of the protruding region of the superstructure frame, EI represents the bending stiffness of the superstructure frame, and EI represents the column stiffness coefficient. and Represented as:

[0158]

[0159]

[0160] The average stiffness of the lower column. The average stiffness of the upper column is... Let be the average stiffness of the beam. This refers to the length of the sunken area in the upper frame structure. This refers to the length of the protruding area of ​​the upper frame structure. This refers to the span of the beam in the frame structure.

[0161] To verify the accuracy of the invention, the calculated displacements of the vertical and horizontal deep soil layers during the excavation of a nearby in-service pile tunnel were compared with existing methods, such as... Figure 5 and Figure 6 The diagram shows a comparison of curves obtained under different working conditions (i.e., different soil loss rates). It can be seen that the depth of the zero point of vertical soil displacement is slightly lower than the tunnel centerline, and the vertical displacement above the tunnel centerline is larger. Figure 5The horizontal displacement of the soil initially increases slowly with depth, then decreases sharply, reaching its maximum value H near the tunnel depth. max ( Figure 6 This is because the soil above the tunnel centerline is greatly affected by stratum displacement and has low soil stiffness. Tunnel excavation unloading causes some soil to heave. The proposed calculation method takes into account the soil stiffness-stress correlation and pile foundation restraint effect, and the result is slightly smaller than that of the existing method, indicating that the traditional calculation method is conservative. Figure 7 and Figure 8 The proposed method's calculation results for the vertical and horizontal displacement of a single pile are compared with those of existing numerical simulation methods. It can be seen that the pile foundation displacement curve is similar to that of the deep soil displacement curve. Figure 5 and Figure 6 The vertical displacement of the pile foundation is consistent with the overall trend of existing numerical simulation results. For the pile body as a whole, the difference between the vertical displacement of the pile top and the pile tip is small, while the horizontal displacement of the pile foundation exhibits a parabolic distribution, that is, it first increases slowly to the maximum value at the tunnel burial depth and then decreases sharply. Similarly, since the proposed method considers the pile foundation restraint effect and the soil stiffness-stress correlation, the calculated results of the vertical and horizontal displacements of the pile foundation under different stratum loss rates are all smaller than the numerical simulation results, proving the rationality of the proposed method. Figure 9 The method of the present invention and the existing method are shown to calculate the lateral displacement of pile groups. It can be seen that the calculation result of the method of the present invention is smaller than that of the existing method because the pile group shielding effect is taken into account. Figure 10 and Figure 11 The vertical and horizontal displacements of the soil around the pile group are compared between the method of this invention and the existing method. The data are consistent and the patterns are consistent. The calculation results are smaller than the existing analytical solutions (considering the blocking effect of the pile group). Figure 12 The data diagram of the upper frame structure of the method of the present invention is given, and it is found that the closer to the center of the tunnel, the greater the displacement.

[0162] 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 displacement of a pile-frame structure induced by tunnel excavation, characterized in that, include: S1. Input the calculation parameters for soil, tunnel and pile foundation, and establish the expression for soil displacement caused by tunnel excavation; S2. Considering the influence of soil cohesion, the equivalent internal friction angle of the soil is introduced to modify the soil displacement expression. S3. Establish a pile-soil interaction model that considers the correlation between soil stiffness and stress. S4. Solve for pile-soil interaction forces. Characterizes the restraining effect of in-service piles and calculates the displacement of soil during tunnel excavation; S5. Determine the parameters of the nonlinear spring foundation beam, establish a mechanical model of pile-tunnel-soil interaction considering the correlation between soil stiffness and stress and the restraint effect of in-service piles, obtain the control equation of pile displacement, and calculate and output the soil and pile displacement. S6. Couple the pile-tunnel-soil interaction mechanical model with the superframe structure to obtain the frame-pile-tunnel-soil deformation compatibility equation, calculate and output the frame structure displacement; In step S3, in the pile-soil interaction model, the spring stiffness of the soil along the horizontal pile is... and the soil spring stiffness of vertical piles They are represented as follows: In the formula, The Young's modulus of soil. For the pile diameter, For the moment of inertia, The elastic modulus of the pile foundation. Poisson's ratio of the soil; This is an empirical parameter, and its value is: Depending on the soil heterogeneity, take = 2.5, The length of the pile; Young's modulus of soil E t Considering the correlation of foundation soil stress: In the formula: Reference stress p at different depths ref Young's modulus of the soil below Let K0 be the effective horizontal stress at different depths, m be the stress-related power exponent, and c' be the stress at rest. These are the effective cohesion and effective internal friction angle of the soil, respectively.

2. The method for calculating displacement of a pile-frame structure induced by tunnel excavation according to claim 1, characterized in that, In step S1, the expression for the soil displacement caused by tunnel excavation is as follows: In the formula, This represents the vertical displacement of the soil. Let be the horizontal displacement of the soil, R be the tunnel radius, z be the vertical distance from the ground surface, H be the tunnel depth, and y be the horizontal distance from the tunnel centerline. For formation loss rate, The equivalent internal friction angle of the soil. γ is the Poisson's ratio of the soil, and γ is the natural unit weight of the soil.

3. The method for calculating displacement of a pile-frame structure induced by tunnel excavation according to claim 2, characterized in that, In step S2, considering the influence of soil cohesion, the equivalent internal friction angle of the soil is... It is expressed as follows: In the formula, c' and These represent the effective cohesion and effective internal friction angle of the soil, respectively, and d is the calculated depth of the soil.

4. The method for calculating displacement of a pile-frame structure induced by tunnel excavation according to claim 1, characterized in that, In step S4, the pile-soil interaction force The calculation formula is as follows: In the formula, The pile foundation flexibility matrix, The relative displacement column vector of the soil considering the restraining effect of in-service piles is calculated by the following formula: In the formula: Each of the following points ( Unit force This causes vertical and horizontal displacements of the soil at a given point (x, y, z). The distance between piles and tunnels. For the soil spring stiffness at the vertical pile tip, This represents the relative displacement of the soil at each node. The flexibility at each node of the pile foundation. The elastic modulus of the pile foundation. Let be the cross-sectional area of ​​the pile. Let be the pile length, and the pile be divided into n units, where i is the pile section number (i = 1 to n+1), j is the unit number (j = 1 to n), and the unit length is... , , , any point ( Unit force The expression for the soil displacement at a point (x, y, z) in the surrounding area is: In the formula, unit force This causes vertical displacement of the soil. unit force This causes horizontal displacement of the soil. Let z be the Young's modulus of the soil, and z be the vertical distance from the ground surface. Poisson's ratio of soil Determined by the following formula: In the formula, H represents the tunnel depth.

5. The method for calculating displacement of a pile-frame structure induced by tunnel excavation according to claim 1, characterized in that, In step S4, the soil displacement during tunnel excavation, considering the restraining effect of in-service piles and the correlation between soil stiffness and stress, includes both vertical and horizontal soil displacement. The calculation formula is as follows: In the formula, This represents the vertical displacement of the soil. This represents the horizontal displacement of the soil. The pile-soil interaction forces at each node. unit force This causes vertical displacement of the soil. unit force This causes horizontal displacement of the soil. The pile is divided into n units, where j is the unit number.

6. The method for calculating displacement of a pile-frame structure induced by tunnel excavation according to claim 1, characterized in that, In step S5, the control equation for pile foundation displacement is expressed as follows: In the formula, and These are the vertical and horizontal displacements of a single pile, respectively. and These are the vertical and horizontal displacements of the soil around the pile, respectively. and The parameters for the vertical nonlinear spring foundation beam and the horizontal nonlinear spring foundation beam are respectively: In the formula, These refer to the soil spring stiffness of horizontal piles and the soil spring stiffness of vertical piles, respectively. The elastic modulus of the pile foundation. For the moment of inertia, Let be the cross-sectional area of ​​the pile.

7. The method for calculating displacement of a pile-frame structure induced by tunnel excavation according to claim 1, characterized in that, In step S5, the pile foundation displacement control equations are applicable to both single piles and pile groups; the single pile displacement control matrix equation is expressed as: In the formula, and These are the vertical stiffness matrix and the horizontal stiffness matrix of the pile foundation, respectively. and These are the vertical load column vector and the horizontal load column vector, respectively. and These are the vertical and horizontal displacements of the pile nodes, respectively. and These are the vertical stiffness matrix and the horizontal stiffness matrix of the soil, respectively. and These represent the vertical and horizontal displacements of the soil at the pile joint, respectively. The displacement control matrix equation for a pile group is expressed as follows: In the formula, For displacement decay function, This is the displacement influence coefficient matrix between two adjacent piles.

8. The method for calculating displacement of a pile-frame structure induced by tunnel excavation according to claim 7, characterized in that, Displacement decay function Considering the curtain effect of pile groups, it can be expressed as: In the formula, Let be the pile radius, and s be the pile spacing. The values ​​are empirically determined based on soil heterogeneity; the displacement influence coefficient matrix between two adjacent piles. Represented as: Displacement influence coefficient between two adjacent piles Represented as: In the formula, This represents the displacement influence coefficient between node j of pile 1 and node i of pile 2. Let G be the vertical spring modulus of the soil at node j, G be the soil shear modulus, and h be the tunnel excavation depth. Poisson's ratio of soil and The distances from the ground surface to pile node i and pile node j are respectively, and x is the distance between the pile and the tunnel centerline. (Intermediate variables) .

9. The method for calculating displacement of a pile-frame structure induced by tunnel excavation according to claim 1, characterized in that, By coupling the pile-tunnel-soil interaction mechanical model with the superstructure, the deformation compatibility equations of the frame-pile-tunnel-soil are obtained: In the formula, Here is the vertical stiffness matrix of the soil. Here is the stiffness matrix of the superstructure frame. The stiffness matrix of the pile group is... This is the pile foundation displacement matrix. This represents the external force vector of the pile group caused by tunnel excavation. The deformation compatibility equations for the frame-pile-tunnel-soil structure can be expanded as follows: The subscript F indicates the connection node between the pile and the superstructure, and the subscript E indicates the pre-embedded pile node at the pile head. The displacement vector of the soil caused by tunnel excavation; the equivalent stiffness of the superstructure frame is calculated by the following formula: In the formula, The equivalent stiffness of the sunken area of ​​the upper frame structure. EI represents the equivalent stiffness of the protruding region of the superstructure frame, EI represents the bending stiffness of the superstructure frame, and EI represents the column stiffness coefficient. and Represented as: The average stiffness of the lower column. The average stiffness of the upper column is... Let be the average stiffness of the beam. This refers to the length of the sunken area in the upper frame structure. This refers to the length of the protruding area of ​​the upper frame structure. This refers to the span of the beam in the frame structure.

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