Calculation method of bearing capacity loss of frictional inclined pile caused by excavation of composite stratum with tunnel

Abstract

The application provides a tunnel composite stratum excavation induced frictional inclined pile bearing capacity loss calculation method, comprising obtaining tunnel parameters of a shield tunnel, structure parameters of an existing pile foundation and physical and mechanical parameters of a soil body; equivalent conversion of elastic modulus of a multilayer composite soil body into homogeneous single stratum elastic modulus, analysis of a soil body plastic zone and elastic zone range and boundary radius induced by tunnel excavation, establishment of a soil body arbitrary position radial stress and hoop stress distribution model; discrete treatment of an inclined pile along a pile length, discrimination of a stress region according to distances of pile body points to a tunnel center and calculation of corresponding soil body principal stresses, solving of pile soil contact surface normal stress changes through a pile shaft and stress principal direction angle conversion; calculation of pile body point side friction resistance changes according to normal stress changes, integral obtaining of total bearing capacity losses along the pile length and calculation of frictional pile foundation bearing capacity loss factors. The calculation method has high operability, simple calculation and wide application prospects.

Description

Technical Field

[0001] This invention belongs to the field of underground engineering technology, and in particular relates to a method for calculating the loss of bearing capacity of friction inclined piles caused by excavation of composite strata in tunnels. Background Technology

[0002] With the acceleration of urbanization and the increasing scale of underground space development, close proximity construction to tunnels is becoming more and more common. Tunnel excavation and unloading significantly alter the stress state of the surrounding soil, posing a potential threat to the stability of adjacent existing structures. Friction piles, due to their ability to effectively transfer horizontal loads using pile-soil skin friction, are widely used in projects requiring resistance to significant horizontal loads, such as slope protection, deep foundation pits, tall structures, and port terminals. Compared to vertical piles, they have significant advantages in controlling lateral displacement and improving overturning and sliding stability. However, the disturbance effect of tunnel excavation on adjacent friction piles is complex and severe. Excavation and unloading cause stress relaxation in the soil around the piles, potentially leading to a loss of skin friction, which in turn affects the bearing capacity of the piles and the safety of the superstructure.

[0003] Existing research on the disturbance impact of tunnel excavation on adjacent structures mainly focuses on the deformation prediction of linear structures such as buried pipelines. For example, Chinese patent CN118013802A proposes a pipeline deformation calculation method considering the interaction between the pipe and the soil. However, it relies on empirical input (Gaussian distribution) of the pipe-soil displacement, failing to fully reflect the physical mechanism of soil excavation stress release and deformation, and the theoretical model has limitations. Chinese patent CN110263448A establishes a prediction method for the relationship between relative settlement and stiffness of the pipe and soil based on empirical fitting. This method is mainly for tunnel underpass conditions and is difficult to apply to complex situations such as tunnel sidepasses and oblique passes. Furthermore, it lacks systematic analysis methods for vertical structures such as friction piles.

[0004] The main problems and gaps currently existing:

[0005] Research limitations: Existing research mainly focuses on pipelines, and there is a lack of research on the evolution of the bearing capacity of foundation components such as friction piles, which are extremely sensitive to lateral disturbances, under the influence of tunnel excavation.

[0006] Theoretical model is lacking: In particular, there is a lack of physical mechanism models that can accurately quantify the relationship between the change in stress state of the soil around the pile and the loss of bearing capacity of the inclined pile caused by tunnel construction (especially side-passing and oblique-passing conditions).

[0007] Insufficient analytical methods: There is a lack of systematic theories and methodologies to assess the complex stress response and bearing capacity loss of adjacent friction piles during tunnel construction. Existing engineering techniques are unreliable in predicting and assessing the bearing capacity loss of such pile foundations.

[0008] Therefore, there is an urgent need to develop a calculation method based on the stress change field model of the soil during tunnel excavation, which can accurately assess the relationship between the stress change of the soil around the pile and the loss of the pile's bearing capacity, so as to provide a scientific basis for engineering safety assessment and construction control. Summary of the Invention

[0009] To address the above technical problems, this invention discloses a method for calculating the bearing capacity loss of friction piles caused by excavation in composite strata of tunnels. This method can assess the construction safety of projects that pass through complex underground structures. The calculation method is highly operable and simple to calculate, and has broad application prospects.

[0010] The technical solution adopted by this invention is as follows:

[0011] The calculation method for the bearing capacity loss of friction piles caused by tunnel excavation in composite strata includes the following steps:

[0012] Step S1: Obtain the tunnel parameters of the shield tunnel, the structural parameters of the existing pile foundation, and the physical and mechanical parameters of the soil. The tunnel parameters of the shield tunnel include the initial radius a0 before tunnel excavation, the tunnel depth H, the volume loss rate η (the percentage of the cross-sectional area after tunnel excavation shrinkage to its original cross-sectional area), and the initial pore pressure p0. The structural parameters of the existing pile foundation include the pile diameter d, pile length L, pile angle θ, and horizontal distance D between the pile and the tunnel. h The physical and mechanical parameters of the soil include the soil elastic modulus E. j Poisson's ratio νj, cohesion C, and angle of internal friction (i.e., soil friction angle) and shear dilatation angle ψ;

[0013] Step S2, calculate the tunnel stress field: the elastic modulus of the multi-layer composite soil is equivalently transformed into the elastic modulus of a homogeneous single stratum. Based on the circular tunnel shrinkage theory and the Mohr-Coulomb elastoplastic model, the range of the plastic and elastic zones of the soil caused by tunnel excavation and the plastic boundary radius c are analyzed, and a model of radial and circumferential stress distribution at any position of the soil is established.

[0014] Step S3, stress analysis of friction inclined pile: Discretize the inclined pile along the pile length, calculate the spatial coordinates of each point of the pile and its distance to the center of the tunnel by combining the angle of the inclined pile, identify the stress area according to the distance and calculate the corresponding principal stress of the soil, and solve the change of normal stress at the pile-soil contact surface (i.e. change of normal stress of the pile body) by converting the angle between the pile axis and the principal stress direction.

[0015] Step S4, Friction Pile Bearing Capacity Loss Assessment: Calculate the change in side friction resistance at various points on the pile body based on the change in normal stress, and obtain the total bearing capacity loss by integrating along the pile length. Furthermore, the influence of the inclined pile angle, pile-tunnel distance, and tunnel depth can be evaluated through parametric analysis, outputting the friction pile foundation bearing capacity loss factor curve.

[0016] This technical solution, based on the circular tunnel shrinkage theory and considering the equivalent strength of composite strata, establishes a soil stress change field model during tunnel excavation. It then calculates the change in normal stress in the soil around the pile, derives the redistribution of frictional force along the pile, quantifies the change in the load transfer mechanism at the interface between the friction pile and the soil, and thus calculates and assesses the loss of pile foundation bearing capacity. Finally, it comprehensively evaluates the degree of bearing capacity loss of the friction inclined pile, providing a theoretical basis and engineering support for assessing structural safety during tunnel construction. This technical solution can solve the problem of insufficient accuracy in the analysis of the response of existing structures caused by tunnel excavation disturbance, particularly in predicting the impact of friction inclined pile bearing performance.

[0017] As a further improvement of the present invention, in step S2, the elastic modulus of the multi-layer composite soil is equivalently converted into the elastic modulus of a homogeneous single stratum using equation (1):

[0018]

[0019] In the formula: ē represents the equivalent homogeneous single-stratum elastic modulus; E j Let ν be the elastic modulus of the j-th soil layer; j Let ν be the Poisson's ratio of the j-th layer. n The last soil layer has the Poisson's ratio.

[0020] As a further improvement of the present invention, in step S2, the stress field calculation based on the circular tunnel shrinkage theory includes: assuming that the tunnel excavation is the radial shrinkage of a circular cavity in an infinite homogeneous isotropic medium, using the Mohr-Coulomb yield criterion to divide the elastic zone and the plastic zone, and calculating the hole wall stress, the radius of the plastic zone and the soil stress distribution through equilibrium differential equations and stress-strain relationships.

[0021] As a further improvement of the present invention, the calculation of the tunnel stress field in step S2 is based on the following governing equations:

[0022] Equilibrium differential equations:

[0023]

[0024] σ r | r＝∞ =-p0 (4),

[0025] σ r | r＝a =-p (5),

[0026] In the formula: r is the distance from any point in the polar coordinate system to the center of the tunnel; σ r σ θThe radial and circumferential stresses on the soil at this point are given, with tensile stress being positive and compressive stress being negative; p0 is the isotropic uniform initial pressure on the circular hole; a0 is the initial hole diameter before tunnel excavation; η is the given tunnel volume shrinkage ratio; a and p are the current hole radius and the pressure on the hole wall, respectively.

[0027] The stress in the elastic zone should satisfy:

[0028]

[0029] In the formula, A is an undetermined coefficient;

[0030] During the plastic stage, the soil follows the Mohr-Coulomb yield criterion:

[0031] ασ r -σ θ =Y (14),

[0032]

[0033] In the formula, C represents the soil cohesion. Let be the soil friction angle; α and γ are parameters, respectively.

[0034] During the plastic stage, the stress in the plastic zone should satisfy:

[0035]

[0036] In the formula, B is an undetermined coefficient;

[0037] The undetermined coefficients are calculated using the following formula:

[0038]

[0039] In the formula: c is the radius of the plastic zone of the soil;

[0040] According to the boundary conditions, the ratio of the plastic boundary radius c to the tunnel diameter a after excavation satisfies the following relationship:

[0041]

[0042] In the formula, p0 is the isotropic uniform initial pressure exerted on the circular hole;

[0043] The ratio of the radius c0 of the plastic boundary before deformation to the radius c of the plastic boundary satisfies the following relationship:

[0044]

[0045] In the formula, It is the equivalent homogeneous soil shear modulus;

[0046] The ratio of the initial borehole diameter a0 before tunnel excavation to the borehole diameter a after tunnel excavation satisfies the following relationship:

[0047]

[0048] The parameter D is calculated using the following formula:

[0049]

[0050] Substituting equation (32) into equation (31), we get:

[0051]

[0052] Where β is a function parameter of the shear expansion angle ψ, β=(1+sinψ) / (1-sinψ).

[0053] Finally, the relationship between the borehole wall pressure p and the borehole diameter a after tunnel excavation is as follows:

[0054]

[0055] As a further improvement of the present invention, in step S3, the calculation formula for discretizing the inclined pile along the pile length is as follows:

[0056]

[0057] In the formula, L is the pile length, m is the number of discrete elements, and s k This is the discrete point of the k-th inclined pile;

[0058] Spatial coordinates (x) of discrete points on the pile k ,z k Calculate using the following formula:

[0059]

[0060] In the formula, D h θ is the horizontal distance between the top of the pile and the tunnel axis, and θ is the angle of the inclined pile.

[0061] The distance r from each point on the pile to the center of the tunnel k Calculated using the following formula:

[0062]

[0063] In the formula, H is the tunnel burial depth;

[0064] The principal stress of soil is calculated using the following formula:

[0065]

[0066] The geostress mapping relationship is as follows:

[0067]

[0068] In the formula, p k σ represents the radial pressure at point k on the pile. v0,k and σ v,k These represent the in-situ stresses at discrete point k of the pile body before and after excavation;

[0069] The normal stress at the pile-soil contact surface, i.e., the pile stress, is calculated using the following formula:

[0070] σ n,j =σ v,j sin 2 θ+K0σ v,j cos 2 θ (39),

[0071] In the formula, K0 is the horizontal earth pressure coefficient, obtained through... Seeking, The angle of friction of the soil.

[0072] As a further improvement of the present invention, in step S4, the side friction τ at point k of the pile body s Calculated using the following formula:

[0073] τ s,k =μσ n,k (40),

[0074] The total bearing capacity loss Q is obtained by integrating along the pile length. s Calculated using the following formula:

[0075]

[0076] In the formula, μ is the friction coefficient of the pile-soil interface, and d is the pile diameter.

[0077] Loss of bearing capacity R Q It can be calculated using the following formula:

[0078]

[0079] In the formula: R Q Q is the bearing capacity loss factor of friction pile foundation. s0 This represents the initial load-bearing capacity.

[0080] This invention discloses a calculation system for the bearing capacity loss of frictional inclined piles caused by excavation in composite strata of tunnels, comprising:

[0081] The parameter acquisition module is used to acquire tunnel parameters of the shield tunnel, structural parameters of the existing pile foundation, and physical and mechanical parameters of the soil. The tunnel parameters include the initial radius a0 before excavation, tunnel depth H, volume loss rate η, and initial pore pressure p0. The structural parameters of the existing pile foundation include the pile diameter d, pile length L, pile angle θ, and horizontal distance D between the pile and the tunnel. h The physical and mechanical parameters of the soil include the soil elastic modulus E. j Poisson's ratio j Cohesion C, Angle of Internal Friction Shear expansion angle ψ;

[0082] The tunnel stress field calculation module is used to convert the elastic modulus of multi-layer composite soil into the elastic modulus of homogeneous single stratum. Based on the circular tunnel shrinkage theory and the Mohr-Coulomb elastoplastic model, it analyzes the range of the plastic and elastic zones of the soil caused by tunnel excavation and the plastic boundary radius c, and establishes a model of radial and circumferential stress distribution at any position of the soil.

[0083] The friction inclined pile stress analysis module is used to discretize the inclined pile along the pile length, calculate the spatial coordinates of each point on the pile and its distance to the tunnel center by combining the inclined pile angle, identify the stress area based on the distance and calculate the corresponding principal stress of the soil, and solve the normal stress change of the pile-soil contact surface by converting the angle between the pile axis and the principal stress direction.

[0084] The friction pile bearing capacity loss assessment module is used to calculate the change in side friction resistance at various points on the pile body based on the change in normal stress, and to obtain the total bearing capacity loss by integrating along the pile length. Furthermore, the influence of the pile angle, pile-tunnel distance, and tunnel depth can be evaluated through parametric analysis, outputting the friction pile foundation bearing capacity loss factor curve.

[0085] As a further improvement of the present invention, the tunnel stress field calculation module uses equation (1) to convert the elastic modulus of multi-layer composite soil into the elastic modulus of homogeneous single stratum in the calculation:

[0086]

[0087] In the formula: ē represents the equivalent homogeneous single-stratum elastic modulus; E j Let ν be the elastic modulus of the j-th soil layer; j Let ν be the Poisson's ratio of the j-th layer. n The last soil layer has the Poisson's ratio.

[0088] As a further improvement of the present invention, the stress field calculation module for tunnels includes the following steps in performing stress field calculations based on the theory of circular tunnel shrinkage: assuming that the tunnel excavation is the radial shrinkage of a circular cavity in an infinite homogeneous isotropic medium, the Mohr-Coulomb yield criterion is used to divide the elastic zone and the plastic zone, and the stress on the borehole wall, the radius of the plastic zone, and the stress distribution in the soil are calculated through equilibrium differential equations and stress-strain relationships.

[0089] As a further improvement of the present invention, the calculation of the tunnel stress field is based on the following governing equations:

[0090] Equilibrium differential equations:

[0091]

[0092] σ r | r＝∞ =-p0 (4),

[0093] σ r | r＝a =-p (5),

[0094] In the formula: r is the distance from any point in the polar coordinate system to the center of the tunnel; σ r σ θ The radial and circumferential stresses on the soil at this point are given, with tensile stress being positive and compressive stress being negative; p0 is the isotropic uniform initial pressure on the circular hole; a0 is the initial hole diameter before tunnel excavation; η is the given tunnel volume shrinkage ratio; a and p are the current hole radius and the pressure on the hole wall, respectively.

[0095] The stress in the elastic zone should satisfy:

[0096]

[0097] In the formula, A is an undetermined coefficient;

[0098] During the plastic stage, the soil follows the Mohr-Coulomb yield criterion:

[0099] ασ r -σ θ =Y (14),

[0100]

[0101] In the formula, C represents the soil cohesion. Let be the soil friction angle; α and γ are parameters, respectively.

[0102] During the plastic stage, the stress in the plastic zone should satisfy:

[0103]

[0104] In the formula, B is an undetermined coefficient;

[0105] The undetermined coefficients are calculated using the following formula:

[0106]

[0107] In the formula: c is the radius of the plastic zone of the soil;

[0108] According to the boundary conditions, the ratio of the plastic boundary radius c to the tunnel diameter a after excavation satisfies the following relationship:

[0109]

[0110] In the formula: p0 is the isotropic uniform initial pressure exerted on the circular hole;

[0111] The ratio of the radius c0 of the plastic boundary before deformation to the radius c of the plastic boundary satisfies the following relationship:

[0112]

[0113] In the formula: It is the equivalent homogeneous soil shear modulus;

[0114] The ratio of the initial borehole diameter a0 before tunnel excavation to the borehole diameter a after tunnel excavation satisfies the following relationship:

[0115]

[0116] The parameter D is calculated using the following formula:

[0117]

[0118] β is a function parameter of the shear expansion angle ψ, β=(1+sinψ)(1-sinψ);

[0119] Finally, the relationship between the borehole wall pressure p and the borehole diameter a after tunnel excavation is as follows:

[0120]

[0121] As a further improvement of the present invention, in the stress analysis module for friction inclined piles, the calculation formula for discretization of the inclined pile along the pile length is as follows:

[0122]

[0123] In the formula, L is the pile length, m is the number of discrete elements, and s k This is the discrete point of the k-th inclined pile;

[0124] Spatial coordinates (x) of discrete points on the pile k ,z k Calculate using the following formula:

[0125]

[0126] In the formula, D h θ is the horizontal distance between the top of the pile and the tunnel axis, and θ is the angle of the inclined pile.

[0127] The distance r from each point on the pile to the center of the tunnel k Calculated using the following formula:

[0128]

[0129] In the formula, H is the tunnel burial depth;

[0130] The principal stress of soil is calculated using the following formula:

[0131]

[0132] The geostress mapping relationship is as follows:

[0133]

[0134] In the formula, p k σ represents the radial pressure at point k on the pile. v0,k and σ v,k These represent the in-situ stresses at discrete point k of the pile body before and after excavation;

[0135] The normal stress at the pile-soil contact surface is calculated using the following formula:

[0136] σ n,k =σ v,k sin 2 θ+K0σ v,k cos 2 θ (39),

[0137] In the formula, K0 is the horizontal earth pressure coefficient, obtained through... Seeking, The angle of friction of the soil.

[0138] As a further improvement of the present invention, in the frictional inclined pile bearing capacity loss assessment module, the side friction resistance τ at point k of the pile body is... s Calculated using the following formula:

[0139] τ s,k =μσ n,k (40),

[0140] The total bearing capacity Q is obtained by integrating along the pile length. s :

[0141]

[0142] In the formula, μ is the friction coefficient of the pile-soil interface, and d is the pile diameter;

[0143] The loss of load-bearing capacity is assessed using the following formula:

[0144]

[0145] In the formula: R Q Q is the bearing capacity loss factor of friction pile foundation. s0 This represents the initial load-bearing capacity.

[0146] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0147] First, unlike existing technologies that mostly use empirical formulas or assumed distributions, the technical solution of this invention treats the composite strata as a homogeneous medium and simulates the stress release process caused by tunnel excavation through a circular tunnel shrinkage model. By fully combining the soil mechanics mechanism, it can more accurately predict the stress redistribution behavior caused by tunnel disturbance and improve the reliability of structural response assessment.

[0148] Secondly, this invention considers the spatial distribution characteristics of friction inclined piles and establishes an analytical calculation model for the interaction forces between them and the soil. By discretizing the pile body and identifying stress regions, it can reveal in detail the variation law of normal stress and side friction at different depths of the pile body, thereby reflecting the evolution process of pile-soil coupling behavior under tunnel disturbance more comprehensively and deeply, and realizing a refined expression of the spatial stress response of friction inclined piles.

[0149] Third, the technical solution of this invention, combining the relative position of the pile and tunnel, the angle of the inclined pile, and soil parameters, provides a methodological system for quantifying bearing capacity loss. It can output the pile side friction attenuation curve, providing a scientific basis for tunnel construction risk prediction and the formulation of protection measures for adjacent buildings. This solves the problem that existing methods mostly focus on vertical structures or buried pipelines, lacking sufficient research on the response analysis of friction inclined piles and specific assessment methods.

[0150] Fourth, the technical solution of this invention is based on readily available conventional geological and structural parameters, with a clear calculation process and well-defined steps. It is applicable to different geological conditions and inclined pile layout scenarios, possessing good operability and engineering applicability. Through advance calculation and analysis, it can effectively guide the design optimization and construction sequence adjustment of pile foundation engineering, reduce the risk of structural damage, and ensure project safety. Attached Figure Description

[0151] Figure 1 This is a flowchart of the calculation method according to an embodiment of the present invention.

[0152] Figure 2 This is a schematic diagram of a tunnel excavation shrinkage model according to an embodiment of the present invention.

[0153] Figure 3This is a schematic diagram of the geometric positions of the tunnel and piles in an embodiment of the present invention.

[0154] Figure 4 This is an analysis diagram of the initial ground stress distribution and structural location in an embodiment of the present invention.

[0155] Figure 5 This is an analysis diagram of the stress distribution and plastic zone range after shrinkage according to an embodiment of the present invention.

[0156] Figure 6 This is a distribution diagram of the pile periphery friction along the pile length direction according to an embodiment of the present invention. Detailed Implementation

[0157] The preferred embodiments of the present invention will be described in further detail below.

[0158] A method for calculating the bearing capacity loss of friction pile foundations caused by tunnel excavation, such as... Figure 1 As shown, it includes:

[0159] (1) Parameter acquisition: Acquire tunnel parameters such as initial radius, burial depth, volume loss rate and initial pore pressure of tunnel excavation, structural parameters such as pile diameter, pile length, pile angle and horizontal distance between pile and tunnel of friction inclined pile, as well as physical and mechanical parameters such as soil elastic modulus, Poisson's ratio, cohesion, internal friction angle and shear dilatation angle.

[0160] (2) Tunnel stress field calculation: The elastic modulus of multi-layer composite soil is equivalently transformed into a single homogeneous soil. Based on the circular tunnel shrinkage theory and the Mohr-Coulomb elastoplastic model, the range of the plastic zone and elastic zone of the soil caused by tunnel excavation and its boundary radius are determined by analytical method, and a stress state distribution model at any location of the soil is established.

[0161] (3) Stress analysis of friction inclined pile: Discretize the inclined pile along the pile length, calculate the spatial coordinates of each discrete point and its distance to the center of the tunnel in combination with the angle of the inclined pile, identify the stress area according to the distance and calculate the corresponding principal stress of the soil, and solve the change of normal stress on the pile-soil contact surface by converting the angle between the pile axis and the principal stress direction.

[0162] (4) Assessment of bearing capacity loss of friction inclined piles: The change of side friction resistance at each point of the pile body is calculated based on the change of normal stress, and the total bearing capacity loss is obtained by summing along the pile length. Furthermore, the influence of different inclined pile angles, pile-tunnel distances and tunnel depths is evaluated through parametric analysis, and bearing capacity loss curves under different working conditions can be output to guide the safety assessment of tunnel construction.

[0163] Since analytical methods can typically only calculate stress changes caused by tunnel excavation in a single homogeneous stratum, the elastic modulus of multi-layered elastic soil can be converted into the elastic modulus of a single homogeneous stratum using the following formula:

[0164]

[0165] In the formula: ē is the equivalent elastic modulus of homogeneous soil; E j Let ν be the elastic modulus of the j-th soil layer; j Let be the Poisson's ratio of the j-th layer of soil.

[0166] In theoretical analysis, tunnel excavation can be simplified as a mechanical problem involving the radial contraction of a circular cavity in an infinitely homogeneous isotropic medium. This model treats the strata as a continuous medium, initially in an in-situ stress state. As the tunnel is gradually excavated, it is equivalent to setting up a circular hole with an initial radius of 0 within this medium, with the pressure on the hole wall gradually decreasing to a target value, thus simulating the stress release process caused by excavation.

[0167] During this process, the soil surrounding the borehole wall will undergo stress redistribution and displacement response. Based on the constitutive properties of the soil, elastoplastic theory is used for analysis, and the Mohr-Coulomb yield criterion is selected to divide the elastic and plastic zones. Key mechanical indicators such as borehole wall stress, plastic zone radius, and soil stress distribution are further calculated.

[0168] Typically, when analyzing the shrinkage problem of circular tunnels, it is assumed that the soil is in a plane strain state, such as... Figure 2 As shown. Accordingly, the stress field satisfies the following equilibrium differential equation:

[0169]

[0170]

[0171] σ r | r＝∞ =-p0 (4)

[0172] σ r | r＝a =-p (5)

[0173] In the formula: r is the distance from any point in the polar coordinate system to the center of the tunnel; σ r , σ θ η represents the radial and circumferential stresses on the soil at that point, with tensile stress being positive and compressive stress being negative; p0 represents the isotropic uniform initial pressure on the circular hole; a0 represents the initial hole diameter before tunnel excavation; η represents the given tunnel volume shrinkage ratio; a and p represent the current circular hole radius and the pressure on the hole wall, respectively.

[0174] During tunnel excavation, the pressure on the tunnel borehole wall gradually decreases. In the initial stage, the soil surrounding the tunnel has not yet reached a yield state and is in an elastic deformation stage. In an axisymmetric cylindrical coordinate system, the stress-strain relationship and displacement response of the soil in this stage can be described using elastic theory, and their variation forms are shown below:

[0175]

[0176] Substituting equations (8) and (9) into equation (6), we obtain the expression for the radial displacement u of the soil:

[0177]

[0178] In the formula: It is the equivalent homogeneous soil shear modulus.

[0179] In the elastic stage, the radial displacement of the soil is u = a - a0. Substituting r = a into equation (10), the relationship between the pore pressure p and the orifice radius a can be derived:

[0180]

[0181] From the equilibrium equation (1) and the elastic stress-strain relations (8) and (9), the stress in the elastic region should satisfy the following:

[0182]

[0183]

[0184] In the formula: A is an undetermined coefficient.

[0185] During the plastic stage, the soil follows the Mohr-Coulomb yield criterion:

[0186] ασ r -σ θ =Y (14)

[0187]

[0188] In the formula: C is the soil cohesion; The angle of friction of the soil.

[0189] When the pore pressure p is less than the critical yield pore pressure p 1y Yielding first occurs at the wall of the cylindrical hole. Substituting r = a, equations (8) and (9) into (14), the critical yield pore pressure p is obtained. 1y for:

[0190]

[0191] During the plastic stage, the stress in the plastic zone should satisfy the following conditions, obtained from the equilibrium equation (1) and the yield condition equation (14):

[0192]

[0193] In the formula: B is an undetermined coefficient.

[0194] Since the stress components at the elastoplastic boundary should remain continuous, combining equations (12), (13), (18), and (19), substituting r = c, we can obtain the undetermined coefficients A and B as follows:

[0195]

[0196] In the formula: c is the radius of the plastic zone of the soil.

[0197] Combining equations (5), (18), and (21), and substituting r = c, the relationship between the hole wall pressure p and the plastic boundary radius c can be obtained:

[0198]

[0199] Combining equations (10), (12), and (20), the displacement of the elastic zone can be obtained:

[0200]

[0201] At the elastoplastic interface (r = c), the radial displacement of the soil is:

[0202]

[0203] The ratio of the radius c0 of the plastic boundary before deformation to the radius c of the plastic boundary satisfies the following relationship:

[0204]

[0205] in, It is the equivalent homogeneous soil shear modulus;

[0206] For the circular tunnel contraction problem, to simplify the solution, the effect of elastic strain in the plastic deformation zone can be neglected. The uncorrelated Mohr-Coulomb flow criterion is as follows:

[0207]

[0208] β is a function parameter of the shear expansion angle ψ, β=(1+sinψ)(1-sinψ);

[0209] During the contraction of a circular tunnel, the near-field soil will undergo significant deformation. Therefore, logarithmic strain is required. The logarithmic strain along the normal, radial, and longitudinal directions is defined as follows:

[0210]

[0211] Substituting into the flow criterion (26), we can obtain:

[0212]

[0213] Integrating equation (29) from the initial state (c0 to r0) to the current state (c to r), we obtain:

[0214]

[0215] At the hole wall, r = a, and the initial radius is a0. Substituting into equation (28), we find that a0 and a satisfy the following relationship:

[0216]

[0217] Substituting equation (32) into equation (31), we obtain the following formula:

[0218]

[0219] Finally, the relationship between the borehole wall pressure p and the borehole diameter a after tunnel excavation was obtained:

[0220]

[0221] like Figure 3 As shown, the discretization of the pile body can be expressed by the following formula:

[0222]

[0223] In the formula: L is the pile length; m is the number of discrete elements, s k This is the discrete point of the k-th inclined pile;

[0224] Spatial coordinates (x) of discrete points on the pile k ,z k Calculate using the following formula:

[0225]

[0226] In the formula, D h θ is the horizontal distance between the top of the pile and the tunnel axis, and θ is the angle of the inclined pile.

[0227] The distance r from each point on the pile to the center of the tunnel k Calculated using the following formula:

[0228]

[0229] In the formula, H is the tunnel burial depth;

[0230] The principal stress of soil is calculated using the following formula:

[0231]

[0232] The geostress mapping relationship is as follows:

[0233]

[0234] In the formula, pk σ represents the radial pressure at point k on the pile. v0,k and σ v,k These represent the in-situ stresses at discrete point k of the pile body before and after excavation;

[0235] The normal stress at the pile-soil contact surface is calculated using the following formula:

[0236] σ n,k =σ v,k sin 2 θ+K0σ v,k cos 2 θ (39),

[0237] In the formula, K0 is the horizontal earth pressure coefficient, obtained through... Seeking, The angle of friction of the soil.

[0238] In step S4, the side friction τ at point k of the pile body s Calculated using the following formula:

[0239] τ s,k =μσ n,k (40),

[0240] The total bearing capacity Q is obtained by integrating along the pile length. s :

[0241]

[0242] In the formula: μ is the friction coefficient of the pile-soil interface; d is the pile diameter.

[0243] In summary, the loss of bearing capacity can be assessed using the following formula:

[0244]

[0245] In the formula: R Q Q is the bearing capacity loss factor of friction pile foundation. s0 This represents the initial load-bearing capacity.

[0246] This invention also discloses a computing system employing the above-described calculation method.

[0247] The following description uses specific examples to illustrate the point.

[0248] like Figure 1 As shown, a method for calculating the bearing capacity loss of friction piles caused by excavation in composite strata of tunnels includes the following steps:

[0249] Determine the analytical calculation parameters for the new subway shield tunnel, existing pile foundations, and soil.

[0250] like Figure 4As shown, the physical and mechanical parameters of a shield tunnel crossing an adjacent pile foundation in a certain project are as follows:

[0251] a) Tunnel parameters for newly constructed shield tunnels:

[0252] Excavation radius a0: 3.2m, tunnel depth H: 20m, volume loss rate η: 5%;

[0253] The initial pore pressure p0 is taken as the vertical earth pressure at the depth of the tunnel axis, which is obtained by multiplying the weight of the soil above the tunnel axis by the corresponding soil height.

[0254] b) Structural parameters of existing pile foundations:

[0255] Pile diameter d: 0.5m, pile length L: 25m, inclined pile angle θ: 15°, horizontal distance between pile and tunnel D h : 4m;

[0256] c) Soil physical parameters: See Table 1 for details of the main physical information.

[0257] Table 1 Formation mechanical properties parameters

[0258] Stratigraphic type Formation thickness / m <![CDATA[重度 / (kN / m 3 )]]> Elastic modulus / MPa Poisson's ratio Cohesion / kPa Friction angle / ° Silty clay 8 18.13 22 0.33 22.8 16.5 gravelly clay soil 10 18.52 35.8 0.3 20.4 24.3 Completely weathered granite 15 18.62 45 0.28 21.5 25.6

[0259] Perform the calculation according to the above calculation method. Figure 4 This indicates the initial ground stress distribution before excavation. Figure 5 The diagram shows the distribution of ground stress after excavation, indicating that tunnel excavation significantly altered the distribution of ground stress in the surrounding soil. Figure 6 This is the curve showing the change in pile skin friction along the pile length. Calculations show that the total skin friction of the friction pile changes from 35513 kN to 30693 kN, and the bearing capacity loss factor R... Q It is 13.57%.

[0260] This embodiment considers the equivalent strength of composite strata and uses a circular tunnel shrinkage model to simulate the stress release process during tunnel excavation. The stress changes in the soil caused by tunnel excavation are calculated based on the Mohr-Coulomb yield criterion. Based on the spatial location of the inclined piles, the method expresses the change in the interaction force between the friction piles and the soil, and then calculates the loss of the frictional resistance of the pile sides. This method is simple and practical, and can provide theoretical reference for engineering projects in advance, assessing the impact of adjacent friction pile foundation structures during tunnel excavation.

[0261] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the bearing capacity loss of friction piles caused by excavation in composite strata of tunnels, characterized in that, Includes the following steps: Step S1: Obtain the tunnel parameters of the shield tunnel, the structural parameters of the existing pile foundation, and the physical and mechanical parameters of the soil. The tunnel parameters of the shield tunnel include the initial radius a0 before tunnel excavation, the tunnel depth H, the tunnel volume shrinkage ratio η, and the initial pore pressure. The structural parameters of the existing pile foundation include the pile diameter d, pile length L, pile angle θ, and pile-tunnel horizontal distance D of the friction piles. h The physical and mechanical parameters of the soil include the soil elastic modulus E. j Poisson's ratio j Cohesion C, internal friction angle φ, shear dilatation angle ψ; Step S2, calculate the tunnel stress field: the elastic modulus of the multi-layer composite soil is equivalently transformed into the elastic modulus of a homogeneous single stratum. Based on the circular tunnel shrinkage theory and the Mohr-Coulomb elastoplastic model, the range of the plastic and elastic zones of the soil caused by tunnel excavation and the plastic boundary radius c are analyzed, and a model of radial and circumferential stress distribution at any position of the soil is established. Step S3, stress analysis of friction inclined pile: Discretize the inclined pile along the pile length, calculate the spatial coordinates of each point of the pile body and its distance to the center of the tunnel by combining the inclined pile angle, identify the stress area according to the distance and calculate the corresponding principal stress of the soil, and solve the change of normal stress on the pile-soil contact surface by converting the angle between the pile axis and the principal stress direction. Step S4, Assessment of bearing capacity loss of friction inclined pile: Calculate the change of side friction resistance at each point of the pile body based on the change of normal stress, and integrate along the pile length to obtain the total bearing capacity loss; In step S2, the elastic modulus of the multi-layered composite soil is equivalently transformed into the elastic modulus of a homogeneous single stratum using equation (1): (1), In the formula: Ē is the equivalent homogeneous single-stratum elastic modulus; E j Let ν be the elastic modulus of the j-th soil layer; j Let ν be the Poisson's ratio of the j-th layer. n The Poisson's ratio of the last soil layer; In step S2, the stress field calculation based on the circular tunnel shrinkage theory includes: assuming that the tunnel excavation is the radial shrinkage of a circular cavity in an infinite homogeneous isotropic medium, the Mohr-Coulomb yield criterion is used to determine the elastic zone and the plastic zone, and the hole wall stress, plastic boundary radius and soil stress distribution are calculated through equilibrium differential equations and stress-strain relationships. The calculation of the tunnel stress field in step S2 is based on the following governing equations: Equilibrium differential equations: (2), (3), (4), (5), In the formula: r is the distance from any point in the polar coordinate system to the center of the tunnel; σ r σ θ Let p0 be the radial and circumferential stresses on the soil at that point, with tensile stress being positive and compressive stress being negative; p0 be the isotropic uniform initial pressure on the circular hole; a0 be the initial radius before tunnel excavation; η be the given tunnel volume shrinkage ratio; and a and p be the radius of the circular hole and the pressure on the hole wall in the current state, respectively. The stress in the elastic zone should satisfy: (12), (13), In the formula, A is an undetermined coefficient; During the plastic stage, the soil follows the Mohr-Coulomb yield criterion: (14), (15), (16), In the formula, C is the soil cohesion, φ is the soil internal friction angle; α and Y are parameters. During the plastic stage, the stress in the plastic zone should satisfy: (18), (19), In the formula, B is an undetermined coefficient; The undetermined coefficients are calculated using the following formula: (20), (21), In the formula: c is the radius of the plastic boundary of the soil; According to the boundary conditions, the ratio of the plastic boundary radius c to the radius a after tunnel excavation satisfies the following relationship: (22), In the formula: p0 is the isotropic uniform initial pressure exerted on the circular hole; The ratio of the radius c0 of the plastic boundary before deformation to the radius c of the plastic boundary satisfies the following relationship: (25), In the formula: Ḡ is the equivalent homogeneous soil shear modulus; The ratio of the initial radius a0 before tunnel excavation to the radius a after tunnel excavation satisfies the following relationship: ； The parameter D is calculated using the following formula: ， β is a function parameter of the dilatation angle ψ. ; Finally, the relationship between the borehole wall pressure p and the radius a after tunnel excavation is as follows: (33)； In step S3, the calculation formula for discretizing the inclined pile along its length is: （34）， In the formula, L is the pile length, m is the number of discrete elements, and s k This is the discrete point of the k-th inclined pile; Spatial coordinates (x) of discrete points on the pile k , z k Calculate using the following formula: (35), In the formula, D h θ is the horizontal distance between the top of the pile and the tunnel axis, and θ is the angle of the inclined pile. The distance r from each point on the pile to the center of the tunnel k Calculated using the following formula: (36), In the formula, H is the tunnel burial depth; The principal stress of soil is calculated using the following formula: (37), The geostress mapping relationship is as follows: (38), In the formula, p k σ represents the radial pressure at point k on the pile. v0,k and σ v,k These represent the in-situ stresses at discrete point k of the pile body before and after excavation; The normal stress at the pile-soil contact surface is calculated using the following formula: (39), In the formula, K0 is the horizontal earth pressure coefficient, which is obtained by 1-sinφ, and φ is the internal friction angle of the soil.

2. The method for calculating the bearing capacity loss of friction piles caused by tunnel composite stratum excavation according to claim 1, characterized in that: In step S4, the side friction τ at point k of the pile body s,k Calculated using the following formula: (40), The total bearing capacity Q is obtained by integrating along the pile length. s : (41), In the formula, μ is the friction coefficient of the pile-soil interface, and d is the pile diameter; The loss of load-bearing capacity is assessed using the following formula: (42), In the formula: R Q Q is the bearing capacity loss factor of friction pile foundation. s0 This represents the initial load-bearing capacity.

3. A calculation system for the bearing capacity loss of friction piles caused by excavation in composite strata of tunnels, characterized in that, include: The parameter acquisition module is used to acquire tunnel parameters of the shield tunnel, structural parameters of existing pile foundations, and physical and mechanical parameters of the soil. The tunnel parameters of the shield tunnel include the initial radius a0 before excavation, the tunnel depth H, the tunnel volume shrinkage ratio η, and the initial pore pressure p0; the structural parameters of the existing pile foundation include the pile diameter d, pile length L, pile angle θ, and pile-tunnel horizontal distance D of the friction inclined pile. h The physical and mechanical parameters of the soil include the soil elastic modulus E. j Poisson's ratio j Cohesion C, internal friction angle φ, shear dilatation angle ψ; The tunnel stress field calculation module is used to convert the elastic modulus of multi-layer composite soil into the elastic modulus of homogeneous single stratum. Based on the circular tunnel shrinkage theory and the Mohr-Coulomb elastoplastic model, it analyzes the range of the plastic and elastic zones of the soil caused by tunnel excavation and the plastic boundary radius c, and establishes a model of radial and circumferential stress distribution at any position of the soil. The friction inclined pile stress analysis module is used to discretize the inclined pile along the pile length, calculate the spatial coordinates of each point on the pile and its distance to the tunnel center by combining the inclined pile angle, identify the stress area based on the distance and calculate the corresponding principal stress of the soil, and solve the normal stress change of the pile-soil contact surface by converting the angle between the pile axis and the principal stress direction. The friction inclined pile bearing capacity loss assessment module is used to calculate the change of side friction resistance at each point of the pile body based on the change of normal stress, and to obtain the total bearing capacity loss by integrating along the pile length. In the calculation of the tunnel stress field, the elastic modulus of the multi-layer composite soil is equivalently transformed into the elastic modulus of a homogeneous single stratum using equation (1): (1), In the formula: Ē is the equivalent homogeneous single-stratum elastic modulus; E j Let ν be the elastic modulus of the j-th soil layer; j Let ν be the Poisson's ratio of the j-th layer. n The Poisson's ratio of the last soil layer; In the tunnel stress field calculation module, the stress field calculation based on the circular tunnel shrinkage theory includes: assuming that the tunnel excavation is the radial shrinkage of a circular cavity in an infinite homogeneous isotropic medium, using the Mohr-Coulomb yield criterion to divide the elastic zone and the plastic zone, and calculating the hole wall stress, plastic boundary radius and soil stress distribution through equilibrium differential equations and stress-strain relationships. The calculation of the tunnel stress field is based on the following governing equations: Equilibrium differential equations: (2), (3), (4), (5), In the formula: r is the distance from any point in the polar coordinate system to the center of the tunnel; σ r σ θ Let p0 be the radial and circumferential stresses on the soil at that point, with tensile stress being positive and compressive stress being negative; p0 be the isotropic uniform initial pressure on the circular hole; a0 be the initial radius before tunnel excavation; η be the given tunnel volume shrinkage ratio; and a and p be the radius of the circular hole and the pressure on the hole wall in the current state, respectively. The stress in the elastic zone should satisfy: (12), (13), In the formula, A is an undetermined coefficient; During the plastic stage, the soil follows the Mohr-Coulomb yield criterion: (14), (15), (16), In the formula, C is the soil cohesion, φ is the soil internal friction angle; α and Y are parameters. During the plastic stage, the stress in the plastic zone should satisfy: (18), (19), In the formula, B is an undetermined coefficient; The undetermined coefficients are calculated using the following formula: (20), (21), In the formula: c is the radius of the plastic boundary of the soil; According to the boundary conditions, the ratio of the plastic boundary radius c to the radius a after tunnel excavation satisfies the following relationship: (22), In the formula: p0 is the isotropic uniform initial pressure exerted on the circular hole; The ratio of the radius c0 of the plastic boundary before deformation to the radius c of the plastic boundary satisfies the following relationship: (25), In the formula: Ḡ is the equivalent homogeneous soil shear modulus; The ratio of the initial radius a0 before tunnel excavation to the radius a after tunnel excavation satisfies the following relationship: ； The parameter D is calculated using the following formula: ， β is a function parameter of the dilatation angle ψ. ; Finally, the relationship between the borehole wall pressure p and the radius a after tunnel excavation is as follows: (33)； In the stress analysis module for friction inclined piles, the calculation formula for discretizing the inclined pile along its length is as follows: （34）， In the formula, L is the pile length, m is the number of discrete elements, and s k This is the discrete point of the k-th inclined pile; Spatial coordinates (x) of discrete points on the pile k , z k Calculate using the following formula: (35), In the formula, D h θ is the horizontal distance between the top of the pile and the tunnel axis, and θ is the angle of the inclined pile. The distance r from each point on the pile to the center of the tunnel k Calculated using the following formula: (36), In the formula, H is the tunnel burial depth; The principal stress of soil is calculated using the following formula: (37), The geostress mapping relationship is as follows: (38), In the formula, p k σ represents the radial pressure at point k on the pile. v0,k and σ v,k These represent the in-situ stresses at discrete point k of the pile body before and after excavation; The normal stress at the pile-soil contact surface is calculated using the following formula: (39), In the formula, K0 is the horizontal earth pressure coefficient, which is obtained by 1-sinφ, and φ is the internal friction angle of the soil.

4. The calculation system for the bearing capacity loss of friction piles caused by tunnel composite stratum excavation according to claim 3, characterized in that: In the friction pile bearing capacity loss assessment module, the side friction τ at point k of the pile body is... s,k Calculated using the following formula: (40), The total bearing capacity Q is obtained by integrating along the pile length. s : (41), In the formula, μ is the friction coefficient of the pile-soil interface, and d is the pile diameter; The loss of load-bearing capacity is assessed using the following formula: (42), In the formula: R Q Q is the bearing capacity loss factor of friction pile foundation. s0 This represents the initial load-bearing capacity.

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