Buffer layer-based deformation calculation method for high-rise building overpass existing tunnel

Abstract

This invention relates to the field of deformation calculation of existing tunnels spanning high-rise buildings, and discloses a method for calculating the deformation of existing tunnels spanning high-rise buildings based on a buffer layer, comprising the following steps: Step 1, establishing a soil-raft interaction model; Step 2, approximating the raft deflection as the buffer layer compression to obtain the vertical displacement w of the soil caused by the raft. se Based on w se The vertical displacement w of the soil at any point at the bottom of the buffer layer was calculated. s1 Step 3: Assume the initial value w of the vertical displacement of the pile foundation. p Calculate the relative displacement w between the pile and the soil. r According to w p and w r Calculate the vertical displacement w at any point around the pile. s2 Step 4: Iterative calculations are performed based on the soil-raft interaction model to obtain the vertical additional load at the existing tunnel caused by the self-weight load of the superstructure. This is used to analyze and evaluate the settlement, convergence, inter-ring deformation, and structural stress response of the tunnel under the superstructure load.

Description

Technical Field

[0001] This invention relates to the field of deformation calculation of high-rise buildings crossing existing tunnels, and specifically to a method for calculating the deformation of high-rise buildings crossing existing tunnels based on a buffer layer. Background Technology

[0002] When developing high-rise buildings or underground spaces above existing operational subway shield tunnels, conventional raft foundations or pile-raft foundations are typically used as the load-bearing and force-transfer system for the superstructure. Conventional raft foundations generally involve the basement floor slab or raft directly acting on the underlying soil, with the superstructure load diffused through the bottom of the raft onto the soil below. When the existing subway tunnel is within the range of this additional stress, the tunnel arch and surrounding soil will bear significant additional vertical stress, leading to adverse responses such as longitudinal settlement, lateral convergence, inter-ring opening, and inter-ring misalignment. Since shield tunnels are modular structures, their joint stiffness is weaker than that of the tunnel segments themselves. Longitudinal differential deformation and elliptical deformation of the cross-section can both induce operational risks such as joint leakage and segment cracking.

[0003] To mitigate the adverse effects of conventional raft foundations on underlying tunnels, pile-raft foundations are commonly used in existing technologies. This type of foundation, by incorporating piles, transfers part of the superstructure load to deeper soil layers, thereby reducing stress concentration in the shallow foundation and, to some extent, mitigating additional deformation of the underlying tunnel. Compared to conventional raft foundations, pile-raft foundations improve the load transfer path, reducing the vertical additional stress acting on the soil layers near the tunnel. Therefore, pile-raft foundations are a commonly used tunnel protection measure when the superstructure load is large or when an existing tunnel is within the foundation's influence range.

[0004] However, existing conventional pile-raft foundations still have significant shortcomings. First, although pile-raft foundations can share some of the superstructure load through the piles, the bottom of the raft slab is still in direct contact with the underlying soil, and its force transmission method is essentially rigid contact force transmission. When the superstructure load is large, the raft slab span is wide, or the tunnel depth is shallow, the raft slab deflection will lead to a non-uniform distribution of contact pressure at the bottom, and stress concentration may still occur in local areas, which will further propagate to the soil layer where the existing tunnel is located. Second, existing pile-raft foundations mainly rely on increasing the stiffness of the raft slab, increasing the pile length, adjusting the pile spacing, or increasing the overall bearing capacity of the foundation to control tunnel deformation. These measures can reduce overall settlement to some extent, but their ability to control local contact stress at the bottom of the raft slab, elliptic deformation of the tunnel cross-section, and relative deformation between rings is limited.

[0005] In summary, conventional raft foundations suffer from the problem of direct diffusion of superstructure loads to the underlying strata, easily leading to significant additional deformation of the tunnel. While pile-raft foundations can reduce some additional stress through pile transfer, they still suffer from drawbacks such as direct contact force transmission at the bottom of the raft, localized pressure concentration, and insufficient deformation isolation capacity. For existing pile-raft foundation + EPS buffer layer structures (with the buffer layer located below the raft slab) in engineering projects, there is currently a lack of deformation calculation methods that can systematically consider the interaction between the pile-raft foundation, EPS buffer layer, underlying soil, and existing operational shield tunnels. Based on this, this invention proposes a tunnel deformation calculation method for the above-mentioned structural forms, used to analyze and evaluate the settlement, convergence, inter-ring deformation, and structural stress response of the underlying tunnel under the load of a high-rise building. Summary of the Invention

[0006] The present invention aims to provide a method for calculating the deformation of existing tunnels spanning high-rise buildings based on buffer layers, so as to analyze and evaluate the settlement, convergence, inter-ring deformation and structural stress response of the tunnels under the load of the high-rise building.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, comprising the following steps: Step 1: Establish a soil-raft interaction model. The main components of the soil-raft interaction model are piles, raft, buffer layer, and soil. The physical quantity to be determined is the vertical displacement of the soil. Step 2: Simplify the raft foundation as an Euler beam on an elastic foundation model. Approximate the raft foundation deflection as the buffer layer compression. Calculate the vertical compressive strain of the buffer layer based on the buffer layer compression, thereby obtaining the stress transmitted from the raft foundation to the underlying soil through the buffer layer, and further obtaining the vertical displacement w of the soil caused by the raft foundation. se Based on w se The vertical displacement w of the soil at any point at the bottom of the buffer layer was calculated. s1 ; Step 3: Assume the initial value w of the vertical displacement of the pile foundation. p Calculate the relative displacement w between the pile and the soil. r According to w p and w r Calculate the vertical displacement w at any point around the pile. s2 ; Step 4: Perform iterative calculations based on the soil-raft interaction model, repeating steps 2 and 3, and adjusting the initial value w of the vertical displacement of the pile foundation. p until w s1 = w s2 Thus, the vertical displacement w of the soil is obtained. s This leads to the vertical additional load at the existing tunnel caused by the self-weight load of the superstructure; Step 5: Based on the vertical additional load obtained in Step 4, establish a soil-tunnel interaction model and solve for the deformation parameters of the existing shield tunnel.

[0008] The beneficial effects of this plan are: 1. In order to fully consider the control capabilities of local contact stress at the bottom of the raft foundation, elliptic deformation of the tunnel cross section, and relative deformation between rings, this scheme establishes different calculation frameworks in two stages to fill the gap of no complete set of analytical algorithms for the pile-raft + EPS buffer layer system.

[0009] In the first stage (steps one to four), a soil-raft interaction model is established. Without considering the reaction of the existing tunnel on the deformation of the free field soil, and ignoring the reverse compression of the tunnel on the soil, the additional load at the existing tunnel caused by the self-weight load of the superstructure under the action of the pile-raft-EPS buffer layer conversion structure is solved. This stage simplifies the calculations, avoids the complex equations of the bidirectional coupling between the soil and the tunnel; accurately quantifies the unloading of the buffer layer and the distribution of pile foundation loads; and uniformly outputs a unique parameter (additional load) to supply the second stage.

[0010] The second stage (step five) involves establishing a soil-tunnel interaction model based on the additional loads obtained in the first stage to solve for deformation parameters such as longitudinal settlement, lateral convergence, and internal forces in existing shield tunnels. This stage primarily relies on existing empirical formulas for calculation, differing from current technologies in that it utilizes the output values ​​from the first stage: the additional loads.

[0011] 2. To fully reflect the regulating effect of the buffer layer on the force transmission process, only the bending deformation of the raft slab body is considered, and the raft slab is simplified as an Euler beam to improve calculation efficiency.

[0012] 3. In traditional calculations, the raft foundation and buffer pressure are calculated separately, which requires the establishment of a three-dimensional contact coupling model of the raft foundation, EPS, and soil. The solution can only be obtained by finite element numerical iteration, and there is no simple analytical formula. In this scheme, considering the calculation scenario, the bottom surface of the raft foundation is attached to the top surface of the buffer layer. The vertical compression deformation of the soil layer is much smaller than that of the EPS, so the soil layer's own compression can be ignored. Therefore, the downward deflection value at each point of the raft foundation is approximately equal to the thickness of the buffer layer that is flattened at that location. The vertical deformation of the contact interface between the raft foundation and the buffer layer is synchronous, and minor horizontal slippage does not affect the calculation of the vertical compression. The vertical displacement is completely synchronous, satisfying the approximation conditions.

[0013] By approximating the raft slab deflection as the compression of the buffer layer, the deflection is directly output using the analytical solution of an Euler beam, and then converted into the compression of the cushion layer in one step. The entire calculation relies on explicit formulas, requiring no modeling. During the design phase, batch calculations can be performed for different EPS thicknesses and raft slab dimensions. With the compression, the three-segment nonlinear constitutive model of EPS (elastic-yield-strain hardening) can be substituted to calculate the compressive stress borne by the foam at various points. Then, the distributed pressure transmitted from the raft slab to the soil can be calculated, and finally, the vertical displacement w of the soil caused by the raft slab can be calculated. se .

[0014] 4. In steps two through four, soil displacement is calculated using the raft foundation and buffer layer, and soil displacement is also calculated using the pile foundation. Finally, the two are made equal to establish an equation, and the initial value w of the vertical displacement of the pile foundation is adjusted iteratively. p This ensures the equation holds true. The entire iterative process relies entirely on explicit mechanical formulas, without the need for numerical software, and allows for rapid changes in EPS material, thickness, raft span, and pile length to perform comparisons under multiple working conditions.

[0015] w in the calculation equation s1 At that time, the vertical displacement w of the soil caused by the raft foundation was introduced. se w se The derivation is derived from the stress and strain of the buffer layer based on the deflection of the Euler beam, which is the key difference from all traditional iterations.

[0016] Furthermore, the formula for calculating the vertical displacement of the soil at any point at the bottom of the buffer layer is as follows: w s1 = w su + w sp + w se ; w su - Vertical displacement of soil caused by excavation of the foundation of the superstructure; w sp - Vertical displacement of soil caused by the interaction force between piles and soil; w se - Vertical displacement of soil caused by raft foundation.

[0017] Furthermore, in step two, w sp The calculation steps include: 2.1 The pile is considered as a rigid body, and the pile is considered as a friction pile. The internal force of the pile body is borne by the side friction of the pile. The interaction mode between the pile and the soil is considered as an ideal elastic-plastic model. 2.2. Discretize a single pile into several pile units along the pile body direction, and treat the pile-soil interaction force of each pile unit as a concentrated force P acting on the center of the unit; 2.3. Based on Mindlin theory, the vertical displacement effect of the force of each pile element in the soil is calculated, and the vertical displacement w of the soil caused by the pile-soil interaction is obtained through the superposition principle.sp .

[0018] Furthermore, in step two, the elastic foundation model is the Winkler foundation model, and the equivalent Winkler foundation coefficient of the raft slab is taken as the vertical compressive stiffness per unit area of ​​the buffer layer; the governing equation for the raft slab deflection is: ; C t =b t C e ; (EI) t - Equivalent bending stiffness of raft slab; u t (x) - Raft deflection; p u (x) - Vertical loads transferred from the superstructure to the raft slab; C t - Equivalent Winkler subgrade coefficient for raft foundation; b t - The width of the raft board strip taken; C e - Vertical compressive stiffness per unit area of ​​the buffer layer.

[0019] Furthermore, in step two, the raft deflection is approximated as the compression of the buffer layer, and the vertical compressive strain of the buffer layer is... ε e ( x The formula for calculating ) is: ; Δx e - Buffer layer compression amount; ε e (x) - compressive strain; d e - Buffer layer thickness.

[0020] Furthermore, the formula for the vertical compressive stress of the buffer layer is: ; E e - Elastic modulus of the elastic segment of the buffer layer material; ε y - Yield strain of the buffer layer material; ε d - The strain threshold at which the buffer layer material enters the strain hardening stage; σ y - Yield stress of the buffer layer material.

[0021] Furthermore, in step two, w is obtained based on the stress transferred from the raft foundation to the underlying soil through the buffer layer. seThe method is as follows: The vertical additional stress in the underlying soil is obtained through Mindlin theory; based on the vertical additional stress, w is calculated using the layered summation method. se .

[0022] Furthermore, in step three, the vertical displacement at any point in the soil around the pile satisfies: w s2 =w p +w r ; In step four, iterative calculations are performed based on the following displacement compatibility equations: .

[0023] Furthermore, in step five, in the soil-tunnel interaction model, the existing shield tunnel is longitudinally equivalent to a Timoshenko beam located on the Winkler foundation, thus obtaining the longitudinal deformation control equation of the existing shield tunnel; the vertical additional load q from step four is substituted into the longitudinal deformation control equation to obtain the deformation parameters of the existing shield tunnel.

[0024] Furthermore, the deformation parameters of existing shield tunnels include free-field soil displacement, additional load, longitudinal settlement, and structural internal force response.

[0025] This solution also has the following effects: 1. Since the compressive stiffness of the EPS buffer layer is significantly lower than the supporting stiffness of the underlying strata, the buffer layer is directly regarded as the foundation. The equivalent Winkler subgrade coefficient Ct of the lower part of the raft foundation is taken as the vertical compressive stiffness C per unit area of ​​the EPS buffer layer. e There is no need to calculate the soil stiffness; the material stiffness of the EPS buffer layer can be directly obtained for calculation.

[0026] 2. Existing technologies only simplify the EPS buffer layer with simple linear elasticity, never incorporating the three-segment nonlinear compression characteristics of EPS into the analytical beam equations of the raft foundation to achieve quantitative load reduction calculations. This scheme, however, equates the raft foundation deflection to EPS compression and combines this with the segmented calculation of the ground pressure transmitted downwards by the raft foundation using the three-segment nonlinear constitutive model of EPS, resulting in more accurate results.

[0027] 3. Traditional pile-raft iteration does not incorporate the nonlinear deformation term of the EPS buffer layer, thus failing to accurately reflect the load distribution between the piles and soil after the foam layer is unloaded. This scheme, however, establishes a unified displacement compatibility equation. And the vertical displacement of the soil caused by the raft foundation w se By introducing the equation, the vertical additional load q shared by the pile foundation is adjusted iteratively to simultaneously satisfy the overall force balance and the coordination of the relative displacement between the pile and the soil; thus truly reflecting the load distribution law of the pile and soil after the unloading of the foam layer.

[0028] 4. Compared with existing calculation methods for ordinary raft foundations and ordinary pile-raft foundations, this invention is geared towards pile-raft foundation + EPS buffer layer structures. It incorporates pile foundation force transmission, raft foundation span distribution, EPS buffer layer compressive force transmission, underlying soil deformation, and existing shield tunnel structural response into a unified calculation process. This allows for a more complete reflection of the stress and deformation patterns of the underlying operating tunnel under the load of a high-rise building. This method can not only calculate the tunnel's longitudinal settlement and lateral convergence but also further obtain indicators such as inter-ring opening, inter-ring misalignment, circumferential bending moment, and circumferential axial force, thereby achieving a comprehensive evaluation of the tunnel's overall deformation, cross-sectional elliptic deformation, joint deformation, and segment stress state. Furthermore, this method can conduct parametric analysis by adjusting factors such as raft foundation thickness, foundation reaction coefficient, tunnel depth, EPS buffer layer thickness, and material parameters, providing quantitative calculation basis for the protection design of existing subway tunnels under high-rise building conditions, foundation scheme comparison, and buffer layer parameter optimization.

[0029] This invention has good engineering applicability. For new high-rise buildings, underground commercial spaces, station-city integrated projects, or rail transit-related development projects built above existing and operational subway tunnels, it can quickly predict the deformation response of the underlying tunnel during the design phase and compare different foundation types and buffer layer layout schemes. Compared to methods that rely entirely on three-dimensional numerical simulation, the calculation process of this invention is clear, and the physical meaning of the parameters is well-defined, facilitating preliminary design, scheme selection, and sensitivity analysis for engineering designers.

[0030] This invention offers significant social and economic benefits. By predicting and controlling the impact of overpass construction on operating subway tunnels in advance, risks such as tunnel structural cracking and joint leakage can be reduced, thereby improving the operational safety of existing subway lines. Simultaneously, this method provides a basis for foundation optimization and buffer layer parameter design, reducing increased engineering costs caused by excessive reinforcement, excessive piling, and repeated calculations, and contributing to the safe and coordinated development of urban underground space and existing rail transit facilities. Attached Figure Description

[0031] Figure 1 The calculation flowchart is shown in the example. Figure 2 A schematic diagram of the raft foundation, pile foundation, and buffer layer in an embodiment; Figure 3 This is a schematic diagram illustrating the vertical stress evolution of the overlying soil layer of a tunnel during underground space development. Figure 4 Comparison chart of tunnel settlement under different measures; Figure 5 Comparison of tunnel convergence deformation under different measures. Detailed Implementation

[0032] The following detailed description illustrates the specific implementation method: The reference numerals in the accompanying drawings include: pile foundation 1, buffer layer 2, and raft foundation 3.

[0033] Example A method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, wherein the calculation object is as follows: Figure 2 As shown, the calculation flowchart is as follows: Figure 1 As shown, it includes the following steps: Step 1: Establish a soil-raft interaction model. The main components of the soil-raft interaction model are piles, raft, buffer layer, and soil. The physical quantity to be determined is the vertical displacement of the soil. Step 2: Calculate the vertical displacement w of the soil at any point at the bottom of the buffer layer. s1 The formula for calculating the vertical displacement of the soil at any point at the bottom of the buffer layer is: w s1 = w su + w sp + w se ; w su - Vertical displacement of soil caused by excavation of the foundation of the superstructure; w sp - Vertical displacement of soil caused by the interaction force between piles and soil; w se - Vertical displacement of soil caused by raft foundation.

[0034] w su Calculation method: After foundation excavation, the soil layer will undergo rebound deformation after losing the weight of the overlying layer. Therefore, the layered summation method is adopted, combined with the Mindlin solution to calculate the vertical displacement of the free field caused by excavation unloading. w su The vertical stress changes during the excavation process are as follows: Figure 3 As shown; w sp The calculation steps include: 2.1 The interaction between pile and soil is described by an ideal elastic-plastic model. The pile is regarded as a rigid body and is considered as a friction pile. The internal force of the pile is borne by the side friction of the pile. The interaction mode between pile and soil is regarded as an ideal elastic-plastic model. 2.2. Discretize a single pile into several pile units along the pile body direction, and treat the pile-soil interaction force of each pile unit as a concentrated force P acting on the center of the unit; 2.3. Based on Mindlin theory, the vertical displacement effect of the force of each pile element in the soil is calculated, and the vertical displacement w of the soil caused by the pile-soil interaction is obtained through the superposition principle. sp .

[0035] w seCalculation method: To characterize the moderating effect of the EPS buffer layer on the force transmission process, considering only the bending deformation of the raft slab itself, the raft slab is simplified as an Euler-Bernoulli beam located on the Winkler foundation, and its governing equations are: (1) x represents the position coordinate (horizontal coordinate) along the longitudinal length direction of the raft slab (foundation slab); The unknown quantity to be solved in the equation is u t (x) - Raft deflection; (EI) t - Equivalent bending stiffness of raft slab; p u (x) - Vertical loads transferred from the superstructure to the raft slab; C t - Equivalent Winkler subgrade coefficient for raft foundation; Pick ; N u This refers to the total vertical load transferred from the superstructure to the raft slab. l This represents the calculated span of the raft foundation.

[0036] Pick ; E c The elastic modulus of the concrete in the raft foundation; h t For raft slab thickness; b t The width of the selected raft plate strip.

[0037] Considering that the compressive stiffness of the EPS buffer layer is significantly lower than the bearing stiffness of the underlying strata, we take... ; C e The vertical compressive stiffness per unit area of ​​the buffer layer; E e The elastic modulus of the EPS buffer layer. d e This refers to the thickness of the EPS buffer layer.

[0038] The raft deflection is approximated as the compression of the EPS buffer layer, where the compression Δ is the buffer layer compression. x e With compressive strain ε e ( x ) are respectively (2) (3) Δxe - Buffer layer compression amount; ε e (x) - compressive strain; d e - Buffer layer thickness.

[0039] Based on the stress-strain relationship of EPS material, the buffer layer is approximated as an ideal elastoplastic material, and its vertical compressive stress is: (4) E e - Elastic modulus of the elastic segment of the buffer layer material; ε y - Yield strain of the buffer layer material; ε d - The strain threshold at which the buffer layer material enters the strain hardening stage; σ y - Yield stress of the buffer layer material.

[0040] When the buffer layer is in the plastic segment, it can be further approximated as follows:

[0041] Therefore, the force transmitted from the raft slab to the underlying strata via the EPS buffer layer q e ( x )for:

[0042] The vertical additional stress in the underlying soil was obtained through the Mindlin solution, and then calculated using the layered summation method to obtain w. se .

[0043] w se Calculation summary: The core of this embodiment lies in, through calculation based on Figure 2 The model assumes a relationship between the raft foundation, buffer layer, and soil layers to simplify the calculation process, thereby calculating the load transfer process between the raft foundation, buffer layer, and soil layers. Finally, based on existing soil mechanics, w is calculated. se Specifically, the raft deflection is calculated using equation (1); the compressive strain is calculated directly based on the raft deflection using equations (2) and (3). ε e ( x Thus, the force transmitted to the lower strata is obtained. q e ( x ).

[0044] Step 3: Assume the initial value w of the vertical displacement of the pile foundation. p Calculate the relative displacement w between the pile and the soil. r According to w p and w rCalculate the vertical displacement w at any point around the pile. s2 ;w s2 =w p +w r ; Step 4: Check the displacement coordination relationship of the pile-transfer structure-buffer layer-soil system according to the following formula.

[0045] w s1 = w s2 ; Right now ; The left side of the equation represents the actual vertical displacement of the soil, while the right side represents the displacement that the soil should have at that location, calculated based on the movement of the pile. That is, the soil displacement is inferred from the pile displacement. Only when both sides of the equation are equal does it mean that the pile and the soil have not separated or intruded into each other, and the deformation is coordinated.

[0046] Therefore, if the above formula is not satisfied, iterative calculations are performed based on the soil-raft interaction model, repeating steps two and three, and adjusting the load q distributed to the pile foundation. p This allows for the adjustment of the initial value w of the vertical displacement of the pile foundation. p until both displacement coordination and mechanical equilibrium are simultaneously satisfied; After the iteration is completed, the vertical displacement w of the soil is obtained. s w s =w s1 = w s2 This leads to the additional vertical load at the existing tunnel caused by the self-weight of the superstructure. q ; Step 5: Based on the vertical additional load obtained in Step 4, establish a soil-tunnel interaction model and calculate the vertical additional load acting on the existing tunnel. q and longitudinal and vertical deformation of the tunnel ω .

[0047] The existing shield tunnel can be longitudinally equivalent to a Timoshenko beam located on the Winkler foundation. Its longitudinal deformation governing equation is:

[0048] This formula is an existing formula. The q in the formula is obtained based on the calculation in step four. This formula is only used to illustrate the role of q in the calculation of longitudinal deformation. In the formula: ω This refers to the vertical deformation of the existing tunnel; q Additional vertical loads are applied to existing tunnels; k s The ground reaction coefficient of the Winkler foundation; EI ) eq and( κGA ) eqThese are the equivalent bending stiffness and equivalent shear stiffness of the existing tunnel, respectively.

[0049] Through the above calculation process, the free field soil displacement, additional load, longitudinal settlement and structural internal force response of the existing shield tunnel under the action of the pile-raft-EPS buffer layer conversion structure can be obtained, thus providing a calculation basis for the selection of the foundation form of the overpass building, the optimization design of the buffer layer parameters, the evaluation of the protection and control effect of the existing tunnel and the parameter sensitivity analysis.

[0050] The calculation results (settlement and convergence deformation) of this embodiment are compared with those of raft foundations and pile-raft foundations as shown in the figure below. Figure 4 , Figure 5 As shown, the advantages of adding a buffer layer are obvious, therefore this calculation method has broad application prospects.

[0051] Calculation Example Taking a high-rise building development project above an existing shield tunnel in a certain city's rail transit section as an example. The existing shield tunnel has an outer diameter of 6.2m and a center burial depth of 15m. The superstructure adopts a pile-raft foundation-EPS buffer layer foundation system. The calculated span l of the raft foundation is taken as 20m, and a 1m wide strip is taken along the width direction for calculation. The thickness h of the raft foundation is... t For a length of 1.0m, the elastic modulus E of concrete is... c The load is 34.8 GPa, and the uniformly distributed load acting on the raft slab from the superstructure is 600 kPa. The EPS buffer layer thickness is d. e The elastic section is 150mm long, and the elastic modulus E is... e The yield stress is 2500 kPa and σ is 2500 kPa. y The yield strain is ε at 25 kPa. y The strain hardening initiation strain ε is 0.01. d Take 0.90.

[0052] Equivalent bending stiffness (EI) of raft foundation t =E c [(b t h t 3 ) / 12]=2.90×10 6 kN / cm 2 The equivalent subgrade coefficient C of the EPS buffer layer t =b t C e =(b t E e ) / d e =1.667×10 4 kN / m 2 Substituting the above parameters into equation (1), the deflection distribution of the raft slab along the span direction is calculated. The maximum deflection at the mid-span of the raft slab is 36.816 mm, and the average deflection of the raft slab is 19.735 mm.

[0053] (1) According to formula (2), the raft deflection is approximately taken as the compression of the EPS buffer layer, which is 36.816 mm.

[0054] (2) Substituting the maximum compression and buffer layer thickness into equation (3), the maximum compressive strain ε of the EPS buffer layer at the mid-span of the raft slab is calculated. e =24.54%.

[0055] (3) Since 0.01 < 0.2454 < 0.90, the EPS buffer layer is in the plastic plateau stage after yielding. According to equation (4), the vertical pressure transmitted from the EPS buffer layer at the mid-span of the raft foundation to the underlying soil is 25 kPa.

[0056] (4) Subsequently, the vertical pressure transmitted by the EPS buffer layer was used as the input for the calculation of the underlying soil. The vertical displacement of the soil caused by the raft load was calculated using the Mindlin theoretical solution and the layered summation method. At the same time, the vertical displacement of the soil caused by excavation unloading and pile-soil interaction was calculated. By adjusting the load sharing and vertical displacement of the pile foundation, the displacement of the soil at the bottom of the buffer layer and the displacement of the soil around the pile were made to meet the coordination conditions.

[0057] After iterative calculations, the maximum vertical additional load at the existing tunnel location when the EPS buffer layer was installed was found to be 23.618 kPa. Finally, the obtained vertical additional load was substituted into the calculation model of the longitudinal deformation and cross-sectional response of the existing shield tunnel to obtain calculation results for tunnel longitudinal settlement, lateral convergence, inter-ring opening, inter-ring misalignment, and structural internal forces. These results were used to evaluate the protective effect of the pile-raft-EPS buffer layer system on the existing tunnel.

[0058] The above descriptions are merely embodiments of the present invention, and common knowledge such as specific technical solutions and / or characteristics are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, characterized in that, Includes the following steps: Step 1: Establish a soil-raft interaction model. The main components of the soil-raft interaction model are piles, raft, buffer layer, and soil. The physical quantity to be determined is the vertical displacement of the soil. Step 2: Simplify the raft foundation as an Euler beam on an elastic foundation model. Approximate the raft foundation deflection as the buffer layer compression. Calculate the vertical compressive strain of the buffer layer based on the buffer layer compression, thereby obtaining the stress transmitted from the raft foundation to the underlying soil through the buffer layer, and further obtaining the vertical displacement w of the soil caused by the raft foundation. se Based on w se The vertical displacement w of the soil at any point at the bottom of the buffer layer was calculated. s1 ; Step 3: Assume the initial value w of the vertical displacement of the pile foundation. p Calculate the relative displacement w between the pile and the soil. r According to w p and w r Calculate the vertical displacement w at any point around the pile. s2 ; Step 4: Perform iterative calculations based on the soil-raft interaction model, repeating steps 2 and 3, and adjusting the initial value w of the vertical displacement of the pile foundation. p until w s1 = w s2 Thus, the vertical displacement w of the soil is obtained. s This leads to the vertical additional load at the existing tunnel caused by the self-weight load of the superstructure; Step 5: Based on the vertical additional load obtained in Step 4, establish a soil-tunnel-soil-raft interaction model and solve for the deformation parameters of the existing shield tunnel.

2. The method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, as described in claim 1, is characterized in that: The formula for calculating the vertical displacement of the soil at any point at the bottom of the buffer layer is: In s1 = in su + in sp + in se ; w su - Vertical displacement of soil caused by excavation of the foundation of the superstructure; w sp - Vertical displacement of soil caused by the interaction force between piles and soil; w se - Vertical displacement of soil caused by raft foundation.

3. The method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, as described in claim 2, is characterized in that: In step two, w sp The calculation steps include: 2.1 The pile is considered as a rigid body, and the pile is considered as a friction pile. The internal force of the pile body is borne by the side friction of the pile. The interaction mode between the pile and the soil is considered as an ideal elastic-plastic model. 2.

2. Discretize a single pile into several pile units along the pile body direction, and treat the pile-soil interaction force of each pile unit as a concentrated force P acting on the center of the unit; 2.

3. Based on Mindlin theory, the vertical displacement effect of the force of each pile element in the soil is calculated, and the vertical displacement w of the soil caused by the pile-soil interaction is obtained through the superposition principle. sp .

4. The method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, as described in claim 1, is characterized in that: In step two, the elastic foundation model is the Winkler foundation model, and the equivalent Winkler foundation coefficient of the raft foundation is taken as the vertical compressive stiffness per unit area of ​​the buffer layer; the governing equation for the raft foundation deflection is: ； C t =b t C e ; (EI) t - Equivalent bending stiffness of raft slab; u t (x) - Raft deflection; p u (x) - Vertical loads transferred from the superstructure to the raft slab; C t - Equivalent Winkler subgrade coefficient for raft foundation; b t - The width of the raft board strip taken; C e - Vertical compressive stiffness per unit area of ​​the buffer layer.

5. The method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, as described in claim 1, is characterized in that: In step two, the raft deflection is approximated as the compression of the buffer layer, and the vertical compressive strain of the buffer layer is... ε e ( x The formula for calculating ) is: ； Δx e - Buffer layer compression amount; ε e (x) - compressive strain; d e - Buffer layer thickness.

6. The method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, as described in claim 1, is characterized in that: The formula for the vertical compressive stress of the buffer layer is: ； E e - Elastic modulus of the elastic segment of the buffer layer material; ε y - Yield strain of the buffer layer material; ε d - The strain threshold at which the buffer layer material enters the strain hardening stage; σ y - Yield stress of the buffer layer material.

7. The method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, as described in claim 1, is characterized in that: In step two, w is obtained based on the stress transferred from the raft foundation to the underlying soil through the buffer layer. se The method is as follows: The vertical additional stress in the underlying soil is obtained through Mindlin theory; based on the vertical additional stress, w is calculated using the layered summation method. se .

8. The method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer according to claim 1, characterized in that: In step three, the vertical displacement at any point in the soil around the pile satisfies: w s2 =w p +w r ; In step four, iterative calculations are performed based on the following displacement compatibility equations: 。 9. The method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, as described in claim 1, is characterized in that: In step five, in the soil-tunnel-soil-raft interaction model, the existing shield tunnel is longitudinally equivalent to a Timoshenko beam located on the Winkler foundation, thus obtaining the longitudinal deformation control equation of the existing shield tunnel; the vertical additional load q from step four is substituted into the longitudinal deformation control equation to obtain the deformation parameters of the existing shield tunnel.

10. The method for calculating the deformation of a high-rise building spanning an existing tunnel based on a buffer layer, as described in claim 9, is characterized in that: The deformation parameters of existing shield tunnels include free-field soil displacement, additional load, longitudinal settlement, and structural internal force response.

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