A consolidation settlement calculation method suitable for composite foundation of immersed tube tunnel

Abstract

The present application belongs to the field of geotechnical engineering and underground structure engineering, and provides a consolidation settlement calculation method suitable for composite foundation of immersed tunnel. The present application divides the foundation system into three sub-domains of gravel cushion, pile-soil reinforcement area and underlying soft soil area. The external load first acts on the top surface of the cushion, and then is transmitted to the composite foundation in layers from the cushion. The cushion is explicitly introduced into the settlement calculation system as an independent compressible unit, and is strictly connected in series with the consolidation calculation of the underlying "reinforcement area + underlying layer". Compared with the traditional calculation method which only regards the cushion as a "rigid uniform load plate" or directly ignores its deformation, the present method can quantify the settlement contribution of the cushion itself, reveal the coordination relationship among the cushion, the composite foundation and the underlying layer in deformation, and thus make up for the important gap in the existing consolidation settlement theory of composite foundation that "only soft soil is calculated without considering the cushion".

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering and underground structure engineering, and specifically relates to a method for calculating consolidation settlement applicable to composite foundations of immersed tunnels. Background Technology

[0002] With the large-scale construction of cross-sea channels and underwater tunnels, composite foundations formed by deep mixing piles (DCM piles) and CFG piles have become the main type of foundation for immersed tunnels. These composite foundations typically include a pile-soil reinforcement zone, an underlying layer of natural soft soil, and a thick overlying crushed stone cushion layer. After long-term exposure to the tunnel's own weight and operational loads, consolidation settlement directly affects the waterproofing performance of the immersed tunnel joints and the overall structural safety. Therefore, engineering design urgently needs a consolidation settlement calculation method that can reflect both the layered characteristics of the composite foundation and describe the time effect.

[0003] In existing designs, settlement calculations for deep silt composite foundations often employ classical one-dimensional consolidation theory or treat the composite foundation as a single homogeneous foundation, frequently estimating settlement using only empirical reduction factors or equivalent compression moduli. While some studies consider the interaction between piles and soil, they often treat the reinforced zone as a monolithic homogeneous medium or only analyze the radial consolidation process of the soil between piles, failing to reflect the stress transfer and deformation coordination between the reinforced zone and the underlying layer. Furthermore, existing methods generally neglect the impact of differences in consolidation rates among different layers of the composite foundation on the overall settlement evolution, failing to simultaneously provide the degree of consolidation and time relationship of the reinforced zone, the underlying layer, and the overall foundation. This leads to significant uncertainties in assessing the assembly of immersed tunnel segments, water-stop joints, and the long-term operational safety of the tunnel sections. In addition, in actual engineering, a 1.5–3.0 m layer of crushed stone or gravel is typically laid first or later at the bottom of the immersed tunnel to adjust elevation, distribute loads, and improve foundation drainage conditions. However, existing studies in consolidation settlement analysis mostly treat the subgrade as a rigid load-bearing body or an ideal "settlement-free" layer, only considering its influence on the equivalent permeability coefficient and equivalent load distribution, and rarely assess the compressive deformation of the subgrade itself. The characteristics of the evolution of subgrade stiffness during the compaction process are not reflected, making it difficult to use to assess the impact of different subgrade thicknesses, mix proportions, and construction quality on long-term settlement; Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a consolidation settlement calculation method applicable to composite foundations of immersed tunnels, thereby resolving the issues in the prior art. The technical solution adopted by this invention is as follows: A method for calculating consolidation settlement applicable to composite foundations of immersed tunnels, comprising: Step 1: Based on the classical consolidation theory framework, construct idealized assumptions; Step 2, construct a layered foundation calculation model: divide the composite foundation of the immersed tunnel into a crushed stone cushion layer, a reinforcement zone and an underlying layer, perform layered settlement calculation, and solve the total settlement of the composite foundation of the immersed tunnel based on the layered settlement calculation results; The crushed stone cushion layer is located at the top, the immersed tunnel is supported on the crushed stone cushion layer, the reinforced area is below the crushed stone cushion layer, and the underlying layer is the natural soft soil layer below the reinforced area.

[0005] Furthermore, in step 1, the idealization assumptions include: In the composite foundation of the immersed tunnel, the soil and piles in each area are in a saturated state, with uniform and isotropic physical properties. The soil particles and pore water are incompressible, and the consolidation deformation is caused only by the deformation of the soil skeleton. The seepage process follows Darcy's law, the permeability coefficient and compressibility coefficient of each layer are constant, the soil between piles only undergoes vertical drainage, and the pile body is impermeable. The consolidation process assumes small deformation, and the stress-strain relationship follows a linear elastic constitutive model. The surface load is applied instantaneously and remains constant throughout the entire process; The crushed stone cushion layer is treated as an independent compressible unit and does not participate in the pore pressure consolidation solution. The total settlement is the sum of the settlements of each layer.

[0006] Furthermore, in step 2, when performing stratified settlement calculations, the following formula is used for the crushed stone cushion layer: ; in, H cush The thickness of the crushed stone subbase is... E cush For compressibility modulus, q c This represents the average additional stress experienced. This indicates the final compressive settlement of the crushed stone cushion layer.

[0007] Furthermore, in step 2, when performing layered settlement calculations, the reinforced area includes: Based on equilibrium conditions and the assumption of constant strain, we obtain: ; ; in, and These represent the average total stress in the soil and pile at any depth, respectively. The average excess pore pressure of the soil; The volumetric strain at any depth in the composite foundation; The average additional stress / total additional stress increment at any depth z; r cWhere is the pile radius; r e The equivalent radius of influence; Soil compression modulus; The elastic modulus of the pile body can then be obtained: ; In the formula: The pile-soil modulus ratio, i.e. ; The pile replacement ratio is expressed as... ; The rate at which volumetric strain changes with time; The consolidation equation for vertical seepage within the soil is: ; In the formula: The specific gravity of water; The vertical permeability coefficient of the soil; Combining the above formulas, the consolidation governing equation for the reinforced zone is: ; in, This is the vertical consolidation coefficient of the soil.

[0008] Furthermore, in step 2, when performing stratified settlement calculations, the underlying layer includes: The height of the lower layer is taken as The seepage flow of two typical soil units is analyzed, including the columnar soil seepage unit. The data were taken from the unreinforced soil within the area of ​​the bottom of the undrained piles, and from the annular soil seepage unit. The soil sample was taken from the unreinforced soil within the area of ​​the soil base around the ring pile. columnar soil seepage unit Without vertical seepage, the excess pore water pressure is dissipated only through radial seepage. Based on the relationship between the pore water outflow and the change in unit volume, the following two equations can be obtained: ; ; In the formula: and At any time columnar soil seepage unit and annular soil seepage unit volume, , ,in, and These are columnar soil seepage units. and annular soil seepage unit The base area; and They are respectively Time columnar soil seepage unit Radial outflow and annular soil seepage unit Vertical outflow; The following relationship can be obtained: ; In the formula: , For thickness is The volume of the unit; ; Based on the relationship between the increase in effective stress and the decrease in unit volume, we obtain: ; In the formula: The excess pore water pressure at any depth in the underlying layer. The first in the lower layer The compression modulus of the soil layer; Based on Darcy's law of seepage, the following equation is obtained: ; Based on Darcy's law of seepage, the following equation is obtained: ; In the formula: The specific gravity of water; The vertical permeability coefficient of the soil; The equations obtained by simultaneously applying Darcy's law of seepage and Darcy's law of seepage are the consolidation governing equations for the underlying layer as follows: ; In the formula: is the vertical consolidation coefficient of the underlying soil layer.

[0009] Furthermore, in step 2, the total settlement of the immersed tunnel composite foundation is calculated based on the layered settlement calculation results, including: Using the method of separation of variables, the consolidation equation of the layered (layered) calculation model for the composite foundation of immersed tunnels is expressed as: ; in, , , and All are undetermined coefficients; ; ; Based on the boundary conditions and initial conditions, we obtain: ; ; In the formula: ; ; ( ); four elements , , and They are represented as follows: ; Based on the boundary and initial conditions, we obtain information about transcendental equations: ; In the formula: ; Undetermined coefficients Solving based on the boundary and initial conditions, the following is satisfied: ; Based on the orthogonality of the characteristic functions, the undetermined coefficients Represented as: ; The settlement expression is derived as follows: The degree of consolidation is calculated as follows: ; in, S found ( t The sum of the solidification settlement of the reinforced area and the underlying layer at a certain moment is denoted as . S found,∞ This represents the final consolidation settlement between the reinforced area and the underlying layer. Total settlement at the bottom of the immersed tunnel S tot ( t ) is represented as: .

[0010] Furthermore, the boundary and initial conditions include: ; ; ; ; .

[0011] The present invention has the following beneficial effects: This invention can quantify the settlement contribution of the cushion layer itself, reveal the synergistic / coordinated relationship among the cushion layer, the reinforced zone (composite foundation), and the underlying soft soil layer in the process of load transfer and deformation development, and can separately give the instantaneous compressive settlement of the cushion layer, the consolidation settlement of the reinforced zone, and the consolidation settlement of the underlying layer and their evolution over time. This avoids the systematic error caused by simplifying the cushion layer as a "rigid layer / non-settlement layer", makes up for the lack of explicit inclusion of the compressive deformation contribution of the cushion layer in the existing consolidation settlement analysis of composite foundations, and improves the completeness and engineering applicability of the settlement prediction of composite foundations for immersed tunnels. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the composite foundation for an immersed tunnel. Figure 2 This is a schematic diagram of the calculation model for the reinforced area; Figure 3 This is a diagram showing the seepage relationship of the underlying soil unit; Figure 4 For comparison and verification; Figure 5 This is a schematic diagram of the foundation reinforcement for the immersed tunnel section in a case study project. Figure 6 This is a schematic diagram of vertical settlement in the composite foundation and cushion layer area; Figure 7 The effect of different foundation replacement ratios on foundation consolidation settlement. Detailed Implementation

[0013] The following will be described in conjunction with embodiments of the present invention. Figures 1-7 The technical solutions in the embodiments of the invention are clearly and completely described. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0014] This invention proposes a consolidation settlement calculation method applicable to composite foundations of immersed tunnels. Based on Otter's consolidation theory, the foundation system is divided into three subdomains: a gravel cushion layer, a pile-soil reinforcement zone, and an underlying soft soil zone. External loads are first applied to the top surface of the cushion layer and then transferred layer by layer to the composite foundation. The cushion layer is explicitly introduced as an independent compressible unit into the settlement calculation system and is strictly linked with the consolidation calculation of the underlying "reinforcement zone + underlying layer". Compared with traditional calculation methods that only treat the cushion layer as a "rigid uniformly distributed load plate" or directly ignore its deformation, this method can quantify the settlement contribution of the cushion layer itself and reveal the coordination relationship of the cushion layer, composite foundation, and underlying layer in terms of deformation, thus filling the important gap in the existing composite foundation consolidation settlement theory that "only considers soft soil and not the cushion layer".

[0015] A method for calculating consolidation settlement applicable to composite foundations of immersed tunnels, comprising: Step 1: Based on the classical consolidation theory framework, construct idealized assumptions; Step 2, construct a layered foundation calculation model: divide the composite foundation of the immersed tunnel into a crushed stone cushion layer, a reinforcement zone and an underlying layer, perform layered settlement calculation, and solve the total settlement of the composite foundation of the immersed tunnel based on the layered settlement calculation results; The crushed stone cushion layer is located at the top, the immersed tunnel is supported on the crushed stone cushion layer, the reinforced area is below the crushed stone cushion layer, and the underlying layer is the natural soft soil layer below the reinforced area.

[0016] Specifically, the technical content of step 1 includes: Considering the extremely complex boundary conditions of the actual working conditions of deep silt composite foundations, such as Figure 1 As shown, to facilitate the establishment of analytically solvable consolidation governing equations, this invention makes the following idealized assumptions within the framework of classical consolidation theory: (1) In the composite foundation, the soil above and below the groundwater level is saturated, and the piles and the soil between the piles are homogeneous and isotropic in their respective areas. The soil particles and pore water are considered to be incompressible, and the consolidation deformation is caused only by the volumetric deformation of the soil skeleton structure.

[0017] (2) The seepage process satisfies Darcy's law. The permeability coefficient and compressibility coefficient are constant in each layer and do not change with time and stress. Only radial drainage and seepage are allowed in the soil between piles. The pile body is regarded as an impermeable body and only plays the role of bearing and transmitting force, and does not participate in the seepage process.

[0018] (3) The deformation amplitude of the soil is small during the consolidation process, so the small deformation assumption can be adopted; the stress-strain relationship follows the linear elastic constitutive model, and the stress field and strain field inside the soil always remain in balance and coordination after loading.

[0019] (4) The surface additional load is applied instantaneously at the beginning of consolidation and remains constant throughout the consolidation process. The influence of the construction process and the change of load over time on pore pressure and deformation is not considered.

[0020] (5) When considering the influence of the cushion layer, the crushed stone cushion layer is simplified as a compression unit located at the top of the foundation and does not participate in the solution of pore pressure consolidation. It generates additional settlement through its own compression modulus and thickness, and satisfies series compatibility with the underlying composite foundation in terms of vertical displacement (total settlement equals the sum of the settlements of each layer). At the current stage, the influence of the cushion layer on the internal stress-pore pressure field of the composite foundation is indirectly considered through equivalent load and total settlement. The fully coupled three-layer consolidation control equation has not yet been constructed.

[0021] Specifically, the technical content of step 2 includes: Calculation of settlement of the crushed stone cushion layer in layers: Assume there is a layer of gravel at the bottom of the tunnel with a thickness of [missing information]. Hcush The compressive modulus is E cush The value is 10 MPa; q c This represents the average additional stress (transferred from the tunnel and overlying structure). Therefore, without considering the pore pressure consolidation of the cushion layer and only considering its skeletal compression, the final compressive settlement of the crushed stone cushion layer is: (1) Layered settlement calculation of the reinforced area: like Figure 2 For the reinforced zone, from the equilibrium condition, the iso-strain assumption, and the assumptions, we can obtain: (2) (3) in, and These represent the average total stress in the body and pile at any depth, respectively. The average excess pore pressure of the soil; The volumetric strain at any depth in the composite foundation; The average additional stress / total additional stress increment at any depth z; r c Where is the pile radius; r e The equivalent radius of influence; Soil compression modulus; This is the elastic modulus of the pile.

[0022] From equations (2) and (3), we can obtain: (4) In the formula: The pile-soil modulus ratio, i.e. ; The pile replacement ratio is expressed as... ; The rate at which volumetric strain changes with time; The consolidation equation for vertical seepage within the soil is: (5) In the formula: The specific gravity of water; This represents the vertical permeability coefficient of the soil.

[0023] Combining equations (4) and (5), the consolidation control equation for the reinforced zone can be obtained as follows: (6) in, This is the vertical consolidation coefficient of the soil.

[0024] Calculation of layered settlement of the underlying layer: like Figure 3 As shown, the height of the lower layer is taken as... The seepage flow of two typical soil units was analyzed, including the columnar soil seepage unit. The annular soil seepage unit is taken from the unreinforced soil within the area of ​​the bottom of the undrained pile. The soil sample was taken from the unreinforced soil within the area of ​​the soil beneath the ring pile.

[0025] Because the bottom of the undrained pile does not drain water, the columnar soil seepage unit... Without vertical seepage, the excess pore water pressure is dissipated only through radial seepage. Based on the relationship between the pore water outflow and the change in unit volume, the following two equations can be obtained: (7a) (7b) In the formula: and At any time columnar soil seepage unit and annular soil seepage unit volume, , ,in, and Units and unit The base area; and They are respectively Time unit Radial outflow and unit Vertical outflow.

[0026] From equations (7a) and (7b), the following relationship can be obtained: (8) In the formula: For thickness is The volume of the unit; .

[0027] Based on the relationship between the increase in effective stress and the decrease in unit volume, we can obtain: (9) In the formula: The excess pore water pressure at any depth in the underlying layer. The first in the lower layer The compression modulus of the soil layer.

[0028] From equations (8) and (9) and Darcy's law of seepage, the following equation can be obtained: (10) On the other hand, Darcy's law of seepage yields the following equation: (11) In the formula: It is the density of water.

[0029] Solving equations (10) and (11) simultaneously, we can obtain the consolidation control equations for the underlying layer as follows: (12) In the formula: is the vertical consolidation coefficient of the underlying soil layer.

[0030] The governing equations for the composite foundation of immersed tunnels are: The governing equations for seepage in the reinforced zone and the underlying soil are compared as follows: (Reinforced area, (13a) (lower berth, (13b) Since equations (13a) and (13b) are consistent in form, they can be combined into a single equation: (14) In the formula: .

[0031] The boundary and initial conditions can be expressed as: (15a) (15b) (15c) (15d) (15e) Total settlement calculation of composite foundation for immersed tunnel: Using the method of separation of variables, the consolidation equation for layered composite foundations can be expressed as: (16) in, , , and All are undetermined coefficients; ; .

[0032] Based on the boundary conditions (15a)~(15c), we can obtain: (17a) (17b-c) In the formula: ; ; ( ); four elements , , and They can be represented as: ; Based on the boundary condition (15d), we can obtain information about... transcendental equations: (17d) In the formula: .

[0033] Undetermined coefficients The solution can be obtained from the initial condition (15e), which satisfies: (18) Based on the orthogonality of the characteristic functions, the undetermined coefficients It can be represented as: (19) Based on the above solution for excess pore pressure, the settlement expression can be derived as follows: (20) degree of consolidation U ( t This reflects the degree of dissipation of excess pore water pressure in the foundation and the development level of consolidation settlement, enabling a quantitative evaluation of the consolidation progress of the foundation at any given time. By calculating the average degree of consolidation of the reinforced zone, the underlying layer, and the entire structure separately, the deformation coordination relationship of each component in the pile-soil composite foundation during the consolidation process and its impact on overall deformation and bearing capacity can be further revealed. Based on the above settlement calculations, the specific calculation of the degree of consolidation is given as follows: (twenty one) in, S found ( t The sum of the solidification settlement of the reinforced area and the underlying layer at a certain moment is denoted as . S found,∞ This represents the final consolidation settlement between the reinforced area and the underlying layer.

[0034] Under the assumption of series deformation, the total settlement at the bottom of the tunnel Stot ( t This can be represented as: (twenty two) The verification process of this invention is as follows: 1. Verification of existing results: To verify the correctness and applicability of the proposed analytical solution for composite foundation consolidation, a typical composite foundation example was selected as a comparison object. The total thickness of the composite foundation is... H =10 m, pile length is 5 m, pile diameter is 0.5 m, soil permeability coefficient is k s =0.01 m / d, soil compression coefficient is m vs = 0.1MPa -1 Simultaneously satisfying the following relations: (twenty one) in, k vp The permeability coefficient of the pile body. m vp The compression coefficient of the pile body. λ The displacement rate is denoted as .

[0035] Figure 4 A schematic diagram comparing the degree of consolidation of the proposed solution with existing numerical and analytical solutions is shown. As can be seen from the diagram, the curve of the degree of consolidation calculated by the proposed solution with consolidation time is basically consistent with the variation patterns of existing numerical and analytical solutions. Both show a slow increase in the first 1 day of consolidation (i.e., 0-100 days), followed by a rapid increase in the degree of consolidation of the composite foundation within the consolidation time range (1-10 days), indicating that this stage is the critical period for foundation consolidation and settlement. After the consolidation time exceeds 10 days, the degree of consolidation approaches 100%. However, the consolidation rate of the proposed solution during the accelerated consolidation period is slightly higher than that of existing solutions, resulting in the 100% degree of consolidation being reached slightly earlier than in existing solutions. This is mainly due to the idealization of the pile-soil interaction, vertical drainage conditions, and layering parameters in the equivalent model of the composite foundation, which makes the equivalent consolidation coefficient slightly conservative and larger. However, this difference neither alters the dominant law of consolidation evolution nor introduces non-physical phenomena; in terms of amplitude, the error is generally controlled within the engineering allowable range, and it manifests as a safe-side estimate of "slightly faster consolidation". Considering the simplicity of the model assumptions, the convenience of parameter acquisition, and computational efficiency, this method, while ensuring a reasonable physical mechanism, can provide a computational means for consolidation settlement analysis of deep silt composite foundations that is both accurate and engineering-feasible, and has good engineering application value.

[0036] 2. Specific implementation verification: This case study uses a specific example of immersed tunnel foundation reinforcement for analysis. A detailed reinforcement diagram is shown below. Figure 5 As shown in Table 1, this paper discusses the effects of various complex working conditions on the cross-section of an immersed tunnel segment, analyzing its stress characteristics under normal operating conditions. The analysis focuses on the combination of the effects under the serviceability limit state and the ultimate limit state. The load conditions of a cross-river immersed tunnel, as shown in Table 1, are analyzed comprehensively. For the left and right bank sections, the analysis mainly considers the structural self-weight, the weight of the overburden, the possible ballast weight, buoyancy, and the possible traffic load within the tunnel. For the underwater immersed tunnel segment, the segment is significantly affected by the cyclic load of siltation and cleaning during operation; therefore, the scouring effect of silt on the top of the immersed tunnel is further considered in addition to the consideration of the onshore section. The calculation process refers to the "Design Standard for Immersed Tunnels" GB / T 51318-2019. By analyzing the complex stress conditions of the immersed tunnel, the most unfavorable internal force conditions and failure modes of the structure can be determined, providing important reference value for the optimized design of the immersed tunnel cross-section.

[0037] Table 1. Additional stress on the submerged tube foundation

[0038] According to the "Technical Specification for Building Foundation Treatment", the compression modulus of cement-soil mixing piles is (100-120). f cu ,assumed f cu If we take 1.2 MPa, then the compression modulus of the mixing pile is 120-144 MPa, and we take the average value of 132 MPa here.

[0039] The soil self-weight stress is related to the soil unit weight and depth. The soil unit weight is shown in Table 2.

[0040] Table 2 Soil weight

[0041] Figure 6This paper presents the distribution of consolidation settlement of the subgrade and composite foundation in different regions under a 54-year working condition (considered as a near-completely consolidated state) of an immersed tunnel, with varying distances from the longitudinal reinforcement from the left bank. The subgrade thickness is 2 m. As shown in the figure, under constant external loads and foundation conditions, the underlying subgrade exhibits the largest consolidation settlement, peaking at approximately 72 mm, occurring at about 170 m from the left bank. The settlement in the reinforced area is significantly reduced, with a maximum value of only about 11 mm, approximately one-seventh of the peak value of the underlying subgrade, indicating that pile-soil reinforcement can significantly reduce foundation consolidation settlement. Furthermore, based on the calculation results of this method, the compressive settlement of the subgrade under direct external loads is also given. Since it has been assumed that the subgrade itself does not undergo consolidation and that the load application can be considered instantaneous, the subgrade settlement remains essentially stable at a constant level after 54 years, with a maximum settlement of approximately 9.8 mm. The above results show that the calculation method proposed in this invention can not only reasonably distinguish and quantify the proportion of the subbase, reinforcement zone and underlying layer in the total settlement, but also reflect the settlement differences and spatial distribution characteristics of different areas. It has strong rationality and engineering applicability for the settlement prediction of deep silt composite foundation of immersed tunnel.

[0042] Figure 7 This diagram illustrates the overall settlement of the composite foundation and cushion layer under different foundation replacement ratios λ. According to the diagram, when the foundation replacement ratio is 0, the overall settlement of the foundation and cushion layer reaches 202 mm, significantly exceeding the 80 mm compression and opening limit of the GINA waterstop for the immersed tube joint. Therefore, foundation reinforcement becomes a necessary and correct choice. When the foundation replacement ratio is 0.1, the overall settlement decreases significantly, with the maximum settlement value dropping to 102 mm, half the value compared to the unreinforced state (i.e., λ = 0), representing a difference of 49.9%. As the foundation replacement ratio gradually increases, the reduction in the maximum overall settlement value also gradually decreases. When the foundation replacement ratio is 0.2 and 0.3, the difference in the maximum settlement is 6.09%; while when the foundation replacement ratio is 0.4 and 0.5, the difference further decreases to 2.25%. This indicates that when the foundation replacement ratio is between 0.4 and 0.5, the performance in improving foundation settlement is basically consistent, and from the perspective of economy and construction efficiency, it is recommended to choose a suitable replacement ratio within this range. Furthermore, the actual foundation replacement ratio in this project was 0.41, which falls precisely within this range. This further verifies the applicability and accuracy of this method when comprehensively considering both reinforced and unreinforced zones. Therefore, in application, this invention can also provide important guidance for foundation reinforcement design based on different foundation replacement ratios λ.

[0043] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, alterations, alterations, or substitutions made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for calculating consolidation settlement of composite foundations for immersed tunnels, characterized in that, include: Step 1: Based on the classical consolidation theory framework, construct idealized assumptions; Step 2, construct a layered foundation calculation model: divide the composite foundation of the immersed tunnel into a crushed stone cushion layer, a reinforcement zone and an underlying layer, perform layered settlement calculation, and solve the total settlement of the composite foundation of the immersed tunnel based on the layered settlement calculation results; The crushed stone cushion layer is located at the top, the immersed tunnel is supported on the crushed stone cushion layer, the reinforced area is below the crushed stone cushion layer, and the underlying layer is the natural soft soil layer below the reinforced area.

2. The method for calculating consolidation settlement of composite foundations for immersed tunnels according to claim 1, characterized in that, In step 1, the idealization assumptions include: In the composite foundation of the immersed tunnel, the soil and piles in each area are in a saturated state, with uniform and isotropic physical properties. The soil particles and pore water are incompressible, and the consolidation deformation is caused only by the deformation of the soil skeleton. The seepage process follows Darcy's law, the permeability coefficient and compressibility coefficient of each layer are constant, the soil between piles only undergoes vertical drainage, and the pile body is impermeable. The consolidation process assumes small deformation, and the stress-strain relationship follows a linear elastic constitutive model. The surface load is applied instantaneously and remains constant throughout the entire process; The crushed stone cushion layer is treated as an independent compressible unit and does not participate in the pore pressure consolidation solution. The total settlement is the sum of the settlements of each layer.

3. The method for calculating consolidation settlement of composite foundations for immersed tunnels according to claim 1, characterized in that, In step 2, when performing stratified settlement calculations, the following formula is used for the crushed stone cushion layer: ； in, H cush The thickness of the crushed stone subbase is... E cush For compressibility modulus, q c This represents the average additional stress experienced. This indicates the final compressive settlement of the crushed stone cushion layer.

4. The method for calculating consolidation settlement of composite foundations for immersed tunnels according to claim 1, characterized in that, In step 2, when performing layered settlement calculations, the reinforced area includes: Based on equilibrium conditions and the assumption of constant strain, we obtain: ； ； in, and These represent the average total stress in the soil and pile at any depth, respectively. The average excess pore pressure of the soil; The volumetric strain at any depth in the composite foundation; The average additional stress / total additional stress increment at any depth z; r c Where is the pile radius; r e The equivalent radius of influence; Soil compression modulus; The elastic modulus of the pile body can then be obtained: ； In the formula: The pile-soil modulus ratio, i.e. ; The pile replacement ratio is expressed as... ; The rate at which volumetric strain changes with time; The consolidation equation for vertical seepage within the soil is: ； In the formula: The specific gravity of water; The vertical permeability coefficient of the soil; Combining the above formulas, the consolidation governing equation for the reinforced zone is: ； in, This is the vertical consolidation coefficient of the soil.

5. The method for calculating consolidation settlement of composite foundations for immersed tunnels according to claim 1, characterized in that, In step 2, when performing layered settlement calculations, the underlying layer includes: The height of the lower layer is taken as The seepage flow of two typical soil units is analyzed, including the columnar soil seepage unit. The data were taken from the unreinforced soil within the area of ​​the bottom of the undrained piles, and from the annular soil seepage unit. The soil sample was taken from the unreinforced soil within the area of ​​the soil base around the ring pile. columnar soil seepage unit Without vertical seepage, the excess pore water pressure is dissipated only through radial seepage. Based on the relationship between the pore water outflow and the change in unit volume, the following two equations can be obtained: ； ； In the formula: and At any time columnar soil seepage unit and annular soil seepage unit volume, , ,in, and These are columnar soil seepage units. and annular soil seepage unit The base area; and They are respectively Columnar soil seepage unit Radial outflow and annular soil seepage unit Vertical outflow; The following relationship can be obtained: ； In the formula: , For thickness is The volume of the unit; ; Based on the relationship between the increase in effective stress and the decrease in unit volume, we obtain: ； In the formula: The excess pore water pressure at any depth in the underlying layer. The first in the lower layer The compression modulus of the soil layer; Based on Darcy's law of seepage, the following equation is obtained: ； Based on Darcy's law of seepage, the following equation is obtained: ； In the formula: The specific gravity of water; The vertical permeability coefficient of the soil; The equations obtained by simultaneously applying Darcy's law of seepage and Darcy's law of seepage are the consolidation governing equations for the underlying layer as follows: ； In the formula: is the vertical consolidation coefficient of the underlying soil layer.

6. A method for calculating consolidation settlement of composite foundations for immersed tunnels according to any one of claims 1-5, characterized in that, In step 2, the total settlement of the immersed tunnel composite foundation is calculated based on the layered settlement calculation results, including: Using the method of separation of variables, the consolidation equation of the layered (layered) calculation model for the composite foundation of immersed tunnels is expressed as: ； in, , , and All are undetermined coefficients; ; ; Based on the boundary conditions and initial conditions, we obtain: ； ； In the formula: ; ; ( ); four elements , , and They are represented as follows: ； Based on the boundary and initial conditions, we obtain information about transcendental equations: ； In the formula: ; Undetermined coefficients Solving based on the boundary and initial conditions, the following is satisfied: ； Based on the orthogonality of the characteristic functions, the undetermined coefficients Represented as: ； The settlement expression is derived as follows: The degree of consolidation is calculated as follows: ； in, S found ( t The sum of the solidification settlement of the reinforced area and the underlying layer at a certain moment is denoted as . S found,∞ This represents the final consolidation settlement between the reinforced area and the underlying layer. Total settlement at the bottom of the immersed tunnel S tot ( t ) is represented as: 。 7. The method for calculating consolidation settlement of composite foundations for immersed tunnels according to claim 6, characterized in that, Boundary and initial conditions include: ； ； ； ； 。

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