A structure and design method for combining an underpass tunnel and an overpass pier

Abstract

The present invention discloses a structure and design method for the combined construction of an underpass tunnel and an overpass pier. The underpass tunnel structure includes tunnel side walls, a tunnel floor, and a pile foundation; the overpass pier structure includes pier columns, pier bodies, caps, and pile foundations; wherein the overpass piers are rigidly connected to the tunnel, and the pier bodies and caps of the overpass piers are integrally cast with the tunnel floor; a composite pile foundation is provided under the tunnel floor. A thickening layer is integrally provided at the bottom of the tunnel floor corresponding to the overpass pier area; a transition connection of no more than 45° is made between the thickened layer of the tunnel floor and the tunnel floor. While meeting its bearing capacity and deformation control standards, the present invention reduces differential settlement, lowers the internal forces of the tunnel floor and the secondary internal forces of the upper structure through the concept of variable stiffness leveling, thereby increasing the service life of the building and ensuring normal use functions. This achieves a reasonable setting of the lower tunnel construction limit and the overpass piers, improves the comprehensive utilization efficiency of urban space, and saves resources.

Description

Technical Field

[0001] The present invention belongs to the field of civil engineering technology, and in particular relates to a structure combining an underpass tunnel and an overpass pier. The structure adopts a composite pile foundation, takes into account that the piles and the soil between the piles directly bear the load, coordinates the deformation of the piles and the soil between the piles, and adopts the concept of variable stiffness leveling to reduce differential deformation and optimize the internal force of the structure while meeting the bearing capacity and deformation control standards. Background Art

[0002] During construction, due to land use, line orientation, and structural layout, intersection nodes appear between the underpass and the upper bridge piers. The upper bridge piers need to fall onto the underpass tunnel floor. If the two structural types are designed separately, this will affect the planar orientation and cross-sectional layout of the tunnel, increasing the difficulty of design and construction. Secondly, if expansion joints are set locally on the tunnel floor to reserve construction space for the upper bridge, allowing the two to be constructed separately, the different load types will result in different and significant settlements. This differential settlement will cause water leakage at this node during operation, and the foundation soil under the tunnel floor will seep into the tunnel, reducing the foundation bearing capacity and affecting driving safety in the tunnel.

[0003] Traditional pile foundation theory generally doesn't consider the soil between piles as directly contributing to the load, placing the entire load on the piles. This is due to a lack of knowledge about how to assess the conditions under which the piles and soil between piles can directly bear the load, or how to determine the proportion of load shared by the piles and soil. Instead, the soil between piles is considered merely a safety reserve for the load. Traditionally, pile length design relies on estimating foundation settlement while maintaining the foundation's bearing capacity. This is often based on empirical analysis, based on whether the pile tip penetrates a specific bearing stratum. However, pile lengths are often conservative and lack quantitative analysis, leading to unnecessary waste.

[0004] The settlement and deformation distribution of the tunnel floor with uniformly distributed piles exhibits a distinct butterfly-shaped distribution. This butterfly-shaped settlement of the tunnel floor induces additional bending and shear forces within the tunnel floor and the superstructure, and can even cause cracking. Furthermore, as the load and structural stiffness increase, the difference between the reaction forces of the center and side piles gradually increases, forming a distinct saddle-shaped distribution. This negative effect leads to an increase in the overall bending moment of the tunnel floor. Summary of the Invention

[0005] Based on this, according to one embodiment of the present invention, its purpose is to provide a structure and design method for the combined construction of an underpass tunnel and an upper span pier. For the upper span piers that fall into the tunnel floor, a combined structure is adopted in which the upper span piers are rigidly connected to the tunnel, and the pier body and the pedestal are integrally cast with the tunnel floor. A composite pile foundation is used under the tunnel floor. Considering that the piles and the soil between the piles directly bear the load together, the deformation coordination of the piles and the soil between the piles is used. Under the premise of meeting the bearing capacity and deformation control standards, the concept of variable stiffness leveling is used to reduce differential settlement, reduce the internal force of the tunnel floor and the secondary internal force of the upper structure. This saves resources, reduces the overall cost of the project, increases the service life of the building, and ensures normal use functions.

[0006] In order to achieve the above-mentioned purpose, the present invention provides a structure in which an underpass tunnel and an overpass pier are built together. The underpass tunnel structure includes tunnel side walls, a tunnel floor and a pile foundation.

[0007] The upper span pier structure includes pier columns, pier bodies, caps and pile foundations;

[0008] The upper bridge pier is rigidly connected to the tunnel, and the pier body and the cap of the upper bridge pier are integrally cast with the tunnel floor;

[0009] Composite pile foundations are set under the tunnel floor.

[0010] Furthermore, a thickening layer is integrally provided at the bottom of the tunnel floor corresponding to the upper bridge pier area; a transition connection is made between the tunnel floor thickening layer and the tunnel floor at an angle not greater than 45°.

[0011] Furthermore, transverse expansion joints are installed along the longitudinal direction of the tunnel. These expansion joints are 15-25mm wide to limit the impact of the combined structure on the remaining tunnel sections. The rigid spacer length (L) equals the tunnel floor width + 400mm, meaning each side extends 200mm beyond the tunnel edge. The rigid spacer is 1000mm wide and 500mm high.

[0012] Furthermore, a rigid pad is provided under the transverse deformation joint.

[0013] Furthermore, the length L of the rigid pad is equal to the tunnel floor width + 400 mm; the width of the rigid pad is 1000 mm and the height is 500 mm.

[0014] To achieve the above-mentioned object, the design method of the combined structure of the underpass tunnel and the overpass pier of the present invention comprises the following steps:

[0015] (1) Determine the type of piles under the tunnel floor, pile length l, and pile diameter d based on the design loads of the underpass and overpass piers, site engineering geological and hydrological conditions, tunnel cross-sectional dimensions and burial depth, and overpass pier type;

[0016] (2) Determine the characteristic value Ra of the vertical bearing capacity of each pile based on the pile length l and pile diameter d;

[0017] The characteristic value Ra of the vertical bearing capacity of a single pile is estimated according to the following formula:

[0018]

[0019] Where: u is the circumference of the pile (m); q sik is the ultimate lateral resistance of the i-th layer of soil around the pile (kPa); li is the thickness of the i-th layer of soil around the pile (m); α is the pile tip resistance correction coefficient; p sk is the pile tip resistance (kPa); Ap is the pile tip area (m2).

[0020] (3) Considering that a certain proportion of the natural foundation bearing capacity is first utilized, and the insufficient part is supplemented by the bearing capacity of the piles, the number of piles n in the composite pile foundation is determined by the following formula:

[0021]

[0022] Where: n is the number of piles in the composite pile foundation; F k is the vertical force acting on the top surface of the tunnel floor corresponding to the standard combination of load effects (kN); Gk is the standard value of the self-weight of the tunnel structure and the self-weight of the bridge structure above the tunnel floor (kN); Qca is the standard value of the load borne by the soil between the piles under the foundation (kN); α is the utilization rate of the bearing capacity of the pile foundation soil under the tunnel floor, which can be taken as 0.4~0.5; Rai is the characteristic value of the vertical bearing capacity of a single pile in the composite pile foundation (kN).

[0023] (4) Build a three-dimensional finite element model and mesh the joint model. The foundation soil and pile subsoil are simulated as a series of independent springs. The design load and springs act on the unit nodes, and the internal force and deformation are calculated using a finite element analysis program.

[0024] (5) Determine the static side pressure σ of the tunnel side wall based on the tunnel side overload q, tunnel floor depth H and groundwater level h i .

[0025] The static side pressure of the tunnel side wall is calculated according to the geological survey report as follows:

[0026]

[0027] Where: σ i is the static earth pressure at the calculation point (kPa); γ j is the effective density of the j-th layer of soil above the calculation point (kN / m3); Hj is the thickness of the j-th layer of soil above the calculation point (m); q is the tunnel side surload (kPa); Ki is the static earth pressure coefficient at the calculation point; ui is the water pressure at the calculation point (kPa).

[0028] (6) According to the tunnel floor burial depth H and the groundwater level h, determine the tunnel floor water buoyancy uf:

[0029] u f =γ w (Hh) (4)

[0030] Where: γ w It is the density of water, generally taken as 10kN / m3.

[0031] (7) The resistance coefficient ks of the foundation soil at the bottom of the tunnel floor is as follows:

[0032]

[0033] Where: k s is the foundation resistance coefficient (kN / m3); E0 is the deformation modulus of the foundation soil (kPa); A is the bottom area of ​​the tunnel floor; μ0 is the Poisson's ratio of the foundation soil; I0 is the coefficient that reflects the foundation shape and stiffness, which can be taken as 0.866.

[0034] (8) Pile end soil resistance coefficient k b Press the formula:

[0035]

[0036] Where: k b is the soil resistance coefficient at the pile end (kN / m3); E is the soil deformation modulus (kPa); d is the pile diameter; μ is the Poisson's ratio of the foundation soil; ω is the settlement influence coefficient.

[0037] Furthermore, under the action of load, the composite pile foundation is borne jointly by the piles and the soil between the piles. In the design, the pile top load Qi of the i-th pile in the composite pile foundation shall not be greater than the corresponding single pile vertical bearing capacity characteristic value Rai.

[0038] Q i ≤R ai (7)

[0039] Furthermore, the calculated settlement is within the design controlled settlement range, and the settlement Ss of the top surface of the soil between the tunnel floor piles and the settlement of the pile top Sp shall not be greater than the design controlled settlement S0.

[0040] That is s s ≤s0 and s p ≤s0(8)

[0041] Furthermore, the maximum differential settlement is calculated to be within the allowable range, the maximum differential settlement Δs max Not greater than [Δs max ].

[0042] That is, Δsmax ≤[Δs max ](9)

[0043] Where: The maximum allowable differential settlement [Δs max ]=0.002L0, L0 is the horizontal distance between the two measuring points.

[0044] Furthermore, considering that the piles and the soil between the piles directly bear the load together, the vertical support stiffness distribution of the foundation piles under the tunnel floor is adjusted by coordinating the deformation of the piles and the soil between the piles, that is, by adjusting the pile length l, pile diameter d and pile spacing S of the composite pile foundation, so as to minimize the differential settlement of the tunnel floor, significantly reduce the internal force of the tunnel floor structure, and effectively reduce the internal force of the tunnel floor. The design differential settlement of the tunnel floor is determined by the following formula:

[0045]

[0046] Where: s pi is the pile top settlement in the i-th calculation (mm); s si is the settlement of the top surface of the soil between piles in the i-th calculation (mm); s pi -1 is the pile top settlement in the i-1th calculation (mm); s si-1 is the settlement of the top surface of the soil between piles in the i-1th calculation (mm); Δ is the differential settlement control standard, which can be taken as 0.01~0.05.

[0047] When an intersection node appears between the underpass tunnel and the upper span pier during construction, the present invention uses the upper span pier, pier body, and pedestal to be rigidly connected to the tunnel floor for the upper span pier that falls into the tunnel floor, and the structure is cast as a whole. The tunnel floor serves as both the pier body and pedestal of the upper span pier and as part of the tunnel structure. A composite pile foundation is used under the tunnel floor, taking into account that the piles and the soil between the piles directly bear the load. Through the deformation coordination of the piles and the soil between the piles, under the premise of meeting the bearing capacity and deformation control standards, the concept of variable stiffness leveling is used to reduce differential settlement, reduce the internal forces of the tunnel floor and the secondary internal forces of the upper structure, improve the service life of the building, and ensure normal use function. In this way, the reasonable setting of the lower tunnel construction limit and the upper span pier is achieved, the comprehensive utilization efficiency of urban space is improved, resources are saved, the comprehensive development needs of large-scale transportation hubs in urban roads are met, and the overall cost of the project is reduced. It provides a reliable guarantee for the utilization of underground space in large-scale transportation hubs and has good promotion potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of the plan layout of the combined structure of the underpass tunnel and the overpass pier in one embodiment of the present invention;

[0049] Figure 2 for Figure 1Schematic diagram of the middle AA section;

[0050] Figure 3 This is a schematic cross-sectional view of the upper bridge pier;

[0051] Figure 4 for Figure 1 Schematic diagram of the middle BB section;

[0052] Figure 5 Detailed diagram of the deformation joint node of the combined structure of the underpass tunnel and the overpass pier in one embodiment of the present invention;

[0053] Figure 6 Detailed drawing of the rigid pads of the combined structure of the underpass tunnel and the overpass pier in one embodiment of the present invention;

[0054] Figure 7 The figure is a flow chart of a design method for a combined structure of an underpass tunnel and an overpass pier in one embodiment of the present invention. DETAILED DESCRIPTION

[0055] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0056] In the description of the present invention, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention.

[0057] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the technical features being referred to. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, "plurality" means two or more.

[0058] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood broadly. For example, they may refer to fixed connections, detachable connections, or integral connections; they may refer to direct connections, indirect connections through an intermediary, or internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0059] In one embodiment of the present invention, in a structure where an underpass tunnel and an overpass pier are built together, the underpass tunnel structure includes tunnel side walls, a tunnel floor, and a pile foundation. The overpass pier structure includes pier columns, pier bodies, caps, and pile foundations.

[0060] Figures 1 to 4 The following schematically shows a structure of an underpass tunnel and an overpass pier provided in one embodiment. Figures 1 to 4 As shown, the embodiment provides a structure of an underpass tunnel and an upper span pier, including an underpass tunnel structure and an upper span pier structure. The upper span pier that falls into the tunnel floor is rigidly connected to the tunnel, and the pier body and the pedestal are integrally cast with the tunnel floor. A composite pile foundation is used under the tunnel floor. Considering that the piles and the soil between the piles directly bear the load, the deformation coordination of the piles and the soil between the piles is used. Under the premise of meeting the bearing capacity and deformation control standards, the concept of variable stiffness leveling is used to reduce differential settlement, reduce the internal force of the tunnel floor and the secondary internal force of the upper structure. This saves resources, reduces the overall cost of the project, increases the service life of the building, and ensures normal use functions.

[0061] Specifically, if Figure 2 As shown, the underpass tunnel includes: tunnel side walls 11 , tunnel floor 12 and pile foundation 13 .

[0062] Specifically, if Figure 3 As shown, the upper bridge pier includes: a pier column 21, a cap 22 and a pile foundation 23.

[0063] Figure 4 The schematic diagram shows the structure of the underpass tunnel and the overpass pier, which includes tunnel side walls 31, tunnel floors 32-34, bridge piers 35, and composite pile foundations 36 under the tunnel floors.

[0064] Specifically, the Figure 2 The tunnel floor 12 and Figure 3 The upper pier column 21 and the cap 22 are integrally cast and rigidly connected. The tunnel floor in the upper pier area is locally reinforced, that is, within the range of not less than 2.5D+0.5m (D is the diameter of the pile foundation in the upper pier area, unit m) of the joint center line, the local thickening of the tunnel floor is not less than 1.0H, forming Figure 4 The joint construction structure 34. Figure 4 The unthickened portion 32 of the middle tunnel floor and the thickened portion 34 of the tunnel floor are transitionally connected 33 at the bottom of the tunnel floor at an angle of no more than 45° to the horizontal line.

[0065] Specifically, if Figure 1 、 Figure 5As shown, a transverse deformation joint 38 is set along the tunnel cross section at the positions of the tunnel floor 12 and the tunnel floor 32 along the longitudinal direction of the tunnel. The width of the deformation joint is 20 mm to control the influence of the combined structure on the remaining tunnel sections.

[0066] Specifically, if Figure 1 、 Figure 6 As shown, by providing rigid pads 39 under the tunnel floor 12, transverse deformation joints 38, and tunnel floor 32, the differential settlement between the combined structure and the remaining tunnel sections is controlled. The length L of the rigid pads 39 is equal to the width of the tunnel floor + 400 mm, i.e., each side extends 200 mm beyond the tunnel edge. The rigid pads are 1000 mm wide and 500 mm high.

[0067] Figure 7 The schematic diagram shows the design process of the combined structure of the underpass tunnel and the overpass pier in one embodiment. Figure 7 As shown in FIG, the design method of the combined structure of the underpass tunnel and the overpass pier includes the following steps:

[0068] Step S10, determining the type of pile under the tunnel floor, pile length l, and pile diameter d based on the design load of the underpass and overpass piers, site engineering geological conditions and hydrological conditions, tunnel cross-sectional dimensions and burial depth, and overpass pier type;

[0069] Step S20, determining the vertical bearing capacity characteristic value Ra of each foundation pile based on the pile length l and the pile diameter d;

[0070]

[0071] In step S30, a certain proportion of the natural foundation bearing capacity is first utilized, and the insufficient part is supplemented by the bearing capacity of the piles. The number of piles n in the composite pile foundation is determined as follows:

[0072]

[0073] Step S40: Build a three-dimensional finite element model. Mesh the combined node model. Simulate the foundation soil and pile subsoil as a series of independent springs. Apply design loads and springs to the unit nodes, and calculate internal forces and deformations using a finite element analysis program.

[0074] Step S50: Determine the static side pressure σ of the tunnel side wall according to the tunnel side overload q, the tunnel floor depth H and the groundwater level h. i .

[0075]

[0076] Step S60: First, determine the tunnel floor water buoyancy uf according to the tunnel floor burial depth H and the groundwater level h:

[0077] uf =γ w (Hh) (4)

[0078] Then calculate the resistance coefficient ks of the foundation soil at the bottom of the tunnel floor according to the following formula:

[0079]

[0080] Calculate the soil resistance coefficient k at the pile end according to the following formula: b :

[0081]

[0082] Step S70: Verify the bearing capacity of a single pile in the pile foundation. In the design, the pile top load Qi of the i-th pile in the composite pile foundation shall not be greater than the corresponding single pile vertical bearing capacity characteristic value Rai.

[0083] Q i ≤R ai (7)

[0084] Step S80, first verify the calculated settlement to make it within the design control settlement range, that is, the settlement Ss of the top surface of the soil between the tunnel floor piles and the settlement Sp of the pile top shall not be greater than the design control settlement S0.

[0085] s s ≤s0 and s p ≤s0(8)

[0086] Then check that the maximum differential settlement is within the allowable range, i.e. the maximum differential settlement Δs max Not greater than [Δs max ].

[0087] Δs max ≤[Δs max ] (9)

[0088] Finally, by adjusting the pile length l, pile diameter d, and pile spacing S of the composite pile foundation, the design differential settlement of the tunnel floor satisfies the following requirements:

[0089]

[0090] The description of the present invention has been presented for purposes of illustration and description and is not intended to be exhaustive or to limit the invention to the form disclosed. Many modifications and variations will be apparent to those skilled in the art. The embodiments were chosen and described in order to better illustrate the principles of the invention and its practical application and to enable those skilled in the art to understand the invention and design various embodiments with various modifications as are suited for specific applications.

[0091] In the description of this specification, specific features, structures, materials or characteristics may be combined in an appropriate manner in any one or more embodiments or examples.

[0092] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A design method for a structure combining an underpass tunnel and an overpass pier, characterized in that: The underpass tunnel structure includes tunnel side walls, tunnel floor and pile foundation; The upper span pier structure includes pier columns, pier bodies, caps and pile foundations; The upper bridge pier is rigidly connected to the tunnel, and the pier body and the cap of the upper bridge pier are integrally cast with the tunnel floor; Composite pile foundations are set under the tunnel floor; The design method comprises the following steps: (1) Determine the type of piles under the tunnel floor, pile length l, and pile diameter d based on the design loads of the underpass and overpass piers, site engineering geological and hydrological conditions, tunnel cross-sectional dimensions and burial depth, and overpass pier type; (2) According to the pile length l and pile diameter d, determine the characteristic value R of the vertical bearing capacity of each pile a ; Characteristic value of vertical bearing capacity of single pile R a Estimate according to the following formula: Where: K is the safety factor; u is the circumference of the pile (m); q sik is the ultimate lateral resistance of the i-th layer of soil around the pile (kPa); l i is the thickness of the i-th layer of soil around the pile (m); α is the pile tip resistance correction coefficient; p sk is the pile tip resistance (kPa); A p is the pile tip area (m 2 ); (3) The number of piles n in a composite pile foundation is determined by the following formula: Where: n is the number of piles in the composite pile foundation; F k is the vertical force acting on the top surface of the tunnel floor corresponding to the standard combination of load effects (kN); G k is the standard value of the deadweight of the tunnel structure and the deadweight of the bridge structure above the tunnel floor (kN); Q ca is the standard value of the load borne by the soil between piles under the foundation (kN); α is the utilization rate of the bearing capacity of the pile foundation soil under the tunnel floor, which can be taken as 0.4~0.5; R ai is the characteristic value of the vertical bearing capacity of a single pile in a composite pile foundation (kN); (4) Establish a three-dimensional finite element model, mesh the joint node model, and simulate the foundation soil and pile subsoil as a series of independent springs; design loads and springs to act on the unit nodes, and use the finite element analysis program to calculate the internal force and deformation; (5) Determine the static side pressure σ of the tunnel side wall based on the tunnel side overload q, tunnel floor depth H and groundwater level h i ; The static side pressure of the tunnel side wall is calculated according to the geological survey report as follows: Where: σ i is the static earth pressure at the calculation point (kPa); γ j is the effective density of the jth layer of soil above the calculation point (kN / m 3 );H j is the thickness of the jth layer of soil above the calculation point (m); q is the tunnel side surcharge (kPa); K i is the static earth pressure coefficient at the calculation point; u i is the water pressure at the calculation point (kPa); (6) Determine the water buoyancy u of the tunnel floor based on the tunnel floor depth H and the groundwater level h f : u f =γ w (H-h)(4) Where: γ w is the density of water, generally 10kN / m 3 ; (7) Resistance coefficient k of the foundation soil at the bottom of the tunnel floor s Press the formula: Where: k s is the foundation resistance coefficient (kN / m 3 ); E0 is the deformation modulus of the foundation soil (kPa); A is the bottom area of ​​the tunnel floor; μ0 is the Poisson's ratio of the foundation soil; I0 is the coefficient that reflects the shape and stiffness of the foundation, which is taken as 0.866; (8) Pile end soil resistance coefficient k b Press the formula: Where: k b is the soil resistance coefficient at the pile end (kN / m 3 ); E is the soil deformation modulus (kPa); d is the pile diameter; μ is the Poisson's ratio of the foundation soil; ω is the settlement influence coefficient.

2. The design method of a combined structure of an underpass tunnel and an overpass pier according to claim 1 is characterized in that When a composite pile foundation is under load, the load is borne by the pile and the soil between the piles. The top load of the i-th pile in the composite pile foundation is Q i shall not be greater than the corresponding single pile vertical bearing capacity characteristic value R ai ; Q i ≤R ai (7).

3. The design method of a combined structure of an underpass tunnel and an overpass pier according to claim 1 is characterized in that: Calculate the settlement. If the settlement is within the design control range, the settlement S of the top surface of the soil between the tunnel floor piles is: s , pile top settlement S p It shall not be greater than the design controlled settlement S0; That is s s ≤s0 and s p ≤s0(8).

4. The design method of a combined structure of an underpass tunnel and an overpass pier according to claim 1 is characterized in that: Calculate the maximum differential settlement within the allowable range, the maximum differential settlement Δs max Not greater than [Δs max ]; That is, Δs max ≤ [Δs max (9) Where: The maximum allowable differential settlement [Δs max ]=0.002L0, L0 is the horizontal distance between the two measuring points.

5. The design method of a combined structure of an underpass tunnel and an overpass pier according to claim 1 is characterized in that: The design differential settlement of the tunnel floor is determined by the following formula: Where: s pi is the pile top settlement in the i-th calculation (mm); s si is the settlement of the top surface of the soil between piles in the i-th calculation (mm); s pi-1 is the pile top settlement in the i-1th calculation (mm); s si-1 is the settlement of the top surface of the soil between piles in the i-1th calculation (mm); Δ is the differential settlement control standard, which can be taken as 0.01~0.05.

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