Foundation pit soil pressure calculation method considering stress transfer of adjacent existing underground structure

Abstract

The invention discloses a foundation pit soil pressure calculation method considering stress transfer of a proximity existing underground structure, which comprises the following steps of: firstly, collecting relevant stratum parameters as basic parameters according to an actual engineering project; then position parameters of an existing structure and a newly-built foundation pit are determined, a foundation pit construction stratum fracture surface is determined, additional stress transmitted by the existing structure is calculated, and collected relevant stratum parameters and corresponding soil slip surface fracture angles, internal friction angles and the like need to be utilized in the process. Then deducing a calculation formula of the soil pressure through a thin-layer unit method, and finally calculating the soil pressure by utilizing the deduced calculation formula.

Description

Technical Field

[0001] The invention relates to the technical field of foundation pit support, and in particular to a method for calculating soil pressure of a foundation pit close to stress transmission of an existing underground structure. Background Art

[0002] With the acceleration of urbanization, the development and utilization of underground projects are increasing, and the construction environment is relatively complex. Open excavation projects have become an important part of foundation and underground project construction. In the process of excavation of adjacent lateral open excavation pits, there will be a form of considering the influence of additional stress of existing structures. The soil pressure becomes complicated, which will be related to the safety of the foundation pit itself, the safety of adjacent buildings and the normal operation of nearby traffic. Soil pressure is the basis for evaluating safety. Patent CN113128061A discloses a "method for obtaining soil pressure of adjacent underground projects in asynchronous construction". It gives a method for obtaining soil pressure of adjacent underground projects in asynchronous construction, but does not consider the influence of additional stress of existing structures, which is different from the actual situation. Therefore, the calculation of soil pressure of adjacent lateral open excavation pits is particularly important, especially considering the influence of additional stress of existing structures on the newly built foundation pit during the excavation of the foundation pit. Summary of the invention

[0003] In order to solve the above-mentioned technical problems, the present invention provides a complete set of technical solutions, which is a method for calculating the soil pressure of a foundation pit close to the stress transmission of an existing underground structure. During the excavation of the foundation pit, when there is a certain distance between the existing station and the retaining structure, when the failure mode is the failure mode of the present invention, the force on the retaining structure will be affected by the existing structure. During the excavation of the foundation pit, the force on the retaining structure must take into account the influence of the additional stress generated by the existing structure. According to this failure mode, the formula for calculating the soil pressure is derived, thereby obtaining the corresponding soil pressure.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0005] The present invention proposes a method for calculating the earth pressure of a foundation pit taking into account the stress transfer of the adjacent existing underground structure, as follows:

[0006] Step 1: Obtain formation parameters;

[0007] Step 2: Obtaining the position parameters of the existing structure and the newly built foundation pit structure;

[0008] Step 3: Determine the fracture surface of the foundation pit construction stratum and each sliding block according to the location parameters of the existing structure and the newly built foundation pit structure;

[0009] Step 4 determines the additional stress transmitted by the existing structure;

[0010] Step 5: Calculate the earth pressure of each sliding block.

[0011] As a further technical solution, in step 3, the method for determining the fracture surface of the foundation pit construction stratum is as follows:

[0012] The failure angle of soil sliding generated when the station is destroyed, θ, and the distance from the ground to the upper surface of the station, h j , station height h0, distance from the lower surface of the station to the bottom of the pile h s , the horizontal distance b from the left edge of the station to the right edge of the pile is taken as the basis. When it meets When the conditions are met, the fracture surface of the stratum produced during foundation pit construction is determined; is the soil friction angle.

[0013] As a further technical solution, three sliding blocks are determined according to the fracture surface of the foundation pit construction stratum. The first sliding body is the sliding body at the top of the existing structure; the second sliding body is the sliding body formed by the side of the existing structure and the side of the newly built foundation pit; the third sliding body is the sliding body at the bottom of the existing structure.

[0014] As a further technical solution, the sliding surface of the first sliding body is a point on the upper part of the existing structure extending to the ground surface along a destruction angle θ.

[0015] As a further technical solution, the sliding surface of the third sliding body is formed from the bottom of the retaining pile along the rupture angle θ to a point at the lower part of the existing structure.

[0016] As a further technical solution, in step 4, the existing structure transfers additional stress as follows:

[0017]

[0018] Among them, β1 is the stress loss rate of the foundation pit retaining structure, K0 is the static earth pressure coefficient is the internal friction angle, γ is the weight of the soil, f is the distance from the center of the foundation pit to the center of the existing station, B1 is the width of the new foundation pit, μ is the Poisson's ratio of the soil, d is the excavation depth of the foundation pit, τ is the shear stress, and L is the length of the foundation pit; Among them, the coordinates of a point in the foundation pit are (f, y0, z0).

[0019] As a further technical solution, the reaction force caused by the additional stress transmitted by the existing structure is: F1 = K x w; among them, K x is the spring stiffness, β2 is the characteristic coefficient; A1, B2, C1, D1 are the correlation coefficients of the general solution of this fourth-order constant coefficient non-homogeneous linear equation; σ c is the additional stress;

[0020] As a further technical solution, the soil pressure σ1 of the first sliding body is:

[0021]

[0022] Among them: when z=0, σ Z =q, we obtain m1. K a is the Rankine active earth pressure coefficient q is the ground overload, b is the horizontal distance from the left edge of the station to the right edge of the pile, hj is the distance from the ground to the upper surface of the station, θ is the failure angle of the soil sliding surface, z is the soil depth, and the value range of z is 0~h j , γ is the soil weight,

[0023]

[0024]

[0025] As a further technical solution, the earth pressure σ2 of the second sliding body is:

[0026]

[0027] in,

[0028]

[0029] K a is the Rankine active earth pressure coefficient z is the soil depth, and the value range of Z is h j ~h j +h0+h s -btanθ; γ is the weight of soil, F1 is the foundation reaction force generated by the additional stress of the existing structure F1=K x w, the interface friction angle between soil and surrounding structure δ1, the interface friction angle between soil and existing station δ2, b is the horizontal distance from the left edge of the station to the right edge of the pile, and h is the distance from the ground to the upper surface of the station. j , the failure angle θ of the soil slip surface.

[0030] As a further technical solution, the earth pressure σ3 of the third sliding body is:

[0031]

[0032] in,

[0033]

[0034] K a is the Rankine active earth pressure coefficient H is the depth of the foundation pit, P is the distance from the bottom of the foundation pit to the bottom of the pile, z is the depth of the soil, and the value range of z is h j +h0+h s -btanθ~h j +h0+h s ; γ is the soil mass, b is the horizontal distance from the left edge of the station to the right edge of the pile, and h is the distance from the ground to the upper surface of the station j , the distance from the lower surface of the station to the bottom of the pile hs, and the failure angle of the soil sliding surface θ.

[0035] The present invention first collects relevant stratum parameters as basic parameters according to actual engineering projects. Then, the position parameters of the existing structure and the newly built foundation pit are determined, the stratum fracture surface of the foundation pit construction is determined, and the additional stress transmitted by the existing structure is calculated. In this process, the collected relevant stratum parameters and the corresponding soil sliding surface failure angle, internal friction angle, etc. are required. Then, the calculation formula of soil pressure is derived by the thin layer unit method, and finally the derived calculation formula is used to calculate the soil pressure.

[0036] Beneficial effects of the present invention:

[0037] The present invention can calculate the soil pressure and safety reserve of a certain point on the side wall of the newly built foundation pit support more specifically and accurately. In the past, calculations only considered the use of thin-layer units to calculate the soil pressure, and then obtained the stress of the retaining structure. The present invention considers the influence of additional stress on the existing structure caused by foundation pit excavation, so that the existing structure will produce corresponding foundation reaction force. On the basis of the calculation of the thin-layer unit method, the calculation of additional stress is added more finely. The key innovative step is to use the superposition operation of the two in the calculation step of the area affected by the existing structure. Different from the previous method that did not consider the influence of additional stress generated by the existing structure, the soil pressure of the newly built foundation pit is calculated more accurately than the existing technology, which is more in line with the actual stress situation and improves the safety of the newly built foundation pit. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of the overall technical solution;

[0039] Figure 2 It is the parameters of the existing structure and the newly built foundation pit structure;

[0040] Figure 3 It is a schematic diagram of the fracture surface of the stratum during foundation pit construction;

[0041] Figure 4 It is a schematic diagram of Mindlin solution under concentrated force;

[0042] Figure 5 It is a schematic diagram of the foundation pit construction stratum;

[0043] Figure 6It is a schematic diagram of the thin layer unit analysis model;

[0044] Figure 7 It is a schematic diagram of earth pressure calculation;

[0045] In the figure: 1. retaining structure, 2. new foundation pit, 3. existing structure, 4. soil, 5. sliding body ABCD, 6. ground overload, 7. sliding body BEG'C', 8. sliding body EFG, 9. supporting structure, 10. additional stress. DETAILED DESCRIPTION

[0046] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0047] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless otherwise explicitly stated in the present invention, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "include" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof;

[0048] In order to solve the above-mentioned technical problems, this embodiment provides a complete set of technical solutions to calculate the foundation pit soil pressure close to the stress transmission of the existing underground structure. First, according to the actual engineering project, collect relevant stratum parameters as basic parameters. Then determine the location parameters of the existing structure and the newly built foundation pit, determine the stratum rupture surface of the foundation pit construction, and calculate the additional stress transmitted by the existing structure. In this process, it is necessary to use the collected relevant stratum parameters and the corresponding soil sliding surface failure angle, internal friction angle, etc. Then, the calculation formula of soil pressure is derived through the thin layer unit method, and finally the derived calculation formula is used to calculate the soil pressure.

[0049] The schematic diagram of the specific overall technical solution is as follows Figure 1 As shown, the specific process is as follows:

[0050] Step 1: Collect formation parameters

[0051] Conduct geological surveys on the actual project site and collect relevant stratum parameters, including the internal friction angle of the stratum soil, the weight of the soil, etc.

[0052] Step 2: Determine the parameters of the existing structure and the new foundation pit structure

[0053] The parameters of the existing structure and the newly built foundation pit structure are as follows: Figure 2 As shown, the distance from the ground to the upper surface of the station is h j, station height h0, distance from the lower surface of the station to the bottom of the pile h s , horizontal distance b from the left edge of the station to the right edge of the pile, station length b s , foundation pit depth H, distance from the bottom of the foundation pit to the bottom of the pile P.

[0054] Step 3 Determine the fracture surface of the foundation pit construction stratum

[0055] The determination of the rupture surface is based on the soil sliding failure angle θ generated when the station is destroyed, where is the soil friction angle, and the distance from the ground to the upper surface of the station h j , station height h0, distance from the lower surface of the station to the bottom of the pile h s , the horizontal distance b from the left edge of the station to the right edge of the pile is taken as the basis. When When the conditions are met, the fracture surface of the stratum produced during the foundation pit construction is studied. A point on the upper part of the existing structure extends along the failure angle θ to the ground surface, forming a sliding surface of the sliding body ABCD (a trapezoid). The bottom of the retaining pile extends along the fracture angle θ to a point on the lower part of the existing structure, forming a sliding surface of the sliding body EFG. The sliding body BEG'C' must consider the influence of additional stress. The specific fracture surface is as follows Figure 3 The fracture surface of the stratum during foundation pit construction is shown.

[0056] Step 4 Determine the additional stress transferred by the existing structure

[0057] During the excavation of the foundation pit, the stress on the retaining structure will be affected by the additional stress generated by the existing structure. The additional stress of the existing structure will produce a certain foundation reaction force on the newly built foundation pit, and the soil pressure of the newly built foundation pit will be affected. Therefore, it is necessary to consider the additional stress generated by the existing structure, such as Figure 4 Schematic diagram of Mindlin solution under concentrated force. When the concentrated force acting at a point (0,0,-c) in the semi-infinite body is Pv, the additional principal stress at any point (x,y,z) in the semi-infinite body is:

[0058]

[0059] Based on the basic stress solution of horizontal unloading static earth pressure N = βK0γd and Mindlin load, R3 and R4 are the distances from point (B1 / 2, η, τ) and point (B1 / 2, η, -τ) to a point (f, y0, z0) on the foundation pit axis. β1 is the stress loss rate of the foundation pit retaining structure, which is based on the research of Jiang Zhaohua, and its value is β1 = 0.75. K0 is the static earth pressure coefficient is the internal friction angle, γ is the weight of the soil, the distance from the center of the foundation pit to the center of the existing station is f, the width of the new foundation pit is B1, μ is the Poisson's ratio of the soil, d is the excavation depth of the foundation pit, τ is the shear stress, L is the length of the foundation pit, and through integration, under the action of the unit force βK0γπdηdτ at a certain point (η,τ) on the side wall of the foundation pit near the existing station, the horizontal additional stress at a certain point (f,y0,z0) of the foundation pit is as follows:

[0060]

[0061] In the formula The relationship between station deflection and horizontal additional stress is expressed as follows:

[0062]

[0063] in:

[0064] E1 is the elastic modulus of the existing station (kN / m 2 ); I is the inertia moment of the existing station (m 4 ), w is the deflection of the existing station (m), K x E is the spring stiffness, which is an important parameter reflecting the interaction between soil and existing stations. w I is the horizontal bending stiffness of the retaining wall, h is the average vertical spacing of the supports, γ w is the weight of water. To further solve the problem, the formula can be rewritten as follows:

[0065]

[0066] To simplify the formula, let the parameters in the formula for Where β2 is the characteristic coefficient, and its dimension is m -1 , E1 is the elastic modulus of the existing station (kN / m 2 ), I is the inertia moment of the existing station (m 4 ), w is the deflection of the existing station (m), K x is the spring stiffness of each part, which is an important parameter reflecting the interaction between soil and existing stations. β2 is a comprehensive index related to the elastic properties of beams and foundations, which can affect the stress-strain characteristics of elastic foundation beams. A1B2C1D1 is the correlation coefficient of the general solution of this fourth-order constant coefficient non-homogeneous linear equation. After the characteristic coefficient is raised to the fourth power and inserted into the formula, the basic differential equation of the elastic foundation beam changes to the following form:

[0067]

[0068] The above equation is a fourth-order non-homogeneous linear equation with constant coefficients. By solving it, we can get its general solution:

[0069]

[0070] In summary, the foundation reaction force caused by the additional stress is:

[0071] F1=K x w

[0072] Step 5 Calculate earth pressure

[0073] Perform microelement analysis on the sliding body ABCD, such as Figure 5 , Figure 6 As shown, the internal friction angle of the soil is The density of the soil is γ, the thickness of the thin layer element is dz, the width of the upper surface of the thin layer element is bs, the interface friction angle between the soil and the surrounding structure is δ1, the interface friction angle between the soil and the existing station is δ2, and the vertical normal stress on the upper surface of the thin layer element is σ z , the vertical normal stress increment of the thin layer microelement surface σz+dσ, σ x1 and τ1 are the horizontal normal stress and shear stress of the enclosure structure on the thin layer microelement, and the shear stress value is σ x1 .tanδ1, T and τ are the normal stress and shear stress on the slip surface respectively, the shear stress value is τ=c+T·tanθ, c is the soil cohesion, the self-weight of the thin layer microelement is w, its value is γ.A, A2 is the microelement area, and q is the ground overload. K a is the Rankine active earth pressure coefficient. Figure 6 The stress characteristics of thin layer units, the horizontal equilibrium equation and the vertical equilibrium equation established by the thin layer unit method are:

[0074]

[0075] Where: x1 =K a σ z , T=a1σ z +a2, Lianlide: like Figure 5 For the ABCD analysis of the sliding body, the depth range of the sliding body ABCD is 0~h j , and its corresponding earth pressure σ1 is:

[0076]

[0077] Among them: when z=0, σ Z =q, we obtain m1. K a is the Rankine active earth pressure coefficient q is the ground overload, b is the horizontal distance from the left edge of the station to the right edge of the pile, and h is jis the distance from the ground to the upper surface of the station, θ is the failure angle of the soil slip surface, z is the depth of any point, γ is the weight of the soil, a1a2a3a4 are the process coefficients required in the calculation process, which are the same as above.

[0078] For the analysis of the sliding body BEG'C', the value range of Z is h j ~h j +h0+h s -btanθ, because the existing structure affects the soil sliding, the additional stress of the existing structure will affect the soil pressure of the new foundation pit, and the additional stress of the existing structure will cause the foundation reaction of the soil on one side of the retaining structure, so the sliding body BEG'C' should be calculated. The influence of the additional stress of the structure on the new foundation pit should be considered to calculate σ2:

[0079]

[0080] in:

[0081]

[0082] K a is the Rankine active earth pressure coefficient z is the soil depth, γ is the soil weight, F1 is the foundation reaction force generated by the additional stress of the existing structure F1 = K x w, the interface friction angle between soil and surrounding structure δ1, the interface friction angle between soil and existing station δ2, b is the horizontal distance from the left edge of the station to the right edge of the pile, and h is the distance from the ground to the upper surface of the station. j , the failure angle θ of the soil sliding surface, a1a2a3a4a5 are the process coefficients required in the calculation process.

[0083] For the EFG analysis of the sliding body, the value range of z is h j +h0+h s -btanθ~h j +h0+h s , the stress σ3 can be obtained as:

[0084]

[0085] in:

[0086]

[0087] K a is the Rankine active earth pressure coefficient H is the depth of the foundation pit, P is the distance from the bottom of the foundation pit to the bottom of the pile, z is the depth of the soil, γ is the weight of the soil, b is the horizontal distance from the left edge of the station to the right edge of the pile, and h is the distance from the ground to the upper surface of the station. j, the distance from the lower surface of the station to the bottom of the pile hs, the failure angle of the soil sliding surface θ, a1a2a3a4a5 are the process coefficients required in the calculation process, the same as above.

[0088] Example verification:

[0089] Take a certain project as an example. The existing station size is 120×20×15m, and the distance from the ground to the upper surface of the station is h. j＝ 13.14m, the distance from the left edge of the station to the right edge of the pile is b = 29.8m, the stratum is a silty clay layer with a Poisson's ratio of μ = 0.35, soil weight γ = 17kN / m3, foundation pit excavation height H = 40m, foundation pit length 150m, and foundation pit width 24m. The distance from the center of the foundation pit to the center of the existing station is f = 51.8m, the distance from the foundation pit to the bottom of the pile is P = 10m, the soil cohesion c = 8kPa, the failure angle of the soil sliding surface θ = 51°, the interface friction angle δ1 between the soil and the surrounding structure is 15°, and the internal friction angle There is no ground overload, the friction angle δ2 between the soil and the existing station is 20°, the stress loss rate of the foundation pit retaining structure is β1 = 0.75, the elastic modulus of the existing station is E1 = 2000MPa, and the moment of inertia of the existing station is I = 1×10 12 mm 4 , horizontal bending stiffness E of the enclosure wall w I=10000kN / m 2 , the average vertical spacing of supports is h = 8m, and the gravity of water is γ w =9.8kN / m3, calculated as follows Figure 7 Earth pressure calculation is shown.

[0090] The present invention determines that when a lateral open excavation pit is excavated near an underground structure, the fracture surface of the stratum for the foundation pit construction is determined, thereby analyzing the influence of additional stress generated by the existing structure, deriving the corresponding earth pressure formula based on the thin layer element method, and considering the foundation reaction force generated by the additional stress, the earth pressure of the corresponding stratum fracture surface for the foundation pit construction is calculated.

[0091] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the earth pressure of a foundation pit considering the stress transfer of an existing underground structure, characterized in that: as follows: Step 1: Obtain formation parameters; Step 2: Obtaining the position parameters of the existing structure and the newly built foundation pit structure; Step 3: Determine the rupture surface of the foundation pit construction stratum and three sliding blocks according to the position parameters of the existing structure and the newly built foundation pit structure, as well as the sliding failure angle; Step 4 determines the additional stress transmitted by the existing structure; Step 5: Calculate the earth pressure of each sliding block.

2. The method for calculating foundation pit earth pressure considering stress transfer of adjacent existing underground structures as claimed in claim 1, characterized in that: In step 3, the method for determining the fracture surface of the foundation pit construction stratum is as follows: The failure angle of soil sliding generated when the station is destroyed, θ, and the distance from the ground to the upper surface of the station, h j , station height h0, distance from the lower surface of the station to the bottom of the pile h s , the horizontal distance b from the left edge of the station to the right edge of the pile is taken as the basis. When it meets When the conditions are met, the fracture surface of the stratum produced during foundation pit construction is determined; is the internal friction angle of soil.

3. The method for calculating foundation pit earth pressure considering stress transfer of adjacent existing underground structures as claimed in claim 2 is characterized in that: According to the fracture surface of the foundation pit construction stratum, three sliding blocks are determined. The first sliding body is the sliding body at the top of the existing structure; the second sliding body is the sliding body formed between the side of the existing structure and the newly built foundation pit; the third sliding body is the sliding body at the bottom of the existing structure.

4. The method for calculating foundation pit earth pressure considering stress transfer of adjacent existing underground structures as claimed in claim 3 is characterized in that: The sliding surface of the first sliding body is a point on the upper part of the existing structure extending along the destruction angle θ to the ground surface.

5. The method for calculating foundation pit earth pressure considering stress transfer of adjacent existing underground structures as claimed in claim 3, characterized in that: The sliding surface of the third sliding body is formed from the bottom of the retaining pile along the rupture angle θ to a point at the lower part of the existing structure.

6. The method for calculating foundation pit earth pressure considering stress transfer of adjacent existing underground structures as claimed in claim 1, characterized in that: In step 4, the existing structure transfers additional stress as follows: Among them, β1 is the stress loss rate of the foundation pit retaining structure, K0 is the static earth pressure coefficient is the internal friction angle, γ is the weight of the soil, f is the distance from the center of the foundation pit to the center of the existing station, B1 is the width of the new foundation pit, μ is the Poisson's ratio of the soil, d is the excavation depth of the foundation pit, τ is the shear stress, and L is the length of the foundation pit; Among them, the coordinates of a point in the foundation pit are (f, y0, z0).

7. The method for calculating foundation pit earth pressure considering stress transfer of adjacent existing underground structures as claimed in claim 6, characterized in that: The reaction force caused by the additional stress transmitted by the existing structure is: F1 = K x w; among them, K x is the spring stiffness, β2 is the characteristic coefficient; A1, B2, C1, D1 are the correlation coefficients of the general solution of this fourth-order constant coefficient non-homogeneous linear equation; σ c For additional stress.

8. The method for calculating foundation pit earth pressure considering stress transfer of adjacent existing underground structures as claimed in claim 3, characterized in that: The earth pressure σ1 of the first sliding body is: Among them: when z=0, σ Z =q, we obtain m1. K a is the Rankine active earth pressure coefficient q is the ground overload, b is the horizontal distance from the left edge of the station to the right edge of the pile, hj is the distance from the ground to the upper surface of the station, θ is the failure angle of the soil sliding surface, z is the depth of any point, γ is the weight of the soil, 9. The method for calculating the earth pressure of a foundation pit considering the stress transfer of an existing underground structure adjacent to claim 3 is characterized in that: The earth pressure σ2 of the second sliding body is: in, K a is the Rankine active earth pressure coefficient z is the soil depth, and the value range of Z is h j ~h j +h0+h s -btanθ; γ is the weight of soil, F1 is the foundation reaction force generated by the additional stress of the existing structure F1=K x w, the interface friction angle between soil and surrounding structure δ1, the interface friction angle between soil and existing station δ2, b is the horizontal distance from the left edge of the station to the right edge of the pile, and h is the distance from the ground to the upper surface of the station. j , the failure angle θ of the soil slip surface.

10. The method for calculating foundation pit earth pressure considering stress transfer of adjacent existing underground structures as claimed in claim 3, characterized in that: The earth pressure σ3 of the third sliding body is: in, K a is the Rankine active earth pressure coefficient H is the depth of the foundation pit, P is the distance from the bottom of the foundation pit to the bottom of the pile, and z is the depth of the soil, with a range of h j +h0+h s -btanθ~h j +h0+h s ; γ is the soil weight; b is the horizontal distance from the left edge of the station to the right edge of the pile, h j is the distance from the ground to the upper surface of the station, hs is the distance from the lower surface of the station to the bottom of the pile, and θ is the failure angle of the soil sliding surface.

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