Calculation method of earth pressure based on soil support structure with limited width

Abstract

The present invention relates to a soil pressure calculation method based on a soil support structure of limited width, characterized in that it includes: obtaining inherent data of the soil and the support structure, the inherent data at least including soil width, soil weight, internal friction angle, additional load, and support structure height; dividing the soil into zones according to the shape of the horizontal differential unit body of the soil, the soil at least including a first zone and a second zone; determining the height of the first zone and the height of the second zone for soil pressure calculation in different zones; determining the soil pressure strength of the horizontal differential unit body of each zone, and determining the soil pressure of the soil according to the soil pressure strength. The present invention performs zone calculation of soil pressure according to the different zone divisions of the soil of limited width, obtains the soil pressure strength of the support structure according to the horizontal differential unit body, and the method is simple and practical.

Description

Technical Field

[0001] The invention relates to the technical field of earth pressure in civil engineering, and more specifically to an earth pressure calculation method based on a soil support structure with limited width. Background Art

[0002] In the construction of urban infrastructure, due to the limited urban space or the surrounding environment, it is often necessary to use a limited width soil support structure to ensure the stability, safety and economy of the project. The traditional classical earth pressure theory is only applicable to the calculation of earth pressure of infinite width soil support structures, so there is a lack of reasonable and effective calculation methods to assist in the design of support structures. The design of the support structure is closely related to the calculation of earth pressure. Accurate calculation of the earth pressure acting on the retaining wall is of great significance to the design safety of the retaining wall and saving of building materials. Summary of the invention

[0003] To address the above-mentioned deficiencies, the present invention provides a soil pressure calculation method based on a soil support structure with limited width, comprising: obtaining inherent data of the soil and the support structure, the inherent data including at least soil width, soil weight, internal friction angle, additional load, and support structure height; dividing the soil into zones according to the shape of a horizontal differential unit body of the soil, the soil including at least a first zone and a second zone; determining the height of the first zone and the height of the second zone for soil pressure calculation in different zones; determining the soil pressure strength of the horizontal differential unit body of each zone, and determining the soil pressure of the soil according to the soil pressure strength.

[0004] Optionally, the horizontal differential unit body of the first zone is in the shape of a rectangle, and the horizontal differential unit body of the second zone is in the shape of a curved trapezoid.

[0005] Optionally, the curved side of the curved-side trapezoid of the horizontal differential unit body of the second zone is set to be a quadratic function parabola shape.

[0006] Optionally, the soil pressure strength of the horizontal differential unit body in the first zone is determined according to the equilibrium equation of the symmetrical circular arc arch and the vertical direction, and the soil pressure strength of the horizontal differential unit body in the second zone is determined according to the equilibrium equation of the symmetrical semicircular arc arch, the vertical direction and the horizontal direction.

[0007] Optionally, the earth pressure strength of the horizontal differential unit body in the first zone satisfies the following formula:

[0008]

[0009] Where z is the depth of the horizontal differential unit; γ is the weight of the soil; B is the width of the soil; δ is the wall-soil friction angle; q is the additional load; k1 is the lateral pressure coefficient of the first zone.

[0010] Optionally, the earth pressure strength of the horizontal differential unit body in the second zone satisfies the following formula:

[0011]

[0012] in,

[0013]

[0014]

[0015] Where k2 is the lateral pressure coefficient of the second zone; is the average normal stress on the upper boundary of the horizontal differential unit; θ l is the angle between the deflection direction of the major principal stress at the back of the wall and the horizontal direction; θ r It is the angle between the deflection direction of the largest principal stress at the slip surface and the horizontal direction.

[0016] The embodiment of the present invention divides the soil body of limited width into different zones, sets the soil arch shape, takes into account the uniformly distributed load on the soil surface, performs zone calculation on the soil pressure, and obtains the soil pressure strength of the support structure based on the horizontal differential unit body. The method is simple and practical, and has important guiding significance for the design of the support structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The following are drawings of exemplary embodiments of the present invention, and the same or similar reference numerals are used in the drawings to represent the same or similar elements. In the drawings:

[0018] Figure 1 A flow chart of a method for calculating earth pressure based on a finite width earth support structure according to an exemplary embodiment of the present invention is shown.

[0019] Figure 2 A schematic diagram of a horizontal differential unit of soil of an exemplary embodiment of the present invention is shown in the soil pressure calculation method based on a finite width soil support structure.

[0020] Figure 3 A force analysis diagram of a horizontal differential unit cell in a first zone of an exemplary embodiment of the present invention is shown.

[0021] Figure 4 A schematic diagram of a small principal stress circular arc arch of a horizontal differential unit cell in the first zone of an exemplary embodiment of the present invention is shown.

[0022] Figure 5 A force analysis diagram of a horizontal differential unit cell in the second zone of an exemplary embodiment of the present invention is shown.

[0023] Figure 6A schematic diagram of a small principal stress semicircular arc arch of a horizontal differential unit cell in the second zone of an exemplary embodiment of the present invention is shown.

[0024] Figure 7 A comparison diagram showing a theoretical calculation solution and a numerical simulation solution of the earth pressure of a supporting structure according to an exemplary embodiment of the present invention is shown.

[0025] Figure 8 A comparison diagram between a theoretical calculation solution and experimental data of the earth pressure of a support structure according to an exemplary embodiment of the present invention is shown. DETAILED DESCRIPTION

[0026] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation modes in conjunction with the accompanying drawings.

[0027] In the present invention, the term "and / or" is intended to cover all possible combinations and sub-combinations of the listed elements, including any one, any sub-combination or all of the elements listed separately, without excluding other elements. Unless otherwise specified, the terms "first", "second", etc. are used to describe various elements without intending to limit the positional relationship, timing relationship or importance relationship of these elements. Such terms are only used to distinguish one element from another. Unless otherwise specified, the orientation or positional relationship indicated by the terms "front, back, up, down, left, right", etc. is usually based on the orientation or positional relationship shown in the accompanying drawings, which is only for the convenience and simplification of description, and cannot be understood as limiting the scope of protection of the present invention.

[0028] In the theoretical calculation of earth pressure, the classical Coulomb and Rankine earth pressure theories are usually used. In these theories, the soil behind the retaining wall is often assumed to be infinite width (or semi-infinite width) and a single homogeneous soil. However, in actual projects, the width of the soil behind the retaining wall is often limited. Since the actual situation does not conform to the above assumptions, it is necessary to improve the existing calculation method to more accurately reflect the actual engineering situation. This improvement will help to improve the understanding of the behavior of the retaining wall and the soil behind it, and can more accurately guide engineering design and construction practice. In addition, in the classical theoretical calculation, for the sake of simplicity of calculation, the deflection of the principal stress inside the soil caused by the soil arch effect is often ignored, which causes a large difference between the calculated results and the measured results, resulting in the design of the support structure being too conservative and not conducive to cost saving. Finally, in actual projects, the retaining wall is often subjected to various loads (such as building material loading, surrounding building loads, etc.), and the traditional earth pressure theory does not effectively consider the load effect. Therefore, it is necessary to include the load effect in the calculation method of earth pressure.

[0029] In some embodiments of the present invention, with soil pressure as the center, a discrete element numerical simulation method is used to focus on analyzing the influence of factors such as the shape of the sliding soil wedge of soil with different widths, the deflection direction of the internal principal stress and the adjustment value of the internal friction angle on the strength of soil pressure. For this RT mode, the horizontal differential unit method is used to obtain a soil pressure calculation method suitable for a soil support structure with limited width.

[0030] Figure 1 A flow chart of a method for calculating earth pressure based on a finite width earth support structure according to an exemplary embodiment of the present invention is shown.

[0031] S102: Acquire inherent data of the soil and the supporting structure, wherein the inherent data at least includes soil width B, soil weight γ, internal friction angle Additional load, and support structure height H.

[0032] Furthermore, in some embodiments, the inherent data also includes a wall-soil friction angle δ.

[0033] S104: Dividing the soil body into zones according to the shape of the horizontal differential unit body, wherein the soil body includes at least a first zone and a second zone.

[0034] like Figure 2 As shown, the horizontal differential unit body of the first zone (zone I) is in the shape of a rectangle, and the horizontal differential unit body of the second zone (zone II) is in the shape of a curved trapezoid. Further, the curved side of the curved trapezoid is set to a quadratic function parabola shape, that is, the highest degree of the quadratic function is quadratic.

[0035] S106: Determine the height of the first zone and the height of the second zone for calculating the earth pressure of different zones. The height h1 of the first zone satisfies the following formula:

[0036] h1=A1B 2 +A2B+A3; (1)

[0037] in,

[0038]

[0039] A2=-tanα;(3)

[0040] A3=H;(4)

[0041] Where B is the width of the soil (behind the retaining wall), K p is the Coulomb passive lateral earth pressure coefficient, α is the inclination angle of the soil sliding zone, and H is the height of the support structure.

[0042] The height h2 of the second zone is the height H of the supporting structure minus the height h1 of the first zone.

[0043] S108: Determine the soil pressure strength of the horizontal differential unit bodies in the first zone and the second zone, and determine the soil pressure of the soil body according to the soil pressure strength.

[0044] Combination Figure 3 and Figure 4 As shown in the figure, the stress conditions of the horizontal differential unit in the first zone (zone I) satisfy the following:

[0045]

[0046] Where N is the normal force, T is the tangential force, N h1 、T h1 is acting on the left boundary of the horizontal differential unit, N he 、T he Acts on the right boundary of the horizontal differential unit; N p is the stress acting on the upper and lower boundaries of the horizontal differential unit; σ is the normal stress, τ is the shear stress, σ h1 , τ h1 is acting on the left boundary of the horizontal differential unit, σ he , τ he is acting on the right boundary of the horizontal differential unit; is the average normal stress on the upper boundary; dG1 is the gravity of the horizontal differential unit; γ is the soil weight.

[0047] according to,

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] The horizontal earth pressure at a certain point of the sliding soil wedge in the first zone can be solved by the equilibrium equation of the horizontal differential unit in the vertical direction:

[0054] T h1 +T he +dN p =dG1; (11)

[0055]

[0056] The earth pressure intensity in the first zone is:

[0057]

[0058] Where z is the depth of the horizontal differential unit; γ is the weight of the soil; B is the width of the soil; δ is the wall-soil friction angle; q is the additional load (on the soil behind the wall); k1 is the lateral pressure coefficient of the first zone.

[0059] Combination Figure 5 and Figure 6 As shown, the soil pressure strength of the second zone (Zone II) is calculated, and the stress conditions of the horizontal differential unit body in the second zone (Zone II) meet the following requirements:

[0060]

[0061] Where N is the normal force, T is the tangential force, N h2 , T h2 is acting on the left boundary of the horizontal differential unit, N r , T r is the right slip surface acting on the horizontal differential unit; N p Acting on the upper and lower boundaries of the horizontal differential unit; σ is the normal stress, τ is the shear stress, σ h2 , τ h2 is acting on the left boundary of the horizontal differential unit, σ r , τ r Acting on the right slip surface of the horizontal differential unit, is the average normal stress on the upper boundary; dG2 is the gravity of the horizontal differential unit; β is the angle between the slip surface and the horizontal plane, B Z is the width of the differential unit cell.

[0062] By calculating as follows,

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] B0=Rcosθ l ;(twenty one)

[0070] B z =B0-Rcosθ r ;(twenty two)

[0071]

[0072]

[0073] The earth pressure intensity in the second zone is:

[0074]

[0075] in,

[0076]

[0077] Where k2 is the lateral pressure coefficient of the second zone; is the average normal stress on the upper boundary of the horizontal differential unit; θ l is the angle between the deflection direction of the major principal stress at the back of the wall and the horizontal direction; θ r It is the angle between the deflection direction of the largest principal stress at the slip surface and the horizontal direction.

[0078] The horizontal earth pressure at a certain point of the sliding soil wedge in the second zone can be solved by the equilibrium equations of the horizontal differential unit in the vertical and horizontal directions:

[0079] dN p +T h2 +T r sinβ+N r cosβ=dG2;(27)

[0080] N h2 +T r cosβ=N r sinβ; (28)

[0081]

[0082]

[0083] According to the equilibrium equations (27)-(29) and boundary conditions (30), the parameters on the right side of formula (25) can be obtained by using the finite difference method. That is, by substituting the boundary condition formula (30) and the finite difference method into formula (29), the average stress on the upper boundary of the unit cell at different depths in the second zone can be obtained: Then substitute it into formula (25) to calculate the soil pressure intensity at different depths.

[0084] Finally, in the RT mode, the horizontal (active) earth pressure of the finite width soil support structure and the resultant horizontal (active) earth pressure.

[0085]

[0086]

[0087] Verification experiment

[0088] The soil pressure of the supporting structure is calculated according to the formula obtained above and compared with the numerical simulation results and model test results.

[0089] 1. DEM numerical simulation is used to compare and verify the calculation method of the embodiment of the present invention. The physical and mechanical parameters of the soil in the model are set as follows:

[0090]

[0091] The calculation parameters are selected as follows:

[0092]

[0093] like Figure 7 As shown, by changing the width B of the soil after the support structure, the soil pressure in the model at this time is selected to compare with the calculation result of the calculation method of the present invention. The calculation of the present invention is highly consistent with the numerical simulation result.

[0094] 2. Comparison and verification are performed using a model test and the calculation method of the embodiment of the present invention. The physical and mechanical parameters of the soil in the test are set as follows:

[0095]

[0096] The calculation parameters are selected as follows:

[0097] like Figure 8 As shown, by changing the wall-soil friction angle δ of the interaction between the supporting structure and the soil, the calculation results of the calculation method of the present invention are compared with the actual results of the model test. The calculation results of the present invention are highly consistent with the model test results.

[0098] The embodiments of the present invention divide the soil into different areas with limited width, set the soil arch shape (especially, set it as a middle symmetrical semicircular arch), take into account the uniformly distributed load on the soil surface, and perform zone calculation on the soil pressure. The soil pressure strength of the support structure is obtained based on the horizontal differential unit body. The method is simple and practical, and has important guiding significance for the design of the support structure.

[0099] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A method for calculating earth pressure based on a soil support structure with limited width, characterized in that: include: Acquire inherent data of the soil and the supporting structure, wherein the inherent data at least includes soil width, soil weight, internal friction angle, additional load, and supporting structure height; Dividing the soil into zones according to the shape of the horizontal differential unit body of the soil, the soil body at least includes a first zone and a second zone, wherein the shape of the horizontal differential unit body of the first zone is a rectangle, and the shape of the horizontal differential unit body of the second zone is a curved trapezoid; determining the height of the first zone and the height of the second zone for use in calculating earth pressures in different zones; Determine the earth pressure strength of the horizontal differential unit body in each zone, and determine the earth pressure of the soil body according to the earth pressure strength, wherein, The soil pressure strength of the horizontal differential unit body in the first zone is determined according to the equilibrium equation of the symmetrical circular arc arch and the vertical direction, and the soil pressure strength of the horizontal differential unit body in the second zone is determined according to the equilibrium equation of the symmetrical semicircular arc arch, the vertical direction and the horizontal direction. The earth pressure strength of the horizontal differential unit body in the first zone satisfies the following formula: Where z is the depth of the horizontal differential unit; γ is the weight of the soil; B is the width of the soil; δ is the wall-soil friction angle; q is the additional load; k1 is the lateral pressure coefficient of the first zone; The earth pressure strength of the horizontal differential unit in the second zone satisfies the following formula: in, Where k2 is the lateral pressure coefficient of the second zone; is the average normal stress on the upper boundary of the horizontal differential unit; θ l is the angle between the deflection direction of the major principal stress at the back of the wall and the horizontal direction; θ r It is the angle between the deflection direction of the largest principal stress at the slip surface and the horizontal direction.

2. The soil pressure calculation method based on the soil support structure with limited width according to claim 1 is characterized in that: The curved side of the curved-side trapezoid of the horizontal differential unit body of the second region is set to be a quadratic function parabola shape.

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