A method for calculating active earth pressure of finite soil body considering width of slope platform

Abstract

The present application belongs to the technical field of active earth pressure calculation, and discloses a kind of finite soil active earth pressure calculation method considering the width of slope platform, comprising the following steps: step one: under the condition of finite platform width, according to the position of soil slip surface, the sliding soil is divided into zones;And determine the design condition of finite soil;Step two: determine the sliding soil volume per meter;Step three: force analysis is carried out on the sliding body;Step four: according to the force analysis of the sliding body in step three, the critical crack angle θcr is solved, and the resultant force of active earth pressure is calculated according to the angle δ between the horizontal component of active earth pressure and the resultant force.The present application divides the sliding soil into two different areas according to the position of soil slip surface under the condition of finite platform width, determines the sliding body volume per meter of finite soil in different areas, and carries out force analysis on the soil, to calculate the active earth pressure.The earth pressure value calculated by the present application is objective and reasonable, and can be used to guide the construction correctly.

Description

Technical Field

[0001] This invention relates to the field of active earth pressure calculation technology, specifically to a method for calculating active earth pressure on finite soil masses that takes into account the width of a slope platform. Background Technology

[0002] In many slope protection projects, the earth pressure acting on the retaining structure is generally calculated using the classical earth pressure theory. Both the classical Rankine earth pressure theory and the Coulomb earth pressure theory are derived under the condition of semi-infinite soil.

[0003] In various engineering fields such as open-pit mines, foundation pits, and water conservancy and hydropower, it is inevitable to encounter situations where there is a finite soil mass behind the retaining structure (the failure surface of the soil mass is greater than the distance between the retaining structure and the existing underground structure). The earth pressure generated by the finite soil mass will differ from the traditional semi-infinite earth pressure. If the calculation is performed according to the semi-infinite earth pressure formula, the force exerted by the soil on the retaining structure will be overestimated. The calculated earth pressure value will often be larger than the actual value, thus failing to correctly guide the design and construction.

[0004] Therefore, it is necessary to find a finite soil pressure calculation method that conforms to the actual situation, and to objectively and reasonably analyze and calculate the active earth pressure acting on the retaining structure, so as to carry out more scientific design and construction. Summary of the Invention

[0005] This invention aims to provide a method for calculating active earth pressure on finite soil masses considering the width of a slope platform. Under the condition of a finite platform width, the sliding soil mass is divided into two distinct regions based on the location of the slip surface. The volume of the sliding mass per meter of soil is determined for each region, and a stress analysis is performed on the finite volume of soil to calculate the active earth pressure. The earth pressure values ​​calculated by this invention are objective and reasonable, and can be correctly used to guide construction.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for calculating active earth pressure on finite soil masses considering the width of a slope platform includes the following steps:

[0008] Step 1: Under the condition of limited platform width, divide the sliding soil mass into zones according to the location of the soil slip surface; and determine the design conditions for the limited soil mass.

[0009] Step 2: Determine the volume of the sliding soil per meter;

[0010] Step 3: Perform force analysis on the sliding body;

[0011] Step 4: Based on the force analysis of the sliding body in Step 3, solve for the critical rupture angle θcr, and calculate the resultant force of the active earth pressure based on the angle δ between the horizontal component of the active earth pressure and the resultant force.

[0012] Furthermore, in step one, the method for dividing the sliding soil mass into zones is as follows: Zone I is defined as the sliding surface that slides out through the slope platform; Zone II is defined as the sliding surface that slides out through the slope slope. The design conditions for the finite soil mass include the finite soil mass height h, platform width l, slope inclination angle α, soil fracture surface inclination angle θ, friction angle between the soil and the wall back δ, and internal friction angle of the soil. And soil weight γ.

[0013] Furthermore, in step two, the method for determining the volume of the sliding soil per meter is as follows:

[0014] When the slip surface is located in Zone I, the slip surface slides out through the slope platform, and the slip surface dip angle θ is:

[0015]

[0016] The area of ​​the sliding soil mass at this time is:

[0017]

[0018] When the slip surface is located in zone II, the slip surface slides out through the slope surface, and the slip surface dip angle θ is:

[0019]

[0020] The area of ​​the sliding soil mass at this time is:

[0021]

[0022] In summary, the volume of the sliding body per meter is:

[0023]

[0024] Furthermore, in step three, when the retaining structure deforms away from the soil, the sliding body is subjected to the following forces: the left side of the element experiences a horizontal reaction force E from the retaining structure. ax The force is influenced by the upward friction T between the soil and the wall, the normal reaction force N1 exerted by the unslidable soil, and the upward friction T1 between the soil masses. Additionally, there is the gravity W of the sliding soil mass. The force analysis for zones I and II is as follows:

[0025] When the slip surface is located in zone I, the slip body is triangular. According to the force equilibrium conditions of the soil in the horizontal and vertical directions, we can obtain:

[0026]

[0027] Furthermore, according to the limiting equilibrium condition, we know that:

[0028]

[0029] The sliding gravity per meter of thickness is:

[0030]

[0031] Combining equations (6) to (8), we obtain the basic equation for the horizontal active earth pressure of a finite soil mass:

[0032]

[0033] When the slip surface is located in zone II, the slip body is quadrilateral, and the weight of the slip body per meter of thickness is:

[0034]

[0035] Similarly, based on the static equilibrium conditions of the soil in the horizontal and vertical directions, the basic equation for the active earth pressure in the horizontal direction of the finite soil is obtained as follows:

[0036]

[0037] In summary, the fundamental equation for the active earth pressure in the horizontal direction on a finite soil mass is obtained as follows:

[0038]

[0039] Furthermore, in step four, let Find the critical fracture angle θ cr At the same time, the resultant force of the active earth pressure is obtained as:

[0040]

[0041] Furthermore, according to the active earth pressure formula in step four, the active earth pressure coefficient of the finite soil mass can be obtained as follows:

[0042]

[0043] Furthermore, according to the active earth pressure formula in step four, if the distribution pattern of the active earth pressure behind the wall is consistent with the traditional classical active earth pressure, and is linearly distributed along the wall height, the active earth pressure intensity σ is obtained. a The distribution equation along the wall height is:

[0044]

[0045] The beneficial effects of the technical solution are as follows: This invention starts from reality, considers the determined width of the slope platform according to the actual scenario, divides the slip surface into two cases: slipping out from the slope platform and slipping out from the slope slope, establishes static equilibrium condition equations for each case, and obtains the expression for the active earth pressure of the finite soil mass, so that the calculation results are more in line with the actual engineering situation and have great promotion and application value. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the sliding body partitioning in step one of the finite soil active earth pressure calculation method considering the width of the slope platform in this invention.

[0047] Figure 2 This is a diagram showing the geometric characteristics of the sliding body in step two of the method for calculating active earth pressure on finite soil considering the width of a slope platform in this invention.

[0048] In the figure, (a) is the sliding body in zone I, and (b) is the sliding body in zone II;

[0049] Figure 3 This is a force analysis diagram of the triangular sliding body in zone I in step three of the active earth pressure calculation method for finite soil considering the width of the slope platform in this invention.

[0050] Figure 4 This is a force analysis diagram of the quadrilateral sliding body in zone II in step three of the active earth pressure calculation method for finite soil considering the width of the slope platform in this invention. Detailed Implementation

[0051] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments:

[0052] A method for calculating active earth pressure on finite soil masses considering the width of a slope platform includes the following steps:

[0053] Step 1: Under the condition of limited platform width, such as Figure 1 As shown, the sliding soil mass is divided into two regions based on the location of the slip surface: Region I is where the slip surface slides out through the slope platform surface AB; Region II is where the slip surface slides out through the slope slope surface BC (or BE). The design conditions for the finite soil mass are determined, including the finite soil mass height h, platform width l, slope inclination angle α, soil rupture surface inclination angle θ, friction angle between the soil and the wall back δ, and internal friction angle within the soil. Soil weight γ;

[0054] Step 2: Determine the volume of the sliding body per meter, such as Figure 2 As shown,

[0055] (1) As Figure 2 As shown in (a), when the slip surface is located in Zone I, the slip surface slides out through the slope platform, and the slip surface dip angle θ is:

[0056]

[0057] The area of ​​the sliding soil mass at this time is:

[0058]

[0059] (2) Figure 2 As shown in (b), when the slip surface is located in zone II, the slip surface slides out through the slope surface, and the slip surface dip angle θ is:

[0060]

[0061] The area of ​​the sliding soil mass at this point is calculated based on its geometric properties:

[0062]

[0063] In summary, the volume of the sliding body per meter is:

[0064]

[0065] Step 3: Perform a force analysis on the sliding body. When the retaining structure deforms away from the soil, the force situation of the sliding body is as follows: The left side of the element is subjected to the horizontal reaction force E from the retaining structure. ax The wall experiences an upward frictional force T between itself and the soil, and is subjected to a normal reaction force N1 from the unslidable soil and an upward frictional force T1 between the soil masses. Additionally, there is the weight W of the sliding soil mass.

[0066] (1) As Figure 3 As shown, when the slip surface is located in zone I, the slip body is triangular. According to the force equilibrium conditions of the soil in the horizontal and vertical directions, we can obtain:

[0067]

[0068] Furthermore, according to the limiting equilibrium condition, we know that:

[0069]

[0070] The sliding gravity per meter of thickness is:

[0071]

[0072] By combining equations (6) to (8), the basic equation for the active earth pressure in the horizontal direction of a finite soil mass can be obtained as follows:

[0073]

[0074] (2) Figure 4 As shown, when the slip surface is located in zone II, the slip body is quadrilateral, and the weight of the slip body per meter of thickness is:

[0075]

[0076] Similarly, based on the static equilibrium conditions of the soil in the horizontal and vertical directions, the basic equation for the active earth pressure in the horizontal direction of the finite soil is obtained as follows:

[0077]

[0078] In summary, the fundamental equation for the horizontal active earth pressure on finite soil masses is:

[0079]

[0080] Step 4: Let Find the critical fracture angle θ cr Meanwhile, based on the angle δ between the horizontal component of the active earth pressure and the resultant force, the resultant force of the active earth pressure can be obtained as:

[0081]

[0082] The present invention will be further illustrated below with reference to a simple embodiment:

[0083] The soil parameters used in the example are: wall height h = 10m, platform width l = 3m, slope angle α = 30°, and soil internal friction angle. The friction angle between the wall and the soil is δ = 0°, and the soil weight is γ = 19 kN / m. 3 .

[0084] Based on the above calculation method, the fundamental equation for active earth pressure in the horizontal direction of finite soil is:

[0085]

[0086] make Find the critical fracture angle θ cr =67°, θ cr Substituting δ into equation (13), the resultant force E of the active earth pressure on the finite soil mass can be obtained. a The magnitude is approximately 201.9 kN. Using the traditional Coulomb active earth pressure method, the active earth pressure value for the finite soil in the above embodiment is approximately 206.6 kN. Compared with the traditional method, the calculated value in this invention is lower and more in line with the actual situation.

[0087] The above descriptions are merely embodiments of the present invention, and common knowledge regarding specific technical solutions or characteristics is not elaborated upon here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for calculating active earth pressure on finite soil masses considering the width of a slope platform, characterized in that, Includes the following steps: Step 1: Under the condition of limited platform width, divide the sliding soil into sections according to the location of the soil slip surface; And determine the design conditions for the finite soil mass; Step 2: Determine the volume of the sliding soil per meter; Step 3: Perform force analysis on the sliding body; Step 4: Based on the force analysis of the sliding body in Step 3, solve for the critical failure angle θcr, and determine the angle between the horizontal component of the active earth pressure and the resultant force. δ The resultant force of active earth pressure was calculated. In step one, the method for dividing the sliding soil mass into zones is as follows: Zone I is defined as the sliding surface that slides out through the slope platform; Zone II is defined as the sliding surface that slides out through the slope slope. The design conditions for the finite soil mass include the finite soil mass height h, platform width l, slope inclination angle α, soil fracture surface inclination angle θ, friction angle between the soil and the wall back δ, internal friction angle φ of the soil, and soil weight γ. In step two, the method for determining the volume of the sliding soil per meter is as follows: When the slip surface is located in Zone I, the slip surface slides out through the slope platform, and the slip surface dip angle is... θ for: (1) The area of ​​the sliding soil mass at this time is: (2) When the slip surface is located in Zone II, the slip surface slides out through the slope surface, and the slip surface dip angle is... θ for: (3) The area of ​​the sliding soil mass at this time is: (4) In summary, the volume of the sliding body per meter is: (5)。 2. The method for calculating active earth pressure on finite soil considering the width of a slope platform according to claim 1, characterized in that: In step three, when the retaining structure deforms away from the soil, the sliding body is subjected to the following forces: the left side of the element experiences a horizontal reaction force from the retaining structure. E ax Upward friction between the wall and the soil T The lower part is subjected to the normal reaction force exerted by the unslidable soil. N 1. The upward frictional force between the soil and the soil. T 1. In addition, there is the gravity of the sliding soil. W The force analysis for regions I and II is as follows: When the slip surface is located in zone I, the slip body is triangular. According to the force equilibrium conditions of the soil in the horizontal and vertical directions, we can obtain: (6) Furthermore, according to the limiting equilibrium condition, we know that: (7) The sliding gravity per meter of thickness is: (8) Combining equations (6) to (8), we obtain the basic equation for the horizontal active earth pressure of a finite soil mass: (9) When the slip surface is located in zone II, the slip body is quadrilateral, and the weight of the slip body per meter of thickness is: (10) Similarly, based on the static equilibrium conditions of the soil in the horizontal and vertical directions, the basic equation for the active earth pressure in the horizontal direction of the finite soil is obtained as follows: (11) In summary, the fundamental equation for the active earth pressure in the horizontal direction on a finite soil mass is obtained as follows: (12)。 3. The method for calculating active earth pressure on finite soil considering the width of a slope platform according to claim 2, characterized in that: In step four, let Find the critical fracture angle θ cr At the same time, the resultant force of the active earth pressure is obtained as: (13)。 4. The method for calculating active earth pressure on finite soil considering the width of a slope platform according to claim 3, characterized in that: According to the active earth pressure formula in step four, the active earth pressure coefficient for finite soil masses can be obtained as follows: (14)。 5. The method for calculating active earth pressure on finite soil considering the width of a slope platform according to claim 3, characterized in that: According to the active earth pressure formula in step four, if the distribution pattern of the active earth pressure behind the wall is consistent with the traditional classical active earth pressure, and is linearly distributed along the wall height, the active earth pressure intensity can be obtained. σ a The distribution equation along the wall height is: (15)。

Images