A method for calculating the earth pressure of any vertical load on the top of a slope of a retaining wall of a slope engineering

Abstract

The application provides a method for calculating the earth pressure of a retaining wall of a slope engineering, comprising the following steps: obtaining the height of the retaining wall of the slope engineering, obtaining the function relationship between the arbitrary vertical load on the top of the slope behind the retaining wall and the vertical plane, obtaining the specific gravity of the slope soil, obtaining the cohesion of the slope soil, and obtaining the internal friction angle of the slope soil; projecting the arbitrary vertical load on the top of the slope behind the retaining wall to the back of the retaining wall at an angle; calculating the active earth pressure generated by the arbitrary vertical load on the top of the slope behind the retaining wall at the projection position on the back of the retaining wall; calculating the active earth pressure and the resultant force of the active earth pressure; and performing size design or stability checking of the retaining wall according to the calculated active earth pressure and the resultant force. The function relationship between the arbitrary vertical load on the top of the slope and the distance between the load and the top vertex of the back of the retaining wall is obtained, the active earth pressure of the retaining wall under the arbitrary vertical load on the top of the slope and the resultant force of the active earth pressure are calculated, the calculation principle is clear and simple, and the method is convenient for engineers to use.

Description

Technical Field

[0001] This invention relates to the field of geotechnical design and construction, specifically to a method for calculating the earth pressure of arbitrary vertical loads on the top of retaining wall slopes in slope engineering. Background Technology

[0002] Retaining walls are structures that prevent soil collapse and are widely used in building construction, water conservancy projects, railway projects, and bridges. They are especially common in slope engineering as a support system.

[0003] The vertical load at the top of the slope behind the retaining wall has a significant impact on the active earth pressure of the retaining wall. However, there is currently a lack of calculation methods for arbitrary vertical loads on retaining walls, which may lead to safety hazards in actual construction projects due to the lack of design verification. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the earth pressure of any vertical load on the top of the slope of a retaining wall in slope engineering. By calculating the earth pressure of any vertical load on the top of the slope behind the retaining wall, the safety of construction can be determined.

[0005] To address the above problems, this invention provides a method for calculating the earth pressure under arbitrary vertical loads at the top of a retaining wall slope in slope engineering, comprising the following steps:

[0006] Step 001: Obtain the height of the retaining wall of the slope project, obtain the arbitrary vertical load function relationship of the slope top behind the retaining wall, obtain the weight of the slope soil, obtain the cohesion of the slope soil, and obtain the internal friction angle of the slope soil.

[0007] Step 002: Arbitrarily adjust the vertical load at the top of the slope behind the retaining wall to the vertical plane. Angle projection onto the back of the wall;

[0008] Step 003: Calculate the active earth pressure generated at the projection position of any vertical load on the top of the slope behind the retaining wall at the back of the retaining wall.

[0009] Step 004: Calculate the active earth pressure and the resultant force of the active earth pressure. Use the calculated active earth pressure and its resultant force to perform dimensional design or stability verification of the retaining wall.

[0010] Furthermore, step 004 in the above-mentioned method for calculating the earth pressure of arbitrary vertical loads at the top of the retaining wall slope in slope engineering includes:

[0011] The active earth pressure e at a distance z from the top of the slope behind the retaining wall az The calculation formula is as follows:

[0012]

[0013] Wherein, γ is the weight of the slope soil; c is the cohesion of the slope soil. K is the internal friction angle of the slope soil; a The active earth pressure coefficient, and H is the height of the retaining wall; f is the functional relationship between the vertical load p at the top of the slope behind the retaining wall and the distance x from the load p to the top of the wall, i.e.: p = f(x). z∈[0,H]; the resultant force of the active earth pressure E a The calculation formula is as follows:

[0014]

[0015] At the same time, when the active earth pressure e at the top of the slope behind the retaining wall is calculated by formula (1), az When < 0, take e. az =0.

[0016] Furthermore, in the above-mentioned method for calculating the earth pressure of arbitrary vertical loads at the top of the retaining wall slope in slope engineering, when the slope behind the retaining wall is a semi-infinite slope, the angle between the semi-infinite slope and the horizontal plane is obtained; then the functional relationship f between p and x is as follows:

[0017]

[0018] Where α is the angle between the semi-infinite inclined plane and the horizontal plane; therefore, according to equation (1), the active earth pressure e at a distance z from the top of the slope behind the retaining wall is obtained. az As shown in the following formula:

[0019]

[0020] Furthermore, in the above-mentioned method for calculating earth pressure under arbitrary vertical loads at the top of the retaining wall slope in the slope engineering, let e in formula (4) az =0, when the active earth pressure e at a distance z from the top of the slope behind the retaining wall is 0. az When z = 0, the corresponding value of z is z0, and the formula for calculating z0 is as follows:

[0021]

[0022] Therefore, we can conclude that when z∈[0, z0], e az ≤0; when z∈[z0, H], e az ≥0.

[0023] Furthermore, in the above-mentioned method for calculating the earth pressure of arbitrary vertical loads at the top of the retaining wall slope in the slope engineering, according to formula (2), e in formula (4) is... az By definite integral of the part ≥0, we can obtain:

[0024]

[0025] Furthermore, in the above-mentioned method for calculating the earth pressure of arbitrary vertical loads at the top of the retaining wall slope in slope engineering, when the slope behind the retaining wall is first an inclined plane and then a horizontal plane, the angle between the inclined plane and the horizontal plane, and the distance from the interface between the inclined plane and the horizontal plane to the back of the retaining wall are obtained; then the functional relationship f between p and x is a piecewise function as follows:

[0026]

[0027] Where β is the angle between the inclined plane and the horizontal plane, and x f Let e ​​be the distance from the interface between the inclined plane and the horizontal plane to the back of the retaining wall; therefore, according to equation (1), the active earth pressure e at the top of the slope behind the retaining wall at a distance z is obtained. az As shown in the following formula:

[0028]

[0029] in,

[0030] Furthermore, in the above-mentioned method for calculating the earth pressure of arbitrary vertical loads at the top of the retaining wall slope in the slope engineering, let e in formula (8) az =0, since equation (8) is a piecewise function, z0 may be in [0, z f In the interval [z], z0 may also be in the interval [z]. f If the interval is H, then the formula for calculating z0 has the following two cases:

[0031]

[0032]

[0033] Therefore, we can conclude that:

[0034] When z∈[0, z0], e az ≤0;

[0035] When z∈[ z0 ,H],e az ≥0.

[0036] Furthermore, in the above-mentioned method for calculating the earth pressure of arbitrary vertical loads at the top of the retaining wall slope in the slope engineering, according to formula (2), e in formula (9) is... az Integrating the part ≥0 yields the following two cases:

[0037] When z0∈[0, z f At that time, E a The calculation formula is as follows:

[0038]

[0039] When z0∈[z f When H], E a The calculation formula is as follows:

[0040]

[0041] By projecting any vertical load at the top of the slope behind the retaining wall at a specific angle to the vertical plane onto the back of the wall, the active earth pressure generated by the arbitrary vertical load at the top of the slope behind the retaining wall at the projection position on the back of the retaining wall can be obtained. Then, the active earth pressure and its resultant force can be obtained, and it can be used to determine whether the construction process is safe and whether there are any safety hazards. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the process according to an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of the earth pressure distribution when the top of the slope behind the retaining wall is a semi-infinite slope according to an embodiment of the present invention.

[0044] Figure 3 This is a schematic diagram of the earth pressure distribution when the top of the slope behind the retaining wall is first a sloping surface and then a flat surface, according to an embodiment of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0046] The calculation principle of the embodiments shown in this invention will be explained below.

[0047] First, any vertical load on the top of the slope behind the retaining wall is projected onto the back of the wall at a specific angle to the vertical plane. In this embodiment, the angle of projection is: in It is the internal friction angle of the slope soil. This is used to obtain the active earth pressure generated at the projection position of any vertical load on the top of the slope behind the retaining wall at the back of the retaining wall. Then, the active earth pressure and its resultant force are obtained. Finally, the retaining wall is dimensionally designed or its stability is verified based on the calculated active earth pressure and its resultant force.

[0048] The active earth pressure e at a distance z from the top of the slope behind the retaining wall az The calculation formula is as follows:

[0049]

[0050] Where γ is the weight of the slope soil, and c is the cohesion of the slope soil. K is the internal friction angle of the slope soil. a The active earth pressure coefficient, and H is the height of the retaining wall, and f is the functional relationship between the vertical load p at the top of the slope behind the retaining wall and the distance x from the load p to the top of the slope behind the wall, i.e.: p = f(x).

[0051] in, z∈[0,H].

[0052] The resultant force of active earth pressure E a The calculation formula is as follows:

[0053]

[0054] The active earth pressure e at the top of the slope behind the retaining wall, calculated using formula (1), is given by formula (1). az When < 0, take e. az =0.

[0055] When the slope behind the retaining wall is a semi-infinite slope, the functional relationship f between p and x is as follows:

[0056]

[0057] Where α is the angle between the semi-infinite inclined plane and the horizontal plane.

[0058] Substituting formula (3) into formula (1), we obtain the active earth pressure e at a distance z from the top of the slope behind the retaining wall. az As shown in the following formula:

[0059]

[0060] Let e ​​in formula (4) az =0, when the active earth pressure e at a distance z from the top of the slope behind the retaining wall is 0. az When z = 0, the corresponding value of z is z0, and the formula for calculating z0 is as follows:

[0061]

[0062] The following conclusion can then be drawn:

[0063] When g∈[0, z0], e az ≤0;

[0064] When z∈[z0, H], e az ≥0.

[0065] According to formula (2), e in formula (4)az By definite integral of the part ≥0, we can obtain:

[0066]

[0067] When the slope behind the retaining wall is first a sloping surface and then a horizontal surface, the angle between the sloping surface and the horizontal surface, and the distance from the interface between the sloping surface and the horizontal surface to the back of the retaining wall are obtained.

[0068] Then the functional relationship f between p and x is a piecewise function as follows:

[0069]

[0070] Where β is the angle between the inclined plane and the horizontal plane, and x f This is the distance from the interface between the inclined plane and the horizontal plane to the back of the retaining wall;

[0071] Therefore, according to equation (1), the active earth pressure e at a distance z from the top of the slope behind the retaining wall is obtained. az As shown in the following formula:

[0072]

[0073] in,

[0074] Let e ​​in formula (8) az =0, since equation (8) is a piecewise function, z0 may be in [0, z f In the interval [z], z0 may also be in the interval [z]. f If the interval is H, then the formula for calculating z0 has the following two cases:

[0075]

[0076]

[0077] Therefore, we can conclude that:

[0078] When z∈[0, z0], e az ≤0;

[0079] When z∈[z0, H], e az ≥0.

[0080] According to formula (2), e in formula (9) az Integrating the part ≥0 yields the following two cases:

[0081] When z0∈[0, z f At that time, E a The calculation formula is as follows:

[0082]

[0083] When z0∈[z f When H], E a The calculation formula is as follows:

[0084]

[0085] Based on Equation (11) for the calculation of the anti-sliding stability of the retaining wall and Equation (12) for the calculation of the anti-overturning stability of the retaining wall, the design calculations are performed on the top a and bottom b of the right trapezoidal retaining wall.

[0086]

[0087]

[0088] Where, γ w Let μ be the unit weight of the retaining wall, μ be the coefficient of friction between the retaining wall and the ground, and a be the unit weight of the retaining wall. w Let a be the distance from the center of gravity of the retaining wall to its toe. a The resultant force of active earth pressure E a The distance to the toe of the wall.

[0089] The calculated active earth pressure and its resultant force are used to design the dimensions or verify the stability of the retaining wall.

[0090] The following is a calculation example: A slope engineering project has a retaining wall with a height H = 5m, the slope soil is in the form of a semi-infinite slope, and the unit weight of the fill soil is γ = 20kN / m. 3 Cohesion c = 10 kPa, internal friction angle The angle α between the inclined plane and the horizontal plane is 20°.

[0091] Substituting into formula (3), we get:

[0092] p=20°·x·tan20°=20°·z·tan(45°-30° / 2)·tan20°

[0093] Next, the active earth pressure e is obtained from formula (4). az :

[0094] e az =6.67·z-11.54+1.4z=8.07z-11.54

[0095] z0 is obtained from formula (5):

[0096]

[0097] E is obtained from formula (6) a :

[0098]

[0099] Active earth pressure e az If the distribution is triangular, then E a Distance a to the toe of the wall a =1.19m, unit weight of retaining wall γ w 25kN / m 3 μ = 0.3, a = 0.8b at the bottom of the retaining wall, a w =2.41m, a =1.6m and b =2m are calculated from equation (11); a =0.29m and b =0.36m are calculated from equation (12); according to the unfavorable principle, the design result is a =1.8m and b =2m.

[0100] It should be understood that the specific embodiments described above are merely illustrative or explanatory of the principles of the invention and do not constitute a limitation thereof. Therefore, any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and scope of the invention should be included within the protection scope of the invention. Furthermore, the appended claims are intended to cover all variations and modifications falling within the scope and boundaries of the appended claims, or equivalent forms of such scope and boundaries.

Claims

1. A method for calculating earth pressure under arbitrary vertical loads at the top of a retaining wall slope in slope engineering, characterized in that, Includes the following steps: Step 001: Obtain the height of the retaining wall of the slope project, obtain the arbitrary vertical load function relationship of the slope top behind the retaining wall, obtain the weight of the slope soil, obtain the cohesion of the slope soil, and obtain the internal friction angle of the slope soil. Step 002, align any vertical load on the top of the slope behind the retaining wall with the vertical plane. The angle of the projection onto the back of the wall; Step 003: Calculate the active earth pressure generated at the projection position of any vertical load on the top of the slope behind the retaining wall at the back of the retaining wall. Step 004: Calculate the active earth pressure and the resultant force of the active earth pressure, and use the calculated active earth pressure and the resultant force of the active earth pressure to perform dimensional design or stability verification of the retaining wall. Step 004 includes: Distance from the top of the slope behind the retaining wall The active earth pressure mentioned above The calculation formula is as follows: （1） in, The weight of the slope soil; The cohesion of the slope soil; The internal friction angle of the slope soil; The active earth pressure coefficient, and ; The height of the retaining wall; The vertical load at the top of the slope behind the retaining wall. With this load Distance to the top of the wall The functional relationship between them is: , , ; The resultant force of active earth pressure The calculation formula is as follows: （2） At the same time, when the distance calculated by formula (1) is to the top of the slope behind the retaining wall, Active earth pressure At that time, take ; When the slope behind the retaining wall is a semi-infinite slope, the angle between the semi-infinite slope and the horizontal plane is obtained. Then there is and The functional relationship between them is as follows: （3） in, The angle between the semi-infinite inclined plane and the horizontal plane; Therefore, according to equation (1), the distance from the top of the slope behind the retaining wall is obtained. Active earth pressure As shown in the following formula: （4）； When the slope behind the retaining wall is first a sloping surface and then a horizontal surface, the angle between the sloping surface and the horizontal surface, and the distance from the interface between the sloping surface and the horizontal surface to the back of the retaining wall are obtained. Then there is and Functional relationship between The piecewise function is as follows: （7）； in, β The angle between the inclined plane and the horizontal plane is... x f This is the distance from the interface between the inclined plane and the horizontal plane to the back of the retaining wall; Therefore, according to equation (1), the distance from the top of the slope behind the retaining wall is obtained. Active earth pressure As shown in the following formula: （8） in, .

2. The method for calculating earth pressure under arbitrary vertical loads at the top of retaining wall slopes in slope engineering according to claim 1, characterized in that: Let the formula (4) When the distance from the top of the slope behind the retaining wall Active earth pressure At this time, corresponding to The value is , The calculation formula is as follows: （5） Therefore, we can conclude that: when , ; when , .

3. The method for calculating earth pressure under arbitrary vertical loads at the top of retaining wall slopes in slope engineering according to claim 2, characterized in that: According to formula (2), in formula (4) By definite integral of the part, we can obtain: （6）。 4. The method for calculating earth pressure under arbitrary vertical loads at the top of retaining wall slopes in slope engineering according to claim 3, characterized in that: Let the formula (8) Since equation (8) is a piecewise function, then The calculation formula has the following two cases: （9.1） （9.2） Therefore, we can conclude that: when , ; when , .

5. The method for calculating earth pressure under arbitrary vertical loads at the top of retaining wall slopes in slope engineering according to claim 4, characterized in that: According to formula (2), in formulas (9.1) and (9.2) Integrating the part by definite integral yields the following two cases: when , E a The calculation formula is as follows: （10.1） when , E a The calculation formula is as follows: （10.2）。

Images