A method for calculating additional earth pressure of any load on top of retaining structure of foundation pit engineering

Abstract

The application provides a kind of additional arbitrary load earth pressure calculation method of retaining structure top in foundation pit engineering, and belongs to the field of foundation pit engineering.The method includes: carrying out strip block division to effective arbitrary load, for the i th strip block, the additional load F i Is calculated, and according to stress diffusion principle, the additional stress Δσ i After diffusion, additional stress acting on local soil is calculated i ;According to Rankine active earth pressure calculation principle, the resultant force E ai Of active earth pressure in the influence range of each strip block is calculated;According to the resultant force E ai Of active earth pressure in the influence range of each strip block, the total resultant force of active earth pressure acting on retaining structure is calculated.The application calculates the earth pressure of retaining structure based on strip block division method and stress diffusion principle, and provides a feasible method for the calculation of earth pressure of retaining structure top under the action of arbitrary additional load.

Description

Technical Field

[0001] This invention belongs to the field of foundation pit engineering, and in particular relates to a method for calculating the earth pressure of an arbitrary additional load on the top of the retaining structure in foundation pit engineering. Background Technology

[0002] The design of retaining structures for foundation pits should begin with calculating the earth pressure acting on the retaining structure. For the earth pressure generated by the soil outside the retaining structure, Rankine's active earth pressure theory is uniformly used for calculation. However, for additional loads acting on the top of the retaining structure, existing standards only provide calculation methods for earth pressure under several types of regularly shaped additional loads. However, in actual engineering projects, the additional loads acting on the top of the retaining structure are not always regular in shape, but may be of arbitrary shape. Engineers often simplify arbitrary additional loads into regular loads during the design process, resulting in calculations that do not reflect reality.

[0003] Therefore, there is currently no method for calculating earth pressure for any additional load applied to the top of a retaining structure. Summary of the Invention

[0004] In view of the above-mentioned defects or deficiencies in the prior art, the present invention aims to provide a method for calculating the earth pressure under an arbitrary additional load on the top of the retaining structure in foundation pit engineering, so as to make the calculation of earth pressure under an arbitrary additional load on the top of the retaining structure more accurate.

[0005] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0006] A method for calculating earth pressure under an arbitrary additional load on the top of a retaining structure in foundation pit engineering, the method comprising the following steps:

[0007] Divide the effective arbitrary load into blocks. For the i-th block, calculate its additional load F. i And based on the stress diffusion principle, the additional load F is calculated. i The additional stress Δσ acting on the local soil after diffusion i Wherein, the effective arbitrary load refers to the load acting on the retaining structure after being diffused by a stress diffusion angle of 45°; the number of blocks is n, where n is a natural number greater than or equal to 10, and i is greater than or equal to 1 and less than or equal to n;

[0008] Based on Rankine's active earth pressure calculation principle, calculate the resultant active earth pressure E within the influence range of each block. ai ;

[0009] Based on the resultant force E of the active earth pressure within the influence range of each block ai Calculate the resultant of the total active earth pressure acting on the retaining structure.

[0010] Wherein, the effective arbitrary load horizontal range is 0 to H, and H is the height of the support structure.

[0011] Wherein, the value of n ranges from 10 to 100.

[0012] For the i-th block, the calculation range of the additional load is: Additional load F i The following formula can be used for calculation.

[0013]

[0014] Where, x i f(x) is the horizontal distance between the midpoint of the bottom surface of the i-th block and the top surface of the support structure. i ) represents the additional load distribution function, and H represents the height of the retaining structure.

[0015] For the i-th block, the additional load F i The additional stress Δσ acting on the local soil after diffusion i Size is

[0016]

[0017] Among them, the resultant force E of the active earth pressure within the influence range of each block ai The following formula is used for calculation:

[0018]

[0019] Where γ is the weight of the soil outside the retaining structure, c is the cohesion of the soil outside the retaining structure, and k a The active earth pressure coefficient, The internal friction angle of the soil on the outer side of the retaining structure.

[0020] The total resultant force of active earth pressure acting on the retaining structure is calculated using the following formula:

[0021]

[0022] The technical solutions provided by the embodiments of the present invention have the following beneficial effects:

[0023] This invention provides a method for calculating earth pressure on the top of a retaining structure under an arbitrary additional load in foundation pit engineering. The method involves dividing the additional load on the top of the retaining structure into blocks, calculating the additional load in each block, and, based on the stress diffusion principle, calculating the additional stress acting on the local soil after stress diffusion. Considering the increased additional stress in the soil, the resultant active earth pressure within the influence range of each block is calculated using Rankine's active earth pressure principle. The total resultant active earth pressure acting on the retaining structure is obtained by summing the resultant active earth pressures within the influence range of each block. This invention, based on the block division method and the stress diffusion principle, provides a practical method for calculating earth pressure when an additional load acts on the top of a retaining structure, making the calculation of earth pressure under arbitrary additional loads more accurate.

[0024] Of course, implementing any product or method of the present invention does not necessarily require achieving all of the advantages described above at the same time. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating a method for calculating earth pressure under an arbitrary additional load on the top of a retaining structure in foundation pit engineering, as described in an embodiment of the present invention.

[0027] Figure 2 This is a schematic diagram illustrating the calculation of additional stress within the influence range of the i-th block according to an embodiment of the present invention;

[0028] Figure 3 This is a schematic diagram illustrating the calculation of active earth pressure within the influence range of the i-th block as described in an embodiment of the present invention. Detailed Implementation

[0029] After discovering the aforementioned problems, the inventors of this application conducted research on the active earth pressure on the retaining structure of the foundation pit. The research revealed that the additional stress in the soil caused by the additional load on the top of the retaining structure follows the principle of stress diffusion, and that in actual engineering, the load distribution on the top of the retaining structure can be diverse, rather than just meeting a few specific forms specified in the code. However, currently there is no method for calculating the earth pressure when any form of load acts on the top of the retaining structure.

[0030] It should be noted that the defects in the above-mentioned prior art solutions are all the result of the inventors' practice and careful research. Therefore, the discovery process of the above problems and the solutions proposed by the embodiments of the present invention in the following text should be the inventors' contributions to the present invention.

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. It should be noted that, without conflict, the embodiments and features in the embodiments of the present invention can also be combined with each other.

[0032] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of the invention, the terms "first," "second," "third," "fourth," etc., are used only to distinguish descriptions and should not be construed as merely or implying relative importance.

[0033] Following the above in-depth analysis, this application analyzes the earth pressure on the retaining structure of a foundation pit. It finds that the additional stress in the soil caused by the additional load at the top of the retaining structure follows the stress diffusion principle. Furthermore, by using the slice method to divide the additional load into slices, the calculation can be performed regardless of the load distribution. Based on this, this application provides a method for calculating the earth pressure under any additional load at the top of the retaining structure in foundation pit engineering. The earth pressure calculated using this method can be used for the design calculation of foundation pit retaining structures; however, this invention is not limited to this.

[0034] like Figure 1 The diagram shows a flowchart of a method for calculating earth pressure under an arbitrary additional load on the top of a retaining structure in a foundation pit project, provided by an embodiment of the present invention. The design method includes the following steps:

[0035] Step S1: Divide the effective arbitrary load into blocks. For the i-th block, calculate its additional load F. i And based on the stress diffusion principle, the additional load F is calculated. i The additional stress Δσ acting on the local soil after diffusion i ;

[0036] Since the height of the retaining structure is limited, only the effective arbitrary load acting on the retaining structure after being diffused by a 45° stress diffusion angle needs to be considered. That is, the effective arbitrary load mentioned in this invention refers to the load acting on the retaining structure after being diffused by a 45° stress diffusion angle, and the horizontal range of the effective arbitrary load is 0 to H.

[0037] The number of blocks is n, where n is a natural number greater than or equal to 10. In practical applications, the precision can be increased as needed, and the value of n can range from 10 to 100. The width of the block is 1 / n of the height of the support structure; that is, for a support structure with a height of H, the width of the block is H / n. i is greater than or equal to 1 and less than or equal to n.

[0038] For the i-th block, the calculation range of the additional load is: Additional load F i The following formula can be used for calculation.

[0039]

[0040] Where, x i f(x) is the horizontal distance between the midpoint of the bottom surface of the i-th block and the top surface of the support structure. i ) represents the additional load distribution function, and H represents the height of the retaining structure.

[0041] like Figure 2 As shown, according to the principle of stress diffusion, the additional load acts on the local soil after diffusion, x i The additional load at the point diffuses and acts on the retaining structure z. i At point z i Let z be the distance from the point of application of the additional load after diffusion on the retaining structure to the top of the retaining structure. The stress diffusion angle is 45°, therefore numerically z i =x i .

[0042] For the i-th block, the additional load F acting on it i The additional stress Δσ acting on the local soil after diffusion i The range of action on the supporting structure is Size:

[0043]

[0044] A i =2x i (3)

[0045] In the formula, A i This represents the area for additional stress diffusion.

[0046] Substituting formulas (1) and (3) into formula (2) yields the additional load F. i The additional stress Δσ acting on the local soil after diffusion i :

[0047]

[0048] Step S2: Calculate the resultant force E of active earth pressure within the influence range of each block, based on Rankine's active earth pressure calculation principle. ai ;

[0049] The additional load on the top surface of the retaining structure causes an increase in the vertical stress within the soil within a local area of ​​the retaining structure, which in turn increases the active earth pressure at various points within that local area. According to Rankine's principle of active earth pressure calculation, such as... Figure 3 As shown, for the i-th block, the distance from the top of the support structure is z. i The active earth pressure at the location is:

[0050]

[0051] In the formula, γ is the weight of the soil outside the retaining structure, c is the cohesion of the soil outside the retaining structure, and k a The active earth pressure coefficient, e is the internal friction angle of the soil on the outer side of the retaining structure. a <0 is taken as e a =0. The soil weight γ, cohesion c, and internal friction angle on the outer side of the retaining structure can be obtained through experiments.

[0052] The resultant force of active earth pressure within the influence range of block i is:

[0053]

[0054] Substitute equations (4) and (5) into equation (6), and use z i =x i The resultant force E of the active earth pressure within the influence range of each block can be obtained. ai :

[0055]

[0056] Step S3, based on the resultant force E of the active earth pressure within the influence range of each block. ai Calculate the resultant of the total active earth pressure acting on the retaining structure.

[0057]

[0058] Substituting formula (7) into formula (8), we get:

[0059]

[0060] The invention will be further explained in detail below through a specific example.

[0061] A foundation pit is supported by a gravity cement-soil wall, with a wall height of 10m. The soil cohesion on the outer side of the pit is 10kPa, the internal friction angle is 30°, and the unit weight is 20kN / m³. 3 The expression for the load distribution form on the top of the wall is p = 20x, and the load distribution width is 10m.

[0062] The load is divided into blocks with a width of 1m and a total of 10 blocks. The additional stresses acting on the local soil after the additional load of each block is diffused, as shown in the table below, obtained from formula (4):

[0063]

[0064] The resultant force of active earth pressure within the influence range of each block, calculated using formula (7), is shown in the table below:

[0065]

[0066] The total active earth pressure resultant force acting on the gravity-type cement-soil wall, calculated by formula (9), is:

[0067] E a =252.9kN / m

[0068] This invention provides a method for calculating earth pressure on the top of a retaining structure under an arbitrary additional load in foundation pit engineering. The method divides the additional load on the top of the retaining structure into blocks, calculates the additional load acting on each block, and, based on the stress diffusion principle, calculates the additional stress acting on the local soil after stress diffusion. Considering the increased additional stress in the soil, the resultant active earth pressure within the influence range of each block is calculated using Rankine's active earth pressure principle. The total resultant active earth pressure acting on the retaining structure is obtained by summing the resultant active earth pressures within the influence range of each block. This invention, based on the block division method and the stress diffusion principle, provides a practical method for calculating earth pressure when an additional load acts on the top of a retaining structure, making the calculation of earth pressure under arbitrary additional loads more accurate.

[0069] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed, and is not intended to limit the scope of the claimed invention, but merely to illustrate preferred embodiments of the invention. Those skilled in the art should understand that the scope of the invention is not limited to the specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A method for calculating earth pressure under an arbitrary additional load on the top of a retaining structure in foundation pit engineering, characterized in that, The method includes: Divide the effective arbitrary load into blocks, for the first... i Calculate the additional load for each block. F i And based on the stress diffusion principle, the additional load is calculated. F i Additional stress acting on the local soil after diffusion Wherein, the effective arbitrary load refers to the load acting on the retaining structure after being diffused at a stress diffusion angle of 45°; the number of blocks divided is n , n For natural numbers greater than or equal to 10, the stated i Greater than or equal to 1, less than or equal to n ; For the i The calculation range for the additional load is [number] blocks. Additional load F i The following formula can be used for calculation. ， in, x i For the first i The horizontal distance between the midpoint of the bottom surface of each block and the top surface of the retaining structure. f(x i ) For the additional load distribution function, H The height of the support structure; For the i Each block, the additional load F i Additional stress acting on the local soil after diffusion Size is Based on Rankine's active earth pressure calculation principle, calculate the resultant active earth pressure within the influence range of each block. The following formula is used for calculation: ， in, γ The weight of the soil on the outside of the retaining structure. c For the cohesion of the soil outside the retaining structure, k a The active earth pressure coefficient, , φ The internal friction angle of the soil on the outer side of the retaining structure; Based on the resultant force of active earth pressure within the influence range of each block. Calculate the resultant of the total active earth pressure acting on the retaining structure.

2. The method for calculating earth pressure under an arbitrary additional load on the top of a retaining structure in foundation pit engineering according to claim 1, characterized in that, The effective arbitrary load range is 0~ H , H The height of the support structure is given.

3. The method for calculating earth pressure under an arbitrary additional load on the top of a retaining structure in foundation pit engineering according to claim 1, characterized in that, The n The value range is 10 to 100.

4. The method for calculating earth pressure under an arbitrary additional load on the top of a retaining structure in foundation pit engineering according to claim 1, characterized in that, The total resultant force of the active earth pressure acting on the retaining structure is calculated using the following formula: 。

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