Method and device for calculating residual sliding force of arc sliding slope

Abstract

The invention discloses a method and a device for calculating residual sliding force of an arc sliding side slope, which are characterized in that the method for calculating the residual sliding force of the arc sliding side slope is provided based on a simplified Bishop method, a calculation formula of the residual sliding force of the arc sliding side slope is obtained, and load boundary conditions related to a sliding surface are provided for the design of an arc sliding side slope engineering support structure. The design process of the supporting structure is simplified and perfected, and the defect that a calculation method is not given in the aspect according to existing relevant standards is overcome. The calculation process is simple and accurate, the method is convenient and reliable, and the method has obvious guiding significance for geotechnical engineering technicians.

Description

Technical Field

[0001] The present invention belongs to the field of geotechnical engineering design, and particularly relates to a method and device for calculating the remaining sliding force of an arc sliding slope based on the simplified Bishop method. Background Art

[0002] At present, the load-structure method is often used in the design of geotechnical engineering slope support structures. Among them, the load value is usually taken as the larger value of the two results of the remaining sliding force and the earth pressure. For a broken-line sliding slope, there are clear calculation methods in the national standard for calculating the remaining sliding force of the slope. However, for an arc sliding slope, there is currently no relevant standard to provide the calculation of the remaining sliding force of the slope. How to simply, conveniently and accurately calculate the remaining sliding force of an arc sliding slope has become an urgent problem to be solved in the field of geotechnical engineering. Summary of the Invention

[0003] In view of the above situation, the present invention aims to provide a method and device for simply and accurately calculating the remaining sliding force of an arc sliding slope, so as to facilitate the design process of the support structure system of the arc sliding slope and meet the needs of rapid design and reinforcement under specific conditions.

[0004] The design idea of the present invention is: based on the basic principle of the simplified Bishop method, the horizontal resistance of the support structure is applied as an unbalanced force to the strip block in contact with the support structure, and the acting position of the unbalanced force is assumed, and the horizontal resistance of the support structure is re-derived from the simplified Bishop method, and this horizontal resistance is the remaining sliding force of the arc sliding slope.

[0005] The present invention is realized by the following technical solutions:

[0006] A method for calculating the remaining sliding force of an arc sliding slope, the specific steps include:

[0007] Step 1: Use geotechnical design software programmed based on the limit equilibrium principle to establish an original slope model without a support structure, and determine the position of the arc sliding surface of the slope by the way of automatically searching for the arc sliding surface by the geotechnical design software.

[0008] Step 2: Set the proposed support structure on the arc sliding slope to re-establish a slope model including the support structure and the arc sliding surface, only retain the slope sliding body behind the support structure, divide the slope sliding body into n strip blocks, i is the strip block number, the strip block connected to the support structure at the bottom of the slope is i = 1, and the strip block at the top of the slope is i = n.

[0009] Step 3: According to the limit equilibrium condition, the anti-sliding force T at the arc sliding surface i The calculation formula is:

[0010]

[0011] Wherein, c i is the cohesion of the slip surface of slice i; is the internal friction angle of the slip surface of slice i; l i is the length of the slip surface of slice i; F s is the slope safety factor.

[0012] The normal force N on the slip surface of slice i i The calculation formula is:

[0013] N i = W i cosθ i (2)

[0014] Wherein, W i is the self-weight of slice i; θ i is the angle between the slip surface of slice i and the horizontal plane.

[0015] Substitute Equation (2) into Equation (1), the calculation formula of T i is:

[0016]

[0017] Step 4: Set the horizontal resistance T provided by the support structure to slice 1 支护 as an unknown. The acting point of T 支护 is located at 1 / 3 of the slice height above the slip surface. The lever arm R from the center O of the circular arc slip surface to T 支护 The calculation formula is: 支护 is:

[0018]

[0019] Wherein, R is the radius of the circular arc slip surface; θ1 is the angle between the slip surface of slice 1 and the horizontal plane; h1 is the height of slice 1; l1 is the length of the slip surface of slice 1.

[0020] Step 5: The sum of the overall anti-sliding moment on the slip surfaces of all slices and the anti-sliding moment provided by the horizontal resistance of the support structure is as follows:

[0021]

[0022] The overall sliding moment generated by all slices is as follows:

[0023]

[0024] Wherein, d i is the lever arm from the center O of the circular arc slip surface to the self-weight W of slice i i of slice i.

[0025] According to the calculation principle of the simplified Bishop method, equating Equation (5) and Equation (6) gives Equation (7):

[0026]

[0027] Rearranging Equation (7) gives the calculation formula for the unknown T 支护 :

[0028]

[0029] T 支护 is the remaining sliding force of the circular-arc sliding slope that the support structure needs to provide.

[0030] A data processing device uses geotechnical design software programmed based on the limit equilibrium principle to establish an original slope model without a support structure, determines the position of the circular-arc sliding surface of the slope by automatically searching for the circular-arc sliding surface using the geotechnical design software, sets the proposed support structure on the circular-arc sliding slope to re-establish a slope model including the support structure and the circular-arc sliding surface, retains only the slope sliding mass behind the support structure, divides the slope sliding mass into n slices, i is the slice number, the slice in contact with the support structure at the slope bottom is i = 1, and the slice at the slope top is i = n. The device specifically includes:

[0031] The first unit calculates the anti-sliding force of slice i at the circular-arc sliding surface according to the limit equilibrium condition and the normal force of the sliding surface of slice i, specifically including:

[0032] The anti-sliding force T i at the circular-arc sliding surface has the calculation formula:

[0033]

[0034] In the formula, c i is the cohesion of the sliding surface of slice i; is the internal friction angle of the sliding surface of slice i; l i is the length of the sliding surface of slice i; F s is the slope safety factor;

[0035] The normal force N i of the sliding surface of slice i has the calculation formula:

[0036] N i = W i cosθ i

[0037] In the formula, W i is the self-weight of slice i; θ i is the angle between the sliding surface of slice i and the horizontal plane;

[0038] Substitute the calculation formula of N i into the calculation formula of T i , Ti The calculation formula is:

[0039]

[0040] In the second unit, according to the geometric relationship, the lever arm R from the center O of the circular arc slip surface to the horizontal resistance T 支护 is obtained. 支护 Specifically, it includes:

[0041] Set the horizontal resistance T provided by the support structure to block 1 支护 as the unknown. The acting point of T 支护 is located at 1 / 3 of the height of the block above the slip surface. The lever arm R from the center O of the circular arc slip surface to T 支护 is obtained. 支护 The calculation formula is:

[0042]

[0043] In the formula, R is the radius of the circular arc slip surface; θ1 is the angle between the slip surface of block 1 and the horizontal plane; h1 is the height of block 1; l1 is the length of the slip surface of block 1.

[0044] In the third unit, according to the calculation principle of the simplified Bishop method, the sum of the overall anti-sliding moments on the slip surfaces of all blocks and the anti-sliding moments provided by the horizontal resistance of the support structure is equal to the overall sliding moment generated by all blocks. Calculate the remaining sliding force of the circular arc sliding slope that the support structure needs to provide. Specifically, it includes:

[0045] The sum of the overall anti-sliding moments on the slip surfaces of all blocks and the anti-sliding moments provided by the horizontal resistance of the support structure is as follows:

[0046]

[0047] The overall sliding moment generated by all blocks is as follows:

[0048]

[0049] In the formula, d i is the lever arm from the center O of the circular arc slip surface to the self-weight W of block i i ;

[0050] According to the calculation principle of the simplified Bishop method, the sum of the overall anti-sliding moments on the slip surfaces of all blocks and the anti-sliding moments provided by the horizontal resistance of the support structure is equal to the overall sliding moment generated by all blocks. After arranging the above formula, we get:

[0051]

[0052] After arrangement, the calculation formula for the unknown T 支护 is obtained:

[0053]

[0054] T 支护 That is the remaining sliding force of the arc sliding slope that the support structure needs to provide.

[0055] A device for data processing includes a memory and more than one program. The more than one program is stored in the memory and is configured to be executed by more than one processor. The more than one program includes instructions for performing the calculation method of steps 1 to 5 of the above-mentioned calculation method for the remaining sliding force of an arc sliding slope.

[0056] A readable storage medium stores instructions thereon. When the instructions are executed by one or more processors of a device, the device is caused to execute the calculation method of steps 1 to 5 of the above-mentioned calculation method for the remaining sliding force of an arc sliding slope.

[0057] For the calculation method and device for the remaining sliding force of an arc sliding slope according to the present invention, by proposing a calculation method for the remaining sliding force of an arc sliding slope based on the simplified Bishop method, it provides load boundary conditions related to the slip surface for the design of the support structure of the arc sliding slope project, improves the support structure design process, and supplements the deficiency that the existing relevant standards do not give a calculation method in this regard. The calculation process is simple and accurate, the method is convenient and reliable, and it has obvious guiding significance for geotechnical engineering technicians. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0059] Figure 1 It is a schematic diagram of automatically searching for the position of the arc slip surface by geotechnical design software in the calculation method for the remaining sliding force of an arc sliding slope according to the present invention;

[0060] Figure 2 It is a schematic structural diagram of the division of the support structure and the slope sliding mass blocks in the calculation method for the remaining sliding force of an arc sliding slope according to the present invention;

[0061] Figure 3 It is a force analysis diagram of block i in the calculation method for the remaining sliding force of an arc sliding slope according to the present invention;

[0062] Figure 4 It is a force analysis diagram with the support structure and block 1 connected to the support structure as the research object in the calculation method for the remaining sliding force of an arc sliding slope according to the present invention. Detailed implementation manners

[0063] The present invention will be further introduced below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. The components of the embodiments of the present invention described and illustrated in the accompanying drawings here can be arranged and designed in various different configurations. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can also be combined with each other.

[0064] It should be noted that: similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. In the description of the present invention, the terms "first", "second", "third", etc. are only used for distinguishing descriptions, and cannot be understood as indicating or implying relative importance.

[0065] The following further describes the present invention in detail with reference to the accompanying drawings:

[0066] A method for calculating the remaining sliding force of an arc-sliding slope according to the present invention specifically includes the following steps:

[0067] Step 1: Use geotechnical design software programmed based on the limit equilibrium principle to establish an original slope model without a support structure, and determine the position of the arc sliding surface of the slope by the method of automatically searching for the arc sliding surface using the geotechnical design software.

[0068] As Figure 1 shown, geotechnical design software such as Lizheng Geotechnical and Geostudio is used to establish an original slope model without a support structure through such geotechnical design software. In the figure, point O is the center of the arc sliding surface, and R is the radius of the arc sliding surface. And the position of the arc sliding surface of the slope is determined by the method of automatically searching for the arc sliding surface.

[0069] Step 2: Set the proposed support structure on the arc-sliding slope to re-establish a slope model including the support structure and the arc sliding surface. Only keep the slope sliding mass behind the support structure, and divide the slope sliding mass into n blocks. i is the block number. The block in contact with the support structure at the bottom of the slope is i = 1, and the top block of the slope is i = n.

[0070] As Figure 2 shown, in this example, anti-slide piles are used as the support structure, and the slope sliding mass behind them is divided into n blocks. i is the block number, and the block in contact with the anti-slide pile is i = 1.

[0071] Step 3: According to the limit equilibrium condition, the anti-sliding force T at the arc sliding surface i The calculation formula is:

[0072]

[0073] Wherein, c i is the cohesion of the slip surface of block i; is the internal friction angle of the slip surface of block i; l i is the length of the slip surface of block i; F s is the slope safety factor.

[0074] The normal force N on the slip surface of block i i The calculation formula is:

[0075] N i = W i cosθ i (2)

[0076] Wherein, W i is the self-weight of block i; θ i is the angle between the slip surface of block i and the horizontal plane.

[0077] Substitute Equation (2) into Equation (1), the calculation formula of T i is:

[0078]

[0079] As Figure 3 shown, perform a force analysis on block i to obtain the calculation formula of the anti-sliding force T of block i at the circular arc slip surface. i

[0080] Step 4. Set the horizontal resistance T provided by the support structure to block 1 支护 as an unknown. The acting point of T 支护 is located at 1 / 3 of the height of the block above the slip surface. The lever arm R from the center O of the circular arc slip surface to T 支护 The calculation formula is: 支护

[0081]

[0082] Wherein, R is the radius of the circular arc slip surface; θ1 is the angle between the slip surface of block 1 and the horizontal plane; h1 is the height of block 1; l1 is the length of the slip surface of block 1.

[0083] In this example, as Figure 4 shown, take the anti-slide pile and block 1 connected to the anti-slide pile as the research object for force analysis. Among them, assume that the horizontal resistance provided by the anti-slide pile to block 1 is T 支护 , which is the required support force, that is, the remaining sliding force of the circular arc sliding slope to be calculated. According to the calculation principle of the simplified Bishop method, the sum of the overall anti-sliding moments on all block slip surfaces and the anti-sliding moment provided by the horizontal resistance of the support structure is equal to the overall sliding moment generated by all blocks, and then the remaining sliding force of the circular arc sliding slope that the anti-slide pile needs to provide can be successfully calculated. ​​

[0084] Step 5. The sum of the overall anti-sliding moment on all the slip surfaces of the blocks and the anti-sliding moment provided by the horizontal resistance of the support structure is as follows:

[0085]

[0086] The overall sliding moment generated by all the blocks is as follows:

[0087]

[0088] In the formula, d i is the lever arm from the center O of the circular arc slip surface to the self-weight W i of block i.

[0089] According to the calculation principle of the simplified Bishop method, equating formula (5) and formula (6) gives formula (7):

[0090]

[0091] Rearranging formula (7) gives the calculation formula for the unknown T 支护 :

[0092]

[0093] T 支护 is the remaining sliding force of the circular arc sliding slope that the support structure needs to provide.

[0094] So far, the entire calculation process is completed.

[0095] A data processing device according to the present invention uses geotechnical design software programmed based on the limit equilibrium principle to establish an original slope model without a support structure, determines the position of the circular arc slip surface of the slope by automatically searching for the circular arc slip surface using the geotechnical design software, sets the proposed support structure on the circular arc sliding slope to re-establish a slope model including the support structure and the circular arc slip surface, only retains the slope sliding mass behind the support structure, divides the slope sliding mass into n blocks, where i is the block number, the block in contact with the support structure at the bottom of the slope is i = 1, and the top block of the slope is i = n. The device specifically includes:

[0096] The first unit calculates the anti-sliding force of block i at the circular arc slip surface according to the limit equilibrium condition and the normal force of the slip surface of block i.

[0097] The second unit obtains the lever arm R 支护 from the center O of the circular arc slip surface to the horizontal resistance T 支护 according to the geometric relationship.

[0098] In the third unit, according to the calculation principle of the simplified Bishop method, the sum of the overall anti-sliding moment on the sliding surfaces of all slices and the anti-sliding moment provided by the horizontal resistance of the support structure is equal to the overall sliding moment generated by all slices, and the remaining sliding force of the circular sliding slope that the support structure needs to provide is calculated.

[0099] Regarding the above data processing device, the specific methods for each unit to perform operations have been described in detail in the specific implementation manners of the method, and will not be elaborated here.

[0100] A device for data processing according to the present invention includes a memory and more than one program. The more than one program is stored in the memory and is configured to be executed by more than one processor. The more than one program includes instructions for performing the calculation methods in steps 1 to 5 of the above method for calculating the remaining sliding force of a circular sliding slope.

[0101] A readable storage medium according to the present invention stores instructions, and when the instructions are executed by one or more processors of the device, the device is caused to execute the calculation methods in steps 1 to 5 of the above method for calculating the remaining sliding force of a circular sliding slope. Of course, the readable storage medium can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, and an optical data storage device, etc.

[0102] The above description is only the preferred embodiment of the present invention and the explanation of the applied technical principles, and is not intended to limit the scope of the present invention claimed, but only represents the preferred embodiments of the present invention. Those skilled in the art should understand that the scope of the invention involved in the present invention is not limited to the technical solutions formed by the specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the inventive concept. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present invention.

Claims

1. A calculation method for the remaining sliding force of an arc-sliding slope, characterized in that The specific steps include: Step 1: Use geotechnical design software programmed based on the limit equilibrium principle to establish an original slope model without a retaining structure, and determine the position of the circular slip surface of the slope by using the automatic search of the circular slip surface by the geotechnical design software; Step 2: Set the proposed retaining structure on the circular sliding slope to re - establish a slope model containing the retaining structure and the circular slip surface. Only retain the slope slide mass behind the retaining structure, and divide the slope slide mass into n slices. i is the slice number. The slice in contact with the retaining structure at the bottom of the slope is i = 1, and the slice at the top of the slope is i = n; Step 3: According to the limit equilibrium condition, the anti-sliding force T at the circular slip surface i The calculation formula is as follows: where c i is the cohesion of the slip surface of slice i; is the internal friction angle of the slip surface of slice i; l i is the length of the slip surface of slice i; F s is the slope safety factor; The normal force N of the sliding surface of block i i The calculation formula is as follows: N i = W i cosθ i (2) Where, W i is the self-weight of slice i; θ i is the angle between the slip surface of slice i and the horizontal plane; Substitute Equation (2) into Equation (1), T i The calculation formula is: Step 4: Set the horizontal resistance force T provided by the support structure to block 1 支护 as an unknown, T 支护 acts at a position 1 / 3 of the block height above the slip surface, and the lever arm R from the center O of the circular slip surface to T 支护 is calculated by the formula: 支护 The calculation formula is: In the formula, R is the radius of the circular slip surface; θ1 is the angle between the slip surface of slice 1 and the horizontal plane; h1 is the height of slice 1; l1 is the length of the slip surface of slice 1; Step 5: The sum of the overall anti - sliding moments on the slip surfaces of all slices and the anti - sliding moments provided by the horizontal resistance of the retaining structure is as follows: The overall sliding moment generated by all slices is as follows: where d i is the lever arm from the center O of the circular arc slip surface to the self-weight W i of slice i; According to the calculation principle of the simplified Bishop method, making Equation (5) equal to Equation (6) gives Equation (7): The calculation formula for the unknown T is obtained by rearranging Equation (7). 支护 as follows: T 支护 Namely, it is the remaining landslide thrust of the arc sliding slope that the support structure needs to provide.

2. A data processing device, characterized in that, Use geotechnical design software programmed based on the limit equilibrium principle to establish an original slope model without a retaining structure, and determine the position of the circular slip surface of the slope by using the automatic search of the circular slip surface by the geotechnical design software. Set the proposed retaining structure on the circular sliding slope to re - establish a slope model containing the retaining structure and the circular slip surface. Only retain the slope slide mass behind the retaining structure, and divide the slope slide mass into n slices. i is the slice number. The slice in contact with the retaining structure at the bottom of the slope is i = 1, and the slice at the top of the slope is i = n. The device specifically includes: The first unit, calculate the anti - sliding force of slice i at the circular slip surface according to the limit equilibrium condition and the normal force of the slip surface of slice i, specifically including: The anti-sliding force T at the arc sliding surface i The calculation formula is as follows: where c i is the cohesion of the sliding surface of slice i; is the internal friction angle of the sliding surface of slice i; l i is the length of the sliding surface of slice i; F s is the slope safety factor; The normal force N of the sliding surface of block i i The calculation formula is as follows: N i = W i cosθ i Where, W i is the self-weight of slice i; θ i is the angle between the slip surface of slice i and the horizontal plane; Substitute N i into the calculation formula for T i The calculation formula for T i is as follows: The second unit calculates the lever arm R of the center O of the circular arc sliding surface to the horizontal resistance T according to geometric relationships 支护 of the force 支护 , specifically including: Set the horizontal resistance force T provided by the support structure to block 1 支护 as the unknown, T 支护 The acting point is located at 1 / 3 of the block height above the slip surface, and the lever arm R from the center O of the circular arc slip surface to T 支护 is 支护 The calculation formula is: In the formula, R is the radius of the circular slip surface; θ1 is the angle between the slip surface of slice 1 and the horizontal plane; h1 is the height of slice 1; l1 is the length of the slip surface of slice 1; The third unit, according to the calculation principle of the simplified Bishop method, the sum of the overall anti - sliding moments on the slip surfaces of all slices and the anti - sliding moments provided by the horizontal resistance of the retaining structure is equal to the overall sliding moment generated by all slices, and calculate the remaining sliding force of the circular sliding slope that the retaining structure needs to provide, specifically including: The sum of the overall anti - sliding moments on the slip surfaces of all slices and the anti - sliding moments provided by the horizontal resistance of the retaining structure is as follows: The overall sliding moment generated by all slices is as follows: where d i is the lever arm from the center O of the circular arc slip surface to the self-weight W i of slice i; According to the calculation principle of the simplified Bishop method, the sum of the overall anti - sliding moments on the slip surfaces of all slices and the anti - sliding moments provided by the horizontal resistance of the retaining structure is equal to the overall sliding moment generated by all slices. Rearranging the above formula gives: Obtain the unknown T after sorting 支护 The calculation formula of: T 支护 Namely, the remaining sliding force of the arc sliding slope that the support structure needs to provide.

3. A device for data processing, characterized in that, It includes a memory and more than one program. The more than one program is stored in the memory and is configured to be executed by more than one processor; the more than one program contains instructions for performing the calculation methods of steps 1 to 5 in claim 1.

4. A readable storage medium, characterized in that, Instructions are stored thereon. When the instructions are executed by one or more processors of the device, the device executes the calculation methods of steps 1 to 5 in claim 1.

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