A slope limit equilibrium method based on shear deformation coordination

Abstract

The embodiment of the application provides a slope limit equilibrium method based on shear deformation coordination, relates to the technical field of slope stability analysis, and introduces the mechanical concept of shear deformation coordination into the limit equilibrium method, and after the target slope is discretized into a plurality of strips, mechanical calculation is carried out on each strip, the shear force at the bottom of the first strip to the shear force at the bottom of the n-th strip, the normal force at the bottom of the first strip to the normal force at the bottom of the n-th strip, the interstrip shear force and the interstrip normal force are sequentially solved, the H n+1 of the last strip node is obtained, and iteration is carried out to obtain the safety factor F n+1 of the target slope when the condition is met s , which is the safety factor F s of the target slope finally obtained. In the calculation of the interstrip shear force, the method introduces the basic assumption of deformation coordination, combines the calculation of the interstrip force with deformation, has clear physical meaning, avoids the randomness of the interstrip force assumption of the traditional limit equilibrium method, and makes the calculation result more scientific and reliable.

Description

Technical Field

[0001] This invention relates to the field of slope equilibrium analysis technology, and more specifically, to a slope limit equilibrium method based on shear deformation coordination. Background Technology

[0002] The limit equilibrium method for slopes is the mainstream method for slope stability analysis. It is characterized by clear concepts, simple implementation, and ease of mastery by engineering technicians, and has been widely used in slope and landslide prevention and control.

[0003] Research has found that the inter-strip force assumption in the traditional limit equilibrium method is merely to increase constraints and transform statically indeterminate problems into statically determinate solvable problems. It does not consider mechanical rationality, lacks mechanical basis, and has a large degree of arbitrariness. The reasonableness of the calculated safety factor cannot be guaranteed. Summary of the Invention

[0004] The beneficial effects of the embodiments of the present invention include, for example, the slope limit equilibrium method based on shear deformation coordination proposed in the present invention introduces the mechanical concept of shear deformation coordination into the limit equilibrium method, avoids arbitrariness in the analysis, and makes the calculation results more scientific and reliable.

[0005] The embodiments of the present invention can be implemented as follows:

[0006] In a first aspect, the present invention provides a slope limit equilibrium method based on shear deformation coordination, comprising:

[0007] S100: Discretize the target slope and divide it into n blocks from top to bottom by n+1 vertical planes. The multiple blocks are denoted as the i-th block from top to bottom, where i≥1. The two nodes above and below the bottom surface of the i-th block are the i-th node and the (i+1)-th node, respectively. The vertical plane corresponding to the i-th node is the i-th dividing plane.

[0008] S200: Obtain the strip model data, which includes the strip's geometric parameters, strength parameters, deformation parameters, and horizontal displacement of the sliding surface;

[0009] Let the initial safety factor of the slope be Between 0.5 and 2;

[0010] S300: Let the normal force between the first noodle be... =0, inter-strip shear force =0, and intermediate result data are calculated based on model data and inter-strip shear strain calculation formula, and then the inter-strip normal force of the corresponding n+1 facet is obtained based on the intermediate result data. ;

[0011] S400: Judgment And confirmation ;

[0012] S410: Judgment Whether the absolute value is greater than the allowable error delta, when The absolute value of the slope is not greater than the allowable error delta, and the safety factor of the slope is determined as follows: ;when If the absolute value is greater than the allowable error delta, then proceed to S420;

[0013] S420: Judgment Is it greater than 0? If the value is greater than 0, then reduce the safety factor. ,like If the value is less than 0, then increase the safety factor. Then repeat steps S300~S410.

[0014] In an optional implementation, the geometric parameters of the strip include the angle between the bottom surface of the i-th strip and the horizontal plane. The width of the i-th strip The length of the base of the i-th block The length of the (i+1)th facet The strength parameters of the strips include the cohesion of the i-th strip. The friction angle of the i-th strip And the gravity of each block The deformation parameter of the strip is the weighted average of the shear modulus of the soil on the (i+1)th face of the i-th strip. The horizontal displacement of the sliding surface of the i-th block is the horizontal displacement of the corresponding (i+1)-th node. Intermediate result data includes the interstrip shear force of the i-th facet. Inter-strip normal force The shear strain of the (i+1)th facet represents the width. Shear displacement Shear strain Shear stress inter-strip shear force Inter-strip normal force The normal force at the bottom of the i-th block and bottom shear force ;

[0015] according to and The shear displacements of the i-th and (i+1)-th strips at the slice plane were calculated. ,according to and The width of the shear strain was calculated. ,according to and Shear strain was calculated ,according to and Shear stress was calculated ,according to and Calculation of interstrip shear force ,according to , , , as well as The normal force at the base of the i-th strip was calculated. ,according to , , as well as Calculate the shear force at the bottom of the strip. ,according to , , , Calculated ,in = , = / .

[0016] In an optional implementation, according to , and The shear displacements at the slice plane of the i-th and (i+1)-th slices were calculated. The steps include:

[0017] = *(tan( )-tan( )).

[0018] In an optional implementation, according to and The width of the shear strain was calculated. The steps include:

[0019] = ( + ) / 2.

[0020] In an optional implementation, according to and Shear strain was calculated The steps include:

[0021] = / .

[0022] In an optional implementation, according to and Shear stress was calculated The steps include:

[0023] = * .

[0024] In an optional implementation, according to and Calculation of interstrip shear force The steps include:

[0025] = * .

[0026] In an optional implementation, according to , The above , , , as well as The normal force at the base of the i-th strip was calculated. The steps include:

[0027] =( + - - * *sin( )) / (tan( sin( )+cos( )).

[0028] In an optional implementation, according to , , as well as Calculate the shear force at the bottom of the strip. The steps include:

[0029] = *tan( )+ * .

[0030] In an optional implementation, according to , , , Calculated The steps include:

[0031] = *sin( )- *cos( )+ . Attached Figure Description

[0032] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 A schematic flowchart of the slope limit equilibrium method based on shear deformation coordination provided for embodiments of the present invention;

[0034] Figure 2 A strip-block discretization diagram of the slope limit equilibrium method based on shear deformation coordination provided in an embodiment of the present invention;

[0035] Figure 3 A schematic diagram of the geometric dimensions of the i-th strip provided in an embodiment of the present invention;

[0036] Figure 4 The shear displacement between blocks on the (i+1)th facet provided in the embodiment of the present invention Calculation diagram;

[0037] Figure 5 The stress analysis diagram of the slope strip provided in the embodiment of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 some embodiments of the present invention, and not all embodiments. 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.

[0039] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0040] It should be noted that similar labels 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.

[0041] In the description of this invention, it should be noted that if terms such as "upper," "lower," "inner," or "outer" are used to indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of this invention is usually placed, they are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0042] Furthermore, the terms "first" and "second" are used only to distinguish descriptions and should not be interpreted as indicating or implying relative importance.

[0043] It should be noted that, where there is no conflict, the features in the embodiments of the present invention can be combined with each other.

[0044] The limit equilibrium method for slopes is the mainstream method for slope stability analysis. It is characterized by clear concepts, simple implementation, and ease of mastery by engineering technicians, and has been widely used in slope and landslide prevention and control.

[0045] Research has found that the inter-strip force assumption in the traditional limit equilibrium method is merely to increase constraints and transform statically indeterminate problems into statically determinate solvable problems. It does not consider mechanical rationality, lacks mechanical basis, and has a large degree of arbitrariness. The reasonableness of the calculated safety factor cannot be guaranteed.

[0046] To address the aforementioned issues, the slope limit equilibrium method based on shear deformation coordination proposed in this invention introduces the mechanical concept of shear deformation coordination into the limit equilibrium method, avoiding arbitrariness in the analysis and making the calculation results more scientific and reliable.

[0047] The following detailed description, in conjunction with the accompanying drawings, outlines the specific steps of the slope limit equilibrium method based on shear deformation coordination provided by this invention, as well as the corresponding technical effects it brings.

[0048] Please refer to Figure 1 The slope limit equilibrium method based on shear deformation coordination provided by this invention includes:

[0049] S100: Discretize the target slope:

[0050] Please refer to Figure 2 and Figure 5 The target slope is discretized, divided into n segments by n+1 vertical planes from top to bottom. These segments are then designated as the i-th segment, where i ≥ 1. The two nodes above and below the bottom surface of segment i are the i-th node and the (i+1)-th node, respectively. In other words, the bottom surfaces of the i-th segment from top to bottom are the i-th node and the (i+1)-th node, respectively. The vertical plane corresponding to the i-th node is the i-th segment.

[0051] In other words, for any strip i, the side furthest from the next strip is denoted as i, and the side closest to the next strip is denoted as node i+1. It is easy to understand that the node number between two adjacent strips can also represent the number of the vertical face, that is, the number of the strip face.

[0052] S200: Please refer to Figure 3 as well as Figure 4 The model data for each block is obtained, including the geometric parameters, strength parameters, deformation parameters, and horizontal displacement of the sliding surface.

[0053] The geometric parameters of the strips include the angle between the bottom surface of the i-th strip and the horizontal plane. The length of the base of the i-th block The width of the i-th strip and the length of the (i+1)th facet .

[0054] The strength parameters of the strips include the cohesion of the i-th strip. The friction angle of the i-th strip And the gravity of each block The horizontal displacement of the sliding surface of the i-th block is the horizontal displacement of the corresponding (i+1)-th node. .

[0055] The intermediate results data include the conditional shear force of the i-th facet. Inter-strip normal force The shear strain of the (i+1)th slice represents the width Shear displacement Shear strain Shear stress inter-strip shear force Inter-strip normal force The normal force at the bottom of the i-th block and bottom shear force .

[0056] The deformation parameter of the strip is the weighted average of the shear modulus of the soil on the (i+1)th strip surface of the i-th strip. All of this data can be obtained through existing measurement methods, and will not be elaborated upon here.

[0057] S300: Obtain the inter-strip normal force on the last slice face. .

[0058] Let the interstrip normal force of the first facet be... =0 and interstrip shear force =0, and intermediate result data are calculated based on model data and inter-strip shear strain calculation formula, and then the inter-strip normal force on the corresponding (n+1)th strip surface is obtained based on the intermediate result data. .

[0059] Specifically, the shear displacement at the slice plane of the i-th and (i+1)-th slices. According to , and The calculations yielded the following results: = *(tan( )-tan( )).

[0060] Shear strain represents width Able to be based on and The calculations yielded the following results: = ( + ) / 2.

[0061] Shear strain Able to be based on and The calculations yielded the following results: = / .

[0062] Able to be based on and Shear stress was calculated Specifically, it includes: = * .

[0063] interstrip shear force Able to be based on Narrative The calculations are as follows: = * The interstrip shear force on the first slice facet is zero.

[0064] Normal force at the base of the i-th strip Able to be based on , , , , as well as The calculations yielded the following results: =( + - - * *sin( )) / (tan( sin( )+cos( )).

[0065] Shear force at the bottom of the strip Able to be based on , , as well as The calculations specifically include = *tan( )+ * .

[0066] Intersegmental normal force on the slice surface According to , , , The calculations yielded the following results: = *sin( )- *cos( )+ Then, based on the above formula, force analysis is performed on the first to the nth (i.e., the last) strip, and the inter-strip normal force on the last strip (i.e., the (n+1)th) strip is calculated. It should be noted that the above... = / , = i / It should be noted that, The bottom cohesion of the i-th strip is... Let be the internal friction angle of the i-th strip, and the angle of friction of the first node. = =0.

[0067] S400: Judgment And confirmation :

[0068] S410: Judgment Whether the absolute value is greater than the allowable error delta, when The absolute value of the slope is not greater than the allowable error delta, so the safety factor of the slope is determined. That is, based on the determined safety factor The calculated inter-strip normal force on the last slice facet is within the preset allowable error delta. It should be noted that the allowable error delta can be determined based on the specific circumstances, but this will not be elaborated upon here.

[0069] It should be noted that, Let be the safety factor of the slope, and denote the initial safety factor. Between 0.5 and 2, in this embodiment, the initial safety factor is set to be between 0.5 and 2. =1. Of course, in other embodiments, the initial safety factor is... It is not limited to 1.

[0070] And when When the absolute value of the error is greater than the allowable error delta, then proceed to S420.

[0071] S420, judgment Is it greater than 0, when When the value is greater than 0, reduce the safety factor. ,when When the value is less than 0, increase the safety factor. Then repeat steps S300-S410.

[0072] In other words, it needs to be based on the changed calculate as well as Further calculations Specifically, it also needs to be based on the changed... as well as Recalculate as well as And then based on the re-obtained , and Calculated Then repeat steps S300-S410.

[0073] It's easy to understand, when entering the judgment... After the step of checking if it is greater than 0, according to Check if it is greater than zero The increase or decrease is used to recalculate. as well as Then, based on the newly obtained , and Calculated until Within the allowable error range, the safety factor of the target slope is then determined. .

[0074] In summary, the slope limit equilibrium method based on shear deformation coordination proposed in this invention introduces the mechanical concept of shear deformation coordination into the limit equilibrium method. By discretizing the target slope into multiple segments, mechanical calculations are performed on each segment to obtain the slope on the last segment surface. Based on the judgment steps, the safety factor of the target slope is finally obtained. Mechanical analysis was introduced into the analysis to avoid arbitrariness in the analysis and to make the calculation results more scientific and reliable.

[0075] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A slope limit equilibrium method based on shear deformation coordination, characterized in that, include: S100: Discretize the target slope and divide it into n blocks from top to bottom by n+1 vertical planes. The blocks are denoted as the i-th block from top to bottom, where i≥1. The two nodes above and below the bottom surface of the i-th block are the i-th node and the (i+1)-th node, respectively. The vertical plane corresponding to the i-th node is the i-th dividing plane. S200: Obtain the strip model data, which includes the geometric parameters, strength parameters, deformation parameters, and horizontal displacement of the sliding surface of the strip; Let the initial safety factor of the slope be Between 0.5 and 2; S300: Let the normal force between the first noodle be... =0, inter-strip shear force =0, and intermediate result data is calculated based on the model data and the inter-strip shear strain calculation formula. The intermediate result data includes the inter-strip shear force of the i-th segment. Inter-strip normal force The shear strain of the (i+1)th facet represents the width Shear displacement Shear strain Shear stress inter-strip shear force Inter-strip normal force The normal force at the bottom of the i-th strip and bottom shear force Then, based on the intermediate result data, the inter-strip normal force of the corresponding (n+1)th facet is obtained. ; S400: Determine the... And confirm the above ; S410: Determine the... Whether the absolute value is greater than the allowable error delta, when the The absolute value of the slope is not greater than the allowable error delta, therefore the safety factor of the slope is determined to be... When the stated If the absolute value is greater than the allowable error delta, then proceed to S420; S420: Determine the... Is it greater than 0? If the value is greater than 0, then decrease the safety factor. ,like If the value is less than 0, then increase the safety factor. Then repeat steps S300~S410.

2. The slope limit equilibrium method based on shear deformation coordination according to claim 1, characterized in that: The geometric parameters of the strip include the angle between the bottom surface of the i-th strip and the horizontal plane. The width of the i-th strip The bottom length of the i-th strip The length of the (i+1)th facet The strength parameters of the strips include the cohesion of the i-th strip. The friction angle of the i-th strip And the gravity of each block The deformation parameter of the strip is the weighted average of the shear modulus of the soil on the (i+1)th face of the i-th strip. The horizontal displacement of the sliding surface of the i-th block is the horizontal displacement of the (i+1)-th node. ; According to the above and the aforementioned The shear displacements of the i-th and (i+1)-th strips at the slice plane were calculated. According to the above and The width representing the shear strain was calculated. According to the above and the aforementioned The shear strain was calculated. According to the above and the aforementioned The shear stress was calculated. According to the above and the aforementioned The interstrip shear force was calculated. According to the above The above , The above The above as well as The normal force at the base of the i-th strip is calculated. According to the above The above , and the Calculate the shear force at the bottom of the strip. ,according to , , , Calculated ,in = , = / .

3. The slope limit equilibrium method based on shear deformation coordination according to claim 2, characterized in that, According to the and the aforementioned , The shear displacements at the slice plane of the first and (i+1)th slices were calculated. The steps include: = *(so( )-so( ))。 4. The slope limit equilibrium method based on shear deformation coordination according to claim 2, characterized in that, According to the above and The width representing the shear strain was calculated. The steps include: =（ + ） / 2。 5. The slope limit equilibrium method based on shear deformation coordination according to claim 2, characterized in that, According to the and The shear strain was calculated. The steps include: = / 。 6. The slope limit equilibrium method based on shear deformation coordination according to claim 2, characterized in that, According to the and the aforementioned The shear stress was calculated. The steps include: = * 。 7. The slope limit equilibrium method based on shear deformation coordination according to claim 2, characterized in that, According to the and the aforementioned The interstrip shear force was calculated. The steps include: The = * .

8. The slope limit equilibrium method based on shear deformation coordination according to claim 2, characterized in that, According to the The above The above The above The above The above as well as The normal force at the base of the i-th strip is calculated. The steps include: The =( + - - * *sin( )) / (tan( sin( )+cos( )).

9. The slope limit equilibrium method based on shear deformation coordination according to claim 2, characterized in that, According to the The above , and the Calculate the shear force at the bottom of the strip. The steps include: The = *tan( )+ * .

10. The slope limit equilibrium method based on shear deformation coordination according to claim 2, characterized in that, According to , , , Calculated The steps include: = *without( )- *cos( )+ 。

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