A slope stability verification method combining the Swedish circular arc method and monitoring data

Abstract

This invention is a slope stability verification method combining the Swedish circular arc method with monitoring data. Specifically, it involves: reviewing geological survey data of the target slope to obtain initial soil and rock strength parameters and slope angle; installing deformation sensors on the slope surface and underground to acquire real-time slope deformation data; identifying the potential circular arc slip surface of the slope using the three points with the largest deformation; dividing the soil within the potential circular arc slip surface into equal parts of fixed width; and directly calculating the center height and vertical angle of the i-th soil strip using a geometric analytical method based on the geometric parameters of the potential circular arc slip surface and the slope angle; and performing limit equilibrium stability calculations based on the initial soil and rock strength parameters, the calculated soil strip height, and the vertical angle to obtain the stability coefficient of the potential circular arc slip surface, thus verifying the slope stability. This invention not only provides a scientific basis for slope safety management but also makes preventative maintenance and precise management possible, effectively preventing disasters.

Description

Technical Field

[0001] This invention relates to the technical field of geotechnical engineering and geological disaster prevention, and in particular to a slope stability verification method that combines the Swedish circular arc method with monitoring data. Background Technology

[0002] During long-term service, the stability of numerous artificial and naturally modified slopes undergoes dynamic changes due to factors such as rainfall, earthquakes, human engineering activities, and weathering. Traditional slope stability analysis often employs rigid body limit equilibrium methods (such as the Swedish circular arc method and the Janbu method) and is conducted during the design phase based on specific working conditions.

[0003] The Swedish circular arc method is one of the most widely used limit equilibrium methods in the stability analysis of circular sliding slopes. Its basic principle is to calculate the safety factor of the slope by considering the overall moment balance between soil strips. Although this method is very mature in engineering design, directly applying the traditional Swedish circular arc method to verify the stability of existing slopes has significant limitations: in the verification stage, the traditional Swedish circular arc method is a static, one-time calculation model. It cannot utilize real-time data obtained from various monitoring instruments deployed on the slope (such as inclinometers and displacement gauges) to correct and calibrate itself, and cannot reflect the dynamic changes in slope stability.

[0004] Therefore, it is necessary to improve the traditional Swedish circular arc method and develop a verification calculation method specifically for dynamic updating of slope stability. Summary of the Invention

[0005] This invention aims to address the shortcomings of existing technologies by providing a slope stability verification method that combines the Swedish circular arc method with monitoring data.

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

[0007] A slope stability verification method combining the Swedish circular arc method and monitoring data includes the following steps:

[0008] S1: Review the geological survey data of the target slope to obtain the initial soil and rock strength parameters and slope angle. Meanwhile, deformation sensors are installed on the slope surface and underground to obtain real-time monitoring data on slope deformation. The three points with the largest deformation are used to determine the potential circular arc slip surface of the slope, with the center of the potential circular arc slip surface being O and the radius being R.

[0009] S2: Divide the soil within the potential circular slip surface into equal parts of a fixed width b. For the i-th soil strip, the horizontal distance between the center of the soil strip and the toe of the slope is calculated. The horizontal distance between the center O and the slope toe A is... Find the horizontal distance between the slip point of the soil strip and the center of the circle, and the vertical angle between the soil strip and the center of the circle. The vertical distance between the soil strip slip point and the center of the circle can be obtained from the horizontal distance and radius R. This allows us to determine the vertical distance between the soil strip slip point and the vertical intersection of the center of the circle and the potential circular slip surface. The vertical distance between the soil strip slope points and the center of the circle can be calculated using the vertical distances between the soil strip slope points and the horizontal line at the bottom of the slope, and the vertical distance between the center of the circle and the horizontal line at the bottom of the slope. Finally, the soil strip height... The height of the i-th soil strip on the potential circular arc slip surface is derived step by step by the difference between the radius R, the vertical distance between the soil strip slip point and the vertical intersection of the center of the circle and the potential circular arc slip surface, and the vertical distance between the soil strip slope points relative to the center of the circle. We can obtain:

[0010] ;

[0011] ;

[0012] S3. Based on the initial soil and rock strength parameters in step S1 and the soil strip height derived in step S2 on the potential circular arc slip surface. and vertical angle Limit equilibrium stability calculations are performed to obtain the stability coefficient of the potential circular arc slip surface, and the slope stability is verified.

[0013] In step S1, the initial soil and rock strength parameters include cohesion. internal friction angle and soil bulk density .

[0014] The specific steps of step S2 are as follows:

[0015] S21. The potential circular arc slip surface of the slope determined in step S1, with center O and radius... Let the slope toe be A, and the horizontal distance between the center O and the slope toe A be... ;

[0016] S22. First, divide all the soil on the potential circular arc slip surface into equal parts with the same width b. Then, arbitrarily select the i-th soil strip GE on the potential circular arc slip surface. The height of soil strip GE is hi, and the vertical angle between the center O and the line OE connecting soil strip GE is... ;

[0017] Let C be the vertical intersection of the soil strip GE and the horizontal line at the bottom of the slope, and let AC be the horizontal distance between point G on the slope surface and the toe A of the slope.

[0018] ;

[0019] Draw a perpendicular line downwards from the center O of the circle. The perpendicular intersection of the center O and the horizontal line at the bottom of the slope is B. Therefore, the horizontal distance between the center O and the toe A of the slope is AB.

[0020] ;

[0021] Let D be the vertical intersection of the center O and the potential circular slip surface. Draw EF perpendicular to OD through the slip point E of the soil strip. That is, let EF be the horizontal distance between the slip point E and the center O.

[0022] ;

[0023] At the same time, we can obtain:

[0024] ;

[0025] S23. From the vertical distance OF of the soil strip slip point E from the center O, combined with EF obtained in step S22, we can obtain...

[0026] ;

[0027] Therefore, the vertical spacing FD between the soil strip slip points E and D can be obtained:

[0028] ;

[0029] S24. Given that the vertical distance from the center O of the circle to the horizontal line at the bottom of the slope is OB, and the vertical distance from point G on the soil strip surface to the horizontal line at the bottom of the slope is GC, we can obtain...

[0030] ;

[0031] ;

[0032] Draw GH perpendicular to OD through G, meaning the vertical distance from point G on the soil slope surface to the center O is OH.

[0033] ;

[0034] S25: From FD obtained in step S23 and OH obtained in step S24, the height hi of the soil strip is:

[0035]

[0036] .

[0037] In step S3, based on the initial soil and rock strength parameters in step S1 and the soil strip height on the potential circular arc slip surface derived in step S2... and vertical angle Perform limit equilibrium stability calculations, where the i-th soil strip has its own weight. Normal reaction force acting on the slip surface of the soil strip Tangential resistance acting on the slip surface of soil strips Correspondingly, the sliding torque caused by gravity is Anti-slip moment caused by normal reaction force R, the anti-slip torque caused by the tangential resistance of the sliding surface. The ratio of the anti-slip moment to the sliding moment is used as a safety factor, and the stability coefficient of the potential circular arc slip surface is:

[0038] = .

[0039] The beneficial effects of this invention are as follows: By integrating slope monitoring data into the calculation process in real time or periodically, this invention divides the soil on the potential circular arc slip surface of the slope into equal parts, derives the height of the soil strips on the potential circular arc slip surface using geometric relationships, and uses the derived soil strip heights to perform limit equilibrium stability calculations to obtain the stability coefficient of the potential circular arc slip surface. This allows for slope stability verification, enabling the model to self-update based on the actual deformation of the slope. A closed loop of "monitoring-analysis-prediction" is established, making stability analysis no longer an isolated point-in-time judgment, but a continuous assessment reflecting the dynamic evolution of slope stability under the influence of environmental factors. This greatly improves the timeliness and practical guiding significance of the verification calculation; it not only provides a scientific basis for slope safety management but also makes preventive maintenance and precise management possible, effectively avoiding the occurrence of disasters. Attached Figure Description

[0040] Figure 1 This is a schematic diagram illustrating the principle of target slope stability verification calculation in this invention;

[0041] Figure 2 This is an example diagram of the stability verification calculation for target slope 1 in this invention;

[0042] Figure 3 This is an example diagram of the stability verification calculation of target slope 2 in this invention;

[0043] The following will describe in detail, with reference to the accompanying drawings, embodiments of the present invention. Detailed Implementation

[0044] The principles and features of the present invention are described below with reference to the accompanying drawings. The embodiments given are for illustrative purposes only and are not intended to limit the scope of the invention. The invention is described more specifically in the following paragraphs by way of example with reference to the accompanying drawings. The advantages and features of the invention will become clearer from the following description. It should be noted that the drawings are in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the invention.

[0045] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0047] A slope stability verification method combining the Swedish circular arc method and monitoring data includes the following steps:

[0048] S1: Review the geological survey data of the target slope to obtain the initial soil and rock strength parameters and slope angle. According to the slope angle A two-dimensional profile model of the slope was created using CAD software. Meanwhile, deformation sensors were installed on the slope surface and underground to obtain real-time monitoring data of slope deformation. The three points with the largest deformation were used to determine the potential circular arc slip surface of the slope, with the center of the potential circular arc slip surface being O and the radius being R.

[0049] Initial soil and rock strength parameters include cohesion. internal friction angle and soil bulk density .

[0050] S2: Divide the soil within the potential circular slip surface into equal parts with a fixed width b, based on the geometric parameters (O, R, ...) of the potential circular slip surface. and slope angle The center height hi and vertical angle of the i-th soil strip are directly calculated using a geometric analytical method. ,like Figure 1 As shown, the specific steps are as follows:

[0051] S21. The potential circular arc slip surface of the slope determined in step S1, with center O and radius... Let the slope toe be A, and the horizontal distance between the center O and the slope toe A be... ;

[0052] S22. First, divide all the soil on the potential circular arc slip surface into equal parts with the same width b. Then, arbitrarily select the i-th soil strip GE on the potential circular arc slip surface. The height of soil strip GE is hi, and the vertical angle between the center O and the line OE connecting soil strip GE is... ;

[0053] Let C be the vertical intersection of the soil strip GE and the horizontal line at the bottom of the slope, and let AC be the horizontal distance between point G on the slope surface and the toe A of the slope.

[0054] ;

[0055] Draw a perpendicular line downwards from the center O of the circle. The perpendicular intersection of the center O and the horizontal line at the bottom of the slope is B. Therefore, the horizontal distance between the center O and the toe A of the slope is AB.

[0056] ;

[0057] Let D be the vertical intersection of the center O and the potential circular slip surface. Draw EF perpendicular to OD through the slip point E of the soil strip. That is, let EF be the horizontal distance between the slip point E and the center O.

[0058] ;

[0059] At the same time, we can obtain:

[0060] ;

[0061] S23. From the vertical distance OF of the soil strip slip point E from the center O, combined with EF obtained in step S22, we can obtain...

[0062] ;

[0063] Therefore, the vertical spacing FD between the soil strip slip points E and D can be obtained:

[0064] ;

[0065] S24. Given that the vertical distance from the center O of the circle to the horizontal line at the bottom of the slope is OB, and the vertical distance from point G on the soil strip surface to the horizontal line at the bottom of the slope is GC, we can obtain...

[0066] ;

[0067] ;

[0068] Draw GH perpendicular to OD through G, meaning the vertical distance from point G on the soil slope surface to the center O is OH.

[0069] ;

[0070] S25: From FD obtained in step S23 and OH obtained in step S24, the height hi of the soil strip is:

[0071]

[0072] .

[0073] S3. Based on the initial soil and rock strength parameters in step S1 and the soil strip height derived in step S2 on the potential circular arc slip surface. and vertical angle Limit equilibrium stability calculations are performed to obtain the stability coefficient of the potential circular arc slip surface, and the slope stability is verified.

[0074] The i-th soil strip has its own weight. Normal reaction force acting on the slip surface of the soil strip Tangential resistance acting on the slip surface of soil strips Correspondingly, the sliding torque caused by gravity is Anti-slip moment caused by normal reaction force R, the anti-slip torque caused by the tangential resistance of the sliding surface. The ratio of the anti-slip torque to the sliding torque is used as a safety factor. Therefore, the stability coefficient of this potential circular arc slip surface is:

[0075] = .

[0076] Example 1:

[0077] A slope stability verification method combining the Swedish circular arc method with monitoring data, such as... Figure 2 As shown, it includes the following steps:

[0078] S1, the unit weight of the soil on a certain slope. 19KN / m 3 Cohesion The internal friction angle is 7 kPa. The slope angle is 28°. The slope is 16.906°. Deformation sensors are used to obtain real-time monitoring data of slope deformation. The three points with the largest deformation are used to determine the potential circular arc slip surface of the slope.

[0079] S2: Divide the soil within the potential circular slip surface into equal parts with a fixed width b, based on the geometric parameters (O, R, ...) of the potential circular slip surface. and slope angle The center height hi and vertical angle of the i-th soil strip are directly calculated using a geometric analytical method. ,like Figure 2 As shown, the specific steps for deriving using geometric relationships are as follows:

[0080] S21: Determine the potential circular arc slip surface according to step S1. Let the center of the circle be point O, and the radius of the potential circular arc slip surface be... =1429.019cm, the horizontal distance between the center O and the toe of the slope. =617.590cm.

[0081] S22: First, divide all the soil on the potential circular arc slip surface into equal parts of the same width b. Then, arbitrarily select the i-th soil strip on the potential circular arc slip surface, with height hi and the perpendicular angle between the center of the circle and the line connecting the soil strip and the i-th soil strip. ,but

[0082] ;

[0083] S23-S25: ​​The center O, radius R, and horizontal distance of the center O relative to the slope toe of the potential circular slip surface determined based on the slope deformation data in step S1. and slope angle The soil height hi can be obtained, combined with the length of the soil strip slip surface. The stability coefficient of the potential circular arc slip surface can be obtained by combining the results. :

[0084] ;

[0085] ;

[0086] .

[0087] Substituting the known data from steps S1 and S21 into the formulas for steps S22-S25, we can obtain Table 1:

[0088] Table 1. Calculation of Circular Arc Slip Stability Moments in Example 1

[0089]

[0090] Based on this, limit equilibrium stability calculations are performed, and the i-th soil strip has its own weight. Normal reaction force acting on the slip surface of the soil strip Tangential resistance acting on the slip surface of soil strips Correspondingly, the sliding torque caused by gravity is Anti-slip moment caused by normal reaction force R, the anti-slip torque caused by the tangential resistance of the sliding surface. The ratio of the anti-slip torque to the sliding torque is used as a safety factor. Therefore, the stability coefficient of this potential circular arc slip surface is:

[0091] ;

[0092] This indicates that the safety factor of the potential circular arc slip surface is 2.283, meaning that the stability meets the specifications: 1.35 (Level 1 slope), 1.3 (Level 2 slope), and 1.25 (Level 3 slope).

[0093] Example 2:

[0094] A slope stability verification method combining the Swedish circular arc method with monitoring data, such as... Figure 3 As shown, it includes the following steps:

[0095] S1, the unit weight of the soil on a certain slope. 18KN / m 3 Cohesion The internal friction angle is 5 kPa. The slope angle is 25°. The angle is 32.636°. Deformation sensors are used to obtain real-time monitoring data of slope deformation, and the three points with the largest deformation are used to determine the potential circular arc slip surface of the slope.

[0096] S2: Divide the soil within the potential circular slip surface into equal parts with a fixed width b, based on the geometric parameters (O, R, ...) of the potential circular slip surface. and slope angle The center height hi and vertical angle of the i-th soil strip are directly calculated using a geometric analytical method. ,like Figure 3 As shown, the specific steps for deriving using geometric relationships are as follows:

[0097] S21: Determine the potential circular arc slip surface based on the slope deformation data obtained in step S1. Let the center of the circle be point O, and the radius of the potential circular arc slip surface be... =1246.556cm, the horizontal distance between the center O and the toe of the slope. =531.302cm.

[0098] S22: First, divide all the soil on the potential circular arc slip surface into equal parts of the same width b. Then, arbitrarily select the i-th soil strip on the potential circular arc slip surface, with height hi and the perpendicular angle between the center of the circle and the line connecting the soil strip and the i-th soil strip. ,but

[0099] ;

[0100] S23-S25: ​​The center O, radius R, and horizontal distance of the center O relative to the slope toe of the potential circular slip surface determined based on the slope deformation data in step S1. and slope angle The soil height hi can be obtained, combined with the length of the soil strip slip surface. The stability coefficient of the potential circular arc slip surface can be obtained by combining the results. :

[0101] ;

[0102] ;

[0103] .

[0104] Substituting the known data from steps S1 and S21 into the formulas for steps S22-S25, we can obtain Table 2:

[0105] Table 2. Calculation of Circular Slip Stability Moments in Example 2

[0106]

[0107] Based on this, limit equilibrium stability calculations are performed, and the i-th soil strip has its own weight. Normal reaction force acting on the slip surface of the soil strip Tangential resistance acting on the slip surface of soil strips Correspondingly, the sliding torque caused by gravity is Anti-slip moment caused by normal reaction force R, the anti-slip torque caused by the tangential resistance of the sliding surface. The ratio of the anti-slip torque to the sliding torque is used as a safety factor. Therefore, the stability coefficient of this potential circular arc slip surface is:

[0108] ;

[0109] This indicates that the safety factor of the potential circular arc slip surface is 1.248, meaning that the stability does not meet the specifications: 1.35 (Level 1 slope), 1.3 (Level 2 slope), and 1.25 (Level 3 slope).

[0110] This invention extends the functionality of the mature and reliable traditional Swedish circular arc method by dividing the soil on the potential circular arc slip surface of the slope into equal parts, deriving the height of the soil strips on the potential circular arc slip surface using geometric relationships, and using the derived soil strip heights to perform limit equilibrium stability calculations to obtain the stability coefficient of the potential circular arc slip surface, thus verifying the slope stability. This improvement allows the method to seamlessly integrate with a large amount of existing slope engineering design data and monitoring systems, making it easy for engineering technicians to understand and accept, and facilitating large-scale promotion and application in engineering practice. It is particularly suitable for the long-term health diagnosis and safe operation and maintenance of existing slopes.

[0111] The present invention has been described above by way of example with reference to the accompanying drawings. Obviously, the specific implementation of the present invention is not limited to the above-described manner. Any improvements made using the inventive concept and technical solution of the present invention, or direct application to other occasions without modification, are all within the protection scope of the present invention.

Claims

1. A slope stability verification method combining the Swedish circular arc method and monitoring data, characterized in that, Includes the following steps: S1: Review the geological survey data of the target slope to obtain the initial soil and rock strength parameters and slope angle. Initial soil and rock mass strength parameters include cohesion. internal friction angle and soil bulk density Meanwhile, deformation sensors are installed on the slope surface and underground to obtain real-time monitoring data on slope deformation. The three points with the largest deformation are used to determine the potential circular arc slip surface of the slope, with the center of the potential circular arc slip surface being O and the radius being R. S2: Divide the soil within the potential circular slip surface into equal parts of a fixed width b. For the i-th soil strip, the horizontal distance between the center of the soil strip and the toe of the slope is calculated. The horizontal distance between the center O and the slope toe A is... Find the horizontal distance between the slip point of the soil strip and the center of the circle, and the vertical angle between the soil strip and the center of the circle. The vertical distance between the soil strip slip point and the center of the circle can be obtained from the horizontal distance and radius R. This allows us to determine the vertical distance between the soil strip slip point and the vertical intersection of the center of the circle and the potential circular slip surface. The vertical distance between the soil strip slope points and the center of the circle can be calculated using the vertical distances between the soil strip slope points and the horizontal line at the bottom of the slope, and the vertical distance between the center of the circle and the horizontal line at the bottom of the slope. Finally, the soil strip height... The height of the i-th soil strip on the potential circular arc slip surface is derived step by step by the difference between the radius R, the vertical distance between the soil strip slip point and the vertical intersection of the center of the circle and the potential circular arc slip surface, and the vertical distance between the soil strip slope points relative to the center of the circle. We can obtain: ； ； S3. Based on the initial soil and rock strength parameters in step S1 and the soil strip height derived in step S2 on the potential circular arc slip surface. and vertical angle Combined with the length of the soil strip slip surface Perform limit equilibrium stability calculations, where the i-th soil strip has its own weight. Normal reaction force acting on the slip surface of the soil strip Tangential resistance acting on the slip surface of soil strips ; Correspondingly, the sliding torque caused by gravity is Anti-slip moment caused by normal reaction force R, the anti-slip torque caused by the tangential resistance of the sliding surface. The ratio of the anti-slip moment to the sliding moment is used as a safety factor, and the stability coefficient of the potential circular arc slip surface is: = ； The slope stability is verified based on the calculated stability coefficient of the potential circular arc slip surface.

2. The slope stability verification method combining the Swedish circular arc method and monitoring data according to claim 1, characterized in that, The specific steps of step S2 are as follows: S21. The potential circular arc slip surface of the slope determined in step S1, with center O and radius... Let the slope toe be A, and the horizontal distance between the center O and the slope toe A be... ; S22. First, divide all the soil on the potential circular arc slip surface into equal parts with the same width b. Then, arbitrarily select the i-th soil strip GE on the potential circular arc slip surface. The height of soil strip GE is hi, and the vertical angle between the center O and the line OE connecting soil strip GE is... ; Let C be the vertical intersection of the soil strip GE and the horizontal line at the bottom of the slope, and let AC be the horizontal distance between point G on the slope surface and the toe A of the slope. ； Draw a perpendicular line downwards from the center O of the circle. The perpendicular intersection of the center O and the horizontal line at the bottom of the slope is B. Therefore, the horizontal distance between the center O and the toe A of the slope is AB. ； Let D be the vertical intersection of the center O and the potential circular slip surface. Draw EF perpendicular to OD through the slip point E of the soil strip. That is, let EF be the horizontal distance between the slip point E and the center O. ； At the same time, we can obtain: ； S23. From the vertical distance OF of the soil strip slip point E from the center O, combined with EF obtained in step S22, we can obtain... ； Therefore, the vertical spacing FD between the soil strip slip points E and D can be obtained: ； S24. Given that the vertical distance from the center O of the circle to the horizontal line at the bottom of the slope is OB, and the vertical distance from point G on the soil strip surface to the horizontal line at the bottom of the slope is GC, we can obtain... ； ； Draw GH perpendicular to OD through G, meaning the vertical distance from point G on the soil slope surface to the center O is OH. ； S25: From FD obtained in step S23 and OH obtained in step S24, the height hi of the soil strip is: 。

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