A general analysis method for stability of arbitrary shape slope based on external force moment correction

Abstract

This invention provides a general analysis method for the stability of slopes of arbitrary shapes based on the moment correction of the resultant external force of the blocks, including the following steps: S1, construction of a two-dimensional analysis model of the slope; S2, force analysis of the blocks; S3, finding the center of gravity of the sliding body; S4, acquisition of key geometric parameters; S5, analysis of the overall force and moment balance of the sliding body; S6, solution of stability coefficients. This invention achieves dual analysis of force and moment balance by adopting a unified expression of the resultant external force of the blocks, thus unifying the basic mechanical framework of stability analysis methods. This makes well-known methods and their upgraded versions special cases of this invention, and also overcomes the significant technical limitations of some current methods that can only consider mechanical rigor or applicability on one hand. This invention provides a completely new analytical method system, which not only enables more scientific acquisition of stability analysis results but also provides the most essential path for those in the field to comprehensively understand the theory of stability analysis.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering theoretical analysis, specifically involving a general analysis method for the stability of slopes of arbitrary shapes based on the moment correction of the combined external forces of the blocks. Background Technology

[0002] Slope stability analysis is a long-standing and classic topic in geotechnical engineering. Over decades of development, a variety of stability analysis methods have emerged, which can be broadly categorized into two types: circular arc methods and non-circular arc methods. However, to date, each method has its own drawbacks, and their systematicity and integration are relatively poor. While each method has very distinct characteristics, it is difficult to form a unified analytical form or theoretical framework.

[0003] For example, the transfer coefficient method, which is prevalent in China, only considers projecting the forces on the strips onto the center of the strip base to derive the residual sliding force of the strips, and only considers force equilibrium, thus its mechanical derivation is not rigorous. Similarly, the Janbu method, while considering the force and moment equilibrium conditions of the strips, decomposes the forces vertically and horizontally during the force analysis, making the force analysis too fragmented and lacking a holistic view. Furthermore, its assumptions about the location of inter-strip forces lack a solid mechanical basis, resulting in poor stability analysis performance. The Spencer method derives the formula for the resultant force between strips, but its method is based on a circular arc sliding surface and assumes that the inter-strip forces are parallel, thus limiting its application. The internationally renowned Morgenstern method overcomes the shortcomings of the Spencer method, expanding the applicability of stability analysis; however, its differential process is extremely complex, making it difficult to integrate with various methods and failing to form a unified analytical framework. In summary, the current technology still lacks systematicity and versatility. Summary of the Invention

[0004] The main objective of this invention is to provide a general analysis method for the stability of slopes of arbitrary shapes based on the moment correction of the combined external force of the blocks, in order to address the problems mentioned above.

[0005] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution: A general analysis method for the stability of slopes of arbitrary shapes based on the moment correction of the resultant external force of the blocks includes the following steps: S1. Construction of two-dimensional slope analysis model: Select the main sliding profile of the slope and express multiple information of the main sliding profile of the slope. Then, divide the sliding body into a limited number of blocks. S2. Force analysis of the strip: S21. Select any strip. i Perform force analysis to obtain arbitrary blocks i Right side inter-strip force Z i ; S22. Construct arbitrary blocks i The resultant force Q between the strips i That is, any block i The resultant force vector Q between the left and right side strips i Obtain the resultant force vector Q i The expressions for the horizontal component force, vertical component force, numerical expression, and direction angle expression are given. Since the inter-strip forces are internal forces and the remaining forces are external forces, the resultant force Q of the inter-strip forces is... i In reality, this is the resultant internal force of the block, which is also the reaction force of the resultant external force of the block. The resultant internal force and the resultant external force are equal in magnitude and opposite in direction, therefore the magnitude of the resultant external force of the block is also denoted as Q. i When performing force analysis, the direction must be indicated in the opposite direction to the resultant internal force of the block.

[0006] S3. Finding the center of gravity of the sliding body: Establish a coordinate system, then subdivide the sliding body into vertical and horizontal segments to determine the x-coordinate of the center of gravity of the entire sliding body. x g y-axis y g ; S4. Acquisition of key geometric parameters: Directly measure the key geometric parameters of the blocks and the geometric parameters of key external forces in the two-dimensional analysis model; S5. Overall force and moment balance analysis of the sliding body: Resultant external force Q of each block i The overall force balance analysis, and based on the resultant external force Q of each block. i Overall moment balance analysis with moment correction applied to the moment center point O of the slope; S6. Stability coefficient solution: Based on the overall force balance and overall moment balance analysis, the stability coefficient is solved by iterative solution.

[0007] While adopting the above technical solutions, the present invention may also adopt or combine the following technical solutions: As a preferred embodiment of the present invention, step S1 further includes the following sub-steps: S11. Select the main sliding profile of the slope to obtain multiple information such as slope morphology, sliding body, sliding surface, soil and rock properties, reservoir water in front of the slope, fissure water behind the slope, groundwater level conditions within the slope, boundary conditions, anti-sliding facilities, and moment center O. S12. Arbitrarily select the center point O of the moment and divide the sliding body into finite vertical strips. The hydraulic heights on both sides of the strip are the heights from the two ends of the base of the strip to the groundwater level on both sides of the strip. S13. For areas where the front of the slope is submerged by reservoir water, the soil part of the strip, together with the upper reservoir water within the range extending upward from its two sides, needs to be used to construct a new strip for treatment. At this time, the hydraulic heights on both sides of the new strip are the heights from the two ends of the strip base to the reservoir water surface.

[0008] As a preferred embodiment of the present invention: step S3 specifically involves quantitatively determining the coordinates of the center of gravity of the entire sliding body, including the abscissa of the center of gravity. x g y-axis y g When searching x g First, establish a coordinate system, then subdivide the sliding body into vertical blocks, and denote the x-coordinate of the vertical center line of any block as . x iv The weight of any vertical strip is W. iv Then we obtain the x-coordinate of the centroid; when searching y g Similarly, establish a coordinate system, and then subdivide the sliding body into horizontal blocks. Let the ordinate of the horizontal centerline of any block be denoted as... y ih The weight of any vertical strip is W. ih Then we obtain the ordinate of the centroid.

[0009] As a preferred embodiment of the present invention: in step S4, the key geometric parameters of the strip include the strip width b. i Hydraulic height h on the left side of the strip i-1 and the hydraulic height h on the right i α, the dip angle of the base of the strip i .

[0010] As a preferred embodiment of the present invention: in step S4, the geometric parameters of the key external force include the length H of the load-bearing section of the anti-slide pile. Pi Angle of incidence of anchor bolt tension The force arm L of the water pressure K0 on the front side of the first block is located at the moment center point O. K0 Water pressure K on the rear side of the last strip n The lever arm L from the moment center point O Kn The vertical seismic moment at the center of gravity of the entire sliding body is taken as the moment arm L at the center point O. Ev The horizontal seismic moment at the center point O of the entire sliding body's center of gravity is taken as the lever arm L. Eh The moment arm L of the block's gravity is taken as the moment center point O. 1i The lever arm L of the resultant external force component of the strip block in the direction parallel to the base and passing through the center of the base block is taken as the center point O. 2i The moment arm L of the component of the resultant external force on the strip perpendicular to the base center is taken as the center point O.3i .

[0011] As a preferred technical solution of the present invention: the positive and negative values ​​of the lever arm value need to be determined according to the clockwise or counterclockwise direction of the corresponding force rotating around the torque center point O. When rotating clockwise, it is a sliding torque, so the lever arm value is negative; when rotating counterclockwise, it is a resisting torque, so the lever arm value is positive.

[0012] As a preferred technical solution of the present invention: In step S5, the overall force balance analysis is based on the theory of balance between internal forces and external forces in the sliding body. Since only the inter-strip forces are internal forces, and the inter-strip forces appear in pairs and cancel each other out, the total internal force is 0. Therefore, the sum of the external forces of all strips is also 0. At this time, the sum of the external forces of each strip is decomposed horizontally or vertically, and then the sum of the horizontal external forces or the sum of the vertical external forces is taken as 0, which can represent the overall force balance.

[0013] As a preferred technical solution of the present invention: In step S5, the overall torque balance analysis is divided into two steps. First, the resultant external force Q of each block is analyzed. i The initial moment is taken about the moment center point O of the slope. Then, the lever arm of the external force factor that does not pass through the center of the base of the segment is obtained and the moment is corrected. Finally, the true moment of the resultant external force on each segment about the moment center point O is obtained, as well as the total resultant external moment of all external forces on all segments about the moment center point O. Since the internal forces appear in pairs, the resultant moment of the internal forces about the moment center point O must be 0. According to the overall moment balance of the slope, the total resultant external moment of all external forces on all segments about the moment center point O is taken as 0 for the overall external moment balance analysis.

[0014] As a preferred technical solution of the present invention: step S6 specifically involves: introducing the inter-strip force tilt angle function θ ( x The tilt angle is adjusted by the expansion coefficient λ. After setting different λ values, the inter-strip force Z is calculated sequentially from the first strip to the last strip. i Constructing a combined external force Q i The initial stability value F0 is iterated to obtain the coefficients F0(1) and F0(2) that satisfy the overall force balance and the moment balance, respectively. The two are then equalized by adjusting λ. * =F0(1)=F0(2), and finally determine the stability coefficient F=F * .

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1) It has a rigorous mechanical derivation process. By constructing a unified expression formula for the resultant external force of each block, the slope stability analysis process is clearer and easier to understand than internationally renowned methods such as the Janbu method. At the same time, it adopts the condition of dual equilibrium of force and moment for solution control, which completely overcomes the roughness of the single equilibrium condition of related domestic methods. 2) The method provided by this invention, through the application of the formula for the resultant external force of the block, unifies the basic mechanical framework of most current methods, possessing an all-encompassing essential characteristic. This makes the well-known Spencer method, Morgenstern method, and Bhsiop method all special cases of this invention, while also encompassing upgraded versions of domestic transfer coefficients. Therefore, this invention provides a completely new analytical method system for the field of slope stability, not only enabling the acquisition of more scientific stability analysis results but also providing the most essential path for researchers in this field to more comprehensively understand stability analysis theory. 3) This invention takes into account the rigor of mechanics, the convergence of the solution, and the universality of the method. It can be used under any complex conditions of slope with any shape. It overcomes the huge problem that most current methods can only take into account the rigor or convergence of mechanics, or the applicability of the method. Attached Figure Description

[0016] Figure 1 This is a two-dimensional analysis model for the slope.

[0017] Figure 2 A schematic diagram showing the determination of the center of gravity position for the entire sliding motion.

[0018] Figure 3 This is a force diagram of the block.

[0019] Figure 4 The force-bearing polygon is a strip.

[0020] Figure 5 This is a flowchart for stability analysis.

[0021] Figure 6 This describes the process of solving for the stability coefficient.

[0022] Figure 7 The stability coefficient is solved for the example.

[0023] In the diagram: 1. Water level in front of the slope reservoir; 1b. Water pressure K0 on the front side of the first block; 2. Hydraulic height h0 on the front side of the first block; 3. Anti-slide pile; 3b. Thrust P of the anti-slide pile; 3c. Length H of the loaded section of the anti-slide pile. Pi 3-1, Anchor bolt; 3-1b, Anchor bolt tension T; 3-1c, Anchor bolt incident angle 4. Arbitrary blocks i Vertical seismic force E v W i 4b. Arbitrary blocks i Horizontal seismic force E h W i 5. Sliding surface; 6. Arbitrary block numbering i6b. Center of any block foundation; 6c. Coordinates of the center of any block foundation; 7. Groundwater level within the slope; 8. Lateral water pressure K behind the slope. n 9. Water body within the fissure behind the slope; 9b. Hydraulic height on the back side of the slope; 10. Water pressure K on the back side of the slope. n The lever arm L from the moment center O Kn 11. Slope surface; 11b. Sliding body; 12. Moment center O; 13. L of the entire sliding body's center of gravity perpendicular to the moment point O. Ev 14. The lever arm L of the entire sliding body's center of gravity in the horizontal direction from the moment point O. Eh 15. The position of the center of gravity of the entire sliding motion ( x g , y g ), 15b, when finding the center of gravity of the sliding body, the horizontal coordinate of the vertical center line of any vertically subdivided block. x iv 15c. When finding the center of gravity of the sliding mass, the ordinate of the horizontal centerline of any horizontally subdivided block is... y ih 16. Reservoir water surface; 17. L of the lever arm L of the water pressure on the front side of the first block from the moment point O. K0 18. Strips and blocks i The moment arm L of the gravitational moment is taken at point O. 1i 19. Arbitrary blocks i The moment of force in the base direction is taken at point O, and the lever arm L is... 2i 20. Pass through any block i The moment arm L of the force applied at point O, which is located at the center of the base and perpendicular to the base. 3i 21. The lever arm L of the anti-slide pile thrust moment taken at point O. P 22. Arbitrary blocks i Left side water pressure K i-1 22b, Arbitrary blocks i Left hydraulic height h i、1 22c, any block i Correction arm of water pressure on the left L Ki-1 23. Arbitrary blocks i Base pressure N i 24. Arbitrary blocks i Base pressure U i 25. Arbitrary blocks i Base friction S i 26. Arbitrary blocks i Base dip angle α i 27. Arbitrary blocks i Total external force Q i Inclination angle of the component along the base direction of the strip Qi- α i 28. Arbitrary blocks i Right side water pressure K i 28b, Arbitrary blocks i Right hydraulic height h i 28c, arbitrary blocks i Correction arm of water pressure on the right side L Ki 29. Arbitrary blocks i Total external force Q i 29b, Arbitrary blocks i Total external force Q i Inclination angle Qi 30. Arbitrary blocks i Right side inter-strip force Z i 30b, arbitrary blocks i Right side inter-strip force Z i Inclination angle i 31. Arbitrary blocks i width b i 32. Arbitrary blocks i gravity W i 33. Arbitrary blocks i Left side inter-strip force Z i-1 33b, Arbitrary blocks i Left side inter-strip force Z i-1 Inclination angle i-1 34. Arbitrary blocks i Side water pressure difference K i 35. Expansion coefficient λ axis; 36. Stability coefficient F0(2) axis under torque equilibrium condition; 37. Stability coefficient F0(1) axis under force equilibrium condition; 38. Intersection of torque equilibrium stability coefficient and force equilibrium stability coefficient; 39. Stability coefficient value F corresponding to the intersection of stability coefficients. * 40. The expansion factor λ corresponding to the intersection of stability coefficients * . Detailed Implementation

[0024] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0025] A general analysis method for the stability of slopes of arbitrary shapes based on the moment correction of the resultant external force of the blocks includes the following steps: S1. Construction of a two-dimensional analysis model for the slope; S11. Select the main sliding profile of the slope to obtain multiple information such as slope morphology, sliding body, sliding surface, soil and rock properties, reservoir water in front of the slope, fissure water behind the slope, groundwater level conditions within the slope, boundary conditions, anti-sliding facilities, and moment center O. The sliding mass refers to the entire area of ​​rock and soil that deforms or slides within the slope. The sliding surface is the interface between the deformed or sliding sliding mass and the relatively stationary rock and soil mass below. The boundary conditions are the actual mechanical conditions at the two end boundaries of the sliding mass, namely, the interstrip force Z0=0 at the foremost side of the sliding mass and the interstrip force Z at the rearmost side of the sliding mass. n =0; The sliding mass refers to the entire area of ​​rock and soil that deforms or slides within the slope. The sliding surface is the interface between the deformed or sliding sliding mass and the relatively stationary rock and soil mass below. The boundary conditions are the actual mechanical conditions at the two end boundaries of the sliding mass, namely, the interstrip force Z0=0 at the foremost side of the sliding mass and the interstrip force Z at the rearmost side of the sliding mass. n =0; S12. Arbitrarily select the center point O of the moment and divide the sliding body into finite vertical strips. The hydraulic heights on both sides of the strip are the heights from the two ends of the base of the strip to the groundwater level on both sides of the strip. S13. For areas where the front of the slope is submerged by reservoir water, the soil part of the strip, together with the upper reservoir water within the range extending upward from its two sides, needs to be used to construct a new strip for treatment. At this time, the hydraulic heights on both sides of the new strip are the heights from the two ends of the strip base to the reservoir water surface.

[0026] S2, Force analysis of the strip block; S21. Select any strip. i Perform force analysis to obtain arbitrary blocks i Right side inter-strip force Z i The unified expression formula: (1); In the formula, W i For gravity, E h W i For horizontal seismic force, E v W i For vertical seismic force, Z i-1 For the inter-strip force on the left, Z i For the inter-strip force on the right side, K i-1 Water pressure on the left side, K i P is the water pressure on the right side, P is the thrust of the anti-slide pile, and N is the thrust of the anti-slide pile. i For the base pressure of the strip, U i For the uplift pressure of the strip base, S i Let T be the frictional resistance of the base layer, T be the anchor bolt tension, and θ be the anchor bolt tension. i-1 θ is the angle of inclination of the force between the strips on the left. i c is the angle of inclination of the inter-strip force on the right side; i' represents the cohesive force of the slip surface, ϕ i ' is the angle of friction between the surfaces. K i =K i -K i-1 All are known quantities; α i The dip angle of the strip base. The incident angle of the anchor bolt is the angle of inclination of the anchor bolt tension, which can be measured; E h For horizontal seismic force coefficient, E v , where is the vertical seismic force coefficient, and both are known levels of seismic force in the slope area; F is the stability coefficient (required solution). For blocks without the action of anti-slide pile thrust P or anchor bolt tension T, P or T can be ignored in equation 1).

[0027] Among them, gravity W i Vertical seismic force E v W i The horizontal seismic force E passes through the center of the block foundation and is a known quantity. h W i The known quantity, the location of application is unknown; the force between the left and right side strips (Z) i-1 Z i The unknown quantity is the solution to be found, and its inclination angle is denoted as (θ). i-1 θ i ); left and right side water pressure (K) i-1 K i Based on the hydraulic height (h) on both sides of the strip i-1 h i Measurements and calculations were performed, and the quantities are known; the total pressure N of the strip base was measured. i Represented by other forces, it is an unknown quantity; the lifting pressure U i The hydraulic height on both sides of the block can be measured and calculated, which is a known quantity. The total pressure at the base is N. i Subtract the lifting pressure U i This is the effective pressure of the base (N). i -U i ); Frictional resistance S of the strip substrate i The effective pressure of the block base and the friction parameters of the sliding surface are used for characterization; the anti-slide pile thrust P and the anchor bolt tension T are known quantities preset in the design stage.

[0028] S22. Construct arbitrary blocks i The resultant force Q between the strips i That is, any block i The force between the left and right side strips (Z) i-1 Z i The resultant force vector of ) is obtained as follows: Q i Horizontal component: (2); Qi Vertical component: (3); Q i Value: (4); Q i inclination: (5); Of all the forces acting on the strip, the inter-strip forces are internal forces, and the remaining forces are external forces. Therefore, the resultant force of the inter-strip forces is Q. i In reality, this is the resultant internal force of the block, which is also the reaction force of the resultant external force of the block. The resultant internal force and the resultant external force are equal in magnitude but opposite in direction. Therefore, the magnitude of the resultant external force of the block is also denoted as Q. i However, the direction of the force analysis must be indicated in the opposite direction to the resultant internal force.

[0029] The resultant external force Q of the strip i Due to the weight W of the strip i Horizontal seismic force E h W i Vertical seismic force E v W i Water pressure on the left side K i-1 Water pressure on the right side K i Anti-slide pile thrust P, and strip foundation pressure N i , block foundation uplift pressure U i Frictional resistance S of the strip base i It consists of components such as anchor bolt tension T. Among them, the water pressure on the left side K... i-1 Water pressure K on the right side i The thrust P of the anti-slide pile does not necessarily pass through the center of the strip base, while all other forces pass through the center of the strip base.

[0030] S3, Finding the center of gravity of the glider; Quantitatively determine the coordinates of the center of gravity of the entire sliding body, including the x-coordinate of the center of gravity. x g y-axis y g , When searching x g First, establish a coordinate system, then subdivide the sliding body into vertical blocks, and denote the x-coordinate of the vertical center line of any block as . x iv The weight of any vertical strip is W. iv Then we get the x-coordinate of the centroid. ; When searching y g Similarly, establish a coordinate system, and then subdivide the sliding body into horizontal blocks. Let the ordinate of the horizontal centerline of any block be denoted as... y ihThe weight of any vertical strip is W. ih Then the ordinate of the centroid is obtained. .

[0031] The degree of segmentation in this process is much greater than the degree of segmentation in the construction of a two-dimensional analysis model, ensuring that the center position is found accurately enough.

[0032] S4. Obtaining key geometric parameters; In the two-dimensional analysis model, the key geometric parameters of the strip and the key external forces are directly measured. The key geometric parameters of the strip include the strip width b. i Hydraulic height h on the left side of the strip i-1 and the hydraulic height h on the right i α, the dip angle of the base of the strip i The geometric parameters of key external forces include the length H of the loaded section of the anti-slide pile. Pi Angle of incidence of anchor bolt tension The force arm L of the water pressure K0 on the front side of the first block is located at the moment center point O. K0 Water pressure K on the rear side of the last strip n The lever arm L from the moment center point O Kn The vertical seismic moment at the center of gravity of the entire sliding body is taken as the moment arm L at the center point O. Ev The horizontal seismic moment at the center point O of the entire sliding body's center of gravity is taken as the lever arm L. Eh The moment arm L of the block's gravity is taken as the moment center point O. 1i The lever arm L of the resultant external force component of the strip block in the direction parallel to the base and passing through the center of the base block is taken as the center point O. 2i The moment arm L of the component of the resultant external force on the strip perpendicular to the base center is taken as the center point O. 3i .

[0033] The sign of the lever arm value depends on the clockwise or counterclockwise direction of the force rotating around the torque center point O. When rotating clockwise, it is a sliding torque, so the lever arm value is negative. When rotating counterclockwise, it is a resisting torque, so the lever arm value is positive.

[0034] S5. Overall force and moment balance analysis of the sliding body; The resultant external force Q of each block i The overall force balance analysis, and the overall moment balance analysis based on the moment correction of the slope center point O based on the resultant external force Qi of each block; The overall force balance analysis is based on the theory of equilibrium between internal and external forces in the sliding block. Since only the inter-strip forces are internal forces, and these forces appear in pairs and cancel each other out, the total internal force is 0. Therefore, the sum of the external forces of all the strips is also 0. At this point, the sum of the external forces of each strip is decomposed horizontally or vertically, and then the sum of the horizontal external forces or the sum of the vertical external forces is taken as 0 to represent the overall force balance. (6); The torque balance analysis consists of two steps. First, the resultant external force Q of each block is... i The initial moment is taken about the moment center point O of the slope, and then the moment is corrected for the external force factor that does not pass through the center of the base of the block. Finally, the true moment of the resultant external force on each block about the moment center point O is obtained, as well as the moment balance of the external forces on all blocks about the moment center point O. Specifically: First, the resultant external force Q of the block is... i Treating the force as passing through the center of the base of the strip, we obtain the resultant external force Q of any strip. i Preliminary moment term about the center point O of the slope Because the resultant external force includes the lateral water pressure K, which does not necessarily pass through the center of the base of the block. i-1 K i Anti-slide pile thrust P, horizontal seismic force E h W i In the initial moment calculation, all moments are assumed to pass through the base center. Therefore, moment calculation correction is required, which involves adding a step-by-step adjustment to the initial moment calculation. After modification, we obtain the formula for the torque of the resultant external force on any block about the moment center point O: (7); Finally, since internal forces occur in pairs, the resultant torque of the internal forces about the moment center point O must be zero. According to the torque balance of the total force of the slope, the overall torque balance can be represented by taking the sum of the external forces on all blocks about the moment center point O as zero. (8); In the formula, The water pressure K on the left side of the strip i-1 The corrected lever arm about the moment center point O means that under the resultant external force Q i Lieutenant General K i-1 When the moment is taken as passing through the center of the base, it is overcalculated relative to its actual position. The length of the anti-slip lever arm, therefore, needs to be subtracted. This item; The water pressure K on the right side of the strip i The corrected lever arm about the moment center point O means that under the resultant external force Q i Lieutenant General K iWhen the moment is taken as passing through the center of the base, it is overcalculated relative to its actual position. The length of the sliding lever arm, therefore, needs to be added. This item; The corrected lever arm of the anti-slide pile thrust P about the moment center point O is defined as the force arm of the resultant external force Q. i When P is considered to pass through the center of the base for taking moments, its actual position is over-calculated. The length of the anti-slip lever arm, therefore, needs to be subtracted. In this aspect, when correcting for horizontal seismic force moments, it is first necessary to clarify that the weight of each block is equivalent to the weight concentrated at the center of gravity of the entire sliding body. x g , y g Therefore, the horizontal seismic force E in each block h W i In fact, it is equivalent to gathering at the center of gravity of the entire sliding body, as shown in formula (8). That is, the horizontal seismic force E h W i The corrected lever arm about the moment center point O means that under the resultant external force Q i Lieutenant General E h W i Considered as passing through the strip i When taking moments from the base center, the ordinate relative to its true centroid position is... y g That's overestimating. The length of the sliding lever arm, therefore, needs to be added. This item.

[0035] S6. Solving for the stability coefficient.

[0036] like Figure 5 The diagram illustrates the process of stability coefficient analysis, which involves solving for the stability coefficient through an iterative method. Based on the overall force balance and overall moment balance analysis, the stability coefficient is solved iteratively. First, a function θ(…) describing the inter-strip force inclination angle θ is introduced. x ), x The x-coordinate of the sliding body, specifically the two sides of the block. x The coordinates then correspond to the corresponding θ ( x The numerical value is then introduced, followed by the expansion coefficient λ and θ. x The product of these two components is used to adjust the increase in the angle of inclination between the bars.

[0037] By setting different λ values, the inter-strip force Z on the back side of each strip can be calculated sequentially from the first strip according to formula (1) by inputting the initial stability value F0. i (e.g., the first block) iWhen Z = 1, Z0 = 0 is the boundary condition, and the corresponding Z1 value can be calculated according to formula (1); then the strip i When Z1 = 2, the inter-strip force Z1 on the left side is the same as the inter-strip force Z1 on the right side of the first strip block that has already been calculated. It can be substituted into formula (1) as a known quantity to calculate the value of Z2. This process is repeated until the value of the last strip block is obtained. i When =n, the interstic force Z on the right side is obtained. n Then construct the resultant external force Q of each block. i The initial stability value F0 is calculated iteratively, so that the stability coefficient satisfying the overall force balance formula (6) is denoted as F0(1), and the stability coefficient satisfying the overall moment balance formula (8) is denoted as F0(2). If the two are not equal, the value of λ is adjusted and the iterative calculation of the stability coefficients satisfying the overall force balance formula (6) and the overall moment balance formula (8) is continued until F0(1) is obtained. * =F0(1)=F0(2), then the stability coefficient F=F * .

[0038] like Figure 1 As shown, a typical two-dimensional slope analysis model is presented, including multiple information such as the slope surface, sliding body, sliding surface, reservoir water in front of the slope, groundwater level within the slope, fissure water behind the slope, boundary conditions, anti-slide piles, anchor bolts, and seismic forces. The sliding body is further divided into a limited number of blocks. It can be seen that the sliding surface is the interface between the deformed or sliding part of the slope and the relatively stationary rock and soil mass below. The sliding body is the entire rock and soil mass bounded by the sliding surface and the slope surface. The boundary conditions are the actual mechanical conditions at the two ends of the sliding body, i.e., the front and rear ends of the sliding body are unsupported. Therefore, the boundary conditions are the inter-strip force Z0=0 at the front end and the inter-strip force Z at the rear end of the sliding body. n =0. Additionally, the foremost side of the slope is subjected to water pressure from the reservoir, while the rearmost side is subjected to water pressure from fissure water. The landslide body is divided into uniform vertical strips. In the area at the front of the slope submerged by the reservoir, the soil portion of each strip, along with the upper reservoir water extending upwards from its two boundaries, is used to construct new strips. The hydraulic heights on both sides of the new strip are the heights from the two endpoints of the strip's base to the reservoir water surface (for example, in strip 1, the hydraulic height h0 on its left side is the height from the left endpoint of strip 1's base to the reservoir water surface). Anti-slide piles are installed between the strips, applying an additional anti-slide force P to the landslide body. Anchor bolts pass through the center of gravity of the strip's base, applying an anchoring force T to the landslide body. Under seismic action, the horizontal seismic force on any strip is E. h W i The vertical seismic force is E v W i The length H of the loaded section of the anti-slide pile is also marked. Pi Angle of incidence of anchor bolt tension The force arm L of the water pressure K0 on the front side of the first block is located at the moment center point O.K0 Water pressure K on the rear side of the last strip n The lever arm L from the moment center point O Kn The vertical seismic moment at the center of gravity of the entire sliding body is taken as the moment arm L at the center point O. Ev The horizontal seismic moment at the center point O of the entire sliding body's center of gravity is taken as the lever arm L. Eh Equal geometric parameters.

[0039] like Figure 2 As shown, the display Figure 1 The process of finding the center of gravity during the entire slide. First, establish a coordinate system, and then find the ordinate of the center of gravity point. y g When the sliding body is subdivided into vertical strips, the horizontal coordinate of the vertical center line of any strip is denoted as . x iv The weight of any vertical strip is W. iv The x-coordinate of the centroid is obtained. When searching for the centroid's ordinate y g When the sliding body is subdivided into horizontal blocks, the ordinate of the horizontal centerline of any block is denoted as . y ih The weight of any vertical strip is W. ih Then the ordinate of the centroid is obtained. .

[0040] like Figure 3 As shown, arbitrary blocks are displayed. i The forces acting on it, including gravity W i Horizontal seismic force E h W i Vertical seismic force E v W i Left side inter-strip force Z i-1 The force Z between the right side bars i Water pressure on the left side K i-1 Water pressure K on the right side i Anti-slide pile thrust P, and strip foundation pressure N i , block foundation uplift pressure U i Frictional resistance S of the strip base i Anchor bolt tension T, etc. Total pressure N of the block foundation. i Includes lifting pressure U i Therefore, the effective pressure of the base is N. i -U i Of the forces mentioned above, the known quantity is gravity W. i Horizontal seismic force E h W i Vertical seismic force E v W iAnti-slide pile thrust P, anchor bolt tension T, uplift pressure U i =0.5( w gh i-1 + w gh i )b i / cosα i Water pressure on the left and right sides K i-1 =0.5 w gh i-1 2 K i =0.5 w gh i 2 The known quantity is the force between the left and right side strips (Z). i-1 Z i Total base pressure N i It can be characterized by the remaining forces, the frictional resistance S of the block base. i The effective pressure of the base and the sliding friction parameters are used for characterization. Except for the inter-strip force, which is an internal force, all other forces are external forces, using Q. i The resultant external forces acting on the block are called the net external force. In addition, key geometric parameters of the block are shown, including the block width b. i Hydraulic height h on the left side of the strip i-1 and the hydraulic height h on the right i α, the dip angle of the base of the strip i The forces between the left and right side strips (Z) are marked. i-1 Z i The angle of inclination (θ) i-1 θ i ), combined external force Q i Inclination angle θ Qi Angle of incidence of anchor bolt tension And the lever arm L of the block's gravity moment at the center point O. 1i The lever arm L of the component of the resultant external force on the strip block, parallel to the base and passing through the center of the base block, is located at the moment center point O. 2i The lever arm L of the component of the resultant external force on the strip perpendicular to the base from the center of the base is taken from the moment center point O. 3i Water pressure K on the left side of the strip i-1 Correction arm about the moment center point O Water pressure K on the right side of the strip i Correction arm about the moment center point O The lever arm L of the anti-slide pile thrust P about the moment center point O P and corrective lever arm .

[0041] like Figure 4 As shown, arbitrary blocks are displayed. i Force equilibrium analysis can yield arbitrary blocks i Right side inter-strip force Z i The unified expression formula (1). Strips i The force between the left and right side strips (Z) i-1 Z i The resultant force vector of ) is the resultant force Q between the strips. i Q can be constructed i The value of Q is shown in formula (4). i The angle of inclination is shown in formula (5). Since only the force between the left and right strips is an internal force among all the forces acting on the strip, and the rest are external forces, the resultant force Q between the strips is... i In reality, it's the combined internal force of the blocks. Because any block... i The forces are in equilibrium, so the net internal force and the net external force are equal in magnitude but opposite in direction. Therefore Figure 4 In this context, the value of the net external force on the block is also denoted as Q. i However, the direction is opposite to the resultant internal force.

[0042] like Figure 6 The diagram illustrates the process of solving for the stability coefficient. It shows how the scaling factor is adjusted. Under the condition of iterative calculation of the initial value of the stability coefficient F0, different expansion coefficients are obtained. The initial value curve of the stability coefficient F0(1) under the condition of satisfying the overall force equilibrium, and different expansion coefficients. The initial value of the stability coefficient F0(2) under the condition of satisfying the overall force balance is given by the curve. The stability coefficient value F* corresponding to the point where the two curves intersect is the accurate value of the slope stability coefficient that simultaneously satisfies the overall force balance and the overall moment balance.

[0043] like Figure 7 As shown in the figure, combined with the embodiment, the solution values ​​for specific slope stability are illustrated. This mainly focuses on an actual slope in a hydroelectric reservoir area, with a water unit weight of 9.8 kN / m³. 3 The bulk density of the natural soil is 18.9 kN / m³. 3 The saturated soil has a unit weight of 21.6 kN / m³. 3 ,θ( x )=sin x The sliding surface cohesion was set at 25.2 kPa, the friction angle at 19.6°, and the horizontal seismic force coefficient E. h =0.15, Vertical seismic force coefficient E vTaking a slope stability analysis as an example with a slope stability coefficient of 0.1, anti-slide pile thrust P=560 kN / m, anchor bolt tension T=90 kN / m, and incident angle of 60°, the analysis shows that when both overall force balance and overall moment balance are satisfied, the slope stability coefficient is 1.383, achieving the expected slope reinforcement effect.

[0044] The technical solution of the present invention has been described in conjunction with the specific experimental procedures shown in the accompanying drawings. However, the scope of protection of the present invention is not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions resulting from such changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A general analysis method for the stability of slopes of arbitrary shapes based on the moment correction of the resultant external force of the blocks, characterized in that, Includes the following steps: S1. Select the main sliding profile of the slope and express multiple information about the main sliding profile of the slope. Then, divide the sliding body into a limited number of blocks. S2. Force analysis of the strip: S21. Select any strip i Perform force analysis to obtain arbitrary blocks i Right side inter-strip force Z i S22. Construct arbitrary blocks i The resultant force between the strips is calculated, and its horizontal and vertical components, numerical values, and direction angles are expressed. The reaction force is then obtained, and this reaction force is combined with the resultant external force Q of the strips. i The values ​​are equal but the directions are opposite; S21. Select any strip. i Perform force analysis to obtain arbitrary blocks i Right side inter-strip force Z i A unified expression formula; S22. Construct arbitrary blocks i The resultant force Q between the strips i That is, any block i The force between the left and right side strips (Z) i-1 Z i The resultant force vector of ) is obtained as follows: Q i Horizontal component: (2); Q i Vertical component: (3); Q i Value: (4); Q i inclination: (5); S3. Establish a coordinate system, then subdivide the sliding body into vertical and horizontal segments to determine the x-coordinate of the center of gravity of the entire sliding body. x g y-axis y g ; S4. Directly measure the key geometric parameters of the blocks and the geometric parameters of the key external forces in the two-dimensional analysis model; S5, the resultant external force Q of each block i The overall force balance analysis, and based on the resultant external force Q of each block. i Overall moment balance analysis with moment correction applied to the moment center point O of the slope; S6. Based on the overall force balance and overall moment balance analysis, the stability coefficient is solved by iterative solution.

2. The method according to claim 1, characterized in that: The specific process of step S1 is as follows: S11. Select the main sliding profile of the slope to obtain multiple information such as slope morphology, sliding body, sliding surface, soil and rock properties, reservoir water in front of the slope, fissure water behind the slope, groundwater level conditions in the slope, boundary conditions, anti-sliding facilities, and moment center O. S12. Arbitrarily select the center point O of the moment and divide the sliding body into finite vertical strips. The hydraulic heights on both sides of the strip are the heights from the two ends of the base of the strip to the groundwater level on both sides of the strip. S13. For areas where the front of the slope is submerged by reservoir water, the soil part of the strip, together with the upper reservoir water within the range extending upward from its two sides, needs to be used to construct a new strip for treatment. At this time, the hydraulic heights on both sides of the new strip are the heights from the two ends of the strip base to the reservoir water surface.

3. The method according to claim 1, characterized in that: The specific process of step S3 is as follows: quantitatively determine the coordinates of the center of gravity of the entire sliding body, including the x-coordinate of the center of gravity. x g y-axis y g When searching x g First, establish a coordinate system, then subdivide the sliding body into vertical blocks, and denote the x-coordinate of the vertical center line of any block as . x iv The weight of any vertical strip is W. iv Then we obtain the x-coordinate of the centroid; when searching y g Similarly, establish a coordinate system, and then subdivide the sliding body into horizontal blocks. Let the ordinate of the horizontal centerline of any block be denoted as... y ih The weight of any vertical strip is W. ih Then we obtain the ordinate of the centroid.

4. The method according to claim 1, characterized in that: In step S4, the key geometric parameters of the strip include the strip width b. i Hydraulic height h on the left side of the strip i-1 and the hydraulic height h on the right i α, the dip angle of the base of the strip i .

5. The method according to claim 1, characterized in that: In step S4, the geometric parameters of the key external forces include the length H of the loaded section of the anti-slide pile. Pi Angle of incidence of anchor bolt tension The force arm L of the water pressure K0 on the front side of the first block is located at the moment center point O. K0 Water pressure K on the rear side of the last strip n The lever arm L from the moment center point O Kn The vertical seismic moment at the center of gravity of the entire sliding body is taken as the moment arm L at the center point O. Ev The horizontal seismic moment at the center point O of the entire sliding body's center of gravity is taken as the lever arm L. Eh The moment arm L of the block's gravity is taken as the moment center point O. 1i The lever arm L of the resultant external force component of the strip block in the direction parallel to the base and passing through the center of the base block is taken as the center point O. 2i The moment arm L of the component of the resultant external force on the strip perpendicular to the base center is taken as the center point O. 3i .

6. The method according to claim 5, characterized in that: The sign of the lever arm value depends on the clockwise or counterclockwise direction of the force rotating around the torque center point O. When rotating clockwise, it is a sliding torque, so the lever arm value is negative. When rotating counterclockwise, it is a resisting torque, so the lever arm value is positive.

7. The method according to claim 1, characterized in that: In step S5, the overall force balance analysis is based on the theory of the balance between internal and external forces in the sliding body. Since only the inter-strip forces are internal forces, and the inter-strip forces appear in pairs and cancel each other out, the total internal force is 0. Therefore, the sum of the external forces of all strips is also 0. At this time, the sum of the external forces of each strip is decomposed horizontally or vertically, and then the sum of the horizontal external forces or the sum of the vertical external forces is taken as 0, which indicates that the overall force balance is achieved.

8. The method according to claim 1, characterized in that: In step S5, the overall moment balance analysis is divided into two steps. First, the resultant external force Q of each block is... i The initial moment is taken about the center point O of the slope, and then the moment is corrected for the external force factor that does not pass through the center of the base of the block. Finally, the resultant external force Q on each block is obtained. i The true torque about the moment center point O, and the sum of the external torques of all external forces on the blocks about the moment center point O, are taken. Since the internal forces appear in pairs, the sum of the internal forces about the moment center point O must be 0. According to the overall moment balance of the slope, the sum of the external forces on all blocks about the moment center point O is taken as 0 for the overall external moment balance analysis.

9. The method according to claim 1, characterized in that: The specific process of step S6 is as follows: by introducing the inter-strip force tilt angle function θ ( x The tilt angle is adjusted by the expansion coefficient λ. After setting different λ values, the inter-strip force Z is calculated sequentially from the first strip to the last strip. i Constructing a combined external force Q i The initial stability value F0 is iterated to obtain the coefficients F0(1) and F0(2) that satisfy the overall force balance and the moment balance, respectively. The two are then equalized by adjusting λ. =F0(1)=F0(2), and finally determine the stability coefficient F=F .

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