A general inclined strip method for slope stability analysis considering equivalent moment of gravity factor

Abstract

The application provides a general inclined strip method for slope stability of any shape considering equivalent treatment of gravity factor, comprising the following steps: S1, construction of a two-dimensional analysis model of a main sliding section; S2, force analysis of an inclined strip block; S3, searching for a gravity center position of a sliding body; S4, acquisition of key geometric parameters; S5, analysis of overall force balance and moment balance of a landslide; and S6, solution of a stability coefficient. The application first proposes an equivalent treatment method of a gravity factor of an inclined strip block, aggregates the gravity of each inclined strip block on the gravity center of the whole sliding body, realizes simple and reasonable treatment of the gravity factor of each inclined strip block on the center point O of the moment of the slope body, solves the technical problem of difficult treatment of the gravity factor moment in the inclined strip method, realizes general solution of the slope stability under various conditions, not only meets all the mechanical conditions, but also ensures the convergence problem in the solution process of the stability solution, and avoids the problem of one-sided consideration of mechanical rigor or solution convergence in the prior art.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering theoretical analysis, specifically involving a general oblique strip method for the stability of slopes of arbitrary shapes that considers the equivalent moment of gravity factor. Background Technology

[0002] Slope stability analysis is a long-standing and classic topic in geotechnical engineering. Over decades of development, various stability analysis methods have emerged, which can be broadly categorized into two types: circular arc methods and non-circular arc methods. Currently, due to the vertical orientation of gravity, most methods focus on vertical slice methods, such as the transfer coefficient method popular in China, and the internationally prevalent Janbu method, Spencer method, and Morgenstern method. Of course, some oblique slice methods have also emerged, such as the Sarma method. As is well known, in the vertical slice method, the gravity of the slice is parallel to its vertical direction. Therefore, when analyzing the forces acting on the slice, the treatment of the gravity term is very convenient. It can be considered that the weight of the slice passes directly through the center of the slice base, and the position of its center of gravity relative to the moment point is clear, thus the moment calculation for the gravity term can be directly solved. However, in inclined strip analysis, the weight of the strip intersects the inclined strip at an angle, and the location of the center of gravity is unclear. Taking moments for the weight of the strip becomes very complicated, requiring corrections or special treatments, which are not yet seen in current technology. Moreover, among the above methods, few are applicable to slope stability analysis in all situations; they are usually limited by applicability.

[0003] On the other hand, for some landslides / slopes reinforced with anti-slide piles, the piles may tilt or bend as the slope continues to deform. This causes the thrust of the anti-slide piles to twist at a certain angle. In such cases, dividing the slope into diagonal strips based on the bending of the anti-slide piles is more convenient for real-time stability analysis. For landslides / slopes reinforced with anchor bolts or other anti-slide structures, the applied anchoring force is incident at an oblique angle due to the specific angle of incidence. Therefore, using diagonal strips at the same angle is more suitable for the stability analysis of this type of landslide / slope. Summary of the Invention

[0004] The main objective of this invention is to provide a general oblique strip method for the stability of slopes of arbitrary shapes that considers the equivalent moment of gravity factor, 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 oblique slice method for the stability of slopes of arbitrary shapes, considering the equivalent moment of gravity factor, includes the following steps: S1. Construction of two-dimensional analysis model of main sliding profile: 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 oblique blocks. S2. Force analysis of the inclined block: S21. Select any diagonal strip. i Force analysis was performed to obtain arbitrary oblique blocks. i Right side inter-strip force Z i ; S22. Construct arbitrary oblique blocks i The resultant force Q between the strips i That is, any diagonal strip 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 among all the forces acting on the inclined strip, the inter-strip forces are internal forces, and the remaining forces are external forces, therefore the resultant force Q of the inter-strip forces is... i In reality, it is the resultant internal force of the inclined block, which is also the reaction force of the resultant external force on the inclined block. The resultant internal force and the resultant external force are equal in magnitude and opposite in direction, so the magnitude of the resultant external force on the inclined 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.

[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 inclined strip and the geometric parameters of the key external forces in the two-dimensional analysis model; S5. Overall force and moment balance analysis of the landslide: Resultant external force Q of each inclined block i The overall force balance analysis, and the various external forces (W) of each inclined block. i N i S i P, T, K i-1 K i E h W i E v W i The moment balance analysis is performed on the slope's moment center point O; in the moment balance analysis, it is necessary to find the center of gravity of the entire sliding body and then equivalently concentrate the gravity of each inclined block at the center of gravity of the entire sliding body. x g , y g On the above, for each inclined block, the gravity factor (W) in each external force is... i E h W i E v Wi The lever arm obtained by taking the moment center point O of the slope is equivalent to that obtained by taking the center of gravity of the entire sliding body. x g , y g The direct measurement of the moment arm distance of the location relative to the center point O of the slope (i.e., the moment arm of the gravity of the inclined strip and the vertical seismic moment at the center point O is equivalent to the direct measurement of the moment arm L of the vertical seismic moment at the center point O of the entire sliding mass) is equivalent to the direct measurement of the moment arm L of the vertical seismic moment at the center point O of the entire sliding mass. Ev The lever arm of the horizontal seismic moment taken at the center point O of the inclined strip is equivalent to the lever arm L of the horizontal seismic moment taken at the center point O of the entire sliding mass. Eh This achieves the equivalent moment taking of the slope's moment center point O by the gravity factor of the inclined strip block; 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 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 inclined strips. The hydraulic heights on both sides of the inclined strip are the heights from the two ends of the base of the inclined strip vertically upward to the groundwater level. The actual immersion heights on both sides of the inclined strip are the vertical heights from the two ends of the base of the inclined strip to the intersection of the two sides of the inclined strip with the groundwater level. S13. For areas where the front of the slope is submerged by reservoir water, the soil part of the inclined strip block, together with the reservoir water within the range of its two sides extending obliquely upward, needs to be used to construct a new inclined strip block for treatment. At this time, the hydraulic height on both sides of the new inclined strip block is the height from the vertical upward of the two ends of the inclined strip block base to the reservoir water surface. The actual immersion height on both sides of the new inclined strip block is the vertical height from the two ends of the inclined strip block base to the intersection of the two sides of the inclined strip block with 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, a coordinate system is established, and then 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 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 diagonal strip include the horizontal width b of the diagonal strip. i Hydraulic height h on the left side of the inclined strip i-1 and the hydraulic height h on the right i Inclination angle α of the oblique strip base i Inclination angle of diagonal strip .

[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 first inclined block's front water pressure K0 is the lever arm L of the moment center point O. K0 Water pressure K on the rear side of the end inclined 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 inclined block is taken as the center point O of the moment of gravity. 1i The moment arm L of the force passing through the center of the inclined strip base parallel to the base direction is taken as the moment center point O. 2i The moment of force perpendicular to the base of the inclined strip is taken as the moment arm L at 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 inclined strips is also 0. At this time, the sum of the external forces of each inclined 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 torque balance analysis is based on the theory that the resultant internal torque of all internal forces of the sliding body about the moment center O and the resultant external torque of all external forces about the moment center O are balanced. Since only the inter-strip forces are internal forces, and the inter-strip forces appear in pairs and cancel each other out, the total resultant internal torque is 0. Therefore, the total resultant external torque of each external force of each inclined strip of the sliding body about the moment center point O of the slope is also 0.

[0014] As a preferred technical solution of the present invention: step S6 specifically involves using the function θ( x Define the inter-strip force inclination angle and introduce a coefficient λ to adjust its amplitude; by setting different λ values, calculate the inter-strip force Z sequentially from the first strip block to the last strip block. i This leads to the construction of the combined external force Q of each block. i The coefficients F0(1) and F0(2) for satisfying overall force balance and moment balance are calculated iteratively. By adjusting λ, the two are made to be consistent, and finally the stability coefficient F = F0(2) is obtained. * .

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1) This invention has a rigorous mechanical derivation process, which can comprehensively consider the force balance and moment balance of the sliding body. Moreover, the introduction of oblique strips is more suitable for the stability analysis of slopes under special conditions (such as the tilting and bending of anti-slide piles, the oblique injection of anchor bolts, etc.), and can overcome the inconvenience, defects and versatility problems of the previous vertical strip method; 2) This invention proposes for the first time an equivalent treatment method for the gravity factor of inclined strips, which effectively concentrates the gravity of each inclined strip at the center of gravity of the entire sliding body. x g , y g On the above, a simple and reasonable moment taking of the gravity factor of each inclined strip about the center point O of the slope is realized, which solves the technical problem of difficulty in taking the moment of the gravity factor in the inclined strip. 3) This invention realizes a universal solution for slope stability under various conditions (anti-slide piles, anchors, earthquakes, reservoir water levels, etc.), which not only satisfies all mechanical conditions, but also ensures the convergence problem in the stability solution process; it successfully avoids the huge technical problem that many existing methods can only take into account mechanical rigor or solution convergence on one side. Attached Figure Description

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

[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 general force diagram for any oblique block.

[0019] Figure 4 This is a general force-bearing polygon for any oblique 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 slope stability coefficient is used as an example.

[0023] In the diagram: 1-Water level in front of the reservoir, 1b-Water pressure K0 in front of the first inclined block, 2-Hydraulic height h0 in front of the first inclined block, 3-Anti-slide pile, 3b-Thrust P of the anti-slide pile, 3c-Lever arm L of the anti-slide pile thrust from the moment point O. P 4-Arbitrary diagonal strip i Vertical seismic force E v W i 4b-arbitrary diagonal strip i Horizontal seismic force E h W i 5 - Sliding surface, 6 - Arbitrary oblique strip number i 6b-Arbitrary Diagonal Strip i The base center position ( x i , y i ), 6c-arbitrary diagonal strip i tilt angle 7-Groundwater level within the slope, 7b-Groundwater level within the slope, 8-Water pressure K on the back side of the slope n 9-Water body within the fissure behind the slope, 9b-Hydraulic height h on the back side of the slope n 10-Slope back side water pressure K n The lever arm L from the moment center O Kn11-Slope surface, 12-Moment center O, 13-Lever arm 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 entire sliding center of gravity position ( x g , y g ), 15b - Vertical strip block suitable for seismic force moment analysis i midline x coordinate x iv 15c - Horizontal strips suitable for seismic force moment analysis i midline y coordinate y ih 16 - Reservoir water surface; 17 - L of the lever arm L of the water pressure on the front side of the first inclined block from the moment point O. K0 18-Anchor bolt, 18b-Anchor bolt tension T, 18c-Anchor bolt incident angle 19-Arbitrary diagonal strip i The moment arm L of the gravitational moment taken at point O 1i 20-arbitrary diagonal strips i The moment of force in the base direction is taken at point O, and the lever arm L is... 2i 21-Arbitrary diagonal strip 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 22-Arbitrary diagonal strip i gravity W i 23-Arbitrary diagonal strip i Hydraulic height h at the left end of the base i-1 ',24-arbitrary diagonal strip i Actual immersion height h on the left side i-1 25-arbitrary diagonal strips i Left side inter-strip force Z i-1 25b - Arbitrary oblique strip i Left side inter-strip force Z i-1 Inclination angle i-1 26-Arbitrary diagonal strips i Left side water pressure K i-1 27-Arbitrary diagonal strip i Base pressure N i 28-Arbitrary diagonal strips i Base pressure U i 29-Arbitrary diagonal strip i Base friction, 30-arbitrary oblique block i Horizontal width b i 31-Arbitrary diagonal strip i Base dip angle αi 32-Arbitrary diagonal strip i Total external force Q i 32b - Arbitrary Diagonal Strip i Total external force Q i Inclination angle Qi 33-Arbitrary diagonal strip i Right side water pressure K i 34 - Arbitrary diagonal strips i Right side inter-strip force Z i 34b - Arbitrary Diagonal Strip i Right side inter-strip force Z i Inclination angle i 35-arbitrary diagonal strip i Hydraulic height h at the right end of the base i ', 36 - Arbitrary diagonal strips i Actual immersion height h on the right side i 37-Arbitrary diagonal strip i Side water pressure difference K i 38 - Expansion coefficient λ axis; 39 - Stability coefficient F0(2) axis under torque equilibrium condition; 40 - Stability coefficient F0(1) axis under force equilibrium condition; 41 - Intersection of torque equilibrium stability coefficient and force equilibrium stability coefficient; 42 - Stability coefficient value F corresponding to the intersection of stability coefficients. * 43 - The expansion coefficient value λ corresponding to the intersection of the 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 oblique slice method for the stability of slopes of arbitrary shapes, considering the equivalent moment of gravity factor, specifically includes the following steps: S1. Construction of the two-dimensional analysis model of the main sliding profile: Select the main sliding profile of the slope and express multiple information about the main sliding profile. Then, divide the sliding mass into a limited number of oblique strips. 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.

[0026] S12. Arbitrarily select the center point O of the moment and divide the sliding body into finite inclined strips. The hydraulic heights on both sides of the inclined strip are the heights from the two ends of the base of the inclined strip vertically upward to the groundwater level. The actual immersion heights on both sides of the inclined strip are the vertical heights from the two ends of the base of the inclined strip to the intersection of the two sides of the inclined strip with the groundwater level. S13. For areas where the front of the slope is submerged by reservoir water, the soil part of the inclined strip block, together with the reservoir water within the range of its two sides extending obliquely upward, needs to be used to construct a new inclined strip block for treatment. At this time, the hydraulic height on both sides of the new inclined strip block is the height from the vertical upward of the two ends of the inclined strip block base to the reservoir water surface. The actual immersion height on both sides of the new inclined strip block is the vertical height from the two ends of the inclined strip block base to the intersection of the two sides of the inclined strip block with the reservoir water surface.

[0027] Anti-slide facilities include anti-slide piles and anchor bolts. Both anti-slide piles and anchor bolts pass through the sliding surface and serve to support the sliding mass. Due to the deformation of the slope, the anti-slide piles deform in coordination with the slope, thus exhibiting a certain degree of tilting or bending.

[0028] S2. Force analysis of the inclined strip: S21. Select any diagonal strip. i Force analysis was performed to obtain arbitrary oblique 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- i For the base pressure of the inclined strip block, U i For the uplift pressure of the inclined strip base, S i Let T be the frictional resistance of the inclined strip base, 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 angle of inclination of the strip. 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 represents the vertical seismic force coefficient, and both represent the horizontal seismic force in the slope area, which is known; F is the stability coefficient that needs to be solved. For inclined blocks without the action of anti-slide pile thrust P or anchor bolt tension T, P or T can be ignored in Equation 1.

[0029] Among them, gravity W i Vertical seismic force E v W i The horizontal seismic force E passes through the center of the inclined strip base and is a known quantity. h W i The quantity is known, but the location of its action is unknown; the force between the left and right side strips (Z) i-1 Z i The unknown quantity is the solution required, and its inclination angle is denoted as (θ). i-1 θ i ), can be achieved through the tilt angle morphology function θ( x ) Proposed; left and right side water pressure (K) i-1 K i The hydraulic height (h) on both sides of the inclined strip can be used as a reference. i-1 '、h i ') and actual immersion height (h) i-1 h i ) Perform measurement and calculation, K i-1 =0.5 h i-1 w gh i-1 ', K i =0.5h i w gh i ' is a known quantity, w The density of water; the total pressure N of the inclined strip base. i It can be represented by other forces and is an unknown quantity; the lifting pressure U i U can be calculated by measuring the hydraulic height on both sides of the inclined strip. i =0.5( w gh i-1 '+ w gh i ')b i / cosα i Given the total base pressure 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 inclined strip base i It can be characterized by the effective pressure of the inclined strip base and the friction parameters of the sliding surface; the anti-slide pile thrust P and the anchor bolt tension T are both known quantities preset in the design stage.

[0030] S22. Construct arbitrary oblique blocks i The resultant force Q between the strips i That is, any diagonal strip i The resultant force vector of the forces between the left and right side strips is obtained as follows: Q i Horizontal component: (2) Q i Vertical component: (3) Q i Value: (4) Q i inclination: (5) 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 inclined block, which is also the reaction force of the resultant external force on the inclined 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 on the inclined 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.

[0031] The resultant external force on the block is the weight W of the block. 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, base pressure N i Base pressure U i Base friction S 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 on the right side K i The thrust P of the anti-slide pile does not necessarily pass through the center of the inclined block base, while all other forces pass through the center of the inclined block base.

[0032] S3. Finding the center of gravity in gliding: 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 searchingx 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 ih The weight of any vertical strip is W. ih Then the ordinate of the centroid is obtained. .

[0033] The degree of subdivision of the blocks in this process is much greater than the degree of detail in the diagonal block division in the construction of the two-dimensional analysis model, to ensure that the center position is found accurately enough.

[0034] S4. Obtaining key geometric parameters: In the two-dimensional analysis model, the key geometric parameters of the inclined strip and the geometric parameters of the key external forces are directly measured; The key geometric parameters of the diagonal strip include the horizontal width b of the diagonal strip. i Hydraulic height h on the left side of the inclined strip i-1 and the hydraulic height h on the right i Inclination angle α of the oblique strip base i Inclination angle of diagonal strip .

[0035] 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 first inclined block's front water pressure K0 is the lever arm L of the moment center point O. K0 Water pressure K on the rear side of the end inclined 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 inclined block is taken as the center point O of the moment of gravity. 1i The moment arm L of the force passing through the center of the inclined block base in the direction parallel to the base is taken as the moment center point O. 2i The moment of force perpendicular to the base of the inclined strip is taken as the moment arm L at the center point O. 3i .

[0036] After measuring the value of the lever arm, the sign of the lever arm value is determined by 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.

[0037] S5. Overall force and moment balance analysis of the landslide: Overall force balance analysis of the resultant external force Qi of each inclined block, and moment balance analysis of the resultant external force Qi of each inclined block about the moment center point O of the slope; 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 inclined blocks is also 0. At this point, the sum of the external forces of each inclined block is decomposed into horizontal or vertical components, and then the sum of the horizontal or vertical external forces is taken as 0 to represent the overall force balance. (6) The moment balance analysis is based on the theory that the resultant internal moment of all internal forces of the sliding body about the moment center O and the resultant external moment of all external forces about the moment center O are in balance. Since only the inter-strip forces are internal forces, and the inter-strip forces appear in pairs and cancel each other out, the total resultant internal moment is 0. Therefore, the various external forces (W) of each inclined strip of the sliding body are equal. i N i S i P, T, K i-1 K i E h W i E v W i The sum of external forces acting about the center point O of the slope is also zero. This is because the lateral water pressures between the sections are paired interaction forces, and their moments cancel each other out. The water pressures on the front and rear sides of the slope, K0 and K... n The torques of these two external forces still exist.

[0038] For each inclined block, the gravity factor W is used in the various external forces. i E h W i E v W i The positions of action of all three are definitely related to gravity, located at the center of gravity of the inclined block. However, the center of gravity of the inclined block is difficult to find and is unknown. The center of gravity of the inclined block will almost never pass through the center of the base. Therefore, it is difficult to find the accurate lever arm when taking the moment of the inclined block's gravity factor about the moment center point O of the slope. An equivalent concept needs to be introduced, that is, in finding the center of gravity of the entire sliding body (… x g, y g Based on this, the gravity of each inclined block can be equivalently concentrated at the center of gravity of the entire sliding body. x g , y g On the above, the gravity factor (W) of each inclined block is obtained in this way. i E h W i E v W i The lever arm of the moment about the center point O of the slope can be equivalently represented by the center of gravity of the entire sliding body. x g , y g The direct measurement of the moment arm distance of the location relative to the center point O of the slope (i.e., the moment arm of the gravity of the inclined strip and the vertical seismic moment at the center point O is equivalent to the direct measurement of the moment arm L of the vertical seismic moment at the center point O of the entire sliding mass) is equivalent to the direct measurement of the moment arm L of the vertical seismic moment at the center point O of the entire sliding mass. Ev The lever arm of the horizontal seismic moment taken at the center point O of the inclined strip is equivalent to the lever arm L of the horizontal seismic moment taken at the center point O of the entire sliding mass. Eh This allows for a simple and reasonable calculation of the gravity factor of the inclined blocks. In summary, the moment balance of all external forces acting on all blocks about the moment center point O of the slope can be obtained as follows: (7) S6. Solving for the stability coefficient: like Figure 5 As shown, the stability coefficient is solved by iterative solution based on the overall force balance and overall moment balance analysis.

[0039] First, we introduce the function θ( ) to describe the inclination angle θ of the inter-strip forces. x ), x The x-coordinate represents the horizontal coordinate of the sliding body, specifically the two sides of the inclined 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.

[0040] By setting different λ values, the inter-strip force Z on the back side of each inclined strip can be calculated sequentially according to formula (1) starting from the first inclined strip by inputting the initial stability value F0. i (e.g., the first diagonal block) i When Z = 1, Z0 = 0 is the boundary condition, and the corresponding Z1 value can be calculated according to formula (1); then the oblique strip block iWhen 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 inclined 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 inclined 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 (7) is denoted as F0(2). If the two are not equal, the value of λ is adjusted and the iterative calculation of the stability coefficient satisfying the overall force balance formula (6) and the overall moment balance formula (7) is continued until F0(1) is obtained. * =F0(1)=F0(2), then the stability coefficient F=F * .

[0041] like Figure 1 As shown, a typical two-dimensional slope analysis model is presented, including multiple information such as slope surface, sliding mass, 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. Furthermore, the sliding mass is divided into a limited number of inclined strips with an inclination angle of [value missing]. 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, while the sliding body is the entire rock and soil mass enclosed by the sliding surface and the slope surface. The boundary conditions are the actual mechanical conditions of the two end boundaries of the sliding body, that is, the frontmost and rearmost ends of the sliding body are unsupported. Therefore, the boundary conditions are the interstrip force Z0 = 0 on the frontmost side and the interstrip force Z on the rearmost side 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 uniformly oriented strips. The hydraulic heights on both sides of each strip are the vertical upward heights from the two endpoints of the strip's base to the groundwater level (h). i-1 ',h i The actual immersion heights on both sides of the inclined strip are the vertical heights from the two endpoints of the inclined strip base to the intersections of the inclined strip with the groundwater level (h). i-1 h i In the area where the front of the slope is submerged by reservoir water, the soil portion of the inclined strip, along with the upper reservoir water extending obliquely upwards from its two sides, is used to construct new inclined strips for treatment. At this point, the hydraulic heights on both sides of the new inclined strip are the vertical heights from the two endpoints of the strip base to the reservoir water surface, and the actual immersion heights on both sides are the vertical heights from the two endpoints of the inclined strip base to the points where the inclined strip intersects with the reservoir water surface (e.g., in inclined strip 1, because the reservoir water surface is horizontal, both the hydraulic height and the actual immersion height on its left side are h0). The anti-slide piles tilt or bend as the slope deforms, along their tilt angle... The diagonal blocks and anti-slip piles apply an additional anti-slip force P to the sliding body. This anti-slip force P is also inclined to the horizontal direction at an angle of [angle missing]. The anchor bolt passes through the center of gravity of the inclined block base, applying an anchoring force T to the sliding body. Under seismic action, the horizontal seismic force on any inclined block 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 first inclined block's front water pressure K0 is the lever arm L of the moment center point O. K0 Water pressure K on the rear side of the end inclined 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.

[0042] 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. .

[0043] like Figure 3 As shown, this demonstrates an arbitrary diagonal strip. 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 on the right side K i Anti-slide pile thrust P, inclined strip base pressure Ni Uplift pressure U of the inclined strip base i , the frictional resistance S of the inclined strip base i Anchor bolt tension T, etc. Total pressure N of the inclined strip base. 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 i Anti-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 h i-1 w gh i-1 ', K i =0.5h i w gh i ' is a known quantity; the unknown quantity is the force between the left and right side strips (Z) i-1 Z i Total base pressure N i The frictional resistance S of the inclined strip base can be characterized by the remaining forces. 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 strip are called the resultant external force. In addition, key geometric parameters of the inclined strip are shown, including the width b of the inclined strip. i Hydraulic height h on the left side of the inclined strip i-1 'and the hydraulic height h on the right side i 'The actual water immersion height h on the left side of the inclined strip i-1 And the actual immersion height h on the right side i Inclination angle α of the oblique strip base i Inclination angle of diagonal strip 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 θQi The thrust P of the anti-slide pile and the horizontal inclination angle Angle of incidence of anchor bolt tension T And the lever arm L of the block's gravity moment at the center point O. 1i The moment arm L, which is the moment arm at point O parallel to the base and passing through the center of the base block, is taken as the moment of the base block. 2i The moment arm L, perpendicular to the base and passing through the center of the base block, is taken as the moment center point O. 3i The lever arm L of the anti-slide pile thrust P about the moment center point O P .

[0044] like Figure 4 As shown, this demonstrates an arbitrary diagonal strip. i Force equilibrium analysis can be used to obtain arbitrary oblique blocks. i Right side inter-strip force Z i The unified expression formula (1). Diagonal strip 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 inclined block, and the rest are external forces, the resultant force Q between the strips is... i In reality, it is the resultant internal force of the inclined blocks. Because any inclined 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, as... Figure 4 In the diagram, the net external force on the inclined block is also denoted as Q. i However, the direction is opposite to the resultant internal force.

[0045] like Figure 6 The diagram illustrates the process of solving the stability coefficient, showing 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.

[0046] 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 v =0.1, anti-slide pile thrust P=560 kN / m, inclination angle =6° Anchor bolt tension T=60 kN / m, incident angle Taking a slope angle of 45° as an example, a slope stability analysis was conducted. Under the condition that both overall force balance and overall moment balance are satisfied, the stability coefficient of the landslide is 1.403, achieving the expected slope reinforcement effect.

[0047] 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 oblique strip method for slope stability of arbitrary shapes considering the equivalent moment of gravity factor, characterized in that, Includes the following steps: S1. Construction of two-dimensional analysis model of main sliding profile: 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 oblique blocks. S2. Force analysis of the inclined strip: S21. Select any diagonal strip. i Force analysis was performed to obtain arbitrary oblique blocks. i Right side inter-strip force Z i ; S22. Construct arbitrary oblique blocks i The resultant force Q between the strips i That is, any diagonal strip 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 among all the forces acting on the inclined strip, the inter-strip forces are internal forces, and the remaining forces are external forces, therefore the resultant force Q of the inter-strip forces is... i In reality, it is the resultant internal force of the inclined block, which is also the reaction force of the resultant external force on the inclined block. The resultant internal force and the resultant external force are equal in magnitude and opposite in direction, so the magnitude of the resultant external force on the inclined 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; 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 inclined strip and the geometric parameters of the key external forces in the two-dimensional analysis model; S5. Overall force and moment balance analysis of the landslide: Resultant external force Q of each inclined block i The overall force balance analysis, and the various external forces W of each inclined block. i N i S i P, T, K i-1 K i E h W i E v W i Moment equilibrium analysis of the slope's moment center point O; in the moment equilibrium analysis, it is necessary to find the center of gravity of the entire sliding body and then equivalently concentrate the gravity of each inclined block at the center of gravity of the entire sliding body. x g , y g For each inclined block, the gravity factor W in each external force is... i E h W i E v W i The lever arm obtained by taking the moment center point O of the slope is equivalent to that obtained by taking the center of gravity of the entire sliding body. x g , y g The direct measurement of the moment arm distance from the slope center point O is equivalent to directly measuring the moment arm L of the vertical seismic moment at the entire sliding body's center of gravity. Ev The lever arm of the horizontal seismic moment taken at the center point O of the inclined strip is equivalent to the lever arm L of the horizontal seismic moment taken at the center point O of the entire sliding mass. Eh This achieves the equivalent moment taking of the slope center point O by the gravity factor of the inclined strip block; S6. Stability coefficient solution: Based on the overall force balance and overall moment balance analysis, the stability coefficient is solved through iterative solution. 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, a coordinate system is established, and then 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 we obtain the ordinate of the centroid; The specific process of step S6 is as follows: through the function θ( x Define the inter-strip force inclination angle and introduce a coefficient λ to adjust its amplitude; by setting different λ values, calculate the inter-strip force Z sequentially from the first inclined strip to the last strip. i This leads to the construction of the combined external force Q of each block. i The coefficients F0(1) and F0(2) for satisfying overall force balance and moment balance are calculated iteratively. By adjusting λ, the two are made to be consistent, and finally the stability coefficient F = F0(2) is obtained. .

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 inclined strips. The hydraulic heights on both sides of the inclined strip are the heights from the two ends of the base of the inclined strip vertically upward to the groundwater level. The actual immersion heights on both sides of the inclined strip are the vertical heights from the two ends of the base of the inclined strip to the intersection of the two sides of the inclined strip with the groundwater level. S13. For areas where the front of the slope is submerged by reservoir water, the soil part of the inclined strip block, together with the reservoir water within the range of its two sides extending obliquely upward, needs to be used to construct a new inclined strip block for treatment. At this time, the hydraulic height on both sides of the new inclined strip block is the height from the vertical upward of the two ends of the inclined strip block base to the reservoir water surface. The actual immersion height on both sides of the new inclined strip block is the vertical height from the two ends of the inclined strip block base to the intersection of the two sides of the inclined strip block with the reservoir water surface.

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

4. 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 first inclined block's front water pressure K0 is the lever arm L of the moment center point O. K0 Water pressure K on the rear side of the end inclined 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 inclined block is taken as the center point O of the moment of gravity. 1i The moment arm L of the force passing through the center of the inclined block base in the direction parallel to the base is taken as the moment center point O. 2i The moment of force perpendicular to the base of the inclined strip is taken as the moment arm L at the center point O. 3i .

5. The method according to claim 4, 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.

6. The method according to claim 1, characterized in that: In step S5, the overall force balance analysis is based on the theory of 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 inclined strips is also 0. At this time, the sum of the external forces of each inclined strip is decomposed into horizontal or vertical directions, 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.

7. The method according to claim 1, characterized in that: In step S5, the torque balance analysis is based on the theory that the resultant internal torque of all internal forces of the sliding body about the moment center O and the resultant external torque of all external forces about the moment center O are balanced. Since only the inter-strip forces are internal forces, and the inter-strip forces appear in pairs and cancel each other out, the total resultant internal torque is 0. Therefore, the total resultant external torque of each external force of each inclined strip of the sliding body about the moment center point O of the slope is also 0.

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