A method for constructing a two-dimensional potential sliding surface model of slope under principal stress deflection mode

Abstract

The present invention relates to a method for constructing a potential sliding surface model for two-dimensional slope stability analysis, which belongs to the field of engineering disaster prevention and reduction and computer-aided design, and specifically provides a method for constructing a two-dimensional slope potential sliding surface model under a principal stress deflection mode. The present invention uses a physical and mechanical model of slope shear failure to combine principal stress deflection with the most unfavorable shear direction to construct a potential sliding surface model that can effectively show the actual sliding surface morphology when the slope slides. At the same time, the known boundary conditions of the lower sliding point and the upper sliding point on the sliding surface are introduced to achieve the dual goals of rationality and simplicity of potential sliding surface generation, thereby reliably improving the accuracy of slope stability assessment under complex conditions, and further providing strong scientific guidance for the definition of the slope landslide range and the determination of the reinforcement area. The implementation method of the present invention has the advantages of strong practicality, wide application range, good versatility, and high calculation efficiency.

Description

Technical Field

[0001] The invention belongs to the field of engineering disaster prevention and reduction and computer-aided design, and specifically relates to a method for constructing a two-dimensional slope potential sliding surface model under a principal stress deflection mode. Background Art

[0002] According to statistics from the Ministry of Natural Resources, landslide disasters account for about a quarter of natural geological disasters in my country. In order to effectively curb or reduce the losses caused by landslides, there is an urgent need for an accurate and reliable method to identify the most dangerous potential sliding surface, so as to accurately evaluate the stability of the slope. In this process, a reasonable theoretical model of potential sliding surface can effectively show the failure characteristics of the slope rock and soil, thereby providing a prerequisite for the accurate calculation of the slope safety factor and the precise search for the most dangerous potential sliding surface. Therefore, constructing a reasonable and effective theoretical model of potential sliding surface is the core of determining the accuracy and reliability of the evaluation results.

[0003] In the existing slope stability analysis methods, the potential sliding surface theoretical model is mainly divided into two types: specific curve sliding surface model and arbitrary random sliding surface model. For specific curve sliding surface models, including straight line, arc and logarithmic spiral, it mainly applies different mathematical geometric specific curve models to simulate the sliding behavior of different types of rock and soil slopes based on actual geological conditions and engineering experience. For example, in sandy soil slopes, two boundary points on a straight line are given to define a straight sliding surface. In clay soil slopes, arc or logarithmic spiral boundary points are given and the polar diameter is controlled to rotate around a certain center point to realize the construction of arc or logarithmic spiral sliding surface. For arbitrary random sliding surface models, they can be mainly divided into two categories. One is to determine the distribution state of discrete points on the potential sliding surface through a certain assumed relationship, and on this basis, connect the discrete points in a certain way to construct an arbitrary sliding surface model. The other is to construct a mathematical function expression and give different random parameters of the mathematical function to obtain a random curve to fit different forms of sliding surfaces.

[0004] Among the current theoretical models of potential sliding surfaces, the specific curve sliding surface model has the advantages of involving fewer parameters and a simple construction method. However, if the slope surface shape and geological conditions are relatively complex, the specific curve sliding surface model is often difficult to accurately and effectively capture the most dangerous potential sliding surface position, and it is also difficult to reflect the complex and changeable sliding characteristics. Therefore, there is a defect of insufficient applicability. As for the arbitrary random sliding surface model, the random characteristics of its sliding surface construction make it more accurate in theory to obtain the most dangerous potential sliding surface of the slope, but it often has the disadvantage of involving more parameters and low calculation efficiency. In addition, the random sliding surface does not consider the physical and mechanical mechanism of slope failure and brings many unreasonable potential sliding surfaces. In order to limit the irrationality of the potential sliding surface generation, a large number of constraints need to be introduced, so that the construction of the potential sliding surface model is relatively cumbersome, which is not conducive to the efficient operation of slope stability analysis.

[0005] With the increasing complexity of slope geological conditions and the refinement of engineering construction in actual projects, it is necessary to conduct slope stability analysis in a simple, accurate and reasonable manner. However, the potential sliding surface theoretical model used in existing slope stability analysis still has some shortcomings and is difficult to meet the needs of actual engineering analysis. Specifically, in the current potential sliding surface theoretical model construction method, in order to reflect the failure characteristics of complex slopes and accurately obtain the most dangerous potential sliding surface, it is often necessary to involve a large number of sliding surface shape parameters and introduce many constraints, making the determination of the most dangerous potential sliding surface more cumbersome and inefficient, and difficult to be widely used in actual slope engineering. However, the widely used specific curve sliding surface model ignores the influencing factors such as complex slope shape and geological conditions, which leads to the problem of insufficient accuracy and reliability of potential sliding surface construction. Therefore, the existing method faces the contradiction between the accuracy and practicality of the potential sliding surface theoretical model construction.

[0006] For example, patent application CN202311847890.5 provides an ant colony optimization method and system for searching for critical sliding surfaces of slopes, which relates to the fields of civil engineering and geological engineering technology. The method includes establishing a slope analysis model according to slope engineering; using Visual Fortran language to write ABAQUS UMAT subroutine to establish a unified strength criterion material model; based on the unified strength criterion material model, obtaining normal stress values ​​and shear stress values ​​at discrete points; defining safety factors based on the unified strength criterion according to the normal stress values, shear stress values, and maximum and minimum principal stress values ​​at discrete points; constructing an ant colony optimization algorithm to search for critical sliding fields, and obtaining critical sliding fields and safety factors of slopes. This method can fully consider the shapes of various slopes, search for critical sliding surfaces of slopes based on the finite element limit equilibrium method and the ant colony optimization algorithm, and consider the influence of the intermediate principal stress of the soil. The results obtained are more reasonable than those based on the Mohr-Coulomb criterion. However, the sliding surface generation and search process of this patent not only requires the use of numerical simulation calculations to obtain the slope stress field in advance, but also requires the combination of mathematical ant colony optimization algorithms to generate random sliding surfaces. As a result, the calculation method of this patent method is relatively complicated and heavily relies on existing numerical simulation software without independence. In addition, the physical and mechanical mechanism of slope shear failure is not applied to ensure the rationality of sliding surface generation, which requires this patent method to spend a lot of time to determine the irrationality of the generated sliding surface during the calculation process, thereby affecting the calculation efficiency and reliability.

[0007] Therefore, exploring a simple, practical, applicable and reliable potential sliding surface model and its construction method is an important issue that needs to be solved urgently in the field of slope engineering. Summary of the invention

[0008] To this end, the present invention designs a new method for constructing a potential sliding surface model. With the help of the physical and mechanical model of slope shear failure, the principal stress deflection is combined with the most unfavorable shear direction to construct a potential sliding surface model that can effectively show the actual sliding surface morphology when the slope slides. At the same time, the known boundary conditions of the sliding out point under the sliding surface and the upper sliding out point are introduced to achieve the dual goals of rationality and simplicity of potential sliding surface generation. Furthermore, the accuracy of slope stability assessment under complex conditions is reliably improved, and strong scientific guidance is further provided for the definition of the slope landslide range and the determination of the reinforcement area. The implementation method of the present invention has the advantages of strong practicality, wide application range, good versatility, and high computational efficiency.

[0009] Therefore, the present invention provides a method for constructing a potential sliding surface model of a two-dimensional slope under a principal stress deflection mode, wherein the method is a method for constructing a general potential sliding surface model of a two-dimensional slope under a mode combining principal stress deflection with the most unfavorable shear direction.

[0010] In a specific embodiment, in the method, with the help of the physical and mechanical model of slope shear failure, the stress state of the sliding surface rock and soil is considered, and combined with the known boundary conditions of the sliding out point A and the upper sliding out point B on the sliding surface, a discrete method is used to generate a sliding surface model.

[0011] In a specific embodiment, the method comprises the following steps:

[0012] S1: Given the coordinates of the sliding out point A and the sliding out point B on the potential sliding surface (x A ,y A ) and (x B ,y B );

[0013] S2: Obtain the horizontal inclination angle β of the slope tangent line at the sliding exit point A and the upper sliding exit point B on the potential sliding surface A and β B ;

[0014] S3: Use equation (1) to calculate the coordinates (x c ,y c );

[0015]

[0016] Among them, θ A is the polar angle of the sliding surface at the sliding out point A, θ B is the polar angle of the sliding surface at the upper sliding point B;

[0017] S4: Use equations (2), (3) and (4) to calculate the angle θ at the midpoint O of triangle OAB: AB , the sliding surface polar diameter r at point A A and the sliding surface polar radius r at point BB ;

[0018]

[0019]

[0020]

[0021] Among them, the sliding surface polar diameter r at point A A That is, OA, the sliding surface polar radius r at point B B That is, OB;

[0022] S5: Let i = 1, and place the starting point of the sliding surface at the sliding exit point A;

[0023] Among them, point i is an arbitrary point on the discrete sliding surface;

[0024] S6: Obtain the internal friction angle of the sliding surface at point i–1 on the potential sliding surface

[0025] S7: Use equations (6) and (7) to calculate the sliding surface polar angle θ at point i on the discrete sliding surface: i and the sliding surface diameter r i ;

[0026] Previously, the point-by-point discrete generation method was used to divide ∠AOB into n equal parts to obtain an equal sliding surface polar angle increment dθ=θ AB / n, and the potential sliding surface is divided into n segments and controlled by n+1 discrete points;

[0027]

[0028]

[0029] Among them, r i–1 is the polar radius of point i–1 on the discrete sliding surface; when i = 0, r0 is the polar radius OA, that is, r0 = r A , when i = n, r n is the polar diameter OB, i.e. r n =r B ; is the internal friction angle of the sliding surface at point i–1 on the discrete sliding surface; when i = 0, is the internal friction angle of the sliding surface at the sliding exit point A on the potential sliding surface. When i = n, is the internal friction angle of the sliding surface at the upper sliding point B on the potential sliding surface;

[0030] S8: Calculate the coordinates (x) of point i on the discrete sliding surface using equation (8) i ,y i );

[0031] Among them, first establish the xy axis rectangular coordinate system;

[0032]

[0033] S9: Determine whether i is equal to n. If i≠n, set i=i+1 and repeat steps S6 to S8. If i=n, ​​it is considered that the discrete sliding surface is generated and the sliding surface is output.

[0034] The present invention also provides a device for constructing a two-dimensional slope potential sliding surface model under a principal stress deflection mode. The device is a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, each step of the method described above is implemented.

[0035] The present invention also relates to a computer device, including a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the various steps of the method for constructing a two-dimensional slope potential sliding surface model under the principal stress deflection mode as described above are implemented.

[0036] The advantages of the present invention include at least: the present invention uses the physical and mechanical model of slope shear failure, considers the stress state of the sliding surface rock and soil, and combines the known boundary conditions of the sliding exit point and the upper sliding exit point on the sliding surface to construct a sliding surface generation model, thereby ensuring the rationality of the sliding surface generation and being able to effectively show the actual sliding surface morphology during slope sliding. At the same time, the potential sliding surface generation only needs to clarify the coordinates of the sliding exit point and the upper sliding exit point on the potential sliding surface, and can be generated in a discrete manner. Therefore, the method of the present invention has the advantages of good simplicity, strong practicality, wide application range, good versatility, high calculation efficiency, etc. It can reliably improve the accuracy of slope stability assessment under complex conditions, and can further provide strong scientific guidance for defining the scope of slope collapse and determining the reinforcement area. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic diagram of the two-dimensional slope and its potential sliding surface of the present invention.

[0038] Figure 2 It is a schematic diagram of the potential sliding surface of a two-dimensional slope under the rotation curve of the present invention.

[0039] Figure 3 It is a schematic diagram of the most unfavorable shear direction deflection law of the potential sliding surface of the two-dimensional slope of the present invention and the spatial relationship between the Mohr stress circle and the shear strength curve at any point on the potential sliding surface.

[0040] Figure 4 It is a schematic diagram of the relationship between the most unfavorable shear direction of the potential sliding surface of the two-dimensional slope and the direction of action of the minor principal stress of the present invention.

[0041] Figure 5It is a schematic diagram of the direction of action of the minor principal stress at the sliding point under the potential sliding surface of the two-dimensional slope of the present invention.

[0042] Figure 6 It is a schematic diagram of the direction of action of the minor principal stress at the sliding point on the potential sliding surface of the two-dimensional slope of the present invention.

[0043] Figure 7 It is a schematic diagram of the spatial geometric relationship of the rotation center point of the potential sliding surface of the two-dimensional slope of the present invention.

[0044] Figure 8 It is a schematic diagram of the geometric relationship between the polar diameter and polar angle micro-units at any point on the potential sliding surface of a two-dimensional slope of the present invention.

[0045] Fig. 9 It is a schematic diagram of the discrete generation method of the potential sliding surface of a two-dimensional slope according to the present invention.

[0046] Fig.10 The present invention is a flowchart of the steps for constructing a two-dimensional potential sliding surface model of a slope.

[0047] In the figure: 1. Two-dimensional slope, 2. Potential sliding surface, 3. Slope surface, 4. Sliding surface tangent, 5. Most unfavorable shear direction, 6. Sliding surface rotation center, 7. Sliding surface polar angle, 8. Sliding surface polar diameter, 9. Vertical direction, 10. Any point on the potential sliding surface, 11. Moore stress circle, 12. Shear strength curve, 13. Minor principal stress action surface, 14. Major principal stress action surface, 15. Minor principal stress action direction, 16. Sliding out point on potential sliding surface, 17. Sliding out point on potential sliding surface, 18. Slope tangent, 19. Horizontal direction, 20. Discrete points on potential sliding surface. DETAILED DESCRIPTION

[0048] In order to solve the above problems, the present invention applies the law of deflection change of the principal stress direction of the potential sliding surface and the characteristic that the tangential direction of the potential sliding surface is equivalent to the most unfavorable shear direction to construct a two-dimensional slope potential sliding surface model, wherein the principal stress direction of the potential sliding surface is represented by the direction of action of the small principal stress at any point on the potential sliding surface, the direction of action of the small principal stress at any point on the potential sliding surface is continuously deflected from bottom to top around the rotation center point, and the direction of action of the small principal stress at any point on the potential sliding surface is the direction of the line connecting any point on the potential sliding surface to the rotation center point, and the rotation center point is obtained based on the sliding out point and the upper sliding out point on the potential sliding surface under known boundary conditions. The potential sliding surface is determined by the intersection of the two directions of minor principal stress. The deflection of the principal stress direction of the potential sliding surface is related to the change of the tangent of the potential sliding surface. The angular relationship between the tangent of the sliding surface at any point on the potential sliding surface and the direction of the minor principal stress is established by applying the spatial position relationship between the Moore stress circle reflecting the stress state of any point on the potential sliding surface and the shear strength curve reflecting its strength characteristics. The potential sliding surface is generated by controlling the determined rotation center point and the angular relationship between the tangent of the sliding surface at any point on the established potential sliding surface and the direction of the minor principal stress. In addition, in order to generalize and simplify the construction of the potential sliding surface, a discrete method is adopted to generate it.

[0049] The specific model building method and implementation process of the present invention are as follows:

[0050] (1) Figure 1 As shown in the figure, the instability of the two-dimensional slope is caused by the fact that the slope rock and soil mass reaches the shear failure state and forms a connected potential sliding surface, which causes the potential unstable sliding body to rotate and slide along the potential sliding surface. Therefore, it means that the potential sliding surface of the slope is the shear failure surface of the slope rock and soil mass, and the tangent direction of the potential sliding surface is the most unfavorable shear direction of the rock and soil mass here. At the same time, the rotational sliding failure of the potentially unstable sliding body indicates that the potential sliding surface of the two-dimensional slope is a rotational curve.

[0051] (2) Figure 2 As shown in the figure, if the potential sliding surface of the two-dimensional slope is a rotational curve, the potential sliding surface can be set as a curve obtained by rotating around a certain center point in a certain direction and distance. In order to easily describe such a curve, the rotation center point of the sliding surface is taken as O, and the sliding surface polar diameter r and sliding surface polar angle θ are used to represent the characteristics of the potential sliding surface, where the sliding surface polar diameter r is the distance from a certain point on the potential sliding surface to the rotation center point, and the sliding surface polar angle θ is the angle between the direction from a certain point on the potential sliding surface to the rotation center point and the vertical direction, and the value is taken in the counterclockwise direction.

[0052] (3) Figure 3As shown in the figure, if the potential sliding surface of the two-dimensional slope is a rotational curve, the tangent direction of the sliding surface will continuously deflect from bottom to top around the rotation center point O. Since the tangent direction of the potential sliding surface represents the most unfavorable shear direction of the rock and soil mass here, it also means that the most unfavorable shear direction of the rock and soil mass on the potential sliding surface will also continuously deflect from bottom to top around the rotation center point O.

[0053] (4) Figure 3 As shown in the figure, the most unfavorable shear direction of the rock and soil on the potential sliding surface can be determined based on the positional relationship between the stress state of the rock and soil on the sliding surface and the shear strength curve. Taking any point P on the potential sliding surface as an example, let the major and minor principal stresses on any point P on the potential sliding surface be σ 1_P and σ 3_P At the same time, the Moore stress circle reflecting the spatial stress state information of the rock and soil at point P is drawn in the normal stress and shear stress rectangular coordinate system. In addition, the shear strength curve of the rock and soil is drawn in the same coordinate system, and the shear strength function of the rock and soil is τ f =f(σ), where σ is the normal stress acting on the potential sliding surface, τ f is the shear strength of the rock mass on the potential sliding surface. For the Mohr stress circle at any point P on the potential sliding surface, its center point is O P And it is located on the normal stress axis, and its two endpoints on the normal stress axis are respectively at D P and E P , and point D P and E P Represent the minor principal stress σ 3_P and major principal stress σ 1_P , according to the definition of Mohr stress circle, O P D P It can represent the direction of the minor principal stress action surface, O P E P It can represent the direction of the major principal stress action surface, passing through the center point O P Draw a vertical line O of the shear strength curve of the rock and soil P F P , point F P Located on the shear strength curve of rock and soil, due to O P F P is the center point O of the Mohr stress circle at any point P on the potential sliding surface P The shortest distance to the shear strength curve of the rock mass, therefore, O P F P It can represent the direction in which shear failure is most likely to occur at any point P on the potential sliding surface, that is, the most unfavorable shear direction at any point P on the potential sliding surface.

[0054] (5) Figure 3 As shown in the figure, let the normal stress and shear stress acting on the potential sliding surface at any point P be σ P and τP , and let the horizontal inclination angle of the sliding surface tangent at any point P on the potential sliding surface be α P Since the tangent direction of the potential sliding surface represents the most unfavorable shear direction of the rock mass here, the Mohr stress circle at any point P on the potential sliding surface is O P F P is the most unfavorable shear direction at any point P on the potential sliding surface, and the Moore stress circle at any point P on the potential sliding surface reflects the spatial stress state information at this point. Therefore, O P F P The intersection G with the Mohr stress circle at any point P on the potential sliding surface P The implied normal stress and shear stress are the normal stress σ of the sliding surface at any point P on the potential sliding surface. P and shear stress τ P At the same time, passing point F P Draw a tangent to the shear strength curve of the rock and soil mass. The horizontal inclination angle of this tangent is Represents the internal friction angle of the sliding surface at any point P on the potential sliding surface. When the shear strength curve of the rock mass is a straight line (i.e., the linear strength criterion), is a constant. When the shear strength curve of the rock mass is nonlinear (i.e., nonlinear strength criterion), is P The relevant variables need to be calculated using a cyclic iterative calculation strategy. Then, based on the triangle geometric relationship, the O in the Mohr stress circle can be obtained. P F P With O P D P The angle between Furthermore, according to the double angle relationship between the Moore stress circle model and the actual physical model, the angle between the tangent direction of the sliding surface and the direction of the minor principal stress action surface at any point P on the potential sliding surface in the actual physical model can be obtained as follows:

[0055] (6) Figure 4 As shown in the figure, for the potential sliding surface curve of the rotating two-dimensional slope, the sliding surface tangent continuously deflects from bottom to top around the rotation center point O. At the same time, according to the relationship between the Moore stress circle at any point P on the potential sliding surface and the shear strength curve of the rock and soil mass here, it can be seen that the sliding surface tangent at any point P on the potential sliding surface has a fixed mathematical relationship with the direction of the small principal stress action surface, that is, the angle between the two is Furthermore, the direction of the surface of the small principal stress of the rock and soil on the potential sliding surface will also deflect continuously from bottom to top around the rotation center point O, and it also means that the direction of the small principal stress (or the direction of the large principal stress) perpendicular to the direction of the surface of the small principal stress of the rock and soil on the potential sliding surface will deflect continuously from bottom to top around the rotation center point O.

[0056] (7) Figure 4As shown in the figure, in the two-dimensional potential sliding surface of the slope, point A and point B are the sliding out point and the upper sliding out point on the potential sliding surface respectively. Since the direction of the small principal stress of the rock and soil on the potential sliding surface continuously deflects from bottom to top around the rotation center point O, if OA is the direction of the small principal stress of the rock and soil at the sliding out point A on the potential sliding surface (or the direction of the large principal stress action surface) and OB is the direction of the small principal stress of the rock and soil at the sliding out point B on the potential sliding surface (or the direction of the large principal stress action surface), then OP can represent the direction of the small principal stress of the rock and soil at any point P on the potential sliding surface (or the direction of the large principal stress action surface).

[0057] (8) Figure 5 As shown in the figure, for the sliding point A on the potential sliding surface of the two-dimensional slope, if there is no tangential external load on the slope surface, the slope surface here is the small principal stress action surface, that is, the tangent direction of the slope surface here is the direction of the small principal stress action surface, which also means that the direction perpendicular to the tangent direction of the slope surface here is the direction of the small principal stress action surface (or the direction of the large principal stress action surface), let the inclination angle of the tangent direction of the slope surface in the horizontal direction be β A , and when the slope tangent is above the horizontal direction, the value is positive, otherwise it is negative. Therefore, the inclination angle of the small principal stress direction (or the large principal stress direction) OA at the slide-out point A in the horizontal direction is (β A +π / 2), further, let the sliding surface polar angle at the sliding out point A be θ A , then according to the spatial geometric relationship, the sliding surface polar angle θ at the sliding point A can be obtained A =β A .

[0058] (9) Figure 6 As shown in the figure, for the sliding point B on the end of the potential sliding surface of the two-dimensional slope, if there is no tangential external load on the slope surface here, the surface perpendicular to the slope surface here is the small principal stress action surface, that is, the tangent direction of the slope surface here is the direction of the small principal stress action (or the direction of the large principal stress action surface), let the inclination angle of the tangent direction of the slope surface here in the horizontal direction be β B , and when the slope tangent is above the horizontal direction, the value is positive, otherwise it is negative. Therefore, the inclination angle of the small principal stress direction (or the large principal stress direction) OB at the sliding point B in the horizontal direction is β B , further, let the sliding surface polar angle at the upper sliding point B be θ B , then according to the spatial geometric relationship, the sliding surface polar angle θ at the sliding point B can be obtained B =β B +π / 2.

[0059] (10) Figure 7 As shown in the figure, the xy axis coordinate system is established with the foot point of the slope as the origin, and the coordinates of the sliding out point A and the sliding out point B on the potential sliding surface are (x A ,y A) and (x B ,y B ), and the coordinates of the sliding surface rotation center point O are (x c ,y c ), and then, according to the spatial geometric relationship of the intersection of the straight lines OA and OB at the sliding surface rotation center point O, the mathematical relationship between the coordinates of the sliding surface rotation center point O and the coordinates of the sliding out point A and the upper sliding out point B on the potential sliding surface and their corresponding sliding surface polar angles can be established. The specific calculation formula is:

[0060]

[0061] Furthermore, in triangle OAB, let the angle at point O (i.e. ∠AOB) be θ AB , the sliding surface polar diameter (OA) at point A is r A , and the sliding surface polar diameter at point B (ie OB) is r B , then according to the geometric relationship of triangle OAB, we can get:

[0062]

[0063]

[0064]

[0065] (11) Figure 8 As shown, let the sliding surface polar angle at any point P on the potential sliding surface of the two-dimensional slope be θ P The horizontal inclination angle of the sliding surface is α P Then, using the fixed mathematical relationship between the tangent direction of the potential sliding surface and the direction of the minor principal stress action surface at any point on the potential sliding surface and the spatial geometric relationship, we can get

[0066] (12) Figure 8 As shown in the figure, for any point P on the potential sliding surface, OP is the direction of the minor principal stress (or the direction of the major principal stress surface) at any point P on the potential sliding surface, which uses the sliding surface polar angle θ P It means that the tangent at any point P on the potential sliding surface is the most unfavorable shear direction of the rock and soil mass at this point, which is the inclination angle α of the sliding surface tangent in the horizontal direction. P Then, applying the geometric relationship of the micro-unit at any point P on the potential sliding surface, the differential control equations of the polar radius and polar angle of the potential sliding surface can be obtained as follows:

[0067]

[0068] In the formula, r P is the polar diameter of the sliding surface at any point P on the potential sliding surface; dr is the polar diameter increment at any point P on the potential sliding surface; dθ is the polar angle increment at any point P on the potential sliding surface.

[0069] Using equation (5) and combining with known boundary conditions, the potential sliding surface of the two-dimensional slope under the principal stress deflection mode can be determined.

[0070] (13) Fig. 9 As shown, in order to easily obtain the potential sliding surface shape, a point-by-point discrete generation method is adopted. Here, ∠AOB is divided into n equal parts to obtain an equal sliding surface polar angle increment dθ=θ AB / n, at the same time, on this basis, the potential sliding surface is divided into n segments and controlled by n+1 discrete points, among which, except for the determined downward sliding out point A and upward sliding out point B, the remaining discrete points are recursively obtained from the known previous point.

[0071] (14) Fig. 9 As shown, for point i on the potential sliding surface, let its polar angle be θ i and the polar diameter is r i , due to the angle equal division method, the polar angle θ of point i on the potential sliding surface can be obtained i The calculation formula is:

[0072]

[0073] At the same time, the radius r of point i on the potential sliding surface can be established using formula (5): i The recursive formula is as follows:

[0074]

[0075] In the formula, r i–1 is the polar radius of point i–1 on the discrete sliding surface. When i = 0, r0 is the polar radius OA, that is, r0 = r A , when i = n, r n is the polar diameter OB, i.e. r n =r B ; is the internal friction angle of the sliding surface at point i–1 on the discrete sliding surface. When i=0, is the internal friction angle of the sliding surface at the sliding out point A on the potential sliding surface. When i = n, is the internal friction angle of the sliding surface at the upward sliding point B on the potential sliding surface.

[0076] (15) Fig. 9 As shown in the figure, in order to facilitate the calculation and analysis, the xy-axis rectangular coordinate system is established with the slope foot point as the origin (or the slide-out point A as the origin), and the coordinates of the sliding surface rotation center point O and the polar angle and polar diameter of the potential sliding surface point i are used to obtain the x and y axis coordinates of the potential sliding surface point i. The specific calculation formula is:

[0077]

[0078] (16) Fig.10 As shown in the figure, the steps of constructing the potential sliding surface model of the two-dimensional slope under the principal stress deflection mode are as follows: ① Given the coordinates of the sliding out point A and the upper sliding out point B on the potential sliding surface (x A ,y A ) and (x B ,y B );② Obtain the horizontal inclination angle β of the slope tangent line at the sliding exit point A and the upper sliding exit point B on the potential sliding surface A and β B ; ③ Use formula (1) to calculate the coordinates of the rotation center point O (x c ,y c );④Use equations (2), (3) and (4) to calculate the angle θ at the midpoint O of triangle OAB AB , the sliding surface polar diameter r at point A A and the sliding surface polar radius r at point B B ; ⑤ Let i = 1, and place the starting point of the sliding surface at the sliding exit point A; ⑥ Obtain the internal friction angle of the sliding surface at the point i-1 on the potential sliding surface ⑦Use equations (6) and (7) to calculate the sliding surface polar angle θ at point i on the discrete sliding surface: i and the sliding surface diameter r i ⑧ Use equation (8) to calculate the coordinates (x i ,y i );⑨Judge whether i is equal to n. If i≠n, set i=i+1 and repeat steps ⑥ to ⑧. If i=n, ​​it is considered that the discrete sliding surface is generated and the sliding surface is output.

[0079] The principal stress deflection method of the present invention is characterized in that the principal stress deflection is the deflection of the principal stress direction of the potential sliding surface, the principal stress direction of the potential sliding surface is expressed by the direction of action of the small principal stress at any point on the potential sliding surface, the principal stress direction deflection of the sliding surface is expressed as the continuous deflection of the direction of action of the small principal stress at any point on the potential sliding surface from bottom to top around the rotation center point, and the direction of action of the small principal stress at any point on the potential sliding surface is the direction of the line connecting any point on the potential sliding surface to the rotation center point, and the rotation center point is determined based on the intersection of the small principal stress action directions obtained from the sliding out point and the upper sliding out point on the potential sliding surface under known boundary conditions.

[0080] The most unfavorable shear direction of the present invention is characterized in that the most unfavorable shear direction is the most unfavorable shear direction of the rock and soil body on the potential sliding surface, which is equivalent to the tangent of the potential sliding surface. The tangent of the potential sliding surface is related to the principal stress direction of the potential sliding surface. The angular relationship between the two is established by applying the spatial position relationship between the Moore stress circle reflecting the stress state of any point on the potential sliding surface and the shear strength curve reflecting its strength characteristics. The generation of the potential sliding surface is controlled by the angular relationship between the tangent of the sliding surface at any point on the established potential sliding surface and the direction of action of the small principal stress.

[0081] Example

[0082] A kind of Figures 1 to 10 The method for constructing a two-dimensional slope potential sliding surface model under the principal stress deflection mode is shown in the figure. In a slope along a highway, the slope height is 40m, the average slope angle is 50°, and the slope soil weight is 19kN / m 3 According to the early on-site survey, it was found that the slope was likely to slide. In order to efficiently and accurately evaluate the slope stability and provide a scientific basis for the implementation of necessary slope protection measures, it was necessary to accurately capture the most dangerous potential sliding surface shape and position of the slope when it was unstable and damaged. To this end, the sliding surface model construction method of the present invention was introduced and applied, and the specific operations are as follows:

[0083] (1) According to the requirements of the Code for Geotechnical Engineering Investigation (GB50021-2001), a field survey was conducted on the highway slope to obtain the two-dimensional slope surface shape and stratigraphic data and the corresponding rock and soil strength parameters in the potential sliding area. The shear failure of the slope rock and soil obeys the linear MC strength criterion, and the soil strength parameters are c = 25 kPa and

[0084] (2) The two-dimensional potential sliding surface model of the slope in the present invention is selected, and then the end position of the sliding surface is estimated according to the possible range of the potential sliding body, thereby determining the horizontal coordinates x of the sliding out point and the upper sliding out point on the potential sliding surface. A and x B The value range is: when the xy axis coordinate system is established with the slope foot point as the origin, the horizontal coordinate x of the sliding point on the potential sliding surface is A The value range is -5m to 5m. The horizontal coordinate x of the sliding point on the potential sliding surface is B The value range is 35m to 45m. Further, within the range of the horizontal coordinates of the sliding out point and the upper sliding out point on the given potential sliding surface, the vertical coordinate value of the sliding out point on the corresponding potential sliding surface is obtained based on the measured slope surface shape. A =0m(x A <0m) and y A =x A tan50°(x A ≧0m), and the vertical coordinate of the sliding point on the corresponding potential sliding surface is y B =40m. In addition, the horizontal inclination angle of the slope tangent at the sliding point under the potential sliding surface is β A =0°(x A <0m) and β A =50°(x A ≧0m), and the horizontal inclination angle of the slope tangent at the sliding point on the corresponding potential sliding surface is β B =0°;

[0085] (3) Set the search step length of the potential sliding surface sliding out point and the upper sliding out point in their value range to 0.1m, and then the horizontal coordinate x of the sliding out point A on the sliding surface A There are 101 search values ​​(corresponding to x A The range of values ​​is -5m to 5m, with a total distance of 10m). The horizontal coordinate x of the sliding point B on the sliding surface is B There are also 101 search values ​​(corresponding to x B The value range is 35m to 45m, with a total distance of 10m). Then, the different search values ​​of the horizontal coordinates of the upper and lower slide-out points are combined. By applying the patented method of the present invention, 10201 potential sliding surfaces can be obtained. Based on this, the number of segments n of each potential sliding surface is taken as 100. Combined with the limit equilibrium method, the slope safety factor corresponding to the 10201 potential sliding surfaces is solved. At the same time, the minimum value is found from these calculated slope safety factors, and the potential sliding surface corresponding to the minimum value is taken as the most dangerous potential sliding surface, thereby completing the purpose of slope stability analysis. Among them, the horizontal coordinates of the sliding out point and the upper sliding out point on the most dangerous potential sliding surface are x A =0m and x B =39.8m;

[0086] (4) Based on the slope stability analysis results, the slope stability is evaluated in accordance with the stability evaluation standard of the Technical Code for Building Slope Engineering (GB 50330-2013). At the same time, the potential instability range of the slope is clarified to provide a scientific basis for subsequent safe construction and reliable reinforcement of the slope.

[0087] In general, the present invention relates to a method for constructing a potential sliding surface model for two-dimensional slope stability analysis, and specifically provides a method for constructing a two-dimensional slope potential sliding surface model under a principal stress deflection mode. With the help of a physical and mechanical model of slope shear failure, the present invention combines the principal stress deflection with the most unfavorable shear direction to construct a potential sliding surface model that can effectively show the actual sliding surface morphology when the slope slides. At the same time, the known boundary conditions of the lower sliding point and the upper sliding point on the sliding surface are introduced to achieve the dual goals of rationality and simplicity of potential sliding surface generation, thereby reliably improving the accuracy of slope stability assessment under complex conditions, and further providing strong scientific guidance for the definition of the slope landslide range and the determination of the reinforcement area. The implementation method of the present invention has the advantages of strong practicality, wide application range, good versatility, and high calculation efficiency.

[0088] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for constructing a two-dimensional slope potential sliding surface model under a principal stress deflection mode, characterized in that: The method is a method for constructing a two-dimensional slope general potential sliding surface model in a mode combining principal stress deflection with the most unfavorable shear direction; in the method, by means of a physical and mechanical model of slope shear failure, the stress state of the sliding surface rock and soil is considered, and the known boundary conditions of the sliding out point A and the upper sliding out point B on the sliding surface are combined, and a sliding surface model is constructed by using a discrete method; and the method includes the following steps: S1: Given the coordinates of the sliding out point A and the sliding out point B on the potential sliding surface (x A ,y A ) and (x B ,y B ); S2: Obtain the horizontal inclination angle β of the slope tangent line at the sliding exit point A and the upper sliding exit point B on the potential sliding surface A and β B ; S3: Use equation (1) to calculate the coordinates (x c ,y c ); Among them, θ A is the polar angle of the sliding surface at the sliding out point A, θ B is the polar angle of the sliding surface at the upper sliding point B; S4: Use equations (2), (3) and (4) to calculate the angle θ at the midpoint O of triangle OAB: AB , the sliding surface polar diameter r at point A A and the sliding surface polar radius r at point B B ; Among them, the sliding surface polar diameter r at point A A That is, OA, the sliding surface polar radius r at point B B That is, OB; S5: Let i = 1, and place the starting point of the sliding surface at the sliding exit point A; Among them, point i is an arbitrary point on the discrete sliding surface; S6: Obtain the internal friction angle of the potential sliding surface at point i–1 S7: Use equations (6) and (7) to calculate the sliding surface polar angle θ at point i on the discrete sliding surface: i and the sliding surface diameter r i ; Previously, the point-by-point discrete generation method was used to divide ∠AOB into n equal parts to obtain an equal sliding surface polar angle increment dθ=θ AB / n, and the potential sliding surface is divided into n segments and controlled by n+1 discrete points; Among them, r i–1 is the polar radius of point i–1 on the discrete sliding surface; when i = 0, r0 is the polar radius OA, that is, r0 = r A , when i = n, r n is the polar diameter OB, i.e. r n =r B ; is the internal friction angle of the sliding surface at point i–1 on the discrete sliding surface; when i = 0, is the internal friction angle of the sliding surface at the sliding exit point A on the potential sliding surface. When i = n, is the internal friction angle of the sliding surface at the upper sliding point B on the potential sliding surface; S8: Calculate the coordinates (x) of point i on the discrete sliding surface using equation (8) i ,y i ); Among them, first establish the xy axis rectangular coordinate system; S9: Determine whether i is equal to n. If i≠n, set i=i+1 and repeat steps S6 to S8. If i=n, ​​it is considered that the discrete sliding surface is generated and the sliding surface is output.

2. A device for constructing a two-dimensional slope potential sliding surface model under a principal stress deflection mode, characterized in that: The device is a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, each step of the method as claimed in claim 1 is implemented.

3. A computer device, characterized in that: It comprises a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, each step of the method for constructing a two-dimensional slope potential sliding surface model under the principal stress deflection mode as claimed in claim 1 is implemented.

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