Slope Stability Evaluation Method, Device and Computer Equipment under Complex Conditions

Abstract

The present invention provides a method for evaluating slope stability under complex conditions, belonging to the fields of engineering disaster prevention and mitigation and computer-aided design. Based on the function relationship between the major principal stress and the minor principal stress of the general non-linear strength criterion in the form of the principal stress, by using the tangent direction of the slip surface at any point on the potential slip surface as its most unfavorable shear direction, the correlation calculation formula of the slip surface stress with its major principal stress and minor principal stress is derived. Then, according to the spatial position relationship between the Mohr stress circle and the shear strength envelope, the mathematical equation of the slip surface shear strength parameter associated with the general non-linear strength criterion in the form of the principal stress is obtained. Subsequently, a cyclic iterative solution strategy is adopted to break the mutual nesting relationship among the slip surface acting force, the slip surface stress and the slip surface shear strength parameter in the evaluation method. The present invention provides a scientific basis for reliably preventing slope collapse and implementing reinforcement measures, and has the advantages of high calculation efficiency, wide application range, strong practicability, etc.

Description

Technical Field

[0001] The present invention belongs to the fields of engineering disaster prevention and mitigation and computer-aided design, and particularly relates to a slope stability evaluation method, device and computer equipment under complex conditions. Background Art

[0002] Landslide is a common geological disaster. Its occurrence often causes casualties and property losses, and sometimes the casualties and losses caused are very huge. Therefore, landslide prevention is very important. In order to reduce the occurrence frequency of landslides and mitigate the losses caused by landslide disasters, theoretical analysis of slope stability is carried out to predict the stable state and development trend of slopes, which has become a key link in preventing landslides.

[0003] The limit equilibrium method is a slope stability analysis method recommended by current engineering design and industry specifications. When using the limit equilibrium method for slope stability analysis, the slope sliding mass needs to be divided into multiple vertical strips, and reasonable assumptions are made about the forces between the strips. Then, the safety factor solution of the slope is established by using the mechanical equilibrium conditions of the strips to evaluate the slope stability. In this process, the strength criterion is embedded in the limit equilibrium mechanical equation as a known function for calculating the shear force of the slip surface. Therefore, whether the strength criterion can truly reflect the shear failure characteristics and failure behavior of slope rock and soil masses will affect the accuracy of the slope stability analysis results and the reliability of guiding engineering design.

[0004] Experimental data show that the shear strength of geotechnical materials shows non-linear characteristics during failure. Therefore, the non-linear strength criterion can better reflect the true mechanical behavior of materials during failure. At the same time, the establishment of the non-linear strength criterion usually comes from the triaxial test data of rock and soil masses. Thus, the general non-linear strength criterion is mainly expressed in the form of principal stresses. However, in the slope stability limit equilibrium method, the principal stresses of the rock and soil masses in the slope cannot be solved, resulting in the difficulty of embedding the general non-linear strength criterion in the form of principal stresses. This limitation of the current slope stability limit equilibrium method restricts its significance in revealing the true slope instability characteristics and failure behavior under complex conditions, and reduces the expectation of reliably preventing slope collapse and implementing reinforcement measures.

[0005] That is to say, in actual engineering, the shear failure behavior of slope rock and soil masses is very complex. Using the general non-linear strength criterion in the form of principal stresses is an effective way to effectively describe this complex behavior. However, it is still difficult to embed the general non-linear strength criterion in the form of principal stresses in the current slope stability limit equilibrium analysis, resulting in its failure to reveal the true slope instability characteristics and failure behavior under complex conditions, and affecting the reliability of preventing slope collapse and implementing reinforcement measures.

[0006] Patent CN201910908421.7 provides a method for evaluating the stability of a spherical crown slope under the action of group tensile force based on the plane sliding method. The implementation process is as follows: Obtain the radius r of the annular sliding mass; Select a sector-shaped sliding mass with an included angle of Δψ, and obtain the height h, bottom length l, and inclination angle θ of the bottom surface with respect to the horizontal plane of the sector-shaped sliding mass; Iteratively calculate the slope safety factor F through the following formula s . Considering the arch effect of the spherical crown slope, new assumptions are introduced to improve the simple plane sliding method, and at the same time, group tensile force is added to the formula. The improved simple plane sliding method can be used to evaluate the stability of the spherical crown slope under the action of group tensile force, and the calculation process is simple, providing a method with more reasonable calculation results for the stability evaluation of the spherical crown slope under the action of group tensile force.

[0007] However, this patent neither solves the limitations of the current slope stability limit equilibrium method, nor can the patent method evaluate the slope stability under complex conditions. Therefore, there is a need in the art for a new method, device, and computer equipment for evaluating slope stability under complex conditions. Summary of the Invention

[0008] To this end, the present invention proposes a method for evaluating slope stability by embedding a general non-linear strength criterion in the form of principal stress into the slope stability limit equilibrium method, which is used to solve the difficult problem of slope stability limit equilibrium analysis under complex strength criteria, so as to ensure the reliability and effectiveness of engineering slope stability evaluation.

[0009] The present invention first provides a method for evaluating slope stability under complex conditions. In this method, based on the functional relationship between the major principal stress and the minor principal stress of the general non-linear strength criterion in the form of principal stress proposed, using the tangent direction of the slip surface at any point on the potential slip surface is equivalent to its most unfavorable shear direction, the correlation calculation formula of the slip surface stress with its major principal stress and minor principal stress is derived. Then, according to the spatial position relationship between the Mohr stress circle and the shear strength envelope, the mathematical equation of the slip surface shear strength parameter related to the general non-linear strength criterion in the form of principal stress is obtained. Subsequently, a cyclic iterative solution strategy is adopted to solve the mutual nesting relationship among the slip surface acting force, slip surface stress, and slip surface shear strength parameter in the evaluation method, that is, the method for evaluating slope stability under complex conditions.

[0010] In a specific embodiment, the method is based on the general non-linear strength criterion in the form of principal stress, introduces the intermediate principal stress action coefficient, constructs a simple relationship between the intermediate principal stress and the major principal stress and the minor principal stress, and thus proposes a functional relationship between the major principal stress and the minor principal stress of the general non-linear strength criterion in the form of principal stress applicable to slope stability analysis.

[0011] In a specific embodiment, the method includes the slip surface strength parameter c Pand The cyclic iteration calculation steps, that is, when the normal stress σ P and shear stress τ P of the slip surface are known, the slip surface strength parameters c P and are solved; the specific steps are as follows:

[0012] Step S3-1: Obtain the normal stress σ P of the slip surface and the shear stress τ P of the slip surface;

[0013] Step S3-2: Let the initial value of the minor principal stress σ 3_P at any point P on the slip surface be σ 3_P (0) , and in the first calculation, take σ 3_P (0) = 0;

[0014] Step S3-3: Calculate the internal friction angle

[0015]

[0016] of the slip surface at point P using Equation (8), where d is the differential symbol and g is the function;

[0017] Step S3-4: Calculate the cohesion c P of the slip surface at point P using Equation (9);

[0018]

[0019] Step S3-5: Calculate the new σ 3_P using Equation (5);

[0020]

[0021] where σ P is the normal stress of the slip surface at point P, and τ P is the shear stress of the slip surface at point P;

[0022] Step S3-6: If |σ 3_P - σ 3_P (0) | ≤ ε, stop the cyclic calculation and output the final results of the slip surface strength parameters c P and ; otherwise, let σ 3_P (0) = σ 3_P , and repeat steps S3-3 to S3-5; preferably, ε = 0.001;

[0023] Thus, the minor principal stress σ at any point P on the slip surface is established 3_P , the normal stress σ on the slip surface P , and the shear stress τ on the slip surface P , as well as the shear strength parameters c P and The nested relationship between them is established

[0024] In a specific embodiment, the method includes the following steps

[0025] Step S1: Ignoring the unknown inter-slice forces of the vertically divided slices, and using the known forces on the vertical slices, calculate the normal force N on the initial slice slip surface P (0) and the shear force T on the initial slice slip surface P (0) ;

[0026] Step S2: Use equations (1) and (2) to calculate σ P and τ P respectively;

[0027] σ P =N P / l P (1)

[0028] τ P =T P / l P (2) where N P is the normal force on the slice slip surface, T P is the shear force on the slice slip surface, and l P is the corresponding length of the slice slip surface;

[0029] Step S3: Implement the above steps S3-1 to S3-6, that is, using the nested relationship between the minor principal stress σ at any point P on the slip surface 3_P , the normal stress σ on the slip surface P , and the shear stress τ on the slip surface P , as well as the shear strength parameters c P and to calculate and obtain the shear strength parameters c P and

[0030] Step S4: Introduce the assumption conditions of the inter-slice forces, and use the mechanical equilibrium conditions of the slices to carry out the limit equilibrium solution of the slope stability, so as to obtain the limit equilibrium solution of the slope stability and the normal force N on the slice slip surface P and the shear force T on the slice slip surface P ;

[0031] Step S5: If the limit equilibrium solution of slope stability tends to be stable, that is, the relative difference between the slope stability results calculated twice before and after is controlled within the allowable error range, stop the iterative loop and output the slope stability result; otherwise, let N P (0) = N P and T P (0) = T P , and repeat steps S2 to S4.

[0032] The present invention also provides a slope stability evaluation device under complex conditions. 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 above-mentioned method is realized.

[0033] The present invention also provides a computer device, including a processor and a memory. The memory stores a computer program. When the computer program is executed by the processor, each step of the slope stability evaluation method under complex conditions as described above is realized.

[0034] The advantages of the present invention are as follows: The limit equilibrium analysis of slope stability is carried out by combining the general non-linear strength criterion in the form of principal stress, revealing the instability characteristics and failure behaviors of real slopes under complex conditions, providing a scientific basis for reliably preventing slope landslides and implementing reinforcement measures. At the same time, the coefficient of the action of the intermediate principal stress is introduced, and by using the feature that the tangent direction of the slip surface at any point on the potential slip surface is the most unfavorable shear direction of the rock and soil mass here, the nested calculation among the minor principal stress, the normal stress and shear stress of the slip surface, and the strength parameters of the slip surface at any point on the slip surface is realized, providing an effective way to embed the general non-linear strength criterion in the form of principal stress into the limit equilibrium method of slope stability. In addition, by adopting the iterative loop solution strategy, the successive approximation solution and calculation accuracy control of the nested calculation in the limit equilibrium analysis of slope stability are realized, with the advantages of high calculation efficiency, wide application range, and strong practicability.

[0035] Generally speaking, the present invention reveals the instability characteristics and failure behaviors of real slopes under complex conditions, provides a scientific basis for reliably preventing slope landslides and implementing reinforcement measures, and has the advantages of high calculation efficiency, wide application range, and strong practicability. Description of the Drawings

[0036] Figure 1 It is a schematic diagram of the general non-linear strength criterion in the form of principal stress of the present invention.

[0037] Figure 2 It is a schematic diagram for calculating the normal stress and shear stress of the slip surface at any point on the potential slip surface in the limit equilibrium method of the present invention. The enlarged view of the slip surface at point P is shown in the lower left corner, and the stress state diagram at point P is shown in the lower right corner.

[0038] Figure 3 It is a schematic diagram of the spatial position relationship between the Mohr stress circle at any point on the potential slip surface of the present invention and its slip surface shear strength envelope line.

[0039] Figure 4 It is a schematic diagram of the spatial position relationship between the slip surface strength envelope line and the general non-linear strength criterion in the principal stress space at any point on the potential slip surface of the present invention.

[0040] Figure 5 It is a schematic diagram of the cyclic iterative calculation process of the slip surface strength parameters of the present invention.

[0041] Figure 6 It is a schematic diagram of the cyclic iterative calculation process when the general non-linear strength criterion in the form of principal stress of the present invention is embedded in the limit equilibrium method for slope stability.

[0042] In the figure: 1. General non-linear shear strength criterion in the form of principal stress; 2. Potential slip surface; 3. Slope sliding mass; 4. Vertical strip; 5. Inter-strip force; 6. Any point on the potential slip surface; 7. Tangent direction of the slip surface; 8. Most unfavorable shear direction; 9. Normal force of the strip slip surface; 10. Shearing force of the strip slip surface; 11. Length of the strip slip surface; 12. Major principal stress; 13. Minor principal stress; 14. Normal stress of the slip surface; 15. Shear stress of the slip surface; 16. Cohesion of the slip surface; 17. Internal friction angle of the slip surface; 18. Shear strength envelope line of the slip surface at any point; 19. Mohr stress circle; 20. Slip surface strength envelope line at any point in the principal stress space. Detailed implementation mode

[0043] To solve the above technical problems, the present invention provides an implementation approach and implementation process for embedding a general non-linear strength criterion in the form of principal stresses into the limit equilibrium method for slope stability. Based on the general non-linear strength criterion in the form of principal stresses, the present invention introduces the coefficient of the intermediate principal stress effect, constructs a simple relationship between the intermediate principal stress and the major and minor principal stresses, and thereby proposes a functional relationship between the major and minor principal stresses of the general non-linear strength criterion in the form of principal stresses applicable to slope stability analysis. Then, by equating the tangent direction of the slip surface at any point on the potential slip surface to its most unfavorable shear direction, a calculation formula for the slip surface stress associated with its major and minor principal stresses is derived. According to the spatial position relationship between the Mohr stress circle reflecting the slip surface stress state information and the shear strength envelope reflecting the shear characteristics of the slip surface, a mathematical equation for the slip surface strength parameter associated with the general non-linear strength criterion in the form of principal stresses is obtained, and further, a mutual feedback channel between the slip surface stress and the slip surface strength parameter is established by embedding the general non-linear strength criterion in the form of principal stresses into the limit equilibrium method for slope stability. At the same time, in the limit equilibrium method for slope stability, the slope sliding mass is divided into multiple vertical blocks, and the slip surface stress can be calculated by the ratio of the slip surface acting force of the block to the slip surface length of the block. However, the slip surface acting force of the block needs to be solved by applying the mechanical equilibrium conditions of the block under the known slip surface strength parameters. Therefore, the present invention adopts a cyclic iterative solution strategy to break the mutual nesting relationship between the slip surface acting force, the slip surface stress, and the slip surface strength parameter of the block when the general non-linear strength criterion in the form of principal stresses is embedded in the limit equilibrium method for slope stability, so as to achieve the purpose of slope stability evaluation under complex conditions.

[0044] The specific implementation approach and implementation process of the present invention are as follows:

[0045] (1) Obtain the functional expression of the general non-linear strength criterion in the form of principal stresses as σ1 = f(σ2, σ3), where σ1, σ2, and σ3 are the major, intermediate, and minor principal stresses respectively.

[0046] (2) Let the simple relationship between the intermediate principal stress and the major and minor principal stresses be σ2 = σ3 + λ(σ1 - σ3), where λ is the coefficient of the intermediate principal stress effect, and its value range is [0, 1]. Furthermore, substituting it into the general non-linear strength criterion in the form of principal stresses, the functional relationship between the major and minor principal stresses of the general non-linear strength criterion in the form of principal stresses can be established as σ1 = g(σ3).

[0047] (3) As Figure 1 shown, for the general non-linear strength criterion in the form of principal stresses, its functional relationship between the major and minor principal stresses σ1 = g(σ3) represents a curve in the principal stress space. At the same time, the linear strength criterion is only a special case of the general non-linear strength criterion.

[0048] (4) As Figure 2As shown, when the limit equilibrium method is used to carry out slope stability analysis, the slope sliding mass is required to be divided into multiple vertical slices, and reasonable assumptions need to be made for the forces between the slices. Then, the limit equilibrium solution of slope stability is established by using the mechanical equilibrium conditions of the slices. In this process, the strength criterion is used as a known function to calculate the shear force of the slice slip surface. However, the limit equilibrium method of slope stability cannot solve the principal stresses of the rock and soil mass in the slope, resulting in the difficulty of embedding the general non-linear strength criterion in the form of principal stresses. Therefore, using the fact that the tangent direction of the slip surface at any point on the potential slip surface is the most unfavorable shear direction of the rock and soil mass here, and then establishing the relationship between the slip surface stress and its corresponding principal stress.

[0049] (5) As Figure 2 shown, for the vertical slices divided by numbers, for any point P on the potential slip surface, analyze its stress state. The major and minor principal stresses acting on it are σ 1_P and σ 3_P , the normal stress and shear stress of the slip surface at point P are σ P and τ P respectively, and the horizontal inclination angle of the tangent direction of the slip surface at point P is α P . Among them, σ P and τ P can be obtained from the normal force N P and shear force T P of the slice slip surface at point P solved by the limit equilibrium method and the ratio of the corresponding slice slip surface length l P . The specific mathematical calculation formula is:

[0050] σ P =N P / l P (1)

[0051] τ P =T P / l P (2)

[0052] (6) In the limit equilibrium method, if the shear strength parameters of the slip surface at a given point P are c P and , where c P and are the cohesion and internal friction angle of the slip surface at point P respectively, then the existing calculation methods or means can be directly used to carry out slope stability analysis. However, c P and are not the parameters involved in the general non-linear shear strength criterion in the form of principal stresses. Therefore, based on the spatial position relationship between the Mohr stress circle reflecting the stress state at point P and the shear strength envelope of the slip surface at point P, establish c P and Relationship with the general non-linear strength criterion σ1 = g(σ3) in the form of principal stresses.

[0053] (7) As Figure 3 shown, establish a rectangular coordinate system of normal stress σ and shear stress τ, with c P as the intercept of the shear stress axis, and with as the horizontal inclination angle, construct the shear strength envelope of the slip surface at point P, which is a straight line. At the same time, based on the major principal stress σ 1_P and minor principal stress σ 3_P at point P, establish a Mohr stress circle reflecting the stress state at point P. The center O of this Mohr stress circle is on the normal stress axis. The two intersection points of the Mohr stress circle and the normal stress axis are A and B respectively, and point A and point B correspond to the minor principal stress σ 3_P and major principal stress σ 1_P respectively. According to the definition of the Mohr stress circle, OA can represent the direction of the plane of the minor principal stress at point P, and OB can represent the direction of the plane of the major principal stress at point P. Further, draw a perpendicular line OE from the center point O to the shear strength envelope. Since OE is the shortest path from the center point O to the shear strength envelope of the slip surface at point P, it represents that the rock and soil mass at point P is most likely to undergo shear failure along the direction of OE. Therefore, OE represents the most unfavorable shear direction of the rock and soil mass at point P.

[0054] (8) As Figure 3 shown, on the Mohr stress circle at point P, the angle between OE and OA is OE represents the most unfavorable shear direction of the rock and soil mass at point P, and OA represents the direction of the plane of the minor principal stress at point P. At the same time, the tangent direction of the slip surface at point P is the most unfavorable shear direction of the rock and soil mass here. Thus, it can be obtained that the angle between the tangent direction of the slip surface at point P and the direction of the plane of the minor principal stress at point P is the angle between OE and OA. Since there is a 2-fold angle relationship between the Mohr stress circle model and the actual physical model, in the actual mechanical model, the angle between the tangent direction of the slip surface at point P and the direction of the plane of the minor principal stress at point P is

[0055] (9) As Figure 3 shown, on the Mohr stress circle at point P, the intersection point of OE and the Mohr stress circle is F. Since the Mohr stress circle reflects the spatial stress state information of any point P on the slip surface and OE represents the tangent direction of the slip surface at point P, it can be known that point F corresponds to the stress state of the slip surface at point P. Furthermore, according to the spatial relationship of the triangle, the mathematical relationships between the normal stress σ P and shear stress τ P of the slip surface at point P and its major principal stress σ 1_P and minor principal stress σ 3_P are deduced as:

[0056]

[0057] Combining Equation (3) and Equation (4), the minor principal stress σ at point P can be obtained as 3_P and the normal stress σ P on the slip surface and the shear stress τ P on the slip surface have the following mathematical relationship:

[0058]

[0059] (10) As shown in Figure 4 , the shear strength envelope of the slip surface at point P is converted into the strength envelope of the slip surface at point P in the principal stress space, which is also a straight line, and its mathematical expression is:

[0060]

[0061] where σ1′ _P is the major principal stress required for the stress on the slip surface at point P to reach the shear failure state under σ 3_P .

[0062] The strength envelope in this principal stress space is equivalent to the general non - linear strength criterion σ1 = g(σ3) in the form of principal stresses at point P, and it is the tangent of the strength curve expressed by the general non - linear strength criterion in the form of principal stresses at point P. Thus, according to the same slope at point P of the two, we can obtain:

[0063]

[0064] Further simplifying Equation (7), we can obtain:

[0065]

[0066] In addition, using the equivalence of the two at point P and substituting the general non - linear strength criterion σ1 = g(σ3) in the form of principal stresses into Equation (6), the calculation formula for c P can be obtained as:

[0067]

[0068] (11) Combining Equation (5), Equation (8) and Equation (9), the nested relationship between the minor principal stress σ 3_P , the normal stress σ P and the shear stress τ P on the slip surface, as well as the slip surface strength parameters c P and can be established. When the normal stress σ P and the shear stress τ P on the slip surface are known, to solve for the slip surface strength parameters c P and , a cyclic iteration calculation strategy needs to be adopted, such asFigure 5 As shown, the steps are as follows: 3.1. Obtain the normal stress σ P and shear stress τ P ; 3.2. Let the initial value of σ 3_P be σ 3_P (0) , and in the first calculation, take σ 3_P (0) = 0; 3.3. Calculate using Equation (8); 3.4. Calculate c P using Equation (9); 3.5. Calculate the new σ 3_P using Equation (5); 3.6. If |σ 3_P - σ 3_P (0) | ≤ ε (ε can be taken as 0.001), stop the iterative calculation and output the final results of the slip surface strength parameters c P and , otherwise, let σ 3_P (0) = σ 3_P , and repeat steps 3.3 to 3.5.

[0069] (12) When solving the slip surface strength parameters c P and , the slip surface stresses σ P and τ P need to be known. However, to obtain the slip surface stresses σ P and τ P , the normal force N P and shear force T P of the corresponding slice slip surface need to be obtained. In the limit equilibrium method for slope stability, the calculation of the normal force N P and shear force T P of the slice slip surface requires the slip surface strength parameters c P and to be given. Therefore, when embedding the general non - linear strength criterion in the form of principal stresses into the limit equilibrium method for slope stability, a cyclic iterative solution strategy between the slip surface strength parameters and the normal force and shear force of the slip surface is also required. As Figure 6 shown, the steps are as follows: ①Ignore the unknown inter - slice forces in the vertical slices, and use the known forces on the vertical slices to calculate the initial normal force N P (0) and shear force T P (0) of the slice slip surface; ②Calculate σ P and τ P using Equations (1) and (2) respectively; ③Use the minor principal stress σ 3_P at any point P on the slip surface and the normal stress σ Pand shear stress τ P and the shear strength parameter c of the slip surface P and calculate the shear strength parameter c of the slip surface through their nested relationship P and ④ Introduce the assumption conditions of the inter-slice force, and use the mechanical equilibrium conditions of the slices to carry out the limit equilibrium solution of the slope stability. Thus, obtain the limit equilibrium solution of the slope stability and the normal force N P and shear force T P ; ⑤ If the limit equilibrium solution of the slope stability tends to be stable, that is, the relative difference between the slope stability results calculated twice before and after is controlled within the allowable error range, then stop the iterative loop and output the slope stability result. Otherwise, let N P (0) = N P and T P (0) = T P , and repeat steps ② to ④.

[0070] The characteristics of the general non-linear strength criterion in the form of principal stress of the present invention are: based on the general non-linear strength criterion in the form of principal stress, introduce the intermediate principal stress action coefficient, construct a simple relationship between the intermediate principal stress and the major and minor principal stresses, and thus propose a functional relationship between the major and minor principal stresses of the general non-linear strength criterion in the form of principal stress applicable to slope stability analysis.

[0071] The characteristics of the slip surface stress of the present invention are: use the tangent direction of the slip surface at any point on the potential slip surface as its most unfavorable shear direction, and derive the calculation formula of the slip surface stress associated with its major and minor principal stresses. At the same time, in the limit equilibrium method of slope stability, combined with the vertical slice division, the slip surface stress is equivalent to the ratio of the slip surface force of the slice to the slip surface length.

[0072] The characteristics of the slip surface strength parameter of the present invention are: according to the spatial position relationship between the Mohr stress circle reflecting the slip surface stress state information and the shear strength envelope reflecting the shear characteristics of the slip surface, obtain the mathematical equation of the slip surface strength parameter associated with the general non-linear strength criterion in the form of principal stress. At the same time, in the limit equilibrium method of slope stability, specifying the slip surface strength parameter is a prerequisite for solving the slip surface force using the mechanical equilibrium conditions of the slices.

[0073] The characteristics of the above-mentioned embedding implementation approach of the present invention are as follows: By utilizing the mutual nesting relationship among the acting force, stress, and strength parameters of the strip-block sliding surface constructed, in the limit equilibrium method, a cyclic iteration solution strategy is adopted, combined with the initial value assignment and iterative approximation calculation method. First, the acting force of the strip-block sliding surface is solved, and then the sliding surface stress and sliding surface strength parameters are solved in sequence until the allowable calculation accuracy is reached, thereby realizing the embedding of the general non-linear strength criterion in the form of principal stress.

[0074] The present invention proposes an implementation approach and implementation process for solving the embedding of the general non-linear strength criterion in the form of principal stress into the limit equilibrium method for slope stability. Based on the functional relationship between the major and minor principal stresses of the general non-linear strength criterion in the form of principal stress, by using the tangent direction of the sliding surface at any point on the potential sliding surface to be equivalent to its most unfavorable shear direction, the correlation calculation formula between the sliding surface stress and its major and minor principal stresses is derived. Then, according to the spatial position relationship between the Mohr stress circle and the shear strength envelope, the mathematical equation for the sliding surface shear strength parameters related to the general non-linear strength criterion in the form of principal stress is obtained. Subsequently, by adopting a cyclic iteration solution strategy, the mutual nesting relationship among the sliding surface acting force, sliding surface stress, and sliding surface shear strength parameters in the embedding of the general non-linear strength criterion in the form of principal stress into the limit equilibrium method for slope stability is solved, achieving the purpose of slope stability evaluation under complex conditions.

[0075] Embodiment

[0076] A method for evaluating the stability of a slope with the general non-linear strength criterion in the form of principal stress embedded as shown in Figures 1 to 6 . This slope project is a supporting project for a construction project in the northwest region. The geological conditions of this slope are complex. The upper part of the slope is composed of newly filled soil, which only contains a small amount of silty clay, and the underlying bedrock. Through special exploration and field investigation of this area slope, the following slope occurrence and physical and mechanical parameters of the rock and soil mass are obtained: The slope height is 48m, the average slope angle is 22°, the average unit weight of the rock and soil mass is 17.8kN / m 3 , the average uniaxial compressive strength σ c of the rock and soil mass is 10MPa, and the average uniaxial tensile strength σ t of the rock and soil mass is 25MPa. Based on the present invention, combined with the limit equilibrium analysis method for slope stability, the stability analysis of this slope is carried out, thereby accurately evaluating the stability status of this slope, and thus providing a scientific basis for effectively preventing the landslide of this slope and reliably implementing reinforcement measures.

[0077] The specific operation is as follows:

[0078] (1) According to the "Code for Geotechnical Investigation" (GB50021-2001) and the "Standard for Geotechnical Test Methods" (GB / T50123-2019), drilling and sampling were carried out on the slope of the analysis object, and triaxial tests were conducted on the sampled samples. The test data show that the shear failure of the rock and soil mass in the slope of the analysis object conforms to the unified strength criterion of double shear. The principal stress expression form of this strength criterion is:

[0079]

[0080] In the formula, the parameter K is the tensile-compressive strength ratio of the soil mass, and K = σ t / σ c = 2.5; b is a parameter reflecting the influence degree of the intermediate principal shear stress and the normal stress on the corresponding plane on the material failure, and b = 0.24 is obtained through the curve fitting method.

[0081] (2) Based on the existing geological data and the in-situ stress test experiment carried out on the slope of the analysis object, it is determined that the influence coefficient λ of the intermediate principal stress is 0. Furthermore, the calculation of the intermediate principal stress is simplified to σ2 = σ3. At the same time, substituting the simplified calculation formula of the intermediate principal stress, K = 2.5, and b = 0.24 into the unified strength criterion of double shear, the functional relationship between the major principal stress and the minor principal stress under the unified strength criterion of double shear in the slope of the analysis object is obtained as σ1 = 25 + 2.5σ3.

[0082] (3) According to the "Technical Code for Building Slope Engineering" (GB 50330-2013), it is assumed that the slope of the analysis object is in a circular arc failure mode. Furthermore, taking the circular arc as its potential slip surface, and at the same time, given the reasonable value range of the circular arc slip surface parameters, the potential critical circular arc slip surface is searched to achieve the purpose of slope stability analysis.

[0083] (4) For a specific slip surface among the numerous circular arc slip surfaces generated by the reasonable value range of the given circular arc slip surface parameters, the slope slip body constructed by it and the slope surface is divided into multiple vertical strips, and the unbalanced thrust method is used to make reasonable assumptions about the forces between the strips. At the same time, combined with the implementation process of this invention patent, iterative solutions are carried out for the slip surface strength parameters, the normal force and the shear force of the slip surface, and thus the slope stability result corresponding to the specific slip surface, that is, the slope safety factor, is obtained. Among them, combined with the implementation steps S3-1 to step S3-6, the slip surface strength parameters c P and are 7.906 kPa and 25.377° respectively.

[0084] (5) Embed a mathematical optimization method. Within the reasonable value range of the given parameters of the circular arc slip surface, with the minimum value of the slope safety factor as the optimization objective, search for and find the circular arc slip surface corresponding to the minimum value of the slope safety factor, and call it the critical circular arc slip surface, while the minimum value of the corresponding slope safety factor is called the minimum slope safety factor.

[0085] (6) According to the stability evaluation standard of the "Technical Code for Building Slope Engineering" (GB 50330 - 2013), combined with the minimum slope safety factor of the analyzed slope of the object obtained by calculation (the value is 1.399), which is greater than the requirement in the code that the slope safety factor for the general working conditions of the first-level safety grade slope should not be less than 1.35, the evaluation result is that the slope is in a stable state. At the same time, the range of the critical circular arc slip surface is predicted, providing boundary conditions for further adopting reinforcement measures in the future.

[0086] (6) It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for evaluating slope stability under complex conditions, characterized in that In the method, based on the functional relationship between the major principal stress and the minor principal stress of the general non-linear strength criterion in the proposed major principal stress form, by using the fact that the tangent direction of the slip surface at any point on the potential slip surface is equivalent to its most unfavorable shear direction, the correlation calculation formula of the slip surface stress with its major principal stress and minor principal stress is derived. Then, according to the spatial position relationship between the Mohr stress circle and the shear strength envelope, the mathematical equation of the slip surface shear strength parameter related to the general non-linear strength criterion in the major principal stress form is obtained. Subsequently, a cyclic iterative solution strategy is adopted to break the mutual nesting relationship among the slip surface acting force, the slip surface stress, and the slip surface shear strength parameter in the evaluation method; And the method includes the following steps: Step S1: Ignore the unknown inter-slice forces for dividing the vertical slices, and calculate the initial normal force N of the slice sliding surface using the known forces on the vertical slices P (0) and the initial shear force T of the slice sliding surface P (0) ; Step S2: Calculate σ and τ respectively using Equation (1) and Equation (2); P and τ P ; σ P = N P / l P (1) τ P = T P / l P (2) Wherein, N P is the normal force of the strip block sliding surface, T P is the shear force of the strip block sliding surface, and l P is the corresponding length of the strip block sliding surface; Step S3: Using the minor principal stress σ 3_P at any point P on the slip surface, the normal stress σ P on the slip surface, and the shear stress τ P on the slip surface, as well as the slip surface strength parameters c P and the nested relationship between them, calculate the slip surface strength parameters c P and Step S4: Introduce the assumption condition of the inter-slice force, and use the mechanical equilibrium condition of the slices to carry out the limit equilibrium solution of the slope stability, so as to obtain the limit equilibrium solution of the slope stability and the normal force N of the slice slip surface P and the shear force T of the slice slip surface P ; Step S5: If the limit equilibrium solution of the slope stability tends to be stable, that is, the relative difference between the slope stability results calculated twice before and after is controlled within the allowable error range, stop the iterative loop and output the slope stability result; otherwise, let N P (0) = N P and T P (0) = T P , and repeat steps S2 to S4.

2. The evaluation method according to claim 1, wherein Step S3 specifically includes the following steps: Step S3-1: Obtain the normal stress σ on the slip surface P and the shear stress τ on the slip surface P ; Step S3-2: Let the initial value of the minor principal stress σ 3_P at any point P on the sliding surface be σ 3_P (0) , and in the first calculation, take σ 3_P (0) = 0; Step S3-3: Calculate the in-plane friction angle of the slip surface at point P using Equation (8) Wherein, d is the differential symbol and g is the function; Step S3-4: Calculate the cohesive force c of the slip surface at point P using Equation (9) P ; Step S3-5: Calculate the new σ using Equation (5) 3_P ; where, σ P is the normal stress on the slip surface at point P, and τ P is the shear stress on the slip surface at point P; Step S3-6: If |σ 3_P -σ 3_P (0) |≤ε, stop the loop calculation and output the final results of the slip surface strength parameters c P and ; otherwise, let σ 3_P (0) =σ 3_P , and repeat steps S3-3 to S3-5; Thus, the minor principal stress σ 3_P , the normal stress σ P on the slip surface, and the shear stress τ P on the slip surface, as well as the shear strength parameters c P and are nested with each other.

3. A slope stability evaluation device under complex conditions, 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 described in claim 1 or 2 is implemented.

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