Slope safety coefficient calculation method considering inclined drainage holes

Abstract

The invention belongs to the field of geological disaster prevention and control, and particularly discloses a slope safety coefficient calculation method considering an upward inclined drainage hole, which comprises the following steps: establishing a slope seepage numerical simulation model containing the upward inclined drainage hole, and obtaining space coordinates of nodes in a slope and pore water pressure data through finite element calculation; generating a potential slip plane based on an upper limit theorem of limit analysis, and calculating a pore water pressure value at each discrete point on the potential slip plane by using a Kriging interpolation method and taking node space coordinates and pore water pressure data as samples; according to the potential slip plane, the soil body strength parameter and the pore water pressure value obtained through interpolation, a balance equation of the soil body gravity power, the pore water pressure power and the internal energy dissipation power when the slope is in the critical failure state is established; and solving the balance equation to obtain the slope safety coefficient considering the inclined drainage hole. According to the method, the slope safety coefficient considering the inclined drainage hole can be efficiently and accurately calculated.

Description

Technical Field

[0001] This application belongs to the field of geological disaster prevention and control, and more specifically, relates to a method for calculating the slope safety factor considering inclined drainage holes. Background Technology

[0002] Slope stability is a long-standing challenge in the field of geological disaster prevention and control. Slope instability can trigger landslides, debris flows, and other disasters, posing a serious threat to infrastructure construction and public safety. Groundwater activity is one of the key factors leading to slope instability, especially in areas with high rainfall or glacial meltwater induced by global warming. Timely measures, such as installing drainage holes to drain groundwater to the slope surface or lowering the water level below the potential sliding surface, can effectively improve slope stability and significantly reduce the probability of landslides. Current research on this type of problem largely relies on numerical simulation methods, but these methods have limitations such as high computational costs, long cycles, complex parameter settings, and high professional requirements, making them difficult to widely apply in engineering practice.

[0003] Therefore, how to efficiently and accurately calculate the slope safety factor considering the inclined drainage hole is an urgent problem to be solved. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the purpose of this application is to provide a method for calculating the slope safety factor considering inclined drainage holes, which can efficiently and accurately calculate the slope safety factor considering inclined drainage holes.

[0005] To achieve the above objectives, in a first aspect, this application provides a method for calculating the slope safety factor considering inclined drainage holes, comprising the following steps: S10. Based on the slope geometric parameters, soil strength parameters and inclined drainage hole layout parameters, a slope seepage numerical simulation model with inclined drainage holes is established. The spatial coordinates of internal nodes and pore water pressure data of the slope are obtained through finite element calculation. S20. Based on the upper limit theorem of limit analysis, potential slip surfaces are generated point by point starting from the toe of the slope. Using the Kriging interpolation method, the spatial coordinates of the nodes and the pore water pressure data are used as samples to interpolate and calculate the pore water pressure values ​​at each discrete point on the potential slip surface. S30. Based on the potential slip surface, soil strength parameters, and interpolated pore water pressure values, establish a balance equation for the soil gravity power, pore water pressure power, and internal energy dissipation power when the slope is in a critical failure state. S40, using the rotation center position parameter of the potential slip surface as the optimization variable, the equilibrium equation as the constraint, and minimizing the safety factor as the objective, the optimization solution is performed to obtain the most dangerous slip surface of the slope and the corresponding safety factor.

[0006] This application provides a method for calculating the slope safety factor considering inclined drainage holes, which has the following advantages: By combining finite element seepage simulation with the upper bound theorem of limit analysis, it utilizes the advantages of numerical methods in simulating complex boundaries and drainage conditions, while also leveraging the characteristics of analytical methods in terms of clear mechanical mechanisms and high computational efficiency. Furthermore, it achieves accurate mapping of pore water pressure on the slip surface through Kriging interpolation, and automatically determines the most dangerous slip surface through an optimization algorithm, thereby significantly improving computational efficiency while ensuring computational accuracy. This overcomes the shortcomings of traditional pure numerical methods, such as complex parameter settings and high computational costs, and is suitable for rapid stability assessment and design of slopes under drainage conditions in practical engineering.

[0007] As a further preferred embodiment, in step S10, in the slope seepage numerical simulation model, the inside of the drainage hole is set to be without mesh, the area around the drainage hole is set to be with a dense mesh, the slope surface and the area around the drainage hole are set to be the head boundary, and the remaining boundaries are set to be impermeable boundaries.

[0008] As a further preferred embodiment, in step S20, the step of generating the potential slip surface point by point is specifically as follows: Establish a rectangular coordinate system with point A at the toe of the slope as the origin. XOY Set initial value R A , i A ;in, R A Let O be the distance from the center of rotation O to A. i A Let line OA and X The angle between the positive axes; Based on a known point P on the slip surface i Generate the next point P along the slip surface i+1 Its coordinates x i+1 , y i+1 The following formula is used to determine it:

[0009] In the formula, ( x i , y i Let P be a point. i coordinate;( x o , y o () represents the coordinates of point O; R i For the line OP i Length; d i For P i OPi+1 included angle; The effective internal friction angle of the soil; i i For OP i and x The angle between the positive axes; when y i+1 Greater than or equal to the slope height H Generation stops when the time is right, and the complete potential slip surface is obtained.

[0010] As a further preferred embodiment, in step S20, the formula for calculating pore water pressure using the Kriging interpolation method is as follows:

[0011] In the formula, P i Let be the pore water pressure at point i on the slip surface; β 0 represents the coefficient of the trend term; r (P i () represents the correlation coefficient vector between the i-th point and the known points; R The correlation matrix between known points; u is the pore water pressure vector at a known point; 1 is a vector consisting of elements 1.

[0012] As a further preferred embodiment, in step S30, the equilibrium equation is expressed as:

[0013] In the formula, W g ，W f ，W p These represent the soil gravity power, internal energy dissipation power, and pore water pressure power when the slope is in a critical failure state.

[0014] As a further preferred embodiment, in step S30, the soil gravity power W g The expression is:

[0015] In the formula, g i For the first i The weight of each block; oh The angular velocity at which the slope fails; R gi Let O be the distance from the center of mass of the block to the center of rotation O. The internal energy dissipation power W f The expression is:

[0016] In the formula, c s = c / Fs , c For the effective cohesion of the soil, Fs This refers to the slope safety factor. ;|P i P i+1 |for P i P i+1 The modulus; R fj For the first i The distance from the center of the sliding surface of each block to the rotation center O; The pore water pressure power W p The expression is:

[0017] In the formula, p Point P obtained by Kriging interpolation i and point P i+1 The average pore water pressure at the location.

[0018] As a further preferred embodiment, in step S40, the optimization variable is the distance from the rotation center to the toe of the slope. R A and its angle with the positive X-axis direction i A The sequential quadratic programming algorithm is used for optimization and solution.

[0019] As a further preferred embodiment, in step S40, the rotation center position parameter of the potential slip surface is used as the optimization variable, and the reasonable value range of the equilibrium equation and the optimization variable is used as constraints, with the goal of minimizing the safety factor, the following optimization framework is established:

[0020] In the formula, R A Let O be the distance from the center of rotation O to A. i A Let line OA and X The angle between the positive axes; H This refers to the slope height; W g ， W f ，W p These are the soil gravity power, internal energy dissipation power, and pore water pressure power when the slope is in a critical failure state, respectively. Fs This is the slope safety factor.

[0021] Secondly, this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the slope safety factor calculation method considering the inclined drainage hole as described in any of the above-mentioned methods.

[0022] Thirdly, this application provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the slope safety factor calculation method considering inclined drainage holes as described in any one of the above.

[0023] It is understood that the beneficial effects of the second and third aspects mentioned above can be found in the relevant descriptions in the first aspect above, and will not be repeated here. Attached Figure Description

[0024] Figure 1 This is a flowchart of the slope safety factor calculation method considering inclined drainage holes provided in this application; Figure 2 This is a schematic diagram of the slope rotation failure mechanism provided in the embodiments of this application; Figure 3 This is a schematic diagram illustrating the calculation of the power of external forces on any block provided in the embodiments of this application; Figure 4 This is a schematic diagram of the hydraulic boundary setting of the slope seepage numerical model considering the inclined drainage hole provided in the embodiments of this application; Figure 5 This is a schematic diagram of the mesh generation of a slope seepage numerical model considering inclined drainage holes provided in an embodiment of this application; Figure 6 This is a diagram showing the distribution of pore water pressure inside a slope, provided in an embodiment of this application. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0026] like Figure 1 As shown, this application provides a method for calculating the slope safety factor considering inclined drainage holes, including steps S10 to S40, which are detailed below: Step S10: Based on the slope geometric parameters, soil strength parameters, and inclined drainage hole layout parameters, establish a slope seepage numerical simulation model with inclined drainage holes, and obtain the spatial coordinates of internal nodes and pore water pressure data of the slope through finite element calculation.

[0027] In step S10, by precisely setting parameters such as the slope's geometry, dimensions, and soil strength characteristics, and combining this with the specific arrangement of the inclined drainage holes, a seepage numerical simulation model that reflects the actual condition of the slope is constructed. Using the finite element method, the seepage process inside the slope can be simulated with high precision, thereby obtaining the spatial coordinates of each node inside the slope and the corresponding pore water pressure data, providing fundamental and accurate data support for subsequent calculations and analyses.

[0028] Specifically, in the slope seepage numerical simulation model, the inside of the drainage hole is set to be without mesh, the area around the drainage hole is set to have a dense mesh, the slope surface and the area around the drainage hole are set as the head boundary, and the other boundaries are set as impermeable boundaries.

[0029] Step S20: Based on the upper bound theorem of limit analysis, potential slip surfaces are generated point by point starting from the toe of the slope. Then, using the Kriging interpolation method, the pore water pressure values ​​at each discrete point on the potential slip surface are calculated by interpolation using the spatial coordinates of the nodes and the pore water pressure data as samples.

[0030] In step S20, by generating slip surfaces point by point and combining them with Kriging interpolation, high-precision point-to-point matching of pore water pressure on slip surfaces can be achieved, overcoming the calculation errors caused by the mismatch between slip surfaces and meshes in traditional methods, and improving the accuracy of characterizing the influence of pore water pressure.

[0031] The formula for calculating pore water pressure using the Kriging interpolation method is as follows:

[0032] In the formula, P i Let be the pore water pressure at point i on the slip surface; β 0 represents the coefficient of the trend term; r (P i () represents the correlation coefficient vector between the i-th point and the known points; R The correlation matrix between known points; u is the pore water pressure vector at a known point; 1 is a vector consisting of elements 1.

[0033] Specifically, the steps for generating potential slip surfaces point by point can be as follows: Establish a rectangular coordinate system with point A at the toe of the slope as the origin. XOY Set initial value R A , i A ;in, R A Let O be the distance from the center of rotation O to A. i A Let line OA and X The angle between the positive axes; Based on a known point P on the slip surface i Generate the next point P along the slip surface i+1 Its coordinates x i+1 , y i+1 The following formula is used to determine it:

[0034] In the formula, ( x i , y i Let P be a point. i coordinate;( x o , y o () represents the coordinates of point O; R i For the line OP i Length; d i For P i OP i+1 included angle; The effective internal friction angle of the soil; i i For OP i and x The angle between the positive axes; when y i+1 Greater than or equal to the slope height H Generation stops when the time is right, and the complete potential slip surface is obtained.

[0035] Step S30: Based on the potential slip surface, soil strength parameters, and interpolated pore water pressure values, a balance equation is established for the soil gravity power, pore water pressure power, and internal energy dissipation power when the slope is in a critical failure state. This equation comprehensively considers the influence of soil self-weight, pore water pressure, and internal energy dissipation on slope stability. By establishing such a balance equation, the mechanical behavior of the slope in a critical failure state can be comprehensively analyzed from an energy perspective, providing a crucial theoretical basis for the subsequent accurate calculation of the slope safety factor.

[0036] In step S30, the equilibrium equation can be expressed as:

[0037] In the formula, W g ，W f ，W p These represent the soil gravity power, internal energy dissipation power, and pore water pressure power when the slope is in a critical failure state.

[0038] Specifically, the gravity power of the soil W g The expression is:

[0039] In the formula, g i For the first i The weight of each block; oh The angular velocity at which the slope fails; R gi Let O be the distance from the center of mass of the block to the center of rotation O.

[0040] Internal energy dissipation power W f The expression is:

[0041] In the formula, c s = c / Fs , c For the effective cohesion of the soil, Fs This refers to the slope safety factor. ;|P i P i+1 |for P i P i+1 The modulus; R fj For the first i The distance from the center of the sliding surface of each block to the rotation center O.

[0042] Pore ​​water pressure power W p The expression is:

[0043] In the formula, p Point P obtained by Kriging interpolation i and point P i+1 The average pore water pressure at the location.

[0044] Step S40: Using the rotation center position parameter of the potential slip surface as the optimization variable, the equilibrium equation as the constraint, and minimizing the safety factor as the objective, the optimization solution is performed to obtain the most dangerous slip surface of the slope and the corresponding safety factor.

[0045] Specifically, the optimized framework is as follows:

[0046] In step S40, the optimization variable is specifically the distance from the rotation center to the toe of the slope. R Aand its angle with the positive X-axis direction i A By using multivariate optimization algorithms (such as sequential quadratic programming) to optimize the rotation center parameters, the most dangerous slip surface and its corresponding minimum safety factor are automatically searched, thus achieving high efficiency and automation in slope stability analysis.

[0047] This application provides a method for calculating the slope safety factor considering inclined drainage holes, which has the following advantages: By combining finite element seepage simulation with the upper bound theorem of limit analysis, it utilizes the advantages of numerical methods in simulating complex boundaries and drainage conditions, while also leveraging the characteristics of analytical methods in terms of clear mechanical mechanisms and high computational efficiency. Furthermore, it achieves accurate mapping of pore water pressure on the slip surface through Kriging interpolation, and automatically determines the most dangerous slip surface through an optimization algorithm, thereby significantly improving computational efficiency while ensuring computational accuracy. This overcomes the shortcomings of traditional pure numerical methods, such as complex parameter settings and high computational costs, and is suitable for rapid stability assessment and design of slopes under drainage conditions in practical engineering.

[0048] In one embodiment, the technical solution to achieve the above objective can be as follows: This embodiment provides a method for calculating the slope safety factor considering inclined drainage holes, including the following steps: (1) Establish a slope geometric model based on parameters such as slope gradient and slope height, establish a rectangular coordinate system with the slope toe as the origin, and initialize the distance from the rotation center of the failure mechanism to the slope toe. R A And the connection between the two X Angle along the positive axis i A Based on the upper bound theorem of limit analysis, point P on the slope slip surface is generated point by point, starting from the toe of the slope. i ; (2) For example Figure 5 As shown, a mesh was generated for the slope geometric model containing inclined drainage holes. The seepage boundary was reasonably set according to the simulation conditions. Finite element numerical simulation of slope seepage was conducted, and the spatial coordinates of the mesh nodes were extracted. s and pore water pressure data u ; (3) Using location information s and pore water pressure information u Using the sample, the P-value on the slope slip surface was established using the Kriging interpolation method. i Point pore water pressure p Predictive models; (4) Establish the permissible velocity field of slope motion based on the upper bound theorem of limit analysis, and introduce the safety factor. Fs soil cohesion c and the tangent of the internal friction angle tan fThe slope is reduced to a critical failure state. The gravity power, pore water pressure power and internal energy dissipation power of each discrete block are calculated under this state. By summing the power of each part of the discrete block, the power balance equation of the critical failure state of the slope is established. (5) with R A , i A To optimize variables and minimize Fs To optimize the objective, the power balance equation is used as a constraint, and a sequential quadratic programming optimization algorithm is employed to solve the constrained optimization problem, thereby obtaining the safety factor of the slope under drainage conditions.

[0049] In this embodiment, as Figure 2 As shown, first according to R A , i A The value determines the rotation center O of the breaking mechanism. x o , y o Then, a point-by-point slip surface generation method is used, starting from the toe A, i.e., P1(0, 0), based on point P... i ( x i , y i Generate point P i+1 ( x i+1 , y i+1 Based on the geometric relationship of the slope failure mechanism, the following system of equations is established: (1) In the formula: R i For OP i Length; d i For ∠P i OP i+1 Angle value; i i For OP i and X Angle along the positive axis; f The friction angle within the soil.

[0050] Solving this system of quadratic equations yields: (2) The formulas for calculating Г and Λ are as follows: (3) exist xi+1 Among the possible values ​​of ∠OP, it is guaranteed that ∠OP i+1 P i The value greater than π / 2 is the desired value. Based on this, determine the next point P along the slip surface. i+1 ( x i+1 , y i+1 ),when y i+1 Greater than or equal to the slope height H When the time is reached, the generation algorithm is terminated, and the construction of the slope slip surface is completed.

[0051] In this embodiment, a finite element numerical simulation model of slope seepage is established based on the layout parameters of the slope's inclined drainage holes, such as... Figure 4 As shown, the drainage holes are set without a mesh, while the area around them is set with a denser mesh. The hydraulic boundary on the slope surface is a head boundary to simulate continuous rainfall conditions, and a head boundary is set around the drainage holes to simulate drainage resistance. The remaining boundaries are impermeable boundaries. Based on these settings, a finite element numerical simulation of slope seepage is conducted. After the calculation results converge, the spatial coordinates of each node are extracted. s and the corresponding pore water pressure u .

[0052] In this embodiment, Kriging interpolation is used, with [ s , u Calculate the distance between each sample point for the sample. d ij and semivariance r ij : (4) (5) The distance between sample points is simulated using an exponentially fitted curve. d ij and semivariance r ij The functional relationship between them, and for the unknown point P i The semivariance is estimated. The coefficient of the trend term in the formula for pore water pressure at unknown points is calculated using regression analysis. β 0, and then the following formula is used to estimate P. i Pore ​​water pressure value p i : (6) In the formula, r (P i ) is P i The vector of correlation coefficients between a point and a known point; R Given the correlation coefficients and correlation matrix of the points; uis the pore water pressure vector at a known point; 1 is a vector consisting of elements 1.

[0053] In this embodiment, based on the upper bound theorem of limit analysis and the rotational failure mechanism, a motion-permitted rotational velocity field is constructed to... oh This represents the rotational angular velocity. A slope safety factor is introduced. Fs The soil shear strength parameter is reduced, and the reduced soil cohesion is... c s satisfy c s = c / Fs Reduced internal friction angle of soil f s satisfy f s = arctan(tan f / Fs ).like Figure 3 As shown, assuming the reduced soil shear strength just brings the slope to a critical failure state, at which point the total power of all external forces in the failure zone is equal to the internal energy dissipation power, i.e.: (7) In the formula, W g , W p , W f These represent the gravity power, pore water pressure power, and internal energy dissipation power of the slope when it is in a critical failure state.

[0054] The gravity power of the soil in the slope failure area can be expressed as: (8) In the formula, g i For the first i The weight of each block; R gi Let O be the distance from the center of mass of the block to the center of rotation O.

[0055] The pore water pressure power can be expressed as: (9) In the formula, p Point P obtained by Kriging interpolation i and point P i+1 Average pore water pressure at the location, R fj For the first i The distance from the center of the sliding surface of each block to the rotation center O.

[0056] Internal energy dissipation power can be expressed as: (10) In the formula, |P i P i+1 |for P i P i+1 The modulus.

[0057] In this embodiment, in the slope failure mechanism that meets the above conditions, Fs The slope slip surface corresponding to the minimum value is the most dangerous slip surface. Based on this, the following optimization framework is established: (11) in, R A , i A The values ​​of the optimization variables determine the slope failure mechanism and slip surface; the constraints ensure the physical rationality of the range of values ​​for the optimization variables, while satisfying the balance equation between external force power and internal energy dissipation of the slope; the optimization objective is to minimize... Fs The corresponding slope slip surface is the most dangerous slip surface. The optimization process uses a sequential quadratic programming algorithm to consider the slope safety factor for the inclined drainage holes. Fs Solve the problem.

[0058] Compared with the prior art, this embodiment has the following beneficial effects: (1) This embodiment constructs a slope rotation failure mechanism based on the upper bound theorem of limit analysis. The slip surface composed of discretized points can be matched point-to-point with the pore water pressure inside the slope. This makes the calculation of the influence of pore water pressure on slope stability more in line with the actual situation, improves the calculation accuracy to a certain extent, and has important engineering guidance significance.

[0059] (2) When meshing the numerical model of the slope with inclined drainage holes, the inside of the inclined drainage holes is set to be unmesh, and the water head boundary is set around the inclined drainage holes. This can effectively simulate the drainage effect of the inclined drainage holes on groundwater and the drainage resistance inside the drainage holes, thereby obtaining a more realistic distribution of pore water pressure inside the slope under the action of the inclined drainage holes.

[0060] (3) The slope safety factor calculation method considering inclined drainage holes proposed in this embodiment effectively combines analytical methods and finite element numerical simulation technology. The former is responsible for the mechanical calculation module of slope stability, while the latter constitutes the internal seepage calculation module of the slope under the action of inclined drainage holes. Therefore, compared with pure analytical methods, this method has the characteristics of high accuracy and wide applicability; compared with pure numerical simulation methods, it has the characteristics of high efficiency and simple parameter setting.

[0061] The following is a specific implementation example of this application: A highway slope has an inclination angle of 60° and a height of 10 m. Geotechnical tests show that the soil cohesion... = 10 kPa, internal friction angle = 25°, natural severity c = 19 kN / m 3 saturated density c sat = 21.8 kN / m 3 Porosity 0.3, permeability coefficient 1×10 -10 m / s. Two rows of inclined drainage holes are installed at 3 m and 6 m from the bottom of the slope to improve the stability of the slope under heavy rainfall conditions. The drainage holes have an elevation angle of 10° and a depth of 6 m.

[0062] The method for calculating the slope safety factor considering inclined drainage holes, as provided in the example of this application, is processed according to the following steps: Step 1: Set the angle appropriately i A and length R A The values ​​of are used to determine the coordinates of the rotation center O of the slope failure mechanism, with the toe point A (0, 0) as the origin, as follows: (12) Points P on the potential slip surface are generated one by one using formulas (1)-(3). i By connecting P i P i+1 Determine the current parameter combination ( i A , R A The lower slope slip surface.

[0063] The second step is to establish a numerical simulation model of slope seepage with inclined drainage holes based on the finite element theory.

[0064] Under heavy rainfall conditions, the infiltration rate of the surface soil on the slope reaches its maximum value and forms surface runoff. At this time, the surface soil unit is in a saturated state, so a water head boundary is adopted and the water head pressure is set to 0. A water head boundary is set at the inclined drainage hole and the water head pressure is set to 1 kPa to simulate the drainage resistance in the hole caused by the accumulation of filter gauze or mud.

[0065] Figure 6 The distribution of pore water pressure inside the slope is shown, and the changes in pore water pressure demonstrate the actual effect of the inclined drainage holes.

[0066] The third step is to use formulas (4)-(6) to perform Kriging interpolation on point P on the potential slip surface. iThe pore water pressure at the location was estimated, and P was taken as the value. i and P i+1 The average pore water pressure at point P is used as the slip surface. i P i+1 Upper pore water pressure value.

[0067] Step 4: Calculate the gravity power, pore water pressure power, and internal energy dissipation power of the potential sliding block using formulas (8)-(10), and determine the slope safety factor using the bisection search method. Fs This makes formula (9) hold true, thus establishing the slope power balance equation.

[0068] Step 5: Using a sequential quadratic programming algorithm, an optimization function for the slope safety factor considering the inclined drainage hole is established for formula (11). By optimizing different parameter combinations ( i A , R A Obtaining the slope safety factor Fs The minimum value of is the safety factor of the slope considering the inclined drainage holes. The calculated slope safety factor can provide a theoretical basis for slope safety design and construction.

[0069] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for calculating the slope safety factor considering inclined drainage holes, characterized in that, Includes the following steps: S10. Based on the slope geometric parameters, soil strength parameters and inclined drainage hole layout parameters, a slope seepage numerical simulation model with inclined drainage holes is established. The spatial coordinates of internal nodes and pore water pressure data of the slope are obtained through finite element calculation. S20. Based on the upper limit theorem of limit analysis, potential slip surfaces are generated point by point starting from the toe of the slope. Using the Kriging interpolation method, the spatial coordinates of the nodes and the pore water pressure data are used as samples to interpolate and calculate the pore water pressure values ​​at each discrete point on the potential slip surface. S30. Based on the potential slip surface, soil strength parameters, and interpolated pore water pressure values, establish a balance equation for the soil gravity power, pore water pressure power, and internal energy dissipation power when the slope is in a critical failure state. S40, using the rotation center position parameter of the potential slip surface as the optimization variable, the equilibrium equation as the constraint, and minimizing the safety factor as the objective, the optimization solution is performed to obtain the most dangerous slip surface of the slope and the corresponding safety factor.

2. The method for calculating the slope safety factor considering inclined drainage holes as described in claim 1, characterized in that, In step S10, in the slope seepage numerical simulation model, the inside of the drainage hole is set to be without mesh, the area around the drainage hole is set to be with dense mesh, the slope surface and the area around the drainage hole are set to be water head boundaries, and the remaining boundaries are set to be impermeable boundaries.

3. The method for calculating the slope safety factor considering inclined drainage holes as described in claim 1, characterized in that, In step S20, the step of generating the potential slip surface point by point is as follows: Establish a rectangular coordinate system with point A at the toe of the slope as the origin. XOY Set initial value R A , θ A ; in, R A Let O be the distance from the center of rotation O to A. θ A Let line OA and X The angle between the positive axes; Based on a known point P on the slip surface i Generate the next point P along the slip surface i+1 Its coordinates x i+1 , y i+1 The following formula is used to determine it: In the formula, ( x i , y i Let P be a point. i coordinate;( x o , y o () represents the coordinates of point O; R i For the line OP i Length; δ i For P i OP i+1 included angle; The effective internal friction angle of the soil; θ i For OP i and x The angle between the positive axes; when y i+1 Greater than or equal to the slope height H Generation stops when the time is right, and the complete potential slip surface is obtained.

4. The method for calculating the slope safety factor considering inclined drainage holes as described in claim 1, characterized in that, In step S20, the formula for calculating pore water pressure using the Kriging interpolation method is as follows: In the formula, P i Let be the pore water pressure at point i on the slip surface; β 0 represents the coefficient of the trend term; r (P i () represents the correlation coefficient vector between the i-th point and the known points; R The correlation matrix between known points; u is the pore water pressure vector at a known point; 1 is a vector consisting of elements 1.

5. The method for calculating the slope safety factor considering inclined drainage holes as described in claim 1, characterized in that, In step S30, the equilibrium equation is expressed as: In the formula, W g ，W f ，W p These represent the soil gravity power, internal energy dissipation power, and pore water pressure power when the slope is in a critical failure state.

6. The method for calculating the slope safety factor considering inclined drainage holes as described in claim 1, characterized in that, In step S30, the soil gravity power W g The expression is: In the formula, g i For the first i The weight of each block; ω The angular velocity at which the slope fails; R gi Let O be the distance from the center of mass of the block to the center of rotation O. The internal energy dissipation power W f The expression is: In the formula, c s = c / Fs , c For the effective cohesion of the soil, Fs This refers to the slope safety factor. ;|P i P i+1 |for P i P i+1 The modulus; R fj For the first i The distance from the center of the sliding surface of each block to the rotation center O; The pore water pressure power W p The expression is: In the formula, p Point P obtained by Kriging interpolation i and point P i+1 The average pore water pressure at the location.

7. The method for calculating the slope safety factor considering inclined drainage holes as described in claim 1, characterized in that, In step S40, the optimization variable is the distance from the rotation center to the toe of the slope. R A and its X Angle in the positive direction of the axis θ A The sequential quadratic programming algorithm is used for optimization and solution.

8. The method for calculating the slope safety factor considering inclined drainage holes as described in claim 1, characterized in that, In step S40, using the rotation center position parameter of the potential slip surface as the optimization variable, and the reasonable value range of the equilibrium equation and the optimization variable as constraints, the following optimization framework is established with the goal of minimizing the safety factor: In the formula, R A Let O be the distance from the center of rotation O to A. θ A Let line OA and X The angle between the positive axes; H This refers to the slope height; W g ，W f ，W p These are the soil gravity power, internal energy dissipation power, and pore water pressure power when the slope is in a critical failure state, respectively. Fs This is the slope safety factor.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the slope safety factor calculation method considering the inclined drainage hole as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When executed by the processor, the computer instructions implement the method for calculating the slope safety factor considering the inclined drainage hole as described in any one of claims 1 to 8.

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