A binary stratigraphic structure type slope earthquake stability evaluation method and device

Abstract

This application discloses a method and apparatus for evaluating the seismic stability of slopes with a binary stratigraphic structure, relating to the field of geotechnical engineering. A soil-rock differentiated constitutive model is established, and the spatiotemporal effects of seismic waves are simulated using simple harmonic waves. Dynamic response characteristics are calculated, and a logarithmic spiral slip surface is determined. The vertically segmented slip body is analyzed, and the inertial force resultant is obtained by integrating seismic acceleration. Using the limit equilibrium method, the slope seismic stability coefficient corresponding to the logarithmic spiral slip surface is solved. All potential slip surfaces within the slope are iteratively searched, and the slip surface corresponding to the smallest slope seismic stability coefficient is taken as the most dangerous slip surface. The displacement and acceleration dynamic response laws of the slip body under seismic loading are analyzed to form a comprehensive evaluation system. This method solves the problems of existing methods that still use a single viscoelastic constitutive model, failing to fully consider the differences in dynamic characteristics between soil and bedrock, failing to reflect the geometric boundary conditions of the slope model, and potentially overestimating seismic forces within the slope.

Description

Technical Field

[0001] This application relates to the technical field of geotechnical engineering, and in particular to a method and apparatus for evaluating the seismic stability of a binary stratum structure slope. Background Technology

[0002] Soil-rock binary strata slopes are a common geological formation in engineering construction. They consist of a soil overburden layer and a bedrock substructure, exhibiting significant differences in mechanical properties and dynamic response characteristics compared to homogeneous soil slopes. Under seismic loading, the stability of such slopes is influenced not only by static factors such as soil strength and slope geometry, but also by dynamic processes such as reflection, refraction, and energy attenuation of seismic waves at the soil-rock interface. Therefore, conducting seismic stability assessments of soil-rock binary strata slopes is of great significance for the seismic design and geological hazard prevention of mountainous highways, railways, water conservancy projects, and building construction.

[0003] However, current technologies primarily employ the quasi-static method, which determines the comprehensive horizontal seismic coefficient of the sliding body or strip based on the basic seismic intensity, and then calculates the seismic inertial force of the strip. In this case, the seismic force on the slope's soil and rock mass is a constant in both magnitude and direction. The quasi-dynamic method simplifies the seismic wave propagation process by setting the seismic acceleration as a spatiotemporally varying function, but the soil and rock materials still employ a rigid constitutive model, which cannot reflect the dynamic response characteristics of the slope under seismic loads. Therefore, an artificial amplification factor is required.

[0004] Although the modified pseudo-dynamic method employs a viscoelastic constitutive model that can reflect the amplification effect of soil and rock materials on seismic waves, it still focuses on homogeneous slopes. Furthermore, due to its use of rigid base boundary conditions, downflow waves reflected from the free surface are completely reflected when they contact the rigid soil base, which can easily over-amplify the seismic forces in the soil. Summary of the Invention

[0005] In this embodiment of the application, a binary stratigraphic structure slope seismic stability evaluation method is provided, which solves the problem that the existing methods still use a single viscoelastic constitutive model, do not fully consider the difference in dynamic characteristics between soil and bedrock, cannot reflect the geometric boundary conditions of the slope model, and may over-amplify the seismic forces in the slope.

[0006] In a first aspect, embodiments of this application provide a method for evaluating the seismic stability of a soil-rock two-dimensional strata-structure slope. The method includes: Step 101, taking the soil-rock two-dimensional strata-structure slope as the research object, setting a differentiated constitutive model for the soil and bedrock, and simplifying seismic waves into incident harmonic waves to simulate spatiotemporal effects; Step 102, based on the slope's geometric parameters and slip surface search parameters, determining the shape and location of a logarithmic spiral slip surface, which is used to define the range of the sliding body within the slope; Step 103, calculating the slope's seismic acceleration by setting multiple sets of boundary conditions to obtain the dynamic response characteristics of the slope's displacement and acceleration; Step 104, based on the dynamic response characteristics of the slope's displacement and acceleration, and the range of the sliding body defined by the logarithmic spiral slip surface, vertically segmenting the sliding body, calculating the resultant horizontal seismic inertial force of each segment by integrating the seismic acceleration along the height of each segment, and then combining this with limit equilibrium... The method involves solving for the slope seismic stability coefficient corresponding to the logarithmic spiral slip surface; step 105, using the length of the slope top shear point from the slope shoulder and the central angle of the logarithmic spiral as iterative variables, adjusting the slip surface search parameters to generate a new logarithmic spiral slip surface, and iteratively executing steps 103 to 104 based on the new logarithmic spiral slip surface; comparing the slope seismic stability coefficients corresponding to each set of iterative variables, and after completing the iterative search of all potential slip surfaces in the slope, selecting the slip surface corresponding to the smallest slope seismic stability coefficient as the most dangerous slip surface; step 106, taking the most dangerous slip surface under static conditions as the object, using the multiple sets of boundary conditions set in step 103 to calculate the slope seismic acceleration, analyzing the displacement and acceleration dynamic response law of the sliding body under seismic action, and forming a slope seismic stability evaluation system including the slope seismic stability coefficient, the location of the most dangerous slip surface, and the dynamic response characteristics, in order to realize the slope seismic stability evaluation.

[0007] In one possible implementation, the soil in the differentiated constitutive model is defined by an equivalent linear viscoelastic model to define the dynamic constitutive relation, while the bedrock is defined by an ideal elastic model to define the dynamic constitutive relation. The seismic waves are simplified into simple harmonic waves in the incident form, specifically simple harmonic waves incident vertically from the basement, to replace random seismic waves in the soil.

[0008] In one possible implementation, the multiple sets of boundary conditions include zero-stress boundary conditions for the free surface at the slope crest, stress continuity conditions for the soil-rock contact surface, displacement continuity conditions for the soil-rock contact surface, and input harmonic wave amplitude conditions; the zero-stress boundary condition is: ;in, For the shear stress of the soil, The depth of the free surface from the top of the slope; the stress continuity condition is: ;in, This represents the depth of the bedrock from the top of the slope. This represents the depth of the soil element from the top of the slope. For bedrock shear stress, The depth of the rock mass unit from the top of the bedrock; the displacement continuity condition is: ;in, This represents the horizontal displacement of the soil. The horizontal displacement of the bedrock; input harmonic wave amplitude conditions: the vertically incident upward wave in the bedrock... The displacement amplitude corresponds to the amplitude of the simple harmonic wave. ;in, The amplitude of the simple harmonic wave. This represents the amplitude of the horizontal displacement of the soil. It is the angular frequency.

[0009] In one possible implementation, the slope geometry parameters include slope height, slope angle, and depth of bedrock from the slope crest; the sliding surface search parameters include the slope crest shear point search range, the slope crest shear point search amount, the logarithmic spiral central angle search range, and the logarithmic spiral central angle search amount.

[0010] In one possible implementation, the logarithmic spiral sliding surface is defined as follows: when the logarithmic spiral intersects the soil-rock contact surface, the slope is set to slide along the contact surface of the soil and rock, and the logarithmic spiral sliding surface is the combination of the logarithmic spiral and the contact surface of the soil and rock.

[0011] In one possible implementation, the vertical segmentation of the sliding body and the calculation of the resultant horizontal seismic inertial force of each segment by integrating seismic acceleration along the height of each segment include: vertically dividing the sliding body into a predetermined number of segments; determining the depth of the bottom and top of each segment from the slope crest based on the geometric relationship between the segment and the sliding surface; and calculating the resultant horizontal seismic inertial force of each segment by integrating seismic acceleration along the height of each segment based on the depth of the bottom and top of each segment from the slope crest, using the following formula: ;in, For strips exist The horizontal seismic force that is constantly subjected to For strips The depth from the bottom to the top of the slope. For strips The depth from the top of the slope to the top of the hill. It is the density of the soil. It is a strip width, for Time depth is The seismic acceleration experienced by the soil element. It is an integral infinitesimal element of the soil element in the depth direction from the top of the slope.

[0012] In one possible implementation, the step of combining the limit equilibrium method to solve for the slope seismic stability coefficient corresponding to the logarithmic spiral slip surface includes: using the Simplified Method as the limit equilibrium method, and determining the slope seismic stability coefficient based on the Simplified Method. The calculation formula is: , ;in, This represents the total number of vertical strips in the sliding body. Number the blocks. For strips Cohesion at the bottom For strips width, It is a strip The weight, For strips The difference in lateral forces, For strips The internal friction angle at the bottom, For strips The iteration factor, For strips The angle of inclination at the bottom, For strips exist The horizontal seismic force constantly acting on it; where the sliding surface is located inside the soil mass, and These are the soil's cohesion and internal friction angle; when the bottom of the strip is located at the contact surface between the soil and rock mass... and It refers to the cohesion and internal friction angle at the soil-rock interface.

[0013] In one possible implementation, adjusting the sliding surface search parameters refers to adjusting the length of the slope crest shear point from the slope shoulder and the central angle of the logarithmic spiral; the adjustment range of the length of the slope crest shear point from the slope shoulder is the slope crest shear point search interval. Search range of the central angle of the logarithmic spiral And the central angle of the logarithmic spiral is less than ;in, This is the starting value for the search interval at the slope crest cut-in point. This is the termination value of the search interval for the slope crest cut-in point. The starting angle for the search range of the central angle of the logarithmic spiral. The terminating angle of the search range for the central angle of the logarithmic spiral. The internal friction angle of the soil. The slope angle is given.

[0014] In one possible implementation, the most dangerous sliding surface under static conditions refers to the sliding surface corresponding to the minimum slope seismic stability coefficient when the simple harmonic wave amplitude is zero. When analyzing the acceleration dynamic response of the sliding body under seismic loading, the free surface amplification factor and the average sliding body amplification factor are used for quantification, and the calculation formulas are as follows: , ;in, x-axis The magnification factor of the corresponding free surface, The x-coordinate is The maximum acceleration of a free surface under the action of a simple harmonic wave. x-axis The corresponding depth of the free surface from the top of the slope. For time, The amplitude of the simple harmonic wave. The operator for extracting the real part of a complex number. For complex wave number, This represents the depth of the bedrock from the top of the slope. The imaginary unit, The ratio of complex impedances. This is the average magnification factor of the sliding body. Let be the maximum average acceleration of the sliding body under the action of a simple harmonic wave. This represents the maximum horizontal load on the sliding body under simple harmonic wave action. The weight of the sliding body.

[0015] Secondly, this application provides a device for evaluating the seismic stability of a two-dimensional strata-structure slope. The device includes: a model setting module, used to set a differentiated constitutive model of the soil and bedrock as the research object for a soil-rock two-dimensional strata-structure slope, simplifying seismic waves into incident harmonic waves to simulate spatiotemporal effects; a determination module, used to determine the shape and location of a logarithmic spiral sliding surface adapted to the dynamic response characteristics based on slope geometric parameters and sliding surface search parameters, the logarithmic spiral sliding surface being used to define the range of the sliding body within the slope; a dynamic response characteristic acquisition module, used to calculate the slope's seismic acceleration by setting multiple sets of boundary conditions, obtaining the dynamic response characteristics of the slope's displacement and acceleration; and a solution module, used to vertically segment the sliding body based on the dynamic response characteristics of the slope's displacement and acceleration, and the range of the sliding body defined by the logarithmic spiral sliding surface, calculating the horizontal seismic inertial force of each segment by integrating the seismic acceleration along the height of each segment. The combined force, combined with the limit equilibrium method, is used to solve for the slope seismic stability coefficient corresponding to the logarithmic spiral slip surface. The iteration module is used to adjust the slip surface search parameters to generate a new logarithmic spiral slip surface by using the length of the slope top shear point from the slope shoulder and the central angle of the logarithmic spiral as iteration variables. Based on the new logarithmic spiral slip surface, steps 103 to 104 are iteratively executed. The slope seismic stability coefficients corresponding to each set of iteration variables are compared. After completing the iterative search of all potential slip surfaces in the slope, the slip surface corresponding to the smallest slope seismic stability coefficient is selected as the most dangerous slip surface. The analysis module is used to calculate the slope seismic acceleration using the most dangerous slip surface under static conditions and following the multiple sets of boundary conditions set in step 103. The displacement and acceleration dynamic response laws of the sliding body under seismic action are analyzed to form a slope seismic stability evaluation system including the slope seismic stability coefficient, the location of the most dangerous slip surface, and the dynamic response characteristics, so as to realize the slope seismic stability evaluation.

[0016] The one or more technical solutions provided in this application have at least the following technical effects: This application provides a method for evaluating the seismic stability of slopes with a two-dimensional stratum structure. Specifically, this application optimizes the seismic stability evaluation of slopes with a soil-rock two-dimensional stratum structure by achieving precise and systematic technical optimization. It effectively solves the problems of existing pseudo-dynamic methods that use a single viscoelastic constitutive model, fail to fully consider the differences in dynamic characteristics between soil and bedrock, cannot reflect the geometric boundary conditions of the slope model, and may excessively amplify seismic forces within the slope. Specifically, it sets differentiated constitutive models for soil and bedrock. The soil uses an equivalent linear viscoelastic model to characterize elastic deformation and damping energy dissipation characteristics, while the bedrock uses an ideal elastic model to adapt to its deformation characteristics. This completely eliminates the unreasonable setting of a rigid constitutive model for bedrock, accurately matches the mechanical essence of the soil-rock two-dimensional stratum, and solves the problem of insufficient consideration of the differences in dynamic characteristics between soil and rock. This application simplifies seismic waves into simple harmonic waves incident vertically from the basement, and calculates slope seismic acceleration by combining multiple sets of boundary conditions. It accurately obtains the dynamic response characteristics of the slope at any depth and time, fully simulating the temporal periodicity and spatial variability of seismic wave propagation, thus overcoming the deficiency of existing methods that may excessively amplify the energy of seismic waves in the soil. This application calculates the stability coefficient through vertical slice analysis and the limit equilibrium method, iteratively searches for and locates the most dangerous slip surface, and finally forms a comprehensive evaluation system. This application balances computational efficiency and practicality, improving the accuracy of stability evaluation and providing comprehensive support for seismic design in engineering. It completely solves the core deficiencies of existing technologies and has significant engineering application value. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating a method for evaluating the seismic stability of a binary stratigraphic slope, as provided in this application embodiment.

[0019] Figure 2 This is a schematic diagram of a soil-rock binary stratum structure slope model provided in an embodiment of this application.

[0020] Figure 3 This is a schematic diagram illustrating the variation of the slope seismic stability coefficient over time for the most dangerous sliding surface, as provided in an embodiment of this application.

[0021] Figure 4 This is a schematic diagram illustrating the variation of acceleration over time on the free surface at the top of a slope, as provided in an embodiment of this application.

[0022] Figure 5 This is a schematic diagram illustrating the change of acceleration of the free surface at the bottom of the slope over time, as provided in an embodiment of this application.

[0023] Figure 6 This is a schematic diagram illustrating the change of acceleration at the center point of the slope over time, as provided in an embodiment of this application.

[0024] Figure 7 This is a schematic diagram illustrating the variation of the slope free surface magnification factor with the abscissa, as provided in the embodiments of this application.

[0025] Figure 8 This is a schematic diagram illustrating the variation of the average amplification factor of the sliding body with the frequency of the simple harmonic wave, as provided in the embodiments of this application.

[0026] Figure 9 This is a schematic diagram of a binary stratigraphic slope seismic stability evaluation device provided in an embodiment of this application.

[0027] Figure 10 This is a schematic diagram of a binary stratigraphic slope seismic stability evaluation server provided in an embodiment of this application. Detailed Implementation

[0028] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0029] The following description of some technologies involved in the embodiments of this application is provided to aid understanding and should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, some descriptions of well-known functions and structures are omitted in the following description.

[0030] This application provides a method for evaluating the seismic stability of a two-dimensional stratigraphic slope, such as... Figure 1 As shown, the method includes steps 101 to 106. Wherein, Figure 1 This is merely one execution order shown in the embodiments of this application and does not represent the only execution order for a binary stratigraphic slope seismic stability evaluation method. The execution order can be adjusted to achieve the desired final result. Figure 1 The steps shown can be performed in parallel or in reverse order.

[0031] This application requires obtaining the parameters needed for seismic stability calculations of slopes with a soil-rock binary stratigraphic structure: Through field reconnaissance, drilling, and other methods, a cross-sectional diagram of the soil-rock binary stratigraphic slope is drawn. Based on the slope profile structure, the model is appropriately generalized to obtain the model's geometric parameters, including the slope height. slope angle Depth of bedrock from the top of the slope Representative undisturbed samples were collected from each layer of soil and rock to conduct laboratory geotechnical tests: the density of the soil was measured using the ring sampler method. The density of the rock mass was measured using the volumetric method. The cohesion and internal friction angle of soil are measured using triaxial or direct shear tests, while the cohesion and internal friction angle of the soil-rock interface are measured using large-scale compression direct shear tests. When relevant test conditions are unavailable, cohesion and internal friction angle can be defined based on empirical values ​​or by reducing the strength parameters of the soil. When the bedrock is deeply buried and the sliding surface is significantly independent of the soil-rock interface, the influence of the cohesion and internal friction angle of the soil-rock interface can be ignored.

[0032] In this embodiment, the target slope was artificially excavated, and the slope surface was landscaped. The slope geometry is regular, and the slope engineering safety level is Level II. The strata mainly consist of clay and bedrock, which can be considered a homogeneous isotropic body with no obvious structural planes. Referring to the "China Seismic Ground Motion Parameter Zoning Map" (GB 18306-2015), the peak ground acceleration is 0.2g (gravitational acceleration). According to the "Technical Specification for Building Slope Engineering" (GB 50330-2013), the importance level of this slope is Level I, and the design stability safety factor is 1.15.

[0033] 1. Geometric parameters: By drilling at 8-meter intervals (5 rows of exploration holes arranged at the bottom, top, and top of the slope, with 3 holes in each row), a stratigraphic profile was drawn and generalized into a 2D model to obtain the slope height. The slope is 25m long and the angle is... The angle is 42°, and the depth of the bedrock from the top of the slope is... It is 43m.

[0034] 2. Basic physical and mechanical parameters of the soil: The density of the soil was obtained by taking the average value of parallel tests using the ring cutter method on undisturbed samples from the top, bottom, and top of the slope. It is 1.62 g / cm 3 Through four sets of triaxial undrained tests (surrounding pressures of 50 kPa, 100 kPa, 200 kPa, and 300 kPa), the soil cohesion was found to be 46 kPa and the internal friction angle was 35°.

[0035] 3. Bedrock and soil-rock interface parameters: density of bedrock It is 2.05 g / cm³ 3(3 sets of parallel tests using the volumetric method); through large-scale compression direct shear tests at 100kPa, 200kPa, 300kPa and 500kPa, the cohesion of the soil-rock interface was found to be 15kPa and the internal friction angle was 30°.

[0036] 4. Dynamic parameters: The dynamic shear modulus of the soil was measured by the resonant column test. The damping ratio of the soil is 35 MPa. The dynamic shear modulus of bedrock is 0.08. 2580MPa

[0037] 5. Seismic motion parameters: Simple harmonic wave amplitude The value is 0.2g (taken as peak ground acceleration), and the frequency is f=2.5Hz (selected as the characteristic period of the ground acceleration response spectrum of 0.4s).

[0038] 6. Sliding surface search and strip division parameters: Search interval for the slope crest shear point Search range of the central angle of the spiral ( Specifically, the search amount for the slope crest shear point is n1=20, and the search amount for the central angle of the logarithmic spiral is n2=20 (a second search is conducted near the point of lowest stability coefficient after the initial search); the total number of vertical strips of the sliding body. It is 30.

[0039] Step 101: Taking the soil-rock binary strata structure slope as the research object, a differentiated constitutive model of soil and bedrock is set up, and the seismic wave is simplified into a simple harmonic wave in the incident form to simulate the spatiotemporal effect.

[0040] Step 102: Based on the slope geometry parameters and sliding surface search parameters, determine the shape and location of the logarithmic spiral sliding surface that matches the dynamic response characteristics. The logarithmic spiral sliding surface is used to define the range of the sliding body within the slope.

[0041] Step 103: Calculate the slope seismic acceleration by setting multiple sets of boundary conditions to obtain the dynamic response characteristics of the slope's displacement and acceleration.

[0042] The soil in the differentiated constitutive model uses an equivalent linear viscoelastic model to define the dynamic constitutive relationship, while the bedrock uses an ideal elastic model to define the dynamic constitutive relationship.

[0043] The seismic wave is simplified into a simple harmonic wave in the incident form, specifically a simple harmonic wave that is perpendicularly incident from the base, to replace random seismic waves in the soil.

[0044] Specifically, an equivalent linear viscoelastic model is used to describe the dynamic mechanical behavior of soil. This model can simultaneously reflect the elastic deformation characteristics and viscous damping energy dissipation characteristics of soil, which is consistent with the actual mechanical response of soil under seismic load. Its core expression is the relationship between soil shear stress and shear strain: .in, It is the shear stress of the soil. It is the shear strain of the soil. It is the dynamic shear modulus of the soil. It is the viscosity coefficient of the soil. It's time.

[0045] Specifically, considering that the stiffness of bedrock is much greater than that of soil, and that its deformation under seismic load is mainly elastic with negligible damping energy, an ideal elastic model is used to define the dynamic constitutive relationship of bedrock.

[0046] Multiple sets of boundary conditions include zero-stress boundary conditions for the free surface at the top of the slope, stress continuity conditions for the soil-rock contact surface, displacement continuity conditions for the soil-rock contact surface, and input harmonic wave amplitude conditions.

[0047] The zero-stress boundary condition is: .in, For the shear stress of the soil, The depth of the free surface from the top of the slope.

[0048] The stress continuity condition is: .in, This represents the depth of the bedrock from the top of the slope. This represents the depth of the soil element from the top of the slope. For bedrock shear stress, This represents the depth of the rock mass unit from the top of the bedrock.

[0049] The displacement continuity condition is: .in, This represents the horizontal displacement of the soil. This represents the horizontal displacement of the bedrock.

[0050] Input harmonic wave amplitude conditions: The upward wave incident vertically in bedrock... The displacement amplitude corresponds to the amplitude of the simple harmonic wave. .in, The amplitude of the simple harmonic wave. This represents the amplitude of the horizontal displacement of the soil. It is the angular frequency.

[0051] Specifically, harmonic waves are used to replace random seismic waves in the soil, through defined frequencies and This simulates the spatiotemporal effects of seismic waves propagating in soil and rock materials.

[0052] Slope geometry parameters include slope height, slope angle, and depth of bedrock from the top of the slope.

[0053] The sliding surface search parameters include the slope crest shear point search range, the slope crest shear point search amount, the logarithmic spiral central angle search range, and the logarithmic spiral central angle search amount.

[0054] The logarithmic spiral slip surface is defined as follows: when the logarithmic spiral intersects the soil-rock contact surface, the slope is assumed to slide along the contact surface between the soil and rock. The logarithmic spiral slip surface is the combination of the logarithmic spiral and the contact surface between the soil and rock.

[0055] The formula for calculating the distance from any point on the sliding surface of a logarithmic spiral to the origin of the spiral is: .in, Let be the distance from any point on the logarithmic spiral sliding surface to the origin of the spiral. The distance from the point of entry to the origin of the spiral is [missing information]. Let be the angle between the line connecting any point on the logarithmic spiral sliding surface and the origin of the spiral, and the horizontal plane. Let be the angle between the line connecting the point of entry and the origin of the spiral and the horizontal plane. The internal friction angle of the soil.

[0056] Specifically, the formula for calculating the distance from any point on a logarithmic spiral sliding surface to the origin of the spiral is used to define the shape of the sliding surface.

[0057] Figure 2 This is a schematic diagram of a soil-rock binary strata structure slope model provided in an embodiment of this application. This application establishes a rectangular coordinate system with the slope toe (point A) as the origin (x-axis positive horizontally to the right, y-axis positive vertically upwards). The coordinates of point A are (0m, 0m), and the coordinates of point B on the slope shoulder are (27.765m, 25m). The horizontal distance from point A to the left boundary of the model is 0.5 times the slope height, and the horizontal distance from point B to the right boundary of the model is 1.5 times the slope height (the furthest search distance for the sliding surface shear point). After inputting the above soil and rock material parameters into the model, the distance from the slope top shear point to the slope shoulder is calculated. Given the central angle ∠AOC of the logarithmic spiral, draw the sliding surface and determine its relationship with the soil-rock contact surface. When the sliding surface cuts down into the soil-rock contact surface, it is determined that the sliding body slides along the soil-rock contact surface. and These are the amplitudes of the ascending and descending waves in the soil, respectively. and These are the amplitudes of the ascending and descending waves in the rock mass, respectively. This represents the depth of the soil element from the top of the slope. This represents the depth of the rock mass unit from the top of the bedrock. Let be the angle between the line connecting the point of entry and the origin of the spiral and the horizontal plane. Let the angle between the line connecting the cut-out point (point A at the foot of the slope) and the origin of the spiral and the horizontal plane be denoted by .

[0058] Step 104: Based on the dynamic response characteristics of the slope displacement and acceleration, and the range of the sliding body defined by the logarithmic spiral sliding surface, the sliding body is vertically segmented. By integrating the seismic acceleration along the height of each segment, the resultant horizontal seismic inertial force of each segment is calculated. Then, combined with the limit equilibrium method, the slope seismic stability coefficient corresponding to the logarithmic spiral sliding surface is solved.

[0059] The sliding body is vertically segmented, and the resultant horizontal seismic inertial force of each segment is calculated by integrating the seismic acceleration along the height of each segment, including the following:

[0060] The sliding body is vertically divided into a predetermined number of strips, and the depth of the bottom and top of each strip from the top of the slope is determined based on the geometric relationship between the strips and the sliding surface.

[0061] Specifically, according to the preset number of blocks (Total number of vertically divided segments of the sliding body), dividing the sliding body evenly along the vertical direction into... Each segment is an independent block; based on the geometric positional relationship between each segment and the logarithmic spiral sliding surface, and combined with the slope coordinate system (with the toe of the slope as the origin, the horizontal direction to the right as the x-axis, and the vertical direction upward as the y-axis), the depths of the bottom and top of each segment from the top of the slope are calculated (denoted as ). and At the same time, determine the width of the strip. The horizontal and vertical coordinates of the bottom control points (top left, bottom left, top right, bottom right) and the center point.

[0062] Based on the depth of the bottom and top of each block from the slope crest, the resultant horizontal seismic inertial force of each block is calculated by integrating the seismic acceleration along the height of each block. The calculation formula is as follows: .in, For strips exist The horizontal seismic force that is constantly subjected to For strips The depth from the bottom to the top of the slope. For strips The depth from the top of the slope to the top of the hill. It is the density of the soil. It is a strip width, for Time depth is The seismic acceleration experienced by the soil element. It is an integral infinitesimal element of the soil element in the depth direction from the top of the slope.

[0063] Specifically, . . . . . . . . . .in, This is the first intermediate parameter representing the overall dynamic characteristics of the slope. This is the second intermediate parameter representing the overall dynamic characteristics of the slope. The first intermediate parameter for the local dynamic characteristics of the strip block. The second intermediate parameter is the local dynamic characteristic of the strip block. The actual wave number of the soil. For the imaginary wave number of the soil, The depth of the free surface from the top of the slope. This represents the depth of the bedrock from the top of the slope. Let be the real part of the soil-rock complex impedance ratio. Let be the imaginary part of the soil-rock complex impedance ratio. For parameters related to the normalized real wavenumber of soil, For parameters related to the normalized imaginary wavenumber of soil, The slope height The shear wave velocity of the soil. The damping ratio of the soil. It is the dynamic shear modulus of the soil. This represents the dynamic shear modulus of the bedrock. This represents the shear wave velocity of the bedrock.

[0064] In this embodiment, based on the above parameters and formulas, the resultant force of horizontal seismic inertial forces at different times within one cycle is calculated for the 30 blocks.

[0065] Using the limit equilibrium method, the seismic stability coefficient of the slope corresponding to the logarithmic spiral slip surface is solved, including the following:

[0066] The limit equilibrium method uses the simplified distribution method, and the slope seismic stability coefficient is based on the simplified distribution method. The calculation formula is: , .in, This represents the total number of vertical strips in the sliding body. Number the blocks. For strips Cohesion at the bottom For strips width, It is a strip The weight, For strips The difference in lateral forces, For strips The internal friction angle at the bottom, For strips The iteration factor, For strips The angle of inclination at the bottom, For strips exist The horizontal seismic force constantly acting on it. Specifically, when the sliding surface is located inside the soil mass, and These are the soil's cohesion and internal friction angle. When the bottom of the strip is located at the contact surface between the soil and rock mass... and It refers to the cohesion and internal friction angle at the soil-rock interface.

[0067] Specifically, .in, It is a strip The ordinate of the top center point, It is a strip The ordinate of the bottom center point The density of the soil. It is gravitational acceleration. .in, For strips The ordinate of the bottom right point For strips The ordinate of the point on the bottom left.

[0068] Specifically, since the slope seismic stability coefficient appears on both sides of the calculation formula, it needs to be solved using an iterative method. The specific process is as follows: assuming Set the initial slope seismic stability coefficient ,Will Substituting the values ​​into the formula for calculating the slope seismic stability coefficient based on the Jance method, we calculate the first approximation of the slope seismic stability coefficient. .like , If the preset calculation accuracy threshold is used, then Let be the slope seismic stability coefficient at that moment; if it does not meet the preset calculation accuracy threshold, let Repeat the above steps until the preset calculation accuracy threshold is met. The preset calculation accuracy threshold can be 0.001.

[0069] Step 105: Using the length of the slope crest shear point from the slope shoulder and the central angle of the logarithmic spiral as iteration variables, adjust the slip surface search parameters to generate a new logarithmic spiral slip surface. Based on the new logarithmic spiral slip surface, iteratively execute steps 103 to 104. Compare the slope seismic stability coefficients corresponding to each set of iteration variables. After completing the iterative search of all potential slip surfaces within the slope, select the slip surface corresponding to the smallest slope seismic stability coefficient as the most dangerous slip surface.

[0070] Adjusting the sliding surface search parameters refers to adjusting the length of the slope crest shear point from the slope shoulder and the central angle of the logarithmic spiral.

[0071] The adjustment range of the distance between the slope crest shear point and the slope shoulder is the slope crest shear point search interval. Search range of the central angle of the logarithmic spiral And the central angle of the logarithmic spiral is less than .in, This is the starting value for the search interval at the slope crest cut-in point. This is the termination value of the search interval for the slope crest cut-in point. The starting angle for the search range of the central angle of the logarithmic spiral. The terminating angle of the search range for the central angle of the logarithmic spiral. The internal friction angle of the soil. The slope angle is given.

[0072] Specifically, It can take the value 0. The value can be 1-2 times the slope height. It can be determined by searching for the preset logarithmic spiral center angle. The system uniformly selects a preset number of discrete values ​​for the central angle of the logarithmic spiral, thereby achieving gradual adjustment of the central angle of the logarithmic spiral.

[0073] Step 106: Taking the most dangerous sliding surface under static conditions as the object, the slope seismic acceleration is calculated using multiple sets of boundary conditions set in Step 103. The dynamic response law of displacement and acceleration of the sliding body under seismic action is analyzed, and a slope seismic stability evaluation system including the slope seismic stability coefficient, the location of the most dangerous sliding surface and dynamic response characteristics is formed to realize the slope seismic stability evaluation.

[0074] The most dangerous slip surface under static conditions refers to the slip surface corresponding to the minimum slope seismic stability coefficient when the amplitude of the simple harmonic wave is zero.

[0075] When analyzing the dynamic acceleration response of a sliding body under seismic loading, the free surface amplification factor and the average amplification factor of the sliding body are used for quantification. The calculation formulas are as follows: , .in, x-axis The magnification factor of the corresponding free surface, The x-coordinate is The maximum acceleration of a free surface under the action of a simple harmonic wave. x-axis The corresponding depth of the free surface from the top of the slope. For time, The amplitude of the simple harmonic wave. The operator for extracting the real part of a complex number. For complex wave number, This represents the depth of the bedrock from the top of the slope. The imaginary unit, The ratio of complex impedances. This is the average magnification factor of the sliding body. Let be the maximum average acceleration of the sliding body under the action of a simple harmonic wave. This represents the maximum horizontal load on the sliding body under simple harmonic wave action. The weight of the sliding body.

[0076] Specifically, . .in, The actual wave number of the soil. For the imaginary wave number of the soil, The imaginary unit, Let be the real part of the soil-rock complex impedance ratio. This is the imaginary part of the soil-rock complex impedance ratio.

[0077] Figure 3 This is a schematic diagram illustrating the variation of the seismic stability coefficient of the most dangerous sliding surface of the slope over time, as provided in this embodiment of the application. In this embodiment, combined with the stability safety factor, it can be seen that the slope has strong stability under the action of a seismic wave with an amplitude of 0.2g and a characteristic period of 2.5s, and the evaluation result is stable.

[0078] Figure 4 This is a schematic diagram illustrating the variation of acceleration over time on the free surface at the top of a slope, as provided in an embodiment of this application. Figure 5 This is a schematic diagram illustrating the change of acceleration of the free surface at the bottom of the slope over time, as provided in an embodiment of this application. Figure 6 This is a schematic diagram illustrating the change of acceleration at the center point of the slope over time, as provided in an embodiment of this application. Figures 4 to 6 The variation of acceleration with time at different locations on the free surface of the slope is presented.

[0079] Figure 7 This is a schematic diagram illustrating the variation of the slope free surface magnification factor with the abscissa, as provided in the embodiments of this application. Figure 7 This indicates that the dynamic response characteristics of different parts of the slope are different and exhibit nonlinear changes, suggesting that this application can reflect the influence of slope geometry on slope seismic stability.

[0080] Figure 8 This diagram illustrates the variation of the average amplification factor of the sliding body with the frequency of a simple harmonic wave, as provided in an embodiment of this application. With increasing frequency, the average amplification factor of the sliding body first increases and then decreases, exhibiting a peak value. At this peak, the slope's dynamic response is strongest, its stability is lowest, and it is in a resonant state. Figure 8 In It is the frequency of a simple harmonic wave.

[0081] This application also provides a binary stratigraphic structure type slope seismic stability evaluation device 900, such as... Figure 9 As shown, the device includes: a model setting module 901, a determination module 902, a dynamic response characteristic acquisition module 903, a solution module 904, an iteration module 905, and an analysis module 906.

[0082] The model module 901 is used to set up a differentiated constitutive model of soil and bedrock for a soil-rock binary strata structure slope as the research object, and to simplify the seismic wave into a simple harmonic wave in the incident form to simulate the spatiotemporal effect.

[0083] The determination module 902 is used to determine the shape and location of a logarithmic spiral sliding surface adapted to the dynamic response characteristics based on the slope geometric parameters and sliding surface search parameters. The logarithmic spiral sliding surface is used to define the range of the sliding body within the slope.

[0084] The dynamic response characteristic acquisition module 903 is used to calculate the slope seismic acceleration by setting multiple sets of boundary conditions, and obtain the dynamic response characteristics of the slope displacement and acceleration.

[0085] The solver module 904 is used to vertically segment the sliding body based on the dynamic response characteristics of the slope displacement and acceleration, and the range of the sliding body defined by the logarithmic spiral sliding surface. By integrating the seismic acceleration along the height of each segment, the resultant horizontal seismic inertial force of each segment is calculated. Then, combined with the limit equilibrium method, the slope seismic stability coefficient corresponding to the logarithmic spiral sliding surface is solved.

[0086] The iteration module 905 uses the length of the slope crest shear point from the slope shoulder and the central angle of the logarithmic spiral as iteration variables to adjust the slip surface search parameters to generate a new logarithmic spiral slip surface. Based on the new logarithmic spiral slip surface, steps 103 to 104 are iteratively executed. The slope seismic stability coefficients corresponding to each set of iteration variables are compared. After completing the iterative search of all potential slip surfaces within the slope, the slip surface corresponding to the smallest slope seismic stability coefficient is selected as the most dangerous slip surface.

[0087] Analysis module 906 is used to calculate the slope seismic acceleration using the most dangerous sliding surface under static conditions and multiple sets of boundary conditions set in step 103. It analyzes the displacement and acceleration dynamic response of the sliding body under seismic action and forms a slope seismic stability evaluation system including the slope seismic stability coefficient, the location of the most dangerous sliding surface and dynamic response characteristics, so as to realize the slope seismic stability evaluation.

[0088] Some modules in the apparatus described in this application can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc., that perform a specific task or implement a specific abstract data type. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0089] The apparatus or module described in the above embodiments can be implemented by a computer chip or physical entity, or by a product with a certain function. For ease of description, the above apparatus is described by dividing it into various modules according to their functions. When implementing the embodiments of this application, the functions of each module can be implemented in one or more software and / or hardware. Of course, a module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.

[0090] The methods, apparatus, or modules described in this application can be implemented in a computer-readable program code manner. The controller can be implemented in any suitable manner, for example, as a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. A memory controller can also be implemented as part of the control logic of a memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code manner, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included within it for implementing various functions can also be considered as structures within the hardware component. Alternatively, the device used to implement various functions can be viewed as either a software module that implements the method or a structure within a hardware component.

[0091] like Figure 10 As shown in the figure, this application embodiment also provides a binary stratigraphic structure type slope seismic stability evaluation server, including a memory 1001 and a processor 1002; the memory 1001 is used to store computer-executable instructions; the processor 1002 is used to execute computer-executable instructions to implement the binary stratigraphic structure type slope seismic stability evaluation method described above in this application embodiment.

[0092] This application also provides a computer-readable storage medium storing executable instructions, which, when executed by a computer, can implement the seismic stability evaluation method for a binary stratigraphic slope described above in this application.

[0093] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary hardware. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product, or it can be embodied in the process of data migration. The computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to execute the methods described in the embodiments of this application.

[0094] The various embodiments described in this specification are presented in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. All or part of this application can be used in numerous general-purpose or special-purpose computer system environments or configurations.

[0095] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of this application.

Claims

1. A method for evaluating the seismic stability of slopes with a binary stratigraphic structure, characterized in that, include: Step 101: Taking the soil-rock binary stratigraphic structure slope as the research object, a differentiated constitutive model of soil and bedrock is set up, and the seismic wave is simplified into a simple harmonic wave in the incident form to simulate the spatiotemporal effect. Step 102: Based on the slope geometric parameters and the sliding surface search parameters, determine the shape and location of the logarithmic spiral sliding surface. The logarithmic spiral sliding surface is used to define the range of the sliding body within the slope. Step 103: Calculate the slope seismic acceleration by setting multiple sets of boundary conditions to obtain the dynamic response characteristics of the slope's displacement and acceleration; Step 104: Based on the dynamic response characteristics of the slope displacement and acceleration, and the range of the sliding body defined by the logarithmic spiral sliding surface, the sliding body is vertically segmented. By integrating the seismic acceleration along the height of each segment, the resultant horizontal seismic inertial force of each segment is calculated. Then, combined with the limit equilibrium method, the slope seismic stability coefficient corresponding to the logarithmic spiral sliding surface is solved. Step 105: Using the length of the slope crest shear point from the slope shoulder and the central angle of the logarithmic spiral as iteration variables, adjust the slip surface search parameters to generate a new logarithmic spiral slip surface. Based on the new logarithmic spiral slip surface, iteratively execute steps 103 to 104. Compare the slope seismic stability coefficients corresponding to each set of iteration variables. After completing the iterative search of all potential slip surfaces in the slope, select the slip surface corresponding to the smallest slope seismic stability coefficient as the most dangerous slip surface. Step 106: Taking the most dangerous sliding surface under static conditions as the object, the slope seismic acceleration is calculated using multiple sets of boundary conditions set in Step 103. The dynamic response law of displacement and acceleration of the sliding body under seismic action is analyzed, and a slope seismic stability evaluation system including the slope seismic stability coefficient, the location of the most dangerous sliding surface and dynamic response characteristics is formed to realize the slope seismic stability evaluation.

2. The method for evaluating the seismic stability of a binary stratigraphic slope according to claim 1, characterized in that, The dynamic constitutive relationship of soil in the differentiated constitutive model is defined by an equivalent linear viscoelastic model, while the dynamic constitutive relationship of bedrock is defined by an ideal elastic model. The seismic wave is simplified into a simple harmonic wave in the incident form, specifically a simple harmonic wave that is perpendicularly incident from the base, to replace random seismic waves in the soil.

3. The method for evaluating the seismic stability of a binary stratigraphic slope according to claim 1, characterized in that, The multiple sets of boundary conditions include the zero-stress boundary condition of the free surface at the top of the slope, the stress continuity condition of the soil-rock contact surface, the displacement continuity condition of the soil-rock contact surface, and the input simple harmonic wave amplitude condition. The zero-stress boundary condition is: ;in, For the shear stress of the soil, The depth of the free surface from the top of the slope; The stress continuity condition is: ;in, This represents the depth of the bedrock from the top of the slope. This represents the depth of the soil element from the top of the slope. For bedrock shear stress, This represents the depth of the rock mass unit from the top of the bedrock. The displacement continuity condition is: ;in, This represents the horizontal displacement of the soil. This represents the horizontal displacement of the bedrock. Input harmonic wave amplitude conditions: The upward wave incident vertically in bedrock... The displacement amplitude corresponds to the simple harmonic wave amplitude. ;in, The amplitude of the simple harmonic wave. This represents the amplitude of the horizontal displacement of the soil. It is the angular frequency.

4. The method for evaluating the seismic stability of a binary stratigraphic slope according to claim 3, characterized in that, The slope geometry parameters include slope height, slope angle, and depth of bedrock from the slope crest; The sliding surface search parameters include the slope crest shear point search range, the slope crest shear point search quantity, the logarithmic spiral central angle search range, and the logarithmic spiral central angle search quantity.

5. The method for evaluating the seismic stability of a binary stratigraphic slope according to claim 1, characterized in that, The definition of a logarithmic spiral sliding surface is: When the logarithmic spiral intersects the soil-rock interface, the slope is set to slide along the soil-rock interface. The logarithmic spiral sliding surface is the combination of the logarithmic spiral and the soil-rock interface.

6. The method for evaluating the seismic stability of a binary stratigraphic slope according to claim 5, characterized in that, The method of vertically segmenting the sliding body and calculating the resultant horizontal seismic inertial force of each segment by integrating the seismic acceleration along the height of each segment includes: The sliding body is vertically divided into a predetermined number of strips, and the depth of the bottom and top of each strip from the top of the slope is determined according to the geometric relationship between the strips and the sliding surface. Based on the depth of the bottom and top of each block from the slope crest, the resultant horizontal seismic inertial force of each block is calculated by integrating the seismic acceleration along the height of each block. The calculation formula is as follows: ;in, For strips exist The horizontal seismic force that is constantly subjected to For strips The depth from the bottom to the top of the slope. For strips The depth from the top of the slope to the top of the hill. It is the density of the soil. It is a strip width, for Time depth is The seismic acceleration experienced by the soil element. It is an integral infinitesimal element of the soil element in the depth direction from the top of the slope.

7. The method for evaluating the seismic stability of a binary stratigraphic slope according to claim 6, characterized in that, The method of combining limit equilibrium to solve for the slope seismic stability coefficient corresponding to the logarithmic spiral slip surface includes: The limit equilibrium method uses the simplified distribution method, and the slope seismic stability coefficient based on the simplified distribution method is... The calculation formula is: , ;in, This represents the total number of vertical strips in the sliding body. Number the blocks. For strips Cohesion at the bottom For strips width, It is a strip The weight, For strips The difference in lateral forces, For strips The internal friction angle at the bottom, For strips The iteration factor, For strips The angle of inclination at the bottom, For strips exist The horizontal seismic force constantly acting on it; where the sliding surface is located inside the soil mass, and These are the soil's cohesion and internal friction angle; when the bottom of the strip is located at the contact surface between the soil and rock mass... and It refers to the cohesion and internal friction angle at the soil-rock interface.

8. The method for evaluating the seismic stability of a binary stratigraphic slope according to claim 7, characterized in that, The adjustment of the sliding surface search parameters refers to adjusting the length of the slope crest shear point from the slope shoulder and the central angle of the logarithmic spiral. The adjustment range of the distance between the slope crest shear point and the slope shoulder is the slope crest shear point search interval. Search range of the central angle of the logarithmic spiral And the central angle of the logarithmic spiral is less than ;in, This is the starting value for the search interval at the slope crest cut-in point. This is the termination value of the search interval for the slope crest cut-in point. The starting angle for the search range of the central angle of the logarithmic spiral. The terminating angle of the search range for the central angle of the logarithmic spiral. The internal friction angle of the soil. The slope angle is given.

9. The method for evaluating the seismic stability of a binary stratigraphic slope according to claim 8, characterized in that, The most dangerous slip surface under static conditions refers to the slip surface corresponding to the minimum slope seismic stability coefficient when the amplitude of the simple harmonic wave is zero. When analyzing the dynamic acceleration response of a sliding body under seismic loading, the free surface amplification factor and the average amplification factor of the sliding body are used for quantification. The calculation formulas are as follows: , ;in, x-axis The magnification factor of the corresponding free surface, The x-coordinate is The maximum acceleration of a free surface under the action of a simple harmonic wave. x-axis The corresponding depth of the free surface from the top of the slope. For time, The amplitude of the simple harmonic wave. The operator for extracting the real part of a complex number. For complex wave number, This represents the depth of the bedrock from the top of the slope. The imaginary unit, The ratio of complex impedances. This is the average magnification factor of the sliding body. Let be the maximum average acceleration of the sliding body under the action of a simple harmonic wave. This represents the maximum horizontal load on the sliding body under simple harmonic wave action. The weight of the sliding body.

10. A device for evaluating the seismic stability of a slope with a binary stratigraphic structure, characterized in that, include: The model module is set up to study soil-rock binary strata slopes, and to set up differentiated constitutive models of soil and bedrock, simplifying seismic waves into incident simple harmonic waves to simulate spatiotemporal effects. The determination module is used to determine the shape and location of the logarithmic spiral sliding surface that is adapted to the dynamic response characteristics based on the slope geometric parameters and sliding surface search parameters. The logarithmic spiral sliding surface is used to define the range of the sliding body within the slope. The module for obtaining dynamic response characteristics is used to calculate the seismic acceleration of the slope by setting multiple sets of boundary conditions, and to obtain the dynamic response characteristics of the slope's displacement and acceleration. The solution module is used to vertically segment the sliding body based on the dynamic response characteristics of the slope displacement and acceleration, and the range of the sliding body defined by the logarithmic spiral sliding surface. By integrating the seismic acceleration along the height of each segment, the resultant horizontal seismic inertial force of each segment is calculated. Then, combined with the limit equilibrium method, the slope seismic stability coefficient corresponding to the logarithmic spiral sliding surface is solved. The iterative module uses the length of the slope crest shear point from the slope shoulder and the central angle of the logarithmic spiral as iterative variables to adjust the slip surface search parameters to generate a new logarithmic spiral slip surface. Based on the new logarithmic spiral slip surface, steps 103 to 104 are iteratively executed. The slope seismic stability coefficients corresponding to each set of iterative variables are compared. After completing the iterative search of all potential slip surfaces in the slope, the slip surface corresponding to the smallest slope seismic stability coefficient is selected as the most dangerous slip surface. The analysis module is used to calculate the slope seismic acceleration using the most dangerous sliding surface under static conditions and multiple sets of boundary conditions set in step 103. It analyzes the displacement and acceleration dynamic response of the sliding body under seismic action and forms a slope seismic stability evaluation system that includes the slope seismic stability coefficient, the location of the most dangerous sliding surface and the dynamic response characteristics, so as to realize the slope seismic stability evaluation.

Images