A method for analyzing characteristics of three-dimensional slope resistance under influence of seismic wave incidence direction

Abstract

The present application provides a kind of three-dimensional slope resistance characteristic analysis method under the influence of seismic wave incidence direction.The three-dimensional slope resistance characteristic analysis method under the influence of seismic wave incidence direction includes the following steps:S1, three-dimensional numerical modeling;S2, full-dimensional seismic wave incidence working condition construction;S3, closed loop iteration to solve critical seismic resistance, in step S3, iteration to solve critical peak acceleration process is set closed loop feedback logic: when monitoring plastic zone is not through, increase input seismic wave peak acceleration and continue iteration.The three-dimensional slope resistance characteristic analysis method under the influence of seismic wave incidence direction provided by the present application accurately simulates P wave, SV wave, SH wave different incidence angle-azimuth full combination oblique incidence working condition, identifies the most unfavorable seismic incidence direction of slope, reveals the internal mechanism of reflection, wave type conversion, ray convergence superposition amplification, outputs seismic correction coefficient, and improves the reliability of seismic evaluation of three-dimensional slope in mountainous area.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering, geological disaster and slope seismic numerical simulation technology, and in particular relates to a method for analyzing the three-dimensional slope resistance characteristics under the influence of the incident direction of seismic waves. Background Technology

[0002] Loess slopes are widely distributed in mountainous areas, and earthquakes can easily trigger landslides. Most existing numerical simulation analyses of slope seismic stability simplify the earthquake input conditions, assuming that the seismic wave is perpendicularly incident on the bottom of the slope, and neglecting the differences in dynamic disturbances caused by variations in the incident angle and spatial azimuth of the seismic wave.

[0003] The existing technology has the following drawbacks: The simulation of the full combination of incident angle and azimuth angle was not carried out, making it impossible to locate the most unfavorable earthquake incident direction in the three-dimensional slope space; the lack of a precise loading method for oblique incident earthquakes supported by the Huygens wavefront propagation principle resulted in poor loading accuracy of oblique incident earthquake waves at the boundary of the three-dimensional slope model.

[0004] Therefore, it is necessary to provide a new method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction to solve the above-mentioned technical problems. Summary of the Invention

[0005] The technical problem solved by this invention is to provide a method for analyzing the resistance characteristics of three-dimensional slopes under the influence of seismic wave incident direction, which accurately simulates the full combination of oblique incidence conditions of P-waves, SV-waves, and SH-waves with different incident angles and azimuths, identifies the most unfavorable seismic incident direction of the slope, reveals the intrinsic mechanism of reflection, wave type conversion, and ray convergence superposition and amplification, outputs seismic correction coefficients, and improves the reliability of three-dimensional slope seismic assessment in mountainous areas.

[0006] To address the aforementioned technical problems, the present invention provides a method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction, comprising the following steps: S1, three-dimensional numerical modeling; S2, construction of full-dimensional seismic wave incident conditions; S3, closed-loop iterative solution of critical seismic resistance; S4, quantitative analysis of resistance regulation mechanism; S5, engineering correction and seismic assessment output; S6, database archiving and engineering reuse iteration.

[0007] In step S1, by collecting on-site geological survey data of the target three-dimensional slope, the slope geometry, soil physical and mechanical parameters, and soil layer information are obtained; based on the Huygens wavefront propagation principle, a three-dimensional slope numerical model matching the real terrain and geology is constructed using the FLAC3D finite difference platform, and the static boundary, soil constitutive model, and damping parameters of the model are set to complete the initialization of ground stress equilibrium. In step S2, a set of coupling parameters for the incident direction of seismic waves is constructed, which includes the seismic wave type and incident angle. Azimuth The seismic wave types include P-waves, SV-waves, and SH-waves; incident angle The value range is 0°-75°, azimuth angle The value range is 0°-315°, and a full combination of working conditions is traversed for the incident angle and azimuth angle. In step S3, the complete penetration of the plastic zone is used as the threshold for judging the instability of the three-dimensional slope. For each set of incident combination conditions, the seismic waves are iteratively input using an incremental loading method. The distribution of the plastic zone and the acceleration response within the slope model are collected in real time, and the program sequence is used. The critical peak acceleration corresponding to the slope under each condition is solved using a bisection iterative algorithm. ; In step S4, by establishing a mapping model between the incident direction and the critical peak acceleration, the variation function of the critical peak acceleration with the incident angle and azimuth angle under different seismic wave types is calculated:

[0008] In the formula: Critical peak acceleration, in g; The angle of incidence of the seismic wave is expressed in degrees (°). The azimuth angle of the seismic wave is expressed in degrees (°). These are seismic wave mode types, including P-wave, SV-wave, and SH-wave. In step S5, the slope surface reflection coefficient is calculated by extracting the most unfavorable incident direction and combining it with elastic wave theory. Waveform conversion coefficient Quantify the convergence effect of incident waves behind the slope and analyze the regulation mechanism of seismic wave incident direction on slope resistance through reflection intensity, wave type conversion and reflection wave superposition amplification effect; In step S6, by outputting the slope seismic resistance assessment results, comparing the difference in critical peak acceleration between the vertical incident seismic wave condition and the full-angle incident seismic wave condition, the slope seismic capacity correction coefficient is output for use in the seismic design and stability assessment of mountain slopes. In the S3 step iterative solution of the critical peak acceleration, a closed-loop feedback logic is set up: when the plastic zone is not detected to be fully connected, the input seismic wave peak acceleration is increased and the iteration continues; when the plastic zone is determined to be fully connected, the acceleration amplitude of the previous step is used as the critical peak acceleration for this condition; when the iteration step size is less than the preset accuracy threshold, the logic is applied. The calculation for this condition is terminated, and the simulation proceeds to the next incident combination condition.

[0009] As a further aspect of the present invention, the construction of a three-dimensional slope numerical model based on the Huygens wavefront propagation principle in step S1 specifically includes: treating each discrete grid node on the seismic wavefront as an equivalent wavelet vibration source, with the wavelet propagation radius as follows: ; Shear wave velocity in soil and rock media The numerical calculation time step is updated by the entire wavelet envelope surface to update the wavefront position of the seismic wave inside the slope medium at each calculation time, so as to achieve accurate loading of obliquely incident seismic waves at the boundary of the three-dimensional slope model.

[0010] As a further aspect of the present invention, in step S1, the Mohr-Coulomb constitutive model is selected as the soil and rock constitutive model, and a static free-field viscous boundary is set in the model to eliminate seismic wave reflection artifacts at the boundary of the numerical model; the criterion for achieving geostress equilibrium is: the ratio of the maximum unbalanced force of the model to the total external force is less than 1. .

[0011] As a further aspect of the present invention, in step S2, the incident angle... Sampling interval set to 5°-15°, azimuth angle The sampling interval is set to 22.5°-45° to form a discrete full-combination simulation working condition matrix; the seismic wave uses Ricker wavelet as the input source waveform, and the center frequency of the wavelet matches the dominant frequency of the slope soil and rock medium.

[0012] As a further aspect of the present invention, in step S3, the method for determining the complete connection of the plastic zone is as follows: statistically analyze the plastic state of all units along the connection path from the slope to the slope top in the slope model. When the proportion of plastic units along the connection path is greater than or equal to 95%, it is determined that the plastic zone is connected and the slope has reached the critical state of instability.

[0013] As a further aspect of the present invention, the binary iterative algorithm in step S3 includes: setting an acceleration search interval. Iteration precision threshold Take 0.005g; take the midpoint of the interval in each round. Input the model, and update the upper and lower limits of the search based on the feedback results of the plastic zone connection, until... The median value of the interval is taken as the critical peak acceleration for this working condition. .

[0014] As a further aspect of the present invention, the formula for calculating the slope reflection coefficient in step S5 is as follows:

[0015] In the formula: The incident rock and soil medium wave impedance is expressed in kg / (m2⋅s). The impedance of the transmitted rock and soil medium is expressed in kg / (m2⋅s). The angle of incidence of the seismic wave is expressed in degrees (°). The angle of reflection of the seismic wave is expressed in degrees (°). By reflectance coefficient The wave type conversion coefficient represents the degree of amplification of seismic waves reflected from the slope surface; it also represents the proportion of energy of P, SV, and SH waves that undergo wave type conversion at the rock-soil interface of the slope.

[0016] As a further aspect of the present invention, in step S5, the convergence effect of incident wave rays behind the slope is identified by statistically analyzing the superimposed amplitude of ground motion in the grid cells inside the slope under the incident conditions. When the vibration amplitude of a local cell is amplified by a factor greater than 1.3 compared to the original incident amplitude, the area is determined to be a wave ray convergence amplification zone and is taken as the priority failure site of the slope.

[0017] As a further aspect of the present invention, the formula for calculating the slope seismic resistance correction coefficient Kcorr in step S6 is as follows: , In the formula: The critical peak acceleration of the slope when seismic waves are incident perpendicularly, in g; The critical peak acceleration of the slope corresponding to the most unfavorable incident direction, in g; Correction coefficient The calculation of the seismic safety factor of the slope is introduced to correct the evaluation bias caused by using only vertical seismic wave input.

[0018] As a further aspect of the present invention, the most unfavorable seismic wave incident combination, critical peak acceleration, and seismic capacity correction coefficient are output to the slope seismic design module for the selection of slope support structure parameters, thereby realizing a three-dimensional quantitative seismic assessment of slope considering the azimuth effect of oblique seismic wave incidence.

[0019] Compared with related technologies, the three-dimensional slope resistance characteristic analysis method provided by this invention under the influence of seismic wave incident direction has the following beneficial effects: This invention introduces the Huygens wavefront propagation principle, updates the wavefront of seismic waves inside the slope at each moment by using the equivalent wavelet source of the wavefront grid nodes, and achieves accurate three-dimensional oblique incidence loading of P-waves, SV-waves, and SH-waves at arbitrary incident angles and azimuth angles. It suppresses false reflections at the model boundary, overcomes the distortion defects of traditional simplified oblique incidence loading, and the simulation results closely match the physical process of real seismic wave propagation.

[0020] This invention uses the plastic zone continuity as the criterion for slope instability, embeds a binary iterative closed-loop feedback process, automatically increases or decreases the seismic acceleration input, and has controllable iteration accuracy; it eliminates the need for repeated manual calculations, solves the critical peak acceleration for all working conditions in batches, significantly reduces the manpower cost of simulation, and ensures that the results of different incident conditions are comparable horizontally.

[0021] This invention introduces slope reflection coefficient and wave type conversion coefficient to quantify the convergence effect of incident wave rays behind the slope; it clarifies how the incident angle and azimuth angle change the slope resistance through reflection intensity, wave type conversion, and superposition and amplification of reflected waves, and locates the most unfavorable earthquake incident direction of the slope, thus solving the pain point of existing technologies that can only provide qualitative descriptions and lack quantitative indicators. Attached Figure Description

[0022] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings.

[0023] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a schematic diagram illustrating the Huygens wavelet propagation loading principle of seismic waves in this invention; Figure 3 This is a block diagram of the binary iterative closed-loop feedback logic in this invention; Figure 4 This is a schematic diagram of the wave convergence and reflected wave superposition amplification effect under the back-slope incident condition in this invention. Detailed Implementation

[0024] Please refer to the following: Figure 1 and Figure 4 ,in, Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a schematic diagram illustrating the Huygens wavelet propagation loading principle of seismic waves in this invention; Figure 3 This is a block diagram of the binary iterative closed-loop feedback logic in this invention; Figure 4 This is a schematic diagram illustrating the wave convergence and reflected wave superposition amplification effects under the back-slope incident condition in this invention. The method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction includes the following steps: S1, three-dimensional numerical modeling; S2, construction of full-dimensional seismic wave incident conditions. S3. Closed-loop iterative solution of critical seismic resistance. During the iterative solution of critical peak acceleration, a closed-loop feedback logic is set: when the plastic zone is not detected to be connected, the input peak acceleration of the seismic wave is increased and the iteration continues. When the plastic zone is determined to be fully penetrated, the acceleration amplitude of the previous level is taken as the critical peak acceleration for this working condition. When the iteration step size is less than the preset precision threshold The calculation for this condition is terminated, and the simulation for the next incident combination condition begins. S4. Quantitative analysis of the resistance regulation mechanism: By establishing a mapping model between the incident direction and the critical peak acceleration, the variation function of the critical peak acceleration with the incident angle and azimuth angle under different seismic wave types is calculated.

[0025] In the formula: Critical peak acceleration, in g; The angle of incidence of the seismic wave is expressed in degrees (°). The azimuth angle of the seismic wave is expressed in degrees (°). These are seismic wave mode types, including P-wave, SV-wave, and SH-wave. S5, Engineering correction and seismic assessment output; S6, Database archiving and engineering reuse iteration.

[0026] In step S1, by collecting on-site geological survey data of the target 3D slope, the slope geometry, soil and rock physical and mechanical parameters, and soil layer information are obtained. Based on the Huygens wavefront propagation principle, a 3D slope numerical model matching the real terrain and geology is constructed using the FLAC3D finite difference platform. The static boundary of the model, the soil and rock constitutive model, and the damping parameters are set, and the stress equilibrium initialization is completed. The construction of the 3D slope numerical model based on the Huygens wavefront propagation principle specifically includes: treating each grid node discrete on the seismic wavefront as an equivalent wavelet vibration source, with the wavelet propagation radius as follows: ; Shear wave velocity in soil and rock media The numerical calculation time step is updated by the entire wavelet envelope surface to update the wavefront position of the seismic wave inside the slope medium at each calculation time, so as to achieve accurate loading of obliquely incident seismic waves at the boundary of the three-dimensional slope model.

[0027] In step S2, a set of coupling parameters for the incident direction of seismic waves is constructed, which includes the seismic wave type and incident angle. Azimuth The seismic wave types include P-waves, SV-waves, and SH-waves; incident angle The value range is 0°-75°, azimuth angle The range of values ​​is 0°-315°. A full combination of working conditions is performed for the incident angle and azimuth angle. The Mohr-Coulomb constitutive model is used for the soil and rock. Static free-field viscous boundaries are set in the model to eliminate seismic wave reflection artifacts at the numerical model boundaries. The criterion for achieving geostress equilibrium is: the ratio of the maximum unbalanced force to the total external force is less than... .

[0028] In step S2, the angle of incidence Sampling interval set to 5°-15°, azimuth angle The sampling interval is set to 22.5°-45° to form a discrete full-combination simulation working condition matrix; the seismic wave uses Ricker wavelet as the input source waveform, and the center frequency of the wavelet matches the dominant frequency of the slope soil and rock medium.

[0029] In step S3, the complete penetration of the plastic zone is used as the threshold for judging the instability of the three-dimensional slope. For each set of incident combination conditions, the seismic waves are iteratively input using an incremental loading method. The distribution of the plastic zone and the acceleration response within the slope model are collected in real time, and the program sequence is used. The critical peak acceleration corresponding to the slope under each condition is solved using a bisection iterative algorithm. The method for determining the complete connection of the plastic zone is as follows: statistically analyze the plastic state of all units along the connection path from the slope to the slope top in the slope model. When the proportion of plastic units along the connection path is greater than or equal to 95%, the plastic zone is determined to be connected and the slope reaches the critical state of instability.

[0030] The binary iterative algorithm described in step S3: setting the acceleration search interval. Iteration precision threshold Take 0.005g; take the midpoint of the interval in each round. Input the model, and update the upper and lower limits of the search based on the feedback results of the plastic zone connection, until... The median value of the interval is taken as the critical peak acceleration for this working condition. .

[0031] In step S5, the slope surface reflection coefficient is calculated by extracting the most unfavorable incident direction and combining it with elastic wave theory. Waveform conversion coefficient This study quantifies the convergence effect of incident waves behind the slope and analyzes the mechanism by which the incident direction of seismic waves regulates slope resistance through reflection intensity, wave mode conversion, and the amplification effect of reflected wave superposition. The formula for calculating the slope reflection coefficient in step S5 is as follows:

[0032] In the formula: The incident rock and soil medium wave impedance is expressed in kg / (m2⋅s). The impedance of the transmitted rock and soil medium is expressed in kg / (m2⋅s). The angle of incidence of the seismic wave is expressed in degrees (°). The angle of reflection of the seismic wave is expressed in degrees (°). By reflectance coefficient The wave type conversion coefficient represents the degree of amplification of seismic waves reflected from the slope surface; it also represents the proportion of energy of P, SV, and SH waves that undergo wave type conversion at the rock-soil interface of the slope.

[0033] In step S5, the convergence effect of incident wave rays behind the slope is identified by statistically analyzing the superimposed amplitude of ground motion in the grid cells inside the slope under the incident conditions. When the vibration amplitude of a local cell is amplified by a factor greater than 1.3 compared to the original incident amplitude, the area is determined to be a wave ray convergence amplification zone and is taken as the priority failure site of the slope.

[0034] In step S6, by outputting the slope seismic resistance assessment results, comparing the difference in critical peak acceleration between the vertical incident seismic wave condition and the full-angle incident seismic wave condition, a slope seismic capacity correction coefficient is output for use in the seismic design and stability assessment of mountain slopes. The formula for calculating the slope seismic resistance correction factor Kcorr in step S6 is as follows: , In the formula: The critical peak acceleration of the slope when seismic waves are incident perpendicularly, in g; The critical peak acceleration of the slope corresponding to the most unfavorable incident direction, in g; Correction coefficient The calculation of the seismic safety factor of the slope is introduced to correct the evaluation bias caused by using only vertical seismic wave input.

[0035] The obtained most unfavorable seismic wave incident combination, critical peak ground acceleration, and seismic capacity correction coefficient are output to the slope seismic design module for the selection of slope support structure parameters, realizing a three-dimensional quantitative seismic assessment of slopes that considers the azimuth effect of oblique seismic wave incidence. Example 1: Seismic Resistance Characteristics Analysis of Loess Slope in Changshougou, a Certain Province S1. Collect field survey data of the loess slope in Changshougou: slope height 42m, slope angle 38°; loess layer thickness 34m, underlying paleosol layer; obtain soil unit weight, cohesion, internal friction angle, shear wave velocity, and compression wave velocity geotechnical parameters; construct a three-dimensional slope numerical model in FLAC3D based on Huygens wavefront principle; adopt the Mohr-Coulomb constitutive model and set free field viscous boundaries; perform geostress equilibrium until the ratio of the maximum unbalanced force to the total external force is less than 10⁻⁵, and complete the model initialization.

[0036] S2. Construct a set of incident coupling parameters for seismic waves: Select P-wave, SV-wave, and SH-wave for seismic waves; Angle of incidence : 0°, 15°, 30°, 45°, 60°, 75°; Azimuth : 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°; Complete the full combination of incident angle and azimuth angle working condition matrix; input Ricker wavelet with a center frequency of 2.2Hz to match the dominant frequency of the loess slope rock and soil.

[0037] S3. Set the criteria for determining plastic zone continuity: if the proportion of plastic units in the continuity path is ≥95%, the slope is considered unstable; set the binary iteration search interval to 0.05g-0.50g, and the iteration accuracy threshold. =0.005g; Closed-loop feedback logic: Input simulation; If the plastic region is not fully connected, update the lower limit of the acceleration search upwards; if the plastic region is fully connected, update the upper limit of the acceleration search downwards; until the interval difference is less than the accuracy threshold, output the critical peak acceleration for this working condition. ; Traverse all combinations of working conditions.

[0038] Simulation results show that SV waves have the strongest disturbance on the loess slope of Changshougou, and the critical peak acceleration of SV waves is the lowest under the same incident angle and azimuth conditions. The critical peak acceleration first decreases and then increases with the increase of the incident angle, with 15° being the key critical angle. The most unfavorable incident combination for this slope is obtained: incident angle 15°, azimuth 0°.

[0039] S4. Establish a mapping model Substituting the reflection coefficient into the formula, the slope surface reflection coefficient under different incident angles was calculated, and the wave convergence zone inside the slope under the back-incident condition was identified. The vibration amplification coefficient in the convergence zone can reach 1.42. It was confirmed that the superposition and amplification of reflected waves generated by back-incident is the core cause that makes the slope more prone to instability and failure.

[0040] S5, Comparison with perpendicular incidence condition =0.312g; Most unfavorable incident direction =0.174g; Calculate the seismic resistance correction factor:

[0041] Will =1.79 was used for seismic design correction of the loess slope in Changshougou; it was shown that simulation based solely on vertical incidence would overestimate the seismic capacity of the slope, and a correction factor needs to be applied to reduce it.

[0042] S6 outputs the most unfavorable incident combination, critical peak acceleration of each vibration mode, and seismic correction coefficient for the Changshougou slope, and submits them to the engineering design to guide the selection of slope support and reinforcement parameters.

[0043] Example 2: Comparative Analysis of Seismic Resistance Characteristics of Loess Slopes with Different Slope Gradients This embodiment selects a typical gentle loess slope in northern Shaanxi Province as the research object. The slope height is 40m, the slope angle is 28°, the soil layer is a homogeneous loess layer without underlying paleosol interlayers, and the geophysical parameters, shear wave velocity, and compression wave velocity are the same as those of the Changshougou loess slope in Example 1, ensuring the uniqueness of the variables. Only the slope angle parameter is changed to verify the influence of slope morphology on the seismic wave incident direction effect.

[0044] S1. Collect the geological and geometric parameters of the target slope. Based on the Huygens wavefront propagation principle, build a three-dimensional numerical model matching the characteristics of a 28° gentle slope on the FLAC3D platform. Use the Mohr-Coulomb constitutive model and free-field viscous boundary conditions to perform geostress equilibrium calculations until the ratio of the maximum unbalanced force to the total external force is less than [value missing]. This completes model initialization and eliminates the interference of modeling errors on simulation results.

[0045] S2. The seismic wave incident system is completely consistent with that in Example 1. The seismic waves include P waves, SV waves, and SH waves. Angle of incidence Values: 0°, 15°, 30°, 45°, 60°, 75°; Azimuth Values: 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°, constructing a full combination simulation working condition matrix; The Ricker wavelet with a main input frequency of 2.2Hz is matched to the optimal frequency of the loess medium to ensure uniform seismic input conditions.

[0046] S3. Using the same slope instability criterion and bisection iterative algorithm, the critical condition for instability is set as the proportion of plastic elements in the plastic through-path being ≥95%. The acceleration iteration search range is 0.05g~0.50g, and the iteration accuracy threshold is... =0.005g.

[0047] The critical peak acceleration is calculated iteratively for each working condition using closed-loop feedback logic: if the plastic zone is not fully penetrated, the lower limit of acceleration is adjusted upwards; if the plastic zone is fully penetrated, the upper limit of acceleration is adjusted downwards. After iterating until the accuracy meets the standard, the values ​​for each working condition are output. Iterate through all incident combination conditions.

[0048] S4. Construct the incident direction-critical peak acceleration mapping model: By combining the theory of elastic wave, the slope reflection coefficient and wave type conversion coefficient are calculated to identify the wave convergence zone inside the slope under the incident condition behind the slope.

[0049] Simulation results show that the 28° gentle loess slope still exhibits the strongest SV wave disturbance effect, and the critical peak acceleration is generally higher than that of the steep slope in Example 1. The critical peak acceleration of the slope still shows a variation law of first decreasing and then increasing with the increase of the incident angle, and 15° is still the key critical angle, which verifies the universality of this variation law in loess slopes.

[0050] S5. The most unfavorable incident combination for this slope is an incident angle of 15° and an azimuth angle of 0°, which is consistent with the steep slope. The critical peak acceleration under vertical incidence was measured. =0.356g; Critical peak acceleration under most unfavorable incident conditions =0.213g; Calculate the seismic correction factor: .

[0051] S6. Comparative analysis of the data from the two sets of examples shows that the smaller the slope, the weaker the intensity of seismic wave reflection on the slope surface, the weaker the wave convergence and superposition effect, the overall seismic resistance of the slope is improved, and the seismic correction coefficient is slightly reduced, but still significantly greater than 1.0. This proves that regardless of whether it is a steep or gentle loess slope, using only vertical incidence seismic wave simulation will overestimate the seismic resistance of the slope, and oblique incidence effect correction must be performed.

[0052] Example 3: Analysis of the Incident Seismic Resistance Characteristics of Layered Soil and Rock Slopes with Multiple Vibration Modes. This example selects a layered soil and rock mixed slope in the mountainous area of ​​southern Shaanxi as the research object. It is different from pure loess slopes. The slope height is 45m and the slope is 35°. The upper part is a silty clay layer and the lower part is a weathered rock layer. It belongs to a typical binary layered slope and is widely distributed in engineering sites in the mountainous area of ​​southern Shaanxi. This example verifies the applicability of the method of the present invention in heterogeneous layered slopes.

[0053] S1. Collect geological parameters of the layered slope, and assign mechanical parameters such as unit weight, cohesion, internal friction angle, and wave velocity to silty clay and weathered rock respectively; construct a three-dimensional layered numerical model based on the Huygens wavefront propagation principle, adopt the Mohr-Coulomb constitutive model, set free-field viscous boundaries, and carry out refined geostress equilibrium calculations until the ratio of unbalanced forces in the model is less than Afterwards, the model initialization was completed, accurately restoring the layered medium characteristics of seismic wave propagation on the layered slope.

[0054] S2. A unified full-dimensional incident condition system is adopted, covering three vibration modes: P-wave, SV-wave, and SH-wave, with a full combination of incident angles from 0° to 75° and azimuth angles from 0° to 315°. The Ricker wavelet with a main frequency of 2.2Hz is input to ensure the standardization of the simulation condition system and facilitate horizontal comparison with loess slope results.

[0055] S3. Using a standardized instability criterion and a binary iterative closed-loop algorithm, with the proportion of plastic units from the slope toe to the slope crest ≥95% as the instability threshold and an iteration accuracy of 0.005g, the critical peak acceleration of the layered slope is solved iteratively for each working condition.

[0056] Simulation results show that the seismic response of layered soil and rock slopes differs significantly from that of pure loess slopes. SV waves remain the dominant failure mode, but the layered interface exacerbates the mode conversion effect, generating more secondary vibration energy and increasing the risk of slope instability.

[0057] S4. Quantitative calculations using reflection coefficient and wave type conversion coefficient revealed that the wave impedance difference at the soil-rock interface of layered slopes is greater, and the slope reflection coefficient is significantly higher than that of homogeneous loess slopes. Under the conditions of a 15° incident angle and a 0° azimuth angle behind the slope, the double reflection from the layered interface and the slope surface results in a vibration amplification coefficient of up to 1.51 in the wave convergence zone, which is higher than the 1.42 of pure loess slopes. This is the core reason why layered slopes are more prone to instability.

[0058] S5. Extract key parameters of the layered slope: Critical peak acceleration for vertical incidence =0.298g; Critical peak acceleration for the most unfavorable incident combination (15°, 0°) =0.158g; Calculate the seismic correction factor: .

[0059] S6. Engineering Application Verification: The seismic correction coefficient for the layered slope is greater than that for a pure loess slope, indicating that the negative impact of oblique seismic wave incidence is more significant on layered soil and rock slopes, and the evaluation deviation of traditional vertical incidence simulation is greater. The method of this invention can accurately locate the most unfavorable incidence conditions for layered slopes, quantify the amplification effects of interlayer wave mode transformation and wave convergence, provide a precise correction basis for the seismic design of slopes in complex strata, and further expand the engineering applicability of this invention.

[0060] The working principle of the three-dimensional slope resistance characteristic analysis method under the influence of seismic wave incident direction provided by this invention is as follows: Based on Huygens' principle, each grid node on the wavefront of a seismic wave at a given moment is considered as a wavelet vibration source; each wavelet... Propagation outward; the entire wavelet wavefront envelope is the new wavefront of the seismic wave in the next calculation time step; arbitrarily incident and azimuth angles of P, SV, and SH waves are obliquely incident at the boundary of the three-dimensional model; the free-field viscous boundary absorbs the seismic waves escaping from the model boundary, eliminating false reflection interference from the boundary and ensuring that the propagation of seismic waves inside the three-dimensional slope conforms to the real physical process.

[0061] The seismic loading process continuously tracks the plastic state of all elements along the path from the toe to the crest; the proportion of Mohr-Coulomb plastic elements within the path is statistically analyzed; when the proportion of plastic elements is ≥95%, the plastic zone is considered to be fully connected, and the slope enters a critical state of instability, which serves as the criterion for determining the critical peak acceleration.

[0062] ① Initialize acceleration search upper and lower limits Set precision threshold ; ② Take the midpoint =( + ) / 2 input seismic waves into the three-dimensional slope model; ③ Read the plastic region results after the simulation is completed and execute the feedback branch: Branch A: The plastic zone is not fully connected, and the slope has not yet become unstable → This indicates that the critical acceleration is greater than [a certain value]. ;renew = Then proceed to the next iteration; Branch B: The plastic zone has been completed, and the slope is becoming unstable → the critical acceleration is less than amid; Update = Then proceed to the next iteration; ④ Iterative judgment The current working condition is terminated when the condition is met. (Take (…)) + ) / 2 is the critical peak acceleration under this operating condition. If the condition is not met, return to step ②. ⑤ After completing the calculation for this working condition, switch to the next set of incident angle-azimuth angle combinations and cycle through all simulation working conditions.

[0063] When seismic waves obliquely strike the soil-rock interface of a slope, they undergo reflection, transmission, and wave mode conversion. The reflection coefficient R represents the strength of the reflected energy, while the wave mode conversion coefficient represents the energy conversion ratio between different vibration modes. When the incident direction is behind the slope, multiple seismic wave rays converge towards the shallow area of ​​the slope, forming a wave ray convergence amplification zone. The incident wave and the slope reflected wave superimpose, amplifying the local vibration amplitude, reducing the critical peak acceleration of the slope, and exacerbating the risk of slope instability. This invention analyzes the complete physical chain of "incident direction → reflection - wave mode conversion - ray convergence superposition → change of critical peak acceleration of the slope → change of slope resistance" by quantitatively calculating the reflection coefficient and identifying the convergence amplification zone.

[0064] Traditional methods only use perpendicular incidence to obtain This method obtains the true most unfavorable working condition. ; Calculate the correction factor In the calculation of the seismic safety factor of the project, the slope seismic resistance is reduced by dividing by the correction factor, eliminating the overestimation bias caused by only vertical incident simulation, and outputting evaluation results that can be directly applied to engineering.

[0065] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions, and variations can be made to these embodiments, or they can be used directly or indirectly, without departing from the principles and spirit of the invention. In other related technical fields, the scope of the invention is defined by the appended claims and their equivalents, and they are similarly included within the scope of patent protection of the invention.

Claims

1. A method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction, characterized in that, Includes the following steps: S1, 3D numerical modeling; S2, construction of seismic wave incidence conditions in all dimensions; S3. Closed-loop iterative solution of critical seismic resistance. During the iterative solution of critical peak acceleration, a closed-loop feedback logic is set: when the plastic zone is not detected to be connected, the input peak acceleration of the seismic wave is increased and the iteration continues. When the plastic zone is determined to be fully penetrated, the acceleration amplitude of the previous level is taken as the critical peak acceleration for this working condition. When the iteration step size is less than the preset precision threshold The calculation for this condition is terminated, and the simulation for the next incident combination condition begins. S4. Quantitative analysis of the resistance regulation mechanism: By establishing a mapping model between the incident direction and the critical peak acceleration, the variation function of the critical peak acceleration with the incident angle and azimuth angle under different seismic wave types is calculated. In the formula: Critical peak acceleration, in g; The angle of incidence of the seismic wave is expressed in degrees (°). The azimuth angle of the seismic wave is expressed in degrees (°). These are seismic wave mode types, including P-wave, SV-wave, and SH-wave. S5, Engineering correction and seismic assessment output; S6, Database archiving and engineering reuse iteration.

2. The method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction according to claim 1, characterized in that: In step S1, by collecting on-site geological survey data of the target 3D slope, the slope geometry, soil and rock physical and mechanical parameters, and soil layer information are obtained. Based on the Huygens wavefront propagation principle, a 3D slope numerical model matching the real terrain and geology is constructed using the FLAC3D finite difference platform. The static boundary of the model, the soil and rock constitutive model, and the damping parameters are set, and the stress equilibrium initialization is completed. The construction of the 3D slope numerical model based on the Huygens wavefront propagation principle specifically includes: treating each grid node discrete on the seismic wavefront as an equivalent wavelet vibration source, with the wavelet propagation radius as follows: ; Shear wave velocity in soil and rock media The numerical calculation time step is updated by the entire wavelet envelope surface to update the wavefront position of the seismic wave inside the slope medium at each calculation time, so as to achieve accurate loading of obliquely incident seismic waves at the boundary of the three-dimensional slope model.

3. The method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction according to claim 1, characterized in that: In step S2, a set of coupling parameters for the incident direction of seismic waves is constructed, which includes the seismic wave type and incident angle. Azimuth The seismic wave types include P-waves, SV-waves, and SH-waves; incident angle The value range is 0°-75°, azimuth angle The range of values ​​is 0°-315°. A full combination of working conditions is performed for the incident angle and azimuth angle. The Mohr-Coulomb constitutive model is used for the soil and rock. Static free-field viscous boundaries are set in the model to eliminate seismic wave reflection artifacts at the numerical model boundaries. The criterion for achieving geostress equilibrium is: the ratio of the maximum unbalanced force to the total external force is less than... .

4. The method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction according to claim 3, characterized in that: In step S2, the angle of incidence Sampling interval set to 5°-15°, azimuth angle The sampling interval is set to 22.5°-45° to form a discrete full-combination simulation working condition matrix; the seismic wave uses Ricker wavelet as the input source waveform, and the center frequency of the wavelet matches the dominant frequency of the slope soil and rock medium.

5. The method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction according to claim 1, characterized in that: In step S3, the complete penetration of the plastic zone is used as the threshold for judging the instability of the three-dimensional slope. For each set of incident combination conditions, the seismic waves are iteratively input using an incremental loading method. The distribution of the plastic zone and the acceleration response within the slope model are collected in real time, and the program sequence is used. The critical peak acceleration corresponding to the slope under each condition is solved using a bisection iterative algorithm. The method for determining the complete connection of the plastic zone is as follows: statistically analyze the plastic state of all units along the connection path from the slope to the slope top in the slope model. When the proportion of plastic units along the connection path is greater than or equal to 95%, the plastic zone is determined to be connected and the slope reaches the critical state of instability.

6. The method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction according to claim 1, characterized in that: The binary iterative algorithm described in step S3: setting the acceleration search interval. Iteration precision threshold Take 0.005g; take the midpoint of the interval in each round. Input the model, and update the upper and lower limits of the search based on the feedback results of the plastic zone connection, until... The median value of the interval is taken as the critical peak acceleration for this working condition. .

7. The method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction according to claim 1, characterized in that: In step S5, the slope surface reflection coefficient is calculated by extracting the most unfavorable incident direction and combining it with elastic wave theory. Waveform conversion coefficient This study quantifies the convergence effect of incident waves behind the slope and analyzes the mechanism by which the incident direction of seismic waves regulates slope resistance through reflection intensity, wave mode conversion, and the amplification effect of reflected wave superposition. The formula for calculating the slope reflection coefficient in step S5 is as follows: In the formula: The incident rock and soil medium wave impedance is expressed in kg / (m2⋅s). The impedance of the transmitted rock and soil medium is expressed in kg / (m2⋅s). The angle of incidence of the seismic wave is expressed in degrees (°). The angle of reflection of the seismic wave is expressed in degrees (°). By reflectance coefficient The wave type conversion coefficient represents the degree of amplification of seismic waves reflected from the slope surface; it also represents the proportion of energy of P, SV, and SH waves that undergo wave type conversion at the rock-soil interface of the slope.

8. The method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction according to claim 7, characterized in that: In step S5, the convergence effect of incident wave rays behind the slope is identified by statistically analyzing the superimposed amplitude of ground motion in the grid cells inside the slope under the incident conditions. When the vibration amplitude of a local cell is amplified by a factor greater than 1.3 compared to the original incident amplitude, the area is determined to be a wave ray convergence amplification zone and is taken as the priority failure site of the slope.

9. The method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction according to claim 1, characterized in that: In step S6, by outputting the slope seismic resistance assessment results, comparing the difference in critical peak acceleration between the vertical incident seismic wave condition and the full-angle incident seismic wave condition, a slope seismic capacity correction coefficient is output for use in the seismic design and stability assessment of mountain slopes. The formula for calculating the slope seismic resistance correction factor Kcorr in step S6 is as follows: , In the formula: The critical peak acceleration of the slope when seismic waves are incident perpendicularly, in g; The critical peak acceleration of the slope corresponding to the most unfavorable incident direction, in g; Correction coefficient The calculation of the seismic safety factor of the slope is introduced to correct the evaluation bias caused by using only vertical seismic wave input.

10. The method for analyzing the three-dimensional slope resistance characteristics under the influence of seismic wave incident direction according to any one of claims 1-9, characterized in that, The obtained most unfavorable seismic wave incident combination, critical peak ground acceleration, and seismic capacity correction coefficient are output to the slope seismic design module for the selection of slope support structure parameters, realizing a three-dimensional quantitative seismic assessment of slope considering the azimuth effect of oblique seismic wave incidence.

Images