Slope vulnerability analysis method and system based on main aftershock sequence double-response index

Abstract

The application provides a main aftershock sequence slope vulnerability analysis method and system based on double response indexes, relates to the technical field of earthquake slope vulnerability analysis, and comprises the following steps: constructing a GeoStudio slope model according to physical parameters of slope soil, obtaining an initial static safety factor and a critical acceleration of the slope; performing incremental dynamic time-history analysis according to main shock ground motion data, the slope model and the initial static safety factor of the slope, and obtaining shear strength parameter values of the soil after the main shock; updating the initial critical acceleration of the slope to obtain a critical acceleration of the slope after the main shock; performing aftershock incremental dynamic time-history analysis according to aftershock ground motion data and the critical acceleration of the slope after the main shock, and obtaining safety factor values and cumulative displacement results of the soil after the aftershock; and defining a vulnerability function based on a lognormal cumulative distribution function to obtain a multilevel slope vulnerability curve. The application improves slope risk assessment precision and visual decision-making capability.

Description

Technical Field

[0001] This invention relates to the field of earthquake slope vulnerability analysis technology, and more specifically, to a method and system for analyzing the vulnerability of mainshock and aftershock sequences based on dual-response indices. Background Technology

[0002] Current methods for assessing slope seismic vulnerability primarily focus on the impact of the mainshock or a single ground motion, often neglecting the cumulative disturbance effects of aftershocks. Real-world earthquake events demonstrate that strong earthquakes are often followed by multiple aftershocks, which can cause landslides to recur or further develop. This is especially true for slopes in a critically stable state; repeated aftershock disturbances can further weaken their structure, leading to delayed landslides or expanding the deformation range of existing landslide bodies. Therefore, the exceedance probability calculated solely based on the mainshock intensity significantly underestimates landslide risk in actual seismic environments, failing to meet the needs of accurate disaster prevention and dynamic assessment.

[0003] On the other hand, traditional seismic slope vulnerability analysis typically considers only a single response index, such as the safety factor or permanent displacement. The former reflects the overall stability of the slope but struggles to capture the cumulative effects of sliding under strong earthquakes; the latter, while quantifying earthquake-induced deformation, fails to reflect the degradation trend of the slope's initial anti-sliding capacity. Especially in the critical stability state, the slope may not have yet slipped, but already possesses a high potential risk of instability. A single response index is insufficient to characterize the entire evolutionary path of a slope from "performance degradation" to "actual failure."

[0004] Therefore, there is an urgent need for a method and system for analyzing the vulnerability of slopes based on the main shock sequence with dual response indices to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for analyzing the vulnerability of slopes based on mainshock and aftershock sequences using dual-response indices, in order to improve the aforementioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows:

[0006] Firstly, this application provides a method for analyzing the vulnerability of slopes based on a mainshock-aftershock sequence using dual-response indices, including:

[0007] Acquire seismic ground motion data of the main shock and aftershocks, and physical parameters of the slope soil;

[0008] Based on the physical parameters of the slope soil, a GeoStudio slope model was constructed, and initial stress state analysis and limit equilibrium analysis were performed to obtain the initial static safety factor and critical acceleration of the slope.

[0009] Incremental dynamic time history analysis was performed based on the main shock ground motion data, slope model and initial static safety factor of the slope to determine the safety factor value and permanent displacement value of the soil after the main shock, and the soil shear strength degradation was calculated based on the permanent displacement value to obtain the soil shear strength parameter value after the main shock.

[0010] The soil shear strength parameters and the initial critical acceleration of the slope after the main shock are sent to the critical acceleration calculation model for updating, and the critical acceleration of the slope after the main shock is obtained.

[0011] Based on aftershock ground motion data and the critical acceleration of the slope after the main shock, dynamic time history analysis of aftershock increments was performed to obtain the safety factor value and cumulative displacement result of the soil after the aftershock.

[0012] Based on the log-normal cumulative distribution function, a vulnerability function is defined, and the safety factor and cumulative displacement of the soil after the main shock and aftershock are calculated to obtain the vulnerability curve of multi-level slopes.

[0013] Secondly, this application also provides a slope vulnerability analysis system based on a dual-response index for mainshock and aftershock sequences, including:

[0014] The acquisition unit is used to acquire main and aftershock ground motion data and slope soil physical parameters;

[0015] The building unit is used to construct the GeoStudio slope model based on the physical parameters of the slope soil, and to perform initial stress state analysis and limit equilibrium analysis to obtain the initial static safety factor and critical acceleration of the slope.

[0016] The calculation unit is used to perform incremental dynamic time history analysis based on the main shock ground motion data, slope model and initial static safety factor of the slope, to determine the safety factor value and permanent displacement value of the soil after the main shock, and to calculate the shear strength degradation of the soil based on the permanent displacement value, so as to obtain the shear strength parameter value of the soil after the main shock.

[0017] The update unit is used to send the soil shear strength parameters and the initial critical acceleration of the slope after the main shock to the critical acceleration calculation model for updating, so as to obtain the critical acceleration of the slope after the main shock.

[0018] The analysis unit is used to perform dynamic time history analysis of aftershock increments based on aftershock ground motion data and critical acceleration of slopes after the main shock, so as to obtain the safety factor value and cumulative displacement results of the soil after the aftershock.

[0019] The processing unit is used to define the vulnerability function based on the log-normal cumulative distribution function, and to calculate the safety factor value and cumulative displacement result of the soil after the main shock and aftershock, so as to obtain the vulnerability curve of the multi-level slope.

[0020] The beneficial effects of this invention are as follows:

[0021] This application simulates the intermittency of real earthquakes by dynamically coupling the effects of the mainshock and aftershock seismic sequences and setting a zero-acceleration interval between the mainshock and aftershock time histories. It combines this with a piecewise linear model based on permanent displacement to dynamically update the soil shear strength parameters (cohesion, internal friction angle) and critical acceleration after the mainshock, enabling continuous degradation analysis of the slope's mechanical response. Innovatively, it employs a safety factor (stability reserve) and permanent displacement (slip result) as dual response indicators for joint judgment, constructing a failure identification standard for the entire "stability-critical-failure" process, overcoming the limitations of traditional single-indicator models. Through incremental dynamic time history analysis of the mainshock and aftershocks, it generates layered vulnerability curves, quantifying the exceedance probability of multi-level performance indicators under multiple aftershock intensities, significantly improving the accuracy of slope risk assessment and visualization decision-making capabilities. This method is applicable to various slope types and earthquake scenarios, supporting dynamic disaster prevention planning and precise emergency response, and solving problems such as neglecting cumulative aftershock damage, static assumptions about shear strength, and a single dimension of risk assessment in traditional methods.

[0022] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0023] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a schematic diagram of the slope vulnerability analysis method based on the main shock sequence with dual response indices as described in this embodiment of the invention.

[0025] Figure 2 This is a schematic diagram of the slope vulnerability analysis system based on the main shock sequence according to the dual response index, as described in this embodiment of the invention.

[0026] Figure 3 The vulnerability curve of a single mainshock is generated by the mainshock sequence slope vulnerability analysis method based on dual response index as described in this embodiment of the invention.

[0027] Figure 4 The vulnerability curve of the mainshock sequence generated by the mainshock sequence slope vulnerability analysis method based on dual response index described in this embodiment of the invention.

[0028] In the diagram: 701, Acquisition Unit; 702, Construction Unit; 703, Calculation Unit; 704, Update Unit; 705, Analysis Unit; 706, Processing Unit. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention 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 the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0030] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0031] Example 1:

[0032] This embodiment provides a method for analyzing the vulnerability of slopes based on the main shock sequence with dual response indices.

[0033] See Figure 1 , Figure 3 and Figure 4 The figure shows that the method includes steps S1, S2, S3, S4, S5 and S6.

[0034] Step S1: Obtain the ground motion data of the main shock and aftershocks and the physical parameters of the slope soil;

[0035] Understandably, this step involves screening ground motion records from the NGA-West2 database for mainshocks and aftershocks with magnitudes ≥ 5.0, mainshock PGA > 0.1g, and each mainshock and aftershock sequence originating from the same station. This condition not only ensures the consistency of ground motion spectral characteristics and propagation paths but also implicitly constrains the spatiotemporal continuity of earthquake energy release, avoiding the introduction of non-physical noise due to differences in multiple source mechanisms or site conditions. Simultaneously, inserting zero-acceleration intervals to simulate the interval between mainshocks and aftershocks essentially provides a time window for stress redistribution on the slope, ensuring the physical rationality of the dissipation of excess pore water pressure and the relaxation process of the soil structure after the mainshock. This operation directly affects the convergence of the slope's dynamic response in subsequent IDA analysis. In obtaining slope parameters, soil physical parameters (unit weight, cohesion, internal friction angle, etc.) need to be calibrated jointly through in-situ tests (such as CPT, SPT) and indoor dynamic triaxial tests. In particular, the strain softening characteristics of cohesion and internal friction angle under cyclic loading must be considered, rather than directly using static parameters.

[0036] Step S2: Construct a GeoStudio slope model based on the physical parameters of the slope soil, and perform initial stress state analysis and limit equilibrium analysis to obtain the initial state parameters and critical acceleration of the slope.

[0037] It is understandable that the introduction of the dynamic shear modulus equation in this step incorporates the nonlinear dynamic response characteristics of the soil into the initial stress field, laying the foundation for accurate simulation of material hysteretic behavior in the limit equilibrium analysis of the main shock. The calculation of critical acceleration realizes the dynamic correlation between shear strength parameters and slope geometry, ensuring the physical rationality of critical acceleration degradation in subsequent aftershock analysis. The accurate extraction of the initial static safety factor and critical acceleration provides key thresholds for setting the seismic amplitude modulation range, avoiding insufficient or redundant intensity interval coverage in the limit equilibrium analysis. In this step, step S2 includes steps S21, S22, and S23.

[0038] Step S21: Perform slope geometry modeling based on slope soil physical parameters. Input parameters and define slope geometry, soil layer distribution and boundary conditions using GeoStudio software to obtain the GeoStudio slope model.

[0039] Understandably, this step involves creating a parametric template using GeoStudio, defining the slope geometry based on borehole data or geological profiles, and dynamically binding the physical parameters (unit weight, cohesion, internal friction angle, etc.) of multiple soil layers to spatial coordinates using layered mapping technology, rather than simply inputting homogeneous parameters. For example, for heterogeneous slopes, material partitioning needs to be set based on soil layer distribution data in the survey report (such as the location of weak interlayers), and a continuously transitioning soil interface needs to be generated based on the Kriging interpolation algorithm to avoid stress abrupt changes caused by traditional "hard stratification" (such as the gradual transition between the clay layer and the underlying sand layer at the slope toe). Through refined modeling and physical constraints, our team provides a numerical carrier with dual geometric and mechanical fidelity for subsequent analysis, and its output model directly determines the reliability of the dynamic response analysis.

[0040] Step S22: Perform initial stress state analysis based on the slope model. Specifically, the stress field distribution under the action of soil self-weight is solved by GeoStudio static analysis module to obtain the initial static stress field of the slope.

[0041] Understandably, this step identifies potential slip surface locations (such as maximum shear stress traces) through stress field visualization and cross-validates them with limit equilibrium analysis results, providing a spatial reference benchmark for subsequent critical acceleration calculations. In this application, the stress distribution of the slope under natural conditions is restored through accurate static equilibrium calculations. In GeoStudio, a nonlinear constitutive model and iterative solution algorithm are used to achieve a 95% agreement between the initial vertical stress distribution and the field pore pressure static cone penetration test (CPTU) data, especially improving the characterization accuracy of the shear stress concentration zone at the slope toe.

[0042] Step S23: Perform limit equilibrium analysis based on the initial static stress field to obtain the initial static safety factor and critical acceleration value of the slope.

[0043] It is understandable that this step, in order to describe the nonlinearity of the soil's dynamic properties, and considering both the dynamic shear model and the dynamic damping ratio, adopts a modified dynamic shear modulus equation G / G. max The initial stress state and limit equilibrium analysis of the slope were performed using dynamic damping λ to obtain the initial static safety factor and critical acceleration of the slope model. The calculation formula for the critical acceleration is shown in formula (3).

[0044] Step S3: Based on the main shock ground motion data, slope model and initial static safety factor of the slope, perform incremental dynamic time history analysis to determine the safety factor value and permanent displacement value of the soil after the main shock, and calculate the soil shear strength degradation based on the permanent displacement value to obtain the soil shear strength parameter value after the main shock.

[0045] It is understood that in this process, step S3 includes steps S31, S32 and S33.

[0046] Step S31: Based on the initial static safety factor of the slope and the preset amplitude modulation range of the ground motion intensity parameters, process the main shock ground motion data at equal intervals or logarithmic intervals to generate multiple sets of amplitude-modulated main shock ground motion time history data, and obtain the amplitude modulation parameter sequence.

[0047] It is understandable that this step, based on the initial critical acceleration of the slope, uses a piecewise amplitude modulation algorithm to dynamically divide the intensity interval: a high-resolution logarithmic interval is used in the interval close to the critical value to capture the nonlinear abrupt drop in the safety factor from 1.5 to 1.0; while an equal interval is used in the high-intensity interval to balance computational efficiency and the smoothness of the displacement accumulation trend. The amplitude modulation process requires amplitude scaling of the original ground motion time history using wavelet packet decomposition-reconstruction technology, retaining the energy proportion error of the main frequency components ≤3%, avoiding spectral distortion caused by traditional linear scaling. Furthermore, the amplitude modulation interval is determined based on the seismic intensity parameters used. For example, if peak ground acceleration (PGA) is used, an equal interval can be used if the numerical range is small; if Arias intensity (Ia) is used, a logarithmic interval can evenly represent values ​​of multiple orders of magnitude with a large numerical range. The pre-set seismic intensity parameters IM used in the project include, for example, peak ground acceleration (PGA), peak ground velocity (PGV), and Arias intensity (Ia). a For the safety factor, a safety factor of 1 is used as the critical condition for slope instability, and safety factors of 1, 1.25, and 1.5 are defined as low safety, medium safety, and high safety, respectively. For permanent displacement, under a single mainshock, 5, 15, and 30 cm are used as the limit states for the three capacity levels of low, medium, and high risk. Under the action of mainshock and aftershock ground motion data, 5, 50, and 100 cm are used as the limit states for the three capacity levels of low, medium, and high risk.

[0048] Step S32: Input the amplitude modulation parameter sequence into the GeoStudio dynamic analysis module in sequence to dynamically solve the stress-strain response of the slope under the action of seismic motion, and obtain the safety factor value and permanent displacement cumulative value corresponding to multiple seismic intensity parameters.

[0049] Understandably, this step utilizes the GeoStudio dynamic analysis module for numerical simulation analysis, directly calculating the safety factor and cumulative permanent displacement values ​​corresponding to the seismic intensity parameters. This accurately reflects the mainshock energy input and slope resonance effect. The seismic intensity parameters used in this step include peak ground acceleration (PGA), peak ground velocity (PGV), and Arias intensity. The safety factor and cumulative permanent displacement values ​​are directly determined using the GeoStudio dynamic analysis module.

[0050] Step S33: Calculate the soil shear strength parameters after the main shock based on the cumulative value of permanent displacement and the preset piecewise linear degradation formula.

[0051] It is understandable that the slope stability under seismic load will be affected after the main shock. At this time, the physical parameters of the soil and rock materials will also change. Specifically, the degradation of the shear strength parameter is described by the piecewise linear relationship between the soil shear strength parameter and the permanent displacement. In this step, the values ​​of soil cohesion and internal friction angle after the main shock are determined by the following equations (1) and (2).

[0052]

[0053] Where c is the cohesive force. It is the internal friction angle, c p It is the peak cohesion of the soil, c r It is the residual cohesion of the soil. It is the peak internal friction angle of the soil. s1 is the residual friction angle of the soil. s2 is the threshold of permanent displacement, that is, the displacement at which shear strength begins to degrade. s3 is the maximum displacement of the soil. When the displacement reaches this value, the cohesion degrades to the residual cohesion. s1 and s2 are closely related to factors such as soil type, seismic intensity, and geological conditions, and can be determined by experimental data, theoretical models, or empirical values ​​in references.

[0054] Step S4: Send the soil shear strength parameters and the initial critical acceleration of the slope after the main shock to the critical acceleration calculation model for updating, and obtain the critical acceleration of the slope after the main shock;

[0055] It is understandable that this step, through the closed-loop coupling of the mechanical model and the optimization algorithm, transforms the damage quantity of the main shock into a dynamic stability index that can drive the aftershock analysis. The updated critical acceleration value output directly defines the aftershock amplitude adjustment benchmark, which solves the problem of misjudgment of aftershock risk caused by neglecting strength degradation in traditional methods. In this step, step S4 includes step S41.

[0056] Step S41: Input the soil shear strength parameter value after the main shock into the preset critical acceleration calculation formula for calculation, obtain the critical acceleration calculation result, and update it under preset conditions based on the critical acceleration calculation result to obtain the critical acceleration of the slope after the main shock.

[0057] The formula for calculating the critical acceleration is shown in formula (3):

[0058]

[0059] In the formula, c represents cohesion. γ is the internal friction angle, β is the slope inclination angle, H is the height of the soil column, and γ is the slope angle.s k is the unit weight of soil. y This represents the critical acceleration. When the displacement is less than the threshold s1, the cohesion and internal friction angle remain at their peak values ​​c. p , The initial yield acceleration remains at the initial value k. y,p When the displacement increases to be greater than s1, the critical acceleration begins to increase with c. Decrease. When the displacement is greater than s2, c, Maintain residual value c r , The critical acceleration remains unchanged, retaining its residual value k. y,r .

[0060] Step S5: Define the vulnerability function based on the log-normal cumulative distribution function, and calculate the safety factor value and cumulative displacement result of the soil after the main shock and aftershock to obtain the vulnerability curve of the multi-level slope.

[0061] It is understood that in this process, step S5 includes steps S51, S52 and S53.

[0062] Step S51: Based on the critical acceleration of the slope after the main shock and the aftershock ground motion data, perform aftershock ground motion amplitude modulation processing. Specifically, the aftershock ground motion record is amplitude-modulated by a preset relative intensity ratio of aftershocks to obtain amplitude-modulated aftershock ground motion data that matches the intensity parameters of the main shock.

[0063] It is understandable that in this step, the amplitude of the aftershock ground motion intensity is adjusted, and the relative intensity of the aftershock is defined as shown in formula (4):

[0064]

[0065] In the formula: IM AS IM represents the seismic intensity parameters of aftershocks. MS These are the seismic intensity parameters of the main shock. Specifically, for each IM of the main shock's ground motion... MS The values ​​ΔIM, corresponding to the relative intensities of aftershock ground motions, are taken from 0.5 to 1.0 to simulate the impact of aftershocks of multiple intensities. For each ΔIM value, the scaled aftershock records are used as input for incremental dynamic analysis. A series of safety factor values ​​and permanent displacement values ​​corresponding to ΔIM are output. The calculated mainshock displacement values ​​are accumulated with these values ​​to obtain the cumulative displacement of the slope under the action of the mainshock-aftershock sequence.

[0066] Step S52: Input the amplitude-modulated aftershock ground motion data into the GeoStudio dynamic analysis module to solve the dynamic response under the action of aftershocks, obtain the safety factor and permanent displacement accumulation value corresponding to multiple aftershock intensities, and obtain the dynamic response data under the action of aftershocks alone.

[0067] Understandably, this step uses the GeoStudio dynamic analysis module for numerical simulation analysis, directly calculating the safety factor value and cumulative permanent displacement value corresponding to multiple aftershock intensities, accurately reflecting the main shock energy input and slope resonance effect.

[0068] Step S53: Accumulate the permanent displacement cumulative values ​​of the mainshock and aftershocks using the linear superposition formula to generate a slope cumulative displacement dataset of the mainshock and aftershock sequence, and obtain the safety factor value and cumulative displacement result of the soil after the aftershock under multiple earthquake intensity combinations.

[0069] It is understandable that this step simplifies the calculation by accumulating the permanent displacement values ​​of the main shock and aftershocks, thereby achieving efficient generation of cumulative displacement data for the main shock and aftershocks, and providing basic data support for the plotting of slope vulnerability curves and risk classification.

[0070] Step S6: Define the vulnerability function based on the log-normal cumulative distribution function, and calculate the safety factor value and cumulative displacement result of the soil after the main shock and aftershock to obtain the vulnerability curve of the multi-level slope.

[0071] It is understood that in this step, step S6 includes steps S61, S62 and S63.

[0072] Step S61: Perform vulnerability function parameter estimation on the safety factor value and cumulative displacement result of the soil after the main and aftershocks to obtain the estimation result, which includes the median and standard deviation parameters of the safety level corresponding to each safety factor;

[0073] In this step, a safety factor of 1 is used as the critical condition for slope instability. Safety factors of 1, 1.25, and 1.5 are defined as low, medium, and high safety, respectively. For permanent displacement, under a single mainshock, 5, 15, and 30 cm are used as the limit states for low, medium, and high risk levels, respectively. Under a mainshock-aftershock sequence, 5, 50, and 100 cm are used as the limit states for low, medium, and high risk levels, respectively. This allows the determination of the safety level of the safety factor, and based on the safety level of the safety factor, the cumulative displacement results, and the above formula, the slope vulnerability function can be calculated.

[0074] It is understandable that the estimation formulas (6) and (7) in this step are as follows:

[0075]

[0076] in, and It is an estimator of the vulnerability function parameters. It is an estimator of the median of the vulnerability function; is an estimate of the natural logarithmic standard deviation of the IM value; n is the number of seismic records used; IM i This represents the seismic intensity parameter value associated with the performance of a seismic slope reaching a specific vulnerable state.

[0077] Step S62: Calculate the estimation result based on the log-normal cumulative distribution function to obtain the failure probability of the slope;

[0078] It is understandable that this step uses the log-normal cumulative distribution function (CDF) to define the vulnerability function, as shown in equation (5).

[0079]

[0080] Where P(V|IM=x) is the conditional probability that the seismic performance state of the slope exceeds the vulnerability state V when the seismic intensity parameter IM is x; Φ() is the standard log-normal cumulative distribution function; θ is the median of the vulnerability function; β is the natural logarithmic standard deviation of the IM value; and x is a constant.

[0081] Step S63: Generate single mainshock vulnerability curves and mainshock-aftershock sequence vulnerability curves based on the slope failure probability.

[0082] Understandably, the mainshock IDA (mainshock incremental dynamic time history analysis) results obtained in this step are applied to the vulnerability function to determine the failure probabilities corresponding to multiple damage levels of the slope, thus obtaining the vulnerability curves of the slope under each extreme state. Specifically, the vulnerability curve for a single mainshock is plotted with ground motion intensity on the horizontal axis and exceedance probability on the vertical axis. The vulnerability curves for the mainshock-aftershock sequence take into account the changes in the relative intensity of aftershocks and are plotted as vulnerability curves under multiple relative aftershock intensities. Each sub-plot corresponds to multiple relative aftershock intensity values, with the mainshock intensity parameter on the horizontal axis and exceedance probability on the vertical axis.

[0083] Example 2:

[0084] like Figure 2 As shown, this embodiment provides a slope vulnerability analysis system based on the main shock sequence using dual response indices. See [link to documentation]. Figure 2 The system includes an acquisition unit 701, a construction unit 702, a calculation unit 703, an update unit 704, an analysis unit 705, and a processing unit 706.

[0085] Acquisition unit 701 is used to acquire main and aftershock ground motion data and slope soil physical parameters;

[0086] Building unit 702 is used to construct a GeoStudio slope model based on the physical parameters of the slope soil, and to perform initial stress state analysis and limit equilibrium analysis to obtain the initial static safety factor and critical acceleration of the slope.

[0087] The calculation unit 703 is used to perform incremental dynamic time history analysis based on the main shock ground motion data, slope model and initial static safety factor of the slope, to determine the safety factor value and permanent displacement value of the soil after the main shock, and to calculate the soil shear strength degradation based on the permanent displacement value, so as to obtain the soil shear strength parameter value after the main shock.

[0088] Update unit 704 is used to send the soil shear strength parameter value after the main shock and the initial critical acceleration of the slope to the critical acceleration calculation model for updating, so as to obtain the critical acceleration of the slope after the main shock;

[0089] Analysis unit 705 is used to perform dynamic time history analysis of aftershock increments based on aftershock ground motion data and critical acceleration of slope after the main shock, so as to obtain the safety factor value and cumulative displacement result of the soil after the aftershock.

[0090] Processing unit 706 is used to define a vulnerability function based on the log-normal cumulative distribution function, and to calculate the safety factor value and cumulative displacement result of the soil after the main shock and aftershock, so as to obtain the vulnerability curve of multi-level slope.

[0091] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0092] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0093] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for analyzing the vulnerability of slopes based on mainshock and aftershock sequences using dual-response indices, characterized in that, include: Acquire seismic ground motion data of the main shock and aftershocks, and physical parameters of the slope soil; Based on the physical parameters of the slope soil, a GeoStudio slope model was constructed, and initial stress state analysis and limit equilibrium analysis were performed to obtain the initial static safety factor and critical acceleration of the slope. Incremental dynamic time history analysis was performed based on the main shock ground motion data, slope model and initial static safety factor of the slope to determine the safety factor value and permanent displacement value of the soil after the main shock, and the soil shear strength degradation was calculated based on the permanent displacement value to obtain the soil shear strength parameter value after the main shock. The soil shear strength parameters and the initial critical acceleration of the slope after the main shock are sent to the critical acceleration calculation model for updating, and the critical acceleration of the slope after the main shock is obtained. Based on aftershock ground motion data and the critical acceleration of the slope after the main shock, dynamic time history analysis of aftershock increments was performed to obtain the safety factor value and cumulative displacement results of the soil after the aftershocks. Based on the log-normal cumulative distribution function, the vulnerability function is defined, and the safety factor value and cumulative displacement result of the soil after the main shock and aftershock are calculated to obtain the vulnerability curve of multi-level slope. Incremental dynamic time-history analysis was performed based on the mainshock ground motion data, slope model, and initial static safety factor of the slope to determine the safety factor and permanent displacement of the soil after the mainshock. Based on the permanent displacement value, the shear strength degradation of the soil was calculated, including: Based on the initial static safety factor of the slope and the preset amplitude modulation range of the ground motion intensity parameters, the main shock ground motion data are processed by equal intervals or logarithmic intervals to generate multiple sets of amplitude-modulated main shock ground motion time history data, and obtain the amplitude modulation parameter sequence. The amplitude modulation parameter sequence is input into the GeoStudio dynamic analysis module to dynamically solve the stress-strain response of the slope under seismic motion, and obtain the safety factor value and cumulative permanent displacement value corresponding to multiple seismic intensity parameters. The shear strength parameters of the soil after the main shock are calculated based on the cumulative value of permanent displacement and the preset piecewise linear degradation formula. Among them, the dynamic time history analysis of aftershock increments is carried out based on aftershock ground motion data and the critical acceleration of the slope after the main shock, including: Based on the critical acceleration of the slope after the main shock and the aftershock ground motion data, aftershock ground motion amplitude modulation processing is carried out. Specifically, the aftershock ground motion records are amplitude-modulated by a preset relative intensity ratio of aftershocks to obtain amplitude-modulated aftershock ground motion data that matches the intensity parameters of the main shock. The amplitude-modulated aftershock ground motion data is input into the GeoStudio dynamic analysis module to solve the dynamic response under the action of aftershocks, and the safety factor and permanent displacement accumulation value corresponding to multiple aftershock intensities are obtained, and the dynamic response data under the action of aftershocks alone are obtained. By accumulating the permanent displacement values ​​of the mainshock and aftershocks using a linear superposition formula, a slope cumulative displacement dataset of the mainshock and aftershock ground motion data is generated, and the safety factor value and cumulative displacement result of the soil after the aftershock under multiple earthquake intensity combinations are obtained.

2. The method for analyzing the vulnerability of slopes based on the main shock sequence using dual-response indices according to claim 1, characterized in that... A GeoStudio slope model was constructed based on the physical parameters of the slope soil, and initial stress state analysis and limit equilibrium analysis were performed, including: Based on the physical parameters of the slope soil, the slope geometry is processed by inputting parameters and defining the slope geometry, soil layer distribution and boundary conditions through GeoStudio software to obtain the GeoStudio slope model. The initial stress state analysis was performed based on the slope model. Specifically, the stress field distribution under the action of soil self-weight was solved by GeoStudio static analysis module to obtain the initial static stress field of the slope. Limit equilibrium analysis was performed based on the initial static stress field to obtain the initial static safety factor and critical acceleration value of the slope.

3. The method for analyzing the vulnerability of slopes based on the main shock sequence using dual-response indices according to claim 1, characterized in that... The soil shear strength parameters and initial critical acceleration of the slope after the mainshock are sent to the critical acceleration calculation model for updating, resulting in the critical acceleration of the slope after the mainshock, including: The shear strength parameters of the soil after the main shock are input into the preset critical acceleration calculation formula for calculation to obtain the critical acceleration calculation result. Based on the critical acceleration calculation result, the result is updated under preset conditions to obtain the critical acceleration of the slope after the main shock.

4. A slope vulnerability analysis system based on a mainshock and aftershock sequence using dual-response indices, characterized in that, include: The acquisition unit is used to acquire ground motion data of the main shock and aftershocks, as well as the physical parameters of the slope soil. The building unit is used to construct the GeoStudio slope model based on the physical parameters of the slope soil, and to perform initial stress state analysis and limit equilibrium analysis to obtain the initial static safety factor and critical acceleration of the slope. The calculation unit is used to perform incremental dynamic time history analysis based on the main shock ground motion data, slope model and initial static safety factor of the slope, to determine the safety factor value and permanent displacement value of the soil after the main shock, and to calculate the shear strength degradation of the soil based on the permanent displacement value, so as to obtain the shear strength parameter value of the soil after the main shock. The update unit is used to send the soil shear strength parameters and the initial critical acceleration of the slope after the main shock to the critical acceleration calculation model for updating, so as to obtain the critical acceleration of the slope after the main shock. The analysis unit is used to perform dynamic time history analysis of aftershock increments based on aftershock ground motion data and critical acceleration of the slope after the main shock, so as to obtain the safety factor value and cumulative displacement result of the soil after the aftershock. The processing unit is used to define the vulnerability function based on the log-normal cumulative distribution function, and to calculate the safety factor value and cumulative displacement result of the soil after the main shock and aftershock, so as to obtain the vulnerability curve of the multi-level slope. The computing unit includes: The first calculation subunit is used to process the main shock ground motion data with equal or logarithmic intervals based on the amplitude modulation range of the initial static safety factor of the slope and the preset ground motion intensity parameters, and generate multiple sets of amplitude-modulated main shock ground motion time history data to obtain the amplitude modulation parameter sequence. The second calculation subunit is used to input the amplitude modulation parameter sequence into the GeoStudio dynamic analysis module in sequence, dynamically solve the stress-strain response of the slope under the action of seismic motion, and obtain the safety factor value and the cumulative value of permanent displacement corresponding to multiple seismic intensity parameters. The third calculation sub-unit is used to calculate the soil shear strength parameters after the main shock based on the cumulative value of permanent displacement and the preset piecewise linear degradation formula. The analysis unit includes: The first analysis subunit is used to perform aftershock ground motion amplitude modulation processing based on the critical acceleration of the slope after the main shock and the aftershock ground motion data. Specifically, the aftershock ground motion record is amplitude-modulated by a preset relative intensity ratio of aftershocks to obtain amplitude-modulated aftershock ground motion data that matches the intensity parameters of the main shock. The second analysis subunit is used to input the amplitude-modulated aftershock ground motion data into the GeoStudio dynamic analysis module to solve the dynamic response under the action of aftershocks, obtain the safety factor and cumulative permanent displacement value corresponding to multiple aftershock intensities, and obtain the dynamic response data under the action of aftershocks alone. The third analysis sub-unit is used to accumulate the permanent displacement cumulative values ​​of the mainshock and aftershocks using a linear superposition formula, generate a slope cumulative displacement dataset of the mainshock and aftershock ground motion data, and obtain the safety factor value and cumulative displacement result of the soil after the aftershock under multiple earthquake intensity combinations.

5. The slope vulnerability analysis system based on the main shock sequence according to claim 4, characterized in that, The building unit includes: The first construction sub-unit is used to perform slope geometric modeling based on the physical parameters of the slope soil. The parameters are input through GeoStudio software and the slope geometry, soil layer distribution and boundary conditions are defined to obtain the GeoStudio slope model. The second construction sub-unit is used for initial stress state analysis based on the slope model. Specifically, the stress field distribution under the action of soil self-weight is solved by GeoStudio static analysis module to obtain the initial static stress field of the slope. The third sub-unit is used to perform limit equilibrium analysis based on the initial static stress field to obtain the initial static safety factor and critical acceleration value of the slope.

6. The slope vulnerability analysis system based on the main shock sequence according to claim 4, characterized in that, The update unit includes: The first update subunit is used to input the soil shear strength parameter value after the main shock into the preset critical acceleration calculation formula for calculation, to obtain the critical acceleration calculation result, and to update it under preset conditions based on the critical acceleration calculation result to obtain the critical acceleration of the slope after the main shock.

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