Multi-dimensional response slope damage and catastrophe evolution process identification method suitable for vibration table test

Abstract

The invention provides a multi-dimensional response slope damage and catastrophe evolution process identification method suitable for a vibration table test, and the method comprises the steps: carrying out an indoor vibration table test, and extracting acceleration test data; on the basis, firstly, the acceleration peak value is extracted, the most unfavorable position of the side slope under the earthquake condition is determined, and the importance of vertical acceleration response to side slope damage is revealed by defining the response ratio of the acceleration peak value and calculating the response ratio of the peak value in the vertical direction and the horizontal direction. Secondly, performing quadratic integration on the acceleration data based on an SPECTR program to obtain displacement conditions of different positions of the slope in the horizontal and vertical directions, drawing a slope displacement response spectrum (DSR), and emphatically exposing relative slippage conditions of the upper and lower positions of the sliding surface in the horizontal and vertical directions and vertical shear dislocation conditions of the rear edge of the slope; and analyzing the development, development and penetration process of the sliding surface and the development process of the vertical crack at the rear edge of the slope.

Description

Technical Field

[0001] The invention belongs to a method for identifying the seismic damage and catastrophic evolution process of slopes, and particularly relates to a method for identifying the damage and catastrophic evolution process of slopes with multi-dimensional responses suitable for shaking table tests. Background Art

[0002] The research on the stability and failure characteristics of slopes under seismic action mainly focuses on theoretical analysis and numerical simulation. For example, the study of slope stability using the pseudo-static method is developed based on the theoretical achievements of Terzaghi et al., and the relatively typical Mononobe-Okabe formula has been formed. The core of the pseudo-static method is to convert the dynamic problem into a static problem. When using this method for slope stability analysis, factors such as the vibration frequency of seismic waves, the duration, and the dynamic characteristics of the medium cannot be considered, so there are certain defects. When using numerical simulation methods to study the seismic stability and failure modes of slopes, the boundary conditions of slopes and the contact conditions between soil particles under real conditions cannot be simulated. In comparison, the shaking table test is the most effective method for simulating the dynamic response and failure process of slopes under seismic action. By conducting shaking table tests, the location where the slope first fails and the failure process can be visually observed. At the same time, by burying acceleration sensors and analyzing the collected test data, the failure mechanism of the slope can also be understood.

[0003] During the transmission of seismic waves, in addition to considering the reflection and transmission at the soil interface, the propagation characteristics of seismic waves inside the slip surface also need to be considered. For the research on the seismic response of slopes containing weak slip surfaces, the seismic waveform is mainly input through shaking table tests, and sensors of types such as acceleration, displacement, and strain are arranged. The seismic response of the slope is analyzed using the collected test data. Currently, the main focus of research is on studying the seismic response of slopes in the horizontal direction under the input of seismic waves in the horizontal direction, vertical direction, or mixed direction, ignoring the analysis of the vertical response of slopes under seismic action. It cannot be ignored that the vertical seismic response plays a controlling role in the formation and penetration of vertical tensile cracks at the rear of the slope and horizontal shear cracks inside the weak slip surface of the slope. Summary of the Invention

[0004] In order to effectively identify the damage and catastrophic evolution process of slopes under seismic action from multiple dimensions and provide technical guidance for the treatment of seismic slopes, acceleration data at different positions of the slope are measured through shaking table tests. On this basis, by using parameters such as the acceleration peak ratio, displacement response spectrum, and marginal spectrum amplitude, an innovative method for identifying the damage and catastrophic evolution process of slopes with multi-dimensional acceleration responses (horizontal response and vertical response) suitable for shaking table tests is proposed, revealing the damage and catastrophic evolution laws of slopes under seismic action.

[0005] To this end, the present invention adopts the following technical solutions:

[0006] A method for identifying the slope damage and disaster evolution process of multi-dimensional responses applicable to shaking table tests, comprising the following steps:

[0007] 1) Select typical working points of the slope. According to engineering geological data and research results, determine the geological and geomorphic conditions of the slope, and obtain the key physical and mechanical parameters of the landslide site, including cohesion, internal friction angle, and unit weight;

[0008] Carry out model generalization and direct shear tests, select the filling materials for the sliding mass, sliding surface, and sliding bed, and determine the mix ratio;

[0009] Fill the indoor shaking table test model, synchronously arrange acceleration sensors, and design test loading conditions;

[0010] 2) Conduct shaking table tests to obtain acceleration test data at different positions;

[0011] 3) According to the acceleration test data measured in step 2), extract the acceleration peak values at different measuring points and under different loading conditions, draw an acceleration peak value contour map, and determine the most unfavorable positions of the slope under different loading conditions;

[0012] Define the acceleration peak value response ratio in the vertical direction and the horizontal direction. The specific calculation formula is as follows:

[0013]

[0014] In the formula: PAR i represents the peak acceleration response ratio of the i measuring point, dimensionless; VPA i represents the peak acceleration in the vertical direction of the i measuring point, with the unit of m / s 2 ; HPA i represents the peak acceleration in the horizontal direction of the i measuring point, with the unit of m / s 2 ; Determine the acceleration peak value ratio under different loading conditions, and judge the contribution degree of the vertical acceleration to the slope failure;

[0015] 4) According to the acceleration test data measured in step 2), perform secondary integration using the SPECTR program to obtain the horizontal and vertical displacement conditions at different positions of the slope; on this basis, draw a contour map of the slope displacement response spectrum (DSR); judge the shear sliding displacement condition through the contour map of the displacement response spectrum (DSR);

[0016] 5) Based on the acceleration test data measured in step 2), use Matlab software to conduct Hilbert-Huang transform (HHT) processing to obtain the Hilbert spectrum and the cloud diagram of the peak value of the marginal spectrum (PMSA); judge the damage of high- and low-frequency seismic waves to the slope;

[0017] 6) According to the cloud diagram of the displacement response spectrum (DSR) of the slope drawn in step 5), reveal the relative sliding law of the positions on both sides of the slip surface, reveal the vertical shear dislocation law at the rear edge of the slope. On this basis, summarize the development, growth, and penetration process of the slip surface and the development process of the vertical cracks at the rear edge of the slope; on the other hand, according to the cloud diagram of the Hilbert spectrum and the peak value of the marginal spectrum (PMSA) drawn in step 7), study the energy propagation law of seismic waves from the energy perspective, and reveal the energy change and distribution law at different positions of the slope during the development, growth, and penetration of the slip surface.

[0018] In this invention, through carrying out indoor shaking table tests, acceleration test data are extracted. On this basis, first, the peak acceleration is extracted to determine the most unfavorable position of the slope under seismic conditions. By defining the peak acceleration response ratio and calculating the peak response ratios in the vertical and horizontal directions, the importance of the vertical acceleration response to slope failure is revealed. Secondly, based on the SPECTR program, the acceleration data are integrated twice to obtain the horizontal and vertical displacements at different positions of the slope, and the displacement response spectrum (DSR) of the slope is drawn to focus on revealing the relative sliding in the horizontal and vertical directions of the positions on both sides of the slip surface and the vertical shear dislocation at the rear edge of the slope, and analyze the development, growth, and penetration process of the slip surface and the development process of the vertical cracks at the rear edge of the slope. In addition, for the collected acceleration data, Matlab software is used for Hilbert-Huang transform (HHT) processing to obtain the cloud diagrams of the Hilbert spectrum and the peak value of the marginal spectrum (PMSA) in the horizontal and vertical directions. By comparing the peak values of the marginal spectra in the horizontal and vertical directions at the local position (the most unfavorable position), the energy propagation law of seismic waves is revealed from the energy perspective, and the whole process and specific response of the development, growth, and penetration of the slip surface and cracks in the vertical and horizontal directions at the most unfavorable position are revealed. Finally, focus on revealing the crack damage and disaster evolution process of the slope from the rear to the front and from the local to the whole, propose an identification method applicable to the slope damage and disaster evolution process, and thus provide technical guidance for slope treatment.

[0019] The beneficial effects of this invention are as follows:

[0020] The existing technologies mainly focus on the horizontal response in the research on the damage and failure laws of slopes, especially there are few reports on the research of the vertical seismic response of slopes under horizontal loading conditions. In view of this, based on the shaking table acceleration test data, this invention conducts slope damage and failure identification based on the acceleration peak ratio, the amplitude of the displacement response spectrum, and the amplitude of the marginal spectrum, making up for the deficiencies in previous research work. Description of the Drawings

[0021] Figure 1 is the algorithm flowchart of the identification method of the present invention;

[0022] Figure 2 is the flowchart of the shaking table test of the present invention;

[0023] Figure 3 is the layout diagram of acceleration sensors for the shaking table test of the present invention;

[0024] Figure 4 is the design diagram of loading conditions for the shaking table test of the present invention;

[0025] Figure 5 is the acceleration time history curve graph obtained from the embodiment;

[0026] Figure 6 is the contour map of 0.1g acceleration peak value;

[0027] Figure 7 is the contour map of 0.4g acceleration peak value;

[0028] Figure 8 is the acceleration peak ratio;

[0029] Figure 9 is the horizontal displacement response spectrum;

[0030] Figure 10 is the vertical displacement response spectrum;

[0031] Figure 11 is the Hilbert spectrum curve graph;

[0032] Figure 12 is the contour map of marginal spectrum amplitude. Detailed Embodiment

[0033] The present invention will be further described below in conjunction with the drawings and specific embodiments:

[0034] 1) In this case, the method of carrying out an indoor shaking table test is adopted to study the catastrophic evolution process of the slope under earthquake action. First, a typical working point is selected, the model is generalized, the direct shear test is carried out to determine the mix ratio parameters, and then the test model is filled and the acceleration sensors are arranged, and the test loading conditions are designed.

[0035] 2) Carry out the shaking table test to obtain the acceleration test data at different positions. The layout diagram of the acceleration sensors is as Figure 3 .

[0036] 3) According to the acceleration test data measured in step 2), extract the acceleration peak values at different measuring points, and draw the peak acceleration contour maps at different positions of the slope as Figure 6 andFigure 7 From Figure 6 it can be seen that when the amplitude of the input seismic wave is 0.1g, the most unfavorable position is at the top of the slope waist. From Figure 7 it can be seen that when the amplitude of the input seismic wave increases to 0.4g, the most unfavorable position is at the lower side of the slip surface.

[0037] Calculate the peak acceleration ratio and master the peak acceleration ratio under different loading conditions ( Figure 8 ). Figure 8 For the case of the peak acceleration ratio of the vertical acceleration peak value to the horizontal acceleration peak value at different measuring points under the condition that the peak input acceleration is 0.4g, from Figure 8 it can be seen that at the rear edge position of the slope, the vertical acceleration response is more intense. Especially for the measuring point A6-4 at the top of the rear edge of the slope, the ratio between the peak value of the vertical acceleration and the peak value of the horizontal acceleration is close to 0.8. This shows that at the rear edge position of the slope, the contribution degree of the vertical acceleration response to the slope failure cannot be ignored.

[0038] 4) According to the acceleration test data measured in step 2), use the SPECTR program to perform double integration to obtain the displacement response spectrum (DSR) contour maps of different measuring points, as Figure 9 , Figure 10 shown. Figure 9 For the horizontal displacement response spectrum under the condition that the amplitude of the input seismic wave is 0.4g, from Figure 9 it can be seen that there are large differences in the displacement response spectrum amplitudes between the measuring points A6-4 and A6-3 at the rear edge of the main slip surface of the slope. The displacement response spectrum amplitude of the measuring point A6-3 on the lower side of the slip surface is 4.15 cm, and the displacement response spectrum amplitude of the measuring point A6-4 on the upper side of the slip surface is 2.77 cm. There is a large shear sliding displacement between them. For the measuring points A3-3 and A3-2 in the middle of the slope, there is still shear sliding displacement, but the relative shear sliding displacement decreases vertically. This shows that the slope slip surface develops and progresses gradually from the rear to the front and finally penetrates.

[0039] Figure 10 For the vertical displacement response spectrum under the condition that the amplitude of the input seismic wave is 0.4g, from Figure 10 it can be seen that in the A6 vertical section at the rear edge of the slope, the amplitude of the vertical displacement response spectrum is significantly greater than that of the A1 and A3 vertical sections at the front edge of the slope. This shows that with the increase of the input seismic wave intensity, there is shear dislocation in the vertical direction at the rear edge of the slope. Combining with Figure 7 the peak ratio situation in it, it can be concluded that there is tensile-shear dislocation at the rear edge of the slope.

[0040] 5) According to the acceleration test data measured in step 2), using Matlab software, perform Hilbert-Huang Transform (HHT) on the acceleration data monitored in the test to obtain the marginal spectrum and Hilbert spectrum ( Figure 11 ), and extract the contour map of the marginal spectrum amplitude ( Figure 12 ). Figure 11 (a) and Figure 11 (b) are the Hilbert spectra of measuring points A6-3 and A6-4 under the condition that the amplitude of the input seismic wave is 0.1g. It can be seen from this that when the amplitude of the input seismic wave is 0.1g, the energy contained in the low-frequency seismic wave (8 - 42Hz) is relatively large, which plays a key role in slope failure. Figure 11 (c) and Figure 11 (d) are the Hilbert spectra of measuring points A6-3 and A6-4 under the condition that the amplitude of the input seismic wave is 0.4g. It can be seen from this that the high-frequency seismic wave (61 - 100Hz) plays a key role in slope failure. Comprehensive Figure 11 It can be seen that after the seismic wave passes through the slip surface from bottom to top, the slip surface has a filtering effect on the low-frequency seismic wave and an amplifying effect on the high-frequency seismic wave.

[0041] 6) Figure 12 They are the contour maps of the marginal spectrum amplitudes of each measuring point under the conditions that the amplitudes of the input seismic waves are 0.1g, 0.2g, and 0.4g respectively. From Figure 12 it can be seen that when the amplitude of the input seismic wave increases from 0.1g to 0.2g, the rules of the marginal spectrum amplitudes of each measuring point are basically the same. When the amplitude of the input seismic wave increases from 0.2g to 0.4g, there is a sudden increase in the marginal spectrum amplitude. Under the conditions of 0.1g and 0.2g, when the energy carried by the seismic wave passes through the picture, there is an obvious phenomenon of energy attenuation, that is, at measuring point A6-3, the marginal spectrum amplitude decreases significantly. Under the condition of 0.4g, the marginal spectrum amplitude at the middle position of the slope is significantly lower than that at the front edge and the rear edge of the slope, indicating that the energy loss is the most serious at the middle position of the slope (the position where the slip surface is located), which also shows that the existence of the slip surface plays a controlling role in slope failure.

Claims

1. A method for identifying the slope damage and catastrophic evolution process of multi-dimensional responses applicable to shaking table tests, characterized in that, It includes the following steps: 1) Select typical working points of the slope. According to the engineering geological data and research results, determine the geological and geomorphic conditions of the slope, and obtain the key physical and mechanical parameters of the landslide site, including cohesion, internal friction angle, and unit weight; Carry out model generalization and direct shear tests, select the filling materials for the sliding mass, sliding surface, and sliding bed, and determine the mix ratio; Fill the indoor shaking table test model, synchronously arrange acceleration sensors, and design the test loading conditions; 2) Conduct the shaking table test to obtain the acceleration test data at different positions; 3) According to the acceleration test data measured in step 2), extract the acceleration peak values at different measuring points and under different loading conditions, draw the acceleration peak value contour map, and determine the most unfavorable positions of the slope under different loading conditions; Define the acceleration peak value response ratio in the vertical and horizontal directions. The specific calculation formula is as follows: In the formula: PAR i represents the peak acceleration response ratio of the i-th measuring point, dimensionless; VPA i represents the peak value of the vertical acceleration of the i-th measuring point, with the unit of m / s 2 ; HPA i represents the peak value of the horizontal acceleration of the i-th measuring point, with the unit of m / s 2 ; Determine the peak acceleration ratio under different loading conditions, and judge the contribution degree of the vertical acceleration to the slope failure; 4) According to the acceleration test data measured in step 2), perform double integration using the SPECTR program to obtain the horizontal and vertical displacement conditions of different positions of the slope; on this basis, draw the displacement response spectrum (DSR) contour map of the slope; judge the shear sliding displacement condition through the displacement response spectrum (DSR) contour map; 5) According to the acceleration test data measured in step 2), use Matlab software to carry out Hilbert-Huang transform (HHT) processing to obtain the Hilbert spectrum and the contour map of the peak value of the marginal spectrum amplitude (PMSA); judge the damage of the slope by high-frequency and low-frequency seismic waves; 6) According to the displacement response spectrum (DSR) contour map of the slope drawn in step 5), reveal the relative sliding law of the positions above and below the sliding surface, reveal the vertical shear dislocation law of the rear edge of the slope, and on this basis, summarize the development, growth, and penetration process of the sliding surface and the development process of the vertical cracks at the rear edge of the slope; on the other hand, according to the Hilbert spectrum and the contour map of the peak value of the marginal spectrum amplitude (PMSA) drawn in step 7), study the energy propagation law of seismic waves from the energy perspective, and reveal the energy change and distribution law of different positions of the slope during the development, growth, and penetration process of the sliding surface.

2. The method for identifying the slope damage and catastrophe evolution process with multi-dimensional response applicable to shaking table tests according to claim 1, characterized in that: a. The acceleration time series collected by the sensor is denoted as X(t). After performing EMD on it, multiple-order IMFs and the residual term r are obtained n , that is, X(t) can be expressed as: At the same time, after performing HHT on X(t), a new time series Y(t) is obtained. The specific transformation process is as follows: In the formula, P represents the Cauchy principal component value; On this basis, using the acceleration time series X(t) collected in the test and the new time series Y(t) obtained by HHT, a new analytic signal Z(t) is constructed; Z(t) = X(t) + Y(t) = a(t)e iθ(t) In the formula, a(t) and θ(t) represent the instantaneous amplitude and instantaneous phase respectively, and the calculation formulas are as follows: a(t) = [X 2 (t) + Y 2 (t)] 1 / 2 From the instantaneous phase θ(t), the expression of the instantaneous frequency ω(t) can be further derived, that is Therefore, the analytic signal expression can be simplified to where a j (t, ω j ) represents the instantaneous amplitude of the j-th order IMF corresponding to the instantaneous frequency ω j at time t; Through the above analysis process, the expression of the Hilbert spectrum H(t,ω) characterizing the distribution characteristics of the acceleration signal X(t) in the time-frequency domain is finally derived, that is On this basis, by integrating H(t,ω) in time, the marginal spectrum of the acceleration time series X(t) can be obtained, and the expression of the marginal spectrum is

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