A method for calculating soil damage in a loess slope model test

Abstract

The application discloses a method for calculating soil damage in a loess slope model test, and the method comprises the following steps: constructing a loess slope test model on a shaking table surface and installing multiple acceleration sensors; setting an acceleration sensor on the shaking table surface at random; connecting all the acceleration sensors with a computer; loading the model under different loading conditions; after each loading, subtracting the acceleration time sequence of the shaking table surface under the same loading condition from the acceleration time sequence recorded by different acceleration sensors to obtain the relative acceleration time sequence of different positions under a certain loading condition; obtaining the frequency spectrum curve of the relative acceleration transfer function of each point under different loading conditions; the frequency corresponding to the maximum peak value in the smoothed frequency spectrum curve is the first-order natural frequency; obtaining two frequency values corresponding to the 0.707 times amplitude of the amplitude corresponding to the first-order natural frequency, then obtaining the damping ratio of a certain position of the model, and then taking the first loading condition as a reference to calculate the relative damage of the soil under subsequent conditions; and the relative damage of the soil is represented by a normalized damping ratio. The calculation method can well determine the damage degree of the soil under the action of earthquake vibration before the slope model is destroyed.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of loess slope model test in the calculation method of soil damage quantity. BACKGROUND

[0002] Loess is a kind of special soil with extremely developed overhead pore microstructure, and the overhead pore structure formed by the mutual lapping of solid particles belongs to a metastable structure system, and the lapping of particles is mainly contact connection, so the dynamic strength is low, and under the action of reciprocating dynamic load such as seismic wave, it is easy to produce damage deformation. When the natural loess slope is subjected to the action of earthquake, the shear wave is transmitted from bottom to top in the slope body in the form of stress wave, causing tension, compression and shear action between different parts of solid medium. For weakly cemented loess with developed support pores, soil microstructure damage and damage deformation are caused under the action of low dynamic stress, thereby causing the change of slope vibration mode and dynamic response; and with the increase of seismic intensity, soil damage is aggravated, and finally leads to slope instability and failure; therefore, quantitative calculation of soil damage plays an important role in analyzing and studying the slope instability and failure mechanism and evaluating the stability of slope. In slope model test, generally, multiple loading conditions are set, and the method of gradually increasing seismic intensity is used to study the instability and failure phenomenon of slope; the increase of seismic intensity acting on rock and soil mass leads to the increase of residual deformation of soil, and the damping ratio of soil increases with the increase of residual deformation of soil. The increase of damping ratio indicates the increase of energy dissipation capacity of soil in the process of movement, which is the performance of the deterioration of soil mechanical properties. SUMMARY

[0003] The purpose of the present application is to provide a calculation method of soil damage quantity in loess slope model test based on the increase of damping ratio of soil with the increase of loading seismic intensity, to analyze and study the slope instability and failure mechanism and evaluate the stability of slope.

[0004] To achieve the above purpose, the technical solution adopted by the present application is as follows: a calculation method of soil damage quantity in loess slope model test, which is specifically performed according to the following steps:

[0005] 1) A loess slope test model is built on the shaking table table surface using loess; during the construction of the slope test model, a plurality of acceleration sensors are installed on the profile at the center position of the slope test model, and the plurality of acceleration sensors are arranged on the slope surface along the center profile of the slope test model;

[0006] 2) An acceleration sensor A0 is arranged at an arbitrary point on the shaking table table surface, and the acceleration sensor A0 is located outside the slope test model; all acceleration sensors are connected to a computer respectively;

[0007] 3) Start the shaking table and apply different loading conditions to the slope test model. After each loading condition, subtract the acceleration time history of the shaking table surface under the same loading condition from the acceleration time history recorded by the acceleration sensors at different locations in the slope test model. This yields the relative acceleration time history of different locations in the test model under a specific loading condition.

[0008] AR ij = AA ij - AA i0 (1)

[0009] (1) In the formula, i Represents the loading condition. j Represents position, AR ij It is the first i Operating conditions j Point relative acceleration, AA ij For the first i Operating conditions j Point absolute acceleration, AA i0 For the first i Absolute acceleration of the vibration table surface under operating conditions;

[0010] 4) Calculate the frequency spectrum of the relative acceleration transfer function at each point under different loading conditions, and smooth the frequency spectrum of the relative acceleration transfer function. The frequency corresponding to the peak value in the frequency spectrum of the smoothed relative acceleration transfer function is the natural frequency of the loess slope test model, while the frequency corresponding to the maximum peak value in the frequency spectrum is the first natural frequency f0.

[0011] The relative acceleration transfer function is: H a ( ω , z j )= G xy ( ω , z j ) / G xx ( ω (2)

[0012] (2) In the formula, G xx ( ω )for AR ij The self-power spectrum; G xy ( ω , zj )for AR ij The cross-power spectrum between the input acceleration on the shaking table surface and the input acceleration. z j for j Point location.

[0013] 5) Find the two frequency values ​​f1 and f2 corresponding to 0.707 times the amplitude of the first natural frequency f0, and then use the formula to calculate the damping ratio λ of a certain part of the slope test model:

[0014] λ=( f 2- f 1) / 2 f 0 (3)

[0015] Using the first loading condition as a baseline, the relative damage of the soil under subsequent loading conditions is calculated; the normalized damping ratio is used to characterize the relative damage L of the soil. di :

[0016] L di =(λ i -λ1) / (λ u -λ1) (4)

[0017] (4) In the formula, i Representing the loading condition, λ1 is the soil damping ratio of the first loading condition, λ u The soil damping ratio, λ, for the last working condition i It is the first i Soil damping ratio under working conditions.

[0018] This invention's quantitative calculation method is based on the phenomenon that the damping ratio of the soil in a slope model increases with increasing seismic intensity during slope model tests. Since the damping ratio of loess increases with the residual deformation of the slope model, changes in the damping ratio can reflect the degree of soil damage and deformation. In shaking table tests, the damping ratio consistently increases with seismic intensity, indicating that increased seismic intensity leads to increased residual deformation of the slope soil. Therefore, changes in the damping ratio of the shaking table model soil reflect, to some extent, the degree of damage to the slope soil. Using the first loading condition as a baseline and employing the normalized damping ratio to characterize the soil damage variable, the degree of soil damage under seismic loading before slope model failure can be effectively determined. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the slope model and the locations of the sensors within the model.

[0020] Figure 2 It is a time history curve of acceleration under 100 gal operating conditions.

[0021] Figure 3 It is the spectral curve diagram of the relative acceleration transfer function at point A5.

[0022] Figure 4 It is the variation diagram of the damping ratio with the dynamic load intensity.

[0023] Figure 5 It is the variation diagram of the soil damage amount at point A5 with the dynamic load intensity.

[0024] Figure 1 In the figure: 1. Shaking table tabletop. Specific implementation manner

[0025] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0026] The present invention provides a method for calculating the soil damage amount in a loess slope model test, which is specifically carried out according to the following steps:

[0027] 1) Build a Figure 1 loess slope test model as shown on the shaking table tabletop 1. This test model is composed of a first cuboid, a quadrangular prism, and a second cuboid arranged in sequence. The quadrangular prism is horizontally arranged, the bottom surface of the quadrangular prism is a right trapezoid, the right-angled waist of the right trapezoid is located on the shaking table tabletop 1, the side surface where the upper base is located in the right trapezoid is coplanar with one side surface of the first cuboid, and the side surface where the lower base is located in the right trapezoid is coplanar with one side surface of the second cuboid; the included angle between the inclined waist and the horizontal plane in the right trapezoid is α;

[0028] During the construction of the slope test model, a plurality of acceleration sensors are installed on the cross-section at the center position of the slope test model. The plurality of acceleration sensors are arranged along the center cross-section of the slope test model within a certain depth range below the slope surface, which can ensure that during the failure process of the slope under seismic dynamic action, the damage evolution information of the soil within the potential sliding range can be monitored.

[0029] The arrangement of the multiple accelerometers is as follows: Accelerometer A1 is installed on the coplanar surface of the first cuboid and the square prism, with a distance of 250mm between accelerometer A1 and the vibration table surface 1. Accelerometer A5 is installed on the coplanar surface of the square prism and the second cuboid, with a distance of 50mm between accelerometer A5 and the top surface of the second cuboid. Accelerometers A2, A3, and A4 are sequentially arranged within the test model between accelerometers A1 and A5 along the direction from accelerometer A1 to accelerometer A5. The line connecting accelerometers A1, A2, A3, A4, and A5 is parallel to the inclined plane of the square prism. Accelerometers B5, C5, D5, and [other accelerometers] are coaxially and equidistantly arranged below accelerometer A5 along the direction away from accelerometer A5. Accelerometer E5; Accelerometers B4, C4, and D4 are coaxially and equidistantly arranged below accelerometer A4, moving away from accelerometer A3; Accelerometers B3 and C3 are coaxially and equidistantly arranged below accelerometer A3, moving away from accelerometer A3; Accelerometer B2 is coaxially arranged below accelerometer A2; The line connecting accelerometers A1, B2, C3, D4, and E5 is parallel to the vibration table surface 1; The line connecting accelerometers A2, B3, C4, and D5 is parallel to the vibration table surface 1; The line connecting accelerometers A3, B4, and C5 is parallel to the vibration table surface 1; The line connecting accelerometers A4 and B5 is parallel to the vibration table surface 1.

[0030] 2) Select any point on the shaking table surface 1 and set up the acceleration sensor A0. The acceleration sensor A0 is located outside the slope test model.

[0031] Connect all acceleration sensors to the computer individually;

[0032] For example, any accelerometer placement point can be selected within the slope test model as the calculation point; in this example, the placement point of accelerometer A5 is selected as the calculation point.

[0033] 3) Start the shaking table and apply different loading conditions to the slope test model. After each loading condition, subtract the acceleration time history (absolute acceleration) sequence recorded by the acceleration sensors at different locations in the slope test model from the acceleration time history (absolute acceleration) sequence of the shaking table surface 1 under the same loading condition to obtain the relative acceleration time history of different locations in the test model under a certain loading condition:

[0034] AR ij = AA ij - AA i0 (1)

[0035] (1) In the formula, i Represents the loading condition. j Represents position, AR ij It is the first i Operating conditions j Point relative acceleration, AA ij For the first i Operating conditions j Point absolute acceleration, AA i0 For the first i Absolute acceleration of the vibration table surface under operating conditions;

[0036] Continuing the previous example, load conditions of 100 gal, 200 gal, 400 gal, 700 gal, and 1000 gal are applied respectively. The acceleration time history of the shaking table surface under the same loading condition is subtracted from the acceleration time history of point A5 under each different loading condition to obtain the relative acceleration time history of point A5 under different loading conditions, as shown below. Figure 2 .

[0037] 4) Obtain the spectrum curves of the relative acceleration transfer function at each point under different loading conditions, and smooth the spectrum curves of the relative acceleration transfer function; the frequency corresponding to the peak value in the spectrum curve of the smoothed relative acceleration transfer function is the natural frequency of the loess slope test model, and the frequency corresponding to the maximum peak value in the spectrum curve is the first-order natural frequency f0 (JIANG Liangwei, YAO Lingkan, Wu Wei, XU Guangxing. Application of Transfer Function Analysis on Slope Shaking Tabie Model Test[J]. Rock and Soil Mechanics,2010,(05):1368-1374).

[0038] The relative acceleration transfer function is: H a ( ω , z j )=G xy ( ω , z j ) / G xx ( ω (2)

[0039] (2) In the formula, G xx ( ω )for AR ij The self-power spectrum (calculated based on a general function); G xy ( ω , z j )for AR ij The cross-power spectrum of the input acceleration on the shaking table surface (calculated based on a general function); z j for j Point location.

[0040] Continuing the previous example, the first-order natural frequencies f0 of point A5 under loading conditions of 100 gal, 200 gal, 400 gal, and 700 gal are calculated to be 31.25 Hz, 31 Hz, 29.25 Hz, and 26 Hz, respectively. Since a large tensile crack appears at point A5 on the slope shoulder of the slope test model under the 1000 gal loading condition, macroscopic phenomena indicate that the slope test model has become unstable and failed. Furthermore, the relative acceleration transfer function spectrum curve no longer shows a clear peak value, such as... Figure 3 Therefore, the damping ratio at point A5 on the slope shoulder under the 1000gal loading condition is no longer required.

[0041] 5) Find the two frequency values ​​f1 and f2 corresponding to 0.707 times the amplitude of the first natural frequency f0, and then use the formula to calculate the damping ratio λ of a certain part of the slope test model:

[0042] λ=( f 2- f 1) / 2 f 0 (3)

[0043] Using the first loading condition (the loading condition with the smallest value) as a baseline, calculate the relative damage of the soil for subsequent loading conditions; the normalized damping ratio is used to characterize the relative damage of the soil, as shown in the following formula:

[0044] L di =(λ i -λ1) / (λ u -λ1) (4)

[0045] (4) In the formula, i Representing the loading condition, λ1 is the soil damping ratio of the first loading condition, λ u The soil damping ratio, λ, for the last working condition i It is the first i Soil damping ratio under working conditions, L di Defined as the first soil mass i The relative damage amount under the working condition.

[0046] Applying formula (3), the damping ratios at point A5 under loading conditions ranging from 100 gal to 700 gal are found to be 0.21, 0.23, 0.26, and 0.41, respectively. Figure 4 As can be seen, the damping ratio changes little within the seismic intensity of 200 gal, because the first load condition has a loading intensity of 100 gal, and the soil is approximately considered to be undamaged.

[0047] In the shaking table model test, with the increase of dynamic load intensity, the amplitude of the transfer function spectrum, the natural frequency, and the damping ratio of different parts of the slope all change accordingly. The damping ratio of loess increases with the increase of residual deformation, and the change of damping ratio can reflect the degree of damage deformation of the soil. In the shaking table test, the damping ratio shows a regular increase with the intensity of the ground motion. The increase of the ground motion intensity will lead to the increase of the residual deformation of the slope soil. Therefore, the change of the damping ratio of the soil in the shaking table model reflects the degree of damage of the slope soil to a certain extent. Therefore, taking the first loading condition as the benchmark, the normalized damping ratio is used to characterize the damage variable of the soil. From formula (4) and Figure 5 As can be seen, the soil damage increases with the intensity of the ground motion. When there is no damage, the soil damage is 0, and when the soil fails, the damage is 1. Formula (4) can be used to determine the degree of soil damage under ground motion before the slope model fails.

[0048] Figure 4 and Figure 5 The horizontal axis represents the seismic intensity, with the unit being g, where 1 g = 981 gal.

Claims

1. A method for calculating soil damage in a loess slope model test, characterized in that, The calculation method is performed in the following steps: 1) Construct a loess slope test model on the shaking table using loess; during the construction of the slope test model, install multiple acceleration sensors on the profile at the center of the slope test model, and arrange these multiple acceleration sensors along the central profile of the slope test model below the slope surface; 2) Select any point on the shaking table to set up acceleration sensor A0. Acceleration sensor A0 is located outside the slope test model; connect all acceleration sensors to the computer. 3) Start the shaking table and apply different loading conditions to the slope test model. After each loading condition, subtract the acceleration time history of the shaking table surface under the same loading condition from the acceleration time history recorded by the acceleration sensors at different locations in the slope test model. This yields the relative acceleration time history of different locations in the test model under a specific loading condition. AR ij = AA ij － AA i0 （1） (1) In the formula, i Represents the loading condition. j Represents position, AR ij It is the first i Operating conditions j Point relative acceleration, AA ij For the first i Operating conditions j Point absolute acceleration, AA i0 For the first i Absolute acceleration of the vibration table surface under operating conditions; 4) Calculate the frequency spectrum of the relative acceleration transfer function at each point under different loading conditions, and smooth the frequency spectrum of the relative acceleration transfer function. The frequency corresponding to the peak value in the frequency spectrum of the smoothed relative acceleration transfer function is the natural frequency of the loess slope test model, while the frequency corresponding to the maximum peak value in the frequency spectrum is the first natural frequency f0. The relative acceleration transfer function is: H a ( ω , z j )= G xy ( ω , z j ) / G xx ( ω (2) (2) In the formula, G xx ( ω )for AR ij The self-power spectrum; G xy ( ω , z j )for AR ij The cross-power spectrum between the input acceleration on the shaking table surface and the input acceleration. z j for j Point location; 5) Find the two frequency values ​​f1 and f2 corresponding to 0.707 times the amplitude of the first natural frequency f0, and then use the formula to calculate the damping ratio λ of a certain part of the slope test model: λ=( f 2- f 1) / 2 f 0 (3) Using the first loading condition as a baseline, the relative damage of the soil under subsequent loading conditions is calculated; the normalized damping ratio is used to characterize the relative damage L of the soil. di : L di =(λ i -λ1) / (λ u -λ1) (4) (4) In the formula, i Representing the loading condition, λ1 is the soil damping ratio of the first loading condition, λ u The soil damping ratio, λ, for the last working condition i It is the first i Soil damping ratio under working conditions.

2. The method for calculating soil damage in a loess slope model test as described in claim 1, characterized in that, In step 1), the constructed slope test model consists of a first cuboid, a quadrangular prism, and a second cuboid arranged sequentially. The quadrangular prism is horizontally positioned, and its base is a right trapezoid. The right-angled leg of the right trapezoid is located on the vibration table surface. The side of the upper base of the right trapezoid is coplanar with one side of the first cuboid, and the side of the lower base of the right trapezoid is coplanar with one side of the second cuboid.

3. The method for calculating soil damage in a loess slope model test as described in claim 2, characterized in that, Multiple acceleration sensors are arranged within the slope test model: Acceleration sensor A1 is installed on the coplanar surface of the first cuboid and the quadrangular prism; acceleration sensor A5 is installed on the coplanar surface of the quadrangular prism and the second cuboid; acceleration sensors A2, A3, and A4 are sequentially arranged within the test model between acceleration sensors A1 and A5 along the direction from acceleration sensor A1 to acceleration sensor A5; the line connecting acceleration sensors A1, A2, A3, A4, and A5 is parallel to the inclined plane of the quadrangular prism; acceleration sensors B5, C5, D5, and E5 are sequentially and equidistantly arranged coaxially below acceleration sensor A5 along the direction away from acceleration sensor A5; and acceleration sensors B5, C5, D5, and E5 are arranged along the direction away from acceleration sensor A4... Accelerometers B4, C4, and D4 are coaxially and equidistantly arranged below accelerometer A4; accelerometers B3 and C3 are coaxially and equidistantly arranged below accelerometer A3, away from it; accelerometer B2 is coaxially arranged below accelerometer A2; the line connecting accelerometers A1, B2, C3, D4, and E5 is parallel to the vibration table surface; the line connecting accelerometers A2, B3, C4, and D5 is parallel to the vibration table surface; the line connecting accelerometers A3, B4, and C5 is parallel to the vibration table surface; the line connecting accelerometers A4 and B5 is parallel to the vibration table surface.

4. The method for calculating soil damage in a loess slope model test as described in claim 3, characterized in that, The distance between accelerometer A1 and the vibration table surface is 250mm, and the distance between accelerometer A5 and the top surface of the second cuboid is 50mm.

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