A method for determining the speed and attenuation coefficient of infrasonic waves in a non-saturated soil slope

Abstract

The application provides a method for determining the speed of sound and the attenuation coefficient of the infrasonic wave of a non-saturated soil slope, and the steps are as follows: 1. Based on the Biot-Geertsma low-frequency limit theory and the boundary layer viscous loss model, the hypothesis is obtained, and the basic parameters are obtained; 2. The Brutsaert modified equal strain model is used to determine the modulus of the three-phase composite fluid; 3. The equivalent density, dry skeleton modulus and other equivalent medium parameters are calculated; 4. The complex wave number is calculated after the viscous loss is corrected; 5. The speed of sound c and the attenuation coefficient alpha are determined by the real part and the imaginary part of the complex wave number respectively. The application can output the speed of sound and the attenuation coefficient synchronously by coupling the double model, can calibrate the slope instability early warning threshold more accurately, and provides a more comprehensive acoustic characteristic theoretical basis for the slope instability early warning; the three-phase coupling effect (skeleton deformation, fluid viscosity and gas-liquid interface effect) is fully considered, so that the acoustic characteristic parameters can truly reflect the internal physical state of the non-saturated soil, and high credibility support is provided for the monitoring data analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of engineering geology and disaster monitoring, and particularly relates to a method for determining the speed and attenuation coefficient of infrasound waves in unsaturated soil slopes. BACKGROUND

[0002] The instability and destruction of soil slopes (such as landslides and collapses) are frequent geological disasters in the fields of transportation and water conservancy, which not only damage roadbeds, dams and other engineering structures, but also can cause casualties and huge economic losses. Infrasound monitoring technology captures low-frequency acoustic signals (1-100 Hz) generated in the process of micro-damage and sliding evolution in soil, thereby identifying early signs of slope instability. This technology has the characteristics of long-distance propagation, wide monitoring range, strong anti-interference ability, and broad prospects in the field of soil slope disaster monitoring. However, the soil slopes in engineering are usually in a non-saturated state, which is essentially a pore medium coexisting with solid, liquid and gas phases. The propagation behavior of infrasound waves in this medium is affected by the coupling effect of the three phases, which makes it difficult to accurately quantify the core acoustic characteristic parameters (speed and attenuation coefficient) of infrasound waves, directly restricting the transformation of infrasound monitoring from laboratory research to engineering application.

[0003] Currently, some classic models and calculation methods have been developed for the study of acoustic wave propagation in unsaturated soil. The most representative of these include the Brutsaert static sound speed model, the Biot three-phase medium acoustic theory, and numerical simulation-based calculation schemes. For example, the Brutsaert model, as an early widely used three-phase medium sound speed calculation model, can only calculate the static sound speed and ignores the skeleton shear modulus and fluid viscous loss, making it impossible to output the attenuation coefficient. The single parameter cannot meet the demand for accurate monitoring, greatly limiting the engineering value of the model. At the same time, the existing acoustic characteristic calculation methods in the prior art rely on numerical simulation and require a large number of iterations and complex parameter inputs, such as local jet flow coefficients and turbulence correction terms. These methods cannot directly calculate acoustic characteristics from conventional soil force parameters, making them difficult to quickly apply in engineering sites. In addition, the existing models do not explicitly state the simplification conditions for low-frequency sound waves, resulting in a calculation error of more than 20% when high-frequency assumptions are used, which deviates greatly from the measured data.

[0004] In summary, the existing calculation of infrasound wave characteristics in unsaturated soil slopes has the core defects of single function (only calculating sound speed, no attenuation coefficient), non-closed calculation system (relying on complex parameters and iterations), and poor frequency adaptability (large error at low frequencies), which makes it difficult to quantify acoustic characteristics and obtain parameters in engineering.

[0005] Therefore, there is a need to provide an improved technical solution to address the above-mentioned deficiencies of the prior art. SUMMARY

[0006] The purpose of the present application is to provide a method for determining the speed and attenuation coefficient of infrasonic waves in unsaturated soil slopes, so as to solve or alleviate the problems existing in the prior art.

[0007] In order to achieve the above-mentioned purpose, the present application provides the following technical scheme:

[0008] The present application provides a method for determining the speed and attenuation coefficient of infrasonic waves in unsaturated soil slopes, which is based on the Biot-Geertsma low-frequency limit theory of three-phase porous medium and the boundary layer viscous loss model, and realizes the rapid and accurate determination of the speed and attenuation coefficient of infrasonic waves in unsaturated soil slopes by constructing a closed-form calculation link of composite fluid modulus→ equivalent medium parameter→ complex wave number→ speed / attenuation coefficient, and the steps are as follows:

[0009] Step one, based on the core applicable conditions of the Biot-Geertsma low-frequency limit theory of three-phase porous medium and the boundary layer viscous loss model, basic assumptions are proposed, and basic parameters are obtained through field tests and specification values;

[0010] Step two, based on the Brutsaert modified equal strain model, the three-phase composite fluid modulus is determined;

[0011] Step three, the equivalent medium parameters are calculated, including the equivalent density, dry skeleton bulk modulus, skeleton shear modulus and equivalent bulk modulus;

[0012] Step four, viscous loss correction is performed, and the complex wave number is calculated;

[0013] Step five, the speed c and attenuation coefficient a of infrasonic waves are determined; the speed c is calculated from the real part of the complex wave number, and the attenuation coefficient a is calculated from the imaginary part of the complex wave number.

[0014] Further, the basic assumptions include:

[0015] (1) The unsaturated soil slope shallow soil is regarded as a local homogeneous, transversely isotropic solid-liquid-gas three-phase porous medium, which is convenient for estimating the volume ratio and uniform pore size. However, if the site is obviously layered or there are large-scale heterogeneities (such as interlayer cracks), the model prediction may have errors;

[0016] (2) The frequency of the infrasonic wave satisfies 1Hz≤ ≤100Hz, which is much lower than the Biot characteristic frequency ( >1kHz), which meets the low-frequency limit assumption; under the low-frequency limit, the fluid inertia term can be ignored, so that the Biot equation is simplified to an algebraic form, thereby obtaining a closed-form analytical expression. However, if the actual frequency of the infrasonic wave is close to or exceeds , ignoring the fluid inertia term will result in significant errors;

[0017] (3) The soil body is in a small strain state (strain ε < 10 -4 ), the skeleton and the fluid only consider mass coupling, and ignore local jet flow, turbulence and surface tension effect. The small strain assumption, only considering mass coupling, ignoring local jet flow, turbulence, surface tension, can ensure linear elastic skeleton, avoid nonlinear flow dissipation term, and realize simplified model. However, when microcrack expansion, bubble vibration or liquid-gas interface dynamics (such as low saturation) appear before collapse, jet flow, turbulence and interface tension effect may be significant;

[0018] The slope characteristics suitable for the present application are: unsaturated soil subgrade slope which is still in the stable period or the initial stage of creep deformation, has not developed macroscopic through cracks or entered the large deformation failure stage, and the soil structure is relatively uniform. Such subgrade slope meets the premise of linear elastic skeleton and laminar flow, and meets the low frequency limit and small strain assumption of the present method.

[0019] Further, in step one, the basic parameters include skeleton parameters, fluid parameters, soil structure parameters, infrasonic wave parameters and water saturation; the skeleton parameters include skeleton solid bulk modulus, skeleton solid density, soil Poisson's ratio, skeleton viscoelastic loss factor; the fluid parameters include water bulk modulus, air bulk modulus, water density, air density, water dynamic viscosity, air dynamic viscosity; the soil structure parameters include soil porosity, soil absolute permeability; the infrasonic wave parameters include infrasonic wave angular frequency. The symbols, definitions, units and value ranges / sources of the basic parameters are shown in Table 1.

[0020] Table 1 Information table of basic parameters

[0021]

[0022] Further, in step two, the Brutsaert modified equal strain model (ignoring surface tension under low frequency limit) is used to directly calculate the complex fluid modulus through water and gas saturation and the bulk modulus of each phase, and the formula is as follows:

[0023] (1);

[0024] Physical rationality verification: when tends to 1 (complete saturation), the value of is close to ; when tends to 0 (complete dryness), the value of is close to , which is consistent with the physical test law.

[0025] Further, in step three, the calculation methods of each basic parameter are as follows:

[0026] Equivalent density : Considering the three-phase mass distribution of unsaturated soil, the equivalent density is the weighted sum of the densities of solid, water and gas according to the volume ratio, and the formula is as follows:

[0027] (2);

[0028] Dry skeleton bulk modulus : The engineering commonly used empirical formula (applicable to sandy soil, loess unsaturated soil) is used to directly calculate through the porosity, and the formula is as follows:

[0029] (3);

[0030] In the formula: is an empirical coefficient, and the sandy soil takes = 4, the loess soil takes = 3.5, and the cohesive soil takes = 3, which is calibrated by indoor compaction test.

[0031] Skeleton shear modulus G: Based on the elastic assumption under small strain, the formula is derived through the Poisson's ratio v of soil and the dry skeleton bulk modulus , as follows:

[0032] (4);

[0033] Equivalent bulk modulus : Based on the Biot-Geertsma low-frequency limit theory (ignoring the fluid inertia term), the coupling effect of dry skeleton and composite fluid is considered, and the formula is as follows:

[0034] (5);

[0035] Further, in step four, the calculation link of viscous loss correction and complex wave number is effective permeability correction → dynamic viscous length → dissipation function → complex density → complex fluid modulus → skeleton viscoelastic additional term → complex wave number, and the specific calculation steps are as follows:

[0036] Effective permeability correction: The effective permeability of water and gas in unsaturated soil changes with the saturation in a cubic relationship, and the formula is as follows:

[0037] (6);

[0038] In the formula: is the effective permeability of water phase, is the effective permeability of gas phase.

[0039] Dynamic viscous length : The thickness of the viscous boundary layer of fluid flowing in the pore, and the formula is as follows:

[0040] (7);

[0041] in, =w represents the aqueous phase. =a represents the gas phase.

[0042] Furthermore, by introducing boundary layer theory into fluid mechanics and cross-domain transplanting the Bessel function dissipation model, commonly used in high-frequency acoustics, into the analysis of low-frequency infrasound waves in soil and rock, the phase difference between the viscous drag and inertial effects of the fluid at the pore wall can be accurately captured. This allows for a theoretically analytical description of the infrasound energy attenuation mechanism in unsaturated soils. (Boundary layer dissipation function) When the pore size With viscous length When comparisons are made, boundary layer dissipation must be considered. Pore size. From absolute penetration rate With porosity Derivation:

[0043] (8);

[0044] The formula for the dissipation function is as follows:

[0045] (9);

[0046] In the formula, These are the zero-order and first-order Bessel functions of the first kind, respectively.

[0047] Complex density The Bessel function can automatically adjust the weights of fluid inertial forces and viscous forces according to the frequency. This makes the three-phase equivalent complex density considering viscous dissipation applicable not only to extremely low frequencies, but also automatically corrected at slightly higher frequencies, avoiding the calculation errors caused by the narrow frequency applicability of traditional models. The formula is as follows:

[0048] (10);

[0049] In the formula, The porosity of the soil. For water saturation, The angular frequency of infrasound. The density of the skeletal solid. The density of water, For the density of air, Let be the boundary layer dissipation function of the aqueous phase. Let be the boundary layer dissipation function of the gas phase.

[0050] Complex fluid modulus : The complex fluid modulus is corrected by considering the phase loss caused by fluid viscosity, avoiding the phase error caused by the simple linear resistance model, and the formula is as follows:

[0051] (11);

[0052] wherein, is the three-phase complex fluid modulus of unsaturated soil, is the viscous phase factor, is the angular frequency of infrasonic wave, is the dynamic viscosity of water, is the water saturation, is the dynamic viscosity of air, is the porosity of soil.

[0053] Skeleton viscoelastic additional term : The constant Q model suitable for low frequency acoustic wave is used to describe the energy loss caused by skeleton viscoelasticity, and the formula is as follows:

[0054] (12);

[0055] Complex wave number : The complex wave number of infrasonic wave propagating in unsaturated soil (the real part reflects the wave propagation speed, and the imaginary part reflects the energy attenuation), and the formula is as follows:

[0056] (13).

[0057] Further, in step five, the sound speed c is calculated from the real part of the complex wave number The formula is as follows:

[0058] (14);

[0059] Attenuation coefficient The imaginary part of the complex wave number is calculated, and the unit is converted to dB / m, and the conversion coefficient is 20 / ln10≈8.686, and the formula is as follows:

[0060] (15).

[0061] Further, the sound speed c and the attenuation coefficient a calculated by the method are used for the analysis of infrasonic wave monitoring data of unsaturated soil slope, including but not limited to:

[0062] (1) Inversion of key parameters of soil: by minimizing the residual error between the measured infrasonic wave speed and attenuation coefficient of the field and the calculated value of the method, the saturation and the porosity of the soil of the field slope can be inverted.

[0063] (2) Instability early warning threshold calibration: based on correlation with a (a sharp peak occurs when a = 0.85~0.9), combined with other sensor parameters (such as deformation), combined with the division of early warning threshold;

[0064] (3) Monitoring data verification: used to check the measurement accuracy of the field infrasound sensor, and to eliminate abnormal data.

[0065] The technical scheme of the present application has the following beneficial effects:

[0066] The present application couples the Biot-Geertsma low-frequency limit theory with the boundary layer viscous loss model, simultaneously outputs the sound speed and attenuation coefficient, and can more accurately calibrate the slope instability early warning threshold, providing a more comprehensive acoustic characteristic theoretical basis for slope instability early warning.

[0067] The input parameters of the calculation model established in the present application can be obtained through conventional tests, without numerical simulation iteration and complex parameter assumption, greatly improving the calculation efficiency and parameter acquisition convenience of the engineering site.

[0068] The present application clearly defines the simplified calculation conditions of low-frequency sound waves (1~100Hz), and clearly defines that the infrasound frequency f≤100Hz is much lower than the Biot characteristic frequency f c The low-frequency limit assumption, while introducing key correction terms such as pore fluid viscous boundary layer dissipation and skeleton viscoelastic loss, fully considers the three-phase coupling effect (skeleton deformation, fluid viscosity, gas-liquid interface action), ensures that the acoustic characteristic parameters can truly reflect the internal physical state of unsaturated soil, and provides high credibility support for monitoring data analysis.

[0069] The calculation logic of the present application does not need to rely on special hardware devices, and the closed formula can be integrated into the existing slope monitoring Internet of Things platform through simple programming, without the need for additional hardware modification of existing sensors (infrasound microphone, three-component detector), significantly reducing the application cost. BRIEF DESCRIPTION OF DRAWINGS

[0070] The drawings accompanying the specification of the present application serve to provide a further understanding of the present application, and the schematic embodiments of the present application and their descriptions serve to explain the present application and do not constitute an improper limitation on the present application. Among them:

[0071] Figure 1 is a schematic diagram of the size and monitoring position of the roadbed slope;

[0072] Figure 2 is a schematic diagram of the comparison of the infrasound sound speed between the calculated value and the measured value using the method of the present application;

[0073] Figure 3 ​is a schematic diagram of the infrasonic wave attenuation coefficient comparison between the calculated value and the measured value of the method of the present application. DETAILED DESCRIPTION

[0074] The present application will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0075] Taking an unsaturated soil slope of a highway subgrade in the south as an example, the slope height is 10 m, the slope ratio is 1:1.5, the slope top width is 15 m, the slope length is 18 m, and the longitudinal length of the test slope is selected as 50 m. A 10Hz three-component detector for assisting in capturing vibration signals is arranged at the top, bottom and middle of the slope, and a 1Hz infrasonic microphone for low-frequency signal collection is arranged at the center of the slope top.

[0076] A method for determining the infrasonic wave speed and attenuation coefficient of an unsaturated soil slope, specifically comprising the following steps:

[0077] Step one: obtaining basic parameters:

[0078] The following basic parameters are obtained through field tests and specification values:

[0079] Skeleton parameters: =2.6×10 10 Pa, =2650kg / m 3 , v=0.3, Q=25;

[0080] Fluid parameters: =2.2×10 9 Pa, =1.4×10 5 Pa, =1000kg / m 3 , =1.2kg / m 3 , =1.0×10 -3 Pa·s, =1.8×10 -5 Pa·s;

[0081] Soil structure parameters: The soil porosity is determined by the field static sounding test =0.35, and the soil permeability is determined by the indoor permeability test =5×10 -15 m 2 ;

[0082] Infrasonic wave parameters: =20Hz (field sensor working frequency), ;

[0083] Water saturation: = 0.7 (measured by field Time Domain Reflectometry, TDR).

[0084] Step two: Determine the modulus of the three-phase composite fluid :

[0085] ;

[0086] Step three: Calculation of the equivalent medium parameters:

[0087] Equivalent density p:

[0088]

[0089] Dry skeleton volume modulus :

[0090] Due to clay = 3.0, then:

[0091] ;

[0092] Thus, the skeleton shear modulus G is calculated:

[0093] ;

[0094] Therefore, the equivalent bulk modulus :

[0095] ;

[0096] Step four: Calculation of the viscous loss correction and complex wave number :

[0097] Effective permeability:

[0098] ;

[0099] ;

[0100] Dynamic viscous length:

[0101] ;

[0102] ;

[0103] Pore size:

[0104] ;

[0105] Dissipation function:

[0106] ;

[0107] ;

[0108] where the Bessel function is approximated as , ;

[0109] Similarly, ;

[0110] Complex density:

[0111] ;

[0112] Substituting the complex viscosity phase factor:

[0113] ;

[0114] Complex fluid modulus:

[0115] ;

[0116] Skeleton viscoelastic additional term:

[0117] ;

[0118] Substituting to obtain the complex wave number:

[0119]

[0120] Step five: determination of the infrasonic wave speed c and the attenuation coefficient a.

[0121] Speed of sound:

[0122] ;

[0123] Attenuation coefficient:

[0124] .

[0125] The present application can simultaneously calculate the infrasonic wave speed and the attenuation coefficient by using conventional soil mechanics parameters and closed-form formulas without complex numerical iteration by explicitly assuming the simplification conditions of low-frequency sound waves. The simplification calculation conditions of low-frequency sound waves (1-100 Hz) are explicitly assumed to reduce the complexity of the model and improve the reliability and accuracy of the calculation results. The quantitative calculation of the attenuation coefficient makes up for the defects of existing models that can only calculate the speed of sound, provides double-parameter support for soil parameter inversion, and promotes the large-scale and precise application of infrasonic monitoring technology in the early warning of unsaturated soil slope instability.

[0126] Test results verification:

[0127] (1) The infrasonic wave speed of the slope is measured by using a 1Hz infrasonic microphone and a 10Hz three-component geophone on site = 1910 m / s, attenuation coefficient = 3.24 x 10 -3 dB / m; the difference between the calculated value and the measured value of the subsonic wave speed and attenuation coefficient using the method of the application is 0.26%, 5.9%, respectively, the error is ≤10%, which meets the engineering precision requirements.

[0128] (2) In the laboratory, different soil porosities and different soil saturation slope standard subsonic signal attenuation test experiments were carried out, the test device and process: the test used a transparent organic glass model with a size (length x width x height) of 2.0 m x 1.0 m x 1.5 m for scale physical simulation. The test soil was taken from the silty clay of the above-mentioned field slope, and different working conditions of the soil sample were prepared by controlling the filling density and moisture content. The specific settings are as follows:

[0129] Model building: the layered compaction method was used to fill the slope body in the model groove, and the thickness of each layer was 20 cm. By strictly controlling the mass and volume of each layer of filling soil, the porosity of the soil body was accurately controlled;

[0130] Saturation control: the soil sample was dried and crushed before filling, the required water amount was calculated according to the designed saturation, and the soil was evenly sprayed, stirred and sealed for 24 hours to realize the control of the water saturation of the soil;

[0131] Signal testing: a low-frequency sound speaker was set at one end of the model groove as a sound source, and subsonic sensors were buried every 0.5 m along the wave propagation direction, and the signals were collected in the relatively static indoor environment to calculate the sound speed and attenuation coefficient under different working conditions. The soil porosity design has four gradients of 0.25, 0.3, 0.35 and 0.4, and the soil water saturation design has four gradients of 0.2, 0.3, 0.4 and 0.5.

[0132] The test results are shown in Tables 1, 2, Figure 2 , Figure 3 . Figure 2 , Figure 3 are the subsonic wave speed and subsonic wave attenuation coefficient comparison diagrams of the calculated value and the measured value using the method of the application, and Tables 2 and 3 are the original data of the calculated value and the measured value.

[0133] The test results show that:

[0134] With the increase of soil saturation, the sound speed slowly decreases, and the attenuation coefficient slowly increases; the water saturation increases by 0.1, the sound speed decreases by about 6 m / s; but when the water saturation ≤0.40, the change is gentle. With the increase of soil porosity, the sound speed decreases obviously, and the possible reason is that the structure is looser and the pore is larger; at the same time, the attenuation coefficient decreases, which is because the scattering decreases or the impedance matching improves.

[0135] Water saturation =0.50 and soil porosity ≥0.35: the sound speed suddenly drops from 2150 m / s to 1770-1940 m / s, and the attenuation coefficient increases from 0-0.008 dB / m to >0.011 dB / m, indicating that the system enters a nonlinear or resonance-dominated region, which may involve bubble vibration, local cavitation, or two-phase flow instability. The above rules fully comply with objective facts, indicating that this method has certain scientificity and can provide a theoretical basis for the large-scale and precise application of infrasound monitoring technology in the early warning of unsaturated soil slope instability.

[0136] Under different test conditions, the errors between the calculated infrasound wave speed and attenuation coefficient and the laboratory test results are all within 10%, fully meeting the engineering precision requirements.

[0137] Table 2 Comparison of calculated and measured infrasound wave speeds

[0138]

[0139] Table 3 Comparison of calculated and measured infrasound wave attenuation coefficients

[0140]

[0141] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for determining the infrasound velocity and attenuation coefficient of an unsaturated soil slope, characterized in that, Includes the following steps: Step 1: Based on the core applicability conditions of the Biot-Geertsma low-frequency limit theory and boundary layer viscous loss model for three-phase porous media, basic assumptions are proposed, and basic parameters are obtained through field tests and standard values. Step 2: Determine the modulus of the three-phase composite fluid based on the Brutsaert modified iso-strain model; Step 3: Calculate the equivalent medium parameters, including equivalent density, bulk modulus of the skeleton, shear modulus of the skeleton, and equivalent bulk modulus. Step 4: Perform viscous loss correction and calculate the complex wavenumber. The parameters to be calculated include effective permeability, dynamic viscous length, pore size, dissipation function, complex density, complex fluid modulus, skeleton viscoelastic addition, and complex wavenumber. The calculation sequence is as follows: effective permeability correction, dynamic viscous length, dissipation function, complex density, complex fluid modulus, skeleton viscoelastic addition, and complex wavenumber. The effective permeability is calculated using a cubic relational empirical model; the dynamic viscous length is calculated based on boundary layer theory; the dissipation function is calculated using a Bessel function dissipation model; viscous dissipation is introduced into the three-phase equivalent complex density for complex density calculation; the complex fluid modulus calculation considers phase loss caused by fluid viscosity; the skeleton viscoelastic addition is calculated using a constant Q model; and the complex wavenumber is calculated based on the complex density and complex fluid modulus using a standard acoustic wave propagation model. Complex density The calculation formula is as follows: ； In the formula, The porosity of the soil. For water saturation, The angular frequency of infrasound. The density of the skeletal solid. The density of water, For the density of air, Let be the boundary layer dissipation function of the aqueous phase. For the boundary layer dissipation function of the gas phase; Complex fluid modulus The calculation formula is as follows: ； In the formula, The modulus of a three-phase composite fluid for unsaturated soil. For viscous phase factor, The angular frequency of infrasound. The dynamic viscosity of water. For water saturation, The dynamic viscosity of air. Porosity of the soil; Complex wave number The calculation formula is as follows: ； In the formula, Equivalent bulk modulus Additional properties for skeletal viscoelasticity; Step 5: Determine the infrasound velocity c and the attenuation coefficient α; the velocity c is calculated from the real part of the complex wave number, and the attenuation coefficient α is calculated from the imaginary part of the complex wave number.

2. The method for determining the infrasound velocity and attenuation coefficient of unsaturated soil slopes according to claim 1, characterized in that: The basic assumptions include: (1) The shallow soil of the unsaturated soil slope is regarded as a local homogeneous, transversely isotropic solid-liquid-gas three-phase porous medium. (2) Infrasound frequency Satisfying 1Hz≤ ≤100Hz, far below Biot characteristic frequency This conforms to the low-frequency limit assumption; (3) The soil is in a low strain state, with strain ε < 10. -4 The skeleton and fluid are only considered in terms of mass coupling, and the effects of local jets, turbulence and surface tension are ignored.

3. The method for determining the infrasound velocity and attenuation coefficient of unsaturated soil slopes according to claim 1, characterized in that: In step one, the basic parameters include skeleton parameters, fluid parameters, soil structure parameters, infrasound parameters, and water saturation; the skeleton parameters include skeleton solid bulk modulus, skeleton solid density, soil Poisson's ratio, and skeleton viscoelastic loss factor; the fluid parameters include water bulk modulus, air bulk modulus, water density, air density, water dynamic viscosity, and air dynamic viscosity; the soil structure parameters include soil porosity and soil absolute permeability; and the infrasound parameters include infrasound angular frequency.

4. The method for determining the infrasound velocity and attenuation coefficient of unsaturated soil slopes according to claim 1, characterized in that: In step three, the equivalent density is the weighted sum of the densities of the solid, water, and gas phases according to their volume ratios; the bulk modulus of the skeleton is directly calculated using an empirical formula based on porosity; the shear modulus of the skeleton is derived from the Poisson's ratio of the soil and the bulk modulus of the skeleton; the equivalent bulk modulus is calculated based on the Biot-Geertsma low-frequency limit theory, ignoring the fluid inertia term and only considering the coupling effect between the skeleton and the composite fluid.

5. The method for determining the infrasound velocity and attenuation coefficient of unsaturated soil slopes according to claim 1, characterized in that: The infrasound velocity c and attenuation coefficient α obtained in step 5 are used for the analysis of infrasound monitoring data of unsaturated soil slopes, including at least one of the following: inversion of key soil parameters, calibration of instability early warning threshold, and verification of monitoring data.

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