Method for calculating acoustic-electric response characteristics of loess under different water contents

Abstract

The invention discloses a method for calculating acoustic-electric response characteristics of loess under different water contents. The method comprises the following steps: solving soil saturation; establishing a fitting relation between the resistivity and the saturation of the soil body based on the solved saturation of the soil body; based on a classic soil sound wave propagation theory, a theoretical formula of the propagation speed of sound waves in soil is obtained; and correcting the soil body wave velocity propagation theoretical model to obtain a corrected soil body wave velocity propagation model. According to the method, a correction relational expression among the wave velocity, the water content and the saturation is established, and a theoretical basis is provided for stability research of the loess slope.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering, and in particular relates to a method for calculating the acoustic-electric response characteristics of loess under different water contents. Background Art

[0002] In geotechnical engineering, the presence of water can easily induce engineering geological disasters such as slope and roadbed instability. For the determination of soil moisture content, traditional methods include specific gravity method, moisture sensor method, etc., which are cumbersome and cause great disturbance to the soil, and have certain limitations. Wave velocity and resistivity are commonly used indicators in geophysical detection, and are also basic physical properties of soil. At the same time, both are related to the porosity and moisture content of soil. Therefore, the information of physical and mechanical parameters such as electricity and magnetism in soil can be measured by geophysical methods to indirectly obtain soil moisture content. In recent years, researchers have applied resistivity and wave velocity in new forms, such as obtaining one of the parameters to infer another property to reduce the cost of geophysical detection, or jointly inverting wave velocity detection and electrical detection data to improve the accuracy and reliability of geophysical detection results. For example, in well logging engineering, resistivity and acoustic wave velocity complement each other to make up for the lack of a single parameter. Wave velocity is introduced in geotechnical engineering survey to overcome the multi-solution problem in the inversion process of resistivity detection method. Therefore, it is of great significance to the engineering site to reveal the changing patterns of soil wave velocity and resistivity with water content, study the acoustic-electric response characteristics of unsaturated loess under different water contents, and construct a relationship model between soil wave velocity and resistivity with water content as the link. Summary of the invention

[0003] The main purpose of the present invention is to provide a method for calculating the acoustic-electric response characteristics of loess under different water contents. The method establishes a corrected relationship between wave velocity, water content and saturation, providing a theoretical basis for the study of the stability of loess slopes.

[0004] To this end, the present invention provides a method for calculating the acoustic-electric response characteristics of loess at different moisture contents, comprising the following steps:

[0005] S1. Solve the soil saturation S

[0006] S2. Based on the obtained soil saturation, establish the fitting relationship between soil resistivity and saturation

[0007]

[0008] Where: ρ—resistivity;

[0009] k—density;

[0010] G—relative density of soil;

[0011] ρ dmax—maximum dry density;

[0012] S3. Based on the classical soil sound wave propagation theory, the theoretical formula for the propagation speed of sound waves in soil is obtained.

[0013]

[0014] The expression of Z is:

[0015]

[0016] Where: ψ is only related to soil type and can be expressed as ψ = a 1 / 2 b 1 / 3 ;

[0017] a—soil acoustic constant, ranging from [0, 1];

[0018] b—soil acoustic constant, the value range is [10 -12 , 10 -10 ];

[0019] ρ tot - Soil bulk density:

[0020] υ c - sound waves;

[0021] p e — effective stress of soil;

[0022] Z—soil acoustic calculation coefficient;

[0023] k e —effective bulk modulus;

[0024] When the soil moisture content is evenly distributed, Z does not change with the change of saturation S and is very close to 1. Only when the saturation S reaches 1, that is, the soil is completely saturated, will Z suddenly increase. Therefore, the theoretical formula for the propagation speed of sound waves in unsaturated soil with evenly distributed moisture content can be simplified to:

[0025]

[0026] S4. Modify the theoretical model of soil wave velocity propagation to obtain the modified soil wave velocity propagation model

[0027] The wave velocity test was carried out on loess with different water contents to obtain the variation law of longitudinal wave velocity with water content, and the water content and water saturation threshold value S corresponding to the inflection point when the longitudinal wave velocity changes from rapid decline to rapid rise were obtained. t ;

[0028] Based on the water saturation threshold S t, the calculation formula of the variation law of wave velocity in the rapid rising section with water content is corrected, and the corrected formula is:

[0029]

[0030] Where: S t —water saturation threshold;

[0031] v ct —wave velocity corresponding to the saturation threshold value;

[0032] v cs —wave velocity at full saturation;

[0033] Therefore, with the increase of water content and saturation, the modified expression of soil sample wave velocity can be expressed as:

[0034]

[0035] Specifically, according to the calculation formula of saturation S:

[0036]

[0037] In the formula, ω is soil moisture content;

[0038] G—relative density of soil;

[0039] e 0 —Porosity ratio of soil;

[0040] By the porosity ratio e 0 , relative density G, moisture content ω, dry density ρ d And the relationship between the density k:

[0041]

[0042] ρ d =kρ dmax

[0043] According to the above relationship, we can get:

[0044]

[0045] Specifically, the soil bulk density calculation expression is:

[0046] ρ tot =(1-f)ρ s +fSρ ω

[0047] In the formula, ρ s —Soil solid particle density;

[0048] ρ ω —Density of water in the soil.

[0049] Specifically, the calculation formula for effective stress of soil is:

[0050] P e =P t -S.P. c

[0051] Where P t — total soil pressure;

[0052] P c —pore water pressure;

[0053] P t =ρ tot ·g·H

[0054] Where, g is the acceleration due to gravity;

[0055] H—Soil depth.

[0056] Specifically, the expression of pore water pressure is:

[0057]

[0058] In the formula, α, n, m = 1-1 / n - only related to soil type;

[0059] S e —Effective saturation, which can be obtained as follows:

[0060]

[0061] In the formula, the total saturation S tot It can be expressed by porosity f, residual saturation S r is a constant that depends only on the soil type.

[0062] Specifically, if water is uniformly distributed in the soil, the bulk modulus is expressed by:

[0063]

[0064] On the contrary, when water is unevenly distributed in the soil, the bulk modulus is expressed as:

[0065] k e =S·k ω +k α (1-S)

[0066] k ω and k α are the bulk moduli of water and air, respectively.

[0067] Specifically, according to the derived expression of the relationship between resistivity and saturation, we can obtain:

[0068]

[0069] By replacing the saturation S in the soil sample wave velocity correction expression with that in the above formula, the quantitative relationship between wave velocity and resistivity can be obtained.

[0070] Compared with the prior art, the present invention has the following beneficial effects: based on the assumption of the distribution state of pore water in loess samples, a revised relationship between wave velocity and moisture content and saturation is proposed, and compared with the experimental measured data, the accuracy of the revised formula is verified, which can provide support for the stability research of loess slopes, and also provide a theoretical basis for the determination of soil moisture content and the prevention and control of soil disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0072] Figure 1 is a curve of longitudinal wave velocity changing with water content provided by an embodiment of the present invention;

[0073] Figure 2 It is a comparison between the wave velocity theoretical calculation and the test results provided by the embodiment of the present invention;

[0074] Figure 3 The modified wave velocity theoretical calculation and test result comparison provided by the embodiment of the present invention are shown;

[0075] Figure 4 The figure is a comparison between the experimental results and the calculated results of the relationship between the longitudinal wave velocity and the resistivity provided by the embodiment of the present invention. DETAILED DESCRIPTION

[0076] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0077] A method for calculating the acoustic-electric response characteristics of loess at different moisture contents comprises the following steps:

[0078] S1. Solve the soil saturation S

[0079] Saturation describes the degree to which the pores in the soil are filled with water. It is an important characteristic of unsaturated soil and can be calculated through the soil moisture content and porosity. In order to study the relationship between the resistivity and longitudinal wave velocity of unsaturated loess, saturation is introduced for analysis. According to the calculation formula of saturation S:

[0080]

[0081] In the formula, ω is soil moisture content;

[0082] G—relative density of soil;

[0083] e 0 —Porosity ratio of soil;

[0084] By the porosity ratio e 0 , relative density G, moisture content ω, dry density ρ d And the relationship between the density k:

[0085]

[0086] ρ d =kρ dmax (3)

[0087] According to the above relationship, we can get:

[0088]

[0089] S2. Based on the obtained soil saturation, establish the fitting relationship between soil resistivity and saturation

[0090] From formula (4), it can be obtained that when the dry density is constant, as the water content increases, the saturation of the soil sample increases accordingly. According to the above relationship, when the dry density and compactness are constant, the change in saturation can be used to reflect the change in the water content of the reshaped loess. The fitting relationship between the resistivity and saturation of loess can be expressed by formula (5).

[0091]

[0092] Where: ρ—resistivity;

[0093] k—density;

[0094] G—relative density of soil;

[0095] ρ dmax —maximum dry density;

[0096] S3. Based on the classic soil sound wave propagation theory, the theoretical formula for the propagation speed of sound waves in soil is obtained:

[0097]

[0098] In the formula, ψ- is only related to the soil type and can be expressed as ψ = a 1 / 2 b 1 / 3 ;

[0099] a—soil acoustic constant, the value range is [0, 1], and it is taken as 1 in this paper;

[0100] b—soil acoustic constant, the value range is [10 -12 , 10 -10 ], in this paper we take 10 -12 ;

[0101] ρ tot —The bulk density of soil is given by formula (10):

[0102] ρ tot =(1-f)ρ s +fSρ ω (11)

[0103] In the formula, ρ s —Soil solid particle density;

[0104] ρ ω —The density of water in the soil is constant, so ρ tot Depends on soil saturation;

[0105] p e —The effective stress of soil, taking into account the effects of water and air, reflects the ability of soil to resist compression and shear, and can be expressed as:

[0106] P e =P t -χ·P c -P a (12)

[0107] Where P t — total soil pressure;

[0108] P c —pore water pressure;

[0109] P a —pore air pressure;

[0110] Since the air has little influence, P a can be ignored. χ is a parameter closely related to soil saturation and can be approximated as saturation S. Therefore, formula (12) can be simplified as follows:

[0111] P e =P t -S.P. c (13)

[0112] Where P t and Pc It can be obtained from formula (14):

[0113] P t =ρ tot ·g·H (14)

[0114] Where, g is the acceleration due to gravity;

[0115] H—soil depth;

[0116] According to Van Genuchten's theoretical model, the pore water pressure can be expressed by equation (15):

[0117]

[0118] In the formula, α, n, m = 1-1 / n - only related to soil type;

[0119] S e —Effective saturation, which can be obtained from formula (16):

[0120]

[0121] In the formula, the total saturation S tot It can be expressed by porosity f, residual saturation S r is a constant that depends only on the soil type, so the effective saturation depends on S.

[0122] Z is affected by the water distribution in the soil and is expressed as:

[0123]

[0124] From formula (17), we can get that, except for the constant b and the effective stress P e In addition, Z also depends on the effective bulk modulus k e , let k ω and k α are the bulk moduli of water and air respectively. If water is evenly distributed in the soil, the bulk modulus can be expressed by formula (18):

[0125]

[0126] On the contrary, when water is unevenly distributed in the soil, the bulk modulus is expressed as:

[0127] k e =S·k ω +k α (1-S) (19)

[0128] When the soil moisture content is evenly distributed, Z does not change with the change of saturation S and is very close to 1. Only when the saturation S reaches 1, that is, the soil is completely saturated, will Z suddenly increase. Therefore, the theoretical formula for the propagation speed of sound waves in unsaturated soil with evenly distributed moisture content can be simplified to:

[0129]

[0130] In order to verify the accuracy of the model, wave velocity tests were carried out on loess with different moisture contents to obtain the variation law of longitudinal wave velocity with moisture content, such as Figure 1 As shown in the figure, the water content and water saturation threshold S corresponding to the inflection point when the longitudinal wave velocity changes from rapid decline to rapid rise are obtained. t ; From formula (20), we can see that in unsaturated soil, as the water content increases, the wave velocity shows a downward trend, which is basically consistent with the downward section of the test results, such as Figure 2 This shows that in the stage where the wave velocity decreases with the water content, the theoretical value and the measured value are in good agreement, and the pore fluid is approximately evenly distributed in the soil sample.

[0131] In the rapid rise stage, the measured wave velocity increases rapidly with the increase of water content, while the theoretical value decreases slowly with the increase of water content. When the water content reaches 30%, that is, when the soil sample reaches saturation, the wave velocity suddenly increases, and there is a big difference in the change rules of the two.

[0132] The reason why there is a big difference between the theoretical value and the measured value in the rapid rise of wave velocity is that the water content is high in this stage. Due to gravity and other reasons, the fluid is not evenly distributed in the soil sample, which does not meet the premise assumptions of the theoretical formula. Because the theoretical model is based on the complete uniform distribution of the fluid in the soil sample, when the saturation reaches 1, the fluid in the soil sample is only water, no gas, the fluid bulk modulus suddenly increases, and the effective bulk modulus k of the soil sample e The Z value increases accordingly, causing the wave velocity to rise rapidly. When the soil sample is fully saturated, the measured wave velocity is much smaller than the theoretical value.

[0133] S4. Modify the theoretical model of soil wave velocity propagation to obtain the modified soil wave velocity propagation model

[0134] like Figure 1 As shown, in this embodiment, when the moisture content of the soil sample reaches 20%, that is, when the saturation threshold value of 0.72 is reached, the pore fluid in the soil sample is not evenly distributed under the action of gravity, etc. At this time, the soil sample can be regarded as composed of two soil samples with different saturations, namely, fully saturated and saturated 0.72. Therefore, the wave velocity can be expressed by the following formula:

[0135]

[0136] Where: S t —water saturation threshold;

[0137] v ct —wave velocity corresponding to the saturation threshold value;

[0138] v cs —wave velocity at full saturation;

[0139] Therefore, with the increase of water content and saturation, the modified expression of soil sample wave velocity can be expressed as:

[0140]

[0141] The comparison between the corrected theoretical calculation results and the experimental results is shown in Figure 3 It can be seen that the corrected theoretical calculation results are closer to the experimental results and can well describe the variation law of the wave velocity of the loess sample in the second stage.

[0142] According to the relationship between resistivity and saturation derived in step S2, we can obtain:

[0143]

[0144] By replacing the saturation S in equation (20) with equation (23), the quantitative relationship between wave velocity and resistivity can be obtained.

[0145] In order to verify the universality of the revised formula proposed in this paper, another group of loess samples were taken to test their resistivity and wave velocity corresponding to different moisture contents under the same dry density. At the same time, the wave velocity value was calculated by formula (22). The calculated results were compared with the test results. Figure 4 The results show that the calculated values ​​are consistent with the experimental results.

[0146] Through the above comparison, it can be seen that when the moisture content of loess is low, the change of resistivity can well reflect the change of moisture content; but when the moisture content is high, the resistivity tends to be stable, and the moisture content can be analyzed by comprehensively analyzing the wave velocity change trend to avoid the limitation of single factor judgment. With moisture content and saturation as a bridge, the relationship between loess wave velocity and resistivity is obtained. The calculation result of this relationship is basically consistent with the test data, which can provide support for the stability study of loess slopes, and also provide a theoretical basis for the determination of soil moisture content and soil disaster prevention and control. .

[0147] The above embodiments are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. The obvious changes or modifications derived therefrom are still within the scope of protection of the present invention.

Claims

1. A method for calculating the acoustic-electric response characteristics of loess at different moisture contents, characterized in that: The steps include: S1. Solve the soil saturation S S2. Based on the obtained soil saturation, establish the fitting relationship between soil resistivity and saturation Where: ρ—resistivity; k—density; G—relative density of soil; ρ dmax —maximum dry density; S3. Based on the classical soil sound wave propagation theory, the theoretical formula for the propagation speed of sound waves in soil is obtained. The expression of Z is: Where: ψ is only related to soil type and can be expressed as ψ = a 1 / 2 b 1 / 3 ; a—soil acoustic constant, ranging from [0, 1]; b—soil acoustic constant, the value range is [10 -12 , 10 -10 ]; ρ tot - Soil bulk density: υ c — sound waves; p e — effective stress of soil; Z—soil acoustic calculation coefficient; k e —effective bulk modulus; When the soil moisture content is evenly distributed, Z does not change with the change of saturation S and is very close to 1. Only when the saturation S reaches 1, that is, the soil is completely saturated, will Z suddenly increase. Therefore, the theoretical formula for the propagation speed of sound waves in unsaturated soil with evenly distributed moisture content can be simplified to: S4. Modify the theoretical model of soil wave velocity propagation to obtain the modified soil wave velocity propagation model The wave velocity test was carried out on loess with different water contents to obtain the variation law of longitudinal wave velocity with water content, and the water content and water saturation threshold value S corresponding to the inflection point when the longitudinal wave velocity changes from rapid decline to rapid rise were obtained. t ; Based on the water saturation threshold S t , the calculation formula of the variation law of wave velocity in the rapid rising section with water content is corrected, and the corrected formula is: Where: S t —water saturation threshold; v ct —wave velocity corresponding to the saturation threshold value; v cs —wave velocity at full saturation; Therefore, with the increase of water content and saturation, the modified expression of soil sample wave velocity can be expressed as:

2. The method for calculating the acoustic-electric response characteristics of loess at different moisture contents according to claim 1 is characterized in that: According to the calculation formula of saturation S: In the formula, ω is soil moisture content; G—relative density of soil; e0—soil porosity ratio; From the porosity e0, relative density G, water content ω, dry density ρ d And the relationship between the density k: r d =kρ dmax According to the above relationship, we can get:

3. The method for calculating the acoustic-electric response characteristics of loess under different moisture contents according to claim 2 is characterized in that: The calculation expression of soil bulk density is: r tot =(1-f)ρ s +fSρ ω In the formula, ρ s —Soil solid particle density; ρ ω —Density of water in the soil.

4. The method for calculating the acoustic-electric response characteristics of loess at different moisture contents according to claim 3 is characterized in that: The formula for calculating the effective stress of soil is: P e =P t -S·P c Where P t — total soil pressure; P c —pore water pressure; P t =ρ tot ·g·H Where, g is the acceleration due to gravity; H—Soil depth.

5. The method for calculating the acoustic-electric response characteristics of loess at different moisture contents according to claim 4 is characterized in that: The expression of pore water pressure is: In the formula, α, n, m = 1-1 / n - only related to soil type; S e —Effective saturation, which can be obtained as follows: In the formula, the total saturation S tot It can be expressed by porosity f, residual saturation S r is a constant that depends only on the soil type.

6. The method for calculating the acoustic-electric response characteristics of loess at different moisture contents according to claim 5 is characterized in that: If the water is uniformly distributed in the soil, the bulk modulus is given by: On the contrary, when water is unevenly distributed in the soil, the bulk modulus is expressed as: k e =S·k ω +k α (1-S) k ω and k α are the bulk moduli of water and air, respectively.

7. The method for calculating the acoustic-electric response characteristics of loess at different moisture contents according to any one of claims 1 to 5, characterized in that: According to the derived expression of the relationship between resistivity and saturation, we can obtain: By replacing the saturation S in the soil sample wave velocity correction expression with that in the above formula, the quantitative relationship between wave velocity and resistivity can be obtained.

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