A method for calculating effective stress of unsaturated soil based on fluid dynamics theory

Abstract

The present invention discloses a method for calculating the effective stress of unsaturated soil based on fluid dynamics theory. Based on the fluid dynamics theory, the present invention analyzes the effective stress of unsaturated soil based on thermodynamics theory, introduces concepts such as chemical potential and free energy, and describes the effective stress of unsaturated soil from the perspective of physical and chemical principles based on the fluid dynamics theory. Compared with the commonly used method of calculating the effective stress coefficient as saturation, the present invention reveals the intrinsic connection between the water-holding characteristics of unsaturated soil and the effective stress coefficient, and indirectly reflects the influence of the microscopic pore structure on the matrix suction in the expression of effective stress. If only the correlation between matrix suction and saturation is considered, the effective stress coefficient will be restored to the value of saturation. In addition, the present invention can take into account influencing factors such as porosity ratio to more reasonably predict the effective stress and strength index of unsaturated soil, and provide theoretical support for unsaturated soil related engineering applications.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering, and in particular relates to a method for calculating effective stress of unsaturated soil based on fluid dynamics theory. Background Art

[0002] In the field of geotechnical engineering, the understanding and prediction of soil mechanical properties is the cornerstone to ensure the safety and stability of the project. In particular, the importance of effective stress analysis of soil is self-evident. For saturated soil, its pores are completely filled with water. When the compressibility of the soil skeleton is ignored, the Terzaghi effective stress principle can effectively describe the mechanical response of the soil under external loads. This principle is simple and clear. Based on the direct relationship between pore water pressure and total stress in saturated soil, it provides a solid theoretical basis for the mechanical analysis of saturated soil. However, for compressible soil (such as rubber soil), the Biot effective stress coefficient needs to be introduced to correct the Terzaghi effective stress formula.

[0003] In addition, when it comes to unsaturated soil, the situation becomes more complicated. The pores of unsaturated soil contain not only water but also air, forming a complex system of solid-liquid-gas coexistence. The existence of this multiphase system makes the effective stress of unsaturated soil no longer depend solely on the pore water pressure, but on the pore water pressure. , pore gas pressure The interaction and mutual restriction of these factors make the determination of effective stress of unsaturated soil a very challenging problem.

[0004] In order to overcome this problem, the civil engineering community has conducted a lot of research and exploration. Among them, the effective stress principle of unsaturated soil proposed by Bishop has become an important milestone. This principle introduces the effective stress coefficient , the Terzaghi effective stress principle is extended to the field of unsaturated soil, and a quantitative description of the effective stress of unsaturated soil is achieved. Specifically, the effective stress of unsaturated soil can be expressed as a function of pore water pressure, pore gas pressure and effective stress coefficient. In practical applications, pore water pressure and pore gas pressure can be directly measured by special test equipment, while the determination of the effective stress coefficient becomes a key issue.

[0005] However, the effective stress coefficient There is still no broad consensus on the specific expression of . Due to the complex and changeable microscopic pore structure of unsaturated soil, the effective stress coefficient may vary significantly between different soil bodies. Existing studies often simplify the effective stress coefficient to the saturation of unsaturated soil, but this simplification ignores the influence of multiple factors such as porosity, pore shape, and size distribution on the effective stress coefficient. Experimental data show that the effective stress coefficient is not only related to the saturation, but also jointly restricted by multiple factors such as porosity and pore structure.

[0006] In order to more accurately describe the effective stress of unsaturated soil, it is necessary to start from a microscopic perspective and explore the mechanism of the influence of the microscopic pore structure of the soil on the effective stress coefficient. The shape, size and distribution of the pores will directly affect the surface tension of the liquid at the solid-liquid-gas interface, thereby changing the mechanical properties of the soil. However, quantitative analysis of the microstructure is a technical challenge that requires the help of high-resolution imaging technology and advanced testing methods.

[0007] The soil-water characteristic curve (SWRC) of unsaturated soil provides an indirect way to characterize microstructural information. The soil-water characteristic curve reflects the water storage and release capacity of the soil under the action of matrix suction, and it contains rich soil microstructural information. By deeply analyzing the intrinsic relationship between the soil-water characteristic curve and the effective stress coefficient, a prediction model for the effective stress coefficient of unsaturated soil can be established, providing strong support for the mechanical analysis of unsaturated soil.

[0008] With the continuous in-depth application of fluid dynamics theory in the research of geotechnical engineering materials, the research on effective stress of unsaturated soil has also ushered in new opportunities. By constructing a reasonable free energy function, the chemical potential, pressure and other physical and mechanical information of each component of unsaturated soil can be systematically calculated, thereby achieving a comprehensive description of the effective stress of unsaturated soil. This thermodynamics-based analysis method not only enriches the content of unsaturated soil mechanics theory, but also provides a more solid theoretical basis for the calculation of effective stress coefficients. Summary of the invention

[0009] The purpose of the present invention is to provide a method for calculating the effective stress of unsaturated soil based on the theory of fluid dynamics, to determine the effective stress coefficient more accurately and reasonably based on the water holding characteristics of the soil, and to calculate the effective stress of the unsaturated soil under the condition of considering the compressibility of the solid skeleton. The method helps to strengthen the calculation of the shear strength of unsaturated soil and is conducive to solving engineering problems such as slope instability.

[0010] To achieve the above object, the technical solution adopted by the present invention is: a method for calculating the effective stress of unsaturated soil based on fluid dynamics theory, which comprises the following steps in order:

[0011] (1) The effective stress principle of unsaturated soil was constructed based on fluid dynamics theory.

[0012] Following the Landau fluid dynamics theory, under the conditions of satisfying the first law of thermodynamics, the second law of thermodynamics and related physical constraints, the mathematical expressions between free energy and state variables such as elastic strain and density are given. Based on the thermodynamic theory, the intrinsic relationship between the chemical potential and the intrinsic pressure of each component of unsaturated soil is calculated. The functional relationship between the thermodynamic pressure and the effective stress coefficient and physical quantities such as pore gas pressure, pore water pressure, matrix suction, chemical potential, and compressibility coefficient of each component is obtained. The effective stress of unsaturated soil is derived as follows: ,

[0013] In the formula, —apparent matrix suction (referred to as matrix suction), kPa;

[0014] —effective stress tensor, kPa;

[0015] —total stress tensor, kPa;

[0016] — the unit tensor;

[0017] —pore gas pressure, kPa;

[0018] —Biot effective stress coefficient;

[0019] —Bishop effective stress coefficient.

[0020] The effective stress calculation method is based on the fluid dynamics theory, where the Biot effective stress coefficient is related to the compressibility of the solid skeleton and is taken as , usually takes a value of 1; the Bishop effective stress coefficient is related to the SWRC characteristics of the soil.

[0021] In the formula, —bulk modulus of soil skeleton, kPa;

[0022] —Bulk modulus of solid particles, kPa.

[0023] (2) Establishing the mapping relationship between apparent matrix suction, Bishop effective stress coefficient and intrinsic matrix suction

[0024] Given the variables and free energy in the system, the chemical potential and thermodynamic pressure of the material can be calculated by the principle of minimum potential energy, and the relationship between the pore gas pressure and pore water pressure and the intrinsic matrix suction can be obtained. Finally, the functional relationship between the apparent matrix suction, the Bishop effective stress coefficient and the intrinsic matrix suction is established. The functional relationship between the apparent matrix suction and the intrinsic matrix suction is: , the functional relationship between the effective stress coefficient and the intrinsic matrix suction is: ,

[0025] In the formula, —bulk modulus of water, kPa;

[0026] —Intrinsic density of soil particles, water and gas, g / cm 3 ;

[0027] —volume fraction of soil particles;

[0028] — volume fraction of water;

[0029] —Intrinsic matrix suction;

[0030] —Partial derivatives of intrinsic matrix suction with respect to apparent density of soil particles, water and gas.

[0031] (3) Obtaining water holding test data and shear test data of unsaturated soil

[0032] Carry out water holding test and shear test of unsaturated soil to obtain the water holding characteristics and shear strength of unsaturated soil. The water holding test includes moisture absorption test and dehumidification test, and the final data obtained is the relationship between the matrix suction of unsaturated soil and saturation, weight water content or volume water content. Shear test includes direct shear test, triaxial test, etc. Due to the hysteresis characteristics of soil-water characteristic curve under the action of dry-wet cycle, shear test needs to be carried out under moisture absorption path or dehumidification path.

[0033] (4) Select an appropriate empirical model to mathematically fit the test data of the unsaturated soil water retention characteristic curve

[0034] If the matrix suction is only related to the saturation, the Van Genuchten model is used to fit the experimental data, and its expression is: ,

[0035] In the formula, — saturation;

[0036] —Fitting parameters, kPa -1 ;

[0037] , —Fitted parameters of the model.

[0038] At this time, the functional relationship between matrix suction, Bishop effective stress coefficient and intrinsic matrix suction can be simplified as follows: , ,

[0039] In the formula, — Partial derivative with respect to saturation.

[0040] If the matrix suction is related to saturation and porosity, the soil-water characteristic curve model considering porosity is used to fit the test data, and its expression is: ,

[0041] In the formula, —Fitting parameters, kPa;

[0042] , —Fitting parameters;

[0043] —Porosity ratio.

[0044] At this time, the functional relationship between matrix suction, effective stress coefficient, free energy and chemical potential can be simplified as follows: , ,

[0045] In the formula, — porosity;

[0046] — Partial derivative with respect to porosity.

[0047] Beneficial effects of the present invention:

[0048] The present invention analyzes the effective stress of unsaturated soil based on the theory of thermodynamics based on the theory of fluid dynamics. By introducing the concepts of chemical potential, free energy, etc., the effective stress of unsaturated soil is described from the perspective of physical and chemical principles based on the theory of fluid dynamics, providing a new idea for the study of unsaturated soil. Compared with the existing commonly used method of calculating the effective stress coefficient as saturation, the present invention reveals the intrinsic connection between the water-holding characteristics of unsaturated soil and the effective stress coefficient, and indirectly reflects the influence of the microscopic pore structure on the matrix suction in the expression of effective stress. If only the correlation between matrix suction and saturation is considered, the effective stress coefficient will be restored to the value of saturation. In addition, the present invention can take into account influencing factors such as porosity ratio to more reasonably predict the effective stress and strength index of unsaturated soil, providing theoretical support for unsaturated soil related engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 The present invention is a flow chart of a method for calculating effective stress of unsaturated soil based on fluid dynamics theory.

[0050] Figure 2 Soil-water characteristic curve of riverbank soil fitted by Van Genuchten model.

[0051] Figure 3 The soil-water characteristic curve of the embankment soil is obtained by fitting the soil-water characteristic curve model considering the porosity ratio.

[0052] Figure 4 The soil-water characteristic curve of residual soil obtained by fitting the Van Genuchten model.

[0053] Figure 5 The soil-water characteristic curve of residual soil is fitted by the soil-water characteristic curve model considering the porosity ratio. DETAILED DESCRIPTION

[0054] Example 1

[0055] like Figure 1 As shown, a method for calculating effective stress of unsaturated soil based on fluid dynamics theory includes the following steps in order:

[0056] (1) The effective stress principle of unsaturated soil was constructed based on fluid dynamics theory.

[0057] Following the Landau fluid dynamics theory, under the conditions of satisfying the first law of thermodynamics, the second law of thermodynamics and related physical constraints, the effective stress of unsaturated soil is derived as follows: , based on the assumption of linear elastic response of the solid skeleton, the Biot effective stress coefficient is , its value is usually 1,

[0058] In the formula, —apparent matrix suction (referred to as matrix suction), kPa;

[0059] —effective stress tensor, kPa;

[0060] —total stress tensor, kPa;

[0061] — the unit tensor;

[0062] —pore gas pressure, kPa;

[0063] —Biot effective stress coefficient;

[0064] —Bishop effective stress coefficient;

[0065] —bulk modulus of soil skeleton, kPa;

[0066] —Bulk modulus of solid particles, kPa.

[0067] (2) Establishing the mapping relationship between apparent matrix suction, Bishop effective stress coefficient and intrinsic matrix suction

[0068] Given the variables and free energy in the system, the chemical potential and thermodynamic pressure of the material can be calculated by the principle of minimum potential energy, and the relationship between the pore gas pressure and pore water pressure and the intrinsic matrix suction can be obtained. Finally, the functional relationship between the matrix suction, Bishop effective stress coefficient and the intrinsic matrix suction can be established.

[0069] The functional relationship between apparent matrix suction and intrinsic matrix suction is: , the functional relationship between Bishop effective stress coefficient and intrinsic matrix suction is: ,

[0070] In the formula, —matrix suction, kPa;

[0071] —Intrinsic density of soil particles, water and gas, g / cm 3 ;

[0072] —volume fraction of soil particles;

[0073] —Ratio of the volume of water to the total volume;

[0074] —bulk modulus of water, kPa;

[0075] —Partial derivatives of intrinsic matrix suction with respect to apparent density of soil particles, water and gas.

[0076] (3) Obtaining water holding test data and shear test data of unsaturated soil

[0077] The embankment soil from the Secchia River near Modena, Italy, is characterized by a complex alternation of silt and sand. Water retention tests and shear tests were conducted on it. The water retention data of the embankment soil under moisture absorption and dehumidification conditions were measured. The shear test adopted a suction-controlled direct shear test, which can control the suction to remain unchanged during the direct shear test, and only the moisture absorption path is considered in the unsaturated direct shear device (UDS). The test conditions are shown in Table 1 below.

[0078] Table 1 Conditions of riverbank soil shear test

[0079]

[0080] (4) Select an appropriate empirical model to mathematically fit the test data of the unsaturated soil water retention characteristic curve

[0081] If the matrix suction is only related to the saturation, the Van Genuchten model is used to fit the soil-water characteristic curve under the moisture absorption path, and its expression is: ,

[0082] In the formula, — saturation;

[0083] —Fitting parameters, kPa -1 ;

[0084] , —Fitting parameters.

[0085] The fitting result is as follows Figure 2 As shown, the fitting parameters are kPa -1 , , .

[0086] At this time, the functional relationship between matrix suction, effective stress coefficient and intrinsic matrix suction can be simplified as follows: , ,

[0087] In the formula, — Partial derivative with respect to saturation.

[0088] If the matrix suction is related to saturation and porosity, the soil-water characteristic curve model considering porosity is adopted (Einav I, Liu M. Hydrodynamics of non-equilibrium soil water retention [J]. Water Resources Research, 2023, 59(1): e2022WR033409.) to fit the experimental data under the moisture absorption path, and its expression is ,

[0089] In the formula, —Fitting parameters, kPa;

[0090] , —Fitting parameters;

[0091] —Porosity ratio.

[0092] The fitting result is as follows Figure 3 As shown, the fitting parameters are kPa, , .

[0093] At this time, the functional relationship between matrix suction, effective stress coefficient, free energy and chemical potential can be simplified as follows: , ,

[0094] In the formula, — porosity;

[0095] — Partial derivative with respect to porosity.

[0096] (5) According to the effective stress calculation formula obtained in step (1), combined with the shear strength data of unsaturated riverbank soil in step (2), the effective stress of unsaturated soil is calculated by the effective stress principle of unsaturated soil. The calculation results are shown in Table 2.

[0097] Table 2 Calculation of effective stress of river embankment soil

[0098]

[0099] If the matrix suction is considered to be related to saturation and porosity, the fitting parameters are Calculate the matrix suction in each set of data in the suction-controlled direct shear test The corresponding saturation The effective stress of the embankment soil is calculated. At this time, the effective stress coefficient The calculation results are shown in Table 3.

[0100] Table 3 Calculation of effective stress of riverbank soil using the Einav porosity ratio model

[0101]

[0102] Example 2

[0103] like Figure 1 As shown, a method for calculating effective stress of unsaturated soil based on fluid dynamics theory includes the following steps in order:

[0104] (1) The effective stress principle of unsaturated soil was constructed based on fluid dynamics theory.

[0105] Following the Landau fluid dynamics theory, under the conditions of satisfying the first law of thermodynamics, the second law of thermodynamics and related physical constraints, the effective stress of unsaturated soil is derived as follows: , based on the assumption of linear elastic response of the solid skeleton, the Biot effective stress coefficient is , its value is usually 1,

[0106] In the formula, —apparent matrix suction (referred to as matrix suction), kPa;

[0107] —effective stress tensor, kPa;

[0108] —total stress tensor, kPa;

[0109] — the unit tensor;

[0110] —pore gas pressure, kPa;

[0111] —Biot effective stress coefficient;

[0112] —Bishop effective stress coefficient;

[0113] —bulk modulus of soil skeleton, kPa;

[0114] —Bulk modulus of solid particles, kPa.

[0115] (2) Establishing the mapping relationship between apparent matrix suction, Bishop effective stress coefficient and intrinsic matrix suction

[0116] Given the variables and free energy in the system, the chemical potential and thermodynamic pressure of the material can be calculated by the principle of minimum potential energy, and the relationship between the pore gas pressure and pore water pressure and the intrinsic matrix suction can be obtained. Finally, the functional relationship between the matrix suction, Bishop effective stress coefficient and the intrinsic matrix suction can be established.

[0117] The functional relationship between apparent matrix suction and intrinsic matrix suction is: , the functional relationship between Bishop effective stress coefficient and intrinsic matrix suction is: ,

[0118] In the formula, —matrix suction, kPa;

[0119] —Intrinsic density of soil particles, water and gas, g / cm 3 ;

[0120] —volume fraction of soil particles;

[0121] —Ratio of the volume of water to the total volume;

[0122] —bulk modulus of water, kPa;

[0123] —Partial derivatives of intrinsic matrix suction with respect to apparent density of soil particles, water and gas.

[0124] (3) Obtaining water holding test data and shear test data of unsaturated soil

[0125] Residual soil from the Rječina River valley in Croatia was selected, of which clay accounted for 30.3%, sand accounted for 10.4%, silt accounted for 53%, and gravel accounted for 6.3%. Water holding data were obtained by water holding tests using a Hydrocon hydraulic consolidation unit, which saturates the sample by back pressure in a closed system and can be used to perform multiple dry and wet tests on undisturbed samples with different net vertical stresses. A back-pressure unsaturated shear box was used for direct shear tests. The device was operated under the dehumidification path, and a suction control test was performed on the complete sample placed inside or saturated outside the shear box, which was immersed in deaerated water before being placed. The specific test conditions are shown in Table 4, where the samples of UVSCDS05, UVSCDS06, and UVSCDS07 were first saturated outside the shear box.

[0126] Table 4 Conditions for residual soil shear test

[0127]

[0128] (4) Select an appropriate empirical model to mathematically fit the test data of the unsaturated soil water retention characteristic curve

[0129] If the matrix suction is only related to the saturation, the Van Genuchten model is used to fit the soil-water characteristic curve under the moisture absorption path, and its expression is: ,

[0130] In the formula, — saturation;

[0131] —Fitting parameters, kPa -1 ;

[0132] , —Fitting parameters.

[0133] The fitting results are as follows Figure 4 As shown, the fitting parameters are kPa -1 , , .

[0134] At this time, the functional relationship between matrix suction, effective stress coefficient and intrinsic matrix suction can be simplified as follows: , ,

[0135] In the formula, — Partial derivative with respect to saturation.

[0136] If the matrix suction is related to saturation and porosity, the soil-water characteristic curve model considering porosity is used to fit the test data under the moisture absorption path. The expression is: ,

[0137] In the formula, —Fitting parameters, kPa;

[0138] , —Fitting parameters;

[0139] —Porosity ratio.

[0140] The fitting results are as follows Figure 5 As shown, the fitting parameters are kPa, , .

[0141] At this time, the functional relationship between matrix suction, effective stress coefficient, free energy and chemical potential can be simplified as follows: , ,

[0142] In the formula, — porosity;

[0143] — Partial derivative with respect to porosity.

[0144] (5) According to the effective stress calculation formula obtained in step (1), combined with the shear strength data of unsaturated residual soil in step (2), the effective stress of unsaturated soil is calculated by the effective stress principle of unsaturated soil. The calculation results are shown in Table 5.

[0145] Table 5 Calculation of effective stress of residual soil

[0146]

[0147] If the matrix suction is considered to be related to saturation and porosity, the fitting parameters are Calculate the matrix suction in each set of data in the suction-controlled direct shear test The corresponding saturation The effective stress of the embankment soil is calculated. At this time, the effective stress coefficient The calculation results are shown in Table 6.

[0148] Table 6 Calculation of effective stress of residual soil using Einav void ratio model

[0149]

[0150] In summary, the present invention reveals the intrinsic relationship between the water-holding characteristics of unsaturated soil and the effective stress coefficient, and indirectly reflects the influence of the microscopic pore structure on the matrix suction in the expression of effective stress. If only the matrix suction and saturation are considered, the effective stress coefficient will return to the saturation value. In addition, the present invention can take into account influencing factors such as the porosity ratio to more reasonably predict the effective stress and strength index of unsaturated soil, providing theoretical support for unsaturated soil related engineering applications.

Claims

1. A method for calculating effective stress of unsaturated soil based on fluid dynamics theory, characterized in that: The following steps are involved: (1) Constructing the effective stress principle of unsaturated soil based on fluid dynamics theory: According to Landau fluid dynamics theory, under the constraints of the first law of thermodynamics, the second law of thermodynamics and related physics, the effective stress formula of unsaturated soil is derived as follows: ， In the formula, is the apparent matrix suction, kPa; is the effective stress tensor, kPa; is the total stress tensor, kPa; is the unit tensor; is the pore gas pressure, kPa; is the Biot effective stress coefficient; is the Bishop effective stress coefficient; The Biot effective stress coefficient The material elastic strain energy is derived by considering the compressibility of the skeleton, specifically: , In the formula, is the bulk modulus of the soil skeleton, kPa; is the bulk modulus of the solid particles, kPa; (2) Establish the relationship between matrix suction and effective stress coefficient: Under given system variables and free energy conditions, the chemical potential and thermodynamic pressure of the material are calculated by the principle of minimum potential energy, and the mapping relationship between apparent matrix suction, Bishop effective stress coefficient and intrinsic matrix suction is established. The relationship between pore gas pressure, pore water pressure and intrinsic matrix suction is obtained through the principle of minimum potential energy, and the specific functional relationship between apparent matrix suction, Bishop effective stress coefficient and intrinsic matrix suction is further derived. The relationship between apparent matrix suction and intrinsic matrix suction is: ， The functional relationship between the Bishop effective stress coefficient and the intrinsic matrix suction is: ， In the formula, is the bulk modulus of water, kPa; are the intrinsic densities of soil particles, water and gas, g / cm 3 ; is the volume fraction of soil particles; is the volume fraction of water; is the intrinsic matrix suction, kPa; is the partial derivative of intrinsic matrix suction with respect to the apparent density of soil particles, water and gas; (3) Data acquisition: Obtain test data of water retention characteristic curve and shear strength of unsaturated soil; The test of the water holding characteristic curve includes a moisture absorption test and a moisture removal test to obtain the relationship between the apparent matrix suction of unsaturated soil and the degree of saturation, weight water content or volume water content; The shear strength test includes a direct shear test and a triaxial test, and is carried out under a moisture absorption path or a moisture desorption path; (4) Data fitting: Select the corresponding empirical model to mathematically fit the test data of unsaturated soil water retention characteristic curve and get the fitting result; If the apparent matrix suction is only related to the saturation, the Van Genuchten model is used for fitting; the expression of the Van Genuchten model is: ， In the formula, is saturation; is the fitting parameter, kPa -1 ; , are the fitting parameters of the model; If the apparent matrix suction is related to both saturation and void ratio, the soil-water characteristic curve model considering void ratio is used for fitting; Among them, the expression of the soil-water characteristic curve model considering the porosity ratio is: ， In the formula, is the fitting parameter, kPa; , All are fitting parameters; is the void ratio; (5) Calculation of effective stress tensor: Combining the effective stress calculation formula in step (1) and the mapping relationship in step (2), as well as the test data and fitting results obtained in steps (3) and (4), the effective stress tensor of unsaturated soil is calculated by the effective stress principle of unsaturated soil; Among them, according to the test data obtained in step (3), the apparent matrix suction is obtained by fitting in step (4): and Saturation Apparent matrix suction Combined with the mapping relationship in step (2), the Bishop effective stress coefficient is calculated Finally, based on the effective stress calculation formula in step (1), the effective stress tensor of unsaturated soil is obtained.

2. The method for calculating effective stress of unsaturated soil based on fluid dynamics theory according to claim 1 is characterized in that: If the apparent matrix suction is only related to the saturation The functional relationship between apparent matrix suction, Bishop effective stress coefficient and intrinsic matrix suction is simplified as follows: ， ， In the formula, for Partial derivative with respect to saturation.

3. The method for calculating effective stress of unsaturated soil based on fluid dynamics theory according to claim 1 is characterized in that: If the apparent matrix suction and saturation , porosity ratio, the functional relationship between apparent matrix suction, Bishop effective stress coefficient and intrinsic matrix suction is simplified to: ， ， In the formula, is the porosity; for The partial derivative with respect to porosity, for Partial derivative with respect to saturation.

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