A fluid-solid coupling analysis method for clay core wall with tension cracks

Abstract

The present invention belongs to the technical field of clay core wall property change analysis, and specifically relates to a fluid-solid coupling analysis method for a clay core wall with tension cracks, including: establishing a pore water continuity equation in a soil medium and a pore gas continuity equation in a soil medium to describe the movement of pore water and pore gas in the soil medium; establishing a water continuity equation and a gas continuity equation in the cracks based on the seepage exchange between the cracks and the soil medium; establishing a static equilibrium equation for the clay core wall to describe the stress-strain response of the soil particle skeleton under the action of an external load; establishing a water-gas-solid coupling analysis model for a clay core wall with tension cracks, and determining the model's solution conditions, including the initial conditions and boundary conditions of soil deformation, soil pore water pressure, soil pore gas pressure, crack water pressure, and crack gas pressure. The present invention can evaluate the performance of an unsaturated clay core wall under various environmental and load conditions.

Description

Technical Field

[0001] The invention belongs to the technical field of clay core wall property change analysis, and particularly relates to a fluid-solid coupling analysis method for a clay core wall with tension cracks. Background Art

[0002] In modern water conservancy projects, especially in the construction of rockfill dams, the stability of the clay core is of vital importance. The main function of the clay core is to serve as an anti-seepage structure to maintain the stability and safety of the rockfill dam. In its design and analysis, it is particularly important to consider the influence of fluid-solid coupling on the tensile crack behavior of the clay core.

[0003] Traditional clay core wall analysis methods usually take into account the behavior of saturated soil, but there is little research on the properties of unsaturated soil, especially the influence of water-air interaction in pores. This leads to insufficient accuracy when analyzing cracks and weak seepage layers in clay core walls. In particular, when cracks appear inside the clay core wall due to construction, uncoordinated deformation, etc., the interaction between the seepage field and the stress field becomes complicated. The water pressure load in the cracks causes the cracks to open and expand, which affects the soil deformation and crack seepage. Therefore, in order to more accurately analyze and predict the behavior of clay core walls, especially when considering the interaction between unsaturated soil and crack seepage, a more complex fluid-solid coupling analysis model needs to be studied.

[0004] In summary, the existing technologies have obvious deficiencies in the analysis of unsaturated soil properties, the prediction of crack behavior, and the analysis of fluid-solid coupling effects. Therefore, it is particularly important to develop a new model that can accurately evaluate the performance of unsaturated clay core walls with tension cracks under different environmental and loading conditions. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to address the deficiencies of the prior art and provide a fluid-solid coupling analysis method for clay core walls with tension cracks, which can evaluate the performance of unsaturated clay core walls under various environmental and load conditions, and help improve engineering safety and reliability.

[0006] Technical solution: The fluid-solid coupling analysis method of the clay core wall with tension cracks described in the present invention is

[0007] The clay core wall with tension cracks includes soil medium and cracks, the soil medium includes soil particles, pore water and pore gas, and the cracks are filled with soil particles, water and gas;

[0008] The analysis method comprises: establishing a pore water continuity equation in a soil medium and a pore gas continuity equation in a soil medium based on the principle of mass conservation to describe the movement of pore water and pore gas in the soil medium;

[0009] Based on the seepage exchange between the cracks and the soil medium, the water continuity equation and gas continuity equation in the cracks are established;

[0010] The static equilibrium equation of clay core wall is established to describe the stress-strain response of soil particle skeleton under external load.

[0011] By combining the continuity equations of water and air in the soil medium and cracks and the static equilibrium equation of the clay core wall, a water-air-solid coupling analysis model of the clay core wall with tension cracks is established, and the boundary conditions of the model are determined, including the initial conditions and boundary conditions of soil deformation, soil pore water pressure, soil pore air pressure, crack water pressure, and crack air pressure.

[0012] To further improve the above technical solution, the fluid-solid coupling analysis method of the clay core wall with tension cracks is based on the following assumptions: (1) the soil phase and water phase in the clay core wall are both continuous media, and the soil particles and pore water are incompressible; (2) the flow of pore water and pore gas satisfies Darcy's law; (3) the temperature effect is ignored and the core wall is assumed to be an isothermal body; (4) the dissolution and diffusion of gas in water and the movement of water vapor are not considered.

[0013] Furthermore, the masses of each item in the differential unit of the soil medium and the crack are expressed as:

[0014]

[0015] Where: m s 、m w 、m a are the masses of soil particles, pore water and gas in the differential unit respectively; ρ s , w , a are the densities of soil particles, pore water and gas respectively; n is the porosity; S is the saturation; V is the differential unit volume;

[0016] The continuity equation of pore water in soil medium is expressed as:

[0017]

[0018] Where: k w is the permeability coefficient of pore water, γ w is the bulk density of water, p w is the pore water pressure, ε v is the volume strain of soil under load, p a is the pore gas pressure, p s is the matrix suction,

[0019] The pore gas continuity equation in soil medium is expressed as:

[0020]

[0021] Where: k a is the pore gas permeability coefficient, γ a is the bulk density of pore gas, K a is the pore gas bulk modulus.

[0022] Furthermore, the continuity equation of the water body in the crack is expressed as:

[0023]

[0024] The gas continuity equation in the crack is expressed as:

[0025]

[0026] Where: k cw is the water permeability coefficient in the fracture, p cw is the pore water pressure in the crack, w is the crack width, n c is the fracture porosity, q 1c k is the flow rate leaking from the crack surface into the soil; ca is the gas permeability coefficient in the crack, p ca is the pore pressure in the crack; q 1c is the gas flow rate that penetrates into the soil from the crack surface.

[0027] Furthermore, the static equilibrium equation of the clay core wall is expressed as:

[0028]

[0029] Where: D is the elastic matrix, χ is the effective stress coefficient, I is the unit vector, and f is the soil body force.

[0030] Furthermore, the water-gas-solid coupling equation of the clay core wall with tension cracks is obtained by combining the pore water continuity equation in the soil medium, the pore gas continuity equation in the soil medium, the water continuity equation in the cracks, the gas continuity equation in the cracks and the static equilibrium equation of the core wall clay, and its expression is:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] The solution conditions of the water-air-solid coupling equation of the clay core with tension cracks include the initial conditions and boundary conditions of soil medium displacement, pore water pressure, air pressure, and water pressure and air pressure in the cracks.

[0037] The initial conditions are:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Where: u 0 、p w0 、p a0 、p cw 、p ca They are the displacement corresponding to the starting calculation time, the pore water pressure in the soil medium, the pore air pressure, the water pressure in the cracks, and the air pressure in the cracks;

[0044] The first type of boundary condition to be satisfied on the Γ boundary is:

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] Where: They are the displacement constraint of soil medium on the boundary, pore water pressure constraint, pore air pressure constraint, water pressure and air pressure constraint of cracks at the boundary.

[0051] The second type of boundary condition to be satisfied on the Γ boundary is:

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] Where: They are respectively the load value of soil medium on the boundary, the adhesion value at the crack, the pore water flow at the boundary, the pore air flow constraint, the pore water flow and pore air flow constraint of the crack at the boundary.

[0061] Furthermore, the pore water and gas in the soil medium are regarded as a mixed fluid, and it is assumed that: (1) the clay core wall has a small deformation; (2) the pore gas in the clay core wall exists in the form of bubbles, which are completely enclosed by water and do not move relative to the water body;

[0062] Establish the continuity equation of soil medium mixed flow:

[0063]

[0064] Considering the water and gas in the fracture as mixed fluid, the continuity equation of the mixed flow in the fracture is obtained as follows:

[0065]

[0066] The static equilibrium equation of clay core wall is:

[0067] Furthermore, the mixed flow continuity equation and the clay core equilibrium equation are combined to obtain the fluid-solid coupling equation for mixed flow in clay core with tension cracks.

[0068]

[0069]

[0070]

[0071] The solution conditions of the fluid-solid coupling equation of mixed flow in clay core with tension cracks include the initial and boundary conditions of soil partial deformation, mixed flow seepage pressure and mixed flow seepage pressure in cracks, among which the initial conditions are:

[0072]

[0073]

[0074]

[0075] Where: u 0 、p m0、p cm0 are the displacement corresponding to the initial calculation time, the mixed fluid pressure in the soil medium, and the mixed fluid pressure in the crack;

[0076] The first type of boundary condition to be satisfied on the Γ boundary is:

[0077]

[0078]

[0079]

[0080] Where: They are the displacement constraint of soil medium on the boundary, the mixed fluid pressure constraint, and the mixed fluid pressure constraint of cracks at the boundary.

[0081] The second type of boundary condition to be satisfied on the Γ boundary is:

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] Where: t、 They are respectively the load value of soil medium on the boundary, the adhesion value at the crack, the mixed flow flow constraint of soil medium at the boundary, and the mixed flow flow constraint of crack at the boundary.

[0088] Furthermore, the calculation parameters in the water-gas-solid coupling analysis model of the clay core wall with tension cracks include saturation, permeability coefficient, and effective stress coefficient;

[0089] The effective saturation S e and matrix suction s The relational expression is:

[0090]

[0091] Where: S e is the effective saturation, p s is the matrix suction, a, b, c are fitting parameters;

[0092] Effective saturation S e The relationship expression with saturation S is:

[0093]

[0094] Where: S max is the maximum saturation; S r is the residual saturation of soil;

[0095] The relationship between the permeability coefficient K and the porosity ratio e is expressed as follows:

[0096]

[0097] Where: K 0 is the initial intrinsic permeability; e 0 is the initial porosity; e is the porosity;

[0098] The effective stress coefficient σ′ is related to the total stress σ, pore pressure p a , matrix suction p a -p w The relationship between and the effective stress coefficient χ is:

[0099] σ′=(σ-p a I)+χ(p a -p w )I

[0100] Where: σ′ is the effective stress, σ is the total stress, p a is the pore gas pressure, p w is the pore water pressure, p a -p w is the matrix suction, χ is the effective stress coefficient, when χ=1, the soil is in a saturated state, and χ=0, the soil is in a completely dry state.

[0101] Beneficial effect: Compared with the prior art, the advantages of the present invention are: the present invention focuses on the fluid-solid coupling problem of unsaturated clay core wall with tension cracks, analyzes the force relationship among water, gas and soil particles in the clay core wall and the influence of crack seepage and soil fluid-solid coupling, and based on the principle of mass conservation and the principle of effective stress of unsaturated soil, constructs water and gas continuity equations and soil static equilibrium equations; considers the change of crack width and the flow exchange between cracks and soil, establishes crack water and gas continuity equations, and proposes a water-gas-solid coupling analysis model for clay core wall with tension cracks.

[0102] In view of the characteristics of high saturation of clay core wall and complete sealing of pore gas by water, pore water and gas are regarded as mixed fluids. Meanwhile, the influence of pore gas compressibility is taken into consideration, and the conventional mixed flow fluid-solid coupling analysis model is improved. A method for determining the bulk modulus of the mixed fluid is given. On this basis, considering the flow exchange between cracks and soil at the crack surface, a mixed flow fluid-solid coupling analysis model of clay core wall with tension cracks is proposed.

[0103] According to the nonlinear parameter variation characteristics in the fluid-solid coupling analysis model of clay core wall with tension cracks, the influence of deformation and seepage pressure on physical and mechanical parameters was comprehensively considered, and the calculation methods of saturation, permeability coefficient and effective stress coefficient were determined.

[0104] The fluid-solid coupling analysis method for clay core walls with tension cracks provided by the present invention can evaluate the performance of unsaturated clay core walls under various environmental and load conditions, especially considering the influence of cracks and weak seepage layers. Through the mixed flow fluid-solid coupling analysis model, the particularity of the clay core wall under high saturation conditions can be effectively handled, and the understanding and analysis of the interaction between unsaturated soil and crack seepage is improved. In the analysis of core parameters and their mutual relationships, a more reliable theoretical basis and calculation tools are provided for the design and safety assessment of unsaturated clay core walls, especially when dealing with complex engineering conditions and environmental changes. Therefore, the present invention provides a new analysis method for the design and safety assessment of clay core walls, which helps to improve engineering safety and reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 It is a specific implementation flow chart of the present invention;

[0106] Figure 2 It is the schematic diagram of the differential unit structure of unsaturated soil;

[0107] Figure 3 is the fracture seepage differential unit;

[0108] Figure 4 is the mixed fluid differential unit;

[0109] Figure 5 It is the soil-water characteristic curve. DETAILED DESCRIPTION

[0110] The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the embodiments.

[0111] Example 1: The fluid-solid coupling analysis model for analyzing the performance of unsaturated clay core walls provided in this example is particularly suitable for clay core walls in rockfill dams, earth-rock dams and concrete gravity dams. The importance of this model lies in the fact that the stability of the clay core wall is the key to ensuring the safety of these large-scale projects. When constructing the model, the complex interactions between water, air and soil particles in the unsaturated clay core wall are taken into account, and these interactions directly affect the stability and performance of the core wall.

[0112] The core of the model is based on the theoretical framework of fluid-solid coupling analysis, focusing on the interaction between pore water, air and soil particles. In the model, special attention is paid to the complex interaction between the seepage field and the stress field in the unsaturated clay core wall, especially when cracks or weak seepage layers appear inside the core wall due to construction, uncoordinated deformation, etc. In this case, the interaction between the seepage field and the stress field becomes particularly complex, which directly affects the overall stability and function of the core wall.

[0113] In the process of model construction, several key components are involved, including water-gas-solid coupling analysis and mixed flow fluid-solid coupling analysis. In the water-gas-solid coupling analysis, the interaction between pore water, gas and soil particles and the coupling relationship between fracture seepage and soil deformation and seepage are comprehensively considered. This analysis is crucial to understanding the behavior of unsaturated clay core walls in a changing environment, especially when analyzing the development of cracks and seepage characteristics. The mixed flow fluid-solid coupling analysis proposes a novel analysis method for the high saturation characteristics of clay core walls, treating pore water and gas as mixed fluids. This method shows its unique advantages in dealing with the special case of highly saturated clay core walls.

[0114] This model provides a comprehensive analysis of the interaction between the seepage and stress fields of unsaturated soils and cracks. In unsaturated soils, the dynamics of pore water and the physical properties of the soil are closely linked, especially when cracks or weak seepage zones are present inside the soil. In these cases, the development of cracks is affected not only by the movement of water inside the soil, but also by changes in the stress field. Therefore, the movement of pore water and gas and their interaction with the soil particle skeleton are comprehensively considered in this model, providing an effective tool for analyzing and predicting the stability and performance of clay core walls.

[0115] First, the following assumptions are made in the model: (1) The water, gas, and solid phases of the clay core are all continua, and the soil particles and pore water are incompressible; (2) The pore water and gas flows satisfy Darcy's law; (3) The temperature effect is ignored and the core is assumed to be an isothermal body; (4) The dissolution and diffusion of gas in water and the movement of water vapor are not considered.

[0116] The water-gas-solid coupling analysis model of clay core wall with tension cracks includes the water and gas continuity equations of the soil medium, the fluid continuity equation in the cracks, and the static equilibrium equation of the clay core wall.

[0117] The clay core wall with tension cracks is mainly divided into the soil medium part and the crack part. Figure 2As shown in the figure, it is composed of soil particle skeleton, pore water and gas; the crack part includes weak seepage layer and cracks, among which the weak seepage layer is also composed of soil particle skeleton, pore water and gas. When there are cracks on the upstream surface of the clay core wall, the upstream filter material will be brought into the cracks during the process of reservoir water flowing into the cracks. At the same time, the clay around the cracks is soaked in water and loose, which will also fill the cracks. That is, the cracks are filled with granular bodies, water and gas. The mass of each phase in the differential unit of the soil part and the crack part can be expressed as:

[0118]

[0119] Where: m s 、m w 、m a are the masses of soil particles, pore water and gas in the differential unit respectively; ρ s , w , a are the densities of soil particles, pore water and gas respectively; n is the porosity; S is the saturation; V is the differential unit volume.

[0120] In order to more accurately simulate and analyze the behavior of unsaturated clay core walls, this model is based on the principle of mass conservation. To describe the movement of pore water and gas in the pores of the soil, water and gas continuity equations are established. According to the principle of mass conservation, the mass of pore water flowing out of the unit per unit time is equal to the change in the mass of pore water in the unit, and we get:

[0121]

[0122] Where: is the gradient operator, v w is the pore water velocity vector;

[0123] Assuming that the pore water flow in unsaturated clay satisfies Darcy's law, its expression is:

[0124]

[0125] Where: k w is the permeability coefficient of pore water, γ w is the bulk density of water, p w is the pore water pressure;

[0126]

[0127] Where: The first term on the right side represents the change rate of pore water density. Since the pore water is assumed to be incompressible, the first term on the right side is equal to zero; the second term on the right side is expressed as:

[0128]

[0129] Where: ε Vis the volume strain of soil under load; the third term on the right side is expressed as:

[0130]

[0131] Where: p a is the pore gas pressure, p s is matrix suction, p s =p a -p w ,make Therefore, the pore water continuity equation in soil medium is derived by combining the pore water continuity equation and the assumed conditions, and its expression is:

[0132]

[0133] Also based on the principle of mass conservation, the pore gas continuity equation of the soil medium is derived by combining the continuity equation of gas flow in the pores and the continuity equation of pore water in the soil medium. Its expression is:

[0134]

[0135] Where: k a is the pore gas permeability coefficient, γ a is the bulk density of pore gas, K a is the pore gas bulk modulus.

[0136] The pore gas continuity equation describes the movement of pore gas in soil, focusing on the flow rate, pressure and density changes of pore gas. It is crucial to understand the gas movement in unsaturated soils, especially when considering the permeability and porosity changes of soils.

[0137] Since the crack width is much smaller than the crack length, the water and gas flow process perpendicular to the crack surface can be ignored, and only the flow of water and gas along the crack surface is analyzed. The crack is actually filled with soil particles, pore water and gas. The differential unit of water seepage in the crack is as follows: Figure 3 As shown, the differential water inflow velocity is v cw , the outflow speed is The crack width is w, and the crack width change rate is The flow rate from the crack surface to the soil is q 1cw Combining the continuity equation of water in cracks and the continuity equation of pore water and pore gas in soil, the continuity equation of water in cracks and the continuity equation of gas in cracks are derived, and their expressions are:

[0138]

[0139]

[0140] Where: k cwis the water permeability coefficient in the fracture, p cw is the pore water pressure in the crack, w is the crack width, n c is the fracture porosity, q 1cw k is the flow rate leaking from the crack surface into the soil; ca is the gas permeability coefficient in the crack, p ca is the pore pressure in the crack; q 1ca is the gas flow rate that penetrates into the soil from the crack surface.

[0141] Through these equations, it is possible to effectively analyze how the movement of pore water and gas affects the physical properties of the soil, such as permeability, density, and saturation, and thus affects the overall stability and function of the soil.

[0142] For the clay core wall, since clay material has obvious nonlinearity, the stress and strain are taken as incremental form, and the pressure is taken as positive when calculating the soil body. Therefore, the static equilibrium equation of the clay core wall is obtained as follows:

[0143]

[0144] Where: D is the elastic matrix, χ is the effective stress coefficient, I is the unit vector, and f is the soil body force.

[0145] This equation is used to describe the stress-strain response of the soil skeleton under external loads. Through this equation, the relationship between the total stress and effective stress inside the soil can be analyzed, and how these stresses affect the soil structure and the development of cracks. Especially when considering unsaturated soils, the static equilibrium equation becomes an important tool for analyzing the stability of the soil skeleton.

[0146] The water-gas continuity equation of the core wall soil and cracks obtained above and the static equilibrium equation of the core wall clay are combined to obtain the water-gas-solid coupling equation of the clay core wall with tension cracks, and its expression is:

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] The solution conditions of the water-air-solid coupling equation of the clay core wall with tension cracks include the initial conditions and boundary conditions of the soil deformation, pore water pressure, air pressure, and water pressure and air pressure in the crack part. The specific analysis is as follows.

[0153] The initial conditions that the coupled equations must satisfy are:

[0154]

[0155]

[0156]

[0157]

[0158]

[0159] Where: u 0 、p w0 、p a0 、p cw0 、p ca They are the displacement corresponding to the starting calculation time, the pore water pressure in the soil medium, the pore air pressure, the pore water pressure in the cracks, and the pore air pressure.

[0160] The first type of boundary condition to be satisfied on the Γ boundary is:

[0161]

[0162]

[0163]

[0164]

[0165]

[0166] Where: They are respectively the displacement constraint, pore water pressure, pore air pressure constraint of soil medium on the boundary, and the pore water pressure and air pressure constraint of cracks at the boundary.

[0167] The second type of boundary condition to be satisfied on the Γ boundary is:

[0168]

[0169]

[0170]

[0171]

[0172]

[0173]

[0174]

[0175]

[0176] Where: t、 They are respectively the load value of soil medium on the boundary, the adhesion value at the crack, the pore water flow at the boundary, the pore air flow constraint, the pore water flow and pore air flow constraint of the crack at the boundary.

[0177] Aiming at the characteristics that the clay core wall has a high saturation and the pore gas is completely wrapped and sealed by pore water, this model, based on the water-gas-solid coupling analysis model of the clay core wall with tension cracks, regards the pore water and gas as mixed fluids, and considers the influence of the pore gas compressibility, and proposes a mixed flow fluid-solid coupling analysis model for the clay core wall with tension cracks.

[0178] The following assumptions are made when constructing the fluid-solid coupling analysis model of mixed flow in a clay core with tension cracks: (1) the clay core has a small deformation; (2) the pore gas in the clay core exists in the form of bubbles, which are completely enclosed by water and do not move relative to the water body; (3) the soil phase and water phase in the clay core are both continuous media, and both water and soil particles are incompressible; (4) the deformation of bubbles in the pores obeys Boyle's law, and the flow of water phase obeys Darcy's law; (5) the temperature effect is ignored, and the core is assumed to be an isothermal body; (6) the dissolution and diffusion of gas in water and the movement of water vapor are not considered.

[0179] Based on the above assumptions, the mixed fluid has the following properties: (1) The flow law of the mixed fluid conforms to Darcy's law. Since the bubbles are stationary relative to the pore water and flow with the water, the flow law of the mixed fluid composed of the two is similar to the flow law of water and also conforms to Darcy's law. (2) The mixed fluid is compressible, that is, the water part of the mixed fluid is incompressible, while the gas part will be compressed and deformed under pressure, so the mixed fluid exhibits compressibility.

[0180] The density of the mixed flow is:

[0181]

[0182] Where: m , w , a are the density of mixed flow, pore water and pore gas respectively, V n is the volume of the pores, S is the saturation, and ρ a <<ρ w , then the density of the mixed flow is approximately: ρ m =ρ w S.

[0183] Because the pore water and gas are regarded as mixed fluids, such as Figure 4 As shown, it is only necessary to analyze the flow process of the mixed fluid without analyzing the flow of pore gas separately. The continuity equation of the soil medium mixed flow can be derived:

[0184]

[0185] Where: p m is the mixed fluid pressure, γ m is the bulk density of the mixed fluid, k m is the permeability coefficient of the mixed fluid.

[0186] This equation indicates that the compression of the soil is equal to the sum of the mixed fluid flow rate out of the soil and the compression of the mixed fluid in the soil. The bulk modulus of the mixed fluid has a greater influence on the calculated result of the seepage pressure value. When the bulk modulus of the mixed fluid is infinite, it degenerates into the pore water continuity equation in the saturated state.

[0187] The water and gas fluids in the fracture are also regarded as mixed fluids, and the continuity equation of the mixed flow in the fracture can be derived as follows:

[0188]

[0189] Where: q 1cm is the mixed fluid flow rate from the crack into the soil medium; w is the crack width; n c is the fracture porosity; k cm is the permeability coefficient of the fracture mixed fluid; p cm is the osmotic pressure of the mixed fluid in the fracture.

[0190] For the above mixed flow continuity equation, the key point of calculation is to determine the mixed fluid bulk modulus B m To determine B m To determine the matrix suction p s When the saturation S is known, the matrix suction p is calculated by the soil-water characteristic curve s , the soil-water characteristic curve function is expressed as: p s =g(S); The compression of the mixed fluid is essentially the compression of the gas in the mixed fluid. Considering the influence of pore pressure on gas compression, a method for determining the bulk modulus of the mixed fluid is proposed, and the expression is:

[0191]

[0192] Where: p 0 is standard atmospheric pressure.

[0193] The static equilibrium equation of clay core wall is:

[0194]

[0195] The mixed flow continuity equation and equilibrium equation are combined to obtain the fluid-solid coupling equation for mixed flow in clay core with tension cracks, which is expressed as follows:

[0196]

[0197]

[0198]

[0199] The solution conditions of the fluid-solid coupling equation of mixed flow in clay core with tension cracks include the initial and boundary conditions of soil deformation, mixed flow seepage pressure and mixed flow seepage pressure in the cracks, where the initial conditions are:

[0200]

[0201]

[0202]

[0203] Where: u 0 、p m0 、p cm0 They are the displacement corresponding to the starting calculation time, the mixed fluid pressure in the soil medium, and the mixed fluid pressure in the crack.

[0204] The first type of boundary condition to be satisfied on the Γ boundary is:

[0205]

[0206]

[0207]

[0208] Where: They are respectively the displacement constraint of soil medium on the boundary, the mixed fluid pressure constraint, and the mixed fluid pressure constraint of cracks at the boundary.

[0209] The second type of boundary condition to be satisfied on the Γ boundary is:

[0210]

[0211]

[0212]

[0213]

[0214]

[0215] Where: t、 They are respectively the load value of soil medium on the boundary, the adhesion value at the crack, the mixed flow flow constraint at the boundary, and the mixed flow flow constraint of the crack at the boundary.

[0216] There are many parameters involved in the fluid-solid coupling analysis model of clay core wall with tension cracks. The following focuses on determining the relevant parameters. Including: taking pore water, air pressure and soil displacement as state variables, the calculation parameters involved mainly include permeability coefficient, saturation and effective stress coefficient, etc., and these parameters change with the change of state variables. The following mainly discusses the relationship between parameters and state variables, and between parameters in the coupling analysis model.

[0217] Matrix suction reflects the soil's ability to hold water. The water holding characteristics change with the change in the ratio of water and gas, that is, they are closely related to the saturation. The lower the saturation, the greater the matrix suction and the stronger the soil's ability to hold water. The relationship between matrix suction and saturation can be characterized by the soil-water characteristic curve. A typical soil-water characteristic curve is shown in Figure 1. Figure 5 As shown, it can be seen that the characteristic points of the curve include the intake value (p a -p w ) b and residual saturation S r When the soil is in a saturated state, the suction is zero. When a small suction is applied to it, the water in the pores will not be discharged. Only when the suction reaches the intake value (p a -p w ) b When the water in the pores is discharged, the gas enters the pores; as the water is discharged, the saturation decreases and the matrix suction increases. When the saturation decreases to a critical value (residual saturation S r ), the change of suction will no longer cause the change of saturation, and the saturation will be maintained at the residual saturation.

[0218] Based on the soil-water characteristic curve, a mathematical model of the relationship between saturation and matrix suction is proposed, and its expression is:

[0219]

[0220] Where: p s is matrix suction; S e is the effective saturation; a, b, c are fitting parameters.

[0221] The relationship between effective saturation and saturation is:

[0222]

[0223] Where: S max is the maximum saturation; S ris the residual saturation of soil.

[0224] The permeability coefficient of clay core wall is closely related to the type of soil, pore size, fluid properties and saturation degree. It is a function related to porosity and saturation, and its expression is:

[0225]

[0226]

[0227] Where: k w , k a is the permeability coefficient of water and gas; μ w , μ a is the viscosity of water and air; g is the acceleration of gravity; K is the inherent permeability of the soil; k wr , k ar is the relative permeability of water and air.

[0228] During the filling and water storage process, the clay core wall is compressed and deformed under the action of its own weight and water pressure load, the soil particles are arranged more closely, the porosity decreases, the infiltration channel becomes narrower, and the infiltration path becomes longer, resulting in a decrease in the permeability coefficient. The test shows that there is an obvious nonlinear relationship between the permeability coefficient and the porosity ratio. The more practical expression for the relationship between the permeability coefficient and the porosity ratio is:

[0229]

[0230] Where: K 0 is the initial intrinsic permeability; e 0 is the initial porosity; e is the porosity.

[0231] The pore size distribution function and saturation are used to uniformly describe the relative permeability coefficients of water and gas, and the expression is:

[0232] k wr =S e (2+3λ) / λ

[0233] k ar =(1-S e ) 2 (1-S e (2+λ) / λ )

[0234] Where: λ is the pore size distribution function.

[0235] For mixed fluids, since the pore gas is completely wrapped by water and flows with the water, the permeability coefficient of the mixed flow adopts the permeability coefficient of the pore water, and the permeability coefficient of the mixed flow is derived as:

[0236]

[0237] Where: k is the permeability coefficient of the mixed flow; k 0 is the initial saturated permeability coefficient.

[0238] According to Bishop's effective stress principle, the relationship between the total stress and the effective stress of the soil particle skeleton, pore pressure, and matrix suction is obtained as follows:

[0239] σ′=(σ-p a I)+χ(p a -p w )I

[0240] Where: σ′ is the effective stress, σ is the total stress, p a is the pore gas pressure, p w is the pore water pressure, p a -p w is the matrix suction, χ is the effective stress coefficient, when χ=1, the soil is in a saturated state, and χ=0, the soil is in a completely dry state.

[0241] The empirical formula of effective stress coefficient about saturation is:

[0242]

[0243] The model has a wide range of applications, not only for various types of clay core walls, but also for different engineering environments, including rockfill dams, earth-rock dams, and concrete gravity dams. This wide applicability makes the model an effective tool for analyzing the changes in the properties of cracks or weak seepage layers in clay core walls due to construction, uncoordinated deformation, etc. The model can provide engineers with valuable insights and decision support both in the design stage and in the operation and maintenance stage.

[0244] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes in form and details may be made without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A fluid-solid coupling analysis method for a clay core wall with tension cracks, characterized in that: The clay core wall with tension cracks includes soil medium and cracks, the soil medium includes soil particles, pore water and pore gas, and the cracks are filled with soil particles, water and gas; The analysis method comprises: establishing a pore water continuity equation in a soil medium and a pore gas continuity equation in a soil medium based on the principle of mass conservation to describe the movement of pore water and pore gas in the soil medium; The masses of each item in the differential unit of the soil medium and crack are expressed as: Where: m s 、m w 、m a are the masses of soil particles, pore water and gas in the differential unit respectively; ρ s , w , a are the densities of soil particles, pore water and gas respectively; n is the porosity; S is the saturation; V is the differential unit volume; The continuity equation of pore water in soil medium is expressed as: Where: k w is the permeability coefficient of pore water, γ w is the bulk density of water, p w is the pore water pressure, ε V is the volume strain of soil under load, p a is the pore gas pressure, p s is the matrix suction, The pore gas continuity equation in soil medium is expressed as: Where: k a is the pore gas permeability coefficient, γ a is the bulk density of pore gas, K a is the pore gas bulk modulus; Based on the seepage exchange between the cracks and the soil medium, the water continuity equation and gas continuity equation in the cracks are established; The static equilibrium equation of clay core wall is established to describe the stress-strain response of soil particle skeleton under external load. By combining the continuity equations of water and air in the soil medium and cracks and the static equilibrium equation of the clay core wall, a water-air-solid coupling analysis model of the clay core wall with tension cracks is established, and the boundary conditions of the model are determined, including the initial conditions and boundary conditions of soil deformation, soil pore water pressure, soil pore air pressure, crack water pressure, and crack air pressure.

2. The fluid-solid coupling analysis method for clay core wall with tension cracks according to claim 1 is characterized in that: The fluid-solid coupling analysis method for the clay core with tension cracks is based on the following assumptions: (1) the soil phase and water phase in the clay core are continuous media, and the soil particles and pore water are incompressible; (2) the flow of pore water and pore gas satisfies Darcy's law; (3) the temperature effect is ignored and the core is assumed to be an isothermal body; (4) the dissolution and diffusion of gas in water and the movement of water vapor are not considered.

3. The fluid-solid coupling analysis method for clay core wall with tension cracks according to claim 1 is characterized in that: The continuity equation of the water body in the crack is expressed as: The gas continuity equation in the crack is expressed as: Where: k cw is the water permeability coefficient in the fracture, p cw is the pore water pressure in the crack, w is the crack width, n c is the fracture porosity, q 1cw is the flow rate from the crack surface to the soil; k ca is the gas permeability coefficient in the crack, p ca is the pore pressure in the crack; q 1ca is the gas flow rate that penetrates into the soil from the crack surface.

4. The fluid-solid coupling analysis method for clay core wall with tension cracks according to claim 3 is characterized in that: The static equilibrium equation of the clay core wall is expressed as: Where: D is the elastic matrix, χ is the effective stress coefficient; I is the unit vector; f is the soil force.

5. The fluid-solid coupling analysis method for clay core wall with tension cracks according to claim 4 is characterized in that: The water-gas-solid coupling equation of the clay core wall with tension cracks is obtained by combining the pore water continuity equation in the soil medium, the pore gas continuity equation in the soil medium, the water continuity equation in the cracks, the gas continuity equation in the cracks and the static equilibrium equation of the core wall clay. Its expression is: The solution conditions of the water-air-solid coupling equation of the clay core with tension cracks include the initial conditions and boundary conditions of soil medium displacement, pore water pressure, air pressure, and water pressure and air pressure in the cracks. The initial conditions are: Where: u0, p w0 、p a0 、p cw0 、p ca0 They are the displacement corresponding to the starting calculation time, the pore water pressure in the soil medium, the pore air pressure, the water pressure in the cracks, and the air pressure in the cracks; The first type of boundary condition to be satisfied on the Γ boundary is: Where: They are the displacement constraint of soil medium on the boundary, pore water pressure constraint, pore air pressure constraint, water pressure and air pressure constraint of cracks at the boundary. The second type of boundary condition to be satisfied on the Γ boundary is: Where: They are respectively the load value of soil medium on the boundary, the adhesion value at the crack, the pore water flow at the boundary, the pore air flow constraint, the pore water flow and pore air flow constraint of the crack at the boundary.

6. The fluid-solid coupling analysis method for clay core wall with tension cracks according to claim 4 is characterized in that: The pore water and gas in the soil medium are regarded as mixed fluids, and it is assumed that: (1) the clay core wall has a small deformation; (2) the pore gas in the clay core wall exists in the form of bubbles, which are completely enclosed by water and do not move relative to the water body; Establish the continuity equation of soil medium mixed flow: Considering the water and gas in the fracture as mixed fluid, the continuity equation of the mixed flow in the fracture is obtained as follows: The static equilibrium equation of clay core wall is:

7. The fluid-solid coupling analysis method for clay core wall with tension cracks according to claim 6 is characterized in that: The mixed flow continuity equation and the clay core equilibrium equation are combined to obtain the mixed flow fluid-solid coupling equation for the clay core with tension cracks. The solution conditions of the fluid-solid coupling equation of mixed flow in clay core with tension cracks include the initial and boundary conditions of soil partial deformation, mixed flow seepage pressure and mixed flow seepage pressure in cracks, among which the initial conditions are: Where: u0, p m0 、p cm0 are the displacement corresponding to the initial calculation time, the mixed fluid pressure in the soil medium, and the mixed fluid pressure in the crack; The first type of boundary condition to be satisfied on the Γ boundary is: Where: They are the displacement constraint of soil medium on the boundary, the mixed fluid pressure constraint, and the mixed fluid pressure constraint of cracks at the boundary. The second type of boundary condition to be satisfied on the Γ boundary is: Where: They are respectively the load value of soil medium on the boundary, the adhesion value at the crack, the mixed flow flow constraint of soil medium at the boundary, and the mixed flow flow constraint of crack at the boundary.

8. The fluid-solid coupling analysis method for clay core wall with tension cracks according to claim 7 is characterized in that: The calculation parameters in the water-gas-solid coupling analysis model of the clay core wall with tension cracks include effective saturation, permeability coefficient, and effective stress coefficient; The effective saturation S e and matrix suction s The relational expression is: Where: S e is the effective saturation, p s is the matrix suction, a, b, c are fitting parameters; Effective saturation S e The relationship expression with saturation S is: Where: S max is the maximum saturation; S r is the residual saturation of soil; The relationship between the permeability coefficient K and the porosity ratio e is expressed as follows: Where: K0 is the initial inherent permeability; e0 is the initial porosity; e is the porosity; The effective stress coefficient σ′ is related to the total stress σ, pore pressure p a , matrix suction p a -p w The relationship between and the effective stress coefficient χ is: σ′=(σ-p a I)+x(p a -p w )I Where: σ′ is the effective stress, σ is the total stress, p a is the pore gas pressure, p w is the pore water pressure, p a -p w is the matrix suction, χ is the effective stress coefficient, when χ=1, the soil is in a saturated state, and χ=0, the soil is in a completely dry state.

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