A method for establishing a two-domain penetration model, storage medium, and electronic device.

Abstract

This invention discloses a method, storage medium, and electronic device for establishing a dual-domain permeability model, relating to the field of hydrogeology. The method includes: dividing the pore system of clay into matrix and fracture domains; conducting soil shrinkage experiments and plotting soil shrinkage curves; establishing soil fracture swelling and shrinkage models for the matrix and fracture domains based on the shrinkage curves and the pore system; obtaining the saturated permeability coefficient of the soil; and establishing governing equations for the variation of pore permeability coefficients in the matrix and fracture domains with soil fracture swelling and shrinkage based on the two-domain swelling and shrinkage models; setting the relative permeability coefficient of the fracture domain to 1, the instantaneous permeability coefficient of the fracture domain being only related to the saturated permeability coefficient, and the saturated permeability coefficient of the fracture domain being a function of the matrix domain saturation; constructing a dual-permeability model with dynamic fracture changes; and using this model for hydrogeological analysis. This invention establishes a dynamic connection between the matrix and fracture domains, making the simulation results more closely match reality.

Description

Technical Field

[0001] This invention relates to the field of hydrogeology, and in particular to a method for establishing a dual-domain permeability model, a storage medium, and an electronic device. Background Technology

[0002] Clay soils are extremely sensitive to climate change. During drying, they are prone to shrinkage and cracking, creating fissures that provide channels for rainwater infiltration. During rainfall, the soil expands and heals, hindering the evaporation and seepage of internal water. Significant rainwater infiltration leads to high moisture content in clay slopes, increasing pore water pressure, reducing shear strength, causing water levels to rise, increasing hydraulic load on the slope, and exacerbating erosion and landslide risks. Given the widespread distribution and significant hazards of clay soils, research on rainwater infiltration in clay soils in regions experiencing extreme climate change should be strengthened.

[0003] However, traditional permeability models typically assume that the macropores of the soil remain constant during rainfall evaporation, neglecting the characteristics of clay shrinkage and swelling, as well as the influence of changes in clay fissures on soil infiltration. Therefore, they are often unsuitable for studying clay wet-dry cycles. Furthermore, existing two-domain dynamic permeability models either ignore the exchange process between the matrix domain and the fissure domain, resulting in results that are not logically sound; or they contain too many parameters, making calculation difficult; or they lack a physically continuous swelling and shrinkage model to describe the dynamic changes in the volume and permeability coefficient of the two domains under the influence of shrinkage and swelling processes. Summary of the Invention

[0004] The purpose of this invention is to address the problem that existing permeability models have fixed fractures and lack an exchange process between the matrix domain and the fracture domain. A method for establishing a dual-domain permeability model is proposed, comprising the following steps:

[0005] S1. Based on the matrix domain and fracture domain, the pore system of clay is divided, soil shrinkage experiments are carried out and soil shrinkage curves are plotted. Based on the shrinkage curves and pore system, soil fracture expansion and contraction models of matrix domain and fracture domain are established.

[0006] S2. Obtain the saturated permeability coefficient of the soil. Based on the two-domain swelling and shrinkage model, establish the governing equations for the changes in pore permeability coefficients of the matrix domain and fracture domain with the swelling and shrinkage of soil fractures.

[0007] S3. Set the relative permeability coefficient of the fracture domain to 1. The instantaneous permeability coefficient of the fracture domain is only related to the saturated permeability coefficient. The saturated permeability coefficient of the fracture domain is a function of the matrix domain saturation. Construct a dual permeability model of dynamic fracture changes and use the dual permeability model of dynamic fracture changes for hydrogeological analysis.

[0008] The present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described method for establishing a dual-domain penetration model.

[0009] The present invention also proposes an electronic device, including a processor and a memory, wherein the processor and the memory are interconnected, wherein the memory is used to store a computer program, the computer program including computer-readable instructions, and the processor is configured to invoke the computer-readable instructions to execute the above-described method for establishing a dual-domain penetration model.

[0010] The beneficial effects of the technical solution provided by this invention are:

[0011] This invention first establishes a soil fracture expansion and contraction model for the matrix and fracture domains, considering the effects of expansion and contraction on fracture development and evolution, soil permeability coefficient, and water migration paths. Then, it establishes governing equations for the changes in pore permeability coefficients in the matrix and fracture domains with soil fracture expansion and contraction, deriving the dynamically changing permeability coefficients. Finally, it constructs a dual permeability model for dynamic fracture changes, establishing the connection between the matrix and fracture domains. Hydrogeological analysis is then performed using this dual permeability model. This invention solves the problem of traditional seepage models assuming fixed fractures; by establishing a dynamic connection between the matrix and fracture domains, the simulation results more closely match reality. Attached Figure Description

[0012] Figure 1 This is a flowchart of the method for establishing a dual-domain penetration model according to an embodiment of the present invention;

[0013] Figure 2 This is a schematic diagram of soil shrinkage according to an embodiment of the present invention;

[0014] Figure 3 This is a block diagram of an electronic device according to an exemplary embodiment of the present invention. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0016] Example 1: The flowchart of the method for establishing the dual-domain penetration model in this embodiment of the invention is as follows. Figure 1 Specifically, it includes the following steps:

[0017] S1. Based on the matrix domain and fissure domain, the pore system of clay is divided, soil shrinkage experiments are carried out and soil shrinkage curves are plotted. Based on the shrinkage curves and the pore system, soil fissure expansion and contraction models of matrix domain and fissure domain are established.

[0018] In a preferred embodiment of the present invention, based on the dual-pore domain infiltration theory, the cracked soil is divided into matrix domains on both sides of the crack, matrix domains at the bottom of the crack, and crack domains. The pore system of clay is divided into internal pores generated by the matrix domains and external pores generated by the crack domains and soil surface settlement. Based on the matrix domains and crack domains, the pore system of clay is divided into: matrix domain pores, crack domain pores, and soil surface settlement pores.

[0019] The relationship between matrix domain porosity, fracture domain porosity, and soil surface settlement porosity is expressed as follows:

[0020]

[0021]

[0022] n t (w max ) = n m (w max (5)

[0023] n t (w s ) = n min +n c (w s )+n s (w s (6)

[0024] Where w represents the mass moisture content, w max w represents the maximum mass water content of the soil. s n represents the moisture content at the shrinkage limit. min n represents the minimum porosity of the matrix domain. t (w) represents the function of total soil porosity as a function of mass water content, n m (w) represents the function of matrix domain porosity as a function of mass moisture content, n c (w) represents the function of porosity of the fractured domain as a function of mass water content, n s V(w) represents the change in surface settlement porosity of soil as a function of mass water content; V(w) represents the change in total soil volume as a function of mass water content. t (w) represents the function of total pore volume of soil as a function of mass water content, V m (w) represents the function of pore volume within the matrix domain as a function of mass water content, V c (w) represents the function of the fracture domain volume as a function of the mass moisture content, V s (w) represents the function of the volume of the settling space as a function of the mass moisture content; n t (w max ) represents the total porosity of the soil when it is at its maximum mass water content, n m (wmax ) represents the matrix porosity of the soil at its maximum mass water content; n t (w s ) represents the total porosity of the soil at its shrinkage-limiting mass water content, n c (w s ) represents the porosity of the fractured domain in soil at its shrinkage-limited mass water content, n s (w s This indicates the surface settlement porosity of the soil when it is at its shrinkage limit moisture content.

[0025] The water content of soil is the ratio of the mass of water in the soil to the mass of solid particles, expressed as a percentage.

[0026] All three types of pores change with the soil moisture content. When saturated, the soil does not crack or settle, so the matrix porosity is equal to the total soil porosity. As the moisture content gradually decreases, the soil shrinks and gradually develops cracks and settles. At this point, the porosity of the soil consists of matrix pores, cracked pores, and ground settlement pores. When the soil moisture content decreases to near the shrinkage limit, the matrix porosity reaches its minimum.

[0027] Soil shrinkage tests were conducted, and soil shrinkage parameters, including soil moisture content, crack parameters, and surface settlement changes, were monitored in real time using a camera system. Based on the monitoring data, a curve showing the change in porosity with moisture content was plotted, i.e., the soil shrinkage curve.

[0028] This curve can be used to obtain the maximum porosity n of the soil matrix in a saturated and crack-free state. max The minimum porosity n when the soil moisture content drops to near the shrinkage limit min And shape distribution parameters p and q. Where, n max With n min The range between these represents the allowable range within which the matrix domain porosity can be converted into fracture domain porosity and sedimentation porosity. Assuming that this part is reversible during the wet-dry cycle, the porosity of the reversible part satisfies the following relationship:

[0029] n rev =n max -n min =n m (w)+n c (w)+n s (w)-n min (7)

[0030] Where, n rev This indicates reversible porosity.

[0031] Based on the four-parameter shrinkage model proposed by Stewart et al., this invention establishes a shrinkage curve function for the soil matrix domain, with the following equation:

[0032]

[0033] Where W is the standard moisture content, n m (W) represents the function of matrix porosity as a function of standard moisture content.

[0034] Combining equations (7) and (8), we obtain the governing equation for the change in porosity of the external matrix domain of the soil:

[0035]

[0036] Where, n out (W) represents the function of the external matrix domain porosity as a function of the standard moisture content, and is equal to the sum of the fracture domain porosity and the settlement porosity.

[0037] Equation (9) shows that the change in the porosity of the outer matrix domain of the soil is proportional to the change in the reversible porosity of the soil. By analogy, for ease of derivation, it is assumed that the change in the volumetric porosity of soil settlement is proportional to the change in the reversible settlement porosity of the soil, and that the reversible settlement porosity of the soil is between 0 and n. s,max The governing equation for soil settlement porosity variation is as follows:

[0038]

[0039] Where, n s (W) represents the function of soil surface settlement porosity as a function of standard moisture content, n s,max This represents the maximum settlement porosity of the soil surface when the soil moisture content is 0.

[0040] Combining equations (9) and (10), the governing equation for the porosity variation in the soil fracture domain is:

[0041]

[0042] Where, n c (W) represents the function of the porosity of the soil fissure domain as a function of the standard moisture content. For ease of derivation and calculation, it is assumed that the soil settlement during shrinkage is proportional to the total shrinkage of the soil.

[0043] To derive n s,max A shrinkage geometric factor x is introduced. When x = 1, it represents that the soil only undergoes vertical shrinkage. When x approaches infinity, the soil only undergoes lateral shrinkage. It is usually assumed that x = 3 represents that the soil undergoes shrinkage in the same direction. The shrinkage geometric factor x is used to describe the changes in the total volume and thickness of the soil and satisfies the following relationship:

[0044]

[0045] Among them, V ms Let H represent the volume of soil particles, H represent the vertical thickness of the soil mass, ΔV(W) represent the change in soil volume corresponding to different changes in standard moisture content, and V(W) represent the change in total soil volume as a function of standard moisture content. m (W) represents the function of pore volume within the matrix domain as a function of standard moisture content, and ΔH(W) represents the function of the vertical change in soil thickness corresponding to different changes in standard moisture content.

[0046] Soil settlement porosity with the incorporation of shrinkage geometry factor is expressed as:

[0047]

[0048] When the moisture content W approaches 0, n m (W) achieves the minimum value n min n s To obtain the maximum value n s,max ,Right now:

[0049]

[0050] Among them, V s (W) represents the function of the volume of the settling space as a function of the standard moisture content, n s (W=0) indicates the soil settlement porosity when the standard moisture content is 0.

[0051] Based on the above derivation, the governing equations for the changes in soil matrix domain, fracture domain, and settlement porosity are mainly composed of p, q, and n. max n min It consists of five parameters: p, q, n, and W. max and n min The standard moisture content W is determined by measuring the soil shrinkage curve as described above, and is obtained by measuring the soil mass moisture content w and the maximum mass moisture content w. max It can then be calculated.

[0052] The cracked soil mass is discretized into N regular small soil blocks on a plane. Assuming that the cracks in each regular soil block have a regular shape, the governing equations for the pore size changes of the soil matrix domain and crack domain during wet-dry cycles are established. The establishment process is as follows:

[0053] Suppose that the side length of one of the discretized regular soil blocks is A (A is a value taken from A). j j = 1, 2, ..., N, A jLet represent the j-th regular soil block, with height H. Under saturated conditions, the volume of this regular soil block is A × A × H. During shrinkage, assuming the soil block shrinks uniformly inwards from all sides, the width of the shrinkage cracks produced by the shrinkage is a (a is a value derived from a...). j j = 1, 2, ..., N, a j Let j represent the j-th fissure. Assuming the surface settlement of the soil block is ΔH, after shrinkage, the volume of the regular soil block becomes (Aa)×(Aa)×(H-ΔH). When the soil moisture content decreases to a certain point, the volume of the fissure domain formed around the regular soil block is a×(2A-a)×(H-ΔH). A schematic diagram of soil shrinkage in this embodiment is provided for reference. Figure 2 .

[0054] Within the matrix domain, the structural porosity of the soil plays a dominant role in seepage compared to the fine pores between soil particles. Therefore, this invention ignores the fine pores between particles and assumes that the structural porosity of the soil consists of M pores with radius r (r is taken from r). i If a cylinder (i = 1, 2, ..., M) with height H is formed, then the volume of the structural pores is M × H × π × r. 2 During shrinkage, the structural porosity of the soil gradually decreases, manifested as a gradual reduction in the radius of individual pores. At saturation, the soil pore radius reaches its maximum value, r. max When the moisture content is close to 0, the soil porosity radius is at its minimum value r. min Although the pores within the soil matrix are actually irregularly shaped and curved, some studies have shown that clay particles have a fishtail-like shape, making the soil pores exhibit a tubular structure that extends into the soil interior. Therefore, this invention assumes that the structural pores of the soil are cylindrical.

[0055] Based on the above assumptions, the porosity variation of the soil matrix domain satisfies the following relationship:

[0056]

[0057] ΔH can be derived from the soil settlement space porosity calculation equation. Transforming equation (10) yields:

[0058]

[0059] Dividing both the upper and lower parts of the left side of the equation by the soil surface area, the equation becomes:

[0060]

[0061] Where M represents the number of cylindrical structural pores in the cracked soil, r i ΔH represents the radius of the i-th cylindrical structural pore in the soil. max Indicates the maximum settlement height, and A represents the side length of a regular soil block, taken from A...j , j = 1, 2, ..., N.

[0062] During the wet-dry cycle, the structural pore size of the soil changes with the water content. Combining equations (8) and (15), we can obtain:

[0063]

[0064] Where, r max r represents the maximum radius of the cylindrical structural pores in the soil. min The minimum radius of the cylindrical structural pores in the soil.

[0065] Substituting equations (17), (18), and (16) into equation (8), we obtain the governing equation for the structural pore size variation of soil:

[0066]

[0067] Where, r i,max Let r represent the maximum radius of the structural pore in the i-th cylinder. i,min This represents the minimum radius of the structural pore in the i-th cylinder.

[0068] Since the height of the soil block is much greater than the settlement height of the soil during the wet-dry cycle, H >> ΔH, equation (19) is simplified to:

[0069]

[0070] The porosity variation in the soil fracture domain satisfies the following relationship:

[0071]

[0072] Among them, A j Let a represent the side length of the j-th regular block. j a represents the width of the crack caused by the shrinkage of the j-th regular soil block. j,max The maximum crack width caused by the shrinkage of the j-th regular soil block when the standard moisture content W = 0.

[0073] Equation (21) can be rewritten as:

[0074]

[0075] Because the width of the soil block is much larger than the width of the crack, 2A j >>a j,max Divide both sides of equation (22) by 2A j The equation can be rewritten using the maximum crack width a. j,max Predict the width a under a certain moisture content condition j expression:

[0076]

[0077] Since H >> ΔH, equation (23) simplifies to:

[0078]

[0079] Therefore, according to equation (24), we can obtain:

[0080]

[0081] As shown in equation (25), if the maximum crack width at a moisture content of W = 0 can be measured when the shrinkage curve parameters are obtained, the crack width under any moisture content condition can be calculated. At the same time, in field tests, we can also calculate the shape parameters of the shrinkage curve by measuring the crack width and the change in moisture content using this formula.

[0082] S2. Obtain the saturated permeability coefficient of the soil. Based on the two-domain swelling and shrinkage model, establish the governing equations for the changes in pore permeability coefficients of the matrix domain and fracture domain with the swelling and shrinkage of soil fractures.

[0083] In a preferred embodiment of the present invention, specifically:

[0084] Indoor soil permeability tests were conducted based on Darcy's law to obtain the saturated permeability coefficient of the experimental materials. The porosity of the matrix domain, fracture domain, and total porosity were expressed as:

[0085] n t (W)=β(W)δ c (W)+(1-β(W))δ m (W)(26)

[0086]

[0087] Where, n t β(W) represents the total porosity of the soil as a function of standard moisture content, β(W) represents the volumetric weighting factor of the fractured domain as a function of standard moisture content, with a value range of 0 to 1, and δ c (W) represents the function of porosity within the fractured domain as a function of standard moisture content, δ m (W) represents the function of porosity within the matrix domain as a function of standard moisture content, V c1 (W) represents the function of pore volume within the fractured domain as a function of standard moisture content, V m，t (W) represents the total volume of the matrix domain as a function of standard moisture content. In reality, the fracture domain contains a certain volume of loose soil particles, hence V c1 Not entirely equivalent to V c .

[0088] For ease of derivation, this invention does not consider the influence of loose soil particles on cracks, i.e., V c1 =V c δ c =1. Then equation (26) simplifies to: n t (W)=β(W)+(1-β(W))δ m (W).

[0089] Secondly, assume β represents the combined volume proportion of the fractured domain and the settlement space:

[0090]

[0091] Then n m (W)=(1-β(W))δ m (W)(30)

[0092] Combining equations (8), (26), (29), and (30), we get:

[0093]

[0094] According to the definition of volumetric water content, the volumetric water content of the matrix domain, fissure domain, and soil surface settlement space is expressed as:

[0095] θ t =θ m +θ c +θ s (32)

[0096]

[0097] Where, θ t θ represents the total volumetric water content of the soil. m Represents the volumetric water content of the matrix domain, θ c θ represents the volumetric water content of the fractured domain. s V represents the volumetric water content of the soil surface settlement; w，m V represents the volume of water contained within the matrix domain. w，c V represents the volume of water contained within the fractured domain. w，s This represents the volume of water contained in the space created by the settlement of the soil surface.

[0098] Since the soil surface typically does not contain free water, then θ s =0, equation (32) simplifies to:

[0099] θ t =θ m +θ c (33)

[0100] Similar to the porosity expression method in the dual-porosity model, the volumetric water content in the matrix domain and the fracture domain is expressed as:

[0101]

[0102] and then:

[0103]

[0104] in, The function representing the change in volumetric moisture content within the matrix domain with respect to standard moisture content. It is a function representing the change in volumetric water content within the fractured domain with respect to the standard water content.

[0105] The water flux density in the matrix domain and the fracture domain is expressed as:

[0106]

[0107] In the formula, R m R represents the water flux density per unit area of ​​the matrix domain in the vertical direction. c Q represents the water flux density per unit area of ​​the fracture domain in the vertical direction; R represents the water flux density per unit area in the vertical direction. m Q represents the water flux in the matrix domain. c S represents the water flux in the fracture domain. m S represents the cross-sectional area of ​​the matrix domain. c This represents the cross-sectional area of ​​the fracture domain.

[0108] The cross-sectional areas of the matrix domain and the fracture domain are expressed as follows:

[0109]

[0110] Combining equations (42) and (43), equation (41) can be rewritten as:

[0111]

[0112] If soil surface settlement is not considered, then equation (44) simplifies to:

[0113] R = R m [1-β(W)]+R c β(W)(45)

[0114] The water flow velocities within the matrix domain and the fracture domain are expressed as:

[0115]

[0116] Among them, v m The velocity v represents the water flow rate within the matrix domain. c This indicates the flow velocity of water within the fractured region.

[0117] Based on Darcy's law, the relationship between soil saturated permeability coefficient, water flux density, and soil water potential gradient is established:

[0118]

[0119] Where Δω represents the soil water potential gradient. c The water potential gradient in the soil fissure domain is Δω. m For soil matrix water potential gradient; K s (W) represents the function of soil saturated permeability coefficient as a function of standard moisture content, K s,c (W) represents the saturated permeability coefficient of the soil fracture domain as a function of standard moisture content, K s,m (W) represents the function of the saturated permeability coefficient of the soil matrix domain as a function of standard moisture content.

[0120] If we assume that the water potential gradient is the same in all regions, i.e., Δω = Δω c =Δω m Then equation (48) simplifies to:

[0121]

[0122] Traditional dual-permeability models often assume that the soil permeability coefficient remains constant during wet-dry cycles. However, in reality, the cross-sectional area of ​​soil pores changes during wet-dry cycles, and the flow velocity of water flowing through the pores also changes nonlinearly under a given water potential gradient. This leads to nonlinear changes in the soil matrix domain, fracture domain, and overall saturated permeability coefficient.

[0123] Assuming the soil fissures are regular cuboids and the matrix pores are cylindrical as previously assumed, Poiseuille's equations show that the flow rate through the cuboid pore space is proportional to the cube of the pore width, and the flow rate through the cylindrical pore is proportional to the square of the radius. The water flux through the cuboid and cylindrical pore spaces can be expressed as:

[0124]

[0125] In the formula, Q rect Let Q be the water flux through the pore space of the cuboid. rcircle Let ρ be the water flux through the pore space of the cylinder. w Let g be the density of water, g be the acceleration due to gravity, and μ be the acceleration due to gravity. w Let be the viscosity of water, and r represent the radius of the cylinder, taken from r... i Let i = 1, 2, ..., M, and a represent the cracks caused by the shrinkage of regular soil blocks, with values ​​taken from a... j , j = 1, 2, ..., N.

[0126] Assuming the geometry of soil fissures and pores remains unchanged during wet-dry cycles, the permeability coefficient of the soil fissure domain is derived based on the above formula for water flux through rectangular pore spaces:

[0127]

[0128] Substituting equation (24) into equation (52), we get:

[0129]

[0130] Where, τ j K represents the curvature of the soil surrounding the j-th regular block. c,max This represents the maximum saturated permeability coefficient of the soil fissure domain in a dry state.

[0131] The matrix domain permeability coefficient is obtained based on formula (51):

[0132]

[0133] Assuming that the pore volume of all matrix domains shrinks at a certain ratio, the soil matrix domain porosity reaches its maximum at saturation, and cracks are not developed. The expression is:

[0134]

[0135] Substituting equations (20) and (56) into equation (55), we get:

[0136]

[0137] Where, r i,max r represents the maximum radius of the pores in the i-th circular matrix domain. i,min This represents the minimum radius of the pores in the i-th circular matrix domain.

[0138] Based on the above formula, the maximum permeability coefficient K of the soil matrix at saturation (when the standard moisture content is 1) can be obtained. m,max And the minimum permeability coefficient K when dry (when the standard moisture content is 0). m,min :

[0139]

[0140] Substituting equations (58) and (59) into equation (57) simplifies to:

[0141]

[0142] The minimum permeability coefficient of the soil matrix is ​​much smaller than the maximum permeability coefficient at saturation. Further simplification of equation (60) yields:

[0143]

[0144] Substituting equations (53) and (61) into equation (49), we derive the expression for the soil permeability coefficient:

[0145]

[0146] Ignoring soil surface settlement, equation (62) simplifies to:

[0147]

[0148] S3. Set the relative permeability coefficient of the fracture domain to 1. The instantaneous permeability coefficient of the fracture domain is only related to the saturated permeability coefficient. The saturated permeability coefficient of the fracture domain is a function of the matrix domain saturation. Construct a dual permeability model of dynamic fracture changes and use the dual permeability model of dynamic fracture changes for hydrogeological analysis.

[0149] Specifically:

[0150] The existing static dual-permeability model (Gerke et al.) divides the soil into two regions based on the proportions of the matrix and fracture domains. Both regions are continuous media, overlapping and interacting with each other. The water transport processes in the matrix and fracture domains are described by two coupled 2-D Richards equations, as detailed below:

[0151]

[0152] Among them, T w =a w K a (h c -h m (66)

[0153] In the formula, h represents the pressure head, h c and h m K represents the pressure head of the matrix domain and the fracture domain, respectively. a Let z be the permeability coefficient between the two domains, z represent the position head, and t represent time. w a represents the water exchange term between the fracture domain and the matrix domain. w C represents the water exchange coefficient between the two domains; c (h c The expression is C represents the specific water capacity of the soil fractured domain as a function of the fractured domain pressure head. m (h m The expression is K represents the function of the specific water capacity of the soil matrix domain as a function of the pressure head of the matrix domain. c (h) represents the instantaneous permeability coefficient of the fracture domain as a function of pressure head, Km β(h) represents the instantaneous permeability coefficient of the matrix domain as a function of pressure head, and β(h) represents the volume weighting factor of the fracture domain as a function of pressure head. This represents the gradient operator.

[0154] In actual experiments, the soil thickness is much greater than the soil settlement, and the soil settlement space has no substantial impact on the water transport in the soil. Ignoring soil settlement, the relationship between the porosity of the soil matrix and fractured domains and the water content is expressed as follows:

[0155]

[0156] Due to the standard moisture content of the soil Se m To determine the soil matrix saturation, equations (67) and (68) are rewritten as follows:

[0157]

[0158] Where, n m (Se m ) represents the function of soil matrix porosity as a function of soil matrix saturation, n c (Se m β(Se) represents the function of soil fracture domain porosity as a function of soil matrix domain saturation. m ) represents a function of the volume weighting factor of the fractured domain as a function of the saturation of the soil matrix domain.

[0159] The porosity within the matrix domain, the volumetric water content within the matrix domain, the volumetric water content within the fracture domain, the saturated permeability coefficient of the matrix domain, the saturated permeability coefficient of the fracture domain, the saturated permeability coefficient of the soil, and the volume fraction of the fracture domain are expressed using the degree of saturation:

[0160]

[0161]

[0162] Where, δ m (Se m The expression represents a function of porosity within the matrix domain as a function of matrix domain saturation. The function representing the change in volumetric water content within the matrix domain with the matrix domain saturation. K represents the function of volumetric water content within the fracture domain as a function of matrix domain saturation. s,m (Se m K represents the function of the saturated permeability coefficient of the soil matrix domain as a function of the matrix domain saturation. s,c (Se m K represents the saturated permeability coefficient of the soil fracture domain as a function of the matrix domain saturation. s (Sem ) represents the function of soil saturation permeability coefficient as a function of matrix saturation.

[0163] In the above formula, the matrix domain saturation Se m The function can be obtained from the soil-water characteristic curve function expression of the soil matrix domain in the Mualem-van Genuchten model:

[0164]

[0165] in, This represents the volumetric water content corresponding to the volume of each domain. Indicates the saturated volumetric water content of the soil. S represents the residual volumetric water content of the soil. e (h) represents the function of soil effective saturation as a function of pressure head, and α, n and b are the shape parameters of the soil-water characteristic curve, which can be obtained by fitting the soil-water characteristic curve. When the soil-water characteristic curve is known, equations (69) to (76) can be calculated.

[0166] According to the Mualem-van Genuchten model, the instantaneous permeability coefficient of soil is expressed as follows:

[0167]

[0168] In the formula, S e K(S) represents the effective saturation of the soil. e K represents the function K that represents the change of the instantaneous permeability coefficient of soil with the effective saturation of soil. s (S e K represents the function of soil saturation permeability coefficient as a function of soil effective saturation. r (S e The function represents the relative permeability coefficient of soil as a function of the effective saturation of soil.

[0169] The expressions for the instantaneous permeability coefficients of the soil matrix domain and the fracture domain are as follows:

[0170]

[0171] Among them, Se c K represents the saturation degree of the soil fracture domain. m (S e K represents a function of the instantaneous permeability coefficient of the soil matrix domain as a function of the effective saturation of the soil. c (S e K represents a function of the instantaneous permeability coefficient of the soil fracture domain as a function of the effective saturation of the soil. r (Se mK represents the relative permeability coefficient of soil as a function of the saturation of the soil matrix. r (Se c The function represents the relative permeability coefficient of soil as a function of the saturation of the soil fracture domain.

[0172] Unlike traditional static dual-permeability models, this invention sets the relative permeability coefficient of the fracture domain to 1. The instantaneous permeability coefficient of the fracture domain is only related to the saturation permeability coefficient, and the saturation permeability coefficient of this domain is a function of the matrix domain saturation, expressed as:

[0173]

[0174] In the formula K m,max K can be obtained through permeability testing of uncracked soil samples indoors. c,max The maximum width a of the crack can be measured. max The estimation is performed using the Poiseuille equation, which is as follows:

[0175]

[0176] Substituting equations (29), (66), (72), (73), (77), (81), and (82) into equations (64) and (65), we obtain a dual-permeability model for the dynamic changes of fractures:

[0177]

[0178] The model mainly includes seven parameters, including four easily obtainable shrinkage curve parameters: maximum porosity n max Minimum porosity n min The shape distribution parameters p and q, as well as the three soil-water characteristic curve parameters α, n and b that can be obtained through fitting, can all be obtained through geotechnical experiments, which are simple to operate and easy to obtain.

[0179] Hydrogeological analyses can be conducted using a dual-permeability model that utilizes the dynamic changes in fractures, such as soil moisture migration analysis, slope stability analysis, and the migration and diffusion of soil pollutants.

[0180] Example 2: In an exemplary embodiment, a computer-readable storage medium is included, which stores a computer program that, when executed by a processor, implements the above-described method for establishing a dual-domain penetration model.

[0181] Example 3: Please refer to Figure 3 In one exemplary embodiment, the device further includes an electronic device including at least one processor, at least one memory, and at least one communication bus.

[0182] The memory stores a computer program, which includes computer-readable instructions. The processor calls the computer-readable instructions stored in the memory through the communication bus to execute the above-mentioned method for establishing the dual-domain penetration model.

[0183] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for establishing a two-domain penetration model, characterized in that, Includes the following steps: S1. Based on the matrix domain and fracture domain, the pore system of clay is divided, soil shrinkage experiments are carried out and soil shrinkage curves are plotted. Based on the shrinkage curves and pore system, soil fracture expansion and contraction models of matrix domain and fracture domain are established. S2. Obtain the saturated permeability coefficient of the soil. Based on the two-domain swelling and shrinkage model, establish the governing equations for the changes in pore permeability coefficients of the matrix domain and the fracture domain with the swelling and shrinkage of soil fractures. S3. Set the relative permeability coefficient of the fracture domain to 1. The instantaneous permeability coefficient of the fracture domain is only related to the saturation permeability coefficient. The saturation permeability coefficient of the fracture domain is a function of the matrix domain saturation. Construct a dual permeability model of dynamic fracture changes and use the dual permeability model of dynamic fracture changes for hydrogeological analysis. The soil fracture swelling and shrinkage model, based on the shrinkage curve and pore system, is specifically established as follows: The shrinkage curve function of the soil matrix domain is expressed as: （8）， in, Standard moisture content, The function representing the change in matrix porosity with standard moisture content. and Indicates the maximum and minimum porosity of the soil matrix. and These are shape distribution parameters; The governing equation for the porosity variation of the external matrix domain of soil is expressed as: （9）， in, The function representing the change in porosity of the external matrix domain with standard moisture content; The governing equation for soil settlement and porosity variation is: （10）， in, The function representing the change in surface settlement porosity of soil with standard moisture content. This represents the maximum settlement porosity of the soil surface when the soil moisture content is 0. The governing equation for the porosity variation in the soil fracture domain is: （11）， in, The function representing the change in porosity of soil fracture domains with standard moisture content. This represents the maximum settlement porosity of the soil surface when the soil moisture content is 0. For the derivation Introducing a shrinkage geometric factor Shrinkage geometric factor When used to describe changes in the total volume and thickness of soil, the following relationship must be satisfied: （12）， in, Where H represents the volume of soil particles, and H represents the vertical thickness of the soil mass. A function representing the change in soil volume corresponding to different changes in standard moisture content. The function representing the change in total soil volume with standard moisture content. The function representing the change in pore volume within the matrix domain with standard moisture content. A function representing the change in the thickness of the soil in the vertical direction corresponding to different changes in standard moisture content; Soil settlement porosity with the incorporation of shrinkage geometry factor is expressed as: （13） （14）， in, The function representing the change in the volume of the settlement space with standard moisture content. This represents the soil settlement porosity at a standard moisture content of 0. The cracked soil mass is discretized into N regular soil blocks on a plane. The cracks in each regular soil block have a regular shape, and the side length of the discretized regular soil block is... , The vertical thickness is H, and the width of the drying shrinkage crack produced by each regular soil block during shrinkage is... , Let the structural pores of the soil matrix be cylinders penetrating the top and bottom of a regular soil block, with each cylinder having the same height and vertical thickness as the regular soil block, denoted as H. The porosity variation of the soil matrix domain satisfies the following relationship: （15） （16）， Where M represents the number of cylindrical structural pores in the cracked soil. This represents the radius of the i-th cylindrical structural pore in the soil. Indicates the maximum settlement height, and A represents the side length of a regular soil block, with values ​​derived from... , ; Combining equations (8) and (15), we get: （17） （18）， in, This represents the maximum radius of the cylindrical structural pores in the soil. The minimum radius representing the cylindrical structural pores of soil; Substituting equations (17), (18), and (16) into equation (8), we obtain the governing equation for the structural pore size variation of soil: （19）， in, Let represent the radius of the structural pore in the i-th cylinder. , This represents the maximum radius of the structural pore in the i-th cylinder. Represents the minimum radius of the structural pore in the i-th cylinder; Because the height of the soil block is much greater than the settlement height of the soil during the wet-dry cycle, H>> Therefore, equation (19) is simplified to: （20）， The porosity variation in the soil fracture domain satisfies the following relationship: （21）， in, This represents the side length of the j-th regular block. This represents the width of the crack caused by the shrinkage of the j-th regular soil block. Standard moisture content At that time, the maximum crack width generated by the shrinkage of the j-th regular soil block; Equation (21) can be rewritten as: （22）， Because the width of the soil block is much larger than the width of the crack. >> Divide both sides of equation (22) by The equation can be rewritten using the maximum crack width. Predict the width under a certain moisture content condition expression: （23）， And because H>> Equation (23) simplifies to: （24）， Therefore, according to equation (24), we get: （25）。 2. The method for establishing a dual-domain penetration model according to claim 1, characterized in that, The pore system of clay is divided into matrix domains and fissure domains as follows: matrix domain pores, fissure domain pores, and soil surface settlement pores.

3. The method for establishing a dual-domain penetration model according to claim 2, characterized in that, The relationship between matrix porosity, fracture porosity, and soil surface settlement porosity is expressed as follows: （1） （2） （3） （4） （5） （6）， in, Indicates the moisture content by mass. This indicates the maximum mass water content of the soil. Indicates the moisture content of the shrinkage limit mass. Indicates the minimum porosity of the matrix domain. The function representing the change in total porosity of soil with mass moisture content. The function representing the change in matrix domain porosity with mass moisture content. The function representing the porosity of the fractured domain as a function of mass water content. The function representing the change in surface porosity of soil with mass moisture content; The function representing the change in total soil volume with mass moisture content. The function representing the change in total pore volume of soil with mass moisture content. The function representing the change in pore volume within the matrix domain with mass water content. The function representing the change in fracture domain volume with mass moisture content. A function representing the change in volume of the settling space with mass moisture content; This represents the total porosity of the soil when it is at its maximum mass moisture content. This represents the matrix porosity of the soil when it is at its maximum mass moisture content. This represents the total porosity of the soil at its shrinkage-limiting mass moisture content. This represents the porosity of the fractured domain in soil at its shrinkage-limited mass moisture content. It represents the surface settlement porosity of soil when the soil is at its shrinkage limit mass moisture content.

4. The method for establishing a dual-domain penetration model according to claim 3, characterized in that, Soil shrinkage parameters include changes in soil moisture content, crack parameters, and surface settlement. Based on these soil shrinkage parameters, a curve showing the change in porosity with moisture content is plotted to obtain the soil shrinkage curve.

5. The method for establishing a dual-domain penetration model according to claim 4, characterized in that, The maximum porosity of the soil matrix was obtained by measuring the soil shrinkage curve. Minimum porosity of the soil matrix and shape distribution parameters and ; and The range between these two values ​​represents the allowable range within which matrix domain porosity can be converted into fracture domain porosity and sedimentation porosity, expressed as: ， in, This indicates reversible porosity.

6. The method for establishing a dual-domain penetration model according to claim 5, characterized in that, The governing equations for the variation of pore permeability coefficients in the matrix and fracture domains with soil fracture expansion and contraction are as follows: The porosity of the matrix domain, the fracture domain, and the total porosity are expressed as: （26） （27） （28）， in, The function representing the change of total porosity of soil with standard moisture content. The function representing the volumetric weighting factor of the fractured domain as a function of standard moisture content. The function representing the porosity within the fractured domain as a function of standard moisture content. The function representing the porosity within the matrix domain as a function of standard moisture content. The function representing the change in pore volume within the fractured domain with standard moisture content. The function representing the total volume of the matrix domain as a function of standard moisture content; （29）， but (30); Combining equations (8), (29), and (30), we get: （31）， The volumetric water content of the matrix domain, fissure domain, and soil surface settlement space is expressed as: （32） （33） （34） （35）， in, Represents the total volumetric water content of the soil. Represents the volumetric water content of the matrix domain. Represents the volumetric water content of the fractured domain. Volumetric water content representing soil surface settlement; This represents the volume of water contained within the matrix domain. This represents the volume of water contained within the fracture domain. The volume of water contained in the space created by the settlement of the soil surface is given by [the following]. Equation (32) simplifies to: （33）， The volumetric water content within the matrix domain and the fracture domain is expressed as: （34） （35） （36）， and then: （37） （38）， in, The function representing the change in volumetric moisture content within the matrix domain with respect to standard moisture content. The function representing the change in volumetric water content within the fractured domain with respect to the standard water content; The water flux density in the matrix domain and the fracture domain is expressed as: （39） （40） （41）， In the formula, This represents the water flux density per unit area of ​​the matrix domain in the vertical direction. This represents the water flux density per unit area of ​​the fracture domain in the vertical direction. This represents the water flux density per unit area in the vertical direction. Represents the water flux in the matrix domain. Represents the water flux in the fracture domain; Represents the cross-sectional area of ​​the matrix domain. Represents the cross-sectional area of ​​the fracture domain; The cross-sectional areas of the matrix domain and the fracture domain are expressed as follows: （42） （43）， Combining equations (42) and (43), equation (41) can be rewritten as: （44）， Neglecting soil surface settlement, equation (44) simplifies to: （45）， The water flow velocities within the matrix domain and the fracture domain are expressed as: （46） （47）， in, Indicates the flow velocity of water within the matrix domain. This indicates the flow velocity of water within the fracture domain; Based on Darcy's law, the relationship between soil saturated permeability coefficient, water flux density, and soil water potential gradient is established: （48）， in, Represented as the soil water potential gradient, For the water potential gradient in the soil fissure domain, The water potential gradient of the soil matrix domain; The function representing the change of soil saturated permeability coefficient with standard moisture content. The function representing the saturated permeability coefficient of soil fissure domain as a function of standard moisture content. The function representing the saturated permeability coefficient of the soil matrix domain as a function of standard moisture content; To ensure that the water potential gradient is the same in all regions, that is... Then equation (48) simplifies to: （49）， Let the fissures in the soil be regular cuboids. The water flux through the cuboid pore space and the water flux through the cylinder pore space are expressed as follows: （50） （51）， In the formula, The water flux through the pore space of the cuboid. The water flux through the pore space of the cylinder. The density of water, It is the acceleration due to gravity. The viscosity of water, Represents the radius of the cylinder, taken from... , 'a' represents the cracks caused by the shrinkage of regular soil blocks, and its value is taken from... , ; During the wet-dry cycle, while keeping the geometry of soil fissures and pores constant, the permeability coefficient of the soil fissure domain is derived based on the water flux formula for rectangular pore spaces: （52）， Substituting equation (24) into equation (52), we get: （53）， in, (54); in, This represents the curvature of the soil surrounding the j-th regular block. This represents the maximum saturated permeability coefficient of the soil fracture domain in a dry state. The matrix domain permeability coefficient is obtained based on formula (51): （55）， When the pore volume of all matrix domains shrinks proportionally, the soil matrix domain porosity reaches its maximum at saturation, and cracks are not developed. The expression is: （56）， Substituting equations (20) and (56) into equation (55), we get: （57）， in, This represents the maximum radius of the pores in the i-th circular matrix domain. This represents the minimum radius of the pores in the i-th circular matrix domain; The maximum permeability coefficient of the soil matrix at saturation can be obtained from the above formula. and the minimum permeability during drying : （58） （59）， Substituting equations (58) and (59) into equation (57) simplifies to: （60）， The minimum permeability coefficient of the soil matrix is ​​much smaller than the maximum permeability coefficient at saturation. Further simplification of equation (60) yields: （61）， Substituting equations (53) and (61) into equation (49), we derive the expression for the soil permeability coefficient: （62）， Ignoring soil surface settlement, equation (62) simplifies to: （63）。 7. The method for establishing a dual-domain penetration model according to claim 6, characterized in that, S3 specifically refers to: The water transport process in the matrix and fracture domains is described by two coupled 2-D Richards equations: （64） （65） in, (66), In the formula, Indicates pressure head, and These represent the pressure head in the matrix domain and the fracture domain, respectively. The permeability coefficient between the two domains Indicates the position of the water head. Indicates time, This represents the water exchange term between the fracture domain and the matrix domain. Indicates the water exchange coefficient between the two domains; The expression is , representing the specific water capacity of the soil fracture domain as a function of the pressure head of the fracture domain. The expression is , representing the specific water capacity of the soil matrix as a function of the pressure head of the matrix. The function representing the instantaneous permeability coefficient of the fracture domain as a function of pressure head. The function representing the instantaneous permeability coefficient of the matrix domain as a function of pressure head. The function representing the volume weighting factor of the fractured domain as a function of pressure head. Represents the gradient operator; Ignoring soil settlement, the relationship between the porosity of the soil matrix and fractured domains and the water content is expressed as follows: （67） （68）， Due to the standard moisture content of the soil , For the soil matrix saturation, when the residual water content of the soil is low, the soil matrix saturation is equal to the relative saturation. Equations (67) and (68) can be rewritten as follows: （69） （70）， in, The function representing the change in soil matrix porosity with soil matrix saturation. The function representing the change in porosity of the soil fracture domain with the saturation of the soil matrix domain. A function representing the change of the fracture domain volume weighting factor with the saturation of the soil matrix domain; The porosity within the matrix domain, the volumetric water content within the matrix domain, the volumetric water content within the fracture domain, the saturated permeability coefficient of the matrix domain, the saturated permeability coefficient of the fracture domain, the saturated permeability coefficient of the soil, and the volume fraction of the fracture domain are expressed using the degree of saturation: （71） （72） （73） （74） （75） （76）， in, The function representing the change in porosity within the matrix domain with matrix domain saturation. The function representing the change in volumetric water content within the matrix domain with the matrix domain saturation. The function representing the change in volumetric water content within the fracture domain with the saturation of the matrix domain. The function representing the saturated permeability coefficient of the soil matrix domain as a function of the matrix domain saturation. The function representing the saturated permeability coefficient of the soil fracture domain as a function of the matrix domain saturation. The function representing the soil saturation permeability coefficient as a function of the matrix domain saturation. The function is obtained based on the soil-water characteristic curve function expression of the soil matrix domain in the Mualem-van Genuchten model: （77）， in, This represents the volumetric water content corresponding to the volume of each domain. Indicates the saturated volumetric water content of the soil. Indicates the residual volumetric water content of the soil. , and The shape parameters of the soil-water characteristic curve; A function representing the effective saturation of soil as a function of pressure head; The instantaneous permeability coefficient of soil is expressed as follows: （78）， In the formula, The effective saturation of the soil. The function representing the instantaneous permeability coefficient of soil as a function of the effective saturation of soil. The function representing the change of soil saturation permeability coefficient with respect to the effective degree of soil saturation. A function representing the relative permeability coefficient of soil as a function of its effective saturation. The expressions for the instantaneous permeability coefficients of the soil matrix domain and the fracture domain are as follows: （79） （80）， in, Indicates the saturation degree of the soil fissure domain; The function representing the instantaneous permeability coefficient of the soil matrix domain as a function of the effective saturation of the soil. The function representing the instantaneous permeability coefficient of the soil fracture domain as a function of the effective saturation of the soil. The function representing the relative permeability coefficient of soil as a function of the saturation of the soil matrix. The function representing the relative permeability coefficient of soil as a function of the saturation of the soil fracture domain; The relative permeability coefficient of the fracture domain is set to 1. The instantaneous permeability coefficient of the fracture domain is only related to the saturation permeability coefficient, and the saturation permeability coefficient of this domain is a function of the matrix domain saturation, expressed as: （81） （82）， in, (83); in, Indicates the maximum width of the crack; Substituting equations (29), (66), (72), (73), (77), (81), and (82) into equations (64) and (65), we obtain a dual-permeability model that considers the dynamic changes of the fracture: （84） （85）， Hydrogeological analysis was conducted using a dual-permeability model that utilizes the dynamic changes in fractures.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it implements the method as described in any one of claims 1-7.

9. An electronic device, characterized in that, The device includes a processor and a memory interconnected thereto, wherein the memory is used to store a computer program, the computer program including computer-readable instructions, and the processor is configured to invoke the computer-readable instructions to perform the method as described in any one of claims 1-7.

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