Establishment method of double-domain penetration model, storage medium and electronic equipment

Abstract

The invention discloses a method for establishing a double-domain penetration model, a storage medium and electronic equipment, and relates to the technical field of hydrogeology, and the method comprises the steps: dividing a pore system of clay based on a matrix domain and a fracture domain, carrying out a soil shrinkage experiment, and drawing a soil shrinkage curve, according to the shrinkage curve and the pore system, establishing a soil mass fracture expansion and shrinkage model of the matrix domain and the fracture domain; obtaining a saturated permeability coefficient of a soil body, and on the basis of the two-domain swelling and shrinking model, establishing a change control equation of the pore permeability coefficients of the matrix domain and the fracture domain along with the swelling and shrinking of the soil body fracture; the relative permeability coefficient of the fracture domain is set to be 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 saturation function of the matrix domain, a dual-permeability model of dynamic fracture change is constructed, and hydrogeological analysis is conducted through the dual-permeability model of the dynamic fracture change. According to the invention, a dynamic relation is established between the matrix domain and the fissure domain, so that the simulation result is more fit with the reality.

Description

Technical Field

[0001] The invention relates to the technical field of hydrogeology, and in particular to a method for establishing a dual-domain permeability model, a storage medium, and electronic equipment. Background Art

[0002] Clay soil is extremely sensitive to climate change. It is easy to shrink and crack during the drying process. The cracks formed provide channels for rainfall infiltration. When it rains, the soil will expand and heal, hindering the evaporation and seepage of internal water. Large amounts of rainwater infiltration will cause a high moisture content in the clay slope, which will increase the pore water pressure, reduce the shear strength of the soil, and cause the water level to rise, increase the hydraulic load on the slope, and increase the risk of erosion and sliding of the soil. Based on the above characteristics of clay soil, which is widely distributed and has great harm, research on rainfall infiltration of clay soil in areas of extreme climate change should be strengthened.

[0003] However, traditional permeability models usually assume that the macropores of the soil remain unchanged during rainfall and evaporation, ignoring the characteristics of clay shrinkage and swelling and the influence of clay fissure changes on soil infiltration, and are often not suitable for the study of clay dry-wet cycles. In addition, the existing dual-domain dynamic permeability models either ignore the exchange process between the matrix domain and the fracture domain, resulting in unreasonable results; or contain too many parameters and are difficult to calculate; or lack a physically continuous expansion and contraction model to describe the dynamic changes of the volume and permeability coefficient of the two domains under the influence of the shrinkage and swelling process. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that the cracks in the existing permeability model are fixed and there is no exchange process between the matrix domain and the crack domain, and propose a method for establishing a dual-domain permeability model, comprising the following steps:

[0005] S1. Divide the pore system of clay based on the matrix domain and the fracture domain, carry out soil shrinkage experiments and draw soil shrinkage curves, and establish soil fracture expansion and contraction models in the matrix domain and the fracture domain based on the shrinkage curves and pore systems;

[0006] S2. Obtain the saturated permeability coefficient of the soil, and establish a control equation for the change of the pore permeability coefficients of the matrix domain and the fracture domain with the expansion and contraction of the soil fracture based on the two-domain expansion and contraction model;

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

[0008] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for establishing the dual-domain penetration model is implemented.

[0009] The present invention also proposes an electronic device, comprising 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 comprises computer-readable instructions, and the processor is configured to call the computer-readable instructions to execute the above-mentioned method for establishing a dual-domain penetration model.

[0010] The beneficial effects brought by the technical solution provided by the present invention are:

[0011] The present invention first establishes soil fissure expansion and contraction models in the matrix domain and the fissure domain, taking into account the effects of expansion and contraction on the development and evolution of fissures, soil permeability coefficient and water migration path, and then establishes control equations for changes in the pore permeability coefficients of the matrix domain and the fissure domain with the expansion and contraction of soil fissures, derives the dynamically changing permeability coefficient, and finally constructs a dual permeability model of dynamically changing fissures, and establishes a connection between the matrix domain and the fissure domain. Hydrogeological analysis is performed using the dual permeability model of dynamically changing fissures. This solves the problem of assuming that fissures are fixed in traditional seepage models; the present invention establishes a dynamic connection between the matrix domain and the fissure domain, so that the simulation results are more in line with reality. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0014] Figure 3 It is a block diagram of an electronic device in an exemplary embodiment of the present invention. DETAILED DESCRIPTION

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

[0016] Example 1: A flowchart of a method for establishing a dual-domain permeation model according to an embodiment of the present invention is shown in FIG. Figure 1 , specifically including the following steps:

[0017] S1. The pore system of clay is divided into matrix domain and fracture domain, soil shrinkage experiment is carried out and soil shrinkage curve is drawn, and soil fracture expansion and contraction model of matrix domain and fracture domain is established according to the shrinkage curve and pore system.

[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 the clay is divided into internal pores generated by the matrix domain and external pores generated by the crack domain and soil surface settlement. The pore system of the clay is divided based on the matrix domain and the crack domain: matrix domain pores, crack domain pores, and soil surface settlement pores.

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

[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 Indicates the maximum mass moisture content of soil, w s Indicates the moisture content of shrinkage limit, n min represents the minimum porosity of the matrix domain, n t (w) represents the function of soil total porosity changing with mass water content, n m (w) represents the function of matrix porosity changing with mass water content, n c (w) represents the function of the porosity of the fracture domain changing with the mass water content, n s (w) represents the function of soil surface settlement porosity changing with mass water content; V(w) represents the function of soil total volume changing with mass water content, V t (w) represents the function of the total pore volume of soil as a function of mass water content, V m (w) represents the function of the pore volume in the matrix domain as a function of the mass water content, V c (w) represents the function of the fracture domain volume changing with mass water content, V s (w) represents the function of the volume of the sedimentation space changing with the mass water content; n t (w max ) represents the total porosity of the soil when the soil is at the maximum mass water content, n m (wmax ) represents the matrix porosity when the soil is at the maximum mass water content; n t (w s ) represents the total porosity of the soil when the soil is at the shrinkage limit moisture content, n c (w s ) represents the porosity of the fracture domain when the soil is at the shrinkage limit mass moisture content, n s (w s ) represents the surface settlement porosity of soil when the soil is at its shrinkage limit moisture content.

[0025] The mass moisture 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] The three types of pores all change with the moisture content of the soil. When saturated, the soil does not crack and the surface does not settle, and the matrix domain porosity is equal to the total soil porosity. As the moisture content gradually decreases, the soil shrinks and cracks and ground settlement gradually occur. At this time, the porosity in the soil is composed of matrix domain pores, crack domains, and ground settlement pores. When the soil moisture content decreases to near the shrinkage limit moisture content, the soil matrix domain porosity reaches the minimum.

[0027] Soil shrinkage tests were carried out, and soil shrinkage parameters were monitored in real time through a shooting system during the experiment, including soil moisture content, crack parameters, and changes in surface settlement. A curve of porosity versus moisture content, i.e., soil shrinkage curve, was drawn based on the monitoring data.

[0028] The maximum porosity n of the soil matrix domain in a saturated state and without cracks can be obtained through this curve. max , the minimum porosity n when the soil moisture content is lost to the shrinkage limit min And shape distribution parameters p and q. Among them, n max With n min The range between represents the allowable range in which the matrix domain porosity can be converted into the fracture domain porosity and the sedimentation porosity. Assuming that this part is reversible during the dry-wet 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] Among them, n rev represents the reversible porosity.

[0031] The present invention is based on the four-parameter shrinkage model proposed by Stewart et al. to establish the soil matrix domain shrinkage curve function, and the equation is as follows:

[0032]

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

[0034] Combining equations (7) and (8) gives the control equation for the change of the porosity of the matrix domain outside the soil:

[0035]

[0036] Among them, n out (W) represents the porosity of the external matrix domain as a function of the standard water content, which is equal to the sum of the porosity of the fracture domain and the sedimentation porosity.

[0037] From formula (9), it can be seen that the change in porosity of the matrix domain outside the soil is proportional to the change in the reversible porosity of the soil. By analogy, for the convenience of derivation, it is assumed that the change in the porosity volume of the soil settlement is proportional to the change in the reversible settlement porosity of the soil settlement, and the reversible settlement porosity of the soil is between 0 and n. s,max , then the control equation of soil settlement porosity change is as follows:

[0038]

[0039] Among them, n s (W) represents the function of soil surface settlement porosity changing with standard water content, n s,max It indicates the maximum settlement porosity of the soil surface when the soil moisture content is 0.

[0040] Combining equations (9) and (10), the control equation for porosity change in soil crack domain is:

[0041]

[0042] Among them, n c (W) represents the function of the porosity of the soil crack domain changing with the standard water content. For the convenience of derivation and calculation, it is assumed that the soil settlement during the shrinkage process is proportional to the total shrinkage change of the soil.

[0043] To derive n s,max , the shrinkage geometry factor x is introduced. When x = 1, it means that the soil only shrinks vertically. When x approaches ∞, the soil only shrinks horizontally. It is usually assumed that x = 3 means that the soil shrinks in the same direction. The shrinkage geometry 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 is the volume of soil particles, H represents the vertical thickness of the soil, ΔV(W) represents the function of the change in soil volume corresponding to different changes in standard water content, V(W) represents the function of the total volume of the soil as the standard water content changes, V m (W) represents the function of the pore volume in the matrix domain changing with the standard water content, and ΔH(W) represents the function of the vertical thickness change of the soil corresponding to different changes in the standard water content.

[0046] The soil settlement porosity with the shrinkage geometry factor introduced is expressed as:

[0047]

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

[0049]

[0050] Among them, V s (W) represents the function of the volume of the settlement space changing with the standard water content, n s (W=0) represents the soil settlement porosity when the standard water content is 0.

[0051] Through the above derivation, the control equations of soil matrix domain, fracture domain and settlement porosity are mainly composed of p, q, n max 、n min And W are composed of five parameters, among which p, q, n max and n min The standard moisture content W is determined by the soil shrinkage curve measured above, and the standard moisture content W is determined by measuring the soil mass moisture content w and the maximum mass moisture content w max It can be calculated.

[0052] The cracked soil is discretized into N regular small soil blocks on the plane. Assuming that the cracks of each regular soil block have regular shapes, the control equations for the change of pore size between the soil matrix domain and the crack domain during the dry-wet cycle are established on this basis. The establishment process is as follows:

[0053] Assume that the side length of one of the regular soil blocks after discretization is A (A is taken from A j , j = 1, 2, ..., N, A jrepresents the jth regular soil block), with a height of H. Under saturated conditions, the volume of the regular soil block is A×A×H. When shrinking, assuming that the soil block shrinks uniformly inward on all sides, the width of the shrinkage cracks generated by shrinkage is a (a is taken from a j , j = 1, 2, ..., N, a j represents the jth crack), and the surface settlement of the soil block is assumed to be ΔH. After shrinkage, the volume of the regular soil block becomes (Aa)×(Aa)×(H-ΔH). When the soil moisture content decreases to a certain moment, the volume of the crack domain formed around the regular soil block is a×(2A-a)×(H-ΔH). Figure 2 .

[0054] In the matrix domain, compared with the tiny pores between soil particles, the structural pores of the soil play a leading role in the seepage process. Therefore, the present invention ignores the tiny pores between particles and assumes that the structural pores of the soil consist of M pores with a radius of r (r is taken from r i , i=1,2,...,M), and is composed of cylinders with a height of H, then the volume of the structural pores is M×H×π×r 2 During the shrinkage process, the structural pores of the soil gradually become smaller, which is manifested by the gradual decrease in the radius of a single pore. When saturated, the pore radius of the soil is the maximum value r max When the water content is close to 0, the porosity radius of the soil is the minimum value r min Although the pores in the soil matrix are actually irregular and curved, some studies have shown that clay particles have a fishtail shape, which makes the soil pores present a tubular structure and extend into the soil. Therefore, the present invention assumes that the soil structural pores are cylindrical.

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

[0056]

[0057] ΔH can be derived from the soil settlement spatial porosity calculation equation, and the formula (10) can be transformed into:

[0058]

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

[0060]

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

[0062] During the drying and wetting cycle, the size of the soil structural pores changes with the moisture content. Combining equations (8) and (15), we can get:

[0063]

[0064] Among them, r max Represents the maximum radius of the cylindrical structural pores in the soil, r min Represents the minimum radius of the cylindrical structural pores in the soil.

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

[0066]

[0067] Among them, r i,max represents the maximum radius of the structural pores of the i-th cylinder, r i,min represents the minimum radius of the structural pores of the i-th cylinder.

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

[0069]

[0070] The porosity change in the soil crack region satisfies the following relationship:

[0071]

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

[0073] Formula (21) is rewritten as:

[0074]

[0075] Since the width of the soil block is much larger than the width of the crack, 2A j >>a j,max , both sides of formula (22) are divided by 2A j , the equation can be rewritten as j,max Predict the width a under a certain moisture content condition j expression:

[0076]

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

[0078]

[0079] Furthermore, according to formula (24), we can get:

[0080]

[0081] From formula (25), we can see that when obtaining the shrinkage curve parameters, if we can measure the maximum crack width when the water content W = 0, we can calculate the crack width under any water content. At the same time, in the field test, we can measure the crack width and the change of water content, and use this formula to calculate the shape parameters of the shrinkage curve.

[0082] S2. Obtain the saturated permeability coefficient of the soil, and on the basis of the two-domain expansion and contraction model, establish a control equation for the change of the pore permeability coefficients of the matrix domain and the fracture domain with the expansion and contraction of the soil fracture.

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

[0084] Based on Darcy's law, an indoor soil permeability test was carried out to obtain the saturated permeability coefficient of the experimental material. The porosity of the matrix domain and the fracture domain and the total porosity are expressed as:

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

[0086]

[0087] Among them, n t (W) represents the function of soil total porosity changing with standard water content, β(W) represents the function of fracture domain volume weight factor changing with standard water content, with a value range of 0 to 1, and δ c (W) represents the function of porosity in the fracture domain as a function of standard water content, δ m (W) represents the function of the porosity in the matrix domain as a function of the standard water content, V c1 (W) represents the function of the pore volume in the fracture domain changing with the standard water content, V m，t (W) represents the function of the total volume of the matrix domain changing with the standard water content. In actual situations, there is a certain volume of loose soil particles inside the fracture domain, so V c1 Not completely equivalent to V c .

[0088] For the convenience of derivation, the present invention does not consider the influence of loose soil particles on cracks, that is, V c1 =V c , δ c =1. Then equation (26) is simplified to: t (W) = β (W) + (1 - β (W)) δ m (W).

[0089] Secondly, assume that β represents the volume ratio of the fracture 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 moisture content, the volumetric moisture content of the matrix domain, crack domain and soil surface settlement space is expressed as:

[0095] θ t =θ m +θ c +θ s (32)

[0096]

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

[0098] Since the soil surface usually does not contain free water, θ s =0, formula (32) is simplified to:

[0099] θ t =θ m +θ c (33)

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

[0101]

[0102] and then:

[0103]

[0104] in, represents the function of the volumetric water content in the matrix domain changing with the standard water content, A function that represents the change of volumetric water content in the fracture domain with 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 represents the water flux density per unit area of ​​the matrix domain in the vertical direction, R c 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; Q m represents the matrix water flux, Q c represents the water flux in the fracture domain; S m represents the cross-sectional area of ​​the matrix domain, S c Represents the cross-sectional area of ​​the fracture domain.

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

[0109]

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

[0111]

[0112] If the soil surface settlement is not considered, equation (44) can be simplified to:

[0113] R=R m [1-β(W)]+R c β(W)(45)

[0114] The flow rate of water in the matrix domain and the fracture domain is expressed as:

[0115]

[0116] Among them, v m represents the velocity of water in the matrix domain, v c Represents the flow velocity of water in the fracture domain.

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

[0118]

[0119] where Δω is the water potential gradient of the soil, c is the water potential gradient in the soil crack region, Δω m is the water potential gradient in the soil matrix domain; K s (W) represents the function of soil saturated permeability coefficient changing with standard water content, K s,c (W) represents the function of the saturated permeability coefficient of the soil crack domain changing with the standard water content, K s,m (W) represents the function of the saturated permeability of the soil matrix domain changing with the standard water content.

[0120] If we assume that the water potential gradient in each domain is the same, that is, Δω=Δω c =Δω m , then formula (48) is simplified to:

[0121]

[0122] Traditional dual permeability models often assume that the soil permeability coefficient remains constant during the wetting and drying cycle. However, in reality, the pore cross-sectional area of ​​the soil will change during the wetting and drying cycle, and the flow rate of water flowing through the pores under given water potential gradient conditions will also change nonlinearly, resulting in nonlinear changes in the soil matrix domain, fracture domain and total saturated permeability coefficient.

[0123] Assuming that the cracks in the soil are regular cuboids, and the pores in the matrix domain are assumed to be cylindrical as before, it can be seen from the Poiseuille equation that the flow through the cuboid pore space is proportional to the cube of the rectangular pore width, and the flow through the cylindrical pore is proportional to the square of the circular radius. The water flux of the cuboid pore space and the water flux of the cylindrical pore are expressed as:

[0124]

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

[0126] Assuming that the geometric shapes of soil cracks and pores remain unchanged during the drying and wetting cycle, the permeability coefficient of soil crack domain is derived according to the above rectangular pore space water flux formula:

[0127]

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

[0129]

[0130] Among them, τ j represents the curvature around the jth regular block of soil, K c,max It represents the maximum saturated permeability of the soil crack domain in a dry state.

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

[0132]

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

[0134]

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

[0136]

[0137] Among them, r i,max represents the maximum radius of the pore in the i-th circular matrix domain, r i,min represents the minimum radius of the pore in the i-th circular matrix domain.

[0138] According to the above formula, the maximum permeability coefficient K of the soil matrix domain when saturated (when the standard water content is 1) is obtained: m,max And the minimum permeability coefficient K when dry (when the standard moisture content is 0) m,min :

[0139]

[0140] Substituting equation (58) and equation (59) into equation (57), it is simplified to:

[0141]

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

[0143]

[0144] Substituting equations (53) and (61) into equation (49), the permeability coefficient of soil is derived as follows:

[0145]

[0146] Ignoring the soil surface settlement, equation (62) is simplified to:

[0147]

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

[0149] Specifically:

[0150] The existing static dual permeability model (Gerke et al.) divides the soil into two regions according to the proportion of the matrix domain and the fracture domain. Both regions are continuous media, overlapping and interacting with each other. The water migration process in the matrix domain and the fracture domain is described by two coupled 2-D Richards equations, which are described as follows:

[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 represent the pressure head in the matrix domain and the fracture domain, respectively, K a is the permeability coefficient between the two domains, z represents the position head, t represents the time, T w represents the water exchange term between the crack domain and the matrix domain, a w represents the water exchange coefficient between the two domains; C c (h c ) is expressed as represents the function of the soil crack domain specific water capacity changing with the crack domain pressure head, C m (h m ) is expressed as K represents the function of the soil matrix domain specific water capacity changing with the matrix domain pressure head. c (h) represents the function of the instantaneous permeability of the fracture domain changing with the pressure head, Km (h) represents the function of the instantaneous permeability of the matrix domain changing with the pressure head, β(h) represents the function of the volume weight factor of the fracture domain changing with the pressure head, 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 effect on the water transport of the soil. Without considering the soil settlement, the relationship between the porosity of the soil matrix domain and the crack domain and the water content is expressed as follows:

[0155]

[0156] Since the standard soil moisture content Se m is the soil matrix domain saturation, and equations (67) and (68) are rewritten as:

[0157]

[0158] Among them, n m (Se m ) represents the function of the soil matrix porosity changing with the soil matrix saturation, n c (Se m ) represents the function of the porosity of soil crack domain changing with the saturation of soil matrix domain, β(Se m ) represents the function of the volume weight factor of the fracture domain changing with the saturation of the soil matrix domain.

[0159] The porosity in the matrix domain, the volumetric water content in the matrix domain, the volumetric water content in 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 body, and the volume proportion of the fracture domain are expressed as follows:

[0160]

[0161]

[0162] Among them, δ m (Se m ) represents the function of the porosity in the matrix domain as the matrix domain saturation changes. represents the function of the volumetric water content in the matrix domain as the saturation of the matrix domain changes. represents the function of volumetric water content in the fracture domain as a function of matrix domain saturation, K s,m (Se m ) represents the function of the saturated permeability coefficient of the soil matrix domain changing with the saturation of the matrix domain, K s,c (Se m ) represents the function of the saturated permeability coefficient of the soil fracture domain changing with the saturation of the matrix domain, K s (Sem ) represents the function of soil saturated permeability coefficient changing with matrix domain saturation.

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

[0164]

[0165] in, represents the volumetric water content corresponding to the volume of each domain, represents the saturated volumetric moisture content of soil, Represents the residual volume moisture content of soil, S e (h) represents the function of the effective saturation of soil with the pressure head, 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 of the soil. When the soil-water characteristic curve of the soil is known, equations (69) to (76) can be calculated.

[0166] According to the Mualem-van Genuchten model, the function expression of soil instantaneous permeability coefficient is:

[0167]

[0168] In the formula, S e is the effective saturation of soil, K(S e ) represents the function K of the instantaneous permeability of soil changing with the effective saturation of soil s (S e ) represents the function of soil saturated permeability coefficient changing with soil effective saturation, K r (S e ) represents the function of the relative permeability of soil changing with the effective saturation of soil.

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

[0170]

[0171] Among them, Se c Indicates the saturation of soil cracks; K m (S e ) represents the function of the instantaneous permeability of the soil matrix domain changing with the effective saturation of the soil, K c (S e ) represents the function of the instantaneous permeability of the soil crack domain changing with the effective saturation of the soil, K r (Se m) represents the function of the relative permeability of soil as a function of the saturation of the soil matrix domain, K r (Se c ) represents the function of the relative permeability of soil as a inverse function of the saturation of the soil fracture domain.

[0172] Different from the traditional static dual permeability model, the present invention sets the relative permeability of the fracture domain to 1. The instantaneous permeability of the fracture domain is only related to the saturated permeability, and the saturated permeability of the domain is a function of the matrix domain saturation, expressed as:

[0173]

[0174] Where K m,max It can be obtained through the penetration test of indoor uncracked soil samples, K c,max The maximum crack width a can be measured max The Poiseuille equation is used for estimation, and the equation is:

[0175]

[0176] Substituting equations (29), (66), (72), (73), (77), (81) and (82) into (64) and (65), we obtain the dual permeability model of fracture dynamics:

[0177]

[0178] The model mainly includes 7 parameters, including four simple and easy-to-obtain shrinkage curve parameters: maximum porosity n max , minimum porosity n min The shape distribution parameters p and q, and the three soil-water characteristic curve parameters α, n and b control that can be fitted can all be obtained through geotechnical experiments, which are simple to operate and easy to obtain.

[0179] The dual permeability model of fracture dynamics is used for hydrogeological analysis, such as water migration analysis in soil, slope stability analysis, and migration and diffusion of soil pollutants.

[0180] Embodiment 2: In an exemplary embodiment, a computer-readable storage medium is included, the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for establishing the dual-domain penetration model is implemented.

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

[0182] Among them, a computer program is stored in the memory, and the computer program 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 one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one 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 present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for establishing a dual-domain penetration model, characterized in that: The following steps are involved: S1. Divide the pore system of clay based on the matrix domain and the fracture domain, carry out soil shrinkage experiments and draw soil shrinkage curves, and establish soil fracture expansion and contraction models in the matrix domain and the fracture domain based on the shrinkage curves and pore systems; S2. Obtain the saturated permeability coefficient of the soil, and establish a control equation for the change of the pore permeability coefficients of the matrix domain and the fracture domain with the expansion and contraction of the soil fracture based on the two-domain expansion and contraction model; S3. Set the relative permeability of the fracture domain to 1. The instantaneous permeability of the fracture domain is only related to the saturated permeability. The saturated permeability of the fracture domain is a function of the matrix domain saturation. Construct a dual permeability model of dynamic changes in fractures, and use the dual permeability model of dynamic changes in fractures to perform hydrogeological analysis.

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 domain and fracture domain: matrix domain pores, fracture 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 the matrix domain pores, the fracture domain pores, and the soil surface settlement pores is expressed as: n t (w max )=n m (w max ) (5) n t (w s )=n min +n c (w s )+n s (w s ) (6), Where w represents the mass moisture content, w max Indicates the maximum mass moisture content of soil, w s Indicates the moisture content of shrinkage limit, n min represents the minimum porosity of the matrix domain, n t (w) represents the function of soil total porosity changing with mass water content, n m (w) represents the function of matrix porosity changing with mass water content, n c (w) represents the function of the porosity of the fracture domain changing with the mass water content, n s (w) represents the function of soil surface settlement porosity changing with mass water content; V(w) represents the function of soil total volume changing with mass water content, V t (w) represents the function of the total pore volume of soil as a function of mass water content, V m (w) represents the function of the pore volume in the matrix domain as a function of the mass water content, V c (w) represents the function of the fracture domain volume changing with mass water content, V s (w) represents the function of the volume of the sedimentation space changing with the mass water content; n t (w max ) represents the total porosity of the soil when the soil is at the maximum mass water content, n m (w max ) represents the matrix porosity when the soil is at the maximum mass water content; n t (w s ) represents the total porosity of the soil when the soil is at the shrinkage limit moisture content, n c (w s ) represents the porosity of the fracture domain when the soil is at the shrinkage limit mass moisture content, n s (w s ) represents the surface settlement porosity of soil when the soil is at its shrinkage limit moisture content.

4. The method for establishing a dual-domain penetration model according to claim 3, characterized in that: Soil shrinkage parameters include soil moisture content, crack parameters and surface settlement changes. The porosity-water content curve is plotted according to the soil shrinkage parameters 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 n of the soil matrix domain is obtained through the soil shrinkage curve max , the minimum porosity of the soil matrix domain n min and shape distribution parameters p and q; n max With n min The range between represents the allowable range within which the matrix porosity can be converted into the fracture porosity and sedimentation porosity, expressed as: n rev =n max -n min =n m (w)+n c (w)+n s (w)-n min (7), Among them, n rev represents the reversible porosity.

6. The method for establishing a dual-domain penetration model according to claim 5, characterized in that: The soil crack expansion and contraction model of the matrix domain and crack domain is established according to the shrinkage curve and pore system as follows: The soil matrix domain shrinkage curve function is expressed as: Where W is the standard moisture content, n m (W) represents the function of matrix domain porosity changing with standard water content; The control equation for the porosity change of the matrix domain outside the soil is expressed as: Among them, n out (W) represents the porosity of the extracellular matrix domain as a function of the standard water content; The control equation of soil settlement porosity change is: Among them, n s (W) represents the function of soil surface settlement porosity changing with standard water content, n s,max It indicates the maximum settlement porosity of the soil surface when the soil moisture content is 0; The control equation for porosity change in soil crack domain is: Among them, n c (W) represents the function of soil crack porosity changing with standard water content; To derive n s,max , the shrinkage geometry factor x is introduced. The shrinkage geometry factor x is used to describe the change of the total volume and thickness of the soil and satisfies the following relationship: Among them, V ms is the volume of soil particles, H represents the vertical thickness of the soil, ΔV(W) represents the function of the change in soil volume corresponding to different changes in standard water content, V(W) represents the function of the total volume of the soil as the standard water content changes, V m (W) represents the function of the pore volume in the matrix domain changing with the standard water content, and ΔH(W) represents the function of the thickness change in the vertical direction of the soil corresponding to different changes in the standard water content; The soil settlement porosity with the shrinkage geometry factor introduced is expressed as: Among them, V s (W) represents the function of the volume of the settlement space changing with the standard water content, n s (W=0) indicates the porosity of soil settlement when the standard water content is 0; The cracked soil is discretized into N regular soil blocks on the plane. The cracks in each regular soil block have a regular shape. The side length of the discretized regular soil block is A. j , j = 1, 2, ..., N, the vertical thickness is H, and the width of the shrinkage cracks produced by each regular soil block during shrinkage is a j , j = 1, 2, ..., N; let the structural pores of the soil in the matrix domain be cylinders that penetrate the regular soil block from top to bottom, and the height of each cylinder is the same as the thickness of the regular soil block in the vertical direction, which is H. The porosity change in the soil matrix domain satisfies the following relationship: Where M represents the number of cylindrical structural pores in the cracked soil, r i represents the radius of the structural pore of the i-th cylinder in the soil, ΔH max represents the maximum settlement height, A represents the side length of a regular soil block, and the value is taken from A j , j = 1, 2, ..., N; Combining equation (8) and equation (15), we get: Among them, r max Represents the maximum radius of the cylindrical structural pores in the soil, r min It represents the minimum radius of the cylindrical structural pores of the soil; Substituting equations (17), (18) and (16) into equation (8), we can obtain the control equation for the change of soil structural pore size: Among them, r i represents the radius of the i-th cylindrical structural pore, i = 1, 2, ..., M, r i,max represents the maximum radius of the structural pores of the i-th cylinder, r i,min represents the minimum radius of the structural pores of the i-th cylinder; Since the height of the soil block is much greater than the settlement height of the soil during the dry-wet cycle, H>>ΔH, equation (19) is simplified to: The porosity change in the soil crack region satisfies the following relationship: Among them, A j represents the side length of the jth regular soil block, a j represents the crack width caused by the contraction of the jth regular soil block, a j,max is the maximum crack width caused by the shrinkage of the jth regular soil block when the standard moisture content W = 0; Formula (21) can be rewritten as: Since the width of the soil block is much larger than the width of the crack, 2A j >>a j,max , both sides of formula (22) are divided by 2A j , the equation can be rewritten as j,max Predict the width a under a certain moisture content condition j expression: Since H>>ΔH, equation (23) is simplified to: Furthermore, according to formula (24), we can get:

7. The method for establishing a dual-domain permeation model according to claim 6, characterized in that: The control equations for the changes of the pore permeability coefficients in the matrix domain and the fracture domain with the expansion and contraction of soil fractures are established as follows: The matrix domain and fracture domain porosity and the total porosity are expressed as: n t (W)=β(W)δ c (W)+(1-β(W))δ m (W)(26) Among them, n t (W) represents the function of soil total porosity changing with standard water content, β(W) represents the function of fracture domain volume weight factor changing with standard water content, δ c (W) represents the function of porosity in the fracture domain as a function of standard water content, δ m (W) represents the function of the porosity in the matrix domain as a function of the standard water content, V c1 (W) represents the function of the pore volume in the fracture domain changing with the standard water content, V m，t (W) represents the function of the total volume of the matrix domain changing with the standard water content; Then n m (W) = (1 - β(W))δ m (W)(30); Combining equations (8), (29) and (30), we get: The volumetric water content of the matrix domain, crack domain, and soil surface settlement space is expressed as: i t =θ m +θ c +θ s (32) Among them, θ t represents the total volumetric moisture content of the soil, θ m represents the volumetric water content of the matrix domain, θ c represents the volumetric water content of the fracture domain, θ s Represents the volumetric water content of the soil surface settlement; V w，m represents the volume of water contained in the matrix domain, V w，c Represents the volume of water contained in the fracture domain, V w，s represents the volume of water contained in the space generated by the settlement of the soil surface, let θ s =0, formula (32) is simplified to: i t =θ m +θ c (33), The volumetric water content in the matrix domain and the crack domain is expressed as: and then: in, represents the function of the volumetric water content in the matrix domain changing with the standard water content, A function that represents the change of volumetric water content in the fracture domain with the standard water content; The water flux density in the matrix domain and the fracture domain is expressed as: In the formula, R m represents the water flux density per unit area of ​​the matrix domain in the vertical direction, R c 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; Q m represents the matrix water flux, Q c represents the water flux in the fracture domain; S m represents the cross-sectional area of ​​the matrix domain, S c represents the cross-sectional area of ​​the fracture domain; The cross-sectional areas of the matrix domain and the crack domain are expressed as: Combining equations (42) and (43), equation (41) can be rewritten as: Without considering the soil surface settlement, equation (44) is simplified to: R=R m [1-β(W)]+R c β(W)(45), The flow rate of water in the matrix domain and the fracture domain is expressed as: Among them, v m represents the velocity of water in the matrix domain, v c represents the flow rate of water in the fracture domain; According to Darcy's law, the relationship between soil saturated permeability coefficient, water flux density and soil water potential gradient is established: Where Δω represents the water potential gradient of the soil, Δω c is the water potential gradient in the soil crack region, Δω m is the water potential gradient in the soil matrix domain; K s (W) represents the function of soil saturated permeability coefficient changing with standard water content, K s,c (W) represents the function of the saturated permeability coefficient of the soil crack domain changing with the standard water content, K s,m (W) represents the function of the saturated permeability coefficient of the soil matrix domain changing with the standard water content; Let the water potential gradient of each domain be the same, that is, Δω=Δω c =Δω m , then formula (48) is simplified to: Assuming that the cracks in the soil are regular cuboids, the water flux in the pore space of the cuboid and the water flux in the pore space of the cylinder are expressed as: In the formula, Q rect is the water flux in the cuboid pore space, Q rcircle is the water flux in the pore space of the cylinder, ρ w is the density of water, g is the acceleration due to gravity, μ w is the viscosity of water, r represents the radius of the cylinder, and its value is taken from r i , i = 1, 2, ..., M, a represents the cracks caused by the shrinkage of regular soil blocks, and the value is taken from a j , j = 1, 2, ..., N; During the wetting and drying cycle, the geometric shapes of soil cracks and pores remain unchanged, and the permeability coefficient of soil crack domain is derived according to the above rectangular pore space water flux formula: Substituting formula (24) into formula (52), we get: in, Among them, τ j represents the curvature around the jth regular block of soil, K c,max It represents the maximum saturated permeability coefficient of the soil crack domain in the dry state; The matrix permeability coefficient is obtained based on formula (51): The pore volume of all matrix domains is reduced at a certain ratio. When saturated, the pore volume of the soil matrix domain reaches the maximum and cracks are not developed. The expression is: Substituting equation (20) and equation (56) into equation (55), we obtain: Among them, r i,max represents the maximum radius of the pore in the i-th circular matrix domain, r i,min represents the minimum radius of the pore of the i-th circular matrix domain; According to the above formula, the maximum permeability coefficient K of the soil matrix domain when saturated is obtained m,max and the minimum permeability coefficient K when dry m,min : Substituting equation (58) and equation (59) into equation (57), it is simplified to: The minimum permeability coefficient of the soil matrix domain is much smaller than the maximum permeability coefficient at saturation. Further simplifying formula (60) yields: Substituting equations (53) and (61) into equation (49), the permeability coefficient of soil is derived as follows: Ignoring the soil surface settlement, equation (62) is simplified to:

8. The method for establishing a dual-domain penetration model according to claim 7, characterized in that: S3 is specifically: The water migration process in the matrix domain and the fracture domain is described by two coupled 2-D Richards equations: Among them, T w =a w K a (h c -h m )(66), In the formula, h represents the pressure head, h c and h m represent the pressure head in the matrix domain and the fracture domain, respectively, K a is the permeability coefficient between the two domains, z represents the position head, t represents the time, T w represents the water exchange term between the crack domain and the matrix domain, a w represents the water exchange coefficient between the two domains; C c (h c ) is expressed as represents the function of the soil crack domain specific water capacity changing with the crack domain pressure head, C m (h m ) is expressed as K represents the function of the soil matrix domain specific water capacity changing with the matrix domain pressure head. c (h) represents the function of the instantaneous permeability of the fracture domain changing with the pressure head, K m (h) represents the function of the instantaneous permeability of the matrix domain changing with the pressure head, β(h) represents the function of the volume weight factor of the fracture domain changing with the pressure head, represents the gradient operator; Without considering soil settlement, the relationship between the porosity of the soil matrix and the crack domain and the water content is expressed as follows: Since the standard soil moisture content Se m is the soil matrix domain saturation. When the soil residual moisture content is low, the soil matrix domain saturation is equal to the relative saturation. Equations (67) and (68) can be rewritten as: Among them, n m (Se m ) represents the function of the soil matrix porosity changing with the soil matrix saturation, n c (Se m ) represents the function of the porosity of soil crack domain changing with the saturation of soil matrix domain, β(Se m ) represents the function of the volume weight factor of the fracture domain changing with the saturation of the soil matrix domain; The porosity in the matrix domain, the volumetric water content in the matrix domain, the volumetric water content in 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 body, and the volume proportion of the fracture domain are expressed as follows: Among them, δ m (Se m ) represents the function of the porosity in the matrix domain as the matrix domain saturation changes. represents the function of the volumetric water content in the matrix domain as the saturation of the matrix domain changes. represents the function of volumetric water content in the fracture domain as a function of matrix domain saturation, K s,m (Se m ) represents the function of the saturated permeability coefficient of the soil matrix domain changing with the saturation of the matrix domain, K s,c (Se m ) represents the function of the saturated permeability coefficient of the soil fracture domain changing with the saturation of the matrix domain, K s (Se m ) represents the function of soil saturated permeability coefficient changing with matrix domain saturation, Se m The function is obtained according to the soil-water characteristic curve function expression in the soil matrix domain of the Mualem-van Genuchten model: in, represents the volumetric water content corresponding to the volume of each domain, represents the saturated volumetric moisture content of soil, represents the residual volume moisture content of the soil, α, n and b are the shape parameters of the soil-water characteristic curve; S e (h) represents the function of effective soil saturation changing with pressure head; The function expression of soil instantaneous permeability coefficient is: In the formula, S e is the effective saturation of soil, K(S e ) represents the function of the instantaneous permeability of soil changing with the effective saturation of soil, K s (S e ) represents the function of soil saturated permeability coefficient changing with soil effective saturation, K r (S e ) represents the function of the relative permeability of soil changing with the effective saturation of soil; The expressions of the instantaneous permeability coefficient of the soil matrix domain and the instantaneous permeability coefficient of the fracture domain are as follows: Among them, Se c Indicates the saturation of soil cracks; K m (S e ) represents the function of the instantaneous permeability of the soil matrix domain changing with the effective saturation of the soil, K c (S e ) represents the function of the instantaneous permeability of the soil crack domain changing with the effective saturation of the soil, K r (Se m ) represents the function of the relative permeability of soil as a function of the saturation of the soil matrix domain, K r (Se c ) represents the function of the relative permeability of soil as a function of the saturation of the soil fracture domain; The relative permeability of the fracture domain is set to 1. The instantaneous permeability of the fracture domain is only related to the saturated permeability, and the saturated permeability of the domain is a function of the matrix domain saturation, expressed as: in, Among them, a max Indicates the maximum width of the crack; Substituting equations (29), (66), (72), (73), (77), (81) and (82) into (64) and (65), we obtain the dual permeability model considering the dynamic changes of fractures: Hydrogeological analysis was performed using a dual permeability model with fracture dynamics.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 8 is implemented.

10. An electronic device, characterized in that: The method comprises 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 comprises computer-readable instructions, and the processor is configured to call the computer-readable instructions to execute the method according to any one of claims 1 to 8.

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