A method for predicting salt expansion of sulfate-affected soil after electroosmosis treatment

Abstract

The present invention discloses a method for predicting the salt expansion of sulfate-saline soil after electroosmosis treatment, comprising establishing an electric field governing equation in the soil, establishing a temperature field governing equation in the soil, establishing a liquid water migration governing equation in the soil, establishing a gaseous water diffusion governing equation in the soil, establishing an ion migration governing equation in the soil, simultaneously establishing the electric field governing equation, the temperature field governing equation, the liquid water migration governing equation, the gaseous water diffusion governing equation, and the ion migration governing equation, dividing the soil model into grids, performing differential solutions on the five equations using a central difference method, and then determining a salt expansion prediction expression. The present invention can accurately predict the salt expansion of sulfate-saline soil under different electroosmotic conditions, reduce engineering test costs, optimize electroosmotic expansion reduction construction plans, and improve engineering economic benefits.

Description

Technical Field

[0001] The invention belongs to the technical field of saline soil treatment, and in particular relates to a method for predicting salt swelling of sulfate saline soil after electroosmosis treatment. Background Art

[0002] At present, the commonly used measures for saline soil diseases in projects include dynamic compaction, soil replacement and isolation layer setting. Among them, the dynamic compaction method causes relatively large vibrations during construction and is not suitable for areas close to buildings and structures, as it is prone to disturbance and nuisance to residents. The soil replacement method is limited by the scope of construction, has high costs, and is difficult to use on a large scale. When setting faults, when the groundwater level is high, the isolation layer cannot achieve the isolation effect, and salt swelling often occurs.

[0003] Compared with the above improved methods, researchers found that water and salt in saline soil can be quickly discharged under the action of electroosmosis, thereby reducing the amount of mirabilite crystallization and effectively reducing the salt swelling of sulfate soil. However, the use of electroosmosis to inhibit salt swelling in sulfate soil is currently only at the experimental level. In order to achieve a good swelling reduction effect, a large number of tests are usually required. In addition, the tests often only consider single influencing factors such as potential gradient, water content, and salt content. The mutual influence and coupling between factors such as electric field, temperature, moisture, gaseous water, and salt are not fully considered. This is not enough to provide scientific guidance for the application of electroosmosis in saline soil salt swelling prevention and control projects.

[0004] Therefore, it is necessary to develop a method to predict the salt swelling of sulfate-salted soil after electroosmosis treatment, so as to reduce the cost of experiments in engineering and optimize the electroosmosis swelling reduction construction plan. Summary of the Invention

[0005] The main purpose of the present invention is to provide a method for predicting the salt swelling of sulfate-saline soil after electroosmosis treatment, aiming to achieve the prediction of the salt swelling of sulfate-saline soil under different electroosmotic conditions.

[0006] To this end, the method for predicting salt swelling of sulfate soil after electroosmosis treatment provided by the embodiment of the present invention includes the following steps:

[0007] Step 1: Establish the electric field control equation in the soil

[0008] Step 2: Establish the temperature field control equation in the soil

[0009] Step 3: Establish the control equation for liquid water migration in soil

[0010] Step 4: Establish the governing equation for the diffusion of gaseous water in soil

[0011] Step 5: Establish the governing equation for ion migration in soil

[0012] Step 6: Simultaneously establish the electric field control equation, temperature field control equation, liquid water migration control equation, gaseous water diffusion control equation, and ion migration control equation, and divide the soil model into grids. Use the central difference method to perform differential solutions on these five equations, and obtain the temperature T(t, i, j), liquid water content W(t, i, j), relative humidity RH(t, i, j), and sodium ion content C(t, i, j) at each grid point in the soil under different electroosmosis times.

[0013] Where t is the electroosmosis time, i = 1, 2, ..., ny, j = 1, 2, ..., nx, ny and nx are the total number of steps in the vertical and horizontal directions, respectively, which are calculated by dividing the vertical and horizontal lengths of the soil model by the grid width;

[0014] Using the obtained soil temperature T(k, i, j) according to formula (35), the solubility of sodium sulfate in water C is calculated. r :

[0015]

[0016] The standard sodium sulfate content C in water is calculated by combining the obtained soil liquid moisture content W(k, i, j) with formula (35) and formula (36). s :

[0017] C s =C r ·ρ w W(t, i, j) / 100 (36)

[0018] Among them, ρ w is the density of water;

[0019] The obtained C s Substitute into formula (37) to calculate the solid sodium ion content of the first part:

[0020]

[0021] Where C tna1 is the solid sodium ion content of the first part, C i is the initial value of sodium sulfate content, ρ is the density of the soil;

[0022] Using the obtained C s The salt ion content C(k,i,j) obtained by the solution is calculated according to formula (38) to calculate the second part of the solid sodium ion content C tna2 :

[0023]

[0024] Where M tna and M mare the molar masses of sodium sulfate and thenardite, respectively;

[0025] The solid sodium ion content of the above two parts is added according to formula (39) to obtain the total solid sodium ion content C in the soil tna :

[0026] C tna =C tna1 +C tna2 (39)

[0027] Substituting the obtained temperature T(t, i, j) into equations (40) and (41), the critical relative humidity RH1 for the conversion of sodium sulfate crystals to mirabilite and the limiting relative humidity RH2 for the conversion of sodium sulfate solution to mirabilite are calculated:

[0028] RH1=60.02+0.7392×T(t,i,j) (40)

[0029] RH2=97.53sin(0.01695T(t,i,j)+1.515) (41)

[0030] The total solid sodium ion content C tna , relative humidity RH(t, i, j), RH1 and RH2 are determined according to formula (42), and the content of mirabilite in the soil C is calculated. m :

[0031]

[0032] The salt expansion of each grid point in the horizontal direction of the soil model grid is accumulated upward, and finally the calculation formula of the salt expansion at each depth after correction is obtained:

[0033]

[0034] Where Δ is the salt expansion of sulfate soil, ρ m is the density of the mirabilite crystals, L is the total depth of the soil, t k is the number of time steps, i.e., the total electroosmosis time divided by the interval time;

[0035] The content of Glauber's salt C obtained by formula (42) m Substituting into formula (43), the salt expansion of sulfate saline soil under electroosmosis can be calculated.

[0036] Specifically, the expression of the electric field control equation in step 1 is:

[0037]

[0038] Where C p is the capacitance influencing factor in saline soil, t is the electroosmosis time, is the mathematical gradient operator, σ is the electrical conductivity of the soil, and E is the electric potential applied at both ends of the soil.

[0039] Specifically, according to Ohm's law:

[0040]

[0041] Where I is the current density in the soil, σ is the electrical conductivity of the soil, and E is the potential applied across the soil.

[0042] The relationship between the electrical conductivity of the soil and the moisture content and salt content in the soil is calculated according to formula (2):

[0043] σ=m1·C·W+m2·C+m3·W-m4(2)

[0044] Where C is the salt content in the soil, W is the water content in the soil, m1, m2, m3, and m4 are parameters related to the type of salt in the soil. In sulfate saline soil, the values ​​of m1, m2, m3, and m4 are 0.140, -0.773, 0.024, and -0.236, respectively.

[0045] According to the law of conservation of charge:

[0046]

[0047] Among them, C p is the capacitance influencing factor in saline soil, t is the electroosmosis time, is the mathematical gradient operator;

[0048] Substituting equation (1) into equation (3), the electric field control equation in soil is established:

[0049]

[0050] Specifically, the expression of the temperature field control equation in step 2 is:

[0051]

[0052] Where: c is the specific heat capacity of the soil, ρ is the density of the soil, T is the soil temperature, σ is the electrical conductivity of the soil, K t is the thermal conductivity of the soil, E is the electric potential applied at both ends of the soil, t is the electroosmosis time, and the thermal conductivity of the soil K is t It consists of four parts, namely the thermal conductivity of liquid water, sodium sulfate, soil particles and gaseous water, namely K tw , K tc , K ts and K ta ; According to the volume ratio of water content, soil particle content, salt content and gaseous water content in unit volume of soil, that is, W, λtc , C and g are calculated according to the following formula:

[0053] K t =K we ·W+K tc ·λ tc +K ts C+K ta ·g (10).

[0054] Specifically, according to Fourier's heat conduction law, formula (5) is obtained:

[0055]

[0056] Where J is the heat flux in the soil, K t is the thermal conductivity of the soil;

[0057] According to the energy conservation equation, we can get equation (6):

[0058]

[0059] Where c is the specific heat capacity of the soil, ρ is the density of the soil, and T is the soil temperature;

[0060] Q is the heat source of electroosmotic Joule heat, which is calculated as follows:

[0061]

[0062] Substituting Equation (7) into Equation (6) yields the energy conservation equation considering the electroosmotic Joule heating:

[0063]

[0064] (9) Substituting equation (6) into equation (8) yields the temperature conduction control equation in unsaturated sulfate saline soil.

[0065] Specifically, the expression of the liquid water migration control equation in step 3 is:

[0066]

[0067] Where W is the water content in the soil, t is the electroosmosis time, K e is the electric permeability coefficient, is the matrix suction in the soil, K h is the hydraulic permeability coefficient, E is the electric potential applied at both ends of the soil, where

[0068] The expression is:

[0069]

[0070] K h The expression is:

[0071] K h =K s H 0.5 [1-(1-H 1 / M ) M ] 2 (twenty one)

[0072]

[0073] Where: W s and W r They represent the saturated volume liquid water content and residual volume liquid water content in the soil, respectively. N is an empirical parameter characterizing the pore size distribution, with a value of 3. M is a sensitive factor affecting the overall symmetry of the soil-water characteristic curve, with a value of 2 / 3. K s is the saturated permeability coefficient in the soil, H is the effective saturation of the soil, and a is a fitting factor related to the soil properties, with a value of 0.15.

[0074] Specifically, according to Darcy's law, the water flux caused by the matrix potential in the soil is expressed as wei:

[0075]

[0076] Where q1 is the water flux under the action of matrix potential, K h is the hydraulic permeability coefficient, is the matrix suction in the soil,

[0077] Under the action of electric potential gradient, the water flux in the soil is expressed as:

[0078]

[0079] Where q2 is the water flux in the soil under the action of the potential gradient, K e is the electric permeability coefficient;

[0080] Under the combined effect of matrix potential and electric potential gradient, the total water flux in the soil is:

[0081] q=q1+q2 (13)

[0082] Substituting equations (11) and (12) into (13), we can obtain the total water flux in the soil:

[0083]

[0084] According to the energy conservation equation and Richard equation, we can get:

[0085]

[0086] Where W represents the water content in the soil, q is the total water flux,

[0087] Substituting equation (14) into equation (15), we obtain the governing equation for liquid water migration in unsaturated sulfate saline soil under electroosmosis;

[0088] Transform Equation (18) with matrix suction as the dependent variable and effective saturation as the independent variable to obtain:

[0089]

[0090] Substituting formula (17) into formula (19), the relationship between matrix suction and water content is obtained:

[0091]

[0092] Hydraulic permeability coefficient K h The relationship between and effective saturation satisfies formula (21):

[0093] K h =K s H 0.5 [1-(1-H 1 / M ) M ] 2 (twenty one)

[0094] Where K s is the saturated permeability coefficient of the soil;

[0095] Substituting formula (17) into formula (21), the relationship between hydraulic penetration and water content is obtained:

[0096]

[0097] Specifically, the solution process of the gaseous water diffusion control equation in step 4 is:

[0098] The diffusion flux of gaseous water in soil is expressed as:

[0099]

[0100] Where G is the diffusion flux of gaseous water in the soil, and g is the gaseous water content in the soil;

[0101] Based on the law of conservation of mass in soil, the following formula is obtained:

[0102]

[0103] Where D v is the molecular coefficient of gaseous water, calculated according to the following formula:

[0104]

[0105] Where, ρ w is the density of water, t is the electroosmotic time, D va is the diffusion coefficient of water vapor in air, θ a is the volumetric air content in the soil, τ g is the water-salt transport coefficient; where

[0106] D va The expression is:

[0107] D va =2.29×10 -5 ×(T / 273.15) 2 (26)

[0108] θ a The expression is:

[0109]

[0110] τ g The expression is:

[0111] τ g =θ a 7 / 3 / n 2 (28)

[0112] Where θ ar is the residual volume air content in the soil, which is set to 0.04, and n is the porosity of the soil;

[0113] Combining equations (23) and (24) yields the governing equation for gaseous water diffusion in sulfate saline soil:

[0114]

[0115] Specifically, the expression of the ion migration control equation in step 5 is:

[0116]

[0117] Where: C tna is the total solid sodium ion content in solid form per unit volume of soil, C is the salt content in the soil, ρ s is the soil density, D s is the pore diffusion coefficient of salt ions in the soil, F is the Faraday constant, which is 96485C / mol, and Z s is the charge number of the charged ion, R is the gas constant, which is 8.3145 J / mol / K, T is the soil temperature, and E is the electric potential applied across the soil.

[0118] Specifically, according to the distribution and content of gaseous water in the soil, the relative humidity in the soil is obtained according to formula (30):

[0119] RH=g / ρ vs (30)

[0120] Among them, ρ vs is the density of saturated gaseous water, which is calculated according to formula (31) based on the soil temperature:

[0121]

[0122] The expression of ion migration flux is:

[0123]

[0124] Where D s is the pore diffusion coefficient of salt ions in the soil, U is the total flux of ion migration,

[0125] Since sodium ions are continuously precipitated during the electroosmosis process, the total amount is divided into two parts: solid phase and liquid phase. The sodium ions in the liquid phase are related to the solubility and moisture content. The law of conservation of mass in the soil is modified to obtain formula (33):

[0126]

[0127] Where C tna It is the sodium ion content in solid form per unit volume of soil;

[0128] Substituting equation (32) into equation (33) yields the governing equation for ion migration under electroosmosis in sulfate-salted soil.

[0129] Compared with existing technologies, this invention offers the following advantages: Its modeling comprehensively considers the effects of the electric field on soil temperature, liquid water content, gaseous water content, and salt content under electroosmosis, determines the coupling relationships between these fields, and uses the central difference method to solve the model and calculate the soil salt expansion. The salt expansion prediction results are highly consistent with experimental test results. This invention can accurately predict the salt expansion of sulfate-salted soil under different electroosmotic conditions, reducing engineering testing costs, optimizing electroosmotic expansion reduction construction plans, and improving engineering economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0130] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0131] Figure 1 1 is a comparison chart of the test results and the prediction results involved in the embodiments of the present invention. DETAILED DESCRIPTION

[0132] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0133] A method for predicting salt swelling of sulfate soil after electroosmosis treatment comprises the following steps:

[0134] It is assumed that Ohm's law and the law of conservation of charge are valid in sulfate saline soil. According to Ohm's law, we can get:

[0135]

[0136] Where I is the current density in the soil, in A / m 2 ; σ is the electrical conductivity of the soil, in mS / cm, and its value is related to the moisture and salt content in the soil; E is the electric potential applied across the soil, in V.

[0137] In formula (1), the relationship between the electrical conductivity of sulfate soil and the moisture content and salt content in the soil can be calculated according to formula (2):

[0138] σ=m1·C·W+m2·C+m3·W-m4(2)

[0139] Where C is the salt content in the soil, unit is m 3 / m 3 ; W is the moisture content in the soil m 3 / m 3 , unit is %; m1, m2, m3 and m4 are parameters related to the type of salt in the soil. In sulfate saline soil, the values ​​of m1, m2, m3 and m4 are 0.140, -0.773, 0.024 and -0.236 respectively.

[0140] According to the law of conservation of charge, we can get:

[0141]

[0142] Among them, C p is the capacitance influencing factor in saline soil, unit is F, which is affected by the dielectric constant of the soil; t is the electroosmosis time, unit is s; It is a mathematical gradient operator. It should be noted that the subscripts in each character in this application have no physical meaning and are only used to distinguish it from other characters.

[0143] Substituting equation (1) into equation (3), the governing equation of the electric field in the soil is established, namely equation (4):

[0144]

[0145] Assuming that Fourier's heat conduction law and the law of conservation of energy are simultaneously established in sulfate soil, according to Fourier's heat conduction law, Equation 5 can be obtained:

[0146]

[0147] Where J is the heat flux in the soil, in W / m 2 ;K t is the thermal conductivity of the soil, in W / m / K;

[0148] According to the energy conservation equation, we can get formula (6):

[0149]

[0150] Where c is the specific heat capacity of the soil, in J / kg / K; ρ is the density of the soil, in kg / m 3 ; T is soil temperature;

[0151] In formula (6), Q is the heat source, the unit is W, including the Joule heat of electroosmosis, and the calculation formula is shown in formula (7):

[0152]

[0153] Substituting Equation (7) into Equation (6) yields the energy conservation equation considering the electroosmotic Joule heating, as shown in Equation (8):

[0154]

[0155] Substituting equation (6) into equation (8) yields equation (9), which is the governing equation for temperature conduction in unsaturated sulfate saline soil.

[0156]

[0157] In formula (9), the thermal conductivity of soil K t It consists of four parts, namely the thermal conductivity of liquid water, sodium sulfate, soil particles and gaseous water, namely K tw , K tc , K ts and K ta, the unit is W / m / K; according to the volume ratio of water content, soil particle content, salt content and gaseous water content in unit volume of soil, that is, W, λ tc , c and g, in m 3 / m 3 , calculated according to formula (10):

[0158] K t =K tw ·W+K tc ·λ tc +K ts C+K ta ·g (10)

[0159] In unsaturated sodium sulfate saline soils, the driving force for water migration comes from the matrix potential, and the flow pattern follows Darcy's law. When a voltage is applied across the soil, a potential gradient forms between the anode and cathode ends, driving water flow through the soil—a phenomenon known as electroosmosis. Electroosmosis and the flow driven by the matrix potential can be linearly superimposed, resulting in the total water flux in the soil being the sum of the flux due to the potential gradient and the matrix potential.

[0160] According to Darcy's law, the water flux caused by the matrix potential in the soil can be expressed as Equation 11:

[0161]

[0162] Where q1 is the water flux under the action of matrix potential, unit is m 2 / s;K h is the hydraulic permeability coefficient, which is related to the water content W in the soil and is expressed in m / s; is the matric suction in the soil, which is a function of the soil moisture content.

[0163] Under the action of electric potential gradient, the water flux in the soil can be expressed as formula (12):

[0164]

[0165] Where q2 is the water flux in the soil under the action of the potential gradient, and the unit is m 2 / s;K e is the electrical permeability coefficient, in m 2 / s / V;

[0166] Under the combined effect of matrix potential and electric potential gradient, the total water flux in the soil is:

[0167] q=q1+q2 (13)

[0168] Substituting equations (11) and (12) into (13), we can obtain the total water flux in the soil:

[0169]

[0170] The energy conservation equation and Richard equation are valid in unsaturated sulfate saline soil, and we can get:

[0171]

[0172] Where W represents the water content in the soil, and the unit is m 3 / m 3 ; q is the total water flux, unit is m 2 / s.

[0173] Substituting Equation (14) into Equation (15), we obtain Equation (16), which is the governing equation for liquid water migration in unsaturated sulfate saline soil under electroosmosis:

[0174]

[0175] In formula (15), matrix suction It is related to the moisture content W in the soil. To simplify the calculation, a new parameter called effective soil saturation H is introduced and defined as formula (17):

[0176]

[0177] Where W s and W r They represent saturated volume liquid moisture content and residual volume liquid moisture content, both in %.

[0178] According to the VG model, the matrix suction and effective saturation H in the soil satisfy the relationship (18):

[0179]

[0180] Where a is a fitting factor related to soil properties, with a unit of kPa and a value of 0.15; M is a sensitive factor affecting the overall symmetry of the soil-water characteristic curve, with a unit of 1; N is an empirical parameter characterizing the pore size distribution, with a unit of 1, and the relationship between M and N satisfies the following equation: M = 1-1 / N.

[0181] Transform Equation (18) with matrix suction as the dependent variable and effective saturation as the independent variable to obtain Equation (19):

[0182]

[0183] Substituting formula (17) into formula (19), we can obtain the relationship between matrix suction and water content (20):

[0184]

[0185] In formula (15), the hydraulic permeability coefficient K h It is also related to the water content W in the soil. According to the VG model, the hydraulic permeability coefficient K h The relationship between and effective saturation satisfies formula (21):

[0186] K h =K s H 0.5 [1-(1-H 1 / M ) M ] 2 (twenty one)

[0187] Where K s is the saturated permeability coefficient in the soil, in m / s.

[0188] Substituting formula (17) into formula (21), we can obtain the relationship between hydraulic penetration and water content (22):

[0189]

[0190] The diffusion of gaseous water follows Fick's law, and this law is valid in sulfate saline soil. According to Fick's law, we can get formula (23):

[0191]

[0192] Where G is the diffusion flux of gaseous water in the soil, unit is m 2 / s; g is the gaseous water content in the soil, unit is m 3 / m 3 .

[0193] Based on the law of conservation of mass in soil, we can obtain formula (24):

[0194]

[0195] In formula (24), D v is the molecular coefficient of gaseous water, unit is m 2 / s, calculated according to formula (25):

[0196]

[0197] Where, ρ w is the density of water in kg / m 3 .

[0198] In formula (25), D va is the diffusion coefficient of water vapor in air, calculated according to formula (26):

[0199] D va=2.29×10 -5 ×(T / 273.15) 2 (26)

[0200] In formula (25), θ a is the volumetric air content in the soil, in m 3 / m 3 , calculated according to formula (27):

[0201]

[0202] Where θ ar is the residual volume air content in the soil, which is 0.04; p is the porosity of the soil;

[0203] In formula (25), τ g is the water-salt transport coefficient, calculated according to formula (28):

[0204] τ g =θ a 7 / 3 / p 2 (28)

[0205] Substituting Equation (23) into Equation (24) yields Equation (29), which is the governing equation for gaseous water diffusion in sulfate saline soil:

[0206]

[0207] According to the distribution and content of gaseous water in the soil, the relative humidity in the soil can be obtained according to formula (30):

[0208] RH=g / ρ vs (30)

[0209] Among them, ρ vs is the density of saturated gaseous water in kg / m 3 , calculated according to formula (31) based on the soil temperature:

[0210]

[0211] In unsaturated sulfate saline soil, the migration flux of ions can be expressed by the Nernst-Planck equation, that is, equation (32):

[0212]

[0213] Where D s is the pore diffusion coefficient of salt ions in the soil, in m 2 / s; U is the total ion migration flux, unit is mol / m 2 / s; F is the Faraday constant, which is 96485C / mol; Zs is the charge number of the charged ion; R is the gas constant, which is 8.3145 J / mol / K;

[0214] Since sodium ions are continuously precipitated during the electroosmosis process, the total amount is divided into two parts: solid phase and liquid phase. The sodium ions in the liquid phase are related to the solubility and moisture content. Therefore, the law of conservation of mass in the soil is modified to obtain formula (33):

[0215]

[0216] Where C tna The sodium ion content in solid form per unit volume of soil, expressed in kg / m 3 .

[0217] Substituting Equation (32) into Equation (33) yields the governing equation for ion migration under electroosmosis of sulfate-salted soil, namely, Equation (34):

[0218]

[0219] The electric field control equations, temperature field control equations, moisture field control equations, gaseous water field control equations, and salt control equations are combined and the soil model is meshed. The five equations are differentially solved using the central difference method to obtain the temperature T(t, i, j), liquid moisture content W(t, i, j), relative humidity RH(t, i, j), and sodium ion content C(t, i, j) at each point in the soil at different times. Where t is the electroosmosis time, i = 1, 2, ..., ny, j = 1, 2, ..., nx, ny and nx are the total number of steps in the vertical and horizontal directions, respectively. The values ​​are calculated by dividing the vertical and horizontal lengths of the soil model by the mesh width, respectively.

[0220] The obtained soil temperature T(t, i, j) is used to calculate the solubility Cr of sodium sulfate in water according to formula (35), in g / 100g.

[0221]

[0222] The standard sodium sulfate content C in water is calculated by combining the obtained soil liquid moisture content W(t, i, j) with formula (35) and formula (36). s , unit is kg / m 3 .

[0223] C s =C r ·ρ w W(t,i,j) / 100(36)

[0224] The obtained C sSubstitute into formula (37) to calculate the solid sodium ion content in the first part.

[0225]

[0226] Where C tna1 is the solid sodium ion content of the first part; C i is the initial value of sodium sulfate content, unit is kg / m 3 ;

[0227] Using the obtained C s The salt ion content C(t, i, j) obtained by reconciliation is used to calculate the solid sodium ion content of the second part according to formula (38):

[0228]

[0229] Where M tna and M m are the molar masses of sodium sulfate and thenardite, which are 142 g / mol and 322 g / mol respectively.

[0230] The solid sodium ion content of the above two parts is added according to formula (39) to obtain the total solid sodium ion content C in the soil tna .

[0231] C tna =C tna1 +C tna2 (39)

[0232] Substitute the obtained temperature T(t, i, j) into equations (40) and (41) again to calculate the critical relative humidity RH1 for the conversion of sodium sulfate crystals to mirabilite and the limiting relative humidity RH2 for the conversion of sodium sulfate solution to mirabilite:

[0233] RH1=60.02+0.7392×T(t,i,j)(40)

[0234] RH2=97.53sin(0.01695T(t,i,j)+1.515) (41)

[0235] The total solid sodium ion content C tna , relative humidity RH(t, i, j), RH1 and RH2 are determined according to formula (42), and the content of mirabilite in the soil C is calculated. m .

[0236]

[0237] Where C m is the content of mirabilite in the soil, in kg / m 3 .

[0238] Since the salt in the soil is unevenly distributed under the action of electroosmosis, the existing salt expansion calculation formula needs to be modified. The modification idea is to accumulate the salt expansion of each grid point in the horizontal direction upward, and finally obtain the salt expansion at each depth, so that the salt expansion under electroosmosis can be accurately calculated. The modified salt expansion calculation formula is:

[0239]

[0240] Where Δ is the salt expansion of sulfate soil, unit is m; ρ m is the density of the Glauber's salt crystal, in kg / m 3 ; L is the total depth of the soil, in m; t k is the number of time steps, that is, the total electroosmosis time divided by the interval time; ny and nx are the total number of steps in the vertical and horizontal directions, respectively, which are calculated by dividing the vertical and horizontal lengths of the soil model by the grid width.

[0241] Formula (42) is used to obtain the content of Glauber's salt c m Substituting into formula (43), the salt expansion of sulfate saline soil under electroosmosis can be calculated.

[0242] This method comprehensively considers the effects of the electric field on soil temperature, liquid water content, gaseous water content, and salt content under electroosmosis, determines the coupling relationship between these fields, and uses the central difference method to solve the model and calculate the soil salt expansion. The salt expansion prediction results are highly consistent with experimental test results. This method can accurately predict the salt expansion of sulfate-saline soil under different electroosmotic conditions, reduce engineering testing costs, optimize electroosmotic expansion reduction construction plans, and improve project economic benefits.

[0243] In order to verify the accuracy of the salt expansion prediction formula obtained by the above method, the inventors artificially prepared a mixture of 12% water content, 2.5% salt content and 1.74g / cm 3 The sulfate soil was placed in a container with a size of 1000 cm 2 The stainless steel plate is in full contact with the soil, and a displacement sensor is placed to measure the soil salt expansion and temperature. The switch power is turned on to provide a 0.66V / cm potential gradient. The electroosmosis lasts for 30 hours, and the salt expansion displacement data is measured every 5 minutes. At the same time, under the same conditions (the length and height of the sulfate saline soil are set to 600mm and 250mm, the initial water content is set to 12%, the initial sodium sulfate content is set to 2.5%, and the density is set to 1.74g / cm 3 The cooling mode is unidirectional cooling, the potential gradient of electroosmosis is set to 0.66 V / cm, and the electroosmosis time is continued for a total of 30 hours. The method of the present invention is used to predict the salt expansion of sulfate saline soil after electroosmosis.

[0244] The prediction results were compared with the wind tunnel test results. Figure 1 The results show that the salt expansion amount calculated by the method for predicting salt expansion of sulfate saline soil under electroosmosis provided by the present invention is consistent with the salt expansion data obtained from the electroosmotic deswelling test. The present invention can be used to predict salt expansion of sulfate saline soil under electroosmosis.

[0245] The above embodiments are merely examples to clearly illustrate the present invention and are not intended to limit its implementation. Those skilled in the art will readily appreciate that other variations or modifications based on the above descriptions are possible. It is not necessary and impossible to provide an exhaustive list of all embodiments. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for predicting salt swelling of sulfate soil after electroosmosis treatment, characterized in that: The steps include: Step 1: Establish the electric field control equation in the soil Step 2: Establish the temperature field control equation in the soil Step 3: Establish the control equation for liquid water migration in soil Step 4: Establish the governing equation for the diffusion of gaseous water in soil Step 5: Establish the governing equation for ion migration in soil Step 6: Simultaneously establish the electric field control equation, temperature field control equation, liquid water migration control equation, gaseous water diffusion control equation, and ion migration control equation, and divide the soil model into grids. Use the central difference method to perform differential solutions on these five equations, and obtain the temperature T(t, i, j), liquid water content W(t, i, j), relative humidity RH(t, i, j), and sodium ion content C(t, i, j) at each grid point in the soil under different electroosmosis times. Where t is the electroosmosis time, i = 1, 2, ..., ny, j = 1, 2, ..., nx, ny and nx are the total number of steps in the vertical and horizontal directions, respectively, which are calculated by dividing the vertical and horizontal lengths of the soil model by the grid width; Using the obtained soil temperature T(t,i,j) according to formula (35), the solubility of sodium sulfate in water C is calculated. r : The standard sodium sulfate content C in water is calculated by combining the obtained soil liquid moisture content W(t, i, j) with formula (35) and formula (36). s : C s =C r ·ρ w ·W(t,i,j) / 100(36) Among them, ρ w is the density of water; The obtained C s Substitute into formula (37) to calculate the solid sodium ion content of the first part: Where C tna1 is the solid sodium ion content of the first part, C i is the initial value of sodium sulfate content, ρ is the density of the soil; Using the obtained C s The salt ion content C(t,i,j) obtained by reconciliation is calculated according to formula (38) to calculate the second part of the solid sodium ion content: C tna2 Where M tna and M m are the molar masses of sodium sulfate and thenardite, respectively; The solid sodium ion content of the above two parts is added according to formula (39) to obtain the total solid sodium ion content C in the soil tna : C tna =C tna1 +C tna2 (39) Substitute the obtained temperature T(t, i, j) into equations (40) and (41) to calculate the critical relative humidity RH1 for the conversion of sodium sulfate crystals to mirabilite and the limiting relative humidity RH2 for the conversion of sodium sulfate solution to mirabilite: RH1=60.02+0.7392×T(t,i,j)(40) RH2=97.53sin(0.01695T(t,i,j)+1.515)(41) The total solid sodium ion content C tna , relative humidity RH(t, i, j), RH1 and RH2 are determined according to formula (42), and the content of mirabilite in the soil C is calculated. m : The salt expansion of each grid point in the horizontal direction of the soil model grid is accumulated upward, and finally the calculation formula of the salt expansion at each depth after correction is obtained: Where Δ is the salt expansion of sulfate soil, ρ m is the density of the mirabilite crystals, L is the total depth of the soil, t k is the number of time steps, i.e., the total electroosmosis time divided by the interval time; The content of Glauber's salt C obtained by formula (42) m Substituting into formula (43), the salt expansion of sulfate saline soil under electroosmosis can be calculated.

2. The method for predicting salt swelling of sulfate soil after electroosmosis treatment according to claim 1, characterized in that: The expression of the electric field control equation in step 1 is: Where C p is the capacitance influencing factor in saline soil, t is the electroosmosis time, is the mathematical gradient operator, σ is the electrical conductivity of the soil, and E is the electric potential applied at both ends of the soil.

3. The method for predicting salt swelling of sulfate soil after electroosmosis treatment according to claim 2, characterized in that: According to Ohm's law: Where I is the current density in the soil, σ is the electrical conductivity of the soil, and E is the potential applied across the soil. The relationship between the electrical conductivity of the soil and the moisture content and salt content in the soil is calculated according to formula (2): σ=m11·C·W+m2·C+m3·W-m4(2) Where C is the salt content in the soil, W is the water content in the soil, m1, m2, m3, and m4 are parameters related to the type of salt in the soil. In sulfate saline soil, the values ​​of m1, m2, m3, and m4 are 0.140, -0.773, 0.024, and -0.236, respectively. According to the law of conservation of charge: Among them, C p is the capacitance influencing factor in saline soil, t is the electroosmosis time, is the mathematical gradient operator; Substituting equation (1) into equation (3), the electric field control equation in soil is established:

4. The method for predicting salt swelling of sulfate soil after electroosmosis treatment according to claim 1, characterized in that: The expression of the temperature field control equation in step 2 is: Where: c is the specific heat capacity of the soil, ρ is the density of the soil, T is the soil temperature, σ is the electrical conductivity of the soil, K t is the thermal conductivity of the soil, E is the electric potential applied at both ends of the soil, t is the electroosmosis time, and the thermal conductivity of the soil K is t It consists of four parts, namely the thermal conductivity of liquid water, sodium sulfate, soil particles and gaseous water, namely K tw , K tc , K ts and K ta ; According to the volume ratio of water content, soil particle content, salt content and gaseous water content in unit volume of soil, that is, W, λ tc , C and g are calculated according to the following formula: K t =K tw ·W+K tc ·λ tc +K ts ·C+K ta ·g (10)。 5. The method for predicting salt swelling of sulfate soil after electroosmosis treatment according to claim 4, characterized in that: According to Fourier's law of heat conduction, we can get formula (5): Where J is the heat flux in the soil, K t is the thermal conductivity of the soil; According to the energy conservation equation, we can get equation (6): Where c is the specific heat capacity of the soil, ρ is the density of the soil, and T is the soil temperature; Q is the heat source of electroosmotic Joule heat, which is calculated as follows: Substituting Equation (7) into Equation (6) yields the energy conservation equation considering the electroosmotic Joule heating: Substituting equation (6) into equation (8) we can obtain the temperature conduction control equation in unsaturated sulfate saline soil.

6. The method for predicting salt swelling of sulfate soil after electroosmosis treatment according to claim 1, characterized in that: The expression of the liquid water migration control equation in step 3 is: Where W is the water content in the soil, t is the electroosmosis time, K e is the electric permeability coefficient, is the matrix suction in the soil, K h is the hydraulic permeability coefficient, E is the electric potential applied at both ends of the soil, where The expression is: K h The expression is: K h =K s H 0.5 [1-(1-H 1 / M )M] 2 (21) Where: W s and W r They represent the saturated volume liquid water content and residual volume liquid water content in the soil, respectively. N is an empirical parameter characterizing the pore size distribution, with a value of 3. M is a sensitive factor affecting the overall symmetry of the soil-water characteristic curve, with a value of 2 / 3. K s is the saturated permeability coefficient in the soil, H is the effective saturation of the soil, and a is a fitting factor related to the soil properties, with a value of 0.

15.

7. The method for predicting salt swelling of sulfate soil after electroosmosis treatment according to claim 6, characterized in that: According to Darcy's law, the water flux q1 caused by the matrix potential in the soil is expressed as: Where q1 is the water flux under the action of matrix potential, K h is the hydraulic permeability coefficient, is the matrix suction in the soil, Under the action of electric potential gradient, the water flux in the soil is expressed as: Where q2 is the water flux in the soil under the action of the potential gradient, K e is the electric permeability coefficient; Under the combined effect of matrix potential and electric potential gradient, the total water flux in the soil is: q=q1+q2 (13) Substituting equations (11) and (12) into (13), we can obtain the total water flux in the soil: According to the energy conservation equation and Richard equation, we can get: Where W represents the water content in the soil, q is the total water flux, Substituting equation (14) into equation (15), we obtain the governing equation for liquid water migration in unsaturated sulfate saline soil under electroosmosis; Transform Equation (18) with matrix suction as the dependent variable and effective saturation as the independent variable to obtain: The effective soil saturation H is introduced and defined as formula (17): Where W s and W r They represent saturated volume liquid moisture content and residual volume liquid moisture content respectively; Substituting formula (17) into formula (19), the relationship between matrix suction and water content is obtained: Hydraulic permeability coefficient K h The relationship between and effective saturation satisfies formula (21): K h =K s H 0.5 [1-(1-H 1 / M )M] 2 (21) Where K s is the saturated permeability coefficient of the soil; Substituting formula (17) into formula (21), the relationship between hydraulic penetration and water content is obtained:

8. The method for predicting salt swelling of sulfate soil after electroosmosis treatment according to claim 4, characterized in that: The solution process of the gaseous water diffusion control equation in step 4 is: The diffusion flux of gaseous water in soil is expressed as: Where G is the diffusion flux of gaseous water in the soil, and g is the gaseous water content in the soil; Based on the law of conservation of mass in soil, the following formula is obtained: Where D v is the molecular coefficient of gaseous water, calculated according to the following formula: Where, ρ w is the density of water, t is the electroosmotic time, D va is the diffusion coefficient of water vapor in air, θ a is the volumetric air content in the soil, τ g is the water-salt transport coefficient; where D va The expression is: D va =2.29×10 -5 ×(T / 273.15) 2 (26) θ a The expression is: τ g The expression is: t g =θ a 7 / 3 / n 2 (28) Where θ ar is the residual volume air content in the soil, which is set to 0.04, and n is the porosity of the soil; Combining equations (23) and (24) yields the governing equation for gaseous water diffusion in sulfate saline soil:

9. The method for predicting salt swelling of sulfate soil after electroosmosis treatment according to claim 1, characterized in that: The expression of the ion migration control equation in step 5 is: Where: C tna is the total solid sodium ion content in solid form per unit volume of soil, C is the salt content in the soil, ρ s is the soil density, D s is the pore diffusion coefficient of salt ions in the soil, F is the Faraday constant, which is 96485C / mol, and Z s is the charge number of the charged ion, R is the gas constant, which is 8.3145 J / mol / K, T is the soil temperature, and E is the electric potential applied across the soil.

10. The method for predicting salt swelling of sulfate soil after electroosmosis treatment according to claim 9, characterized in that: According to the distribution and content of gaseous water in the soil, the relative humidity in the soil is obtained according to formula (30): RH=g / ρ vs (30) Among them, ρ vs is the density of saturated gaseous water, g is the gaseous water content in the soil, and is calculated according to formula (31) based on the soil temperature: The expression of ion migration flux is: Where D s is the pore diffusion coefficient of salt ions in the soil, U is the total flux of ion migration, Since sodium ions are continuously precipitated during the electroosmosis process, the total amount is divided into two parts: solid phase and liquid phase. The sodium ions in the liquid phase are related to the solubility and moisture content. The law of conservation of mass in the soil is modified to obtain formula (33): Where C tna It is the sodium ion content in solid form per unit volume of soil; Substituting equation (32) into equation (33) yields the governing equation for ion migration under electroosmosis in sulfate-salted soil.

Images