Method for predicting salt expansion amount of sulfuric acid salinized soil after electroosmosis treatment

Abstract

The invention discloses a method for predicting salt expansion of sulfuric acid salinized soil after electroosmosis treatment. Comprising the steps of establishing an electric field control equation in a soil body, establishing a temperature field control equation in the soil body, establishing a liquid water migration control equation in the soil body, establishing a gaseous water diffusion control equation in the soil body, establishing an ion migration control equation in the soil body, and simultaneously establishing the electric field control equation, the temperature field control equation and the liquid water migration control equation. A gaseous water diffusion control equation and an ion migration control equation are established, a soil body model grid is divided, a central difference method is used for carrying out difference solving on the five equations, and then a salt expansion prediction expression is determined. According to the method, the salt expansion amount of the sulfate saline soil under different electroosmosis conditions can be accurately predicted, the engineering test cost is reduced, an electroosmosis expansion reduction construction scheme is optimized, and the engineering economic benefit is improved.

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 cushion layer and setting up isolation layers. Among them, the dynamic compaction method has 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 cushion layer method is limited by the scope of construction, has high costs and is difficult to use on a large scale. When setting up faults and 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 saline soil. However, the use of electroosmosis to inhibit salt swelling of sulfate saline soil is currently only at the experimental level. In order to obtain a better swelling reduction effect, a large number of tests are usually required, and 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, water content, gaseous water and salt are not fully considered, which 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 saline 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 realize 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 saline soil after electroosmosis treatment provided by the embodiment of the present invention comprises 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 control equation for the diffusion of gaseous water in soil

[0011] Step 5: Establish the control equation of ion migration in soil

[0012] Step 6: Combine 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 grid. Use the central difference method to solve 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 of 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 obtained by dividing the length of the soil model in the vertical and horizontal directions by the grid width;

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

[0015]

[0016] The standard sodium sulfate content C in water is calculated by using the obtained soil liquid moisture content W(k, i, j) and formula (35) according to 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] In the formula, 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 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 solid sodium ion content C in the second part tna2 :

[0023]

[0024] Where M tna and M mare the molar masses of sodium sulfate and mirabilite, 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) to calculate the content of mirabilite in the soil C 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 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 sodium sulfate C obtained by formula (42) m Substituting into equation (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] In the formula, C p is the capacitance influencing factor in saline soil, t is the electroosmotic 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 conductivity of the soil, and E is the potential applied at both ends of 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] In the formula, 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 electroosmotic 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 moisture 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, we get formula (5):

[0055]

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

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

[0058]

[0059] In the formula, 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 effect:

[0063]

[0064] (9) Substituting equation (6) into equation (8), we can obtain 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 electrical 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 moisture content and residual volume liquid moisture 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 characteristics, with a value of 0.15.

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

[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 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 penetration 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] In the formula, W represents the moisture content in the soil, q is the total water flux,

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

[0088] Transform formula (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] In the formula, K s is the saturated permeability coefficient in 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] In the formula, 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 as follows:

[0104]

[0105] In the formula, 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] In the formula, θ ar is the residual volume air content in the soil, which is taken as 0.04, and n is the porosity of the soil;

[0113] Combining equations (23) and (24), we can obtain the diffusion control equation of gaseous water 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, whose value is 8.3145 J / mol / K, T is the soil temperature, and E is the electric potential applied at both ends of 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 migration flux of ions is expressed as:

[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 water content. The law of conservation of mass in the soil is corrected to obtain formula (33):

[0126]

[0127] In the formula, C tna 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 of sulfate saline soil.

[0129] Compared with the prior art, the present invention has the following beneficial effects: when modeling, the present invention comprehensively considers the influence of the electric field on the soil temperature, liquid water content, gaseous water content and salt content under the action of electroosmosis, determines the coupling relationship between the fields, solves the model and calculates the salt expansion of the soil using the central difference method, and the salt expansion prediction result is highly consistent with the experimental test result. The present invention can accurately predict the salt expansion of sulfate saline soil under different electroosmotic conditions, reduce engineering test costs, optimize the electroosmotic expansion reduction construction plan, and improve the economic benefits of the project. 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 It 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 be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0133] A method for predicting salt swelling of sulfate saline 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, the unit is mS / cm, and its value is related to the moisture content and salt content in the soil; E is the electric potential applied at both ends of the soil, the unit is V.

[0137] In formula (1), the relationship between the conductivity of sulfate saline 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, in m 3 / m 3 ; W is the moisture content in the soil m 3 / m 3 , the 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, 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 electric field control equation in soil is established, namely equation (4):

[0144]

[0145] Assuming that Fourier's heat conduction law and the law of conservation of energy are both valid 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 soil, in W / m / K;

[0148] According to the energy conservation equation, we can get equation (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), we get the energy conservation equation considering the electroosmotic Joule heat effect, as shown in equation (8):

[0154]

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

[0156]

[0157] In formula (9), the thermal conductivity K of the soil 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, the unit is W / m / K; according to the volume ratio of moisture 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 soil, the driving force of water migration comes from the matrix potential, and the flow pattern follows Darcy's law. When voltage is applied to both ends of the soil, an electric potential gradient is formed between the anode and cathode ends of the soil, which can drive the water flow in the soil, namely, electroosmosis. The water flow driven by electroosmosis and matrix potential can be linearly superimposed, and the total water flux in the soil is the sum of the water flux under the action of the electric potential gradient and 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 matrix potential, in 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 matrix suction in the soil, which is a function of the moisture content of the soil.

[0163] Under the action of 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, in 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 moisture content in the soil, in m 3 / m 3 ; q is the total water flux, in m 2 / s.

[0173] Substituting equation (14) into equation (15), we get equation (16), which is the control 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, soil effective 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 respectively, 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 is: 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] In the formula, K s It is the saturated permeability coefficient of 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, equation (23) can be obtained:

[0191]

[0192] Where G is the diffusion flux of gaseous water in the soil, in 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 equation (24):

[0194]

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

[0196]

[0197] In the formula, 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 the 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] In the formula, 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 the diffusion of gaseous water 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 the soil temperature according to formula (31):

[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 flux of ion migration, in 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 water content. Therefore, the law of conservation of mass in the soil is corrected to obtain equation (33):

[0215]

[0216] In the formula, C tna is the sodium ion content in solid form per unit volume of soil, in kg / m 3 .

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

[0218]

[0219] The electric field control equation, temperature field control equation, moisture field control equation, gaseous water field control equation and salt control equation are combined and the soil model is gridded. 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. 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.

[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 of the first part.

[0225]

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

[0227] Using the obtained C s The salt ion content C(t, i, j) obtained by the solution 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) to calculate the content of mirabilite in the soil C m .

[0236]

[0237] In the formula, 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, it is necessary to correct the existing salt expansion calculation formula. The correction idea is to add 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 the action of electroosmosis can be accurately calculated. The corrected 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 electro-osmosis 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 length of the soil model in the vertical and horizontal directions by the grid width.

[0241] Formula (42) gives the content of sodium sulfate c m Substituting into equation (43), the salt expansion of sulfate saline soil under electroosmosis can be calculated.

[0242] The present invention comprehensively considers the influence of the electric field on the soil temperature, liquid water content, gaseous water content and salt content under the action of electroosmosis, determines the coupling relationship between the fields, solves the model and calculates the salt expansion of the soil using the central difference method, and the salt expansion prediction results are highly consistent with the experimental test results. The present invention can accurately predict the salt expansion of sulfate saline soil under different electroosmotic conditions, reduce engineering test costs, optimize the electroosmotic expansion reduction construction plan, and improve the economic benefits of the project.

[0243] In order to verify the accuracy of the salt expansion prediction formula obtained by the above method, the inventors artificially prepared a water content of 12%, a salt content of 2.5% and a density of 1.74 g / cm 3 The sulfate soil was placed in a container with a size of 1000 cm 2 The stainless steel plate is fully in contact with the soil, and a displacement sensor is placed to measure the salt expansion and temperature of the soil. The switch power supply 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 lasts for a total of 30 hours), and the method of the present invention is used to predict the salt swelling 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 swelling amount obtained by the salt swelling prediction method of sulfate saline soil under electroosmosis provided by the present invention is consistent with the salt swelling data obtained by the electroosmotic swelling reduction test. The present invention can be used for predicting salt swelling of sulfate saline soil under electroosmosis.

[0245] The above embodiments are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. The obvious changes or modifications derived therefrom are still 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 control equation for the diffusion of gaseous water in soil Step 5: Establish the control equation of ion migration in soil Step 6: Combine 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 grid. Use the central difference method to solve 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 of 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 length of the soil model in the vertical and horizontal directions by the grid width; Using the obtained soil temperature T(t, i, h) according to formula (35), calculate the solubility C of sodium sulfate in water: r : The standard sodium sulfate content C in water is calculated by using the obtained soil liquid moisture content W(k, i, j) and formula (35) according to 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: In the formula, 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 soil; Using the obtained C s The salt ion content C(k, i, j) obtained by the solution is calculated according to formula (38): the solid sodium ion content C of the second part tna2 : Where M tna and M m are the molar masses of sodium sulfate and mirabilite, 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 =CV tna1 +C tna2 (39) 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: 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) to calculate the content of mirabilite in the soil C 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 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 sodium sulfate C obtained by formula (42) m Substituting into equation (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: In the formula, C p is the capacitance influencing factor in saline soil, t is the electroosmotic 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 saline 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 conductivity of the soil, and E is the potential applied at both ends of 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=m1·C·W+m2·C+m3·W-m4(2) In the formula, 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 electroosmotic 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 moisture 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 get equation (5): Where J is the heat flux in the soil, K t is the thermal conductivity of soil; According to the energy conservation equation, we get equation (6): In the formula, 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 effect: (9) 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 saline 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 electrical 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 moisture content and residual volume liquid moisture 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 characteristics, 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 caused by matrix potential in 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 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 penetration 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: In the formula, W represents the moisture content in the soil, q is the total water flux, Substituting equation (14) into equation (15), the control equation for liquid water migration in unsaturated sulfate saline soil under electroosmosis is obtained; Transform equation (18) with matrix suction as the dependent variable and effective saturation as the independent variable to obtain: 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) In the formula, K s is the saturated permeability coefficient in 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 1, 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: In the formula, 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 as follows: In the formula, 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) In the formula, θ ar is the residual volume air content in the soil, which is taken as 0.04, and n is the porosity of the soil; Combining equations (23) and (24), we can obtain the diffusion control equation of gaseous water in sulfate saline soil:

9. The method for predicting salt swelling of sulfate saline 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 taa 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, whose value is 8.3145 J / mol / K, T is the soil temperature, and E is the electric potential applied at both ends of 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, which 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 water content. The law of conservation of mass in the soil is corrected to obtain formula (33): In the formula, C tna It is the content of sodium ions in solid form per unit volume of soil; Substituting equation (32) into equation (33) yields the governing equation for ion migration under electroosmosis of sulfate saline soil.

Images