CN115372589A - Method for determining unfrozen water content of frozen soil based on premelting theory - Google Patents
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- 239000002689 soil Substances 0.000 title claims abstract description 100
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 title claims abstract description 85
- 238000000034 method Methods 0.000 title claims abstract description 15
- 239000002245 particle Substances 0.000 claims abstract description 95
- 239000012535 impurity Substances 0.000 claims abstract description 17
- 238000004781 supercooling Methods 0.000 claims abstract description 12
- 150000003839 salts Chemical class 0.000 claims abstract description 9
- 239000004927 clay Substances 0.000 claims abstract description 6
- 239000007788 liquid Substances 0.000 claims description 18
- 239000007787 solid Substances 0.000 claims description 12
- 238000012856 packing Methods 0.000 claims description 11
- 230000008014 freezing Effects 0.000 claims description 6
- 238000007710 freezing Methods 0.000 claims description 6
- 230000009467 reduction Effects 0.000 claims description 3
- 239000011800 void material Substances 0.000 claims description 3
- 239000011148 porous material Substances 0.000 abstract description 9
- 230000014509 gene expression Effects 0.000 abstract description 6
- 230000003746 surface roughness Effects 0.000 abstract description 4
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- 238000004364 calculation method Methods 0.000 description 10
- 230000008859 change Effects 0.000 description 7
- 230000000694 effects Effects 0.000 description 4
- 238000009825 accumulation Methods 0.000 description 3
- 239000005457 ice water Substances 0.000 description 3
- 230000008018 melting Effects 0.000 description 3
- 238000002844 melting Methods 0.000 description 3
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- FAPWRFPIFSIZLT-UHFFFAOYSA-M Sodium chloride Chemical compound [Na+].[Cl-] FAPWRFPIFSIZLT-UHFFFAOYSA-M 0.000 description 2
- 238000013459 approach Methods 0.000 description 2
- 238000006243 chemical reaction Methods 0.000 description 2
- 230000004927 fusion Effects 0.000 description 2
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- 239000007791 liquid phase Substances 0.000 description 2
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- 239000003513 alkali Substances 0.000 description 1
- 238000005452 bending Methods 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
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- 150000002500 ions Chemical class 0.000 description 1
- 239000000463 material Substances 0.000 description 1
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- 238000013508 migration Methods 0.000 description 1
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- 238000010951 particle size reduction Methods 0.000 description 1
- 230000035699 permeability Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
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- 238000004088 simulation Methods 0.000 description 1
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Abstract
The invention relates to a method for determining the unfrozen water content of frozen soil based on a premelting theory, which comprises the following steps of: s1, establishing a relation between the thickness of a water film and supercooling temperature based on a premelting theory and by considering soil properties; s2, establishing an unfrozen water content model based on a soil particle obtaining arrangement mode; s3, collecting a soil sample, and measuring the particle size distribution, the salt concentration and the pore ratio of the soil; s4, characterizing the particle size distribution of the soil particles based on the equivalent particle size, and respectively reducing the equivalent particle size by 0.28, 0.3 and 0.36 for silty clay, loess and sandy soil so as to correct the influence of the shape or surface roughness of the soil particles; the particle surface impurity density was calculated using the maximum water film thickness and the measured salt concentration. And S5, calculating the unfrozen water content of the frozen soil. The invention has less related parameters, a given value range and a simple expression.
Description
Technical Field
The invention relates to the field of calculation of unfrozen water of frozen soil in a cold region, in particular to a method for determining the content of unfrozen water of frozen soil based on a premelting theory.
Background
The content of unfrozen water influences the structure of the pore ice and the cementation strength of soil particles and an ice skeleton in frozen soil, the internal friction angle of a soil body is increased along with the reduction of temperature, and the strength of the soil body is higher at negative temperature. The volume of water and ice in soil is changed due to the phase change of water and ice, the change of the volume share of each component in the soil body also causes the change of the heat conductivity coefficient and the volume heat capacity of the soil body, the related variables have obvious influence on the thermal state of geological structures and geotechnical engineering structures, and the heat stability of cold region engineering can be predicted, so that the determination of the heat transfer rate and the freeze-thaw depth can be facilitated. The unfrozen water content controls the permeability of frozen soil and plays an important role in the water conveying process of a soil-water system in a cold environment. In saline-alkali areas, unfrozen water carries solutes from the unfrozen area to the frozen area due to low temperature suction, and then an ice lens body is formed at the cold end of the frozen edge, and meanwhile, the ice lens body is thickened due to underground water supply, so that moisture migration and solute transport are hindered.
The unfrozen water model can be divided into an empirical model and a theoretical model. The empirical model is used for obtaining data through tests and fitting curves, the physical meaning of parameters in the model is not clear, and the parameters are calibrated in a laboratory again according to different working conditions. The theoretical model has a specific mathematical derivation process, but the model expression is complex and difficult to apply to numerical simulation calculation, and parameters in the expression are more and more difficult to obtain.
Disclosure of Invention
In order to overcome the problems in the prior art, it is important to research a model and a determination method which have fewer related parameters and a given value range and have simple expressions.
The invention aims to provide a frozen soil unfrozen water content determination method based on a premelting theory, which is simple in model expression and accurate in calculation, provides a calculation mode of the unfrozen water content, determines the change of the thickness of a water film in soil along with the doping level and the change rule of the temperature, and can calculate the unfrozen water content of the soil at different temperatures only by measuring common physical indexes of the soil to be measured, such as salt concentration, particle gradation and porosity ratio.
The purpose of the invention is realized by the following technical scheme: a method for determining the unfrozen water content of frozen soil based on a premelting theory comprises the following steps:
s1, establishing a relation between the water film thickness and the supercooling temperature.
In the formula: Δ T represents the supercooling degree, i.e., the initial freezing temperature reduction value, i.e., the deviation value from 273.15K; r is g Is the gas constant; t is a unit of m ＝273.15K；N im Is the concentration of impurities on the surface of the soil particles; a. The H Is Hamaker constant.
S2, establishing the unfrozen water content f l And (3) a model of the relation with the water film thickness.
In the formula, R e Represents the equivalent radius of the particle; d p Represents the thickness of the water film between the ice particles and the solid particles; d gb Represents the water film thickness between ice particles; SC and FCC represent two common types of packing, simple cubic packing (abbreviated as SC) and cubic closest packing (face-c)entried cubic packing, abbreviated FCC), f p (SC) and f p (FCC) represents the percentage of particles in the total volume (packing fraction) in the SC and FCC arrangements, respectively, and can be converted from the void ratio e (f) p = 1/(1+e)); r represents the radius of the ice-liquid contact surface, and is determined by the Gibbs-Thomson relationship.
And S3, collecting a soil sample, measuring the particle size distribution and the salt concentration of the soil, and determining the volume percentage of soil particles with each particle size in the soil.
S4, characterizing the particle size distribution of the soil particles based on the equivalent particle size, and reducing the equivalent particle size by 0.21-0.23, 0.16-0.28, 0.25-0.3 and 0.36 respectively for silt, silty clay, loess and sandy soil so as to correct the influence of the shape or surface roughness of the soil particles; the particle surface impurity density was calculated using the maximum water film thickness and the measured salt concentration.
And S5, calculating the unfrozen water content of the frozen soil.
The invention has less related parameters, a given value range and a simple expression.
Drawings
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a graph showing the particle size distribution of soil particles according to the present invention based on the equivalent particle size.
FIG. 3 is an embodiment SC model;
FIG. 4 illustrates an example FCC model;
FIG. 5a is a graph of water film thickness versus subcooling temperature;
FIG. 5b is a second graph showing the relationship between the water film thickness and the supercooling temperature;
FIG. 5c is a third graph of the relationship between the water film thickness and the supercooling temperature;
FIG. 6a is a graph showing the results of an unfrozen water content model for the type 1 soil of example;
FIG. 6b is a graph of the results of an unfrozen water content model for the type 2 soil of example;
FIG. 6c is a graph of the results of an unfrozen water content model for the type 3 soil of the example;
FIG. 6d is the results of an unfrozen water content model for the type 4 soil of the example;
FIG. 6e is a graph of the results of an unfrozen water content model for the type 5 soil of the example;
FIG. 6f is a graph of the results of an unfrozen water content model for the type 6 soil of example;
FIG. 6g is a graph of the results of an unfrozen water content model for the type 7 soil of the example;
FIG. 6h is the results of an unfrozen water content model for the type 8 soil of example.
Detailed Description
The specific technical scheme of the invention is described by combining the embodiment. The process shown in fig. 1 comprises the following steps:
s1, establishing a relation between the water film thickness and the supercooling temperature.
In the formula: Δ T represents the supercooling degree, i.e., the initial freezing temperature decrease value (deviation from 273.15K). R g Is the gas constant; t is m ＝273.15K；N im Is the concentration of impurities on the surface of the soil particles; pore solution molar density ρ l Can be considered as a constant in the calculation; q. q.s m As latent heat of fusion per mole.
The step S1 includes:
s101, pre-melting is a common phenomenon of all solids. When the system is at ultra-low temperatures, the interstitial spaces in the system are completely filled with ice crystals. When the temperature is raised, surface melting occurs at the interface of ice in contact with the matrix, and grain boundary melting occurs between ice crystals. The existence form of the water comprises film water and interstitial water, and the system can be divided into three layers according to the form of the medium, wherein the layer is a spherical solid layer, the layer is a pre-molten liquid layer (water film) with the width of d, and the last layer is an ice crystal layer. If the liquid in the system contains a certain amount of impurities, the Gibbs free energy per unit area of the system can be written as follows:
G(T,P,N s ,N l ,N im )＝μ s (T,P)N s +μ l (T,P)N l +μ im (T,P)N im +R g T(N s lna s +N l lna l +N im lna im )+G interface (d) (1)
in the formula: t, P are temperature and pressure, μ s ,μ l ,μ im Chemical potential, μ, per mole of solid, liquid and impurity, respectively s ,μ l ,μ im The activity of solid, liquid and impurity respectively, under normal conditions, the activity of ice is 1,N s ,N l ,N im Respectively the number of moles per unit area of solid, liquid, impurities, R g Is a gas constant, G interface Is the interfacial free energy associated with the water film. The solid (ice) and liquid phase (water) are in equilibrium at the freezing point, and the thermodynamic equilibrium conditions are as follows:
at constant pressure, the chemical potential difference per mole of solid and liquid can be determined as:
in the formula: l S,S s entropy of liquid and solid respectively, at T m =273.15K, latent heat of phase change q m Is constant, Δ T is T m -T。G interface There are two contributions:
in the formula: f dis (d) Contribution of dispersive forces to the free energy of the interface, F elec (d) Hamaker constant A due to contribution of ion-trapping surface charges in the liquid layer H Is a common indicator for comparing the strength of van der Waals interactions, q s For surface charge density, van der waals interactions are weak for solid and liquid phases of a single material, and contribute predominantly when electrical forces are present. ε is the relative dielectric constant of liquid water 0 Vacuum dielectric constant, e is the electron charge amount, k B Is Boltzmann constant, N A Is the Avgalois constant and kappa is the constant, 7.237 × 10 7 m -1/2 ·mol -1/2 。
For an ideal dilute solution, -lna l ＝ρ i /ρ l The joint type (2), the formula (3) and the formula (4) can obtain:
in the formula: q. q.s m Is the latent heat of fusion per mole, ρ l Is the molarity of the liquid, N im The segregation coefficient of impurities in ice is small (about 10) because of the number of impurities per unit area -6 ) Therefore, the impurity distribution in the preliminary melt is considered to be uniform.
S102. To obtain the effect of the ice-water interface curvature on the freezing temperature, the present embodiment ignores the anisotropy of the ice surface energy, assuming that a spherical ice crystal with radius r is completely surrounded by liquid water. Considering that the area of the interface is no longer a constant, equation (1) is rewritten as:
G(T,P,N s ,N l ,N im )＝μ s (T,P)N s +μ l (T,P)N l +μ im (T,P)N im +R g T(N s lna s +N l lna l +N im lna im )+4πr 2 γ sl
(7)
for a principal radius of curvature of r 1 And r 2 The temperature drop due to the liquid surface bending at thermodynamic equilibrium can be calculated by equation (2). Between themThe relationship is shown in formula (8):
in the formula: ice crystal radius r in N s Correlation (N) s ＝4πr 3 ρ s /3)，ρ s Is the molar density of ice, gamma sl Is the interface free energy.
As can be seen from fig. 5a to 5c, for the system with larger doping, the water film thickness is almost completely affected by the impurity effect, and the soil is a porous medium with larger doping amount in the subsequent calculation, so the formula (6) can be simplified to the formula (9):
s2, establishing the unfrozen water content f l And (3) a model of the relation with the water film thickness.
In the formula, R e Represents the equivalent radius of the particle; d p Represents the thickness of the water film between the ice particles and the solid particles; d gb Represents the water film thickness between ice particles; f. of p The proportion of spherical particles in the total volume can be obtained by changing the pore ratio e; r represents the radius of the ice-liquid contact surface and can be determined by the Gibbs-Thomson relationship. To simplify the gibbs-thomson equation, larger radii of curvature at the ice-water interface may be excluded. Accordingly, equation (8) is expressed as:
the step S2 includes:
based on two common stacking approaches: simple cubic packing (abbreviated as SC) and cubic closest packing (abbreviated as FCC) establish the relationship between the moisture content and the water film on the surface of the particle and the surface of the ice crystal, the crack at the particle contact and the particle boundary.
(1) Relationship between water content and water film on particle surface and ice crystal surface
The cross sections surrounded by the solid black lines in fig. 3b and 4b are cross sections of the unit cells SC and FCC, and the cubes corresponding to the cross sections are taken as the unit cells. n is p,i Is a sphere with a radius of R i The number of soil particles per unit volume of soil, for SC model and FCC model n p,i Are respectively 1/(8R) i 3 ) And √ 2/(8R) i 3 )，f p，i Is the ratio of the sphere particles to the total volume n p,i There is a conversion relation, i.e. f p，i ＝4πR i 3 n p,i . The soil particle surface area is then expressed as:
for the SC model, the contact area between two adjacent ice crystals is equal to the difference between the area of the square and the area of the soil particles. Considering r i Much less than R i The calculation formula can be written as formula (12 a):
s gb,i (SC)≈(2R i +2r i ) 2 -π(R i +2r i ) 2 (12a)
for the FCC model, the area of each grain boundary is equal to the difference between the area of the triangle and the area of the soil grain. Can be approximately calculated by equation (12 b):
there were 3 grain boundaries per soil particle in the SC model (fig. 3 a) and 8 grain boundaries per soil particle in the FCC model (fig. 4 a). Thus, the total surface area contributed by the ice crystal grain boundaries per unit volume can be estimated as:
S gb,i (SC)＝3n p,i s gb,i (SC) (13a)
S gb,i (FCC)＝8n p,i s gb,i (FCC) (13b)
the unfrozen water content per unit volume of soil particles and particle (ice) boundaries can be written as:
(2) Curvature induced change in water content
There are two regions with curvature, one present between two adjacent spheres (fig. 3 b), which is caused by the formation of ice crystals in the pores consisting of a plurality of particles. The other is the edge between the ice crystal boundary and the sphere (fig. 3 c), which is formed by adjacent ice crystals as they touch on the particle surface.
For the SC model, one sphere has six adjacent spheres, and for the FCC model, one sphere has 12 adjacent spheres. Thus, there are 3 cracks per sphere of SC packing and 6 cracks per sphere of FCC packing. When r is i Much less than R i The volume of each crack is approximately 2 pi r i R i 2 Therefore:
if the curvature of the adjacent spheres and the ice-water interface is neglected, the liquid water in the cross-section (FIG. 3 b) is: s edge，i ＝2(r i 2 -πr i 2 /4). For the SC and FCC models, the number of pores corresponding to the unit volume soil particles (fig. 3b and fig. 4 c) was 1 and 8, respectively.In the SC model, the total side length of each ice crystal boundary is equal to the arc length of the soil-contacting particle (FIG. 3 b), 4X 2 π R i /4＝2πR i . The total edge of each neck in the FCC model is equal to the arc length of three soil-contacting particles (FIG. 4 c), 3X 2 π R i /6＝πR i . Thus, the following equation can be used to calculate the total water content per volume of soil in the neck.
From a radius of R i The total liquid volume fraction of the soil particle composition of (a) can be ascribed to the sum of four contributions:
considering the soil composition at different particle radii, the total liquid fraction in the soil can be found as follows:
in the formula: f. of i The volume of the soil particles with the particle size i is the percentage of the total volume of the soil particles, R i The soil particles have a particle size of i. And (3) representing the particle size distribution of soil particles by adopting equivalent particle sizes, and simplifying the soil body into an equivalent particle size spherical accumulation system. The specific calculation is shown in formula (19):
thus, equation (20) in conjunction with equations (18) and (19) is used to calculate the unfrozen water content, and the applicable porosity ratio of the following equation can be calibrated as discussed in S3.
And S3, collecting a soil sample, measuring the particle size distribution and the salt concentration of the soil, and determining the volume percentage of soil particles under each particle size in the soil.
S4, characterizing the particle size distribution of the soil particles based on the equivalent particle size, and reducing the equivalent particle size by 0.21-0.23, 0.16-0.28, 0.25-0.3 and 0.36 respectively for the silt, the silty clay, the loess and the sandy soil so as to correct the influence of the shape or the surface roughness of the soil particles; the particle surface impurity density was calculated using the maximum water film thickness and the measured salt concentration.
The step S4 includes:
s401, as shown in figure 1, the equivalent particle size is adopted to represent the particle size distribution of soil particles, and the soil body is simplified into an equivalent particle size spherical accumulation system. The specific calculation is shown in equation (19).
S402, the influence of equivalent particle size reduction of 0.21-0.23, 0.16-0.28, 0.25-0.3 and 0.36 on silt, silty clay, loess and sandy soil is corrected to correct the shape of soil particles or the surface roughness. Namely, the alpha pair of silt, silty clay, loess and sandy soil obtained in the S2 are respectively 0.21 to 0.23, 0.16 to 0.28, 0.25 to 0.3 and 0.36.
S403, particles obtained in soil in a natural state are not necessarily contacted with each other, so that no matter which arrangement mode media exist, the space is 2 delta, and a stacking unit system comprises:
the soil void ratio represents the ratio of the total volume of voids in the soil to the total volume of soil particles, and f p There is a conversion relationship: e =1/f p 1, e can be obtained by the equation (21) in the state where the soil particles are in contact with each other (i.e., δ = 0) sc And e fcc Are 0.35 and 0.9.
As the temperature approaches freezing at infinity, assuming the ice crystal is at the center of the pore, infinity can be considered to be a point at which the ice crystal has a maximum water film thickness.
And establishing a correlation between the initial pore volume concentration and the impurity concentration on the surface of the water film under different soil particle stacking according to the particle arrangement geometrical relationship, as shown in a formula (24).
N im ＝ηc 0 d 0 (24)
In the formula: η is the number of electrolytic ions per molecular impurity, for example: sodium chloride eta =2,c 0 Is the concentration of the solution.
And S5, calculating the unfrozen water content of the frozen soil.
The step S5 can refer to fig. 1, and the specific steps are as follows:
and S501, substituting the soil parameters measured in the S3 and the calculation result of the S4 into the model of the relation between the water film thickness and the supercooling temperature established in the S1.
S502, selecting a proper accumulation model according to the actually measured pore ratio of the soil, and establishing an unfrozen water content model of the frozen soil by combining the relation between the thickness of the water film and the supercooling temperature.
Fig. 6a to 6h are the results of the unfrozen water content model for 8 types of soil.
Claims (4)
1. A method for determining the unfrozen water content of frozen soil based on a premelting theory is characterized by comprising the following steps of:
s1, establishing a relation between the thickness of a water film and the supercooling temperature;
s2, establishing the unfrozen water content f l A model relating to water film thickness;
s3, collecting a soil sample, measuring the particle size distribution and the salt concentration of the soil, and determining the volume percentage of soil particles with each particle size in the soil;
s4, characterizing the particle size distribution of the soil particles based on the equivalent particle size, and respectively reducing the equivalent particle size for different soils; calculating the particle surface impurity density using the maximum water film thickness and the measured salt concentration;
and S5, calculating the unfrozen water content of the frozen soil.
2. The method for determining the unfrozen water content of the frozen soil based on the premelting theory as claimed in claim 1, wherein the relation between the thickness of the water film and the supercooling temperature is established in S1 as follows:
in the formula: Δ T represents the supercooling degree, i.e., the initial freezing temperature reduction value, i.e., the deviation value from 273.15K; r g Is the gas constant; t is m ＝273.15K；N im Is the concentration of impurities on the surface of the soil particles; a. The H Is Hamaker constant.
3. The method for determining the unfrozen water content of the frozen soil based on the premelting theory as claimed in claim 1, wherein in S2, the unfrozen water content f is established l The model of the relationship with the water film thickness is:
in the formula, R e Represents the equivalent radius of the particle; d p Represents the thickness of the water film between the ice particles and the solid particles; d gb Represents the water film thickness between ice particles; SC and FCC represent two common stacks, namely simple cubic stack, namely simple cubic packing, abbreviated as SC, and cubic closest stack, namely face-centered cubic packing, abbreviated as FCC; f. of p (SC) and f p (FCC) represents the percentage of particles in the total volume, i.e. the filling ratio, in the SC and FCC arrangements, respectively, as a function of the void ratio e, f p = 1/(1+e); r represents the radius of the ice-liquid contact surface, determined by the Gibbs-Thomson relationship.
4. The method for determining the unfrozen water content of the frozen soil based on the premelting theory as claimed in claim 1, wherein in the step S4, the equivalent particle size of the silt, the silty clay, the loess and the sandy soil is respectively reduced by 0.21 to 0.23, 0.16 to 0.28, 0.25 to 0.3 and 0.36.
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