CN117990889A - Method for determining unfrozen water content of unsaturated soil - Google Patents
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- 239000002689 soil Substances 0.000 title claims abstract description 181
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Abstract
The invention discloses a method for determining the unfrozen water content of unsaturated soil, which relates to the field of the unfrozen water content of soil, and establishes the relation between the thickness of a water film and the temperature change of a gas-premelted layer-crystal system; establishing a relation between the thickness of a water film and the temperature change between different solid material interfaces and between crystal grain boundaries of the same kind in a matrix-premelting layer-crystal system; establishing a Gibbs free energy equation in the ice-water system in the ice water interface curvature induction melting process; taking ice-water system chemical potential balance as a discrimination condition, and establishing a relationship between a curvature radius and temperature change in the curvature-induced melting process; establishing an unfrozen water content model of unsaturated soil; and (3) collecting a soil sample, measuring the soil particle size, the initial water content and the gas saturation, and calculating the unfrozen water content of the unsaturated soil. The method is used for establishing the model of the unfrozen water content of the unsaturated soil and rapidly obtaining the unfrozen water content of the frozen soil.
Description
Technical Field
The invention relates to the field of unfrozen water content of soil, in particular to a method for determining the unfrozen water content of unsaturated soil.
Background
The content of unfrozen water influences the structure of pore ice and the cementing strength of soil particles and an ice skeleton in frozen soil, the internal friction angle of the soil body rises 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 the soil is changed due to the water-ice phase change, the change of the volume proportions 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, and the related variables have obvious influence on the thermal state of geological structures and geotechnical engineering structures, so that the heat transfer rate and the freezing and thawing depth can be determined when the thermal stability of the engineering in a cold region is predicted. The unfrozen water content controls the permeability of frozen soil and plays an important role in the water delivery process of a soil-water system in a cold environment.
Frozen soil tends to be unsaturated, and when the temperature is reduced below the freezing point, the pores of the unsaturated soil are filled with liquid water, ice and air. As the temperature is further reduced, the proportions of water, ice, air and soil change continuously. Thus, thermodynamic, hydrodynamic and mechanical parameters in the earth also change correspondingly with temperature changes. In a seasonal frozen soil area, the moisture in unsaturated soil is redistributed to cause frost heaving under the action of freeze thawing circulation.
The relationship between soil temperature and unfrozen water content is defined as soil freezing profile (SFCC). At present, no mature technology is available for explaining the influence of the initial water content on SFCC, so that an unfrozen water content calculation model of unsaturated soil is proposed in theory, the unfrozen water content is calculated rapidly, and the method has important significance for revealing a freezing mechanism and engineering operation.
Disclosure of Invention
The invention provides a method for determining the unfrozen water content of unsaturated soil, which aims to solve the problems that the influence of the initial water content of soil on SFCC is difficult to explain and the unfrozen water content in frozen soil is difficult to calculate rapidly in the prior art, and realize the purposes of realizing an unfrozen water content model of unsaturated soil and obtaining the unfrozen water content in frozen soil rapidly.
The invention is realized by the following technical scheme:
A method of determining the unfrozen water content of unsaturated soil comprising:
Step S1, establishing a relation between the thickness of a water film and temperature change in a gas-premelting layer-crystal system, wherein the relation is defined as a first equation;
step S2, establishing a relation between the thickness of a water film between different solid material interfaces and between crystal grain boundaries of the same kind and temperature variation in a matrix-premelting layer-crystal system, and defining the relation as a second equation;
Step S3, establishing a Gibbs free energy equation under the ice-water system and in the ice water interface curvature induction melting process based on the gas saturation, and defining the Gibbs free energy equation as a third equation;
S4, establishing a relation between a curvature radius and temperature change in the curvature-induced melting process by taking the chemical potential balance of the ice-water system as a discrimination condition, and defining the relation as a fourth equation;
s5, establishing an unfrozen water content model of unsaturated soil based on the soil particle size, the initial water content, a first equation, a second equation, a third equation and a fourth equation;
And S6, collecting a soil sample, measuring the soil particle size, the initial water content and the gas saturation, substituting the soil particle size, the initial water content and the gas saturation into an unsaturated soil unfrozen water content model, and calculating the unsaturated soil unfrozen water content.
Aiming at the problems that the influence of the initial water content of soil on SFCC and the quick calculation of the unfrozen water content in frozen soil are difficult to explain in the prior art, the invention provides a method for determining the unfrozen water content of unsaturated soil, the method is based on two systems of gas-premelted layer-crystal and matrix-premelted layer-crystal given by premelted theory, the relation between the thickness of a water film and the temperature is respectively established, and a first equation, a second equation and a third equation are respectively obtained by adopting the idea of minimizing free energy; then taking the chemical potential balance of the ice-water system as a discrimination condition, establishing a fourth process for representing the relationship between the curvature radius and the temperature change in the curvature induction melting process, and finally solving the fourth process simultaneously, wherein the first equation, the second equation, the third equation and the fourth process can obtain an unfrozen water content model of unsaturated soil, the position and the size of an ice-gas interface can be determined through the model, and establishing an SFCC model which takes the boundary melting and the curvature effect into consideration under the condition that gas exists, so as to realize the purpose of explaining the influence of the initial water content of soil on the SFCC; in the practical engineering application, the measurement result can be substituted into the obtained model of the unfrozen water content of the unsaturated soil by only collecting the on-site soil sample and measuring the parameters such as the soil particle size, the initial water content and the gas saturation, so that the unfrozen water content of the unsaturated soil is directly calculated and solved, the difficulty in solving the unfrozen water content of the on-site unsaturated soil is obviously reduced, and the aim of rapidly obtaining the unfrozen water content in frozen soil is fulfilled.
Further, the first equation is:
；
Wherein: t is the temperature; d is the thickness of the water film; sigma is a constant on the order of the molecular diameter; Δγ is the difference between the coefficients of the dry and wet interfaces; ρ l is the molar density of water; q m is the latent heat released per mole of water ice phase change; t m =273.15K; delta T is the temperature change; lambda is a fitting parameter related to interfacial interaction potential energy.
It can be seen that the film thickness d is a function of the temperature T.
Further, the second equation is:
；
Wherein: ρ l is the molar density of water; q m is the latent heat released per mole of water ice phase change; t m =273.15K; delta T is the temperature change; d is the thickness of the water film; r g is a gas constant; n im is the density of impurities on the surface of the soil particles; a H is Hamaker constant; q s is the surface charge density; epsilon is the relative dielectric constant of liquid water; epsilon 0 vacuum dielectric constant; k is an intermediate constant.
Further, the calculation formula of the intermediate constant K is:
；
wherein: e is natural logarithm; n A is the Avofacil constant; k is the boltzmann constant.
Further, the step S3 specifically includes:
step S301, assuming that ice crystals are completely surrounded by liquid water in the ice-water system, determining the total Gibbs free energy of the ice-water system;
Step S302, establishing a calculation equation of the change amount of the free energy of the Gibbs interface when the free energy of the Gibbs interface is cooled from the water-gas interface equilibrium state to the ice-gas interface equilibrium state in the process of moving the gas to the solid surface, and taking the calculation equation of the change amount as a third equation.
Further, the total gibbs free energy of the ice-water system is determined by the following formula:
；
wherein: g is the total Gibbs free energy; mu i (T, P) represents the chemical potential per mole of ice at temperature T, pressure P; mu l (T, P) represents the chemical potential per mole of water at temperature T, pressure P; mu im (T, P) represents the chemical potential per mole of impurity at temperature T, pressure P; mu g (T, P) represents the chemical potential per mole of gas at temperature T, pressure P; n i is the number of moles of ice per unit area; n l is the number of moles of water per unit area; n im is the density of impurities on the surface of the soil particles; n g is the number of moles of gas per unit area; r g is a gas constant; a i is the shape factor of ice; a l is the shape factor of water; a im is the shape factor of the impurity; a g is the shape factor of the gas; a lg is the area of the gas-liquid interface; gamma lg is the interface free energy of the gas-liquid interface; gamma li is the interfacial free energy of the ice-liquid interface; r i is the radius of the ice crystals;
The third equation is:
；
Wherein: ΔG S (III-II) is the change in free energy of the Gibbs interface when cooling from the water-gas interface equilibrium state to the ice-gas interface equilibrium state; r g, III is the gas equivalent size radius at state III; gamma ig is the interfacial free energy of the ice-gas interface; gamma lg is the interface free energy of the gas-liquid interface; gamma sg is the interfacial free energy of the earth-gas interface; gamma li is the interfacial free energy of the ice-liquid interface; r g,II is the gas equivalent size radius at state II; θ 2, II is the equilibrium contact angle with respect to gas content and temperature in state II; r p is the equivalent aperture radius of the soil; θ 1, III、θ2, III are equilibrium contact angles related to gas content and temperature for state III;
Wherein, the state II is the state when the gas forms a stable spherical cap on the surface of the substrate; the state III refers to the state when the ice water undergoes phase change volume expansion and the original gas-liquid interface is replaced by the gas-ice interface.
Further, the fourth equation is:
；
Wherein: r is the radius of curvature; gamma ig is the interfacial free energy of the ice-water interface; s g is air saturation; gamma lg is the interface free energy of the gas-liquid interface; q m is the latent heat released per mole of water ice phase change; t m =273.15K; delta T is the temperature change; r g is a gas constant; ρ l is the molar density of water; ρ i is the molar density of ice; d is the thickness of the water film; n im is the density of impurities on the surface of the soil particles.
Further, in step S5, the established model of the unfrozen water content of the unsaturated soil is:
；
Wherein: n u is the unfrozen water content of the unsaturated soil; n r is the unfrozen water content at-15 ℃; n o is the initial moisture content; k 1 is a first coefficient; k 2 is a second coefficient; k 3 is a third coefficient; n im is the density of impurities on the surface of the soil particles; alpha is the soil coefficient; r e is the equivalent particle diameter of the soil; delta T is the temperature change.
Further, the equivalent particle diameter R e of the soil is calculated by the following formula:
；
Wherein: omega i is the ratio of the volume of R i particles to the total particle volume; r i is the radius of the ith soil particle; n is the total number of particles.
Further, when the soil is silty clay, the soil coefficient α=0.27;
when the soil is silt, the soil coefficient α=0.35;
when the soil is silty sandy soil, the soil coefficient α=0.52;
When the soil is sand, the soil coefficient α=0.60.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. according to the method for determining the unfrozen water content of the unsaturated soil, the model of the unfrozen water content of the unsaturated soil can be obtained, the position and the size of an ice-gas interface can be determined through the model, and an SFCC model which takes boundary melting and curvature effects into consideration under the condition that gas exists is established, so that the purpose of explaining the influence of the initial water content of the soil on the SFCC is achieved.
2. According to the method for determining the unfrozen water content of the unsaturated soil, provided by the invention, the unfrozen water content of the unsaturated soil can be directly calculated and solved by substituting the measurement result into the obtained model of the unfrozen water content of the unsaturated soil only by collecting a field soil sample and measuring parameters such as the soil particle size, the initial water content and the gas saturation, so that the difficulty in solving the unfrozen water content of the field unsaturated soil is remarkably reduced, and the purpose of rapidly obtaining the unfrozen water content in the frozen soil is realized.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the principles of the application. In the drawings:
FIG. 1 is a schematic flow chart of an embodiment of the present invention;
FIG. 2 is a schematic view showing the position of the gas-liquid contact surface in the state I according to the embodiment of the present invention;
FIG. 3 is a schematic view showing the position of the gas-liquid contact surface in state II according to the embodiment of the present invention;
FIG. 4 is a schematic view showing the position of the gas-liquid contact surface in the state III according to the embodiment of the present invention;
FIG. 5 is a graph showing a comparison of predicted results and measured results in an embodiment of the present invention; wherein, panel (a) shows the comparison results of three soil samples numbered 1-3; panel (b) shows the results of a comparison of two soil samples numbered 4-5; panel (c) shows the results of a comparison of three soil samples numbered 6-8; panel (d) shows the results of a comparison of two soil samples numbered 9-10; panel (e) shows the results of a comparison of two soil samples numbered 11-12; panel (f) shows the results of a comparison of three soil samples numbered 13-15.
In the drawings, the reference numerals and corresponding part names:
1-water, 2-gas, 3-ice crystals.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present invention and the descriptions thereof are for illustrating the present invention only and are not to be construed as limiting the present invention.
Example 1
A method for determining the unfrozen water content of unsaturated soil, as shown in fig. 1, specifically comprises the following steps:
Step S1, establishing a relation between the thickness of a water film and temperature change in a gas-premelting layer-crystal system, wherein the relation is defined as a first equation; specific:
Considering that the solid and the gas with the temperature of T and the pressure of P are in an equilibrium state, and considering that the interface is wetted by the quasi-liquid layer, the expression of free energy in unit area can be obtained; the expression includes a function f (d) related to film thickness, which in this embodiment is ; Where d is the film thickness and σ is a constant on the order of the molecular diameter.
Then, based on the expression of the free energy, a power law relation between the water film thickness d and the temperature change delta T can be obtained, namely, a first equation is obtained as follows:
；
Wherein: t is the temperature; d is the thickness of the water film; sigma is a constant on the order of the molecular diameter; Δγ is the difference between the coefficients of the dry and wet interfaces; ρ l is the molar density of water; q m is the latent heat released per mole of water ice phase change; t m =273.15K; delta T is the temperature change; lambda is a fitting parameter related to interfacial interaction potential energy.
The first equation may be used to calculate the surface melting of solids and gases; it will be appreciated by those skilled in the art that the temperature change deltat therein is indicative of a reduced value of the initial freezing temperature.
Step S2, establishing a relation between the thickness of a water film between different solid material interfaces and between crystal grain boundaries of the same kind and temperature variation in a matrix-premelting layer-crystal system, and defining the relation as a second equation; specific:
the presence of solute enhances the pre-thawing behavior and reduces the chemical potential of the solvent phase. In the case of freezing of the solution, impurities are driven out of the solid, tending to form a high concentration solution at the interface; considering the influence of the number of electrolyte ions in the premelted layer and the interface charge on the thickness of the water film, and obtaining an equation of total Gibbs free energy in the system;
then, based on thermodynamic principle, establishing a conditional equation for the equilibrium of ice crystals and liquid water in the system;
Then in the aqueous solution, the difference between the chemical potentials of solid (ice) and liquid (water) per mole is approximately equivalent to the following equivalent expression: q m×ΔT/Tm;
Combining the equation, the conditional equation and the equivalent expression of the total Gibbs free energy in the system, the relation between the thickness of the water film and the delta T between different solid material interfaces and between the crystal grain boundaries of the same kind can be obtained, and a second equation is obtained as follows:
；
Wherein: ρ l is the molar density of water; q m is the latent heat released per mole of water ice phase change; t m =273.15K; delta T is the temperature change; d is the thickness of the water film; r g is a gas constant; n im is the density of impurities on the surface of the soil particles, which is related to the concentration of the solution; a H is Hamaker constant; q s is the surface charge density; epsilon is the relative dielectric constant of liquid water; epsilon 0 vacuum dielectric constant; k is an intermediate constant.
Wherein, the calculation formula of the intermediate constant K is:
；
wherein: e is natural logarithm; n A is the Avofacil constant; k is boltzmann constant, taking k=1.38x10 -23 J/K.
This example characterizes the water film thickness between two different material interfaces and between crystals within the same material by a second equation.
Step S3, establishing a Gibbs free energy equation under the ice-water system and in the ice water interface curvature induction melting process based on the gas saturation, and defining the Gibbs free energy equation as a third equation; specific:
The curvature of the ice water interface and the saturation of the gas both can cause the change of the solidifying point; this example ignores the anisotropy of the ice surface and assuming that the ice crystals are completely surrounded by liquid water, the interfacial area is no longer a constant, as opposed to the planar case, and the Gibbs free energy G of the whole system can be written as:
；
wherein: g is the total Gibbs free energy; mu i (T, P) represents the chemical potential per mole of ice at temperature T, pressure P; mu l (T, P) represents the chemical potential per mole of water at temperature T, pressure P; mu im (T, P) represents the chemical potential per mole of impurity at temperature T, pressure P; mu g (T, P) represents the chemical potential per mole of gas at temperature T, pressure P; n i is the number of moles of ice per unit area; n l is the number of moles of water per unit area; n im is the density of impurities on the surface of the soil particles; n g is the number of moles of gas per unit area; r g is a gas constant; a i is the shape factor of ice; a l is the shape factor of water; a im is the shape factor of the impurity; a g is the shape factor of the gas; a lg is the area of the gas-liquid interface; gamma lg is the interface free energy of the gas-liquid interface; gamma li is the interfacial free energy of the ice-liquid interface; r i is the radius of the ice crystals;
Wherein the area a lg of the gas-liquid interface is related to the equilibrium contact angle and the gas saturation.
The embodiment adopts a free energy minimization method to determine the position and the size of the gas-liquid contact surface: a volume of gas is placed in the spherical pores of the immersion liquid, the gas first assuming a spherical distribution (defined as state I) due to the surface tension, as shown in fig. 2, the variables from the initial state, considering the process of gas movement towards the solid surface, include: (1) replacing the initial spherical interface with a gas-liquid interface; (2) The matrix-liquid interface is replaced by a matrix-gas interface portion, and the gibbs interface free energy is changed from the initial state to the equilibrium state (defined as state II), as shown in fig. 3. In addition, pore radius, gas radius and equilibrium contact angle have the following relationship: r gsinθ2=rpsinθ1; wherein r g is the equivalent aperture radius of the earth, r p is the equivalent gas size radius, and θ 1、θ2 is the equilibrium contact angle.
Based on the calculation, a change equation of the free energy of the Gibbs interface can be obtained. And then considering that the liquid and the gas reach an equilibrium state on the solid surface with fixed curvature, obtaining the minimum value of the Gibbs free interface energy change according to the change equation of the Gibbs free interface energy, and calculating the equilibrium contact angle theta 1、θ2 in the state II. The system was cooled, the ice water undergoes a phase change volume expansion, and the original gas-liquid interface was replaced by a gas-ice interface (defined as state III), as shown in fig. 4. The increase in surface energy hinders the formation of ice nuclei, and the variables that change to the equilibrium phase of the gas-liquid interface after cooling include (1) the equilibrium contact angle θ 1, II、θ2, II in state II to the equilibrium contact angle θ 1, III、θ2, III in state III, respectively; (2) replacing the gas-liquid interface with a gas-ice interface; (3) The matrix-gas interface changes due to the change in the equivalent contact angle; (4) adding an ice-liquid interface.
Therefore, according to the change in the free energy of the Gibbs interface from state II (water-gas interface equilibrium) to state III (ice-gas interface equilibrium), the third equation is obtained as follows:
；
Wherein: ΔG S (III-II) is the change in free energy of the Gibbs interface when cooling from the water-gas interface equilibrium state to the ice-gas interface equilibrium state; r g, III is the gas equivalent size radius at state III; gamma ig is the interfacial free energy of the ice-gas interface; gamma lg is the interface free energy of the gas-liquid interface; gamma sg is the interfacial free energy of the earth-gas interface; gamma li is the interfacial free energy of the ice-liquid interface; r g,II is the gas equivalent size radius at state II; θ 2, II is the equilibrium contact angle with respect to gas content and temperature in state II; r p is the equivalent aperture radius of the soil; θ 1, III、θ2, III are equilibrium contact angles with respect to gas content and temperature for state III.
S4, establishing a relation between a curvature radius and temperature change in the curvature-induced melting process by taking the chemical potential balance of the ice-water system as a discrimination condition, and defining the relation as a fourth equation; specific:
Firstly, calculating the areas of a soil particle-gas interface and a gas-liquid/ice interface; the calculation results show that when the interface reaches a stable state, the change of the equilibrium contact angle has smaller and smaller influence on the interface in the state II and the state III along with the increase of the gas saturation degree. Especially for gas-ice/liquid interfaces, when the gas saturation level is greater than 0.25, the rate of change of the gas-ice and gas-liquid interface dimensions is less than 10%. Therefore, for ease of calculation, the present embodiment ignores the effect of angle change on the interface, uses the equilibrium contact angle in state iii to represent the area of the earth particle-gas-liquid interface during phase transition, and can give a regression equation.
In this embodiment, the neck of the soil particle connection pore is considered to be relatively small, and the relationship between the radius of curvature r and Δt can be obtained by using the chemical potential balance of the ice-water system as a discrimination condition, namely, the fourth process is as follows:
；
Wherein: r is the radius of curvature; gamma ig is the interfacial free energy of the ice-water interface; s g is air saturation; gamma lg is the interface free energy of the gas-liquid interface; q m is the latent heat released per mole of water ice phase change; t m =273.15K; delta T is the temperature change; r g is a gas constant; ρ l is the molar density of water; ρ i is the molar density of ice; d is the thickness of the water film; n im is the density of impurities on the surface of the soil particles.
S5, establishing an unfrozen water content model of unsaturated soil based on the soil particle size, the initial water content, a first equation, a second equation, a third equation and a fourth equation; the method comprises the following steps:
And (3) taking the surface charge density of the particles and the concentration of the solution in the soil into consideration to obtain calculation models of the water contents of different soil bodies. For unsaturated soils, the surface melting of ice crystals and their gas phase is further taken into account: assuming that soil particles are uniformly distributed, closely contacted and the pores are spherical, obtaining the relationship between the pore radius and the particle size of the soil; the gas balance moves to the particle surface, so that the interface melting of soil particles and the ice surface is inhibited, an area formula of the interface of the gas and the particles in the unit soil volume is obtained, the surface melting effect of the soil particles and the ice crystals is corrected, and the volume fraction of the pre-melted liquid in the unit soil volume at the interface of the gas and the ice crystals and the unit volume at the interface of the gas and the ice crystals is obtained. In summary, the liquid water content of the earth can be calculated taking into account the presence of the gas.
The total volume content of water also includes the residual water content, which can be described in terms of effective water content. The effective moisture content is related to the unfrozen moisture content n r at-15 ℃ and n u, and the value of n r can be detected by the specific surface area of the soil or obtained by freezing experiments. Taking the randomness of the arrangement of the soil particles into consideration, taking the average value of the two superposition methods, and reconstructing the arrangement of the soil particles.
Because of supercooling of liquid, the freezing point of soil is usually not 0 ℃, and the calculated unfrozen water content curve needs to be moved to the freezing point from the initial value of the volume water content to meet the actual freezing condition. Considering the randomness of the arrangement of the particles in the soil, the embodiment reconstructs the arrangement of the soil particles by combining the average values of the two stacking modes, replaces the saturated water content with the initial water content, and finally obtains a generalized model suitable for the unfrozen water content of the unsaturated soil as follows:
；
；
Wherein: n u is the unfrozen water content of the unsaturated soil; n r is the unfrozen water content at-15 ℃; n o is the initial moisture content; k 1 is a first coefficient; k 2 is a second coefficient; k 3 is a third coefficient; n im is the density of impurities on the surface of the soil particles; alpha is the soil coefficient; r e is the equivalent particle diameter of the soil; delta T is the temperature change; omega i is the ratio of the volume of R i particles to the total particle volume; r i is the radius of the ith soil particle; n is the total number of particles. Wherein, the equivalent particle diameter R e of the soil can be obtained by combining the actually measured soil particle diameter distribution curve.
In this embodiment, when the soil is silty clay, the soil coefficient α=0.27; when the soil is silt, the soil coefficient α=0.35; when the soil is silty sandy soil, the soil coefficient α=0.52; when the soil is sand, the soil coefficient α=0.60.
Wherein k 1、k2、k3 can be calculated by the following formula:
Wherein: f p(SC)、fp (FCC) represents the percentage of the volume of particles in the SC arrangement and the FCC arrangement, respectively, to the total volume; ρ l is the molar density of water; q m is the latent heat released per mole of water ice phase change; t m= 273.15 K;Rg is a gas constant; r is the ice-water interface surface radius; λ is a fitting parameter related to interfacial interaction potential energy; r e is the equivalent particle diameter of the soil; ζ 1、ξ2 are regression parameters, calculated by the following formula:
in this embodiment, for the calculation of the regression parameters, the influence of angle change on the interface is ignored, the equilibrium contact angle in the state iii is used to represent the area of the soil particle-gas-liquid interface in the phase change process, and the corresponding regression equation is given.
Those skilled in the art will appreciate that the SC arrangement, FCC arrangement, is a representation of the type of lattice structure that is two different arrangements of atoms in the crystal.
And S6, collecting a soil sample, measuring the soil particle size, the initial water content and the gas saturation, substituting the soil particle size, the initial water content and the gas saturation into an unsaturated soil unfrozen water content model, and calculating the unsaturated soil unfrozen water content.
In this example, 15 kinds of unsaturated soil samples were taken, the unfrozen water content was predicted by the method of the present application, and the predicted result was compared with the measured result. Specific parameters for the 15 unsaturated soil samples are shown in the following table:
In fig. 5, the following is described: panel (a) shows the results of a comparison of three soil samples numbered 1-3; panel (b) shows the results of a comparison of two soil samples numbered 4-5; panel (c) shows the results of a comparison of three soil samples numbered 6-8; panel (d) shows the results of a comparison of two soil samples numbered 9-10; panel (e) shows the results of a comparison of two soil samples numbered 11-12; panel (f) shows the results of a comparison of three soil samples numbered 13-15.
As can be seen from fig. 5, the method of the present application can reasonably predict the variation of unfrozen water content with temperature. When Δt < 2K, ice crystals nucleate rapidly, and the equivalent pore size is considered a constant during the simulation; the lower saturation soil phase changes more severely at Δt < 2K, which results in a predicted value higher than the experimental value, which is also consistent with the theoretical analysis that shows that the pore size increases slightly with decreasing initial water content in the prior studies.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Claims (10)
1. A method for determining the unfrozen water content of unsaturated soil, comprising:
Step S1, establishing a relation between the thickness of a water film and temperature change in a gas-premelting layer-crystal system, wherein the relation is defined as a first equation;
step S2, establishing a relation between the thickness of a water film between different solid material interfaces and between crystal grain boundaries of the same kind and temperature variation in a matrix-premelting layer-crystal system, and defining the relation as a second equation;
Step S3, establishing a Gibbs free energy equation under the ice-water system and in the ice water interface curvature induction melting process based on the gas saturation, and defining the Gibbs free energy equation as a third equation;
S4, establishing a relation between a curvature radius and temperature change in the curvature-induced melting process by taking the chemical potential balance of the ice-water system as a discrimination condition, and defining the relation as a fourth equation;
s5, establishing an unfrozen water content model of unsaturated soil based on the soil particle size, the initial water content, a first equation, a second equation, a third equation and a fourth equation;
And S6, collecting a soil sample, measuring the soil particle size, the initial water content and the gas saturation, substituting the soil particle size, the initial water content and the gas saturation into an unsaturated soil unfrozen water content model, and calculating the unsaturated soil unfrozen water content.
2. The method of determining the unfrozen water content of unsaturated soil according to claim 1, wherein the first equation is:
；
Wherein: t is the temperature; d is the thickness of the water film; sigma is a constant on the order of the molecular diameter; Δγ is the difference between the coefficients of the dry and wet interfaces; ρ l is the molar density of water; q m is the latent heat released per mole of water ice phase change; t m =273.15K; delta T is the temperature change; lambda is a fitting parameter related to interfacial interaction potential energy.
3. The method of determining the unfrozen water content of unsaturated soil according to claim 1, wherein the second equation is:
；
Wherein: ρ l is the molar density of water; q m is the latent heat released per mole of water ice phase change; t m =273.15K; delta T is the temperature change; d is the thickness of the water film; r g is a gas constant; n im is the density of impurities on the surface of the soil particles; a H is Hamaker constant; q s is the surface charge density; epsilon is the relative dielectric constant of liquid water; epsilon 0 vacuum dielectric constant; k is an intermediate constant.
4. A method of determining the unfrozen water content of unsaturated soil according to claim 3, wherein the intermediate constant K is calculated by the formula:
；
wherein: e is natural logarithm; n A is the Avofacil constant; k is the boltzmann constant.
5. The method of determining the unfrozen water content of unsaturated soil according to claim 1, wherein the step S3 specifically comprises:
step S301, assuming that ice crystals are completely surrounded by liquid water in the ice-water system, determining the total Gibbs free energy of the ice-water system;
Step S302, establishing a calculation equation of the change amount of the free energy of the Gibbs interface when the free energy of the Gibbs interface is cooled from the water-gas interface equilibrium state to the ice-gas interface equilibrium state in the process of moving the gas to the solid surface, and taking the calculation equation of the change amount as a third equation.
6. A method for determining the unfrozen water content of unsaturated soil according to claim 5,
The total gibbs free energy of the ice-water system is determined by the following formula:
；
wherein: g is the total Gibbs free energy; mu i (T, P) represents the chemical potential per mole of ice at temperature T, pressure P; mu l (T, P) represents the chemical potential per mole of water at temperature T, pressure P; mu im (T, P) represents the chemical potential per mole of impurity at temperature T, pressure P; mu g (T, P) represents the chemical potential per mole of gas at temperature T, pressure P; n i is the number of moles of ice per unit area; n l is the number of moles of water per unit area; n im is the density of impurities on the surface of the soil particles; n g is the number of moles of gas per unit area; r g is a gas constant; a i is the shape factor of ice; a l is the shape factor of water; a im is the shape factor of the impurity; a g is the shape factor of the gas; a lg is the area of the gas-liquid interface; gamma lg is the interface free energy of the gas-liquid interface; gamma li is the interfacial free energy of the ice-liquid interface; r i is the radius of the ice crystals;
The third equation is:
；
Wherein: ΔG S (III-II) is the change in free energy of the Gibbs interface when cooling from the water-gas interface equilibrium state to the ice-gas interface equilibrium state; r g, III is the gas equivalent size radius at state III; gamma ig is the interfacial free energy of the ice-gas interface; gamma lg is the interface free energy of the gas-liquid interface; gamma sg is the interfacial free energy of the earth-gas interface; gamma li is the interfacial free energy of the ice-liquid interface; r g,II is the gas equivalent size radius at state II; θ 2, II is the equilibrium contact angle with respect to gas content and temperature in state II; r p is the equivalent aperture radius of the soil; θ 1, III、θ2, III are equilibrium contact angles related to gas content and temperature for state III;
Wherein, the state II is the state when the gas forms a stable spherical cap on the surface of the substrate; the state III refers to the state when the ice water undergoes phase change volume expansion and the original gas-liquid interface is replaced by the gas-ice interface.
7. The method of determining the unfrozen water content of unsaturated soil according to claim 1, wherein the fourth equation is:
；
Wherein: r is the radius of curvature; gamma ig is the interfacial free energy of the ice-water interface; s g is air saturation; gamma lg is the interface free energy of the gas-liquid interface; q m is the latent heat released per mole of water ice phase change; t m =273.15K; delta T is the temperature change; r g is a gas constant; ρ l is the molar density of water; ρ i is the molar density of ice; d is the thickness of the water film; n im is the density of impurities on the surface of the soil particles.
8. The method according to claim 1, wherein in step S5, the unsaturated soil unfrozen water content model is established as follows:
；
Wherein: n u is the unfrozen water content of the unsaturated soil; n r is the unfrozen water content at-15 ℃; n o is the initial moisture content; k 1 is a first coefficient; k 2 is a second coefficient; k 3 is a third coefficient; n im is the density of impurities on the surface of the soil particles; alpha is the soil coefficient; r e is the equivalent particle diameter of the soil; delta T is the temperature change.
9. The method of determining the unfrozen water content of unsaturated soil according to claim 8, wherein the equivalent particle diameter R e of the soil is calculated by the following formula:
；
Wherein: omega i is the ratio of the volume of R i particles to the total particle volume; r i is the radius of the ith soil particle; n is the total number of particles.
10. A method for determining the unfrozen water content of unsaturated soil according to claim 8,
When the soil is a silty clay, the soil coefficient α=0.27;
when the soil is silt, the soil coefficient α=0.35;
when the soil is silty sandy soil, the soil coefficient α=0.52;
When the soil is sand, the soil coefficient α=0.60.
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