Freezing speed comparison method based on frozen soil capillary-film water occurrence evolution model

Abstract

The invention provides a freezing speed comparison method based on a frozen soil capillary-thin film water occurrence evolution model, which comprises the following steps: step 1, constructing a frozen capillary-thin film water occurrence evolution model, step 2, calculating a capillary critical aperture change equation, step 3, constructing an occurrence evolution model when thin film water on the surface of a particle is frozen, step 4, calculating a thin film water thickness change equation, and step 5, comparing the freezing speed with the thin film water thickness change equation. And 5, comparing and analyzing the capillary-thin film water freezing speed. The critical aperture change rate of the frozen capillary under the same negative temperature condition is three times of the thickness change rate of the thin film water, and the freezing sensitivity of the capillary water is far higher than that of the thin film water.

Description

Technical Field

[0001] The invention relates to the field of engineering frost heave and thaw settlement, and in particular to a freezing rate comparison method based on a frozen soil capillary-film water storage evolution model. Background Art

[0002] The study of frost heave development and its control mechanism involves the intersection of multiple disciplines such as thermodynamics, physical chemistry and mechanics, and has always been a core problem in frozen soil research. Frost heave mainly includes in-situ frost heave, which causes the internal in-situ water phase to turn into ice, causing a volume increase of 9.05%, and segregation frost heave, which causes the pore water and external replenishment water to continuously migrate to the freezing front, resulting in a volume increase of 109.05%. Among them, water migration is the main cause of frost heave. At the same time, according to the capillary and adsorption properties of the soil matrix, there are mainly two forms of unfrozen water in the frozen soil, namely: capillary water and film water. Among them, capillary water is mainly present in the volume space inside the capillary, while film water is mainly adsorbed on the surface of particles. However, the existing frost heave theory only considers the occurrence evolution and migration mechanism of one type of unfrozen water, which is difficult to fully and reasonably reveal the frost heave phenomenon of soil. Therefore, research on the occurrence, evolution and migration mechanism of capillary-film water was carried out, the occurrence ratio of capillary water and film water, the freezing phase change rate (or freezing rate) were analyzed, and the evolution law of capillary water and film water during the freezing process was revealed, which has important theoretical value and scientific significance for improving the frost heave theory and guiding engineering practice.

[0003] Since the freezing temperature of capillary water is inversely proportional to the interface curvature, the smaller the pore size, the lower the freezing temperature of capillary water; and the thickness of the film water liquid layer is also inversely proportional to the temperature, the lower the temperature, the smaller the liquid layer thickness; but the freezing speed of the two is still unclear. Current research shows that the pore size D of mesoporous capillaries is ≥ 0.1μm, while the pore size D of microporous film water is < 0.1μm (or the thickness of the single-sided film h < 50nm), so the pore size D = 0.1μm can be used as the dividing line between capillary water and film water. See Table 1:

[0004] Table 1 Pore size and pore water classification by size

[0005]

[0006] It can be seen from Table 1 that the capillary pore size where the capillary water is located is much larger than the thickness of the water layer in the film, so the permeation resistance of capillary water migration is much smaller than the permeation resistance of water migration in the microporous film. Therefore, the unfrozen capillaries in the freezing process are the main channels for water migration.

[0007] Constructing a frozen capillary model and a frozen thin film water model, studying the freezing evolution law of capillary water and thin film water, and exploring the freezing speed of the two will help analyze the comprehensive migration law of capillary-thin film water and propose more effective frost heave control methods. Summary of the invention

[0008] The purpose of the present invention is to provide a freezing rate comparison method based on the frozen soil capillary-film water storage evolution model, study the freezing evolution law of capillary water and film water, explore the freezing speed of the two, analyze the comprehensive migration law of capillary-film water, and propose a more effective frost heave control method.

[0009] In order to achieve the above object, the present invention provides the following technical solutions:

[0010] A freezing rate comparison method based on a frozen soil capillary-film water storage evolution model comprises the following steps:

[0011] Step 1: Construct a frozen capillary-film water storage evolution model.

[0012] R is the effective pore radius; D is the effective pore diameter; h is the film water thickness; T is the temperature variable; T f is the freezing front temperature; T s is the segregation-freezing temperature; γ SL is the interfacial tension; P i-w is the interface pressure, and P i-w =γ SL / R;P C is capillary suction; P S is the actual pressure of pore ice; P S0 is the theoretical pressure of porous ice in equilibrium; P ew is the external water pressure; P Ly is the actual liquid pressure of the film water in the non-equilibrium state; P Lh is the theoretical liquid pressure of the film water in equilibrium state; P Ld It is the driving force for water migration in the film;

[0013] When porous ice forms, the pore ice pressure, capillary suction and external water pressure reach equilibrium on the curved ice-water interface, namely:

[0014] P c +P ew =P S (1)

[0015] Let the curvature be: κ1=1 / R1+1 / R2, where R1 and R2 are the main curvature radii; for an ideal hemispherical interface, we have: κ1=1 / R1+1 / R2=2 / R, and R1=R2=R, where R is the effective radius of the pore. It can be seen that the capillary suction of the curved ice-water interface is:

[0016]

[0017] When the capillary freezes, the theoretical ice pressure in equilibrium is:

[0018]

[0019] Where: P S0 is the theoretical ice pressure in equilibrium; L is the melting heat of water, which can be taken as 3.34×10 9 cm 2 / s 2 ; vS is the specific volume of ice; TA is the absolute freezing temperature of pure water, which is 273.15K,

[0020] Combining equations (1), (2), and (3), we can obtain:

[0021]

[0022] Let: T = T f , is the freezing temperature of the capillary; transform equation (4) to obtain:

[0023]

[0024] From equation (5), we can see that the negative value of the capillary freezing temperature is proportional to the curvature, that is, the larger the curvature, the lower the corresponding capillary freezing temperature.

[0025] Step 2, calculate the capillary critical aperture change equation,

[0026] Let: R = R GT is the maximum pore diameter that can be frozen in the capillary under any negative temperature condition, that is, the critical pore radius. According to equation (4), we can get:

[0027]

[0028] Where: R GT is the critical pore radius for capillary freezing,

[0029] The influence of external water pressure is negligible, that is: P ew = 0, changing equation (6), we can get the critical pore radius equation of capillary freezing under any negative temperature condition:

[0030]

[0031] Where: C1 = (2γ SL ×ν S ×T A ) / L≈0.0558μm·℃ is a constant,

[0032] From equation (7), we can know that the critical pore radius R of the capillary is GT It is inversely proportional to the first power of negative temperature, that is, the lower the freezing temperature, the smaller the aperture of the corresponding frozen capillary.

[0033] In addition, substituting equation (3) into equation (7), we can obtain:

[0034]

[0035] Where: c1 = 2γ SL ≈63.54mN / m, which is a constant.

[0036] From equation (8), we can see that the critical pore radius of the capillary is inversely proportional to the first power of the theoretical ice pressure, which indicates that as the ice pressure increases, the critical pore radius of the capillary that can be invaded by pore ice becomes smaller, resulting in a decrease in the capillary water content.

[0037] Step 3: Construct a model for the evolution of the water in the thin film on the particle surface when it freezes.

[0038] According to the phase thermal equilibrium condition, the chemical potentials of the solid and liquid phases at the ice-water interface are equal, that is:

[0039] μ L =μ S (9)

[0040] Where: μ L is the chemical potential of film water; μ S is the chemical potential of ice, where the liquid phase chemical potential of thin film water can be expressed as:

[0041] μ L =μ L0 -μ Lσ (10)

[0042] Where: μ L0 is the volume water chemical potential under reference conditions (T0, P0); μ Lσ The chemical potential change caused by the surface effect is mainly related to the distance from the particle surface, so it can be defined as:

[0043] μ Lσ =ay -α (11)

[0044] Where: a is a constant; y is the distance from the film water to the particle surface; α is a power; since the decrease in the chemical potential of the film water will lead to an increase in the hydraulic pressure, we can get:

[0045] μ L =μ L0 +v L P L -s L T L -ay -α (12)

[0046] Where: P0 is the reference pressure, which is the standard atmospheric pressure; T0 is the reference temperature, which is the melting point under standard atmospheric pressure; v L is the water specific volume of the film; PL Relative to the reference value P L0 Hydraulic pressure; L is the entropy of film water; T L Relative to the reference value T L0 The liquid layer temperature;

[0047] Assumption: The chemical potential μ of the film water L Always continuous, when the film water is in contact with the bulk water:

[0048] μ L =μ L0 (13)

[0049] Since the film water thickness h is very small, the temperature change along the film water thickness direction is ignored. At this time: T L =T L0 -T0 = 0, then by combining equations (12) and (13), we can obtain:

[0050]

[0051] From equation (14), we can see that the decrease in chemical potential near the surface directly leads to an increase in the hydraulic pressure of the film water. When the external phase of the film water changes to ice, the chemical potential of the ice on the interface is:

[0052] μ S =μ S0 +v S P S -s S T S (15)

[0053] Where: μ S0 is the chemical potential of bulk ice under reference conditions (T0, P0); v S is the specific volume of ice; P S Relative to the reference value P L0 Ice pressure;s S is ice entropy; T S Relative to the reference value T L0 The ice temperature,

[0054] When the film water thickness y = h, assuming that the water-ice phase is still in equilibrium, combining equations (9), (12), and (15), we can obtain:

[0055] μ S0 +v S P S -s S T S =μ L0 +v L P Lh -s L T L -ah-α (16)

[0056] Where: P Lh is the theoretical hydraulic pressure when the film water thickness y = h. Since the particle matrix ice-water interface is convexly curved outward, there is a pressure difference between the ice pressure and the hydraulic pressure at the ice-water interface, that is:

[0057]

[0058] Where: γ SL is the surface tension of the solid-liquid interface; is the mean curvature of the ice-water interface,

[0059] Assumption: The temperature of the thin film water and ice at the ice-water interface is equal, that is: T L =T S =T, substituting formula (17) into formula (16), we can get:

[0060]

[0061] Where: Δv = v S -v L ; L / T A =s L -s S ,

[0062] From formula (18), we can see that when the film water thickness y = h, the hydraulic pressure equation is:

[0063]

[0064] Combining formula (18) and (19), we get:

[0065]

[0066] By parameter transformation, it can be derived:

[0067]

[0068] Combining formula (17) and (21), we get:

[0069]

[0070] Where: P S0 is the theoretical ice pressure on the particle surface,

[0071] Step 4, calculate the film water thickness change equation,

[0072] The equation for the variation of film water thickness with temperature is:

[0073]

[0074] Where: A is the Hamker constant; T K is the absolute temperature variable; T m,K is the absolute freezing temperature of liquid water under critical conditions; ρ i is the density of ice, and ρ i =1 / v S ,

[0075] Due to T m,K =T A , convert the absolute temperature difference in equation (23) into relative temperature difference, and we get:

[0076] T m,K -T K =(T A +0)-(T A +T)=-T (24)

[0077] Combining equations (23) and (24), we can obtain:

[0078]

[0079] Where: C2 = (-A × T A ) / (6π×ρ i ×L), is a constant,

[0080] From equation (25), we can see that the film water thickness is inversely proportional to the 1 / 3 power of the negative temperature, that is, the lower the temperature, the smaller the thickness of the frozen film water.

[0081] Substituting equation (22) into equation (25), we can obtain:

[0082]

[0083] In the formula: c2 = -A / 6π, which is a constant,

[0084] Step 5, comparative analysis of capillary-film water freezing rates,

[0085] By combining equations (8) and (25), we can obtain the critical pore size and the rate of change of film thickness with temperature:

[0086]

[0087] Where: C3 = (12π × γ SL ) / (-A), is a constant,

[0088] When the temperature T→0℃; R GT →+∞、h 3 →+∞, at this time the theoretical value does not match the actual initial value. By removing the influence of the extreme value and transforming equation (27), we can obtain:

[0089] R GT =C3·h 3 , T<0℃ (28)

[0090] It can be seen from equation (28) that the critical aperture change rate of the freezing capillary under the same negative temperature conditions is the cube of the change rate of the film water thickness, indicating that the freezing sensitivity of capillary water is much higher than that of film water.

[0091] Furthermore, in the above-mentioned freezing rate comparison method based on the frozen soil capillary-film water storage evolution model, in step 2,

[0092] The relationship between capillaries with different pore diameters and freezing temperatures is shown in Table 1:

[0093] Table 1 Relationship between pore diameter and freezing temperature

[0094]

[0095]

[0096] Note: γ SL =0.42γ SL =31.77mN / m,

[0097] It can be seen from Table 1 that the smaller the critical pore radius of the pore, the lower the corresponding freezing temperature.

[0098] Combined with Table 2,

[0099] Table 2 Pore size and pore water classification by size

[0100]

[0101] The boundary between capillary water and film water is D = 0.1 μm, and the corresponding boundary freezing temperature is -1.131 °C. It can be seen that the freezing temperature of capillary water is higher, while the freezing temperature of film water is lower.

[0102] Furthermore, in the above-mentioned freezing rate comparison method based on the frozen soil capillary-film water storage evolution model, the critical aperture change rate of the capillary is inversely proportional to the first power of the negative temperature, and the film water thickness is inversely proportional to the 1 / 3 power of the negative temperature.

[0103] It shows that under the same negative temperature conditions, the critical aperture change rate of the capillary is the cube of the film thickness change rate, and the freezing rate of capillary water is much faster than that of film water.

[0104] Furthermore, in the above-mentioned freezing rate comparison method based on the frozen soil capillary-film water storage evolution model, the freezing rate of capillary water is fast and the freezing temperature is high;

[0105] The freezing speed of film water is slow and the freezing temperature is low;

[0106] Due to the suction effect of the interface, the crystallization of capillary water will accelerate the freezing rate of thin film water, but the crystallization of thin film water does not affect the freezing rate of capillary water.

[0107] Analysis shows that the present invention discloses a freezing rate comparison method based on the frozen soil capillary-thin film water storage evolution model, which has important theoretical value and scientific significance for improving the frost heave theory and guiding engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] The drawings constituting a part of the present application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. Among them:

[0109] Figure 1 Force analysis diagram of capillary freezing in the capillary-film water storage evolution model.

[0110] Figure 2 Stress analysis diagram when the thin film water on the tube wall freezes in the capillary-thin film water storage evolution model.

[0111] Figure 3 Schematic diagram of the diffuse double layer of water in a thin film.

[0112] Figure 4 Schematic diagram of the chemical potential and hydraulic pressure distribution when the thin film water on the particle surface freezes.

[0113] Figure 5 Schematic diagram of the storage state of water in the film on the particle surface.

[0114] Figure 6 Schematic diagram of the storage state of thin film water on the inner wall of capillary.

[0115] Figure 7 Distribution curve of capillary-film water in frozen soil with temperature.

[0116] Figure 8 Capillary-film water content versus temperature.

[0117] Fig. 9 Distribution map of freezing works for water collection wells in communication channels under the riverbed.

[0118] Fig.10 Comparative analysis of frost heave with grouting before freezing and without grouting.

[0119] Explanation of reference numerals: R is the effective pore radius; D is the effective pore diameter; h is the film water thickness; T is the temperature variable; T f is the freezing front temperature; T s is the fractionation-freezing temperature (the temperature at which fractional ice forms); γ SL is the interfacial tension; Pi-w is the interface pressure, and P i-w =γ SL / R;P C is capillary suction; P S is the actual pressure of pore ice; P S0 is the theoretical pressure of porous ice in equilibrium; P ew is the external water pressure; P Ly is the actual liquid pressure of the film water in the non-equilibrium state; P Lh is the theoretical liquid pressure of the film water in equilibrium state; P Ld It is the driving force for water migration in the film. DETAILED DESCRIPTION

[0120] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments. Each example is provided by way of explanation of the present invention and does not limit the present invention. In fact, it will be clear to those skilled in the art that modifications and variations may be made in the present invention without departing from the scope or spirit of the present invention. For example, a feature shown or described as a part of one embodiment may be used in another embodiment to produce yet another embodiment. Therefore, it is desired that the present invention encompasses such modifications and variations within the scope of the appended claims and their equivalents.

[0121] One or more examples of the present invention are shown in the accompanying drawings. The detailed description uses numerical and letter designations to refer to features in the drawings. Like or similar designations in the drawings and description have been used to refer to like or similar parts of the present invention.

[0122] like Figure 1-10 As shown, according to an embodiment of the present invention, a freezing rate comparison method based on a frozen soil capillary-film water storage evolution model is provided, comprising the following steps:

[0123] Step 1: Construct a frozen capillary-film water storage evolution model.

[0124] like Figure 1 Schematic diagram of the forces on the capillary-film water in the frozen capillary in the capillary-film water storage evolution model and Figure 2 Schematic diagram of the stress state of thin film water on the tube wall in the capillary-thin film water storage evolution model of frozen capillaries.

[0125] R is the effective pore radius; D is the effective pore diameter; h is the film water thickness; T is the temperature variable; T f is the freezing front temperature; T s is the fractionation-freezing temperature (the temperature at which fractional ice forms); γ SL is the interfacial tension; P i-w is the interface pressure, and P i-w =γ SL / R;P C is capillary suction; P S is the actual pressure of pore ice; P S0 is the theoretical pressure of porous ice in equilibrium; P ew is the external water pressure; P Ly is the actual liquid pressure of the film water in the non-equilibrium state; P Lh is the theoretical liquid pressure of the film water in equilibrium state; P Ld It is the driving force for water migration in the film;

[0126] Since the capillary suction is the capillary cross-sectional surface force, the ice pressure in the pore is also the capillary cross-sectional surface force, and the external water pressure is the phreatic pressure; when pore ice is formed, the pore ice pressure, capillary suction and external water pressure reach equilibrium on the curved ice-water interface, that is:

[0127] P c +P ew =P S (1)

[0128] Let the curvature be: κ1=1 / R1+1 / R2, where R1 and R2 are the principal curvature radii; for an ideal hemispherical interface, we have: κ1=1 / R1+1 / R2=2 / R, and R1=R2=R, where R is the effective radius of the pore.

[0129] It can be seen that the capillary suction force of the curved ice-water interface is:

[0130]

[0131] When the capillary freezes, the theoretical ice pressure in equilibrium is:

[0132]

[0133] Where: P S0 is the theoretical ice pressure in equilibrium; L is the melting heat of water, which can be taken as 3.34×10 9 cm 2 / s 2 ; vS is the specific volume of ice; TA is the absolute freezing temperature of pure water, which is 273.15K,

[0134] Combining equations (1), (2), and (3), we can obtain:

[0135]

[0136] Let: T = T f , is the freezing temperature of the capillary; transform equation (4) to obtain:

[0137]

[0138] From equation (5), we can see that the negative value of the capillary freezing temperature is proportional to the curvature, that is, the larger the curvature, the lower the corresponding capillary freezing temperature.

[0139] Step 2, calculate the capillary critical aperture change equation,

[0140] Let: R = R GT is the maximum pore diameter that can be frozen in the capillary under any negative temperature condition, that is, the critical pore radius. According to equation (4), we can get:

[0141]

[0142] Where: R GT is the critical pore radius for capillary freezing,

[0143] The influence of external water pressure is negligible, that is: P ew = 0, changing equation (6), we can get the critical pore radius equation of capillary freezing under any negative temperature condition:

[0144]

[0145] Where: C1 = (2γ SL ×ν S ×T A ) / L≈0.0558μm·℃ is a constant,

[0146] From equation (7), we can know that the critical pore radius R of the capillary is GT It is inversely proportional to the first power of negative temperature, that is, the lower the freezing temperature, the smaller the aperture of the corresponding frozen capillary.

[0147] In addition, substituting equation (3) into equation (7), we can obtain:

[0148]

[0149] Where: c1 = 2γ SL ≈63.54mN / m, which is a constant.

[0150] From equation (8), we can see that the critical pore radius of the capillary is inversely proportional to the first power of the theoretical ice pressure, which indicates that as the ice pressure increases, the critical pore radius of the capillary that can be invaded by pore ice becomes smaller, resulting in a decrease in the capillary water content.

[0151] Step 3: Construct a model for the evolution of the water in the thin film on the particle surface when it freezes.

[0152] Due to the adsorption effect of the electrostatic force on the particle surface on the film water, a virtual electric field is formed in the form of a diffuse double electric layer. Figure 3 .

[0153] Since the increase in water pressure near the film water offsets the chemical potential caused by the surface adsorption effect, the chemical potential and hydraulic pressure distribution of the film water on the particle surface are obtained, see Figure 4 .

[0154] According to the phase thermal equilibrium condition, the chemical potentials of the solid and liquid phases at the ice-water interface are equal, that is:

[0155] μ L =μ S (9)

[0156] Where: μ L is the chemical potential of film water; μ S is the chemical potential of ice. Among them, the liquid phase chemical potential of thin film water can be expressed as:

[0157] μ L =μ L0 -μ Lσ (10)

[0158] Where: μ L0 is the volume water chemical potential under reference conditions (T0, P0); μ Lσ The chemical potential change caused by the surface effect is mainly related to the distance from the particle surface, so it can be defined as:

[0159] μ Lσ =ay -α (11)

[0160] Where: a is a constant; y is the distance from the film water to the particle surface; α is a power; since the decrease in the chemical potential of the film water will lead to an increase in the hydraulic pressure, we can get:

[0161] μ L =μ L0 +v L P L -s L T L -ay -α (12)

[0162] Where: P0 is the reference pressure, which is the standard atmospheric pressure; T0 is the reference temperature, which is the melting point under standard atmospheric pressure; v L is the water specific volume of the film; P L Relative to the reference value P L0 Hydraulic pressure; L is the entropy of film water; T L Relative to the reference value T L0 The liquid layer temperature;

[0163] Assumption: The chemical potential μ of the film water L Always continuous, when the film water is in contact with the bulk water:

[0164] μ L =μ L0 (13)

[0165] Since the film water thickness h is very small, the temperature change along the film water thickness direction is ignored. At this time: T L =T L0 -T0 = 0, then by combining equations (12) and (13), we can obtain:

[0166]

[0167] From equation (14), we can see that the decrease in chemical potential near the surface directly leads to an increase in the hydraulic pressure of the film water. When the external phase of the film water changes to ice, the chemical potential of the ice on the interface is:

[0168] μ S =μ S0 +v S P S -s S T S (15)

[0169] Where: μ S0 is the chemical potential of bulk ice under reference conditions (T0, P0); v S is the specific volume of ice; P S Relative to the reference value P L0 Ice pressure (actual ice pressure); s S is ice entropy; T S Relative to the reference value T L0 The ice temperature,

[0170] When the film water thickness y = h, assuming that the water-ice phase is still in equilibrium, combining equations (9), (12), and (15), we can obtain:

[0171] μ S0 +v S P S -s S T S =μ L0 +v L P Lh -s L T L -ah -α (16)

[0172] Where: P Lh is the theoretical hydraulic pressure when the film water thickness y = h. Given that the particle matrix ice-water interface is convexly curved outward (see Figure 4 ), so there is a pressure difference between ice pressure and hydraulic pressure at the ice-water interface, that is:

[0173]

[0174] Where: γ SL is the surface tension of the solid-liquid interface; is the average curvature of the ice-water interface (positive toward the liquid side),

[0175] Assumption: The temperature of the thin film water and ice at the ice-water interface is equal, that is: T L =T S =T, substituting formula (17) into formula (16), we can get:

[0176]

[0177] Where: Δv = v S -v L ; L / T A =s L -s S ,

[0178] From formula (18), we can see that when the film water thickness y = h, the hydraulic pressure equation is:

[0179]

[0180] Combining formula (18) and (19), we get:

[0181]

[0182] By parameter transformation, it can be derived:

[0183]

[0184] Combining formula (17) and (21), we get:

[0185]

[0186] Where: P S0 is the theoretical ice pressure on the particle surface,

[0187] The theoretical ice pressure equation derived from this model is completely consistent with the theoretical ice pressure equation (3) derived from the capillary model, but the boundary conditions of the two models are different (the particle surface is a convex interface, and the inner wall of the capillary is a concave interface, see Figure 5 and Figure 6 ). This shows that the theoretical ice pressure development has nothing to do with boundary conditions and is only closely related to temperature; therefore, the theoretical ice pressure equation has wide applicability, and is applicable to both capillary water freezing models and film water freezing models.

[0188] Step 4, calculate the film water thickness change equation,

[0189] The equation for the variation of film water thickness with temperature is:

[0190]

[0191] Where: A is the Hamker constant; T K is the absolute temperature variable; T m,K is the absolute freezing temperature of liquid water under critical conditions; ρ i is the density of ice, and ρ i =1 / v S ,

[0192] Due to T m,K =T A , convert the absolute temperature difference in equation (23) into relative temperature difference, and we get:

[0193] T m,K -T K =(T A +0)-(T A +T)=-T (24)

[0194] Combining equations (23) and (24), we can obtain:

[0195]

[0196] Where: C2 = (-A × T A ) / (6π×ρ i ×L), is a constant,

[0197] From equation (25), we can see that the film water thickness is inversely proportional to the 1 / 3 power of the negative temperature, that is, the lower the temperature, the smaller the thickness of the frozen film water.

[0198] Substituting equation (22) into equation (25), we can obtain:

[0199]

[0200] In the formula: c2 = -A / 6π, which is a constant,

[0201] From equation (26), it can be seen that the film water thickness is inversely proportional to the 1 / 3 power of the theoretical ice pressure; this indicates that as the theoretical ice pressure increases, the depth of ice crystals penetrating into the film increases, so the film water thickness gradually decreases as the temperature decreases, and the film water content decreases synchronously.

[0202] Step 5, comparative analysis of capillary-film water freezing rates,

[0203] By combining equations (8) and (25), we can obtain the critical pore size and the rate of change of film thickness with temperature:

[0204]

[0205] Where: C3 = (12π × γ SL ) / (-A), is a constant,

[0206] When the temperature T→0℃; R GT →+∞、h 3 →+∞, at this time the theoretical value does not match the actual initial value. By removing the influence of the extreme value and transforming equation (27), we can obtain:

[0207] R GT =C3·h 3 , T<0℃ (28)

[0208] To simplify the analysis, the rate of change of capillary water or film water content with temperature (or the crystallization rate of capillary water or film water during freezing) is defined as the freezing rate, and the following assumptions are made:

[0209] 1) Capillaries of various pore sizes are evenly distributed inside the soil, and the change in capillary water content can characterize the change in its critical pore size;

[0210] 2) The water content of each film at each interface is evenly distributed on the surface of the substrate, and the change in the water content of the film can characterize the change in the thickness of the liquid layer.

[0211] From equation (28), it can be seen that the critical pore size change rate of freezing capillaries under the same negative temperature conditions is the cube of the change rate of film water thickness, indicating that the freezing sensitivity of capillary water is much higher than that of film water. Given that capillary water exists in the pore space, while film water is adsorbed on the particle surface, the freezing rate of capillary water and film water (the rate of change of capillary water and film water content with temperature) can be measured to verify the rate of change of the two with temperature.

[0212] Furthermore, in step 2,

[0213] The relationship between capillaries with different pore diameters and freezing temperatures is shown in Table 1:

[0214] Table 1 Relationship between pore diameter and freezing temperature

[0215]

[0216] Note: γ SL =0.42γ SL =31.77mN / m,

[0217] It can be seen from Table 1 that the smaller the critical pore radius of the pore, the lower the corresponding freezing temperature.

[0218] Combined with Table 2,

[0219] Table 2 Pore size and pore water classification by size

[0220]

[0221] The boundary between capillary water and film water is D = 0.1 μm, and the corresponding boundary freezing temperature is -1.131 °C. It can be seen that the freezing temperature of capillary water is higher, while the freezing temperature of film water is lower.

[0222] Furthermore, the capillary critical aperture change rate is inversely proportional to the first power of the negative temperature, and the film water thickness is inversely proportional to the 1 / 3 power of the negative temperature.

[0223] It shows that under the same negative temperature conditions, the critical aperture change rate of the capillary is the cube of the film thickness change rate, and the freezing rate of capillary water is much faster than that of film water.

[0224] According to the low-field nuclear magnetic resonance test and the classification criteria of capillary water and film water in Table 2, the distribution curves of capillary water and film water with temperature can be obtained, see Figure 7 .

[0225] Depend on Figure 7 It can be seen that both capillary water and film water gradually decrease with decreasing temperature. For mesopores or macropores with pore size D ≥ 0.1 μm, it is found that they crystallize in order of pore size, but remain unchanged when the pore size drops to 0.1 μm. Therefore, this pore size can be defined as the minimum critical pore size D of the capillary. GT =0.1μm. For micropores with pore size D<0.1μm, it is found that the film water will continue to decrease with decreasing temperature, but the corresponding pore distribution range remains unchanged. The test results prove that it is reasonable and correct to use D=0.1μm as the dividing point between capillary water and film water pore size.

[0226] In addition, according to the one-to-one correspondence between the total NMR signal and the unfrozen water content, Figure 5 The T2 spectrum distribution area is analyzed, and the total signal intensity of D < 0.1 μm represents film water, and the total signal intensity of D ≥ 0.1 μm represents capillary water. The curves of capillary water content and film water content changing with temperature can be obtained, see Figure 8 .

[0227] Figure 8 In: The ordinate y represents the unfrozen water content, and the abscissa x represents the temperature variable; a is the fitting function coefficient; b is the fitting function power, which represents the rate of change of the unfrozen water content with temperature (freezing speed); R 2 is the degree of fit. Figure 6It can be seen that the initial content of capillary water is 5.48%, while the initial content of film water is 23.32%, and the distribution ratio of the two is 1:4.255. After eliminating the influence of supercooling temperature, the capillary water and film water contents decrease rapidly with the decrease of temperature in the initial freezing stage (0~-1.3℃ / I stage), which is called the rapid freezing stage; when the temperature drops to -1.3℃ (II stage), all the capillary water is frozen, and the remaining film water content decreases with the decrease of temperature, and the decrease rate gradually slows down, which is called the slow freezing stage, which lasts until the end of the freezing process.

[0228] Fitting analysis of the above data shows that the fitting value of capillary water freezing rate b = -1.036 is basically consistent with the theoretical value b = -1.0 of equation (12); while the fitting value of film water freezing rate b = -0.505 is much lower than the theoretical value b = -1 / 3 of equation (28). Given that the freezing rate is inversely proportional to the temperature, it can be seen that the corresponding film water freezing rate experimental value is significantly faster than the theoretical value. In view of this, the film water freezing process is re-divided into two stages, and the film water freezing rate of stage II is fitted. It is found that the fitting value b = -0.397 at this time is close to the theoretical value b = -0.333.

[0229] The above analysis shows that the occurrence evolution and water migration of capillary water and film water during the freezing process are not independent, but are carried out simultaneously and promote each other. Among them, the freezing rate of capillary water is almost unaffected by the freezing state of film water; however, the freezing rate of film water is significantly accelerated in stage I due to the freezing absorption of capillary water, and in stage II, because all the capillary water is frozen, its freezing rate begins to slow down gradually and gradually approaches the theoretical value. The experimental results not only prove the correctness of the capillary-film water occurrence evolution mechanism, but also further explain the influence of water migration on the occurrence evolution process.

[0230] Although, in theory, the freezing rate of capillary water is much faster than that of film water, when capillary water freezes, it not only affects the reduction of its own content, but also draws nearby film water to the capillary wall, where it aggregates and undergoes phase change, thus accelerating the reduction of film water content. Therefore, the storage evolution and migration process of capillary-film water proceed simultaneously and promote each other.

[0231] It is further concluded that capillary water freezes quickly and at a high temperature, while thin film water freezes slowly and at a low temperature. The freezing evolution of capillary water and thin film water does not proceed independently. Due to the suction effect of the interface, the crystallization of capillary water will accelerate the freezing speed of thin film water, but the crystallization of thin film water does not affect the freezing speed of capillary water.

[0232] The freezing sensitivity of capillary water is much higher than that of film water. Combining the freezing characteristics of capillary-film water, the frost heave characteristics of different soil samples can be studied, and corresponding expansion control methods can be proposed, such as:

[0233] Sandy soil has the characteristics of strong capillary properties and weak adsorption, so it has high ice content, strong cementation and small frost heave during freezing, and is a relatively good frozen soil material.

[0234] Powdery soil has both capillary and adsorption characteristics. Therefore, during the freezing process, it has a medium ice content, medium cementation strength, and large frost heave, and is a short-term frost-sensitive material. Based on the above characteristics, measures such as grouting before freezing or high-pressure consolidation and drainage can be used to reduce porosity and frost heave.

[0235] Clay has the characteristics of weak capillary properties and strong adsorption. Therefore, during the freezing process, it has low ice content, poor cementation strength, and small frost heave. Although the frost heave develops slowly, the long-term frost heave force is very large, making it a long-term freeze-sensitive material. Based on the above characteristics, liquid nitrogen ultra-low temperature rapid freezing or intermittent freezing can be used to shorten the freezing time and reduce the development of frost heave force.

[0236] In summary, by analyzing the occurrence and evolution characteristics of capillary water and film water during the freezing process, we can compare the freezing temperature, freezing speed and freezing sensitivity of capillary water and film water, and then propose targeted expansion control measures based on the above characteristics, so as to achieve the purpose of reducing frost heave.

[0237] Example:

[0238] See also Fig. 9 The freezing project of the 8-meter connecting channel and the collection well under the riverbed is a sandy clay layer and belongs to the horizontal freezing project under the riverbed. It is not only highly frost-sensitive but also easy to replenish water. Therefore, grouting is used to suppress frost heave.

[0239] As shown in the figure: the distance between the connecting channel and the riverbed is small, and the overlying layer is mainly gravel interlayer and sandy clay. Since the sandy clay layer is thin and too close to the replenishment water source, if the freezing solution is used alone, the development of frost heave will be difficult to control, which may cause serious damage to the underground structure.

[0240] Based on this, a "pre-grouting + freezing" treatment plan is proposed. First, the grouting pipe is drilled, and the water in the pores is replaced by chemical slurry (cement + water glass slurry, or cement slurry), which blocks the capillary water migration channel and increases the penetration resistance. Then the freezing pipe is actually drilled to make full use of the cementing ability of ice to increase the strength, deformation modulus and impermeability of the frozen curtain.

[0241] See also Fig.10 Schematic diagram comparing frost heave with grouting before freezing and without grouting.

[0242] Fig.10The diamond data represent the freezing test results alone (i.e., only freezing operation), while the square data represent the "pre-grouting + freezing" scheme. The monitoring data show that after the frozen soil wall is formed, if the pre-grouting scheme is not used to block the capillary water migration channel, the frost heave will develop from 7.2 mm to 27.5 mm, causing serious frost heave; while the "pre-grouting + freezing" scheme is used, the frost heave fluctuates between 7.0 ± 5.0 mm, and the frost heave is effectively suppressed. Therefore, the "pre-grouting + freezing" scheme greatly reduces the frost heave, and the frost heave suppression scheme is reasonable and correct.

[0243] From the above description, it can be seen that the above embodiments of the present invention achieve the following technical effects:

[0244] 1. The capillary water migration channel determines the water migration speed;

[0245] 2. For frost-sensitive soils such as silt, silty soil, sandy clay, etc. with strong capillary properties, due to their high capillary water content in the saturated state and large permeability coefficient of the freezing edge, the water migrates quickly during freezing, and the frost heave rate / amount develops relatively large, which is not conducive to the construction of cold region projects; therefore, blocking the capillary water migration channel is the key to controlling the development of frost heave.

[0246] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A freezing rate comparison method based on a frozen soil capillary-film water storage evolution model, characterized in that: The steps include: Step 1: Construct a frozen capillary-film water storage evolution model. R is the effective pore radius; D is the effective pore diameter; h is the film water thickness; T is the temperature variable; T f is the freezing front temperature; T s is the segregation-freezing temperature; γ SL is the interfacial tension; P i-w is the interface pressure, and P i-w =γ SL / R;P C is capillary suction; P S is the actual pressure of pore ice; P S0 is the theoretical pressure of porous ice in equilibrium; P ew is the external water pressure; P Ly is the actual liquid pressure of the film water in the non-equilibrium state; P Lh is the theoretical liquid pressure of the film water in equilibrium state; P Ld It is the driving force for water migration in the film; When porous ice forms, the pore ice pressure, capillary suction and external water pressure reach equilibrium on the curved ice-water interface, namely: P c +P ew =P S (1) Let the curvature be: κ1=1 / R1+1 / R2, where R1 and R2 are the principal curvature radii; for an ideal hemispherical interface, we have: κ1=1 / R1+1 / R2=2 / R, and R1=R2=R, where R is the effective radius of the pore. It can be seen that the capillary suction force of the curved ice-water interface is: When the capillary freezes, the theoretical ice pressure in equilibrium is: Where: P S0 is the theoretical ice pressure in equilibrium; L is the melting heat of water, which can be taken as 3.34×10 9 cm 2 / s 2 ; vS is the specific volume of ice; TA is the absolute freezing temperature of pure water, which is 273.15K, Combining equations (1), (2), and (3), we can obtain: Let: T = T f , is the freezing temperature of the capillary; transform equation (4) to obtain: From equation (5), we can see that the negative value of the capillary freezing temperature is proportional to the curvature, that is, the larger the curvature, the lower the corresponding capillary freezing temperature. Step 2, calculate the capillary critical aperture change equation, Let: R = R GT is the maximum pore diameter that can be frozen in the capillary under any negative temperature condition, that is, the critical pore radius. According to equation (4), we can get: Where: R GT is the critical pore radius for capillary freezing, The influence of external water pressure is negligible, that is: P ew = 0, changing equation (6), we can get the critical pore radius equation of capillary freezing under any negative temperature condition: Where: C1 = (2γ SL ×ν S ×T A ) / L≈0.0558μm·℃ is a constant, From equation (7), we can know that the critical pore radius R of the capillary is GT It is inversely proportional to the first power of negative temperature, that is, the lower the freezing temperature, the smaller the aperture of the corresponding frozen capillary. In addition, substituting equation (3) into equation (7), we can obtain: Where: c1 = 2γ SL ≈63.54mN / m, which is a constant. From equation (8), we can see that the critical pore radius of the capillary is inversely proportional to the first power of the theoretical ice pressure, which indicates that as the ice pressure increases, the critical pore radius of the capillary that can be invaded by pore ice becomes smaller, resulting in a decrease in the capillary water content. Step 3: Construct a model for the evolution of the water in the thin film on the particle surface when it freezes. According to the phase thermal equilibrium condition, the chemical potentials of the solid and liquid phases at the ice-water interface are equal, that is: m L =μ S (9) Where: μ L is the chemical potential of film water; μ S is the chemical potential of ice, where the liquid phase chemical potential of thin film water can be expressed as: m L =μ L0 -m Lσ (10) Where: μ L0 is the volume water chemical potential under reference conditions (T0, P0); μ Lσ The chemical potential change caused by the surface effect is mainly related to the distance from the particle surface, so it can be defined as: μ Lσ =is -α (11) Where: a is a constant; y is the distance from the film water to the particle surface; α is a power; since the decrease in the chemical potential of the film water will lead to an increase in the hydraulic pressure, we can get: μ L =μ L0 +v L P L -s L T L -is -α (12) Where: P0 is the reference pressure, which is the standard atmospheric pressure; T0 is the reference temperature, which is the melting point under standard atmospheric pressure; v L is the water specific volume of the film; P L Relative to the reference value P L0 Hydraulic pressure;s L is the entropy of film water; T L Relative to the reference value T L0 The liquid layer temperature; Assumption: The chemical potential μ of the film water L Always continuous, when the film water is in contact with the bulk water: m L =μ L0 (13) Since the film water thickness h is very small, the temperature change along the film water thickness direction is ignored. At this time: T L =T L0 -T0 = 0, then by combining equations (12) and (13), we can obtain: From equation (14), we can see that the decrease in chemical potential near the surface directly leads to an increase in the film water pressure. When the external phase of the film water changes to ice, the chemical potential of ice on the interface is: m S =μ S0 +v S P S -s S T S (15) Where: μ S0 is the chemical potential of bulk ice under reference conditions (T0, P0); v S is the specific volume of ice; P S Relative to the reference value P L0 Ice pressure;s S is ice entropy; T S Relative to the reference value T L0 The ice temperature, When the film water thickness y = h, assuming that the water-ice phase is still in equilibrium, combining equations (9), (12), and (15), we can obtain: μ S0 +v S P S -s S T S =μ L0 +v L P Lh -s L T L -ah -α (16) Where: P Lh is the theoretical hydraulic pressure when the film water thickness y = h. Since the particle matrix ice-water interface is convexly curved outward, there is a pressure difference between the ice pressure and the hydraulic pressure at the ice-water interface, that is: Where: γ SL is the surface tension of the solid-liquid interface; is the mean curvature of the ice-water interface, Assumption: The temperature of the thin film water and ice at the ice-water interface is equal, that is: T L =T S =T, substituting formula (17) into formula (16), we can get: Where: Δv = v S -v L ; L / T A =s L -s S , From formula (18), we can see that when the film water thickness y = h, the hydraulic pressure equation is: Combining formula (18) and (19), we get: By parameter transformation, it can be derived: Combining formula (17) and (21), we get: Where: P S0 is the theoretical ice pressure on the particle surface, Step 4, calculate the film water thickness change equation, The equation for the variation of film water thickness with temperature is: Where: A is the Hamker constant; T K is the absolute temperature variable; T m,K is the absolute freezing temperature of liquid water under critical conditions; ρ i is the density of ice, and ρ i =1 / v S , Due to T m,K =T A , convert the absolute temperature difference in equation (23) into relative temperature difference, and we get: T m,K -T K =(T A +0)-(T A +T)=-T (24) Combining equations (23) and (24), we can obtain: Where: C2 = (-A × T A ) / (6π×ρ i ×L), is a constant, From equation (25), we can see that the film water thickness is inversely proportional to the 1 / 3 power of the negative temperature, that is, the lower the temperature, the smaller the thickness of the frozen film water. Substituting equation (22) into equation (25), we can obtain: In the formula: c2 = -A / 6π, which is a constant, Step 5, comparative analysis of capillary-film water freezing rates, By combining equations (8) and (25), we can obtain the critical pore size and the rate of change of film thickness with temperature: Where: C3 = (12π × γ SL ) / (-A), is a constant, When the temperature T→0℃; R GT →+∞、h 3 →+∞, at this time the theoretical value does not match the actual initial value. By removing the influence of the extreme value and transforming equation (27), we can obtain: R GT =C3·h 3 ,T<0 oC (28) It can be seen from equation (28) that the critical aperture change rate of the freezing capillary under the same negative temperature conditions is the cube of the change rate of the film water thickness, indicating that the freezing sensitivity of capillary water is much higher than that of film water.

2. The freezing rate comparison method based on the frozen soil capillary-film water storage evolution model according to claim 1 is characterized in that: In step 2, The relationship between capillaries with different pore diameters and freezing temperatures is shown in Table 1: Table 1 Relationship between pore diameter and freezing temperature Note: c SL =0.42g SL =31.77mN / m, It can be seen from Table 1 that the smaller the critical pore radius of the pore, the lower the corresponding freezing temperature. Combined with Table 2, Table 2 Pore size and pore water classification by size The boundary between capillary water and film water is D = 0.1 μm, and the corresponding boundary freezing temperature is -1.131 °C. It can be seen that the freezing temperature of capillary water is higher, while the freezing temperature of film water is lower.

3. The freezing rate comparison method based on the frozen soil capillary-film water storage evolution model according to claim 2 is characterized in that: The capillary critical aperture change rate is inversely proportional to the first power of the negative temperature, and the film water thickness is inversely proportional to the 1 / 3 power of the negative temperature. It shows that under the same negative temperature conditions, the critical aperture change rate of the capillary is the cube of the film thickness change rate, and the freezing rate of capillary water is much faster than that of film water.

4. The freezing rate comparison method based on the frozen soil capillary-film water storage evolution model according to claim 2 is characterized in that: Capillary water freezes quickly and at a high temperature; The freezing speed of film water is slow and the freezing temperature is low; Due to the suction effect of the interface, the crystallization of capillary water will accelerate the freezing rate of thin film water, but the crystallization of thin film water does not affect the freezing rate of capillary water.

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