Construction of occurrence evolution model of frozen capillary and frost heaving inhibition method of frozen capillary

Abstract

The invention provides a method for constructing an occurrence evolution model of a frozen capillary tube. The method comprises the following steps: step 1, calculating freezing temperature of liquid phase water of any interface; step 2, constructing a freezing model of the capillary tube; step 3, calculating a critical pore diameter change equation of the capillary tube; the larger the critical pore radius RGT is, the smaller the decrease amplitude of the permeability coefficient of the frozen edge is, and the smaller the critical pore radius RGT is, the larger the decrease amplitude of the permeability coefficient of the frozen edge is, and the decrease amplitude is amplified by-beta power. The frost heaving inhibition method comprises the following steps that freezing is carried out after pre-grouting to control the capillary water content, and freezing carried out after pre-grouting specifically comprises the steps that firstly, a grouting pipe is drilled, pore water is replaced with chemical grout, so that a capillary water migration channel is blocked, permeation resistance is increased, then a freezing pipe is drilled, and the capillary water content is controlled by utilizing the low-temperature cementation capacity of ice; and the strength, the deformation modulus and the impermeability of the freezing curtain are improved.

Description

Technical Field

[0001] The invention relates to the field of engineering frost heave and thaw settlement, and in particular to a model for constructing an occurrence evolution of frozen capillaries and a method for suppressing frost heave. 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 condensation 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. According to the capillary and adsorption properties of the soil matrix, it can be seen that there are mainly two forms of unfrozen water in frozen soil: capillary water and film water. Among them, capillary water exists in the volume space inside the capillary, mainly affected by interfacial tension; while film water is adsorbed on the surface of the particles, mainly affected by the surface electric field force.

[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, so the lower the temperature, the smaller the liquid layer thickness. In addition, since the pore size of the mesoporous capillary is generally above D = 0.1μm, and the thickness of the microporous film water on one side is generally below h = 50nm (or the thickness of both sides 2h is below 0.1μm), 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] As shown in Table 1, the cross section of the capillary where the capillary water is located is much larger than the micropore cross section where the film water is located, which makes the permeation resistance of the capillary much smaller than the permeation resistance of the microporous film liquid layer, and is the main channel for the migration of unfrozen water. Therefore, the capillary provides a channel for water migration, while the film water provides the driving force for water migration.

[0007] In addition, at different overburden pressures P OB Under these conditions, the driving force of water migration is P Lb The change is small, but the permeability coefficient k of the frozen edge ff The change is very drastic. According to Darcy's law, the permeability coefficient k of the frozen edge is ff Dominant water migration velocity V ff See Table 2 for the changes:

[0008] Table 2 Comparison of driving force, freezing edge permeability and migration velocity under different high pressure and low temperature conditions

[0009]

[0010] In summary, constructing a capillary water freezing model, studying the evolution characteristics of capillary water freezing, and exploring its relationship with the permeability coefficient of the freezing edge will help analyze the changing trend of water migration speed and propose new frost heave control methods. Summary of the invention

[0011] The purpose of the present invention is to construct an occurrence evolution model of frozen capillaries and a frost heave suppression method thereof, analyze the changing trend of water migration velocity, and propose a new frost heave control method.

[0012] In order to achieve the above object, the present invention provides the following technical solutions:

[0013] The construction of the frozen capillary occurrence evolution model includes the following steps:

[0014] Step 1: Calculate the freezing temperature of liquid water at any interface.

[0015] According to capillary theory, when capillary water freezes, it is mainly affected by interfacial tension. For any curved interface, we have:

[0016]

[0017] Where: κ is the curvature of the interface, and κ = 1 / R1 + 1 / R2; R1 and R2 are the principal curvature radii of the interface at a given point,

[0018] Introducing equation (1) into the Gibbs-Thomson equation, we can obtain the freezing temperature equation of liquid water at any curved interface:

[0019]

[0020] Where: ΔH m is the melting enthalpy of ice; T m,K is the absolute freezing temperature of liquid water under critical conditions; T e,K is the absolute freezing temperature of liquid water at any curved interface; γ SL is the ice-water interfacial tension, taken as 31.77 mN / m; ν S is the specific volume of ice,

[0021] According to the transformation relationship between thermodynamic parameters, we get: T m,K =T A , ΔH m =L; where T A is the absolute freezing temperature of pure water, which can be taken as 273.15K; L is the latent heat of fusion of water, which can be taken as 3.34×10 9 cm 2 / s 2 ,

[0022] The temperature decreases due to the bending of the interface, and the temperature decrease is: ΔT = T m,K -T e,K ,have to:

[0023]

[0024] Transforming equation (3) yields:

[0025]

[0026] For ease of analysis, convert the absolute temperature difference into Celsius temperature difference, and we get:

[0027] ΔT=T m,K -T e, K =(T A +0)-(T A +T F )=-T F (5)

[0028] Where: T F is the freezing temperature of liquid water at any curved interface, in degrees Celsius,

[0029] Substituting equation (5) into equation (4), we can obtain:

[0030]

[0031] From equation (6), we can see that the negative value (or absolute value) of the freezing temperature of liquid water at any curved interface is proportional to the curvature of the interface.

[0032] Step 2, construct the freezing model of the capillary,

[0033] R is the effective radius of the capillary; D is the effective diameter of the capillary; L c is the effective cross-sectional perimeter of the capillary; A is the effective cross-sectional area of ​​the capillary; h is the thickness of the thin film water layer; γ SL is the interfacial tension on the curved ice-water interface; P c is the capillary suction force of the capillary on the effective cross section; P f is the film suction of film water on the liquid layer thickness; P i is the pore ice pressure; P ew is the external water pressure,

[0034] Since the interfacial tension on the curved ice-water interface is γ SL , capillary suction force P on the effective cross section of the capillary c The film suction P on the film water layer f The resultant forces in the capillary axis direction are equivalent to each other, that is:

[0035]

[0036] Simplifying equation (7), we get the conversion equation between capillary suction and film suction:

[0037]

[0038] Where n is the proportionality factor between the thickness of the thin film water and the capillary radius, a dimensionless quantity,

[0039] From equation (8), we can see that the capillary suction and the film suction are in linear positive proportion, and the capillary suction and the film suction are equivalent, so the change law of the two with temperature is highly consistent.

[0040] Since capillary suction is the surface force for the entire capillary cross section, and the ice pressure in the pores is also the surface force for the entire capillary cross section; when porous ice is formed, the pore ice pressure, capillary suction, and external water pressure on the curved ice-water interface are balanced, that is:

[0041] P c +P ew =P i (9)

[0042] For the ideal hemispherical interface curvature, let: κ1 = 1 / R1 + 1 / R2 = 2 / R, then R1 = R2 = R, R is the effective radius of the pore,

[0043] It can be seen that the capillary suction force of the curved ice-water interface is:

[0044]

[0045] The theoretical ice pressure when the capillary freezes (under equilibrium state) is:

[0046]

[0047] Where: P i,e is the theoretical ice pressure (under equilibrium state); when the capillary is frozen,

[0048]

[0049] Where: T f is the capillary freezing temperature,

[0050] Combining equations (11) and (12), we can obtain:

[0051]

[0052] Transforming equation (13), we get:

[0053]

[0054] Comparing equations (6) and (14), we can see that when the external water pressure P ew When it approaches zero, the freezing temperature given by the capillary freezing model is completely consistent with the freezing temperature derived from the Gibbs-Thomson equation, indicating that the constructed capillary freezing model is reasonable.

[0055] Step 3, calculate the capillary critical aperture change equation,

[0056] According to equation (14), the capillary freezing temperature equation that varies with the critical pore size can be obtained:

[0057]

[0058] Where: R GT is the critical pore radius of the freezing capillary,

[0059] The influence of external water pressure is negligible, that is: P ew = 0, changing equation (15), we can get the critical pore radius equation under any negative temperature condition:

[0060]

[0061] Where: C1 = (2γ SL ×ν S ×T A ) / L≈0.0558μm·℃ is a constant,

[0062] From equation (16), 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 temperature, the smaller the pore size of the frozen capillary.

[0063] In addition, substituting equation (11) into equation (16), we can obtain:

[0064]

[0065] Where: c1 = 2γ SL ≈63.54mN / m, which is a constant.

[0066] Step 4: Confirm the corresponding relationship between the freezing edge permeability coefficient and the critical pore radius.

[0067] From equation (17), we can see that the critical pore radius of the capillary is inversely proportional to the first power of the theoretical ice pressure. This 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. At the same time, the permeability coefficient of the frozen edge decreases rapidly due to the blocking of the seepage channel by pore ice.

[0068] The permeability equation of the frozen edge under different temperature conditions can be obtained:

[0069]

[0070] Where: k uf is the permeability coefficient of unfrozen soil; k ff is the permeability coefficient of the frozen edge; β is a power, which takes a negative value; T f is the freezing front temperature; T s is the freezing temperature,

[0071] Combining equations (16) and (18), we can obtain the capillary critical pore radius R GT , frozen edge permeability coefficient k ff As temperature changes,

[0072] That is: capillary critical pore radius R GT , frozen edge permeability coefficient k ff The trend of temperature change is consistent.

[0073] Assume that the freezing front temperature is T f Assuming that the temperature is zero degrees Celsius, substituting equation (16) into equation (18) and unifying the dimensions, we can obtain:

[0074]

[0075] From equation (19), we know that the critical pore radius R GT The larger the value, the smaller the decrease of the freezing edge permeability coefficient, and the critical pore radius R GT The smaller it is, the greater the decrease in the permeability coefficient of the frozen edge is, and it is magnified by -β times.

[0076] Furthermore, in the above-mentioned frozen capillary occurrence evolution model, in step 3 and step 4,

[0077] When β is -8, the relationship between the pore diameter, the freezing edge permeability ratio and the freezing temperature is shown in Table 3:

[0078] Table 3 Relationship between pore diameter, freezing temperature and permeability coefficient change rate

[0079]

[0080] Note: γ SL =0.42γ SL =31.77mN / m,

[0081] It can be seen from Table 3 that the smaller the critical pore radius, the lower the corresponding freezing temperature.

[0082] Combined with Table 1, the boundary between capillary water and film water is D = 0.1 μm, the corresponding freezing temperature is -1.131 ° C, and the corresponding freezing edge permeability coefficient decreases by 2.4‰. It can be seen that the freezing state of capillary water plays a dominant role in the change of water migration speed.

[0083] By controlling the capillary water content, water migration can be strongly inhibited, thereby achieving the purpose of reducing frost heave.

[0084] The present invention also discloses a method for suppressing frost heave according to the occurrence evolution model of frozen capillaries, comprising the following steps:

[0085] Controlling the capillary water content by freezing after pre-grouting,

[0086] Freezing after pre-grouting specifically includes:

[0087] First, the grouting pipe is drilled to replace the pore water with chemical slurry, thereby blocking the capillary water migration channel and increasing the penetration resistance.

[0088] Then, the freezing pipe is solidly driven, and the low-temperature bonding ability of ice is used to increase the strength, deformation modulus and impermeability of the freezing curtain.

[0089] Furthermore, in the above-mentioned frost heave suppression method based on the occurrence evolution model of frozen capillaries, an overburden pressure of 1.0 MPa is applied to the soil. At this time, the overburden pressure is equivalent to the ice pressure inside the condensed ice. Substituting it into equation (17), the critical pore radius of the frozen capillary can be obtained as:

[0090]

[0091] From equation (20), we can know that the critical pore diameter is: D GT =2R GT =127.08nm=0.127μm, the corresponding freezing temperature of the warm end of the condensed ice is T s is -0.891℃;

[0092] Substituting equation (20) into equation (19), we find that the permeability coefficient of the frozen edge zone drops significantly to 6.3‰ when it is not frozen.

[0093] This indicates that overburden pressure can strongly inhibit water migration.

[0094] Analysis shows that the present invention discloses a storage evolution model for constructing frozen capillaries and a method for suppressing frost heave, which has important theoretical value and scientific significance for improving frost heave theory and guiding engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] 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:

[0096] Figure 1 Capillary freezing model.

[0097] Figure 2 The trend of freezing edge permeability coefficient changing with temperature.

[0098] Figure 3 Schematic diagram of the freezing project of the water collection well in the communication channel under the riverbed.

[0099] Figure 4 Schematic diagram comparing frost heave with grouting before freezing and without grouting.

[0100] Figure 5 Schematic diagram of frost heave development under different overburden pressures.

[0101] Figure 6 Schematic diagram of the development trend of frost heave rate under different overburden pressures.

[0102] Explanation of reference numerals: R is the effective pore radius; D is the effective pore diameter; L is the effective pore diameter. c is the effective pore cross-section perimeter; A is the effective pore cross-section area; h is the film thickness; γ SL is the interfacial tension; P c is capillary suction; P f is the film suction; P i is the pore ice pressure; P ew is the external water pressure. DETAILED DESCRIPTION

[0103] 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.

[0104] 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.

[0105] like Figure 1-6 As shown, according to an embodiment of the present invention, a method for constructing an occurrence evolution model of frozen capillaries is provided, comprising the following steps:

[0106] Step 1: Calculate the freezing temperature of liquid water at any interface.

[0107] According to capillary theory, when capillary water freezes, it is mainly affected by interfacial tension. For any curved interface, we have:

[0108]

[0109] Wherein: κ is the curvature of the interface, and κ=1 / R1+1 / R2; R1 and R2 are the principal curvature radii of the interface at a given point.

[0110] Introducing equation (1) into the Gibbs-Thomson equation, we can obtain the freezing temperature equation of liquid water at any curved interface:

[0111]

[0112] Where: ΔH m is the melting enthalpy of ice; T m,K is the absolute freezing temperature of liquid water under critical conditions; T e,K is the absolute freezing temperature of liquid water at any curved interface; γ SL is the ice-water interfacial tension, taken as 31.77 mN / m; ν S is the specific volume of ice.

[0113] According to the transformation relationship between thermodynamic parameters, we get: T m,K =T A , ΔH m =L; where T A is the absolute freezing temperature of pure water, which can be taken as 273.15K; L is the latent heat of fusion of water, which can be taken as 3.34×10 9 cm 2 / s 2 .

[0114] The temperature decreases due to the bending of the interface, and the temperature decrease is: ΔT = T m,K -T e,K ,have to:

[0115]

[0116] Transforming equation (3) yields:

[0117]

[0118] For ease of analysis, convert the absolute temperature difference into Celsius temperature difference, and we get:

[0119] ΔT=T m,K -T e, K =(TA +0)-(T A +T F )=-T F (5)

[0120] Where: T F is the freezing temperature of liquid water at any curved interface, in degrees Celsius. Substituting equation (5) into equation (4), we can obtain:

[0121]

[0122] It can be seen from equation (6) that the negative value (or absolute value) of the freezing temperature of liquid water at any curved interface is proportional to the curvature of the interface, that is, the greater the curvature of the curved interface, the lower the freezing temperature of the liquid water due to the surface effect.

[0123] The above is also the analysis of the evolution of the occurrence characteristics of capillary water.

[0124] Step 2: Construct a capillary freezing model.

[0125] In order to clarify the influence of interface effect and reveal the physical meaning of each parameter in the above freezing temperature equation, the freezing state of the capillary was modeled.

[0126] First, according to the Yang-Laplace equation, it can be seen that the ice-water interface at the top of the pore ice is an ideal hemispherical shape when the capillary freezes.

[0127] Combining the distribution characteristics of capillary water and film water in the capillary, a capillary freezing model is constructed. Figure 1 .

[0128] Figure 1 In: R is the effective pore radius of the capillary; D is the effective pore diameter of the capillary; L c is the effective pore cross-sectional perimeter of the capillary; A is the effective cross-sectional area of ​​the capillary pore; h is the thickness of the film water; γ SL is the interfacial tension on the curved ice-water interface; P c is the capillary suction force on the effective cross-section of the capillary; P f is the film suction on the film water; P i is the pore ice pressure; P ew is the external water pressure. Since the unfrozen water film on the capillary wall is at the nanometer level, and the effective pore size of the capillary is at the millimeter or micrometer level, the effect of the thickness of the film water on the effective pore size of the capillary can be ignored.

[0129] Analysis of the capillary freezing model shows that the interfacial tension γ on the curved ice-water interface SL , capillary suction force P on the effective cross section of the capillary c and the film suction P on the film water fThe three forces in the capillary axial direction are equivalent to each other, namely:

[0130]

[0131] Simplifying equation (7), we get the conversion equation between capillary suction and film suction:

[0132]

[0133] Where n is the proportional factor between the thickness of the film water and the capillary radius, a dimensionless quantity. From equation (8), it can be seen that the capillary suction and the film suction are linearly proportional, and the combined force of the two is equivalent. However, the capillary suction mainly considers its cross-sectional force from the perspective of capillary water migration, while the film suction mainly considers its cross-sectional force from the perspective of film water migration. Therefore, the variation of capillary suction and film suction with temperature is highly consistent.

[0134] Since capillary suction is the surface force for the entire capillary cross section, and the ice pressure in the pores is also the surface force for the entire capillary cross section; when porous ice is formed, the pore ice pressure, capillary suction, and external water pressure on the curved ice-water interface are balanced, that is:

[0135] P c +P ew =P i (9)

[0136] For the ideal hemispherical interface curvature, let: κ1 = 1 / R1 + 1 / R2 = 2 / R, then R1 = R2 = R, and R is the effective radius of the pore.

[0137] It can be seen that the capillary suction force of the curved ice-water interface is:

[0138]

[0139] In addition, the theoretical ice pressure when the capillary freezes (under equilibrium conditions) is:

[0140]

[0141] Where: P i,e is the theoretical ice pressure (under equilibrium state); when the capillary is frozen,

[0142]

[0143] Where: T f is the capillary freezing temperature. Combining equations (11) and (12), we can obtain:

[0144]

[0145] Transforming equation (13), we get:

[0146]

[0147] Comparing equations (6) and (14), we can see that when the external water pressure P ew When it tends to zero, the freezing temperature given by the capillary freezing model is completely consistent with the freezing temperature derived from the Gibbs-Thomson equation, indicating that the capillary freezing model is reasonable and correct.

[0148] Step 3, calculate the capillary critical aperture change equation,

[0149] According to equation (14), the capillary freezing temperature equation that varies with the critical pore size can be obtained:

[0150]

[0151] Where: R GT is the critical pore radius of the freezing capillary.

[0152] Normally, the influence of external water pressure is negligible, that is: P ew = 0, changing equation (15), we can get the critical pore radius equation under any negative temperature condition:

[0153]

[0154] Where: C1 = (2γ SL ×ν S ×T A ) / L≈0.0558μm·℃ is a constant.

[0155] From equation (16), 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 temperature, the smaller the pore size of the frozen capillary.

[0156] In addition, substituting equation (11) into equation (16), we can obtain:

[0157]

[0158] Where: c1 = 2γ SL ≈63.54mN / m, which is a constant.

[0159] Step 4: Confirm the corresponding relationship between the freezing edge permeability coefficient and the critical pore radius.

[0160] From equation (17), it can be seen 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.

[0161] In addition, according to Thomas et al. (2009), the permeability equation of the frozen edge can be obtained:

[0162]

[0163] Where: k uf is the permeability coefficient of unfrozen soil; k ff is the permeability coefficient of the frozen edge; β is a power, which takes a negative value; T f is the freezing front temperature; T s is the freezing temperature. Combining equations (16) and (18), we can get the capillary critical pore radius R GT , frozen edge permeability coefficient k ff For temperature variations, see Figure 2 :

[0164] Depend on Figure 2 It can be seen that the capillary critical pore radius R GT , frozen edge permeability coefficient k ff The trend of temperature change is highly consistent. For the convenience of analysis, it is assumed that the freezing front temperature T f is zero degrees Celsius. At this time, substitute equation (16) into equation (18) and unify the dimensions (eliminate the temperature dimension), and we get:

[0165]

[0166] From equation (19), we know that the critical pore radius R GT The larger the value, the smaller the decrease of the freezing edge permeability coefficient, and the critical pore radius R GT The smaller it is, the greater the decrease in the permeability coefficient of the frozen edge is, and it is magnified by -β times.

[0167] When β is -8, the relationship between pore diameter, freezing temperature and permeability coefficient change rate is shown in Table 3:

[0168] Table 3 Relationship between pore diameter, freezing temperature and permeability coefficient change rate

[0169]

[0170] Note: γ SL =0.42γ SL =31.77mN / m.

[0171] It can be seen from Table 3 that the smaller the critical pore radius, the lower the corresponding freezing temperature. Combined with Table 1, the boundary between capillary water and film water is D = 0.1 μm, the corresponding freezing temperature is -1.131 ° C, and the corresponding freezing edge permeability coefficient decreases by 2.4‰. It can be seen that the freezing state of capillary water plays a dominant role in the water migration speed.

[0172] The above description process cited both the critical pore radius and the critical pore diameter because the radius is generally used in the derivation of capillary theory, while the diameter is generally used in the experimental process.

[0173] Therefore, by controlling the capillary water content (or controlling the capillary water freezing percentage), water migration can be inhibited to achieve the purpose of reducing the amount / rate of frost heave.

[0174] The present invention also discloses a method for suppressing frost heave according to the occurrence evolution model of frozen capillaries, comprising the following steps:

[0175] Controlling the capillary water content by freezing after pre-grouting,

[0176] Freezing after pre-grouting specifically includes:

[0177] First, the grouting pipe is drilled to replace the pore water with chemical slurry, thereby blocking the capillary water migration channel and increasing the penetration resistance.

[0178] Then, the freezing pipe is solidly driven, and the low-temperature bonding ability of ice is used to increase the strength, deformation modulus and impermeability of the freezing curtain.

[0179] In the above frost heave suppression method, an overburden pressure of 1.0 MPa is applied to the soil. At this time, the overburden pressure is equivalent to the ice pressure inside the condensed ice. Substituting it into equation (17), the critical pore radius of the frozen capillary can be obtained as:

[0180]

[0181] From equation (20), we can know that the critical pore diameter is: D GT =2R GT =127.08nm=0.127μm, the corresponding freezing temperature of the warm end of the condensed ice is T s is -0.891℃;

[0182] Substituting equation (20) into equation (19), we find that the permeability coefficient of the frozen edge zone drops significantly to 6.3‰ when it is not frozen.

[0183] This indicates that overburden pressure can strongly inhibit water migration.

[0184] Example 1

[0185] See also Figure 3 The freezing project of the 8-meter connecting channel and the collection well under the riverbed uses grouting to suppress frost heave, which is a horizontal freezing project under the riverbed.

[0186] 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, it is difficult to control the frost heave, which will cause serious damage to the underground structure.

[0187] Based on this, a "pre-grouting + freezing" treatment plan is proposed. First, the grouting pipe is drilled, and the capillary water in the pores is replaced by chemical slurry (cement slurry, cement + water glass slurry), thereby blocking the capillary water migration channel and increasing the penetration resistance. Then the freezing pipe is actually drilled, and the bonding ability of ice is used to increase the strength, deformation modulus and impermeability of the frozen curtain.

[0188] See also Figure 4 Schematic diagram comparing frost heave with grouting before freezing and without grouting.

[0189] Figure 4 The 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 effect is effectively suppressed. Therefore, it is reasonable and correct to use "pre-grouting + freezing" to reduce the frost heave rate and suppress frost heave.

[0190] Example 2

[0191] Example of using external load to reduce frost heave rate (loading test of frozen silt).

[0192] A one-dimensional frost heave loading test was carried out on frost-sensitive silt. The test data can be found in Figure 5 , Schematic diagram of frost heave development under different overburden pressures.

[0193] Depend on Figure 5 It can be seen that as the overburden pressure increases, the development of frost heave is strongly suppressed (when 100 kPa, the frost heave is the largest; when 1000 kPa, the frost heave is the smallest). Since the frost heave is linearly proportional to time, the relationship between the overburden pressure and the frost heave rate can be obtained as follows: Figure 6 As shown in Figure 2, a schematic diagram of the development trend of frost heave rate under different overburden pressures.

[0194] Depend on Figure 6It can be seen that as the overburden pressure increases, the frost heave rate decreases rapidly; when the overburden pressure reaches 1.0 MPa, the frost heave rate tends to zero and the water migration almost stops. This shows that the existence of the overburden pressure inhibits the cracking and expansion of porous ice, thereby hindering the formation of segregated ice. If the overburden pressure of 1.0 MPa is equivalent to the internal ice pressure of segregated ice and substituted into equation (17), the critical pore radius of the frozen capillary can be obtained as:

[0195]

[0196] From equation (20), we can know that the critical pore diameter is: D GT =2R GT =127.08nm=0.127μm, and the corresponding freezing temperature of the condensed ice is -0.891℃; in addition, substituting equation (20) into equation (19), it can be seen that the permeability coefficient of the frozen edge zone drops to 6.3‰ when it is not frozen. This shows that the overburden pressure can strongly inhibit the migration of water by preventing the formation of condensed ice, and its theoretical analysis conclusion is highly consistent with the experimental results.

[0197] From the above description, it can be seen that the above embodiments of the present invention achieve the following technical effects:

[0198] 1. The capillary water migration channel determines the water migration speed;

[0199] 2. For frost-sensitive soils such as silt, silty soil, sandy clay, etc. with strong capillary properties, the capillary water content is high in the saturated state and the permeability coefficient of the frozen edge is large. Therefore, the water migration speed is fast during freezing, resulting in a large frost heave rate / amount, which is not conducive to engineering construction in cold regions; therefore, blocking the capillary water migration channel is the key to controlling the development of frost heave. For example:

[0200] 1) By means of formation grouting, cement slurry / water glass slurry is used to replace pore water, thereby blocking the capillary water migration channel and reducing the permeability coefficient by physical methods to achieve the purpose of inhibiting frost heave;

[0201] 2) Through ground loading, the freezing temperature when the condensed ice is formed is reduced, causing a large amount of capillary water in the freezing edge area to freeze, thereby increasing the penetration resistance of the freezing edge area and achieving the purpose of inhibiting frost heave.

[0202] 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. Construct a frozen capillary occurrence evolution model, characterized in that: The steps include: Step 1: Calculate the freezing temperature of liquid water at any interface. According to capillary theory, when capillary water freezes, it is mainly affected by interfacial tension. For any curved interface, we have: Where: κ is the curvature of the interface, and κ = 1 / R1 + 1 / R2; R1 and R2 are the principal curvature radii of the interface at a given point, Introducing equation (1) into the Gibbs-Thomson equation, we can obtain the freezing temperature equation of liquid water at any curved interface: Where: ΔH m is the melting enthalpy of ice; T m,K is the absolute freezing temperature of liquid water under critical conditions; T e,K is the absolute freezing temperature of liquid water at any curved interface; γ SL is the ice-water interfacial tension, taken as 31.77 mN / m; ν S is the specific volume of ice, According to the transformation relationship between thermodynamic parameters, we get: T m,K =T A , ΔH m =L; where T A is the absolute freezing temperature of pure water, which can be taken as 273.15K; L is the latent heat of fusion of water, which can be taken as 3.34×10 9 cm 2 / s 2 , The temperature decreases due to the bending of the interface, and the temperature decrease is: ΔT = T m,K -T e,K ,have to: Transforming equation (3) yields: For ease of analysis, convert the absolute temperature difference into Celsius temperature difference, and we get: ΔT=T m,K -T e,K =(T A +0)-(T A +T F )=-T F (5) Where: T F is the freezing temperature of liquid water at any curved interface, in degrees Celsius, Substituting equation (5) into equation (4), we can obtain: From equation (6), we can see that the negative value (or absolute value) of the freezing temperature of liquid water at any curved interface is proportional to the curvature of the interface. Step 2, construct the freezing model of the capillary, R is the effective radius of the capillary; D is the effective diameter of the capillary; L c is the effective cross-sectional perimeter of the capillary; A is the effective cross-sectional area of ​​the capillary; h is the thickness of the thin film water layer; γ SL is the interfacial tension on the curved ice-water interface; P c is the capillary suction force of the capillary on the effective cross section; P f is the film suction of film water on the liquid layer thickness; P i is the pore ice pressure; P ew is the external water pressure, Since the interfacial tension on the curved ice-water interface is γ SL , capillary suction force P on the effective cross section of the capillary c The film suction force P on the film water layer f The resultant forces in the capillary axis direction are equivalent to each other, that is: Simplifying equation (7), we get the conversion equation between capillary suction and film suction: Where n is the proportionality factor between the thickness of the thin film water and the capillary radius, a dimensionless quantity, From equation (8), we can see that the capillary suction and the film suction are in linear positive proportion, and the capillary suction and the film suction are equivalent, so the change law of the two with temperature is highly consistent. Since capillary suction is the surface force for the entire capillary cross section, and the ice pressure in the pores is also the surface force for the entire capillary cross section; when porous ice is formed, the pore ice pressure, capillary suction, and external water pressure on the curved ice-water interface are balanced, that is: Pc+Pew=Pi(9) For the ideal hemispherical interface curvature, let: κ1 = 1 / R1 + 1 / R2 = 2 / R, then R1 = R2 = R, R is the effective radius of the pore, It can be seen that the capillary suction force of the curved ice-water interface is: The theoretical ice pressure when the capillary freezes (under equilibrium state) is: Where: Pi,e is the theoretical ice pressure (under equilibrium state); when the capillary is frozen, Where: Tf is the capillary freezing temperature, Combining equations (11) and (12), we can obtain: Transforming equation (13), we get: Comparing equations (6) and (14), it can be seen that when the external water pressure Pew approaches zero, the freezing temperature given by the capillary freezing model is completely consistent with the freezing temperature derived from the Gibbs-Thomson equation, indicating that the constructed capillary freezing model is reasonable. Step 3, calculate the capillary critical aperture change equation, According to equation (14), the capillary freezing temperature equation that varies with the critical pore size can be obtained: Where: R GT is the critical pore radius of the freezing capillary, The influence of external water pressure is negligible, that is: P ew = 0, changing equation (15), we can get the critical pore radius equation under any negative temperature condition: Where: C1 = (2γ SL ×ν S ×T A ) / L≈0.0558μm·℃ is a constant, From equation (16), 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 temperature, the smaller the pore size of the frozen capillary. In addition, substituting equation (11) into equation (16), we can obtain: Where: c1 = 2γ SL ≈63.54mN / m, which is a constant. Step 4: Confirm the corresponding relationship between the freezing edge permeability coefficient and the critical pore radius. From equation (17), we can see that the critical pore radius of the capillary is inversely proportional to the first power of the theoretical ice pressure. This 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. At the same time, the permeability coefficient of the frozen edge decreases rapidly due to the blocking of the seepage channel by pore ice. The permeability equation of the frozen edge under different temperature conditions can be obtained: Where: k uf is the permeability coefficient of unfrozen soil; k ff is the permeability coefficient of the frozen edge; β is a power, which takes a negative value; T f is the freezing front temperature; T s is the freezing temperature, Combining equations (16) and (18), we can obtain the capillary critical pore radius R GT , frozen edge permeability coefficient k ff As temperature changes, That is: capillary critical pore radius R GT , frozen edge permeability coefficient k ff The trend of temperature change is consistent. Assume that the freezing front temperature is T f Assuming that the temperature is zero degrees Celsius, substituting equation (16) into equation (18) and unifying the dimensions, we can obtain: From equation (19), we know that the critical pore radius R GT The larger the value, the smaller the decrease of the freezing edge permeability coefficient, and the critical pore radius R GT The smaller it is, the greater the decrease in the permeability coefficient of the frozen edge is, and it is magnified by -β times.

2. The occurrence evolution model of frozen capillaries according to claim 1, characterized in that: In step 3 and step 4, When β is -8, the relationship between the pore diameter, the freezing edge permeability ratio and the freezing temperature is shown in Table 3: Table 3 Relationship between pore diameter, freezing temperature and permeability coefficient change rate Note: c SL =0.42g SL =31.77mN / m, It can be seen from Table 3 that the smaller the critical pore radius, the lower the corresponding freezing temperature. Combined with Table 1, the boundary between capillary water and film water is D = 0.1 μm, the corresponding freezing temperature is -1.131 ° C, and the corresponding freezing edge permeability coefficient decreases by 2.4‰. It can be seen that the freezing state of capillary water plays a dominant role in the change of water migration speed. By controlling the capillary water content, water migration can be strongly inhibited, thereby achieving the purpose of reducing frost heave.

3. The method for suppressing frost heave of the frozen capillary occurrence evolution model according to any one of claims 1 to 2, characterized in that: The steps include: Controlling capillary water content by freezing after pre-grouting, Freezing after pre-grouting specifically includes: First, the grouting pipe is drilled to replace the pore water with chemical slurry, thereby blocking the capillary water migration channel and increasing the penetration resistance. Then, the freezing pipe is solidly driven, and the low-temperature bonding ability of ice is used to increase the strength, deformation modulus and impermeability of the freezing curtain.

4. The method for suppressing frost heave of the frozen capillary occurrence evolution model according to claim 3, characterized in that: When the overburden pressure of 1.0 MPa is applied to the soil, the overburden pressure is equivalent to the ice pressure inside the condensed ice. Substituting it into equation (17), the critical pore radius of the frozen capillary is obtained as: From equation (20), we can know that the critical pore diameter is: D GT =2R GT =127.08nm=0.127μm, the corresponding freezing temperature of the warm end of the condensed ice is T s is -0.891℃; Substituting equation (20) into equation (19), we find that the permeability coefficient of the frozen edge zone drops significantly to 6.3‰ when it is not frozen. This indicates that overburden pressure can strongly inhibit water migration.

Images