Method for determining content of unfrozen water in three-dimensional pores of frozen soil under freezing and thawing cycle

Abstract

The invention is suitable for the technical field of frozen soil engineering, and provides a method for determining the content of unfrozen water in three-dimensional pores of frozen soil under freezing and thawing circulation. According to the method, a frozen soil thawing process under a freezing and thawing cycle condition is focused, the adsorption effect and the capillary effect of water are combined, based on a three-dimensional pore structure, the quantitative relation between the unfrozen water content and the temperature, the medium size and the pore size is established, the change of the unfrozen water content is divided into three states, and an expression equation is deduced by combining a microscopic geometrical relation for each state; when the values of variables such as the temperature, the medium size and the pore size are known, the unfrozen water content can be quickly and accurately determined by judging the state of the unfrozen water and substituting the state into the corresponding equation, and the calculation efficiency and accuracy are effectively improved. The method not only provides a new thought for characterizing the unfrozen water content of the frozen soil in the freezing and thawing cycle process, but also can assist the geophysical prospecting work of the underground water in the frozen soil region, and especially has important application value for detecting the underground water content in the frozen soil region by using a magnetic resonance technology.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of frozen soil engineering, and particularly relates to a method for determining the unfrozen water content in three-dimensional pores of frozen soil under freeze-thaw cycles. BACKGROUND

[0002] As a temperature-sensitive geologic body, the physical properties of the active layer frozen soil on the plateau change with temperature. The freeze-thaw process of the frozen soil causes the conversion of water-ice phase, which causes the interaction among the pores, ice and water in the frozen soil medium, accompanied by a series of freeze-thaw cycle phenomena such as pore frost heaving, ice freezing and unfrozen water migration, resulting in the extremely unstable pore structure, unfrozen water content and ice occurrence state of the frozen soil. In this case, it is of great significance to accurately obtain the relationship between the unfrozen water content and the pore distribution and temperature change.

[0003] A method for obtaining the unfrozen water content in rocks under freeze-thaw cycles is disclosed in Chinese patent CN110806422A. The method prepares a rock column sample, saturates the rock column sample with formation water, obtains a T2 spectrum curve through nuclear magnetic resonance testing, converts the T2 spectrum curve into a nuclear magnetic pore throat distribution curve, and then substitutes it into an integral formula to obtain the relationship curves between the unfrozen water content and temperature at the time of melting and freezing, respectively. This method has the advantages of high precision, high reliability and easy access to the unfrozen water content. A method for calculating the unfrozen water content of frozen soil considering the initial water content is disclosed in Chinese patent CN115047032A. The method obtains a theoretical formula for the unfrozen water content in frozen soil considering the initial water content by the steps of soil sampling, parameter measurement and substitution of the calculation coefficient into the function, and uses the obtained formula to calculate the unfrozen water content in the soil freeze-thaw process. This method has the advantages of simple expression, convenient use and fast calculation of the unfrozen water content in the soil freezing and thawing process.

[0004] However, both of the above methods have certain limitations in actual application. For the method disclosed in patent CN110806422A, it needs to prepare a rock sample first, and then perform a series of conversion calculations after nuclear magnetic resonance testing. The overall process is relatively cumbersome, and the calculation process does not consider the geometric relationship between the pore and the unfrozen water system in detail. The method disclosed in patent CN115047032A focuses on the resistivity model, measures the change of soil resistivity in the freeze-thaw process, and analyzes the relationship between the change of resistivity and the change of unfrozen water content and temperature. However, resistivity measurement is an indirect measurement mode, and the measurement result is easily disturbed by various external factors. At the same time, this method does not consider the changes in the form of unfrozen water caused by adsorption and capillary action, and the changes in the form of unfrozen water will directly cause the deviation of the calculation result of the unfrozen water content and affect the accuracy of the calculation.

[0005] In view of the above deficiencies of the prior art, the present application provides a method for determining the unfrozen water content in the three-dimensional pores of frozen soil under freeze-thaw cycles. SUMMARY

[0006] The purpose of the present application is to provide a method for determining the unfrozen water content in the three-dimensional pores of frozen soil under freeze-thaw cycles, aiming to solve the problems raised in the background art.

[0007] The purpose of the present application is achieved by the following technical solutions: A method for determining the unfrozen water content in the three-dimensional pores of frozen soil under freeze-thaw cycles, comprising the following steps: Sample acquisition and parameter determination: acquire a frozen soil sample and determine its basic physical parameters; Temperature measurement: perform a freeze-thaw cycle process on the frozen soil sample and monitor its temperature change in real time; State determination: calculate the numerical value of the capillary water meniscus curvature radius r and determine the unfrozen water state of the frozen soil sample at the current temperature; the state includes: State 1: when r=0, only adsorbed water exists in the system; State 2: when 0 State 3: when r> the inscribed sphere radius of the pore model, the capillary water is connected; Unfrozen water content calculation: according to the determined state, use the corresponding unfrozen water content calculation formula to calculate the unfrozen water content under the corresponding state.

[0008] Further, in the state determination step, the capillary water meniscus curvature radius r is calculated by the following formula: ; Wherein: is the capillary water contact angle; is the ice-water interface free energy coefficient; is the capillary water pressure.

[0009] Further, the capillary water pressure is calculated by the total pressure of water and the adsorbed water pressure , and the relationship is as follows: ; Wherein: the adsorbed water pressure is composed of molecular force , electrostatic force and structural force , and the relationship is as follows: .

[0010] Further, in the state determination step, the inscribed sphere radius of the pore model is solved according to a geometric relationship as ) , wherein is the medium average radius of the sample.

[0011] Further, in the state 1, the unfrozen water content is equal to the adsorbed water content, wherein the adsorbed water volume is equal to the product of the surface area and the adsorbed water thickness d , the unfrozen water content is solved according to a geometric relationship as ; , wherein is the density of water.

[0012] Further, in the state 2, the unfrozen water content is equal to the sum of the adsorbed water content and the capillary water content, the unfrozen water content is solved according to a geometric relationship as ; , wherein the integral upper limit is solved according to a geometric relationship as , is the distance from the vertex of the capillary water meniscus to the bottom edge, is the capillary water cross-sectional area, is the included angle set in the geometric relationship.

[0013] Further, in the state 3, the unfrozen water volume is equal to the difference between the total pore volume and the ice volume, the unfrozen water content is solved according to a geometric relationship as .

[0014] Compared with the prior art, the present application has the beneficial effects that: The present application focuses on the thawing process of frozen soil under freeze-thaw cycle conditions, fully considers the influence of water adsorption and capillary action on the form of unfrozen water, and based on the dense distribution structure of the medium, a technical solution is constructed based on three-dimensional pore structure: on the one hand, the quantitative relationship between the unfrozen water content and temperature, medium size, pore size is established, the change of the unfrozen water content in the thawing process is divided into three states, and the expression formula is derived according to the micro-geometric relationship for each state; on the other hand, when the temperature, medium size and pore size and other variable values are known, the state of the unfrozen water can be determined and substituted into the corresponding formula to quickly and accurately determine the unfrozen water content, effectively improving the calculation efficiency and accuracy. The present application not only provides a new idea for the characterization of the unfrozen water content of frozen soil in the freeze-thaw cycle process, but also assists the groundwater geophysical work in the frozen soil area, especially has important application value for detecting the groundwater content in the frozen soil area by using magnetic resonance technology. BRIEF DESCRIPTION OF DRAWINGS​​​

[0015] Figure 1 This is a flowchart of the method of the present invention.

[0016] Figure 2 This is a schematic diagram of a three-dimensional medium with a tight distribution; where (a) is a left and right isometric axonometric view; and (b) is a front view.

[0017] Figure 3 This diagram illustrates the state changes of unfrozen water during the melting process; (a) represents the initial stage of melting (no capillary water); (b) represents the formation of capillary water before its convergence; (c) represents the critical point of capillary water convergence; (d) represents the stage after capillary water convergence; and (e) represents the end of melting.

[0018] Figure 4 This is a flowchart for determining the state of unfrozen water.

[0019] Figure 5 The diagram shows the solution for the radius of curvature r of the capillary water curve surface. Detailed Implementation

[0020] In order to provide a clearer understanding of the technical features, objectives and beneficial effects of the present invention, the technical solution of the present invention will now be described in detail below, but it should not be construed as limiting the scope of implementation of the present invention.

[0021] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0022] This invention provides a method for determining the unfrozen water content in the three-dimensional pores of frozen soil under freeze-thaw cycles. In freeze-thaw cycle studies, the core variables of frozen soil samples include pore distribution, temperature, and unfrozen water content. Temperature is a variable that is easily measured directly, while pore distribution is relatively stable and unrelated to temperature changes. Unfrozen water content, however, is influenced by both pore distribution and temperature, and these two factors jointly determine the dynamic changes in unfrozen water content. Therefore, the core objective of this invention is to establish a quantitative relationship among pore distribution, temperature, and unfrozen water content. By using directly measurable temperature combined with known pore distribution parameters, the unfrozen water content can be accurately calculated. The specific method is as follows (flowchart shown). Figure 1 (as shown) I. Sample Acquisition and Parameter Measurement; Obtain frozen soil samples and determine their basic physical parameters (mean radius of the medium of the sample). Average pore radius ); II. Temperature Measurement; The frozen soil sample was subjected to a sufficient freeze-thaw cycle (placed for a set duration in a temperature-controlled instrument). During this process, the internal medium distribution of the frozen soil tended to be uniform and densely distributed. Figure 2As shown in (a) and (b), the temperature changes of the frozen soil samples were monitored in real time during the freeze-thaw cycle and subsequent thawing analysis, and the current temperature was recorded. data.

[0023] III. Determination of State and Calculation of Unfrozen Water Content; Taking the melting process as an example, initially only adsorbed water exists in the system, and the unfrozen water content equals the adsorbed water content, which is defined as state 1. As the temperature rises, melting proceeds, the thickness of the adsorbed water changes, and capillary water appears. At this point, the unfrozen water content equals the sum of the adsorbed water content and the capillary water content, which is defined as state 2. When the temperature continues to rise, melting continues until the capillary water reaches contact. At this point, the unfrozen water volume equals the difference between the total pore volume and the ice volume, which is defined as state 3. The above state changes are as follows: Figure 3 As shown in (a)-(e), the methods for calculating the unfrozen water content differ for the three states.

[0024] Regarding the determination of the three states during melting mentioned above, this invention classifies the states based on the radius of curvature r of the capillary manifold surface: when r = 0, the system is in state 1; when 0 < r < the radius of the inscribed sphere of the pore model, the system is in state 2; when r > the radius of the inscribed sphere of the pore model, the system is in state 3. The above-mentioned unfrozen water state determination process is as follows: Figure 4 As shown. Based on geometric relationships, the radius of the inscribed sphere of the pore model can be calculated as ( ) ,in Let r be the average radius of the medium in the sample. The derivation of r is as follows: Step 1: Derivation of the radius of curvature r of the capillary water trap surface (including calculation of secondary correlation parameters); (1) The radius of curvature r of the capillary water trap surface can be obtained from the following formula: Formula 1: ; in: The capillary water contact angle is close to 0°. The free energy coefficient at the ice-water interface; It is the capillary water pressure.

[0025] (2) The capillary water pressure described in Formula 1 It can be solved by the following formula: Formula 2: ; Formula 3: ; in: The total pressure of the water; This represents the pressure of adsorbed water, determined by molecular forces. electrostatic force and structural forces co-constitute.

[0026] (3) The molecular forces , electrostatic forces , and structural forces of the molecule of Formula 3 can be solved by the following equation: Equation 4: ; Equation 5: ; Equation 6: ; where: H is the Hamaker constant (J); h is the thickness of the adsorbed water; ε is the relative permittivity of liquid water; ε0 is the permittivity of vacuum; Δφ is the potential difference of the interacting surfaces; a is the surface correlation length; d is the characteristic thickness of the hydration layer.

[0027] (4) The thickness of the adsorbed water of Equations 4, 5, and 6 can be solved by the following equation: Equation 7: ; where: and are parameters related to the interfacial interaction potential energy; , Tm is the melting point temperature, T is the current temperature; ρ is the density of water; L is the latent heat of phase transition; R is the medium average radius of the sample.

[0028] (5) The melting point temperature of Equation 7 can be solved by the following equation: Equation 8: ; where: 273.15 K; ρ is the density of ice; R is the average radius of the pores.

[0029] (6) The total pressure of water of Equation 2 can be solved by the following equation: Equation 9: ; where: and are the total pressure of ice and the density of ice, respectively.

[0030] Step 2: Summary of the independent variable of the capillary water meniscus curvature radius r; Through the hierarchical derivation of Step 1, it is finally determined that the independent variable of r is only related to the current temperature , the average radius of the pores , and the average radius of the medium of the sample R (solving logic as Figure 5 shown).

[0031] Step 3: Calculation of unfrozen water content; (1) Calculation of unfrozen water content in state 1 : When r = 0, the system is in state 1, and the unfrozen water content is equal to the adsorbed water content, where the adsorbed water volume is equal to the product of its surface area in contact with the medium and the adsorbed water thickness , and the unfrozen water content is solved according to the geometric relationship as: Equation 10: ; (2) Calculation of unfrozen water content in state 2 : When 0 < r < ( ) , the system is in state 2, and the unfrozen water content is equal to the sum of the adsorbed water content and the capillary water content, and the unfrozen water content is solved according to the geometric relationship as: Equation 11: ; where: ; is the distance from the vertex of the capillary water meniscus to the bottom edge; is the capillary water cross-sectional area; is the included angle set in the geometric relationship.

[0032] The distance from the vertex of the capillary water meniscus to the bottom edge and the capillary water cross-sectional area , according to the geometric relationship, can be solved by the following equation: Equation 12: ; Equation 13: ; where and (same as , a set parameter in the geometric relationship solving process, not physically meaningful) are reciprocal, and according to the geometric relationship, we have: Equation 14: ; Equation 15: ; (3) Calculation of unfrozen water content in state 3 : When r > ( ) When the system is in state 3, the ice is completely surrounded by water, and the unfrozen water volume is equal to the difference between the total pore volume and the ice volume. According to the geometric relationship, the unfrozen water content is solved as : Equation 16: .

[0033] The above is only the preferred embodiment of the present application, it should be noted that for those skilled in the art, without departing from the concept of the present application, can also make several variations and improvements, these should also be considered as the protection scope of the present application, these will not affect the effect and the practicality of the patent of the present application.

Claims

1. A method for determining the unfrozen water content in the three-dimensional pore of frozen soil under freeze-thaw cycles, characterized by, The method comprises the following steps: Sample acquisition and parameter determination: acquire frozen soil samples and determine their basic physical parameters; Temperature measurement: perform freeze-thaw cycle process on the frozen soil samples and monitor their temperature changes in real time; State determination: calculate the numerical value of the capillary water meniscus curvature radius r and determine the unfrozen water state of the frozen soil samples at the current temperature; the states include: State 1: when r = 0, only adsorbed water exists in the system; State 2: when 0 < r < the inscribed sphere radius of the pore model, adsorbed water and capillary water coexist in the system; State 3: when r > the inscribed sphere radius of the pore model, capillary water is in contact; Unfrozen water content calculation: according to the determined state, the corresponding unfrozen water content calculation formula is used to calculate the unfrozen water content under the corresponding state.

2. The method of determining unfrozen water content in frozen soil three-dimensional pores under freeze-thaw cycles according to claim 1, characterized in that, In the state determination step, the capillary water meniscus curvature radius r is obtained by calculation through the following formula: ； wherein: is the capillary water contact angle; is the ice-water interfacial free energy coefficient; is the capillary water pressure.

3. The method of determining unfrozen water content in frozen soil three-dimensional pores under freeze-thaw cycles according to claim 2, characterized in that, The capillary water pressure By the total pressure of water With the adsorbed water pressure The relationship is calculated as follows: ； Where: adsorbed water pressure Molecular forces Electrostatic forces Structural forces Together, the relationships are as follows: 。 4. The method of determining unfrozen water content in frozen soil three-dimensional pores under freeze-thaw cycles according to claim 1, characterized in that, In the state determination step, the inscribed sphere radius of the pore model is solved according to a geometric relationship as ) wherein is the medium average radius of the sample.

5. The method of determining unfrozen water content in frozen soil three-dimensional pores under freeze-thaw cycles according to claim 4, characterized in that, In the state 1, the unfrozen water content is equal to the adsorbed water content, where the adsorbed water volume is equal to the product of its surface area and the adsorbed water thickness d The unfrozen water content is solved from the geometric relationship as: ​ ； wherein is the density of water.

6. The method of determining unfrozen water content in frozen soil three-dimensional pores under freeze-thaw cycles according to claim 5, characterized in that, In the state 2, the unfrozen water content is equal to the sum of the adsorbed water content and the capillary water content, and the unfrozen water content is solved according to the geometric relationship is: ； Wherein, according to the geometric relationship, the integral upper limit is solved , The distance from the vertex of the capillary water bend to the bottom edge, The capillary water cross-sectional area, The angle set in the solution of the geometric relationship.

7. The method of determining unfrozen water content in frozen soil three-dimensional pores under freeze-thaw cycles according to claim 5, characterized in that, In the state 3, the unfrozen water volume is equal to the difference between the total pore volume and the ice volume, and the unfrozen water content is solved according to the geometric relationship is: 。

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