CN111830235B - Frozen soil model and method for constructing frozen soil moisture migration model - Google Patents
Frozen soil model and method for constructing frozen soil moisture migration model Download PDFInfo
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Abstract
The invention provides a frozen soil body model and a method for constructing a frozen soil body water migration model. Wherein, freezing soil body model includes: the freezing edge area is arranged on the side of the freezing edge area, and the side of the freezing edge area, which is far away from the freezing edge area, of the frozen area is provided with an overlying pressure towards the freezing edge area; a soil particle matrix and a plurality of capillaries with different diameters are arranged in the freezing edge area, and each capillary penetrates through the soil particle matrix to be communicated with the ice lens body and the non-freezing area; pore ice is formed in the first number of capillaries, and unfrozen water films are formed on the soil particle matrix and the inner wall surfaces of the first number of capillaries; the inner walls of the second number of capillaries form an unfrozen water film, and the capillary water is filled in the capillaries. The frozen soil body model provided by the invention combines a capillary water migration mechanism and a film water migration mechanism, and can comprehensively and reasonably explain the soil body frost heaving phenomenon.
Description
Technical Field
The invention relates to the field of frozen soil physics, basic thermodynamics and hydrodynamics, in particular to a frozen soil body model and a construction method of a frozen soil body water migration model.
Background
For the research of frost heaving mechanism, two frost heaving theories are widely accepted at present. Namely: the capillary theory proposed by Everett (1961), also known as the first frost heave theory. Capillary suction is considered as the driving force for water migration during ice segregation, and the amount of frost heave and frost heave force are quantitatively estimated. However, the capillary theory cannot explain the formation of freezing edges and discontinuous partial ice, and also underestimates the water migration rate and the frost heaviness of fine-grained soil. In view of the deficiencies of capillary theory, Miller (1978) proposed the freezing edge theory, also known as the second frost heave theory. It is believed that a region with low water content, low moisture permeability and no frost heaving exists at the freezing frontal surface and the warmest ice lens bottom surface, called the freezing edge, and water migrates through the thin film water on the particle surface to the warm end of the ice lens body under the action of generalized driving forces such as temperature gradient, resulting in the growth of the ice lens body. However, the influence of unfrozen water is not considered by the freezing edge theory, and the phenomenon of uneven frost heaving is difficult to explain, so that further improvement is needed.
Currently, there are two moisture migration mechanisms widely recognized, namely: capillary water migration mechanism and thin film water migration mechanism. However, the scholars at home and abroad only study on a single water migration mechanism, and the scholars do not organically combine the two water migration mechanisms, so that a capillary-film water migration mechanism model for comprehensively and reasonably explaining the soil frost heaving phenomenon is lacked.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art or the related art.
In view of the above, an object of the present invention is to provide a frozen soil mass model.
The invention further aims to provide a method for constructing a frozen soil body water migration model.
In order to achieve the above object, the technical solution of the present invention provides a frozen soil model, including: the freezing edge area is arranged in the freezing edge area, the freezing lens body is formed on one side of the freezing edge area close to the freezing edge area, the covering pressure towards the freezing edge area is applied to one side of the freezing edge area far away from the freezing edge area, the warm end of the freezing lens body is arranged on one side of the freezing lens body close to the freezing edge area, and the freezing front surface is formed on one side of the freezing edge area close to the non-freezing area; a soil particle matrix and a plurality of capillaries with different diameters are arranged in the freezing edge area, and each capillary penetrates through the soil particle matrix to be communicated with the ice lens body and the non-freezing area; wherein pore ice forms within the first number of capillaries and a curved ice-water interface forms within the first number of capillaries; the soil particle matrix and the inner wall surfaces of the first number of capillaries form unfrozen water films, the second number of capillaries are unfrozen, the inner walls of the second number of capillaries form unfrozen water films, and the capillaries are filled with capillary water.
The frozen soil body model comprises a frozen area, a frozen edge area and an unfrozen area which are sequentially arranged, the basic structure of natural frozen soil is simulated through the frozen area, the frozen edge area and the unfrozen area, a soil particle matrix and a plurality of capillaries with different diameters are arranged in the frozen edge area, each capillary penetrates through the soil particle matrix to be communicated with an ice lens body and the unfrozen area, the capillaries are used for simulating the frozen area in the naturally formed frozen soil, the pores between the frozen edge area and the unfrozen area, pore ice is formed in a first number of capillaries, and a bent ice-water interface is formed in a first number of capillaries; the capillary-thin film water migration model is characterized in that unfrozen water films are formed on the soil particle matrixes and the inner wall surfaces of the capillaries of the first quantity, thin film water migration data are obtained according to the unfrozen water films formed on the wall surfaces of the capillaries of the first quantity which are frozen, the unfrozen water films are formed on the inner walls of the capillaries of the second quantity which are not frozen, capillary water is filled in the capillaries, and migration data of the capillary water in a freezing edge area are obtained, so that the model can provide the capillary water migration data of the freezing edge area and the thin film water migration data in the capillaries, and a frozen soil body model can combine a capillary water migration mechanism and a thin film water migration mechanism to comprehensively and reasonably explain a frost heaving phenomenon.
Furthermore, the pore diameter of the plurality of capillaries ranges from 0.1 μm to 1000 μm.
Furthermore, the capillaries are normally distributed according to the diameter, and the capillaries are randomly distributed in the freezing edge area.
Furthermore, the thickness of the unfrozen water film is in a range of 0.1nm to 50 nm.
The invention provides a method for constructing a frozen soil body water migration model, which comprises the following steps:
obtaining a theoretical ice pressure equation under an equilibrium state according to a generalized Clapperon (Clapeyron) equation;
acquiring a freezing temperature equation of the capillary according to a theoretical ice pressure equation and a freezing soil body model;
acquiring a segregation-freezing temperature equation according to a theoretical ice pressure equation and a frozen soil body model;
acquiring a migration driving force equation at the warm end of the ice lens body according to a film water hydraulic pressure equation and a frozen soil body model of Gilpin (translation);
obtaining a relational expression between the total permeability coefficient of the freezing edge and the temperature according to the statistical result of a Thomas test;
and (4) obtaining an explicit equation of the water migration speed according to Darcy's law in combination with a relational expression between the total permeability coefficient of the freezing edge and the temperature and a migration driving force equation, and completing the construction of a frozen soil water migration model.
Further, the step of obtaining the freezing temperature equation of the capillary according to the theoretical ice pressure equation and the frozen soil model specifically comprises the following steps:
acquiring a capillary suction equation on a curved ice water interface according to a capillary theory;
and acquiring a capillary freezing temperature equation according to the theoretical ice pressure equation and the capillary suction equation.
Further, the step of obtaining the segregation-freezing temperature equation according to the theoretical ice pressure equation and the frozen soil model specifically comprises the following steps:
acquiring actual ice pressure;
acquiring the sum of the overlying pressure and the separation pressure;
determining that the actual ice pressure is greater than the sum of the overlying pressure and the separation pressure, and acquiring a partial condensation ice forming condition equation;
and acquiring a segregation-freezing temperature equation according to the segregation ice forming condition equation.
Further, the method for obtaining the migration driving force equation at the warm end of the ice lens body according to the film hydraulic pressure equation of Gilpin (Gilpin) and the frozen soil body model specifically comprises the following steps:
obtaining the thickness h of the unfrozen water film in an equilibrium state;
acquiring the thickness y of the unfrozen water film in the non-equilibrium state;
acquiring a theoretical hydraulic equation when y is h in an equilibrium state and an actual hydraulic pressure when y is h in a non-equilibrium state according to a film water hydraulic equation;
acquiring a hydraulic migration driving force equation when the unfrozen water film is in a non-equilibrium state and y is equal to h according to a theoretical hydraulic equation when y is equal to h in the equilibrium state and actual hydraulic pressure when y is equal to h in the non-equilibrium state;
acquiring a normal equilibrium equation of the unfrozen water film in an equilibrium state and a normal equilibrium equation of the unfrozen water film in a non-equilibrium state according to the pressure difference between the ice pressure and the hydraulic pressure;
acquiring an ice pressure migration driving force equation at the position of y & lth & gt according to a hydraulic migration driving force equation at the position of y & lth & gt, a normal balance equation of the unfrozen water film in a balanced state and a normal balance equation of the unfrozen water film in an unbalanced state;
according to the ice pressure migration driving force equation at the position where y is h; and acquiring a migration driving force equation of the warm end of the ice lens body under the condition of forming the segregation ice layer.
Further, the obtaining of the relation between the total permeability coefficient of the freezing edge and the temperature according to the permeability experiment of the frozen soil model specifically includes:
obtaining the permeability coefficient of a saturated soil body under the normal temperature condition;
acquiring the freezing temperature of the freezing frontal surface;
acquiring the segregation-freezing temperature of the warm end of the ice lens;
and determining a relational expression between the total permeability coefficient of the freezing edge and the temperature according to the permeability coefficient of the saturated soil body under the normal temperature condition, the freezing temperature of the freezing frontal surface and the segregation-freezing temperature of the warm end of the ice lens.
Further, the theoretical ice pressure equation is specifically:
the freezing temperature equation is specifically:
the segregation-freezing temperature equation is specifically as follows:
the migration driving force equation is specifically:
the relation between the total permeability coefficient of the freezing edge and the temperature is specifically as follows:
the explicit equation of the water migration speed is as follows:
wherein, the parameters in the formula are specifically as follows: t is the temperature in centigrade of the ice-water interface, TA is the absolute freezing temperature of pure ice, K, and TA 273.15K, PS0 is the theoretical ice pressure in equilibrium, MPa, and gamma SL is the ice-water interface tension, g/s2R is the effective radius of a capillary, the unit is mum, PS is the actual ice pressure, the unit is MPa, POB is the overlying pressure, the unit is MPa, Psep is the separation pressure, the unit is MPa, PLd is the migration driving force, the unit is MPa, kuf is the permeability coefficient of the saturated soil body under the normal temperature condition, the unit is cm/s, kff is the total permeability coefficient of a freezing edge, the unit is cm/s, Tf is the freezing temperature of the freezing front surface, the unit is Ts is the segregation-freezing temperature of the warm end of the ice lens, the unit is ℃, g is the gravity acceleration, and the unit is m/s2Vff is the water migration velocity in cm/s, Vs is the specific volume of ice in s2The/m and the L are the phase change latent heat of pure water, and the unit is cm2/s2Lt is a permeation path of water migration, the unit is cm, beta is power, and the unit is dimensionless, the value is 8, rho w is the density of water, and the unit is g/cm3。
The technical scheme provided by the embodiment of the invention has the following beneficial effects: the capillary-film water migration mechanism model combines a capillary water migration mechanism and a film water migration mechanism to comprehensively and reasonably explain the soil body frost heaving phenomenon, and particularly, the capillary-film water migration mechanism model simultaneously considers the capillary water and film water dual migration mechanisms, overcomes the defects and shortcomings of a single water migration mechanism, and enriches the existing frost heaving mechanism; analysis of water migration driving force of the film is given, and the migration driving force is found to be derived from normal hydraulic pressure difference or ice pressure difference and represents the difference between theoretical pressure and actual pressure in an equilibrium state; establishing a freezing edge permeability coefficient model and giving a relational expression between the freezing edge permeability coefficient and the segregation-freezing temperature; an explicit equation of the water migration speed is given, the number of parameters is simplified, and the frost heaving rate and the frost heaving amount of the saturated soil body can be rapidly predicted.
Drawings
Figure 1 shows a schematic view of a frozen earth model of the invention;
FIG. 2 shows a stress analysis diagram of a frozen soil moisture migration model of the present invention;
FIG. 3 shows a schematic of the freeze edge permeability coefficient model of the present invention;
FIG. 4 shows a schematic of the calculated flow rate versus the experimental flow rate of the present invention.
The symbols in the figures are as follows:
1 frozen region, 2 frozen margin region, 3 non-frozen region, 4 ice lens body, 5 soil particle matrix, 7 capillary tube, 9 pore ice, 10 non-frozen water film, 11 capillary water, 12 bending ice-water interface, 14 overlying pressure, 16 warm end of ice lens body, 8 capillary pore freezing junction connecting lines with different pore diameters, 13 maximum pore diameter of non-frozen pore, 15 space x coordinate axis, 17 freezing front, 18 temperature coordinate axis, 19 front freezing temperature, 20 fractional freezing-freezing temperature, 21 theoretical ice pressure, 22 actual ice pressure, 23 migration driving force, 24 overlying pressure and separation pressure sum, 25 non-frozen region permeability coefficient, 26. permeability coefficient of thin film water in frozen capillary tube, 27 capillary water permeability coefficient in non-frozen capillary tube, 28 frozen margin total permeability coefficient, 29 frozen region permeability coefficient, 30 permeability coefficient coordinate axis.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention and advantageous effects thereof will be described in further detail below with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides a frozen earth model defining:
the technical scheme of the invention provides a frozen soil body model, which comprises the following steps: the frozen area 1, the freezing edge area 2 and the non-frozen area 3 are sequentially arranged, the basic structure of natural frozen soil is simulated through the frozen area 1, the freezing edge area 2 and the non-frozen area 3, an ice lens body 4 is formed on one side of the frozen area 1 close to the freezing edge area 2, an overlying pressure 14 facing the freezing edge area 2 is applied to one side of the frozen area 1 far away from the freezing edge area 2, an ice lens body warm end 16 is arranged on one side of the ice lens body 4 close to the freezing edge area 2, and a freezing frontal surface 17 is formed on one side of the freezing edge area 2 close to the non-frozen area 3; a soil particle matrix 5 and a plurality of capillaries 7 with different diameters are arranged in the freezing margin area 2, each capillary 7 penetrates through the soil particle matrix 5 to be communicated with the ice lens body 4 and the non-freezing area 3, and the capillary 7 is used for simulating the naturally formed holes among the frozen area 1, the freezing margin area 2 and the non-freezing area 3 in the frozen soil; wherein pore ice 9 is formed within the first number of capillaries 7 and a curved ice-water interface 12 is formed within the first number of capillaries 7; the soil particle matrix 5 and the inner wall surfaces of the first number of capillaries 7 form an unfrozen water film 10, whereby within the capillaries 7 having the pore ice 9, thin film water within the unfrozen water film 10 can flow from the unfrozen zone 3 to the ice lens body warm end 16 of the frozen zone 1; the second quantity of capillaries 7 are not frozen, the inner walls of the second quantity of capillaries 7 form an unfrozen water film 10, and the capillaries 7 are filled with capillary water 11, specifically, the capillaries 7 with the pore diameters smaller than the maximum pore diameter 13 of the unfrozen pores are not frozen, so that the water in the unfrozen area 3 flows to the warm end of the ice lens body in the frozen area 1 in a capillary water 11 mode; according to the unfrozen water film 10 formed on the surface of the tube wall of the first number of the frozen capillaries 7, the film water permeability coefficient 26 of the unfrozen water film 10 is obtained, the unfrozen water film 10 is formed through the inner wall of the second number of the unfrozen capillaries 7, the capillaries 7 are filled with the capillary water 11, and the permeability coefficient 27 of the capillary water 11 in the freezing edge area 2 is obtained, so that the model can provide the capillary water 11 migration data of the freezing edge area and the film water migration data in the capillaries 7, and the frozen soil model can combine the capillary water 11 migration mechanism and the film water migration mechanism to explain the frost heaving phenomenon in a comprehensive and reasonable soil body.
As shown in fig. 1 and 2, the frozen soil model proposed by the present invention further defines:
the pore diameter range of the capillaries 7 is 0.1-1000 μm to simulate the diameter of pores in the frozen soil in nature, so that the migration data of the capillary water 11 and the thin film water obtained by the capillaries 7 is closer to the real migration data of the capillary water 11 and the thin film water in the pores in the frozen soil.
As shown in fig. 1, according to an embodiment of the invention, further defined is:
the plurality of capillaries 7 are normally distributed in diameter, and the plurality of capillaries 7 are randomly distributed in the freezing edge region, and specifically, the pore distribution is found to substantially conform to the positive distribution by a low-field nuclear magnetic resonance test.
Wherein, it should be noted that fig. 1 is a water migration schematic diagram, which illustrates that the capillary water migration and the film water migration exist in the freezing edge region at the same time, and gives a freezing temperature equation and a segregation-freezing temperature equation; FIG. 2 is a water migration driving force analysis, unifying the migration driving force of frozen macro-pores and unfrozen micro-pores at the warm end of the ice lens body. FIG. 3 is a permeability coefficient analysis of frozen, frozen margin and unfrozen regions, showing the relationship between frozen margin permeability coefficient and temperature; specifically, 19 represents the freezing temperature of the front, 25 represents the permeability coefficient of the unfrozen area, 26 represents the permeability coefficient of the film water in the freezing capillary tube, 27 represents the permeability coefficient of the capillary water in the unfrozen capillary tube, 28 represents the total permeability coefficient of the freezing edge, 29 represents the permeability coefficient of the frozen area, 30 represents the coordinate axis of the permeability coefficient, and by combining the graph 1, the graph 2 and the graph 3, the change rule of each parameter along with the segregation-freezing temperature is obtained, and finally, an explicit equation of the water migration speed is given.
As shown in fig. 1, according to an embodiment of the present invention, further defined are:
the thickness of the unfrozen water film 10 ranges from 0.1nm to 50nm, so that the thickness of the unfrozen water film 10 existing in the frozen soil in the natural environment is simulated, and the accuracy of the film water migration data of the unfrozen water film 10 is improved.
Another embodiment of the present invention provides a method for constructing a frozen soil moisture migration model, including the following steps:
step 1: obtaining a theoretical ice pressure equation under an equilibrium state according to a generalized Clapperon (Clapeyron) equation;
and 2, step: acquiring a freezing temperature equation of the capillary 7 according to a theoretical ice pressure equation and a freezing soil body model;
and step 3: acquiring a segregation-freezing temperature equation according to a theoretical ice pressure equation and a frozen soil body model;
and 4, step 4: acquiring a migration driving force equation at the warm end 16 of the ice lens body according to a film hydraulic pressure equation and a frozen soil body model of Gilpin (Gilpin);
and 5: obtaining a relation between the total freezing edge permeability coefficient 28 and the temperature according to the statistical result of the Thomas test;
step 6: and (4) obtaining an explicit equation of the water migration speed according to Darcy's law in combination with a relational expression between the total permeability coefficient 28 of the freezing edge and the temperature and a migration driving force equation, and completing the construction of a frozen soil water migration model.
Specifically, as shown in fig. 1 and fig. 2, by modifying the freezing edge region, a set of capillaries 7 are added inside, and a layer of film water is added on the inner wall of the capillary 7, both capillary water 11 migration in the freezing edge region and film water migration inside the capillary 7 are considered; according to the capillary theory, a freezing temperature equation of the capillary 7 is deduced, the freezing temperature is found to be inversely proportional to the pore diameter of the capillary 7, as shown by a capillary pore freezing point connecting line 8 with different pore diameters in fig. 1, fig. 2 and fig. 3, the smaller the pore diameter of the capillary 7 is, the smaller the total amount of pore ice 9 in the capillary 7 is gradually reduced, when the diameter of the capillary 7 is smaller than or equal to the maximum pore diameter 13 of the unfrozen pore, the capillary 7 is not frozen, and the capillary 7 is filled with capillary water 11, so that the capillary 7 in the freezing edge is sequentially frozen according to the pore diameter; in view of the interfacial tension, part of the small-hole capillary 7 is still in an unfrozen state all the time, so that two migration mechanisms of capillary water 11 and film water exist in the area of the freezing edge; through the analysis of the driving force of the film water migration, the model unifies the driving force equation of the capillary water 11 and the unfrozen water film 10 (also called as film water) at the warm end 16 of the ice lens body, in addition, according to the Poisea flow equation, the permeability coefficient equations of two migration mechanisms can be obtained, and the relational expression between the total permeability coefficient 28 of the freezing edge and the segregation-freezing temperature 20 is given by combining the results of the permeability test; combining with the law of Darcy, an explicit equation of the water migration speed of the unified model can be provided, and in detail, the freezing temperature of the capillary pores is reduced along with the reduction of the pore diameter according to the freezing temperature equation; when the actual ice pressure 22 is greater than the sum 24 of the overlying pressure and the separation pressure, new fractional ice is generated, and a fractional ice forming condition can be obtained by combining a theoretical ice pressure equation so as to obtain a fractional ice-freezing temperature equation; then, acquiring a migration driving force equation at the warm end 16 of the ice lens body according to a film water hydraulic equation and a frozen soil body model of Gilpin (Gilpin), thereby acquiring a tangential driving force for driving the film water in the capillary 7 to migrate; and obtaining a relational expression between the total permeability coefficient 28 of the freezing edge and the temperature according to the statistical result of the Thomas test, obtaining an explicit equation of the water migration speed according to the Darcy's law in combination with the relational expression between the total permeability coefficient 28 of the freezing edge and the temperature and the migration driving force equation, completing the construction of a frozen soil water migration model, and comprehensively and reasonably explaining the soil body frost heaving phenomenon according to the frozen soil water migration model.
As shown in fig. 2, according to an embodiment of the present invention, it is further defined that obtaining the freezing temperature equation of the capillary 7 according to the theoretical ice pressure equation and the frozen soil model specifically includes the following steps:
step 1: acquiring a capillary suction equation on a curved ice water interface according to a capillary theory;
step 2: and acquiring a freezing temperature equation of the capillary tube 7 according to the theoretical ice pressure equation and the capillary suction equation.
According to an embodiment of the present invention, it is further defined that obtaining the segregation-freezing temperature equation according to the theoretical ice pressure equation and the frozen soil model specifically includes the following steps:
step 1: acquiring an actual ice pressure 22;
and 2, step: acquiring the sum 24 of the overlying pressure and the separation pressure;
and step 3: it is determined that the actual ice pressure 22 is greater than the sum 24 of the overburden pressure and the separation pressure to obtain a partial ice formation condition equation.
And 4, step 4: and acquiring a segregation-freezing temperature equation according to the segregation ice forming condition equation.
According to an embodiment of the present invention, it is further defined that the obtaining of the migration driving force equation at the warm end 16 of the ice lens body according to the thin film hydraulic pressure equation of Gilpin (translation) and the frozen soil body model specifically comprises the following steps:
and 3, step 3: acquiring a theoretical hydraulic equation when y is h in an equilibrium state and an actual hydraulic equation of the unfrozen water film 10 when y is h in an non-equilibrium state according to the film water hydraulic equation and the thickness of the unfrozen water film 10;
and 4, step 4: acquiring a hydraulic migration driving force equation when the unfrozen water membrane 10 is in the non-equilibrium state and y is equal to h according to a theoretical hydraulic equation when y is equal to h in the equilibrium state and an actual hydraulic equation when yh is in the non-equilibrium state;
and 5: acquiring a normal equilibrium equation of the unfrozen water film 10 in an equilibrium state and a normal equilibrium equation of the unfrozen water film 10 in an unbalanced state according to the pressure difference between the ice pressure and the hydraulic pressure;
step 6: acquiring an ice pressure migration driving force equation at the position of y-h according to a hydraulic migration driving force equation at the position of y-h, a normal balance equation of the unfrozen water film 10 in a balanced state and a normal balance equation of the unfrozen water film 10 in an unbalanced state;
and 7: according to the ice pressure migration driving force equation at the position where y is h; the migration driving force equation of the ice lens body warm end 16 under the formation condition of the segregated ice layer is obtained.
Wherein y represents the thickness of the membrane water in the non-equilibrium state, h represents the thickness of the membrane water in the equilibrium state, the freezing process is a process that y approaches h infinitely, and it should be noted that y is h approaches h infinitely, and when calculating, y is h.
According to an embodiment of the present invention, it is further defined that obtaining the relationship between the total permeability coefficient 28 of the freezing edge and the temperature according to the permeability experiment of the frozen soil model specifically includes the following steps:
step 1: obtaining the permeability coefficient of a saturated soil body under the normal temperature condition;
and 2, step: the freezing temperature of the freezing front 17 is obtained, and generally 0 ℃ can be taken;
and step 3: acquiring the segregation-freezing temperature 20 of the warm end of the ice lens;
and 4, step 4: and determining a relation between the total permeability coefficient 28 of the freezing edge and the temperature according to the permeability coefficient of the saturated soil body under the normal temperature condition, the freezing temperature of the freezing frontal surface 17 and the segregation-freezing temperature 20 of the warm end of the ice lens.
In detail: fig. 1 and 2 are a frozen soil moisture migration unified model and a stress analysis diagram thereof, and fig. 3 is a freezing edge permeability coefficient analysis diagram. The explicit equation of the water migration speed can be deduced by combining a driving force equation and a freezing edge permeability coefficient equation.
The construction method of the frozen soil moisture migration model is specifically implemented as follows:
1. freezing temperature determination
As shown in fig. 2, the theoretical ice pressure equation is obtained: according to the generalized Clapeyron equation, the theoretical ice pressure 21 in the equilibrium state is:
in the formula: pS0The theoretical ice pressure in equilibrium 21; l is latent heat of fusion of water, and can be 3.34 × 109cm2/s2；vSSpecific volume of ice; t isAThe absolute freezing temperature of pure ice can be 273.15K; t is the temperature in degrees Celsius of the ice-water interface.
Acquisition of capillary attraction equation: according to the capillary theory, the equation of the capillary suction force on the curved ice water interface can be obtained:
in the formula: p isCCapillary attraction caused by interfacial tension; gamma raySLThe ice-water interfacial tension can be 29 mN/m; r is the effective radius of the capillary 7; theta is the contact angle.
Acquisition of freezing temperature equation: combining formula (1) and formula (2), and further according to the pore ice 9 formation conditions, PS0＝PCAnd θ is 180 °, the freezing temperature equation of the capillary 7 can be obtained:
from the formula (3), the freezing temperature of the capillary pores decreases as the pore diameter decreases.
2. Determination of the segregation-freezing temperature 20
As shown in fig. 2, as can be seen from the theoretical ice pressure equation (1), the theoretical ice pressure 21 gradually increases with decreasing temperature, and when the actual ice pressure 22 is greater than the sum 24 of the overlying pressure and the separation pressure, new segregated ice is generated, that is:
PS≥POB+Psep (4)
acquiring a partial ice forming condition equation: in formula (4): pSActual ice pressure 22; pOBIs an overburden pressure 14; psepIs the separation pressure. Combining the formulas (1) and (4), the formation condition of the partial freezing ice can be obtained:
transforming the formula (5) to obtain a segregation-freezing temperature equation:
3. migration driving force determination
The film water pressure equation is obtained from Gilpin (1979):
obtaining a theoretical hydraulic pressure equation at y-h under an equilibrium state:
from equation (7), the smaller the film thickness, the stronger the adsorption force. When y is h, the following is obtained:
in formula (8): pLThe inner part of the film water is hydraulically distributed; pLhThe theoretical hydraulic pressure at y-h under the equilibrium state; v. ofLSpecific volume of water; a is a universal constant; alpha is a power; h is the film water thickness.
And (5) obtaining a driving force equation of h hydraulic migration:
according to the hydraulic equilibrium condition, when the membrane water is in an unbalanced state, the thickness y of the membrane water is infinitely close to h, so that a hydraulic driving force is generated, namely, the hydraulic migration driving force equation at the position where y is h:
PLb＝PLh-PLy (9)
in formula (9): pLbIs the migration driving force 23; pLyIn an unbalanced state, the actual hydraulic pressure at h is infinitely close to y.
Acquiring a normal balance equation of the unfrozen water film 10 under equilibrium and a normal balance equation of the unfrozen water film 10 under non-equilibrium:
since the capillary 7 ice-water interface is curved, there is a pressure difference between the ice pressure and the hydraulic pressure:
wherein, the formula (10) is a normal equilibrium equation of the film water in an equilibrium state; equation (11) is the normal equilibrium equation of membrane water in the non-equilibrium state.
And (5) acquiring an ice pressure migration driving force equation at the position of y-h:
by combining the formulas (9), (10) and (11)
Acquisition of migration driving force equation of the ice lens body warm end 16:
as can be seen from equation (12), the migration driving force 23 can be expressed by either the hydraulic pressure difference or the ice pressure difference, each representing the difference between the theoretical pressure and the actual pressure in the equilibrium state. When the ice layer is formed, the ice alone will bear the full overburden pressure 14, so the migration driving force equation at the warm end 16 of the ice lens is:
4. freezing edge permeability coefficient
As shown in fig. 3, the statistical results of Thomas test give the relationship between freezing edge total permeability coefficient 28 and temperature:
in the formula: k is a radical ofufThe permeability coefficient of a saturated soil body under the normal temperature condition is shown; k is a radical offfTotal permeability coefficient for frozen rim 28; t isfThe freezing temperature of the freezing front 17; t issThe segregation-freezing temperature of the warm end of the icelens is 20. As can be seen from equation (14), the total freezing edge permeability coefficient 28 increases as a higher order power function with decreasing temperature between the freezing front 17 and the warm end 16 of the ice lens body, so that the lower the segregation-freezing temperature 20, the lower the total freezing edge permeability coefficient.
5. Rate of water migration
Acquiring an explicit equation of moisture migration speed:
assuming that the water migration in the freezing edge region conforms to Darcy's law, it can be obtained
Combining equations (13), (14) and (15), an explicit equation for the water migration velocity can be obtained:
as can be seen from the formula (16), the segregation-freezing temperature is 20TsIs the main control parameter of the explicit equation of the moisture migration speed.
Wherein L istIs the permeation path for moisture migration, β is the power, and ρ w is the density of water.
One embodiment of the invention also provides a frozen soil water migration model inspection method, which comprises the following specific inspection processes:
6. calculation model
Firstly, introducing main parameters and values thereof:
table 1 calculation model principal parameter values
Furthermore, the separation pressure PsepThe value is 25kPa, POBValues of 100kPa, with reference to Konrad and Morgenstrin (1980) experimental data,
TABLE 2 Experimental data on partial ice formation
The new segregation-freezing temperature 20 is obtained from equation (6):
konrad and Morgenstrin (1980) experimentally determined the average of the segregation-freezing temperatures 20 at-0.1 ℃ and thus the theoretical and experimental values for the above-described segregation-freezing temperature 20 were approximately the same. Further, the formula of the migration driving force of the warm end 16 of the ice lens body can be obtained from the formula (13):
according to the theoretical calculation value of the segregation-freezing temperature 20, the freezing edge permeability coefficient equation of the sample NS-1 can be obtained:
from equation (16), a moisture migration velocity value can be obtained:
with reference to additional experimental data of Konrad and Morgenstern (1980), the following table can be found.
TABLE 3 theoretical calculation and test values of water migration velocity of different samples
For the purpose of analysis, the theoretical calculation of the water migration velocity in Table 3 was compared with the test values of Konrad and Morgenstrin (1980),
as shown in fig. 4, the average relative error between the theoretical calculation value and the test value of the water migration speed is within 10%, and the rules are consistent, so that the frozen soil water migration unified model can accurately predict the frost heaving conditions of different soil bodies.
Wherein T is the centigrade temperature of the ice-water interface, TA is the absolute freezing temperature of pure ice, PS0 is the theoretical ice pressure under the equilibrium state, γ SL is the ice-water interface tension, R is the effective radius of the capillary, PS is the actual ice pressure, POB is the overlying pressure, Psep is the separation pressure, PLd is the migration driving force, kuf is the permeability coefficient of the saturated soil body under the normal temperature condition, kff is the total permeability coefficient of the freezing edge, Tf is the freezing temperature of the freezing front, Ts is the segregation-freezing temperature of the warm end of the ice lens, g is the gravity acceleration, Vff is the moisture migration speed, Vs is the specific volume of ice, L is the phase transition latent heat of pure water, Lt is the permeation path of moisture migration, β is the power, and ρ w is the density of water.
The invention has the following beneficial effects: the capillary-film water migration mechanism model combines a capillary water migration mechanism and a film water migration mechanism to comprehensively and reasonably explain the soil body frost heaving phenomenon, and particularly, the capillary-film water migration mechanism model simultaneously considers the capillary water and film water dual migration mechanisms, overcomes the defects and shortcomings of a single water migration mechanism, and enriches the existing frost heaving mechanism; analysis of water migration driving force of the film is given, and the migration driving force is found to be derived from normal hydraulic pressure difference or ice pressure difference and represents the difference between theoretical pressure and actual pressure in an equilibrium state; establishing a freezing edge permeability coefficient model and giving a relational expression between the freezing edge permeability coefficient and the segregation-freezing temperature; an explicit equation of the water migration speed is given, the number of parameters is simplified, and the frost heaving rate and the frost heaving amount of the saturated soil body can be rapidly predicted.
In the present invention, the terms "first", "second", and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance; the term "plurality" means two or more unless explicitly defined otherwise. The terms "mounted," "connected," "fixed," and the like are to be construed broadly, and for example, "connected" may be a fixed connection, a removable connection, or an integral connection; "coupled" may be direct or indirect through an intermediary. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the description of the present invention, it is to be understood that the terms "upper", "lower", "left", "right", "front", "rear", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplification of description, but do not indicate or imply that the referred device or unit must have a specific direction, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention.
In the description herein, the description of the terms "one embodiment," "some embodiments," "specific embodiments," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A frozen soil mass water migration model, comprising:
the freezing device comprises a frozen area, a freezing edge area and an unfrozen area which are sequentially arranged, wherein an ice lens body is formed on one side of the frozen area close to the freezing edge area, overlaying pressure towards the freezing edge area is applied to one side of the frozen area far away from the freezing edge area, the warm end of the ice lens body is arranged on one side of the ice lens body close to the freezing edge area, and a freezing front surface is formed on one side of the freezing edge area close to the unfrozen area;
a soil particle matrix and a plurality of capillaries with different diameters are arranged in the freezing edge area, and each capillary penetrates through the soil particle matrix to be communicated with the ice lens body and the non-freezing area;
wherein pore ice forms within a first number of the capillaries and a curved ice-water interface forms within the first number of capillaries; the soil particle matrix and the inner wall surfaces of the first number of capillaries form an unfrozen water film, a second number of capillaries are not frozen, the inner walls of the second number of capillaries form the unfrozen water film, and capillary water is filled in the capillaries;
the freezing edge region has two migration mechanisms of capillary water and unfrozen water membrane.
2. The frozen soil mass water migration model of claim 1,
the pore diameter of the capillaries ranges from 0.1 μm to 1000 μm.
3. The frozen soil mass water migration model of claim 2,
the plurality of capillary tubes are normally distributed according to the diameters, and the plurality of capillary tubes are randomly distributed in the freezing edge area.
4. The frozen soil mass water migration model of claim 1,
the thickness of the unfrozen water film is in a range of 0.1nm to 50 nm.
5. The method for constructing the frozen soil body water migration model according to any one of claims 1 to 4, which is characterized by comprising the following steps:
freezing temperature determination
According to the generalized Clapeyron equation, the theoretical ice pressure in the equilibrium state is as follows:
in the formula: pS0The theoretical ice pressure is in the equilibrium state; l is the latent heat of fusion of water; v. ofSSpecific volume of ice; t is a unit ofAIs the absolute freezing temperature of pure ice; t is the temperature in degrees Celsius of the ice-water interface;
obtaining the capillary suction equation on the curved ice water interface according to the capillary theory:
in the formula: pCCapillary attraction caused by interfacial tension; gamma raySLIs the ice-water interfacial tension; r is a capillary tubeAn effective radius; theta is a contact angle;
combining the formula (1) and the formula (2), and then according to the pore ice forming condition, PS0＝PCAnd theta is 180 degrees, and a capillary freezing temperature equation is obtained:
as can be seen from the formula (3), the freezing temperature of the capillary pores decreases with the decrease of the pore diameter;
segregation-freezing temperature determination
As can be seen from the theoretical ice pressure equation (1), the theoretical ice pressure gradually increases with decreasing temperature, and when the actual ice pressure is greater than the sum of the overlying pressure and the separation pressure, new segregated ice is generated, that is:
PS≥POB+Psep (4)
in equation (4): pSThe actual ice pressure is obtained; pOBIs an overburden pressure 14; psepIs the separation pressure;
combining the formulas (1) and (4), scoring the forming condition of the ice congelation:
and (5) transforming the formula (5) to obtain a segregation-freezing temperature equation:
migration driving force determination
And obtaining a film water hydraulic equation according to Gilpin:
as can be seen from the formula (7), the smaller the film thickness is, the stronger the adsorption force is;
when y is h, the following is obtained:
in equation (8): pLThe inner part of the film water is hydraulically distributed; pLhThe theoretical hydraulic pressure at y ═ h in an equilibrium state; v. ofLSpecific volume of water; a is a universal constant; alpha is a power; h is the film water thickness;
when the film water is in an unbalanced state, the film water thickness y is infinitely close to h, so that a hydraulic driving force is generated, namely the hydraulic migration driving force equation at the position where y is h:
PLb＝PLh-PLy (9)
in formula (9): pLbIs the driving force for migration; pLyIn an unbalanced state, the actual hydraulic pressure at y infinitely approaches h;
since the capillary ice-water interface is curved, there is a pressure difference between the ice pressure and the hydraulic pressure:
wherein, the formula (10) is a normal equilibrium equation of the film water in an equilibrium state; equation (11) is the normal equilibrium equation of the film water in the non-equilibrium state;
by combining the formulas (9), (10) and (11)
When the ice layer is formed, the ice will bear all the overlying pressure alone, so the migration driving force equation at the warm end of the ice lens body is:
freezing edge permeability coefficient
The result of statistics by the thomas test, the frozen edge total permeability coefficient versus temperature is:
in the formula: k is a radical ofufThe permeability coefficient of a saturated soil body under the normal temperature condition is shown; k is a radical of formulaffThe total permeability coefficient of the frozen edge; t isfThe freezing temperature of the freezing frontal surface; t is a unit ofsThe segregation-freezing temperature of the warm end of the ice lens;
as can be seen from equation (14), the total permeability coefficient of the freezing edge increases as a high-order power function with decreasing temperature between the freezing front and the warm end of the ice lens body, so that the lower the segregation-freezing temperature, the smaller the total permeability coefficient of the freezing edge;
rate of water migration
Assuming that the water migration of the freezing edge region conforms to Darcy's law
Combining the formulas (13), (14) and (15), obtaining an explicit equation of the water migration speed:
wherein L istIs the permeation path for moisture migration, β is the power, and ρ w is the density of water.
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