CN108549617B - Frozen soil phase change latent heat calculation method considering non-linear change of unfrozen water content - Google Patents

Frozen soil phase change latent heat calculation method considering non-linear change of unfrozen water content Download PDF

Info

Publication number
CN108549617B
CN108549617B CN201810349127.2A CN201810349127A CN108549617B CN 108549617 B CN108549617 B CN 108549617B CN 201810349127 A CN201810349127 A CN 201810349127A CN 108549617 B CN108549617 B CN 108549617B
Authority
CN
China
Prior art keywords
latent heat
frozen soil
phase change
change
unfrozen water
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201810349127.2A
Other languages
Chinese (zh)
Other versions
CN108549617A (en
Inventor
陈之祥
李顺群
张勋程
潘林娜
冯彦芳
夏锦红
姚士霞
赵磊
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Tianjin Chengjian University
Original Assignee
Tianjin Chengjian University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Tianjin Chengjian University filed Critical Tianjin Chengjian University
Priority to CN201810349127.2A priority Critical patent/CN108549617B/en
Publication of CN108549617A publication Critical patent/CN108549617A/en
Application granted granted Critical
Publication of CN108549617B publication Critical patent/CN108549617B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • General Physics & Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Computational Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Operations Research (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Investigating Or Analyzing Materials Using Thermal Means (AREA)
  • Investigation Of Foundation Soil And Reinforcement Of Foundation Soil By Compacting Or Drainage (AREA)

Abstract

The invention provides a frozen soil phase change latent heat calculation method considering non-linear change of the content of unfrozen water in frozen soil. The method has the advantages that the fact that the latent heat is constantly changed along with the change of the content of the unfrozen water is considered, and the change relation between the latent heat and different negative temperatures can be drawn through the provided method. Multiple times of actual measurement and calculation show that the prediction accuracy of the calculation method is improved by 72.4% compared with that of the traditional method. The improvement of the precision can realize the calculation of the non-linear phase change latent heat of the frozen soil to the maximum extent, and the calculation of the temperature field in the frozen soil engineering is facilitated.

Description

Frozen soil phase change latent heat calculation method considering non-linear change of unfrozen water content
Technical Field
The invention belongs to the field of latent heat calculation in the field of frozen soil engineering, and particularly relates to a method for calculating frozen soil phase change latent heat by considering non-linear change of unfrozen water content, which can be used for equation description of frozen soil phase change latent heat and calculation of latent heat total under the condition of known frozen soil unfrozen water content.
Background
Latent heat of phase change refers to the heat absorbed or released by a substance changing from one phase to another under isothermal and isobaric conditions, such as freezing and evaporation of water, and melting of ice. The research on the influence of latent heat on the frozen soil temperature field has important significance and engineering value on the research on the frozen soil temperature field in cold regions and in the process of artificial freezing method.
Under the influence of various factors such as mineral composition in soil, external load, salt content, soil particle surface tension and the like, when a soil body is frozen, part of liquid water in the soil is kept in an unfrozen state, and the part of liquid water is called unfrozen water. The existing research shows that the unfrozen water content of the frozen soil is nonlinearly changed with different negative temperatures. It can be seen that the latent heat of phase change resulting from the non-linear change in the unfrozen water of the frozen earth is also non-linear.
The existing latent heat of phase change is calculated according to the variation of unfrozen water at two temperature points before and after phase change, and because a certain distance exists between the two temperature points all the time, a nonlinear equation cannot be formed by a method for calculating latent heat according to the difference of the content of the unfrozen water at the two temperature points, namely the latent heat obtained by calculation by a conventional method is a constant, and the variation trend of the latent heat between the two temperature points cannot be considered. Meanwhile, the problem of different values of the temperature range also leads to the fact that the obtained latent heat change trend cannot reflect the nonlinear phase change latent heat of the frozen soil. The analytical solution problem requires a specific equation that can characterize the trend of change, and therefore, the conventional latent heat calculation method cannot be used for solving the analytical solution equation.
The method is limited to the large difference of the properties of soil bodies with different regionalities and different causes, provides a general method capable of calculating and expressing the phase change latent heat of frozen soil, and is an important choice for solving the construction problem of the manual freezing method. With the wide application of the artificial freezing method in underground and mining engineering, a frozen soil phase change latent heat calculation method capable of reflecting the nonlinear change of frozen soil is urgently needed, and the method has important significance for the research of the analysis solution problem of the frozen soil temperature field and the improvement of the temperature field prediction precision.
Disclosure of Invention
The invention aims to provide a frozen soil phase change latent heat calculation method considering non-linear change of the content of unfrozen water, so as to be beneficial to calculation of the non-linear phase change latent heat of the frozen soil.
In order to achieve the purpose, the invention provides a method for calculating the phase change latent heat of frozen soil considering the non-linear change of the content of unfrozen water, which comprises the following steps:
1) the relation of the variation of the unfrozen water content of the frozen soil along with the negative temperature is expressed as a form of an equation (1), wherein the equation (1) is as follows:
Wu(T)＝AeBT+CT3+DT2+ET+F (1)
in the formula, Wu(T) is the unfrozen water content of the frozen soil at the time of temperature T,%; A. b, C, D, E, F is a fitting constant; t is temperature, DEG C; e is the override number.
2) The derivative of T in equation (1) is:
Wu(T)'＝ABeBT+3CT2+2DT+E (2)
3) the latent heat change dQ in an infinitely small negative temperature range can be expressed as
Figure BDA0001632659590000021
In the formula, dQ is the latent heat variable quantity in an infinitesimal negative temperature interval, and the unit is kJ/kg; l is the heat released by water condensation and ice formation, and the unit is kJ/kg; rhodIs the dry density of the soil sample in kg/m3(ii) a Rho is the density of the soil sample and has the unit of kg/m3(ii) a dT is infinitesimal negative temperature range, and the unit is ℃.
4) Certain negative temperature interval [ T ]n～Tj](Tn＜Tj) The frozen soil in the section has latent heat of phase change of
Figure BDA0001632659590000031
In the formula (I), the compound is shown in the specification,
Figure BDA0001632659590000032
is a negative temperature interval [ Tn～Tj](Tn＜Tj) The phase change latent heat of the frozen soil in the section is kJ/kg. According to the method, the non-linear change of the content of unfrozen water can be considered to represent and calculate the phase change latent heat of the frozen soil, and a foundation is laid for calculating the temperature field of the frozen soil.
The method has the advantages that the fact that the latent heat is constantly changed along with the change of the content of the unfrozen water is considered, and the change relation between the latent heat and different negative temperatures can be drawn through the provided method. Multiple times of actual measurement and calculation show that the prediction accuracy of the calculation method is improved by 72.4% compared with that of the traditional method. The improvement of the precision can realize the calculation of the nonlinear phase change latent heat of the frozen soil to the maximum extent, and the calculation of the temperature field in the frozen soil engineering is facilitated.
Detailed Description
The method for calculating the phase change latent heat of the frozen soil considering the non-linear change of the content of the unfrozen water is explained.
The invention discloses a method and a principle for calculating the phase change latent heat of frozen soil by considering the non-linear change of the content of unfrozen water, which comprises the following steps: the gradient of the change of the content of unfrozen water is obtained, the latent heat change quantity of the frozen soil in an infinite negative temperature interval is obtained by a differential means, and on the basis, the phase change latent heat of the frozen soil with nonlinear change is calculated by an integral method.
The invention provides a method for calculating phase change latent heat of frozen soil considering non-linear change of unfrozen water content, which comprises the following steps of:
1) the relation of the variation of the unfrozen water content of the frozen soil along with the negative temperature is expressed as a form of an equation (1), wherein the equation (1) is as follows:
Wu(T)＝AeBT+CT3+DT2+ET+F (1)
in the formula, Wu(T) is the unfrozen water content of the frozen soil at the time of temperature T,%; A. b, C, D, E, F is a fitting constant; t is temperature, DEG C; e is the override number.
2) The derivative of T in equation (1) is:
Wu(T)'＝ABeBT+3CT2+2DT+E (2)
3) the latent heat change dQ in an infinitely small negative temperature range can be expressed as
Figure BDA0001632659590000041
In the formula, dQ is the latent heat variable quantity in an infinitesimal negative temperature interval, and the unit is kJ/kg; l is the heat released by water condensation and ice formation, and 333.51kJ/kg is taken; rhodIs the dry density of the soil sample, kg/m3(ii) a Rho is the density of the soil sample, kg/m3(ii) a dT is infinitesimal negative temperature range, DEG C.
4) Certain negative temperature interval [ T ]n～Tj](Tn＜Tj) The frozen soil in the section has latent heat of phase change of
Figure BDA0001632659590000042
In the formula (I), the compound is shown in the specification,
Figure BDA0001632659590000043
is a negative temperature interval [ Tn～Tj](Tn＜Tj) The frozen soil in the section has latent heat of phase change, kJ/kg. According to the method, the non-linear change of the content of unfrozen water can be considered to represent and calculate the phase change latent heat of the frozen soil, and a foundation is laid for calculating the temperature field of the frozen soil.
The dry density was determined by testing to be 1.8g/cm3，dsThe powder clay sample with the temperature of 2.72 has the unfrozen water content of-1 ℃, 2 ℃ and 3 ℃, and the phase change latent heat at the temperature of-2 ℃ is calculated and obtained by utilizing the proposed method for calculating the phase change latent heat of the frozen soil considering the nonlinear change of the unfrozen water content. And calculating the phase change latent heat Q of the frozen soil according to the unfrozen water content difference between-1 ℃ and-3 ℃ by adopting a conventional method(-1～-3)Will be
Figure BDA0001632659590000044
Obtained at-2 ℃ determined by conventional methodsLatent heat of phase change of frozen earth. Compared with the conventional method and the calculation method of the frozen soil phase change latent heat considering the non-linear change of the content of the unfrozen water, the calculation method provided by the invention has the advantage that the prediction precision is improved by 72.4% compared with the traditional method.
The above description is only for the purpose of illustration in conjunction with the present calculation process, and it will be apparent to those skilled in the art that various changes and modifications may be made in the present invention. 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 (1)

1. A method for calculating the phase change latent heat of frozen soil considering the non-linear change of the content of unfrozen water comprises the following steps:
1) the relation of the variation of the unfrozen water content of the frozen soil along with the negative temperature is expressed as a form of an equation (1), wherein the equation (1) is as follows:
Wu(T)＝AeBT+CT3+DT2+ET+F (1)
in the formula, Wu(T) is the percentage of the unfrozen water content of the frozen soil at the time of temperature T; A. b, C, D, E, F is a fitting constant; t is the temperature; e is the overrun number;
2) the derivative of T in equation (1) is:
Wu(T)'＝ABeBT+3CT2+2DT+E (2)
3) the latent heat change dQ in an infinitely small negative temperature range can be expressed as
Figure FDA0001632659580000011
In the formula, dQ is the latent heat variable quantity in an infinitesimal negative temperature interval, and the unit is kJ/kg; l is the heat released by water condensation and ice formation, and the unit is kJ/kg; rhodIs the dry density of the soil sample in kg/m3(ii) a Rho is the density of the soil sample and has the unit of kg/m3(ii) a dT is an infinite small negative temperature interval, and the unit is;
4) certain negative temperature interval [ T ]n～Tj](Tn＜Tj) The frozen soil in the section has latent heat of phase change of
Figure FDA0001632659580000012
In the formula (I), the compound is shown in the specification,
Figure FDA0001632659580000013
is a negative temperature interval [ Tn～Tj](Tn＜Tj) The phase change latent heat of the frozen soil in the section is kJ/kg.
CN201810349127.2A 2018-04-18 2018-04-18 Frozen soil phase change latent heat calculation method considering non-linear change of unfrozen water content Active CN108549617B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810349127.2A CN108549617B (en) 2018-04-18 2018-04-18 Frozen soil phase change latent heat calculation method considering non-linear change of unfrozen water content

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810349127.2A CN108549617B (en) 2018-04-18 2018-04-18 Frozen soil phase change latent heat calculation method considering non-linear change of unfrozen water content

Publications (2)

Publication Number Publication Date
CN108549617A CN108549617A (en) 2018-09-18
CN108549617B true CN108549617B (en) 2021-06-29

Family

ID=63515289

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810349127.2A Active CN108549617B (en) 2018-04-18 2018-04-18 Frozen soil phase change latent heat calculation method considering non-linear change of unfrozen water content

Country Status (1)

Country Link
CN (1) CN108549617B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109507234B (en) * 2019-01-02 2020-07-03 大连理工大学 Frozen soil heat conductivity coefficient test correction method based on hot wire method
CN111380906B (en) * 2020-03-30 2021-08-17 大连理工大学 Refinement method for converting phase change latent heat of frozen soil into equivalent specific heat

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2318710A1 (en) * 2000-04-26 2001-10-26 Robert C. Tsigonis Sewage treatment plant
CN102135513A (en) * 2011-01-04 2011-07-27 刘波 Method for testing content of unfrozen water in frozen earth
CN103675232A (en) * 2013-11-22 2014-03-26 河海大学 Measuring and calculating method for water conserving and storing capacity of drainage basin based on soil freeze-thawing
CN104792818A (en) * 2015-04-07 2015-07-22 河南大学 Method for calculating specific heat at clay freezing stage by performing energy substitution on phase-change latent heat of water in soil
CN105241920A (en) * 2015-11-06 2016-01-13 天津城建大学 Method for determining content of unfrozen water in soil freezing process by using specific heat calculation
CN105973746A (en) * 2016-01-25 2016-09-28 天津城建大学 Apparatus for testing unfrozen water content of frozen soil, and method thereof
CN106120506A (en) * 2016-06-29 2016-11-16 中交第公路勘察设计研究院有限公司 Permafrost Area based on principle of energy balance hot-mix recycling Parameters design
CN106872529A (en) * 2017-04-07 2017-06-20 天津城建大学 The method that content of unfrozen water in frozen earth is determined by measured resistivity
CN106918624A (en) * 2017-04-07 2017-07-04 天津城建大学 Unfrozen water content computational methods based on thermal conductivity of frozen soils

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2318710A1 (en) * 2000-04-26 2001-10-26 Robert C. Tsigonis Sewage treatment plant
CN102135513A (en) * 2011-01-04 2011-07-27 刘波 Method for testing content of unfrozen water in frozen earth
CN103675232A (en) * 2013-11-22 2014-03-26 河海大学 Measuring and calculating method for water conserving and storing capacity of drainage basin based on soil freeze-thawing
CN104792818A (en) * 2015-04-07 2015-07-22 河南大学 Method for calculating specific heat at clay freezing stage by performing energy substitution on phase-change latent heat of water in soil
CN105241920A (en) * 2015-11-06 2016-01-13 天津城建大学 Method for determining content of unfrozen water in soil freezing process by using specific heat calculation
CN105973746A (en) * 2016-01-25 2016-09-28 天津城建大学 Apparatus for testing unfrozen water content of frozen soil, and method thereof
CN106120506A (en) * 2016-06-29 2016-11-16 中交第公路勘察设计研究院有限公司 Permafrost Area based on principle of energy balance hot-mix recycling Parameters design
CN106872529A (en) * 2017-04-07 2017-06-20 天津城建大学 The method that content of unfrozen water in frozen earth is determined by measured resistivity
CN106918624A (en) * 2017-04-07 2017-07-04 天津城建大学 Unfrozen water content computational methods based on thermal conductivity of frozen soils

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
Adsorbed cation effects on unfrozen water in fine-grained frozen soil measured using pulsed nuclear magnetic resonance;Aaron M. Kruse 等;《Cold Regions Science and Technology》;20170721;第42-54页 *
Sensible and latent heat flux response to diurnal variation in soil surface temperature and moisture under different freeze/thaw soil conditions in the seasonal frozen soil region of the central Tibetan Plateau;Donglin Guo 等;《Environmental Earth Sciences》;20100724;第97-107页 *
土体冻融特征研究现状与展望;张熙胤 等;《冰川冻土》;20161231;第38卷(第6期);第1644-1657页 *
基于未冻水含量的冻土热参数计算分析;陈之祥 等;《岩土力学》;20171130;第38卷(第2增刊期);第67-74页 *
基于连续介质热力学的冻土中未冻水含量与温度的关系;覃英宏 等;《青岛大学学报（工程技术版）》;20080331;第23卷(第1期);第78-82页 *

Also Published As

Publication number Publication date
CN108549617A (en) 2018-09-18

Similar Documents

Publication Publication Date Title
CN108549617B (en) Frozen soil phase change latent heat calculation method considering non-linear change of unfrozen water content
Kane et al. Water movement into seasonally frozen soils
Tice et al. The prediction of unfrozen water contents in frozen soils from liquid limit determinations
CN104833693B (en) The thermal conductivity factor of sand, silt and silty clay determines method
CN104792818B (en) The clay that native reclaimed water latent heat of phase change is carried out into energy replacement freezes stage specific heat computational methods
Rui et al. Field experimental study of the characteristics of heat and water transfer during frost heaving
Shreve et al. Internal deformation and thermal anomalies in lower Blue Glacier, Mount Olympus, Washington, USA
Kozlowski Soil freezing point as obtained on melting
Brown Difficulties associated with predicting depth of freeze or thaw
Zhang et al. Effectiveness of ionic polymer soil stabilizers on warm frozen soil
Chen et al. Effect of temperature on the strength characteristics of unsaturated silty clay in seasonal frozen region
Flerchinger et al. Freezing and thawing processes
CN112685884B (en) Method for determining liquid water content at different temperatures in soil
Wasif Naqvi et al. Investigating the Frost Action in Soils
CN106289939A (en) A kind of method obtaining sandy soil undisturbed sample
Hou et al. Thermal and deformational repairing effect of crushed rock revetment acting as reinforcement along Qinghai–Tibet railway in permafrost regions
Romero-Juarez A note on the theory of temperature logging
CN111380906B (en) Refinement method for converting phase change latent heat of frozen soil into equivalent specific heat
Goodrich A numerical model for assessing the influence of snow cover on the ground thermal regime
Kim et al. Thermodynamic evaluation of the pressure occurring at frost penetration in confined space of the soil
Galkin Improvement of openings strength in criolithic zone
Unold et al. Cryosuction–a model to describe the mechanism during ground freezing
Langleben Some physical properties of sea ice. II
Ziegler Artificial freezing method in geotechnical and tunneling applications
Yamamoto et al. The hydraulic conductivity of soils during frost heave

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant