Study of moisture migration in clay soils considering rate of freezing

S.A.Kudriavtcev ,A.V.Kazharskii ,E.D.Goncharova ,I.B.Berestianyi

1.Far Eastern State Transport University (FESTU),Khabarovsk 680021,Russia

2.Research Construction and Engineering Company (DV-GEOSYNTHETICS),Khabarovsk 680021,Russia

1 Introduction

Freezing,frost heaving,and thawing of wet ground are complex thermodynamic processes.Freezing and thawing take place simultaneously with changes in the temperature field and are accompanied by moisture migration to the freezing front.Previous numerous researches have shown that moisture redistribution due to water migration during freezing is the main negative process in frozen soils because it changes features of soils and their physical and mechanical characteristics.

Thus,when conducting a study of freezing,frost heaving,and thawing activity,it is reasonable to take into account a ratio of frost heaving deformations versus the freezing rate of foundation soils because frost heaving is significantly determined by migration water suction from underground water to the freezing front.The lower the rate of freezing front advance,the greater amount of moisture moves to the freezing front,and consequently considerable deformations of frost heaving in a frozen foundation appear.

A quantitative assessment of soil deformations considering frost heaving and thawing is one of the most challenging tasks of geomechanics.The main difficulty in solving this problem is the necessity to consider changes in the condition of freezing and thawing soils in the foundation as well as the thermal and physical characteristics of the changing environment.

The purpose of our study was to analyze the changes of soil characteristics when water migrates during freezing-thawing,and a parabolic equation of lateral resistance versus moisture was established which makes it possible to determine the relation between lateral resistance and soil moisture.

2 Numeric modeling processes of freezing,frost heaving,and thawing

The numeric modeling was done on the FEM-models program complex developed by geotechnical engineers in St.Petersburg,Russia (Ulitskyet al.,2003a,2003b;Kudriavtcevet al.,2009,2012,2013a,b).A component of the FEM-models is the"Thermoground" program,which enables study of the processes of freezing,frost heaving,and thawing in a yearly cycle by spatial programming of numerical modeling by the finite element method.The core of a mathematical modeling of thermophysical processes in the "Thermoground" program is the model of high ice,and thawed and frozen soils offered by Guidiceet al.(1978).In the following equations,the thermotechnical part of the numerical modeling task is solved where moisture and temperature fields are determined for every period of time.

A general equation describing the freezing and thawing processes for a transient thermal regime in a three-dimensional soil space can be expressed as:

whereCth(f)is the specific heat of soils (frozen or thawed),J/(kg·K);ρis the soil consistency,kg/m3;Tis the temperature,λth(f)is the thermal conductivity of soil(frozen and thawed),W/(m·K);x,y,zare the coordinates,m;andqVis the internal heat source capacity,W/m3.

Under steady conditions,the flow in and from the elementary unit of soil is the same at any time.Thus,as the left hand side of the equation is eliminated,the equation is reduced to:

The heat capacity function consists of two parts:a)volume-specific heat of soil (thawed or frozen);and b)latent heat of transition (within a range of negative temperatures) which is absorbed or yielded by soil due to phase changes in groundwater.This can be expressed as:

whereCth(f)is the volume-specific heat of thawed or frozen soil;L0= 335×106J/m3= 335×103kJ/m3=79.760 kcal/m3,is the water-ice latent heat of transition;andWWis the moisture content unit of unfrozen water.

The volume-specific heatCth(f)can be presented graphically on the heat exchange curve in thawed and frozen areas,as shown in figure 1.

Figure 1 Curve of heat exchanges in soil (freezing-thawing).Tbf :temperature void water freezing/thawing point;Tbwf :temperature bound water freezing point;Tf :temperature of frozen soil.

The average soil moisture within a migration layer(amount of migration moisture is considered) is determined from:

whereQwfis the amount of migration moisture,andγdis the specific weight of dry soil.The mass of migration soil is determined from:

whereqwfis the migration flow intensity of moisture;Аis the cross-sectional area of migration flow;andtis the impact time.

Because the migration flow is measured in the unit volume,the specific weight of dry soilγdequals the mass of dry soilQd.Thus,the delta of average migration moisture per time period equals:

Having analyzed all existing ratios of the moisture increment Δw1versus the rate of freezingVfin different types of soil,relevant approximating functions were selected (Ulitskyet al.,2003b).The average values of the approximating functions of ratios of moisture increment Δw1versus rate of freezingVfon the freezing front for different soils are expressed by a common formula:

wherevis the rate of soil freezing,andbandcare the empirical coefficients.

The correlation index for the given function is 0.96–0.99 and root-mean-square deviation is within 0.0053–0.0328.The values of the coefficientsbandcare given in table 1.

Table 1 Values of coefficients b and c

On the basis of abundant surveys in frozen-soil territories of Russia,there are two maximums of groundwater level fluctuations in a year:spring and autumn.The spring maximum is the highest level and the autumn maximum is less,and the lowest level appears by the end of winter.The height of rise and total amplitude of the groundwater level depend on its depth and the grading of the soil above it.

Groundwater recession takes place from the end of autumn up to the end of winter.The rate of ground freezing in the base depends on air temperatures (Figure 2):

Figure 2 Diagram of freezing and level of groundwater in winter.WL:trend of groundwater level.1:possible trends considering rate of ground freezing;2:trend of groundwater level;3:freezing front overlapping groundwater level;4:distance between freezing front and groundwater level

As was previously stated,the total amplitude of the groundwater level depends on its depth and the grading of the soil above it.Numerous measurement analyses in observation wells for groundwater level in the Russian Far East and northwestern parts of Russia showed that it is possible to express the fluctuations trend of groundwater level as:

whereBis the groundwater level before winter;Ais the coefficient of groundwater fluctuation during a year;andtis time.

The farther the freezing front is from the groundwater level,the less is the migration flow (Figure 3):

Figure 3 Diagram of migration water flow rate during ground freezing.(a) small distance between the groundwater level and the freezing front;(b) greater distance

3 Experimental design

Some variants with different levels of groundwater and different rates of freezing were considered in solving the thermophysical problem by numerical modeling methods.The tests were done on low-plastic silt loam because it is widespread in southern regions of the Far East.The numeric modeling tasks considered different rates of soil freezing when an average monthly air temperature was within 2–9 °C below 0 °C which corresponds to the freezing-to-frost interval of soil condition.The level of groundwater varied from 1.0 m to 2.5 m below the surface on each modeled day.

When the thermophysical problem was solved within a day,the interval of changes was split into four periods of 6 h.Every period was set with different air temperatures,both negative and positive.Five series of numerical modeling of freezing with migration moisture changes were conducted at average daily air temperatures ofТ1=-2.08 °C;Т2=-4.16 °C;Т3=-4.33 °C;Т4=-6.08 °C;andТ5=-8.75 °C.

Figure 4 shows the temperature distribution in soil during a month at different depths and at different rates of freezing.Diagrams of moisture changes in soil are given in figure 5.

Figure 4 Daily temperature distribution at various freezing depths at different average daily air temperatures.Т1 =-2.08 °C;Т2 =-4.16 °C;Т3 =-4.33 °C;Т4 =-6.08 °C;Т5 =-8.75 °C.(a) 0.6-m depth of freezing;(b) 1.0-m depth of freezing

Figure 5 Diagrams of moisture changes in soil versus rate of freezing at various average daily air temperatures.(a) Т1 =-2.08 °C;(b) Т2 =-4.16 °C;(c) Т3 =-4.33 °C;(d) Т4 =-6.08 °C;(e) Т5 =-8.75 °C

The moisture changes in soil versus the rate of freezing were determined at the maximum depth during 30 days of first negative temperatures,and they are given in figure 6.

The numerical modeling of moisture changes in frozen soils versus rate of freezing resulted in the following equation:

whereWis the moisture of soil unit,andvis the rate of freezing,m/day.

The parameters of frozen soil stability were determined according to the results of cylindrical test-piece stability in the triaxial cell of the ASIS measuring and computing complex developed by Geotech.R&D Co,Russia.More than 30 silt loam tests resulted in a general diagram of distribution (Figure 7).Silt loam taken from southern parts of the Russian Far East was tested for lateral resistance in clay soil in a wide range of moisture.The outcome dependence enables qualitative and quantitative assessment of how moisture influences lateral resistance and stress and strain conditions of a soil structure and its foundation in general.

Figure 6 Moisture changes in soil versus rate of freezing

Figure 7 Lateral resistance changes in soil due to moisture

This study led to a parabolic equation of lateral resistance versus moisture that helps assess the relation of lateral resistance changes in soil due to moisture:

whereСuis the specific cohesion,andwis the soil moisture unit.

4 Conclusions

This study of moisture changes in frozen soils versus rate of base freezing in a yearly cycle shows that the moisture value increased by 68% while the lateral resistance in clay soils decreased five-fold.

The developed numerical modeling method of determining temperature,moisture,and lateral resistance enables assessment of the impact of frost heaving and the decrease in strength of building and structure foundations due to freeze-thaw action.This will make it possible to efficiently introduce modern reinforcement structures with new materials for soil structures and their foundations to decrease or eliminate the negative impacts of frost heaving and thawing.

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