2. Water in road materials and subgrade soils, terminology

2.1. General about water

A water molecule consists of one oxygen and two hydrogen atoms. Hydrogen atoms form an angle of 104.5° with the oxygen atom. The water molecule is polar, which means that the oxygen atom has a mild negative charge. The oxygen atom, as an electro-negative element, binds electrons closer to itself and that is why hydrogen atoms remain as mild positive atoms. The length of oxygen-hydrogen linkage is 0,96Å.


The temperature and pressure of the local environment affect the local state of water. In road structures and subgrade soils in cold climate areas water can occur in all three main states: the solid state (ice), the liquid state (water) and the gaseous state (water vapour). The amount and the state of the water present (i.e. liquid or frozen) affects the performance of the materials in the road and subgrade soils. It should also be remembered that the form of the water, the dissolved air content and the content of colloids all have a great effect on the stiffness of materials, their permanent deformation properties and frost susceptibility. These factors, and the general terminologies used when discussing water in road materials and subgrade soils, are described in the following paragraphs.


2.2. Free water – bound water, saturation, porosity

In general liquid water in soils and aggregates can be classified as: 1) adsorption water, also called hygroscopic water, 2) viscous water, or capillary water and 3) free water. A more simpler classification divides water into two forms a) bound water and b) free water.


2.2.1. Bound water


Adsorption water

Because the water molecule is polar, and because the greatest part of mineral surfaces have a negative charge, the water molecules closest to the mineral surface are very well arranged. This adsorption water consists of two layers; tightly and loosely bound layers. The thickness of the tightly bound adsorption water layer is about 0.002 ?m. Adsorption water condenses on the surface of soil particles straight from water vapour in the air. Around the tightly bound layer is the loosely bound adsorption water layer. This layer thickness varies from the 0.002 ?m to 0.006 ?m. Salt reduces the thickness of this layer, and thus helps compaction of the material.

Adsorption water can also be called bound water as it can act as a “binder” between soil particles producing the tensile strength of the dry material. That is why in some countries dry unbound materials are also called as “water bound” materials.

The amount of adsorption water is also controlled by the specific surface area of minerals. The higher the specific surface area, the higher is the adsorption water content. However not all the adsorption water is harmful to material performance. For instance, iron oxides can adsorb great amounts of water but this water does not cause performance problems for the aggregates.

Viscous water or capillary water

The moisture in soil which is not bound around mineral grains as hygroscopic water, and does not respond to gravity, is usually called as viscous water, or capillary water. Capillary water can also be divided into “inner” and “outer” layers. When compacting aggregates the optimum water content in road materials is where the inner capillary layer changes to the outer capillary layer. Capillary forces are also very important factors in the frost heave process on roads.

Menisci or contractile skin

Capillary menisci, also called contractile skin, form between the particles and air in unsaturated soils and aggregates. This air-water interface is only a few molecular layers thick but its presence is very important in soil mechanics because of its property of exerting tensile pull. This ability is called surface tension. The magnitude of surface tension depends on temperature; if the temperature increases the magnitude decreases.


The fact that a drying aggregate has a better stiffness with the same water content than an aggregate that is getting wetter has been explained by the fact that the menisci are concave and better structured when drying, compared to the case when the menisci are convex when new water molecules are entering the system and breaking the molecular menisci structure. This phenomenon is also called hysteresis.

Menisci or contractile skin is an important factor in matric suction, which is described later in this lesson.

2.2.2. Free water

Free water (also called gravitation water) moves through the soil voids under the force of gravity. It is important to be conversant with free water as road drainage systems can be affected by the amount of this water type. The amount of free water has an immediate influence in decreasing bearing capacity. It also weakens the stability of road edges and causes edge settlements and erosion. Free water is an important factor in the freeze-thaw process. In the fall when the temperature of mineral aggregates or soil drops below 0°C, free water freezes first forming hexagonal crystals so increasing its volume and causing frost heave.

2.2.3. Saturated and unsaturated materials


The behaviour of material under a traffic load varies greatly based on whether the material is saturated with water or unsaturated. In saturated materials all of the pore spaces are filled with water, as is the case for materials under the groundwater table. In unsaturated materials the pore spaces are filled both with water and air. It is important to keep in mind that in these mineral–water–air mixtures the air is the only compressible material, and that under high pressure air can partly be dissolved in water.

2.2.4. Porosity, void ratio and saturation

Porosity


For road materials and subgrade soils the term porosity (n) means the percent of the ratio of the volume of voids to the total volume. It is calculated

n = (Vv (100)) / V, where

Vv= volume of voids, V = total volume

Porosity varies according to soil type. Typical values are presented in the table:

Reference: Soil mechanics for unsaturated soil.

Soil type Max. Porosity (%) Min. Porosity (%)
Silty sand 47 29
Clean fine to coarse sand 49 17
Sandy or silty sand 64 20
Clay 71 33

Void ratio


Void ratio (e) is determined as the ratio of the volume of voids to the volume of soil solids. It is calculated using the following equation:

e = Vv / Vs , where

Vv= volume of voids, Vs = volume of soil solids

The void ratio also varies with soil type. Typical values are presented in the table:

Reference: Soil mechanics for unsaturated soil.

Soil type Max. Void ratio, e Min. Void ratio, e
Silty sand 0.90 0.30
Clean fine to coarse sand 0.95 0.20
Sandy or silty sand 1.80 0.25
Clay 2.40 0.50

Saturation


The percentage of the void space, which contains water, is seen in the degree of saturation (S).

S = (Vw(100)) / Vv , where

Vw= volume of water, Vv = volume of voids

The void ratio also varies with soil type. Typical values are presented in the table:

Reference: Soil mechanics for unsaturated soil.

Unsaturated soils can be subdivided to another three groups depending on upon whether the air phase is “continuous” or “occluded”. The classification can be made according to the degree of saturation.

  • S < 80%, unsaturated soil with continuous air phase
  • S > 90%, unsaturated soil with occluded air bubbles
  • 80% < S < 90%, transition zone between continuous air phase and occluded air bubbles.

The 80 % limit is an important factor when discussing dynamic loads caused by moving traffic and tells that road materials do not have to be totally saturated when their performance starts to change.

2.3. Interaction of air and water

2.3.1. Water and air blends

Water and air can be joined together as miscible and / or immiscible blends. The immiscible blend is a combination of free air and water without any interaction. The air and water are separated by the contractile skin. A miscible air-water mixture can have two forms; air dissolved in water, and water vapor present in the air. Air dissolved in water can occupy approximately 2% by volume of the water.


When a load is applied to a road material or subgrade soil with water filling more than 80 % of the voids the air starts to blend with the water. This process of air dissolving into water can be divided into two stages. At first the air is compressed (Boyle’s law) and after that the air is dissolved into the water (Henry’s law). The amount of air that dissolves into water is time dependent and when the load is removed a reverse process takes place that can take a longer time. This process can used to explain the recovery time and visco-elastic behaviour of road materials.


2.3.2. Compressibility


The mechanical behaviour of unsaturated soils and road materials is directly affected by changes in the pore-air and pore-water pressures. The pore pressure conditions can be divided into two classes. 1) The pore pressures associated with the flow or seepage of water through soils, and 2) The pore pressure conditions that are generated from the application of an external load.

Pore-air and pore-water do not flow out of the soil during compression. The volume changes as a result of the compression. The volume change of the pore fluid (i.e. free air, water and air dissolved in the water) will be dependant on the change in pore-air and pore-water pressures. Pore-air and pore-water pressures will increase when unsaturated soil is compressed.


2.3.3.Solubility

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A demonstration showing the effect of repeated loading to nearly saturated road material (i.e. a saturation level of 85-95 %). Under wheel loading the dielectric value of the soil increases because of the reduced amount of air with a dielectric value of 1 (the dielectric value of free water is 81). Part of the air dissolves into the pore water and it takes time for this dissolved air to return back to air pores. This process causes the dielectric value to increase as a function of the repeated axle loads.

The volume of dissolved air in water is mainly independent on the air and water pressures. Air solubility can be expressed with the ideal gas law and Henry’s Law. The ideal gas law defines that the absolute pressure of the dissolved air is equal to the absolute pressure of the free air under equilibrium conditions. The equilibrium condition is reached where the pressure in the free air and the dissolved air are equal. If the load is then increased, the process is repeated.

2.4. Chemical and electrical properties of water in soils and aggregates

2.4.1. Chemical components in water

The water in soils and aggregates usually contains inorganic and organic material in a variety of forms. These can be either soluble, or as a component in stable suspension. This latter form is important in the mechanical behaviour of materials. The most important components are described below:

a. Ions. There are two types of ions that always present in water, 1) cations and 2) anions. A cation is an ion with less electrons than protons giving a net positive charge to the ion. These positive ions attract the negative corners of water molecules and vice versa. Cations are attracted to negatively charged mineral surfaces. An anion, on the other hand, is an ion with more electrons than protons giving a net negative charge to the ion.

b. Organic complexes. Organic complexes in road aggregates increase their water adsorption properties and thus reduce their resistance to permanent deformation. This can be seen for instance in gravel roads with high amounts of organic compounds in their wearing course that become easily slippery, losing friction during rainfall. In addition to high plasticity and low strength the presence of organic matter in road material can also increase compressibility and shrinkage leading to cracking when the material dries out again.

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Demonstration of the behaviour of colloids during the thawing period in the spring. When ice starts to thaw, colloids are released into the pore water because of loading. At the same time the value of electric conductivity rises to its maximum level. When the colloids coagulate, the value of electrical conductivity lowers.

c. Suspended colloidal particles. In order to understand the behaviour of pore water it is important to understand the properties of colloidal particles in pore water in differing conditions. Colloidal particles are defined as lying between dissolved compounds and suspended particles with a particle size of between 10-6 – 10-9 m. The dominating features in colloids are high plasticity and molecule adsorption. In road aggregates and subgrade soils colloids can be classified into a) hydrophilic colloids and b) hydrophobic colloids.

The importance of colloidal particles has not been sufficiently recognized in the performance of road materials and subgrade soils. One reason for this is their size, which is much smaller than clay particles. It is also why it is extremely difficult to analyse them.

Research projects in Finland into poorly performing aggregates have found different types of colloids present in the aggregates tested. Colloids were also seen in the data collected from Percostation spring thaw monitoring stations. These show that in the beginning of the surface weakening period, when roads materials are thawing, there is always a peak in electrical conductivity that can be explained by the increase in the amount of colloids being released from the clay mineral surfaces to the water phase. At the same time the road surface becomes very plastic. Later, the electrical conductivity drops indicating that the colloids are flocculating (ie gathering into groups), and at the same time the surface materials start to dry and lose their plasticity. The coagulation and flocculation of colloids is controlled by the pH of the pore water.

Clay minerals and colloids can be compared to similar sized organic compounds. Clay minerals are the size of bacteria and colloids are the size of viruses. In the future it may be discovered that colloids are as dangerous to the health of roads as viruses are to human beings….

d. Ions adsorbed on suspended particles. Hydrofilic colloids adsorb hydrated ions surrounded by loosely bound water to their surfaces causing all hydrophilic colloids to be surrounded by a liquid membrane. Under cycling loading this can cause an increase in pore water pressure.

Pore water pH

One of the most important chemical properties of the pore water in aggregates is the pH value. The pH value has a great effect on the hydrogen bonds within materials and thus the tensile forces. If the salinity of a material, and/or carbon dioxide content, is increased, the pH of the material will decrease. A low pH will increase the tensile forces between the positively charged mineral edges and negatively charged mineral surfaces, and cause the compounds in the pore water to flocculate, or remain flocculated on the mineral surfaces. Conversely, if the pore water pH is high particles will stay in suspension in the pore water and the material will be more susceptible to permanent deformation.

2.4.2. Electrical properties of water

The electrical properties of road materials and subgrade soils can be described by their magnetic susceptibility, electrical conductivity and dielectric value. Of these, magnetic susceptibility can be ignored in Northern Periphery area. Dielectric value and electrical conductivity can, on the other hand, have an effect on a number of phenomenon related to road performance. By measuring and analysing these parameters information can be obtained on a range of issues such as susceptibility to permanent deformation, frost susceptibility, moisture content, content of unfrozen water in frozen soil, fines content, chloride content and damages in asphalt and concrete.


The dielectric value gives a measure of the volumetric water content of a material. It also provides information on the amount of free water in the material by measuring how the polaric molecules move in a changing (AC) electrical field.

Several factors can affect electrical conductivity and dielectricity:

  • structure of medium
  • size of structural elements
  • electrochemical nature of elements
  • porosity
  • volumetric water content
  • water distribution (amount of free water)
  • ion concentration
  • temperature
  • pressure
  • density

2.5. Water content and methods to define it

When discussing water and the properties of road aggregates and subgrade soils the most popular term used is “water content”. Water content is however a general term and a clear definition should be always made whether the discussion is about gravimetric water content or volumetric water content, and how the content is measured, ie confined to free water or including premier-pharmacy.com/product/inderal/ bound water. The definitions of gravimetric and volumetric water contents and their measurement techniques are considered in the following sections.


2.5.1. Gravimetric and volumetric water content


The gravimetric water content (w) of a material is defined as the ratio of the mass of the water to the mass of solid.

w(%) = (Mw(100)) / Ms , where

Mw= mass of water, Ms = mass of soil solids

This means that the mineralogy and density of an aggregate has a great effect on the gravimetric water content, and thus gravimetric water content values cannot be compared between different types of aggregates. Additionally the gravimetric water content does not give any information on the density or degree of saturation of the material. Despite these drawbacks, the gravimetric water content is still the most popular parameter used to describe water content as it is so easy to measure.

The volumetric water content (?w) of a material is defined as the ratio of the volume of water to the total volume.

?w = (Vw / V , where

Vw= volume of water, V = total volume of soil

Volumetric water content ignores the dry density of the minerals involved and is a better parameter for discussing the mechanical behaviour of road materials and subgrade soils. This is because volumetric water content can also be presented in terms of porosity, degree of saturation and void ratio:

?w = (SVv) / V , where

S = saturation degree, Vv= volume of voids, V = total volume of soil

or

?w = Se / (1+e), where

S = saturation degree, e = void ratio

When calculating volume-mass relationships it is good to know a few basic facts about soil density. The total density and the dry density are the most commonly used definitions. The total density, also called the bulk density, of a soil (?) is the ratio of the total mass to the total volume of the soil.

? = M / V, where

M = total mass, V = total volume of soil

The dry density of a soil (?d) is defined as the ratio of the mass of the soil solids to the total volume of the soil.

? = Ms / V, where

Ms = mass of soil solids, V = total volume of soil

The maximum and minimum dry densities vary for different materials. Some typical examples are shown in the table below:

Reference: Fredlund D. G. and Rahardjo H.: Soil mechanics for unsaturated soil

Soil type Max. density ? ( kg / m3 ) Min. density ? ( kg / m3 )
Silty sand 2034 1394
Clean fine to coarse sand 2210 1362
Sandy or silty sand 2162 961
Clay 1794 801

The use of volumetric water content is often more convenient than gravimetric moisture content because it is more directly adaptable to the computation of fluxes, and adding or subtracting water to a soil. These two different ways of calculating moisture content explain the differences between different studies as gravimetric moisture content depends on the bulk density of the material and is approximately 1.5 to 2 times smaller than volumetric moisture content.


The degree of compaction affect the water content. A compacted material has a higher volumetric water content than a loose material. During compaction the volume of the voids (i.e. pores partly filled with water) becomes smaller as the soil particles are set dense



When the soil particles close on each other during compaction, the water bonded to the particles loosens and becomes unbound free water. This causes the dielectric value to rise as the amount of unbound water rises.

2.5.2. Traditional laboratory test methods

There are many ways to measure gravimetric water content in the laboratory but the most commonly used methods are the oven-dry method and the calcium carbide CaC2 gas pressure meter method.


The simplest method to define gravimetric water content is the oven-dry method. A soil sample with natural moisture content is first weighed and then dried in a convection oven at a temperature of 105°C ± 5°C. The drying time depends on various parameters such as soil type, size of sample and properties of the oven. Usually 16-24 hours is adequate. The drying should take as long as necessary so that a constant weight of sample is reached. After the sample has been dried, it is weighed again and the gravimetric water content calculated using the equation below:

w = (m1 – m2) / (m2 – mc) * 100 = mw / md * 100, where

w = water content,
m1 = mass of container + wet sample,
m2 = mass of container + dry sample,
mc = mass of container,
mw = mass of water,
md = mass of dry sample

The calcium-carbide gas pressure method is based on the fact that water in a soil sample is absorbed by calcium-carbonate and forms acetylene gas as a product of the chemical reaction. The pressure of acetylene gas is directly proportional to the amount of acetylene and thus to the amount of water in the sample. Moisture content measured in this way is also gravimetric moisture content.



There are no specified instructions how to measure volumetric water content in the laboratory but in general the measurement starts by first measuring the exact volume of the sample and then drying the sample in an oven similar to the gravimetric water content method. This gives the weight of water and the weight of aggregate. After that the density of aggregate is defined using different methods and the volumetric water content can be calculated assuming that the density of water is 1.0 g/cm3.

2.5.3. Other laboratory and field test methods

Water content can be measured in laboratory and in the field using a variety of test methods and instruments. Currently, time domain reflectometry (TDR) is the most popular technique used to measure the moisture content of soil in the field. Other methods that can be used to measure moisture content in the soil are capacitance-based sensors and ground penetrating radar (GPR). Nuclear gauges and nuclear magnetic resonance (NMR) are used sometimes. Electrical conductivity has also been used to measure water content but the method can be affected by temperature and colloidal state and thus not reliable. Good methods are TDR, capacitance based probes and GPR, all of which measure the dielectric value of the material, which is a function of its volumetric content. Based on the measurement frequency used in these measurements a rough estimate of the free water and bound water in the material can be made. These techniques are described in the following.


The TDR technique transmits an electromagnetic pulse through the soil and records the resulting changes in its dielectric permittivity (dielectric value, dielectric constant). When TDR is used to measure the water content of a frozen soil it should be noted that the value of dielectric constant of frozen soil is approximately 4, rather than 1 which has been assumed in some tests in the past.


Capacitance based sensors can be used to measure the volumetric water content of a soil by measuring of its dielectric value. The sensors detect if there are any changes in the free water content in the soil or aggregate by measuring changes in the capacitancy compared to capacitancy of air. The operating frequency is normally 50 – 100 MHz. Capacitance based sensors can be used in soils which have a higher salt content where the TDR method cannot be used. It is very important to have a good contact between the soil and sensor to get reliable measurements. If water content is measured sensors have to be calibrated to be soil specific. Capacitance based sensors are recommended by the ROADEX project for use in Tube Suction tests to evaluate moisture sensitivity and frost susceptibility of base course materials, and for testing base course stabilisers and treatment chemicals.

Reference: Kolisoja & Vuorimies report: Material Treatment Techniques

Ground Penetrating Radar (GPR) is a non-destructive ground survey method that can be used in researching roads, railways, bridges, airports, environmental objects, etc. Its main advantage is the continuous profile it provides over the road structures and subgrade soils and, as a consequence, the technique is becoming an increasingly important tool especially on the structural evaluation of low volume roads. A further, important advantage in road surveys is that it is not intrusive to other traffic using the road.


The method is based on transmitting short pulses of electromagnetic energy through materials using either an air coupled or ground coupled antenna. When an electromagnetic wave hits a boundary between substances with different dielectric constants, part of the wave reflects back to the surface and the antenna of the receiver picks it up. The rest of the wave either carries on to the underlying substance or scatters in multiple directions. Dielectric value of materials can be measured using different GPR sounding techniques, such as WARR and CMP. The air coupled antenna reflection technique can also be used to detect water. The location of moist areas and the location of unfrozen water in frozen soils or road structures can be also determined from GPR data.


2.6. Water and thermodynamics

2.6.1. General, thermodynamic balance


Seasonal changes have a major effect on the behavior of road structures in the Northern Periphery area through the changing ground temperatures and volumetric water contents. Freeze-thaw processes are a major reason for road defects and the fact is that more than half of the pavement distresses in northern road networks appear during the spring. During the weakest period in spring one single truck can cause substantial road failures. In order to understand the processes behind such problems it is important to understand some basics of thermodynamics.


A road is a thermodynamic system that changes material and energy with its surroundings. The system is said to be in thermodynamic balance if it does not change with time. The conditions of balance are: temperature balance, chemical balance and mechanical balance. A road structure which is under dynamic traffic load and which freezes in winter, and thaws and warms in summer, does not fall within these requirements. And when the thermodynamics of a road are out of balance water is the most important substance that transfers forces to balance the instability.


2.6.2. Suction properties of unsaturated soils and road materials


In soils and unbound aggregates with low moisture contents, suction generates tension between the soil particles in the pore water and increases the stiffness of the material leading to a high modulus value. If the moisture content then increases, the suction decreases until at high water content the positive pore water pressures generated reduce the material’s resistance to permanent deformation. The most important suction components in the mechanical performance of unbound road structures and subgrade soils are 1) matric suction, 2) osmotic suction and, in the cold climate areas 3) cryo suction. The sum of matric suction and osmotic suction is also called “total suction”.


Matric suction is mainly controlled by void ratio, voids’ size and the amount of fines in the material, while the amount of ionic compounds affects the level of osmotic suction. A good example of suction in roads is the way that the tensile strength can be created in a gravel road wearing course material, and its resistance to dusting can be improved, by the application of a dust binder. Increasing the fines content in a wearing course material increases matric suction, and adding a dust binder (chlorides) to the material increases osmotic suction.


Cryosuction becomes effective when the temperature in the soil or road materials drops below 0°C. Cryosuction is independent of total suction. Cryosuction is the force which causes water (if it is available) to flow to the freezing front and then form segregation ice.

2.7. Ground water – capillary zone – intermediate vadose zone


Water in road structures and subgrade soils can be divided into two or three major zones, where the thermodynamic forces are different. The lowest zone is the groundwater zone where the pores of materials are completely saturated with water. The groundwater table separates the unsaturated zone and the saturated zone. The unsaturated zone can also be called the “vadose” zone and the saturated zone can be called the “phreatic” zone.

The vadose zone can be sub-divided into three zones:

  • the capillary zone (or capillary fringe),
  • an intermediate vadose zone (the adsorption water zone) and
  • the surface water zone.

The capillary zone is located above the groundwater table and water in the capillary zone is pulled upward from the groundwater table by matric suction. As described earlier, capillary forces (matric suction) are governed by the pore size distribution of the material and the capillary rise will be larger when the pore sizes are smaller. The thickness of the capillary zone can vary from a few centimetres (as with coarse grained soils) to a few metres (as with fine grained soils).


In the adsorption / intermediate vadose zone the water is held by suction forces. When the surface layer (pavement) is in good condition and impermeable, the water held in this zone should be relatively stable with a water content at or near field capacity. During the spring thaw weakening or wet periods the water content may be higher. When the pavement is cracked, water flows from the road surface through the intermediate vadose zone to the capillary zone.


The surface water zone is the closest to the surface. When the pavement or wearing course is in good condition the water content in this zone should be relatively constant, close to the field capacity or lower depending on atmospheric conditions. When the pavement is cracked or distressed water from the road surface can enter into the road structure through cracks. During rainy periods the water content in the surface water zone can rise, and even become fully saturated. ./p>

2.8. What happens when a road / soil freezes


Different processes and different forces start to dominate in the ground when the temperature drops below 0?C and water in the ground starts to freeze. The first water to freeze is the water in the biggest water filled voids; in other words free water freezes first at temperatures between 0o and minus 0.5o C. At this time a strong cryo-suction force rises at the freezing front. This has the capability to adsorb and trap water molecules quite far beneath the freezing front if there is free water available. This can expand the pores and loosen the aggregate layers. When this material then subsequently thaws, excess water is produced in the layer that makes it weaker and thus sensitive to permanent deformation.


Fine graded soils have a large specific surface area and can hold a high amount unfrozen adsorption water when temperatures drop below 0?C. Below -0,5?C the adsorption water starts to freeze and water flows to the freezing front.

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Demonstration showing the freezing process when the temperature drops fast (e.g. -10°C). Because the freezing happens quickly, the water has no time to flow to the freezing front before the material totally freezes, and as a result no more water can move to the freezing front. In this case the frost heave or frost expansion will be quite low.
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Demonstration showing the process when the temperature drops slowly. Now the freezing takes a long time and the water has enough time to flow to the freezing front and grow segregation ice (ice lenses). In this case the amount of frost heave or frost expansion is now high.

The height of frost heave also depends partly on the temperature of the local environment. If the temperature drops fast, for example to -10°C, ice lenses will not have time to grow so much as when the temperature drops slowly. The features of soil that affect the amount of unfrozen water in the ground are; the mineralogical properties of soil, salt content, its granularity, the specific area of the soil particles and surface tension.

References other than ROADEX information and publications used in this chapter: Andrew Dawson: Water in road structures D. G. Fredlund & H. Rahardjo: Soil mechanics for unsaturated soil

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