Suction and capillarity phenomena in unsaturated soils

Suction and capillarity phenomena in unsaturated soils

Domenico GALLIPOLI Professeur en mécanique des sols Institut Supérieur Aquitain du Bâtiment et des Travaux Publics (école d'ingénieurs) - Université de Pau et des Pays de l'Adour

33èmes Rencontres Universitaires de Génie Civil de l'AUGC

Anglet, 26 mai 2015

1

SUM

MA

RY

Suction and capillarity phenomena in unsaturated soils Summary

Introduction to unsaturated soils What are unsaturated soils? 2 Occurrence of unsaturated soils 3

Capillarity in unsaturated soils Pore pressures 5 Air-water interface 6 Mechanical effect of meniscus water 9

Basic constitutive laws Water retention in soils 13 Shear strength of unsaturated soils 16 Permeability 22

Soil suction measurement Measuring suction in soils 24 Psycrometer 25 Filter paper 27 Tensiometer 29

2

Unsaturated soils are those soils in which the void spaces are partly filled by a liquid and partly filled by a gas

An unsaturated soil is therefore a three-phases material made of solid, liquid and gas Usually the liquid is water and the gas is air

The liquid and gas phases can be continuous or discontinuous

What are unsaturated soils?

Air

Solid

Bulk water

(water flooding pores as

in saturated soils)

Meniscus water

(water present as lenses at inter-particle

contacts surrounded by dry, i.e. empty,

pores)

Occluded air

(air present as bubbles surrounded

by water inside a pore)

3

Unsaturated soils can occur as a natural material or as an artificial (compacted) material Natural unsaturated soils occur over large areas of the Earth, especially in dry environments, in the superficial soil layers above the phreatic surface Typical applications: shallow foundations, slope stability, shallow tunnels, groundwater and pollutant migration It is possible to have a layer above the phreatic surface where the soil presents negative values of pore water pressure while still being saturated

Occurrence of unsaturated soils

4

Artificial unsaturated soils are the product of remolding and compacting a mixture of dry soil and water Compacted soils are commonly used as a construction material Typical applications: road pavements, embankments, dams, retaining structures, nuclear waste disposal, earthen buildings)

Occurrence of unsaturated soils

5

In unsaturated soils the air pressure, ua is greater than the water pressure, uw but why?

The greater pressure at the interface between water and air will always be on the side where the meniscus interface is concave The contact angle and the morphology of soil particles determine whether the meniscus interface is concave on the side of air or the side of water For most soils the menisci at the air-water interface form very small contact angles on the water side (virtually 0 deg)

Pore pressures

Air

ua

Water

uw

6 Air-water interface

• Air pressure is greater than water pressure • Air pressure in unsaturated soils is usually zero (atmospheric value)

Pore water pressure in unsaturated soils is always negative (lower than atmospheric)

• The suction (s) is the pressure differential between air and water pressures: s = ua- uw

hence, if air pressure is zero (atmospheric): s = - uw

• This pressure differential between air and water is absorbed by the air-water interface that acts as a thin membrane

• The presence of this membrane at the interface between air and water explains why some insects can walk on water !

Water pressure uw

Air pressure ua

Infinitesimal portion of two-dimensional (cylindrical) meniscus

r

Tu u s w a

7 Air-water interface

• The pressure differential, i.e. the suction (s), depends on: - the principal radii of curvature (r1 and r2) of the air-water interface

- the magnitude of surface tension (T) within the membrane, which is equal to 7,28 10-2 N/m @ 20 C

1 2

T

Water pressure uw

Air pressure ua

r1 r2

Air-water

interface

T

T

T

r1 1 r2 2

Infinitesimal portion of three-dimensional meniscus

21w a

r

1

r

1Tu u s

(Laplace equation)

8 Question time

• What is the form of Laplace equation for the case of a spherical water meniscus of radius r (r1=r2=r) ? (the Laplace equation for the case of a spherical meniscus is often referred to as Kelvin’s capillary model)

• Calculate the value of suction for two spherical water menisci of radii 1 mm and 0.001 mm respectively

• Use Kelvin’s capillary model to calculate the height to which water will rise inside a glass capillary tube of 1 mm diameter submerged at its base in free water (assume that contact angle between water and glass is equal to zero)

9 Mechanical effect of meniscus water

• Unless saturated soils, in unsaturated soils pore water can be present under two different forms with different effects on the solid skeleton: - meniscus water = water present as lenses at inter-particle contacts surrounded by dry (empty) pores - bulk water = water flooding pores as in saturated soils

• The presence of water under these two different forms is the reason why the engineering behaviour of unsaturated soils differ from that of saturated soils


• By doing an equilibrium of forces, Fisher (1926) calculated the inter-particle reaction N generated by the meniscus pull at the contact between two spherical grains of radius R

• The forces on the soil particles due to the presence of the meniscus are: - the water pressure uw acting inside the meniscus - the surface tension T acting inside the air-water interface - the inter-particle reaction N

T T uw uw

N

ua ua r1

r2

N

uw

R

ua

ua

uw


• By combining the equilibrium equation with Laplace equation, one obtains the relationship between the inter-particle reaction N and suction s = ua- uw

• Curvature r1 is concave on the air while curvature r2 is concave on the water, so they enter with opposite signs in Laplace equation for calculating suction s

T T uw uw

N

ua ua r1

r2

N

uw

R

ua

ua

uw

2 1 w a

r

1

r

1Tuus

(Laplace equation)


• The variation of the inter-particle reaction N is relatively small over the whole range of suctions from zero to infinity: - at a suction s = 0, the inter-particle reaction N= 4/3 TR - at a suction s , the inter-particle reaction is only 50% larger than at s= 0 and equal to N= 2TR

• The cohesion induced by water menisci varies only marginally with suction and could be considered, as a first approximation, to be a function of the number of menisci alone

πTR3

4

ΔN

s = ua-uw

πTR2

0

13 Water retention in soils

• As suction increases and soil dries, water retreats into smaller voids leaving behind empty pores and forming new inter-particle menisci – see figures (a), (b), (c)

• As suction decreases and soil wets, water menisci coalesce and the empty pores are flooded again – see figure (d)

• Drying-wetting cycle shows hysteresis


• Degree of saturation Sr is the fraction of pore volume occupied by water (range 0 to 1)

• As suction increases and the soil is dried from a saturated state (Sr=1), the degree of saturation starts to decrease only after the air entry value of suction is exceeded

• The relationship between degree of saturation and suction is named the “water retention curve” - a soil element follows a different water retention curve depending on whether is being dried or wetted but also depending on the previous history of suction variation


• Soils having different grain size distributions have different water retention curves

• Different particle sizes imply different pore sizes with sand having the larger pore sizes, silt intermediate pore sizes and clay the smallest pore sizes

• Higher suctions are needed to extract water from the smaller clay pores, lower suctions are needed to drain the larger sand pores (i.e. clay has a larger air entry value of suction than sand with silt being in the middle of the two)

1

0

Sand

Sr

s=ua-uw

Clay Silt

16 Shear strength of unsaturated soils

• The analysis of geotechnical problems such as bearing capacity of foundations, slope stability, retaining wall require the knowledge of the shear strength of the soil

• For saturated soils the shear strength is characterised by a linear frictional relationship (the

Mohr-Coulomb relationship) between shear stress and effective normal stress (-uw) on the failure plane where: - is the shear stress on the plane of failure - (-uw) is the effective stress normal to the plane of failure - is the friction angle

Mohr-Coulomb failure envelope for saturated soils

tan uςcτ w


• In unsaturated soils, unlike saturated soils, it is impossible to describe the failure criterion in terms of a single effective stress variable

• Test performed under controlled suction indicate that the shear strength of an

unsaturated soil tends to increase with suction (ua-uw)

• Therefore the Mohr-Coulomb failure criterion changes from a linear relationship for saturated soils into an extended planar relationship for unsaturated soils

where: - is the shear stress on the plane of failure - (-ua) is the net stress normal to the plane of failure - (ua-uw) is the suction - is the friction angle - b is the suction angle

)tanu(ς)tanu(ucτ ab

wa


• The extended Mohr-Coulomb failure envelope provides a smooth transition from unsaturated condition to saturated condition

• As the soil approaches saturation we have:

• Therefore the intersection of the extended planar failure envelope with the plane corresponding to zero suction gives back the failure envelope of a saturated soil

• This also means that the angle coincides with the saturated friction angle in the ( , -uw) plane

wawa uu0uu wa uςuς

)tanu(ς)tanu(ucτ ab

wa

)tanu(ςcτ w


Extended Mohr-Coulomb failure envelope for unsaturated soils

• Suction (ua-uw)=0 corresponds to saturated conditions

• Therefore the intersection of this surface with the frontal plane at zero suction gives the Mohr-Coulomb failure envelope for saturated soils


As the soil approaches saturation at (ua-uw)=0 the total cohesion c tends to the effective cohesion c

Failure envelope projections on the (, -ua) plane

• The extended Mohr-Coulomb envelope can be presented as a number of failure lines projected in the (, -ua) plane, each line corresponding to a different constant suction

• All lines have different “total cohesion” intercepts, depending on their value of suction, but the same slope , which is the same as the saturated friction angle

• Therefore the failure surface intersects the (, ua-uw) plane along a line which describes the variation of total cohesion, c with suction according to the following equation: b

wa )tanu(ucc


Failure envelope projections on the (, ua -uw) plane

• The extended Mohr-Coulomb envelope can also be presented as a number of failure lines projected in the (, ua-uw) plane, each line corresponding to a different constant net normal stresses

• Each line has the same slope angle b but different ordinate intercept depending on the corresponding value of net stress

22 Permeability

• What happens to soil permeability when the soil becomes drier?

• Why the infiltration capacity of a dryer soil is higher than the infiltration capacity of a soil in wetter conditions?

Sr = 1 1 > Sr > Sres Sr = Sres

23 Permeability

• Permeability decreases with increasing values of soil suction

• Volumetric water content (or degree of saturation) decreases as soil suction increases

• Hence permeability decreases as volumetric water content or degree of saturation decreases

c

b a

c

b

a

Log K

s

a = uniform sand

b = silty sand

c = silty clay

s

24 Measuring suction in soils

• Under thermodynamic equilibrium, suction is related to the relative humidity of the air inside the soil pores by means of Kelvin law: - s = suction - R = universal gas constant (8.31432 J/molK) - T = absolute temperature (K) - w = density of water (kg/m3) - w = molecular water mass (18.016 kg/kmol) - RH = relative humidity

RHlnω

TR ρs

w

w

suction, s [kPa]

rela

tive

hu

mid

ity,

RH

[%

]

T

T

T

25 Psychrometer

• Psychrometers measure suction within the soil by measuring the relative humidity of the air inside the pores

• The principle is to measure the temperature difference between a wet (evaporating)

surface and a dry (non evaporating surface) which is related to relative humidity

• Traditional Peltier psychrometers can not measure suctions beyond 8000 kPa but modern transistor psychrometers can measure suctions up to 70000 kPa

Soil sample chamber with sealed psychrometer in place

(after Brown and Collins, 1980)

26 Psychrometer

• Measurements can be taken only after isothermal conditions have been achieved between soil, surrounding air and psychrometer

• Psychrometers are extremely sensitive to temperature changes (a temperature control of

+/- 0.001 C is required for a suction accuracy of +/- 10 kPa - isothermal conditions are ensured by placing psychrometers in a constant temperature bath

• Psychrometers are mainly used in the laboratory because temperature oscillations make their use not viable in situ

Schematic diagram of a constant temperature bath

(after Krahn and Fredlund, 1972)

27 Filter paper

• The filter paper method assumes that a filter paper, placed in contact with a soil sample, will attain suction equilibrium at a given water content

• This method can measure the full range of suction and is mainly used in the laboratory on samples obtained from the field

• Suction is estimated from the water content in the filter paper at equilibrium by using a calibration curve (due to hysteresis appropriate calibration curve should be used)

Calibration curves for two types of filter papers

(after Fredlund and Rahardjo, 1993)

28 Filter paper

• The filter paper technique may be used to determine the water retention curve of a particular soil by testing different samples of that soil at various water content

• Filter paper is also used to establish the in situ suction profile of soil deposits by using undisturbed samples from the field

• Filter paper is also used to establish the in situ suction profile of soil deposits by using undisturbed samples from the field

Scheme for using filter papers to measure total suction in situ

(after Fredlund and Rahardjo, 1993)

29 Tensiometer

• Tensiometers are used to obtain direct measurements of pore water tension in the laboratory or in the field

• The tensiometer is made of a high air entry value porous ceramic cup in contact with the

soil. The water saturated ceramic cup is connected to a pressure-measuring device through a small tube

• Air pressure is usually atmospheric and therefore the pore water pressure is usually tensile

Tensiometers with different pressure-measuring devices

(after Morrison, 1983)

30 Tensiometer

• Once equilibrium has been achieved, the water in the soil and in the measuring system will have the same pressure

• The maximum suction a tensiometer can measure is limited by two factors:

- the air entry value of the porous cup - if the difference between air pressure and water pressure in the soil is higher that the air entry value of the porous cup then air will break into the tensiometer

- water cavitation inside the device - the maximum water tension that a tensiometer can read is 100 kPa after which cavitation occurs and air bubbles form inside the device

Tensiometers with different pressure-measuring devices

(after Morrison, 1983)

Merci de votre attention

CONTACT

Domenico GALLIPOLI Professeur en mécanique des sols

Institut Supérieur Aquitain du Bâtiment et des Travaux Publics (école d'ingénieurs)

[email protected]

http://univ-pau.academia.edu/DomenicoGallipoli

Suction and capillarity phenomena in unsaturated soils

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