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Universitat Politècnica de Catalunya · BARCELONATECH Escola Tècnica Superior d’Enginyers de Camins, Canals i Ports

Soil Mechanics

Chapter 1

Soil characterization

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Chapter 1

1. Phase diagrams and index properties of soils.

2. Grain-size distribution.

3. Soil consistency and Atterberg’s limits

4. Unified Soil Classification System

Exercises

Laboratory: practice 1 (index properties)

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Introduction

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Soils and rocks

• Transition between soft or altered rocks

and soils is not well defined. A hard soil

often behaves similarly to a rock

• A characteristic of a soil is that it is easily

broken up under small loads or when

dissolved in water.

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Scale of observation Geologic (~100 m) Geotechnical/engineering (~10 m)

E.g., for slope stabilty

analysis

Laboratory (~ 10 cm)

Laboratory samples

tipycal size is 7x15 cm

Microscopic (~ 1 μ)

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Soil’s nature

• Material components of a soil

– Solid particles

– Water • free water

• adsorbed water, attached to solid particles surface

• water vapor

– Air • free air

• air dissolved in water

– Dissolved salts (important in some soils)

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Phases of a soil

• Solid phase – solid particles

– adsorbed water

• Liquid phase – free water

– air dissolved in water

– dissolved salts

• Gas phase – free air

– water vapor

GAS PHASE

LIQUID PHASE

SOLID PHASE

Phase diagram

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Saturated and unsaturated soils

• Saturated soil: only two phases – there

is no gas phase

• Unsaturated soil: there are trhee phases

G

L

S

L

S

sat unsat

• Withour gas phase, there are no

surface tension (that appears at the

border between liquid and gas

phases)

• Three-phase soils are more

complicated to study than two-

phase (saturated) ones

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Solid particles

Gravel Sand Silt Clay > 2 mm

> 4.76 mm (3/16″)

0.06 < < 2 mm

0.074 < < 4.76 mm

2 μ < < 0.06 mm

2 μ < < 0.074 mm

< 2 μ (UNE)

< 2 μ (Lambe)

Particles are visible without aid Some apparatus, such as microscopes, are

needed to see the particles

Cohesionless Cohesive

― ― Do not stick to fingers

Rough texture

Stick to fingers

Soft texture

specific surface → s/w : 10-4 m2/g s/w : 1 m2/g

s/w : 103 m2/g montmorillonite

s/w : 20 m2/g kaolinite

Microscopic behaviour:

mechanical contact; very large stresses at

the contacts if φ is large

Microscopic behaviour:

chemical effects, colloidal structure,

physical-chemical effects

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Sand particles

0.42 to 0.48 mm 0.19 to 0.42 mm 0.11 to 0.19 mm

Ottawa Sand (Canada)

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Sand particles

Feldspar cristals,

0.19 to 0.42 mm

Quartz cristals,

0.19 to 0.42 mm Dolomite cristals,

0.19 to 0.42 mm

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Sand particles

Beach Sand, Hawaii Venezuela Sand Venezuela Sand,

compressed to 140 MPa

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Clay particles

Kaolinite Illite

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Chemical composition

• Sands and gravels: originate from mechanical

decomposition of rocks; chemical composition

does not influence their geotechnical behaviour.

• Clays: their composition is different from the

originating rock – usually hydrated silicates.

Their geotechnical behaviour is determined

mainly by:

– their specific surface

– how they react to water (expansive...)

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Clay chemistry

• Silts, sands and gravels may be

considered chemically inert, because of

their low specific surface

• Particle size in clays, is:

L L

L Le ≈3 100

to

Kaolinite: 1 μ 1 μ 0.1 μ Montmorillonite: 0.1 μ 0.1 μ 0.001 μ

Represented as:

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Composition and molecular structure of

the solid phase of clay minerals

• General classification of soils:

– Organic

• peat – large proportion of vegetal material (20% ...)

• dangerous soils for engineering purposes, very compressible

– Inorganic

• amorphous solid particles – scarce, more abundat in North

Europe

• crystalline solid particles :

– sulfates (gypsum) – not abundant, but problematic

– oxides

– hydroxides

– carbonates

– silicates – very abundant, represent more than 90% of all soils

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• The structure of the silicate crystals can be:

– three-dimensional (spatial): quartz, feldspar

– two-dimensional (flat): phyllosilicates (clay) – may

have a different chemical composition from the

originating rock

• In Earth:

– the most abundant anion is oxygen (50%)

– the most abundant cations are:

• Si4+ (27%); Al3+ (8%); Mg++; Ca++; K+; Na+; ...

the most abundant mineral is SiO2 = quartz

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• Molecular structures:

– Silicon (Si) – tetrahedral combinations

– Aluminium (Al) – tetrahedral and octahedral

combinations

– Other elements – in general octahedral

combinations

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• Typical structures of 2D silicates: sheets

or films piled one on another, each formed

by a layer of tetrahedrons or octahedrons:

– Type 1:1

– Type 2:1

tetrahedrons

octahedrons

tetrahedrons

octahedrons (with Al, Fe, Mg, ...)

tetrahedrons

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• A typical clay particle

consists of stacked sheets

of these elemental

structures (e.g. up to 100)

• Depending on the chemical

elements and the structure

type, different minerals

result

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Tetrahedron (SiO4)-4

Octahedron

Al(OH)6-3

Mg(OH)6-4

FLINTSTONE

GIBBSITE

these are electrically neuter

BRUCITE

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structure of serpentine structure of kaolinite

two layers: type 1:1

brucite + one

layer of flintstone

gibbsite + one

layer of

flintstone

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three layers: type 2:1

structure of pyrophyllite structure of moscovite

Gibbsite between

two flint layers

Gibbsite

between two flint

layers. Isomor-

phic substitution

of Al3+ by Si4+.

Electric equilib-

rium with K+ ions

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Double layer

• Silicate chains are not electrically neuter: negative

electrical charges concentrate on the particle surface,

attracting cations that on its turn attract water molecules

• These water molecules are almost part of the solid

particle: it is the adsorbed water

O

HH

HH

O

HH

O

HH

O

O

HH O

HH

DOUBLE LAYER “complete”

particle:

“strict”

particle +

double layer

“strict”

particle

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Double layer

• Cation concentration decreases as distance to

the particle increases

• The double layer is the layer containing a

certain percentage (e.g. 90%) of the cations

attracted by the particle

• The thickness of the double layer sets the

behaviour and interaction of one particle with its

neighbours, depending on the balance of

attractive and repulsive forces.

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Double layer

ca

tio

n c

on

ce

ntr

aio

n

distance to the particle (d)

high cation concentration

(small double layer)

low cation concentration

(large double layer)

(d)

distance

between

particles

rep

uls

ive

fo

rce

s

att

ractive

fo

rce

s

van der Waals forces

increase with the inverse

of distance

electrical forces

large double layer

small double layer

sum, large double layer

sum, small double layer

large double layer (large d)

→ disperse structure

small double layer (small d)

→ flocculated structure

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Double layer

• Surface-to-edge distance between particles

– flocculated

– non-flocculated

• Surface-to-surface distance between particles

– aggregated

– disperse

• Flocculated structures are stiffer and stronger

(except if they are very porous)

• Aggregated structures are less strong, although

they are more plastic and deformable.

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Double layer

• Smaller double layer with increasing

– cation concentration

– cation valence

– temperature

• Smaller double layer with decreasing

– medium’s dielectric constant

– pH

– cation size

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Double layer

• Double layer size:

– K = constant depending on the medium’s dielectric

constant, temperature, etc.

– v = cation valence

– n0 = cation concentration

• Cation Na+ – large d

• Cation Ca++ – small d

d

1/2

0

1 K

v n

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Phyllosilicates

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MICROPHOTOGRAPHS OF CAMPUS NORD SOIL P

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1.1

Phase diagram and index properties of soils

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Index properties of soils

• Model of a discontinuous medium with a continuous one

• Phase diagram: – Gas (air)

– Liquid (water)

– Solid (particles)

• Va+Vw = Vp (Vh)

• Vp+Vs = Vt

• Ww+Ws = Wt

AIR

WATER

SOLID

Vp

Vh

Va

Vw

Vs

Ww

Ws

volume weight

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• Porosity:

• Void ratio:

Vp

Vt

Vp

Vs

Vt

Vs

p

t

Vn

V

p

s

Ve

V

0 1n

0 e

non-

dimensional

non-

dimensional

larger range

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• Relation between porosity and void ratio

• Values (theoretical extremes with spheres):

1 1

1 111

1

p p

st p s

p

V V en

VV V V e

eV

ne

n

emax = 0.92 emin = 0.35

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• Actually, e depends on grain-size distribution,

coarseness and uniformity of the material …

• In general, e > 1 implies high deformability

Soil type emax emin

Clean sand 0.9 0.2

Silt 1.1 0.4

Soft clay 2.3 0.6

Peat 25 2

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• Relative density:

– 0 ≤ Dr ≤ 1 (or in %)

– Difficult to know, since emax and emin are not easily

evaluated

max

max min

r

e eD

e e

dense (100%) loose (0%)

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Vw

Vp

Vs

• Degree of saturation: – 0 ≤ Sr ≤ 1 (or in %)

– For clays, usually Sr > 0.8

– For sands, 0 ≤ Sr ≤ 1

• Water content:

– 0 ≤ w ≤ ∞ (or in %)

– Saturated sand: 20~30%

– Saturated clay: 25~60%

– Peat: 100~3000%

Va

Ww

Ws

Vw

Vp

Vs

Va

Ww

Ws

wr

p

VS

V

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• Natural (total) unit

weight Vp

Vs

Vt

Ww

Ws

Wt

Unit weights – given in kN/m3

tn

t

W

V

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• Average unit weight

of solid constituents

– Kaolinite: 26.3 kN/m3

– Illite: 27.8 kN/m3

– Quartz: 26.3 kN/m3

– Peat: 11~27 kN/m3

Vp

Vs

Vt

Ww

Ws

Wt


ss

s

W

V

Clays: 27 kN/m3

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• Dry unit weight (unit

weight of soil if water is

entirely replaced by air)

– Sand: 14 ~ 18 kN/m3

– Clay: 8 ~ 20 kN/m3

Vp

Vs

Vt

Ww

Ws

Wt


sd

t

W

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• Saturated unit weight (unit weight with pores entirely filled with water)

– Sand: 19 ~ 22 kN/m3

– Clay: 16 ~ 22 kN/m3

• Submerged unit weight

Vp

Vs

Vt

Ww

Ws

Wt


s p w

sat

t

W V

V

sat w WARNING!! w3=10 kN/m

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Relations between index properties

AIR

WATER

SOLID

Vp

Va

Vw

Vs

Ww

Ws

volume weight

Wt Vt

• Known data: w=10 kN/m3

• Known reference volume (e.g., Vt)

• Two known additional volumes, e.g.: (Vp,Vw), (Va, Vw), ...

• Weights: enough to know s, since w is a known constant

• Three independent indices:

– w, s, nat

– obtained from laboratory tests

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Vt=1

1-n

n

n(1-Sr)

nSr nSrw

(1-n)s

w(1-n)s

by definition

=W

wW

w

s(=1)

p

t

=V

nV

Therefore,

Other

relations:

(1 )(1 )

(1 )(1 )

1

(1 ) (1 ) (1 )

sr w s r

w

s sd s

t

tnat s r w s

t

w nnS w n S

n

W nn

V

Wn w nS n

V

volume weight

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1+e

Vs=1

e

e(1-Sr)

eSr eSrw

s

Ws

bydefinition

=W

wW

w

s(=1)

p

s

=V

eV

Therefore, sr w s r

w

weS w S

e

volume weight

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Experimental techniques to obtain index properties

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Laboratory techniques

• Water content from drying soil on a conventional (UNE

103300-1993) o microwave (ASTM 4643-87) oven

Ww

W

WW

Wtw s

ss

-= =

weight of natural

sample:

Wt = Ww + Ws

drying sample at

110ºC

weight of dry sample:

Ws

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• Average unit weight of solid constituents (UNE

103302-1994)

• The dry weight of the

sample is known (Ws)

• Determine the volume of

the solid constituents with

a pycnometer (Vs)

• The unit weight of solid

constituents is:

s

W

Vs

s

=

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• Natural unit weight (UNE 103301-1994)

natural

sample natural

sample

paraffin

Wt

Vt = ?

W1 = Wt + Wpar

V1 = Vt + Vpar

W2 = W1 – V1·w

hydrostatic scale

W W W

W W W VW

VWW WV

WV Vt

par 1 tpar 1 t par

par par t

t1 t1 21 pa

nat

r

w par

-= - = =

=--

= - = -

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Field techniques

In the field, index properties usually need to be know fast:

• s is assumed known

• to measure the water content, w:

– measure the weight of a soil sample on a scale, Wt

– burn the sample with alcohol and weigh again to obtain the

dry weight, Ws

– with these two values, the water content w is obtained as in the

laboratory tests:

Ww

W

WW

Wtw s

ss

-= =

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Field techniques

• to measure the natural unit weight, nat:

– make a hole on the soils surface and measure the weight of the

excavated material, Wt

– fill the hole up to the original surface with a normalized sand,

using an apparatus allowing measurement of the needed sand

volume, which is equal to the volume of excavated soil, Vt

– with these two values the natural unit weight is obtained as in the

laboratory tests:

• with these field techniques the index properties can be

obtained in less than one hour

V

W

t

natt=

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1.2

Grain-size distribution

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Sieve test

• The purpose is to determine the grain-size

distribution of the soil particles:

Classification Size

Gravel > 2.0 mm (4.76 mm)

Sand coarse 0.6 < < 2.0 mm

medium 0.2 < < 0.6 mm

fine 0.06 < < 0.2 mm

Silt coarse 0.02 < < 0.06 mm

medium 0.002 < < 0.02 mm

fine < 2 μ

Clay …

sie

ve test

decanta

tion test

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Sieve test

German-type

sieve (DIN)

US (ASTM) and

Spanish-type

(UNE) sieve

Mechanical sieve apparatus

UNE 103101-1995

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Sieve test Sieve mm ″

4 101.6 4

3-1/2" 88.9 3.5

3" 76.2 3

2-1/2" 63.5 2.5

2" 50.8 2

1-3/4" 44.4 1.75

1-1/2" 38.1 1.5

1-1/4" 31.7 1.25

1" 25.4 1

7/8" 22.2 0.875

3/4" 19.1 0.750

5/8" 15.9 0.625

1/2" 12.7 0.500

7/16" 11.1 0.438

3/8" 9.52 0.375

5/16" 7.93 0.312

coarse ASTM sieves

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Sieve test Sieve mm ″

1/4″ 6.35 0.250

1/2″ 5.66 0.223

# 4 4.76 0.187

# 5 4.00 0.157

# 6 3.36 0.132

# 7 2.83 0.111

# 8 2.38 0.0937

# 10 2.00 0.0787

# 12 1.68 0.0661

# 14 1.41 0.0555

# 16 1.19 0.0469

# 18 1.00 0.0394

# 20 0.84 0.0331

# 25 0.71 0.0280

# 30 0.59 0.0232

# 35 0.50 0.0197

Sieve mm ″

# 40 0.42 0.0165

# 45 0.35 0.0138

# 50 0.297 0.0117

# 60 0.250 0.0098

# 70 0.210 0.0083

# 80 0.177 0.0070

# 100 0.149 0.0059

# 120 0.125 0.0049

# 140 0.105 0.0041

# 170 0.088 0.0035

# 200 0.074 0.0029

# 230 0.062 0.0024

# 270 0.053 0.0021

# 325 0.044 0.0017

# 400 0.037 0.0015

fine ASTM sieves

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Sieve test

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Decantation test • Purpose: to determine the grain-size distribution

of the fine fraction of solid particles (passing sieve # 200) UNE 103102-1995

• Background theory is Stokes Law: decantation velocity of a spherical particle within a liquid medium is:

• where D = diameter of the particle

• η = 0.001009 N·s/m2 is the fluid viscosity

• v is constant if 0.02 μ ≤ D ≤ 0.05 mm

2

18

s wv D

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Decantation test

• At depth z, and time t after initiation of the

decantation process, no particles with diameter

larger than the one corresponding to decantation

velocity z/t may exist.

z

v = 0.1 mm/s

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Decantation test

• The size (D) of the particles that at time t are at depth z is at the most:

• The number of particles of size less than D is the same as initially was at that depth because, as they decant, smaller particles are replaced by the ones decanting from above.

18

s w

zD

t

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Decantation test

• The percentage N≤D, in weight, of particles with diameter less than D relative to the total weight can be obtained as the ratio between the weight (concentration) C(z,t) of the particles at depth z and time t, and the initial weight (concentration) C(z,0) at that point:

• To measure the particle concentration at certain depths and times, a small sample is taken from the suspension at the desired depth with a chemical dropper (pipette). The weight of the solid particles can be measured with a precision scale after evaporation of the liquid in an oven.

( , )(%) 100

( ,0)D

C z tN

C z

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Decantation test • Restrictions:

– Particle flow within the fluid must be laminar, implying decant-

ation velocities corresponding to diameters less than 0.05 mm.

– Shape of real particles (especially in clays) is not spherical –

thus one actually measures the diameter of a sphere with the

same decantation velocity as the irregular particle.

– Stokes Law is valid for a single sphere – therefore particle

concentration in the suspension needs to be low (usually 50 g/l)

– Particles with a diameter less than 2 μm will be subjected to

Brownian motion.

– Particles must be in a disperse state, not forming aggregates of

larger size. If necessary, chemicals must be added to ensure

particle dispersion. Also, for clays, the double layer masks the

real particle size.

– Water-soluble salts within the solid matrix may distort the results.

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Decantation test

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Grain-size curves

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Grain-size curves

D60 D30 D10

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Grain-size curves

• Uniformity coefficient:

– Uniform sand: CU < 6

– Uniform gravel: CU < 4

– Uniform ≡ poorly graded

60

10

1 UU CD

CD

single size maximum

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Grain-size curves

• Coefficient of curvature:

– Usually: 1 < CC < 3

2

30

10 60

C

DC

D D

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Grain-size curves

1

2

CU = 3.9

CC = 0.9

CU = 5.2

CC = 2.9

CU = 7.1

CC = 4.3 1 & 2 have the

same CU = 2.9

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Classification of soils according to grain-size

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1.3

Soil consistency and Atterberg’s limits

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Consistency

• Depending on its water content, a soil may

be in one of several states::

– liquid

– plastic

– semi-solid

– solid

more water

content

more

consistency

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Atterberg Limits

• The Atterberg limits are the threshold

water content values between liquid,

plastic, semi-solid and solid consistencies. (proposed by the Swedish engineer Albert Atterberg in

1911, and generalized by Arthur Casagrande in 1932)

solid semi-solid plastic liquid

water content, w w = wR w = wP w = wL

shrinkage

limit

wR

plastic

limit

wP

liquid

limit

wL

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Atterberg Limits

• Liquid limit (UNE 103103-1994)

– Is the water content of a soil at which two

sections of a pat of soil separated by a

standard groove touch each other when

subjected to 25 sharp blows from below using

a standard device (Casagrande’s spoon)

spoon

handle tools to make the groove

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Atterberg Limits

• Liquid limit (UNE 103103-1994)

– The results are affected by:

• the type of tool used to make the groove

• the type of material at the base of the spoon

• speed at which the blows are given

– Alternative: to define liquid limit as the water

content at which a standard cone penetrates

a normalized length into a soil sample

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Atterberg Limits

• Plastic limit (103104-1993)

– Is the water content at which the soil begins

to crumble (cracks begin to form) when rolled

into thin threads of about 3 mm.

– Results are more consistent, independently of

operator and conditions, than results of the

liquid limit.

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Atterberg Limits

• Shrinkage limit

– Is the water content below which further loss

of water by evaporation does not result in a

reduction of volume. As soon as the soil

passes below the shrinkage limit its colour

become slightly lighter.

– Much less used than the other two limits

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Atterberg Limits

wR wP wL

water content, w

tota

l vo

lum

e

unsaturated saturated

within this range the

soil is saturated, but

water is under

tensile stress

(negative porewater

pressure)

drying

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Derived indices

• Plasticity index

• Consistency index

• Liquidity index

• Activity

p L PI w w

Lc

w wI

IP

Pw wI

IP

% 2

pIA

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Plasticity chart (Casagrande)

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• Line A: IP = 0.73(wL–20)

– Points that represent samples of soil from the

same stratum define a straight line that is

roughly parallel to line A.

• High values of the liquid limit are related to

high deformability (compressibility)

• H = high wL; L = low wL

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• Soils with a high clay fraction (percentage

of particles in weight with particle size less

than 2μ) are represented by points above

line A, while silt and organic soils are

represented by points below line A.

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Unified Soil Classification System

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Letter Definition

G gravel

S sand

M silt

C clay

O organic

Letter Definition

P poorly graded (uniform particle sizes)

W well graded (diversified particle sizes)

H high plasticity

L low plasticity

The Unified Soil Classification System (or USCS) is a soil classification

system used in engineering and geology disciplines to describe the texture

and grain size of a soil. The classification system can be applied to most

unconsolidated materials, and is represented by a two-letter symbol. Each

letter is described below (with the exception of Pt):

First and/or second letter Second letter

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Major division Group

symbol Group name

coarse

grained soils

more than

50% retained

on No.200

(0.075 mm)

sieve

gravel

> 50% of

coarse

fraction

retained on

No.4 (4.75

mm) sieve

clean gravel

<5% smaller

than #200

Sieve

GW well graded gravel,

fine to coarse

gravel

GP poorly graded

gravel

gravel with

>12% fines

GM silty gravel

GC clayey gravel

sand

≥ 50% of

coarse

fraction

passes No.4

sieve

clean sand SW well graded sand,

fine to coarse sand

SP poorly graded sand

sand with

>12% fines

SM silty sand

SC clayey sand

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Major division Group

symbol Group name

fine grained

soils

more than

50% passes

No.200 sieve

silt and clay

liquid limit < 50

inorganic ML silt

CL clay

organic OL organic silt,

organic clay

silt and clay

liquid limit ≥ 50

inorganic MH silt of high plasticity

CH clay of high

plasticity

organic OH organic clay,

organic silt

highly organic soils Pt peat

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