void ratio

8/13/2019 Void Ratio

1/11

III-1

PARTICULATE MEDIA:

CHARACTERIZATION OF PARTICULATE MEDIA(Phase relationships, specific gravity)

Phase relationships: indirect measure of particle arrangement (fabric)

Void ratio:

sV

vV

e

Porosity:

vV

sV

vV

Vv

Vn

T

e

en

evV

vV

sV

n

1

11

1

Porosity and void ratio for natural sands depend a great degree upon on the shape and size

distribution of the particles.

e 0.5 to for sand and gravel soils

0.7 to for most common clays

3.0 to for colloidal clays

n 30% to for sand and gravel soils

Water or moisture content:

sW

wW

For sands 10% to

For clays 5% to

Phase relationships (density & volume)

Packing of regular spheres

Friction

Grain size distribution

Solids, 26.5 kN/m3

Water, 9.81 kN/m3

Air, 0.01 kN/m3 VA, WA

VW, WW

VS, WS

VV

V, W


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III-2

Degree of saturation:

vVwVS Extreme values seldom approached

Air content:V

aV

A

Unit weight, Mass density:V

W

V

M

g

, g = 9.81 m/s

2

Specific gravity:w

G

Soil particles G 2.6 to 2.8

w9.81 kN/m3@ 21C

Relative density (granular soils):minee

ee

ma

max

xrD

Very loose: 0% to Loose: 15% to

Medium dense: 35% to Dense: 70% to

Very dense: 85% to

Specific gravities:

Quartz 2.65 Sand 2.65

K-Feldspars 2.65 - 2.57 Silty Sand 2.66 - 2.68

Na-Ca-Feldspars 2.62 - 2.76 Silt 2.67 - 2.68Calcite 2.72 Silty Clay 2.70 - 2.72

Dolomite 2.85 Clay 2.70 - 2.80

Muscovite 2.7 - 3.1

Biotite 2.8 - 3.2 Gs > 2.80 - likely metals present

Chlorite 2.6 - 2.9 Gs < 2.70 - likely organics present

Pyrophyllite 2.84

Serpentine 2.2 - 2.7 Average Gs for sand = 2.65

Kaolinite 2.61a

Average Gs for well mixed soil = 2.70

2.64+/-0.02

Halloysite (2 H2O) 2.55

Illite 2.84a

2.60 - 2.86

Montmorillonite 2.74a

2.75 - 2.78

Attapulgite 2.3

aCalculated from crystal structure.

Specific Gravities of Minerals Specific Gravities of Soils

Figure 1.4 Craigs Soil Mechanics (2012)


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III-3

Some typical values of void ratio, moisture content and dry unit weight for soils are given next

(Das, 2010).


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III-4

Example III-1:

A soil has = 8%, GT= 1.9, GS= 2.65. Find (a) void ratio e, (b) degree of saturation S,

and (c) How much water has to be added to 1m3to increase to 13%?

SOLIDS

WATER

AIR VA, WA

VW, WW

VS, WS

VV

VT,WT


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III-5

a) Void ratio e

b) Degree of saturation S

c) How much water per m3to increase to 13%?


6/11

III-6

PARTICLE SIZE DISTRIBUTION CURVES

Unified Soil Classification System

A soil classification system provides:

a systematic method of categorizing soils according to their probable engineering behaviour;

a common base to communicate soil information between engineers; and

a common system to accumulate experience on the engineering behaviour of soils.

Role of the classification system in geotechnical engineering:

(Holtz and Kovacs, 1981)

Different classification systems have evolved over the years, but the one most comonly used in

geotechnical engineering is the Unified Classification System (USCS). Simplistic model of the

Unified Soil Classification System:

Classification and Index properties

(w, e, , S, GSD, LL, PI etc.)

Classification System

Language

Engineering Properties

(permeability, compressibility,

shrink-swell, shear strength etc.)

Engineering Purpose

(highways, airfields,

foundation, dams etc.)

Sands Gravels

Coarse Grained

Clays Silts

Fine Grained

Soils


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III-7

The system was originally developed in 1948 by Professor A. Casagrande for airfield

construction during World War II. It has been subsequently modified (only slightly).

The basis of the USCS is that: coarse grained soils can be classified according to their grain size

distributions; and the engineering behaviour of fine grained soils is primarily related to their

plasticity. Therefore, sieve analysis and Atterburg limits are needed to classify a soil.

A soil is classified using a two letter symbol:

The first letter describes the major component of the soil according to four major divisions:

coarse grained soils (gravel (G) and sand (S)); fine grained soils (silt (M) and clay (C)); organic

soils (O); and peat (Pt).

The second letter describes the soil relating to: whether a coarse grained soil is well (W) or

poorly (P) graded; whether a coarse grained soil contains appreciable silt (M) or Clay (C); and

whether a fine grained soil has high plasticity (H) or low plasticity (L).

Characterization of particulate materials based on particle sizes:

Coarse-grained soils (Gravel, Sand) form 0.075 mm to 75.0 mm (3 orders of magnitude)

Fine-grained soils (Silt, Clay) from


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III-8

Other classification systems were developed by the Massachusetts Institute of Technology

(MIT), the U.S. Department of Agriculture (USDA) and the American Association of State

Highway and Transportation Officials (AASHTO). The next table shows the particle-size

classifications (Das, 2010).

Particulate size analysis:

Since soil particles are rarely perfect spheres, particle diameter (or size) refers to an equivalentparticle diameter as found from the sieve analysis. In Canada, we often use the U.S. Standard

Sieves.

Sieve

Mesh

W1

W2

W3

W-N

W-pan


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III-9

The sieve sizes are:

Sieve No. Sieve Opening (mm)

3" 75

1.5" 380.75" 19

0.375" 9.5

#4 4.75

#10 2.00

#20 0.85

#40 0.425

#60 0.25

#100 0.15

#140 0.106

#200 0.075

Nested sieves are used for soils with grain sizes larger than 75 m. For finer soils (silts and clays)

the hydrometer test (sedimentation analysis) is used.

After performing a sieve analysis, the percent of passing material (percent finer for each sieve) is

plotted against the sieve opening size (in log scale). This plot is referred to as the particle-size

distribution curve.

Figure 1.13 Craigs Soil Mechanics (2012)


10/11

III-10

Example of sieve analysis. Total weight = 500 g

Sieve # Size (mm) W-retained

(g)

W-r

(g)

W-passing

(g)

% Passing

3/8 9.5 0 500

10 2 70 43020 0.85 90 340

40 0.425 160 180

100 0.15 85 95

200 0.075 50 45

Pan >0.075 45 N/A N/A

0.01 0.1 1 100

20

40

60

80

100

Particle size (mm)

%

Passing

Yi

Xi

Quantitative Characteristics:

Coefficient of uniformity (CU):

10

60

D

DCu

Coefficient of curvature (CC):6010

2

30

DD

DCc

Well graded sand: 1< CC< 3, CU

Well graded gravel: 1< CC< 3, CU

The higher CUthe larger the range of particles sizes in the soil

WP= WT- WR

86= (430/500)*100

Sieve 200

corresponds cosely

to the limit of

coarse-grained soil

(200 wires/inch)


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III-11

Examples of Particle size distributions ( CU= ? CC= ? )

1) Well graded soil: good representation of particle sizes over a wide range; gradationcurve is generally smooth.

2) Poorly graded soil: either excess or a deficiency of certain sizes, or most of the particlesabout the same size. (i.e. uniform soil)

3) Gap graded soil: a proportion of grain sizes within a specific range is low (it is alsopoorly graded).

% Passing

%Passing

Log (Particle size)

%Passing

Log (Particle size)

Log (Particle size)

1) 2)

3)

void ratio

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