Phase Relations 1

1

2

Phase Relations

Phase Relations 2

Rock and Soil: A 3-Phase Material

Solid

WaterAir

4

Three Phase Diagram

Solid

Air

Water

Mineral Skeleton Idealization:

Three Phase Diagram

Phase Relations 3

5

Objectives

To compute the masses (or weights) and volumes of the three different phases.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

Notation

M = mass or weight

V = volumes = soil grains

w = water

a = air

v = voids

t = total

6

Definitions

Water content (w) is a measure of the water present in the soil.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

S

W

M

Mw =

Expressed as percentage.

Range = 0 – 100+%.

X 100%

Phase Relations 4

7

Definitions

Void ratio (e) is a measure of the void volume.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

S

V

V

Ve =

8

Definitions

Porosity (n) is also a measure of the void volume, expressed as a percentage.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

T

V

V

Vn = X 100%

Theoretical range: 0 – 100%

Phase Relations 5

9

Definitions

Degree of saturation (S) is the percentage of the void volume filled by water.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

V

W

V

VS =

Range: 0 – 100%

X 100%

Dr

y Saturate

d

10

A Simple Example

water

air

soil

In this illustration,

e = 1

n = 50%

S = 50%

Phase Relations 6

11

Specific Gravity

Unit weight of Water, γw

γw = 1.0 g/cm3 (strictly accurate at 4°

C)

γw = 62.4 pcf

γw = 9.81 kN/m3

WaterofVolumeEqualanofWeight

ceSubsaofWeightGravitySpecific

tan=

WaterofWeightUnit

ceSubsaofWeightUnitGravitySpecific

tan=

12

Specific Gravity

Iron 7.86

Aluminum 2.55-2.80

Lead 11.34

Mercury 13.55

Granite 2.69

Marble 2.69

Quartz 2.60

Feldspar 2.54-2.62

Phase Relations 7

13

Specific Gravity, Gs

14

Definitions

Bulk density (ρm) is the density of the soil in the

current state.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

T

Tm

V

M=ρ

Units: t/m3, g/ml, kg/m3

Phase Relations 8

15

Definitions

Saturated density (ρsat) is the density of the soil when the voids are filled with water.

Submerged density (ρ’) is the effective density of the soil when it is submerged.

ρ’ = ρsat - ρw

16

Definitions

Dry density (ρd) is the density of the soil in dry

state.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

T

Sd

V

M=ρ

Units: t/m3, g/ml, kg/m3

Phase Relations 9

17

Definitions

Bulk, saturated, dry and submerged unit weights (γ)are defined in a similar manner.

γ = ρg

Here, use weight (kN) instead of mass (kg).

Specific gravity of the soil grains (Gs) typically varies between 2.6 and 2.8.

kg/m3N/m3 m/s2

Phase RelationsConsider a fraction of the soil where Vs = 1.

soil

air

water

1 Gsρρρρw

SeρρρρwSe

e

Phase Diagram

The other volumes can be obtained from the previous definitions.

Mass = Density x Volume

volumes masses

The masses can be obtained from:

Phase Relations 10

19

Phase RelationsFrom the previous definitions,

soil

air

water

1 Gsρρρρw

SeρρρρwSe

e

Phase Diagram

SS

W

G

Se

M

Mw ==

e

e

V

Vn

T

V

+==

1

20

Unit Weights

The bulk unit weight

The saturated unit weight (S = 1)

The dry unit weight (S = 0)

The submerged unit weight

γγ γ γ

bulk

w s s w s

s s

w sW

V

G V eSV

V eV

G eS

e= =

+

+=

+

+

( )

1

γγ

sat

w sG e

e=

+

+

( )

1

γγ

d r y

w sG

e=

+1

γ γ γ' = −sat w

Phase Relations 11

21

Phase Relations

soil

air

water

1 Gsρρρρw

SeρρρρwSe

e

Phase Diagram

WS

T

Tm

e

SeG

V

Mρρ

+

+==

1

WS

T

Tsat

e

eG

V

Mρρ

+

+==

1

WS

T

Sd

e

G

V

Mρρ

+==

1

22

Typical Unit weights

Phase Relations 12

23

Relative Density (Dr)Measure of how densely the grains are packed in a coarse grain soil in %.

0 100

Loosest Densest

minmax

max

ee

eeDr

−

−=

Also known as density index (ID).

24

Try not to memorise the equations. Understand the definitions, and develop the relations from the phase diagram with VS = 1;

Assume GS (2.6-2.8) when not given;

Do not mix densities and unit weights;

Rock and Soil grains are incompressible. Their mass and volume remain the same at any void ratio.

Phase Relations 13

25

Testing Times…

State whether the following are true or false?

(a) Dry density is greater than submerged density

(b) In unsaturated rocks, water content is always

less than 100%.

(c) Larger the void ratio, larger the porosity.

True

False

True

26

Example 1

Phase Trimmings Mass

(g)

Sample Mass, M

(g)

Sample Weight, Mg

(kN)

Total 55 290 2845 × 10-6

Solid 45 237.3 2327.9 × 10-6

Water 10 52.7 517 × 10-6

• Distribution by mass and weight

Phase Relations 14

27

Example 1

Phase Trimmings Mass

(g)

Sample Mass, M

(g)

Sample Weight, Mg

(kN)

Total 55 290 2845 × 10-6

Solid 45 237.3 2327.9 × 10-6

Water 10 52.7 517 × 10-6

• Distribution by mass and weight

• Distribution by volume (assume Gs = 2.65)

Total Volume V = π r2 l

28

Example 1

Phase Trimmings Mass

(g)

Sample Mass, M

(g)

Sample Weight, Mg

(kN)

Total 55 290 2845 × 10-6

Solid 45 237.3 2327.9 × 10-6

Water 10 52.7 517 × 10-6

• Distribution by mass and weight

• Distribution by volume (assume Gs = 2.65)

Total Volume V = π r2 l

Water Volume VW

w

w

w

=γ

Phase Relations 15

29

Example 1

Phase Trimmings Mass

(g)

Sample Mass, M

(g)

Sample Weight, Mg

(kN)

Total 55 290 2845 × 10-6

Solid 45 237.3 2327.9 × 10-6

Water 10 52.7 517 × 10-6

• Distribution by mass and weight

• Distribution by volume (assume Gs = 2.65)

Total Volume V = π r2 l

Water Volume

Solids Volume

VW

w

w

w

=γ

VW

Gs

s

w s

=γ

30

Example 1

Phase Trimmings Mass

(g)

Sample Mass, M

(g)

Sample Weight, Mg

(kN)

Total 55 290 2845 × 10-6

Solid 45 237.3 2327.9 × 10-6

Water 10 52.7 517 × 10-6

• Distribution by mass and weight

• Distribution by volume (assume Gs = 2.65)

Total Volume V = π r2 l

Water Volume

Solids Volume

Air Volume Va = V - Vs - Vw

VW

w

w

w

=γ

VW

Gs

s

w s

=γ

Phase Relations 16

31

Moisture content mW

W

w

s

= = = =10

450 222 22 2. . %

32

Moisture content

Voids ratio

mW

W

w

s

= = = =10

450 222 22 2. . %

eV

V

V V

V

v

s

a w

s

= =+

= 0 755.

Phase Relations 17

33

Moisture content

Voids ratio

Degree of Saturation

mW

W

w

s

= = = =10

450 222 22 2. . %

eV

V

V V

V

v

s

a w

s

= =+

= 0 755.

SV

V

V

V V

w

v

w

a w

= =+

= =0 780 78 0. . %

34

Moisture content

Voids ratio

Degree of Saturation

Bulk unit weight

mW

W

w

s

= = = =10

450 222 22 2. . %

eV

V

V V

V

v

s

a w

s

= =+

= 0 755.

SV

V

V

V V

w

v

w

a w

= =+

= =0 780 78 0. . %

γ bulk

W

VkN m= = 181 3. /

Phase Relations 18

35

Moisture content

Voids ratio

Degree of Saturation

Bulk unit weight

Dry unit weight

mW

W

w

s

= = = =10

450 222 22 2. . %

eV

V

V V

V

v

s

a w

s

= =+

= 0 755.

SV

V

V

V V

w

v

w

a w

= =+

= =0 780 78 0. . %

γ bulk

W

VkN m= = 181 3. /

γ dry

sW

VkN m= = 14 8 3. /

36

Moisture content

Voids ratio

Degree of Saturation

Bulk unit weight

Dry unit weight

Saturated unit weight

Note that γdry < γbulk < γsat

mW

W

w

s

= = = =10

450 222 22 2. . %

eV

V

V V

V

v

s

a w

s

= =+

= 0 755.

SV

V

V

V V

w

v

w

a w

= =+

= =0 780 78 0. . %

γ bulk

W

VkN m= = 181 3. /

γ dry

sW

VkN m= = 14 8 3. /

γ sat

W

VkN m=

+ × ×=

−( . . )

. /14 9 10 981

19 046

3

Phase Relations 19

37

Example 2

Volume and weight distributions

Phase Volume

(m3)

Dry Weight

(kN)

Saturated Weight

(kN)

Voids 0.7 0 0.7 × 9.81 = 6.87

Solids 1.0 2.65 × 9.81 = 26.0 26.0

38

Example 2

Volume and weight distributions

Dry unit weight,

Phase Volume

(m3)

Dry Weight

(kN)

Saturated Weight

(kN)

Voids 0.7 0 0.7 × 9.81 = 6.87

Solids 1.0 2.65 × 9.81 = 26.0 26.0

γ dry

kN

mkN m= =

26 0

17153

3

3.

.. /

Phase Relations 20

39

Example 2

Volume and weight distributions

Dry unit weight,

Saturated unit weight

Phase Volume

(m3)

Dry Weight

(kN)

Saturated Weight

(kN)

Voids 0.7 0 0.7 × 9.81 = 6.87

Solids 1.0 2.65 × 9.81 = 26.0 26.0

γ dry

kN

mkN m= =

26 0

17153

3

3.

.. /

γ sat

kN

mkN m=

+=

( . . )

.. /

260 687

17193

3

3

40

Example 2

Volume and weight distributions

Dry unit weight,

Saturated unit weight

Moisture content (if saturated)

Phase Volume

(m3)

Dry Weight

(kN)

Saturated Weight

(kN)

Voids 0.7 0 0.7 × 9.81 = 6.87

Solids 1.0 2.65 × 9.81 = 26.0 26.0

γ dry

kN

mkN m= =

26 0

17153

3

3.

.. /

γ sat

kN

mkN m=

+=

( . . )

.. /

260 687

17193

3

3

m = = =6 87

26 00 264 26 4%

.

.. .

Phase Relations 21

41

Durability of Rock Materials

Longevity of the materials for use in construction (fill, backfill, rockfill)

Will the rock deteriorate when exposed to the elements, time, freeze-thaw, wet-dry cycles, temperatures, chemicals.

Tests used to accelerate exposure (slake durability, LA abrasion, freeze-thaw).

42

Slake Durability Test of Rocks

Evaluate shales and weak rocks that may degrade in service environment.

Rock fragments of known weight placed in rotating drum apparatus (ASTM D 4644).

Materials are circulated through wet & dry cycles.

reweigh rock fragments to determine the Slake Durability Index (SDI).

Phase Relations 22

43

Slake Durability Test

44

Slake Durability Testpotential weathering of exposed rock

Resistance to two standard cycles of

drying & wetting

Rotating drum (20 rpm); rotates in water

10 small dry lumps rotated for 10 mins

Dried out and repeated

Mass loss recorded

Phase Relations 23

45

Slake Durability Test

mass initial

lumpsdry of mass final index durability slake =