lecture tow

01/05/23 BYDr.IBRAHIM

1

Soil Phase RelationshipsSoil Phase Relationshipsللتربة الظاهرية للتربة العالقات الظاهرية العالقات

01/05/23 Soil Phase Relationships 2

التربة التربة مكونات Soil CompositionSoil Compositionمكونات

Soil Grain or Soil Grain or particleparticle

التربة التربة حبيبات Soil GrainsSoil Grains( ( 11حبيبات

22 & ) & )33 ) )Voids: Water + AirVoids: Water + Air

الفراغات )عبارة عن ماء وهواء(الفراغات )عبارة عن ماء وهواء(

VoidsVoids


الفراغات الفراغات نسبة Void RatioVoid Ratioنسبة

Solid, VSolid, Vss

Void, VVoid, Vvv

e =e =VVvv

VVss

high e =high e = LooseLooseسائبسائب

low e =low e = DenseDenseكثيفكثيف


Saturation Saturation بالمياه بالمياه التشبع التشبع

Voids, VVoids, Vv v = V= Vww + V+ Vaa

Air, Va

Water, VWater, Vww

VVvv = V = Vw w + V+ Vaa

SSrr = =

fully saturatedfully saturatedSSrr = 100 % = 100 %

تماما مشبع تماما مشبع

VVww

VVvv

. 100. 100

DryDry جافجاف SSrr = 0 % = 0 %


Mineral soils are composed of:Mineral soils are composed of:Soil grains Soil grains التربة التربة حبيبات حبيباتWater Water مياهمياهAir Air هواءهواء

Three Phases of Mineral SoilsThree Phases of Mineral Soils


Weight and volume of soil Weight and volume of soil sample depends on:sample depends on:Specific gravity of soil grains Specific gravity of soil grains

(solids)(solids)The size and space between The size and space between

soil grains (voids and pores)soil grains (voids and pores)Volume of void space filled Volume of void space filled

with waterwith water

Weight Volume RelationshipsWeight Volume Relationships

• Water

• Solids

• Air


PHASE DIAGRAMPHASE DIAGRAMTo compute the masses )or weights) and To compute the masses )or weights) and

volumes of the volumes of the threethree different phases. different phases.

soil

air

water

Vs

Va Wa=0

Ws

WwWt

Vw

Vv

Vt

Idealized Prism

NotationNotation W = weight W = weight الوزنالوزنV = volume V = volume الحجمالحجمs = soil grainss = soil grainsw = waterw = watera = aira = airv = voidsv = voidst = totalt = total


DefinitionsWater content )wWater content )wcc)) )) المياه المياه محتوى is a measure is a measure ((محتوى

of the water or Moisture present in the soil.of the water or Moisture present in the soil.

Phase Diagram

s

wc W

Ww

Expressed as percentage.Expressed as percentage.

Range = 0 – 100+%.Range = 0 – 100+%.

X 100%

soil

air

water

Vs

Va Wa=0

Ws

WwWt

Vw

Vv

Vt


DefinitionsDefinitionsVoid ratio (e) Void ratio (e) (( الفراغات الفراغات نسبة is a is a ((نسبة

measure of the volume of voids. measure of the volume of voids.

Phase Diagram

S

V

VVe

soil

air

water

Vs

Va Wa=0

Ws

WwWt

Vw

Vv

Vt


DefinitionsDefinitionsPorosity (n) Porosity (n) ((المساميةالمسامية)) is also a measure of the is also a measure of the

volume of voids, expressed as a percentage. volume of voids, expressed as a percentage.

Phase Diagram

t

vVVn X 100%

Theoretical range: Theoretical range: 0 – 100%0 – 100%

soil

air

water

Vs

Va Wa=0

Ws

WwWt

Vw

Vv

Vt


DefinitionsDefinitionsDegree of saturation (SDegree of saturation (Srr) ) (( التشبع التشبع درجة is the is the ((درجة

percentage of the void volume filled by water.percentage of the void volume filled by water.

Phase Diagram

V

Wr V

VS

Range: 0 – 100%Range: 0 – 100%

X 100%

DryDrySaturatedSaturated

soil

air

water

Vs

Va Wa=0

Ws

WwWt

Vw

Vv

Vt


DefinitionsDefinitions

Bulk density (Bulk density (bb) ) (( الكلية الكلية الكثافة is the density is the density ((الكثافةof the soil in the current state.of the soil in the current state.

Phase Diagram

t

tVW

b

Units: t/mUnits: t/m33, g/cm, g/cm33, kN/m, kN/m33 soil

air

water

Vs

Va Wa=0

Ws

WwWt

Vw

Vv

Vt


DefinitionsDefinitions

Saturated density (Saturated density (satsat) ) (( المشبعة المشبعة الكثافة is the is the ((الكثافةdensity of the soil when the voids are filled with water. density of the soil when the voids are filled with water.

: تكون عندما التربة كثافة هى المشبعة : الكثافة تكون عندما التربة كثافة هى المشبعة الكثافةبالماء مملوءة بالماء الفراغات مملوءة الفراغات

Submerged density )Submerged density )subsub( ( )) المغمورة المغمورة الكثافة ))الكثافةis the effective density of the soil when is the effective density of the soil when it is submerged. it is submerged.

: عندما الفعالة التربة كثافة هى المغمورة : الكثافة عندما الفعالة التربة كثافة هى المغمورة الكثافةالماء فى مغمورة الماء تكون فى مغمورة sub= sat - wتكون


DefinitionsDefinitionsDry density (Dry density (dd) ) (( الجافة الجافة الكثافة is the density of the soil in dry is the density of the soil in dry ((الكثافة

state state : الجافة الحالة فى التربة كثافة هى الجافة : الكثافة الجافة الحالة فى التربة كثافة هى الجافة الكثافة

Phase Diagram

t

sVW

d

Units: t/mUnits: t/m33, kg/m, kg/m33, kN/m, kN/m33 soil

air

water

Vs

Va Wa=0

Ws

WwWt

Vw

Vv

Vt


Phase RelationsPhase RelationsConsider a unit volume of the soil solids,Consider a unit volume of the soil solids,where Vs = 1.

soil

air

water

Vs =1 Gsw

SrewSree

Phase Diagram

The other volumes The other volumes can be obtained can be obtained from the previous from the previous definitions.definitions.

Weight = Density x Weight = Density x VolumeVolume

volumes masses

The weights can The weights can be obtained be obtained from:from:

w

ss

s

ss G ,

VW


Phase RelationsPhase RelationsConsider a unit volume of the soil solids,Consider a unit volume of the soil solids,where Vs = 1.

soil

air

water

Vs =1 Gsw

SrewSree

Phase Diagram

volumes masses

s

vVVe

e S VV x

VV

VV

rs

v

v

w

s

w

wsss

s G VW


للتربة الظاهرية للتربة العالقات الظاهرية Phase PhaseالعالقاتRelationsRelations

From the previous definitions,From the previous definitions,

soilsoil

airair

waterwater

1 Gsw

SrewSr e

e

Phase Diagram

s

r

s

wc G

eSWWw

e1e

VVn

t

v


Phase RelationsPhase Relations

soil

air

water

1 Gsw

SrewSre

e

Phase Diagram

wrs

t

tb e1

eSGVW

ws

t

tsat e1

eGVW

ws

t

sd e1

GVW


النسبية النسبية الكثافة Relative RelativeالكثافةDensityDensityIt is a measure of the soil state of

compactness, and expressed as:

minmax

maxr e - e

e - e = D

الدمك حالة وهى النسبية الكثافة هىالرملية التربة فى غالبا وتستخدم


EXAMPLE 1EXAMPLE 1A sample of saturated clay has a water content Wc = 47.0% and specific gravity Gs = 2.7. Calculate the voids ratio e, the porosity n, and the saturated unit weight sat.

r

sc

SG x W = e

1.27 = 1

2.7 x 0.47 = e

e + 1e =n

x e + 1e + G = w

ssat

2.273.97 = 1 x

1.27 + 11.27 + 2.7 =


EXAMPLE 1Solution Using Prism:Solution Using Prism:

soil

water

Vs =

1/2.7ws= 1.0

Ww = 0.47 gm

Vv = Vw = 0.47

1.27=0.47x2.7=

2.71

0.47=VV=e

s

v

0.56=

2.71+0.47

0.47=VV=n

t

v

3

sat

gm/cm 1.75=

2.7147.0

1+0.47

=VW=


EXAMPLE 2EXAMPLE 2The weight of a wet specimen of clay is 34.62 gm. The The weight of a wet specimen of clay is 34.62 gm. The dry weight = 20.63 gm. Before drying, the specimen was dry weight = 20.63 gm. Before drying, the specimen was immersed in mercury and its volume was found to be immersed in mercury and its volume was found to be 24.26 cm24.26 cm33, if G, if Gss = 2.7, calculate the water content Wc, = 2.7, calculate the water content Wc, the voids ratio e, and the degree of saturation Sthe voids ratio e, and the degree of saturation Srr..

70.40% 100 x 20.3614.26 %

WW =W

s

wc

3s cm 7.54 =

1.0 x 2.720.36 = V

Solution:Ww = 34.62 - 20.36 = 14.26 gm

Water content, Wc = 70.40%where


2.22 = 7.54

16.72 = VV = e

s

v

% VV = S

v

wr

% 85.29 = 100 x 16.72

114.26

= Sr

Vv = V - Vs

Vv = 24.26 - 7.54 = 16.72 cm3

Voids ratio, e = 2.22

Degree of Saturation, Sr = 85.29%.

May 1, 2023 Soil Mechanics 24

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