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Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

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Page 1: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Civil Engineering Department

Soil Mechanics803440-3

Introduction

Lecture 3Week 3

2014/2015

UMM AL-QURA UNIVERSITY

Page 2: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Content

• Phase Diagram

• Specific Gravity

• Volume and Weight Relationships

(Porosity, Saturation, Void Ratio, Moisture Content,

Unit Weight)

• Relationships

• Relative Density

Page 3: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Specific Gravity

Gsis defined as the ratio of the unit weight of a given

material to the unit weight of water.

wwws ρ

ρ

g ρ

g ρ

γ

γG

Density ρ

tUnit Weighγ

Page 4: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Specific Gravity

Page 5: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Phase Diagram

Air

Water

Solids

3 Phase System

Page 6: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Phase Diagram

Air

Solids

2 Phase System (Dry)

Page 7: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Phase Diagram

Water

Solids

2 Phase System (Saturated)

Page 8: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Phase Diagram

Page 9: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Phase Diagram

W Total Weight V Total VolumeWw Water Weight Vw Water VolumeWs Solids Weight Vs Solids VolumeWa Air Weight = 0 Va Air Volume

Page 10: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Phase Diagram

W = Ww +Ws

V =Vs +Vw +Va

Vv =Vw +VaV =Vs +Vv

Page 11: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Volume Relationships

Porosity (n)

V

Vn v

Void Ratio (e)

s

v

V

Ve

Degree of Saturation (S)

v

w

V

VS

n1

ne

Prove!!

e1

en

Page 12: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Volume Relationships

Moisture Content (w)

s

w

M

Mw

Unit Weight (γ)

V

Wγ

Dry Unit Weight (γd)

V

Wγ s

d

Prove!!

w1

γγd

Page 13: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Questions?!

Page 14: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Basic Relations

s

w

W

Ww

V

Wγ

V

Vn v

s

v

V

Ve

v

w

V

VS

w

ss γ

γG

Page 15: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

γ, e, w, Gs Relationships

Solids Weight in Terms of Specific Gravity Gs

swss

ws

s

w

ss

w

ss

VγGW

γV

W

γ

V/W

γ

γG

swssw VγG w WwW

Water Weight in Terms of Specific Gravity Gs

Page 16: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

γ, e, w, Gs Relationships

Soil Unit Weight

vs

swssws

VV

VγwGVγG

Divide by Vs

Page 17: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

γ, e, w, Gs Relationships

With the same substitution for Ws we got:

Dry Unit Weight

Void Ratio

Saturation

Page 18: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

γ, e, w, Gs Relationships

Group Work

e

γeGγ wssat

1

Prove that for Saturation Condition:

swGe

Page 19: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Questions?!

Page 20: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Soil Unit Weight

vs

swssws

VV

VγwGVγG

Divide by Vs

γ, n, w, Gs Relationships

Substitute for (e) by

n1

ne

Page 21: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Soil Unit Weight

nn

nwγG ws

11

11

γ, n, w, Gs Relationships

nwγG ws 11

Dry Soil Unit Weight (w=0) nγG ws 1

Saturated Soil Unit Weight (Ww= nV) ws γnnG 1

Page 22: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Questions?!

Page 23: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Various Unit-Weight Relationships

Page 24: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Typical Values

Page 25: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Example 3.2

Page 26: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY
Page 27: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

Example 3.4

Page 28: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY
Page 29: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY
Page 30: Civil Engineering Department Soil Mechanics 803440-3 Introduction Lecture 3 Week 3 2014/2015 UMM AL-QURA UNIVERSITY

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