civil engineering department soil mechanics 803440-3 introduction lecture 3 week 3 2014/2015 umm...

Civil Engineering Department

Soil Mechanics803440-3

Introduction

Lecture 3Week 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

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

Specific Gravity

Phase Diagram

Air

Water

Solids

3 Phase System

Phase Diagram

Air

Solids

2 Phase System (Dry)

Phase Diagram

Water

Solids

2 Phase System (Saturated)

Phase Diagram

Phase Diagram

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

Phase Diagram

W = Ww +Ws

V =Vs +Vw +Va

Vv =Vw +VaV =Vs +Vv

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

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

Questions?!

Basic Relations

s

w

W

Ww

V

Wγ

V

Vn v

s

v

V

Ve

v

w

V

VS

w

ss γ

γG

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

γ, e, w, Gs Relationships

Soil Unit Weight

vs

swssws

VV

VγwGVγG

Divide by Vs

γ, e, w, Gs Relationships

With the same substitution for Ws we got:

Dry Unit Weight

Void Ratio

Saturation

γ, e, w, Gs Relationships

Group Work

e

γeGγ wssat

1

Prove that for Saturation Condition:

swGe

Questions?!

Soil Unit Weight

vs

swssws

VV

VγwGVγG

Divide by Vs

γ, n, w, Gs Relationships

Substitute for (e) by

n1

ne

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

Questions?!

Various Unit-Weight Relationships

Typical Values

Example 3.2

Example 3.4