CE340 Geotechnical Engineering Equations Sheet by JiLiang Li

1

Soil Mechanics & Foundation Equations Sheet

v Ds w

182

D mm KL cm

t( )

( )

(min)

130

1

18

sws GGK

CD

Du

60

10

CD

D Dc

30

2

60 10

wsws

e

SeG

V

WW

V

W

1

)(

1m=10dm=100cm=1000mm 1=0.3048m 1m2=10000cm2

F=ma 1N=1kg*m/s2 1Pa=1N/m2

g=9.81m/s2

33633 /1)100/(10/1000/1 cmgcmgmkgmtonw

1m=3.281 ft

g=9.81m/s2=32.2ft/s2

33633 /1)100/(10/1000/1 cmgcmgmkgmtonw

PCFftbmKNw 4.62/41.62/81.933

1foot=12incehs 1=12 1inch=1in=1=2.54cm=25.4mm 1m=1odm=100cm=1000mm 1=0.3048m

1m=3.281ft

g=9.81m/s2=32.2ft/s2

F=ma 1N=1kg*m/s2 33633 /1)100/(10/1000/1 cmgcmgmkgmtonw

PCFftbmKNw 4.62/41.62/81.933

1psf=144psi 1pcf=1 lb/ft3 1MPa=145 PSI

CE340 Geotechnical Engineering Equations Sheet by JiLiang Li

2

d

s s wW

V

G

e

1

w

e

wGd

ws

1

1

1

e

eG

e

eG

V

WW wswwswssat

11

GW

Vs

s

w

s

s w

wW

W

w

s

ne

kivs e

V

V

v

s

nV

V

v e

wG

V

VS s

v

w Se wGs

De e

e er

d d

d d

d

d

max

max min

(min)

(max) (min)

(max)

PLP wwIPLLLPI P

PL

I

wwI

PLLL

PLwLI

2073.0 LP wI

zp

hhhw

zp

L

hi

kiAQ k Kw

kQL

Aht

1

10log303.2h

h

At

aLk o

2

10sec)/( CDcmk (mm)

a

b

N

NhkLQ

D

F

wphu

Wa=0 Air Va=e-wGs

Vv=e Ww=wGsYw Water Vw=wGs

Ws=GsYw1 Solid Vs=1

Three Phase Diagram of Soil

PLLL

PLwLI

SL PI=LL--PL PL LL

w

CE340 Geotechnical Engineering Equations Sheet by JiLiang Li

3

A

D

AUBwA Z

N

nhhu

)(

15.0

)(

03.0)(

10 mmDmmdmhc

i

ii

parallelH

Hkk

i

i

i

normal

k

H

Hk

dThd wc

cos4

2 w

cd

Th

cos4

hS

u w

100

icrw

' FS

iav w

'

Hz

uzz ' ; uH inducedzz )('

wij

uHjz )('

Major and minor principal stresses: 22

3,122

xy

xyxy

2sin2cos22

2sincossin 22 xyxyxy

xyyxn

2sin2cos22

xy

xyxy

n

2cos2sin2

xy

xy

n

xy

xy

22tan

22

1

322

xy

xyxy

2cos22

3131

2sin2

31

CE340 Geotechnical Engineering Equations Sheet by JiLiang Li

4

J. Boussinesq Eqs: 2/522

3

5

3

2

3

2

3

zr

zP

L

zPpz

5

3

2

3

R

Pz fz

))(( ffz

zLzB

BLq

Square Foundation: Z

Ln

Z

Bm

Circular Foundation: Z

RI

fillfillfillz H

inducedzzozf )(''

p

pOCR c

zo

c '

'

Das Braja M Das Braja M Das Braja MDas Braja M Das Braja M

Pre Consolidation Pressure Estimation:

For OC: ppe

ec

L

00463.0log1888.0122.1 &

sL GLL

e

100

%

188.0

log00463.0122.1

log

o

L

o

c

pe

e

p

crf Figure

For NC: pe

e

L

00463.0122.1 &

sL GLL

e

100

%

pGLL

e s log2343.0122.1100

%

crf Figure

For Normally Consolidated Clays:

Wa=0 Air Va=e-wGs

Vv=e Ww=wGsYw Water Vw=wGs

Ws=GsYw1 Solid Vs=1

Three Phase Diagram of Soil

Wa=0 Air Va=e-wGs

Vv=e Ww=wGsYw Water Vw=wGs

Ws=GsYw1 Solid Vs=1

Three Phase Diagram of Soil

01 e

e

H

H

He

eHS

01

CE340 Geotechnical Engineering Equations Sheet by JiLiang Li

5

o

oc

p

pp

e

HCS log

1 0

io

iioic

p

pp

e

HCS log

1 0

For Normally Consolidated Clays:

If co ppp then

o

os

p

pp

e

HCS log

1 0

If co ppp then

c

oc

o

cs

p

pp

e

HC

p

p

e

HCS log

1log

1 00

%10060%100log933.0781.1

%600100

%

4

2

2

UForU

UForU

H

tcT

dr

vv

Tv=0.197, U=50%

S

SU tz Where S is the total primary consolidation

Das Braja M Das Braja M Das Braja MDas Braja M Das Braja M Das Braja

M

'

'

0

log1

)(zo

zfcultc

e

HC

for NC

dl

dCDf d

'

'

0

log1

)(zo

zfrultc

e

HC

for OC

'

'

0

'

'

0

log1

log1

)(c

zfc

zo

crultc

e

HC

e

HC

hA

q

t

kn

Empirical Procedures to Estimate Void Ratio-Pressure Relationships:

74/pc IC 370/pr IC

Cc=0.009(LL-10) Cr=Cs=1/5~1/10

vwcw

zv

a

ek

C

ekc

)1(13.2 '

Tc t

Hv

v

dr

2

CE340 Geotechnical Engineering Equations Sheet by JiLiang Li

6

z

e

ultc

c uxU

1%100

)(

tan' cs TTcs tan

245tan2

245tan 231

cff

f 45

2

tanint aerface cs

f

duu

qS

22

Degree of

Consolidation, U%

Time Factor, Tv

0 0

10 0.008

20 0.031

30 0.071

40 0.126

50 0.197

60 0.287

70 0.403

80 0.567

90 0.848

100

wd

1

zav

s w

s

w

s

G

wG wG

11

100(%))(max

)(

labd

fieldd

RC

%1001 x

V

V

cutd

filld

f

sF

sin

tancos ''

W

ulWlcF

cossin

tancos '2'

D

zDcF wwS

CE340 Geotechnical Engineering Equations Sheet by JiLiang Li

7

Wd

sRF

u

180

2

H

cNF F

z

xK

0

'sin

0 )sin1( OCRK

aaza KcK 2

Ka tan245

2

z0 2c

Ka

ppzp KcK 2

Kp tan245

2

22

22

coscoscos

coscoscos

aK

uDA

pq c

uDB

bPq c

/

strip footing

BNNcNq qDcult 5.0'

square footing

BNNcNq qDcult 4.03.1'

circular footing

BNNcNq qDcult 3.03.1'

F

qq ultall

Qu QEB QSF F

QQ ultall

PultEB AqQ QSF f*AS

tanint* aerface csf

shearenormaleh

uuuu