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SOIL - WATER RELATIONSHIPS. Ground Surface (G.S.). Air. Water. Water Table (W.T.). Voids. Solids. By: KAMAL TAWFIQ, Ph.D.; P.E. 1. STRESSES CAUSED BY A POINT LOAD. Boussinesq’s Equation. D P z = (3P/2 p) (Z 3 /L 5 ). P. Using Influence Factor. Y. GROUND SURFACE.

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SOIL - WATER RELATIONSHIPS

Ground Surface (G.S.)

Air

Water

Water Table (W.T.)

Voids

Solids

By: KAMAL TAWFIQ, Ph.D.; P.E.


1. STRESSES CAUSED BY A POINT LOAD

Boussinesq’s Equation

DPz = (3P/2p) (Z3/L5)

P

Using Influence Factor

Y

GROUND

SURFACE

DP = (P/Z2) Ip

X

L

Z

General

Stresses

DP = s1

DP = sv

Principal

Stresses

t

s2

sh

s3

Z

By Kamal Tawfiq, Ph.D; P.E.


2. STRESSES CAUSED BY A LINE LOAD

QO (Load/Unit Length)

QO (Load/Unit Length)

X

Y

WALL

X

Z

Boussinesq’s Equation

DPz = {2 Qo Z3/p (X2 + Z2 )2}

Z

General

Stresses

Using Influence Factor

DP = sv

s1

DP = (P/Z) IL

Principal

Stresses

t

s2

sh

s3

Z

By Kamal Tawfiq, Ph.D; P.E.


4. TRIANGULAR LOAD

3. CONTINUOUS LOAD

DP = (q/p) {(X/B) a - (sin 2d/2)}

DP = q/p [b + sin b cos (b + 2 d)]

Y

X

Z

General

Stresses

HIGHWAY

EMBANKMENT

sv

s1

Principal

Stresses

t

s2

sh

s3

Z

By Kamal Tawfiq, Ph.D; P.E.


5. VERTICAL STRESS DUE TO CIRCULAR LOAD

Qo

X

q

Y

GROUND

SURFACE

X

Z

DP= q { 1- 1/[(R/Z)2 + 1 ]3/2 }

Z

General

Stresses

DP = sv

s1

Principal

Stresses

t

s2

sh

s3

Z

By Kamal Tawfiq, Ph.D; P.E.


6. VERTICAL STRESS DUE TO RECTANGULAR LOAD

DP = q IR

IR = 1/4p {[ (2. m.n (m2 + n2 + 1)1/2 ) / (m2 + n2 + m2. n2 + 1) ] [(m2 + n2 + 2)/(m2 + n2 + 1)] +

tan-1 (2.m .n (m2 + n2 + 1)1/2 / (m2 + n2 - m2 . n2 + 1)}

IR = f (m,n)

L

q = Load /Area

B

Loaded Area

Foundation Level

Corner of

the Building

L

X

Z

B

m = B/Z

DP = sv

m & n from Charts

t

n = L/Z

sh

By Kamal Tawfiq, Ph.D; P.E.


GROUND SURFACE

Water Table

Dpv

+

sv

Stresses due to additional load

H

Geostatic Stress

sh + Δph

A