Transcript Geostatic Stresses

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
GROUND
SURFACE
DP = (P/Z2) Ip
Y
X
L
Z
Principal
Stresses
DP = s1
DP = sv
s2
General
Stresses
t s
h
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
Using Influence Factor
DP = (P/Z) IL
DP = sv
s1
Principal
Stresses
s2
General
Stresses
t s
h
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
HIGHWAY
EMBANKMENT
sv
s1
Principal
Stresses
General
Stresses
s2
t s
h
s3
Z
By Kamal Tawfiq, Ph.D; P.E.
5. VERTICAL STRESS DUE TO CIRCULAR LOAD
Qo
X
GROUND
SURFACE
q
Y
X
Z
DP= q { 1- 1/[(R/Z)2 + 1 ]3/2 }
Z
DP = sv
s1
Principal
Stresses
General
Stresses
s2
t
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
B
q = Load /Area
Loaded Area
Foundation Level
Corner of
X the Building
L
Z
B
DP = sv
m = B/Z
m & n from Charts
n = L/Z
t s
h
By Kamal Tawfiq, Ph.D; P.E.
GROUND SURFACE
Water Table
Dpv Stresses due to additional load
+
sv Geostatic Stress
H
A
sh + Δph