Stress of soil

CHAPTER 3

§3 Stress of soil

§3.1 General§3.2 Self-weight stress §3.3 Stress at the bottom of foundation §3.4 Additional stress in foundation

§3.1 General

§3 Stress of soil

Weight of soil (effective stress)

Surface loads Fill large area Point loads:

Hydro pole, light stand, column, etc Lines loads

Rack or rail loading, strip foundation Rectangular area

Raft or rectangular footing Circular area

Tank Earth embankment

Road, railway, fill, ice, etc.

§3.2 Self-weight stress

§3 Stress of soil

natural ground

cz

cx

cy 11

z

zcz

z

σcz

σcz= z

Due to soil’s self weight

i

n

iinncz hhhh

1

2211

natural ground

h1

h2

h33

2

1

ground water level

1 h1

1 h1 + 2h2

1 h1 + 2h2 + 3h3

czcycx K 0

natural ground

z

cz

cx

cy

zcz

lateral earth pressure coefficient

at restAssumption：no shear stresses on the vertical planes bounding the column in horizontal direction.

Example 1: How to calculate the stress in soils?

Natural ground

Ground water level

Top roof of the aquitard

Clay

sand

57.0kPa

80.1kPa

103.1kPa150.1kPa

194.1kPa

i

n

iinncz hhhh

1

2211

Solution:

Natural ground

Ground water level

Top roof of the aquitard

Clay

sand

F

§3.3 Stress at the bottom of foundation §3 Stress of soil

Filled soil

Base pressureGeotextile polymer

Smaller load

Extreme load

Smaller load

Extreme load

A

GFp

l

e

bl

GF

p

p 61

min

max

W

M

A

GF

p

p

min

max

Outdoor ground

l

e

bl

GF

p

p 61

min

maxDiscussion：

pmax

pmin

e<l/6

pmax

pmin=0

e=l/6

e>l/6

pmax

pmin<0

pmax

pmin=0

redistribution of the base pressure

(1) Point load

M(x,y,z)

Po

y

x

z

xy

z

r

R M(x,y,0)

325

3

cos2

3

2

3

R

P

R

Pzz

2z

PKz

Note:z is independent of

elastic modulus Poisson’s ratio.

§3.4 Additional stress in foundation§3 Stress of soil

Stresses due to point load Rules of the stress distribution

Pa

z

Pb

a b

superposition principle

several point loads:

(2) Strip area carrying uniform pressure

pKcz

blm /bzn /

),( nmfKc

pKKKK ccccz ⅣⅢⅡⅠ

z

M

o

IV

IIIII

I

oI

IIIII

IV

pKK ccz ⅡⅠ II

I

oo

I

IIIo

IVo

pKKKK ccccz ⅣⅢⅡⅠ

II

I

o o

III

IIIV

pKKKK ccccz ⅣⅢⅡⅠ

(3) Strip area carrying linearly increasing pressure

pK tz 11

ttz pK 22

Strifoundation Load :F=400kN/m ， M=20kN•m，

? Additional stress on the middle of base? Plot the distribution of the stress

2m

F

M

0 ＝ 18.5kN/m3

0.1m

1.5m

Example 2

Solution

1.Base pressure

l

e

bl

GF

p

p 61

min

max

F=400kN/m

0 ＝ 18.5kN/m3

M=20kN •m

0.1m

2m

1.5m

319.7kPa140.3kPa

2.Additonal pressure

1.5m

292.0kPa112.6kPa

dp

p

p

p0

min

max

min0

max0

0.1mF=400kN/m

M=20kN •m

2m

0 ＝ 18.5kN/m31.5m

3.Additioanl pressure at the middle point

2m

F=400kN/m

M=20kN •m

0.1m

1.5m0 ＝ 18.5kN/m3

179.4kPa

112.6kPa

292.0kPa112.6kPa

2m

F=400kN/m

M=20kN •m

0.1m

1.5m0 ＝ 18.5kN/m3

202.2kPa193.7kPa

165.7kPa

111.2kPa

80.9kPa

62.3kPa

1m1m

2m

2m

2m

result