Soil Stresses (ch10) Stress Assumptions Continuous material Homogeneous (eng. props. = at all locations) Isotropic (Modulus and are = in all directions)

test #1 - cive 462 sp 04

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Soil Stresses(ch10)

Stress

Assumptions

Continuous material

Homogeneous (eng. props. = at all locations)

Isotropic (Modulus and are = in all directions)

Linear-elastic stress-strain properties

Stress Concept

Stress Concept

xz

x

z

normal stresses

xx

xz

zx

zx

z

z

shear stresses

Ten (-), Comp (+)

Clock (+), CC (-)

Strain Concept

dL

P

L

dL

normal strain

L

shear strain

= shear strain [radians]

Stress vs. Strain = Modulus

E

Gpa

p

Stresses in Soils

1. Geostatic Stresses

Due to soil’s self weight

2. Induced Stresses

Due to added loads (structures)

3. Dynamic Stresses

e.g., earthquakes

0.248811

0.241673

ASi

g

81.950 ti

0 10 20 30 40 50 60 70 80 900.4

0.2

0

0.2

0.4

Geostatic Stresses

TOTAL VERTICAL STRESS AT A POINT

z = depth = 5 m

A

Ground surface

Soil , = 18 kN/m3

AA z “total vertical stress at A”

Geostatic Stresses

SHEAR STRESSES

If ground surface is flat, all geostatic shear stresses = zero

Geostatic Stresses

PORE WATER PRESSURE AT A POINT

z = 5 m

A

Ground surface

Soil , = 18 kN/m3

ApwA hu “pore water pressure at A”

hpA

Geostatic Effective Stress

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Example

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Special Case

Board – submerged soils

Induced Stresses

z

A

z

A

P

= z = z +

= =

Bousinnesq - point loads

zf

A

Point load

See page 324 of your book…

Area loads

q = bearing pressure = P/A

z

A

P

Area, A

B

L

Terminology:

B < or = to L

Area loads – z below corner

zf

B

L

z below corner of a loaded area: see page 327 (book)

Area loads – z below center

Circular loaded area

zf

A

q

5.1

2

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11

f

z

zB

q

Area loads – z below center

Square loaded area

Strip loads

Rectangular area

See page 332 (text)

Lateral Stresses

z

A

Ground surface

Soil , = 18 kN/m3

' = Vertical effective stress = 'v

h' = Horiz. eff. stress = ?

Lateral Stresses

v

hK'

'

“Coefficient of lateral earth pressure”

Superposition

We can only add total stresses

Stresses on other planes…

So far we have x and z Now we want

xx

z

z

Stresses acting on other planes

The Mohr Circle

Describes 2-D stresses at a point in a material

Plots and on an = scale

Each point on the MC represents the and on one side of an element oriented at a certain angle

The angle between two points in the MC is = 2 times the angle between the planes they represent

The Mohr Circle

A 1

A 2B 1

B 2

B2

B1

A2

A1

A2

A1

B2

B1

If we change we will get two more points on the same MC.

A

B

The Mohr Circle

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1

The Mohr Circle – Principal Stresses

Planes A and B are called principal planes when there are no shear stresses (only normal stresses) acting on them.

1 = major principal stress

3 = minor principal stress

The Mohr Circle

Direction of max principal stresses is 17 degrees c.c. from the vertical

Effective Stress Mohr Circle

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Seepage Force

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Seepage Force - Example

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