Geotechnical Engineering

DHARM

456 GEOTECHNICAL ENGINEERING

Unit

area

z

Stretching 45° + /2f

45° + /2f

Horizontal

ground

surface

(minor)

sh

sv

sh

sgvz=

Pattern of failure planes

(major)

Kzog

z

Compression 45° – /2f

45° – /2f

Horizontal

ground

surface

(minor)

sh

sv

sh

sgvz=

Pattern of failure planes

(major)

Kzog

Failure envelopets f= tan

E

Failure planes

t

III

B

P 2

Failure envelope

Vertical stress zg

Passive pressure K zpg

C 2 (45° – /2)f

(45° – /2)f

A

D I II

(45°+

f/2)

(45°+ C 1

f/2)

+f

O –f

Active

pressure

Kzag

At rest

pressure

Kzag

(a) Active Rankine State

(b) Passive Rankine State

1. Mohr’s circle for ‘At rest’ condition


2. Mohr’s circle for ‘Active’ condition


3. Mohr’s circle for ‘Passive’ condition
   (c) Mohr‘s stress circles and failure envelopes for active and passive states

P 1

Kzag

Kzag

Fig. 13.6 Rankine’s states of plastic equilibrium