OBSERVATION AND PREDICTION - Introduction to Soft Soil Geotechnique: Content, Context and Application - page 158

2

: 7

2 xx yy 2

8
9

5
6

m xy

2

At the centre of the Mohr circle, the mean normal stress gives

xx yy xx yy

cos 2

m yy m yy

2 2

The Mohr-Coulomb failure criterion states: sin . This provides

m m

sin cos 2 ( sin cos 2 )

m m yy yy m

With

xy

sin 2 sin sin 2

xy m

m

one obtains

sin sin 2

xy

1 sin cos 2

yy

In similar manner one obtains

sin sin 2 xy

1 sin cos 2

xx

For the coaxial case without dilatancy ( = 0) it follows from (9.16) for the final

stage

cos sin

xy

R sin

1 sin sin

yy

This complies with . Obviously, the main stresses

rotate from the initial state towards final state (Fig 9.13).

= 45 = , and thus

xx yy

application 9.5

Find cr of equation (9.14) and elaborate (9.15b).