elements of the critical state model 1. yield surface the equation for the yield surface is ellipse...

ELEMENTS OF THE CRITICAL STATE MODEL

ByAyam Jabbar Jihad

ELEMENTS OF THE CRITICAL STATE MODEL1. Yield Surface

The equation for the yield surface is ellipse given by :-

2.Critical State Parameters Failure Line in space The failure line in space is

Axisymmetric Compression

Mc We know

Therefore ,

or

Axisymmetric ExtensionIn an axisymmetric extension test , the radial stress is theMajor principal stress .Since in axial symmetry the radial stress is equal

to the circumferential stress,we get

and

or

Failure line in space Let us now find the equation for the critical state line in space .We will use the

plot as shown in Fig.(8.9c)The CSLis parallel to the normal consoldation line and is represented by

The essential critical state parameter are :

Compression index, which is obtained from an isotropic or a one-dimensional consolidation test .

Unloading /reloading index or recompression index, which is obtained from an isotropic or a one-dimensional consolidation test .

Critical state frictional constant .

To use the critical state model , you also know the initial stresses , for example and and the initial void ratio

Example 1-1 calculation of failure stresses

Solution:-

Example 1-2 Determination of

Figure (8.2)

Strategy Make a sketch of the results in

space to provide a visual aid for solve aid for solving this problem .

Solution:-