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:-