ELEMENTS OF THE CRITICAL STATE MODEL By Ayam Jabbar Jihad

ELEMENTS OF THE CRITICAL STATE MODEL Yield Surface The equation for the yield surface is ellipse given by :-

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

Axisymmetric Compression Mc We know Therefore , or

Axisymmetric Extension In an axisymmetric extension test , the radial stress is the Major 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 .

Example 1-1 calculation of failure stresses 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:-