The generalized nonlinear strength criterion unifies all kinds of the nonlinear strength criteria about the friction material

so that the criterion can represent the strength characteristic of these materials. The shape parameter α is one of the factor that affect the shape of the failure curve in the generalized nonlinear strength criterion

the research about the parameter α is done as follows: (1) The generalized nonlinear strength criterion is applied to the sand

and then

according to the character of the failure curve in the generalized nonlinear strength criterion in the ?-plane

for judging the failure curve convex

the relation between the least of the parameter α and the failure stress ratio Mf was deduced. (2) By some test results about the sand

the proposed criterion for general stress state was applied to simulate test results; and it was shown that the criterion could reproduce the test data fittingly. And then the linear relation between the two parameters in the criterion was found. So the failure behavior of the sand could be reproduced by the use of triaxial compression condition for practical application.