Determination of dilatancy angle for geomaterials under non-associated flow rule

Geomaterials are frictional materials, and their strength indexes play a key role in depicting strength characteristics. Illegible knowledge on dilatancy angle has existed for a long time, which caused large errors in theoretical analysis and numerical simulation. It was proved with the generalized geotechnical plastic mechanics principle that the angle of dilatancy should be phi/2 and the corresponding volumetric strain is zero for geomaterials under non-associated flow rule, based on traditional slip line theory. The classic foundation bearing capacity topic of Prandtl's solution, which has accurate theoretical interpretation, was analyzed systemetically with step loading finite elements under the following three conditions: 1) associated flow rule, 2) non-associated flow rule with the dilatancy of phi/2 and 3) non-associated flow rule with the dilatancy of 0. Results showed that the errors of ultimate capacity obtained under the above three conditions were within 2 %, but the slip line fields were quite different. The slip line field obtained under conditon 2) was identical with that by Prandtl's solution, but a large deviation existed between condition 3) and Prandtl's solution. Thus a correct ultimate load and a slip line field with a great error can be acquired under condition 3), but both are precise under condition 2). Therefore, the angle of dilatancy should be phi/2, not 0 widely used at present when non-associated flow rule is applied.