Incorporating Non‐Associated Flow Rule Using Kinematics Based Finite Element Limit Analysis for Plane Strain Problems

ABSTRACT It is understood that most soils follow non‐associated flow rule, and the true volumetric strain is often considerably lower than that predicted with the application of the associated flow rule. For obtaining the solution for any stability problem with the usage of non‐associated flow rule, it is generally recommended to use equivalent values () of cohesion and internal friction angle for a given dilatancy angle () with the usage of the fictitious associated flow rule. The choice of the flow rule, however, affects the kinematics based finite elements limit analysis (FELA) solution; the solution obtained with the usage of the kinematics conditions becomes the upper bound (UB) solution for an associated flow rule material. In the current article, the usage of the non‐associated flow rule has been incorporated while employing the kinematics based FELA. To show the implementation procedure, the bearing capacity of a rough strip footing placed on cohesionless media and subjected to an inclined load has been computed with the usage of the second order cone programming (SOCP) for performing the associated optimization. The computations clearly reveal that the magnitude of the failure load reduces continuously with a decrease in and this computed value of the failure load, especially for small values of , remains generally substantially greater than that obtained simply with the usage of and and using the fictitious associated flow rule.