This paper discusses the application of plasticity theory and limit design in soil mechanics. The authors propose a yield function that generalizes the Mohr-Coulomb criterion, which is used to describe the failure of soils under shear stress. The yield function is given by $ f = \alpha J_1 + J_2^{1/2} = k $, where $ J_1 $ and $ J_2 $ are stress invariants, and $ \alpha $ and $ k $ are constants. The plastic strain rate is derived from this yield function, and it is shown that plastic deformation is accompanied by volume expansion, a phenomenon known as dilatancy. The paper also presents limit theorems for plasticity, which state that collapse will not occur if the stress state satisfies equilibrium and boundary conditions, and that collapse must occur if the rate of external work equals or exceeds the rate of internal dissipation. These theorems are valid when frictional surface tractions are present. The paper then shows that the yield function reduces to the Mohr-Coulomb criterion in the case of plane strain. It also discusses the rate of energy dissipation and the relationship between the plastic strain rate and the yield function. The paper further considers the case of a vertical bank and calculates the critical height using upper and lower bound techniques. The results show that the upper bound is twice the lower bound, indicating the need for a more accurate yield criterion. The authors also propose a modified stress criterion that accounts for the possibility of tension in soil, which is not allowed in the original Mohr-Coulomb criterion. This modified criterion is shown to give a more accurate result for the critical height of a vertical bank. The paper concludes that plasticity theory and limit design have significant implications for soil mechanics, particularly in the prediction of failure and the behavior of soils under shear stress.This paper discusses the application of plasticity theory and limit design in soil mechanics. The authors propose a yield function that generalizes the Mohr-Coulomb criterion, which is used to describe the failure of soils under shear stress. The yield function is given by $ f = \alpha J_1 + J_2^{1/2} = k $, where $ J_1 $ and $ J_2 $ are stress invariants, and $ \alpha $ and $ k $ are constants. The plastic strain rate is derived from this yield function, and it is shown that plastic deformation is accompanied by volume expansion, a phenomenon known as dilatancy. The paper also presents limit theorems for plasticity, which state that collapse will not occur if the stress state satisfies equilibrium and boundary conditions, and that collapse must occur if the rate of external work equals or exceeds the rate of internal dissipation. These theorems are valid when frictional surface tractions are present. The paper then shows that the yield function reduces to the Mohr-Coulomb criterion in the case of plane strain. It also discusses the rate of energy dissipation and the relationship between the plastic strain rate and the yield function. The paper further considers the case of a vertical bank and calculates the critical height using upper and lower bound techniques. The results show that the upper bound is twice the lower bound, indicating the need for a more accurate yield criterion. The authors also propose a modified stress criterion that accounts for the possibility of tension in soil, which is not allowed in the original Mohr-Coulomb criterion. This modified criterion is shown to give a more accurate result for the critical height of a vertical bank. The paper concludes that plasticity theory and limit design have significant implications for soil mechanics, particularly in the prediction of failure and the behavior of soils under shear stress.