Abstract: The problem of earth pressure is studied by using the limit equilibrium variational method and the Culmann analysis method. In the limit equilibrium variational method, the problem of active earth pressure and passive earth pressure is formulated in terms of calculus of variation based on the two force equilibrium equations of the sliding mass, and is transcribed as the functional extreme-value problem of two undetermined function arguments by means of Lagrange multiplier. According to Euler equations that must be satisfied when a functional attains its extremal, the conclusion that the failure of soil mass behind wall is in the mode of sliding on a plane surface is drawn when the active earth pressure and the passive earth pressure get the minimax solutions. In the Culmann analysis method, the assumption that the soil failure is in the mode of sliding along a plane is adopted; however only one force equilibrium equation along some special direction is utilized to derive the computation formula of earth pressure. Compared with the popular proof process of the Coulomb earth pressure theory, the Culmann analysis method is more simple.

Key words: Coulomb earth pressure theory, calculus of variations, limit equilibrium, Culmann analysis method