Calculation of earth pressure on rigid retaining wall based on model indeterminacy

The earth pressure on rigid retaining wall considering model indeterminacy is focused. Based on the force equilibrium equations for sliding mass, the functional extreme-value isoperimetric model for earth pressure in the general case is derived, including active and passive limit state situations. Through the introduction of coordinate transformation, the slip surface function and normal stress function along the slip surface are obtained, the solution of earth pressure is further transcribed as the functional extreme-value problem by means of two Lagrange undetermined multipliers. In the changing curve of function , the minimum varies along with the position factor of action point, and one can find a section of horizontal line segment with. This line segment corresponds to the position factor range of action point of resultant earth pressure, then the corresponding earth pressure scope can be determined, and the two cases of active and passive earth pressures are explained by the calculation example. The calculated results show that the position factor of action point has the upper and lower limit values, which correspond to the maximum and minimum values of earth pressure respectively, and corresponding slip surfaces can also be obtained. It is found that the magnitude of earth pressure and the position of action point depend on the modes of wall movement. The range of values of earth pressure corresponds to the upper and lower limits of the position factor of action point, and it comprises the earth pressures on the rigid retaining wall with all possible wall modes of movement. In a word, the interval estimation of the magnitude of earth pressure and the position of action point for different modes of wall movement can be obtained using the proposed method, so that it is convenient for the engineer to choose.