Study on the indeterminacy of the earth pressure on rigid retaining walls

The insufficient information of the occurrence condition of earth pressure and the spatial characteristic of soil distribution were two main factors leading to the indeterminacy of the earth pressure acting on rigid retaining wall.In calculation,the former was manifested with the indeterminacy of the calculation model;while the latter was related to the indeterminacy of the mechanical parameters.To the indeterminacy problem of the earth pressure,the more reasonable way was to find some range as the proper estimate of the earth pressure in all possible cases to provide for engineering designer to choose;however,for these two types of problem.i.e.model indeterminacy and parameter indeterminacy,different mathematical methods must be employed to determine the corresponding range of earth pressure.Based on the variational method of limit equilibrium,the functional extreme-value problem of limiting earth pressure was transformed into that of finding the minimum solution of functions with restraints,and the problem of the indeterminacy of earth pressure model due to the nondeterministic wall movement mode was studied.By means of mathematical method of interval analysis,taking the Coulomb formula in case of vertical smooth wall for example,the interval operation and the expansion form of real function were discussed,and the indeterminacy of earth pressure calculation on account of uncertain mechanical parameters was preliminarily analyzed.The methods used in the paper could be applied to study other nondeterministic problems in geotechnical engineering.