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Uncertain parameters with inherent spatial variability are commonly encountered in engineering. Modeling of this kind of spatial uncertainty plays a fundamental role in structural uncertainty analysis, which provides a necessary basis for subsequent uncertainty propagation through the system. An interval field model for quantification of spatial uncertain parameters is proposed, by which only the upper and lower bounds of the spatial uncertain parameters rather than their precise probability distributions are required. The dependency can be fully considered by the proposed interval field model. With the information of dependency, an interval K-L expansion is presented as a combination of deterministic functions with uncorrelated standard interval variables, through which the continuous spatial interval field with dependency can be expressed only by very limited intervals. Necessary mathematical illustrations are provided for the proposed interval field model and the interval K-L expansion. The sampling method for the interval field model is given, providing a robust numerical analysis basis for subsequent structural uncertainty analysis. When the interval field model is applied in finite element analysis of structures with spatial uncertain parameters, the non-deterministic equilibrium equations with interval factors is then formulated. The MCS method and the perturbation method are developed for solution of the derived interval equilibrium equations. The feasibility and validity of the proposed interval field model and corresponding interval finite element methods are verified by numerical examples, where the upper and lower bounds of the responses such as the displacements and the stresses of structures with spatial uncertain parameters are computed and compared.

Interval field model; Spatial uncertainty; Interval K-L expansion; Interval finite element method