260 M. K. Ramancha et al. Fig. 29.1 Unscented Kalman Filter Algorithm using scaled unscented transformation Fig. 29.2 (a) Pine Flat Dam, and (b) 2D FE model of the dam The cap plasticity material model is a sophisticated three-dimensional non-smooth multi-surface plasticity model intended to capture realistically the multi-dimensional behavior of plain concrete [6, 12], see Fig. 29.3c. The cap plasticity model is characterized by a set of eleven (11) time-invariant material parameters (i.e., material constants) [5]. Two of these parameters (shear modulus, G, and bulk modulus, K) are linear elastic parameters, while the other nine parameters (T, X0, R, α, λ, D, W, β and θ) characterize the yield surfaces, the flow rule and the hardening law of the cap plasticity model. The three yield surfaces are: an ideal plasticity failure envelope f1(σ) =0 defined by α, λ, β and θ; a strain hardening ellipsoidal cap f2(σ, κ) =0 (κ is the hardening parameter acting as a material history variable) defined by X0 and R; and an ideal plasticity tensile-cutoff surface f3(σ) =0 defined byT. Parameters DandWcharacterize the hardening law. Here, σis the stress tensor with s and (I1/3)I denoting its deviatoric and volumetric components such that σ=s +(I1/3)I (I1 is the first invariant of the
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