Non-linear finite element analyses applicable for the design of large reinforced concrete structures

Abstract

In order to make non-linear finite element analyses applicable during assessments of the ultimate load capacity or the structural reliability of large reinforced concrete structures, there is need for an efficient solution strategy with a low modelling uncertainty. A solution strategy comprises choices regarding force equilibrium, kinematic compatibility and constitutive relations. This contribution demonstrates four important steps in the process of developing a proper solution strategy: 1) definition, 2) verification by numerical experiments, 3) validation by benchmark analyses and 4) demonstration of applicability. A complete solution strategy is presented in detail, including a fully triaxial material model for concrete, which was adapted to facilitate its implementation in a standard finite element software. Insignificant sensitivity to finite element discretization, load step size, iteration method and convergence tolerance were found by numerical experiments. A low modelling uncertainty, denoted by the ratio of experimental to predicted capacity, was found by comparing the results from a range of experiments to results from non-linear finite element predictions. The applicability to large reinforced concrete structures is demonstrated by an analysis of an offshore concrete shell structure.

Numerically Efficient Three-Dimensional Model for Non-Linear Finite Element Analysis of Reinforced Concrete Structures

“…The maximum principal value is set to the residual value, and the stress vector is transformed to a global coordinate system with the following formulas: where: —the residual stress coefficient ( ), and —the transformation matrix (calculated according to Reference [ 17 ]). In contrast to the aforementioned papers (e.g., References [ 20 , 21 , 22 ]), the stress in cracks is not set equal to zero due to different convergence criteria for the Newton scheme. During tests, it was found that the best stability of the incremental process is observed for .…”

“…The implemented smeared crack model is based on the Rashid concept [ 42 ], which later was developed by Vidosa et al [ 43 ], Kotsovos and Spiliopoulos [ 44 ], Spiliopoulos and Lykidis [ 16 ], Markou and Papadrakakis [ 18 ], Mourlas et al [ 20 , 21 ], and Engen et al [ 22 ]. In this approach, the modification of stiffness properties and stress values is introduced in Gauss points, at which the stress state reached the ultimate surface.…”

“…A physical interpretation of this parameter could be the measure of tension softening, which characterises plain concrete. During the following incremental-iterative process, the tangent constitutive matrix is used (in global coordinates): where: —normal retention factor (a value of was adopted as in References [ 22 , 29 ]), and —shear retention factor (a value of 0.1 was adopted as in References [ 17 , 22 ]). Retention factors are introduced mainly to maintain the numerical stability of the incremental process [ 17 , 45 ].…”

“…Hence, the stress vector is mapped on the PJ surface. A similar solution was adopted by Engen [ 22 ]. The value of the threshold angle was selected based on References [ 22 , 46 , 47 ].…”

“…Mourlas et al have adapted the Kotsovos model to non-monotonic loads by the introduction of: an efficient cracks closure algorithm [ 20 ] and damage factors [ 21 ]. Engen et al [ 22 ] implemented this model in the DIANA code and showed its usefulness by the simulation of the behaviour of a large offshore shell structure. Lewinski and Wiech [ 23 ] proposed a modified Kotsovos model for the analysis of moderate-thickness RC plates.…”