Simplified modeling strategies for the non-linear behavior of civil engineering structures

Engineering regulations are in place to deal with ordinary civil engineering structures. However, for irregular structures and/or those requiring precise knowledge of their operation (local critical zones, floor spectra, safety margins, etc.), access to non-linear calculations becomes a necessity.

The non-linear analysis of structures involves a number of challenges: analysis of the structure and its interactions with the ground, analysis of material behavior, but also of the possible stochastic randomness of the loading action and of material properties. In order to integrate uncertainties at all levels and support decision-making when the structure is subjected to severe loading, complex phenomena need to be studied, and a large number of calculations need to be carried out.

Engineering therefore needs fast, efficient and robust models that can reproduce complex phenomena while reducing uncertainties.

The analysis of structures in non-linear dynamics, based solely on detailed finite element models, requires considerable computing resources and delicate, time-consuming resolution techniques. The need for parametric studies, however, calls for the use of simplified techniques, most often based on multi-scale formulations, which help to reduce calculation costs. From soil to structure, simplified modeling strategies have been developed in recent years. With a limited number of input parameters, either geometric or determined by simple experiments (e.g. on materials), they enable the phenomena driving the behavior of a reinforced concrete structure to be modeled finely, robustly and rapidly.

In order to cover a wide range of techniques and simplified applications, the following families of models will be developed:

• the Equivalent Reinforced Concrete model ( – ERC), which reproduces the overall behavior (force/displacement) of a reinforced concrete wall;

• the Timoshenko multi-fibre beam, capable of simulating the behaviour of reinforced concrete beams or walls whose sections are loaded by a torsor of internal forces (moment, shear force, normal force and torsion);

• global models, based on homogenization theory, which give access to the damage and/or cracking of reinforced concrete walls;

• the macro-element which, coupled with the multi-fiber beams, is capable of reproducing soil-structure interaction phenomena and their effects on the structure.

These simplified models have imposed kinematics that restrict the space in which the behavior laws can be used. Unidirectional nonlinear laws are, for example, often used in multi-fiber beams to...