Implementation of PARC_CL 2.0 crack model for reinforced concrete members subjected to cyclic and dynamic loading

Nonlinear finite element analysis (NLFEA) are nowadays strongly used both in research and in design practices. The [fib-Model Code 2010] introduced the concept of Levels of Approximations (LoA) to estimate a reinforced concrete (RC) structural member's behaviour. The LoA approach is a design strategy, based on the assumption that the structural member's response can be progressively refined through a better estimate of the physical parameters. By increasing the level of approximation, a better accuracy in the estimate of the structural response can be obtained; however, more time and resources have to be devoted to the analyses. In particular, the higher level of approximation is associated with the NLFEA. In the last years the rapid increase of computer power contributed to the development of this numerical tool for both the design of new structures and the assessment of existing ones. For the latter, a proper modelling of the nonlinear behaviour is fundamental for the prediction of the structural response. The behaviour of thin RC structural members (e.g. walls and slabs) subjected to monotonic, cyclic and dynamic loading, both in-plane and out-of-plane, has been investigated, by means of NLFEA. In particular, the cyclic response of RC walls has been analysed in detail. RC walls are commonly used as lateral load resisting elements in buildings in seismic region thanks to the high stiffness and resistance they can give to the building. Their principal function is to carry in-plane forces but, as a consequence of particular forces and boundary conditions, they could be subjected also to out-of-plane actions. RC walls can be modelled with different approaches: 1-D models considering lumped or distributed plasticity using beam elements, 2-D models using shell elements and 3-D models using solid elements. In particular, in the present research the behaviour of RC walls was investigated by means of †œmulti-layer shell†� elements (MS) using ABAQUS code. The MS approach, defined within the ABAQUS code, consists in discretizing the thickness of the element in several layers assuming a plane†"stress hypothesis. The aim of this research was to assess the capability of the proposed approach to reproduce the monotonic, cyclic and dynamic behaviour of RC members subjected to in-plane and out-of-plane actions. Since the adopted MS elements are defined in ABAQUS code in plane-stress condition, they do not include the nonlinear behaviour due to shear along the thickness; it is, therefore, not possible to capture shear or punching shear out-of-plane failure. Within this research a post-processing of the NLFEA results is conducted based on Critical Shear Crack Theory (CSCT). CTCT, as reported in [Muttoni, 2008] and [Muttoni and Fernandez, 2008a], allows to calculate shear and punching shear resistance based on few fundamental parameters, such as respectively the axial strain at mid-depth and the out-of-plane rotation of the element. In this context, NLFEA are carried out on several RC slabs experimentally tested in literature. The outcomes highlighted that NLFEA, post-processed according to CSCT, leads to good results when compared with the experimental ones, proving itself able to capture both the bending and shear out-of-plane failure. Moreover, by comparing with simplified analytical formulations, it was underlined that NLFEA allows considering phenomena like redistribution of stresses and membrane effect due to cracking and boundary conditions. The main aim of this research was to investigate the capability of MS elements to predict the cyclic and dynamic response of RC walls. The cyclic response of RC structures was widely investigated in literature associated to 1-D elements (e.g. plastic hinge models to study the nonlinear flexural behaviour). On the other hand, concerning 2-D shell and 3-D solid modelling, recent developments in seismic engineering underlined the lack of cyclic crack models for reinforced concrete, while the monotonic behaviour was widely studied in the past. A cyclic crack model for RC members, defined PARC_CL 2.0 and implemented as a user subroutine UMAT.for within the ABAQUS code, allows, differently from the previous PARC_CL 1.0 crack model, to account for plastic and irreversible deformation in the unloading phase. As a consequence of this it permits to consider the hysteretic cycles both in concrete and steel. Moreover, within the PARC_CL 2.0 crack model, was implemented a formulation able to account for stiffness proportional damping in dynamic analyses. The implemented PARC_CL 2.0 crack model was primarily validated by means of comparison with experimental tests run on simple RC panels carried out at the University of Houston [Mansour and Hsu, 2005] and in a second phase it was applied to more complex structural members, such as RC walls, with the aim to assess the capability of the implemented model to predict the cyclic and dynamic behaviour and to underline the improvement with respect to the previous PARC_CL 1.0 crack model. In order to evaluate the generalizability of the implemented model, different walls, characterized by different layouts were analysed: squat walls tested at ISPRA laboratory [Pegon, 1998] and slender walls with different cross sections tested at EPFL in Lausanne (two †œT-shaped†� walls [Rosso et al., 2016] and a †œU-shaped†� wall [Constantin and Beyer, 2016]). The results obtained by means of NLFEA with PARC_CL 2.0 crack model was in good agreement with the experimental tests, demonstrating its ability to capture not only cyclic in-plane behaviour but also phenomena associated to the out-of-plane instability.