The non-linear behaviour of RC structures is related to the highly non-linear response of material to cyclic loading, in particular seismic one. For this reason, realistic cyclic constitutive models are required to obtain reasonably accurate simulations of RC members.
Existing commercial finite-element codes often have limitations in representing cyclic behaviour, due to idealizations in material models, or due to the fact that they are not able to consider particular failure modes, for example, those associated to existing buildings.
The need to handle every single constitutive law and to add, as needed, different contributions led to the creation of a new crack model for reinforced concrete elements, called PARC_CL 2.1 (Physical Approach for Reinforced Concrete under Cyclic Loading condition).
The PARC_CL 2.1 model is a smeared and fixed crack model for the cyclic and dynamic response provision of RC structures, able to consider plastic and irreversible deformation occurring during the unloading/reloading phases. The PARC_CL 2.1 crack model is implemented as a user subroutine, written in the fortran language, for the Abaqus software.
In the PARC_CL 2.1 crack model, the quantities that control the problem are the opening and the sliding of the crack lips, as well as the strain of the concrete struts that are located between cracks. Applied to a local analysis of cracked reinforced concrete, the above variables
allow for the effective modeling of compatibility and equilibrium conditions and take into account phenomena such as aggregate interlock, tension stiffening, and buckling.
Once the knowledge of the behaviour of a single element is reached, it is easily possible to study entire structures as an assemblage of many elements, Figure 1.2.
More specifically, the user subroutine is created for the application to multi-layered shell elements. The advantages of multi-layered shell finite element modelling are many, including the ability to consider the interaction between the stresses acting both in the plane and out of the element's main plane.
Figure 1.2: (a) Entire structure considered as the assembly of multi-layered shell elements: (b) shell element in plane and (c) shell section.
The thesis presents formulations implemented in the PARC_CL 2.1 and demonstrates the reliability of the model through the methodical comparison with the experimental results of different types of structural elements. After demonstrating the efficiency of the model for the prediction of the structural response of new buildings, it was possible to extend the formulation to existing buildings as well. This interest arises from the need for a correct analysis of the vulnerability of existing structures, in which unexpected local and global mechanisms may develop, linked to lack of details and often accompanied by poor material characteristics.
Herein lies the true peculiarity of the PARC_CL 2.1 model. The knowledge of such mechanisms would lead to great advantages in the "conceptual design" of the seismic assessment, so as to maximize its effectiveness. This procedure is essential for the safeguard and development of the existing building.
The buckling failure mode due to the instability of the vertical bars, often anticipated by corrosive phenomena, turns out to be pernicious for existing RC structures characterized by a lack of detail. For this reason, the first step to extend the model to existing buildings concerned the study of buckling of longitudinal rebars.
The aim of the thesis is therefore to develop a model for RC elements capable of evolving according to the type of problem that needs to be explored, in order to overcome the limits imposed by the commercial programs.
Lacunae in Current Knowledge
This research aims to provide a contribution to a correct methodological and engineering approach to the problem of predictive evaluation of the collapse mechanisms typical of new and existing structures. In fact, there is only limited research available that combines deterioration modelling with numerical analyses of the member resistance of existing structures.
Some collapse mechanisms typical of existing structures are not observed in new buildings, such as the buckling of longitudinal reinforcements caused by insufficient stirrups. This is due to the fact that reinforced concrete structures, built before the modern seismic codes, were designed only for gravitational loads, without considering the horizontal actions induced by earthquakes. The elements of these structures generally have a sub-dimensioned cross-section which, when subjected to large transverse and/or cyclic deformations, fail for spalling of concrete cover with consequent buckling of the longitudinal reinforcement.
There are currently a very limited models able to predict the non-linear response of RC elements accounting for the combined effect of inelastic buckling and cycle fatigue degradation.
This aspect led to extend the PARC_CL 2.1 formulation to existing RC structures. The first step of this work was the implementation of constitutive models able to take into account for buckling effect.
Research Objectives
This Ph.D. research focuses on the following main objectives:
• Develop a new crack model, called PARC_CL 2.1, for the response prevision of RC elements or structures subjected to static and dynamic loading;
• Develop a numerical model to assess the contribute given by bond-slip mechanism between steel and concrete and shrinkage effects;
• Validate the PARC_CL 2.1 model by means of comparison, both in terms of global and local response, with experimental data available in literature;
• Extend the PARC_CL 2.1 crack model to the structural response assessment of existing RC structures. In this sense the first step consists in the implementation of constitutive laws for steel accounting for buckling of the longitudinal rebars;
• Develop a numerical model capable of evolving according to the type of problem that needs to be explored.
Thesis Outline
This thesis work is divided into six chapters each of which is organized in the following way, Figure 1.3:
• introduction to literature background;
• presentation of the implemented formulation;
• validation of the PARC_CL 2.1 model by means of comparison with experimental tests inherent the implemented contribute;
• conclusion and remarks about potentiality and possible improvements of the PARC_CL 2.1 crack model.
This methodology of work has allowed to create a cracking model increasingly more complex and able to grasp various aspects that affect the RC structures. For clarifying the versatility of the proposed model, the systematic verification is carried out through comparison with some experimental test.
In Chapter 2 the concepts underlying the different theoretical approaches will be described, highlighting the peculiarities of the proposed model and the common aspects to other approaches. It will thus be possible to place the proposed model more accurately within the studies carried out by other authors on RC elements subject to in-plane stresses. Furthermore,
the main formulations for RC elements subjected to cyclic loading are presented and the comparison with the results obtained by another NLFEA program are shown.
Chapter 3 presents a proper numerical modelling able to consider the concrete shrinkage effect. Shrinkage is an important contribute because it affects the cracking resistance of structural elements, as well as their deformations even under short-term loading. To this aim, concrete shrinkage is explicitly considered by treating it as a prescribed deformation. This permits to avoid inaccurate predictions of structural performances at serviceability conditions.
Figure 1.3: Thesis outline.
The combined effect of shrinkage deformations and tension-stiffening will be treated in Chapter 4. In fact, shrinkage causes time-dependent cracking and gradually reduces the beneficial effects of tension stiffening. On the other hand, the tension stiffening is the effect induced by the interaction between concrete and steel after cracking: concrete between cracks of RC elements carries tensile stress due to the bond between the reinforcing bars and the surrounding concrete. Moreover, the modeling of the tension stiffening will allow taking into
Basic Formulation Chapter 2
Shrinkage effect Chapter 3
Tension Stiffening contribute Chapter 4
Buckling of longitudinal rebars
Chapter 5 Introduction Chapter 1
Conclusion Chapter 6
- literature background - implemented
formulation - validation by
NLFEA
newstructures
existingstructures
PARC_CL 2.1
account splitting failure and the sliding of the bars due to debonding, caused by lack of details as bad anchoring of the bars.
Chapter 5 presents the first development of the PARC_CL 2.1 model to RC existing structures. Existing structures, designed and built before seismic codes, are characterized by lack of details, often associated with high stirrups spacing. This aspect is relevant above all in Italy where there is a high building heritage dating back to the 60s and 70s, a period of great building growth. The first step of this study consists in the implementation of the buckling of longitudinal rebars. The constitutive laws chosen for steel offer the possibility to be extended also to corrosion.
Eventually, major findings and conclusions together with suggesting for further developments are exposed in Chapter 6.