Neither damage mechanics model nor elastoplastic constitutive law can solely describe the behavior of concrete satisfactorily. In fact, they both fail to represent proper unloading slopes during cyclic loading. To overcome the disadvantages of pure plastic models and pure damage approaches, the combined effects need to be considered. In this regard, various classes of plastic-damage models have been recently proposed. Here, the theoretical basics of the plastic-damage model originally proposed by Lubliner et al. and later on modified by Lee and Fenves is initially presented and its numerical aspects in three-dimensional space are subsequently emphasized. It should be mentioned that a part of the implementation in 3-D space needs to be reformulated due to employing a hyperbolic potential function to treat the singularity of the original linear form of plastic flow proposed by Lee and Fenves. The consistent algorithmic tangent stiffness, which is utilized to accelerate the convergence rate in solving the nonlinear global equations, is also derived. The validation and evaluation of the model to capture the desired behavior under monotonic and cyclic loadings are shown with several simple one-element tests. These basic simulations confirm the robustness, accuracy, and efficiency of the algorithm at the local and global levels. At the end, a four-point bending test is examined to demonstrate the capabilities of the model in real 3-D applications.

Elevated water tanks as one of the main lifeline elements are the structures of high importance. Since they are extremely vulnerable under lateral forces, their serviceability performance during and after strong earthquakes is a matter of concern. As such, in recent years, the seismic behavior of water tanks has been the focus of a significant amount of studies. In the present work, three reinforced concrete elevated water tanks, with a capacity of 900 cubic meters and height of 25, 32 and 39 m were subjected to an ensemble of earthquake records. The behavior of concrete material was assumed to be nonlinear. Seismic demand of the elevated water tanks for a wide range of structural characteristics was assessed. The obtained results revealed that scattering of responses in the mean minus standard deviation and mean plus standard deviation are approximately 60% to 70 %. Moreover, simultaneous effects of mass increase and stiffness decrease of tank staging led to increase in the base shear, overturning moment, displacement and hydrodynamic pressure equal to 10 - 20 %, 13 - 32 %, 10 - 15 % and 8 - 9 %, respectively.