Lattice discrete particle modeling of time dependent behavior of prestressed concrete beams

Time dependent behavior of prestressed concrete (PC) structures is an essential factor in defining their serviceability limit states. Excessive creep and shrinkage deformations pose structural serviceability problems such as the 1.5 m beyond design camber that occurred in Koror-Babeldaob Bridge in 1996[1]. With the current trend of using advanced cementitious materials to produce higher strength concretes, these long-term effects (including self desiccation) become more evident. In this paper, coupled creep, shrinkage and aging evolution in prestressed concrete beams is simulated using a recently developed Discrete-Solidification-Microprestress (DSM) formulation within the Lattice Discrete Particle Model (LDPM). Spatial and temporal evolutions of temperature, humidity and cementitious materials hydration are simulated using a Hygro-Thermo-Chemical (HTC) model. SDMP, DSM and LDPM are coupled in one framework to capture the interplay between environmental changes, creep and shrinkage deformation and damage. The formulations can capture early age as well as multi-decade creep and shrinkage deformations relevant to different design stages of prestressed/post tensioned concrete beams. Tendons are modeled using 1D finite element 2 with a relaxation formulation that could be bound to concrete using a bond-slip type formulation. Calibration and validation is performed through the simulation of multiple experimental data sets from literature. Introduction Time dependent deformations, such as creep and shrinkage, are considered major factors while design for serviceability limits of concrete structures. These deformations have more impact on prestressed concrete structures, as they could cause excessive deformations and loss of prestressing forces. An example for that is Koror-Babeldaob Bridge [1], where camber exceeded design limit of 1.5 meters. Although the bridge was retrofitted, it ended up collapsing few months later. Several experimental programs studied long-term behavior of prestressed concrete structures, covering creep and shrinkage deformations [2,3] and relaxation [4]. These studies provided the needed database for design codes and numerical modeling developments. In parallel, several finite element models were used to simulate and predict instantaneous and long-term behavior of prestressed concrete structures [5,6,7]. The main disadvantage of these models is the lack of concrete heterogeneity representation. Thus, discrete models are needed to better model and predict the complex short and long behavior of prestressed concrete structures. In this paper, a multi-physics framework is used to model long-term behavior of post tensioned concrete beams under its own weight or sustained load. The discrete model used is Lattice Discrete Particle Model (LDPM) [8,9] that is used to replicate elastic and damage behavior of concrete at the meso-scale (large aggregate pieces interaction scale) Visco-elastic and viscous deformations are modeled using a recently developed Discrete-Solidification-Microprestress (DSM)[10] formulation that was based on the Solidification-Microprestress Model by [11,12,13], to model the time dependency of strains with loading and environmental conditions. The comprehensive creep/shrinkage formulations are informed by a Hygro-Thermo-Chemical (HTC) Model [14] that evolves temperature, humidity, and cementitious materials hydration degree over both space and time. Thus, point-wise analysis of the structural elements is accurately performed accounting for the variations in environmental conditions and material aging. Steel relaxation was accounted 3 for using the Eurocode 2 model [15]