Multi-scale computational modeling of interplay of fibers, reinforcement and cementitious matrix for ultra-high performance concrete in fluid and solid states

Abstract

Ultra-High-Performance Concrete (UHPC) is a special class of concrete with superior mechanical and rheological properties. Optimal gradation with only very fine aggregate (typically less than 1 mm) and the presence of discrete smeared fiber reinforcements holds the key behind its special features. UHPC has significantly higher compressive strength ($>$ 150 MPa) and much lower permeability compared to regular concrete which makes it much more durable. The presence of fibers enables UHPC to sustain large tensile stresses for much larger strains compared to regular concrete too. Thus, the contribution from tension zones in UHPC beams due to fiber crack bridging is not negligible as it was in regular concrete. These additional features come at a price. From a mechanical behavior complexity point of view, previous research works have shown that the key failure modes of reinforced-UHPC (R-UHPC) beams are governed by the relative proportion of continuous and discrete reinforcements which originates from the mechanics of interplay. However, not only the interplay is a complex phenomenon, but also, the tensile capacity of UHPC is not an isotropic property. This is because of the highly flowable nature of UHPC that creates flow-induced fiber orientation based on the casting geometry as well as rheological properties of UHPC at fresh state. This phenomenon makes UHPC behavior anisotropic. Therefore, the macroscopic tensile strength (and to some extent its shear strength) of UHPC becomes an extrinsic property and hence increases the uncertainty during the structural design process. Additionally, the quantification of these complex interactions is challenging even with the most rigorous experimental tools given the challenges of measuring individual fiber contributions and their orientations. Therefore, this presented research aims to address these issues with a comprehensive multi-state multi-scale computational framework that links fresh state to hardened state of UHPC and mesoscale description to structural length scale via multi-scaling modeling. The numerical framework can be broadly divided into three projects. In the first project, a state-of-the-art discrete numerical model, the Lattice Discrete Particle Model with Fibers (LDPM-F) is used to probe into shear and flexural failure mechanisms of R-UHPC beams. In this work, a UHPC material model was calibrated and validated based on lab-scale companion specimen tests. The calibrated model was then used to simulate R-UHPC beams with different fiber and rebar reinforcement contents followed by sectional analysis to quantitatively evaluate the different contributions of UHPC matrix, rebar, and fiber in load-carrying capacity. The detailed probing of failure mechanisms was able to furnish a fundamental understanding of stress redistribution for different failure modes. Next, the second project was focused on enabling the computationally cost-effective simulation of R-UHPC structural beams while keeping as much rich physics of their constituents interactions. This was done by extending an energy-based coarse-graining model for plain concrete to account for discrete fibers explicit contribution. To study the applicability of the model and the ranges of its scaling factor, a parametric study was designed for different coarse realizations to show that the length scale of the fiber dictates the limit of the coarse realization to reliably preserve the complex energy dissipation mechanisms of the fine-scale. The results showed the capabilities of the new coarse-graining model in achieving very large computational cost reductions with high accuracy in predicting the same failure mode and load-displacement response for a large number of lab-scale and full structural scale experiments. Finally, the third project intends to link the flow-induced fiber orientation during casting to the hardened mechanical behavior of UHPC. An orientation tensor-based approach was used to predict the evolution of fiber orientation in a semi-explicit manner where instead of tracking each fiber due to hydrodynamic interaction, a fiber orientation state is predicted in a statistical sense. This model successfully predicted the fiber orientation state which was subsequently validated by simulating the hardened behavior of UHPC in presence of a preferential fiber alignment. Collectively, the presented research provides a virtual numerical framework of R-UHPC structural elements that allow for investigating and evaluating complex failure mechanisms as functions of reinforcement ratio, fiber content, and flow-induced fiber orientation. At the same time, this framework is capable of simulating large-scale elements thanks to its cost-effective multi-scale modeling capability. Collectively, the presented research serves as a digital twin for R-UHPC beams that can be used to understand and link the Processing-Structure-Properties-Performance relationships of this complex and advanced class of reinforced cementitious composites.