Ultra-High Performance Concrete (UHPC) is an evolving structural material that has attracted interest in the civil engineering industry recently. Currently, it is being used mainly for highway infrastructure in the US and also being explored for various other applications. The existing design guides on UHPC in countries like Japan, Australia and France are not as detailed as the concrete or steel guides. Most of the sections made of UHPC are slender due to its superior mechanical properties which are expected to simplify construction. Being an expensive material to use, making slender sections also helps to minimize the overall cost of the structure and makes it competitive with that of high strength steel and prestressed concrete. It has also been demonstrated to have very high compressive strength and considerable tensile strength. To begin with, an introduction on UHPC and its current applications around the world is presented, followed by a review of the existing design guides on UHPC. The importance as well as the methodology to measure fracture energy of concrete with factors to be considered for fiber reinforced concrete is discussed in detail. The main motive of this research is to introduce a creative modeling concept which served as the theoretical basis for the development of a computer program called Lattice 3D. The program is a modeling tool for engineers studying the behavior of UHPC, and in the future will be developed into a finite element protocol for analyzing complex structures made of UHPC. Parametric studies on lattice models of thin simply supported plates in compression and three-point bending of beams have been demonstrated in this research. Experimental tests conducted on briquette specimens under uniaxial tension are also discussed. / Master of Science

Hydraulic fracturing is a multi-physics multi-scale problem related to natural processes such as the formation of dikes. It also has wide engineering applications such as extraction of unconventional resources, enhanced geothermal energy and carbon capture and storage. Current simulators are highly simplified because of the assumption of homogeneous reservoir. Unconventional reservoirs are heterogeneous owing to the presence of natural fracture network. Because of high computational effort, three-dimensional multi-scale simulations are uncommon, in particular, modelling material as a heterogeneous medium. Lattice Element Method (LEM) is therefore proposed for multi-scale simulation of heterogeneous material. In LEM, material is discretised into cells and their interactions are modelled by lattices, hence a three-dimensional model is simplified to a network of one-dimensional lattice. Normal, shear and rotational springs are used to define the constitutive laws of a lattice. LEM enables desktop computers for simulation of a lattice model that consists of millions of lattices. From simulations, normal springs govern the macroscopic bulk deformation while shear springs govern the macroscopic distortion. There is fluctuation of stresses even under uniform loading which is one of the characteristics of a lattice model. The magnitude increases with the stiffness ratio of shear spring to normal spring. Fracturing process can be modelled by LEM by introducing a microscopic tensile strength and a microscopic shear strength to the lattice properties. The strength parameters can be related to fracture toughness with the length scales of cells. From simulations, the relationships between model parameters and macroscopic parameters that are measurable in experiments are identified. From the simulations of uni-axial tension tests, both the spring stiffness ratio and the applied heterogeneity govern the fracturing process. The heterogeneity increases the ductility at the expense of the reduction on the macroscopic strengths. Different stages of fracturing are identified which are characterised by the model heterogeneity. Heterogeneous models go through the stages of the spatially distributed microscrack formation, the growth of multiple fracture clusters to the dominant fracture propagation. For homogeneous models, one of the microcracks rapidly propagates and becomes a dominant fracture with the absence of intermediate stages. From the uni-axial compression test simulations, the peak compressive stress is reached at the onset of the microscopic shear crack formation. Ductility is governed by the stiffness reduction ratio of a lattice in closed fractured stage to its unfractured stage. A novel Dual Lattice Model (DLM) is proposed for hydraulic fracture simulation by coupling a solid lattice model with a fluid lattice model. From DLM simulations of hydraulic fracturing of the classical penny shape crack problem under hydrostatic condition, the heterogeneities from both the fracture asperity and the applied heterogeneity increase the apparent fracture toughness. A semi-analytical solution is derived to consider the effect of fluid viscosity in the elastic deformation regime. Two asymptotes are identified that gives steep pressure gradients near the injection point and near the fracture tip which are also identified in the DLM simulations. Simulations also show three evolving regimes on energy dissipation/transfer mechanisms: the viscosity dominant, the elastic deformation dominant and the mixture of elastic deformation and toughness.