Ultra-High Performance Concrete Compression and Fracture Response Parameters for Lattice Discrete Particle Model Simulations

Lattice Discrete Particle Model (LDPM) simulation parameters are obtained for Lafarge Ductal Ultra-High Performance Concrete (UHPC) from unconfined compression, fracture, and direct tension tests. The LDPM predicts macroscopic behavior of concrete including compression, shear, and flexure limit states, through mesoscale constitutive relationships. The volume and orientation of fibers were considered as test variables. The experimental results showed a 7% increase in the ultimate compression strength when fibers, 2% by volume, were introduced in the UHPC matrix. The post-peak load carrying capacity also improved where the material maintained 50% of its ultimate carrying capacity at an axial strain 157% greater than the ultimate strain with a 4% fiber volume content. In the fracture tests, the peak load increased by a factor of 5 with the inclusion of 2% fibers by volume and by a factor of 6 when these fibers were oriented perpendicular to the crack plane. The post-peak loads also improved with increasing fiber content. LDPM parameters were obtained by simulating the material tests relevant to plain UHPC (without fiber reinforcement) and comparing the results to experimental data. The simulations will be coupled with fiber-pullout models to validate the model predictive capabilities for fiber-reinforced UHPC in support of a larger research effort to bring simulation-based analysis and design to concrete codes and standards. Keywords: UHPC, LDPM, Fracture, Compression, Tension, Fibers, Material Characterization First International Interactive Symposium on UHPC – 2016 Ultra-High Performance Concrete Compression and Fracture Response Parameters for Lattice Discrete Particle Model Simulations Rafic G. El-Helou, Erol Lale, Gianluca Cusatis, and Cristopher D. Moen 2 1. Introduction and Research Vision Structural-scale computational modeling of concrete components and systems including random cracking, failure patterns, and the influence of discrete fiber reinforcement is now possible because of advances in mechanics, numerical methods, and computational tools. The Lattice Discrete Particle Model (LDPM), for example, predicts the macroscopic behavior of Ultra-High Performance Concrete (UHPC) including compression, shear, and flexure limit states, through mesoscale constitutive relationships (Cusatis et al. 2011a, Schauffert and Cusatis 2011a). This formulation is chosen for the current study for its ability to predict concrete failure modes and crack patterns including the effect of aggregate size, discrete cracking, and fiber-matrix interaction. UHPC is a high-strength material with a compressive strength exceeding 150 MPa, achieved when discrete steel fibers are combined with an optimized packing of cement, silica fume, fine sand, and water (Graybeal 2006). The fibers improve the durability and ductility of the composite by contributing to the resistance to tensile stresses, bridging crack surfaces, and limiting crack propagation (Lin and Li 1997, Lepech and Li, 2009; Wille and Naaman, 2012). When compared to conventional concrete, UHPC has a higher compressive strength with postpeak capacity, a higher tensile strength with enhanced ductility, and increased durability making it a superior alternative for many structural applications (Graybeal 2013). However, efforts made by the government and industry for its broad implementation into civil infrastructure is taking time to catalyze, in large part because design guides and computational tools for analyzing UHPC structural components are yet to be developed. Concrete design equations and failure patterns have been traditionally investigated through experimental programs directed to specific structural applications. Experimental tests produce reliable data but are expensive, time consuming, and not feasible for exploration of a large number of variables. The LDPM provide an analysis-based alternative to tests that can accelerate the design and implementation of state-of-the-art innovative construction materials into civil infrastructure. However, predictive structural-scale UHPC computational simulations depend on careful material characterization that captures the material response in compression, tension, and fracture, and adequately describes interfacial properties between fibers and surrounding matrix. The research summarized herein contributes to this characterization by describing UHPC unconfined compression and fracture responses including post-peak behavior dependent on fiber content and orientation effect. An experimental program is designed and implemented that builds on previous research to bring UHPC material characterization to structural-scale computational modeling. The tests quantify the direct tension strength, the axial and circumferential stress-strain response of unconfined UHPC in compression, and the fracture behavior for different fiber contents and orientation. The details of the computational modeling framework and the experimental program carried out for this research, including the test matrix, are introduced in the next sections. 2. Lattice Discrete Particle Model The LDPM simulates concrete as a two-phase material composed of coarse aggregate grains held together by an embedded cementitious matrix. The mesostructure is constructed by randomly generating the aggregate centers and diameters, whose shapes are approximated as spheres, based on an assumed particle density function (Figure 1a). Zero-radius nodes are randomly generated over the model surface to create its external geometry. A Delaunay tetrahedralization connect the aggregate centers, and a 3D domain tessellation defines the particle interfaces and creates a system of polyhedral cells, each containing an aggregate and its surrounding matrix First International Interactive Symposium on UHPC – 2016 Ultra-High Performance Concrete Compression and Fracture Response Parameters for Lattice Discrete Particle Model Simulations Rafic G. El-Helou, Erol Lale, Gianluca Cusatis, and Cristopher D. Moen 3 (Figure 1b). These cells interact with each other through triangular facets which are also assumed to be potential crack surfaces (Figure 1a and 1c). To ensure that shear interaction between adjacent particles does not depend on the shear orientation, a vectorial constitutive law is imposed at the centroid of the projection of each single facet (contact point) onto a plane orthogonal to the straight line connecting the particle centers (lattice strut). The straight lines connecting the particle centers define the lattice system (Figure 1c). Figure 1: a) Two-dimensional mesostructure tessellation; b) Three-dimensional discrete particle; c) Facet intersecting a discrete fiber (El-Helou, 2014; Schauffert and Cusatis, 2012a) The displacement field along the lattice struts and the displacement jump, [uc], at the centroid of each facet are described through rigid body kinematics. The components of the strain vector in a local system of reference (normal and shear strains) are defined by the displacement jump at the contact point divided by the inter-particle distance, l : ε( = n+ u/l; εM = m+ u/l; ε3 = l+ u/l, where n is a unit vector orthogonal to the projected facet and m and l are mutually orthogonal unit vectors and lie in the projected facet. Equilibrium is imposed using the principle of virtual work by summing all the facet contributions and equating total internal and external work to obtain the discrete equilibrium equations of the LDPM formulation. The elastic behavior is described by assuming that the normal and shear stresses are proportional to the corresponding strains: σ( = E(ε(; σ7 = E+ε(; σ3 = E+ε3, where E( = E8, E+ = αE8, in which E8 is the effective normal modulus of elasticity, and α is the shear-normal coupling parameter. The parameters E8 and α are assumed to be material properties and are related to the macroscopic properties (modulus of elasticity, E, and Poisson’s ratio, ν). Beyond the elastic regime, the inelastic behavior is represented by three physical mechanisms including fracture and cohesion in tension and tension-shear, pore collapse and compaction in compression, and frictional behavior due to compression-shear. A detailed description of model behavior in the nonlinear range can be found in Cusatis et al., 2011a, and Cusatis et al., 2011b. Schauffert and Cusatis (2012a, 2012b) extended the LDPM formulation to incorporate the effect of discrete short circular straight fiber reinforcement on the concrete behavior. The fiber formulation retains the discrete nature of the model generating all the fibers in a given concrete volume (random or preferred orientation) and overlapping it with the cell system of the LDPM as shown in Figure 1c. The LDPM fiber-matrix interaction formulation takes into account fiber pullout resistance considering debonding and frictional slip, matrix spalling, and fiber snubbing phenomena. The current LDPM formulation is implemented in MARS, a multi-purpose computational code for the explicit dynamic simulation of structural performance (Pelessone, 2016). This paper obtains the LDPM parameters for Ductal UHPC governing compression, tension, and fracture behavior, namely, normal modulus E8, alpha α, facet tensile strength σ;, tensile characteristic length l; , shear strength ratio σ=/σ; , initial friction μ8 , and softening First International Interactive Symposium on UHPC – 2016 Ultra-High Performance Concrete Compression and Fracture Response Parameters for Lattice Discrete Particle Model Simulations Rafic G. El-Helou, Erol Lale, Gianluca Cusatis, and Cristopher D. Moen 4 exponent n; , through experimental testing. The details of the experimental investigation, including the test matrix, are introduced in the next section. 3. Experimental Program The experimental program comprised of a total of 31 unconfined compression testing cylinders, 43 direct tension dogbone-shaped specimens, and 37 three-point bending (notched) fracture toughness prisms. Th