ACI SP-306

Abstract

Scope: INTRODUCTION Three-dimensional finite element method (FEM) calculations for concrete structures are now commonplace in many applications. Common applications range from academic studies of structural behaviors under transient loads to informing designs for new structures or retrofits. The objective of this paper is to identify factors that influence response predictions obtained with FEM models for concrete structures under transient loadings. This is accomplished by computing the response of several simple concrete structures and comparing the results with data and observations taken from experiments. The FEM calculations focus on codes solving nonlinear continuum mechanics equations [1] capable of treating concrete behaviors under transient loads and large deformations. All of the computational results presented here are executed using the LS-DYNA code [2], which is a widely used commercial FEM software. It is widely recognized that a competent constitutive model for concrete, and a set of calibrated constitutive parameters for it, are important to producing accurate response predictions using FEM. Several studies already exist comparing many of the widely used models [3] [4] [5] [6]. In this paper, four concrete models available in LS-DYNA are considered. The goal is not to redo some of the comparisons presented in those publications or advocate for use of any one model; instead, our purpose is to demonstrate that although each of these models differ in their assumptions and formulations, the accuracy of structural response predictions computed with them depend on nuanced material model parameters, and often, parameters of the FEM calculations that have little to do with the material model. For this reason, the discussion herein is primarily focused on results obtained using the constitutive model developed and enhanced over the last twenty years by the authors and the late Dr. L. Javier Malvar [7] [8] [9], which is known as the Karagozian & Case Concrete model (KCCM). In LS-DYNA, the model is implemented as MAT072_REL3. The others considered are: the Winfrith Concrete Model (WCM, MAT084); the Continuous Surface Cap Model (CSCM, MAT159); and the Reidel-Hiermaier-Thoma model (RHTM, MAT272). Each of the concrete models can be exercised by entering all of the model variables directly, if mechanical data is available to calibrate those variables, or values can be automatically generated using a “simple input” feature available in each model (e.g., see [8] and [9] for the KCCM). Because data needed to calibrate these models for a specific concrete is costly, and therefore not commonly acquired in practice, the latter is more widely used and the paper focuses on results obtained using this option. Five concrete structures tests are selected for the FEM calculations. Each serves to illustrate an important behavior, feature, or response regime for concrete structures that are highly desirable for the FEM calculation to replicate. • The first are standardized concrete cylinder and cube specimens placed under compression to measure the unconfined compressive strength (ƒC\'). When comparing standard cylinders and cubes, experimental evidence suggests that cube strength is typically greater than cylinder strength, by a factor that varies up to 1.54 for normal strength concretes [10] [11] [12]. In practice, specimen size is standardized to 152-mm diameter, 304-mm tall (6- in diameter, 12-inch tall) cylinders, or 150-mm (6-in) cubes. Typically, cylinder specimens are capped (following ASTM C 617) and placed between grooved platens having various amounts of friction that result in lateral restraint at the top and bottom. An unrestrained form of testing cylinders for compressive strength is relatively recent (ASTM C 1231 was first established in 1993). The DIN 1048 standard for the cube specimens, however, does not prevent restraint at the top and bottom of the cube specimen. The FEM calculations address the factors that affect these specimens, i.e., specimen shape and end restraint. • The second is the splitting tension (or Brazilian) test (DIN 1048 and ASTM C 496), where compression is used to generate failure by indirect tensile stresses. Rupture strengths (ƒr ) measured with the splitting tension tests are known to result in values exceeding the direct tensile strength (ƒt). CEB-FIP reports the ratio of  ƒr/ƒt as 1.11 [11]. Rocco et al. report this ratio between about 1.05 and 1.25 depending on specimen shape, aggregate size, concrete strength, and plywood strip width [13]. For 25-mm (1-inch) aggregates, cylindrical specimens, and increasing strengths from 30 to 80 MPa (4,350 to 11,600 psi), the ratio decreases from 1.16 to 1.08. • The third consists of a split-Hopkinson Pressure Bar (SHPB) test [14], in both compression and tension. SHPB tests generate a dynamic uniaxial stress pulse into a concrete sample, thereby deforming the material rapidly. SHPB tests for concrete are not commonly performed nor are they standardized. SHPB and sample diameters are commonly several times the maximum aggregate size (MAS) of the concrete. In compression, the sample is placed between the two bars and lubricated; in tension, the sample is adhered to the bars. Loading rate effects have been observed from SHPB measurements for decades [15-18]. The data exhibits a two branch behavior when plotted with normalized peak strength versus strain rate in both compression and tension and are often termed Dynamic Increase Factor (DIF) curves [11] [15] [16] [17]. Rate effects in concrete are believed to be due initially to moisture (for example, below 1 s-1), and, at higher strain rates, to inertia effects [18]. • The fourth structure is a thin reinforced concrete (RC) panel blast tested by the U.S. Army Corp of Engineers Engineering Research and Development Center (ERDC) using a blast load simulator. Details of the test, the panel, and the support frame are described in [19]. The RC panel, PH-Set 1a, is loaded by a dynamic pressure loading applied over the front surface of the panel, which deforms the panel in flexure. The panel is reinforced with longitudinal and horizontal mild steel rebars placed on the tensile-side of the panel; no transverse reinforcement is provided that can provide confinement to the concrete. The panel is placed in a support frame with its two long sides supported with structural steel tubes on both sides of it (i.e., on the front and back face of the panel). • The last structure consists of a series of confined RC column tests described in [20]. The column is loaded with a monotonically-increasing uniform lateral loading by way of servo-hydraulic actuators operated under displacement-control. An initial axial load is held constant during the lateral loading. Confinement to the column is provided by Carbon Fiber Reinforced Plastic (CFRP) wraps placed around the column’s cross-section. As the RC column is loaded laterally, the concrete cracks, due to the flexure and shear deformations, dilates, and the CFRP acts to resist the lateral expansion of the concrete, thereby increasing confinement. Contrary to the thin RC panel, the confinement affords the column large levels of strength and ductility until deformations are large enough to break the CFRP wraps. Four tests are of interest, corresponding to the number of CFRP wraps placed around the column (0 wraps, 2 wraps, 4 wraps, and 6 wraps). This paper is organized into five sections. Section 2 provides a brief description of the numerical methods employed in the FEM calculations, the constitutive models, and the FEM models developed for each test. Comparisons produced using each constitutive model are shown for simple triaxial compression and unconfined tension load paths. Triaxial compression behaviors are important in highly confined RC structures while unconfined tension behaviors can dominate in lightly confined RC structures. In Section 3, the results of the FEM calculations are presented. Section 4 provide a brief discussion of the results and Section 5 states our conclusions.