Browsing by Subject "Modulus"
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Item Bayesian prediction of modulus of elasticity of self consolidated concrete(2009-05-15) Bhattacharjee, ChandanCurrent models of the modulus of elasticity, E , of concrete recommended by the American Concrete Institute (ACI) and the American Association of State Highway and Transportation Officials (AASHTO) are derived only for normally vibrated concrete (NVC). Because self consolidated concrete (SCC) mixtures used today differ from NVC in the quantities and types of constituent materials, mineral additives, and chemical admixtures, the current models may not take into consideration the complexity of SCC, and thus they may predict the E of SCC inaccurately. Although some authors recommend specific models to predict the E of SCC, they include only a single variable of assumed importance, namely the compressive strength of concrete, c f ? . However there are other parameters that may need to be accounted for while developing a prediction model for the E of SCC. In this research, a Bayesian variable selection method is implemented to identify the significant parameters in predicting the E of SCC and more accurate models for the E are generated using these variables. The models have a parsimonious parameterization for ease of use in practice and properly account for the prevailing uncertainties.Item Equilibrium Distribution of Charges, Capacities, and Affine Mappings(2011-08) Valles, James R.; Solynin, Alexander Y.; Barnard, Roger W.; Williams, Brock; Dwyer, Jerry F.In this dissertation, we will explore the interactions of potential charges within simple geometric domains. The positions of these charges in reaching an extremal position will then be transitioned to a study on the interaction of the charges based on the shape of the domain changing. This will lead into a final study, where a conformal invariant, based on the shape of a particular domain, is examined as the domain is transformed by a complex mapping. The common thread between all of these topics is that a particular energy for a system is studied; the energy of each system, though, is based on the interactions the charges have in their respective domains. In Chapter 2, we will discuss the historical background of the study of charge placement with regard to minimizing potential energy. Some of the applications of potential energy in other fields will be discussed as well. In Chapter 3, the planar configurations of charges on simple geometric domains will be discussed. Of interest is the placement of charges that produce an extremal logarithmic potential energy based on the domain containing these charges. In Chapter 4, we will discuss the break-of-symmetry effect with regard to the position charges on domains as the shape of the domains changes. We will show that n extremal charges will have a convergent limit set of n charges. However, for one particular system the critical point of the function describing the system’s logarithmic potential energy will be where a “jump” occurs in the extremal position of the charges. In Chapter 5, we will discuss the affine capacity of a system of charges. The affine modulus of a quadrilateral is introduced, and the behavior of the affine modulus of two “essentially different” quadrilaterals under an affine transformation will also be discussed.Item Field measurement of the linear and nonlinear constrained moduli of granular soil(2013-08) LeBlanc, Matthew Thad; Stokoe, Kenneth H.Traditional field seismic measurements have been performed for more than 50 years to determine the small-strain shear and constrained moduli of geotechnical materials under existing conditions. Field measurements to characterize the nonlinear response of the constrained modulus have received essentially no attention in the engineering community. This study was undertaken to characterize the in-situ response of the linear and nonlinear constrained moduli in one testing method. In this dissertation, a field method is presented which uses large shakers to impart vertical sinusoidal excitations directly above an embedded sensor array. This methodology essentially performs parametric studies on the constrained moduli of geotechnical materials in-situ over a wide range of axial strains. In this study, embedded sensor arrays at two different locations were constructed. A staged loading sequence was used to determine the constrained compression wave velocities between sensors in the linear, i.e. small-strain, and nonlinear strain ranges. Constrained moduli were determined using the mass density of the soil and the constrained compression wave velocities. The axial strains generated between sensors were estimated using a displacement-based method. At both sensor arrays, the method successfully measured in the field: (1) the variation of the small-strain constrained compression wave velocity with increasing confining pressure and (2) the effect of axial strain on the constrained moduli of soil in various states of stress. The field measurements indicate that, at lower levels of confining pressure, the constrained modulus increases slightly with increasing axial strain, but then decreases with increasing axial strain. However, in other cases, the constrained modulus increased with increasing axial strain and showed little or no tendency to reach a "peak" value. The nonlinear stress-strain behavior of the constrained modulus is quite complex and appears to be a function of several factors, including the amount of overconsolidation and cementation in the soil and the locations of the sensors in the array. Therefore, while the results of this study indicate that the proposed field method can be successfully used to investigate the constrained modulus, more work is required in this area to fully quantify the response of the constrained modulus in the nonlinear strain range.