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Superelevation transition is often used to help balance the centrifugal forces on vehicles through curved roadway sections. Such transitions have regions with near-zero cross-slope as the pavement cross-section rotates from a negative to positive grade. For drainage of roadway surfaces, regions with near-zero slope constitute 'irregular topography'. This condition promotes extended stormwater runoff drainage path lengths and may result in excessive splash from vehicles and hydroplaning. A critical concern is the effect of longitudinal slope on stormwater drainage through superelevation transition. The overall goal of this study is to provide design guidance on longitudinal slope at superelevation transitions through application of a numerical simulation model of highway drainage. Sheet flow on urban pavement surfaces is very shallow, typically measuring a depth less than one centimeter. For modeling of such flow conditions, any small discontinuity or over-simplification of the surface geometry may result in failure in the flow computation. The kinematic wave approximation to the full Saint-Venant equations is often used in many surface and subsurface water models due to its simplicity in application. However, this model fails when backwater effects, ponding, or flow on reverse slope occurs in the local scale. Furthermore, due to the complexity in the surface geometry and the existence of drainage systems, the kinematic wave model is not sufficient for modeling urban stormwater runoff. On the other hand, the full dynamic wave (DW) model usually requires more computational effort. The long computation time of DW model often compromises the accuracy of the model, making the model practically inefficient. In this study, an algorithm was developed to properly represent the irregularly shaped roadway surfaces near superelevation transition areas with unevenly spaced curvilinear grids based on the geometry profile provided by a roadway design software package such as MicroStation CAD. With this accurately defined geometric representation, a nonlinear hydrodynamic diffusion wave model for hydraulic analysis developed in this research estimates the flow depth and runoff volume on the pavement surfaces. The model computes the flow responses for rising hydrographs using a preconditioned general Conjugate Gradient method. Kinematic boundary conditions developed for the open boundaries at the upstream and downstream boundaries compute the boundary values explicitly at each time step. The result of a numerical experiment shows that the spread and concentration of sheet flow is closely related to the transition in cross slope, longitudinal slope, rainfall intensity, and the width of the road. The characteristics of the sheet flow on superelevation transition areas are analyzed to find the optimal longitudinal slope. It is found that the longitudinal slope in the range of 0.3%-0.4% is the optimal slope at superelevation transition areas which minimizes the depth of stormwater runoff. An example application of the model on a rural highway in Texas is also presented. It is found that a significant amount of stormwater may exist on traffic lanes at the superelevation transitions tested. The predicted ponding depth exceeds the minimum value for potential hydroplaning, and the pattern of the flow concentration may cause differential drag forces on traffic vehicles. / text

It has been shown by Neuman [1990], Di Federico and Neuman [1997, 1998a,b] and Di Federico et al. [1999] that observed multiscale behaviors of subsurface fluid flow and transport variables can be explained within the context of a unified stochastic framework, which views hydraulic conductivity as a random fractal characterized by a power variogram. Any such random fractal field is statistically nonhomogeneous but possesses homogeneous spatial increments. When the field is statistically isotropic, it is associated with a power variogram γ(s) = Cs²ᴴ where C is a constant, s is separation distance, and If is a Hurst coefficient (0 < H< 1). If the field is Gaussian it constitutes fractional Brownian motion (fBm). The authors have shown that the power variogram of a statistically isotropic or anisotropic fractal field can be constructed as a weighted integral from zero to infinity of exponential or Gaussian vario grams of overlapping, homogeneous random fields (modes) having mutually uncorrelated increments and variance proportional to a power 2H of the integral (spatial correlation) scale. Low- and high-frequency cutoffs are related to length scales of the sampling window (domain) and data support (sample volume), respectively. Intermediate cutoffs account for lacunarity due to gaps in the multiscale hierarchy, created by a hiatus of modes associated with discrete ranges of scales. In this dissertation, I investigate the effects of domain and support scales on the multiscale properties of random fractal fields characterized by a power variogram using real and synthetic data. Neuman [1994] and Di Federico and Neuman [1997] have concluded empirically, on the basis of hydraulic conductivity data from many sites, that a finite window of length-scale L filters out (truncates) all modes having integral scales λ larger than λ = μL where μ ≃ 1/3. I confii in their finding computationally by generating truncated fBm realizations on a large grid, using various initial values of μ, and demonstrating that μ ≃ 1/3 for windows smaller than the original grid. My synthetic experiments also show that generating an fl3m realization on a finite grid using a truncated power variogram yields sample variograms that are more consistent with theory than those obtained when the realization is generated using a power variogram. Interpreting sample data from such a realization using wavelet analysis yields more reliable estimates of the Hurst coefficient than those obtained when one employs variogram analysis. Di Federico et al. [1997] developed expressions for the equivalent hydraulic conductivity of a box-shaped support volume, embedded in a log-hydraulic conductivity field characterized by a power variogram, under the action of a mean uniform hydraulic gradient. I demonstrate that their expression and empirically derived value of μ ≃ 1/3 are consistent with a pronounced permeability scale effect observed in unsaturated fractured tuff at the Apache Leap Research Site (ALRS) near Superior, Arizona. I then investigate the compatibility of single-hole air permeability data, obtained at the ALRS on a nominal support scale of about 1 m, with various scaling models including fBm, fGn (fractional Gaussian noise), fLm (fractional Lévy motion), bfLm (bounded fractional Lévy motion) and UM (Universal Multifractals). I find that the data have a Lévy-like distribution at small lags but become Gaussian as the lag increases (corresponding to bfLm). Though this implies multiple scaling, it is not consistent with the UM model, which considers a unique distribution. If one nevertheless applies a UM model to the data, one obtains a very small codimension which suggests that multiple scaling is of minor consequence (applying the UM model to permeability rather than log-permeability data yields a larger codimension but is otherwise not consistent with these data). Variogram and resealed range analyses of the log-permeability data yield comparable estimates of the Hurst coefficient. Resealed range analysis shows that the data are not compatible with an fGn model. I conclude that the data are represented most closely by a truncated fBm model.

A new Farm Package (FMP) was developed for using the U.S. Geological Survey's groundwater modeling program, MODFLOW-2000 (MF2K), to estimate irrigation water allocations to irrigation settings. The FMP dynamically integrates irrigation water demand, surface-water & groundwater supply, and return flow from excess irrigation. Routed surface-water delivery is optional, and can be simulated by coupling FMP with the Streamflow Routing Package (SFR1). MF2K with FMP and SFR1 allows estimating the allocation of surface-water and groundwater to farms for the following applications: (1) historic and future simulations, (2) water rights issues and operational decisions, (3) non-drought and drought situations. Irrigation demand, supply, and return flow are partly subject to head-dependent sinks and sources such as transpiration uptake from groundwater (formulated by FMP) and leakage between the conveyance system and the aquifer (formulated by SFR1). A steady state transpiration uptake, varying with changing water level, is stepwise linearly approximated by FMP. This was validated by ensembles of variably saturated soil column models using HYDRUS2D for different soil types, values of potential transpiration, and root zone depths. A restriction of transpiration uptake is proportional to a reduction of the active root zone. It is approximated in FMP by an analytical solution, which determines inactive ranges of the root zone with pressure heads typical for conditions of anoxia or wilting. At steady state, the transpiration uptake equaled the flux across the water table (plus the irrigation flux, if applied). Therefore, changes in soil water storage are assumed negligible. Based on this assumption, the irrigation flux required is determined in FMP by subtracting transpiratory components from natural sources (groundwater, precipitation) from a maximum transpiration uptake. This transpiratory irrigation requirement is calculated for each finite difference cell, and increased sufficiently to compensate for evaporative losses and for inefficient use. Accumulating the resulting cell delivery requirement over all cells in a farm yields the total farm delivery requirement, which is to be satisfied with surface- or groundwater. Five economic and non-economic drought response policies can be applied, if the potential supply of surface- and groundwater is insufficient to meet the crop demand. The code was verified by a hypothetical example problem run in 55 scenarios (5 drought policy scenarios x 11 parameter-group scenarios). Among all sources and sinks in a cumulative volumetric budget, 'farm well discharge,' and particularly 'farm net recharge,' were most sensitive to changes in drought policies or changes of parameters.

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Solution algorithms are developed for the nonlinear finite element equations, resulting from the discretization of governing incremental equations of equilibrium. The equations of equilibrium in the total Lagrangian formation are derived, based on continuum mechanics principles and by invoking the principle of virtual work. A general purpose computer program, modular in structure, and interactive in nature, is developed, based on the theoretical formulation presented. A brief review of some of the existing solution algorithms for nonlinear structural analysis using the finite element formulation is presented. Arc-length methods, which facilitate the tracing of the load-configuration path beyond limit points, are systematically examined. Specific emphasis is focussed on obtaining the complete structural response in an efficient and reliable way. The arc-length methods treat the load parameter as a variable in addition to the unknown displacements. A constraint equation forms the supplemental equation for the determination of the additional variable. Attention is directed to the constraint equation, comprising the displacements and loads. Realising that the loads and displacements have different magnitudes, several authors had addressed the issue of including a scaling parameter, however, inadequately. In this research, several well formulated automatic means of computing the scaling parameter are suggested. A constant scaling parameter, which remains unchanged throughout all the load steps, and a variable scaling parameter, which is recalculated at each load step are introduced. The latter parameter is related to the current stiffness parameter. In the present investigation, the spherical constraint, the normal plane constraint and the updated normal plane constraint equations are examined with the proposed scaling parameters. An automatic load step calculation, based on the arc-length is suggested. The load step is rendered adaptive by including the load term with the scaling parameter in the constraint equation. Examples from large displacement problems, that exhibit severe geometric nonlinearities, are included to evaluate the proposed algorithms and substantiate their efficacies in tracing the complete load-configuration path. The relative performances of the proposed algorithms reveal their cost-effectiveness.

The purpose of this research was to develop a simplified analytical procedure for determining the optimal timing for upgrading low-volume roads in developing countries. Most roadway upgradings from gravel to surface treated and to asphaltic concrete are carried out when total transport cost on a road becomes high as a result of high traffic and the consequent rapid deterioration of the roadway. Adequate timing of upgrading strategies ensures effective use of resources and lower total transport cost. This study examined existing systems, models, and approaches for estimating total transport cost components. An analytical procedure was then developed using a decision-tree concept to delineate all possible upgrading strategies within a plan period. The decision-tree concept depicts all the possible upgrading strategies within a plan period with decisions on roadway upgrading made at certain decision intervals. The total transport cost of the upgrading strategies is evaluated to establish the optimal strategies and traffic warrants for improving a roadway surface. A computer program PVMNT was written to facilitate the computation of the total transport cost. A case study was presented to demonstrate the application of the analytical procedure. The case study revealed interesting results on the changes of optimal upgrading strategies with changes in base traffic volume and growth rate. However, general conclusions could not be drawn based on the results of the case study. These results, as well as the analytical procedure, should be of interest to engineers responsible for providing low-volume roads in developing countries.

The problems of combining ideas of phase shifting interferometry (PSI) and synthetic-wavelength techniques to extend the phase measurement range of conventional single-wavelength PSI are investigated. This combination of PSI and synthetic-wavelengths gives multiple-wavelength phase-shifting interferometry the advantages of: (1) larger phase measurement range and (2) higher accuracy of phase measurement. Advantages, error sources, and limitations of single-wavelength PSI are discussed. Some practical methods to calibrate the piezoelectric transducer (PZT), used to phase shift the reference beam, are presented with experimental results. Two methods of two-wavelength PSI are used to solve the 2π ambiguity problem of single-wavelength PSI. For the first method, two sets of phase data (with 2π ambiguities) for shorter wavelengths are calculated and stored in the computer which calculates the new phase data for the equivalent-wavelength λ(eq). The "error magnification effect," which reduces the measurement precision of the first method, is then investigated. The second, more accurate method, uses the results of the first method as a reference to correct the 2π ambiguities in the single-wavelength phase data. Experimental results are included to confirm theoretical predictions. The enhancement of two-wavelength PSI is investigated, and requires the phase data of a third wavelength. Experiments are performed to verify the capability of multiple-wavelength PSI. For the wavefront being measured, the difference of the optical-path-difference (OPD) between adjacent pixels is as large as 3.3 waves. After temporal averaging of five sets of data, the repeatability of the measurement is better than 2.5 nm (0.0025%) rms (λ = 632.8 nm). This work concludes with recommendations for future work that should make the MWLPSI a more practical technique for the testing of steep aspheric surfaces.

Determination of the stresses and displacements which occur in response to random excitations cannot be accomplished by traditional deterministic analysis methods. As the specification of the excitation and the response of the structure become more complex, solutions by direct, closed-form methods require extensive computations. Two methods are presented which can be used in the analysis of structures which are subjected to random excitations. The Power Spectrum Method is a procedure which determines the random vibration response of the structure based upon a frequency response analysis of a structural model. The Response Spectrum Method is a method which is based upon specified forces or displacements as a function of time. A derivation of each of the methods is presented and followed by comparisons of the results which were obtained for single and multiple-degree-of-freedom systems. Assumptions and limitations of the methods are discussed as well as their accuracy over ranges of frequency, damping and loading specification. As a direct application and comparison of the two methods, an analysis of the support system for the primary mirror of the Space Infrared Telescope Facility (SIRTF) has been performed. In addition, a method for the evaluation of the critical damping in a single-degree-of-freedom structure is demonstrated.