etd@IISc Collection:http://hdl.handle.net/2005/332016-05-06T06:00:55Z2016-05-06T06:00:55ZWater Balance Studies In A Small Experimental Forested Watershed, South IndiaMurari, Raja Raja Varmahttp://hdl.handle.net/2005/11122011-04-01T20:30:43Z2011-03-31T18:30:00ZTitle: Water Balance Studies In A Small Experimental Forested Watershed, South India
Authors: Murari, Raja Raja Varma
Abstract: Forested watersheds play a dominant role in the global hydrological cycle. Very few experimental observatories especially in tropical forested regions of India have been undertaken. This study has been initiated for this reason and to gain insights into functioning of the hydrological system in such climatic conditions. This study involves experimental setup of a watershed, it’s monitoring till date, modelling of the hydrological processes observed and the challenges in modelling components of the water balance in this watershed.
A Small Experimental Watershed of 4.3 Km2 was set up at Mule Hole, in South India along the Kerala-Karnataka State borders, and is situated inside the Bandipur National park. After an overview of watershed studies, review of literature related to forest watershed studies and processes in the first two chapters, Chapter 3 introduces the study area, Mule Hole Experimental Watershed and explains the methodology used to study this watershed. Model SWAT was used initially to simulate the water balance components. A brief description of the model, methodology adopted and discussion on the results obtained is presented in Chapter 4. The watershed initially modelled as an ungauged watershed using the default parameters in the model, simulated very high groundwater contribution to the runoff. The calibrated model although performed favourably for annual average values and monthly calibration, the daily calibration was unsatisfactory. An auxiliary study on quantification of actual and potential evapotranspiration (ET0) has been carried out in Chapter 5 . Ten methods including Penman-Montieth were compared and evaluated for efficacy of the methods. All methods except for Hargreaves method showed agreement with the Penman-Montieth for annual average values. Priestly-Taylor method was found be the best estimator in comparison with Penman-Montieth method, when used to estimate AET. Adjusted Hargreaves and FAO Blaney -Criddle method were found to be very useful when few or limited climatic data were available for estimation of Potential evapotranspiration. A multidisciplinary approach of estimating recharge consisting of chloride mass balance technique coupled with study of water table fluctuations and groundwater flow analytical modelling has been attempted in Chapter 6. Direct and localized recharge was estimated at 45 mm/yr and indirect recharge 30 mm/yr for the monitored years in the watershed. The low values of recharge rates implied an unexpected very high evapotranspiration rate. It may be inferred that in the absence of groundwater flow to the stream, the recharge joins groundwater flow as outflow of the hydrologic system. An integrated lumped model incorporating the regolith zone and the capability of the tree roots to access this store is presented in Chapter 7. The model was able to simulate the pattern of lag-time between water table rise was observed in shallow piezometers in comparison with hillslope piezometers. The patterns of water table variation among the different hillslope piezometers suggest that they are linked with local processes and not by a regional aquifer dynamics. This study shows that water uptake, combined with the spatial variability of regolith depth, can account for the variable lag time between drainage events and groundwater rise observed for the different piezometers. Chapter 8 discusses the results, conclusions derived from this study and possibility of further scope of studies.2011-03-31T18:30:00ZVibration Analysis Of Structures Built Up Of Randomly Inhomogeneous Curved And Straight Beams Using Stochastic Dynamic Stiffness Matrix MethodGupta, Sayanhttp://hdl.handle.net/2005/2242010-04-28T20:35:47Z2006-07-19T05:49:48ZTitle: Vibration Analysis Of Structures Built Up Of Randomly Inhomogeneous Curved And Straight Beams Using Stochastic Dynamic Stiffness Matrix Method
Authors: Gupta, Sayan
Abstract: Uncertainties in load and system properties play a significant role in reliability analysis of vibrating structural systems. The subject of random vibrations has evolved over the last few decades to deal with uncertainties in external loads. A well developed body of literature now exists which documents the status of this subject. Studies on the influence of system property uncertainties on reliability of vibrating structures is, however, of more recent origin. Currently, the problem of dynamic response characterization of systems with parameter uncertainties has emerged as a subject of intensive research. The motivation for this research activity arises from the need for a more accurate assessment of the safety of important and high cost structures like nuclear plant installations, satellites and long span bridges. The importance of the problem also lies in understanding phenomena like mode localization in nearly periodic structures and deviant system behaviour at high frequencies. It is now well established that these phenomena are strongly influenced by spatial imperfections in the vibrating systems. Design codes, as of now, are unable to systematically address the influence of scatter and uncertainties. Therefore, there is a need to develop robust design algorithms based on the probabilistic description of the uncertainties, leading to safer, better and less over-killed designs.
Analysis of structures with parameter uncertainties is wrought with difficulties, which primarily arise because the response variables are nonlinearly related to the stochastic system parameters; this being true even when structures are idealized to display linear material and deformation characteristics. The problem is further compounded when nonlinear structural behaviour is included in the analysis. The analysis of systems with parameter uncertainties involves modeling of random fields for the system parameters, discretization of these random fields, solutions of stochastic differential and algebraic eigenvalue problems, inversion of random matrices and differential operators, and the characterization of random matrix products. It should be noted that the mathematical nature of many of these problems is substantially different from those which are encountered in the traditional random vibration analysis. The basic problem lies in obtaining the solution of partial differential equations with random coefficients which fluctuate in space. This has necessitated the development of methods and tools to deal with these newer class of problems. An example of this development is the generalization of the finite element methods of structural analysis to encompass problems of stochastic material and geometric characteristics.
The present thesis contributes to the development of methods and tools to deal with structural uncertainties in the analysis of vibrating structures. This study is a part of an ongoing research program in the Department, which is aimed at gaining insights into the behaviour of randomly parametered dynamical systems and to evolve computational methods to assess the reliability of large scale engineering structures. Recent studies conducted in the department in this direction, have resulted in the formulation of the stochastic dynamic stiffness matrix for straight Euler-Bernoulli beam elements and these results have been used to investigate the transient and the harmonic steady state response of simple built-up structures. In the present study, these earlier formulations are extended to derive the stochastic dynamic stiffness matrix for a more general beam element, namely, the curved Timoshenko beam element. Furthermore, the method has also been extended to study the mean and variance of the stationary response of built-up structures when excited by stationary stochastic forces. This thesis is organized into five chapters and four appendices.
The first chapter mainly contains a review of the developments in stochastic finite element method (SFEM). Also presented is a brief overview of the dynamics of curved beams and the essence of the dynamic stiffness matrix method. This discussion also covers issues pertaining to modeling rotary inertia and shear deformations in the study of curved beam dynamics. In the context of SFEM, suitability of different methods for modeling system uncertainties, depending on the type of problem, is discussed. The relative merits of several schemes of discretizing random fields, namely, local averaging, series expansions using orthogonal functions, weighted integral approach and the use of system Green functions, are highlighted. Many of the discretization schemes reported in the literature have been developed in the context of static problems. The advantages of using the dynamic stiffness matrix approach in conjunction with discretization schemes based on frequency dependent shape functions, are discussed. The review identifies the dynamic analysis of structures built-up of randomly parametered curved beams, using dynamic stiffness matrix method, as a problem requiring further research. The review also highlights the need for studies on the treatment of non-Gaussian nature of system parameters within the framework of stochastic finite element analysis and simulation
methods.
The problem of deterministic analysis of curved beam elements is considered first. Chapter 2 reports on the development of the dynamic stiffness matrix for a curved Timoshenko beam element. It is shown that when the beam is uniformly param-etered, the governing field equations can be solved in a closed form. These closed form solutions serve as the basis for the formulation of damping and frequency dependent shape functions which are subsequently employed in the thesis to develop the dynamic stiffness matrix of stochastically inhomogeneous, curved beams. On the other hand, when the beam properties vary spatially, the governing equations have spatially varying coefficients which discount the possibility of closed form solutions. A numerical scheme to deal with this problem is proposed. This consists of converting the governing set of boundary value problems into a larger class of equivalent initial value problems. This set of Initial value problems can be solved using numerical schemes to arrive at the element dynamic stiffness matrix. This algorithm forms the basis for Monte Carlo simulation studies on stochastic beams reported later in this thesis. Numerical results illustrating the formulations developed in this chapter are also presented. A satisfactory agreement of these results has been demonstrated with the corresponding results obtained from independent finite element code using normal mode expansions.
The formulation of the dynamic stiffness matrix for a curved, randomly in-homogeneous, Timoshenko beam element is considered in Chapter 3. The displacement fields are discretized using the frequency dependent shape functions derived in the previous chapter. These shape functions are defined with respect to a damped, uniformly
parametered beam element and hence are deterministic in nature. Lagrange's equations
are used to derive the 6x6 stochastic dynamic stiffness matrix of the beam element. In
this formulation, the system property random fields are implicitly discretized as a set of
damping and frequency dependent Weighted integrals. The results for a straight Timo-
shenko beam are obtained as a special case. Numerical examples on structures made up
of single curved/straight beam elements are presented. These examples also illustrate the characterization of the steady state response when excitations are modeled as stationary random processes. Issues related to ton-Gaussian features of the system in-homogeneities are also discussed. The analytical results are shown to agree satisfactorily with corresponding results from Monte Carlo simulations using 500 samples.
The dynamics of structures built-up of straight and curved random Tim-oshenko beams is studied in Chapter 4. First, the global stochastic dynamic stiffness matrix is assembled. Subsequently, it is inverted for calculating the mean and variance, of the steady state stochastic response of the structure when subjected to stationary random excitations. Neumann's expansion method is adopted for the inversion of the stochastic dynamic stiffness matrix. Questions on the treatment of the beam characteristics as non-Gaussian random fields, are addressed. It is shown that the implementation of Neumann's expansion method and Monte-Carlo simulation method place distinctive demands on strategy of modeling system parameters. The Neumann's expansion method, on one hand, requires the knowledge of higher order spectra of beam properties so that the non-Gaussian features of beam parameters are reflected in the analysis. On the other hand, simulation based methods require the knowledge of the range of the stochastic variations and details of the probability density functions. The expediency of implementing Gaussian closure approximation in evaluating contributions from higher order terms in the Neumann expansion is discussed. Illustrative numerical examples comparing analytical and Monte-Carlo simulations are presented and the analytical solutions are found to agree favourably with the simulation results. This agreement lends credence to the various approximations involved in discretizing the random fields and inverting the global dynamic stiffness matrix. A few pointers as to how the methods developed in the thesis can be used in assessing the reliability of these structures are also given.
A brief summary of contributions made in the thesis together with a few suggestions for further research are presented in Chapter 5.
Appendix A describes the models of non-Gaussian random fields employed in the numerical examples considered in this thesis. Detailed expressions for the elements of the covariance matrix of the weighted integrals for the numerical example considered in Chapter 5, are presented in Appendix B; A copy of the paper, which has been accepted for publication in the proceedings of IUTAM symposium on 'Nonlinearity and Stochasticity in Structural Mechanics' has been included as Appendix C.2006-07-19T05:49:48ZThe Variable Source Area Conceptul Model For Western Ghats, Karnataka, IndiaSawant, Priyadarshi Hhttp://hdl.handle.net/2005/21652013-07-29T09:21:15Z2013-07-28T18:30:00ZTitle: The Variable Source Area Conceptul Model For Western Ghats, Karnataka, India
Authors: Sawant, Priyadarshi H2013-07-28T18:30:00ZUplift Capacity Of Horizontal Strip And Circular Anchors In Homogeneous And Layered SoilsManjunatha, Khttp://hdl.handle.net/2005/18062012-11-21T05:06:08Z2012-11-20T18:30:00ZTitle: Uplift Capacity Of Horizontal Strip And Circular Anchors In Homogeneous And Layered Soils
Authors: Manjunatha, K2012-11-20T18:30:00Z