etd@IISc Collection:
http://hdl.handle.net/2005/33
2017-12-08T02:32:15ZWater Balance Studies In A Small Experimental Forested Watershed, South India
http://hdl.handle.net/2005/1112
Title: 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 Method
http://hdl.handle.net/2005/224
Title: 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, India
http://hdl.handle.net/2005/2165
Title: The Variable Source Area Conceptul Model For Western Ghats, Karnataka, India
Authors: Sawant, Priyadarshi H2013-07-28T18:30:00ZUpper Bound Finite Element Limit Analysis for Problems of Reinforced Earth, Unsupported Tunnels and a Group of Anchors
http://hdl.handle.net/2005/2811
Title: Upper Bound Finite Element Limit Analysis for Problems of Reinforced Earth, Unsupported Tunnels and a Group of Anchors
Authors: Sahoo, Jagdish Prasad
Abstract: This thesis presents the implementation of the upper bound limit analysis in combination with finite elements and linear optimization for solving different stability problems in geomechanics under plane strain conditions. Although the nonlinear optimization techniques are becoming quite popular, the linear optimization has been adopted due to its simplicity in implementation and ease in attaining the convergence while performing the analysis. The objectives of the present research work are (i) to reduce the computational effort while using an upper bound finite element limit analysis with linear programming in dealing with geotechnical stability problems, and (ii) to obtain solutions for a few important geotechnical stability problems associated with reinforced earth, unsupported tunnels and a group of anchors. It is also intended to examine the developments of the failure patterns in all the cases. For carrying out the analysis for different stability problems, three noded triangular elements have been used throughout the thesis. The nodal velocities are treated as basic unknown variables and the velocity discontinuities are employed along the interfaces of all the elements. The soil mass is assumed to obey the Mohr-Coulomb’s failure criterion and an associated flow rule. The Mohr-Coulomb yield surface is linearized by means of an exterior regular polygon circumscribing the actual yield circle so that the finite element formulation leads to a linear programming problem.
A simple technique has been proposed for reducing the computational effort while solving any geotechnical stability problem by using the upper bound finite element limit analysis and linear optimization. In the proposed method, the problem domain has been discretized into a number of different regions in which a particular order (number of sides) of the polygon has been specified to linearize the Mohr-Coulomb yield criterion. A greater order of the polygon needs to be chosen only in that part of the domain wherein the rate of the plastic strains becomes higher. The computational effort required to solve the problem with this implementation reduces considerably. By using the proposed method, the bearing capacity has been computed for smooth as well as rough strip footings and the results obtained are found to be quite satisfactory.
The ultimate bearing capacity of a rigid strip footing placed over granular, cohesive-frictional and purely cohesive soils, reinforced with single and a group of two horizontal layers of reinforcements has been determined. The necessary formulation has been introduced to incorporate the inclusion of reinforcement in the analysis. The efficiency factors, and , to be multiplied with Nc and Nγ for finding the bearing capacity of reinforced foundations, have been established. The results have been obtained (i) for different values of soil friction angles in case of granular and cohesive-frictional soils, and (ii) for different rates at which the cohesion increases with depth for purely cohesive soil under undrained condition. The optimum positions of the reinforcements' layers corresponding to which and becomes maximum, have been established. The effect of the length of the reinforcements on the results has also been analyzed. As compared to cohesive soil, the granular soils, especially with greater values of frictional angle, cause much more predominant increase in the bearing capacity.
The stability of a long open vertical trench laid in a fully cohesive and cohesive-frictional soil has been determined with an inclusion of single and a group of two layers of horizontal reinforcements. For different positions of the reinforcement layers, the efficiency factor (ηs), has been determined for several combinations of H/B, m and where H and B refer to height and width of the trench, respectively, and m accounts for the rate at which the cohesion increases linearly with depth for a fully cohesive soil with = 0. The effect of height to width of the long vertical trench on the stability number has been examined for both unreinforced and reinforced soils. The optimal positions of the reinforcements layers, corresponding to which becomes maximum, have been established. The required length of reinforcements to achieve maximum efficiency factor corresponding to optimum depth of reinforcement has also been determined. The magnitude of the maximum efficiency factor increases continuously with an increase in both m and . The effect of pseudo-static horizontal earthquake body forces on the stability of a long unsupported circular tunnel (opening) formed in a cohesive frictional soil has been determined. The stability numbers have been obtained for various values of H/D (H = tunnel cover, D = diameter of the tunnel), internal friction angle of soil, and the horizontal earthquake acceleration coefficient The computations revealed that the values of the stability numbers (i) decreases quite significantly with an increase in , and (ii) become continuously higher for greater values of H/D and . The failure patterns have also been drawn for different combinations of H/D, and . The geometry of the failure zone around the periphery of the tunnel becomes always asymmetrical with an inclusion of horizontal seismic body forces.
The interference effect on the stability of two closely spaced parallel (twin) long unsupported circular tunnels formed in fully cohesive and cohesive-frictional soils has been evaluated. The variation of the stability number with S/D has been established for different combinations of H/D, m and ; where D refers to the diameter of each tunnel, S is the clear spacing between the tunnels, and is the internal friction angle of soil and m accounts for the rate at which the cohesion increases linearly with depth for a soil with = 0. On account of the interference of two tunnels, the stability number reduces continuously with a decrease in the spacing between the tunnels. The minimum spacing between the two tunnels required to eliminate the interference effect increases with (i) an increase in H/D and (ii) a decrease in the values of both m and . The failure patterns have also been generated for a few cases with different values of S/D. The size of the failure zone is found to become smaller for greater values of m and .
The horizontal pullout capacity of a group of two vertical strip anchors embedded, along the same vertical plane in sand, at shallow depths has been determined. At collapse, it is assumed that the anchor plates are subjected to the same uniform horizontal velocity without any bending or tilt. The pullout resistance increases invariably with increases in the values of embedment ratio, friction angle of the sand mass and anchor-soil interface friction angle. The effect of spacing (S) between the anchors on their group collapse load is examined in detail. For a given embedment ratio, the total group failure load becomes maximum corresponding to a certain optimal spacing (Sopt). The values of Sopt increases with an increase in the value of , but the changes in the value of H/B and do not have any significant effect on Sopt.
The vertical uplift capacity of a group of two horizontal strip plate anchors with the common vertical axis buried in purely cohesive as well as in cohesive frictional soil has been computed. The variation of the uplift factors Fc, Fq and F , due to the contributions of soil cohesion, surcharge pressure and unit weight, respectively, has been evaluated for different combinations of S/B and H/B. As compared to a single isolated anchor, the group of two anchors generates significantly greater magnitude of Fc. On the other hand, the factors Fq and F , for a group of two anchors are found to become almost equal to that of a single isolated anchor as long as the levels of the lower plate in the group and the single isolated anchor are kept the same. For the group of two horizontal strip plate anchors in purely cohesive soil, an increase of cohesion of soil mass with depth and the effect of self weight of the soil have been incorporated. The uplift factor Fcy both due to cohesion and unit weight of the soil has also been computed for the anchors embedded in clay under undrained condition. For given embedment ratios, the factor Fcy increases linearly with an increase in the normalized unit weight of soil mass upto a certain value before attaining a certain maximum magnitude.
The computational results obtained for different research problems would be useful for design.2017-11-26T18:30:00Z