Please use this identifier to cite or link to this item: http://localhost:8081/xmlui/handle/123456789/14666
Authors: Singh, Rakesh Pratap
Keywords: Small Strain;Consolidation Theory;Self Weight of Soil;Variation of Void Ratio
Issue Date: Jun-2015
Publisher: Dept. of Civil Engineering iit Roorkee
Abstract: Small strain one dimensional consolidation theory, based on many simplified assumptions is applicable effectively to thin layers only. Theory of large or finite strain one dimensional consolidation takes into account the self weight of soil, variation of void ratio, compressibility and hydraulic conductivity and offers a generalized approach for consolidation of a homogeneous soil type. These attributes make the theory capable of predicting the settlements of soft soils such as the deposits of dredged materials/ mine tailings under self / overburden loads at their disposal sites and also the consolidation settlement of thicker layers of usual soils. This work presents a novel explicit time marching numerical model based on finite volume method with quadratic three point Lagrangian interpolation function. Model takes into account the geometric non linearity of the governing equation and material nonlinearity of the constitutive equations. Unlike the other numerical models, such as finite element method and finite difference method, this model accounts for the continuity of fluid flow (mass conservation) automatically due to conservation specific formulation of the model at discrete control volume level. The conservativeness and boundedness of the numerical scheme makes the model solutions feasible and stable. The accuracy of the model is maintainable to the level of third order. The time step restrictions are not very tight and depend on consolidation induced velocity and the size of the discrete control volume. The boundary conditions of consolidation for drained and undrained boundaries are presented in terms of void ratio. The initial equilibrium distribution of void ratio due to self load and a pre-existing overburden pressure are determined with the help of quadratic interpolation on data of compressibility constitutive relation. Comparison of the model solutions with analytical and other numerical models affirms the accuracy and efficiency of the model. A parametric study on consolidation behaviour of soft soil having initial void ratio ranging from 3.2 to 2.4, shows almost linear relation of settlement and square root of time up to 80% average degree of consolidation. Model has further been tested on experimental results of consolidation of thicker specimens of 40 mm and 70 mm thickness and has been found to work well. Solute transport through porous media is an important field of research in the context of geoenvironmental issues. The concerned one-dimensional governing equation is also a differential equation of conservation law. An explicit time marching finite volume numerical model for one-dimensional solute transport in rigid porous media is developed on ii the pattern of large strain consolidation. The novelty of the model lies in treating the solute concentrations in liquid and solid phases of the media as combined concentration for developing the numerical scheme and segregating it into solid and liquid concentrations during post processing of the solution. The methodology adopted keeps the solute transport equation linear up to solutions and opens the model at the stage of post processing to accommodate variety of sorption isotherms such as linear-equilibrium, nonlinearequilibrium and nonlinear-nonequilibrium. The model is also set to accommodate the variation of hydrodynamic dispersion with void ratio and decay reaction of first order. The solute concentration boundary conditions taken up are; constant concentration for a boundary with unlimited reservoir, zero concentration gradient for a non-transmitting boundary and constant flux or reservoir boundary condition for a boundary with small well mixed reservoir. The interpolation scheme followed is the quadratic upwinding in general but at critical situations of high gradient or discontinuity the model adopts the exponential upwinding scheme with normalized variables. Model verification and checks through comparative studies with other numerical models show the efficiency of the model and it requires lesser elements to provide an acceptable solution. The model has further been extended to one-dimensional advection with two-dimensional hydrodynamic dispersion. Quadratic interpolation functions for two-dimensional space are derived. The departure from one dimensional interpolation function is found to be only by a small curvature term which can easily be accommodated with exponential upwinding scheme also. Two-dimensional model maintains the accuracy level of third order as well. Comparison of results with exhibits that less number of elements are required in the suggested model as compared to existing linear interpolation models. Consolidation induced solute transport is important in assessing the spread of contaminants in soft deposits of dredged materials and mine tailings as well as in the compacted clay liners of waste disposal sites. The penultimate chapter of the thesis describes the synthesis of computational modules of large strain consolidation and solute transport through rigid porous media to give a semi-coupled numerical model for consolidation induced solute transport through deforming porous media due to mechanical consolidation. The coupling of two modules requires additional provision of computation of Darcy velocity due to existing hydraulic gradient and the consolidation induced Darcy velocity in consolidation module. Thus computed Darcy velocity is used for computing the solute transport. Consolidation induced velocity is computed on kinematical considerations iii on the basis of reduction in void ratio at each time step as calculated during the consolidation. It is obvious that the kinematical provision for consolidation induced advection provides better mass conservation and continuity of fluid flow compared to computations based on dynamic equation of excess pore pressure gradient. The model performance has been tested for four types of problems varying mainly in sorption isotherm. The first one considers the problem of a hypothetical landfill clay liner with linear sorption isotherm, second is about an experimental observation on kaolinite slurry with nonlinearnonequilibrium sorption isotherm, the third one is regarding organoclay modified bentonitesoil mix liner material and shows the influence of consolidation on design of such a clay liner with nonlinear equilibrium sorption. Fourth problem is related to two-dimensional solute transport in dredged material deposit with linear equilibrium sorption. The comparison of results with other models affirms the efficiency of the present model. It may also be inferred that the consolidation induced solute transport is worth considering while designing a clay barrier systems for waste disposal sites. A limited parametric study on twodimensional solute transport for only two parameters, the longitudinal/ lateral dispersivities and effective diffusion coefficient, reveals that the dispersivities have almost negligible influence on two-dimensional spread of contaminants, but the influence of effective diffusion is substantial. Finally, it is concluded that the problems of momentum and mass transfer with deterministic approach can be dealt effectively with finite volume formulation with an advantage of automatic mass conservation and complexity level is less than the finite and boundary element based numerical models.
Research Supervisor/ Guide: Singh, Mahendra
Ojha, C. S. P.
metadata.dc.type: Thesis
Appears in Collections:DOCTORAL THESES (Civil Engg)

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