Stochastic finite element analysis applied to soil media with uncertain material properties

• Main Author: Hoddinott, Terry Keith
• Format: Thesis
• Language: English
• Published: Memorial University of Newfoundland 1986
• Subjects: Arctic
• Online Access: https://research.library.mun.ca/5293/; https://research.library.mun.ca/5293/1/Hoddinott_TerryKeith.pdf; https://research.library.mun.ca/5293/2/Hoddinott_TerryKeith.pdf

This thesis examines how material uncertainty influences the short term settlements and stresses of foundations. Expressing the uncertainty of material strength in terms of elastic modulus, the foundation and layered-soil-medium interaction is analyzed. Two soil models are examined: (i) an elastic, single phase, layered soil medium with undrained material properties and (ii) a piecewise linear elastic, single phase, layered soil medium approximating the nonlinear behaviour of soil. For the piecewise linear approximation, two shear-strain-dependent soil modulus relationships are included to differentiate between clays and sands. -- Utilizing a two-dimensional plane strain triangular element, a stochastic finite element solution is formulated. The procedure incorporates the elastic modulus variation by considering a linear two term Taylor series expansion of the equilibrium equations. -- To limit the extent of errors induced by the omission of second order terms, the coefficient of variation (C.O.V.) for elastic modulus is assumed to be less than 30%. To model the degree of interdependence between finite elements, a decaying exponential correlation distance function in terms of the scalar distance between elements is used. Based on the definition of covariance combined with the linear two-term expansion for elastic modulus, the covariance of nodal displacements and the variance of element stresses are derived. -- To model the stochastic finite element procedure, a FORTRAN computer code is developed for both linear and piecewise linear material elasticity. The displacements and stresses obtained from the plane strain analysis are considered as the mean values. Using the covariance of displacements and variance of stresses computed for selected nodes and elements, the resulting coefficients of variation are determined for actual displacements, relative displacements and stresses. A parametric analysis is carried out to establish the sensitivity of the stochastic finite element procedure to correlation distance, modulus C.O.V. and soil models. This type of analysis is defined as an upper bound due to its maximizing the material uncertainty. Also the random variation of material properties and its influence on displacements and stresses are examined by including a procedure to randomly vary the modulus C.O.V. from zero to maximum. -- Two ocean structure cases are examined to verify the stochastic finite element formulation, viz., (i) the Ekofisk Tank and (ii) the Mobile Arctic Caisson (M.A.C.). The Ekofisk Tank is examined for gravitational loads and guasistatic wave loads representative of an actual storm. Gravitational forces and design ice forces are applied to the M.A.C. structure. In both cases, numerical results compare very well with those published in literature for the prototype structures, differing by less than 10% for most conditions. -- The main conclusions from the parametric study of the stochastic finite element procedure for soil-structure interaction are: -- (i) The effect of elastic modulus uncertainty is more pronounced in the uncertainty of stresses than the displacements. -- (ii) As the correlation distance factor becomes large (greater than 10), the variation of displacements or stresses attributed to local material uncertainty is smaller. Under this condition the soil continuum is highly correlated. -- (iii) The proportion of uncertainty in results are insensitive to the varying loading conditions. -- (iv) The piecewise linear soil model provides closer agreement with the published data for prototype structures and yields lower coefficients of variation for displacements and stresses than the elastic model.