Mathematical model of a single pile.
Creators: name: Sage, Roy.
Publisher: name: Université d'Ottawa / University of Ottawa
Year: 1971
Subjects: subject: Engineering, Civil.

description: The introduction of electronic digital calculating machines in the last decade or two has led to the development of mathematical models of pile foundations. These models are able to overcome many hitherto intractable analytical problems in pile-soil interaction studies, through the use of numerical methods possible only with the computer. These models fall into two classes; those dealing with an elastic system of both pile and soil, with modifications to allow some non-linear pile-soil interaction, and those using only empirical measured values of soil response, thus permitting full non-linear treatment. The first class of models allows the action of the entire soil-pile system to be taken into account. The second, though better coping with the true non-linear behaviour of the pile-soil system, considers only the effects immediately adjacent to the pile. This thesis presents a new model that incorporates the approaches of each class, thus being a completely non-linear model that accounts for the total behaviour of the soil-mass system. Part I of the thesis is concerned with the development of the model. The pile is considered as a series of elastic elements contained in an elastic soil, but between the soil and the pile a layer of soil with plastic properties is assumed. On the pile sides the layer is thin; below the pile a plastic soil element of finite length and the same section as the pile allows a non-linear base response. The properties of these plastic soil regions are determined from empirical soil tests in situ or in the laboratory. The behaviour of the semi-infinite elastic soil mass outside the plastic soil region is accounted for by the use of equations developed by R. D. Mindlin in 1936. A large section of the first part of the thesis is devoted to a discussion of the Mindlin equations and the solution of singularities that arise in their use. The second part of the thesis first compares the model pile results with field tests for which the relevant model input information is also available. Reasonable agreement between model and test results is demonstrated, although there is clearly a scarcity of the information required for input to the model. The thesis then presents a series of studies on typical, arbitrary piles in a variety of soil types, although the general characteristics of the soils considered are those of clay soils. Characteristics typical of piles of a particular type and in soils of a particular type are considered, in the hope of identifying characteristics typical of such piles or soils in the field. Characteristics identified from the load-settlement curve of the pile top are particularly considered, since many such curves are produced daily in the construction industry. Certain trends in the shape of these load-settlement curves are discerned, but no positive unique characteristic of any one soil or pile type has been found. It appears that the pile load-settlement curve with a marked peak, or change in slope, is typical of the friction pile, with the peak corresponding to development of maximum pile side friction. However the trend is not as yet certain enough to be of practical use. It is concluded that the model is valid, but requires a large reserve of information about soil plastic properties and to a lesser extent elastic properties before substantial use of the model can be made. However it appears that much of this reserve of information can be found from existing tests commonly performed, in particular the conventional shear box test. The movements associated with peak shear in this test are the values required for the assumed model plastic soil properties; such movements though often recorded are rarely published and so this information is lost. A technique is suggested at the end of the thesis for adapting the model to forecast the results of cyclic loading tests. Though of little design value such a model, if accurate, would clearly be reliable for use in general design procedures.