Optimization has two faces, minimization of a loss function or maximization of a gain function. We show that the mean absolute deviation about the mean, d, maximizes a gain function based on the power set of the individuals; and nd, where n is the sample size, equals twice the value of the cut-norm of the deviations about the mean. This property is generalized to double-centered and triple-centered data sets. Furthermore, we show that among the three well known dispersion measures, standard deviation, least absolute deviation and d, d is the most robust based on the relative contribution criterion. More importantly, we show that the computation of each principal dimension of taxicab correspondence analysis (TCA) corresponds to balanced 2-blocks seriation. These ideas are applied on two data sets.
SUMMARYThe modified Cam clay (MCC) model is used to study the response of virgin-compressed clay subjected to undrained triaxial compression. The MCC constitutive relationship is obtained in a closed form. Both elastic and plastic deviatoric strains are considered in the analysis. The solution allows to obtain total and effective stress paths followed by the clay in undrained spherical expansion. Pore water pressures are determined from the difference between total and effective mean stresses. For illustration purposes, the analysis is also applied to the well-known reconstituted normally consolidated London clay and the results are compared with the recently published data obtained by a numerical approach. In addition, the Almansi large strains are used in the analysis, as these allow to obtain limit expansion and pore pressures, whereas both small-strain and logarithmic-strain approaches do not permit to determine them.
This article presents the analytical solution of Laplace equation for the steady flow around open-ended cylindrical piezometers located in an infinite, isotropic, and incompressible saturated soil. Shape factors are obtained for piezometers with varying length-to-diameter ratios. Comparisons are made with published factors obtained by means of approximate analytical solutions, numerical approaches, and measurements in electric analog models. It is shown that some expressions that are currently used in practice are inadequate and should be abandoned.
This paper presents the results of analytical and numerical analyses of the effects of performing a pressuremeter test or driving a pile in clay. The geometry of the problem has been simplified by the assumptions of plane strain and axial symmetry. Pressuremeter testing or installation of driven piles has been modelled as an undrained expansion of a cylindrical cavity. Stresses, pore water pressures, and deformations are found by assuming that the clay behaves like normally consolidated modified Cam clay. Closed-form solutions are obtained which allow the determination of the principal effective stresses and the strains around the cavity. The analysis which indicates that the intermediate principal stress at critical state is not equal to the mean of the other two principal stresses, except when the clay is initially isotropically consolidated, also permits finding the limit expansion and excess pore water pressures by means of the Almansi finite strain approach. Results are compared with published data which were determined using finite element and finite difference methods.
The objective of this paper is to compare field test results obtained in a stiff sensitive clay from Quebec using prebored, instrumented sharp cone tests (ISCTs) with those deduced from prebored and self-boring pressuremeter tests (PMTs and SBPMTs, respectively) and vane shear tests (VSTs). Comparisons are also made with triaxial test results. It is shown that undrained shear strengths Su deduced from PMTs and ISCTs are greatly overestimated with respect to the values inferred from SBPMTs and VSTs. As for the shear modulus G, the opposite is true. These discrepancies are considered to arise from initial disturbance and unloading caused by drilling of pilot holes in the case of PMTs and ISCTs. Interpretation problems may be also related to the existence of very high lateral pressures at rest in the clay deposit.
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