Narrow Results

In this paper we discuss how to implement a Bayesian thinking for multistate reliability analysis. The Bayesian paradigm comprises a unified and consistent framework for analysing and expressing reliability, but in our view the standard Bayesian procedures gives too much emphasis on probability models and inference on fictional parameters. We believe that there is a need for a rethinking on how to implement the Bayesian approach, and in this paper we present and discuss such a rethinking for multistate reliability analysis. The starting point of the analysis should be observable quantities, expressing states of the world, not fictional parameters.

The influence of anisotropic properties and layering of saturated soils on dynamic response of a circular foundation under time-harmonic vertical loading is studied in this paper. The foundation is modeled as a rigid disk, with either permeable or impermeable and smooth contact surface, whereas a multilayered transversely isotropic poroelastic half-space is defined for the supporting soil. To investigate the dynamic interaction problem, a displacement and flow boundary condition at the contact surface is constituted by employing a discretization technique and the displacement influence functions, which are obtained from the exact stiffness matrix scheme, with the stiffness matrices being presented explicitly for the first time. A set of numerical results are presented to portray the effects of anisotropic and poroelastic properties, hydraulic boundary conditions, soil heterogeneity, and frequency of excitation on vertical dynamic response of rigid circular foundations. In addition, vertical vibrations of a ring foundation and a massive circular foundation are also investigated.

This paper presents a simple technique 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 is discretized into a number of different regions in which a particular order (number of sides) of the polygon is chosen to linearize the Mohr–Coulomb yield criterion. A greater order of the polygon needs to be selected only in that region 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 and rough strip footings and the results are found to be quite satisfactory.

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker–Prager (D–P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D–P yield cone with the Mohr–Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors N_c, N_q and N_γ have been computed, as a function of ϕ, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.

Selected case histories recording the behaviour of piled foundations in lateral-spreading fields are reviewed. From these observations and from laboratory experiments in the centrifuge and on the shaking table, it is clear that the resistance of liquefied soil is very small and that the critical points for a pile are at the bottom as well as near the top of the liquefied layer. It is also apparent that liquefaction does not occur until a significant threshold level of shaking is exceeded, and that even then it does not occur instantaneously. Thus damaging motions can be felt by the pile and transmitted to the superstructure before liquefaction and lateral spreading occurs. There is a critical period early in the shaking when the soil has softened enough for ground motion to be amplified but is still stiff enough to induce large bending moments in the pile, near the top of the liquefiable layer. Liquefaction is certainly not a dependable base-isolation mechanism. A controversial issue concerns the continuity or localisation of displacement within the liquefied layer. There is evidence that, in the majority of cases, displacement within the liquefied layer is continuous with depth; although when a sufficiently impermeable layer overlies the liquefiable one, a layer of free water can accumulate and localise displacement. Another old controversy, which now seems to be resolved, concerns the generation of passive earth pressures in non-liquefiable surface layers. There is clear field and laboratory evidence for the development of the passive state in superficial layers. For use in every-day design, two simple methods of analysis have recently emerged. They are the earth pressure method and the seismic deformation method. They have been calibrated against the Kobe data and appear to work well in the few cases where they have been checked on other soils. It remains for them to be verified against a broader range of soils and for further soil-spring models.

The quantum Liouville equation, which describes the phase space dynamics of a quantum system of fermions, is analyzed from stochastic point of view as a particular example of the Kramers–Moyal expansion. Quantum mechanics is extended to relativistic domain by generalizing the Wigner–Moyal equation. Thus, an expression is derived for the relativistic mass in the Wigner quantum phase space presentation. The diffusion with an imaginary diffusion coefficient is discussed. An imaginary stochastic process is proposed as the origin of quantum mechanics.

Standardization in software engineering plays an important role for integrating, regulating, and optimizing existing best practices and fundamental theories in software development and organization. An idiom says that one can “gain new knowledge by reviewing the past”. This chapter reviews current software engineering and software quality related standards and the history of their development. Usability and open issues in applications of the major software engineering standards are discussed. Future trends and research topics considered significant and worthy of being explored are suggested in this chapter.

The problem of increasing the understanding of algorithms by considering the foundations of numerical analysis and computer science is considered. The schism between scientific computing and computer science is discussed from a theoretical perspective. These theoretical considerations have an intellectual importance when viewing the computer. In particular, the legitimacy and importance of models of machines that accept real numbers is considered.