Application of Simplified Models to Qualitative Geotechnical Analysis

The paper describes an approach for qualifying soil-structure systems behavior, using simple numeric models – “geotoys”, reflecting the main features of the systems behavior and enabling numeric simulation of various case histories. Three case histories of major karstic sinkholes are analyzed to show that man-made structures above a karstic cavity prevent formation sinkhole. When plastic zones reach the structure periphery, the soil-structure system becomes unstable. Prior settlements could be negligible to serve as precursors. Another soil-footing-superstructure (SFSS) model is a 2D geotoy - an exact mathematical solution, used for multiple simulations (about 10,000) of SFSS sensitivity i.e., response to input parameters variations. The sensitivity was rated for each input-output pair [1]. The most interesting findings are the following: 1) SFSS stress state is very sensitive to soil strength parameters c and φ, which are responsible for formation of soil disruption zones (‘plastic zone’) under footing edges. 2) If a structure rests on a homogeneous soil base then it is practically insensitive to soil base compressibility i.e., soil modulus E variations. 3) 3D FEM analysis confirmed that 2D simulations can be used for qualitative SFSS analysis. 4) Geotoys can be used for case histories analysis, risk assessment, training practical intuition, education purposes and international exchange and cooperation

Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio

Seismic Behavior of Nailed Soil Massifs

Soil nailing technology can be successfully applied to strengthen natural soil massifs in seismic regions, provided adequate analysis is available. Conventionally, the design of soil nailing is performed iteratively: firstly parameters of nailing and their distribution are assigned, the safety factor of the nailed massif is calculated, if its value is less than 1 then nailing parameters are reassigned, etc. Such “trial and error” approach is laborious and especially so, because different types of ULSs shall be analyzed. The method, discussed in the paper, is based on assumption that the effect of nailing in soil with internal cohesion c=c(x,y) could be simulated by equivalent internal cohesion Δc=Δc(x,y) (deficit) of unreinforced massif. Formulae for calculating nailing parameters are determined on the basis of deficit distribution. A MathCad code has been developed, examples are given. The method can be easily applied to assess seismic stability of nailed soil massifs

Study of the electrodes length influence on the trajectories of water droplets dispersed in oil and affected by non-uniform electric field

The paper presents the results of numerical modelling of the processes accompanying movement of drop viscous media (water) in oil under the influence of exterior forces of the electric and dynamic nature. Systematic calculations of influence on the electric field heterogeneity drops, created by a symmetric and asymmetrical configuration of electrodes are carried out both in inter electrode and behind electrode areas taking into account a complex operation of dielectrophoresis forces, buoyancies and drag, as well as the variability of electrode sizes. The analysis of drop movement trajectories shows that the asymmetrical configuration of electrodes can be applied for an electro-coalescence intensification of water-in-oil emulsion. Correctness of calculations of the mathematical model and numerical methods are confirmed by good results if compared with the available data of the other authors