On the solution of steady unconfined seepage towards semi-infinite slopes

Analytical solutions for the two-dimensional problem of unconfined seepage towards semi-infinite slopes are described. The analysis employs complex variable techniques. Conformal mappings have been used to reduce the problem to solving an ordinary differential equation. The resulting integrals are presented in terms of special functions. The solutions for the location of the phreatic surface and the exit point have been obtained in parametric form. Some additional results and asymptotic expansions of the solutions are also presented. The numerical results have been calculated and plotted for different values of the slope angle in dimensionless co-ordinate space.     

Lunar evolution: How well do we know it now?

The currently known astronomical, chemical and magnetic data are not uniquely indicative of an extensively and globally molten Moon. We argue here for an accretional layering in the Moon, but at temperatures below solidus. The excess mass in the near side of the Moon compatible with a 2 km displacement in the center of mass relative to the centre of figure and the moment of inertia data is considered to be due to Fe-FeS liquid formation and inhomogeneous segregation. These Fe-FeS bodies, termed fescons, are shown to be capable of accounting for the presently available magnetization data, by acting as small regenerative dynamos with a time-stability less than that of the terrestrial equivalent. The chemical characteristics of the highly differentiated materials (KREEP, granite etc.) are considered to be due to small scale localized melting caused by collisional events, from sources in which accessory phases play a significant role. Mare basalts are considered to be melts in the overlying material produced at a later time by⁴⁰K radioactivity in the fescons. Some consequences of the present hypothesis are suggested.We conclude that these and other characteristics of the lunar materials are reconcilable with a cold Moon such as discussed by Urey over the past two decades.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

Dynamic analysis of piles and pile groups embedded in non-homogeneous soils

A hybrid boundary element formulation for the steady state analysis of piles and pile groups embedded in a soil stratum in which the modulus increases linearly with depth is presented. The piles are represented by compressible columns or flexible beams and the soil as a hysteretic, layered medium. The explicit Green's function corresponding to dynamic loads in the interior of a layered stratum, developed earlier by Kausel is used in the study. The governing differential equations for the pile domain are solved for a distributed periodic loading intensity and those for the soil domain by a system of boundary elements at the pile-soil interface. These are then assembled into a system of algebraic equations by satisfying interface equilibrium and compatibility. The results of the analysis have been compared against those from alternative formulations, e.g. finite elements, and confirm the accuracy of the proposed formulation. Representative results for single piles and pile groups are presented.