7R23. Boundary Element Method in Contact Problems for Elastic Spatial-and-Nonhomogeneous Bases. (Russian). - SM Aleinikov (Dept of Math, Voronezh State Academy of Construction and Architecture, ul Kirova 3-75, Voronezh, 394018, Russia).Publ House of Civil Eng, Moscow. 2000. 754 pp. ISBN 5-93093-053-8.
Reviewed by RO Simionescu-Panait (Dept of Mech, Univ of Bucharest, Str Academiei nr 14, Bucharest, 70109, Romania).
This book deals with the numerical modeling of contact interaction of rigid foundations with soil bases via the boundary element method (BEM). It presents a systematic approach for a wide range of spatial contact problems arising in geotechnics. New numerical techniques and the corresponding computing algorithms are developed, their implementation leads to the design of complex shaped foundations, subject to spatial loadings, resting on an elastic soil.
The book is divided in six chapters, eight appendices, and an extensive reference list, containing 819 titles, which focuses mainly on the Russian literature in the field.
The first chapter reviews the classical spatial contact models applied to geotechnics, gives the useful fundamental solutions for spatial problems in elasticity, and analyzes the behavior of the influence function for some elastic-type bases (soldered half-spaces with variable thickness layers, and elastic half-spaces with variable soil deformation modulus).
Chapter 2 is devoted to the analytical solutions, and their approximation, of mixed problems for the spatial contact of a rigid foundation with an elastic half-space. One reduces the problem to solve a system of integral equations which is performed, in the case of Mindlin fundamental solutions, using triangular and quadrilateral boundary elements. One presents some examples concerning the contact of a rigid body, at axial loading and torsion, with an elastic half-space, for complex shaped punches with flat and smooth base.
The third chapter deals with the numerical implementation of the developed algorithms into a program package. One investigates here the stress and strain behavior due to the interaction of foundations with the soil, under the action of various kind of forces. The accuracy and efficiency of BEM are shown by several examples, regarding the problems of contact for flat punches of circular, annular, or polygonal shape with an elastic half-space. Finally, the author analyzes some spatial contact problems concerning rigid spherical, cylindrical, and conical punches deepened into an elastic half-space.
In Chapter 4, one considers the BEM solutions of spatial contact problems for complex shaped footings resting an elastic nonhomogeneous half spaces. Some optimization problems have been solved, controlling the loading parameters and the shapes of base, to provide a uniform settlement of rigid foundation plates. Combining BEM with Finite Difference Method the author investigates contact problems with orthotropic plates situated on elastic nonhomogeneous bases.
The fifth chapter contains the application of BEM for solving the problem of a deepened foundation in a spatial formulation. One obtains the solutions for deepened monolithic foundations most used: pyramidal piles; foundations made of short vertical and inclined bored piles with caps; bored pile foundations with supporting widening; slot foundations having longitudinal section of various shapes. Quantitative estimates of the foundations’ shape influence on the displacements and slopes, for different loadings, are given.
The last chapter deals with the important problem of the spatial contact of a rigid punch with a poroelastic half-space. One derives the numerical modeling of the strains in soil mass due to the reducing of pore pressure in soil. The approach is based on the integral representation of displacements for a poroelastic half-space, saturated with fluid. It has various applications in underground gas and oil deposits design, or in the withdrawing of underground water.
In conclusion, Boundary Element Method in Contact Problems for Elastic Spatial-and-Nonhomogeneous Bases is recommended by this reviewer to graduate students, researchers, and engineers working in the field of geotechnics and civil engineering, and can be purchased by the libraries. However, its impact is linked to the knowledge of Russian language.
