747
Using 3D numerical solutions for the simplified modelling of interaction of soil and
elongated structures
Utilisation de solutions 3D numériques pour la modélisation simplifiée de l'interaction des sols et
des structures allongées
Kholmyansky M.L., Sheynin V.I.
NIIOSP Research Institute, Moscow, Russian Federation
ABSTRACT: The problem of interaction of linearly deformable structure and linearly deformable soil is stated in a general form and
then defined more precisely for an elongated structure that is rigid in transversal direction. Both loads acting on the structure and on
the soil outside the structure (induced by of surface and/or subsurface construction, geological processes etc.) are considered.
Numerical method for solution of corresponding equations is developed based on Galerkin boundary elements and numerically
implemented. Examples of concentrated load and tunnelling effects on beam-like structure resting on half-space are considered.
RÉSUMÉ : Le problème de l'interaction d’une structure déformable linéaire et d’un sol linéaire est posé sous une forme générale puis
défini plus précisément pour une structure allongée rigide dans le sens transversal. Les charges agissant sur la structure et sur le sol à
l'extérieur de la structure (induite par une construction en surface ou en souterrain, par des processus géologiques, etc) sont
considérées. Une méthode numérique pour la solution des équations correspondantes est développée sur la base des éléments de
frontière de Galerkin et mise en œuvre numériquement. Des exemples de charge concentrée et d’effets dus au creusement de tunnels
sont étudiées pour des structures assimilables à une poutre reposant sur un demi-espace.
KEYWORDS: half-space, deformable structure, soil-structure interaction, tunnelling effects, boundary elements, Galerkin method.
1 INTRODUCTION
Development of methods of soil-structure interaction with most
adequate simulation of real conditions is one of the most
important of research in structural mechanics and soil
mechanics. The extensive literature and review of some
problems may be found elsewhere (e.g., Gorbunov-Posadov e.a.
1984).
In recent years the researchers’ attention is increasingly
attracted to the study of soil mass effect due to natural or man-
induced processes on above-surface and sub-surface structures.
In such problems it is usually impossible to be restricted to
conventional idealizations.
At the same time it is possible to choose a class of structures
with elongated zone of contact with soil, when one zone
dimension is significantly less than another: buildings with strip
foundations, underground pipelines, transportation tunnels etc.
Three-dimensional soil-structure interaction analysis in these
cases may be simplified.
In such a way, analysis of solution for a beam on a half-
space under concentrated load (Biot 1937) has led to the
Winkler model that was used for calculation of beams on soil
surface and pipes within it (Vesic 1961, Attewell e.a. 1986).
Corresponding model has some known disadvantages and needs
some development. Comparison of Winkler and half-space
models for elongated structures was performed in the papers
(Klar 2004, Fischer and Gamsjäger 2008).
At present time finite element is widely used for solving the
problems of soil-structure interaction. However its application
in case of domain with length and breadth of different orders of
magnitude encounters additional difficulties in course of
numerical implementation.
As a consequence, in case of elongated contact zones of
deformable structures interacting with soil continuum another
approach is needed that allows for geometrical features of the
problems and makes it possible to develop a numerical
calculation algorithm simple and providing sufficient accuracy.
2 SOIL-STRUCTURE INTERACTION
2.1
Problem statement
2.1.1
The soil
A problem of interaction between structure and linearly
deformable soil is considered in discrete or continuum
statement. In many instances, for example for tunnels and
pipelines, the pressure exerted on soil is of small or moderate
level; that makes possible disregarding nonlinearity. Effects
both on structure and soil are permitted. The general form of the
flexibility method for the linearly deformable soil is the
following:
*ˆ ˆˆ ˆ
wpCw
,
(1)
where
= vector of displacements in the contact zone;
C
=
flexibility matrix in discrete case or – corresponding operator in
continuum case; = vector of loads on the ground in the
contact zone;
= vector of displacements in the contact zone
due to the forces exerted on soil outside the structure under
consideration.
w
ˆ
ˆ
p
ˆ
*ˆ
w
The last value is non-zero when other structures are present
or some geological processes are developing; it is supposed that
corresponding loads on do not depend on the presence of the
structure considered, i.e. back effect does not take place.
2.1.2
The structure
The .structure is supposed linearly deformable too. The
equations of the stiffness method for it read
*
p Kw p
,
(2)
where
p
= vector of loads transferred to the structure from its
(strip) footing;
K
= matrix (or operator) of the stiffness of the
structure, reduced to the nodes of footing axis;
w
= vector of
SOIL-STRUCTURE INTERACTIOn
2.1
Problem statement
