Numerical analysis and shape optimisation of concrete gravity dams.
The Finite Element and Boundary Element Methods are both well established
numerical techniques for analysing a wide range of engineering problems. In the
present thesis these numerical techniques are used for obtaining a more realistic picture
of various characteristics of concrete gravity dams. The present work addresses the
behaviour of gravity dams under static loading, and the developed analysis
procedure/computer package can cater for a wide range of dam characteristics
including: the three-dimensional behaviour of a gravity dam-foundation-abutments
system; the non-linear behaviour of a dam and foundation materials; the sequential
construction of a dam and impounding of the reservoir loading on the structure; the
effect on stresses of interfaces and joints existing between a dam and its foundation,
and in the body of a dam itself; the action of pore water pressure within the
foundation, at the dam-foundation interface, and in the body of a gravity dam; etc.
Using the purpose written computer package which can cater (in an efficient and
accurate way) for the influence of all such factors, mathematical programming methods
are, then, used to produce a powerful tool for the shape optimisation of gravity dams
leading to safe, functional and economical solutions to the problem.
In the course of developing the computer program, much care has been
exercised as regards the appropriate selection of the finite element types, mesh
configurations and mesh densities, in order to reflect (in an efficient fashion) the
variation of stress gradients in the body of a gravity dam.
In order to reduce high costs associated with a full three-dimensional analysis,
a rather efficient method is developed which enables one to carry out equivalent twodimensional
computer runs which will effectively simulate the actual three-dimensional
behaviour of gravity dams in, for example, narrow valleys. The proposed approach
reduces the dimensionality of an actual problem by one, thus, eliminating the main
disadvantage of the finite element method in terms of high solution costs for threedimensional
problems. As a result, the proposed method makes the solution procedure
highly cost effective.
By coupling the finite element-boundary element (FEBE) techniques, which
can cater for the material non-linearities in the appropriate regions of the foundation,
an attempt is made to by-pass the individual disadvantages of both these numerical
techniques. It has, then, been possible to exploit the advantages of reducing the
dimensionality of the foundation region by one using the boundary element technique,
and, hence, come up with significant savings in terms of computer running times.
Anisotropic tangent constitutive models for plain concrete under a general state
of biaxial static monotonic loading for, both, plane-stress and plane-strain states of
stresses are proposed which are simple in nature, and use data readily available from
uniaxial tests. These models have been implemented into the computer program which
is, then, used to investigate the influence of the step-by-step construction of the dam
and the sequential impoundment of the reservoir loading on the state of stresses. The
non-linear program is also used to analyse various characteristics of Bratsk concrete
gravity darn (in Russia). The correlations between the numerical results and extensive
field measurements on this darn, have been found to be encouraging.
Isoparametric quadratic interface finite elements for analysing the darnfoundation
interaction problem have also been developed. These elements have zero
thickness and are based on an extension of the linear interface elements reported by others. The numerical problems of ill-conditioning (usually associated with zero
thickness elements) are critically investigated using test examples, and have been found
to be due to inadequate finite element mesh design. Non-linear elastic tangent
constitutive models for simulating the shear stress-relative displacement behaviour of
interfaces have also been developed, and are used to analyse the effects of including
interface elements at the dam-foundation region of contact. It is shown that the
inclusion of interface elements in the numerical analyses of the dam-foundation system
leads to rather significant changes in the magnitudes of the critical tensile stresses
acting at the heel of the dam, which have previously been evaluated (by others) using a
rigid dam-foundation interconnection scheme.
Effects of pore water pressure, acting as a body force throughout the
foundation, the dam-foundation interface and the body of a gravity dam, are also
critically studied, with the pore pressure values predicted by seepage analysis. Using an
extensive set of numerical studies, a number of previously unresolved issues as regards
the influence of pore pressures on the state of stresses are clarified. The effect of
drainage on the state of stresses within the body of a dam is investigated, and an
insight is also given into the effect of the uplift acting at the lift lines between
successive layers of Roller Compacted Concrete (ReC) dams.
A shape optimisation procedure for gravity dams based on the penalty function
method and a sequential unconstrained minimisation technique is also developed. A
number of shape optimisations of idealised gravity dams are carried out in order to
compare the numerical results with previously available analytical solutions. The
present work also caters for the effects of foundation elasticity and uplift on the
optimal shape of a gravity dam. A numerical example is provided covering the shape
optimisation of a hollow gravity dam. Finally, the shape optimisation of an actual dam
(i.e. Tvishi gravity dam in Georgia) using the presently proposed procedures is carried
out with the fmal results compared with those available from the project design team.
Wherever possible. numerical outputs have been checked against available
small or full scale test data or previously reported closed form solutions. Throughout
this thesis very encouraging correlations between the present predictions and such
experimental and theoretical data have been obtained.