The document discusses optimizing the cost of a raft foundation for a building in Bahrain. It considers variables like the pile group design, soil improvement, and uses genetic algorithms to optimize the total cost which includes costs for the raft, piles, soil excavation and filling, and settlement constraints. The authors conclude that the optimal number of piles is closer to the lower limits considered and gradual relaxation of the variable limits can help identify consistently optimal solutions.

1. Georgios K. Bekasa
, Georgios E. Stavroulakisb
a,b
Department of Production Engineering and
Management, Technical University of Crete, Greece
Cost optimization of a raft foundation
including pile group design optimization
and soil improvement considerations
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

2. Outline
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

3. Outline
 Objectives
 Optimization scenarios
 Variables of the optimization problem
 Model
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

4. Outline
 Objective function
 Constraints
 Optimization methodology
 Conclusions
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

5. Resources
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

6. Resources
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

7. Objectives
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

8. Objectives
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

9. Optimization scenarios
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

10. Optimization scenarios
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

11. Variables of the optimization
problem
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

12. Variables of the optimization
problem
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

13. Variables of the optimization
problem
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

14. Model
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

15. Model
 A multi-
storeyed
building,
located on
Bahrain.
 Plan view:
Rectangular
shaped,
30x35 m.
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

16. Model
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

17. Model
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

18. Model
 A depth equal to: 1.5B
+ Lp (where: B is the
smaller dimension of
the foundation and Lp
is the length of piles) is
used to estimate the
depth, where the
applied loads have a
negligible effect (≈
0.1q, where q is the
applied load).
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

19. Model
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

20. Model
 The efficiency
of the pile
group is taken
conservatively
as equal to 1.
 The soil layers
are treated as
one equivalent
layer by
following the
method
described by
Bowles.
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

21. Model
•The pressures below
each column are
calculated and compared
with the ultimate bearing
capacity of the soil.
•The structural design of
the raft is based on its
division into 3 intermediate
strips and 2 edge strips
(that have half of the width
of the intermediate strips).
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

22. Model
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

23. Model
 The adjusted elasticity method is used for
the estimation of the settlement caused by
the raft assisted by a surrogate model for
the calculation of the influence factor
described in the formula.
 The total settlement of the group of piles
is calculated by the methodology proposed
by Randolph and Worth.
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

24. Objective function
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

25. Objective function
Total cost = Cost of raft forming +
Cost of the concrete and the steel
reinforcement of the raft + Cost of
the piles + Excavation costs related
to the soil improvement layer +
Filling costs related to the soil
improvement layer + ∑pi
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

26. Constraints
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

27. Constraints
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

28. Constraints
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

29. Constraints
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

30. Optimization methodology
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

31. Optimization methodology
 Genetic
algorithms
via the use
of the
optimization
toolbox of
Matlab.
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

32. Conclusions
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

33. Conclusions
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

34. Conclusions
 Furthermore, for both scenarios, the optimal
number of piles for a typical row or a typical
column of the pile group is closer to the lower
limits than the upper limits.
 A gradual relaxation of the limits of the
variables can take place by accepting the
solutions that appear with a higher frequency
-as optimal solutions- and accordingly by
excluding those that appear as not optimal.
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations

35. Georgios K. Bekasa
, Georgios E. Stavroulakisb
a,b
Department of Production Engineering and
Management, Technical University of Crete, Greece
Cost optimization of a raft foundation
including pile group design optimization
and soil improvement considerations
Georgios K. Bekas and Georgios Stavroulakis - Cost optimization of a raft foundation including pile group design
optimization and soil improvement considerations