2011
Calculation method of optimization the soil-cement mass dimensions to reduce the
enclosure displacements in deep excavation
Calcul des dimensions optimales du massif du sol-ciment pour réduire les déplacements de fouilles
profondes
Ilyichev V.A.
Russian Academy of Architecture and Construction Sciences, Moscow, Russia
Gotman Y.A.
Company Ltd ‘Podzemproekt’, Moscow,Russia
ABSTRACT: In the article basic condition to the calculation the soil-cement massif optimum dimensions, which ensure the assigned
value of deep excavation wall displacement are presented. Problem statement and it's solution with the application of a Winkler-bed
model, standard procedures for analysis of massive retaining walls and theory of optimum design are described. Some results of
calculations and benchmark of these results with the use of
PLAXIS 2D software package
are given.
RÉSUMÉ : Le procédé de calcul est décrit pour la détermination des dimensions d'une masse de sol-ciment en utilisant un modèle de
“Winkler-bed”, des procédures standard pour l'analyse des murs de soutènement poids, et la théorie de la conception optimale. Les
résultats des calculs et leur évaluation à l'aide du logiciel PLAXIS 2D sont présentés.
KEYWORDS: diaphragm wall, optimal design, Winkler-bed model, coefficient of stiffness.
1
INTRODUCTION
Acceleration of work execution for underground space
constructing in dense urban conditions with the minimum
influence upon surrounding buildings is one of the main
problems of underground structures design today. The given
paper presents the design method of optimization of the raised
problem design decision. The method of excavation “top-down”
is used as technological scheme only with upper floor
installation and as optimized (variable) parameter, the
dimensions of soil-cement mass (SCM) combined with
enclosure (diaphragm wall) that provides the excavation without
intermediate strutting system and minimization of wall
displacement (Fig. 1).
So the main task is to determine the minimum volume of the
SCM with the condition that the horizontal displacements of the
enclosure during excavation of the pit do not exceed the
assigned value
S
v
max
≤ S
pred
.
Figure 1.
Problem condition
1
PROBLEM STATEMENT
The computational model of the optimized "wall-SCM-
soil" system can be represented as a beam on an elastic
Winkler bed, where the beam simulates the pit enclosure, and
the SCM working in consort with the soil of the elastic bed. The
stiffness coefficient of the bed, which varies over the height of
the enclosure, is the only parameter of the model used to
determine the dimensions of the SCM. The stiffness coefficient
of the elastic bed, and the development of a procedure to
determine the SCM dimensions corresponding to the optimal
solution will therefore be the subject of optimization problem.
In its initial state of rest, the enclosure is treated as a beam
affixed on two sides by prestressed springs that describe the
"SCM-soil" system (Fig. 2, a, b), whereupon the prestress
corresponds to the lateral pressure of the soil
q
01
in a state of
rest (Fig. 2, c, d). As the pit is excavated, the prestressed springs
(soil) then disappears on one side together with the pressure,
which they have created, and the system is taken out of
equilibrium. To attain equilibrium, the enclosure is displaced
within the pit (Fig. 2, e). Here, the springs below the bottom of
the pit are mutually disturbed on the inside, but are undisturbed
on the outside, altering the pressure of the springs against the
enclosure (Fig. 2, f). During compression, this pressure is
increased, and is
q
2
=
q
02
+
kz
,
(1)
but is diminished on release
q
1 =
q
01
−
kz
,
(2)
whereupon the change in pressure will depend on the
coefficient of stiffness
k
of each spring, and the displacement z
of the enclosure at the corresponding point.
During excavation, therefore, the SCM as a component part
of the soil, which is simulated by the springs (Fig. 2, g) is
displaced inside the pit, and the pressure against the enclosure is
changed in conformity with (1) and (2), and the pressure against
the SCM remains as before
q
02 and
q
01 on the side of the soil,
when no Coulomb active or passive pressure is formed.
Considering that the displacement of the soil and beam
below the bottom of the pit is less than that within the bounds of
the pit over its height, let us simplify the computational
diagram. The work of the springs on the outside of the pit below
its bottom can be neglected (Fig. 2, h), and replaced by a
constant pressure of the soil in a state of rest. If these springs are
eliminated from the computational diagram of the beam on the
outside of the pit, the pressure of the soil against the enclosure
below the bottom of pit will be
q
0 =
q
01
−
q
02 , and the
springs on the inside beneath its bottom will be under no
prestress.
