1889
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
1
Development of Method for Evaluating and Visualizing 3-dimensional Deformation
of Earth Retaining Wall for Excavation
Développement des méthodes d’évaluation et de visualisation de la déformation tridimensionnelle
des murs de soutènement dans les excavations
T. Matsumaru & K. Kojima
Railway Technical Research Institute
ABSTRACT: Monitoring of deformation of earth retaining wall for excavation is important in order to keep surrounding environment
and structures safe during construction. However, there are some problems in monitoring of earth retaining walls. For example, it is
difficult for the partial measurement by plum bobs to evaluate the overall behavior of the retaining walls, and the multipoint
measurement using multi-element inclinometers tends to be expensive. In this paper, we developed a system to evaluate and visualize
retaining wall as three-dimensional curved surface. The validity was confirmed by the simulation of the loading test on the model
wall. In order to confirm the effectiveness of the proposed system to actual monitoring, we tried to apply the system to the on-site
measurement. Furthermore, we proposed a method to conduct monitoring of retaining walls using this system and simple
inclinometers.
RÉSUMÉ : Le contrôle de la déformation des murs de soutènement dans les excavations est important pour assurer la sécurité de
l’environnement et des structures
lors de la construction. Toutefois, le contrôle des murs de soutènement pose un certain nombre de
problèmes. Il est par exemple difficile de procéder à des mesures partielles au fil à plomb pour évaluer le comportement général des
murs de soutènement et les mesures multipoint à l'aide d’inclinomètres multié
léments sont plutôt onéreuses. Dans cet article, nous
présentons un système d’évaluation et de visualisation des murs de soutènement sous forme d’une surface courbe tridimensionne
lle.
La validité du système a été confirmée par simulation d’un essai de charge sur la paroi du mur testé. Afin de vérifier l’efficacit
é du
système proposé dans des conditions de contrôle réelles, nous avons tenté de l’appliquer lors de mesures sur le terrain. Nous
proposons également une méthode de conduite du contrôle des murs de
soutènement à l'aide de ce système et d’inclinomètres simples.
KEYWORDS: earth retaining wall, 3-dimensional deformation, cubic B-spline function, measurement, incline
1 INTRODUCTION
Monitoring of deformation of earth retaining wall for
excavation is important in order to keep surrounding
environment and structures safe during construction. However,
there are some problems in monitoring of earth retaining walls.
For example, it is difficult for the partial measurement by plum
bobs to evaluate the overall behavior of the retaining walls, and
the multipoint measurement using multi-element inclinometers
tends to be expensive.
Considering these problems as backgrounds, we developed a
system to evaluate and visualize retaining wall as three-
dimensional curved surface. In this system, the cubic B-spline
function is adopted as analytical technique, which is employed
for describing shape of land as three-dimensional curved surface
based on sets of data of the elevation altitude (Nonogaki et. al.,
2008). We proposed a method to evaluate inclinometer data as
surface without transforming incline into displacement. The
validity and the adequacy was confirmed by loading test and
field measurement. Furthermore, we seached the way two
conduct measurement easily by using the proposed method.
2 EVALUATING AND VISUALIZING DEFORMATION
OF RETAINING WALL IN 3-DIMENSIONAL SPACE
2.1
Cubic B-spline function
Figure 1 shows the 3-dimensional coordinate space for
describing the deformation of the earth retaining wall. In this
figure,
x
,
y
, and
z
axis means the direction of the retaining wall,
the depth, and the direction toward which the wall deforms. The
earth retaining wall is expressed as smooth and continuous
surface by the following equation.
z yxf
,
(1)
In the cubic B-spline function (Nonogaki et. al., 2008), the
region for drawing the surface is divided in
M
x
and
M
y
equally-
spaced areas in
x
and
y
axis. By setting the
M
x
+7 and
M
y
+7
equally-spaced nodes, the surface is expressed by the following
equation:
3
1
3
1
,
Mx
i
My
j
j
i
ij
yNxNc
yxf
(2)
where
N
i
(
x
) and
N
j
(
y
) is the cubic B-spline function, and
c
ij
is
unknown coefficient.
In order to determine the surface, objective function
Q
was
defined as following equation:
fR fJ
fQ
;
(3)
where
J
(
f
) is the functional for evaluating the smoothness of the
surface,
R
(
f
) is the function which expresses the sufficiency
degree of data, and
α
is the parameter balancing for these two
functions. The surface is determined by substituting
c
ij
into
equation (2) obtained from
∂
Q
(
f
;
α
)/
∂
c
ij
=0.
J
(
f
) is written by
Shiono et al (2001).
The function which expresses the sufficiency,
R
(
f
), is
mentioned as below. The coordinate (
x
p
,
y
p
,
z
p
), where a
measurement equipment is placed, and the measured
displacement
u
p
has following relationship.
p
p
p p
u z y xf
,
(4)
Therefore, using the error average
ε
p
of squares between the
curved surface and the obtained displacement data,
R
(
f
) is
evaluated as following equation.
h p
n
fR
/
2
(5)
Development of Method for Evaluating and Visualizing 3-dimensional
Deformation of Earth Retaining Wall for Excavation
Développement des méthodes d’évaluation et de visualisation de la déformation
tridimensionnelle des murs de soutènement dans les excavations
Matsumaru T., Kojima K.
Railway Technical Research Institute
