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Transactions on Engineering and Computing Sciences - Vol. 12, No. 2
Publication Date: April 25, 2024
DOI:10.14738/tecs.122.16787.
Toma, S. (2024). Model Experiments for Floating Stability of Self-Elevating Platform and Assessment Based on Theory of Structural
Stability. Transactions on Engineering and Computing Sciences, 12(2). 121-130.
Services for Science and Education – United Kingdom
Model Experiments for Floating Stability of Self-Elevating
Platform and Assessment Based on Theory of Structural Stability
Shouji Toma
Hokkai-Gakuen University, Sapporo, Japan
ABSTRACT
A self-elevating platform (referred to as SEP hereafter), used as a pier, capsized
during construction work at sea in March 2014. The structural characteristics of the
SEP include a notably high center of gravity due to its long legs and a large
rectangular plane, resulting in a shallow draft, which significantly differs from
conventional vessels. While the stability of floating bodies is typically assessed
using metacentric height and restoring moment curves based on conventional ship
algorithms, it is essential to ascertain whether the same principles can be applied
to the SEP, given its distinct structural features. In this study, an evaluation method
based on structural stability theory, distinct from ship algorithms, was validated
through model experiments. An analysis of overturning, based on structural
stability theory previously employed for pile drivers on land, was conducted using
the experimental results. As a result, it was discovered that both ship algorithms
and structural stability theory essentially serve the same purpose in assessing the
floating stability of SEP.
Keywords: Self-Elevating Platform, Floating Stability, Okinotorishima SEP, Overturning
Model Test, Pile Driver Overturning, Overturning Mechanism, Structural Stability, Soft
Foundation
INTRODUCTION
A self-elevating platform (hereinafter referred to as SEP) capsized during afloat construction
work at the site of Okinotorishima on March 30, 2014 [1]. The SEP was supposed to be used as
a part of permanent pier after placed at the site. Figure 1 illustrates floating SEP schematically.
The structural features of SEP shown in Fig. 1 include a very high center of gravity due to its
long legs (4 in total, 47.5m long) and a large rectangular pontoon (20m width and 30m length)
resulting in a shallow draft, which significantly differ from conventional vessels.
While the stability of floating bodies is typically evaluated using metacentric height and
restoring moment curves based on conventional ship algorithms, it is necessary to verify
whether the same methods can be applied to SEP, which has significantly different structural
characteristics.
In this study, the evaluation method based on structural stability theory will be applied, which
is different from ship algorithms. In order to research its applicability, a model experiment was
conducted and analyzed based on structural stability theory. It was found through the
experiments the assessment of structural stability theory consequently gave the same results
as ship algorithms.
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Transactions on Engineering and Computing Sciences (TECS) Vol 12, Issue 2, April - 2024
Services for Science and Education – United Kingdom
Figure 1: Self-Elevating Platform
Overturning mechanisms using structural stability theory have been studied in the past for pile
drivers and other heavy machines on land [2] ~ [6]. The study here will verify the past
researches.
EXPERIMENTAL AND ANALYTICAL MODELS
A model experiment has been conducted on the overturning (capsizing) of the floating body of
the SEP illustrated in Fig. 1. In order to perform the experimental study on stability, SEP in Fig.
1 is simplified to experimental model as shown in Fig. 2. The experimental model consists of
three parts: a box type of pontoon for the floating body, a leg concentrated at the center, and
spacers for height adjustment. A cylindrical water tank at the center was used for the legs, and
water was poured into this tank during the experiment until the model capsized, measuring the
weight and height. Here, the four legs at the corners were simplified into one central leg as
shown in Fig. 2. The water inside the tank has a free surface.
The model shown in Fig. 2 is further simplified as a rigid bar-rotation spring system, as depicted
in Fig. 3, for structural stability analysis. This structural model has been utilized in previous
studies on the overturning problems of cranes and pile drivers [2~6], and this experiment also
serves as a verification of its analytical approach. While the rotational spring stiffness in the
overturning of onshore heavy machines is uncertain because they are supported by soil
foundation, it is clear for offshore vessels which are supported by water.
In the structural system shown in Fig. 3, the structural stability theory derives the following
critical load (buckling) Pcr and critical height Lcr from the rotational spring stiffness Ks [7].
Pcr=Ks /Lcr (1)
When the load on SEP (own weight) exceeds this critical load Pcr, SEP becomes structurally
unstable, and it overturns even if the overturning moment is zero, similarly to the elastic
buckling of a long column. Note that the rotational stiffness Ks is assumed as linear in Eq. (1).
When the vessel is tilted as shown in Fig. 2(b), the rotational stiffness will be calculated from
the buoyancy change. The change of buoyancy volume V in Fig. 2(b) can be calculated by the
following Eq. (2).
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Toma, S. (2024). Model Experiments for Floating Stability of Self-Elevating Platform and Assessment Based on Theory of Structural Stability.
Transactions on Engineering and Computing Sciences, 12(2). 121-130.
URL: http://dx.doi.org/10.14738/tecs.122.16787
V =
b
2
12
l tanθ (2)
in which b=width of pontoon, l =length of pontoon.
Assuming the water density 1g/cm3, which results in f =V, the righting moment MR induced by
the force f can be obtained as follows:
MR=
2
3
fbcosθ =
b
2
12
l sinθ (3)
Equation (3) is plotted in Fig. 4, disregarding the height of freeboard. Since sinθ ≈θ for small θ,
the rotational spring stiffness Ks can be obtained from the definition shown in Fig. 4 as follows:
KS =
b
2
12
l = Iy (4)
in which Iy = moment of inertia of draft area with respect to long axis of pontoon.
It is interesting to know that the rotational stiffness is equal to the moment of inertia of the
draft area. In general vessels, the center of buoyancy shifts with incline, causing a variation in
Iy. However, it is assumed to remain constant in structural stability theory.
(a)
(b)
Figure 2: Experimental Model of SEP.