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International Conference on Civil and Environmental Engineering, ICCEE 2019/
Oct.
28-30, 2019/ Pukyong National University/
1
Settlement Estimation of a Cube-type Artificial Reef Installed on
Clay by Finite Element and Regression Analyses
Van-Than CHAU
1
and Won-Bae NA
1
Keywords: settlement, artificial reefs, clay, regression analysis, finite element analysis
Introduction
Benefits of artificial reefs (ARs) have been proved for
decades. Shapes and sizes of ARs have been studied to
maximize the benefits of ARs. However, the
settlement of ARs during installation may reduce their
working capacity (Han, 2016; Kim, 2018). Thus,
evaluating influence of clay soil, considering its
characteristic parameter, can help engineers estimate
the working capacity of ARs. Thus, we simulated the
installation of a cube-type AR and found the influence
of each parameter of clay soil on the settlement of the
AR. Thereby, it is possible to highlight each parameter
that greatly affects the AR settlement.
Material and Method
The AR is made from concrete and reinforcing bars
with typical dimension of 2m (𝐻) × 2m (𝐵) × 2m (𝐿)
and the vertical and horizontal thickness of 0.25m. It
was dropped from a height above seabed for installing
and this process was modeled by the ANSYS
AUTODYN with an initial velocity, as shown in Fig 1.
The clay was modeled according to Carton (2014), as
shown in Table 1. The installation velocity was set to
0.5m/s, a practice in South Korea. For the parameter
study, we made variations of the parameters of clay
and accordingly found the influence of each parameter
to the settlement.
Ta bl e 1 Characteristic parameters of clay soil
Density
(kg/m3)
Bulk
Modulus
(kPa)
Shear
Modulus
(kPa)
Yield
Stress
(kPa)
Friction
angle
(degree)
1800 833.33 200 0.15 19
Mathematics
Regression is an algorithm to get an equation, which
can describe the law of variability of data. The clay is
characterized by density (𝑑), bulk modulus (𝑏), shear
modulus (𝑠), yield stress (𝑦), and friction angle (
);
hence, the equation to estimate settlement ( ℎ ) is
described as Eq. 1, and rewritten as Eq. 2.
2345 6
1
xxxxx
hxd b s y
(1)
12 3 4
ln( ) ln( ) ln( ) ln( ) ln( )hxxdxbxs
56
ln( ) ln( )xsx
(2)
Fig. 1. Model of the installation process of a cube-type
AR in clay soil.
From the simulation data (Table 2) and regression
analysis, we can find the coefficients 𝑥, 𝑥, 𝑥, 𝑥,
𝑥, and 𝑥, respectively.
Result and Discussion
From the regression analysis, Eq. 2 becomes Eq. 3, and
the settlement of the AR can be estimated by Eq. 4.
𝑙𝑛ℎ 16.3833 2.1036 𝑙𝑛𝑑
0.0066 𝑙𝑛𝑏 0.0087 𝑙𝑛𝑠 0.2476 𝑙𝑛𝑠
0.1757𝑙𝑛 𝜑 (3)
ℎ7.67
10𝑑.𝑏.𝑠.𝑦.𝜑. (4)
Figure 2 shows the settlement history of the first run
in Table 2. It is found that Eq. 4 can estimate the
settlement of the AR with high accuracy, when
installed on the seabed of clay with the initial velocity
of 0.5 m/s. The errors between the values of simulation
and regression are under 5%, as shown in Fig. 3. The
coefficients whose exponents are approximately zero
in Eq. 4 are negligible; hence, the influence of bulk and
shear moduli is considered small on the AR settlement.
1 Department of Ocean Engineering, Pukyong
national University, 45 Yongso-ro, Nam-gu, Busan,
48513, Korea
2
/
International Conference on Civil and Environmental Engineering, ICCEE 2019/ Oct.. 28-30, 2019/ Pukyong National University
Ta bl e 2 Simulation results by ANSYS AUTODYN software
Fig. 2. The settlement of the AR vs. time.
Fig. 3. Comparison the settlement of regression and
simulation.
The exponential coefficients of negative sign indicate
that their effect on the settlement is inversely
proportional. In other words, bulk modulus and yield
stress are inversely proportional to the settlement
while density, shear modulus, and the friction angle are
proportional. The most significant parameter is density
because its index number is the largest in the
proportional manner. Eq. 4 is especially useful for an
engineer to evaluate or estimate the settlement of the
AR. If it is installed on the other type of soils (rather
than clay), the regression equation should be adjusted.
References
E. Carton, G.H.J.J Roebroeks, J.P.F. Broos, V. Halls, J.
Zheng (2014): Characterization of dynamic
properties of ballistic clay, Personal Armour
Systems Symposium, Robinson College,
Cambridge, UK.
S. Han (2016): Estimation of seabed settlement and
impact force for a box-type artificial reef
considering seabed soil conditions in the initial
installation stage, Master thesis, Department of
Ocean Engineering, Pukyong National
University.
M. Kim (2018): Estimation of initial seabed settlement
of artificial reefs according to installation
velocities, Master thesis, Department of Ocean
Engineering, Pukyong National University.
Run Density
(kg/m3)
Bulk
Modulus
(kPa)
Shear
Modulus
(kPa)
Yield Stress
(kPa)
Friction
angle
(degree)
Settlement
(m)
1 1800 833.333 200 0.15 19 0.7374
2 1800 2000 1000 0.15 19 0.7518
3 1800 3000 4000 0.30 19 0.6367
4 1800 3000 4000 0.50 25 0.5728
5 1800 3000 4000 1.00 30 0.5255
6 2000 1500 200 0.30 19 0.7650
7 2000 3000 4000 1.00 30 0.6099
8 2200 2000 1500 0.50 25 0.8779
9 2200 3000 4000 1.00 30 0.7737