A NUMERICAL STUDY ON SEDIMENT MANAGEMENT IN A
VOLCANIC BASIN
NAOKI MIYAZAWA
Interdisciplinary Graduate School of Medicine and Engineering, University of
Yamanashi, 4-3-11 Takeda,
Kofu, Yamanashi 400-8511, Japan
KENGO SUNADA AND SATORU OISHI
Interdisciplinary Graduate School of Medicine and Engineering, University of
Yamanashi, 4-3-11 Takeda,
Kofu, Yamanashi 400-8511, Japan
A methodology for sediment management in a basin where the sediment yield is severe
is studied. The study basin is the Pasig-Potrero River basin near the Mt. Pinatubo in the
Philippines, where the thick deposits of pyroclastic material were emplaced due to the
eruption of Mt. Pinatubo. Using the lahar model developed by Miyazawa et al. [1], the
deposition areas of lahar-sediment to the several-scale flood determined virtually are
calculated numerically and are estimated. Based on the calculation results, which
countermeasure is better for the sediment management in this basin is studied.
INTRODUCTION
Active volcanoes, Mt. Pinatubo in the Philippines, Mt. Kelue and Mt. Semeru in the
Indonesia belong to the monsoon Asia. The sediment yield is severe in these volcanic
basins.
Mt. Pinatubo in the Philippines erupted on June 1991. During the post-eruption stage,
lahars occurred several times in basins around it. The lahars occurred by erosion of large
quantities of volcanic ash and pyroclastic deposits covered around the volcano due to
heavy rainfall and the lahar-sediments deposited in the lower basin, causing the serious
damage to several towns and villages. By river piracy on October 1993, the pyroclastic
sediments flowed into the Pasig-Potrero River. In the present stage, large quantities of
lahar-sediments deposited near the Megadikes and the riverbed aggradations occurred
downstream of them. The risk of flood inundation in the Pasac Delta by the riverbed
aggradations is pointed out. Also, runoff sediments greatly affect the ecological
environment of the Pampanga Bay. From these backgrounds, it is necessary to study the
comprehensive sediment management in the Pasig-Potrero River basin and the Pasac
Delta.
In this paper, a methodology for sediment management in a basin where the
sediment yield is severe is studied.
1
STUDY BASIN
The study basin is the Pasig-Potrero River basin near the Mt. Pinatubo in the Philippines,
where the thick deposits of pyroclastic material were emplaced due to the eruption of Mt.
Pinatubo. The Pasig-Potrero River rises from the foot of Mt. Pinatubo and flows into the
Pampanga Bay. The Volume of pyroclastic deposit is 500 million cubic meters in the
river basin. The catchment area at the transverse dike is 144 km2. Total rainfall in rainy
season is 2172mm from Clark Camp rainfall station, Angeles City. Rainy season is from
May to October. The volume of sediment runoff along the River is 135 million cubic
meters in 1994. The existing structural measures in the River basin are a sabo dam in
upstream reach and the Megadikes and the transverse dike in middle reach. The sediment
dredging is conducted in lower reach of the River.
2D LAHAR MODEL
The governing equations are the volumetric conservation of lahar (Eq. (1)), the
volumetric conservation of sand (Eq. (2)), the momentum equations in the x and y
directions (Eq. (3) and (4), respectively), and the equation of bed elevation change (Eq.
(5)):
h M N
1



( E  D)
t x
y C*
(1)
(Ch) (CM ) (CN )  
C   
C 
 E D



Kxh
   K y h
t
x
y
x 
x  y 
y 
(2)
( z b  h)  bx
(UM )
(VM )
M


  gh

t
x
y
x
m

 ( z b  h)
 (UN )
 (VN )
N
by


  gh

t
x
y
y
m
z b
1

( E  D)
t
C*
(3)
(4)
(5)
where h = flow depth; U, V = depth-averaged velocity in the x, y directions, respectively;
M, N = discharge flux in the x, y directions, respectively; C* = sediment concentration of
bed; E = volumetric rate of erosion per unit bed area; D = volumetric rate of deposition
per unit bed area; C = depth-averaged sediment concentration; Kx, Ky = diffusive
coefficients of suspended sediment in the x, y directions, respectively; β = momentum
coefficient, β = 1.0; g = gravity acceleration; zb = bed elevation; τbx, τby = shear stress at
the bed in the x, y directions, respectively; ρm = mass density of lahar, ρm= (σ – ρ)C+ρ; σ
= mass density of sand; and ρ = mass density of water.
2
The resistance law for turbulent mudflows proposed by Arai & Takahashi [2] is used
in the present model. The shear stresses at the bed are expressed as follow:
 by
 bx
f
f
 V U 2 V 2
 U U 2 V 2 ,
m 8
m 8
 

1 1  2
1

f  8  ln
 1   2   
2
2





  Z0  Z0 

(6)
2
0   d 
1
  , 
 2 m  h 
(C * / C ) 1 / 3  1
(7)
2
 2  2
(8)
where f = resistance factor; κ = Karman constant; Z0 = z0/h; z0 = ks/30; ks = roughness
height; λ = linear concentration of the particles in the lahar; α0 = 0.022= empirical
constant; and d = diameter of sand. Arai & Takahashi [2] stated that when empirical
constant α0 was set 0.022, their theoretical equation for velocity distribution had a good
correlation with the experimental velocity distributions conducted by them.
The Karman constant of Arai and Takahashi [3] is used:
 0 1  2C  4C 2

{1  1  52 0 (1  2C  4C 2 ) s1

2
f
gsws C (h  k s )
s1  3
U 2 V 2
, u* 
u * ln( h / k s )(1  sC )
2 2
(9)
(10)
where κ0 = Karman constant for plain water; s = specific gravity of sediment in water, s =
σ/ρ-1; u* = friction velocity; and ws = settling velocity of the suspended sediment which
is obtained by Rubey’s equation (Izumi & Ikeda [4], Ikeda & Izumi [5], Ikeda et al. [6]).
The volumetric rate of deposition is expressed as,
m(m  1) 2 

Cb 
D  wscb Cb , w scb  w s 1  mC b 
2


(11)
where wscb = settling velocity of sand particles adjacent to the bed (Hindered settling); Cb
= concentration of suspended sediment adjacent to bed; and m = exponent (2.39~4.65)
depending on the particle Reynolds number.
The volumetric rate of erosion into suspension per unit bed area is expressed as,
E  K z
dc
| z  0  w scb E *
dz
(12)
3
where E* = dimensionless erosion rate equal to Cb at the equilibrium condition; Kz =
diffusion coefficient of suspended sediment in the vertical direction; and c =
concentration of suspended sediment. Fig.1 (a) shows the relationship between the
dimensionless erosion rate E* and the friction velocity-settling velocity ratio u*/wscb
obtained by fitting the experimental data of Hirano et al. [7], Egashira et al. [8] and
Winterwerp et al. [9] the following dimensionless expression.

E*
u
 1  exp   Kd * *
C*
w
scb

 sg 

 , d*  d 2 

 

 0 
1/ 3
(13)
where d* = dimensionless grain parameter; ν0 = kinematical viscosity of water; and K =
dimensionless coefficient = 0.0105. Thus, Eq. (12) upon substitution of the dimensionless
erosion rate E* from Eq. (13) yields


u

E  C* 1  exp   0.0105 d * *
wscb





wscb



(14)
5.0
1.0
E*/C*=1-exp(-Kd*u*/wscb)
0.9
(a)
4.0
0.7
3.5
0.6
3.0
Kz (cm2/s)
E*/C*=Cb/C*
0.8
0.5
0.4
0.3
0.1
40
60
80
100
120
2.0
1.0
0.5
0.0
0.0
20
Kz=0.0475u*h
2.5
1.5
Hirano et al. d=0.17mm
Hirano et al. d=0.29mm
Hirano et al. d=0.55mm
Egashira et al. d=0.16mm
Winterwerp et al. d=0.12mm
Winterwerp et al. d=0.225mm
0.2
0
Hirano et al. d=0.17mm
Hirano et al. d=0.29mm
Hirano et al. d=0.55mm
Egashira et al. d=0.16mm
Winterwerp et al. d=0.12mm
Winterwerp et al. d=0.225mm
(b)
4.5
0
140
10
20
30
40
50
60
70
u*h (cm2/s)
d*u*/wscb
Figure 1. (a) Relationship between the dimensionless erosion rate E* and the friction
velocity-settling velocity rate u*/wscb. Solid line indicates best-fit empirical relation, Eq.
(13), in which K = 0.0105. (b) Relationship between u*h and Kz plotted using
experimental data of Hirano et al. [7], Egashira et al. [8] and Winterwerp et al. [9].
Fig.1 (b) shows the relationship between u*h and Kz. The solid line indicates a linear
relationship between them. Therefore, the diffusion coefficient in the vertical direction
can be expressed as follows,
K z  u * h ,   0.0475
(15)
4
The transverse diffusion coefficients of highly concentrated sediment-laden flows have
not yet been fully understood. For simplicity, the diffusion coefficient Kz in Eq. (15) is
used to represent the corresponding ones in the transverse directions, namely, Kx and Ky.
NUMERICAL CALCULATION RESULTS
Using the lahar model mentioned above, the deposition areas of lahar-sediment to the
several-scale flood determined virtually are calculated numerically and are estimated.
Based on the calculation results, which countermeasure is better for the sediment
management in this basin is studied
The discharge hydrograph is an important hydrological data for reproducing the lahar.
The discharge observation and rainfall observation aren’t done on site. Therefore, the
triangle discharge hydrograph was specified (Fig.2). The peak discharge per unit width is
6.25 ~ 100 m2/s and the duration is 2 hours. Because the sediment discharge at the inflow
point was not known, the equilibrium sediment concentration was specified.
Fig.3 shows the topography in the southeast area of Mt. Pinatubo (23.2 km x 21.7
km). This topography was obtained by interpolating the 30 second x 30 second
(approximate 1km) DEM data (GTOPO30) published in the U. S. Geological Survey
(U.S.G.S) website. The grid size is 7.28 second x 7.28 second. The arrow in Fig. 3 shows
the inflow direction at inflow point, ● the location of the main town or city, and ■ the
sediment-sampling point.
120
15.16
ANGELES
No.3
15.12
No.2
100m
80 m
60 m
15.10
80
40 m
15.08
Latitude
Discharge at inflow point (m2/s)
15.14
100
60
40
20
PORAC
20 m
15.06
15.04
15.02
No.4
15.00
STA RITA
14.98
FLORIDABLANCA
GUAGUA
14.96
0
0.0
0.5
1.0
1.5
SAN FERNANDO
MINALIN
120.51 120.54 120.57 120.60 120.63 120.66 120.69
2.0
Longitude
Time (hours)
Figure 2. Discharge hydrograph used for
Calculation
Figure 3. Topography in the southeast area
area of Mt. Pinatubo.
The sediment diameter is one of important parameters for discussing the erosion and
deposition of sediment. Particles size distributions of the sediment at three locations
(points Nos.2, 3, and 4 in Fig. 3) along the Pasig-Potrero River were measured in March
5
2002. Fig.4 shows the measured distributions of the lahar deposits at all the sites. The
maximum diameter is 20mm and minimum diameter is 0.07 mm. Particle sizes range
from very fine sand to medium gravel. The median diameter is 0.45 mm at point No.2
and 0.85 mm at points No.3 and No.4.
100
Cumulative percent passing
90
80
70
60
50
40
30
No.2
No.3
No.4
20
10
0
0.01
0.1
1
10
100
Diameter (mm)
Figure 4. Particle size distribution of lahar deposits
The model parameters are as follows; the diameter of sand d = 0.7 mm
(representative diameter of lahar deposits from Fig.4), the sediment concentration of bed
C* = 0.6 (measured concentration of lahar deposits), the mass density of sand σ = 2.6
g/cm3 (mass density corresponding to d = 0.7mm from measured mass density of lahar
deposits), the threshold depth of flow hth = 0.05 m, and time step Δt = 0.5 s. If Δt was
taken as 0.5 second, the numerical calculation was found to be stable. Otherwise, the
threshold depth is assumed to have more than 30 times the representative diameter of
lahar deposits. The model domain was discretized into an array of nodes each measuring
225 m by 217 m.
Fig.5 shows the final deposition areas of lahar-sediment to the several-scale flood.
The lahar flows toward the east side of the basin. However, the model expresses the
tendency of sediment deposition on the whole. Though the model isn’t perfect, it is useful
to be applied to the overland lahar in the Mt. Pinatubo basin. Because the DEM data with
resolution of about 1 km was used in present stage, the location of river or small-scale
topography did not reflect the overland flow calculation. It is found that it is necessary to
calculate using the high-resolution elevation data.
6
15.15
ANGELES
LATITUDE
15.10
PORAC
0
15.05
q100.0
=100m2/s
peak
q200.0
=50m2/s
peak
SAN FERNANDO
300.0
15.00
qpeak=25m2/s
400.0
qmax=12.5m2/s
STA RITA
500.0
qpeak=6.25m2/s
600.0
120.55
MINALIN
GUAGUA
120.60
120.65
120.70
LONGITUDE
Figure 5. Deposition areas of lahar-sediment
As mentioned in INTRODUCTION, it is necessary to managing the sediment
comprehensively in the Pasig-Potrero River basin. It is important to develop the model
for estimating from the sediment yield to the sediment deposition coherently in the study
basin. Present study is defined as the preparatory stage for developing the coherent
simulation model.
In order to understand the sediment environment in the Pasig-Potrero River basin
and the Pasac Delta, the topographical data is going to be acquired by a detail survey or
an analysis of satellite images. It is planned to mount Synthetic Aperture Radar (SAR) on
the satellite for the future earth observation mission. Getting the topographical data by
SAR is expected for the future practical usage. There is an example for measuring the
topography of volcanic area, Mt. Unzen, using the SAR mounted on an airplane. A laser
profiler mounted on an airplane is also effective method for acquiring the high-resolution
and high-precision topographical data.
CONCLUSIONS
The conclusions drawn from this study are itemized below:
Using the lahar model developed by Miyazawa et al. [1], the deposition areas of
lahar-sediment to the several-scale flood determined virtually are calculated numerically
and estimated. The deposition environment of sediment in the Pasig-Potrero River basin
can be understood by enforcement of present study.
7
The importance of grasping the sediment problems of specific area within the
framework of the comprehensive system of sediment environment is recognized. Present
study will become a concrete example toward the direction.
In order to understand the sediment environment in the Pasig-Potrero River basin
and the Pasac Delta, the topographical data is going to be acquired by a detail survey, an
analysis of satellite images and so on.
ACKNOWLEDMENT
This work has been supported by CREST of JST (Japan Science and Technology
Agency).
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8