PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011
Ramli, M 1 , & Ohnishi Y 2
1 Teknik Pertambangan Universitas Hasanuddin, Makassar, 90245
2 Urban and Environmental Engineering, Kyoto University, 606-8501, Kyoto
ABSTRACT
Slope failure frequently occurs in the rainy season indicating pore water pressure along the potential sliding planes during or after rainfall plays important roles. The pore water pressure changes correspond to water table fluctuation that is mainly associated with the rainfall. However, numerical modeling for seepage flow analysis is commonly performed by setting boundary conditions at upper and lower gradient as a fixed head. This simple assumption may lead to inaccurate estimation results. Therefore, evaluation of the pore water pressure distribution and its time evolution needs a new technique. A coupling of tank model and groundwater flow model was proposed in this paper. Using this technique, the effect of rainwater infiltration to the slope seepage flow can be represented more realistic in adjusting boundary conditions as time-dependent hydraulic head. The proposed method was implemented into the real field problem of slope in Japan
INTRODUCTION
The important of groundwater to slope instability is depicted with a number of slope failures occurred during the wet season, or following heavy rainfall or snowmelt events. Triggering mechanism of this failure is the increase in pore water pressure along the potential failure planes due to a rising water table. However, geotechnical analysis of slope stability often invokes incorrect pore water pressure distribution (Freeze et al
1979). The pore water pressure distribution is estimated based on steady state flow approach, or the flow line is assumed to be linear along the slope profile. These simple assumptions are
Seepage flow analysis by using numerical model has been realized as important and effective method to represent physical process of the system. However, a number of simplifications according to problem interest are required to be adjusted with capability of software and hardware.
In many cases, the modeling has being performed by setting upper-and-lower gradient as a fixed head source boundary is only condition. infiltrated
In this rainfall, study, representation of the essential boundary condition on the slope seepage flow model is emphasized.
For analysis covering all slope and recharge this representation is reasonable, but for a slope with open hydrogeologic system in which recharge come from rainfall and underflow, such kind of seldom happen in the field, because the hydrogeologic system of a slope involves complex problem; transient, saturated-unsaturated interaction that usually leads to a water table rise in which very difficult to be predicted. The amount and duration of rise, and time lag between the rainfall event and the resulting rise may vary widely depending of the slope configuration, the rainfall intensity and duration, the initial moisture content, and hydro-geologic properties of saturated-unsaturated zone. To find a better estimation result, analysis should be done without too much simplification of the field problem. assumption may produce a significant bias of result. In order to overcome this problem, timedependent head (pore water pressure) boundary condition is proposed to be applied on the numerical simulation.
With record of past occurrence of rainfall and groundwater level fluctuation, the time-dependent boundaries can be defined simply. However, in order to anticipate a lack of this kind of data particularly for forecasting of slope stability, an estimation method becomes necessity. In this

PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011 study, tank model and numerical flow model was investigated to be integrated by using a loose coupling approach. The tank model is applied to forecast the groundwater level fluctuation caused by rainfall, and the numerical flow model is used to understand physical process of groundwater flow. Implementation of proposed method is demonstrated for the flow analysis on a slope at
Mizusawa-Yamagata, Japan (Figure 1).
METHODOLOGY
Analysis of slope stability in this research is aimed to develop a new method by coupling two methods of the tank model and the numerical flow model. In order to integrate these models, two codes for both methods have been developed. In groundwater modeling, integrating two models can be done by using loose coupling, tight coupling, and embedded coupling (Gogu, et al,
2001). In this case, these two codes are integrated by using the loose coupling system. As a loose coupling technique, the tank model code organizes output files according to structure of data requirement of the numerical flow model.
The tank model code will produce a set of estimated groundwater level, and the data will be read as an input file by the flow model code.
Such as aforementioned, the main constraint of this new model is to represent the boundary conditions more accurately on upper-and-down gradient or both vertical sides of slope cross section. The boundary condition that is mainly set as a constant head is modified to be a time dependent boundary condition of fluctuated pore water pressure head. Therefore, the input file as the groundwater level will be generated automatically into pore water pressure head along boundary by the flow model code. The number of set data produced by the tank model code determines number of time steps in the numerical flow simulation. For each time step, the pore pressure head is assumed to be constant on the vertical boundaries.
The Tank Model
Tank model was initially developed as a run-off model in field of water resource engineering. Now days, this method has been widely applied for recharge estimation method through some modifications according to problem interest. The tank model requires recorded data of rainfall and groundwater level. Similar with some other recharge estimations method using the groundwater level data, the tank model has simplicity and insensitivity to the mechanism by which water moves through the unsaturated zone.
Some disadvantages associated with this method are less accurate for conditions in which groundwater fluctuation sensitive to rainfall, and groundwater level located quite deep from top surface. Comparing with the recharge estimation purpose, interest of application this model has been focused in generating a number of the Tank
Model parameter to forecast the groundwater level fluctuation due to rainfall, and the volume of water comes into and out from a system.
The tank model is a method of modeling the rainfall – river flow volume response in present drainage basin. A conceptual diagram of the tank model is shown in figure 2. Rainfall coming into a particular area composes two main components.
One is surface runoff occurs immediately after rainfall. The other is the base flow, in which rainwater infiltrated to the underground, and then reappears in surface as groundwater base flow. In order to represent the process in the model, a number of tanks are arranged with arbitrary connections. Each water tank has outlets on its bottom and/or side. Water in a tank flows out through each outlet in proportion to the water depth above the outlet.
Application of the tank model to estimate groundwater level within a slope due to infiltrated rainfall has been concentrated on the model of single tank. This kind of model usually composes of two layers called upper tank and lower tank.
Configuration of the tank model and related coefficient are shown in figure 3. The upper tank represents surface runoff and infiltration, and the lower tank for underground flow and groundwater level. In order to represent the water flowing out from the system, every tank has outlets on its bottom and/or vertical side. Some symbols used in this model are

11
,

12
,

21
,

22
to represent conductance of run-off, infiltration, intra-flow, and groundwater flow, respectively. H
A
is head control of run-off (unsaturated zone storage), H
B for intra-flow, and H
C
for groundwater flow. The rate of each component of flow is estimated by

PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011 multiplying these conductances with gap between water level and height of related outlet.
Interpretation of the tank model to the physical problem may be described by using following approaches. Water initially supplied to the top tank by rainfall and/or irrigation flows to the lower tank in connection. The upper tank corresponds to a shallower part of the subsurface, and the lower tank to a deeper part of sub-surface.
By assuming the lower tank is fully saturated, inflow to this tank is considered as recharge.
Actual evapotranspiration is simulated by subtracting from the tank concern starting form the upper tank. If the upper tank is empty, the evaporation will be subtracted form the lower tank for a case of depth of groundwater level is smaller than extinction depth. Storage in each tank is calculated as remainder after addition and deduction of inflow and outflow. All these calculation are performed successively for every time interval. Position of groundwater level is obtained by dividing water height on the lower tank with effective porosity of soil (

).
A numerical code was developed to incorporate all above mentioned procedures. In a common sense, the tank model analysis needs to determine the seven unknown parameters to produce groundwater level fluctuation due to rainfall pulse. However, since the model is developed to forecast groundwater fluctuation, the code was organized with data input of these seven parameters and the rainfall intensity. Therefore, a pre-defined these seven parameters is required to find a verified values. These verified values of the seven parameters are determined through trialand-error procedure to achieve a best fit between observed and estimated hydraulic head. The best fit is obtained by minimizing the root means square error (RMSE) and mean error (ME) of those hydraulic heads. It is also important to consider time range of a series record data form past occurrence in which there is a no significant changes in variable affecting the recharge to the slope. Since the fitting process is counted by trialand-error procedure, the accuracy is specified by user. Finally, with these verified value of the seven parameters, the groundwater level fluctuation can be produced accurately based on the forecasting rainfall intensity.
The Flow Model
The second numerical code developed in this study is the groundwater flow model. Modeling of the groundwater flow on slope employs the equation of fluid mass balance that can be formulated for saturated-unsaturated media as follow (Bear, in Voss et al 2003);
(

S op
)
 p
 t

(
 v )

Q p
Where

is fluid density (kg.m
-3 ), S op
1)
is specific pressure storativity (kg.m
-1 sec -1 water pressure (kg.m
-1 sec -2
), p is the pore
),

is volumetric porosity of medium (-), v is fluid velocity (m. sec -1 ), and Q p
is fluid mass source (kg.m
-3 sec -1 ).
The specific pressure storativity is given;
S op

( 1
 
)
  
2)
Where;

and

are compressibility of matrix and water (kg.m
-1 sec -2 ), respectively. In addition, fluid velocity can be calculated through the application of Darcy’s law; v
 

 k .
k r



  p
  g

3)
Where k r
is relative permeability (-), k is intrinsic permeability (m m -1 sec -1
2 ), u is the fluid viscosity (kg.
),

is the porosity (-), and g is the gravitational acceleration (m.sec
-2 ). For the current study, it is assumed that both fluid viscosity and fluid density are constant.
The relative permeability is calculated in term of pressure and saturation that is carried out by employing a general function based on saturationcapillary pressure. The relation can be written as follow (Van Genutchten, in Voss et al 2003); k r

S w
* 1 / 2



1




1

S
* w n n

1



 n n
1
 2


4)
Where the a dimensionless saturation, S w
* is given by;
S w
* 
S w
1


S wres
S wres
5)
S w

S wres

( 1

S wres
)


1

1
( ap c
) n


 
1 n
6)

PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011
S wres
is a residual saturation below which saturation is not expected to fall because the fluid becomes immobile, a and n are van Genucthen soil parameters.
The governing equations is formulated numerically based on a hybridization of finite element and integrated with finite different method (Voss et al, 2003). These methods are in the framework of a method of weighted residual.
Standard finite element approximation is used only for terms in the balance equation that describe fluxes of fluid mass. All other non-flux terms are approximated with finite-difference method. In order to represent fluid mass balance, the simulation produces values of pore pressure for all nodes within domain instead of hydraulic head. The linearization of equation is generated by iterative solver of Pre-conditioned bi-conjugate gradient.
INTEGRATION RECHARGE MODEL AND
GROUNDWATER FLOW MODEL
Study Area of Mizusawa-Yamagata, Japan
The proposed method was applied to investigate the pore pressure changes due to rainfall pulse on a slope at Mizusawa-Yamagata Prefecture. This application is concerned more about the verification of the proposed method than prediction to occurrence in the future. Therefore, this paper mainly describes strengthen of the proposed method to produce the observed groundwater level within modeling area more accurately than the previous method.
The Mizusawa area is well known for heavy snowfall with a number of landslides in the snow melting season of March to April. Configuration of the investigated slope is shown in figure 4 composed two types of geological material; mudstone and colluvial soil. The colluvial soil takes place in upper layer with thickness varying from 10 m in up-hill to 20 m in down-hill. Four observation wells constructed in this slope, B3-
D-1, B3-D-2, B3-D-3, and B3-D-5, were used to investigate reliability of this proposed method.
The modeling area covers slope between bore holes B3-D-5 to B3-D-3, which horizontal length of 280 m from surface elevation of 240 – 320 m with lower boundary at elevation of 220 m from mean sea level. Consequently, data from these two holes are used to find the seven parameter of the tank model, and then the estimated groundwater level is applied to run the groundwater flow model. Two others holes, B3-
D-2 and B3-D-3, within the investigation area are functioned as a control of pore pressure head produced by the groundwater flow model.
Slope Response to Rainfall by Tank Model
The response of the slope to precipitation intensity was investigated on well of B3-D-5 at downstream boundary, and on well of B3-D-3 at upstream boundary. Analysis was based on data of rainfall intensity and groundwater observation within 183 days (June – November, 1994). The monitoring data of rainfall occurrence is available in one observation point. Since the observed data depict that fluctuation of groundwater level at the well of B3-D-3 is higher than the well of B3-D-5, therefore representation of the hydrogeological parameter into coefficient of tank model has significant difference.
The tank model was applied without considering the component of intra-flow (parameter of

21
and
H
B on figure 3). This was based on assumption that there is no significant lateral flow occurred from the infiltrated water before reaching water table. Since the position of water table is deeper than the extinction depth and the slope profile and hydraulic gradient shows that the groundwater will flow continuously over time, therefore the H
C also can be set to zero. By using these simplification, unknown variable of the tank model parameters remain four coefficients;

12
,


11
,
22
, and

. In order to obtain these parameters, a number of set of approximation values were input to the tank model to estimate hydraulic heads on each well. This is a trial-anderror procedure to find a best match between the observation hydraulic heads with the calculation results. The obtained parameters of tank model is shown in table 1, with matching of the hydraulic head at well of B3-D-3 and of B3-D-5 are shown in figure 5 and 6, respectively. By using these values, the transient response of the slope to the rainfall pulse can be predicted.

PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011
Assignment of Numerical Model Parameter
Simulation of groundwater flow on the slope of
Mizusawa-Yamagata was carried out by using 2D
(two-dimensional) model with considering saturated-unsaturated medium. The area is discretized with a regularly spaced of Cartesian grid constructed with mesh size of 1.0 by 5.0 m square in the vertical place. The domain descritization results 2979 nodes and 2818 elements shown in figure 7. The 183 daily stress periods was simulated to investigate groundwater behavior within slope. For each stress period, the average hydrologic conditions are assumed to remain constant. The simulation was carried by setting boundary conditions as time-dependent boundary condition of fluctuated pore pressure at both vertical sides and of rainfall form top side.
The bottom side of the domain was set as no-flow boundary.
To perform simulation, natural initial pore pressure are required to be set everywhere in the aquifer. This value is obtained through an extra initial simulation for steady state case. The timedependent boundary conditions depicted on figure
6 were also modified by using fixed pore pressure instead of the fluctuated one, and the rainfall is set to be zero. The pore pressures on the vertical side boundaries were generated as a linear function from bottom aquifer to top surface.
Assignment of hydrogeological parameter of the system was obtained through calibration procedure of transient problem by employing the boundary conditions such as in figure 7. In this step, intrinsic permeability was adjusted to achieve a reasonable representation of the observed hydraulic head. The estimated pore pressure was converted to hydraulic head to compare with the observed head. Two monitoring wells with observation data of 183 days were used to compare both hydraulic heads. With a number of simulations, calibrated intrinsic permeability were obtained such as depicted in table 2.
Matching between the observed and the simulated hydraulic heads produced by using the calibrated parameters are shown in figure 8.
DISCUSSIONS
The Tank Model and Numerical Flow Model were integrated to simulate groundwater flow at a slope. In order to investigate the effectiveness of the proposed method, the simulation was run by setting the up-gradient and down-gradient boundary with two difference boundary conditions, fixed and time-dependent pore pressure, while others boundaries are set such as shown in figure 7. The simulated hydraulic head at two observation points, well of B3-D-1 and B3-
D-5, are plotted on figure 8. The graph shows clearly that by defining the both vertical sides as fixed pore pressure (head) boundary, the fluctuation of groundwater level within problem domain can not be represented in both inside wells, even though a same of rainfall intensity is imposed in the top layer to emerge groundwater recharge from infiltration. This means the underflow recharge has a higher influence to pore pressure changes in the evaluated site than the precipitation.
From point of view of slope stability analysis, slope configuration poses a non-uniform surface inclination with stratified material exist with a different permeability or conductivity values.
Such kind type of slope, the sliding failure is mostly on the contact of both materials (Lourence et al, 2006; McCarthy, 1993). Three cross sections, AA, BB, and CC, shown in figure 7 are made on the slope to observe the pore pressure on potential failure plane. Within the observation period, there was no occurrence of slope movement, and the pore pressure at the potential failure plane shown in figure 9. The potential failure plane on cross section AA is located below water table, but at two other cross sections of BB and CC in above water table. The graph also shows that up-hill is more sensitive to the pore pressure changes than down-hill zone.
The above example is aimed to examine the reliability of proposed method in analysis the pore pressure changes on the slope by verifying the model with a field problem. It is commonly understood that prediction of slope stability before failure is more important than analyzed the past occurrence to find a better counter measure of the problem. However, the past occurrence of slope movement may affect the sensitivity of slope as a

PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011 response to rainfall event. Therefore, the observation data before the latest slope movement occurrence should not be used to obtain of the parameter of tank model. In addition, it is also recognized that value of intrinsic permeability is quite significant effect in calculating pore pressure distribution. Therefore, coupling both tank model and numerical flow model is useful in assigning the conductance of material.
CONCLUSIONS
Integrating Tank model and numerical flow model is demonstrated to find a better representation of natural water balance on a slope affecting distribution of the pore pressure values. The estimation of recharge rate can be set according to time interval employed in the numerical flow analysis. By this coupling, underflow recharge is represented as time-dependent boundary condition, so that an error of calculation due to defining both vertical side of slope as fixed head boundary can be avoid. Another advantage of this coupling is that the material conductance can be assigned through calibration process of transient problem with a higher confidence than using a fixed head boundary. However, application of this method for slope stability analysis should studied combination of the tank model and coupled stressflow simulation to evaluate the mechanical behavior of slopes.
REFERENCES
Arai Y., Ohnishi M., Imai G., Kisanuki T., and
Hirayama M., 2003, Preservation countermeasures for groundwater flow against the linear open cut tunnel in low alluvial plain with dissected valley, Groundwater engineering –
Recent advances, Balkema, pp. 255-262.
Freeze, R.A. and Cherry, J.A. (1979),
Groundwater. Prentice Hall Inc, Englewood
Cliffs, N.J.
Jiao, J.J. Wang X.S. and Nandy, S. (2005).
Confined groundwater zone and slope instability in weathered igneous rocks in Hong Kong.
Engineering Geology 80; pp. 71-92.
Koyama, T. Takahashi, K. Ramli, M. and Ohnishi,
Y. (2008). Slope stability analysis using coupled tank model and saturated-unsaturated flow simulation, The 3 rd Taiwan Japan Joint Workshop on Geotechnical Natural Hazards, Keelung,
Taiwan.
Kinzelbach, W. (2002) A survey of methods for groundwater recharge in arid and semi-arid regions, United Nations Environment Programme,
UNEP/DEWA/RS.02-2.
Lourenco, S.D.N. Sassa, K. and Fukuoka, H.
(2006) Failure process and hydrologic response of a two layer physical model: Implications for rainfall-induced landslides. Geomorphology 73, pp. 115-130.
McCarthy, D.F. (1993) Essentials of soil mechanics and foundations. Basic Geotechnics,
Regents/Prentice Hall, Englewood Cliff, New
Jersey.
Ohnishi, Y. Ohtsu, H. Nishioka, T. Naka, Y.
Yasuda, T. and Takahashi, K. (2003).
Observational method for tunnel construction considering environmental impact to groundwater.
Groundwater Engineering – Recent Advances,
Balkema, pp. 17-24.
Rahardjo, H. Hritzuk, K.J. Leong, E.C. and
Rezaur, R.B. (2003). Effectiveness of horizontal drains for slope stability, Engineering Geology 69, pp. 295-308.
Simoni, A. Berti, M. Generali, M. Elmi, C. and
Ghirotti, M. (2004). Preliminary result from pore pressure monitoring on an unstable clay slope.
Engineering Geology 73; pp. 117-128.
Voss C.I. (2003). SUTRA, A Model for
Saturated-Unsaturated Variable-Density Groundwater Flow with Solute or Energy Transport,
Water-Resources Investigation Report 02-4231,
U.S. Geological Survey.

PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011
Parameter
Run-off coefficient (

11
)
Infiltration coefficient (

12
)
Groundwater flow coef (

22
)
Head of outlet of upper tank (H
A
)
Effective porosity (

RMSE
ME
Unity
-
-
-
M
%
M
M
B3-D-5
0.80
0.75
0.075
0.030
0.08
0.23
-0.02
Values at Well
TABLE 1 : Obtained value of tank model parameters.
B3-D-3
0.85
0.75
0.065
0.020
0.015
2.39
-0.43
Material
Colluvium soil
Mudstone k x
(m/s)
9.18E-14
3.58E-15 k y
(m/s)
9.18E-15
3.58E-16
Porosity (%)
0.30
0.25
TABLE 2 : Calibrated Hydrogeological parameter of the evaluated slope
FIGURE 1 : Landslide area in Mizusawa, Yamagata, Japan

PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011
FIGURE 2 : Outline of the tank model (JRA in Arai et al, 2003)
FIGURE 3: Configuration of tank model

PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011
FIGURE 4 : Feature of investigated slope at Mizusawa-Yamagata Prefecture.
FIGURE 5 : Matching observed (H_obs) and estimated hydraulic head (H_est) at bore hole of B3-D-3 by using parameters of tank model at table 1.

PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011
FIGURE 6 . Matching observed (H_obs) and estimated hydraulic head (H_est) at bore hole of B3-D-5 by using parameters of tank model at table 1.
FIGURE 7 : Discretization of domain by employing Cartesian grid with mesh size 1 x 5 m, and applied boundary conditions. AA, BB, and CC are cross sections.

PROCEEDIGS JCM MAKASSAR 2011
The 36 th HAGI and 40 th IAGI Annual Convention and Exhibition
Makassar, 26 – 29 September 2011
FIGURE 8 : Matching observed head ( Observation ) and estimated head by using tank model ( Time_bc ) and fixed boundary ( Fix_bc ) at both vertical side.
FIGURE 9 : Pore pressure distribution on potential failure plane at cross sections of AA, BB, CC