iRIC Software
Changing River Science

Morpho2DH ver.2

Solver Manual- Debris/Mud flow Produced by Hiroshi Takebayashi

Copyright iRIC Project, All Right Reserved.

Contents
I. OUTLINE ............................................................................................................................... 2
I.1 MORPHO2DH ........................................................................................................................ 2
I.2 CHARACTERISTICS OF FLOW MODEL ...................................................................................... 3
II. GOVERNING EQUATIONS ................................................................................................. 3
II.1 GOVERNING EQUATIONS OF FLOW ............................................................................................ 3＜REFERENCES＞........................................................................................................................... 6
III. CALCULATION CONDITION ............................................................................................. 7
III.1 SETTING OF CALCULATION PARAMETERS ............................................................................. 7
III.2 SETTING OF CALCULATION CONDITIONS .............................................................................. 9
III.3 SETTING OF BED MATERIAL CONDITIONS ........................................................................... 11
III.4 SETTING OF VEGETATION CONDITIONS .............................................................................. 12
III.5 SETTING OF OBSTACLE CONDITION ................................................................................... 13
III.6 SETTING OF HOT START FUNCTION .................................................................................... 14

I. Outline
I.1 Morpho2DHMorpho2DH is a calculation solver that a debris/mud flow model is added to Morpho2D.
Morpho2D is the unsteady horizontal two dimensional bed deformation analysis solver of bed
material load, which is developed by Hiroshi Takebayashi, Kyoto University. The governing
equations are written in boundary fitted general coordinate system. In 2009, the solver was installed
to RIC-Nays Version 1.0 which is the free software developed by RIC. Some functions are added tothe original version and the improved version is installed into iRIC Version2.0 on March 2011. On
March 2014, Morpho2D was unified with Nays2D and Nays2DH was developed.
Morpho2DH is the horizontal two dimensional debris/mud flow analysis solver which can reproduce
the transport and deposition process of debris/mud flow due to the landslides. Structures (ex. sabodam, weir, house and so on) and horizontal distribution of maximum erosion depth can beconsidered in the analysis.
The unsteady horizontal two dimensional bed deformation analysis of bed material load which canbe performed as it used to be.

2

I.2 Characteristics of flow model①

TVD-MacCormack scheme (2nd order accuracy) is used for the convection term in the
momentum equations as the difference method.

②

Energy dissipation is calculated by the constitutive lows of two layers model. The laminar flow
layer near the bed and the turbulence flow layer on the laminar flow are considered in the twolayer model.

③

Movements of the mixtures of water and sediment due to landslides are used as the initialconditions of debris flow④

The horizontal distribution of maximum erosion depth can be considered.

⑤

Structures (ex. sabo dam, weir and so on) can be considered by use of the height data of the
fixed bed area.

⑥

Houses and buildings can be considered as fixed bed elevations as well as river structures,
allowing for the calculation of sediment deposition on top of buildings and the transport ofdebris/mud flows. Very tall obstacles can also be considered by specifying the calculation cell
where the obstacle exists as a polygon.

⑦

The time of occurrence of slope failure can be varied for each slope failure.

II. Governing equations
II.1 Governing equations
The relationship between the Cartesian coordinate system and the generalized curvilinear coordinate
system is expressed as:J1 x y x y       



(1-1)


y
J
x


(1-2)


y
 J
x


(1-3)


x
 J
y


(1-4)


x
J
y


(1-5)

In Eqs. (1-1) – (1-5),  and  represent coordinates along the longitudinal and transverse directionsin the generalized curvilinear coordinate system, respectively; x and y represent the coordinates in
the Cartesian coordinate system.

3

Debris/mud flows comprise a mixture of flowing water and sediments; this mixture is treated as asingle-phase continuum fluid body (Egashira and Itoh, 2004). The mass conservation equation for
the water and sediment mixture is:  h    hU    hV  E   t  J    J    J  c* J

(2)where t, h, and U and V represent the time, flow depth, and contravariant depth-averaged flow
velocities above the bed along the  and  coordinates, respectively. These velocities are defined as:

U



u v
x
y

(3)

V



u v
x
y

(4)

where u and v represent the depth-averaged flow velocities above the bed along the x and ycoordinates, respectively. The term on the right-hand side of Eq. (2) indicates the sink and source ofthe mass and expresses the development and decrescence of a debris flow caused by the exchange ofthe mixture of water and sediment between the bed surface and debris flow, where c* denotes theconcentration of the sediment in the static deposition layer (bed layer) and E represents the erosion
rate of the bed. When the cohesive characteristics of the bed layer on the bedrock can be neglected
and the equilibrium bed condition wherein the bed erosion rate is the same as the sedimentdeposition rate, the bed erosion rate can be estimated using (Egashira and Ashida, 1992)Eu  v22 c* tan    e 

(5)where  denotes the bed slope in the flow direction and it is calculated usingsin  u sin  x  v sin  y
u 2  v2

(6)

where xand y denote the bed slope in the x-direction and bed slope in the y-direction, respectively.
A laminar flow layer is dominant when the sediment size is large; therefore, the flow becomes a
debris flow. When the sediment size is small, a turbulent flow layer is formed on the laminar flow
layer near the bed, and this becomes a mud flow. Considering the formation of both laminar andturbulent flows and referring to the averaged depth and sediment concentration, the equilibrium bed
slope e in the flow direction can be obtained as:    1 c hstan e  tan sh    1 c  1



(7)

where s denotes the angle of repose. The mass conservation of sediments in the debris and the mudflow is4  ch    chU    chV  E   t  J    J    J  J(8)The momentum conservation equations are given as  hU    hU    hU 


U

V

t  J   J   J hu          hv              U    V
U    V
J    x   x   J    y   y  
 1     2    2   z
1        zb       b    gh J   x   y     J  x x y y    

 

2
2
1  1         P 1       P  b        m  J   x   y     J  x x y y     m J



(9)

  hV    hV    hV 


U

V

t  J    J   J hu          hv              U    V
U    V
J    x   x   J    y   y  22
 1        z
1          zb b  gh  J  x x y y    J   x   y     




2
2
1  1       P 1         P  b




  

    m  J  x x y y    J   x   y      m J



(10)

where g and zb represent the gravitational acceleration and bed elevation, respectively. Pressure P isassumed to be static pressure, which is given ashP   m g  h  z  cos dz
0(11)

where z represents the vertical coordinate. The density of the debris flow m ism       c  (12)where  and  represent the water density and sediment density, respectively. bξ and bη in Eqs. (9)and (10) represent the contravariant shear stresses in the  and  directions, respectively. These shear
stresses are defined as

b 



bx  by
x
y

(13)

b 



bx 
by
x
y

(14)

where bx and byrepresent the shear stresses in the x- and y-directions, respectively, as5 u u v

 u v v

bx   y  f b  u 2  v 2 2

by   y  f b  u 2  v 2 

2

(15)

2

(16)

2

The energy dissipation of both the solid and fluid motion bases was considered to estimate the shear
stress. ys denotes the yield stress, which uses the following relation for non-cohesive materials.
1nc y         cgh cos  tan s c* 

(17)

where n is a constant, and it is set to 5 here. Further, fb in Eqs. (20) and (21) denotes the resistancecoefficient, for which the following relation is used.

f b  72 2 ，  25  1  c
fb 
k f
4 
c

2
3


6

（Turbulence flow layer）(18)

  k  1  e c  h  （Laminar flow layer）
5
3

d





2

  d 
1
3




2



2)

(19)

The second term is from the inelastic collisions of sediment particles, where kf = 0.16, kd = 0.0828,
and e represents the inelastic coefficients of the particles herein; dm represents the mean particle sizeof the sediment in the debris flow. The bed elevation equation is  zb E t  J 
c* J

(20)

where, zb is the bed elevation.

＜References＞
Egashira, S., Ashida, K., 1992. Unified view of the mechanics of debris flow and bed-load, in: Stud.
Appl. Mech. Elsevier 31, 391–400.
Egashira, S., Itoh, T., 2004. Numerical simulation of debris flow. J. Jap. Soc. Comput. Fluid Dyn. 12,
33–43.
Takebayashi, H., Fujita, M., Ohgushi K.: Numerical modeling of debris flows using basic equations
in generalized curvilinear coordinate system and its application to debris flows in Kinryu River
Basin in Saga City, Japan, Journal of Hydrology, 615, Part A, 128636, 2022.

6III. Calculation condition
In this chapter, calculation condition of Morpho2DH is described by use of the setting dialog boxesof iRIC.

III.1 Setting of calculation parameters
Calculation type and data (ex. calculation time and so on) are set.

Figure III－1

#

1

2
3

4

5

Setting dialog box of Calculation type and data

Table III－1
Items

Explanation of setting of calculation parameters
Setting method
Else
Select [Debris/Mud flow] for bed
deformation analysis by debris/mud
flow. [Flow only] is for flow calculation.
Calculation Type
[Bed material load] is for bed
deformation analysis by bed materialload.
Start time of the calculation isStart Time （s）
Unit is second.
set.
End time of the calculation is
End Time （s）
Unit is second.
set.
Unit is second. The
time step is decided
Calculation
Time
Time step Δt is set.
considering
CFL
Step （s）
condition.
Output Time Step forUnitissecond.
Output time step for file is set.
File （s）
Short
time
step
7

makesaanimation.
second.
6

Output Time Step for
Screen （s）

7

Bed
Deformation
Start Time （s）

Output Time Step of calculation
condition for Screen is set.
When
thedebris/mud
flow
calculation is performed, please
input 0.

8

smoothUnit isUnit is second.
Unit is second.

III.2 Setting of calculation conditions
Calculation conditions are set.

Figure III－2

#
1

2

3
4

5

6

Setting dialog box of calculation conditions

Table III－2
Items

Explanation of setting of calculation conditions
Setting method
Else
Please select [Change] when you want
Sediment
to consider the spatiotemporal change
Concentrationof sediment concentration.
When [Constant] is selected in[Sediment Concentration], please
Sediment
input
value
to
sediment
Concentration Value
concentration.
Original
Liquid The original liquid here is water
Densityand 1 is used.
Thedensityof
Sediment Density
Please input sediment density.
granite
is
about
2.65.
deposition
sediment
StaticDeposition Staticconcentration is between 0.54 andSediment
0.8.
Concentration
Fine material behaves as liquid
LiquidBehavior phase. Content rate of 0.2mm andfiner diameter is rough standard
Sediment Ratio
to decide the value.

9

7

Minimum Flow Depth

8Internal
Angle

9

Laminar Flow Depth

10Laminar Flow Depth
Ratio

11

Resistance
Coefficient

12

Fixed Bed Elevation

Friction

Minimum flow depth must be set toget stable calculation results.
Smaller value is recommended.
Input measured internal friction
angle of the sediment.
When the temporal change oflaminar flow depth is considered,please select [Change].
When the flow characteristics aredebris flow, the laminar flow
depth ratio is about 1. When theflow characteristics are mudflow, the laminar flow depth
ratio must be smaller than 1.
Value of resistance coefficientmust be set to reproduce flow
depth.
When some parts of the bed
composed of rock or sabo dams is
set in the calculation area,
please select [Enable] in [Fixed
Bed Elevation]. When [Fixed Bed
Elevation] is [Enable], the fixed
bed area must be set using
polygons.

10

The unit is m.
The unit is degree.

III.3 Setting of bed material conditions
Bed material conditions are set.

Figure III－3#
1
2

Setting dialog box of bed material conditions

Table III－3
Items

Explanation of setting of bed material conditions
Setting method
Else
When debris/mud flow calculation is
Bed Material Typeperformed, please select [Uniform].
Input mean grain diameter of the
Mean Grain Diameter
sediment that does not change Unit is m.
（m）phase into liquid.

11III.4 Setting of vegetation conditions
Set calculation conditions for vegetation. Note that this function is currently only available for flow
only calculations and for bed deformation analysis with bed load and suspended load.

Figure III－4

#

1

2

3

Setting dialog box of vegetation conditions

Table III－4
Items

Explanation of setting of vegetation conditions
Setting methodElse
If vegetation is considered, [Enabled] isalwaysselectedin[Vegetation
Density]. Polygons of vegetation
Vegetation Density
regions must be set and the vegetation
density values must be inputted.
If vegetation height is considered,[Enabled] is selected in [Vegetation
Height]. Polygons of vegetation regions
must be set and the vegetation height
Vegetation Heightvalues must be inputted. If [Disabled] isselected in [Vegetation Height], thevegetation height becomes infinity.
Calculation conditions for vegetation
loss due to land erosion. If the land
Vegetation Erosion erodes more than this value from theinitial land surface, the vegetation is
Depthconsidered to have flowed out and thevegetation density is zero.

12III.5 Setting of Obstacle condition
Sets calculation conditions related to obstacles.

Figure III－5#
1

Table III－5
Items
Obstacle

Setting dialog box of obstacle conditions

Explanation of setting of obstacle conditions
Setting methodElse
If obstacles are considered, [Enabled]is selected in [Obstacle] and polygonsof obstacle regions must be set.

13

III.6 Setting of Hot start function
Set hot start function. Note that this function is currently only available for flow only calculations
and for bed deformation analysis with bed load and suspended load.

Figure III－6#

Table III－6
Items

1

Hot start

2

Continue File

Setting dialog box of Hot start function

Explanation of setting of Hot start function
Setting method
Else
When users perform new calculation,please select [New]. When users want
to start the calculation from the end of
the previous calculation, please select[Continue].
In case of continue calculation,please load files in the previous
calculation.

14