# IJEGE-11_BS-Uchida-et-alii

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*DOI: 10.4408/IJEGE.2011-03.B-018*

**THE ROLE OF GRID CELL SIZE, FLOW ROUTING ALGOLITHM**

**AND SPATIAL VARIABILITY OF SOIL DEPTH ON SHALLOW**

**LANDSLIDE PREDICTION**

shallow landslide susceptibility have been developed,

and such models are potentially a powerful way to

evaluate the spatial pattern of shallow landslide sus-

ceptibility (e.g., o

*et alii*, 1985; H

*et*

*alii*, 1990; m

*et alii*, 1998; k

*et alii*, 2002;

*et alii*, 2006; t

*et alii*, 2007).

simplest approaches combines an infinite slope stabil-

ity analysis with a steady-state shallow subsurface

flow model (e.g., o

*et alii*, 1985; m

*et alii*, 1998). Recently, more

have been incorporated into physically based models

predicting the spatial patterns of shallow landslide

susceptibility (e.g., H

*et alii*, 1990; w

*et alii*, 2006; t

*et alii*, 2007).

*et alii*

surface flow into their models, and H

*et alii*

*et alii*(2002) considered the ef-

improving the precision of landslide susceptibility

prediction by the models.

the spatial patterns of many parameters be specified.

**ABSTRACT**

infinite slope stability model to predict the spatial pat-

tern of critical steady-state rainfall required to cause

slope instability. We studied a headwater in the Aratani

River basin, western Japan. To clarify soil depth spa-

tial patterns, we measured soil depth on the hillslope

by using knocking pole tests. We compared two wide-

ly used procedures for determining local slope angle

and upslope contributing area: a single-flow-direction

procedure and an algorithm based on proportioning

flow into two downslope pixels. Further, we examined

the role of the analysis grid cell size on the precision

of landslide prediction. We showed that by choosing

an optimal grid cell size and using an optimal proce-

dure for calculation of the upslope contributing area

and by performing a detailed field survey to determine

soil depth, the precision of landslide susceptibility as-

sessment could be remarkably improved

**K**

**ey**

**words**

**:**shallow landslide, soil depth, physically based*model, grid cell size, procedure for calculation of topogra-*

phic indices

phic indices

**INTRODUCTION**

landslides are likely to occur is key to preventing

debris flow disasters. Since the pioneering work of

*T. UCHIDA, k. TAMURA, & k. AkIYAMA*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

not examine in detail the optimal grid cell size or ups-

lope contributing area calculation to use for assessing

landslide susceptibility.

a physically based model could be improved by (1)

choosing the optimal grid cell size; (2) using the opti-

mal method for calculating topographic index parame-

ter values; and (3) inputting more detailed information

about (a) soil depth and (b) bedrock surface topogra-

phy. Here, we examine these hypotheses by comparing

model results obtained by using grid cell sizes from 5

to 25 m and between two different methods for cal-

culating topographic indexes, and by conducting a de-

tailed field survey to obtain data on soil depth and bed-

rock surface topography and then comparing results

obtained by using bedrock surface topography with

those obtained by using ground surface topography.

**STUDY SITE**

western Hiroshima Mountains, western Japan (Fig.

1). The region is humid and temperate: the mean an-

nual precipitation in this region is around 1700 mm,

and the mean temperature is around 15 °C. The site is

deeply incised and dominated by hillslopes, with no

riparian area. Slope angles range from 20 to 45°, and

the values of such parameters as bedrock topography,

soil depth, soil mechanical parameters, and soil hy-

draulic parameters, have generally been lacking. So,

it can be thought that even though the complex nu-

merical simulation models, most of processes can not

fully described, since the parameters controls these

processes cannot be measured. w

*et alii*

bility analysis with a steady-state shallow subsurface

flow was used as a reasonable approximation of a

shallow landslide occurrence.

by back-calculations or by calibration against past

observed events, which often were represented by

mean values of a limited number of observed data. For

example, although soil depth exerts a first-order con-

trol on shallow landslide potential on steep hillslopes

(e.g., d

*et alii*, 1995; i

a limited number of field measurements (e.g., H

*et alii*, 1990; m

steep, wet, soil-mantled hillslopes, the bedrock sur-

face and not the ground surface topography may be

the most important surface controlling the routing of

mobile water laterally downslope (e.g., f

*et alii*,

surface is also strongly controlled by bedrock surface

topography. Most landslide prediction studies have

used a ground surface digital elevation model (DEM)

to calculate values of parameters used as topographic

indexes, such as local slope angle and upslope con-

tributing area, because information about the bedrock

surface topography is often lacking.

ed to affect the precision of shallow landslide assess-

ment. t

shallow landslide assessment and the optimal grid cell

size in Miozza catchment in north-eastern Italy was 10

m. In addition, researchers have proposed a variety of

procedures as optimal for calculation of upslope con-

tributing area by hydrological models (e.g., t

*Fig. 1 - Topography and soil depth of the Aratani hillslo-*

*pe study site*

**THE ROLE OF GRID CELL SIZE, FLOW ROUTING ALGOLITHM AND SPATIAL VARIABILITY OF SOIL DEPTH**

**ON SHALLOW LANDSLIDE PREDICTION**

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*Φ*is the friction

surface,

*γ*and

*γ*

*w*

saturated water depths, respectively. We assumed that

*γ*

can be described by the equation

*γ*

*s*

*γ*

*t*

be described as

length, and

*k*

*s*

*h ≤ h*, then the critical

steady-state rainfall required to cause shallow landslid-

ing, rc, can be determined with equations 1 through 3

by setting

*FS*= 1, as follows:

*FIELD MEASUREMENTS*

DEM. We also mapped the edges of the shallow land-

slides that occurred in June 1999 during a field survey

(Fig. 1). Soil depth on the Aratani hillslope was meas-

ured with a cone penetrometer (knocking pole test)

with a cone diameter of 25 mm, a weight of 5 kg, and

a fall distance of 50 cm. Nd represents the number of

blows required for 10 cm of penetration. Knocking pole

tests were conducted at intervals of 10–15 m in 2005.

In all, we conducted the tests at 181 points, 16 of which

were on the shallow landslide scars (Fig. 1).

showed that the Nd value of weathered bedrock was

around 20, indicating that a layer with an Nd of less

than 20 can potentially fail, causing a shallow land-

slide. Therefore, in this study we assumed that Nd val-

ues greater than 20 indicated bedrock and we defined

the depth of the layer with Nd < 20 as the soil depth.

by Hiroshima Granite, and the soils are sandy. The site

is covered by secondary forest, predominately Pinus

densiflora. Specific weights of saturated (17.9 kN/m

measured in the laboratory in five undisturbed 100

cm

*et alii*, 2009).

and these landslides triggered many debris flows. Four

of these shallow landslides occurred in the study area.

The landslide scars range from 9 to 15 m in width. The

total rainfall amount and maximum rainfall intensity

of the triggering event were 417 mm and 63 mm/h,

respectively, measured at Uokiri dam (1.4 km north

of Aratani).

flow rate have been conducted on the hillslope since

2003(u

*et alii*, 2009). These hydrometric obser-

surface water flow can be observed at the lower end

of the catchment. Stream water was sensitive to rain-

fall intensities during storm runoff. Groundwater level

and soil pore water pressure measurements showed

that within most of the hillslope area, the soil-bedrock

interface was not commonly saturated between events.

Several monitored large storms produced saturation at

the soil-bedrock interface and the soil pore pressures

were sensitive to the rainfall intensity.

**METHOD**

*THEORY*

ods of o

*et alii*(1985) and m

is small with respect to the length of the slope, as in the

case of our hillslope (e.g., o

*et alii*, 1985; m

*et alii*, 2006). Thus, if saturated depth is less than soil

depth, an infinite slope stability analysis can be used to

compute the factor of safety (FS) as follows:

*T. UCHIDA, k. TAMURA, & k. AkIYAMA*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

used procedures for determining local slope angle and

upslope contributing area, a single-flow-direction pro-

cedure (hereafter referred to as D8; o’C

to as D-infinity; t

one of its eight neighbours, either adjacent or diagonal,

in the direction with steepest downward slope. While,

D-infinity is based on representing flow direction as a

single angle taken as the steepest downward slope on

the eight triangular facets centred at each grid point.

Upslope area is then calculated by proportioning flow

between two downslope pixels according to how close

this flow direction is to the direct angle to the downs-

lope pixel (t

*SOIL MANTLE PARAMETERS*

disturbed soil samples. Soil cohesion was estimated

by using data on both soil depth and topography. We

assumed that if the soil mantle was unsaturated (

*h*

*s*

*=*

larger than 1.0. Therefore, we used equations 1 and

2 to calculate the minimum cohesion, including root

strength, required for all grid cells to remain stable,

excepting one grid cell where the soil was very deep

and the local slope was very steep. We also back-cal-

culated cohesion for each of our test cases (Tab. 1, see

below) as the minimum cohesion required for all grid

cells to remain stable. The calculated cohesion data

are shown in Table 2.

*et alii*(1997) and u

*et alii*(2003) de-

a hand auger. The depth of the layer with Nd < 20 was

almost the same as the depth of the layer that could

be penetrated with a hand auger, so our definition is

consistent with that of a

*et alii*(1997) and

*et alii*(2003).

**DATA PREPARATION**

*TOPOGRAPHY*

pre-landslide surface topography across the landslide

scars on the 1-m DEM. In addition, we made the 5-m

DEM of the ground surface from the 1-m DEM made

using the LiDAR data. Then, we used a Kriging inter-

polation scheme to make a 5-m DEM of the bedrock

surface from a 5-m ground surface DEM and the soil

depth data. Thus, we calculated slope angle and ups-

lope drainage area data sets for both the ground surface

topography and the bedrock surface topography. Also,

we compiled a 5-m-grid soil depth data set by subtract-

ing the bedrock surface elevation from the ground sur-

face elevation at each grid point.

study site, we made DEMs of the bedrock surface to-

pography at three additional grid cell sizes (10, 15, and

25 m) using a Kriging interpolation scheme. We made

4, 9, and 25 datasets for the 10-, 15-, and 25-m DEMs,

respectively (see an example of 10-m DEM in Fig. 2)

so that the same number of elevation data was used to

*Fig. 2 - Schematic illustration of grid cell creation. Cir-*

*cle represents center of grid which has elevation*

*data. Black and white circles in the lower panel*

*represent used and non-used data, respectively.*

*Bold and solid lines in the lower panel represent*

*created 10-m grid and original 5-m grid, respec-*

*tively*

*Tab 1 - Simulated case*

**THE ROLE OF GRID CELL SIZE, FLOW ROUTING ALGOLITHM AND SPATIAL VARIABILITY OF SOIL DEPTH**

**ON SHALLOW LANDSLIDE PREDICTION**

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

We compared differences between detailed and less

detailed soil data and between use of the ground sur-

face instead of the bedrock surface in Cases 1 and 6–8.

We used rc, the critical steady-state rainfall amount, as

an index for assessing shallow landslide susceptibil-

ity. We interpreted grid cells with lower

*r*

*c*

with higher rc to be more stable, because the higher

the rc value was, the less frequent would be the oc-

currence of a rainfall event sufficient to cause shallow

landsliding.

lating the “landslide ratio,” as follow. If the centre

of a given grid cell was inside an observed landslide

polygon, we defined the grid cell as a landslide cell.

We defined the ratio of landslide grid cells to all grid

cells as landslide ratio.

*h*

*s*

*= h*in equation 3 and rearranging,

lows:

*FS*is larger

than 1.0. Therefore, we interpreted such grid cells as

“unconditionally stable” with regard to shallow land-

sliding, and other grid cells as “potentially unstable.”

Then, we calculated landslide ratio for grid cells

which grouped into “unconditionally stable” and “po-

tentially unstable”, respectively.

*r*

*c*

unstable cells. We calculated the landslide ratio and

mean

*r*

*c*

*r*

*c*

*k*

*s*

the simulated

*r*

*c*

the 20

*r*

*c*

ple (e.g., b

*et alii*, 1994; u

*et alii*,

*et*

*alii*(1994) and u

*et alii*(2003), we estimated

*k*

*s*

observed total amount of subsurface flow discharge

and the mean soil pore pressure in the lower part of

the hillslope. Such an estimate can be made assuming

the applicability of Darcy’s law

*Q*

*s*

*dh/dI*is the hydraulic gradient.

We assumed that the

*Q*

*s*

of the site. The hydraulic gradient (

*dh/dI*) of 0.72 was

assumed to be equal to the mean surface gradient in

the hillslope.. The width and the depth of the flux area

were assumed to be equal to the twice of ephemeral

stream length and the observed soil pore water pres-

sure head at the lower part of the hillslope, respective-

ly. Using the hydrometric data of the heaviest rainfall

during the observation period (total rainfall, 236 mm;

maximum rainfall intensity, 53 mm/h), we calculated

Ks of the Aratani hillslope to be 5.2 × 10

measured in the undisturbed 100 cm

*et alii*(2009)

*SIMULATED CASES AND DATA ANALYSIS*

in Table 2. Briefly, we compared the effects of grid

cell size in Cases 1–4 and the effect of the calculation

*Tab 2 - Parameter values*

*T. UCHIDA, k. TAMURA, & k. AkIYAMA*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

*r*

*c*

calculation continuously. We interpreted a clear in-

verse relationship between rc and the landslide ratio

and a large difference in the landslide ratio between

potentially unstable cells and unconditionally stable

cells to demonstrate better model performance.

**RESULTS**

unstable cells was 0.28 (Fig. 3). We observed a clear

inverse relationship between rc and the landslide ratio

(Fig. 4a). These results indicate that the predicted rc

of Case 1 well described landslide locations and the

rainfall amount required to cause shallow landslid-

ing. In the Case 1 simulation result, in at least one

mesh in each landslide scar, rc was smaller than the

observed maximum 1-hour rainfall (63 mm/h) (Fig.

the landslide area.

mained around 0.11, whereas that of potentially unsta-

ble cells was 0.20 (Fig. 3). There was a weak inverse

relationship between rc and the landslide ratio, but the

apparent slope of the relationship was smaller than it

was in Case 1 (Fig. 4b). Further, in Cases 3 (15-m grid

cell) and 4 (25-m grid cell), the landslide ratio differed

between unconditionally stable grid cells (0.10 and

0.11 in Cases 3 and 4, respectively) and potentially

unstable grid cells (0.20 and 0.17, respectively) (Fig.

3). However,

*r*

*c*

*and the landslide ratio did not show a*

grid cells were 0.11 and 0.30, respectively (Fig. 3),

almost the same as those of Case 1. However, there

was no clear inverse relationship between rc and the

landslide ratio (Fig. 4e).

was similar to that of Case 1, so there was a large dif-

ference in the landslide ratio between unconditionally

*F*

*ig. 3 - Landslide ratios and relative ratio (the ratio of*

*potentially unstable landslide ratio to the uncon-*

*ditionally stable landslide ratio)*

*Fig. 4 - Relationship between r*

*c*

*and landslide ratio*

*Fig. 5 - Spatial patter of simulated r*

*c*

*in Case 1*

**THE ROLE OF GRID CELL SIZE, FLOW ROUTING ALGOLITHM AND SPATIAL VARIABILITY OF SOIL DEPTH**

**ON SHALLOW LANDSLIDE PREDICTION**

predicted rc and the landslide ratio was not obtained

when D8 was used, whereas when D-infinity was

used, a clear inverse relationship resulted. Both cal-

culation procedures, however, resulted in a large dif-

ference in the landslide ratio between unconditionally

stable and potentially unstable grid cells.

cells are not affected by the upslope contributing area,

which is determined by the local slope angle, soil

depth, and soil properties, whereas equation 4 shows

that the upslope contributing area does affect the pre-

dicted

*r*

*c*

*.*These results indicate that the effectiveness

area, as reported by t

*et*

*alii*(2004), improves the precision with which shal-

low landslide susceptibility can be determined. D8, in

contrast, can reasonably distinguish between uncon-

ditionally stable and potentially unstable grid cells

because the upslope contributing area does not affect

this determination.

*BEDROCk SURFACE VERSUS GROUND SUR-*

FACE TOPOGRAPHY

FACE TOPOGRAPHY

*et alii*,

tion to be improved by using the bedrock topography

instead of the ground surface topography. However,

predicted rc calculated using the ground surface DEM

(Case 6) was almost the same as that calculated using

the bedrock surface DEM (Case 1). Thus, the differ-

ence between the ground surface and bedrock surface

DEMs had little effect on the precision of landslide

susceptibility prediction. We think it likely therefore

that the difference between these two DEMs is small

on the Aratani hillslope.

*SPATIAL VARBILITY OF SOIL DEPTH*

depth by using averaged depths, grid cells with lower

rc (<20 mm/h) had higher landslide ratios than grid

cells with higher

*r*

*c*

grid cells with higher

*r*

*c*

(Fig. 3). Further, there was a clear inverse relationship

between rc and the landslide ratio, also similar to Case

1 (Fig. 4f).

ment point, the differences in the landslide ratio be-

tween unconditionally stable (0.12 and 0.14 in Cases

7 and 8, respectively) and potentially unstable (0.17

and 0.18) grid cells were small (Fig. 3). Although the

landslide ratio clearly decreased as the predicted rc in-

creased (Figs. 4g and 4h), the landslide ratios of grid

cells with

*r*

*c*

*= 20–30 mm/h were similar to those of*

ratios of grid cells with

*r*

*c*

**DISCUSSION**

*ROLE OF GRID CELL SIZE*

cell size increased (Fig. 3, Cases 1–4). We observed

an inverse relationship between predicted rc and the

landslide ratio, however, only in Cases 1 (5-m grid)

and 2 (10-m grid), indicating that when a grid cell size

of 15 m or greater is used, the predicted

*r*

*c*

tionally stable. These results suggest that the most ef-

fective grid cell size at this study site is around 5 m.

slide susceptibility using a physically based model,

reported that the optimal grid cell size at their site was

10 m. i

*et alii*(2009) investigated the optimal

tibility by discriminant analysis and reported that it

was strongly controlled by landslide size. Our result

is consistent with these findings, because both the

optimal grid cell size and the landslide size on our

hillslope are smaller than those reported by t

*CALCULATION PROCEDEURE FOR FLOw*

ROUTING

ROUTING

*et alii*(2004) re-

calculating the upslope contributing area. Here we

showed that even when the input data, including the

*T. UCHIDA, k. TAMURA, & k. AkIYAMA*

*et alii*, 1997; f

*et alii*, 2002; t

*et*

*alii*, 2009). Therefore, spatial variability in soil depth is

likely to be important in determining shallow landslide

susceptibility on other steep landscapes.

**CONCLUSIONS**

topography, and the choice of an optimal grid cell size

and topographic index calculation procedure, can im-

prove the precision of shallow landslide susceptibility

assessment. We showed that the choice of an optimal

grid cell size and an optimal procedure for calculat-

ing the upslope contributing area, and a detailed field

survey of soil depth remarkably improves the precision

of landslide susceptibility assessment. Use of a ground

surface DEM instead of a bedrock surface DEM, how-

ever, had little effect on the precision of landslide sus-

ceptibility prediction. These findings indicate that the

existing simple models, if an optimal grid cell size and

procedure for topographic index calculation are cho-

sen and a detailed field survey is conducted, can yield

results useful for landslide susceptibility assessment.

We consider, of course, that improvement of numerical

simulation models is important, but this study shows

that detailed field surveys to clarify the spatial vari-

ability of soil depth and fine-resolution topographic

measurements and hydrometric observations are also

very important to improve the precision of landslide

susceptibility assessment.

for Case 1 and 25 m

on

*r*

*c*

conditionally stable and potentially unstable grid cells

are strongly affected by the soil depth. That is, if the

averaged soil depth was used instead of observed soil

depth, several potentially unstable grid cells predicted

by using observed soil depth were assessed as uncon-

ditionally stable. These results indicate that if we ig-

nore the spatial variability of soil depth, the precision

of distinguishing between unconditionally stable and

potentially unstable grid cells becomes worse.

*Fig. 6 - Relationship between soil depth and r*

*c*

*calculated*

*using parameters for Case 1 and 25 m*

*2*

*/m of ups-*

*lope contributing area*

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