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Estimating the effects of heavy rainfall conditions on shallow landslides using a distributed landslide conceptual model
Physics and Chemistry of the Earth 49 (2012) 44–51
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Estimating the effects of heavy rainfall conditions on shallow landslides using a distributed landslide conceptual model Yasuhiro Shuin a,⇑, Norifumi Hotta b, Masakazu Suzuki b, Ki-ichiro Ogawa c a
Faculty of Agriculture, Utsunomiya University, 350 Mine-cho, Utsunomiya, Tochigi 321-8505, Japan Graduate School of Agricultural and Life Sciences, University of Tokyo, 1-1-1,Yayoi, Bunkyo-ku, Tokyo 113-8657, Japan c Asia Air Survey Co., Ltd., 1-2-2,Manpukuji, Aso-ku, Kawasaki, Kanagawa 215-0004, Japan b
a r t i c l e
i n f o
Article history: Available online 21 June 2011 Keywords: Distributed landslide conceptual model Effective soil cohesion Heavy rainfall Sediment-related disaster
a b s t r a c t This study used a distributed landslide conceptual model to examine the effects of variable, heavy-rainfall conditions on shallow landslides. A digital terrain model with 50-m resolution was used to calculate the regional potential for shallow landslides based on the distribution of shallow infiltration water, Darcy’s law, and a safety factor estimated by infinite slope stability analysis. The model was applied to the upper Miyagawa River basin at Odai-cho in Mie Prefecture, Japan. In 2004, Typhoon Meari caused severe landslides in areas adjacent to the study area, whereas other heavy-rainfall events in the same year did not cause severe landslides. Response analysis of data collected hourly during heavy-rainfall events revealed that temporal changes in shallow landslide potentials were influenced by both temporal rainfall patterns and effective soil cohesion. Two indices obtained from the model were found to be useful for discriminating between rainstorms with and without sediment-related disasters. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In highly populated and mountainous countries such as Japan, quantifying landslide hazard and other risks associated with heavy rainfall is important. Quantification of the threshold rainfall condition for soft sediment failure is fundamental for the establishment of effective warning and evacuation systems. Broadly, there are three ways in which the rainfall condition can be estimated: using rainfall intensity–duration analysis (I–D method) (Caine, 1980; Guzzetti et al., 2007; Cannon et al., 2008; Dahal and Hasegawa, 2008); using a conceptual model with a function that converts rainfall fluctuations into indices related to soil moisture content (Crozier and Eyles, 1980; Crozier, 1999; Glade et al., 2000); and using a process-based model with indices based on physical soil parameters such as hydraulic conductivity, soil strength, and soil depth (Okimura and Ichikawa, 1985; Montgomery and Dietrich, 1994; Wu and Sidle, 1995; Iverson, 2000; Dhakal and Sidle, 2004). For the I–D method, Caine (1980) was the first to propose the global threshold curve defining the relationship between rainfall duration and intensity based on data from 73 rainfall events worldwide that resulted in shallow landslides and debris flows. Caine’s (1980) threshold curve equation is as follows:
I ¼ 14:82D0:39 ⇑ Corresponding author. E-mail address: [email protected] (Y. Shuin). 1474-7065/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.pce.2011.06.002
ð1Þ
where D is rainfall duration in hours and I is the mean rainfall intensity in millimetres per hour. The development of this method of analysis is recognised as a landmark in the field, and since Caine’s (1980) work, many researchers have proposed rainfall I–D threshold curves based on data from other sites and regions (Larsen and Simon, 1993; Chen-Yuan et al., 2005; Guzzetti et al., 2007). However, the I–D method does not provide information on the effects of antecedent soil moisture on landslide initiation during rainfall events. Thus, Crozier and Eyles (1980) and Crozier (1999) proposed the conceptual antecedent soil water status (ASWS) model as a means by which estimated antecedent soil moisture may be related to landslide occurrence on a daily basis. Their results showed that this model was able to discriminate between days with landslides and days without landslides during 1974 in Wellington, New Zealand. Although Glade et al. (2000) modified the ASWS model and confirmed its usefulness on a regional scale, elaborative model parameterisation based on a larger regional data set is still needed. Moreover, this method does not provide information on other regions with different types of land use. The process-based model uses a combination of water infiltration and slope stability analysis to predict the time, location, and magnitude of a landslide. Various approaches to process-based modelling have been conducted (Okimura and Ichikawa, 1985; Montgomery and Dietrich, 1994; Wu and Sidle, 1995; Iverson, 2000; Dhakal and Sidle, 2004; Tsutsumi and Fujita, 2008) at various spatial scales ranging from slopes to catchments. At the catchment scale, Okimura and Ichikawa (1985) proposed an authentic
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
numerical simulation model that combined digital terrain data with saturated lateral flow and infinite slope stability analysis. They applied their model to a test field (approximately 11 ha) in Gifu Prefecture, Japan, and showed that the model could precisely predict the locations of past shallow landslides. When using a smaller spatial scale, process-based models require more parameters linked to physical soil properties. At the slope scale, Tsutsumi and Fujita (2008) used an elaborate process-based model that could estimate the effect of soil pore size on unsaturated–saturated infiltration and the effects of pipe flow on preferential flow. Their results demonstrated that more accurate prediction of landslide occurrence requires detailed information about subsurface geomorphology, including preferential flow pathways. When using a process-based model at the catchment scale, estimation of the potential hazard area becomes almost impossible because of the difficulty in obtaining detailed spatial information about geomorphology, subsurface soil surfaces, and hydrological and soil characteristics over such a large area. However, using the I–D method or a conceptual model such as the ASWS, it is possible to simulate hazards on a broader spatial scale; such simulation is even more possible with the I–D method, which requires basic information such as past rainfall and landslide occurrences. However, the threshold curve derived from the I–D method does not discriminate between heavy-rainfall events with landslides and those without landslides. In this paper, a process-based model was used as a conceptual, not physical, model. The model was applied to part of the Miyagawa Dam catchment in Mie Prefecture, Japan. This area receives some of the highest amounts of rainfall in Japan, making it particularly suitable for estimating the effects of variable, heavy rainfall conditions on shallow landslide potential. The simulation results were compared with results by the I–D method, and a discriminating method was proposed that optimises the computed effect of variations in heavy rainfall on the potential for shallow landslides.
1979 to 2007 was approximately 3200 mm, and the maximum annual rainfall in 2004 was 5200 mm. 3. Materials and methods 3.1. Topographic and rainfall data A digital terrain model with a 50-m cell resolution was used to model the regional terrain. Rainfall data measured at the automated meteorological data acquisition system (AMeDAS) station in Miyagawa (34°16.70 N, 136°12.50 E) in 2004 were used, with the exception of the period between 28 September and 3 October because of a deficiency of data. During that period, rainfall data from the Miyagawa Dam rain gauge (34°17.60 N, 136°11.60 E) administrated by Mie Prefecture were used. The locations of the two rain gauges are shown in Fig. 1. 3.2. Outline of the analytical procedure Fig. 2 shows a flowchart of the analytical procedure. The outline of the analytical procedure is as follows: 1. Consecutive rainfall in 2004 was divided into individual rainstorms bounded by no-rainfall periods of at least 24 h in duration (i.e., an individual rainstorm was defined as a period of rainfall that was preceded and followed by 24-h periods of no rainfall) (Step 1 in Fig. 2). 2. Heavy-rainfall events were chosen based on the criterion that the rainstorm, 24-h rainfall, or hourly rainfall intensity ranked in the top 10 events for the study period (Step 2). 3. The model results were calculated and displayed using the I–D method and the threshold curve equation (Eq. (1)), and estimations of rainfall properties with and without sediment-related disasters were calculated using the index derived from the I–D method (Steps 3-1, 3-2, and 3-3). 4. The response analysis of the index value of the potential landslide risk induced from the distributed landslide conceptual model was calculated and displayed (Steps 4-1, 42, and 4-3). 5. Rainfall properties with and without sediment-related disasters and the effect of varying rainstorm conditions were estimated using the results of the distributed landslide conceptual model (Step 4-4).
2. Study area The study area (72 km2) is part of the Miyagawa Dam catchment (126 km2) located in the upper Miyagawa River basin at Odai-cho in southern Mie Prefecture, Japan (Fig. 1). The study area is hilly, with gradients ranging from 30° to 50°, and constitutes 68% of the Miyagawa Dam catchment area. Palaeozoic sandstones and slates predominate. Soils range in thickness from tens of centimetres to more than a metre with most soil classified as brown forest soil (Imaizumi and Sidle, 2007). In 2004, Typhoon Meari caused many landslides in the upper Miyagawa River basin. Fig. 1 shows the spatial distribution of the landslides caused by Typhoon Meari. In an aerial photograph taken immediately after the sediment-related disaster, more than 800 landslides were identified in the upper Miyagawa River basin (Nagata et al., 2009). Six people were killed and one went missing in association with landslides in the area adjacent to the study area. In the Miyagawa Dam catchment area, which includes the study area, the landslide area ratio caused by Typhoon Meari was 0.14% (Kuroiwa and Hiramatsu, 2010); rather surprisingly, however, other heavy-rainfall events that year did not cause any landslides. Landslides triggered by heavy-rainfall events in the study area have a large effect on sediment yields, indicating that fluvial systems in the Miyagawa Dam catchment are supply-limited with respect to sediment (Imaizumi and Sidle, 2007). The volume of new deposits in the dam lake supplied by landslides in 2004 was 596,000 m3/year; this value is over seven times the average yearly value from 1958 to 2007, with the exception of 2004 (Kuroiwa and Hiramatsu, 2010). Rainfall over the study area is most abundant from June through the typhoon season in late August to early October. The mean annual rainfall from
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3.3. Distributed landslide conceptual model The model framework, proposed by Okimura and Ichikawa (1985), uses a digital terrain model with a 50-m resolution to calculate the regional potential for shallow landslides. This model was initially proposed to be entirely process-based. However, we used this model as a conceptual, distributed landslide model not linked to any physical parameters. The model consists of a groundwater table calculation and an infinite slope analysis, as described below. 3.3.1. Groundwater table calculations The entire study area consists of a grid of 50 m 50-m unit cells. At each cell unit, an hourly fluctuation in the level of the groundwater table is calculated using Eq. (2) and Darcy’s law, expressed as Eqs. (3) and (4) as follows:
k
@h @qx @qy þ þ ¼r @t @x @y
ð2Þ
where h (m) is the apparent groundwater table above the bedrock, q (m2/h) is the flow volume per unit width of each cell per unit time, r (m/h) is the effective hourly rainfall, which is equivalent to the
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Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
Rain gauge Landslide Miyagawa Dam (MIE pref.) 34 17.6’N, 136 11.6’E
136 E Japan Sea
Miyagawa (AMeDAS) 34 16.7’N, 136 12.5’E 34 N
N
Miyagawa
0
4
Pacific Ocean
8 km
Fig. 1. Map of spatial landslides caused by Typhoon Meari in the Miyagawa upstream area (from Nagata et al., 2009) and the study area (72 km2), which is enclosed by the dashed line.
Division of consecutive rainfall into an individual event
No Heavy Heavy rainfall rainfall
(Step 1)
Yes
(Step 2) Yes (Step 4-1) (Step 3-1)
(Step 3-2)
I-D method
Distributed landslide conceptual model (Step 4-2)
Index of potential landslide risk
Index of potential landslide risk
(Step 3-3)
(Step 4-3)
Estimation of rainfall properties with and without sediment-related disasters
Response analysis with the variation in model parameters (Step 4-4)
Except for analysis data
Estimation of rainfall properties with and without sediment-related disasters Fig. 2. Analytical procedure in this study.
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
hourly rainfall value measured by a rain gauge, and k is the effective porosity of the soil layer. Darcy’s law is given as
qx ¼ hkIx
ð3Þ
qy ¼ hkIy
ð4Þ
where k (m/h) is the hydraulic conductivity and I is the hydraulic gradient. Subscript x indicates groundwater flow in an east–west direction, and subscript y indicates a north–south direction. When calculating the groundwater table using Eqs. (2)–(4), this study used the same assumptions as in Okimura and Ichikawa (1985): 1. The effective hourly rainfall immediately infiltrates the soil profile and reaches the groundwater table. 2. The groundwater table is at the centre of the cell unit. 3. Before any rainstorms occur, the initial conditions of the groundwater tables are set to 0 in all cells. 4. The hydraulic gradient I is identical to the inclination in each cell unit determined from neighbouring grid elevations. 5. The values for hydraulic conductivity k and effective porosity k are set to uniform values for all cells. Similarly, the effective hourly rainfall given to each cell is also the same (not considering the spatial variability in soil properties and rainstorms). 6. The outflow volume from a cell does not exceed the water storage volume at any time. In the case of a summation outflow volume exceeding a storage volume, the storage volume is distributed in each direction as a proportion of the hydraulic gradient of the cell. 3.3.2. Infinite slope analysis To calculate the potential for landslide occurrence in each cell, an infinite slope stability analysis model for natural slopes (Simons et al., 1978) was used (Fig. 3). The safety factor for each cell was determined using Eqs. (5)–(7):
F¼
C total þ A cos2 a tan / B sin a cos a
ð5Þ
A ¼ q0 þ ðcsat cw Þðh zÞ þ ct ðd hÞ
ð6Þ
B ¼ q0 þ csat ðh zÞ þ ct ðd hÞ
ð7Þ
where F is the safety factor, Ctotal is the effective soil cohesion (kPa), / is the soil internal friction angle (°), a is bedrock inclination (de-
47
grees), csat is the saturated unit weight of the soil (kgf/m3), ct is the unit weight of soil (kgf/m3), cw is the unit weight of water (kgf/m3), h is the groundwater table above the bedrock surface (m), d is the depth of regolith above the bedrock surface (m), z is the height of the slip surface above the bedrock surface (m), and q0 is the tree surcharge (kPa). When calculating the safety factor of each cell unit, this study used the same assumptions as in Okimura and Ichikawa (1985): 1. The inclination of the bedrock surface is the same as the inclination of the unit cell. 2. The slip surface appears at the boundary between regolith and bedrock (z = 0). 3. The tree surcharge q0 is zero. 3.3.3. Setting model parameters In the model runs, only effective soil cohesion varied. Other parameters were kept constant or set to adjusted values associated with the effective soil cohesion. The parameters were set in this way because soil cohesion, above all, has the greatest effect on shallow landslide occurrence (e.g. O’Loughlin, 1974; Swanston, 1974; Schmidt et al., 2001; Dhakal and Sidle, 2003). Although variation in regolith depth also has an effect on shallow landslide occurrence (e.g. Okimura, 1989; DeRose et al., 1991; Dietrich et al., 1995), fluctuations in effective soil cohesion occur on a shorter timescale compared with changes in regolith depth. Moreover, effective cohesion is simple to change for various vegetation and land-use types. For model parameters related to soil strength, the angle of internal friction (/) and the range of effective soil cohesion (Ctotal) were set at 30° and 0.5–9.0 kPa (every 0.5 kPa), respectively. The parameters linked to hydraulic properties were set at k = 0.35 and k = 1.8 (m/h). Other parameter values used in this study were ct = 1700 (kgf/m3), csat = 1900 (kgf/m3), and cw = 1000 (kgf/m3). For the regolith depth (d), to stabilise every cell under the condition of no rainfall, the initial safety factors of all cells were set at more than 1.2 by infinite slope analysis. In the case of regolith depth reaching infinite value (e.g. the gradient of a cell was less than the internal friction angle), 1.2 m was set as the maximum value. 4. Results and discussion 4.1. Characteristics of heavy rainstorms in 2004 Consecutive rainfall was divided into 66 rainstorms in 2004; of these events, 13 were heavy-rainfall events selected for the I–D
rainfall
gth en l t i Un
Regolith Regolithdepth depth dd
z ock dr
Be
Height of the slip surface (Z=0)
groundwater table h slope inclination Fig. 3. Infinite slope model for stability analysis.
48
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
Table 1 Characteristics of the 13 heavy rainfall events detected in 2004. ⁄TR: total rainfall amount; R24: 24-h rainfall amount; MHI: maximum hourly rainfall intensity; Event number 53: Typhoon Meari. Event number of rainstorm
TR (mm)
Rank of TR
R24 (mm/24 h)
Rank of R24
MHI (mm/h)
Rank of MHI
Duration (h)
27 30 32 33 39 45 47 52 53 55 56 58 62
90 76 76 431 1200 520 146 87 957 180 455 116 144
10 14 15 5 1 3 7 13 2 6 4 9 8
70 54 76 357 570 275 122 87 892 146 398 80 143
13 16 12 4 2 5 8 9 1 6 3 10 7
8 22 24 60 89 40 19 22 114 14 73 9 17
18 8 6 4 2 5 9 7 1 12 3 17 10
61 41 12 44 168 98 79 12 102 54 42 52 30
20
Mean rainfall intensity (mm/h)
Typhoon Meari (Event 53)
10
DMI 5
Caine’s threshold curve
2
1 10
20
50
100
200
Duration (hours) Fig. 4. Relationships between mean rainfall intensity and duration for the 13 heavy rainstorms. ⁄DMI: difference between mean rainfall intensity in each rainstorm and Caine’s (1980) threshold curve over the same duration.
As shown in Table 2, comparison of DMI indicates that Typhoon Meari ranked second largest when using the I–D method. In this empirical approach, the probability of sediment-related disasters occurring during rainstorms increases with increases in the difference between mean rainfall intensity and the threshold curve. Although the mean intensity and duration derive broadly applicable thresholds for the occurrence of sediment-related disasters, this approach may be insufficient for determining the degree of
method and model simulation. The characteristics of the 13 heavyrainfall events are shown in Table 1. Fig. 4 lists the rainfall events chronologically with mean intensity and duration together with Caine’s (1980) threshold curve. Differences between mean rainfall intensity and Caine’s (1980) threshold curve at the same duration (DMI) are shown in Table 2. Of the 13 selected rainstorms, only Typhoon Meari (Rainstorm 53) caused a severe sediment-related disaster.
Table 2 Difference between mean rainfall intensity and Caine’s (1980) threshold curve over the same duration for 13 detected heavy rainfall events. ⁄MI: mean rainfall intensity; DMI: difference between MI and Caine’s (1980) threshold curve over the same duration; Event number 53: Typhoon Meari. Event number of rainstorm
TR (mm)
Duration (h)
MI (mm/h)
Caine’s threshold (mm/h)
DMI (mm/h)
Rank
27 30 32 33 39 45 47 52 53 55 56 58 62
90 76 76 431 1200 520 146 87 957 180 455 116 144
61 41 12 44 168 98 79 12 102 54 42 52 30
1.48 1.85 6.33 9.80 7.14 5.31 1.85 7.25 9.38 3.33 10.83 2.23 4.80
2.98 3.48 5.62 3.39 2.01 2.48 2.70 5.62 2.44 3.13 3.45 3.17 3.93
1.51 1.63 0.71 6.41 5.13 2.83 0.85 1.63 6.94 0.21 7.38 0.94 0.87
12 13 8 3 4 5 10 6 2 9 1 11 7
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
influence of high-intensity precipitation events on shallow landslides. 4.2. Simulation using the distributed landslide conceptual model
Hourly rainfall (mm/h)
Here, an example of results using the distributed landslide conceptual model is given. Fig. 5 shows the ratio of unstable cells (safety factor <1.0) to total cells (ARU) and the difference in ARU in hour-long time intervals (HRC) within Typhoon Meari (Rainstorm 53), where effective soil cohesion was equal to 8.0 kPa. ARU shows the hourly temporal change. The peak of ARU (PARU in Fig. 5) was 6.5%, and the emerging duration was 13:00–14:00 on 29 September after 3 h emerging duration of maximum hourly rainfall (Fig. 5A). The peak of HRC (PHRC in Fig. 5) was 3.1%/h, and the emerging duration (10:00–11:00 on 29 September) corresponds to that of maximum hourly rainfall (Fig. 5B). The change in PARU varied with the effective soil cohesion and with the difference in the properties of the 13 heavy rainstorms. Fig. 6 shows the results with variation of effective soil cohesion between 0.5 and 9.0 kPa. The maximum, minimum, and average values of the unstable cells/total cells ratio decreases with increases in the value of the effective soil cohesion parameter. Rainstorms 53 and 30 produce the maximum and minimum unstable area ratios, respectively, for all changes in the effective soil cohesion parameter (Fig. 6A). At an effective soil cohesion of 9.0 kPa, none of the rainstorms produces unstable cells. The standard deviations and coefficient of variance of PARU are shown in Fig. 6B. The standard deviations form a convex upward line. Although the standard deviations for the 13 rainstorms are considered to indicate the extent of the effect of rainstorm variability on the area ratio of unstable cells under the same value of effective soil cohesion, the standard deviations do not indicate the normalised differences in the effects of the 13 rainstorms on the unstable cells area ratio under different values of effective soil cohesion because the average peak of the unstable cells area ratio for the 13 rainstorms decreases with the increase in effective soil cohesion as shown in Fig. 6A. Thus, to reveal the normalised effect of rainstorm variability at different values of effective soil cohesion, the relationship between effective soil cohesion and the coefficient of variance for the peak area ratios
150
of unstable cells during the 13 rainstorms was examined. As shown in Fig. 6B, the coefficient of variance values increase with increased effective soil cohesion between 0.5 and 8.0 kPa, but slightly decrease at an effective soil cohesion of 8.5 kPa. Although it is well known that rainstorm influences vary with the effective soil cohesion and that different rainfall conditions result in different peak area ratios of unstable cells, the results of this study indicate that the potential for rainfall characteristics to cause sediment-related disasters varies with changes in the effective soil cohesion parameter. For example, Fig. 7 shows the coefficients of variance for the 13 rainstorms at effective soil cohesion values of 1.0 and 8.0 kPa, expressed as the relationship between the normalised peak area ratio of unstable cells (NPARU, defined as the PARU in each rainstorm divided by the value of Typhoon Meari) and DMI. Differences in NPARU among the 13 rainstorms are not clear at an effective soil cohesion of 1.0 kPa (Fig. 7A). In contrast, at an effective soil cohesion of 8.0 kPa, NPARU increases within the bounds of the positive and negative differences between mean rainfall intensity and Caine’s (1980) threshold, and the difference in NPARU between Typhoon Meari and the other rainstorms is comparatively clear (Fig. 7B). 4.3. Method of estimating rainstorm properties This section examines which rainstorm properties may be effective for discriminating between rainstorms with and without sediment-related disasters. As shown in Figs. 6 and 7, model performance differed with the effective soil cohesion parameter values. Thus, two normalised indices for comparison of different effective soil cohesion parameters were used. One was NPARU, and the other was NPHRC (PHRC in each rainstorm divided by the value for Typhoon Meari). Sediment-related disasters are mostly caused by combinations of long-term rainfall characteristics (e.g. cumulative rainfall) and short-term effects (e.g., hourly rainfall intensity) (e.g. Dhakal and Sidle, 2004; Nakai et al., 2006). The NPARU values are considered to be an index of the characteristics of long-term rainfall, while the NPHRC values are considered to be an index of short-term rainfall effects. Fig. 8 shows the relationships between NPARU and
Typhoon Meari (Event 53)
Maximum of hourly rainfall: 114 mm/h (29 Sep 10:00–11:00)
100 50 0 10 8
ARU (%)
49
Peak of ARU (PARU): 6.5% (29 Sep 13:00–14:00)
A
6 4 2
HRC (%/h)
0 4 3
Peak of HRC (PHRC): 3.1%/h (29 Sep 10:00–11:00)
B
2 1 0 -1 Sep 28
Sep 29
Sep 30
Fig. 5. Temporal change in ARU (A) and HRC (B) for Typhoon Meari with the parameter of effective soil cohesion equal to 8.0 kPa. ⁄ARU, percentage of unstable cells (safety factor <1.0) to total cells; HRC, difference in ARU in hour-long time intervals.
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Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
100
60
A
Standard deviation (%)
PARU (%)
80 60 40 20 0
1.5
B
Standard deviation Coefficient of variance
40
1.0
20
0.5
0.0 10
0 0
2
4
6
8
0
10
Effective soil cohesion (kPa)
2
4
6
Coefficient of variance
maximum Event 53 average minimum Event 30
8
Effective soil cohesion (kPa)
Fig. 6. Model results with variation of effective soil cohesion between 0.5 and 9.0 kPa. Relationships between effective soil cohesion and PARU (A) and between the standard deviation and coefficient variance of PARU (B). ⁄PARU, peak area ratio of unstable cells.
B
Typhoon Meari
Typhoon Meari
1.0
1.0
0.8
0.8
NPARU
NPARU
A
0.6 0.4 0.2 0.0 -2
0.6 0.4 0.2
0
2
4
6
0.0 -2
8
0
2
DMI (mm/h)
4
6
8
DMI (mm/h)
Fig. 7. Relationships between NPARU and DMI with the effective soil cohesion parameter equal to 1.0 kPa (A) and 8.0 kPa (B). ⁄NPARU, normalised value of PARU (i.e., PARU in each rainstorm divided by the value for Typhoon Meari); DMI, difference between mean rainfall intensity and Caine’s (1980) threshold curve over the same duration.
Typhoon Meari 32
NPHRC
B
1.5
53
45 62 52
0.5
1.5 Typhoon Meari
39
1.0
NPHRC
A
30 47
33
1.0
53
56
0.5
55
33 39
58
0.0 0.0
27
56
45
0.0 0.5
1.0
1.5
NPARU
0.0
0.5
1.0
1.5
NPARU
Fig. 8. Relationships between NPARU and NPHRC for the 13 rainstorms with the effective soil cohesion parameter equal to 1.0 kPa (A) and 8.0 kPa (B). ⁄NPHRC, peak of hourly rate change in the unstable cells area ratio divided by the value for Typhoon Meari (Event 53); numbers in the figure correspond to the event numbers shown in Table 1.
NPHRC for the 13 rainstorms with the effective soil cohesion parameter equal to 1.0 kPa (Fig. 8A) and 8.0 kPa (Fig. 8B). In Fig. 8, to clarify the difference in model performance between effective soil cohesion parameters of 1.0 and 8.0 kPa, a straight dotted line (gradient, 1.0; intercept, 1.5) was drawn. With the exception of Typhoon Meari (Rainstorm 53), none of the heavy rainstorms in 2004 caused a severe sediment-related disaster. The difference between Typhoon Meari and other heavy rainstorms is relatively clear at an effective soil cohesion of 8.0 kPa compared with the model performance at an effective soil cohesion of 1.0 kPa. In detail, with the parameter of effective soil cohesion
equal to 1.0 kPa, two rainstorms (33 and 62) are located nearly on the straight dotted line, and four rainstorms (32, 39, 45, and 53) are located over the line. In contrast, at an effective soil cohesion of 8.0 kPa, only Typhoon Meari (Rainstorm 53) is located over the line, and other rainstorms are shifted under the line. Although the straight dotted line is not the critical threshold line, these results indicate that sediment-related disasters are determined by the interaction between rainfall characteristics and soil strength. Furthermore, the two indices produced by the distributed landslide conceptual model may allow for clear discrimination between rainstorms with and without sediment-related disasters and may
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
contribute to the determination of a critical threshold line with accumulation of case studies related to heavy rainstorm- and sediment-related disasters.
5. Conclusions In this study, a method to discriminate the characteristics that identify heavy rain events with and without sediment-related disasters was examined across a wide area in Japan. The conclusions of this study are summarised as follows: 1. Comparison between a rainstorm with a sediment-related disaster and another rainstorm without a sediment-related disaster using the relationship between the mean intensity and duration of rainfall is insufficient for discriminating differences in rainstorm characteristics. 2. A distributed landslide conceptual model consisting of a water infiltration process and infinite slope analysis indicated that variation in the parameter of effective soil cohesion led to variation in the potential of a heavy rain event to cause landslides. Differences in the effects of rainstorms are clear with increased effective soil cohesion. 3. Two indices were obtained from the model calculations: the peak area ratio of unstable cells and the peak hourly rate of change in the area ratio of unstable cells. These indices are effective for discriminating between rainstorms with and without sediment-related disasters over a wide area. To predict the location, timing, and extent of sediment-related disasters, a process-based model based on rigorous physical processes would undoubtedly be very useful. However, limitations exist in process-based modelling, such as in developing a rigorous physical model and in acquiring input data to apply the model over a wide area. Thus, in this study a process-based model was used as a conceptual model, not as a physical model. The study results will contribute to the prediction and mitigation of sediment-related disasters caused by heavy rain events. Acknowledgments This research was partly supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan; a Grant-in-Aid for Scientific Research (C) No. 19580161; and the SABO Technical Center, Japan. References Caine, N., 1980. The rainfall intensity–duration control of shallow landslides and debris flows. Geogr. Ann. Ser. A. Phys. Geogr. 62, 23–27. Cannon, S., Gartner, J., Wilson, R., Bowers, J., Laber, J., 2008. Storm rainfall conditions for floods and debris flows from recently burned areas in southwestern Colorado and southern California. Geomorphology 96, 250–269.
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Chen-Yuan, C., Tien-Chien, C., Fan-Chien, Y., Wen-Hui, Y., Chun-Chieh, T., 2005. Rainfall duration and debris-flow initiated studies for real-time monitoring. Environ. Geol. 47, 715–724. Crozier, M.J., 1999. Prediction of rainfall-triggered landslides: a test of the antecedent water status model. Earth Surf. Process. Landforms 24, 825–833. Crozier, M.J., Eyles, R.J., 1980. Assessing the probability of rapid mass movement. In: Technical Groups (Eds.), Proceedings of the 3rd Australia–New Zealand Conference on Geomechanics, Wellington, vol. 6. New Zealand Institution of Engineers, Wellington, pp. 2.47–2.51. Dahal, R., Hasegawa, S., 2008. Representative rainfall thresholds for landslides in the Nepal Himalaya. Geomorphology 100, 429–443. DeRose, R.C., Trustrum, N.A., Blascke, P.M., 1991. Geomorphic change implied by regolith–slope relationships on steepland hillslopes, Taranak, New Zealand. Catena 18, 489–514. Dhakal, A.S., Sidle, R.C., 2003. Long-term modeling of landslides for different management practices. Earth Surf. Process. Landforms 28, 853–868. Dhakal, A.S., Sidle, R.C., 2004. Distributed simulations of landslides for different rainfall conditions. Hydrol. Process. 18, 757–776. Dietrich, W.E., Reiss, R., Hsu, M.-L., Montgomery, D.R., 1995. A process-based model for colluvial soil depth and shallow landsliding using digital elevation data. Hydrol. Process. 9, 383–400. Glade, T., Crozier, M.J., Smith, P., 2000. Applying probability determination to refine landslide-triggering rainfall thresholds using an empirical ‘‘Antecedent Daily Rainfall Model’’. Pure Appl. Geophys. 157, 1059–1079. Guzzetti, F., Peruccacci, S., Rossi, M., Stark, C.P., 2007. Rainfall thresholds for the initiation of landslides in central and southern Europe. Meteorol. Atmos. Phys. 98, 239–267. Imaizumi, F., Sidle, R.C., 2007. Linkage of sediment supply and transport processes in Miyagawa Dam catchment, Japan. J. Geophys. Res. 112, F03012. doi:10.1029/ 2006 JF000495. Iverson, R.M., 2000. Landslide triggering by rain infiltration. Water Resour. Res. 36, 1897–1910. Kuroiwa, C., Hiramatsu, S., 2010. Study on hillside landslides caused by typhoon T0421 in Miyagawa-Dam basin, Mie prefecture (in Japanese with English abstract). J. Jpn. Soc. Erosion Control Eng. 63 (4), 16–21. Larsen, M., Simon, A., 1993. A rainfall intensity–duration threshold for landslides in a humid-tropical environment, Puerto Rico. Geogr. Ann. Ser. A. Phys. Geogr. 75, 13–23. Montgomery, D.R., Dietrich, W.E., 1994. A physically based model for the topographic control on shallow landsliding. Water Resour. Res. 30, 1153–1171. Nagata, H., Inuma, T., Hagiwara, Y., 2009. Topographical and subsurface geological characteristics of surface failures induced by heavy rainfall of the Typhoon Meari (No. 0421) at Miyagawa Village, Mie Prefecture, Japan (literature in Japanese). J. Jpn. Landslide Soc. 46 (3), 49–55. Nakai, S., Sasaki, S., Kaibori, M., Moriwaki, T., 2006. Rainfall index for warning and evacuation against sediment-related disaster: reexamination of rainfall index Rf and proposal of R0 . Soils Found. 46, 465–475. Okimura, T., 1989. Prediction of slope failure using the estimated depth of potential failure layer. J. Nat. Disaster Sci. 11, 67–89. Okimura, T., Ichikawa, R., 1985. A prediction method for surface failures by movements of infiltrated water in surface soil layer. J. Nat. Disaster Sci. 7, 41–51. O’Loughlin, C.L., 1974. The effect of timber removal on the stability of forest soil. J. Hydrol. (NZ) 13, 121–134. Schmidt, K.M., Roering, J.J., Stock, J.D., Dietrich, W.E., Montgomery, D.R., Schaub, T., 2001. The variability of root cohesion as an influence on shallow landslide susceptibility in the oregon coast range. Can. Geotech. J. 38, 995–1024. Simons, D.R., Li, M.M., Ward, T.J., 1978. Mapping of potential landslide areas in terms of slope stability. USDA Forest Service, Rocky Mountain Forest and Range Experiment Station, 75 pp. Swanston, D.N., 1974. Slope stability problems associated with timber harvesting in mountainous regions of the western United States. USDA Forest Service General Technical Report pnw-21, 14 pp. Tsutsumi, D., Fujita, M., 2008. Relative importance of slope material properties and timing of rainfall for the occurrence of landslides. Int. J. Erosion Control Eng. 1, 79–89. Wu, W., Sidle, R.C., 1995. A distributed slope stability model for steep forested hillslopes. Water Resour. Res. 31, 2097–2110.
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Physics and Chemistry of the Earth journal homepage: www.elsevier.com/locate/pce
Estimating the effects of heavy rainfall conditions on shallow landslides using a distributed landslide conceptual model Yasuhiro Shuin a,⇑, Norifumi Hotta b, Masakazu Suzuki b, Ki-ichiro Ogawa c a
Faculty of Agriculture, Utsunomiya University, 350 Mine-cho, Utsunomiya, Tochigi 321-8505, Japan Graduate School of Agricultural and Life Sciences, University of Tokyo, 1-1-1,Yayoi, Bunkyo-ku, Tokyo 113-8657, Japan c Asia Air Survey Co., Ltd., 1-2-2,Manpukuji, Aso-ku, Kawasaki, Kanagawa 215-0004, Japan b
a r t i c l e
i n f o
Article history: Available online 21 June 2011 Keywords: Distributed landslide conceptual model Effective soil cohesion Heavy rainfall Sediment-related disaster
a b s t r a c t This study used a distributed landslide conceptual model to examine the effects of variable, heavy-rainfall conditions on shallow landslides. A digital terrain model with 50-m resolution was used to calculate the regional potential for shallow landslides based on the distribution of shallow infiltration water, Darcy’s law, and a safety factor estimated by infinite slope stability analysis. The model was applied to the upper Miyagawa River basin at Odai-cho in Mie Prefecture, Japan. In 2004, Typhoon Meari caused severe landslides in areas adjacent to the study area, whereas other heavy-rainfall events in the same year did not cause severe landslides. Response analysis of data collected hourly during heavy-rainfall events revealed that temporal changes in shallow landslide potentials were influenced by both temporal rainfall patterns and effective soil cohesion. Two indices obtained from the model were found to be useful for discriminating between rainstorms with and without sediment-related disasters. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In highly populated and mountainous countries such as Japan, quantifying landslide hazard and other risks associated with heavy rainfall is important. Quantification of the threshold rainfall condition for soft sediment failure is fundamental for the establishment of effective warning and evacuation systems. Broadly, there are three ways in which the rainfall condition can be estimated: using rainfall intensity–duration analysis (I–D method) (Caine, 1980; Guzzetti et al., 2007; Cannon et al., 2008; Dahal and Hasegawa, 2008); using a conceptual model with a function that converts rainfall fluctuations into indices related to soil moisture content (Crozier and Eyles, 1980; Crozier, 1999; Glade et al., 2000); and using a process-based model with indices based on physical soil parameters such as hydraulic conductivity, soil strength, and soil depth (Okimura and Ichikawa, 1985; Montgomery and Dietrich, 1994; Wu and Sidle, 1995; Iverson, 2000; Dhakal and Sidle, 2004). For the I–D method, Caine (1980) was the first to propose the global threshold curve defining the relationship between rainfall duration and intensity based on data from 73 rainfall events worldwide that resulted in shallow landslides and debris flows. Caine’s (1980) threshold curve equation is as follows:
I ¼ 14:82D0:39 ⇑ Corresponding author. E-mail address: [email protected] (Y. Shuin). 1474-7065/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.pce.2011.06.002
ð1Þ
where D is rainfall duration in hours and I is the mean rainfall intensity in millimetres per hour. The development of this method of analysis is recognised as a landmark in the field, and since Caine’s (1980) work, many researchers have proposed rainfall I–D threshold curves based on data from other sites and regions (Larsen and Simon, 1993; Chen-Yuan et al., 2005; Guzzetti et al., 2007). However, the I–D method does not provide information on the effects of antecedent soil moisture on landslide initiation during rainfall events. Thus, Crozier and Eyles (1980) and Crozier (1999) proposed the conceptual antecedent soil water status (ASWS) model as a means by which estimated antecedent soil moisture may be related to landslide occurrence on a daily basis. Their results showed that this model was able to discriminate between days with landslides and days without landslides during 1974 in Wellington, New Zealand. Although Glade et al. (2000) modified the ASWS model and confirmed its usefulness on a regional scale, elaborative model parameterisation based on a larger regional data set is still needed. Moreover, this method does not provide information on other regions with different types of land use. The process-based model uses a combination of water infiltration and slope stability analysis to predict the time, location, and magnitude of a landslide. Various approaches to process-based modelling have been conducted (Okimura and Ichikawa, 1985; Montgomery and Dietrich, 1994; Wu and Sidle, 1995; Iverson, 2000; Dhakal and Sidle, 2004; Tsutsumi and Fujita, 2008) at various spatial scales ranging from slopes to catchments. At the catchment scale, Okimura and Ichikawa (1985) proposed an authentic
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
numerical simulation model that combined digital terrain data with saturated lateral flow and infinite slope stability analysis. They applied their model to a test field (approximately 11 ha) in Gifu Prefecture, Japan, and showed that the model could precisely predict the locations of past shallow landslides. When using a smaller spatial scale, process-based models require more parameters linked to physical soil properties. At the slope scale, Tsutsumi and Fujita (2008) used an elaborate process-based model that could estimate the effect of soil pore size on unsaturated–saturated infiltration and the effects of pipe flow on preferential flow. Their results demonstrated that more accurate prediction of landslide occurrence requires detailed information about subsurface geomorphology, including preferential flow pathways. When using a process-based model at the catchment scale, estimation of the potential hazard area becomes almost impossible because of the difficulty in obtaining detailed spatial information about geomorphology, subsurface soil surfaces, and hydrological and soil characteristics over such a large area. However, using the I–D method or a conceptual model such as the ASWS, it is possible to simulate hazards on a broader spatial scale; such simulation is even more possible with the I–D method, which requires basic information such as past rainfall and landslide occurrences. However, the threshold curve derived from the I–D method does not discriminate between heavy-rainfall events with landslides and those without landslides. In this paper, a process-based model was used as a conceptual, not physical, model. The model was applied to part of the Miyagawa Dam catchment in Mie Prefecture, Japan. This area receives some of the highest amounts of rainfall in Japan, making it particularly suitable for estimating the effects of variable, heavy rainfall conditions on shallow landslide potential. The simulation results were compared with results by the I–D method, and a discriminating method was proposed that optimises the computed effect of variations in heavy rainfall on the potential for shallow landslides.
1979 to 2007 was approximately 3200 mm, and the maximum annual rainfall in 2004 was 5200 mm. 3. Materials and methods 3.1. Topographic and rainfall data A digital terrain model with a 50-m cell resolution was used to model the regional terrain. Rainfall data measured at the automated meteorological data acquisition system (AMeDAS) station in Miyagawa (34°16.70 N, 136°12.50 E) in 2004 were used, with the exception of the period between 28 September and 3 October because of a deficiency of data. During that period, rainfall data from the Miyagawa Dam rain gauge (34°17.60 N, 136°11.60 E) administrated by Mie Prefecture were used. The locations of the two rain gauges are shown in Fig. 1. 3.2. Outline of the analytical procedure Fig. 2 shows a flowchart of the analytical procedure. The outline of the analytical procedure is as follows: 1. Consecutive rainfall in 2004 was divided into individual rainstorms bounded by no-rainfall periods of at least 24 h in duration (i.e., an individual rainstorm was defined as a period of rainfall that was preceded and followed by 24-h periods of no rainfall) (Step 1 in Fig. 2). 2. Heavy-rainfall events were chosen based on the criterion that the rainstorm, 24-h rainfall, or hourly rainfall intensity ranked in the top 10 events for the study period (Step 2). 3. The model results were calculated and displayed using the I–D method and the threshold curve equation (Eq. (1)), and estimations of rainfall properties with and without sediment-related disasters were calculated using the index derived from the I–D method (Steps 3-1, 3-2, and 3-3). 4. The response analysis of the index value of the potential landslide risk induced from the distributed landslide conceptual model was calculated and displayed (Steps 4-1, 42, and 4-3). 5. Rainfall properties with and without sediment-related disasters and the effect of varying rainstorm conditions were estimated using the results of the distributed landslide conceptual model (Step 4-4).
2. Study area The study area (72 km2) is part of the Miyagawa Dam catchment (126 km2) located in the upper Miyagawa River basin at Odai-cho in southern Mie Prefecture, Japan (Fig. 1). The study area is hilly, with gradients ranging from 30° to 50°, and constitutes 68% of the Miyagawa Dam catchment area. Palaeozoic sandstones and slates predominate. Soils range in thickness from tens of centimetres to more than a metre with most soil classified as brown forest soil (Imaizumi and Sidle, 2007). In 2004, Typhoon Meari caused many landslides in the upper Miyagawa River basin. Fig. 1 shows the spatial distribution of the landslides caused by Typhoon Meari. In an aerial photograph taken immediately after the sediment-related disaster, more than 800 landslides were identified in the upper Miyagawa River basin (Nagata et al., 2009). Six people were killed and one went missing in association with landslides in the area adjacent to the study area. In the Miyagawa Dam catchment area, which includes the study area, the landslide area ratio caused by Typhoon Meari was 0.14% (Kuroiwa and Hiramatsu, 2010); rather surprisingly, however, other heavy-rainfall events that year did not cause any landslides. Landslides triggered by heavy-rainfall events in the study area have a large effect on sediment yields, indicating that fluvial systems in the Miyagawa Dam catchment are supply-limited with respect to sediment (Imaizumi and Sidle, 2007). The volume of new deposits in the dam lake supplied by landslides in 2004 was 596,000 m3/year; this value is over seven times the average yearly value from 1958 to 2007, with the exception of 2004 (Kuroiwa and Hiramatsu, 2010). Rainfall over the study area is most abundant from June through the typhoon season in late August to early October. The mean annual rainfall from
45
3.3. Distributed landslide conceptual model The model framework, proposed by Okimura and Ichikawa (1985), uses a digital terrain model with a 50-m resolution to calculate the regional potential for shallow landslides. This model was initially proposed to be entirely process-based. However, we used this model as a conceptual, distributed landslide model not linked to any physical parameters. The model consists of a groundwater table calculation and an infinite slope analysis, as described below. 3.3.1. Groundwater table calculations The entire study area consists of a grid of 50 m 50-m unit cells. At each cell unit, an hourly fluctuation in the level of the groundwater table is calculated using Eq. (2) and Darcy’s law, expressed as Eqs. (3) and (4) as follows:
k
@h @qx @qy þ þ ¼r @t @x @y
ð2Þ
where h (m) is the apparent groundwater table above the bedrock, q (m2/h) is the flow volume per unit width of each cell per unit time, r (m/h) is the effective hourly rainfall, which is equivalent to the
46
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
Rain gauge Landslide Miyagawa Dam (MIE pref.) 34 17.6’N, 136 11.6’E
136 E Japan Sea
Miyagawa (AMeDAS) 34 16.7’N, 136 12.5’E 34 N
N
Miyagawa
0
4
Pacific Ocean
8 km
Fig. 1. Map of spatial landslides caused by Typhoon Meari in the Miyagawa upstream area (from Nagata et al., 2009) and the study area (72 km2), which is enclosed by the dashed line.
Division of consecutive rainfall into an individual event
No Heavy Heavy rainfall rainfall
(Step 1)
Yes
(Step 2) Yes (Step 4-1) (Step 3-1)
(Step 3-2)
I-D method
Distributed landslide conceptual model (Step 4-2)
Index of potential landslide risk
Index of potential landslide risk
(Step 3-3)
(Step 4-3)
Estimation of rainfall properties with and without sediment-related disasters
Response analysis with the variation in model parameters (Step 4-4)
Except for analysis data
Estimation of rainfall properties with and without sediment-related disasters Fig. 2. Analytical procedure in this study.
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
hourly rainfall value measured by a rain gauge, and k is the effective porosity of the soil layer. Darcy’s law is given as
qx ¼ hkIx
ð3Þ
qy ¼ hkIy
ð4Þ
where k (m/h) is the hydraulic conductivity and I is the hydraulic gradient. Subscript x indicates groundwater flow in an east–west direction, and subscript y indicates a north–south direction. When calculating the groundwater table using Eqs. (2)–(4), this study used the same assumptions as in Okimura and Ichikawa (1985): 1. The effective hourly rainfall immediately infiltrates the soil profile and reaches the groundwater table. 2. The groundwater table is at the centre of the cell unit. 3. Before any rainstorms occur, the initial conditions of the groundwater tables are set to 0 in all cells. 4. The hydraulic gradient I is identical to the inclination in each cell unit determined from neighbouring grid elevations. 5. The values for hydraulic conductivity k and effective porosity k are set to uniform values for all cells. Similarly, the effective hourly rainfall given to each cell is also the same (not considering the spatial variability in soil properties and rainstorms). 6. The outflow volume from a cell does not exceed the water storage volume at any time. In the case of a summation outflow volume exceeding a storage volume, the storage volume is distributed in each direction as a proportion of the hydraulic gradient of the cell. 3.3.2. Infinite slope analysis To calculate the potential for landslide occurrence in each cell, an infinite slope stability analysis model for natural slopes (Simons et al., 1978) was used (Fig. 3). The safety factor for each cell was determined using Eqs. (5)–(7):
F¼
C total þ A cos2 a tan / B sin a cos a
ð5Þ
A ¼ q0 þ ðcsat cw Þðh zÞ þ ct ðd hÞ
ð6Þ
B ¼ q0 þ csat ðh zÞ þ ct ðd hÞ
ð7Þ
where F is the safety factor, Ctotal is the effective soil cohesion (kPa), / is the soil internal friction angle (°), a is bedrock inclination (de-
47
grees), csat is the saturated unit weight of the soil (kgf/m3), ct is the unit weight of soil (kgf/m3), cw is the unit weight of water (kgf/m3), h is the groundwater table above the bedrock surface (m), d is the depth of regolith above the bedrock surface (m), z is the height of the slip surface above the bedrock surface (m), and q0 is the tree surcharge (kPa). When calculating the safety factor of each cell unit, this study used the same assumptions as in Okimura and Ichikawa (1985): 1. The inclination of the bedrock surface is the same as the inclination of the unit cell. 2. The slip surface appears at the boundary between regolith and bedrock (z = 0). 3. The tree surcharge q0 is zero. 3.3.3. Setting model parameters In the model runs, only effective soil cohesion varied. Other parameters were kept constant or set to adjusted values associated with the effective soil cohesion. The parameters were set in this way because soil cohesion, above all, has the greatest effect on shallow landslide occurrence (e.g. O’Loughlin, 1974; Swanston, 1974; Schmidt et al., 2001; Dhakal and Sidle, 2003). Although variation in regolith depth also has an effect on shallow landslide occurrence (e.g. Okimura, 1989; DeRose et al., 1991; Dietrich et al., 1995), fluctuations in effective soil cohesion occur on a shorter timescale compared with changes in regolith depth. Moreover, effective cohesion is simple to change for various vegetation and land-use types. For model parameters related to soil strength, the angle of internal friction (/) and the range of effective soil cohesion (Ctotal) were set at 30° and 0.5–9.0 kPa (every 0.5 kPa), respectively. The parameters linked to hydraulic properties were set at k = 0.35 and k = 1.8 (m/h). Other parameter values used in this study were ct = 1700 (kgf/m3), csat = 1900 (kgf/m3), and cw = 1000 (kgf/m3). For the regolith depth (d), to stabilise every cell under the condition of no rainfall, the initial safety factors of all cells were set at more than 1.2 by infinite slope analysis. In the case of regolith depth reaching infinite value (e.g. the gradient of a cell was less than the internal friction angle), 1.2 m was set as the maximum value. 4. Results and discussion 4.1. Characteristics of heavy rainstorms in 2004 Consecutive rainfall was divided into 66 rainstorms in 2004; of these events, 13 were heavy-rainfall events selected for the I–D
rainfall
gth en l t i Un
Regolith Regolithdepth depth dd
z ock dr
Be
Height of the slip surface (Z=0)
groundwater table h slope inclination Fig. 3. Infinite slope model for stability analysis.
48
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
Table 1 Characteristics of the 13 heavy rainfall events detected in 2004. ⁄TR: total rainfall amount; R24: 24-h rainfall amount; MHI: maximum hourly rainfall intensity; Event number 53: Typhoon Meari. Event number of rainstorm
TR (mm)
Rank of TR
R24 (mm/24 h)
Rank of R24
MHI (mm/h)
Rank of MHI
Duration (h)
27 30 32 33 39 45 47 52 53 55 56 58 62
90 76 76 431 1200 520 146 87 957 180 455 116 144
10 14 15 5 1 3 7 13 2 6 4 9 8
70 54 76 357 570 275 122 87 892 146 398 80 143
13 16 12 4 2 5 8 9 1 6 3 10 7
8 22 24 60 89 40 19 22 114 14 73 9 17
18 8 6 4 2 5 9 7 1 12 3 17 10
61 41 12 44 168 98 79 12 102 54 42 52 30
20
Mean rainfall intensity (mm/h)
Typhoon Meari (Event 53)
10
DMI 5
Caine’s threshold curve
2
1 10
20
50
100
200
Duration (hours) Fig. 4. Relationships between mean rainfall intensity and duration for the 13 heavy rainstorms. ⁄DMI: difference between mean rainfall intensity in each rainstorm and Caine’s (1980) threshold curve over the same duration.
As shown in Table 2, comparison of DMI indicates that Typhoon Meari ranked second largest when using the I–D method. In this empirical approach, the probability of sediment-related disasters occurring during rainstorms increases with increases in the difference between mean rainfall intensity and the threshold curve. Although the mean intensity and duration derive broadly applicable thresholds for the occurrence of sediment-related disasters, this approach may be insufficient for determining the degree of
method and model simulation. The characteristics of the 13 heavyrainfall events are shown in Table 1. Fig. 4 lists the rainfall events chronologically with mean intensity and duration together with Caine’s (1980) threshold curve. Differences between mean rainfall intensity and Caine’s (1980) threshold curve at the same duration (DMI) are shown in Table 2. Of the 13 selected rainstorms, only Typhoon Meari (Rainstorm 53) caused a severe sediment-related disaster.
Table 2 Difference between mean rainfall intensity and Caine’s (1980) threshold curve over the same duration for 13 detected heavy rainfall events. ⁄MI: mean rainfall intensity; DMI: difference between MI and Caine’s (1980) threshold curve over the same duration; Event number 53: Typhoon Meari. Event number of rainstorm
TR (mm)
Duration (h)
MI (mm/h)
Caine’s threshold (mm/h)
DMI (mm/h)
Rank
27 30 32 33 39 45 47 52 53 55 56 58 62
90 76 76 431 1200 520 146 87 957 180 455 116 144
61 41 12 44 168 98 79 12 102 54 42 52 30
1.48 1.85 6.33 9.80 7.14 5.31 1.85 7.25 9.38 3.33 10.83 2.23 4.80
2.98 3.48 5.62 3.39 2.01 2.48 2.70 5.62 2.44 3.13 3.45 3.17 3.93
1.51 1.63 0.71 6.41 5.13 2.83 0.85 1.63 6.94 0.21 7.38 0.94 0.87
12 13 8 3 4 5 10 6 2 9 1 11 7
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
influence of high-intensity precipitation events on shallow landslides. 4.2. Simulation using the distributed landslide conceptual model
Hourly rainfall (mm/h)
Here, an example of results using the distributed landslide conceptual model is given. Fig. 5 shows the ratio of unstable cells (safety factor <1.0) to total cells (ARU) and the difference in ARU in hour-long time intervals (HRC) within Typhoon Meari (Rainstorm 53), where effective soil cohesion was equal to 8.0 kPa. ARU shows the hourly temporal change. The peak of ARU (PARU in Fig. 5) was 6.5%, and the emerging duration was 13:00–14:00 on 29 September after 3 h emerging duration of maximum hourly rainfall (Fig. 5A). The peak of HRC (PHRC in Fig. 5) was 3.1%/h, and the emerging duration (10:00–11:00 on 29 September) corresponds to that of maximum hourly rainfall (Fig. 5B). The change in PARU varied with the effective soil cohesion and with the difference in the properties of the 13 heavy rainstorms. Fig. 6 shows the results with variation of effective soil cohesion between 0.5 and 9.0 kPa. The maximum, minimum, and average values of the unstable cells/total cells ratio decreases with increases in the value of the effective soil cohesion parameter. Rainstorms 53 and 30 produce the maximum and minimum unstable area ratios, respectively, for all changes in the effective soil cohesion parameter (Fig. 6A). At an effective soil cohesion of 9.0 kPa, none of the rainstorms produces unstable cells. The standard deviations and coefficient of variance of PARU are shown in Fig. 6B. The standard deviations form a convex upward line. Although the standard deviations for the 13 rainstorms are considered to indicate the extent of the effect of rainstorm variability on the area ratio of unstable cells under the same value of effective soil cohesion, the standard deviations do not indicate the normalised differences in the effects of the 13 rainstorms on the unstable cells area ratio under different values of effective soil cohesion because the average peak of the unstable cells area ratio for the 13 rainstorms decreases with the increase in effective soil cohesion as shown in Fig. 6A. Thus, to reveal the normalised effect of rainstorm variability at different values of effective soil cohesion, the relationship between effective soil cohesion and the coefficient of variance for the peak area ratios
150
of unstable cells during the 13 rainstorms was examined. As shown in Fig. 6B, the coefficient of variance values increase with increased effective soil cohesion between 0.5 and 8.0 kPa, but slightly decrease at an effective soil cohesion of 8.5 kPa. Although it is well known that rainstorm influences vary with the effective soil cohesion and that different rainfall conditions result in different peak area ratios of unstable cells, the results of this study indicate that the potential for rainfall characteristics to cause sediment-related disasters varies with changes in the effective soil cohesion parameter. For example, Fig. 7 shows the coefficients of variance for the 13 rainstorms at effective soil cohesion values of 1.0 and 8.0 kPa, expressed as the relationship between the normalised peak area ratio of unstable cells (NPARU, defined as the PARU in each rainstorm divided by the value of Typhoon Meari) and DMI. Differences in NPARU among the 13 rainstorms are not clear at an effective soil cohesion of 1.0 kPa (Fig. 7A). In contrast, at an effective soil cohesion of 8.0 kPa, NPARU increases within the bounds of the positive and negative differences between mean rainfall intensity and Caine’s (1980) threshold, and the difference in NPARU between Typhoon Meari and the other rainstorms is comparatively clear (Fig. 7B). 4.3. Method of estimating rainstorm properties This section examines which rainstorm properties may be effective for discriminating between rainstorms with and without sediment-related disasters. As shown in Figs. 6 and 7, model performance differed with the effective soil cohesion parameter values. Thus, two normalised indices for comparison of different effective soil cohesion parameters were used. One was NPARU, and the other was NPHRC (PHRC in each rainstorm divided by the value for Typhoon Meari). Sediment-related disasters are mostly caused by combinations of long-term rainfall characteristics (e.g. cumulative rainfall) and short-term effects (e.g., hourly rainfall intensity) (e.g. Dhakal and Sidle, 2004; Nakai et al., 2006). The NPARU values are considered to be an index of the characteristics of long-term rainfall, while the NPHRC values are considered to be an index of short-term rainfall effects. Fig. 8 shows the relationships between NPARU and
Typhoon Meari (Event 53)
Maximum of hourly rainfall: 114 mm/h (29 Sep 10:00–11:00)
100 50 0 10 8
ARU (%)
49
Peak of ARU (PARU): 6.5% (29 Sep 13:00–14:00)
A
6 4 2
HRC (%/h)
0 4 3
Peak of HRC (PHRC): 3.1%/h (29 Sep 10:00–11:00)
B
2 1 0 -1 Sep 28
Sep 29
Sep 30
Fig. 5. Temporal change in ARU (A) and HRC (B) for Typhoon Meari with the parameter of effective soil cohesion equal to 8.0 kPa. ⁄ARU, percentage of unstable cells (safety factor <1.0) to total cells; HRC, difference in ARU in hour-long time intervals.
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Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
100
60
A
Standard deviation (%)
PARU (%)
80 60 40 20 0
1.5
B
Standard deviation Coefficient of variance
40
1.0
20
0.5
0.0 10
0 0
2
4
6
8
0
10
Effective soil cohesion (kPa)
2
4
6
Coefficient of variance
maximum Event 53 average minimum Event 30
8
Effective soil cohesion (kPa)
Fig. 6. Model results with variation of effective soil cohesion between 0.5 and 9.0 kPa. Relationships between effective soil cohesion and PARU (A) and between the standard deviation and coefficient variance of PARU (B). ⁄PARU, peak area ratio of unstable cells.
B
Typhoon Meari
Typhoon Meari
1.0
1.0
0.8
0.8
NPARU
NPARU
A
0.6 0.4 0.2 0.0 -2
0.6 0.4 0.2
0
2
4
6
0.0 -2
8
0
2
DMI (mm/h)
4
6
8
DMI (mm/h)
Fig. 7. Relationships between NPARU and DMI with the effective soil cohesion parameter equal to 1.0 kPa (A) and 8.0 kPa (B). ⁄NPARU, normalised value of PARU (i.e., PARU in each rainstorm divided by the value for Typhoon Meari); DMI, difference between mean rainfall intensity and Caine’s (1980) threshold curve over the same duration.
Typhoon Meari 32
NPHRC
B
1.5
53
45 62 52
0.5
1.5 Typhoon Meari
39
1.0
NPHRC
A
30 47
33
1.0
53
56
0.5
55
33 39
58
0.0 0.0
27
56
45
0.0 0.5
1.0
1.5
NPARU
0.0
0.5
1.0
1.5
NPARU
Fig. 8. Relationships between NPARU and NPHRC for the 13 rainstorms with the effective soil cohesion parameter equal to 1.0 kPa (A) and 8.0 kPa (B). ⁄NPHRC, peak of hourly rate change in the unstable cells area ratio divided by the value for Typhoon Meari (Event 53); numbers in the figure correspond to the event numbers shown in Table 1.
NPHRC for the 13 rainstorms with the effective soil cohesion parameter equal to 1.0 kPa (Fig. 8A) and 8.0 kPa (Fig. 8B). In Fig. 8, to clarify the difference in model performance between effective soil cohesion parameters of 1.0 and 8.0 kPa, a straight dotted line (gradient, 1.0; intercept, 1.5) was drawn. With the exception of Typhoon Meari (Rainstorm 53), none of the heavy rainstorms in 2004 caused a severe sediment-related disaster. The difference between Typhoon Meari and other heavy rainstorms is relatively clear at an effective soil cohesion of 8.0 kPa compared with the model performance at an effective soil cohesion of 1.0 kPa. In detail, with the parameter of effective soil cohesion
equal to 1.0 kPa, two rainstorms (33 and 62) are located nearly on the straight dotted line, and four rainstorms (32, 39, 45, and 53) are located over the line. In contrast, at an effective soil cohesion of 8.0 kPa, only Typhoon Meari (Rainstorm 53) is located over the line, and other rainstorms are shifted under the line. Although the straight dotted line is not the critical threshold line, these results indicate that sediment-related disasters are determined by the interaction between rainfall characteristics and soil strength. Furthermore, the two indices produced by the distributed landslide conceptual model may allow for clear discrimination between rainstorms with and without sediment-related disasters and may
Y. Shuin et al. / Physics and Chemistry of the Earth 49 (2012) 44–51
contribute to the determination of a critical threshold line with accumulation of case studies related to heavy rainstorm- and sediment-related disasters.
5. Conclusions In this study, a method to discriminate the characteristics that identify heavy rain events with and without sediment-related disasters was examined across a wide area in Japan. The conclusions of this study are summarised as follows: 1. Comparison between a rainstorm with a sediment-related disaster and another rainstorm without a sediment-related disaster using the relationship between the mean intensity and duration of rainfall is insufficient for discriminating differences in rainstorm characteristics. 2. A distributed landslide conceptual model consisting of a water infiltration process and infinite slope analysis indicated that variation in the parameter of effective soil cohesion led to variation in the potential of a heavy rain event to cause landslides. Differences in the effects of rainstorms are clear with increased effective soil cohesion. 3. Two indices were obtained from the model calculations: the peak area ratio of unstable cells and the peak hourly rate of change in the area ratio of unstable cells. These indices are effective for discriminating between rainstorms with and without sediment-related disasters over a wide area. To predict the location, timing, and extent of sediment-related disasters, a process-based model based on rigorous physical processes would undoubtedly be very useful. However, limitations exist in process-based modelling, such as in developing a rigorous physical model and in acquiring input data to apply the model over a wide area. Thus, in this study a process-based model was used as a conceptual model, not as a physical model. The study results will contribute to the prediction and mitigation of sediment-related disasters caused by heavy rain events. Acknowledgments This research was partly supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan; a Grant-in-Aid for Scientific Research (C) No. 19580161; and the SABO Technical Center, Japan. References Caine, N., 1980. The rainfall intensity–duration control of shallow landslides and debris flows. Geogr. Ann. Ser. A. Phys. Geogr. 62, 23–27. Cannon, S., Gartner, J., Wilson, R., Bowers, J., Laber, J., 2008. Storm rainfall conditions for floods and debris flows from recently burned areas in southwestern Colorado and southern California. Geomorphology 96, 250–269.
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Chen-Yuan, C., Tien-Chien, C., Fan-Chien, Y., Wen-Hui, Y., Chun-Chieh, T., 2005. Rainfall duration and debris-flow initiated studies for real-time monitoring. Environ. Geol. 47, 715–724. Crozier, M.J., 1999. Prediction of rainfall-triggered landslides: a test of the antecedent water status model. Earth Surf. Process. Landforms 24, 825–833. Crozier, M.J., Eyles, R.J., 1980. Assessing the probability of rapid mass movement. In: Technical Groups (Eds.), Proceedings of the 3rd Australia–New Zealand Conference on Geomechanics, Wellington, vol. 6. New Zealand Institution of Engineers, Wellington, pp. 2.47–2.51. Dahal, R., Hasegawa, S., 2008. Representative rainfall thresholds for landslides in the Nepal Himalaya. Geomorphology 100, 429–443. DeRose, R.C., Trustrum, N.A., Blascke, P.M., 1991. Geomorphic change implied by regolith–slope relationships on steepland hillslopes, Taranak, New Zealand. Catena 18, 489–514. Dhakal, A.S., Sidle, R.C., 2003. Long-term modeling of landslides for different management practices. Earth Surf. Process. Landforms 28, 853–868. Dhakal, A.S., Sidle, R.C., 2004. Distributed simulations of landslides for different rainfall conditions. Hydrol. Process. 18, 757–776. Dietrich, W.E., Reiss, R., Hsu, M.-L., Montgomery, D.R., 1995. A process-based model for colluvial soil depth and shallow landsliding using digital elevation data. Hydrol. Process. 9, 383–400. Glade, T., Crozier, M.J., Smith, P., 2000. Applying probability determination to refine landslide-triggering rainfall thresholds using an empirical ‘‘Antecedent Daily Rainfall Model’’. Pure Appl. Geophys. 157, 1059–1079. Guzzetti, F., Peruccacci, S., Rossi, M., Stark, C.P., 2007. Rainfall thresholds for the initiation of landslides in central and southern Europe. Meteorol. Atmos. Phys. 98, 239–267. Imaizumi, F., Sidle, R.C., 2007. Linkage of sediment supply and transport processes in Miyagawa Dam catchment, Japan. J. Geophys. Res. 112, F03012. doi:10.1029/ 2006 JF000495. Iverson, R.M., 2000. Landslide triggering by rain infiltration. Water Resour. Res. 36, 1897–1910. Kuroiwa, C., Hiramatsu, S., 2010. Study on hillside landslides caused by typhoon T0421 in Miyagawa-Dam basin, Mie prefecture (in Japanese with English abstract). J. Jpn. Soc. Erosion Control Eng. 63 (4), 16–21. Larsen, M., Simon, A., 1993. A rainfall intensity–duration threshold for landslides in a humid-tropical environment, Puerto Rico. Geogr. Ann. Ser. A. Phys. Geogr. 75, 13–23. Montgomery, D.R., Dietrich, W.E., 1994. A physically based model for the topographic control on shallow landsliding. Water Resour. Res. 30, 1153–1171. Nagata, H., Inuma, T., Hagiwara, Y., 2009. Topographical and subsurface geological characteristics of surface failures induced by heavy rainfall of the Typhoon Meari (No. 0421) at Miyagawa Village, Mie Prefecture, Japan (literature in Japanese). J. Jpn. Landslide Soc. 46 (3), 49–55. Nakai, S., Sasaki, S., Kaibori, M., Moriwaki, T., 2006. Rainfall index for warning and evacuation against sediment-related disaster: reexamination of rainfall index Rf and proposal of R0 . Soils Found. 46, 465–475. Okimura, T., 1989. Prediction of slope failure using the estimated depth of potential failure layer. J. Nat. Disaster Sci. 11, 67–89. Okimura, T., Ichikawa, R., 1985. A prediction method for surface failures by movements of infiltrated water in surface soil layer. J. Nat. Disaster Sci. 7, 41–51. O’Loughlin, C.L., 1974. The effect of timber removal on the stability of forest soil. J. Hydrol. (NZ) 13, 121–134. Schmidt, K.M., Roering, J.J., Stock, J.D., Dietrich, W.E., Montgomery, D.R., Schaub, T., 2001. The variability of root cohesion as an influence on shallow landslide susceptibility in the oregon coast range. Can. Geotech. J. 38, 995–1024. Simons, D.R., Li, M.M., Ward, T.J., 1978. Mapping of potential landslide areas in terms of slope stability. USDA Forest Service, Rocky Mountain Forest and Range Experiment Station, 75 pp. Swanston, D.N., 1974. Slope stability problems associated with timber harvesting in mountainous regions of the western United States. USDA Forest Service General Technical Report pnw-21, 14 pp. Tsutsumi, D., Fujita, M., 2008. Relative importance of slope material properties and timing of rainfall for the occurrence of landslides. Int. J. Erosion Control Eng. 1, 79–89. Wu, W., Sidle, R.C., 1995. A distributed slope stability model for steep forested hillslopes. Water Resour. Res. 31, 2097–2110.