The influence of rainstorm pattern on shallow landslide

3 downloads 0 Views 612KB Size Report
greater than the minimum landslide-triggering rainfall amount, the occurrence of landslide significantly depends not only on the rainfall duration but also on the ...
Environ Geol (2008) 53:1563–1569 DOI 10.1007/s00254-007-0767-x

ORIGINAL ARTICLE

The influence of rainstorm pattern on shallow landslide Tung-Lin Tsai

Received: 11 January 2007 / Accepted: 18 April 2007 / Published online: 10 May 2007  Springer-Verlag 2007

Abstract In this study, the influence of the rainstorm pattern on shallow landslide is examined. The physicallybased shallow landslide model is used to conduct this examination with considering four representative rainstorm patterns including uniform, advanced, central, and delayed rainstorms. The results show that in spite of the rainfall duration and the rainfall pattern, the rainstorm with less than the minimum landslide-triggering rainfall amount will not trigger landslide. However, for the rainstorm with greater than the minimum landslide-triggering rainfall amount, the occurrence of landslide significantly depends not only on the rainfall duration but also on the rainfall pattern. Among the four representative rainstorm patterns, the delayed rainstorm has the greatest rainfall duration threshold for landslide occurrence, followed by the central rainstorm, and then the uniform rainstorm. In addition, for each rainstorm pattern, the corresponding rainfall duration threshold for landslide occurrence decreases with the increase of rainfall amount, and seems to be constant for large rainfall amount. Keywords Landslide  Rainstorm pattern  Infiltration  Slope stability List of symbols C the change in volumetric water content per unit change in pressure head C0 the minimum value of C c soil cohesion

T.-L. Tsai (&) Department of Civil and Water Resources Engineering, National Chiayi University, 300 Sefu Road, Chiayi City 60004, Taiwan e-mail: [email protected]

D0 dZ dLZ FS IZ Ksat T Z w h a / csat and cw

Ksat =C0 water depth slope depth factor of safety rainfall intensity saturated hydraulic conductivity rainfall duration the coordinates groundwater pressure head soil volumetric water content slope angle soil friction angle the unit weights of saturated soil and water

Introduction Landslide often poses a serious threat to both lives and property in many places around the world. Although slope failures may happen due to human induced factors such as the loading of the slope or the cutting away of the toe for construction purposes, many slope failures occur simply due to rainfall, especially in regions with residual soil subjected to a rainstorm. Up to now, the assessment of rainfall-induced landslide has still been a widely concerned research topic for soil scientists. The empirical rainfall threshold concept and the physically-based model are two commonly used approaches. Based on historical records of landslides and the corresponding rainfall data, the rainfall threshold for landslide occurrence can be simply related either to the critical cumulative rainfall amount (Campbell 1975) or to the rainfall intensity (Brand et al. 1984), but the most

123

1564

commonly used that was developed by simultaneously considering the rainfall intensity and the rainfall duration (Caine 1980). In order to take the climatic effect into account, the rainfall intensity-duration threshold for landslide occurrence was further refined by normalizing the rainfall intensity with the mean annual rainfall amount (Cannon and Ellen 1985; Jibson 1989; Wieczorek et al. 2000). Another frequently used rainfall threshold correlates the amount of rainfall until landslide initiation with the maximum rainfall intensity (Govi et al. 1985). In addition, the influence of the antecedent rainfall was also considered in the rainfall threshold for landslide occurrence (Glade et al. 2000). The empirical rainfall threshold concept can be very simple to practically apply to the assessment of rainfallinduced landslide, but it seems to provide a minimal amount of insight into the actually physical processes that trigger landslide. In addition, the empirical rainfall threshold for landslide initiation is probably associated with the rainfall amount, the rainfall duration, the rainfall mean and maximum hourly intensity, or the antecedent rainfall, but it seems not to take the rainstorm pattern into consideration. In order to investigate the importance of the rainstorm pattern to shallow landslide, the physically-based model needs to be used (Brooks et al. 1994; Dhakal and Sidle 2004). With assumptions of steady or quasi-steady water table, and groundwater flows parallel to hillslope, various physically-based models coupling the infinite slope stability analysis with hydrological modeling (Montgomery and Dietrich 1994; Wu and Sidle 1995; Borga et al. 1998) were developed to assess landslide induced by land use and hydrological conditions. Iverson (2000) developed a flexible modeling framework of landslide with approximations of Richards’ equation (1931) valid for more general hydrological conditions. The extension version of Iverson’s model was further proposed to take variable rainfall intensity into account for hillslope with finite depth (Baum et al. 2002). Due to its simplicity and practicability, the Iverson’s model was popular (Crosta and Frattini 2003; Keim and Skauqset 2003; Frattini et al. 2004; Lan et al. 2005; D’Odorico et al. 2005). By amending the boundary condition at top of hillslope to take general infiltration process into account, the modified Iverson’s model without the assumption of constant infiltration capacity was proposed by Tsai and Yang (2006). The modified Iverson’s model can avoid the unrealistically high pressure heads which could happen from Iverson’s model due to the overestimation of infiltration rate under the assumption of constant infiltration capacity. In addition, even though the beta-line correction (Iverson 2000) is applied to eliminate the unrealistically high pressure heads, the Iverson’s model

123

Environ Geol (2008) 53:1563–1569

with the beta-line correction could still produce greater pressure heads and overestimates soil failure potential as compared with the modified Iverson’s model. The purpose of this study is to examine the influence of the rainstorm pattern on shallow landslide. The modified Iverson’s model (Tsai and Yang 2006) is applied to conduct this investigation with considering four representative rainstorm patterns including uniform, advanced, central and delayed rainstorms (Ng et al. 2001; de Lima and Singh 2002). In the following sections, both hydrological modeling and soil failures modeling used herein are first described. The demonstrations and the examinations of the effect of the rainstorm pattern on shallow landslide are then conducted.

Hydrological modeling and slope failures modeling Hydrological modeling The governing equation for rainfall infiltration into hillslope can be written as ow o2 w ¼ D0 cos2 a 2 ot oZ

ð1Þ

in which w is groundwater pressure head; h is soil volumetric water content; a is the slope angle; t is time. D0 ¼ Ksat =C0 in which C0 is the minimum value of C(w) and Ksat is the saturated hydraulic conductivity. CðwÞ ¼ dh=dw is the change in volumetric water content per unit change in pressure head. The elevation Z shown in Fig. 1 is vertically measured downward from a horizontal reference plane. The appropriate initial and boundary conditions are needed for solving (1). For initially steady state with water table of dZ in vertical direction shown in Fig. 1, the initial condition in terms of pressure head can be expressed as wðZ; 0Þ ¼ ðZ  dZ Þ cos2 a

ð2Þ

For a slope with depth of dLZ measured in vertical direction, the boundary condition in terms of pressure head at impervious base can be written as ow ðdLZ ; tÞ ¼ cos2 a oZ

ð3Þ

The ground surface of hillslope subjected to a rainfall with intensity of Iz yields  ow ð0; tÞ ¼ IZ Ksat þ cos2 a oZ

if wð0; tÞ60 and t\T

ð4Þ

Environ Geol (2008) 53:1563–1569

1565 Assume that infiltration rate equals rainfall intensity

x dZ Apply Eqs. (1)- (4) to find pressure head

( x, t )

d LZ (0, t )

z water flow

0

Check ponding

Z (0, t )

α

Fig. 1 Schematic illustration of the finite slope stability analysis integrated with hydrological modeling

wð0; tÞ ¼ 0 if wð0; tÞ[0 and t\T

ð5Þ

ow ð0; tÞ ¼ cos2 a oZ

ð6Þ

0

Calculate factor of safety

Apply Eqs. (1)-(3) and

using (8)-(10)

(5) to find

( x, t )

Move forward to the next time step

if t[T

where T is the rainfall duration. Equations (1)–(6) need to be numerically solved with an iterative procedure due to the nonlinearity. The solution procedure for (1)–(6) is shown in Fig. 2. The pressure head at ground surface of hillslope, i.e. w (0,t), is first obtained by assuming that the infiltration rate equals the rainfall intensity shown in (4). If w (0,t) is less than or equals zero, that is, the ponding does not happen, the calculated results are accepted. The computation moves forward to the next time step. If the calculated w (0,t) is greater than zero, that is, the ponding occurs, with neglecting the water depth of overland flow (Hsu et al. 2002; Wallach et al. 1997) w (0,t) = 0 is used as boundary condition to recalculate once more for the same time step. Soil failures modeling Once the pressure heads w (Z,t) are obtained from the hydrological modeling mentioned above, the hillslope failure potential can be estimated using the infinite slope stability analysis. The infinite slope stability analysis is a preferred tool to evaluate landslides due to its simplicity and practicability (Montgomery and Dietrich 1994; Wu and Sidle 1995; Borga et al. 1998; Iverson 2000; Morrissey et al. 2001; Crosta and Frattini 2003; Collins and Znidarcic

Fig. 2 Flow chart of hydrological modeling with considering general infiltration process

2004). This concept is generally valid for the case of landside with a small depth compared to its length and width. This assumption is also compatible with that used to previously develop hydrological modeling of hillslope. A hillslope failure at a certain depth Z occurs when the acting stress equals the resisting stress due to friction and cohesion. In other words, failure happens at a certain depth Z with satisfying FS ¼ Ff þ Fw þ Fc ¼ 1

ð7Þ

where the dimensionless value FS is so-called safety factor. The gravity performing term Ff, the water pressure performing term Fw, and the cohesion performing term Fc in the safety factor can be respectively, expressed as Ff ¼

tan u tan a

ð8Þ

Fw ¼

wðZ; tÞcw tan u csat Z sin a cos a

ð9Þ

Fc ¼

c csat Z sin a cos a

ð10Þ

123

1566

Environ Geol (2008) 53:1563–1569

where / is the soil friction angle; c denotes the soil cohesion; cw and csat represent the unit weights of water and saturated soil, respectively.

Demonstrations and examinations The importance of rainstorm pattern to shallow landslide The demonstration of the importance of the rainstorm pattern to shallow landslide is first conducted. Four representative rainstorm patterns including uniform, advanced, central, and delayed rainstorms (Ng et al. 2001; de Lima and Singh 2002) shown in Fig. 3 are used. The hillslope has slope angle of 23 and depth of 4 m. The initial water table is 2 m below the ground surface of hillslope. The following soil parameters are adopted: / = 38, c = 500 N/m2, csat = 19,000 N/m3, cw = 9800 N/m3,

uniform

Rainfall intensity (mm)

advanced

The influence of rainstorm pattern on rainfall threshold for landslide occurrence central

delayed

Time (hrs)

Fig. 3 Four representative rainstorm patterns

123

D0 = 0.001 m2/s, Ksat = 3 · 10–5m/s. The rainstorm with rainfall amount of 250 mm lasts for 4 h. The simulated pressure heads with respect to time from different rainstorm patterns are displayed in Fig. 4. It can be clearly observed from Fig. 4 that the pressure heads due to rainfall infiltration are strongly related to the rainstorm pattern. The time to the ponding is first reached by the advanced rainstorm at 1 h after the rainfall, followed by the central rainstorm, and then the uniform rainstorm. The delayed rainstorm latest causes the ponding at 3 h after the rainfall. The steady state seems to be reached at 2 h after the end of the rainfall. At steady state, the advanced rainstorm has the greatest water table rise among the four representative rainstorm patterns. The water table rise of the uniform rainstorm is greater than that of the central rainstorm. The least water table rise is caused by the delayed rainstorm as compared with the other three rainstorm patterns. This outcome seems consistent with the simulated cumulative infiltrations from different rainstorm patterns shown in Fig. 5. Due to the close relation between soil failure potential and water table rise, it can be expected that the occurrence of landslide is significantly affected by the rainstorm pattern. The simulated soil failure potential in terms of safety factor with respect to time from different rainstorm patterns are shown in Fig. 6. From Fig. 6, one can find that the advanced rainstorm and the uniform rainstorm induce soil failures at 4.5 and 5.5 h after the rainfall, respectively. However, the central rainstorm and the delayed rainstorm can not cause the landslides. This is due to the fact that the temporal difference in rainfall intensity largely influences the infiltration rate that is related to landslide-triggering water table rise. Therefore, it can be concluded from mentioned above that the occurrence of soil failure strongly depends on the rainstorm pattern.

After the importance of the rainstorm pattern to shallow landslide is demonstrated, the influence of the rainstorm pattern on the rainfall threshold for landslide occurrence is examined. With the same soil parameters, soil depth, slope angle, initial water table as previous case, and different rainfall amounts and rainfall durations, the simulated rainfall threshold for landslide initiation from the four representative rainstorm patterns are shown in Fig. 7. In Fig. 7, one can observe that for each rainstorm pattern, the corresponding rainfall threshold curve can divide the graph into two parts. The landslides are not induced if the rainstorm lies to the left side of the threshold curve. On the other hand, the rainstorm lying to the right side of the threshold curve can trigger landslides. For example, the

Environ Geol (2008) 53:1563–1569

1567

Fig. 4 Simulated results of pore water pressures from various rainstorm patterns

0

0 uniform advanced central delayed

1

1

2

2

t =1 hr

3

4

0.5

1.0

1.5

2.0

2.5

0.0

0

0

1

1

Z direction (m)

Z direction (m)

4 -1.5 -1.0 -0.5 0.0

2

3

t =2 hr

4 -1.0 -0.5 0.0

0.5

1.0

1.5

2.0

2.5

0

1

1

2

2

4 -0.5

1.5

2.0

2.5

3.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

uniform advanced central delayed

t =6 hrs

3

t =2.5 hr

1.0

t =4 hrs

3

4 -0.5 0.0

3.0

0.5

2

0

3

t =3 hrs

3

4 0.0

0.5

1.0

1.5

2.0

2.5

3.0

-1

Pore water pressures (m)

0

1

2

3

4

Pore water pressures (m)

Z direction (m)

0

1

2

Steady state

3

4 -1

0

1

2

3

4

Pore water pressures (m)

delayed rainstorm with rainfall amount of 250 mm and rainfall duration of 6 h can not induce landslide because it lies to the left side of the rainfall threshold curve for the delayed rainstorm, whereas the advanced rainstorm with the identical rainfall amount and rainfall duration can cause soil failure. In addition, the four rainstorm patterns, respectively, together with rainfall amount of 300 mm and rainfall duration of 8 h will all induce landslides. One can clearly find from Fig. 7 that regardless of the rainfall pattern and the rainfall duration, the rainstorm with less than rainfall amount of 200 mm can not cause soil failure, that is, the minimum landslide-triggering rainfall amount seems existent. This is because that the rainstorm

with less than rainfall amount of 200 mm entirely infiltrates into soil, the resulting water table rise is not enough to trigger landslide. However, for the rainstorm with greater than rainfall amount of 200 mm, the occurrence of landslide is related not only to the rainfall duration but also to the rainfall pattern. It can be observed from Fig. 7 that the rainstorm with greater than rainfall amount of 200 mm will induce landslide if the duration of the rainfall is larger than the rainfall duration threshold. For instance, the delayed rainstorm with rainfall amount of 240 mm has the corresponding rainfall duration threshold of 7 h. In other words, the landslide will be induced by the delayed rainstorm with rainfall amount of 240 mm if the rainfall

123

1568

Environ Geol (2008) 53:1563–1569

and seems to remain unchanged for large rainfall amount. For example, the uniform rainstorm has constant rainfall duration threshold of about 3.5 h when the rainfall amount is greater than 350 mm. Therefore, one can conclude from mentioned above that the occurrence of rainfall-induced shallow landslide is associated with the rainfall amount and the rainfall duration as well as the rainfall pattern.

The cumulative rainfall infiltration (m)

0.25 uniform advanced central delayed

0.20

0.15

0.10

Conclusions

0.05

In many places all over the world, both lives and property are often threatened by landslide. The empirical rainfall threshold concept and the physically-based model are two approaches to the assessment of rainfall-induced landslide. Due to its simplicity and practicability, the empirical rainfall threshold for landslide occurrence, probably related to the rainfall amount, the rainfall duration, the rainfall mean and maximum hourly intensity, or the antecedent rainfall, is commonly used, but it seems not to clearly analyze the actually physical processes of landslide, and seems not to take the rainstorm pattern into consideration. In this study, the physically-based shallow landslide model developed by the modified Iverson’s concept (Tsai and

0.00 0

1

2

3

4

Time (hrs)

Fig. 5 Cumulative rainfall infiltration form different rainstorm patterns

duration is greater than 7 h. Among the four representative rainstorm patterns, the delayed rainstorm has the greatest rainfall duration threshold, followed by the central rainstorm, and then the uniform rainstorm. In addition, for each rainstorm pattern, the corresponding rainfall duration threshold decreases with the increase of rainfall amount, Fig. 6 Simulated results of soil failure potentials from various rainstorm patterns

0

0 uniform advanced central delayed

1

1

t =5.5 hr

2

2

t =1 hr 3

3

4 0.5

4 1.0

1.5

2.0

0.6

2.5

1 2

t =3 hr

3

0.6

0.8

1.0

1.2

1.4 1.6

1.8

1.4

1.6

1.8

2.0

1.2

1.4

1.6

1.8

2.0

1.2

1.4

1.6

1.8

2.0

uniform advanced central delayed

1 2

t =6 hr 3

0.6

2.0

0.8

1.0

0

0

1

t =4.5 hr

2

2

3

3

Steady state

4

4 0.6

0.8

1.0

1.2

1.4 1.6

Safety factor

123

1.2

4

4

1

1.0

0

Z direction (m)

Z direction (m)

0

0.8

1.8

2.0

0.6

0.8

1.0

Safety factor

Environ Geol (2008) 53:1563–1569

1569

uniform advanced central delayed

Rainfall duration(hr)

10

8

6

4

2 150

200

250

300

350

400

450

500

Rainfall amount (mm)

Fig. 7 Rainfall threshold curves for landslide occurrence from different rainstorm patterns

Yang 2006) is applied to examine the influence of the rainstorm pattern on shallow landslide. The four representative rainstorm patterns including uniform, advanced, central, and delayed rainstorms are used to conduct this examination. The results indicate that among the four representative rainstorm patterns, the advanced rainstorm has the least rainfall duration threshold for landslide occurrence, followed by the uniform rainstorm, whereas the delayed rainstorm has the greatest rainfall duration threshold for landslide occurrence. For each rainstorm pattern, with the increase of rainfall amount, the corresponding rainfall duration threshold decreases to constant. Thus, one can conclude that the shallow landslide is strongly affected not only by the rainfall amount and the rainfall duration of the rainstorm but also by the rainstorm pattern.

References Baum RL, Savage WZ, Godt JW (2002) TRIGRS-a Fortran program for transient rainfall infiltration and grid-based regional slopestability analysis, Virginia, US Geological Survey Open file report 02-424 Borga M, Fontana GD, De Ros D, Marchi L (1998) Shallow landslide hazard assessment using a physically based model and digital elevation data. Environ Geol 35:81–88 Brand EW, Premchitt J, Phillipson HB (1984) Relationship between rainfall and landslides in Hong Kong. In: Proceedings of the IV international symposium on landslides, Toronto 1:377–384 Brooks SM, Richards KS (1994) The significance of rainstorm variations to shallow translational hillslope failure. Earth Surf Process Landforms (19):85–94 Caine N (1980) The rainfall intensity duration control of shallow landslides and debris flow. Geogr Ann 62(1):23–27

Campbell RH (1975) Debris flow originating from soil slip during rainstorm in southern California. Q Eng Geol 7:339–349 Cannon SH, Ellen SD (1985) Rainfall conditions for abundant debris avalanches, San Francisco Bay region, California. Calif Geol 38(12):267–272 Collins BD, Znidarcic D (2004) Stability analyses of rainfall induced landslides. J Geotech Geoenviron Eng 130(4):362–372 Crosta GB, Frattini P (2003) Distributed modeling of shallow landslides triggered by intense rainfall. Nat Hazards Earth Syst Sci 3:81–93 Dhakal AS, Sidle RC (2004) Distributed simulations of landslides for different rainfall conditions. Hydrol Process 18:757–776 D’Odorico P, Fagherazzi S, Rigon R (2005) Potential for landsliding: Dependence on hyetograph characteristics. J Geophys Res Earth Surf 110(F1) Frattini P, Crosta GB, Fusi N, Negro PD (2004) Shallow landslides in pyroclastic soil: a distributed modeling approach for hazard assessment. Eng Geol 73:277–295 Glade T (2000) Modelling landslide-triggering rainfalls in different regions of New Zealand- the soil water status model. Z Geomorphol NE 122:63–84 Govi M, Mortara G, Sorzana P (1985) Eventi idrologici e frane. Geol Appl Idrogeol 20(2):395–401 Hsu SH, Ni CF, Hung PF (2002) Assessment of three infiltration formulas based on model fitting on Richards’ equation. J Hydrol Eng 7(5):373–379 Iverson RM (2000) Landslide triggering by rain infiltration. Water Resour Res 36:1897–1910 Jibson RW (1989) Debris flow in southern Porto Rico. In: Schultz, Jibson (eds) Landslide processes of the eastern United States and Puerto Rico. Geological Society of American Special Paper 236:29–55 Keim RF, Skaugset AE (2003) Modelling effects of forest canopies on slope stability. Hydrol Processes 17:1457–1467 Lan HX, Lee CF, Zhou CH, Martin CD (2005) Dynamic characteristics analysis of shallow landslides in response to rainfall event using GIS. Environ Geol 47:254–267 de Lima JLMP, Singh VP (2002) The influence of the pattern of moving rainstorm on overland flow. Adv Water Resour 25:817– 828 Montgomery DR, Dietrich WE (1994) A physically based model for the topographic control on shallow landslide. Water Resour Res 30:83–92 Morrissey MM, Wieczorek GF, Morgan BA (2001) A comparative analysis of hazard models for predicting debris flows in Madison County, Virginia. US Geological Survey Open file report 01-67 Ng CWW, Wang B, Tung YK (2001) Three-dimensional numerical investigation of groundwater responses in an unsaturated slope subjected to various rainfall patterns. Can Geotech J 38:1049– 1062 Richards LA (1931) Capillary conduction of liquids in porous mediums. Physics 1:318–333 Tsai TL, Yang JC (2006) Modeling of rainfall-triggered shallow landslide. Environ Geol 50(4):525–534 Wallach R, Grigorin G, Rivlin J (1997) The errors in surface runoff prediction by neglecting the relationship between infiltration rate and overland flow depth. J Hydrol 200:243–259 Wieczorek GF, Morgan BA, Campbell RH (2000) Debris flow hazards in the Blue Bridge of Central Virginia. Environ Eng Geosci 1(1):11–27 Wu W, Slide RC (1995) A distributed slope stability model for steep forested basins. Water Resour Res 31:2097–2110

123