Debris Flow Assessment from Rainfall Infiltration Induced Landslide
7th International Conference on Debris-Flow Hazards Mitigation Debris flow assessment from rainfall infiltration induced landslide
Yu-Charn Hsu a,*, Ko-Fei Liu a, Hung-Ming Shu b
aDepartment of Civil Engineering National Taiwan University, No.1, Sec.4, Roosevelt Rd., Taipei 10617, Taiwan ( R.O.C.) b Taitung Branch of Taiwan Soil and Water Conservation Bureau, No.665, Sec. 1, Zhonghua Rd., Taitung City 950, Taiwan (R.O.C.)
Abstract
In the study, debris flows induced by landslides are studied through physical models. TRIGRS and DEBRIS-2D models are integrated for simulation of rainfall infiltration induced shallow landslide and the subsequent debris flows. TRIGRS is used to estimate unstable mass on the hillslope and provide the initial volume for debris flow simulation, and DEBRIS-2D is applied to simulate mass motion and assess the hazard zone mapping. The method is applied to Daniao tribe’s sediment disaster during Typhoon Morakot in Taiwan. The simulated final deposition zone and the disaster area in the real event are almost identical. All the geophysical parameters are obtained through official values and rheological parameters are obtained by in situ measurements.
Keywords: TRIGRS, DEBRIS-2D, estimate unstable mass, the hazard zone;
1. Introduction
Rainfall infiltration will increase soil moisture. As a result, shear strength is reduced and pore pressures and seepage forces are increased. Enough rainfall causes hillside failure, and the failure mass will slide down or turn into debris flows with enough water. Many studies used empirical or statistical method to obtain landslide potential analysis and realize the hazard zone mapping for debris flow. But physical process combining landslide prediction and debris flow simulation is considered more precise in smaller scale. Many researches have used coupled methodology to simulate a debris flow mobilization from a shallow landslide. Chiang et al. (2012) have combined a landslide susceptibility model in landslide prediction, an empirical model to select debris flow initiation points among predicted landslide area and a debris flow model to simulate the spread and inundated region of failed materials from the identified source areas. Gomes et al. (2013) have combined two physical models of SHALSTAB and FLO-2-D to model debris flow spreading area. Wang et al. (2013) have combined limit equilibrium theorem and 2-D depth-integral flow model to assess landslide and a debris flow processes. In this study, TRIGRS (Baum et al., 2010) and DEBRIS-2D (Liu and Huang, 2006) models are coupled in an assessment with rainfall infiltration amount. TRIGRS is a well-known model used in estimating collapse region from rainfall infiltration. DEBRIS-2D has been successfully applied to a hazard zone simulation of debris flow, but DEBRIS-2D needs input for failure volume and location. Therefore, TRIGRS is used to estimate unstable mass on the hillslope and provide the initial volume for debris flow simulation, and DEBRIS-2D is applied to simulate mass motion and assess the hazard zone mapping. This way, TRIGRS and DEBRIS-2D models are integrated for simulation of rainfall infiltration induced shallow landslide and the subsequent debris flows.
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* Corresponding author e-mail address: [email protected] Hsu / 7th International Conference on Debris-Flow Hazards Mitigation (2019)
2. Fundamentals
2.1. Rainfall Infiltration
Rainfall infiltration causes soil water content to increase until saturation and then raise the water table. Therefore, the pore pressure in the saturated state needs to be calculated first. Consider a rectangular Cartesian coordinate system with its origin at an arbitrary point on the ground (see Fig.1), the x axis points to down slope, the y axis points to tangents the topographic contour, and the z axis is normal to x - y plane and points into the slope. The fundamental of rainfall infiltration simulation is based on Iverson’s (2000) linearized solution of Richard’s equation. A generalized solution with an infinite basal boundary is expressed in equation (1), and an impermeable basal boundary at a finite depth is given by equation (2). The first term on the right hand side in equations (1) and (2) represents the steady solution and remaining terms on the right hand side represent the transient solution.
(,)[Z tZd ] , (1) N I Z 2()[()][nz Ht t Dt t1/2 ierfc ] nn1 1/2 n1 KDttzn2[1 ( ) ] N I Z 2()[()][nz Ht t Dt t1/2 ierfc nn+1 1 1 1/2 n1 KDttzn2[11 ( ) ]
(,)[Zt Z d ] . (2) (2md 1) ( d Z ) ierfc[]LZ LZ N 1/2 Inz 1/2 2[Dt1 ( tn ) ] 2()[()]Ht tnn Dt1 t K (2md 1) ( d Z ) nm11z ierfc[]LZ LZ 1/2 2[Dt1 ( tn ) ] (2md 1) ( d Z ) ierfc[ LZ LZ ] N 2[Dt ( t )1/2 ] Inz 1/2 1+1n 2()[()]Ht tnn+1 Dt 1 t +1 K (2md 1) ( d Z ) n1 z m1 ierfc[]LZ LZ 1/2 2[Dt1+1 ( tn ) ]
Fig.1 Coordinate system diagram of TRIGRS model. Hsu / 7th International Conference on Debris-Flow Hazards Mitigation (2019)
Equation (1) applies where hydraulic properties are uniform and equation (2) applies where a well-defined decrease in hydraulic conductivity exists at a finite depth. In the equations φ is the groundwater pressure head, t is time, θ is the slope angle of x axis, Z = z / cosθis the failure depth, d is the initial depth of the water table measured in Z direction in steady state, dLz is a depth of impermeable basal boundary measured in Z direction, β = λcosθ[λ = cos θ- (Iz - Kz)LT, with Kz the hydraulic conductivity in Z and Iz initial surface flux], Inz means a surface flux of a given th 2 intensity in n time interval, D1 = D0 cos θ with D0 the saturated hydraulic diffusivity), H(t - tn) is Heaviside function. The function ierfc is defined as
1 ierfc() exp(2 )erfc () (3)
Iverson (2000) used an infinite-slope stability analysis to model a hillslope stability. The ratio Fs called the factor of safety is calculated at Z depth by (4).
tan CZt(,)w tan (4) FS tans Z sin cos
where is the friction angle, C is the cohesion of soil, both for effective stress, w is specific gravity of water and s is specific gravity of soil. Equation (4) expresses the failure of the infinite slope by the ratio between resisting from basal Coulomb friction to gravitationally induced downslope basal driving stress. The hillslope fails for Fs < 1. Therefore, the depth H = z and area A of the hillside in unstable (Fs < 1) condition, the product H and A will provide volume for the mass motion simulation.
2.3. Debris flow
A hillside fails when Fs < 1, and this mass will mix with water and become debris flow as it moves down slope. A physical model, DEBRIS-2D (Liu and Hung, 2006) adopted depth integrated form of conservation law under long wave approximation in the plug flow region and has been successfully applied in debris flow simulation, which is original developed by Liu and Huang (2006). DEBRIS-2D with inclined coordinate system (see Fig. 2), x coincides with flow direction, y tangent to topographical contour direction and z normal to x - y plane and points to depth direction. The velocity components in the x, y directions are u and v respectively, θ is the inclined angle, τ0 is the yield stress, H = h - B is the flow depth (where h is the free surface and B is the natural bottom of the debris flow). The momentum equations in conservative form are shown in equation (5) and (6), the continuity equation is shown in equation (7).
uH u2 H uvH ()BH 1 u gHcos gHsin 0 , (5) txy x uv22
vH uvH v2 H ()1 B H v gHcos 0 , (6) txy y uv22
HuHvH 0 , (7) txy
The initial velocities when the hillslope just fails are u = 0 and v = 0, and the initial depth H is obtained from the slope stability analysis results under the instability condition Fs < 1 in equation (4). Three unknowns H, u and v could be solved from three independent equations (5), (6), and (7). Hsu / 7th International Conference on Debris-Flow Hazards Mitigation (2019)
Fig.2 Coordinate system diagram of DEBRIS-2D model.
3. Descriptions of Environment and Modelling
3.1. Surface Survey
The landslide is located on the upper hillside of the Daniao tribe as in Fig. 3. The failure source on the ground was composed of slate, mudstone, sandstone and weathered gravel, which are all easily movable under external forces. The sieve analysis gives D10 = 0.98 mm, Dm = 55.94 mm and maximum is Dmax = 420 mm.
(a) Photographs of Daniao tribe’s landslide after Typhoon Morakot (b) Particle distribution of Daniao tribe’s landslide
Fig. 3 Surface survey results.
3.2. Topographical Analysis
The 2 m × 2 m digital terrain model is used for the topographic analysis of the Daniao tribe’s sediment disaster. The watershed area is approximately 52.38 ha, and the elevation changes from 60 m to 480 m, and the slope distribution is from 0° to 70°, the major stratigraphic trend is from the east to the west. The landslide occurred mostly within the steeper area (slope greater than 15°). The distributions of elevation, slope and flow direction of the hazard zone are shown in Fig. 4. Hsu / 7th International Conference on Debris-Flow Hazards Mitigation (2019)
Fig. 4 Topographic analysis results.
3.3. Rainfall Event
During 2009 August, Typhoon Morakot struck Taiwan and induced sediment disasters throughout Taiwan. Daniao tribe watershed landslide is one of sediment disasters which is occurred in Eastern Taiwan. Typhoon Morakot produced heavy rainfall to Daniao tribe watershed from 2009/08/07 09:00 to 2009/08/10 03:00. The hyetograph is shown in Fig. 5. The rainstorm accumulated 759 mm in 65 hours, and maximal rainfall intensity reached 45.5 mm/hour on 2009/08/07 06:00. The rainstorm accumulation reached 740.5 mm at 2009/08/08 15:00, and induced landslides and debris flows.
Fig. 5 Hyetograph during Typhoon Morakot struck Daniao tribe watershed.
3.4. Geological Properties
There were 10 boreholes drilled to understand the geological formation of the Daniao tribe’s landslide after the disaster. The boreholes BH-1, BH-3, BH-5, BH-7, BH-9, and BH-10 were sampled using the Standard Penetration Test (SPT) every 1.5 m. The soil samples of the landslide were obtained from the split tube samplers, and all of the samples were tested for soil properties in a laboratory. According to the drilling results, there are two stratums underground. The first formation is composed of brown colluvial rock, concrete, backfill layer and gray sand, whose Hsu / 7th International Conference on Debris-Flow Hazards Mitigation (2019)
depth ranged from 0 m to 0.75 ~ 12.65 m underground. The second formation is constituted by brown slate, gray slate, shear gouge, rust staining and quartz. The geological profiles of the boreholes and field particle distribution survey results are shown in Fig. 6.
Fig. 6 Geological profiles of boreholes.
The remolded soil samples are used in the soil properties test, the soil properties of the Daniao tribe landslide region are shown in the Table 1. Direct Shear Test (DST) is applied to obtain the friction angle is 34.5o and cohesion is 1.6 ton/m3 of the remolded soil sample. According to the Plasticity Chart from Casagrande (1932), the stratum’s soil of Daniao tribe landslide could be classified as inorganic clays of low plasticity soil (CL-ML). The hydraulic conductivity -8 -10 Ks is about from 5.0 × 10 to 5.0 × 10 m/Sec. Liu and Wu (2008) found the diffusivity value D0 of the colluvium soil is about 10 to 500 times that of the hydraulic conductivity Ks. Furthermore, if the soil is saturated that the steady infiltration rate Iz could be the same as the hydraulic conductivity Ks. Therefore, the diffusivity value selects 200 times -5 2 of the Ks equals D0 = 1.0 × 10 m /Sec, and the steady infiltration rate Iz equals zero under fully saturated soil condition.
Table 1 Geological characteristics of soil samples in Daniao tribe landslide
Number of Specific Water Liquid Plasticity Distributed Depth Material Porosity Soil layer SPT Gravity Content Limit Index (m) Constituted Ratio (N) (ton/m3) (%) LL (%) PI (%)
Brown clastic rock From 0.00 m to 8 ~ >100. 2.11 ~ 2.28. 6.7 ~ 12.7. 0.26 ~ 0.43. 17.2 ~ 19.2. 6.8 ~ 8.7 blocks of concrete Collapse, Backfill 0.75 ~ 12.65 m or backfill layer layer underground Average： Average： Average： Average： Average： Average： with gray sand 62.2 2.21 8.9 0.32 18.5 8.0 Brown, gray turn black and gray From 0.75 ~ 12.65 50 ~ >100. 1.86 ~ 2.20. 8.5 ~ 9.8. 0.31 ~ 0.57. 17.6 ~ 19.5 6.8 ~ 9.5 broken slate clip m to 30~50 m Broken Slate scissors mud and underground Average： Average： Average： Average： Average： Average： rust-strained quartz 69.0 2.03 9.0 0.45 18.4 8.0 Hsu / 7th International Conference on Debris-Flow Hazards Mitigation (2019)
4. Results of Simulation and Discussion
The topographic data were from 2 m × 2 m DTM. The hyetograph from Typhoon Morakot record is used to calculate infiltration. The geological parameters are obtained from boreholes and laboratory tests.
4.1. Estimation and Validation of Landslide Volumes
According to report of Soil and Water Conservation Bureau in 2011, the landslide volume is 319,875 m3 and failure area equals 51,873 m2 using the DTM before and after the landslide disaster. The average depth is 5.2 m. Assuming soil is already saturated just before the disaster, with the input information in Table. 1. TRIGRS model applied to assess the volume of the collapsed zone in the Daniao tribe’s upstream hill, the infiltration model of TRIGRS equation (2) was used to calculate the total pressure head φ, we ran the TRIGRS model by increased the depth Z from 1 m to 6 m, the domain is almost the same as real event at Z = 6 m, then the area where Fs < 1 is shown in Fig.7. The corresponding failure depth is 6 m which is 1.15 times of the average failure depth from the report (SWCB, 2011). The landslide volume by TRIGRS is 367,085 m3. The TRIGRS’s result is within 15% error of the report (SWCB, 2011). These values are inputs to DEBRIS-2D for calculate the hazard zone of debris flow.
Fig.7 Factor of safety distribution due to failure depth equal to 6 m.
4.2. Simulation of Debris Flow
The yield stress was measured in the field as 256.8 dyne/cm2. A time step of 0.005 seconds was set up, and the computational grid size was 2 m × 2 m. The TRIGRS’s results provide 367,085 m3 initial volume was distributed on the head of the Daniao tribe’s hillslope as shown in Fig. 7. The debris flow simulated results are shown in Fig. 8. The points P1, P2, P3 and P4 located at watershed gap, with maximal depths 12.99 m, 13.99 m, 13.09 m and 12.12 m, respectively. When the debris flow flows out of the watershed gap, at the positions P5 and P6, the maximal velocities equal 2.44 m/Sec and 1.48 m/Sec. Then debris flow begins to slow down, and the maximal flow depths reduced from 9.99 m to 7.46 m. The debris flow crossed the upstream of the Daniao tribe at the positions P7 and P10, then followed two diversion ditches on both sides Daniao tribe. Points P7 to P9 are a located on the left ditch and simulation indicated that debris flow arrived P7 at 334 Sec with maximal velocity 1.12 m/Sec and maximal flow depth 7.84 m at P8. And, the debris flow flows over Daniao tribe after crossing the P9 at 1008 Sec. The P10 to P11 is a right ditch, and simulation represented that debris flow arrived P10 at 488 Sec, which’s maximal velocity reduced to 0.51 m/Sec and maximal flow depth of 6.37 m. And, the debris flow was stopped on P11 at 1200 Sec. We compared the final deposition zone for both of the simulation (colored contours) and the real event (purple line), the simulation results were nearly consistent with the field measurements. Hsu / 7th International Conference on Debris-Flow Hazards Mitigation (2019)
(b) Debris Flow Depths in Time Variations
(a) Final Deposition Mapping of Debris flow (c) Debris Flow Velocities in Time Variations
Fig.8 Final deposition mapping of debris flow and debris flow depths and velocities in time variations.
5. Conclusions
TRIGRS and DEBRIS-2D models are integrated for a rainfall infiltration inducing shallow landslide simulation. The result of the simulation is tested by Daniao tribe‘s landslide induced debris flow in 2009. All input parameters for the model are obtained from field measurements, no data fitting is involved. TRIGRS leads to a stability analysis of a hillslope and gives instability zone as well as failure depth. This provided the initial volumes for DEBRIS-2D in the simulation. The simulated hazard zone from DEBRIS-2D are nearly consistent to the aerial map measurements.
Acknowledgements
The authors wish to thank Soil and Water Conservation Bureau Taitung Branch for information providing.
References
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