# Combining TRIGRS and DEBRIS-2D Models for the Simulation of a Rainfall Infiltration Induced Shallow Landslide and Subsequent Debris Flow

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## Abstract

**:**

## 1. Introduction

## 2. Environment Information and TRIGRS Inputs

#### 2.1. Description of Environment

^{3}and the watershed of almost 14.85 ha was buried [23].

#### 2.2. Geological Properties

#### 2.3. Short Term Water Table Monitoring

#### 2.4. Model Inputs

_{z}= 0 because an infiltration is ignored before a rainfall occurs. The friction angle is selected at a minimal value of inorganic clays in low plasticity soil equal to 18° [24] and the cohesive value is 22 kPa [25]; the hydraulic conductivity of silty clay loam is K

_{s}= 2.382 × 10

^{−7}m/s [26]; the diffusivity value using D

_{0}= 4.764 × 10

^{−5}m

^{2}/sec is about 200 times of the saturated hydraulic conductivity K

_{s}[27]; the geological parameters are all taken from Table 1. According to the results of that boreholes, the maximal failure depth set 12.65 m underground is equal to the first stratum depth, and the initial water table is from the BH-3 monitoring result, which equals 4.56 m underground.

## 3. Analysis of Rainfall Infiltration Induced Shallow Landslide

#### 3.1. Rainfall Infiltration

_{z}means an infiltration rate; P means the rainfall intensity, R

_{U}means the upstream runoff, R

_{D}means downstream runoff, and K

_{S}means the hydraulic conductivity of soil in saturation. The rainfall infiltration modules of TRIGRS [17,18] have shown that the rainfall would completely infiltrate under a P + R

_{U}< K

_{S}condition, the infiltration rate I

_{z}= P + R

_{U}, and without downstream runoff, R

_{D}occurs under this condition. Then, the infiltration rate I

_{z}= K

_{S}under P + R

_{U}> K

_{S}condition, and the downstream runoff R

_{D}= P + R

_{U}–K

_{S}would occur. In this study, rainfall infiltration induced a shallow landslide and debris flow case for the Daniao tribe, and Typhoon Morakot produced heavy rainfall from 09:00 7 August 2009 to 03:00 10 August 2009. The rainstorm accumulated 758 mm in 62 h, and the maximal rainfall intensity reached 45.5 mm/h at 06:00 7 August 2009. The rainstorm accumulation reached 740.5 mm at 15:00 8 August 2009 and induced considerable landslides and debris flow [28]. Because of the Typhoon Morakot’s heavy rainfall, the intensity of the rainfall P was smaller than hydraulic conductivity K

_{S}, which only appeared at 1, 3, 5, 8, 59 and 60 h, and the rainfall intensity was all greater than the hydraulic conductivity K

_{S}at other times. The hyetography of rainfall infiltration analysis during Typhoon Morakot Struck appears in Figure 4.

#### 3.2. Total Pressure Head Response

_{max}as an impermeable boundary, and based on the linear solution of the Richard Equation by Iverson [14], we found a groundwater head φ expressed in Equation (1) [17,18]:

_{LZ}means the depth of an impermeable basal boundary measured in the Z direction, β = λ cos θ, where λ = cos θ – (I

_{z}/K

_{z})

_{LT}, and in which K

_{z}is a hydraulic conductivity in the Z direction and I

_{z}is an initial surface flux, I

_{nz}is a surface flux of a given intensity in n

^{th}time interval, D

_{1}= D

_{0}cos 2θ (where D

_{0}is the saturated hydraulic diffusivity), a script LT means long term, a script N means total number interval, a form of H(t – t

_{n}) is Heavy side function, and a form of the function ierfc means:

_{nz}/K

_{Z}= 0 before a rainfall occurs, Equation (1) appears as φ = (Z − d) cos2θ, and the total pressure head of groundwater almost maintains a steady state. As a rainfall infiltration has begun to occur, the steady state almost maintains itself until a time equal to 1 h, and the total pressure head is almost similar to a hydrostatic distribution (see the orange color lines in Figure 5a–e). Subsequently, a rainfall infiltration occurs in I

_{nz}/K

_{Z}> 0, and the β and transient terms of Equation (1) will increase. Therefore, the rainfall infiltration leading to the suction pressure head tends to be smaller in unsaturated regions of soil, and the water table tends to rise (see Figure 5a–e. The phenomena implies that the water content of soil tends to saturate.

#### 3.3. Safety Factor Response

_{w}means a unit weight of water, γ

_{S}is a unit weight of soil, and φ is a groundwater pressure head. F

_{S}expresses the failure of the infinite slope, which is characterized by the ratio of resisting basal Coulomb friction to gravitationally induced downslope basal driving stress and called the factor of safety is shown in Equation (3) [17,18]. As the rainfall infiltration (I

_{nz}/K

_{Z}> 0) would cause the total pressure head of groundwater φ to rise, and the hill would tend to be unstable (F

_{S}< 1).

_{S}changed at θ = 17.7° due to a rainfall infiltration, where the safety factor were all maintained in F

_{S}> 1 during a rainfall infiltration, the result implied that the hillslope were all maintained in a stable state where the slopes satisfied the θ ≤ 17.7° condition. The collapse occurred where the slopes satisfied θ > 17.7° condition, and where the depths were reduced as the slopes increased on the zone that satisfied the θ ≤ 45° condition, but an inverse result occurred as the slope’s θ > 45°. This is because the driving force’s term included a tan θ function (the denominator of Equation (3)). This result implied that the driving force would increase where the slope satisfied θ ≤ 45°, but would reduce where the slope satisfied θ > 45°. Figure 6b–e shows that the factors of safety changed due to a rainfall infiltration at θ = 22°, 32°, 42°, and 52°, and the collapse (F

_{S}< 1) occurred at depths that were greater than 8.22 m, 4.09 m, 2.55 m, and 5.68 m, respectively. The results demonstrate such phenomena, too.

#### 3.4. Validation of Potential Collapse Zone

^{2}, and the deposited volume equals 93,574 m

^{3}. The collapsed zone is the region with terrain reduction, whose range is where a yellow color line is included in Figure 7. The collapse area equals 77,969 m

^{2}and the collapsed volume equals 319,875 m

^{3}(without including the deposited zone).

^{2}is represented by the blue colored block in Figure 7, whose distributions of depth and slope on the collapsed zone are shown in Figure 8a,b, respectively. Therefore, the depth distribution and area of the collapse zone used to calculate the collapsed volume is 391,894 m

^{3}(without including the deposited zone). Therefore, the TRIGRS simulated results are shown with 8% errors for the collapsed area and 23% errors for the collapse volume, compared to the DTM analysis results.

## 4. Analysis of Subsequent Motion of Collapsed Mass

#### 4.1. Debris Flow Spreading Model and Inputs

_{S}< 1; then, the collapsed mass mixed with enough water and became a debris flow that moved to a downslope. A physical model, DEBRIS-2D, is used to analyze the subsequent motion of the collapsed mass. The DEBRIS-2D model is an adopted depth integral form of the conservation law under long wave approximation in the plug flow region, which was originally developed by Liu and Huang [2]. DEBRIS-2D has an inclined coordinate system, where x coincides with the flow direction, y tangents to a topographical contour direction and z is normal at the x − y plane and points to the depth direction. The velocity components in the x, y directions are u and v respectively, θ is the inclined angle, τ

_{0}is the yield stress, and 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 Equations (4) and (5), and the continuity equation is shown in Equation (6).

^{3}, and the initial depth H distributed on the upstream of Daniao tribe as in Figure 5a. The three unknowns H, u, and v could be solved from three independent Equations (4)–(6).

#### 4.2. Description of Debris Flow Motion

#### 4.3. Validation of Hazard Zone

^{2}; the DEBRIS-2D result appeared in the hazard zone with 146,316 m

^{2}and with a 25% positive error relative to the real hazard zone. In spite of that, the hazard zone from the DEBRIS-2D simulation could almost include the real disaster range. Figure 15 shows a photo of the Daniao tribe’s debris flow fan, and we used the features of the landscape in the photo as the scale for estimating the deposited depth of the debris flow. Roughly estimated, the deposited depths were 10 m, 10 m, 7 m, and 7 m on the A, B, C, and D location, respectively (see Figure 15). However, the DEBRIS-2D results are shown at 10 m, 10 m, 8 m and 6 m on the locations (see Figure 14).

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**The total pressure heads change due to a rainfall infiltration at 1, 3, 7, 12, 24, 36, 45, 54, and 62 h where slopes equal to 17.7°, 22°, 32°, 42°, and 52°.

**Figure 6.**The factors of safety change due to rainfall infiltration at 1, 3, 7, 12, 24, 36, 45, 54, and 62 h where slopes equal to 17.7°, 22°, 32°, 42°, and 52°.

**Figure 9.**The velocity distributions results of debris flow spreading from the DEBRIS-2D simulation.

Soil Layer | Distributed Depth (m) | Material Constituted | SPT Number (N) | Unit Weight (ton/m^{3}) | Water Content (%) | Porosity Ratio | Liquid Limit LL (%) | Plasticity Index PI (%) |
---|---|---|---|---|---|---|---|---|

Brown clastic rock, concrete, gray sand backfill layer | From 0.00 m to 12.65 m underground | Collapse, Backfill layer | 8–>100 | 2.11–2.28 | 6.7–12.7 | 0.26–0.43 | 17.2–19.2 | 6.8–8.7 |

Average 62.2 | Average 2.21 | Average 8.9 | Average 0.32 | Average 18.5 | Average 8 | |||

Brown, gray, black and gray broken slate, shear gouge, and rust-strained quartz | From 0.75 m to 50 m underground | Broken Slate | 50–>100 | 1.86–2.20 | 8.5–9.8 | 0.31–0.57 | 17.6–19.5 | 6.8–9.5 |

Average 69.0 | Average 2.03 | Average 9.0 | Average 0.45 | Average 18.4 | Average 8 |

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**MDPI and ACS Style**

Hsu, Y.-C.; Liu, K.-F.
Combining TRIGRS and DEBRIS-2D Models for the Simulation of a Rainfall Infiltration Induced Shallow Landslide and Subsequent Debris Flow. *Water* **2019**, *11*, 890.
https://doi.org/10.3390/w11050890

**AMA Style**

Hsu Y-C, Liu K-F.
Combining TRIGRS and DEBRIS-2D Models for the Simulation of a Rainfall Infiltration Induced Shallow Landslide and Subsequent Debris Flow. *Water*. 2019; 11(5):890.
https://doi.org/10.3390/w11050890

**Chicago/Turabian Style**

Hsu, Yu-Charn, and Ko-Fei Liu.
2019. "Combining TRIGRS and DEBRIS-2D Models for the Simulation of a Rainfall Infiltration Induced Shallow Landslide and Subsequent Debris Flow" *Water* 11, no. 5: 890.
https://doi.org/10.3390/w11050890