Hydrological Modelling of Shallow Landslides

Hydrological Modeling of Shallow LandslidesInternal Seminar, 12 October 2009

Anagnostopoulos Grigoris

1.Introduction

Landslides triggered by rainfall occur in most mountainous landscapes.

Most of them occur suddenly and travel long distancesat high speeds.

They can pose great threats to life and property.

1.Introduction 2.PhD plan 3.Theoretical Background 4.State of the art 5.Cellular Automata 6.Field Campaign 7.Future plans

1.Introduction

Figure 1: Landslides in Urseren Valey Figure 2: Rutschung Hellbüchel, Lutzenberg, AR – Sept. 1st, 2002

Typical dimensions: Width ~ tens of meters. Length ~ hundreds of meters. Depth ~ 1-2 meters.

Main triggering mechanisms: Rainfall intensity and duration. Antecedent soil moisture conditions. Pore pressure change due to saturated and unsaturated flow of

water through soil pores. Cohesion and friction (c,φ) angle of soil. Hydraulic conductivity and hysteretic behaviour of soil during

wetting and drying cycles. Topography and macropores.


1.Introduction

Hyd

rolo

gica

lSo

il Pr

oper

ties

2.PhD Plan

Development of a physically based model for the prediction of the location and timing of shallow landslides.

Produce results in various scales varying from the hillslope to the catchment scale.

Take into account as many as possible factors that contribute to the phenomenon (unsaturated conditions, hysteresis, macropores etc).

Verification of the produced model with experimental data from a landslide-prone location.


2.PhD Plan

3.Theoretical Background

Water flow through soil: The depth of the swallow landslides is 1-2 meters. The failure surface may be located in the vadoze zone

where unsaturated flow conditions exist. The hillslope subsurface flow that considers also the

unsaturated zone is described by the fully three dimensional Richard`s equation:



( ) ( ) ( )s rK K zt

,ww s s w

s

dSS S Sd

Limitations of the Richard`s equation: RE model is highly non-linear due to pressure head

dependencies in the storage and conductivity terms. It is solved numerically using Finite differences or Finite

element techniques. For large-scale problems the conventional numerical

methods are complex and time-consuming. RE cannot describe accurately some flows like gravity-

driven fingers, which occur in an initially dry medium infiltrated at small supply rates.



Soil-Water Characteristic Curve Models (SWCC): Van Genuchten (1980) model is commonly adopted for

engineering applications:

The parameters are computed directly from special lab tests or indirectly from the grain size distribution.



(1 ) , 0

1, 011

n mre

s r

e

S

S

mn

Hysteretic phenomenon: Hysteresis is observed during consequent wetting and

drying cycles.

Models: Conceptual, based mainly on the dependent domain theory

(Mualem, 1974). Empirical, most of them based on VG model for the prediction

of main drying-wetting curves (Kool & Parker, 1983 – Huang et al, 2005).



Saturated soil mechanics: One stress variable (σ-uw) controls the saturated soil behaviour

(Terzaghi, 1936). Pore pressure is isotropic and invariant in direction (“neutral

stress”).

Unsaturated soil mechanics: Two stress variables (σ-ua), (ua-uw) mustmust be used for

unsaturated soils (Fredlung & Morgenstern, 1977). Pore pressure (no longer “neutral”) disintegrates in:

1. Air pressure acting on dry or hydrated grain surfaces.2. Water pressure acting on the wetted portion of grain

surfaces in menisci (ink-bottle effect).3. Surface tension along the air-water interfaces.



Unsaturated shear strenght: It is described in terms of the independent stress state

variables:



( - ) tan ( ) tanbf wc u u u

φb is highly non linear function ofmatric suction and can vary from a value close to φ (saturatedconditions) to as low as 0o (neardryiness).

It can be expressed as:tan tanb r

s r

Infinite slope analysis (Factor of Safety concept): Appropriate for long continuous slopes where the

thickness is small compared to the height. The end effects can be neglected. Each vertical block of soil above the failure plane have

the same forces acting on it.



tan 2tan sin 2

( ) (tan cot ) tan(1 ( ) )

ss

a wn m

a w ss

cFoSH

u uu u H

Constitutive models for unsaturated soils: Elasto-plastic models for unsaturated soils are based

on the Cam Clay model. Barcelona Basic Model (Alonso et al, 1990) is the

basis of many unsaturated elasto-plastic models: The yield surface is three dimensional in the p-q-s

space and the elastic domain increases as the suction increases.

A volumetric stress-strain relationship (influenced by sunction) is considered.

An hysteresis model is incorporated.



4.State of the Art

SHALSTAB (Montgomery and Dietrich, 1994) The model couples digital terrain data with a steady-

state water flow model and a slope stability model. Assumptions

Rainfall influences water flow only by modulating steady water table heights.

Water flow is exclusively parallel to the slope. Slope stability is computed using an infinite slope analysis.

Limitations: Neglects slope-normal redistribution of pore-water

pressures associated with transient infiltration of rain.


4.State of the art

dSLAM (Wu and Sidle, 1995) It is a distributed physically based model combining a slope

stability model with a 1-D kinematic wave model for the water flow accounting for vegetation and root strength.

Assumptions Rainfall influences water flow only by modulating quasi-

steady water table heights. Water flow is exclusively parallel to the slope. Slope stability is computed using an infinite slope analysis.

Limitations: Neglects the water flow in the unsaturated zone of soil,

which is crucial for triggering landslides.


4.State of the art

TRIGRS (Baum, Savage and Godt, 2002) It computes transient pore-pressure changes and

attendant changes in the factor of safety based on the Iverson`s (2000) linearised solution of Richard`sequation.

Linearised Richard`s equation:


4.State of the art

2

2

( ) 1[ ( sin )]

( ) [ ( cos )]

Lo

L z

C KC t x x

K Ky y z z

TRIGRS (Baum, Savage and Godt, 2002) If ε<< 1 ( ε= H/Α1/2, where H is the soil depth and A is the

catchment area that influences ψ) the terms multiplied by εcan be neglected.

If we assume Kz=Ksat and C=Co the equation becomes a 1-D linear diffusion equation which can be solved analytically:

Limitations: The model assumes flow in saturated or nearly saturated

homogenous, isotropic soil. Pore water pressure is only function of depth and time. The results are very sensitive to initial conditions.


4.State of the art

22

2cosoDt t

D`Odorico et al framework, 2005 An existing body of modeling approaches is put together in

order to calculate the return period of landslide-triggering precipitation.

The relative importance of long-term (slope parallel) flow with respect to short-term (vertical) infiltration combined with the characteristics of the hyetograph are explored.

Several features of previous models are coupled: A model of subsurface lateral (steady, long-term) flow

(Montgomery and Dietrich, 1994). A model of transient (short-term) rainfall infiltration (Iverson 2000). Intensity-duration-frequency relations of extreme precipitation are

used to determine the return period of landslides.


4.State of the art

GeoTOP-FS (Simoni et al, 2007) It is a distributed, hydrological-geotechnical model which

simulates the probability of shallow landslides and debris flow. Characteristics:

It is based on GEO-top distributed hydrological model which models latent and sensible heat fluxes and surface runoff.

Soil suction and moisture are computed by numerically integrating Richard`s equation in a 3-D scheme.

The relation between the suction ψ and volumetric water content θis given through the van Genuchten (1980) model.

Soil failure mechanisms are described through an infinite slope model.

Accounts for additional root cohesion, tree weight and surface runoff to the calculation of FS.


4.State of the art

Statistical framework for predicting landslides. Approaches:

Most statistical models rely on either multivariate correlation between mapped landslides and landscape attributes or general associations with soil properties (Carrara et al, 1995; Chung et al, 1995).

Other models analyze the intensity and duration of rainfalls triggering landslides. They built the critical rainfall threshold curves (Wieczorek,1987; Wieczorek et al, 2000; Crosta and Frattini, 2003).

Limitations: Lack of process-based analysis. Unable to assess the stability of a particular slope with respect to

certain storm characteristics. Unable to assess the return period of the landslide-triggering

precipitation.


4.State of the art

5.Cellular Automata

Basic definitions CA are dynamical systems discrete both in space and time. In space, a finite state automata is distributed over the nodes

of regular lattice. Each automaton can be in one of any finite number of states. Each automaton is connected to every other automaton at

pre-determined distance. In time, each automaton updates its state synchronously with

all other automata. This update is done according to fixed mapping function (local

transition function) from the present states of the automata to their future states.


5.Cellular Automata

Macroscopic Cellular Automata for Unsaturated flow All existing numerical methods for solving field equations have a

differential formulation as their starting point. To obtain a discrete formulation of the fundamental equation is

not necessary to go down to the differential form and then go upto the discrete (as most of numerical algorithms do).

CA can be used for the simulation of 3-D unsaturated water flow by considering the macroscopic equation of mass balance between the cells of the lattice:


5.Cellular Automata

( )a c cc a c c c

a

h h hK A V C Sl t

Macroscopic Cellular Automata for Unsaturated flow The states of the cell must account for all the characteristics

relevant to the evolution of the system. The discrete mass balance equation plays the role of the local

transition function used to update the states of the cells. CA can be used for the simulation of 3-D unsaturated water flow by

considering the macroscopic equation of mass balance between the cells of the lattice.


5.Cellular Automata

At the beginning the cells are in arbitrary states representing the initial conditions of the system.

The CA evolves by changing the states of all cells according to the transition function.

Why Cellular Automata? It`s how nature works: simple local rules produce a very complex

global behavior. Simulation of large-scale problems using fully coupled system

equations shows computational limitations. Both the dimension of the grid and the time step should be small

in order to achieve convergence. CA allow to increase the spatial and temporal domain of

simulations with acceptable computational requirements. CA are inherently parallel, as a collection of identical transition

functions simultaneously applied to all cells. Thus, the simulation can be accelerated tremendously by

running it simultaneously in many processors. 1.Introduction 2.PhD plan 3.Theoretical Background 4.State of the art 5.Cellular Automata 6.Field Campaign 7.Future plans

5.Cellular Automata

Sample problem for testing a CA algorithm A simple case, for which analytical solutions of Richard` s

equation exist (Tracy, 2006), is selected for testing the accuracy of a CA algorithm.


5.Cellular Automata

2

( )2

( )

, ,

( ),

1( , , , ) ln[ (1 ) sin cos ], ( , , , 0)

1 ln{ (1 ) sin cos

sinh 2[ ( 1) sin( )sinh

r

r r

r r

ahah ahs r r

s r

s

ah ahr

a L zah ah

k kk

kk ht z

k k k k e h e eah hh a c c

z t kx yh x y L t e e h x y z h

a a bx yh e e e

a a bz z eL Lc

1

]}t

k

Sample problem for testing a CA algorithm


5.Cellular Automata

(x=5, y=5), t=30s

01

23

456

78

910

-10-8-6-4-20Pressure height h (m)

dept

h (m

)

CAAnalytical

(x=5, y=5), t=60s

01

234

5678

910


dept

h (m

)

CAAnalytical

(x=5, y=5), t=120s

01

23

456

78

910


dept

h (m

)

CAAnalytical

(x=5, y=5), t=240s

0

12

34

56

78

910


dept

h (m

)

CAAnalytical

(x=5, y=5), t=480s

0

12

34

567

89

10


dept

h (m

)

CAAnalytical

(x=5, y=5), t=960s

0123

4

56

789

10


dept

h (m

)

CAAnalytical

6.Field Campaign


6.Field Campaign

Urseren Valley, Kanton Uri, 21/7-31/7/2009.

Persons involved: Grigoris Anagnostopoulos Markus Konz Marco Sperl Stefan Carpentier David Finger Kathi Edmaier Florian Köck


6.Field Campaign

Simulation of shallow landslides requires detailed knowledge of soil parameters and their spatial variability.

Parameters to be determined: Subsurface topography (Ground Penetration Radar). Grain size distribution. Atterberg limits. Soil Water Characteristic Curves (SWCC). Dry bulk density and porosity. Cohesion (c) and friction angle (φ). Saturated hydraulic conductivity (Ks).


6.Field Campaign

Dis

turb

ed

sam

ples

Und

istu

rbed

sa

mpl

es a

nd

in s

itu te

sts

In situ shear box test


6.Field Campaign

0

100

200

300

400

500

600

700

0 10 20 30 40 50

Horizontal diplacement (mm)

She

ar fo

rce

(N)

Shearbox 1Shearbox 2Shearbox 3Shearbox 4Shearbox 5

0

2

4

6

8

10

12

14

16

18

0 5 10 15 20 25 30 35 40 45 50

Horizontal diplacement (mm)

Ver

tical

dip

lace

men

t (m

m)

Shearbox 1Shearbox 2Shearbox 3Shearbox 4Shearbox 5

Inverse Auger Test


6.Field Campaign

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

1.00E-06 1.00E-05 1.00E-04

Hydraulic Conductivity (m/s)

Rel

ativ

e fr

eque

nce

(%)

Classification tests


6.Field Campaign

Ground Penetration Radar (GPR)


6.Field Campaign

High resolution GPR measurements (100,250 MHz) revealed deformations of a clay layer around the cutting edge of a landslide.

7.Future Plans

The CA algorithm, combined with a FS concept for the slope stability, will be implemented for a real case study for which data before and after the event exist.

Compare its results to other popular models (TRIGRS) and TOPKAPI.

If the results are satisfactory the algorithm will be programmed in parallel environment for greater efficiency in larger scales.

Establish regionalization methods for soil parameters. Incorporate subsurface topography anomalies

(macropores, deformation of soil layers etc) which can lead to local failures.


7.Future plans

Thank you for your attention!

Education

Hydrological Modelling of Shallow Landslides