physical based models of landslides' triggering

Riccardo Rigon, Giuseppe Formetta, Giovanna Capparelli, Fabio Ciervo, Mariolina Papa

Process -based models of landslide triggering (especially the hydrological parts)

Giornata di Studio su: “La modellazione dell’innesco dei movimenti franosi - Rende 7 Novembre 2013

We feel clearly that we

are only now beginning to acquire reliable

material for welding together the sum total of all

that is known into a whole; but, on the other

hand, it has become next to impossible for a

single mind fully to command more than a small

specialized portion of it.

!E. Schroedinger (What is life ?)

!3

What’s the physics of landslides ?

Hillslope Hydrology

Introduction

Rigon et al.

Hillslope stability

+

!4

Hillslope Hydrology

bricks

Introduction

Darcy hypothesis

Mass conservation

Soil water retention curves (SWRC)

Fluxes Hypothesis

Eventually assume a theory that relates SWRC to fluxes

Rigon et al.

!5

Darcy’s hypothesis

Hillslope hydrology

Rigon et al.

This is the REV Representative Elementary Volume

!6

Richards’ equation core

is that what it is true is this

Mass conservation (no nuclear reactions) ! but actually true if the continuum (a.k.a. Darcy) hypothesis is valid

Hillslope hydrology

Rigon et al.

!7

Assume a parametric form of soil water retention curves

Se :=�w � �r

⇥s � �r

Parametric van Genuchten (1981)

C(⇥) :=⇤�w()⇤⇥

Se = [1 + (��⇥)m)]�n

But other forms are possible ...

Hillslope hydrology

Rigon et al.

!8

Flux hypothesis

Darcy-Buckingham Law

Volumetric flow through the surface of the infinitesimal volume

Hydraulic conductivity times gradient of the hydraulic head

Bu

ckin

gh

am, 1

90

7, R

ich

ard

s, 1

93

1

~Jv = K(✓w)~r h

Hillslope hydrology

Rigon et al.

!9

A theory for getting hydraulic conductivity from soil water retention curves

K(�w) = Ks

⇧Se

⇤�1� (1� Se)1/m

⇥m⌅2

But other forms are possible also here...

Hillslope hydrology

Rigon et al.

!10

Now you can simplify it

Hillslope hydrology

http://abouthydrology.blogspot.it/2013/06/ezio-todini-70th-symposium-my-talk.html

Rigon et al.

!11

Simplifications with more details

http://abouthydrology.blogspot.it/2013/07/hillslope-hydrology-from-point-of-view.html

An outcome of this project

Rigon et al.

!12!12

Soil depth

Soil

rocks

Where does water flow ?

The medium is the message

Rigon et al.

!13

Because is usually believed that it is the perched water

table that can form at soil

discontinuity that causes shallow landslides

Soil depth is particularly important for landslides

The medium is the message

Rigon et al.

Perched water table

Water table

http://abouthydrology.blogspot.it/2012/09/soil-depth-estimation.html

!14

Hillslope stability

bricks

Stresses (and strains)

Effective stresses

Soil stresses characteristics curves (SSCC)

Material strength (Coulomb Hypotesis)

Factor of safety

Rigon et al.

Geomechanics

!15

I do not enter into

the geotechnical

details

Rigon et al.

http://www.camilab.unical.it/summer_school/index.html

Geomechanics

!16

Commercial a good book save a lot of searching

N. Lu, J. Godt,Hillslope Hydrology and Stability, Cambridge University Press, 2012

Rigon et al.

Geomechanics

http://www.amazon.com/Ning-Lu/e/B001HMLJ3W/ref=ntt_athr_dp_pel_1

http://www.amazon.com/s/ref=ntt_athr_dp_sr_2?_encoding=UTF8&field-author=Jonathan%20Godt&search-alias=digital-text&sort=relevancerank

!17

Advancing Knowledge Promoting Learning�

6.#Effec(ve#Stress#in#Soil�

!  Suction stress is the effective stress (skeleton stress) with zero total stress.

!  Suction stress is the work done by the inter-particle stress or internal stress due to water.

!  What are the components of the inter-particle stress σs?

What is Suction Stress?

11

s

s

s s

Dry: no stress (a)

Wet: internal suction stress (b)

Dry: equivalent suction stress (c)

dε1 dε1

dε 2

dε 2

! s = !!C = !! cap !! pc ! S ua !uw( )

Rigon et al.

However, let me say something

Dry: no stress Dry: equivalent suction stressWet: internal

suction causes , and correspondent

strain

Geomechanics L

u a

nd

God

t, 2

01

2

!18

Ning Lu

Geomechanics

!19

Lu

an

d G

od

t, 2

01

2

Effective stress at REV is the composition of several

forces acting at micro scale

Advancing Knowledge Promoting Learning�

6.#Effec(ve#Stress#in#Soil�

!  To define a stress that accounts for soil saturation and is “effective” in describing strength and deformation at Representative Elementary Volume (REV).

Stresses at sub-pore scale " forces at pore scale " stress at soil REV scale

Rationale for Suction Stress Characteristic Curve

10

Fc

uw

Fcap

ua

Fpc

A

Aa2

Aa3

Aw1

Aw2

Aw3

Ac1

Ac2

Ac3

Area of REV Cross-Section

Aa1

Aa4

Fc

uw

Fcap

ua

Fpc

A

Aa2

Aa3

Aw1

Aw2

Aw3

Ac1

Ac2

Ac3

Area of REV Cross-Section

Aa1

Aa4

w uwSa ua 1 S( )cap = fcap (S)pc = fpc (S)

' = ua( ) + S ua uw( ) + cap + pc

' = ua( ) s

s = S ua uw( ) cap pc

c = - s

Soil-Water-Air REVContinuum Media

cap a

c = -

wpc

c = -Soil-Water-Air REVContinuum Media

cap a

c = -

wpc

c = -Soil-Water-Air REVContinuum Media

cap a

c = -

wpc

Ft

Suction stress�

Rigon et al.

Geomechanics and vadose zone hydrology

!20

Effective suction stress is then:

Effective stress

Lu

an

d G

od

t, 2

01

2

Rigon et al.

Stress in material

air pressure

Suction stress


!21

Effective suction stress is then:

capillarity

interparticle stresses

relative water content

water pressure

Rigon et al.


!22

Soil Suction Characteristic Curves

SSCC

As a result of Lu et al. 2010 work, suction stress can be expressed as a

function of the SWRC:

Se :=�w � �r

⇥s � �r

Parametric van Genuchten (1981) Se = [1 + (��⇥)m)]�n

from slide 7


Rigon et al.

!23

Therefore

Rigon et al.


The determination of the SWRC is of fundamental

importance, and the key to predict both soils

suction and stress evolution in hillslopes

What about hillslope

failure ?

!24


FoS

Factor of Safety

Rigon et al.

Both Material Strength and Design Loads, in

the hillslope game are function of the stresses

Details in Lu and Godt, 2012 and references therein

!25

To sum up

We have a sound and comprehensive theory

!

GEOtop and its brothers and sisters

!27

So what ? We have the theory (and the equations)!

However we have to

implement it in sound numerical code

to identify the parameters (and there are quite a few)

treat the input and the output data

Rigon et al.

!28

GEOtop

!• it models: !- subsurface saturated and unsaturated flows !

- surface runoff !

- turbulent fluxes across the soil-atmosphere interface.

Rig

on

et

al.,

20

06

, En

dri

zzi

et a

l., 2

01

3GEOtop as a tool of this project

Rigon et al.

!29

GEOtop

• 3D physically based finite-difference model !!

• spatially distributed

Rig

on

et

al.,

20

06

, En

dri

zzi

et a

l., 2

01

3GEOtop as a tool of this project

Rigon et al.

!30

Dav

id

et

al.,

20

13

Model integration with OMS

The Object Modeling System is a modular modeling framework that,

using an open source software approach, enables all members of the

scientific community to address collaboratively the many complex

issues associated with the design, development, and application of

distributed hydrological and environmental models.

Features

Components interoperability

Data interoperability

Language interoperability

GEOtop as a tool of this project

Rigon et al.

!31

In reality GEOtop is the most complex of a series

of models

and one scope is to compare many of them, and eventually use them for different purposes. In red those already implemented for the project.

Other tools

Rigon et al.

!32

GEOtop:

https://code.google.com/p/geotop/

CISLAM and SHALSTAB:

https://code.google.com/p/jgrasstools/

code at:

code at:

information at: http://abouthydrology.blogspot.it/search/label/GEOtop

information at:http://abouthydrology.blogspot.it/2012/09/my-past-research-on-shallow-landslide.html

Every is free … as “free of speech"

https://code.google.com/p/geotop/

!33

Many landslides models with many physical approximations !• Does exist a minimum physical degree of simplification to

model a landslide? !

• Is it possible create a unique modeling framework where different models can be executed and compared? !!!!!!

Research but also practical questions

Rigon et al.

Questions

!34

Waiting for the data

… an application where we have some

TuostoloRigon et al.

It works!

!35

Measurement station

Some results

Rigon et al.

It works!

!36

Measurement station

• Suction [KPa] simulation at 0.35 m depth !

• Simulation period: 01-12-2007 to 01-05-2008

PBIAS=1.90 NSE=0.83

Rigon et al.

It works!

Tuostolo - Campania- Italy

!37

Tuostolo - Campania- Italy

• Soil moisture simulation at 0.35 m depth !

• Simulation period: 01-12-2007 to 01-05-2008 !• Time step: hourly

PBIAS=2.1 NSE=0.70

!38

Drake River - CO - USA

Trento 17 June 2011G. Formetta, Trento 24 June 2011G. Formetta,

C1

C3

Input data: • Radiation • Rainfall • Air Temperature • Relative Humidity !Output: • soil moisture at

different depths

!39

Simulation period: 01/09/2008-01/02/2009 !Simulation timestep: hourly


!40



Suction (mm)

30 cm depth

50 cm depth

!41



Suction (mm)

30 cm depth

50 cm depth

!42



Suction (mm)

30 cm depth

50 cm depth

!43

Safety factor


!44

Comments

• GEOtop seems able to reproduce decently suction and water contents

• Therefore it can be reliably used for trying a forecasting of these quantities

• Certainly more analysis and data are required

It works!

Rigon et al.

The IWL3 Round Robin

!46

Thanks to Neaples Group: the IWL3 experiment

R. Greco1, L. Comegna1, E. Damiano1, A. Guida1,2, L. Olivares1, and L. Picarelli1

1Dipartimento di Ingegneria Civile Design Edilizia e Ambiente, Seconda Università di Napoli, via Roma 29, 81031 Aversa (CE), Italy 2Centro Euro-Mediterraneo sui Cambiamenti Climatici, via Maiorise, Capua (CE) 81043, Italy

GEOtop in the lab

Rigon et al.

!47

Tes t

nr.

Soi l Thickness (cm)

Slope Length (cm)

Initial porosity n0

Rainfal l intensity (mm/h)

Init ial mean suction (kPa)

Duration of test (min)

D3 10.0 100 0.75 55 17.5 36

D4 10.0 120 0.76 56 41.0 30

The inclination of the slope is 40°. !The test are carried out with constant and spatially homogeneous rainfall intensity.

Several devices (tensiometer, pore pressure transducer, TDR and laser

Rigon et al.

GEOtop in the lab

!48

. !!

first displacementfailure

first displacement

factor of safety here is 1.2

Suctions and pressures

-5 cm

-10 cm

Rigon et al.

Analysis of the data

!49

Water Content

Rigon et al.


!50

Water Content talks

Hydraulic conductivity was measured in the lab. The value given was around one order of magnitude less than the artificial rainfall

So we expect an Hortonian flux: saturation at the top and movement downward.

Which we do not have!

Rigon et al.


!51

So we expect an Hortonian flux: saturation at the top and movement downward.

red line is more ore less what we expect just after the beginning of irrigation in a Hortonian interpretation of infiltration

Rigon et al.


!52

What about the Darcy scale here ?

Rigon et al.

Questions

!53

Water Content talks

Is irrigation really stationary ? What happens after the 28th minute ? Lateral flow triggers ?

Rigon et al.


!54

Two hydraulic conductivities

One hypothesis we did is that, despite the homogeneity of the

preparation of the experiment, hydraulic conductivity (at

saturation) at the bottom is different from hydraulic conductivity at

the top of the mock-up.

Due to packing of particles ? Due to some unavoidable imperfection

in preparation ? Due to avoidable imperfection of the preparation ?

What else ?

Rigon et al.

Let’s go !

!55

Suction talks

Both suction and water content data were used to calibrate van Genuchten parameters. Also the hydraulic conductivity is among

Se :=�w � �r

⇥s � �r

Se = [1 + (��⇥)m)]�n

Also hydraulic conductivity at saturation is a calibration parameter

K(�w) = Ks

⇧Se

⇤�1� (1� Se)1/m

⇥m⌅2

Rigon et al.

Which parameters ?

!56

Calibrated Parameters

alfa n m0.052 1.805 0.445983

Ksat_layer superficiale (0-5cm) = 0.178 mm/s

Ksat_layer di fondo (5-10cm) = 0.117 mm/s

Rigon et al.

Which parameters ?

!57

Rigon et al.

Suctions

!58

Averaging does not get the right result

even if water contents are reproduced fairly well until the 21th minute

Rigon et al.

Water content

!59

Discussion

The friction angle of the material is 38 degrees. Therefore the stability

depends mainly on suction.

The FoS has been calculated into 2 different ways, by using the Fos

below that includes both the “classical” and “Lu’ Fos:

Rigon et al.

Analysis of the set up

!60

Stresses (FoS)

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Stresswise

!61

Stresses (FoS)

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Stresswise

!62

Comment

The way you calculate the FoS matters. While with the classical approach,

FoS remains consistently higher than 1 (close to 2), with Lu approach the

FoS comes close to 1.

In a sense, also this is not satisfactory, since we would like to have a

safety factor well below 1.

Do we neglected something ?

Rigon et al.

Stresswise

!63

Conclusion

We are close … but also far away …

The project allowed to set up an infrastructure that can be used to

investigate real cases, and to better tune experiments

On the present infrastructure can be incrementally built

“Real Time” physical modelling of these phenomena is feasible

Rigon et al.

What we gain

Thank you for your attention

G.U

lric

i, 2

00

0 ?

!64

La presentazione può essere scaricata da http://abouthydrology.blogspot.com

R. Rigon

Closing

http://abouthydrology.blogspot.com

!65

Do the physics simplify at hillslope scale ?

Which measures can we envision to make a verification of the theory ?

Can lab measures reproduce field ?

Questions

How we characterise spatial patterns (needed to check real cases) ?

The theory is sound … where it fails ?

What the relation between mass waste and erosion ?

How can we validate the overall process ?

What is the influence of these phenomena on landscape evolution ?

Rigon et al.

Closing

!66

What the role of plants’ roots in stability?

Questions

Rigon et al.

Closing

physical based models of landslides' triggering

Education