Slope Stability Analysis under Variably Saturated Conditions

Advancing the Predictability of Infiltration Induced Landslidesof Infiltration‐Induced Landslides

Ning Lug

Currently Shimizu Visiting Professor, Stanford University

Can Pervasive Landsliding Occur under Rainfall Conditions?

Photograph showing geomorphologic evolution and land use dynamics near Hayward, CA. 

Can Pervasive Landsliding Occur under Rainfall Conditions?

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0.45

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4.5

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0.30

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ter Co

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3.0

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depth = 10 cm (mm

/hr)

0 10

0.15

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lumetric Wat

1 0

1.5

2.0

Precipita

tiodepth = 35 cmdepth = 60 cmdepth = 85 cmPrecipitation

Prec

ipita

tion

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0 0 0 0 1 1 1 1 1 1 1

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9‐Jan

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Date

Photograph showing landsliding around March 28, 2011 near Hayward, CA. 

How Does Pervasive Landsliding Occur under Rainfall Conditions?

Photograph showing abundant shallow landslides near Valencia CA The un‐vegetatedPhotograph showing abundant shallow landslides near Valencia, CA. The un‐vegetated scars are shallow failures caused by heavy rainfall in the winter of 2005.

How Long This Will Last?

Photograph showing on‐going landslides at Santa Monica beach, CA. 

Objectives( )(Partnership Team of CSM and USGS on Landslides)

T d l f k bl f t lTo develop a framework capable of accurately accounting for coupled hydrological and mechanical processes in hillslope environment.p p

To quantify, analyze, and predict infiltration‐induced landslides.

“ f h l h h h dl d d“If there is one single thing that is mishandled and leads to problems, it’s pore pressure.”

T Willi L bT. William LambeIn 2010 in an interview with graduate students from Virginia Tech.

Coupled Hydro‐Mechanical Framework

climatic data

hydrologic properties

SWCC, HCF

hydro-mechanical properties,

SSCC

Suction Stress Characteristic Curve (SSCC)

ijs

Geomorphologic Model

Landslide Analysis & Prediction

Hydrologic Model

Stress-Strain-Deformation

Model

GIS datavegetation

data

governing stress & strength

ti

governing head

equation

governing stress-strain &

deformation ti equationsequations

0bii3ji

sijijij '

)h(:(SWCC) Cure sticCharacteri WaterSoil

th

hthhC

xhk

x j3jj

)()(

x ii3j

ij E kk 'ij

1 E

ij '

f c ' n ' tan '

LFS = ’/*)k( :(HCF) Functionty Conductivi Hydraulic)(( )

i

j

j

iij x

uxu

21 CSM-USGS Landslide

Partnership Team

Conventional Slope Stability Analysis 

 

Bi h ’ M P i ’J b ’

Moment ResistantFS or

Force ResistantFS N

N

1ii

N

N

1ii

Bishop’s method

Morgenstern-Price’s method

Janbu’s methodFellenius’s method

Moment DrivingForce DrivingN

1ii

N

1ii

Presetting failure surface precludes accurate assessment of factor of safety!

Local Factor of Safety Based on Coulomb Stress

'G

'

D

c

'

'

'°+

'A B '

'c

Local Factor of Safety (LFS) is defined as the potential Coulomb stress at failure to the current Coulomb stress:

LFS = ’/* 

Local Factor of Safety Based on Coulomb Stress

'G

D

c

'O A B 'C

'E F

c

LFSDABG

DEGF

ACBC

*

'

sin*)''(sin 31 cBCBG

sin)2tan

(sin BCBG

DE = failure Coulomb stressGF = current Coulomb stress

Field of LFS )tan)''((*''

cos),,,(

3131

c2tzyxFLFS

Vertical Cut: Equilibrium Analysis         LFS from FEM 

Hcm

dry or saturated

kN/m20m 10H

H

3

New York Times, April 15, 2011

variesc35o

Vertical Cut: Progressive Analysis of LFS from FEMdry ordry or 

saturated

LFS has potentials to identify initiation and progression of landslides!

60° Slope: Equilibrium Analysis         LFS from FEM

dry ordry or saturated

LFS has potentials to identify zones venerable to instability!

45° Slope: Equilibrium Analysis         LFS from FEM

dry ordry or saturated

LFS has potentials to delineate shape evolution of venerable zone!

dry or

30° Slope: Equilibrium Analysis         LFS from FEM

dry or saturated

Identification of realistic failure initiation and progressionIdentification of realistic failure initiation and progression zone cannot be done

by conventional slope stability methodologies!

30° Slope: Equilibrium Analysis         LFOS from FEMdry or

Unsaturated fluid flow and stress changes have not been accounted for correctlydry or 

saturatedy

by conventional slope stability methodologies!

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wijij u '

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wijij

Effective stress for saturated conditions cannot be used for failure prediction!

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Unified Effective Stress for Variably Saturated Porous Mediay

sijijij 'Unified effective stress (Lu and Likos, 2006):

1000 0Suction Stress Characteristic Curve (SSCC)Soil‐Water Characteristic Curve (SWCC)

100.0

1000.0

a) Pa)

10000

100000

Series1

Series2

Series3

Sand: = 0.3 kPa-1, n = 3.0

Clay: = 0.01 kPa-1, n = 1.8Silt: = 0.05 kPa-1, n = 2.5

10.0

n st

ress

s, (

kPa

n st

ress

(-kP

100

1000

c su

ctio

n (k

Pa)

1.0suct

ion

Sand: alpha = 0.3 kPa-1, n = 3.0Silt: alpha = 0.05 kPa-1, n = 2.5

suct

ioSeries1

Series2

Sand: = 0.3 kPa-1, n = 3.0

Silt: = 0.05 kPa-1, n = 2.51

10Mat

ri

1

0.10.0 0.2 0.4 0.6 0.8 1.0

effective saturation, unitless

Clay: alpha = 0.01 kPa-1, n = 1.8

0 20 40 60 80 100

Saturation (%)

Series3Clay: = 0.01 kPa-1, n = 1.8

1

0.10 20 40 60 80 100

Saturation (%)

-air entry pressure n-pore size spectrum

(van Genuchten, 1980)

nn1

n

ewa 1S1uu

(Lu and Likos, 2004)

n1

n1n

ees 1SS

Unified Effective Stress for Variably Saturated Porous Mediay

sijijij 'Unified effective stress (Lu and Likos, 2006):

Soil‐Water Characteristic Curve (SWCC) Suction Stress Characteristic Curve (SSCC)

10000

100000

Series1

Series2

Series3

Sand: = 0.3 kPa-1, n = 3.0

Clay: = 0.01 kPa-1, n = 1.8Silt: = 0.05 kPa-1, n = 2.5

100

1000

a)

Series1

Series2

Series3

Sand: = 0.3 kPa-1, n = 3.0

Clay: = 0.01 kPa-1, n = 1.8Silt: = 0.05 kPa-1, n = 2.5

100

1000

c su

ctio

n (k

Pa)

10

ion

stre

ss (-

kPa

1

10Mat

ric

1

Suc

t

1

0.10 20 40 60 80 100

Saturation (%)

0.10 100 200 300 400 500

Matric suction (kPa)

n1nn

wa

was

uu1

uu/

(Lu and Likos, 2004)(van Genuchten, 1980)

n1

n1n

ewa 1S1uu

, n

FEM‐Based HILLSLOPE (FS)2 Framework Flow and Stress & Factor of SafetyFlow and Stress & Factor of Safety

• Finite element method model

l d h d h l f k• Coupled hydro‐mechanical framework

Geomorphologic Model

Stress-Strain-Deformation

Model

Hydrologic Model

Landslide Analysis & Prediction

Automesh2D/3D

FEM2D/3D

FEM2D/3D

Effective stress and

climatic dataelevation data

vegetation data

local F.S. distributions

Novel Features in Landslide Analysis & Prediction 

Unified effective stress (Lu and Likos, 2006)

sijijij '1.

ewas Suu

n111SS

/

Suction stress (Lu and Likos, 2004)

S il i

2.

nwar

re uu1

1S1SSS

Soil‐water retention curve (van Genuchten, 1980)

3.

n1nn

wa

was

uu1

uu/

Suction stress characteristic curve  

(Lu and Likos, 2004; Lu et al., 2010)4.

t)2(2*cos sLFS Local factor of safety

Plant root strength (Wu et al., 1978)rootccc '5.

6 tan)2(2* 31

31

scLFS

Local factor of safety  (Lu et al., 2010)

6.

Case Illustration 1: Hydro‐Mechanical Modeling of a 5‐day SnowMelting on a 30° Silty Slopeof a 5‐day Snow Melting on a 30 Silty Slope

4 0E-78.0E-71.2E-61.6E-6

infa

ll (m

/s)a

A

15m

0.0E+04.0E-7

0 5 10 15 20 25 30

Rai

Time (days)θr  0.034 θs  0.46 α  1.6 m‐1 

Total 500 mm of water!

5 m

n  1.37 Ks  1.39e‐6 m/s C  10 kPa   20 kN/m3   30 

            30 m

5  0.33 E  10000 kPa 

Moisture, Suction Stress and LFS Responses

 

1E+3

1E+4

1E+5

1E+6

1E+3

1E+4

1E+5

1E+6ss

(-kP

a)

Pa)

SWRC

SSCCSilty soil

1E+0

1E+1

1E+2

1E+3

1E+0

1E+1

1E+2

1E+3

Suc

tion

Stre

s

Suc

tion

(kP

1E-11E-10 0.1 0.2 0.3 0.4 0.5

Volumetric Water Content, θ

Variations of Moisture and Suction Profiles

rs

reS

)( wa uu

Variations of Suction Stress and Local Factor of Safety ProfilesLocal Factor of Safety Profiles

tan)2(2*cos 31

31

swae

s cFSuuS

Case Illustration 2: Landslide Monitoring and PredictionShallow Landslides on sandy slopes at Edmonds Site, Seattle, WAy p

• Steep (45°) costal bluff about 50 m high

•Most slides result from prolonged heavy rainfall

• Shallow landslides typically involve colluviumShallow landslides typically involve colluvium

overlying well‐consolidated glacial/non‐glacial sediments

• Hillside vegetation is Alder, Blackberry, and grasses (Godt, Baum, and Lu, 2009, GRL)

Rainfall Characteristics

• 500 mm of rain between Sept‐05 and Feb‐06

• Wet period begins middle of Dec‐05; heaviest rainfall around Christmasp g

•~200 mm of rain between 17‐Dec‐05 and 15‐Jan‐06

• Heavy rainfall in early Jan‐06 increases pressure and water contents at shallow depths

Shallow Landslide, 14 January 2006

d• Adjacent to instrumentation

• Did not reach tracks

• 0 6 ‐ 1 5 m thick in colluvium• 0.6  1.5 m thick in colluvium

Geologic and Contour Map of Shallow Landslide

Rootwad

Moisture Profiler

Suction Probe

Wet‐season Hydrologic Response to Rainfall• 500 mm of rain between Sept‐05• 500 mm of rain between Sept‐05 and Feb‐06

• Drastic moisture changes aroundDrastic moisture changes around Nov. 5, Nov. 22, and Dec. 22.

• Vertical moisture movement follows advective‐diffusive pattern.

• Soil suction drastic reduced around Nov. 5, Nov. 22, and Dec. 22.

• Suction/pore pressure remains tensile and soil unsaturated duringtensile and soil unsaturated during the entire monitoring period.

•Suction stress variations:Suction stress variations:

war

rs uuSSStz

1

),(

Wet‐season Mechanical Response to Rainfall• Suction stress due to wetting:

• Factor of safety by infinite slope

war

rs uuSSS

1

y y pmodel from the classical:

'tancottantan

'tan)(

urzFS

Slid t d d i th 2 d

tan

ss

s

u Hr

• Slides reported during the 2nd week of Jan-06

• Slides roughly coincident withSlides roughly coincident with water content and suction peaks at depths > 80 cm

Summary and Conclusions

• Coupled hydro‐mechanical framework can capture major physical processes in hillslopes, implying in‐situ monitoring of p y p p p y g gsuction and moisture variations are important tools.

• Unified effective stress is valid for variably saturated hillslopeUnified effective stress is valid for variably saturated hillslope materials.

S i i b d fi ld f f f f i f l• Stress‐invariant based field of factor of safety is very powerful in capturing slope instability initiation and evolution.

• Three constitutive relationships or material properties are sufficient and necessary to characterize unsaturated hydro‐mechanical behavior: SWCC HCF and SSCCmechanical behavior: SWCC, HCF, and SSCC.

Questions?

ReferencesLu, N. and Likos, W.J., Unsaturated Soil Mechanics, John Wiley & Sons,  2004.

NING LUG U

JONATHAN W. GODT

HILLSLOPE HYDROLOGY AND STABILITY

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

AcknowledgementGrants from USGS, NSF, and CDOT make this research sustainable.

ninglu@mines.edu, http://inside.mines.edu/~ninglu/

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