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Numerical Analysis of the Influence of
Initial Hydraulic Boundary Conditions on
the Infiltration Behaviour of Unsaturated
Soil Slopes
Patrick P. Pichler
Institute of Soil Mechanics, Foundation Engineering and Computational Geotechnics
Graz University of Technology
2
▪ Introduction – Why unsaturated soil mechanics?
▪Numerical back-calculation of Lysimeter-data
▪Safety analyses on benchmark slope geometry
▪Rainfall infiltration into a real slope
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
Content
3
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
Introduction – Why unsaturated soil mechanics?
Collapse in Via Luigi Settembrini, Naples (2001)La Conchita, California (2005)
4
Introduction
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
5
Matric suction & Capillary forces
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
𝒔 =𝟐 𝑻𝒔 𝒄𝒐𝒔𝜶
𝑹= 𝒖𝒂 −𝒖𝒘
6
The initial pore-water-pressure conditions, before a (heavy)rainfall event starts, can play a major role in the instability ofsoil slopes!
▪Numerical analyses:
Due to equilibrium reasons the solely use of the initialgroundwater-level would lead to a linearly increasing negativepore-water-pressure above the groundwater-level, which maynot be realistic!
Focus on initial conditions
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
7
▪Given data (continuously measured):
▪Precipitation▪Evapotranspiration
▪Suction in certain depths
Lysimeter
Grass-covered Lysimeter, testfield “Wagna”, Styria
(Klammler et. al, ongoing)
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
8
Lysimeter – Climatic hydrograph
Grass-covered Lysimeter, testfield “Wagna”, Styria
(Klammler et. al, ongoing)
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
-10
0
10
20
30
40
50
60
70
80
90
100
-10
0
10
20
30
40
50
60
70
80
90
100
19.04.2013 19.04.2014 19.04.2015 18.04.2016 18.04.2017
Su
ctio
n [
kP
a]
Pre
cip
ita
tion
/ E
va
po
tran
spir
ati
on
[m
m]
Timeline
P [mm] ETr [mm] ET0 [mm] suction 20 cm [kPa] suction 50 cm [kPa]
9
Lysimeter – SWCC & relative permeability
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,01 0,1 1 10 100 1000
Sa
tura
tio
n [
-]
suction [kN/m²]
Layer1 0-30
Layer2 30-50
Layer3 50-80
Layer4 80-130
Layer5 >130
1,0E-15
1,0E-14
1,0E-13
1,0E-12
1,0E-11
1,0E-10
1,0E-09
1,0E-08
1,0E-07
1,0E-06
1,0E-05
1,0E-04
1,0E-03
0,01 0,1 1 10 100 1000
un
satu
ra
ted
per
mea
bil
ity
[m
/s]
suction [kN/m²]
Layer1 0-30
Layer2 30-50
Layer3 50-80
Layer4 80-130
Layer5 >130
g
p
w
wp
=
( ) ( ) ( )c
ng
g
paressatresp gSSSS
+−+= 1
ressat
rese
SS
SSS
−
−=
( ) ( )
21
111
−−=
−
− n
n
ng
ng
lg
g
eg
erel SSSk
10
Lysimeter – Backcalculation results
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
-5
0
5
10
15
20
25
30
35
40
-5
0
5
10
15
20
25
30
35
40
1 6 11 16 21 26 31 36 41 46 51 56 61
Pre
cip
ita
tion
/ E
va
po
tran
spir
ati
on
[m
m]
suct
ion
[k
Pa
]
Timeline [days]
suction 20 cm depth (kPa) suction 50 cm depth [kPa] precipitation-evapotranspiration [mm]
11
Lysimeter – Backcalculation results
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
-5
0
5
10
15
20
25
30
35
40
-5
0
5
10
15
20
25
30
35
40
1 6 11 16 21 26 31 36 41 46 51 56 61
Pre
cip
ita
tion
/ E
va
po
tran
spir
ati
on
[m
m]
suct
ion
[k
Pa
]
Timeline [days]
suction 20 cm depth (kPa) PLAXIS suction -20 cm [kPa] suction 50 cm depth [kPa] precipitation-evapotranspiration [mm]
12
Lysimeter – Backcalculation results
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
-5
0
5
10
15
20
25
30
35
40
-5
0
5
10
15
20
25
30
35
40
1 6 11 16 21 26 31 36 41 46 51 56 61
Pre
cip
ita
tion
/ E
va
po
tran
spir
ati
on
[m
m]
suct
ion
[k
Pa
]
Timeline [days]
suction 20 cm depth (kPa) PLAXIS suction -20 cm [kPa] suction 50 cm depth [kPa]
PLAXIS suction -50 cm [kPa] precipitation-evapotranspiration [mm]
13
Goals & Questions
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
Important Question: When do manually & automatically
generated pwp‘s match?
14
Goals & Questions
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
-5
0
5
10
15
20
25
30
35
40
-5
0
5
10
15
20
25
30
35
40
1 6 11 16 21 26 31 36 41 46 51 56 61
Pre
cip
ita
tion
/ E
va
po
tran
spir
ati
on
[m
m]
suct
ion
[k
Pa
]
Timeline [days]
suction 20 cm depth (kPa) PLAXIS suction -20 cm [kPa] PLAXIS suction -20cm GW [kPa]
suction 50 cm depth [kPa] PLAXIS suction -50 cm [kPa] PLAXIS suction -50cm GW [kPa]
precipitation-evapotranspiration [mm]
15
Lysimeter – Backcalculation (suction prediction)
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
-10
0
10
20
30
40
50
60
70
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 120 140 160 180
Su
ctio
n[k
Pa
]
Net
-Pre
cip
ita
tio
n[m
m]
Time [days]
P-Etr [mm]
suction 20 cm [kPa]
suction 50 cm [kPa]
PLAXIS suction 20 cm [kPa]
PLAXIS suction 50 cm [kPa]
From here on:
Only numerical prediction in 20 cm depth!
16
Benchmark slope - Geometry
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
Same stratigraphy as in simple
Lysimeter „box-studies“
GW table initially ALWAYS
3.5 m below ground surface
Different slope angles
▪ Geometry A → 2,00:1 ( = 26.57°)
▪ Geometry B → 2,50:1 ( = 21,80°)
▪ Geometry C → 2,25:1 ( = 23,94°)
17
Completed investigations
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
pwp’s
Auto / Manual
Run-off criteria
max= 1 mm / 15 mm
Saturated (reference)
permeability
kref / kref:10 / kref:100
Climatic hydrograph
192 / 120-120 / const.
Hydraulic BC’s
Closed / Head
Modified hydrographs
“cutting of rainfall peaks”Location gw-level
-3.5 / -7.0 m
18
Influence of max
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
-10
0
10
20
30
40
50
60
70
80
90
100
-10
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140 160 180
Pre
cip
ita
tion
/E
va
po
rati
on
[m
m]
Su
ctio
n [
kP
a]
Timeline [days]
192 days
kref & Influence of max
P-Etr [mm] M_192_m_psi_1 M_192_50_psi_1 A_192_20_psi_1 A_192_50_psi_1
M_192_20_psi_30 M_192_50_psi_30 A_192_20_psi_30 A_192_50_psi_30
Once suction is equal to zero,
there‘s no influence of the initially
defined suction anymore!
19
kref/100 & Influence of max
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
-10
0
10
20
30
40
50
60
70
80
90
100
110
120
-10
0
10
20
30
40
50
60
70
80
90
100
110
120
0 20 40 60 80 100 120 140 160 180
Pre
cip
ita
tion
/ E
va
po
rato
pn
[m
m]
Su
ctio
n [
kP
a]
Timeline [days]
192 days
kref/100 & Influence of max
P-Etr [mm] M_192_20_psi_1 M_192_50_psi_1 A_192_20_psi_1 A_192_50_psi_1
M_192_20_psi_30 M_192_50_psi_30 A_192_20_psi_30 A_192_50_psi_30
20
-10
0
10
20
30
40
50
0 20 40 60 80 100 120 140 160 180
Net
-Pre
cip
ita
tio
n[m
m]
Timeline [days]
P-Etr [mm]
Safety calculations on Benchmark slope
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
First 40 days [of 192 days dataset]
21
-10
0
10
20
30
40
50
0 20 40 60 80 100 120 140 160 180
Net
-Pre
cip
ita
tio
n[m
m]
Timeline [days]
P-Etr [mm]
Safety calculations on Benchmark slope
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
Starting with day 40 [of 192 days dataset]
22
Safety calculations on Benchmark slope
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
kref
max = 1 mm
suction in all phases
Model A
initial 1.58
after day 39 1.17
after day 40 1.15
kref
max = 1 mm
suction in all phases
Model A
initial 1.58
after day 40 only 1.21
23
Real slope geometry
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
24
Climatic hydrograph
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
0
1
2
3
4
5
6
7
Vo
lum
e [m
m/m
²
da
y]
Timeline [months]Precipitation A Precipitation B Potential evaporation APotential evaporation B Infiltration A Infiltration B
-10
0
10
20
30
40
50
Vo
lum
e [m
m/m
²d
ay
]
Timeline [days]
25
Results of using the monthly precipitation dataset while varying SWCCs and saturated permeabilities and either considering the antecedent on year of precipitation or not
Influence of previous rainfall events
Type
Sliding mass Transition zone Original data Additional rainfall
SWCC ksat [m/s] SWCC ksat [m/s] FoS before FoS after q [m/day]duration
[days]FoS
1-33 Coarse 1.0 e-3 Coarse 1.0 e-3 1.28 1.14 0.3 2 1.13
1-33 Coarse 1.0 e-6 Coarse 1.0 e-6 1.28 1.26 0.3 10 1.24
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
26
Influence of previous rainfall events
Type
Sliding mass Transition zone Original data Additional rainfall
SWCC ksat [m/s] SWCC ksat [m/s] FoS before FoS after q [m/day]duration
[days]FoS
1-33 Coarse 1.0 e-3 Coarse 1.0 e-3 1.28 1.14 0.3 2 1.13
- 1 year Coarse 1.0 e-3 Coarse 1.0 e-3 1.28 - 0.3 2 1.20
1-33 Coarse 1.0 e-6 Coarse 1.0 e-6 1.28 1.26 0.3 10 1.24
- 1 year Coarse 1.0 e-6 Coarse 1.0 e-6 1.28 - 0.3 10 1.28
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
Results of using the monthly precipitation dataset while varying SWCCs and saturated permeabilities and either considering the antecedent on year of precipitation or not
27
▪ With respect to the reproduction of real-life suction profiles in unsaturated soils, the back-calculation of Lysimeter-data in a column-test with PLAXIS 2D delivers very satisfactory results
▪ The application of the described procedure avoids the use of uncertain hydraulic input-parameters, which could affect the infiltration behavioursignificantly
▪ Antecedent precipitation greatly influences the pore water pressure profile in slopes and should therefore always be considered
Conclusions
Numerical analysis of the influence of initial hydraulic boundary conditions on the infiltration behaviour of unsaturated soil slopes
Thank you for your attention!
Patrick P. Pichler
Institute of Soil Mechanics, Foundation Engineering and Computational Geotechnics
Graz University of Technology
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