Liquefaction Mechanisms of
Upper and Lower San Fernando Dams
in the 1971 Earthquake
X. S. Li
Hong Kong University of Science and Technology
11/10/2003
Lower and Upper San Fernando Dams after 1971 Earthquake
Steinbrugge Collection, Earthquake Engineering Research Center
University of California, Berkeley
Photo: Cluff, LLoyd
Observations (Seed et al. 1973)
• Upper dam
– Liquefied and weakened in certain zones;
– A significant body of the hydraulic fill still retained
considerable resistance;
– Complete flow slide did not occur.
• Lower dam:
– A large part of hydraulic fill liquefied;
– The shear resistance of the soil could no longer
withstand the initial driving forces;
– Slide developed consequently.
Question
• Why the two dams responded so differently to the
same earthquake?
Given that they were
– founded on similar natural alluvium
– constructed using similar borrowing material
and similar hydraulic filling method
– located only two miles away from each other
Objective of the Numerical Analysis
• To investigate the failure and deformation
mechanism of the San Fernando dams
– Fully coupled finite element procedure
(SUMDES2D, Li & Ming 2001)
– Bounding surface critical state model (Li &
Dafalias 2000, Li 2002)
Fully-coupled Approach
• Physical Laws
– Balance of Linear Momentum
σ ij , j − ρ bi = − ρ u&&i
– Conservation of Mass
q j , j + nε&vwc = ε&v
• Three Constitutive Relationships
– Soil skeleton
∆σ ij = Dijkl ∆ε kl + H ijkl ∆ε&kl
– Pore fluid
∆uw = Γ w ∆ε vwc
– Interaction between solid and fluid phases
∆q j = k  ρ w (∆bi − ∆u&&i ) − ∆uw,i 
*
ij
State-Dependent Dilatancy Model
• Stress Dilatancy Theory (Rowe 1962)
D = D(η , C )
• State-Dependent Dilatancy (Li and Dafalias 2000)
D = D (η ,ψ , Q, C )
Variation of Dilatancy
Test of Toyoura Sand (Verdugo and Ishihara 1996)
1,600
2,000
(a)
(b)
Dense State, D < 0
1,500
η = constant
800
e=0.735
Dr=63.7%
400
0
p' (kPa)
800
1,000
Loose State
D>0
Dense State, D < 0
Loose State, D > 0
400
η = constant
500
e=0.907
Dr=18.5%
0
q (kPa)
q (kPa)
1,200
e=0.833
Dr=37.9%
1,200
0
0
500
1,000
p' (kPa)
1,500
2,000
Model Parameters based on SF7
Elastic
parameters
G0 = 125
ν = 0.25
Parameters
Parameters
Critical State
associated with associated with
parameters
dr-mechanism dp-mechanism
M = 1.375
c = 0.7
Default
parameters
d1 = 0.41
d2 = 1
a =1
m = 3.5
h4 = 3.5
b1 = 0.005
eΓ = 0.813
h1 = 3.15
b2 = 2
λc = 0.206
h2 = 3.05
b3 = 0.01
ξ = 0.2
h3 = 2.2
n = 1.1
(Based on data from Castro et al. 1989)
600
600
500
500
400
400
q (kPa)
q (kPa)
Model Response
300
200
100
100
0
100
200
300 400
p' (kPa)
500
600
e=0.567
300
200
0
e=0.500
0
e=0.660
0
5
10
15
Axial Strain (%)
20
Undrained
Triaxial
Compresstion
200
200
(a) e=0.660, τ/p'0=0.2
(b) e=0.660, τ/p'0=0.2
100
τ (kPa)
τ (kPa)
100
0
-100
-200
0
-100
0
100
200
p' (kPa)
300
-200
-6
400
(c) e=0.567, τ/p'0=0.2
τ (kPa)
τ (kPa)
6
4
6
100
0
-100
0
-100
0
100
200
p' (kPa)
300
-200
-6
400
-4
-2
0
2
Shear Strain γ (%)
200
200
(e) e=0.500, τ/p'0=0.2
(f) e=0.500, τ/p'0=0.2
100
τ (kPa)
100
τ (kPa)
4
(d) e=0.567, τ/p'0=0.2
100
0
-100
-200
-2
0
2
Shear Strain γ (%)
200
200
-200
-4
0
-100
0
100
200
p' (kPa)
300
400
-200
-6
-4
-2
0
2
Shear Strain γ (%)
4
6
Undrained
Cyclic
Simple
Shear
Upper San Fernando Dam
Rolled Fill
Water Table
0
Hydraulic Fill
Hydraulic Fill
Upper Alluvium
unit: m
2.3
15.3
Phreatic Line
Lower Alluvium
95
131
95
Acceleration (g)
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
0
5
10
Time (sec)
15
20
20
40
Flow Deformation of the Upper dam t = 00sec
Click on the mesh to start the animation
Flow Deformation of the Upper dam t = 40sec
(0.91m)
(1.52m) 1.61m
1.31m
0.46m
2.76m
(0.61m) - Seed et al. (1973)
0.73m - by SUMDES2D
2.19m
Typical response of hydraulic fill material
100
100
(a)
80
40
0
50
50
-40
σ13 (kPa)
σ13 (kPa)
-80
-10
0
-8
-6
-4
-2
0
0
-50
-50
-100
-100
200-40
(b)
0
50
100
p' (kPa)
150
-30
-20
-10
γ13 (%)
0
10
Typical response of alluvium in foundation
150
(a)
100
100
50
50
σ13 (kPa)
σ13 (kPa)
150
0
-50
0
-50
-100
-100
-150
(b)
0
100
200
p' (kPa)
-150
300 -2
-1
γ13 (%)
0
1
Lower San Fernando Dam
Ground Shale
Rolled Fill
Upper Alluvium
Hydraulic Fill
Lower Alluvium
104
Phreatic Line
Rolled Fill
Hydraulic Fill
104
274
0.4
0.2
0
-0.2
-0.4
-0.6
0
5
10
Time (sec)
15
25
unit: m
0.6
Acceleration (g)
31.1
Water Table
0
20
50
Flow Failure of the Lower Dam t = 00sec
Click on the mesh to start the animation
Flow Failure of the Lower Dam t = 40sec
Response of soil in lower part of hydraulic fill
(upstream side)
100
100
100
80
60
40
50
20
50
0
σ13 (kPa)
σ13 (kPa)
-20
0
-50
-100
0
5
10
15
0
t=17s
-50
0
50
100
p' (kPa)
150
-100
200
0
20
40
γ13 (%)
60
80
100
Response of soil in lower part of hydraulic fill
(downstream side)
150
150
100
50
100
100
0
-50
50
σ13 (kPa)
σ13 (kPa)
-100
0
-50
-150
-10
0
100
200
p' (kPa)
-8
-6
-4
-2
0
2
0
-50
-100
-100
-150
50
-150
300-40
t=40s
-30
-20
γ13 (%)
-10
0
Shear Stress Distribution along the Bottom of
the Hydraulic fill in Embankment
(a) Upper San Fernando Dam
Shear Stress (kPa)
40
Gravity-induced Shear Stress
Shear Stress Distribution
20
0
-20
Bottom of Hydraulic Fill
Residual Strength Envelope (15 kPa)
-40
-60
-40
-20
0
20
40
Horizontal Coordinate (m)
60
80
100
Shear Stress Distribution along the Bottom of
the Hydraulic fill in Embankment
(b) Lower San Fernando Dam
120
Gravity-induced Shear Stress
Shear Stress (kPa)
90
Shear Stress Distribution
60
Downstream Berm
30
0
-30
-60
-90
-120
Bottom of Hydraulic Fill
Residual Strength Envelope (15 kPa)
-90
-60
-30
0
30
60
90
Horizontal Coordinate (m)
160 kPa
120
150
180
Conclusions
1. Upper Dam: The static driving forces were
marginally higher than the steady state strength
of the hydraulic fill only on the downstream
side. As a result, the dam moved downstream
restrictively upon liquefaction.
2. Lower Dam: The static driving forces were
significantly higher than the steady state strength
of the hydraulic fill on both sides of the
embankment. However, as the downstream
hydraulic fill was supported by the well
constructed downstream berm, the liquefied soil
moved towards the reservoir.
3. Fully coupled procedure that incorporates
an appropriate soil model can be used as
an effective tool to study the failure and
deformation mechanisms of earth dams.
Thank you
Animation USF
– flow failure
Flow Deformation of the Upper dam t = 01sec
Flow Deformation of the Upper dam t = 02sec
Flow Deformation of the Upper dam t = 03sec
Flow Deformation of the Upper dam t = 04sec
Flow Deformation of the Upper dam t = 05sec
Flow Deformation of the Upper dam t = 06sec
Flow Deformation of the Upper dam t = 07sec
Flow Deformation of the Upper dam t = 08sec
Flow Deformation of the Upper dam t = 09sec
Flow Deformation of the Upper dam t = 10sec
Flow Deformation of the Upper dam t = 11sec
Flow Deformation of the Upper dam t = 12sec
Flow Deformation of the Upper dam t = 13sec
Flow Deformation of the Upper dam t = 14sec
Flow Deformation of the Upper dam t = 15sec
Flow Deformation of the Upper dam t = 16sec
Flow Deformation of the Upper dam t = 17sec
Flow Deformation of the Upper dam t = 18sec
Flow Deformation of the Upper dam t = 19sec
Flow Deformation of the Upper dam t = 20sec
Flow Deformation of the Upper dam t = 21sec
Flow Deformation of the Upper dam t = 22sec
Flow Deformation of the Upper dam t = 23sec
Flow Deformation of the Upper dam t = 24sec
Flow Deformation of the Upper dam t = 25sec
Flow Deformation of the Upper dam t = 26sec
Flow Deformation of the Upper dam t = 27sec
Flow Deformation of the Upper dam t = 28sec
Flow Deformation of the Upper dam t = 29sec
Flow Deformation of the Upper dam t = 30sec
Flow Deformation of the Upper dam t = 31sec
Flow Deformation of the Upper dam t = 32sec
Flow Deformation of the Upper dam t = 33sec
Flow Deformation of the Upper dam t = 34sec
Flow Deformation of the Upper dam t = 35sec
Flow Deformation of the Upper dam t = 36sec
Flow Deformation of the Upper dam t = 37sec
Flow Deformation of the Upper dam t = 38sec
Flow Deformation of the Upper dam t = 39sec
Click on the mesh to return
Animation LSF
– flow failure
Flow Failure of the Lower Dam t = 01sec - Original
Flow Failure of the Lower Dam t = 02sec
Flow Failure of the Lower Dam t = 03sec
Flow Failure of the Lower Dam t = 04sec
Flow Failure of the Lower Dam t = 05sec
Flow Failure of the Lower Dam t = 06sec
Flow Failure of the Lower Dam t = 07sec
Flow Failure of the Lower Dam t = 08sec
Flow Failure of the Lower Dam t = 09sec
Flow Failure of the Lower Dam t = 10sec
Flow Failure of the Lower Dam t = 11sec
Flow Failure of the Lower Dam t = 12sec
Flow Failure of the Lower Dam t = 13sec
Flow Failure of the Lower Dam t = 14sec
Flow Failure of the Lower Dam t = 15sec
Flow Failure of the Lower Dam t = 16sec
Flow Failure of the Lower Dam t = 17sec
Flow Failure of the Lower Dam t = 18sec
Flow Failure of the Lower Dam t = 19sec
Flow Failure of the Lower Dam t = 20sec
Flow Failure of the Lower Dam t = 21sec
Flow Failure of the Lower Dam t = 22sec
Flow Failure of the Lower Dam t = 23sec
Flow Failure of the Lower Dam t = 24sec
Flow Failure of the Lower Dam t = 25sec
Flow Failure of the Lower Dam t = 26sec
Flow Failure of the Lower Dam t = 27sec
Flow Failure of the Lower Dam t = 28sec
Flow Failure of the Lower Dam t = 29sec
Flow Failure of the Lower Dam t = 30sec
Flow Failure of the Lower Dam t = 31sec
Flow Failure of the Lower Dam t = 32sec
Flow Failure of the Lower Dam t = 33sec
Flow Failure of the Lower Dam t = 34sec
Flow Failure of the Lower Dam t = 35sec
Flow Failure of the Lower Dam t = 36sec
Flow Failure of the Lower Dam t = 37sec
Flow Failure of the Lower Dam t = 38sec
Flow Failure of the Lower Dam t = 39sec
Click on the mesh to return