Seismic Analysis of Retaining...
Transcript of Seismic Analysis of Retaining...
Seismic Analysis of Retaining Structures
Nanjundaswamy P.Department of Civil Engineering
S J College of Engineering, Mysore
ship
warehouse
sheet pile
Sheet PilesSheets of interlocking steel or timber
driven into the ground, forming a continuous sheet
Retaining Walls….
19
Shoring
propping and supporting the exposed walls to resist lateral earth pressures
Retaining Walls….
Reconstruction of the slope of embankment using GRS-RWs having a FHR facing for a
track of bullet trains (Shinkan-Sen)
Retaining Walls….
Interlocking stretchers
and headers
filled with soil
Good drainage & allow plant growth.
CRIB WALL
Retaining Walls….
Forces acting on retaining wall
L0
L
H
z
LELR
Sv`
45+/2
P2(live loads)P1
DSurcharge
+hs
Soil pressure
+hq
Surcharge pressure
=ht
Live load pressure
h
Total lateral pressure
Under Static Conditions
Concept of Lateral Earth Pressures
v
v
hh
Conceptual Steps:
• Stick a thin plate through soil w/o causing any strain
• Assume we remove soil on left side w/o causing any strain on right side
• Assume we can move plate left or right
o
expansion n;compressio with
(-) (+)
Kp
Ka
Ko
“Passive State” -failure due to compression
“At Rest” - no strain
“Active State” -failure due to expansion
Classical methods
Coulomb Theory (1776)
Rankine Theory (1857)
Static Earth Pressures . . . .
C.A.Coulomb1736-1806
WJM Rankine1820-1872
Coulombs Earth Pressure Theory Isotropic & Homogeneous Rupture surface is plane Failure wedge is a rigid body Pressure surface is a plane Wall friction exists on the pressure surface 2 – D failure Cohesionless Force equilibrium of the failure wedge is determined. Force acting on the back of wall is due to the weight
of soil wedge above the planar failure surface. Failure plane is inclined to horizontal by α that
depends on Φ, β, δ & θ Frictional force on the failure surface causes the wall
movement
Static Earth Pressures . . . .
2
2
1HKP AA
2
2
2
)cos()cos(
)sin()sin(1)cos(cos
)(cos
AK
3
Hh
)cot()tan()tan(1
)cot()tan(1)cot()tan()tan(
)tan(tan
2
1
2
11
C
C
C
CA
Coulombs Earth Pressure Theory
Static Earth Pressures . . . .
Isotropic & homogeneous
Rupture surface is plane inclined at 45+Φ/2 for active case & 45-Φ/2 for passive case
Failure is 2 – D and is by shear
Wall is smooth & vertical
AA
A
KHP
K
2
22
22
2
1
coscoscos
coscoscoscos
Rankines Earth Pressure Theory
Static Pressures . . . .
Dynamic Response
Quite Complex Inherent variability
Uncertainty
Properties and behaviour of Soil
Response depends on Sub-soil
Backfill
Inertial and Flexural response of wall
Nature of input motion
Interaction between wall and soil
Dynamic Response . . . .
Current understanding come from
Model tests
• Shaking table tests
• Centrifuge tests
Numerical analyses Simplified Analysis (pseudo-static)
Simplified Dynamic Analysis (Sliding block model)
Dynamic Analysis
Finite Element Technique
Finite Difference Technique
To measure and understand the response of
ground at different locations under dynamic loading• Manual one directional shaking table
• Frequency 2 Hz
• Acceleration 0.5g
• Period 12 to 20 seconds
• Accelerometers• To measure the acceleration of ground
• Pore water pressure sensors• To measure pore water pressure variation
Model testing . . .
Model testing . . .
10
20100 140 160150130120110100908050 70604030
50
40
30
20
0 10 20
10
50
40
30
20
30 40 60 7050 80 90 100 110 120 130 150 160140
Deformation Pattern of Model Ground after Shaking
Responses recorded
Responses recorded
Model testing . . .
Typical Time histories of acceleration and excess pore water pressure
1 0 2 0 3 0
-3
0
3
T im e (s )
In p u t
-3
0
3
Ac
ce
lera
tio
n (
m/s
2)
Ex
ce
ss
PW
P (
kP
a)
A 3 - C a s e 1
-3
0
3 A 3 - C a s e 2
0
2 P 4 - c a s e 1
0
2 P 4 - c a s e 2
Processed records
Numerical Analysis
Pseudo Static Methods
• Pseudo-static seismic actions are added to the static problem as external forces
• Common in most codes
• Simple to use
• Relatively low computational & simpler boundary condition requirements
Pseudo Static Methods . . .
• Applied PS force is based on PGA and will not represent true dynamic nature of earthquake load on structure
• Does not consider the effects of
• Amplification
• Soil hysteric damping
• Development of cyclic pore pressures
Numerical Analysis . . .
Pseudo Dynamic Methods
• Processing and modeling requirements are lower
• Addresses the shortcomings of PS
• Does not consider the effects of
• Non-linear soil behaviour
• Soil hysteric damping
• Development of cyclic pore pressures
Numerical Analysis . . .
Dynamic Methods
• Mode of failure is not defined
• Any constitutive model to represent the soil behaviour
• Quite complex and requires many input parameters
Numerical Analysis . . .
Numerical Analysis . . .
Contours of the pore pressure ratio (Ru), at the end of analyses for SPT=20
Numerical Analysis . . .
Contours of the pore pressure ratio (Ru), at the end of analyses for SPT=40
13121110987654321100
200
300
400
500
600
700
800
900
Height of wall (m)
MSE (Metal)
Co
st (
dolla
rs/m
2) Mean Values