Seismic Analysis of Retaining Structures Nanjundaswamy P. Department of Civil Engineering S J College of Engineering, Mysore pnswamy@yahoo.com
Retaining Walls
Retaining Walls. Where?
Retaining Walls. Road Train
Retaining Walls.
Retaining Walls.
Retaining Walls.
Retaining Walls.
Retaining Walls. highway
Retaining Walls.
Retaining Walls.
Retaining Walls. Sheet Piles Sheets of interlocking steel or timber driven into the ground, forming a continuous sheet warehouse ship sheet pile
Retaining Walls.
Retaining Walls.
Retaining Walls. Cofferdam Sheet pile walls enclosing an area, to prevent water seeping in
Retaining Walls. Tieback wall
Retaining Walls.
Retaining Walls. Columbia Tower, Seattle, Washington
Retaining Walls. Shoring propping and supporting the exposed walls to resist lateral earth pressures 19
Retaining Walls.
Retaining Walls.
Retaining Walls.
Retaining Walls.
Retaining Walls. High-rise building basement wall
Retaining Walls.
Retaining Walls.
Retaining Walls.
Retaining Walls. Geogr i d-r ei nf or ced soi l RW al ong JR Kobe Li ne ( 1995)
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. Steel rods placed into holes drilled into the walls & grouted Soil Nailing
Retaining Walls. Soil Nailing
Retaining Walls.
Retaining Walls. CRIB WALL Good drainage & allow plant growth. filled with soil Interlocking stretchers and headers
Retaining Walls.
Why? Poor Performance
Retaining walls Failures
Failures....
Failures....
Failures....
Failures....
Failures....
Failures.... MSE Wall Failure
Failure Mechanism
Failure Mechanism.... Tension Failure Pull Out Failure
Failure Mechanism....
Forces acting on retaining wall Under Static Conditions P 1 P 2 (live loads) Surcharge D z H L R L E S v` s hs + s hq + s ht = s h 45+/2 L 0 L Soil pressure Surcharge pressure Live load pressure Total lateral pressure
Static Earth Pressures Two types Active Earth Pressure Passive Earth Pressure
Concept of Lateral Earth Pressures Conceptual Steps: s v Stick a thin plate through soil w/o causing any strain s h o s h s v Assume we remove soil on left side w/o causing any strain on right side Assume we can move plate left or right K p Passive State - failure due to compression with compression; expansion K o K a (-) (+) At Rest - no strain Active State - failure due to expansion
Static Earth Pressures....
Static Earth Pressures.... Classical methods Coulomb Theory (1776) Rankine Theory (1857) C.A.Coulomb 1736-1806 WJM Rankine 1820-1872
Static Earth Pressures.... 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
2 2 1 H K P A A 2 2 2 ) )cos( cos( ) )sin( sin( 1 ) cos( cos ) ( cos K A 3 H h ) cot( ) tan( ) tan( 1 ) )cot( tan( 1 ) cot( ) tan( ) tan( ) tan( tan 2 1 2 1 1 C C C C A Coulombs Earth Pressure Theory Static Earth Pressures....
Static Pressures.... Rankines Earth Pressure Theory 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 K A cos cos cos cos cos 2 2 cos cos 2 2 P A 1 H 2 2 K A
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
Model Testing
Model testing... 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...
Model testing...
Model testing... Responses recorded 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 Deformation Pattern of Model Ground after Shaking
Model testing... Responses recorded E x c e s s P W P (k P a ) A c c e le ra tio n (m /s 2 ) 2 0 0 0-3 3 0-3 3 0-3 P 4 - c a s e 2 2 P 4 - c a s e 1 3 A 3 - C a s e 2 A 3 - C a s e 1 In p u t Processed records 1 0 2 0 3 0 T im e (s ) Typical Time histories of acceleration and excess pore water pressure
Model testing...
Model testing...
Model testing...
Model testing... Centrifuge
Model testing... Centrifuge
Model testing...
Model testing...
Model testing... Movie
Model testing...
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
Numerical Analysis... 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... The soil zones and the applied models in each zone
Numerical Analysis... The selected finite difference mesh for numerical analysis by FLAC-2D.
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
Numerical Analysis...
Numerical Analysis...
900 Cost (dollars/m 2 ) 800 700 600 500 400 300 Mean Values MSE (Metal) 200 100 1 2 3 4 5 6 7 8 9 Height of wall (m) 10 11 12 13
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