"Pile-Group Response to Large Soil Displacements and Liquefaction: Centrifuge Experiments Versus A Physically Simplified Analysis", Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 139(2), pp. 223-233, 2013. Piles in Lateral Spreading due to Liquefaction: A Physically Simplified Method Versus Centrifuge Experiments Panagiota Nikos Takashi George TA S I O P O U LO U G E R O LY M O S TA Z O H G A Z E TA S
What is liquefaction? Ϭ vo Շ Ϭ v = Ϭ vo ε v DRY Loose Sand
What is liquefaction? Ϭ vo Շ Ϭ vo ε v DRY Loose Sand Ϭ vo Շ Δu = Ϭ vo ε v = 0 SATURATED Loose Sand
Christchurch 2011 Manifestation of liquefaction Lateral spreading El Centro 1979 Sand boils
Piles subjected to lateral spreading Oil Tank Seaward rotation of the quay-wall Σημασία του Προβλήματος Pile Failure Lateral Spreading Kobe Earthquake 1995
Centrifuge Tests ( Sato et al. 2001 ) Plan view water 0 m 6.6 m 1.8 m 6 m 8.1 m 9 m Silica Sand D r = 50 % Silica Sand D r = 50 % Silica Sand D r = 90 % Toyoura Sand D r = 90 % 3.6 m 0.2g 24 m 10 sec
Centrifuge Tests ( Sato et al. 2001 ) Plan view water 0 m 2.75 m 6.6 m 1.8 m 6 m 8.1 m 9 m Silica Sand D r =50 % Silica Sand D r =50 % Silica Sand D r =90 % Toyoura Sand D r =90 % 3.6 m 0.2g 24 m 10 sec
Centrifuge Tests ( Sato et al. 2001 ) Quay-wall Displacement at top (m) 1 0.5 0 0 2 4 6 8 10 12 14 time (sec) time (sec) 0.8 m 0.45 m Model With Piles Model Without Piles
Centrifuge Tests ( Sato et al. 2001 ) 2.75 m behind the quay-wall (at the position of the pile group) Displacement at top (m) 0.6 0.5 0.4 0.3 0.2 0.1 0 Free-field 0.5 m Pile cap 0.05 m 0 2 4 6 8 10 12 14 time (sec) time (sec) Model With Piles Model Without Piles
Problem Definition Δu σ νο 1. Δu generation 2. Displacement + rotation of quaywall 3. Induced Soil flow 4. Pile deformation
Problem Definition Δu σ νο 1. Δu generation 2. Displacement + rotation of quaywall 3. Induced Soil flow 4. Pile deformation + 3D geometry
The 3D problem Δu σ νο as a combination of 2 PLANE subproblems
The 3D problem Δu σ νο as a combination of 2 PLANE subproblems 2D Dynamic Analysis of Plane Vertical Slice Without Piles 2D Static Analysis of a Horizontal Slice Containing the Piles
Vertical Section Without Piles Δu (t) G l u fp u fc Seismic Base Excitation Computation of the residual lateral soil displacement, u fp : at the mid-depth of the liquefiable layer at the location potentially occupied by piles
Vertical Section Without Piles H L Δu (t) G l u fp u fc Seismic Base Excitation Computation of the equivalent shear modulus of the liquefiable layer: G l H L 0 ( z) ( z) dz
G l Horizontal Slice containing the Piles
Horizontal Slice containing the Piles G l A A G l quaywall displacement piles: rigid inclusions!
Horizontal Slice containing the Piles HOW can the rigid pile inclusions express the real lateral stiffness of the pile group??? G l quaywall displacement piles: rigid inclusions!
Horizontal Slice containing the Piles HOW can the rigid pile inclusions express the real lateral stiffness of the pile group??? G l quaywall displacement
Horizontal Slice containing the Piles out of plane springs K 2 K 1 K 3 quaywall displacement G l
Horizontal Slice containing the Piles out of plane springs Appropriate kinematic constraints at the boundaries K δ = 1 l K 2 K 1 K 3 quaywall displacement G l
Horizontal Slice containing the Piles K 1 section G l K 3 K 2 Unit quaywall displacement Plan view G l Pseudo static analysis
Free-field displacement u fp Soil displacement line under soil flow conditions, modified by the presence of the pile group Pile-group displacement u p Ratio α = u p u fp Liquefiable soil G l
ratio a 1 0.8 0.6 single pile 2 x 2 pile group 2 x 4 pile group 0.4 0.2 0 0.1 1 10 100 K / K G/ l G(m) L
ratio a 1 0.8 0.6 single pile 2 x 2 pile group 2 x 4 pile group 0.4 0.2 0 0.1 1 10 100 K / K G/ l G L (m) The ratio α is affected only by the relative stiffness between soil + pile for each pile configuration.
Development of Simplified Method STEP 1: 2D Dynamic Analysis of the Vertical Slice WITHOUT the piles Computation of the free-field soil displacement STEP 2: Relative Stiffness between soil + pile ratio α Estimation of the pile displacement within the liquefiable zone STEP 3: Prediction of the displacement and bending moment distribution along the pile
Centrifuge Test ( Tazoh et al. 2005 ) Plan view water 0 m 2.1 m 5.7 m 8.1 m 9 m Silica Sand D r =50 % Silica Sand D r =50 % Silica Sand D r =90 % Toyoura Sand D r =90 % 24 m 0.27g 3 m 6 m 3.6 m 15 sec
Numerical model w/out piles (STEP 1) u fc (t) 9 m 1 2 beam element 5 3 0.27g 24 m 4 15 sec FLAC, Constitutive model by Byrne (1991) 1. Dry Silica Sand No. 8 (D r = 50%) 3. Toyoura Sand (D r = 90%) 5. Sea water 2. Liquefiable Silica Sand No. 8 (D r = 50%) 4. Silica Sand No. 3 (D r = 90%)
Excess Pore Pressure Ratio Distribution (STEP 1) r u = Δu σ νο 1.000 Contour interval = 0.1 0 0.2 0.4 0.6 0.8 1 0.500 0.000 0.27g 10 sec -0.500
Excess Pore Pressure Ratio Distribution (STEP 1) r u = Δu σ νο 1.000 Contour interval = 0.1 0 0.2 0.4 0.6 0.8 1 0.500 0.000 1 0.27g r u 0.5 0 Numerical model Centrifuge model 10 sec -0.500 0 5 10 15 time (sec)
Deformed grid w/out piles (STEP 1) u fc = 1.15 m 1 Quay-wall 9 m 2 3 4 0.27g 24 m 10 sec 1. Dry Silica Sand No. 8 (D r = 50%) 3. Toyoura Sand (D r = 90%) 5. Sea water 2. Liquefiable Silica Sand No. 8 (D r = 50%) 4. Silica Sand No. 3 (D r = 90%)
Deformed grid w/out piles (STEP 1) Center of pile group u fc = 1.15 m 1 Quay-wall 9 m 2 u fp = 0.505 m 3 4 0.27g 24 m 10 sec 1. Dry Silica Sand No. 8 (D r = 50%) 3. Toyoura Sand (D r = 90%) 5. Sea water 2. Liquefiable Silica Sand No. 8 (D r = 50%) 4. Silica Sand No. 3 (D r = 90%)
ratio a Pile Displacement within the liquefiable layer (STEP 2) K K = 585 KN/m liquefiable zone G l = 126 kpa (from STEP 1) K / G l = 4.6 Ratio α = u fp u p 0.5 0.4 0.3 0.2 0.1 0.0 1 K / G 10 l
ratio a Pile Displacement within the liquefiable layer (STEP 2) K K = 585 KN/m liquefiable zone G l = 126 kpa (from STEP 1) K / G l = 4.6 Ratio α = u fp u p 0.5 0.4 0.3 0.2 0.146 0.1 0.0 K / G l 4.6 1 10
ratio a Pile Displacement within the liquefiable layer (STEP 2) K K = 585 KN/m liquefiable zone G l = 126 kpa (from STEP 1) K / G l = 4.6 Ratio α = u p u fp 0.5 0.4 0.3 0.146 = u p 0.505 m 0.2 0.146 0.1 u p = 0.074 m 0.0 K / G l 4.6 1 10
Pile Displacement Distribution (STEP 3) So far, we only predicted the pile displacement at the mid-depth liquefiable zone of the liquefiable zone u p = 0.074 m HOW can we estimate the pile displacement at the top OR even the pile deflection at all depths???
Pile Displacement Distribution (STEP 3) So far, we only predicted the pile displacement at the mid-depth liquefiable zone of the liquefiable zone u p = 0.074 m HOW can we estimate the pile displacement at the top OR even the pile deflection at all depths??? We consider different load distributions
Pile Displacement Distribution (STEP 3) 0 w/w max 0 0.5 1 x w max w (x) L 0.2 x/l 0.4 The deformation shape 0.6 of each pile is controlled primarily p 1.5p 2p by the boundary conditions 0.8 and only marginally by the load distribution along it 1 0.5p
Depth (m) Simplified Method Vs Centrifuge Results 0 1 Pile Deflection (m) 0 0.02 0.04 0.06 0.08 0.1 0.12 Pile cap Bending Strains (10-6 ) -1500-1000 -500 0 500 1000 1500 Pile cap 2 3 Centrifuge results 4 5 6 p 1.5p 2p 7 8 9 0.5p
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Piles subjected due to lateral spreading Christchurch 2011
Span collapse due to outward movement of foundation Nishinomiya-ko bridge Kobe Earthquake 1995
Seaward Quay-wall Tilt and Displacement Kobe Earthquake 1995