2. Complexity of the Soil Structure Interaction Problem The Soil-Foundation-Structure Problem involves Kinematic Soil-Foundation Interaction occurring during large (cyclic and permanent) ground deformations as well as Inertial Foundation-Structure Interaction occurring during shaking all of which take place while the soil and possibly structural properties degrade with time.
3.
4. Major Causes of Damage Ground Shaking Site Response Near Fault Effects Ground Deformation Liquefaction Related Soft Soil Related
8. Hanshin Expressway Route 5 1995 Kobe Earthquake Permanent Horizontal Displacement of Bridge Piers vs Distance to Waterfront Permanent Horizontal Displacements of Bridge Piers versus Free Field Ground Displacement
9. Important Factors to be considered in Solution of the Complex SSI Problem Thickness and properties (shear strength and passive pressure) of soil strata Geometry and Properties of Foundation Elements Restraining stiffness and strength of Structural Elements Pile Types - Vertical or Batter/End Bearing or Floating
15. Berth 37 - Damage Calibration Study Calibration Target Deformations Permanent Horiz. Deck Displacement = 2 - 4 inches Permanent Horiz. Soil Deformation = 6 inches Visible Damage to the Piles Damage to the Piles at Depth ?
16. SUMMARY OF PILE TOP DAMAGE BERTH 37 - LOMA PRIETA EARTHQUAKE Note: Pile Integrity Testing suggests some E-Row piles may be damaged below the liquefiable layer.
17. Orbital Plots of Loma Prieta Records - Port of Oakland (Acceleration) (Velocity) (Displacement) Input Time History to FLAC Model
22. Pile Displacement Vector Diagram Permanent Horizontal Deck Displacement = 0.30 feet (feet) Berth 37 (Pre-Loma Prieta Condition) Loma Prieta, S r = 400 PSF
23. 1 2 3 4 Pore Pressure Monitoring Locations Loma Prieta, S r = 400 PSF Berth 37 (Pre-Loma Prieta Condition) B D E F G H A C
24. Pore Pressure Ratios Time (Seconds) Berth 37 Loma Prieta, S r = 400 PSF (Pre-Loma Prieta Condition) Pore Pressure Ratio 4 3 1 2
25. Soil Deformation Time History Near Top of Batter Pile Liquefaction triggered, soil deformation occurs Cyclic motions, no liq.
26. Pile Top Shear Time History - Waterside Batter Pile Inertia Loading Kinematic Loading
27. Berth 37 Loma Prieta, S r = 400 PSF (Pre-Loma Prieta Condition) Time (Seconds) Axial Force at Pile/Deck Connection, Pile Row H -336 kip Axial Force per foot pile spacing (lb) 480 kip
28. Bending Moment at Pile/Deck Connection, Pile Row H 60 ft-kip Mp = 60 ft-kip Berth 37 Loma Prieta, S r = 400 PSF (Pre-Loma Prieta Condition) Time (Seconds) Moment per foot pile spacing (ft/lb)
29. Time (Seconds) Horizontal Deck Displacement Time History Displacement (Feet) Berth 37 Loma Prieta, S r = 400 PSF (Pre-Loma Prieta Condition) 3.6 inches 4.4 inches
34. Computer Program DFSAP D eep F oundation S ystem A nalysis P rogram developed using Strain Wedge Method for Washington State Department of Transportation for Analysis of Laterally and Axially Loaded Group of Shafts and Piles
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36.
37. What are the differences between the SWM approach and the p-y method?
38.
39. Laterally Loaded Pile as a Beam on Elastic Foundation (BEF) y p ( E s ) 1 ( E s ) 3 ( E s ) 4 ( E s ) 2 p p p y y y ( E s ) 5 p y M o P o P v
40. LARGE DIAMETER SHAFT z T y p S o i l - S h a f t H o r i z o n t a l R e s i s t a n c e S o i l - S h a f t S h e a r R e s i s t a n c e T i p R e a c t i o n D u e t o S h a f t R o t a t i o n N e g l e c t e d w i t h L o n g S h a f t s P o M o P v T P o o M o o P v y F P v M t F v F P F P F v F v V t F t
41. The p-y method provides a unique p-y curve for the equal diameter piles in the same soil regardless of the pile’s EI EI & D = 1 ft 0.1 EI & D = 1 ft
42. Variation of soil reaction with the change of the footing stiffness (EI) as presented by Terzaghi (1955) and Vesic (1961) q per unit area B C L q 0.5q K r = K r = 0 Rigid Footing, K r = Flexible Footing, K r = 0 Footing H (1- 2 s ) E P H 3 6 (1- 2 P ) E s B 3 K r =
43. The p-y method provides a unique p-y curve for the equal diameter piles in the same soil for piles with free- or fixed-head conditions Load Test by Kim et al. (ASCE J., 2004) to Show the Effect of Pile-Head Fixity on the p-y curve SW Model Analysis
44. Laterally Loaded Pile as a Beam on Elastic Foundation (BEF) Effect of Structural Element Cross-Sectional Shape on Soil Reaction P P K 1 K 2 4 ft 4 ft
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46. Horizontal and Vertical Growth in the Soil Passive Wedge Pile Pile Pile head load P o Successive mobilized wedges m m Mobilized zones as assessed experimentally
47. Simplified SW Model 6 P o Soil Strain = y/d , From Triaxial Test Concept , and Stress-Strain Curve, d = h , Stress Level= SL & Mobilized friction angle = m d y x Y o h m m m Pile Real stressed zone F 1 F 1 Triaxial test principle stresses A Side shear ( ) p = CD * h + Pile Side Shear (b) Force equilibrium in a slice of the wedge at depth x p Plane taken to simplify analysis (i.e. F 1 ’s cancel) C D A h d Horizontal Slice (c) Forces at the face of the soil passive wedge (Section elevation A-A) ds dx h h * CD * dx = * CD * ds sin m VO m K VO Y o h x H i i Sublayer i+1 Sublayer 1 Vertical Slice Beam on Elastic Foundation
48. L = SHAFT LENGTH T = (EI/f ) 0.2 f = Coefficient. of Modulus of Subgrade Reaction Varying Deflection Patterns Based on Shaft Type h = 0.69 X o X o Zero Crossing Deflection Pattern Linearized Deflection Y o Long Shaft L/T 4 X o > h > 0.69 X o X o Zero Crossing Y o Linearized Deflection Intermediate Shaft 4 > L/T > 2 Zero Crossing h = X o Y o Deflection Pattern Short Shaft L/T 2
53. Measured and Predicted Shaft Response of the Las Vegas Test (8-ft Diameter and 32-ft long Shaft) P o COM624P
54. P o 15 ft 4 ft Stiff Clay Su = 5500 psi R/C Shaft Measured and Predicted Shaft Response of the Southern California Test (Pier 1) 0.0095 5500 0 130 22 Clay Layer 1 50 ** S u (psf) (deg.) (pcf) Thickness (ft) Soil type Soil layer
58. y p p group = P mult x p single p single Pile in a group Single pile (P mult. ) 1 = (P mult. ) 2 = (P mult. ) 3 =
59. The Overlapping of Passive Soil Wedges and the Interaction among the Piles in a Group at any Step of Lateral Loading 6 Pile Group Analysis in SWM Model No P-multiplier)
60. Horizontal Passive Wedge Interference in Pile Group Response Pile Pile Overlap of stresses based on elastic theory (and nonuniform shaped deflection at pile face) Overlap employed in SW model based on uniform stress and pile face deflection (P o ) g (P o ) g Uniform pile face movement
61. Horizontal (Lateral and Frontal) Interaction for a Particular Pile in a Pile Group at a Given Depth 8
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63.
64. Treasure Island 3 x 3 Pile Group Test (Rollins et al., ASCE J., No. 1, 2005)
67. Traditional p-y curves were modified using LPILE to match the measured p-y data (Brown et al. 2001)
68. 0 40 80 120 160 200 P i l e H e a d D e f l e c t i o n , Y o , m m 0 1000 2000 3000 4000 P i l e H e a d L o a d , P o , k N M e a s u r e d ( B r o w n e t a l . 2 0 0 1 ) P r e d i c t e d ( S W M o d e l ) N o V . S i d e S h e a r W i t h V . S i d e S h e a r S i n g l e 1 . 5 - m - D i a m e t e r Shaft (B1) F r e e - h e a d
76. Effect of Pile-Head Conditions on Cap Resistance at the Same Deflection Value in DFSAP Piles + Cap Piles Cap 320 Piles + Cap Piles Cap 410 Free-Head Fixed-Head
82. Current Available Procedures That Assess the Pile/Shaft Behavior in Liquefied Soils (Using the Traditional P-y Curve): 1. Construction of the p-y curve of soft clay based on the residual strength of liquefied sand presented by Seed and Harder (1990) 2. Reduce the unit weight of liquefied sand with the amount of R u (Earthquake effect in the free-field ) and then build the traditional p-y curve of sand based on the new value of the sand unit weight.
83. Pile Deflection, y Soil-Pile Reaction, p Upper Limit of S r using soft clay p-y curve API Procedure Corrected blowcount vs. residual strength, S r (Seed and Harder, 1990) P-Y Curve of Completely Liquefied Soil Lower Limit of S r Treasure Island Test Result (Rollins and Ashford)
84.
85. Effect of Cyclic Loading upon Subsequent Undrained Stress-Strain Relationship for Sacramento River Sand (Dr = 40%) (Seed 1979)
86.
87. Peak Ground Acceleration (a max ) = 0.1 g Earthquake Magnitude = 6.5 Induced Porewater Pressure Ratio (r u ) = 0.9 - 1.0 Soil Profile and Properties at the Treasure Island Test S h a f t W i d t h x x L o n g i t u d i n a l S t e e l Steel Shell Soil-Pile Reaction, p Pile Deflection, y Treasure Island Test Result (Rollins and Ashford) Upper Limit of S r using soft clay p-y curve Lower Limit of S r API Procedure
88. 0 100 200 300 400 P i l e - H e a d D e f l e c t i o n , Y o , m m 0 100 200 300 400 500 P i l e - H e a d L o a d , P o , k N C I S S , 0 . 6 1 m E I = 4 4 8 3 2 0 k N - m 2 O b s e r v e d P r e d i c t e d ( S W M ) P r e d i c t e d ( C o m 6 2 4 ) N o - L i q u e f a c t i o n P o s t - L i q u e f a c t i o n ( u x s , f f + u x s , n f )
90. p-y Curve of 0.61-m Diameter CISS in Liquefied Soil ( Treasure Island, After Rollins et al. 2005) 0.2 m Below Ground 1.5 m Below Ground 3.2 m Below Ground
91. p-y Curve Empirical Formula in Liquefied Sand by Rollins et al. 2005 p (d=324 mm) = A(By) C for D r = 50% where: A = 3 x 10 -7 (z+1) 6.05 , B = 2.8 (z+1) 0.11 C = 2.85(z+1) -0.41 z is depth in (m) y is lateral deflection (mm) p multiplier = 3.81 ln d + 5.6 p = p (d=324 mm) x p multiplier
92. p-y Curves for loose and dense sand for M=6.5 and amax=0.35g
93. Loose Sand Profile for Three Levels of Earthquake M=4.5, amax=0.15g; M=5.0, amax=0.25g; M=6.5, amax=0.35g
97. Clay Shaft Diameter Clay Liquefiable Soil “ Full” Pile-Soil Response Under Lateral Soil Spread Liquefiable Soil “ Partial” P o A x i a l L o a d M o M o M o Phase I y p P-y Curve for Fully Liquefied Soil y p P-y Curve for Partially Liquefied Soil y p P-y Curve for Non- Liquefied Soil y p Lateral Spread Effect P-y Curve for Crust Layer Phase II
98. Comparison of Pile Behavior for - As Is Condition - Liquefaction - Liquefaction with Lateral Spread
99. Pile head load = 100 kN Pile head moment = 316 kN-m No-Liquefaction Liquefaction Liquefaction + Lateral Spread
100. Pile head load = 100 kN Pile head moment = 316 kN-m No-Liquefaction Liquefaction Liquefaction + Lateral Spread
101. UC Davis, Centrifuge Test (Boulanger et al. 2003, and Brandenberg and Boulanger 2004) Dense Sand Loose Sand Clay = 6 kN/m 3 , Dr = 21-35% = 30 o , 50 = 0.01 = 7 kN/m 3 , Dr = 69-83% = 36 o , 50 = 0.004 Cu= 44 kPa = 16 kN/m 3 14.3 9.2 2.2 4.6 0.051 1.17 23.5 Pile Cap Length (m) Pile Cap Width (m) Pile Cap Height (m) Pile Spacing (m) Wall Thick. (m) Diameter (m) Pile Length (m)
102. UC Davis, Centrifuge Test on 2 x 3 Fixed-Head Pile Group (After Brandenberg and Boulanger, 2004) Pile Displacement a max = 0.67 g Magnitude = 6.5 Bending Moment
103. Niigata Court House Bld. 0.35-m-Diam. RC Pile, 1964 Niigata EQ, Yoshida and Hamada, 1991
104. Niigata Court House Bld. 1964 Niigata EQ 0.35-m-Diam. RC Pile (Yoshida and Hamada, 1991)
106. h = 0.69 X o X o Zero Crossing X o > h > 0.69 X o X o Zero Crossing Zero Crossing h = X o Deflection Pattern Linearized Deflection Y o Y o Y o Linearized Deflection Deflection Pattern Long Shaft L/T 4 Intermediate Shaft 4 > L/T > 2 Short Shaft L/T 2 L = SHAFT LENGTH T = (EI/f ) 0.2 f = Coefficient. of Modulus of Subgrade Reaction Varying Deflection Patterns Based on Shaft Type
107.
108. T P o M o P v y 75 ft 6 ft P v = 100 kip P o = 150 kip M o = 800 kip-ft L/T = 3.1 Intermediate Shaft Soil Profile – S5 Short Shaft Analysis Intermediate Analysis Short Shaft Analysis Intermediate Analysis
109. T P o M o P v y 90 ft 6 ft P v = 100 kip P o = 150 kip M o = 800 kip-ft L/T = 4.0 Long Shaft Soil Profile – S5 Short Shaft Analysis Long Shaft Analysis
110. Effect of Soil Liquefaction on Response of Shafts of Different Lengths Effect of Shaft Length and Soil Layers on p-y Curve at Certain Depth
111. T P o M o P v y 65 ft 6 ft P v = 100 kip P o = 800 kip M o = 3000 kip-ft M EQ = 6.0 Soil Profile – S7 Liquefaction
112. T P o M o P v y L 6 ft Soil Profile – S5 Shaft-Length Effect on the p-y Curve P-y Curve at 5 ft depth P-y Curve at 20 ft depth
113. T P o o M o P v y 90 ft 6 ft P v = 100 kip P o = 800 kip M o = 3000 kip-ft M EQ = 6.0 Soil Profile – S7 Liquefaction
114. T P o M o P v y 65 ft 6 ft Soil Profile – S7 Liquefaction Effect of Soil Profile (Liquefaction) on the p-y Curve at the Same Depth
115. Pile and Pile Group Stiffnesses with/without Pile Cap
116. Loads and Axis F1 F2 F3 M1 M2 M3 X Z Y F 1 F 2 F 3 M 1 M 2 M 3 X Z Y
117.
118. Shaft Deflection, y Line Load, p y P, M > y P + y M y M y P y P, M y p ( E s ) 1 ( E s ) 3 ( E s ) 4 ( E s ) 2 p p p y y y ( E s ) 5 p y M o P o P v Nonlinear p-y curve As a result, the linear analysis (i.e. the superposition technique ) can not be employed Actual Scenario
119.
120. Pile Load-Stiffness Curve Linear Analysis Pile-Head Stiffness, K11, K33, K44, K66 Pile-Head Load, P o , M, P v P 1, M 1 P 2, M 2 Non-Linear Analysis
121. P L P v M (K22) (K11) (K66) x x K11 0 0 0 0 0 0 K22 0 0 0 0 0 0 K33 0 0 0 0 0 0 K44 0 0 0 0 0 0 K55 0 0 0 0 0 0 K66 1 2 3 1 2 3 (K11) = P L / 1 (K22) = P v / 2 (K33) = M 3 Group Stiffness Matrix (p v ) M (p v ) M (p v ) Pv (p v ) Pv P L P v (1) M (p L ) PL (Fixed End Moment)