1

Geotechnical Modeling and Capacity Assessment

byGeoffrey R. Martin

Chapter 6 : Geotechnical Modeling and Capacity Assessment

Foundation Modeling (Evaluation Methods D and E)

Equivalent linear stiffness modelsCapacity modelsShallow footing, piles, shafts, abutments

Ground Displacement DemandsSettlement (Appendix B)Liquefaction Induced Lateral Spreads

2

Geotechnical Modeling and Capacity Assessment

Seismic Bridge Response May Be Significantly Influenced by the Stiffness and Strength of the Foundation System (abutments, footings, pile foundations)Stiffness and Strength of Foundations can Influence Both the Force and Displacement on the Bridge and the Distribution of Loads to the Structure and Foundation ComponentsBecause of the Cost of Retrofit Construction, More Detailed Foundation Analysis May be Warranted for Retrofit Projects than for New Construction

Foundation Modeling

3

Foundation Modeling

Stiffness and Capacity:Shallow Footing Foundations

Assume idealized elasto-plastic behaviorUse uncoupled spring model for rigid footings or Winkler spring modelWinkler spring model can capture progressive mobilization of plastic capacity during rocking behaviorUpper and lower bound approaches capture uncertainties in soil properties

4

Shallow Footing Foundations :Stiffness Parameters

Uncoupled stiffness parameters obtained from theoretical solutions for a rigid plate on a semi-infinite elastic half-space

Shallow Footing Foundations :Stiffness Parameters (cont.)

5

Shallow Footing Foundations :Stiffness Parameters (cont.)

Shallow Footing Foundations :Capacity Parameters

Winkler springs assumed for capacity evaluationSoil yield, rocking and uplift can reduce ductility demands on bridge structure

Settlement < few inches for Fv>2.5

6

Shallow Footing Foundations :Capacity Parameters (cont.)

Non-linear moment rotation behavior is generated by yield and upliftLengthens fundamental period –dissipates energy by soil yielding

Shallow Footing Foundations :Capacity Parameters (cont.)

Column shear forces resisted by friction at base and passive resistance at footing face

7

Pile Footing Foundations :Stiffness and Capacity

Pile Group – footing or pile cap normally uncoupled from the piles – contributions from two components evaluated separatelyPile Cap treated as a footing but base friction neglected

Primary source of lateral resistance stiffness and capacity is passive pressure on vertical face

Pile Lateral Load – nonlinear load-deflection characteristics determined by pushover analysis assuming nonlinear p-y Winkler springsAxial nonlinear load-deflection characteristics uncoupled from lateral load behavior, and govern moment-rotation behaviorPile-Pile Cap connection details influence lateral load-deflection characteristics

Pile Footing Foundations :Stiffness and Capacity (cont.)

8

Pile Footing Foundations :Stiffness and Capacity (cont.)

Pile Footing Foundations :Stiffness and Capacity (cont.)

9

Pile Head Stiffness :Lateral Loading

Non-linear p-y curves may be linearized to determine coupled 6x6 stiffness matrix for a pile groupStiffness coefficients obtained from beam-column solutions for single piles assuming elastic subgradereaction theory

Pile Head Stiffness :Lateral Loading (cont.)

10

Pile Head Stiffness :Lateral Loading (cont.)

Pile Head Stiffness :Lateral Loading (cont.)

11

Pile Head Stiffness :Lateral Loading (cont.)

Pile Head Stiffness :Lateral Loading (cont.) - Example

12

Pile Head Stiffness :Axial Loading

A graphical simplified solution may be used for initial estimatesAlternatively, a simple estimate is given by αAE/L, where:α=1 for end bearing

piles on rock

α=2 for friction piles

1. Obtain single pile axial and lateral stiffnessSuperimpose single pile stiffnessSuperimpose pile cap stiffness

Example: 3x3 pile group – 1-ft. diameter pipe piles (0.25in wall thickness filled with concrete) driven into sand (φ=30o) 70 ft.

Pile Group Stiffness :Example Calculations

13

Pile Group Stiffness :Example Calculations (cont.)

Lateral Stiffness of Pile:Comments

14

Lateral Stiffness of Pile:Comments (cont.)

Lateral Stiffness of Pile:Issues

15

Pile Group:Moment-Rotation Capacity

Moment Capacity of a pile group depends on

Number of piles and spatial dimensionsAxial capacity of piles in compression and uplift

The study on the right illustrates a modeling procedure

Pile Group:Moment-Rotation Capacity (cont.)

Analytical studies have shown that for pile footings where the static factor of safety for dead load is >3, the settlement generated from mobilizing moment capacity during earthquake is unlikely to be significant.

16

Pile Group:Moment-Rotation Capacity (cont.)

Traditional Moment Retrofit Example

Abutments:Stiffness and Capacity

The stiffness and capacity of abutments under longitudinal inertial loading depends on the structural design of the abutment walls and the resistance of mobilized fill soils.

17

Abutments:Stiffness and Capacity (cont.)

Abutment Stiffness Longitudinal Direction:

Default Passive Pressures:Non-plastic backfill

Pp = 2H/3 ksfCohesive backfill

Pp = 5 ksf (UCS > 4 ksf)

ForcePP

Dg

D

D

K Keff2 eff2

ForcePP

Actual Behavior

K = Keff1

eff1

Deflection

Seat Abutments Integral or Diaphragm Abutments

i

i

K

K

eff

eff

Approach Slab Active Pressure Zone

Tie

GranularDrainageMaterial

H

Passive Pressure Zone

45 60

H

o o

Footing

peffl

PK

0.02H=

( )p

efflg

PK

0.02H D=

+

(integral)

(Seat)

Abutments:Stiffness and Capacity (cont.)

Knock-off backwalls are commonly used to avoid damage to piled abutment foundations or to avoid backward tilt of walls

18

Free Standing Full Height Abutment Retaining Walls

6.3 Ground Displacement Demands on Foundations

Earthquake Induced Settlement (Appendix B)Liquefaction Induced Lateral Spreads

Large rigid body movements of abutments and piersCan cause catastrophe damage to piers and foundations and/or unseat the superstructure

• 1990 Philippines Earthquake

• 2m lateral spread

19

Ground Displacement Demands on Foundations• 1987 Edgecombe

N.Z. Earthquake• 2m lateral spread• Piles resisted

passive pressure

Ground Displacement Demands on Foundations (cont.)

1995 Kobe EarthquakePlastic hinge development at interfaces between liquefied and non-liquefied layers