Testing and design of bridge deck- column-rocking foundation systems

Bruce L. Kutter, Lijun Deng and Sashi M. Kunnath

Caltrans‐PEER Seismic Research Seminar, Sacramento8 June 2009

System conceptsCentrifuge tests and resultsGood observed performance of rocking foundationsDraft design procedureConclusions, questions, and future work

Units: mmIn prototype setup

Column elements: beamWithHingesTop pin elements: nonlinear rot. springsFoundation elements: Qzsimple1, EPP...

X100911

12

13

500921

22

23

31

32

33

Y

Z

311

312

313

333332

331

(11)

(12)

(13)

(21)

(22)

(23)

(33) (34)

(311)

(313)(312)

(333)

(331)

(332)

(120) (220)120 220

313131

42

3131 41

43

44

45

46

47

48

49

50

(411)

(412)

(413)

(414)

(415)

(416)

(417)

(418)

(419)

(420)

(421)

(422)

Destroyed columns from 1995 Kobe earthquake

Inspectable, controllable with proper reinforcing, but catastrophic results if ductility capacity is exceeded.

(a) fixed‐fixed (b) fixed‐hinged (c) fixed‐rocking; (d) hinged‐rocking

(b)

Seismic  load

Plastic hinges Plastic hinges

(d)Plastic hinges

Column is protected by rocking 

isolation in case (d)

(a)

(c)

There is a critical (minimum) contact  length, Lc, required to support the vertical load, V. Moment capacity (from equilibrium) is

Define Ac = Lc Bwhere B =

footing width

note Ac /A = Lc /L for 1‐D loadingLc/L << 1 for typical bridge foundations. 

∴ Mo,ult is insensitive to Lc /L

⎥⎦⎤

⎢⎣⎡ −=

LLLVM c

ulto 12,

7

6774

3660

1680

Unit: mm

8956

I-15

Camino del Norte Rd

I-15

Camino del Norte Rd

169.

35

91.5 Unit: mm

Camino del Norte bridge, San Diego, CA

Prototype

mdeck , Kz , Kθ

Hcol , Kcol

Notches

Structural hinges

L/D=3, and 4.5

R0.5

4.53

2 68

0.5 0.5

R1.5Clear holes for 5/16-18screws 42 places

1.3

0.5

1.5" radius, typical 4 places

Model

Plan view of model bridge deck

1.5 1 0.5 0 0.5

1 .104

0

1 .104

Moment vs rotationTheo ftg moment capTheo ftg moment cap

Foot

ing

mom

ent (

kN*m

)

1 .5 1 0.5 0 0.5

1 .104

0

1 .104

Moment vs rotationTheo ftg moment capTheo ftg moment cap

Footing rotation (%)

Foot

ing

mom

ent (

kN*m

)

2 0 21.5 .104

1 .104

5000

0

5000

1 .104

1.5 .104

Centrifuge tes tsStatic loading tests

g ,

Col

umn

mom

ent (

kN*m

)

2 0 21.5 .104

1 .104

5000

0

5000

1 .104

1.5 .104

Centrifuge tes tsStatic loading tests

Column rotation (%)

Col

umn

mom

ent (

kN*m

)

Footing Rotation (%) Column Rotation (%)

Small- footing bridge

Large- footing bridge

10 15 20 25 30

2

0

2

SN columnSS columnSN footingSS footing

Column and footing rotation time histori

Rot

atio

n (%

)

10 15 20 25 301

2

3

4

5Settlement of SN footing

Sett

lem

ent (

cm)

10 15 20 25 30

2

0

2

LN columnLS columnLN footingLS footing

g

Time (s)

Rot

atio

n (%

)

10 15 20 25 301

2

3

4

5

6g

Time (sec)

Sett

lem

ent (

cm)

Small-footing bridge

Large-footing bridge

Systems with small footings may perform better than systems with large footingsdrift, ductility demand on columns

Rocking foundations provideSelf‐centering tendencyNon‐degrading moment capacityIsolation mechanismEnergy dissipation

Difficult aspect of the problem: How to evaluate settlement (or uplift) associated with rocking. 

Lc

Bearing Failure over length Lc under toe during rockingRounding of surface and local bearing failure during reversal of rotationMain factors controlling are:

s/L ~ (Lc/L)(θ)

Soil falls under the footing under large rotation

Cohesion of backfill limits fall backSuction could enhance fallback

Dilatancy during sliding (but sliding is small for typical bridge foundations)

Small FSvLarge FSv

Settlement per cycle, s/L Uplift, -s/L

Half Amplitude of Rotation (radians)

Assume: ordinary bridge, multi column bents, hinge  at top of column, no sliding of shallow 

foundation, seat‐type abutments.1. Footings initially sized based on serviceability criteria 

and static loads. If weight of deck is mdeck

, then the  fraction of the vertical load taken by the columns is:  x mdeck g

The factor x may be affected by footing or abutment  settlement 

a)

AASHTO: settlement = 0.004*spanb)

Caltrans

often uses: 1”

(maybe too strict?)

3. Compute rocking acceleration

And “Rocking Force”: 

hdeckr amF =

2. Ground motion selectiona)

ARS may be sufficient for MCE, safety evaluation

b)

Time histories for Functional‐Evaluation Earthquake (FEE) 

(MTD 20‐1 1999)

mdeck * ah

mdeck/2 * g

Assume half deck weight shared equally by columns

mdeck * g/4

mdeck * ah/2 Mc_foot

mdeck * g/4Mc_foot

Hdcg

LfcH

hdeckam21

gmxdeck2

gmxdeck2

gxmdeck

cc

c

h

HLxLL

HLx

ga

2)/1(

2≈−=

4. Drift demand in MCE 

a)

Estimate using ARS 

b)

Nonlinear dynamic  analysis of SDOF;

BISPEC example:PGA = 0.45g Rocking acceleration = 0.13g

ARS 

Demand

Rocking 

Force

Δrock ΔD

Relativ

e Horizon

tal 

Displacem

ent (in.) Time (s)

5. Estimate the Settlement in the 

Functional Evaluation Earthquake; 

(work in progress) some current 

ideas:a)Count number and size of cycles 

from BISPEC analysisb)Correlate number of cycles to 

Magnitude of EQ

6. Check potential range in vertical loads on footing (the x‐ factor defined earlier); this will be affected by 

settlement/uplift of the footings or abutments. The x‐ factor will affect the yield acceleration and moment 

capacity of footings. Effect can be limited by increasing  deck flexibility. May need to repeat above steps.

7. Check for overturning instability in  transverse direction (unlikely to be a problem unless drift ~ L/2).

8. Design columns to have over‐strength over the upper  bound of moment capacity of footing. Detailing can be 

for limited ductility demand.

Performance of bridges on small rocking foundations can be superior to that on larger foundations. What is the allowable settlement?Statically: 1” seems smallFunctional Evaluation Earthquake: 0.004 x span (AASHTO)MCE: avoid collapse due to excessive bending of deck

Working  on  simplified  procedures  to  estimate drift/rotation demand and associated settlementWorking  on  an  example  design  procedure,  with  real numbersOne more centrifuge testNonlinear  finite element simulations  (parametric studies on soil‐fdn‐col‐deck‐abutment systems. )

Financial support from California Department of Transportation and PEERCaltrans collaborators Mark Desalvatore, Steve McBride, Tom Shantz, Mahmoud Khojasteh, Craig Whitten, FadelAlameddinePEER collaborators – Steve Mahin, Tara Hutchinson, Boris JeremicNSF: NEES (Network for Earthquake Engineering Simulation):  NEES@UCDavisUCD students: Tom Algie , Jose Ugalde, and SivapalanGajan, Emrah Erduran, Yunlei Fan