RC Shear Wall and MRF Building

EERI TechnicalSeminar Series

Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations

Practical Modeling Considerations

Impact of Foundation Modeling on the

Earthquake Responseof a

RC Shear Wall and MRF Building

Mark A. Moore S.E. and Emma Goodson P.E.



Overview

Case Study – Shallow FoundationFoundation Flexibility

Soil Stiffness, G and G0

“K” by Method 1 through Method 3 and moreSE / GE collaboration

Impact on Global and Local ResponsesSuggested Modeling Improvements



FEMA 440/ASCE 41

FEMA 440/ASCE 41

FEMA 440/ASCE 41

FEMA 356/ASCE 41

Overview con’t

Inertial effectsFoundation stiffness and strengthRadiation damping

Kinematic effectsBase slab averaging (x,y)Embedment (z)



Related documents

FEMA 356 (2000): Prestandard and Commentary for the Seismic Rehabilitation of Buildings [References herein are to this document]FEMA 440ASCE 41 + Supplement 1



FEMA 440 – Chapter 8:Procedures for Including Soil-Structure Interaction Effects

Acceleration Reponse Spectra

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2

Period (sec)

Spec

tral

Acc

eler

atio

n, S

a (g

)

BSE-2BSE-13/4 BSE-1SSI

Used for DBE

BSE 1 reduced forkinematics effectsand radiationdamping



Effects of Foundations on Performance

Foundation stiffness and strength affectvarious structural components differently.

Δ, small

Stiff and Strong Foundation

Smalldisplacementsprotect framefrom damage

High forcescause shearwall damage Δ, large

Flexible and Weak Foundation

Largedisplacementscause frame

damageFoundationyielding androcking protectsshear wall

Stiff and strong is not always favorable;nor is flexible and weak always conservative.

Foundation stiffness and strength affectvarious structural components differently.Foundation stiffness and strength affectvarious structural components differently.

Δ, smallΔ, smallΔ, small

Stiff and Strong Foundation

Smalldisplacementsprotect framefrom damage

High forcescause shearwall damage

High forcescause shearwall damage Δ, largeΔ, largeΔ, large

Flexible and Weak Foundation


damage


damageFoundationyielding androcking protectsshear wall





Case Study

1965 ConstructionReinforced Concrete 6 Stories Above Grade24’ by 24’ Bays (31,000 SF)Two-way Slab with Drop PanelsFull Basement with Shallow FoundationsSite Class DSeismic Design Category CAt ¾ BSE 1: S-3; N-D



Typical Floor Plan

Transverse Shear Walls

Longitudinal Shear Walls(Two coupled walls)

Perimeter Moment-Resisting Frame with Precast Infill



Two rigid foundations coupled by structural components

Longitudinal Wall Elevation

Ground Floor

Basement

General wall element modeling

One rigid foundation response



Displacement Compatibility

Basement SOG

Ground Floor

LBW supports slab and roof (not shown)

Nonlinear elastic bar – NSPInelastic bar + gap - NDP

General wallInelastic section

Inelastic frame element



Typical Atypical Condition

Beam

Column

Two-waySlab

Plan Elevation

Exterior Beam-Column Joint

Torsional deformation?

Precast betweenand connected to columns and beams



Displacement Compatibility

Summary of Component Actions to TrackShear of foundation coupling walls

Shear of LBW lintel

Torsion of perimeter beam-column joint

Slab strips parallel and orthogonal to wall



ASCE 41 Supplement 1

Proposed Figure 2-3Component Force versus Deformation Curves

Lateral deformation following loss oflateral strength capacity

b

Notes:1. Only secondary component actions permitted between points 2 and 4.2. The force, Q, after point 3 diminishes to approximately zero.

Type 1 Curve Type 2 Curve Type 3 Curve



Foundation Plan

Individual Footings Coupled toForm Krot for Wall Line

Type A(Vertical springBeneath col.)

Type D (3 springs)

Type C

Type B(2 vert. springsto capture Krot)

Foundation Plan – Vertical Spring ID

One storyshear wall

Postulate shear overstressdue to foundation flexibility

Plenum



Chapter 4:Effective Stiffness of “Foundation”

Initial Soil StiffnessInitial Shear Modulus, G, Derived By

1> Soil Shear Wave Velocity (Eq 4-4)2> Standard Penetration Test (Blow Count – N1/60) ) (Eq 4-5)

Effective Soil StiffnessEffective Stiffness, Go

Modulus Reduction Factors (Table 4-7)

Foundation StiffnessRelative Stiffness Between Soil and Structure (C4-1 & C4-2)Method 1 to Method 3 Proportional to Go



Quantitatively Define Soil Properties

Nominal “N” value used by GEInfluence depth – B or 4B?

Site Class “D”v= 600 ft/sec 1,200 ft/sec(over great depth)

G0 proportional to v2

Strain level dependent –10%/50yr or 2%/50yr (Go/G 0.80 & 0.66)

OriginalGround

22

280’

260’

47

64

21

65

Footing location

? How deep?



Other Means of Arriving at Soil Properties:Modulus of Subgrade Reaction and Units

In lieu of FEMA 356, the GE may provide othersoil property recommendations. The following may help the SE, but collaboration with GE is the bestanswer:

Soil with cohesive properties reacts independent of depth and may be recommended in terms of F/L3, which when multiplied by contact area (BxL) gives F/L.

Soil reliant on internal friction for strength reacts dependent on depth and may be recommended in terms of F/L4, which when multiplied by depth (h) and contact area (BxL) gives F/L.



Foundation Overturning Stiffness:

Model vertical foundation stiffness and couple those with explicit structure modeling. Determine Kvert by:

Method 1: Rigid isolated foundation 18’ by 18’coupled by explicit structure modeling

Method 2: Decoupled end and middle zones by considering footing as 64’ by 18’

Method 3: Unit subgrade modulusMethod 1 Revised: Determine Rotational stiffness

and convert to vertical stiffness



Foundation Plan

Individual Footings Coupled toForm Krot for Wall Line


Type D (3 springs)

Type C

Type B(2 vert. springsto capture Krot)

Foundation Plan – Vertical Spring ID

One storyshear wall

Postulate shear overstressdue to foundation flexibility

Plenum



Foundation Partial Plan

Type D Foundation Elevation

Ground Floor

Basement

24’ 24’

Partial Plan

K vert K vert K vert

Considered as:3 No. 18’ by 18’ Pads

or64’ long by 18’ wide pad



Chapter 4, Method 1:Rigid Foundation Structure?

rigid test 4 k sν⋅

1

5

m_m 1

5

nn

sinm_m π⋅

2⎛⎜⎝

⎞⎟⎠

2sin

nn π⋅

2⎛⎜⎝

⎞⎟⎠

2⋅

π4 D f⋅m_m2

L1( )2nn2

B1( )2+

⎡⎢⎢⎣

⎤⎥⎥⎦

⋅ k sν+∑=

∑=

⋅:=

Use of elastic properties to determine relative rigidities… perhaps strengthwould be a better test? See C4-2 for equation, discussion and limitations.

whereFor a 3’-3” thick by 18’ square footingwith a point load, the structuralcomponent is considered rigid. Strength(shear and flexure) would likely deemotherwise.

D fE f t3×

12in 1 ν f−( )2×:=



Chapter 4, Method 1 Con’t:Gazetas’ Equation: 18’ by 18’ pad

Use isolated footing vertical stiffness (Figure 4-4)

Modify for embedment

β zi1

121

Di

Bi⋅ 2 2.6

Bi

Li⋅+

⎛⎜⎝

⎞⎟⎠

⋅+⎡⎢⎣

⎤⎥⎦

1 0.32di Bi Li+( )⋅

Bi Li⋅

⎡⎢⎣

⎤⎥⎦

23

⋅+

⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

⋅:=

K z_suri

G Bi⋅

1 ν−1.55

Li

Bi

⎛⎜⎝

⎞⎟⎠

0.75

⋅ 0.8+⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=



Chapter 4, Method 1 Con’t:Gazetas’ Equation: 18’ by 18’ Pad

q ult 12 ksf=L 18 ft=B 18 ft=

Ultimate bearing pressure provided byGE and not discussed herein

For a unit ft2

For lower bound use 80% (discussed later) of the ultimate bearing pressure. A nominal tension force and stiffness, and strain hardening is assumed.

Sq Ftg Axial F-Defl

Defl

Forc

e FD1 Δ( )

Δ

.

K z 6378kipin

=K z

2 L⋅ B⋅9.8

ksfin

=



Chapter 4, Method 2:End Stiffening/Decoupling P and M For a 64’ by 18’ footing

K z6.83 G⋅ B⋅

1 ν−( ):=

Note: B or L/6 used in lieu of B/6. For High L/B ratios, this is judged as moreappropriate. For this case “B/6”is made equal to “B”.

Kz

2 L⋅ B⋅23

ksfin

=

Again, 1/2 is introduced to determinea lower bound stiffness.

End footing (zone)

K z_mid0.736.83

K z⋅:=

Middle footing (zone)

K z_mid

2 L⋅ B⋅2.5

ksfin

=

PlanL

B

B/6 B or L/6or



Chapter 4, Method 3:Unit Coef. Of Subgrade Reaction: 18’ by 18’ Pad

K z1.3 G⋅

B 1 ν−( )⋅B⋅ L⋅:= The multiplication of B and L converts

to force per footing versus deformation.

K z

2 L⋅ B⋅4.4

ksfin

=QED!



Chapter 4, Method 1 Revised:Gazetas’ Equation: 64’ by 18’ pad

K yy_suri

G Bi( )3⋅

1 ν−0.47

Li

Bi

⎛⎜⎝

⎞⎟⎠

2.4

⋅ 0.034+⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

Modify for embedment

β yyi1 1.4

di

Li

⎛⎜⎝

⎞⎟⎠

0.6

⋅ 1.5 3.7di

Li

⎛⎜⎝

⎞⎟⎠

1.9 di

Di

⎛⎜⎝

⎞⎟⎠

0.6−

⋅+⎡⎢⎢⎣

⎤⎥⎥⎦

⋅+:=

Use isolated footing rotational stiffness (Figure 4-4)



Chapter 4, Method 1 Revised:Gazetas’ Equation: 64’ by 18’ pad

I 2 242( )⋅ ft2⋅:=

Performing a rivet-type analysis with a unit area for each pad:

The equivalent vertical spring for each pad is

K yy

I

2 L⋅ B⋅10.9

ksfinch

= Again, 1/2 is introduced to determinea lower bound stiffness.



Foundation Plan


Type D (3 springs)

Type C

Foundation Plan – Type A, Method 2

One storyshear wall Plenum

Middle Zone(Strip Footing)

End Zone, Typical(Say “B/6” = 2 ftg’s)



Chapter 4, Method 2 Revised For Type A ftgEnd Stiffening/Decoupling P and M

KMethod2 9982kipin

= KMethod2_mid 1067kipin

= rKMethod2_mid

KMethod2:=

IM2 2 1 1082⋅ 1 842⋅+ r 602⋅+ r 362⋅+ r 122⋅+( )⋅ ft2⋅:=

IM2 KMethod2⋅ 5.536 1010×kip in⋅rad

=

KMethod2IM2

I⋅ 8091

kipin

=KMethod2

IM2

I⋅

2 L1⋅ B1⋅28.1

ksfin

=



Foundation Mechanism:

Soil Foundation Flexure Flexural-shear/Shear

==>

qult qult

< qult

qult

PSoil + 2 Vngoverns and equalsabout 80% of soil-governed capacity:0.8 * qult = 9.6 ksf

VnVn

P ~



Limit State StrengthShear Capacity - to one side and at d/2 from face of wall

Vsoil L1B1 12inch wall⋅−

2

d1

2−

⎛⎜⎝

⎞⎟⎠

⋅ qult⋅:= Vsoil 612 kip=

φVn 2 4500⋅lb

in2⋅ 0.8⋅ d1⋅ L1⋅:= φVn 464kip=

At 3 root f'c, soil governs.

For lower bound strength capacity, use a factor of

qult B1 2B1 12 inch⋅ wall⋅−

2

d1

2−

⎛⎜⎝

⎞⎟⎠

⋅−⎡⎢⎣

⎤⎥⎦

⋅ L1⋅⎡⎢⎣

⎤⎥⎦

2 φVn⋅+

B1 L1⋅ qult⋅0.83=



Lower Bound Stiffness SummaryEffective Shear Modulus (1200/645)2 = 3.5(GE rec. versus SE’s Guess)

Method 1 9.8 ksf/inchMethod 2

End Zone 23 ksf/inchMiddle Zone 2.5 ksf/inch

Method 3 4.4 ksf/inchMethod 1 Revised 11 ksf/inch

Range of variation:All methods : 23/4.4= 5.2Considering Method 1 and 3 only: 11/4.4 = 2.5

Worst case scenario ==> 3.5 x 5.2 x 1/2 = 9.1 x too stiff

Note: Even with this range, any springs are far better than fixed base!



Spectral Acceleration versus Displacement

0

0.05

0.1

0.15

0.2

0.25

0.3

0.0 1.0 2.0 3.0 4.0

Spectral Displacement (in)

Spec

tral

Acc

eler

atio

n (g

)

3/4 BSE-1

BSE-1

BSE-2

Fixed Base

Lower Bound

Global Response

Target displacement increase by 75 %



Foundation Response – Longitudinal Wall

Foundation "Tension" Spring - Longitudinal Wall

-1200

-1000

-800

-600

-400

-200

0 1 2 3 4 5


Axia

l For

ce (

kips

)

3/4 BSE-1BSE-1

BSE-2Lower Bound

Foundation Compression Spring Longitudinal Wall

-2500

-2000

-1500

-1000

-500

0 1 2 3 4 5


Axi

al F

orce

(ki

ps)

3/4 BSE-1

BSE-1

BSE-2

Lower Bound

Nonlinear Elastic Springs – Lower Bound Stiffness and Strength

Ground Floor

Basement

K vert K vert K vert

System not dominated by rocking



Local (Component) Response

Longitudinal WallsCoupling Beam

0.0

0.1

0.2

0.3

0.0 0.5 1.0 1.5 2.0 2.5 3.0


Shea

r St

ress

(ks

i) Fixed BaseLower Bound3/4 BSE-1BSE-1BSE-2




Longitudinal WallsCoupling Beam, Lower Bound

0.0

0.1

0.2

0.3

0.0 0.5 1.0 1.5 2.0 2.5 3.0


Shea

r St

ress

(ks

i)

3/4 BSE-1BSE-1BSE-2Lower BoundLSCP




Outrigger Wall - Above OpeningLBW

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0


Shea

r St

ress

(ks

i)

Fixed Base

Lower Bound

3/4 BSE-1

BSE-1

BSE-2

LS

CP



Beam

Column

Two-waySlab

Plan Elevation


Torsional deformation?

Precast betweenand connected to columns and beams

Beam-Column Joint Torsion

0.000

0.005

0.010

0.0 0.5 1.0 1.5 2.0 2.5 3.0


Tors

ion

Def

orm

atio

n (r

adia

ns)

3/4 BSE-1 LB

BSE-1 LB

BSE-2 LB

Joint Rotation

3/4 BSE-1 FB

BSE-1 FB

BSE-2 FB




Local (Component) ResponseSlab End Moment on Line D at Column Face

-10

100

210

320

430

540

0 1 2 3 4 5


Slab

End

Mom

ent

(kip

-ft)

3/4 BSE-1BSE-1BSE-2Fixed BaseLower Bound

Slab End Moment on Line D at Wall Face

-750

-600

-450

-300

-150

0

0 1 2 3 4 5


Slab

End

Mom

ent (k

ip-f

t)

3/4 BSE-1BSE-1BSE-2Fixed BaseLower Bound

Indicates significant slab stress demandbut no inelastic behavior for 24’ span.Short spans showed inelastic behavior.




Beam (E)

Col. (E)

Plan Elevation


Slab (E)

Col. (N)



Typical Floor Plan

New columns (Wall Piers)

Deleted columns as aresult of the analysis



Seismic Rehabilitation RecommendationsDo nothing to overstressed coupling beam that is between the longitudinal wallsProvide “catcher” to LBW at 5th floor and at other locationsDo nothing to beam-column joint in longitudinal direction:

• Deformation levels• Higher confidence in determining deformations due to inclusion of

SSI effectsSlabs proven to within acceptance limits.

Without modeling foundation flexibility and capturing the kinematics three dimensionally, wall piers may have been added in the longitudinal direction and the LBW deficiency may not have been identified.



Displacement-Based Design

More liberal evaluation techniques

ASCE 41 Supplement 1 will require more comprehensive modeling

Foundation flexibility and strength:Adds to total lateral deflectionChanges the distribution of inelastic displacement demand between components and may change strength hierarchy



Ways to Improve SSI ModelingGE and SE collaboration

Consider displacement compatibility in 3D

Use Winkler models calibrated by testing

Use capacity spectrum for systems dominated by rocking

Identify and include uncertainty in the evaluation

Determine residual displacements - NDP

RC Shear Wall and MRF Building

Documents

Transcript of RC Shear Wall and MRF Building