FEMA 365 Foundation Example

Practical Modeling Considerations Impact of Foundation Modeling on the

Earthquake Response of a

RC Shear Wall and MRF Building Mark A. Moore S.E. and Emma Goodson P.E.

EERI Technical

Impact of Soil-Structure Interaction on Response of Structures

Overview 

Case Stu Case Study dy – Sh Shal allow low Fo Foun unda dati tion on  Foundation Flexibility   

Soil Stiffness, G and G0 “K” by Method 1 through Method 3 and more SE / GE collaboration



Impact on Global and Local Responses  Suggested Modeling Improvements

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Overview con’t

Inertial effects Foundation stiffness and strength  Radiation damping 

FEMA 356/ASCE 41 FEMA 440/ASCE 41

Kin inem ema ati ticc ef effe fect ctss Base slab averaging (x,y)  Embedment (z) 

EERI Technical

FEMA 440/ASCE 41 FEMA 440/ASCE 41


Related documents

FEMA

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

EERI Technical


FEM EMA A 44 440 0 – Ch Chap apte terr 8: Procedures for Including Soil-Structure Interaction Effects Acceleration Reponse R eponse Spectra ) g ( a S , n o i t a r e l e c c A l a r t c e p S

0.8 0.7

BSE-2 BSE-1 3/4 BSE-1 SSI

0.6 0.5

Used for DBE

0.4

BSE 1 reduced for kinematics effects and radiation damping

0.3 0.2 0.1 0.0 0

0.5

1

1.5

2

Period (sec)

EERI Technical


Effects of Foundations on Performance Foun ounda dation tion stiffn ess and st re rengt ngth h affect various va rious st ructu ra rall comp onents differently differently . High forces cause shear wall damage

Δ,

smal s malll

Foundation yielding and rocking protects shear wall

Large displacements cause frame damage Δ, large

Small displacements protect frame from damage

Stif Stiff ti fff and and Stron tro tr ong g Foundation Founda Found ation

Flexible Flexibl e and Wea Weak k Fou Found ndation ation

Stif tifff and and stron st rong g is not alwa always ys fa f avor able; nor is flexible flexib le and and wea weak k always con s erv rva ative.

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Case Study 1965

Construction Reinforced Concrete 6 Stories Above Grade 24’ Bays (3 (31,000 SF SF) 24’ by 24 Two-way Slab with Drop Panels Full Basement with Shallow Foundations Site Class D Seismic Design Category C  At ¾ BSE 1: S-3; N-D

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Typical Floor Plan

Transverse Shear Walls Longitudinal Shear Walls (Two coupled walls)

Perimeter Moment-Resisting Frame with Precast Infill EERI Technical


Longitudinal Wall Elevation General wall element modeling

Ground Floor One rigid foundation response

Basement

Two rigid foundations coupled by structural components

EERI Technical


Displacement Compatibility General wall Inelastic section

L B BW s W up u p p o p r o r o r t oo f t s o f ( n s s l l a ab a n no ot b t s h nd ho w d o wn ) n

Inelastic frame element G r ro u o un d n F l d l o o o o r r B a a s se e m me n nt t S O OG G

Nonlinearr elast Nonlinea elastic ic bar bar – NSP Inelast Inel astic ic bar bar + gap gap - NDP

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Typical Atypical Condition Beam

Two-way Slab

Torsio Tor sional nal def deform ormatio ation? n?

Precast between and connected to columns and beams

Column

P l an

Elevation Exterior Beam-Column Joint

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Displacement Compatibility Summary of Component Actions to Track 

Shear of foundation coupling walls



Shear of LBW lintel



Torsion of perimeter beam-column joint



Slab strips parallel and orthogonal to wall

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ASCE 41 Supplement 1 Proposed Figure 2-3 Component Force versus Deformation Curves Lateral deformation following loss of lateral strength capacity

b

Type 1 Curve

Type 2 Curve

Type 3 Curve

Notes: 1. Onl Only y seconda secondary ry compo componen nentt action actions s permit permitted ted betwe between en points points 2 and and 4. 2. The forc force, e, Q, aft after er point point 3 dimi diminis nishes hes to to approx approxima imatel tely y zero. zero.

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Foundation Plan Type B (2 vert. springs to capture K rot)

Individual Footings Coupled to Form K rot for Wall Line

One story shear wall

Type A (Vertical spring Beneath col.)

Plenum

Type D (3 springs) Type C

Postulate shear overstress due to foundation flexibility

Foundat Fou ndation ion Plan – Ver Vertic tical al Sprin Spring g ID ID

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Chapter 4: Effective Stiffness of “Foundation” Initial

Soil Stiffness

Initial Init ial Shear Shear Modul Modulus, us, G, G, Deriv Derived ed By By 1> Soil Soil Shear Shear Wave Wave Velocity Velocity (Eq (Eq 4-4 4-4)) 2> Standard Standard Penet Penetratio ration n Test (Blow (Blow Count Count – N1/60) ) (Eq 4-5) Effective Soil Stiffness Effective Stiffness, Go

Modulus Reduction Factors (Table 4-7) Foundation Stiffness Relative Stiffness Between Soil and Structure (C4-1 & C4-2) Method 1 to Method 3  Proportional to Go

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Quantitatively Define Soil Properties Nominal “N” val Nominal value ue used used by by GE Influen Infl uence ce dept depth h – B or 4B? Site Class “D” v= 600 ft/sec  1,200 ft/sec (over great depth) G0 proportional to v2

Original Ground

22 Footing location

280’

65 21

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

47 64 260’ ? How deep? deep?

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Other Means of Arriving at Soil Properties: Modulu Mod uluss of Sub Subgra grade de Rea Reacti ction on and and Uni Units ts In lieu of FEMA 356, the GE may provide other soil property recommendations. The following may help the SE, but collaboration with GE is the best answer: 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.

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Foundation Overturning Stiffness: Model vertical foundation stiffness and couple those with explicit structure modeling. Determine K vert by: 

Method Met hod 1: R Rigid igid isolat isolated ed founda foundatio tion n 18’ by 18’ coupled by explicit structure modeling  Method 2: Decoupled end and middle zones by conside con sidering ring foo footing ting as 64’ by 18’ Metho thod d 3: Unit Unit subgr subgrade ade mo modul dulus us  Me  Method 1 Revised: Determine Rotational stiffness and convert to vertical stiffness

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Foundation Plan Type B (2 vert. springs to capture K rot)

Individual Footings Coupled to Form K rot for Wall Line



Plenum


Postulate shear overstress due to foundation flexibility

Foundat Fou ndation ion Plan – Ver Vertic tical al Sprin Spring g ID ID

EERI Technical


Foundation Partial Plan 24’

Considered as:

24’

3 No No. 18 18’ by 18 18’ Pads or 64’’ lo 64 long ng by 18 18’’ wi wide de pa pad d Partial Plan

Ground Floor Basement

K

vert

K

vert

K

vert

Type D Foundation Elevation

EERI Technical


Chapt Cha pte er 4, Me Meth thod od 1: Rigid Foundation Structure? Use of elastic properti properties es to determine determine relative relative rigidities… rigidities… perhap perhapss strength would be a better test? See C4-2 for equation, discussion and limitations. limitations. 5

5

∑= ∑=

rigid test := 4 ⋅ k sν ⋅

m_m

1 nn

1

⎛ m_m ⋅ π ⎞ 2 ⎛ nn ⋅ π ⎞ 2 sin ⋅ sin 2 ⎝ ⎠ ⎝ 2 ⎠ ⎡ m_m2 nn2 ⎤ 4

π ⋅ D f ⋅

⎣ ( L1)

2

+

2

( B1) ⎦

+ k sν

where D f :=

E f × t

3

12in × ( 1 − ν f )

EERI Technical

2

For a 3’For 3’-3” 3” thi thick ck by by 18’ 18’ sq squa uare re foo footin ting g with a point load, the structural component is considered rigid. Strength (shear and flexure) would likely deem otherwise.


Chapte Chap terr 4, Me Meth thod od 1 Co Con’ n’t: t: Gazetas’ Equation: 18’ by 18’ pad Use isolated footing vertical stiffness (Figure 4-4)

⎤ ⎛ Li ⎞ 0.75 K z_sur := ⋅ 1.55 ⋅ + 0.8 i 1−ν ⎣ ⎝ Bi ⎦ G ⋅ Bi

⎡

Modify for embedment

2⎤ ⎡ Bi ⎞ ⎤ ⎢ ⎡ ⎡ di ⋅ ( Bi + Li) ⎤ 3 ⎥ 1 Di ⎛ β z := 1 + ⋅ ⋅ 2 + 2.6 ⋅ ⋅ 1 + 0.32 ⋅ i 21 Bi ⎝ Li ⎦ ⎣ ⎣ ⎣ Bi ⋅ Li ⎦ ⎦

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Chapte Chap terr 4, Me Meth thod od 1 Co Con’ n’t: t: Gazetas’ Equation: 18 18’ by 18 18’ Pad L = 18 ft B = 18 ft K z = 6378

q ult = 12ksf kip

For a unit

in

Sq Ftg Axial F-Defl

e c r o F

Ultimate bearing pressure provided by GE and not discussed herein

FD1 ( Δ )

K z

ft2

2⋅L⋅B .

= 9.8

ksf in

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

Δ Defl

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Chaptter 4, Me Chap Meth thod od 2: End Stiffening/Decoupling P and M For a 64’ by 18’ footing End footing (zone) K z :=

6.83 ⋅ G ⋅ B

(1 − ν)

Middle footing (zone) K z_mid := B/6

0.73 6.83

or

⋅ K z

Note: B or L/6 used in lieu of B/6. For High L/B ratios, this is judged as more appropriate. For this case “B/6” is made equal to “B”. K z 2⋅L⋅B

= 23

ksf

K z_mid

in

2⋅L⋅B

= 2.5

B or L/6

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

B

L Plan

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ksf in

Chap Ch apte terr 4, Met etho hod d 3: 3: Unit Co Coef. Of Of Su Subgrade Reaction: 18’ by 18 18’ Pad K z :=

1.3 ⋅ G B ⋅ (1 − ν) QED!

EERI Technical

⋅B⋅L

The multiplication of B and L converts to force per footing versus deformation. K z 2⋅L⋅B

= 4.4

ksf in


Chapte Chap terr 4, Me Meth thod od 1 Rev Revise ised: d: Gazetas’ Equation: 64 64’ by 18’ pad Use isolated footing rotational stiffness (Figure 4-4)

⎤ ⎛ Li ⎞ 2.4 K yy_sur := ⋅ 0.47 ⋅ + 0.034 i 1−ν ⎣ ⎝ Bi ⎠ ⎦ G ⋅ ( Bi)

3

⎡

Modify for embedment

⎛ di ⎞ 0.6 ⎡ ⎛ di ⎞ 1.9 ⎛ di ⎞ − 0.6 ⎤ β yy := 1 + 1.4 ⋅ ⋅ 1.5 + 3.7 ⋅ i ⎝ Li ⎣ ⎝ Li ⎠ ⎝ Di ⎠ ⎦

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Chapte Chap terr 4, Me Meth thod od 1 Rev Revise ised: d: Gazetas’ Equation: 64 64’ by 18 18’ pad Performing a rivet-type analysis with a unit area for each pad:

( 2)

I := 2 ⋅ 24 ⋅ ft

2

The equivalent vertical spring for each pad is K yy I

2⋅L⋅B

= 10.9

EERI Technical

ksf inch

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


Foundation Plan



Plenum


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

Middle Zone (Strip Footing)

Foundat Fou ndation ion Plan – Typ Type e A, A, Metho Method d2

EERI Technical


Chapterr 4, Met Chapte Method hod 2 Revis Revised ed For Typ Type e A ftg End Stiffening/Decoupling P and M K Method2 = 9982

(

2

IM2 := 2⋅ 1⋅ 108

IM2⋅ K Method2

K Method2_mid = 1067

in

kip in

r :=

K Method2_mid K Method2

+ 1⋅ 842 + r⋅ 602 + r⋅ 362 + r⋅ 122)⋅ ft2

= 5.536 ×

IM2 K Method2⋅ I

EERI Technical

kip

= 8091

10

10

kip in

kip⋅ in rad K Method2⋅

IM2 I

2⋅ L1⋅ B1


= 28.1

ksf in

Foundation Mechanism:

< qult qult

Soil

qult

qult

Foundation Flexure

P~

P

Soil + 2 V n

==> V n

EERI Technical

Flexural-shear/Shear

V n

governs and equals about 80% of soilgoverned capacity: 0.8 * qult = 9.6 ksf


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

⎛ B1 − 12inch⋅ wall − Vsoil := L1 ⋅ 2 ⎝ φ Vn := 2 ⋅ 4500 ⋅

lb in

2

d1 ⎞ 2 ⎠

⋅ qult Vsoil = 612kip

⋅ 0.8 ⋅ d1 ⋅ L1

φ Vn = 464 464 kip

At 3 root f'c, soil governs. governs. For lower bound strength capacity, use a factor of

⎡ ⎡ ⎛ B1 − 12 ⋅ inch⋅ wall − qult ⋅ B1 − 2 ⋅ 2 ⎣ ⎣ ⎝ B1 ⋅ L1 ⋅ qult

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d1 ⎞ ⎤

⎤ ⋅ L1 + 2 ⋅ φ Vn 2 ⎠ ⎦ ⎦ = 0.83


Lower Bound Stiffness Summary Effective Shear Modulus (GE rec. versus SE’s Guess) Method 1 Method 2 End Zone Middle Zone Method 3 Method 1 Revised

(1200/645)2 = 3.5

9.8 ksf/inch 23 ks ksf/inch 2.5 ks ksf/inch 4.4 ksf/inch 11 ksf/inch

Range of variation: All methods : 23/4.4= 5.2 Considering 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 any springs are are far better than fixed base!

EERI Technical


Global Response Spectral Acceleration versus Displacement 0.3

Target displacement increase by 75 %

0.25 ) g ( n o 0.2 i t a r e l e 0.15 c c A l a r t c 0.1 e p S

3/4 BSE-1 BSE-1 BSE-2 Fixed Base

0.05

Lower Bound

0

0.0

1.0

2.0

3.0

4.0

Spectral Displacement (in)

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Founda Fou ndation tion Res Respon ponse se – Lon Longit gitudin udinal al Wa Wallll Nonlinearr Elastic Nonlinea Elastic Springs – Lower Bound Bound Stiffness Stiffness and Strength Strength Foundation Compression Spring Longitudinal Wall

Foundation "Tension" Spring - Longitudinal Wall -200 -500

-400 ) s p i k ( -600 e c r o F -800 l a i x A -1000

3/4 BSE-1 BSE-1

) -1000 s p i k ( e c r -1500 o F l a i x A

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

BSE-2 Lower Bound

-2000

-1200

-2500

0

1

2

3

4

0

5

2

3



Ground Floor

System not dominated by rocking

Basement

K

EERI Technical

1

vert

K

vert

K

vert


4

5

Local (Component) Response Longitudinal Longitudin al Walls Coupling Beam

0.3

) i s k ( s 0.2 s e r t S r a e h S 0.1

Fixed Fi xed Base Ba se Lower Bound 3/4 BSE-1 BSE-1 BSE-2

0.0 0.0

0 .5

1 .0

1.5

2.0

2 .5

3 .0

Spectral Spect ral Displ Displac acement ement (in)

EERI Technical


Local (Component) Response Longitudinal Walls Coupling Beam, Lower Bound 3/4 BSE-1 BSE-1 BSE-2 Lower Bound LS CP

0.3

) i s k ( s s 0.2 e r t S r a e h 0.1 S

0.0 0.0

0.5

1.0

1.5

2.0

2.5


EERI Technical


3.0

Local (Component) Response Outrigger Wall - Abov Ab ove e Opening LBW 0.6 Fix Fi x ed Base

0.5

Lower Bound

) i s k 0.4 ( s s e r 0.3 t S r a e h 0.2 S

3/4 BSE-1 BSE-1 BSE-2 LS CP

0.1

0.0 0 .0

0.5

1.0

1 .5

2 .0

2 .5

Spectral Sp ectral Displacement D isplacement (in)

EERI Technical


3.0

Local (Component) Response Beam Joint Tor Beam-Column Torsion sion 0.010

) s n a i d a r ( n o i t a 0.005 m r o between Precast f e and connected to D columns n and beams o i s r o T

3/4 BSE-1 LB

Two-way Slab

BSE-1 LB BSE-2 LB Joint Rotati Ro tation on 3/4 BSE-1 FB BSE-1 FB

Torsio Tor sional nal def deform ormatio ation? n?

BSE-2 FB

Column

P l an

0.000 0 .0

0.5

Elevation 1 .0

1 .5

2.0

2.5

Spectral Displacement (in) Exterior Beam-Column Joint

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3 .0

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

Slab End Moment on Line D at Wall Face

540

0

) t f p-150 i k ( t n e m-300 o M d n-450 E b a l S-600

) t f p430 i k ( t n e320 m o M d n210 E b a l S100

3/4 BSE-1 BSE-1 BSE-2 Fixed Base Lower Bound

3/4 BSE-1 BSE-1 BSE-2 Fixed Base Lower Bound

-10

-750 0

1

2

3


4

5

0

1

2

3

4

5


Indicates significant slab stress demand but no inelastic beha be havi vior or for for 24’ sp span. an. Short spans showed inelastic behavior.

EERI Technical


Exterior Beam-Column Joint Col. (N)

Beam (E)

Slab (E)

Col. (E)

P l an

Elevation Exterior Beam-Column Joint

EERI Technical


Typical Floor Plan Deleted columns as a result of the analysis New columns (Wall Piers)

EERI Technical


Seismic Rehabilitation Recommendations  Do

nothing to overstressed coupling beam that is between the longitudinal walls Prov ovide ide “ca “catc tche her” r” to LBW LBW at at 5th floor and at other locations  Pr  Do nothing to beam-column joint in longitudinal direction: • •

Deformation levels Higher confidence in determining deformations due to inclusion of SSI effects

 Slabs

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.

EERI Technical


Displacement-Based Displacement-Ba sed Design  More

liberal evaluation techniques

 ASCE

41 Supplement 1 will wil l require more comprehensive modeling

 Foundation

flexibility and strength:  Adds to total lateral deflection  Changes the distribution of inelastic displacement demand dema nd betwe between en comp componen onents ts and may cha change nge strength hierarchy

EERI Technical


Ways to Improve SSI Modeling 

GE 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



Determi Det ermine ne residu residual al displa displacem cements ents - NDP

EERI Technical


FEMA 365 Foundation Example

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