Post on 03-Oct-2021
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Performance-based guidelines for practitioners
Foundations and SSI aspects of FEMA 356 and 440
Craig D. Comartin
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Outline
Example buildingFoundation modelingInertial effectsKinematic effectsResponse spectrum for analysisBearing capacity
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Example building plan
160’-0”
100’
-0”
Plan
8” R/C wall – 20’Ltypical
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Example building wall elevation and section
Elevation @ wall Section @ wall
Roof
2nd
1st
20’-0”
Footing 26’L x 3’B x 1.5’d
3’D
10’-0”typical
Elevation @ wall Section @ wall
Roof
2nd
1st
20’-0”
Footing 26’L x 3’B x 1.5’d
3’D
10’-0”typical
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Example building description
• Two story concrete structure: FEMA model building Type C2• Story to story heights 10 ft: total building height of 20 ft. • Plan dimensions: 100 ft. by 160 ft. • Floors and roof construction: two-way reinforced concrete flat slab
• Roof DL = 140 psf• Floor DL = 160 psf
• Vertical support: concrete columns and interior and exterior reinforced concretebearing walls
• Lateral system: six shear walls in each direction, 12 total – L=20 ft., t=8 in. • Foundations: spread footings bearing 3 ft. below grade and reinforced concrete
slab on grade• Soils conditions: very stiff alluvium, u= 1200 fps, NEHRP Site Class C• Ground motion: shaking with a 10% chance of being exceed in 50 yrs.• Analysis objective: Maximum global displacement for specified ground motion
NOTE: See FEMA 440 for complete example.
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Generic Foundation Element Models
Fy
Fx
Mz
SθSx
Sy
Sx
Siy i=1 to 5
c. Winkler Component Model
b. Uncoupled ComponentModel
a. Foundation Actions
Structural Component Geotechnical Components
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Flexible base properties
Flexible base model
20’-0”
10’-0”typical
Mroof
Mfloor
Footing 26’L x 3’B x 1.5’d
3’D
Flexible base model
20’-0”
10’-0”typical
Mroof
Mfloor
Footing 26’L x 3’B x 1.5’d
3’D
Flexible base model
20’-0”
10’-0”typical
Mroof
Mfloor
Footing 26’L x 3’B x 1.5’d
3’D
Flexible base model
20’-0”
10’-0”typical
Mroof
Mfloor
Footing 26’L x 3’B x 1.5’d
3’D
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Gazetas’ equations (stiffness)
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Gazetas’ equations (embedment)
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Flexible base properties
Soil properties Foundation dimensions
initial shear modulus 31 ksi length, L= 26 ftwidth, B= 3 ft
unit wt. of soil, 100 pcf thickness, d 1.5 ft shear wave velocity, 1200 fps depth, D= 3 ft
effective shear modulus 0.75
23 ksi
Poisson's ratio 0.3
0/G G =
γ =
sν =
20 sG
gγ ν= =
G=
υ=
ATC 40Sect. 10.4.1.2
FEMA 356Table 4.7
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Soil properties
shear wave velocity = 1200 ft/secsoil unit weight = 100 pcf
gravity = 32.2 ft/sec2
G0 = 31 ksi
G = 0.75 G0
= 23 ksi
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Flexible base properties
Rotational stiffness
at surface 780,342,531 k-in/rad
embedment factor 1.39
at depth 1,081,161,315 k-in/rad
θ υ
⎡ ⎤⎛ ⎞= + =⎢ ⎥⎜ ⎟− ⎝ ⎠⎢ ⎥⎣ ⎦
2.43
, 0.47 0.034 61surGB LK X walls
B0.6 1.9 0.6
1 1.4 1.5 3.7d d dL L Dθβ
−⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + + =⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦
,surK Kθ θ θβ= =
FEMA 356Fig. 4.4ATC 40
Table 10.2&3
7.8 x 108
1.1 x 109
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Flexible base properties
Translational stiffness
at surface 44,505 k/in
embedment factor 1.86
at depth 82,607 k/in
υ
⎡ ⎤⎛ ⎞= + =⎢ ⎥⎜ ⎟− ⎝ ⎠⎢ ⎥⎣ ⎦
0.65
, 3.4 1.2 62x surGB LK X walls
B
( ) 0.4
21 0.21 1 1.6x
Dd B LDB BL
β⎡ ⎤⎛ ⎞ ⎛ ⎞+⎢ ⎥= + + =⎜ ⎟ ⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦
,x x sur xK K β= =
FEMA 356Fig. 4.4ATC 40
Table 10.2&3
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Linear periodsEvaluate the linear periods for the structural model
assuming a fixed base, , and a flexible base, , using appropriate foundation modeling assumptions.
Fixed base model
20’-0”
10’-0”typical
Mroof
Mfloor
T
0.20sec=%T
T%
0.14sec=TFlexible base model
20’-0”
10’-0”typical
Mroof
Mfloor
Footing 26’L x 3’B x 1.5’d
3’D
Flexible base model
20’-0”
10’-0”typical
Mroof
Mfloor
Footing 26’L x 3’B x 1.5’d
3’D
xK Kθ
Flexible base model
20’-0”
10’-0”typical
Mroof
Mfloor
Footing 26’L x 3’B x 1.5’d
3’D
Flexible base model
20’-0”
10’-0”typical
Mroof
Mfloor
Footing 26’L x 3’B x 1.5’d
3’D
xK Kθ
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Initial spectrum for analysis
Select ground motion spectrum
Site class C and shear wave velocity,
Acceleration parameters for MCE shaking Damping coefficients for initial short period 1.5 glong period 0.6 g
Adjustment for site class Cshort periodlong period
short period 1.0 g
long period 0.5 g
To reduce to design level motions (e.g.10% chance of being exceeded in 50 years), multiply accelerations by 2/3
sv =1200fps
sS =5%β =
1.0sB =
1 1.0B =
FEMA 356Sect. 1.6ATC 40
Sect. 4.4
S1 =
( )xs a sS F S g= = 11.5=1.5( )1 1= = 1.3 0.6 =0.78x vS FS g
1.0aF =
=1.3vF
DS XSS S2= =3
D XS S1 12= =3
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Acceleration vs. period
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.50 1.00 1.50
Period, T (sec)
Sa
free field motion (FFM) @5% damping
Initial design spectrum for β =5%
T=0.2 sec
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Foundation (inertial) damping
2
1 21 1eff efff
eff eff
T Ta a
T Tβ
⎛ ⎞ ⎛ ⎞= − + −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
% %
( )*exp . . /1 4 7 1 6ea c h rθ= −
( )*ln /2 25 16ea c h rθ⎡ ⎤= −⎣ ⎦( )1.5 / 1e xc e r= +
Fixed to flexible base period shift
Ratio of effective height to foundation radius for rotation
Ratio of effective height to foundation radiusfor translation
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Foundation (inertial) dampingParameters necessary to compute:
%eff
eff
TT
*h
rθ
xr
e
Effective period shift
Effective building height
Equivalent foundation radius for rotation
Embedment of structure
Equivalent foundation radius for translation
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Effective period shift
0.5211 1μ
⎧ ⎫⎡ ⎤⎛ ⎞⎪ ⎪⎢ ⎥= + −⎨ ⎬⎜ ⎟⎢ ⎥⎝ ⎠⎪ ⎪⎣ ⎦⎩ ⎭
% %eff
eff
T TT T
μ is the expected ductility demand for the system (i.e. including structure and soil effects). This is an approximation that assumes all inelastic behavior is concentrated in the structure.
Fixed to flexible base period shift
FEMA 440Eqn. 8-8
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Example building
Effective period lengthening
Assume μ = 3
1.2 FEMA 440Eqn. 8-8
0.5211 1eff
eff
T TT Tμ
⎧ ⎫⎡ ⎤⎛ ⎞⎪ ⎪⎢ ⎥= + − =⎨ ⎜ ⎟ ⎬⎢ ⎥⎝ ⎠⎪ ⎪⎣ ⎦⎩ ⎭
% %
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Effective building height
174 in.* 1
1
N
i iiN
ii
h Mh
M
ϕ=
=
= =∑
∑FEMA 440Sect. 8-3
This is a simple dynamic property of the structure.
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Foundation radius for rotation
( )133 1
8K
rG
θθ
υ⎛ ⎞−= ⎜ ⎟⎝ ⎠
FEMA 440Eqn. 8-7
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Foundation radius for rotation
( )133 1
8K
rG
θθ
υ⎛ ⎞−= ⎜ ⎟⎝ ⎠
91.1 x 10θ =K
231in.=
From previous calculation
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Alternative approximation
( )2* *
2 *
1
fixed
fixed
x
K hK
KTT K
θ =⎛ ⎞
− −⎜ ⎟⎝ ⎠
%FEMA 440
Eqn.8-6
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Fixed base stiffness
2* * 2fixedK M
Tπ⎛ ⎞= ⎜ ⎟
⎝ ⎠*M is the effective mass for the first mode calculated as
the total mass times the effective mass coefficient (see ATC 40 Eqn. 8-21).
FEMA 440Eqn. 8-3
23,250 k/in2
* * 2fixed mK M M
Tπ α⎛ ⎞= = =⎜ ⎟
⎝ ⎠
where0.77
2
1
2
1 1
/
/ /
N
i imi
m N N
i i imi i
w g
w g w g
φα
φ
=
= =
⎡ ⎤⎢ ⎥⎣ ⎦= =
⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦
∑
∑ ∑
ATC 40Eqn 8-21
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Translational stiffness of the foundation
This can be evaluated using the procedures in FEMA 356 (Chap. 4) or ATC 40 (Chap. 10). For many applications, it can be estimated as
82x xK Gr
υ=
−
where G = effective, strain-degraded soil shear modulus and υ = soil Poisson’s ratio (∼0.3 for sand, ∼0.45 for clay).
FEMA 440Eqn. 8-5
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Foundation radius for translation
/x fr A π=
fA is the area of the foundation footprint if the foundation components are inter-connected laterally.
FEMA 440Eqn. 8-4
71 ft. = 856 in./x fr A π= =
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Translational stiffness of the foundation
This can be evaluated using the procedures in FEMA 356 (Chap. 4) or ATC 40 (Chap. 10). For many applications, it can be estimated as
82x xK Gr
υ=
−
where G = effective, strain-degraded soil shear modulus and υ = soil Poisson’s ratio (∼0.3 for sand, ∼0.45 for clay).
FEMA 440Eqn. 8-5
93,867 k/in82x xK Gr
υ= =
−
83,000=xKFrom previous calculation
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Foundation rotational stiffness
6.0E+08 k-in/rad( )2* *
2 *
1
fixed
fixed
x
K hK
KTT K
θ = =⎛ ⎞
− −⎜ ⎟⎝ ⎠
%
88.4 x 10θ =K
91.1 x 10θ =KFrom previous calculation
Adjust for embedment
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Foundation radius for rotation
189 in( ) θ
θυ−⎛ ⎞
= =⎜ ⎟⎝ ⎠
133 1
8K
rG
86.0 x 10θ =KNeglecting embedment and using
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Foundation (inertial) damping
Determine the basement embedment, e, if applicable and calculate
x
er
Relative translational stiffness index
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Example building
No basement so e = 0
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Example buildingCalculate foundation damping
3.73 %2
1 21 1eff efff
eff eff
T Ta aT T
β⎛ ⎞ ⎛ ⎞
= − + − =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
% % FEMA 440Eqn. 8-9a
⎩ ⎭
where25.19
-18.06
1.00
( )1 exp 4.7 1.6 /ea c h rθ= − =
( )2 25ln / 16ea c h rθ⎡ ⎤= − =⎣ ⎦
( )1.5 / 1e xc e r= + =
FEMA 440Eqn. 8-9b
FEMA 440Eqn. 8-9c
FEMA 440Eqn 8-9d
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Foundation dampingGraphical approach
1 1.5 2Period Lengthening
0
10
20
30
Foun
dati o
nD
amp i
ng,β
f( %
)= 0
(radiation damping only)
= 0.5
1.0
2.0 /h
/e r
1 1.5 2Period Lengthening
0
10
20
30
Foun
dati o
nD
amp i
ng,β
f( %
)= 0
(radiation damping only)
= 0.5
1.0
2.0 /h
/e r
4%
1.2
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Flexible base damping ratio
where 5 %iβ =
6.9 %( )0 3
if
eff effT T
ββ β= + =%
FEMA 440Eqn. 8-10
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Reduce spectrum for increased damping
Evaluate the effect on spectral ordinates of the change in damping ratio accordance with Section 6.3.
1.09
( ) ( ) ( )0
0 0
5%
( ) ( )
a a FIMa
S SS
B Bββ β
= =
00
4(5.6 ln (in %))
Bβ β= =
−FEMA 440Eqn.6-17
FEMA 440Eqn.6-16
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Acceleration vs. period
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.50 1.00 1.50
Period, T (sec)
Sa
free field motion (FFM) @5% damping
free field motion includingfoundation damping
Spectrum adjusted for foundation damping
T=0.2 sec
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Kinematic effectsEvaluate the spectral reduction from base slab
averaging (RRSbsa) as a function of period.
0 0.2 0.4 0.6 0.8 1 1.2
Period (s)
0.4
0.5
0.6
0.7
0.8
0.9
1
Foun
datio
n/fre
e-fie
ld R
RS
fro
m b
ase
slab
ave
ragi
ng (R
RS
bsa)
Simplified Modelbe = 65 ft
be = 130 ft
be = 200 ft
be = 330 ft
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Kinematic effects
An approximation to curves is given by:
≥ the valuefor T= 0.2 sec.
1.21114100
ebsa
bRRST
⎛ ⎞= − ⎜ ⎟⎝ ⎠
FEMA 440Eqn. 8-1
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Kinematic effects
Evaluate effective foundation size where aand b are the full footprint dimensions (in feet) of the building foundation in plan view.
abbe =
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Kinematic effectsIf the structure has a basement embedded a depth e
from the ground surface, evaluate an additional spectral reduction from embedment (RRSe) as a function of period.
0 0.4 0.8 1.2 1.6 2
Period (s)
0
0.2
0.4
0.6
0.8
1
1.2Fo
unda
tion/
Free
-Fie
ld R
RS
e = 30 ftVs = 2500 ft/sVs = 1200 ft/sVs = 600 ft/s
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Kinematic effectsAn approximation to curves is given by:
vs = shear wave velocity n = shear wave velocity
reduction factor for the expected PGA
cos
.
2
the larger of 0.453or the RRS value efor T=0.2sec
es
eRRST nvπ⎛ ⎞
= ≥⎜ ⎟⎝ ⎠ FEMA 440
Eqn. 8-2
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Adjust for kinematic interactionModify kinematic soil-structure interaction
Effective foundation size: Embedment:a = 100 ft. e = 0b = 160 ft.
126 ft.
Ratio of response spectra for base slab averaging
Foundation input motion (FIM)
no basement
eb ab= =
1.211 the value for = 0.2 sec.14100
ebsa
bRRS TT⎛ ⎞= − ≥⎜ ⎟⎝ ⎠
FEMA 440Eqn. 8-1
( ) ( )a FIM bsa e a FFMS RRS RRS S=
eRRS =1.0
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Acceleration vs. period
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.50 1.00 1.50
Period, T (sec)
Sa free field motion (FFM) @5% damping
free field motion includingfoundation damping
foundation input (FIM) withfoundation damping
Final spectrum
T=0.2 sec
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5
Roof displacement, D
Base shear,V/W
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5
Roof displacement, D
Base shear,V/W
Displacement demand and base shear
0.4 gVW
=
.0.4 inroofΔ =
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Elasto-Plastic Behavior
Possible Stress States
1
l
Elastic prior touplift
2Elastic at uplift
3Elastic after uplift
4
l
Yield prior touplift
5Yield afteruplift
6 Inelastic limit
q< qu
q< qu
q< qu qu
qu
qu
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Elasto-Plastic Behavior
Moment,M
Rotation,θ
3
1
2
6
5
4
Infinitely strong soil
P
M
l
BStress (q) distribution
Ultimate soil capacity = q
u
55
Pl2
Pl2 - P2
2quB
P l6
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Check soil bearing capacity
( ) ( )13 23 3( ) 41932OTM floor roof floor roof slab slabLM F F F F M V ft k⎛ ⎞= + − + − + =⎜ ⎟
⎝ ⎠∑ ∑
2OTM DLL aM P −⎛ ⎞= ⎜ ⎟
⎝ ⎠
149yroof
Vm ft k
W= =
171yfloor
Vm ft k
W= =
20’-0”
10’-0”typical
F floor
20’-0”
10’-0”typical
F roof
PDL
PDL
qu
−2
L a
Mslab,Vslab
F total
20’-0”
10’-0”typical
F floorF floor
20’-0”
10’-0”typical
F roofF roof
PDL
PDL
qu
−2
L a
Mslab,Vslab
F totalF total
540k≈
17.2DLu
Pq ksfBa
= =2 10.4OTM
DL
Ma L ftP
→ = − =
5002slab slabLM V ft k+ ≈∑ ∑
EERI TechnicalSeminar Series
Impact of Soil-Structure Interaction on Response of StructuresSeminar 1: Practical Applications to Shallow Foundations
Ultimate capacities for shallow foundations
Presumptive values tabulated for classes of materialsVertical bearing pressures increase with depth and widthLateral passive pressures increase with depth
Prescriptive values based on original design data3.0 times specified "allowable" dead plus live loads1.5 times all required "working loads"
Site-specific values based on geotechnical investigation