Monotonic and Cyclic Tests of Long Steel-Frame Shear Walls with ...
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![Page 1: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic and cyclic loading Introduction Prof. ing.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5514583c550346494e8b5495/html5/thumbnails/1.jpg)
Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic and cyclic loading
IntroductionProf. ing. Claudio di Prisco
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Prof. ing. Claudio di Prisco
Indice
Outlook of the presentationOutlook of the presentation
a) Introduction
b) Failure mechanisms and punching
c) The macro-element concept
d) Cyclic soil-structure interaction: constitutive modeling observations
e) A simplified approach
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Prof. ing. Claudio di Prisco
Definitions: shallow foundations
GEOMETRIESGEOMETRIES
• Shallow (B/H>4) and deep foundations (B/H<4)
• Strip footings
• Mat foundations
• Grid foundations
Lancellotta e Calavera, 1999
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Prof. ing. Claudio di Prisco
The soil-structure interaction
Statically determinate interaction
Redundantly constrained interaction
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Prof. ing. Claudio di Prisco
What are the consequences? Irreversible differential settlements, damage to the structureenergy dissipation
The soil structure interaction
site amplification
Depending on topography and stratigraphy
Soil- foundation interaction
Dynamic structural response
3
1
2
4
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Prof. ing. Claudio di Prisco
1. The pseudo-static approach: the rigid-plastic approach
Static equivalent horizontal load: step 2 is disregarded whereas step 4 is abruptly simplified.
A design pseudo-static distribution of forces is applied to the structure, additional loads H and M are applied on the foundation and new limit conditions have to be accounted for
In this perspective the design of the shallow foundation under inclined and eccentric loads become essential
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Prof. ing. Claudio di Prisco
Failure mechanisms: the interaction domain in quasi static conditions
Failure mechanisms: Failure mechanisms: small scale 2D experimental test results (drained and small scale 2D experimental test results (drained and undrained conditions, cohesive and granular soils)undrained conditions, cohesive and granular soils)
Nova e Montrasio, 1988
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Prof. ing. Claudio di Prisco
Punching mechanisms
Punching mechanisms and 2nd order effectsPunching mechanisms and 2nd order effects
Lancellotta e Calavera, 1999
Lancellotta, 1993
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Prof. ing. Claudio di Prisco
The limit analysis
The limit analysis and the Prandtl mechanismThe limit analysis and the Prandtl mechanism
• Rigid-plastic mechanical behavior of the material• Associated flow-rule• Mohr-Coulomb failure criterion
The kinematic limit analysis approachThe kinematic limit analysis approach
Lancellotta, 1993
Nova, 2008
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Prof. ing. Claudio di Prisco
The Terzaghi Theory
The Terzaghi bearing capacity equation for vertical and centered The Terzaghi bearing capacity equation for vertical and centered loadsloads
Lancellotta, 1993
1
2LIM c qq B N cN qN
( ')
( ')
( ')c c
q q
N N
N N
N N
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Prof. ing. Claudio di Prisco
Inclined and eccentric loads: Brinch-Hansen coefficientsInclined and eccentric loads: Brinch-Hansen coefficients
Lancellotta, 1993
H/M
V
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Prof. ing. Claudio di Prisco
The interaction domain for rigid shallow footings
m = M/ψBVMAX,
h = H/μVMAX
ξ = V/VMAX
1. To each point belonging to the failure locus a distinct failure mechanism corresponds
2. Difficulty in defining the failure locus when loose sand strata are concerned
3. Extension to rectangular footings
4. Extension for D/B>0
5.
MONOTONOUSLY INCREASING LOADING
22 2
2 1 0c
M H Vf V
B V
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Prof. ing. Claudio di Prisco
Centered vertical load Centered inclined load
Elasto-plastic finite element numerical analyses
Tochnog perfect elasto-plastic numerical analyses
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The uplift
Shirato et al. 2007
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Prof. ing. Claudio di Prisco
The uplift of rigid shallow foundations
Confronto tra il Dominio di Interazione fornito dal modello Nova- Montrasio e i valori puntuali valutati con il modello numerico
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500 600 700 800 900 1000
V[kN/m]
M [
kN
m/m
]
Modello Elasto-Plastico
Modello Nova-Montrasio
Poli. (Modello Nova-Montrasio)
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Prof. ing. Claudio di Prisco
M
HV
Q
qv
u
Inclined LOADS
Rigid strip footing
0
0
1
2
3
4
H
V
Dense sand
B
0.5B
0.5B
0.5B
INTERACTION DIAGRAMS
GENERALISED STRESS PATHS
LOAD CONTROLLED TESTS
THE EXPERIMENTAL TEST SERIES
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Prof. ing. Claudio di Prisco
Failure mechanism
in unreinforced dense sand layer
Failure mechanism
in unfastened reinforced dense sand layer
DENSE SAND, vertical loading
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Prof. ing. Claudio di Prisco
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30 35 40 45 50 55 60 65
v [mm]
V [ kPa]
Unreinforced
Unfastened reinforced
fastened reinforced
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35 40 45
u [mm]
H [ kPa]
H/V = 0.1
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Sabbia sciolta non rinforzata
0
2
4
6
0 10 20 30 40 50V [kPa]
H [
kP
a]
Sabbia sciolta rinforzata con geosintetici non allacciati
0
2
4
6
8
10
0 20 40 60 80 100 120 140
V [kPa]
H [
kP
a]
Sabbia sciolta rinforzata con geosintetici allacciati
0
5
10
15
20
25
-20 0 20 40 60 80 100 120 140 160 180 200
V [kPa]
H [
kP
a]
EXPERIMETNAL DATA and NUMERICAL INTERPOLATION
INTERACTION DIAGRAMS
Unreinforced loose sand Unfastened reinforced loose sand
Fastened reinforced loose sand
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Prof. ing. Claudio di Prisco
Numerical simulations Tochnnog finite element codeelasto-perfectly plastic constitutive model
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
2
0 0,05 0,1 0,15 0,2 0,25 0,3
v / B
V /
VM
AX
Legge associata
Legge non associata
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0 0,2 0,4 0,6 0,8 1 1,2 1,4
u [m]
v [
m]
mohr-coulomb associata
mohr-coulomb non associata
Non associated flow rule ( = 0)
Truss elements
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1
2
4
K =k() ?
= () ?
The visco-elastic approach
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M - curves
-0.08 -0.04 0 0.04 0.08-0 .1 -0 .06 -0 .02 0.02 0.06 0.1
(rad)
- 2
- 1
0
1
2
-1 .5
-0 .5
0.5
1.5
M (
kN.m
)
-0.08 -0.04 0 0.04 0.08-0 .1 -0 .06 -0 .02 0.02 0.06 0.1
(rad)
- 2
- 1
0
1
2
-1 .5
-0 .5
0.5
1.5
M (
kN.m
)
PWRI experimental test results,2005
Dense sand stratum Loose sand stratum
FOOTING UPLIFT
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Prof. ing. Claudio di Prisco
Cross section
Plan view
Ispra Laboratory Elsa (Pedretti, 1998)
Ispra Laboratory Elsa di Elsa di (Pedretti, 1998)
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A simplified approach
A sA symmetricymmetric generalised stress-paths generalised stress-paths
1E-005 0.0001 0.001 0.01 0.1
(rad)
0
0.2
0.4
0.6
0.8
1
0.1
0.3
0.5
0.7
0.9
Kf
/ Kf,
0 (-
)
1E-005 0.0001 0.001 0.01 0.1 1
(rad)
0
0.1
0.2
0.3
0.4
0.5
0.05
0.15
0.25
0.35
0.45
f (
-)
Medium Relative DensityDR = 50-60%
ISPR A phase 1
ISPR A phase 2
ISPR A phase 3
N um erica l phase 1
N um erica l phase 2
PW R I test n .10
PW R I test n .11
c) Rotational SecantStiffness
d) Damping Factor
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1E-005 0.0001 0.001 0.01 0.1rocking angle (rad)
0
0.2
0.4
0.6
0.8
1
K/K0(-)
1E-005 0.0001 0.001 0.01displacement (m)
0
0.2
0.4
0.6
0.8
1
K/K0(-)
0.0001 0.001 0.01 0.1rocking angle (rad)
0
0.1
0.2
0.3
0.4
0.5
(-)
High relative densityDR = 90%
ISPRA phase 1ISPRA phase 2ISPRA phase 3
numerical phase 1numerical phase 2PWRI test n. 5PWRI test n. 8
Rotational SecantStiffness
Translational SecantStiffness
Damping Factor