1. Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic and cyclic loading
Introduction
Prof. ing. Claudio di Prisco

2. Outlook of the presentation
Indice
Outlook of the presentation
Introduction
Failure mechanisms and punching
The macro-element concept
Cyclic soil-structure interaction: constitutive modeling observations
A simplified approach

3. Definitions: shallow foundations
GEOMETRIES
Shallow (B/H>4) and deep foundations (B/H<4)
Strip footings
Mat foundations
Grid foundations
Lancellotta e Calavera, 1999

4. The soil-structure interaction
Statically determinate interaction
Redundantly constrained interaction

5. The soil structure interaction
What are the consequences? Irreversible differential settlements, damage to the structure energy dissipation 3 Dt 1 2 4
Dynamic structural response
Soil- foundation interaction
site amplification
Depending on topography and stratigraphy

6. 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

7. Failure mechanisms: the interaction domain in quasi static conditions
Failure mechanisms: small scale 2D experimental test results (drained and undrained conditions, cohesive and granular soils)
Nova e Montrasio, 1988

8. Punching mechanisms and 2nd order effects
Lancellotta e Calavera, 1999
Lancellotta, 1993

9. The limit analysis and the Prandtl mechanism
Rigid-plastic mechanical behavior of the material
Associated flow-rule
Mohr-Coulomb failure criterion
The kinematic limit analysis approach
Nova, 2008
Lancellotta, 1993

10. The Terzaghi bearing capacity equation for vertical and centered loads
The Terzaghi Theory
The Terzaghi bearing capacity equation for vertical and centered loads
Lancellotta, 1993

11. Inclined and eccentric loads: Brinch-Hansen coefficients
H/M V
Lancellotta, 1993

12. The interaction domain for rigid shallow footings
MONOTONOUSLY INCREASING LOADING
To each point belonging to the failure locus a distinct failure mechanism corresponds
Difficulty in defining the failure locus when loose sand strata are concerned
Extension to rectangular footings
Extension for D/B>0
m = M/ψBVMAX,
h = H/μVMAX
ξ = V/VMAX

13. Elasto-plastic finite element numerical analyses
Centered vertical load
Centered inclined load
Tochnog perfect elasto-plastic numerical analyses

14. The uplift
Shirato et al. 2007

15. The uplift of rigid shallow foundations

16. THE EXPERIMENTAL TEST SERIES
GENERALISED STRESS PATHS
Inclined LOADS
INTERACTION DIAGRAMS
Rigid strip footing
Dense sand B
0.5B
LOAD CONTROLLED TESTS
THE EXPERIMENTAL TEST SERIES

17. DENSE SAND, vertical loading
Failure mechanism
in unreinforced dense sand layer
Failure mechanism
in unfastened reinforced dense sand layer

18. H/V = 0.1 v [mm] V [ kPa] Unreinforced Unfastened reinforced20 40 60 80
100
120
140 5 10 15 25 30 35 45 50 55 65
v [mm]
V [
kPa]
Unreinforced
Unfastened reinforced
fastened reinforced 2 4 6 8 10 12 14 5 15 20 25 30 35 40 45
u [mm]
H [
kPa]
H/V = 0.1

19. INTERACTION DIAGRAMS EXPERIMETNAL DATA and NUMERICAL INTERPOLATION
Unreinforced loose sand
Unfastened reinforced loose sand
Sabbia sciolta non rinforzata
Sabbia sciolta rinforzata con geosintetici non allacciati 6 10 8 4 6
H [kPa]
H [kPa] 4 2 2 20 40 60 80
100
120
140 10 20
V [kPa] 30 40 50
V [kPa]
Fastened reinforced loose sand
Sabbia sciolta rinforzata con geosintetici allacciati 25
INTERACTION DIAGRAMS 20 15
H [kPa] 10 5
EXPERIMETNAL DATA and NUMERICAL INTERPOLATION
-20 20 40 60 80
100
120
140
160
180
200
V [kPa]

20. Truss elements Numerical simulations Tochnnog finite element code
elasto-perfectly plastic constitutive model
Truss elements
Non associated flow rule (y = 0)

21. The visco-elastic approachDt 1 2 4
K =k() ?
 =  () ?

22. PWRI experimental test results,2005
M -  curves
PWRI experimental test results,2005
Loose sand stratum
Dense sand stratum
FOOTING UPLIFT

24. Ispra Laboratory Elsa di Elsa di (Pedretti, 1998)
Cross section
Plan view

29. A simplified approach
A symmetric generalised stress-paths