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

2. 2 Experimental device Max= 712 gal Max= 608 gal Shear stacks

3. Prof. ing. Claudio di Prisco 3 Experimental evidence

4. Prof. ing. Claudio di Prisco 4 The elasto-perfectly plastic approach

5. Prof. ing. Claudio di Prisco 5 Coupled elastoplastic CONSTITUTIVE RELATIONSHIP Defined in quasi static conditions: THE MACRO-ELEMENT CONCEPT Incremental constitutive relationship FOUNDATION NEAR FIELD FAR FIELD

6. Prof. ing. Claudio di Prisco 6 The interaction domain for rigid footings Interaction domain for rigid strip footings and elasto-perfectly plastic approach m = M/ψBV MAX, h = H/μV MAX ξ = V/V MAX 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.Non-associated flow rule 4.Within the failure locus the mechanical behaviour is assumed to be elastic and uncoupled 5.Extension to rectangular footings MONOTONOUSLY INCREASING LOADING

7. Prof. ing. Claudio di Prisco 7 Settlements Centered vertical load Centered inclined load Cyclic inclined loading anisotropic hardening Cremer et al, 2001

8. Prof. ing. Claudio di Prisco 8 Hardening Isotropic hardening (Nova and Montrasio, 1991) Swipe tests Butterfield and Gottardi, 2003 H V V M/B c =V c / V MAX Hardening parameter

9. Prof. ing. Claudio di Prisco 9 Inclined-eccentric loads Nova and Montrasio, 1991 Inclined and eccentric loading

10. Prof. ing. Claudio di Prisco 10 How can R 0 be determined? Some hints about settlement evaluation Homogeneous stratigraphic profiles

11. Prof. ing. Claudio di Prisco 11 Settlement evaluation Irreversibility of the material mechanical response Non-linearity Dependency of stiffness on confining pressure

12. Prof. ing. Claudio di Prisco 12 The elastic solution Poulos e Davis (1974) Gibson (1973) Winkler (1867) Dependency of stiffness on confining pressure: Eo/λD 1 0 0.5 r/D 0 1 = 0.5

13. Prof. ing. Claudio di Prisco 13 Settlement evaluation The elastic solution Linear loading distribution Strip loading distribution Rectangular loading distribution

14. Prof. ing. Claudio di Prisco 14 Generalised plasticity

15. Prof. ing. Claudio di Prisco 15 Numerical validation

16. Prof. ing. Claudio di Prisco 16

17. Prof. ing. Claudio di Prisco 17 Cyclic loads Loose sand Dense sand

18. Prof. ing. Claudio di Prisco 18 Numerical validation

19. Prof. ing. Claudio di Prisco 19 Numerical results

20. Prof. ing. Claudio di Prisco 20 Cyclic consequences of the mechanical coupling

21. Prof. ing. Claudio di Prisco 21

22. Prof. ing. Claudio di Prisco 22

23. Prof. ing. Claudio di Prisco 23 A dynamic/non seismic problem

24. Prof. ing. Claudio di Prisco 24