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

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

Prof. ing. Claudio di Prisco 3 Experimental evidence

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

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

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

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

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

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

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

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

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 r/D 0 1 = 0.5

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

Prof. ing. Claudio di Prisco 14 Generalised plasticity

Prof. ing. Claudio di Prisco 15 Numerical validation

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

Prof. ing. Claudio di Prisco 18 Numerical validation

Prof. ing. Claudio di Prisco 19 Numerical results

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

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

Prof. ing. Claudio di Prisco 24