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

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

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

The soil-structure interaction Statically determinate interaction Redundantly constrained interaction

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

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

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

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

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

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

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

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

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

The uplift Shirato et al. 2007

The uplift of rigid shallow foundations

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

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

H/V = 0.1 v [mm] V [ kPa] Unreinforced Unfastened reinforced 20 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

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]

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

The visco-elastic approach Dt 1 2 4 K =k() ?  =  () ?

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

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

A simplified approach A symmetric generalised stress-paths