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

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**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

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**Definitions: shallow foundations**

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

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**The soil-structure interaction**

Statically determinate interaction Redundantly constrained interaction

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**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

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**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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**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

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**Punching mechanisms and 2nd order effects**

Lancellotta e Calavera, 1999 Lancellotta, 1993

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**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

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**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

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**Inclined and eccentric loads: Brinch-Hansen coefficients**

H/M V Lancellotta, 1993

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**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

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**Elasto-plastic finite element numerical analyses**

Centered vertical load Centered inclined load Tochnog perfect elasto-plastic numerical analyses

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The uplift Shirato et al. 2007

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**The uplift of rigid shallow foundations**

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**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

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**DENSE SAND, vertical loading**

Failure mechanism in unreinforced dense sand layer Failure mechanism in unfastened reinforced dense sand layer

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**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

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**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]

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**Truss elements Numerical simulations Tochnnog finite element code**

elasto-perfectly plastic constitutive model Truss elements Non associated flow rule (y = 0)

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**The visco-elastic approach**

Dt 1 2 4 K =k() ? = () ?

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**PWRI experimental test results,2005**

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

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**Ispra Laboratory Elsa di Elsa di (Pedretti, 1998)**

Cross section Plan view

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A simplified approach A symmetric generalised stress-paths

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