Il dissesto idrogeologico:dalla conoscenza del territorio alla sua protezione

Milano, 20 Maggio 2015

Progettazione di opere di difesa passiveFrancesco Calvetti

Francesco Calvetti

Rockfall shelter typology: artificial tunnels covered by soil layers

1 Near field impact (F1, impact force)2 Stress propagation (F2, applied actions)3 Structural response (F3, internal actions)

NB: 4 supports

Francesco Calvetti

M = 100, 500, 1000 kg,

H = 1-10 m

Soil layer: 0.25-1 m thick, dense

Small scale experiments 3

Francesco Calvetti

F2 > F1 dynamic (wave propagation) amplification

F2 F2

F1 F1

Experiments: stress propagation 4

Francesco Calvetti

F2F2

F3 F3

F3 > F2 dynamic (structural) amplification

Experiments: Structural response 5

Francesco Calvetti

M = 850 kg

H = 5 -50 m

Soil layer: 2 m thick, dense

Real scale experiments 6

Francesco Calvetti

0 0.04 0.08 0.120.02 0.06 0.1

t [s]

0

400

800

1200

1600

200

600

1000

1400

1800

F [k

N]

0 0.04 0.08 0.120.02 0.06 0.1

t [s]

0

200

400

600

100

300

500

∆σ

v [kP

a]

Soil-slab stress

0 0.04 0.08 0.120.02 0.06 0.1

t [s]

4

0

-4

6

2

-2

-6

s [m

m]

deflectionImpact Force

ResultsTypical impact (H = 36 m)

0 0.2 0.4 0.60.1 0.3 0.5

t [s]

0

400

800

1200

1600

200

600

1000

1400

1800

F [k

N]

0 0.2 0.4 0.60.1 0.3 0.5

t [s]

4

0

-4

6

2

-2

-6

s [m

m]

deflection

0 0.2 0.4 0.60.1 0.3 0.5

t [s]

0

200

400

600

100

300

500

∆σ

v [kP

a]

Impact force Soil-slab stress

T1 T3 T3T2

2T2

rigorously

Impact force ⇒ Actions on the slab ⇔ Structural response

Conservative simplification

Impact force ⇒ Actions on the slab ⇒ Structural response

7

Francesco Calvetti

IMPACT FORCE STRUCTURAL RESPONSE

Structural response in dynamic conditions

First impactSecond impact

8

Francesco CalvettiClaudio di Prisco

9

BIMPAM MODEL (boulder kinematics & impact force)derived from MACROELEMENT for shallow foundations

boulder - soil interaction

deformability of the layer and 3D damping

ξ=V/VMAX

V

B

Modelling impact force 9

Francesco CalvettiFrancesco Calvetti, Claudio di Prisco

10

block deceleration - block velocity – block penetration (vs time)

model vs. experiments

model:dense and loose sand layers

Modelling impact force 10

Francesco Calvetti

Modelling impact force

Falling height H = 50 mMass = 100 – 10000 kg

Falling height H = 5 – 50 mMass = 1000 kg

11

Francesco Calvetti

Uncoupled design approach, STEP 1: Impact force

CHARTS FOR n and F0 as a function of block size

(dense sand-gravel soil layer)

Francesco Calvetti

T1,2,3&4 as a function of falling height and block mass (dense sand-gravel soil layer)

Uncoupled design approach, STEP 1: Impact force

Francesco Calvetti

r

Francesco Calvetti, Claudio di Prisco

14Modelling stress propagation

NUMERICL ANALYSIS (FLAC, GEOELSE)finite differences - spectral element codes

wave propagation

stress increment on structure

Δσ(t,r)

F(t) σ(t) = F(t)/A(t)

14

Francesco CalvettiClaudio di Prisco

15Modelling stress propagation

stress increment at r = 0, as a function of timeexperimental and numerical results

Elasticsoil layer

elasto-plasticsoil layer

elasto-viscoplasticsoil layer

15

Francesco CalvettiClaudio di Prisco

16Modelling stress propagation, geometric effect

maximum stress increment, as a function of rexperimental and numerical results

16

Francesco Calvetti

Stre

ss [k

Pa]

Time [s]

Uncoupled design approach, STEP 2: Actions on shelter

Impact wave propagation - dynamic stress diffusion

r

Elastic solution

Francesco Calvetti

18