DYNAMIC BEHAVIOUR OF ROCKFALL SHELTERS

I n t e r d i s c i p l i n a r y R o c k f a l l W o r k s h o p 2 0 1 1 – I n n s b r u c k -‐ I g l s DYNAMIC BEHAVIOUR OF ROCKFALL SHELTERS Francesco Calvetti, Claudio di Prisco, Vittorio MoriggiFrancesco Tondini

Rockfall shelter typology: artificial tunnels covered by soil layer Calvetti & di Prisco: An uncoupled approach for the design of rockfall protection shelters WSL Interdisciplinary Workshop on Rockfall Protection 2008 June 23-25, Morschach, CH F1 F2 F3 F1 Impact force  F2 Actions on the shelter  F3 Structural actionsLocal interaction: boulder-soil surface Structural response Stress propagation Calvetti, di Prisco, Moriggi & Tondini

Uncoupled design approach, STEP 1: Impact force CHARTS FORn and F0 as a function of block size (dense sand-gravel soil layer) Calvetti, di Prisco, Moriggi & Tondini

Impact Force: design charts T1,2,3&4 as a function of falling height and block mass (dense sand-gravel soil layer) Calvetti, di Prisco, Moriggi & Tondini

Uncoupled design approach, STEP 2: Actions on shelter Impact wave propagation - dynamic stress diffusion Elastic solution B S ! MAX ( r ) = ! MAX ! f d ! f g r B ! MAXStress [kPa] Time [s] Calvetti, di Prisco, Moriggi & Tondini

Reference structure: cantilever shelter covered by soil cushion Calvetti, di Prisco, Moriggi & Tondini

FEM model of 1 moduleTendons “GAP” elements (unilateral contact) Hinge Calvetti, di Prisco, Moriggi & Tondini

FEM model of assembled structure •  6 Modules (10 metres) • 12 Modules (20 metres) • 18 Modules (30 metres) • 24 Modules (40 metres) “GAP” Elements Calvetti, di Prisco, Moriggi & Tondini

Reference impacts: Block mass: 7.8 tons Soil thickness 2-3 m (dense sand-gravel); Impact Energy : E= 1000-2000-5000 kJ (H = 13-26-65 m) 10000 9000 8000 1000 kJImpact force (kN) 7000 6000 2000 kJ 5000 kJ σMAX [kPa] 5000 4000 3000 2000 1000 0 0 0,02 0,04 0,06 0,08 0,1 time (s) r Calvetti, di Prisco, Moriggi & Tondini

Structural response as a function number of modules6 modules 24 modules Comparison 18 – 24 modules E 1000 kJ 2000 kJ 5000 kJ UY -1,8 % -1,9 % -0,06 % UX -6,1 % -7,7 % -10,5 % Calvetti, di Prisco, Moriggi & Tondini

Structural response as a function number of modules Tendon action Comparison 1000 kJ 2000 kJ 5000 kJ 6-‐24 modules -‐38,43 % -‐45,58 % -‐54,71 % 18-‐24 modules -‐6,42 % -‐8,44 % -‐11,48 % Moment @ C 2,00E+07 1,50E+07 1,00E+07 5,00E+06 T[s] 0,00E+00 M [N*m] 0 0,05 0,1 0,15 0,2 0,25 0,3 -‐5,00E+06 -‐1,00E+07 -‐1,50E+07 -‐2,00E+07 -‐2,50E+07 Calvetti, di Prisco, Moriggi & Tondini

Structural response as a function of distance from impact point Impact point d = 0 [m] Ux [m] d = 8,3 [m] d = 18,26 [m]Uy [m] M [N*m] Calvetti, di Prisco, Moriggi & Tondini

Structural response as a function of impulse shape 2,5 2 Impulse Factor [-‐] Molto impulsivo R piccoli 2 1,5 Carico Normale 1 1 0.5 Poco impulsivo R piccoli 0,5 0 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 T [s] 2 1 0.5 Ux [m]Uy [m] 2 1 0.5 Calvetti, di Prisco, Moriggi & Tondini

Structural response as a function of distance from impact point Impulse factor 2.0 Vertical displacements @ AUy [m] Impulse factor 0.5 T [s] Uy [m] T [s] Calvetti, di Prisco, Moriggi & Tondini

Structural response: dynamic amplification factors Impulse factor 1.0 1,6 Max. displacement under impulse load 6 ElemenS 1,55 12 ElemenS 1,5 18 ElemenS Rd [-‐] Static displacement under peak of impulsive force 1,45 24 ElemenS 1,4 1,35 1,3 0 1000 2000 3000 4000 5000 6000 Impact Energy [kJ] Impulse factor 0.5 Impulse factor 1.0 Impulse factor 2.0 Calvetti, di Prisco, Moriggi & Tondini

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DYNAMIC BEHAVIOUR OF ROCKFALL SHELTERS

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