PSI - Issue 44

Simona Coccia et al. / Procedia Structural Integrity 44 (2023) 1356–1363 Simona Coccia et al. / Structural Integrity Procedia 00 (2022) 000–000

1362

7

88 ( < ) = $6;!!

(34)

The ratio between the rotation at the foot of the wall at the ends of the second and first pulse is = . %% (A ' . ) % (A ' ) = . #)++ . #)++ B (( + ' '$C(*"+ ℎ @A ' '$) = $ B (( + ' '$C(*"+ ℎ @A ' '$) > 1 We therefore recognize that, in spite that the second pulse acts in the opposite direction to the first, the rotation of the basis of the wall continues to grow in the same direction induced by the first. An accumulation of rotation takes place (Fig. 4(b)). (35)

(a)

(b)

Fig. 4. (a) Simple seismic input; (b) Accumulation of rotation during the rocking motion

The collapse acceleration A 0 , related to the acceleration of the static collapse A L , i.e. the ratio: = : , : + is obtained as a solution of Eq.s (33) and (34). More specifically, the pulse acceleration drags the wall at the critical configuration at the end of the second pulse of the three pulse sequence. The quantity q is therefore the so called performance factor, or strength reduction factor, obtained with reference to the actual dynamical nature of the wall collapse and is equal to: = # *"+ ℎ ! @A ' '$ # *"+ ℎ @A ' (*"+ ℎ @A ' '$) (37) The critical rotation q COLL at the foot of the wall is attained at the end of the second pulse. The collapse occurs with the arrival of the third pulse. Fig.5 shows the trend of the limit curve defined by (37). As already done for the unreinforced wall (Coccia et al, 2022), these results must be extended to a larger number of pulses. 3. Safety of the wall in the site The reinforced wall is identified by its geometry and by the values of the ratio Q/G between the weights applied at the head and distributed along its height. Let further A L /g be the static limit acceleration. The seismic condition of the site indicate that T t and PGA respectively are the expected values of the period of the quake and of the maximum horizontal acceleration . We assume t 0 equal to the maximum expected pulse duration (= T t /2 ) and let us evaluate, by using the eq. (35) the value q corresponding to the chosen pulse duration pT t /2 (Fig. 5). (36)