Table 3. Strains, pore pressure changes,...

Table 3.

Strains, pore pressure changes, stiffness and damping ratio variations during cyclic loading, considering changes from the first cycle up to the N_f cycle, or final cycle in the unfailed tests

Test	q_mean/(2S_u)	q_cyc/(2S_u)	q_max/(2S_u)	Imposed cycles, N_max	N_f*	ε_a at N_f: %	ε_a/N_f: %	r_u: %†	Secant cyclic $E_{\sec}^{u, cyc}$ ⁠: MPa	Damping ratio, D: %‡
DCy-A1	0	0·30	0·30	10 024	Unfailed	0·078	7·78 × 10⁻⁶	0·10→34·5	903→1166	4·80→3·70
DCy-B1	0	0·45	0·45	717	486^(A)	−0·210	−4·32 × 10⁻⁴	1·91→85·3	951→14·0	6·51→21·2
DCy-C1	0·30	0·30	0·60	10 058	Unfailed	0·085	8·45 × 10⁻⁶	32·1→54·1	1067→1155	9·53→8·06
DCy-C2	0·15	0·45	0·60	676	645^(B)	0·829	1·29 × 10⁻³	20·2→95·7	918→9·3	12·8→26·4
DCy-C3	0	0·60	0·60	181	65^(A)	−0·023	−3·54 × 10⁻⁴	3·86→77·2	841→23·2	13·0→21·3
DCy-CX	−0·15	0·45	−0·60	361	357^{(A, B)}	−0·516	−1·45 × 10⁻³	10·1→80·3	1067→13·9	4·82→19·9
DCy-D1	0·79	0·17	0·96	9600	Unfailed	0·147	1·53 × 10⁻⁵	42·8→67·4	1334→1444	5·56→2·95
DCy-D2	0·57	0·30	0·87	10 614	5528^(B)	0·984	1·78 × 10⁻⁴	40·1→82·7	1160→269·7	6·90→20·1
DCy-D3	0·44	0·44	0·88	240	183^(B)	0·926	5·06 × 10⁻³	22·2→92·4	1045→35·6	10·9→25·9
DCy-D4	0·28	0·60	0·88	58	47^{(A, B)}	0·523	0·011	30·3→90·2	955→21·6	11·1→25·7
DCy-D5	0	0·75	0·75	170	≈18	−0·005	−2·78 × 10⁻⁴	6·45→76·9	508·0→46·9	17·9→23·9
DCy-A1-E	0	0·30	0·30	10 085	Unfailed	0·036	3·57 × 10⁻⁶	0·40→64·2	1428→1023	4·51→7·35
DCy-B1-E	0	0·45	0·45	149	142^(A)	−0·071	−5·0 × 10⁻⁴	1·81→89·0	1236→34·3	8·15→22·1
DCy-C3-E	0	0·60	0·60	57	50^(A)	−0·080	−1·6 × 10⁻³	2·70→82·5	1190→57·3	12·2→24·1
DCy-D5-E	0	0·75	0·75	18	16^{(A, B)}	−0·085	−5·31 × 10⁻³	6·56→67·3	815·0→80·9	17·0→23·3

Test	q_mean/(2S_u)	q_cyc/(2S_u)	q_max/(2S_u)	Imposed cycles, N_max	N_f*	ε_a at N_f: %	ε_a/N_f: %	r_u: %†	Secant cyclic $E_{\sec}^{u, cyc}$ : MPa	Damping ratio, D: %‡
DCy-A1	0	0·30	0·30	10 024	Unfailed	0·078	7·78 × 10⁻⁶	0·10→34·5	903→1166	4·80→3·70
DCy-B1	0	0·45	0·45	717	486^(A)	−0·210	−4·32 × 10⁻⁴	1·91→85·3	951→14·0	6·51→21·2
DCy-C1	0·30	0·30	0·60	10 058	Unfailed	0·085	8·45 × 10⁻⁶	32·1→54·1	1067→1155	9·53→8·06
DCy-C2	0·15	0·45	0·60	676	645^(B)	0·829	1·29 × 10⁻³	20·2→95·7	918→9·3	12·8→26·4
DCy-C3	0	0·60	0·60	181	65^(A)	−0·023	−3·54 × 10⁻⁴	3·86→77·2	841→23·2	13·0→21·3
DCy-CX	−0·15	0·45	−0·60	361	357^{(A, B)}	−0·516	−1·45 × 10⁻³	10·1→80·3	1067→13·9	4·82→19·9
DCy-D1	0·79	0·17	0·96	9600	Unfailed	0·147	1·53 × 10⁻⁵	42·8→67·4	1334→1444	5·56→2·95
DCy-D2	0·57	0·30	0·87	10 614	5528^(B)	0·984	1·78 × 10⁻⁴	40·1→82·7	1160→269·7	6·90→20·1
DCy-D3	0·44	0·44	0·88	240	183^(B)	0·926	5·06 × 10⁻³	22·2→92·4	1045→35·6	10·9→25·9
DCy-D4	0·28	0·60	0·88	58	47^{(A, B)}	0·523	0·011	30·3→90·2	955→21·6	11·1→25·7
DCy-D5	0	0·75	0·75	170	≈18	−0·005	−2·78 × 10⁻⁴	6·45→76·9	508·0→46·9	17·9→23·9
DCy-A1-E	0	0·30	0·30	10 085	Unfailed	0·036	3·57 × 10⁻⁶	0·40→64·2	1428→1023	4·51→7·35
DCy-B1-E	0	0·45	0·45	149	142^(A)	−0·071	−5·0 × 10⁻⁴	1·81→89·0	1236→34·3	8·15→22·1
DCy-C3-E	0	0·60	0·60	57	50^(A)	−0·080	−1·6 × 10⁻³	2·70→82·5	1190→57·3	12·2→24·1
DCy-D5-E	0	0·75	0·75	18	16^{(A, B)}	−0·085	−5·31 × 10⁻³	6·56→67·3	815·0→80·9	17·0→23·3

Superscripts (A) and (B) denote the applied cyclic failure criteria. Cycling control of test DCy-D5 deteriorated as specimen softened significantly after 13 cycles.

†

r_u, pore water pressure ratio (%), defined as: r_u = (p₀′ − p′)/p₀′ = Δu/p₀′.

‡

Damping ratio calculated as: D = A_loop/(4πA_elastic); A_loop – area enclosed by a stress–strain (q–ε_a) loop for a complete sinusoidal stress cycle; A_elastic – unloading half-cycle elastic triangle area with height as q_cyc ( = (q_peak − q_trough)/2) and width as cyclic strain ( = (ε_peak − ε_trough)/2).

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