Frequency-Domain Assessment of Integration Schemes for Earthquake Engineering Problems

Table 3

Permanent slope displacements computed by Newmark sliding method for the strong ground motion Gilroy number 1 (Bedrock) and Gilroy number 2 (Soil), applying different integration formulae and several values of . The corresponding deviations (in percentage) with respect to the trapezoidal rule are also listed for comparison purposes.

	(cm)	Deviation (%)	(cm)	Deviation (%)	(cm)	Deviation (%)
Gilroy number 1 (Bedrock)
Trapezoidal	11.5954	—	3.7081	—	0.663	—
Simpson	11.597	0.0143	3.6869		0.6861	3.4829
Simpson 3-8	11.6022	0.0585	3.7256	0.4719	0.622
Newton-Cotes	11.3222		3.6338		0.466
Rectangle	11.6881	0.7998	3.7432	0.9445	0.6769	2.1014
Tick	11.5924		3.6832		0.6837	3.1203
Schuessler-Ibler	11.7432	1.2745	3.7292	0.5693	0.5402
Gilroy number 2 (Soil)
Trapezoidal	17.0186	—	2.8038	—	0.3117	—
Simpson	17.0514	0.1932	2.8074	0.126	0.312	0.0936
Simpson 3-8	17.0043		2.7929		0.301
Newton-Cotes	17.3194	1.768	2.7726		0.2968
Rectangle	17.0362	0.1038	2.812	0.2921	0.3142	0.8138
Tick	17.0496	0.1826	2.8063	0.089	0.3119	0.0596
Schuessler-Ibler	17.4455	2.5086	2.8077	0.1364	0.3119	0.0585