Displacement-based seismic assessment of masonry buildings for global and local failure mechanisms

Figures & data

Figure 1. Global failure mechanisms of masonry structures.

Notes: From left to right: Storey mechanism in case of strong spandrels and weak piers and spandrel mechanism in case of strong piers and weak spandrels (Penna, 2005).

Figure 2. Observed out-of-plane failure modes for masonry structures (D’Ayala & Speranza, 2003).

Figure 3. Damage mechanisms of rubble stone masonry.

Notes: From left to right and top to bottom: Coupled in-plane/out-of-plane damage of structures during 1995 Aegion earthquake in Greece (Penna, 2005), in-plane shear damage of field stone masonry during 1999 Athens earthquake in Greece (Tassios & Syrmakezis, 2002), and out-of-plane delamination failure mode for masonry structures (Javed, 2008).

Figure 4. Graphical representation of DBELA.

Notes: From left to right and top to bottom: Idealized displacement response spectrum and the limit state overdamping, analytical seismic fragility functions and damage scenario, where DS represents different damage state of structures on regional scale.

Figure 5. Nonlinear static SDOF idealization and capacity curve, mechanical model, for global mechanism.

Figure 6. Nonlinear static SDOF idealization, mechanical model, of masonry wall for out-of-plane failure modes, after Doherty et al. (2002).

Figure 7. Flow chart for the derivation of vector-based displacement-based fragility functions, global mechanism.

Figure 8. Flow chart for the derivation of vector-based displacement-based fragility functions, local mechanism.

Figure 9. Definition of seismic demand on the out-of-plane walls.

Notes: From top to bottom and left to right: load path for out-of-plane walls, absolute spectrum to define floor absolute displacement demand and out-of-plane amplification spectrum.

Figure 10. Equivalent frame method.

Notes: From left to right: equivalent frame idealization of masonry structural wall and Nonlinear force-displacement response of frame element, considering either multilinear or bilinear behavior.

Figure 11. Lateral force-displacement response of case study masonry walls.

Notes: From left to right: experimentally obtained response through quasi-static cyclic test on full scale wall (Javed, 2008) and simplified used in the present study.

Figure 12. Ductility capacity model for masonry walls.

Figure 13. Validation of the proposed modelling hypothesis for masonry structure, tested at the University of Pavia (Magenes et al., 1995).

Notes: From left to right: equivalent capacity curve and ultimate damage state.

Figure 14. The effect of different wall density and floor area on the yield strength, exemplificative chart.

Table 1. Structural properties considered to generate proto type structural models for masonry structures

Parameter	Mean value	C.O.V. (%)	Lower bound	Upper bound	Probabilistic distribution type
Brick masonry
fu,mc (Mpa)	3.44	30.86	2.00	5.58	Truncated Lognormal
ft (kPa)	104	30.86	60.16	167.13	Truncated Lognormal
Eeff (Mpa)	859.16	30.86	501.36	1394.26	Truncated Lognormal
Geff (Mpa)	343.67	30.86	200.54	557.70	Truncated Lognormal
γm (kN/m^3)	18	10	15	21	Truncated Lognormal
Wd (%)	5.34	47.68	2.38	10.91	Truncated Lognormal
Af (m^2)	73.11	56.34	25.01	175.06	Truncated Lognormal
Block masonry
fu,mc (Mpa)	2.01	29.33	1.21	3.32	Truncated Lognormal
ft (kPa)	60.35	29.33	36.45	99.57	Truncated Lognormal
Eeff (Mpa)	502.95	29.33	303.72	829.72	Truncated Lognormal
Geff (Mpa)	201.18	29.33	121.49	331.89	Truncated Lognormal
γm (kN/m^3)	13	10	12	14	Truncated Lognormal
Wd (%)	4.90	49.29	2.41	10.34	Truncated Lognormal
Af (m^2)	70.58	54.34	26.97	156.28	Truncated Lognormal
Stone masonry
fu,mc (Mpa)	2.63	4.93	2.42	2.861	Truncated Lognormal
ft (kPa)	79.00	4.93	72.67	85.84	Truncated Lognormal
Eeff (Mpa)	658.29	4.93	605.62	715.36	Truncated Lognormal
Geff (Mpa)	263.32	4.93	242.25	286.14	Truncated Lognormal
γm (kN/m^3)	19	10	16	22	Truncated Lognormal
Wd (%)	12.05	10.88	10.11	14.86	Truncated Lognormal
Af (m^2)	54.18	17.95	40.34	72.62	Truncated Lognormal

Note: Characteristic values are considered which has 84 percent chances of exceedance.

Figure 15. Pushover curves for case study two-storey low-rise structures and the derivation of capacity curves parameters.

Table 2. Capacity curve parameters (median, lower and upper bound) for case study masonry structures

Masonry typology		Distribution parameter	Meq (Ton)	H (m)	Ty (sec)	Fyeq (m/sec^2)	∆y (mm)	∆u (mm)	μ
Wooden floors	Brick	Mean	115	5.40	0.14	4.33	2.09	9.91	4.97
		β	0.27	0.04	0.12	0.12	0.13	0.11	0.11
		5th Percentile	73	5.10	0.12	3.53	2.59	11.89	6.00
		95th Percentile	179	5.73	0.18	5.32	1.68	8.26	4.12
	Block	Mean	109	5.51	0.22	3.00	3.68	13.22	4.51
		β	0.27	0.03	0.17	0.12	0.23	0.10	0.19
		5th Percentile	69	5.24	0.17	2.46	5.41	15.45	6.14
		95th Percentile	170	5.81	0.30	3.66	2.51	11.30	3.31
	Stone	Mean	184	5.39	0.18	3.71	3.08	18.68	6.07
		β	0.08	0.03	0.05	0.02	0.08	0.08	0.02
		5th Percentile	161	5.12	0.17	3.56	3.51	21.35	6.29
		95th Percentile	210	5.67	0.20	3.86	2.70	16.35	5.87
RC slab floors	Brick	Mean	171	5.40	0.19	3.82	3.29	10.80	3.77
		β	0.24	0.04	0.15	0.12	0.19	0.09	0.14
		5th Percentile	115	5.10	0.15	3.12	4.51	12.60	4.78
		95th Percentile	253	5.73	0.24	4.68	2.40	9.25	2.97
	Block	Mean	165	5.51	0.28	2.56	5.06	13.87	3.43
		β	0.26	0.03	0.18	0.12	0.24	0.11	0.18
		5th Percentile	108	5.24	0.21	2.09	7.52	16.49	4.61
		95th Percentile	253	5.81	0.38	3.13	3.41	11.67	2.55
	Stone	Mean	221	5.39	0.20	3.46	3.52	19.46	5.53
		β	0.25	0.03	0.05	0.02	0.08	0.08	0.02
		5th Percentile	195	5.12	0.19	3.34	3.99	22.11	5.74
		95th Percentile	251	5.67	0.22	3.58	3.11	17.13	5.33

Figure 16. Mean spectrum of the selected accelerograms and comparison with the EC8 Type I-C soil spectrum.

Table 3. Drift limits computed for case study masonry structures, in percent

Typology	Distribution parameter	RC slab floors				Timber floors
		DS1	DS2	DS3	DS4	DS1	DS2	DS3	DS4
Brick	Mean	0.06	0.09	0.29	0.44	0.04	0.06	0.26	0.39
	β	0.12	0.13	0.08	0.08	0.11	0.10	0.13	0.13
	5th Percentile	0.05	0.07	0.26	0.39	0.03	0.05	0.21	0.32
	95th Percentile	0.07	0.11	0.33	0.49	0.05	0.07	0.33	0.49
Block	Mean	0.09	0.13	0.37	0.55	0.06	0.10	0.35	0.52
	β	0.17	0.18	0.08	0.08	0.14	0.15	0.07	0.07
	5th Percentile	0.06	0.10	0.32	0.48	0.05	0.08	0.31	0.46
	95th Percentile	0.11	0.18	0.42	0.62	0.08	0.13	0.39	0.59
Stone	Mean	0.07	0.10	0.49	0.74	0.06	0.09	0.47	0.71
	β	0.05	0.04	0.04	0.04	0.05	0.05	0.04	0.04
	5th Percentile	0.06	0.09	0.46	0.69	0.06	0.08	0.44	0.67
	95th Percentile	0.07	0.11	0.52	0.78	0.06	0.10	0.50	0.76

Figure 17. Collapse multiplier for typical out-of-plane failure of façade walls obtained experimentally (Restrepo-Velez & Magenes, 2009).

Table 4. Parameters used in the random generation of structures for fragility functions derivation for South-Asia countries

Parameter	Mean value	C.O.V. (%)	Lower bound	Upper bound	Probability distribution type
HT (m)	3.00	30.00	2.50	3.50	Truncated Lognormal
hS (m)	2.50	30.00	2.00	3.00	Truncated Lognormal
k1	0.727	01.15	0.69	0.75	Truncated Lognormal
k2	0.807	14.22	0.44	1.23	Truncated Lognormal
c	0.400	20.00	0.28	0.50	Truncated Lognormal
t (mm)	230	20.00	300	500	Truncated Lognormal
Ψ	0.8	10.00	0.50	1.00	Truncated Lognormal
ϕ	0.75	16.00	0.60	0.90	Truncated Lognormal
λ	0.23	35.00	0.13	0.42	Truncated Lognormal

Figure 18. Vector-based fragility functions for case study masonry structures.

Notes: From left to right: masonry structures with rc floors (in-plane mechanism), wooden floors (in-plane mechanism) and wooden floors (out-of-plane mechanism).

Figure 19. Scalar-based, SA (0.30 s), fragility functions for case study masonry structures.

Notes: From left to right: masonry structures with rc floors (in-plane mechanism), wooden floors (in-plane mechanism) and wooden floors (out-of-plane mechanism).

Figure 20. Scalar-based, PGA, fragility functions for case study masonry structures.

Notes: From left to right: masonry structures with rc floors (in-plane mechanism), wooden floors (in-plane mechanism) and wooden floors (out-of-plane mechanism).

Figure 21. Percentage of structure typology to total stock subjected to 2005 Kashmir earthquake.

Figure 22. Percentage of structures damaged during 2005 Kashmir earthquake.

Notes: From left to right and top to bottom: stone masonry structures, block masonry structures, reinforced concrete structures and brick masonry structures.

Table 5. Input parameters for vector-based (inelastic spectral displacement) fragility functions, lognormal distribution is conservatively considered

Typology		Slight		Moderate		Extensive		Complete
		Mean	SD	Mean	SD	Mean	SD	Mean	SD
Brick	UFB5	2.32	0.30	3.47	0.31	8.14	0.48	11.59	0.52
	UFB4	1.55	0.31	2.34	0.31	7.02	0.53	10.09	0.55
Block	UCB4-O							89.56	0.54
	UCB5	2.39	0.31	3.90	0.32	9.66	0.49	13.64	0.53
	UCB4	2.39	0.31	3.90	0.32	9.66	0.49	13.64	0.53
	UCB4-O							90.14	0.56
Stone	DS4	2.60	0.30	3.96	0.29	13.00	0.52	18.76	0.56
	DS3	2.29	0.30	3.44	0.30	12.45	0.54	18.00	0.56
	DS3-O							85.96	0.53

Table 6. Input parameters for scalar-based (elastic spectral acceleration), SA (0.30 s), fragility functions, lognormal distribution is conservatively considered

Typology		Slight		Moderate		Extensive		Complete
		Mean	SD	Mean	SD	Mean	SD	Mean	SD
Brick	UFB5	0.16	0.32	0.25	0.32	0.51	0.32	0.63	0.32
	UFB4	0.15	0.32	0.22	0.31	0.52	0.32	0.65	0.32
	UFB4-O							0.21	0.49
Block	UCB5	0.16	0.33	0.24	0.33	0.46	0.32	0.57	0.32
	UCB4	0.14	0.32	0.24	0.32	0.51	0.32	0.63	0.32
	UCB4-O							0.21	0.50
Stone	DS4	0.17	0.30	0.27	0.30	0.67	0.31	0.83	0.31
	DS3	0.17	0.30	0.25	0.30	0.68	0.31	0.85	0.31
	DS3-O							0.20	0.45

Table 7. Input parameters for scalar-based (peak ground acceleration) fragility functions, lognormal distribution is conservatively considered

Typology		Slight		Moderate		Extensive		Complete
		Mean	SD	Mean	SD	Mean	SD	Mean	SD
Brick	UFB5	0.08	0.58	0.12	0.58	0.15	0.60	0.16	0.55
	UFB4	0.09	0.58	0.14	0.58	0.18	0.60	0.19	0.60
	UFB4-O							0.08	0.48
Block	UCB5	0.07	0.61	0.10	0.61	0.14	0.47	0.17	0.38
	UCB4	0.08	0.59	0.13	0.59	0.17	0.55	0.19	0.44
	UCB4-O							0.08	0.49
Stone	DS4	0.11	0.59	0.16	0.59	0.22	0.53	0.25	0.42
	DS3	0.11	0.57	0.17	0.57	0.23	0.54	0.26	0.43
	DS3-O							0.08	0.45

Figure 23. Test and validation of the UPAV methodology against the 2005 Kashmir earthquake.

Notes: From left to right: the likelihood of randomly generated ground motions in the affected areas and the percentage of structures heavily damaged/collapsed (mean estimate).

Penna, A. (2005). Seismic vulnerability assessment of masonry structures. Earthquake Rehabilitation Conference, Islamabad, Pakistan.

 Google Scholar

D’Ayala, D. F., & Speranza, E. (2003). Definition of collapse mechanisms and seismic vulnerability of historic masonry buildings. Earthquake Spectra, 19, 479–509.10.1193/1.1599896

 Web of Science ®Google Scholar

Tassios, T. P., & Syrmakezis, K. (2002). Load-bearing stone masonry buildings. In World Housing Encyclopedia (Report No. 16). Oakland, CA: Earthquake Engineering Research Institute (EERI).

 Google Scholar

Javed, M. (2008). Seismic risk assessment of unreinforced brick masonry building system of northern Pakistan ( PhD Thesis). Civil Engineering Department, NWFP University of Engineering and Technology, Peshawar.

 Google Scholar

Doherty, K., Griffith, M. C., Lam, N., & Wilson, J. (2002). Displacement-based seismic analysis for out-of-plane bending of unreinforced masonry walls. Earthquake Engineering and Structural Dynamics, 31, 833–850.10.1002/(ISSN)1096-9845

 Web of Science ®Google Scholar

Magenes, G., Calvi, G. M., & Kingsley, G. R. (1995). Seismic testing of a full-scale two-storey masonry building: Test procedure and measured experimental response (Technical Report). Pavia: Structural Mechanics Department, University of Pavia.

 Google Scholar

Restrepo-Velez, L. F., & Magenes, G. (2009). Static tests on dry stone masonry and evaluation of static collapse multiplier (Technical Report). Pavia: IUSS Press.

 Google Scholar