Abstract
Regional seismic damage prediction is an important approach to discover the weakness of a city so as to effectively mitigate seismic losses. A major proportion of regional seismic losses is caused by masonry buildings. As a result, an accurate prediction of the regional seismic damage to masonry buildings has significant engineering and scientific values. Various parameters of the computational models for regional seismic damage predictions usually involve considerable uncertainty, especially for masonry buildings. Therefore, a parametric sensitivity analysis for the regional seismic damage prediction of reinforced masonry buildings is performed in some detail in this study. Damage to this kind of buildings is predicted through nonlinear time-history analysis using the multiple-degree-of-freedom shear model, which can better represent the features of different buildings and ground motions. In the sensitivity analysis, two widely used methods, the first-order second-moment (FOSM) method and the Monte Carlo method, are adopted and their prediction results are compared. The outcomes of this study indicate that the uncertainty of parameters has a small influence on the analysis results when the total number of regional buildings is large. However the uncertainty cannot be neglected for individual building analysis. In addition, the FOSM method, which is more time-saving, can achieve a similar level of prediction as the Monte Carlo simulation.
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Acknowledgements
The authors would like to acknowledge the financial supports of the National Natural Science Foundation of China (Nos. 51578320, 51378299) and the National Key Technology R&D Program (No. 2015BAK14B02). The authors would like also to acknowledge Professor Quanwang Li and Mr. Xiang Zeng for their contributions to this work.
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Appendices
Appendix 1: Typical parameters of reinforced masonry test specimens considered in this study
Reference | Number of specimens | Typical parameters of specimens | |||
|---|---|---|---|---|---|
Length (mm) | Height (mm) | Thickness (mm) | Size of tie columns (mm) | ||
Liu et al. (1981) | 9 | 4500 | 2800 | 240 | 240 |
Yan (1985) | 15 | 2140 | 1080 | 240 | 120 |
Shi and Yi (2000) | 7 | 2320 | 1220 | 240 | 120 |
Yang et al. (2000) | 3 | 1400 | 1120 | 190 | 200 |
Wang et al. (2003) | 9 | 1920, 2220, 4520 | 1750 | 240 | 120 |
Yu (2003) | 4 | 3000 | 1500 | 120 | 120 |
Wang et al. (2004) | 4 | 2550 | 1800 | 240 | 150 |
Ye et al. (2004) | 1 | 2800 | 2000 | 240 | 200 |
Zhou (2004) | 6 | 4410 | 2700 | 190 | 210 |
Zhang (2005) | 4 | 2800 | 2000 | 270 | 200 |
Huang (2006) | 2 | 2380 | 1480 | 190 | 120 |
Sun et al. (2006) | 6 | 4410 | 2700 | 190 | 210 |
Zhou et al. (2006) | 2 | 4410 | 2700 | 190 | 210 |
Zhang (2007a) | 3 | 2110, 2200 | 2180, 1500 | 240 | 120, 200 |
Zhang (2007b) | 2 | 2720 | 1520 | 120 | 120 |
Gong (2008) | 4 | 1830, 2730 | 2160, 1740 | 240 | 240 |
Hao et al. 2008 | 4 | 1830, 2730 | 2160, 1740 | 240 | 240 |
Yang (2008) | 1 | 2800 | 1400 | 240 | 120 |
Yang et al. (2008) | 3 | 1480, 1730, 2230 | 1250 | 120 | 120 |
Fang (2009) | 4 | 2800 | 1360 | 120 | 120 |
Han (2009) | 4 | 2800 | 1650 | 240 | 120 |
Gu et al. (2010) | 8 | 666, 2000 | 413, 1240 | 80, 240 | 40, 120 |
Weng (2010) | 2 | 4770 | 3230 | 250 | 250 |
Zhang (2010) | 1 | 2050 | 1500 | 240 | 150 |
Zheng (2010) | 7 | 3000 | 1500 | 240 | 240 |
Liu et al. (2011) | 4 | 2720 | 1580 | 120 | 120 |
Wu et al. (2012) | 4 | 3300 | 1650 | 240 | 78, 120 |
Wu (2012) | 3 | 1500, 2000 | 1750 | 240 | 120 |
Xiao et al. (2012) | 3 | 3200 | 2200 | 220 | 200 |
Guo et al. (2014) | 3 | 2650 | 1900 | 240 | 200 |
Wang et al. (2014) | 1 | 2000 | 1860 | 240 | 120 |
Zhang (2014) | 2 | 2000 | 1860 | 240 | 120 |
Appendix 2: Parameters obtained for reinforced masonry test specimens considered in this study
References | ID | Ω y | Ω p | δ p | δ s |
|---|---|---|---|---|---|
Liu et al. (1981) | WZI-1 | 2.8275 | 1.2967 | – | – |
WZI-2 | 3.0066 | 1.1097 | – | – | |
WZI-3 | 2.8747 | 1.1672 | – | – | |
WZII-1 | 2.9987 | 1.0851 | – | – | |
WZII-2 | 3.0944 | 1.1289 | – | – | |
WZII-3 | 3.0465 | 1.0576 | – | – | |
WZIII-1 | 2.4423 | 1.1143 | – | – | |
WZIII-2 | 2.3585 | 1.1479 | – | – | |
WZIII-3 | 2.3236 | 1.1021 | – | – | |
Yan (1985) | A-1 | – | – | 0.0035 | – |
A-2 | – | – | 0.0015 | – | |
A-3 | – | – | 0.0026 | – | |
B-1 | – | – | 0.0023 | – | |
B-2 | – | – | 0.0019 | – | |
B-3 | – | – | 0.0020 | – | |
B-4 | – | – | 0.0020 | – | |
C-1 | – | – | 0.0019 | – | |
C-2 | – | – | 0.0025 | – | |
C-3 | – | – | 0.0025 | – | |
C-4 | – | – | 0.0019 | – | |
D-1 | – | – | 0.0020 | – | |
D-2 | – | – | 0.0019 | – | |
D-3 | – | – | 0.0021 | – | |
D-4 | – | – | 0.0025 | – | |
Shi and Yi (2000) | W7 | 3.4207 | 1.1628* | 0.0065 | 0.0152 |
W8 | 3.0708 | 0.0055 | 0.0170 | ||
W9 | 3.5095 | 0.0038 | 0.0143 | ||
W10 | 3.3294 | 0.0093 | 0.0196 | ||
W11 | 3.0076 | 0.0096 | 0.0188 | ||
W12 | 2.8930 | 0.0046 | 0.0161 | ||
W13 | 4.0790 | 0.0054 | 0.0179 | ||
Yang et al. (2000) | Z2-1 | 2.2011 | 2.0755 | 0.0050 | 0.0062 |
Z2-2 | 2.1596 | 2.1154 | 0.0037 | 0.0071 | |
Z3-1 | 2.3257 | 2.0179 | 0.0044 | 0.0070 | |
Wang et al. (2003) | W1-t | 2.0288 | 1.8130 | 0.0034 | – |
W1-m | 1.9898 | 1.6273 | 0.0019 | – | |
W1-b | 2.0883 | 1.5086 | 0.0033 | – | |
W2-t | 2.1669 | 1.7027 | 0.0020 | – | |
W2-m | 2.4135 | 1.7273 | 0.0034 | – | |
W2-b | 2.1892 | 1.4599 | 0.0025 | – | |
W3-t | 2.3573 | 1.3944 | 0.0042 | – | |
W3-m | 1.9380 | 1.7772 | 0.0021 | – | |
W3-b | 1.9544 | 1.5771 | 0.0012 | – | |
Yu (2003) | W-I | 3.7781 | 1.4207 | 0.0088 | – |
W-II | 3.9181 | 1.3707 | 0.0098 | – | |
WH-I | 4.4380 | 1.3333 | 0.0056 | – | |
WH-II | 4.1940 | 1.4306 | 0.0073 | – | |
Wang et al. (2004) | MK-1 | 2.8656 | 1.0807 | 0.0033 | 0.0089 |
MK-2 | 2.8907 | 1.1304 | 0.0027 | 0.0061 | |
MK-3 | 2.6974 | 1.2000 | 0.0047 | 0.0078 | |
MK-4 | 1.9920 | 1.5833 | 0.0052 | 0.0075 | |
Ye et al. (2004) | SW2 | 3.0766 | 1.1968 | 0.0017 | 0.0050 |
Zhou (2004) | A-1 | 1.8439 | 2.7953 | 0.0015 | 0.0034 |
A-2 | 2.1267 | 2.2667 | 0.0015 | 0.0025 | |
A-3 | 1.4171 | 3.7337 | 0.0016 | 0.0021 | |
A-4 | 2.3503 | 1.8199 | 0.0008 | 0.0021 | |
A-5 | 2.3538 | 1.9746 | 0.0007 | 0.0032 | |
A-6 | 2.3538 | 1.9135 | 0.0009 | 0.0023 | |
Zhang (2005) | W-1 | 1.9529 | 1.5840 | 0.0036 | 0.0064 |
W-2 | 2.1012 | 1.5375 | 0.0018 | 0.0041 | |
W-3 | 2.5296 | 1.8042 | 0.0016 | 0.0050 | |
W-4 | 2.5830 | 1.7826 | 0.0014 | 0.0056 | |
Huang (2006) | CMC-1 | 4.2835 | 1.4194 | – | – |
CMC-2 | 4.6267 | 1.2475 | – | – | |
Sun et al. (2006) | E-1 | 1.8225 | 2.4579 | 0.0008 | 1.822 |
E-2 | 1.8284 | 2.9180 | 0.0008 | 1.828 | |
F-1 | 3.0506 | 1.8205 | 0.0016 | 3.051 | |
F-2 | 2.4274 | 2.2051 | 0.0018 | 2.427 | |
G-1 | 3.0352 | 1.6771 | 0.0011 | 3.035 | |
G-2 | 3.0352 | 1.7740 | 0.0011 | 3.035 | |
Zhou et al. (2006) | W-1 | – | 1.6499 | 0.0006 | – |
W-4 | – | 1.4059 | 0.0028 | – | |
Zhang (2007a) | W1 | 2.2558 | 1.6286 | 0.0029 | – |
W4 | 3.7276 | 1.1500 | 0.0051 | – | |
W11 | 2.7010 | 1.4143 | 0.0023 | – | |
Zhang (2007b) | WA-3 | – | 3.3375 | 0.0114 | 0.0144 |
WA-4 | – | 3.8619 | 0.0186 | 0.0220 | |
Gong (2008) | WA-1 | 4.0302 | 1.4762 | 0.0068 | 0.0097 |
WA-2 | 4.1756 | 1.4069 | 0.0083 | 0.0126 | |
WA-3 | 3.8397 | 1.5000 | 0.0081 | 0.0095 | |
WA-4 | 4.0620 | 1.3810 | 0.0094 | 0.0119 | |
Hao et al. (2008) | WL1 | 4.0302 | 1.3810 | 0.0068 | 0.0104 |
WL2 | 3.7437 | 1.5692 | 0.0035 | 0.0062 | |
WL3 | 3.8397 | 1.5625 | 0.0107 | 0.0131 | |
WL4 | 3.7120 | 1.3810 | 0.0076 | 0.0119 | |
Yang (2008) | Q5 | 1.4807 | 2.0600 | 0.0053 | 0.0063 |
Yang et al. (2008) | W-1b | 1.7569 | 2.3395 | 0.0085 | 0.0131 |
W-2b | 1.7517 | 2.4249 | 0.0055 | 0.0102 | |
W-3b | 2.0738 | 2.3175 | 0.0054 | 0.0115 | |
Fang (2009) | GP-0.6-1 | 2.3574 | 1.5416 | 0.0005 | – |
GP-0.3-1 | 2.4899 | 1.3942 | 0.0038 | – | |
GP-0.3-2 | 2.4953 | 1.2692 | 0.0020 | – | |
GD-0.6-1 | 1.1680 | 1.8968 | 0.0033 | – | |
Han (2009) | FQZ-1 | 2.4913 | 1.3653 | 0.0004 | – |
FQZ-2 | 2.7654 | 1.3133 | 0.0013 | 0.0015 | |
FQZ-3 | 3.3201 | 1.0451 | 0.0007 | 0.0030 | |
FQZ-4 | 2.8531 | 1.2771 | 0.0009 | 0.0018 | |
Gu et al. (2010) | PD10-5-0.6C | 4.6932 | 1.1367 | 0.0029 | 0.0051 |
PD10-10-0.3C | 3.4254 | 1.3550 | 0.0043 | 0.0108 | |
PD10-10-0.6C | 4.5262 | 1.3829 | 0.0041 | 0.0140 | |
PD10-10-0.9C | 5.6517 | 1.2369 | 0.0035 | 0.0077 | |
PD15-15-0.6C | 5.8121 | 1.1118 | 0.0042 | 0.0155 | |
PD15-15-0.9C | 5.5556 | 1.1682 | 0.0037 | 0.0155 | |
PM-0.3C | 4.7068 | 1.3871 | 0.0043 | 0.0075 | |
PM-0.6C | 5.2397 | 1.3043 | 0.0085 | 0.0120 | |
Weng (2010) | W-1 | – | 3.0000 | 0.0011 | – |
W-2 | – | 2.4000 | 0.0016 | – | |
Zhang (2010) | W-1 | – | – | 0.0011 | 0.0039 |
Zheng (2010) | BCW-1 | 2.0498 | 1.7450 | 0.0017 | 0.0065 |
BCW-2 | 2.2208 | 1.4000 | 0.0016 | 0.0049 | |
BC2 W-1 | 1.2769 | 2.0464 | 0.0018 | 0.0054 | |
BC2 W-2 | 1.2980 | 1.5909 | 0.0016 | 0.0042 | |
BC2 W-3 | 1.6656 | 1.3700 | 0.0020 | 0.0099 | |
BC2 W-4 | 2.2076 | 1.6824 | 0.0021 | 0.0072 | |
BC2 W-5 | 1.6874 | 1.7297 | 0.0020 | 0.0060 | |
Liu et al. (2011) | WB-1 | – | 3.2461 | 0.0080 | 0.0166 |
WB-2 | – | 3.1937 | 0.0107 | 0.0131 | |
WB-3 | – | 3.1623 | 0.0174 | 0.0185 | |
WB-4 | – | 3.9083 | 0.0150 | 0.0173 | |
Wu et al. (2012) | HQ2 | 2.0012 | 1.5969 | 0.0016 | 0.0100 |
HQ3 | 2.3499 | 1.5540 | 0.0017 | 0.0120 | |
HQ4 | 3.0572 | 1.2482 | 0.0015 | 0.0102 | |
HQ5 | 3.0572 | 1.4475 | 0.0015 | 0.0175 | |
Wu (2012) | LSGZ-01 | 2.7991 | 1.4044 | 0.0036 | 0.0053 |
ZYGZ-01 | 2.5177 | 1.2694 | 0.0027 | 0.0058 | |
ZYGZ-02 | 1.9270 | 1.3667 | 0.0030 | 0.0089 | |
Xiao et al. (2012) | TJ-W-1 | 3.6664 | 1.4923 | 0.0026 | 0.0051 |
TJ-W-3 | 4.6799 | 1.4936 | 0.0026 | 0.0075 | |
TJ-W-4 | 3.7058 | 1.6317 | 0.0029 | 0.0043 | |
Guo et al. (2014) | W-1 | 2.4650 | 1.7404 | 0.0044 | 0.0060 |
W-2 | 1.8429 | 2.4290 | 0.0050 | 0.0074 | |
W-3 | 1.8182 | 2.5225 | 0.0050 | 0.0080 | |
Wang et al. (2014) | TW-2 | – | – | 0.0033 | – |
Zhang (2014) | TW-2 | 2.8318 | 2.0603 | 0.0083 | – |
LW-2 | 1.5588 | 3.3669 | 0.0165 | – |
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Lu, X., Tian, Y., Guan, H. et al. Parametric sensitivity study on regional seismic damage prediction of reinforced masonry buildings based on time-history analysis. Bull Earthquake Eng 15, 4791–4820 (2017). https://doi.org/10.1007/s10518-017-0168-9
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DOI: https://doi.org/10.1007/s10518-017-0168-9