Question 17.9: Construct Newmark–Hall broad-banded design spectrum for a si......
Construct Newmark–Hall broad-banded design spectrum for a site. Develop spectrum curves using the program for damping factors 0.02, 0.05, 0.1. Estimate the maximum horizontal ground displacement assuming the maximum ground acceleration = 0.4 g, assuming group L and 84.1% on 50 m alluvium by bed rock.
Maximum ground acceleration = 0.4g = 0.4 × 981 cm/s² = 392.4 cm/² From Table 17.6 v/a = 117/g; ad/v² = 7.8
v = 117 × 0.4 = 46.8 cm/s
d = 7.8 v² /a = 7.8 × 46.8² /392.4 = 43.53 cm
a = 392.4 cm/s² ; v = 46.8 cm/s d = 43.53 cm
Construct the maximum ground motion polygon with the values of a, v and d. Apply appropriate amplification factors to the maximum ground motion components in a manner similar to that described in this chapter.
| Table 17.6 Summary of v/a and ad/v² ratios (log normal distribution) | ||||||
| Soil | Group | v/a (cm s/g) | ad/v² | d/a (cm/g) 50 |
||
| 50% | 84.1% | 50% | 84.1% | |||
| Rock | L | 60 | 97 | 5.3 | 11 | 20 |
| S | 69 | 112 | 5.2 | 11.2 | 25 | |
| V | 71 | 114 | 6.1 | 11.8 | 30 | |
| <10m
alluvium
underlain
by rock |
L | 76 | 145 | 4.5 | 7.7 | 28 |
| S | 99 | 157 | 4.2 | 8.2 | 43 | |
| V | 84 | 135 | 6.8 | 13.3 | 48 | |
|
10–70m
alluvium
underlain
by rock |
L | 76 | 117 | 5.1 | 7.8 | 30 |
| S | 91 | 147 | 3.8 | 6.4 | 33 | |
| V | 76 | 117 | 7.6 | 13.7 | 46 | |
| Alluvium | L | 122 | 175 | 3.9 | 6 | 58 |
| S | 145 | 216 | 3.5 | 4.9 | 74 | |
| V | 122 | 178 | 4.6 | 7 | 69 | |
Adapted from ‘A study of Earthquake Response spectra for different geological conditions’, by B Mohraz, Bulletin of the Seismological Survey of America, vol. 66, No. 3, 1976.