Civil Insight: A Technical Magazine Volume 2

CIVIL INSIGHT 2018 TEACHERS’ SECTION 21 Calculation of the free-fi eld deformation ( free-fi eld) As per the collected earthquake data The peak ground acceleration at the depth of tunnel (a s ) = (0.9 * a max ) = 0.9 * 0.49 = 0.44 g. 0.9 is the ratios of ground motion at depth to motion at ground surface obtained from Table 1 (Y M AHashash et al., 2001). For stiff soil medium, (Source to site distance = 59.9 km) peak ground velocity at the depth of tunnel can be calculated as, Peak ground velocity at the depth of tunnel = V s = (k ×a s ) From table 2, (Y M A Hashash et al., 2001), k = ratio of peak ground displacement (cm) to peak ground acceleration (g), (corresponding to source to site distance) = 135.7 (cm/sec)/g V s = 135.7* 0.44 = 59.708 cm /sec = 0.597 m/sec ௏ ೞ Maximum free-fi eld shear strain at the elevation of tunnel = ɀ ୫ୟ୶ = ஼ ೞ C s = Apparent velocity of s-wave propagation in soil C s (for rock) 750 m/sec For stiff soil = 200-750 m/sec For soft soil < 200 m/sec. ɀ ୫ୟ୶ = 0.597 / 750 = 0.000796. Free-fi eld deformation = free-fi eld= ɀ ୫ୟ୶ *H = 0.000796 * 6.8 = 0.0054128m = 5.4128 mm Calculation of Flexibility ratio (FR) [J H Wood, 2007] Figure 3: Unit force applied at the roof level In assessing soil-structure interaction effects on underground structures it is usual to defi ne fl exibility ratio. ୰ ൌ ୋ ౣ ൈ୛ ୗ భ ൈୌ In these expressions, the unit racking stiffness is simply the reciprocal of the lateral racking defl ection, ଵ ܵ ଵ ൌ , caused by unit concentrated force ο For a rectangular frame with arbitrary confi guration, the fl exibility ratio can be determined by ୫ ൌ ሺɏ ሺ ୫ ሻ ଶ ൈ ሺ ୫ ሻ ଶ = (2000 / 1000) * (75 50) 2 = 11250000 K pa ܵ ଵ ൌ ୰ ൌ ͳ ൌ Ͷ͹͸ͳͻͲǤͲ ͲͶ‫ܭ‬ ‫ܽ݌‬ ʹ Ǥͳ ൈ ͳͲ ି଺ ଵଵ ଵଶହ଴଴଴ൈଶଶǤଵ ସ଻ ଻଺ଵଽ଴Ǥ଴ସൈ଺Ǥଽ ൌ ൌ7.567

Civil Insight: A Technical Magazine Volume 2 | Page 21