A Designer’s Approach for Estimation of Nuclear-Air-Blast-Induced Ground Motion

Table 5

Parametric studies carried out on the proposed closed-form solution.

Parameter	Parametric study	Observation	Recommended value
M1 and M2	Parameters M1 and M2 based on six different methods are adopted from Table 3.	Peak ground displacements are very sensitive to the constrained modulus value.	Observed results are consistent with the observations of Wilson and Sibley [17].
	Other parameters kept constant at r = 0.6; f = 2; adopted from Table 4.	Average coefficient of variation in peak displacement estimates = 83%.	(1) Shallow ground layers are likely to have modulus values determined by unconfined or triaxial compression test, and deep ground layers are likely to have modulus values computed from seismic velocity test or resonant column test. The justification to this variation in selection of modulus values can be attributed to the small strains associated with deeper layers and higher strains at shallow depths.
	Variation of absolute percentage errors in estimated peak ground displacements is plotted against peak overpressures in Figures 6(a) and 6(b).	Estimates are close to measured values if higher modulus values are used for smaller overpressures.	(2) Constrained modulus increases with decreasing ratio of applied stress to overburden. For higher overpressures, the overstress ratio would be higher and therefore modulus value will be lower compared to lower overpressures. An optimal choice of constrained modulus values is adopted as shown in Table 6. The computed displacements are found to be in good agreement with measured displacements (Table 6).
	is varied from 10 m to 250 m.	As increases (or decreases), peak displacement increases.	Attenuation has to be taken into account under low overpressures, and it can be ignored under high overpressures.
	Other parameters kept fixed at M1 and M2 adopted from Table 6; f = 2; r = 0.6.
	Estimated peak displacements are plotted against as shown in Figure 7.	Beyond of 250 m, the peak ground displacement does not increase, and  ≥ 250 is considered as the non-attenuating medium.
	Errors in estimated peak displacements for the attenuating medium and non- attenuating medium are also plotted against peak overpressure in Figure 8(a).
r	Two cases are considered: (i) full strain recovery r = 1 and (ii) partial strain recovery r = 0.6.	Assumption of full strain recovery gives less errors as compared to partial strain recovery under low overpressures.	Under low overpressure, ground is not stressed beyond its elastic limit, and hence full strain recovery is a better representation of actual conditions in low overpressure zones.
	Other parameters fixed at M1 and M2 adopted from Table 6; f = 2; adopted from Table 4.		A lower strain recovery causes higher permanent deformations and increases peak ground displacement compared to elastic case (i.e., unit strain recovery ratio). Under higher overpressures, the ground is stressed beyond its elastic limit and the assumption of partial strain recovery is recommended.
	Errors in estimated peak displacement for the two cases are plotted as shown in Figure 8(b).
f	f is varied from 1.0 to 2.2.	Under high overpressure (P1 and P2), error in occurrence time of peak displacement reduces significantly with increasing f.	f has insignificant effect on magnitude of estimated peak displacements. However, as the velocity ratio increases, the rise-time of overstress pulse with depth also increases and affects the occurrence time of the peak displacement.
	Other parameters fixed at M1 and M2 adopted from Table 6; r = 0.6; adopted from Table 4.	Error increases marginally under lower overpressures as the velocity ratio is close to 1 under lower stress (in (3) when ).
	Estimated peak displacements are plotted against f (Figure 8(c)).
	Error in occurrence time of peak displacement are also plotted against f (Figure 8(d)).