The design of underground critical facilities for anticipated effects of nuclear-air-blast is becoming a challenge. Moving air-shock waves on the earth surface generated due to above-ground nuclear-explosions induce ground displacements. An accurate estimate of nuclear-air-blast-induced free-field ground displacement is crucial for the design of such protective structures. This thesis provides a computationally efficient and reliable estimate of ground displacements considering nuclear-air-overpressure, stress-strain characteristics of geomaterials, and associated uncertainties.
Of several blast load models available in literature, the ASCE manual No.-42 model captures the mean trend of the decay portion of the air-overpressure time-history reasonably well. This model predicts nuclear-air-overpressure time-history in terms of distance from ground-zero (R), height-of-burst (HOB), and yield of the explosion (W). The ASCE model is further modified to account for the uncertainties associated with (i) the ASCE model, (ii) occurrence of an explosion, and (iii) inherent variability of nuclear-attack parameters (R, W, and HOB) by (i) comparing the field data with model estimates, (ii) developing a probabilistic threat scenario model, and (iii) assigning appropriate probability distributions to the nuclear-attack parameters, respectively. The incorporation of these uncertainties into the ASCE model leads to the probabilistic characterization of nuclear-blast loads. For the direct use in design, two simple correlations are proposed for peak overpressure and positive phase duration in terms of their respective probability of exceedance along with another equation that represents a normalized air-overpressure time-history.
An appropriate description of stress-strain relationship of geomaterials subjected to blast loading is the next important step. Previous experimental and theoretical research efforts indicated that the constitutive behaviour of geomaterials under blast loading depends upon strain rate, stress level, and interaction among the three phases (solid, liquid, and gases) and various advanced constitutive models are available to model such a stress-strain behavior of geomaterials. However, these models are based on large number of material parameters which needs to be calibrated through different experimental studies and numerical computations. Furthermore, the inherent variability of geomaterials, uncertainties of the nuclear-air-blast overpressures, epistemic uncertainties of the constitutive model itself would add significantly to the cost of computation of ground displacements. Therefore, as an alternative to advanced constitutive models, new functional forms, based on three parameters, namely, weight factor, initial modulus ratio, and strain recovery ratio, are proposed to capture the loading and unloading branches of experimentally determined or numerically simulated stress-strain curve of geomaterials subjected to blast loads. The three parameters are determined for an exhaustive data set of experimental stress-strain curves of different types of geomaterials (sands, silts, and clays) under different types of conditions (dry, saturated, partially saturated, confined, and unconfined) subjected to various loads (dynamic loads, blast loads, impact loads, and static loads) and a catalogue of the parameters is prepared for direct use by practitioners. It is observed that the functional forms reasonably capture the mean trend of the stress-strain data corresponding to not only blast loads and high strain rates but also to static and dynamic loads. The functions were also able to capture the stress-strain behaviour simulated from advanced constitutive models. The dependence of model parameters on strain-rate, lateral confinement, degree of saturation, initial compaction, and locking-initiation stress is also analyzed and some simple models or thumb-rules are proposed for reasonable estimation of the three parameters.
In the last step, to estimate the nuclear-air-blast-induced free-field vertical ground displacement a model is proposed in terms of air-overpressure time-history and depth-dependent geotechnical parameters (stress wave velocity, stress attenuation, and stress-strain model). The estimated displacement time-histories are compared with the nuclear as well as non-nuclear test data and a reasonable agreement is found between the recorded and estimated displacements. It is observed that the model significantly overestimates the displacements at greater depths and at larger distances from ground-zero (GZ). The displacement model is utilized further to study the effect of loading and geotechnical parameters on peak ground displacement through parametric variations and sensitivity analysis. The analysis indicates that the peak ground displacement is highly sensitive to R, HOB, and constrained modulus.
The field data is utilized further to characterize the epistemic uncertainties associated with the displacement model. Since the quantification of model uncertainties is computationally tedious if model parameters are also uncertain, an approximate approach is proposed for model uncertainty characterization that is based on Taylor’s series approximation and accounts for deterministic as well as uncertain input parameters. The proposed approach is compared with the computationally rigorous Bayesian approach and is observed to be in close agreement for prediction of mean model factors. Based on the proposed model uncertainty characterization approach, it is found that the mean model uncertainty factor (corresponding to peak displacement) varies between 0.78 and 0.99 for coefficients of variation of input parameters in the range of 0-20%. Since all the mean model uncertainty factors are less than unity, it indicates that the proposed model provides, on an average, conservative estimate of peak ground displacement.
Thus, using the proposed (i) probabilistic nuclear-blast load model, (ii) stress-strain function of geomaterials, (iii) displacement model, and (iv) model uncertainty factors, a reliable and computationally efficient estimate of nuclear-air-blast-induced ground displacements can be arrived at.