Uncertainty Analysis

# Pathak, S., & Ramana, G. V. (2018c). Uncertainties of a nuclear-air-blast induced ground displacement model. In B. Fatahi, A. Mwanza, & D. Chang (Eds.), Geochina 2018: Civil infrastructures confronting severe weathers and climate changes conference (pp. 183–196). Springer, Cham.

Scenario based design of strategic underground structures is increasingly becoming important with increasing capacities of nuclear warheads. The ground displacement caused by nuclear-air-blast is an important design parameter for such structures. A simplified model to compute ground displacement, proposed earlier by authors, is recommended for preliminary designs in professional practice. This paper quantifies the uncertainties associated with this simplified model as well as its input parameters namely P-wave velocity, strain recovery ratio, velocity ratio, and constrained modulus, while estimating the nuclear blast induced ground displacement. The model uncertainty quantification is generally accomplished using sampling based Bayesian updating techniques. However, this is a computationally time-consuming process and not suitable with increasing number of model parameters. To circumvent this, an alternate simplified model uncertainty characterization approach is developed based on Taylor’s series approximation. The validity of the proposed approach is established by comparing the results for a simple case of an earth pressure problem, routinely encountered in geotechnical engineering, against Bayesian approach. Subsequently, this simplified approach has been used to quantify the model uncertainties of air-blast induced ground displacement model and it is observed that this model is biased towards conservative side.

# Pathak, S., & Ramana, G. V. (2019). A first order quantification of effects of uncertainties in hydro-fracturing parameters on tunnel ovalization estimates. Geotechnical and Geological Engineering, 37 (4), 3049–3064.

In-situ stresses are always present in rock-masses due to gravitational and tectonic forces. Excavation of a tunnel in such a pre-stressed media causes deformation of tunnel cross-section. Ovalization of tunnels due to in-situ stresses in rock-mass is an important design parameter. For estimation of tunnel ovalization, state of in-situ stresses needs to be determined first. In-situ stresses determined through hydro-fracturing technique (HFT) are dependent upon the three HFT parameters: (a) shut-in pressure, (b) re-opening pressure, and (c) fracture orientation. A critical review of previous studies indicates that HFT parameters are subjected to uncertainties due to (1) limitations of testing procedures and equipment, (2) assumptions and subjective engineering judgment associated with interpretation of test results, and (3) inherent variability of geological formations. Therefore, tunnel deformation estimates based on in-situ stresses determined through HFT would also be affected by these uncertainties. In this paper, a framework based on the first-order second moment method is developed to evaluate the effects of uncertainties in hydro-fracturing test data on tunnel deformation. The analysis indicates that uncertainty in tunnel deformation depends upon the uncertainty levels as well as magnitude of the three HFT parameters along with Poisson’s ratio, height of overburden, and the angular location of the point on the tunnel periphery where deformation is being estimated. It is also found that among the three parameters, the shut-in pressure has the maximum relative contribution in the resulting uncertainties in tunnel ovalization with an average of 68% (± 8% standard deviation). The proposed methodology is explained through an example case-study from Bukit Timah Granite rock-mass of Singapore. It is found that for a range of coefficient of variation of shut-in and re-opening pressure from 0 to 50%, the maximum coefficient of variation of tunnel deformation varies between 63 and 332%. In view of such high uncertainties, it is recommended that uncertainties of HFT parameters must be taken into account in the design procedure to avoid unsound engineering judgments.

# Pathak, S., & Ramana, G. V. (2020). Probabilistic characterization of nuclear blast loads. Journal of Structural Engineering, ASCE, 146 (5).

With increasing stockpiles of nuclear warheads, it has become essential to fortify critical infrastructure against nuclear blast. Therefore, a reliable estimation of nuclear-blast load is crucial for design of such hardened facilities. Several previous studies analyzed nonnuclear explosion scenarios without specific attention to nuclear explosions. In this paper, a standard nuclear-blast model from the literature is compared with the declassified nuclear test data, and it is observed that the standard model reasonably captures the mean trend of the decay portion of the air-overpressure history. This study accounts for the uncertainties associated with (1) the standard model, (2) occurrence of an explosion, and (3) inherent variability of nuclear-attack parameters (range, yield, and height of burst) by (1) comparing the field data with the model estimates, (2) developing a probabilistic threat scenario model, and (3) assigning appropriate probability distributions to the nuclear-attack parameters, respectively. The incorporation of these uncertainties into the standard model leads to the probabilistic characterization of nuclear-blast loads. For direct use in design, two simple equations are proposed for peak overpressure and positive phase duration in terms of probability of exceedance, and an equation is proposed that represents a normalized air-overpressure history.

# Crollen-Vandromme, E., Pathak, S., Soltani, P., Collette, C., & Deraemaeker, A. (2020). Robust design of tuned mass dampers attached to host structures containing uncertainties in the form of fuzzy parameters. In Proceedings of international conference on noise and vibration engineering and international conference on uncertainty in structural dynamics (7-9 September 2020), Leuven, Belgium (p. 3811-3824).

A robust design of tuned mass dampers (TMDs) must consider the influence of uncertainties associated with structural parameters to avoid detuning and malfunctioning. The existing robust equal-peak approach accounts for uncertainties in stiffness and damping of single degree-of-freedom (SDOF) host structures but may lead to a high computational cost and sub-optimal design in practical cases where host structures are represented by a large number of degrees-of-freedom and also exhibit some damping. To overcome these limitations, a numerical optimization technique is proposed which has the advantage of a low computational cost and generalization to any type of model of the host structure, including damping. Additionally, to account for the fact that the bounds of the uncertainty intervals are never known exactly for real-life conditions, this study employs fuzzy numbers to represent the structural uncertainties. The proposed approach is illustrated in case of an existing footbridge located in Durbuy (Belgium).

# Pathak, S., & Ramana, G. V. (2021). A note on partial safety factors for in-situ shear strength parameters of rock-mass. In Garg, A. et al. (Ed.), Proceedings of the 1st Indo-China Research Series in Geotechnical and Geoenvironmental Engineering, Lecture Notes in Civil Engineering (Vol. 123, p. 129-138). Springer Nature Singapore Pte Ltd.

The design of retaining structures founded on jointed rock-mass must ensure their safety against sliding instability. For this purpose, generally, in-situ direct shear tests are conducted and shear strength parameters (cohesion and friction-angle) are determined using the popular Mohr–Coulomb criterion. However, due to assumptions associated with such a simple shear strength criterion and various other uncertainties, random errors and limitations associated with in-situ testing, the shear strength parameters are also associated with uncertainties. The present study discusses a practise-friendly procedure to account for such uncertainties and investigates the efficacy of the current design practice (IS 6512) in accounting for these uncertainties. The proposed procedure is explained through four case-studies of in-situ direct shear tests conducted in Phyllite and Granitic rock-masses and evaluating sliding safety of a hypothetical concrete gravity dam founded on those rock-masses. The study highlights the fact that IS 6512 may lead to an unsafe design in cases when uncertainties associated with in-situ shear test data are significant.