Fluid-filled tanks in tank farms of industrial plants can experience severe damage and trigger cascading effects in neighboring tanks due to large vibrations induced by strong earthquakes. In order to reduce these tank vibrations, we have explored an innovative type of foundation based on metamaterial concepts. Metamaterials are generally regarded as manmade structures that exhibit unusual responses not readily observed in natural materials. If properly designed, they are able to stop or attenuate wave propagation. Recent studies have shown that if locally resonant structures are periodically placed in a matrix material, the resulting metamaterial forms a phononic lattice that creates a stop band able to forbid elastic wave propagation within a selected band gap frequency range. Conventional phononic lattice structures need huge unit cells for low-frequency vibration shielding, while locally resonant metamaterials can rely on lattice constants much smaller than the longitudinal wavelengths of propagating waves. Along this line, we have investigated 3D structured foundations with effective attenuation zones conceived as vibration isolation systems for storage tanks. In particular, the three-component periodic foundation cell has been developed using two common construction materials, namely concrete and rubber. Relevant frequency band gaps, computed using the Floquet-Bloch theorem, have been found to be wide and in the low-frequency region. Based on the designed unit cell, a finite foundation has been conceived, checked under static loads and numerically tested on its wave attenuation properties. Then, by means of a parametric study we found a favorable correlation between the shear stiffness of foundation walls and wave attenuation. On this basis, to show the potential improvements of this foundation, we investigated an optimized design by means of analytical models and numerical analyses. In addition, we investigated the influence of cracks in the matrix material on the elastic wave propagation, and by comparing the dispersion curves of the cracked and uncracked materials we found that small cracks have a negligible influence on dispersive properties. Finally, harmonic analysis results displayed that the conceived smart foundations can effectively isolate storage tanks.

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Bolted Flange Joints (BFJs) represent the most common and critical components used nearly in all industrial piping systems, including Oil & Gas plants. Owing to their strategic importance and heavy consequences both to the environment and human lives due to both damage and leakage, BFJs are considered very important in industrial plant design. Therefore, their behaviour becomes critical also under seismic actions. Along this line, in the first part of this paper the experimental test campaign performed on enhanced bolted flange joints subject to both monotonic and cyclic loading is presented and discussed. Then, specific values of both stiffness and strength with reference to leakage are estimated. Successively, a reliable model capable of predicting the leakage force for a generic BFJ, including the interaction between the axial and shear load, is proposed and validated; in particular, both actual and previous full scale experimental data were involved in the validation. As a result, the values predicted by the model agree well with those obtained by the experiments. This model is also adopted to predict leakage stiffness values for thick flanges. Overall, the proposed analytical model can represent a promising tool for the leakage prediction of BFJs in complex piping systems.

Dynamic analysis is an integral part of seismic risk assessment of industrial plants. Such analysis often neglects actual boundary conditions or proper coupling between structures of coupled systems, which introduces uncertainty into the system and may lead to erroneous results, e.g., an incorrect fragility curve, in comparison with the actual behaviour of the analyzed structure. Hence, it is important to study the effect of uncertainties on the dynamic characteristics of a system, when coupling effects are neglected. Along this line, this paper investigates the effects of uncertain boundary conditions on the dynamic response of coupled tank-piping systems subjected to seismic loading. In particular, to take into account the presence of the tank as boundary condition for the piping system, two sources of uncertainty were considered: the tank aspect ratio and the piping-to-tank attachment height ratio. Moreover, to model the seismic input, a Filtered White Noise (FWN) characterized by a Kanai-Tajimi spectrum was used. Finally, to study the dynamic interaction of a set of coupled tank-piping systems, the non-intrusive stochastic collocation (SC) technique was applied. It allowed for calculating surface responses of stresses and axial loads of a pair of components of the coupled system with a reduced number of deterministic numerical simulations.

Piping systems of energy industries in oil & gas play a critical role in meeting the increasing global energy demand. A great portion of these pipelines is located in high seismic-prone areas. Such systems have been found to be quite vulnerable to seismic events. Current seismic design approaches to piping systems are mainly based on the allowable stress method, even though more modern design methods are currently available for buildings or nuclear power plants; for example, the Performance-Based Earthquake Engineering (PBEE) framework has not been applied yet to piping systems and relevant structures. In this respect, both information about the quantification of limit states for pipes and adequate non-linear structural models for seismic analysis of piping systems and relevant structures are very limited. One of the key ingredients of PBEE approach for the assessment of the seismic vulnerability of existing structures is the evaluation of fragility curves, namely the probability of exceeding a certain level of damage for a given seismic intensity measure (IM). However, the contributions in the literature on this delicate aspect are very limited. This paper deals with such a problem by using a very popular method, namely the Cloud Analysis, originally developed as a method for probabilistic seismic demand analysis of civil structures. This method is here applied to a typical piping system for process plants. For this purpose, the structure is properly modelled, especially support structure and pipe, including pipe fittings like elbows and bolted flange joints. Using natural accelerograms selected from the PEER database and in accordance with given hazard conditions, the probabilistic seismic demand analysis is performed adopting different engineering demand parameters (EDP) consistent with the damage states expected in the pipes and fittings and in the support structure. According to the results of experimental tests campaign performed in the past by some of the authors on flanged joints, and elbows, different damage states (leakage, yielding, rupture) have been identified and related to the corresponding EDP and the corresponding probability of exceeding has been determined by assuming a lognormal distribution of the response. The analysis intends to recognise the most probable damage condition in a refinery piping system subjected to a seismic input.

Dynamic analysis is an integral part of seismic risk assessment of industrial plants. Such analysis often neglects proper coupling between structures of coupled systems, which introduces uncertainty into the system and may lead to erroneous results, e.g., incorrect fragility curves, in comparison with the actual behavior of the analyzed structure. Hence, it is important to study the effect of uncertainties on the dynamic characteristics of a system, when coupling effects are both neglected and included. Along this line, this paper intends to define and compare the fragility curves of both an isolated (decoupled) and a coupled tank-piping system subjected to seismic loading. In particular, for the decoupled case, we estimated the probability of exceedance of main engineering demand parameters within the Performance-Based Earthquake Engineering (PBEE) framework. Moreover, for the coupled case, to take into account the presence of the tank as boundary condition for the piping system, two sources of uncertainty were considered: i) the tank aspect ratio; ii) the piping-to-tank attachment height ratio. In addition, to model the tank slippage, both a Filtered White Noise (FWN) characterized by a Kanai-Tajimi spectrum and the non-stationarity of the seismic input were taken into account by means of the stochastic linearization. All these elements allow for the estimation of fragility curves for different limit states in the coupled case.

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