This dissertation investigates the use of probabilistic models, including copulas, vine-copulas, and Bayesian Networks, to enhance the understanding and reliability of submerged floating tunnels (SFTs). Despite their potential for challenging water crossings, no SFTs have been constructed beyond a prototype in Qingdao Lake, China, highlighting significant uncertainties related to their reliability under complex loading conditions. Through a case study of a hypothetical SFT in the Qiongzhou Strait, China, this research investigates the joint probability distribution of traffic and environmental loads, including wave height, wave period, and current velocities. The study develops methodologies for reliability analysis, focusing on the interactions between traffic loads, metocean conditions, and potential cascading failure scenarios. The findings demonstrate the importance of accounting for complex dependencies among variables to enhance the safety and stability of SFTs. The flexible models proposed in this research can be updated with new data, enabling continuous safety assessments and providing valuable insights for the design and planning of future SFT structures.@en

Vine copulas have become the standard tool for modelling complex probabilistic dependence. It has been shown that the number of regular vines grows extremely quickly with the number of nodes. Chimera is the first attempt to map the vast space of regular vines. Software for operating with regular vines is available for R, matlab and Python. However, no dataset containing all regular vines is available. Our atlas of regular vines, Chimera, comprises all 24 4 × 4 matrices representing regular vines on 4 nodes, 480 5 × 5 matrices representing regular vines on 5 nodes, 23,040 6 × 6 matrices representing regular vines on 6 nodes, 2,580,480 7 × 7 matrices representing regular vines on 7 nodes and 660,602,880 8 × 8 matrices representing regular vines on 8 nodes. Regular vines in Chimera are classified according to their tree-equivalence class. We fit all regular vines to synthetic data to demonstrate the potential of Chimera. Chimera provides thus a tool for researchers to navigate this vast space in an orderly fashion.

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Before the year 1519, the Valley of Mexico was a closed basin and at the bottom of the valley, an extensive system of shallow lakes was formed. Within this lacustrine system, the capital of the Aztec empire, Tenochtitlan, was built. The Aztecs were known for their impressive constructions and complex hydraulic structures, of which the most impressive structure was the Nezahualcoyotl dike. This structure was constructed across Lake Texcoco. Its principal function was to protect the city of Tenochtitlan from high water levels at the lake. However, there is not enough information about the reliability of this dike. Mainly due to two reasons, today there are no remains left of the dike and most of the lacustrine system is drained. In this paper, we present a method to study the reliability of the Nezahualcoyotl dike under two failure modes, overturning and sliding. This is done by following up on the work presented by Torres-Alves & Morales-Nápoles (2020) where they developed a hydrological characterization of the lacustrine system and studied the dike under one failure mode, overflow. The proposed analysis aims to provide a more realistic assessment of the reliability of the dike as a flood defense mechanism. @en

Investigating the reliability of ancient hydraulic structures constructed without modern probabilistic criteria allows an understanding of why and how the structure fails. In this paper, we present an extended method, firstly introduced by Torres-Alves and Morales-N´apoles (2020), to perform the reliability analysis of the Nezahualcoyotl’s dike that was designed (most likely) without probabilistic criteria. The dike was built around 1450 by the Aztec empire dividing Lake Texcoco from north to south (present-day Mexico City). We estimate the probability of failure due to overflow. By using a discrete time-state Markov chain and bi-variate copulas to generate large synthetic observations of the environmental variables precipitation and evaporation. In addition to the previous methodology, two sources of uncertainty were taken into account (i) the characterization of the environmental conditions during the dry season to estimate initial water levels on the lake and (ii) the influence of surface runoff and subsurface seepage losses on the water levels. The extended method allows for better characterization of the lacustrine system. Therefore an improved extent of the hydrology of the system and a more reliable estimation of the probability of failure of Nezahualcoyotl’s dike are presented. @en

Investigating the reliability of ancient hydraulic structures constructed without modern probabilistic criteria allows an understanding of why and how the structure fails. In this paper, we present an extended method, firstly introduced by Torres-Alves and Morales-Nápoles (2020), to perform the reliability analysis of the Nezahualcoyotl's dike that was designed (most likely) without probabilistic criteria. The dike was built around 1450 by the Aztec empire dividing Lake Texcoco from north to south (present-day Mexico City). We estimate the probability of failure due to overflow. By using a discrete time-state Markov chain and bi-variate copulas to generate large synthetic observations of the environmental variables precipitation and evaporation. In addition to the previous methodology, two sources of uncertainty were taken into account (i) the characterization of the environmental conditions during the dry season to estimate initial water levels on the lake and (ii) the influence of surface runoff and subsurface seepage losses on the water levels. The extended method allows for better characterization of the lacustrine system. Therefore an improved extent of the hydrology of the system and a more reliable estimation of the probability of failure of Nezahualcoyotl's dike are presented. @en

A submerged floating tunnel (SFT) is a structure that has been proposed as an innovative solution for waterway crossings around the world. However, to this day, no SFT has been constructed yet. One of the main reasons is that there is an insufficient insight into the structural reliability of the SFT. Here, a method to assess the expected structural response of an SFT under traffic loads and a reliability assessment of the results is presented. To do this, traffic models and structural response and reliability are coupled. The methodology presented herein proposes an innovative way to combine copula-based models and structural models to obtain more a more realistic structural response of the SFT. The focus will be on one failure mechanism, leakage caused by bending failure of the SFT in the longitudinal direction. The method utilizes a copula-based model to characterize the traffic loads and simulate traffic loads on the SFT (axle weight, inter-axle distance, and inter-vehicle distance). Next, a structural model is used to assess the structural response and derive stresses. Using a probabilistic analysis, the design of the cross-section can be adapted so that it meets the requirements for leakage caused by bending moments. For the case study is demonstrated that for a buoyancy weight ratio (BWR) of 1.1 an optimal design can be achieved based on a probabilistic method. This methodology could be extended to other failure modes of an SFT or to other structures.

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A submerged floating tunnel (SFT) is a novel structure that allows crossing waterways where immersed tunnels or bridges are not viable. However, no SFT has been built yet mainly, due to lack of experience. In consequence, there are several uncertainties regarding its design and construction. An effect that should be further investigated is the structural response of the SFT under the simultaneous action of waves and currents. For this purpose, extreme values of waves and currents that were generated through a vine-copula model are used as input in a statistical model based on Bayesian Networks (BNs). The BNs are used to study the conditional correlation (i.e the correlation between random variables conditionalized on a given event) between the hydrodynamic forces acting on the SFT and metocean variables such as waves and currents. This methodology was applied to a case study in China for a SFT aimed to be built at the Qiongzhou Strait. Moreover, the BN model was used to test twelve different configurations of the SFT, with varying submergence depths and diameter sizes. The proposed methodology can be used to provide a more realistic estimation of the forces on the SFT by considering the dependence between the variables of interest. Moreover, this methodology can be extended to test different configurations of the SFT and other hydraulic or maritime structures subjected to simultaneous loading. @en

The generation of synthetic time series is important in contemporary water sciences for their wide applicability and ability to model environmental uncertainty. Hydroclimatic variables often exhibit highly skewed distributions, intermittency (that is, alternating dry and wet intervals), and spatial and temporal dependencies that pose a particular challenge to their study. Vine copula models offer an appealing approach to generate synthetic time series because of their ability to preserve any marginal distribution while modeling a variety of probabilistic dependence structures. In this work, we focus on the stochastic modeling of hydroclimatic processes using vine copula models. We provide an approach to model intermittency by coupling Markov chains with vine copula models. Our approach preserves first-order auto-and cross-dependencies (correlation). Moreover, we present a novel framework that is able to model multiple processes simultaneously. This method is based on the coupling of temporal and spatial dependence models through repetitive sampling. The result is a parsimonious and flexible method that can adequately account for temporal and spatial dependencies. Our method is illustrated within the context of a recent reliability assessment of a historical hydraulic structure in central Mexico. Our results show that by ignoring important characteristics of probabilistic dependence that are well captured by our approach, the reliability of the structure could be severely underestimated.

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In past decades, the construction of a submerged floating tunnel (SFT) has been presented as an innovative solution for water crossings. One of the main challenges surrounding the design of this type of structure is the lack of data since no SFT has been constructed yet, except for a prototype in Qingdao Lake in China (Mazzolani, Faggiano, & Martire 2010). Additionally, there are uncertainties related to the environmental variables relevant for the construction and operation of a SFT. Wave and current data will be considered for this study. These variables are usually taken as deterministic for design of marine and hydraulic structures and its values represent extreme events. In this paper, a joint probability distribution analysis is proposed to characterize the variables and their dependence. This task was carried out using a copula-based model. In this way, the design conditions for the SFT can be modeled more realistically. The results are several synthetic time series of hourly values and extreme values of all the variables involved.

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