ABSTRACT


All civil engineering structures, and particularly dams and reservoirs, should meet the highest requirements of safety and economy. Large dams provide extraordinary benefits to society, but, at the same time, dams impose high potential risks over population and properties downstream.

Spanish legislation in dam safety has evolved in the last years and nowadays risk management is explicitly invoked as one of the basic tasks that modern countries must face. In fact, risk management is considered a key issue in the design of actions oriented to protect people, goods and the environment. In this context, and in the field of dam engineering, risk-based analysis techniques are being developed, offering not only a complementary view to the classical approach to dam safety, but also an entire new tool that can help out robust management of dam safety, including some useful criteria to rationalize dam investments and a better understanding of the risk posed by dams.

Risk analysis methodologies need risk quantification. For an initial state of the dam-reservoir system, and for a certain failure mode, this risk quantification means the estimation of both the probability of the loading scenarios and the conditional probability of the response of the dam-reservoir system for a certain loading scenario, together with the estimation of the consequences for a certain response of the system.

In dam engineering, the main loading scenarios are those of hydrological and seismic nature. Hydrology and seismic engineering are well established sciences with a wide and solid body of knowledge which is constantly in development, as the estimation of the probability of floods and earthquakes has been on the focus of researchers and engineers for a long time.

The estimation of the conditional probability of the response of a system for a certain loading scenario can be done with the help of the reliability theory, which is based on a powerful mathematical framework, that has been used successfully on the field of structural analysis.

The estimation of the consequences (in terms of loss of lives and impacts on economy), for a certain response of the dam-reservoir system (partial or total failure for a given loading scenario), represents a much more recent landmark in dam safety engineering. However, the development of this issue during the last decades of the past century has been remarkable.
 

Following the distinction between the probabilities aforementioned, this dissertation deals with the second of them: conditional probability of the response of a dam-reservoir system for a certain loading scenario, but considering only the case of gravity dams. In the context of risk analysis, the conditional probability can be assessed by means of three different methods, namely historical references, probability elicitation, and reliability analysis. Probability estimation of the response of complex systems such as dams is an issue subjected to much controversy and discussion by dam engineering community.

Reliability techniques have been used in structural analysis while its application to other civil engineering fields, such as dam engineering, has been scarce, due to a variety of reasons such as the prototype character of each dam, uncertainties associated with the foundation, presence of water flow, and others. The complexity of the dam-reservoir behaviour, with several phenomena of different nature interacting simultaneously, has been tackled by following strong simplifications in the models of analysis together with the adoption of large safety margins on loads and resistances. On the other hand, the development of advanced numerical models (finite element and finite difference based methods) and the growing calculation power of computers, allow to use complex mathematical models in the analysis of dam safety problems.

Within this general context, a methodology is presented herein to improve the estimation of the conditional probability of the response of the gravity dam-reservoir system, which is accomplished linking numerical models with reliability techniques of several levels of precision, and in particular with level 3 reliability methods, using Monte Carlo simulation. Both natural variability and epistemic uncertainty of parameters are incorporated into the process using probability distribution functions.

A full application of the proposed methodology is carried out for a Spanish gravity dam. Following the formulation of the dam risk model, and for a single failure mode, conditional probability of the response of the system is obtained. In addition, the methodology includes the evaluation of the sensibility of the global results of the risk model of the dam for the different conditional probabilities calculated