# Reliability-based evaluation of concrete dams

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## Abstract

Swedish concrete dams are designed and assessed based on deterministic design using safety factors. The combination of increasing age, new methods for calculation of design floods and increasing demands by society to ensure a high level of safety, has resulted in upgrading and rebuilding needs for dams. When safety is re-evaluated it is important that evaluation is based on modern safety concepts. The objective of this thesis is to describe how reliability based methodology can be used for assessment of concrete dams, how it fits into the dam safety risk management process and the present state of knowledge of relevant statistic information of resistance and load parameters. Risk management is becoming more frequently used in dam safety all over the world and structural reliability analysis can be used for safety assessment of existing dams. Since object specific information, monitoring results, known loads etcetera can be included in the analysis it gives more reliable results than a more general assessment procedure based on traditional dam safety design guidelines. In this thesis the sliding and overturning failure modes are used for analysis, but there are reasons to further analyse the failure mode formulation. Overturning is not considered in several guidelines, instead resultant location is used as an indicator, and failure is associated with sliding or overstressing. The Swedish guideline on dam safety, RIDAS, does not, unlike guidelines used elsewhere in the world, take account to cohesion when the sliding stability is estimated. Even so, cohesion is included in the sliding criterion used for analysis in this thesis. In structural reliability analysis the failure mode of interest is described by a limit state function, which is a function of a number of basic variables, described by their statistical distribution. For a concrete dam the basic variables for the sliding failure mode are self-weight (G), cohesion (c), base area (A), friction angle (), uplift pressure (U), hydrostatic water pressure (H) and ice load (I) and the limit state function becomes Limit state functions for overturning or other failure modes can be defined in the same way. When statistical distributions are known for the basic variables, the safety index, , can be calculated. is related to the probability of failure by , where is the standardized normal distribution function. For safety evaluation, is compared to a target safety index, T. For dams no such target value exists. There are different approaches how to set a target and the most straightforward is calibration to existing practice, but there are also reasons to believe that target safety for dams should be based also on tolerable risk concepts. The basic variables affecting concrete dam stability are described and special attention is given to uplift, where a thorough state-of-the art is given, as it has been shown in previous research to have a large influence on dam stability. Uplift varies depending on temperature (higher uplift during cold periods), due to loads (increasing water levels may give rise to uplift pressure to increase more than the linear design assumption), is highly dependant on foundation treatment and drainage and is difficult to monitor (uplift in one point represent only a local area). A promising approach on how to use geostatistical modelling to derive statistical distribution for uplift is shown. The hydraulic conductivity beneath the dam is assumed to have certain properties (mean value and variance) and is quantified by a spatial correlation structure. Flow and uplift pressure distribution is then solved by use of a finite element program. A large number of simulations is used to obtain a statistical distribution of uplift force and moment on the whole dam base area. The uplift force active on the dam is described as where u is the uplift force, calculated from the linear uplift reduction assumption used in design, and C is a random variable based on the simulations. The treatment of moment of uplift is similar. This concept can and should be further developed, e.g. by investigating real rock properties and analyzing 3-D modelling of hydraulic conductivities. Even though there are questions to be solved, this approach gives useful results. In the first of two examples, the capacity of a wall in a spillway chute is analyzed. The result is that the wall can withstand approximately 20 % higher water levels than that resulting from design according to RIDAS. In the second example a dam, fulfilling the requirements in RIDAS, is analysed. The results reveal that the cohesion and the friction coefficient gives the largest contribution to the uncertainty of for sliding failure, whereas self-weight, followed by uplift and ice load, dominates the uncertainty for overturning failure. The main conclusions are that structural reliability analysis can be used as a tool in the dam safety risk management process and that the most important factors for further analysis are cohesion, friction coefficient, ice load, uplift and self-weight. The examples shown, and the results of a master thesis, indicates that today’s guideline (RIDAS) results in a number of “problems”, among them that the safety index seems to be dependant on dam type and dam height and that cross-sectional design is, at least in one example, conservative.

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