Reliability Updating with Survival Information for Dike Slope Stability Using Fragility Curves

Abstract

Dikes and levees play a crucial role in flood protection. The main causes of levee failures are of geotechnical nature. Geotechnical failure modes are also the main contributors to the probability of failure of flood defenses such as levees due to the large uncertainties in ground conditions. Hence, information on ground conditions and soil properties is crucial in safety assessments and retrofitting designs of levees. The experience in practice with designs and risk assessments is that even with a substantial amount of site investigation and laboratory testing the uncertainties in soil properties often remain large. One way to further reduce uncertainties is to include past performance information.The present papers shows how information of survived loads in the past can be incorporated in reliability assessments by means of Bayesian posterior analysis using the same (physics-based) performance models as the prior reliability assessments. The incorporation of survival information leads to reduced uncertainties and probabilities of failure. Furthermore, an approximate approach using fragility curves is proposed, mainly to make problems with computationally expensive performance functions tractable.After briefly recapping Bayesian reliability updating, we provide examples for slope stability of (flood protection) dikes. The examples illustrate that posterior analysis enables us to reduce the large prior uncertainties in soil strength parameters by "eliminating" implausible samples or regions of the joint PDF of the strength properties using the evidence of survived load conditions (i.e. water levels). The results suggest that the effect of updating the probability of failure with survival evidence can be considerable, especially when the uncertainty in the strength properties dominates the reliability. Dominant strength uncertainties are rather typical in geotechnical engineering, as opposed to, for example, structural engineering, implying that using the method is promising also for other geotechnical applications.

Improving dike reliability estimates by incorporating construction survival

“…The results, however, are presented conditional to the water level, whereas the total probability of failure is the probability-weighted sum of the conditional failure probabilities for all water levels in the relevant range; two of which are considered by loading condition B and C. To provide a rough estimate of the total annual failure probability for the characteristic dike cases, we combined the conditional failure probabilities P(F) | h with the probability density of the water level f(h), using the approach in Schweckendiek et al (2017). We used a Gumbeldistributed probability distribution of the water level based on the assumption that the flood level of loading condition C corresponds to an exceedance probability of 1/100 per year.…”

Value of Information of Structural Health Monitoring in Asset Management of Flood Defences

“…Probabilistic calculations of flood defence reliability often show that strength uncertainties have a major influence on flood defence reliability estimates. In practice, reduction of such uncertainties often results in a major change in such estimate [23,24,48], leading towards different reinforcement and maintenance decisions. The general aim of this paper is to show in what circumstances reduction of epistemic strength uncertainty improves asset management decisions for flood defences, focusing on long-term reinforcement investments.…”

“…There are various ways in which the influence of epistemic uncertainty on reliability estimates can be reduced, most notably the inclusion of survival observations in general due to correlation of resistance parameters in time [49], survival of past extreme events [48,50] or actively reducing uncertainties by monitoring or site investigation. The latter has been investigated in this paper, and neither of the former two are considered in the computations.…”

Value of information of combinations of proof loading and pore pressure monitoring for flood defences

“…Here, fragility curves are used to calculate the slope reliability of dikes, see Schweckendiek et al (2017). Fragility curves describe the conditional failure probability given a (load) variable.…”

“…This is in line with expectations because the survived proof load becomes more valuable if a high phreatic line is less likely. Note that the failure probability for water levels lower than the survived proof load level is not reduced to 0 (infinite beta) because of irreducible uncertainty (see Schweckendiek et al (2017) for a consideration of reducible and irreducible uncertainty). In this case this mostly concerns uncertainty in time-variant variables, such as the rainfall intensity.…”