Hydra Ring Scientific Documentation Ferdinand Diermanse Kathryn Roscoe Juliana Lopez de la Cruz Henri Steenbergen Ton Vrouwenvelder 1206006-004 © Deltares, 2013 Title Hydra Ring Scientific Documentation Client Project Reference Pages Rijkswaterstaat 1206006-004 1206006-004-ZWS-0001 249 Keywords System reliability, failure probability, dike ring, probabilistic techniques, failure mechanisms, load models, flood risk Summary This document describes the scientific background of Hydra-Ring, a probabilistic model used for the computation of failure probabilities for interconnected systems of flood defences. It includes background on the probabilistic techniques, the way in which the statistics and correlations of the hydraulic load and strength variables are handled, and the built-in failure mechanism models. The current version of this document is a preliminary work-in-progress document that is largely intended for developers and programmers in the development phases of Hydra-Ring. The most relevant topics in the scientific documentation are the probabilistic techniques, including techniques for combining failure probabilities, the correlation models which are used to describe the interdependence of load variables, the statistical distributions which are used to describe the load and strength variables, and the description of hydraulic load models. Examples of load models in the Netherlands are presented in appendices. Version Date Author Initials Review Initials Approval Initials Jan 2013 F. Diermanse State draft This is a draft report, intended for discussion purposes only. No part of this report may be relied upon by either principals or third parties. Hydra Ring Scientific Documentation 1206006-004-ZWS-0001, 2 January 2013, draft Contents 1 Introduction 5 1.1 Background 5 1.2 Purpose and scope of this document 5 1.3 Global setup of Hydra-Ring 5 1.4 The role of Hydra-Ring in the safety assessment procedure of flood defences in the Netherlands 7 1.5 Predecessors of Hydra-Ring 8 1.6 Outline 10 2 Probabilistic computation techniques for system reliability 11 2.1 Introduction 11 2.2 Basic techniques and terminology 11 2.2.1 Systems and components 11 2.2.2 Formulation of the probability of failure of a single component 12 2.2.3 Conversion between standard normal variables (U-domain) and real variables (X-domain) 14 2.2.4 Reliability index E 16 2.2.5 Linearisation of Z-functions 19 2.3 Failure probability for a single component 22 2.3.1 Introduction 22 2.3.2 Numerical Integration 23 2.3.3 Crude Monte Carlo 25 2.3.4 Monte Carlo Importance Sampling 27 2.3.5 Monte Carlo directional sampling 30 2.3.6 First-order reliability method (FORM) 32 2.3.7 Computing Į values for other methods than FORM 41 2.3.8 Rationale 43 2.4 Combining failure probabilities for components - generic methods 45 2.4.1 Introduction 45 2.4.2 Combining n components: the Hohenbichler method 45 2.4.3 Upscaling for systems with identical components: numerical integration with constant correlation 64 2.4.4 System analysis with Monte Carlo methods or numerical integration 72 2.4.5 Techniques for time and space dependent processes 73 2.5 Combining failure probabilities of components – choices and implementations in Hydra- Ring 77 2.5.1 General overview 77 2.5.2 Temporal upscaling 77 2.5.3 Combining over wind directions 87 2.5.4 Closure scenarios for flood barriers 94 2.5.5 Spatial upscaling - from cross section to flood defence segment 101 2.5.6 Combination order over mechanisms and flood defense segments 106 2.5.7 Order of combining: wind directions 108 2.6 Procedure for computing the failure probability of a flood defence system 109 2.6.1 Introduction 109 2.6.2 Procedure for FBC 109 2.6.3 Procedure for NTI 115 Hydra Ring Scientific Documentation i 1206006-004-ZWS-0001, 2 January 2013, draft 2.6.4 Procedure for APT 116 3 Hydraulic load models: generic set-up 117 3.1 Introduction 117 3.2 Hydraulic load models in probabilistic failure computations 117 3.2.1 Introduction 117 3.2.2 Hydraulic load models in probabilistic failure computations for single components 118 3.2.3 Generic, modular set-up of load models in Hydra-Ring 120 3.3 Statistical distribution functions of random variables 121 3.3.1 Generic description of the application of distribution functions 121 3.3.2 Standard distribution functions and parameter values 127 3.3.3 Temporal scaling of statistical distribution functions 127 3.3.4 Statistics of durations 129 3.4 Correlation models 131 3.4.1 Introduction 131 3.4.2 Correlations between random variables 132 3.4.3 Correlation in time and space 137 3.5 Hydrodynamic models 138 3.5.1 Simulating water levels and waves in an entire water system 138 3.5.2 Models for quantification of local (corrections on) hydraulic loads 139 3.5.3 Transformation module for a breakwater 143 3.5.4 Spatial interpolation methods 146 4 Hydraulic load models for primary water systems in the Netherlands 147 4.1 Introduction 147 4.2 System characteristics 149 4.2.1 Upper rivers 149 4.2.2 Rhine Meuse delta 149 4.2.3 Lakes 149 4.2.4 Lake delta 149 4.2.5 Coastal zone; dikes 150 4.2.6 Oosterschelde 150 4.2.7 Coastal zone; dunes 150 4.3 Random variables 150 4.4 Load model for the upper rivers and tidal rivers 154 4.4.1 Distribution functions of random variables 154 4.4.2 Hydrodynamic models 160 4.5 Load model for the lakes 160 4.5.1 Distribution functions of random variables 160 4.5.2 Hydrodynamic models 162 4.6 Load model for the lake delta 162 4.6.1 Distribution functions of random variables 162 4.6.2 Hydrodynamic models 165 4.7 Load model for the coastal dikes 165 4.7.1 Distribution functions of random variables 165 4.7.2 Hydrodynamic models 172 4.8 Load model for the Oosterschelde 180 4.8.1 Distribution functions of random variables 180 4.8.2 Hydrodynamic models 181 4.9 Load model for the coastal dunes 183 ii Hydra Ring Scientific Documentation 1206006-004-ZWS-0001, 2 January 2013, draft 4.9.1 Distribution functions of random variables 183 4.9.2 Hydrodynamic model 189 4.10 Spatial correlations between load models of different regions 192 5 Failure mechanisms 198 5.1 Introduction 198 5.2 Models of failure mechanisms in probabilistic failure computations 199 5.2.1 Introduction 199 5.3 Overtopping and Overflow 199 5.3.1 Limit State Function Overflow 201 5.3.2 Limit State Function Overtopping 201 5.3.3 Introduction to the overtopping discharge models 202 5.3.4 Overtopping: PC-overslag approach 203 5.3.5 Overtopping: PC-Ring approach 214 5.3.6 Critical overtopping discharge (CIRIA model) 216 5.3.7 Relevant variables for overtopping and overflow failure mechanisms 218 5.4 Failure mechanism ‘Macrostability’ 220 5.4.1 Introduction 220 5.4.2 Deelmechanisme Stab: Afschuiving MProStab 220 5.4.3 Deelmechanisme StPf: Kans op falen na afschuiving 223 5.4.4 Variabelen voor het mechanisme afschuiving 224 5.5 Pipsing and heave’ 224 5.5.1 Mechanismebeschrijving 224 5.5.2 Deelmechanisme ZfOPBA: Opbarsten 225 5.5.3 deelmechanisme ZfPIPE: Piping 226 5.5.4 Variabelen voor het mechanisme opbarsten/piping 228 6 Statistical distribution functions 230 6.1 Introduction 230 6.2 General method to avoid influence of rounding errors 230 6.3 Uniform distribution 230 6.4 Normal distribution 232 6.5 (Shifted) Lognormal distribution 233 6.6 (Shifted) Exponential distribution 234 6.7 Gumbel distribution 235 6.8 Weibull distribution 237 6.9 Rayleigh distribution 237 6.10 Pareto distribution 237 6.11 Triangular distribution 237 6.12 Linear and log-linear interpolation 237 6.13 Conditional Weibull distribution 238 6.14 Modified Gumbel 239 6.15 Truncated Gumbel 241 7 References 243 Appendices A Dutch Hydraulic Boundary Conditions – version TMR2006 1 A.1 Overview of stochastic input variables and regions 1 Hydra Ring Scientific Documentation iii 1206006-004-ZWS-0001, 2 January 2013, draft A.1.1 TMR2006 parameters 3 iv Hydra Ring Scientific Documentation 1206006-004-ZWS-0001, 2 January 2013, draft 1 Introduction 1.1 Background In compliance with the Dutch Water Act (‘Waterwet, 2009’), the safety of the Dutch primary sea and flood defences must be assessed periodically for the required level of protection. In the Netherlands, the safety assessment of flood defences is carried out by evaluating dike sections, dune transects and structures individually, using representative hydraulic load conditions in combination with mathematical descriptions of failure mechanisms. From 2017 onwards, the evaluation will be done for entire ‘dike rings’, using the probability of flooding of he protected area as the main criterion. A dike ring area is an area that is protected from flooding by a dike ring, i.e. a closed system of flood defences (dikes, dunes, hydraulic structures, barriers). The differences with respect to the present assessment are twofold: - Safety assessment per dike-ring in stead of per dike stretch; - Quantification of the probability of failure instead of an assessment ‘dike stretch is safe or unsafe’. The advantage of the new approach is that it provides valuable insights in the weaker spots in the flood defence chain and, consequently, on the effciency of investments of improvement works in terms of “risk reduction per invested euro”. The computation of failure probabilities for dike rings is a complex matter. Over the last decades, significant research was carried out to explore the possibility carrying out a safety assessment based on failure probabilities for all dike ring areas in the Netherlands.