Comprehensive Risk Assessment for Natural Hazards - Planat

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Comprehensive risk assessment for natural hazards guaranteed only if the probability of failure of the system is less than or equal to 10 –7 per year. The joint distribution of storm-surge level, basin level and wave energy was developed for The Netherlands as follows. Frequency analysis was applied to available storm-surge-level data. Knowledge of the physical laws governing the stormsurge phenomenon was used to determine whether extreme water levels obtained by extrapolation were physically realistic.A conditional distribution between storm-surge levels and basin levels was derived from a simple mathematical model of wind set-up and astronomical tide applied to simulation of different strategies for closing the barrier gates. The basin level was found to be statistically independent of the wave energy.A conditional distribution between storm-surge levels and wave energy could not be derived because of lack of data. Therefore, a mathematical model was developed considering the two sources of wave energy: deep-water waves originating from the North Sea and local waves generated by local wind fields. The advanced first-order second-moment reliability analysis method (Ang and Tang, 1984, p. 333-433; Yen et al., 1986) was applied to determine the failure probability of each major system component of the storm-surge barrier. An advantage of this method is that the contribution of each basic variable (model parameters, input data, model correction or safety factors, etc.) to the probability of failure of a given component can be determined. Thus, problematic aspects of the design can be identified and research effort can be directed to the variables that have the greatest effect on the probability of failure. Application of the failure criterion of 10 –7 to the design of each major component of the storm-surge barrier was a substantial step in achieving a societally acceptable safety level. However, the appropriate approach is to determine the safety of the entire barrier as a sea-defence system. Thus, the probability of system failure was determined as a function of the probability of component failure, and the probability of failure resulting from mismanagement, fire and ship collision through application of fault-tree analysis (Ang and Tang, 1984, p. 486-498). The fault tree for determining the probability that parts of Zeeland are flooded because of failure of components of the barrier, mismanagement, and/or malfunction of the gates is shown in Figure 8.1. By using the fault tree, the design of the barrier was refined in every aspect and the specified safety criterion of 10 –7 per year was achieved in the most economical manner. Through application of sophisticated probabilistic techniques, Dutch engineers were able to reduce the design load for the storm-surge barrier by 40 per cent relative to traditional design methods and still achieve a societally acceptable failure probability or hazard level. In this case, the societally acceptable hazard was defined by setting the fatality rate equal to levels resulting from accidents in The Netherlands. Thus, the completed structure reduced the risk resulting from storm surges to fatality rates accepted by the people of The Netherlands in their daily lives. It could be considered that the application of the new design procedures resulted in an increase in the hazard level resulting from storm surges faced by society relative to the application of the previous design standards. However, the previous design standards were implicitly set without any consideration of the consequences of a storm surge and societally acceptable hazard levels. The population in the southwestern region of The Netherlands to be protected by the storm-surge barrier was already facing a substantial hazard. Thus, the question was to what level should the hazard be reduced? The Dutch Government decided that people in The Netherlands would be willing to accept a possibility of dying because of a failure of the sea defences that was equal to the probability of dying because of an accident. This resulted in substantial savings relative to the use of the implicit societally acceptable hazard level. The key point of this example is that when faced with the construction of a large, complex and expensive structure for the protection of the public, the Dutch Government abandoned implicit societally acceptable hazard levels and tried to determine real, consequence-based societally acceptable hazard levels. 8.3 MINIMUM LIFE-CYCLE COST EARTHQUAKE DESIGN Earthquake-resistant design and seismic-safety assessment should explicitly consider the underlying randomness and uncertainties in the earthquake load and structural capacity and should be formulated in the context of reliability (Pires et al., 1996). Because it is not possible to avoid damage under all likely earthquake loads, the development of earthquake-resistant design criteria must include the possibility of damage and an evaluation of the consequences of damage over the life of the structure. To achieve this risk assessment for structures in earthquake-prone regions, Professor A. H-S. Ang and his colleagues at the University of California at Irvine have proposed the design of earthquake-resistant structures on the basis of the minimum expected total life-cycle cost of the structure including initial (or upgrading) cost and damage-related costs (Ang and De Leon, 1996, 1997; Pires et al., 1996) and a constraint on the probability of loss of life (Lee et al., 1997). The minimum life-cycle cost approach consists of five steps as follows (Pires et al., 1996; Lee et al., 1997). (1) A set of model buildings is designed for different levels of reliability (equal to one minus the probability of damage, p f ) or performance following the procedure of an existing design code. For reinforced concrete buildings, this is done by following the design code except that the base-shear coefficient is varied from code values to yield a set of model buildings having different strengths, initial costs (construction or upgrading), and probabilities of damage. (2) A relation between the initial cost of the structure and the corresponding probability of damage under all possible earthquake loads is established from the designs made in step 1. (3) For each design, the expected total cost of structural damage is estimated as a function of the probability of damage under all possible earthquake loads and is expressed on a common basis with the initial cost. The damage cost includes the repair and replacement cost, C r , loss of contents, C c , economic impact of structural 79
80 Chapter 8 — Strategies for risk assessment — case studies PARTS OF ZEELAND ARE FLOODED 05 BASIN LEVEL >N.A.P. -4.3 SCHOJVEN AND/OR N-BEVELAND ARE FLOODED DISCHARGE VIA COMPLETELY FAILING 558 DISCHARGE VIA PARTIALLY FAILING 558 DISCHARGE VIA FAILING ABUTM (FAILING TDPL) DISCHARGE VIA FAILING ABUTM (FAILING PIER) DISCHARGE VIA 558 IN OPERATION DISCHARGE VIA CLOSABLE PART DISCHARGE VIA DAM SECTION AND FG = O FAILING CONTROL FAILING GATE SLIDING SYSTEM FAILING OF 4 OR MORE PIERS CHAIN REACTION A FAILING OF DAM SECTION CHAIN REACTION B FG = 1.2.3.4 FAILING MANAGEMENT DISCHARGE VIA • DAM SECTION • LEAKAGE • PIPING • WAVE OVER TOPPING LOADS ON PIERS > BEARING CAP FAILURE OF 1 PIER FAILING GATE SLIDING SYSTEM FAILING FOUNDATION LOADS ON FOUNDATION > BEARING CAP DEFORMATION OF SUBSOIL > EXPECTED FAILING OF SUBSOIL SUPP. FAILING OF SILL SUPPORT FAILURE OF SUBSOIL FAILURE OF FOUNDATION MATTRESS FAILURE BED PROTECTION FAILURE OF MATTRESS OTHER REASONS FAILING OF SILL CORE FAILURE OF BED PROTECTION. OTHER REASONS THAN DISCHARGE VIA 1 FG FAILURE OF SILL CORE OTHER REASONS DISCHARGE VIA 1 FAILING GATE FAILURE OF UPPER- AND/OR SILLBEAM FAILING GATE BECAUSE OF COLLAPSED UPPER- AND/OR SILLBEAM FAILING GATE LOADS ON GATE > BEARING CAP 1 GATE DOES NOT SLIDE GATE COLLAPSES UPPER BEAM COLLAPSES SILL BEAM COLLAPSES SHIPS COLLISION FAILURE GATE SLIDING SYSTEM GATE IS STUCK FAILURE OF BEARING CONSOLE LOADS UPPER BEAM > BEARING CAP LOADS SILL BEAM > BEARING CAP FAILING CONTROL DEFORMATIONS > EXPECTED EXCESS OF TOLERANCES DEFORMATION SUBSOIL > EXPECTED Figure 8.1 — Fault tree for computation of the failure probability of the Eastern Schedlt storm-surge barrier in the Netherlands (after Vrijling, 1993) damage, C ec , cost of injuries resulting from structural damage, C in , and cost of fatalities resulting from structural damage, C f . (4) The expected risk of death for all designs under all likely earthquake intensities also is expressed as a function of the probability of damage. (5) A trade-off between initial cost of the structure and the damage cost is then done to determine the target reliability (probability of damage) that minimizes the total expected life-cycle cost subject to the constraint of the socially acceptable risk of death resulting from structural damage. Determination of the relation between damage cost and the probability of damage in step 3 is the key component of the minimum life-cycle-cost earthquake-design method. The estimate of the damage cost is described mathematically as given by Ang and De Leon (1997) and summarized in the following. Each of the damage-cost components will depend on the global damage level, x,as: C j = C j (x) (8.1) where j = r, c, ec, in and f are as previously described in item 3. If the damage level x resulting from a given earthquake with
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CONTENTS AUTHORS AND EDITORS . . .
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AUTHORS AND EDITORS AUTHORS: Chapte
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Chapter 1 INTRODUCTION 1.1 PROJECT
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Comprehensive Risk Assessment for Natural Hazards - Planat

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