1、 I 中文 1300 字 Maritime Engineering 159 December 2006 lssue MA4 Pages 137-140 Specifying seawall crest levels using a probabilistic method Probabilistic methods provise a powerful frame word for the design of coastal defenses. However, present knowledge of the behavior of these structures is insuffici
2、ent to assess their safety against specific types of failure, such as excessive overtopping by wave action. However, the choice of overtopping model used to describe the failure is crucial to the outcome of the assessment. The paper illustrates the different results obtained from two models used to
3、describe wave overtopping. The models are implemented in a software package known as PARASODE-BALI which employs the Level First Order Reliability Method(FORM)for the design and safety assessment of coastal structures. For the two overtopping models provide similar results. However, the differences
4、are much greater for the small discharges commonly respired to ensure the safety, the two overtopping models provide similar results. However, the differences are much grater for the small discharges commonly repaired to ensure the safety of people and property in urban areas. 1. INTRODUCTION In the
5、 design lf seawalls, it is important to strike the correct balance II between satisfying the structural and functional requirement of the project, avoiding unnecessary expense, and having undesirable impacts on the surrounding environment. one important element in such considerations is the choice o
6、f the seawall crest level(CL)which is necessary to limit to permissible valves the mean wave overtopping discharge per unit length of seawall (Q).Basic variable which are relevant to the choice of CL are(Fig.1):the angle of the seawall front slope measured from horizontal( ),the still-water level(SW
7、L) and the characteristics of the incident waves, such as the significant wave height(Hs) and the peak wave periled (Tp). Probability and consequences f failure, while coping to some degree, with such factors as the incident wave conditions. Besides listing many of the wide range of consequences and
8、 potential effects of wave overtopping in urban areas, this paper provides an example of the use of a probabilistic method in determining the crest level of a seawall subject to the action of a combination of wind-sea and swell (bimodal wave conditions).The purpose is to illustrate the importance in
9、 probabilistic design of the choice of model rest to describe failure. The degree of confidence in the determined crest level will vary depending upon the confidence that can be assigned to the overtopping model and to the statistical distributions adopted for the random variables which are employed
10、 in the model. 2. SINGLE FAILURE MODE PROBABILITY ANALYSIS In probabilistic methods, theoretical expressions or empirical formulae describing single failure modes may be used to define a failure function ,Z=Z(X1,.,XN),where Xi ,i=1,.,N are the N basic variables of the problem (e.g. water level, wave
11、 conditions, structure dimensions and material properties).positive values of Z imply the absence of failure and zero or negative values represent failure in the mode being considered, the surface defined by Z=0 is Calles the failure surface. Variables whose increase leads to an increase in Zaire de
12、signated as resistance variables III whereas those in Z are designated as resistance variables whereas those whose increase leads to a decrease in Z are called load variables. Since some of the resistance or load variables are random (and may even be correlated), the value of the failure function is
13、 also a random variable, and the probability of failure (Pf),during a specified reference period, can be expressed as 0 110Z NXXfdXdXfZPP N （ 1） In which fx1.xn is the joint probability density function of the basic variable X1. Xn. Expiration (10forms the mathematical basis of probabilistic analysi
14、s, with the exception of simple failure functions of just a few random variables, the multiple integrations cannot be performed analytically abed have to be approximated in some way. This is the aim of the various probabilistic methods； these methods are often classified according to the types of ca
15、lculations performed and the approximations made. Three levels are commonly distinguished. They are listed here in order of decreasing accuracy and complexity. （ a） Level :the full distribution approach. This method provides an exact probabilistic analysis, using full joint probability density funct
16、ions including the correlations among the variable. Use is made of numerical integration or, more commonly, sampling techniques. （ b） Level :the limit state approach. Approximation methods are applied in which the generally non-normal and/or correlated variables are transformed into Normal independe
17、nt variables. Reliability indices are used as measures of the reliability. （ c ） Level :the limit state approach. This level involves calculations uncharacteristic values and partial load and resistance factors. The factors represent, for example, the ratio of load at failure to a permissible working load.
