ASSIGNMENT 11   The crest level of embankment over a reach is described by a Gaussian distribution with mean 5 and standard deviation 0

ASSIGNMENT 11

1. The crest level of embankment over a reach is described by a Gaussian distribution with mean 5 and standard deviation 0.5. This is often written as N(5,0.5). Monthly maximum water levels along the reach obey N(3,1). What is the probability of flooding?

2. For a caisson breakwater, the limit state function can be given as

g = f(W-U) –F_h

where W = Overall weight (Weight of material – buoyant force), U = uplift force, f = friction factor, and F_h = horizontal wave forces.

For a certain design, data have been obtained in a variety of ways, and the following estimates are available:

Variable                                               m                                                             s

f                                               0.636                                       0.095

W (KN/m width)                      2331                                        45.7                            

U (KN/m width)                       377                                          90.5

F_h (KN/m width)                                              714                                          171.4

1. Estimate the probability of failure by the Mean Value Approach. (Note: this would be the first step in part 2 below, anyway!)
2. Estimate the probability of failure by the iterative method (which, by the way, is called the “Design Point Approach” or the “First Order Reliability Method (FORM)”). How do the two failure probabilities (MVA and FORM) compare? Plot the Guassian distribution for the limit state function, after obtaining the m and s for the possible values of the g.
3. Now change the values to the ones from the solved problem in your notes and repeat the above calculations. What’s the difference in failure probability relative to the dataset given above? Can you suggest a reason?