90 



20,000 years or so, shown in Fig. 7.1. Sea level rose rapidly (about 

 0.8 m/century) from 20,000 years before present (BP) to about 6,000 years 

 BP. Over the last 6,000 years, sea level has risen at the greatly reduced 

 rate of 0.08 m/century, which is roughly consistent with estimates of 

 0.11 m/century based on tide gage data over the last century. As will be 

 discussed later, the earlier much more rapid rise of sea level may still be 

 having an effect. 



The most widely applied engineering approach to predicting shoreline 

 response to sea level rise is the so-called Bruun Rule. This rule 

 considers: a) the active profile to always be in equilibrium, and to retain 

 its relative position to sea level, and b) the active portion of the 

 profile to be limited by the "depth of effective motion" seaward of which 

 no sediment exchange occurs. With the above assumptions, when sea level 

 rises a vertical distance, S, the entire active profile must rise also by 

 S, requiring a volume ¥g^, of sand per unit beach length 



AVr = SL (7.1) 



in which L is the offshore length of active profile. This required sand is 

 provided by a profile retreat, R, over a vertical distance, h-A-+B (see 

 Fig. 7.2). The volume generated by this retreat is 



A¥+ = (h* + B)R (7.2) 



and equating the two volumes , the retreat R can be shown to be 



R = S n — ^ —n (7.3) 



h* + B tanS ^ ^ 



in which 6 is the average slope of the active profile out to its limit of 

 active motion. Fig. 7.3. From Eq. 7.3, it is clear that beach profiles 

 with mild slopes would experience greater recessions due to a given sea 

 level rise than would steeply sloping profiles. 



