behavior, implying a foreshore which receded or accreted uniformly along its 

 full length. In the model, the transport rate is linearly extended from the 

 end of the surf zone to the runup limit. (The surf zone is arbitrarily ended 

 at a depth of 0.3-0.5 m.) However, as the foreshore erodes, the slope 

 steepens and a pronounced scarp or step develops. Eventually, if erosive 

 waves act for a sufficiently long time, the slope of the step will exceed the 

 angle of initial yield (Allen 1970). In Part IV, time evolution of profile 

 slopes was analyzed and indications of avalanching were found if profile 

 slopes exceeded a value of 28 deg on average. This value is used in the 

 numerical model to limit the growth of slopes along the profile. 



419. Since the transport relationships do not explicitly describe 

 avalanching, an algorithm was developed to simulate avalanching if the profile 

 slope steepened excessively. If the angle of initial yield is exceeded, the 

 profile slope decreases to a lower, stable value known as the residual angle 

 after shearing (Allen 1970). Inspection of the LWT profiles indicated that a 

 stable slope appeared to be reached at a value somewhat smaller than 22 deg on 

 average. In the numerical model the residual angle after shearing was 

 therefore set to 18 deg. The reason for this ambiguity was the difficulty of 

 determining the residual angle after shearing from the profile data; instead, 

 Allen's experimental results were used where the dilatation angle (difference 

 between angle of initial yield and residual angle after shearing) was found to 

 be in the range of 10-15 deg for sand. A dilatation angle of 10 deg was 

 chosen, implying a residual angle after shearing of 18 deg. 



420. If avalanching occurs in the numerical model, that is, if the 

 angle of initial yield is exceeded, sand is redistributed into neighboring 

 cells so that the slope adjusts to the residual angle after shearing. Once 

 avalanching has started in one cell, it proceeds along the grid until a point 

 is reached where the slope is less than the residual angle after shearing. A 

 definition sketch is shown in Figure 56 illustrating a number of calculation 

 cells and one cell where the angle of initial yield is exceeded (cell 1). 

 Depths after avalanching, denoted with a prime in Figure 56, can be determined 

 once the change in depth in the cell where avalanching is initiated is known. 

 The change in depth in the first cell is given by 



171 



