realistic conditions ofH, and T„ varying with time, the rate of damage increase dS/dt is 

 obtained from Equation 6.10 as 



^ = a^bN^T^^'t'-' (6.12) 



at 



which is assumed to be valid at arbitrary time t. To apply Equation 6.12 for H^ and T^ 

 varying with time t, the relation must be integrated numerically with an arbitrary initial 

 value of S. For practical applications, the values of H, and T„ may be assumed to be 

 constant for a short duration. Integration of Equation 6. 12 for the duration of constant 

 Hj and T„ lasting r = /„ to r = t„^, yields the mean damage at arbitrary time t 



5(0 = 5(/„) + aXK\t " - 1„') for t,,<t< /„^, (6.13) 



where S(,t„) = known damage at f = t„. Use of Equation 6. 13 for each interval of 

 constant H^ and T„ in sequence allows one to compute S(t„) for incident wave 

 conditions represented by H^ and T„ varying with time. Alternatively, representing the 

 irregular waves at the toe of the slope using spectral parameters as shown in Equation 

 6.1 1 yields the equation 



5(0 = 5(r„) + a^NlT^-\t " - 1„') for t,^<t< r„,, (6.14) 



Equations 6.13 and 6.14 are valid for an undamaged structure (5 = at r = 0) or 

 damaged structure, S{tf^ = 5, at / = t^. Using the coefficients predicted by Van der 

 Meer's data, a^ = 0.003 and b = 0.5. Equation 6. 13 follows the general trend of the data 



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