دانلود رایگان مقاله برآورد تخلیه متغیر زمان و حجم تجمعی در سرریزی امواج فردی

Abstract

The time variation of discharge per unit dike length in an overtopping wave is characterized by a rapid increase to a maximum discharge that can be several times greater than the mean discharge, followed by a slower decrease in discharge until overtopping for that wave ceases. Measurements of wave overtopping acquired during the European small-scale FlowDike experiments were analyzed to identify individual overtopping waves using a two-step “supervised” procedure that combines the best features of automated wave determination augmented with manual error correction and validation. The result was a well-vetted data set of 5799 individual overtopping waves represented by time-series of flow depth and velocity near the seaward edge of the dike crest. The model dikes had planar seaward dike slopes of either 1V-on-3H or 1V-on-6H. Instantaneous discharge time series were calculated as the product of the flow thickness and velocity time series. In this paper, the two-parameter Weibull probability density function is adopted to represent the time variation of instantaneous discharge in an overtopping wave. Values of the Weibull scale factors, a, and shape factors, b, are obtained through nonlinear best-fitting of the Weibull equation to all 5799 waves. Best fits were also performed for the simpler Rayleigh version of the Weibull equation when b = 2. An empirical equation was developed for scale factor, a, in terms of predicable parameters of the overtopping waves. The shape factor, b, could not be successfully parameterized, but it was found that the shape factors are narrowly distributed about the Rayleigh value of b = 2. Predictions of time-varying discharge made using the Weibull equation with b = 2 (i.e., Rayleigh equation) are assessed in terms of the root-mean-square errors between predictions and measurements. The estimates are reasonable for most of the waves. The capability to estimate the time-varying discharge in individual overtopping waves will improve the art of full-scale wave overtopping simulation, and the resulting empirical equations will contribute to methodologies aimed at quantifying the resiliency of dike erosion protection.

9. Conclusions

This study examined time series of instantaneous discharge associated with individual overtopping waves that were measured at the seaward edge of a laboratory-scale dike crest for incident wave conditions impinging on either a 1-on-3 or 1-on-6 planar seawardside dike slope. The shapes of the time-varying discharge and timevarying cumulative volume (per unit dike length) were well described by the two-parameter Weibull equations, as shown by nonlinear best- fits to measurements from 5799 overtopping waves. The related oneparameter Rayleigh equations with shape factor, b = 2, did almost as well. A reasonable empirical equation was determined that related the best-fit values of the theoretical Weibull scale factor, a, to the individual overtopping wave volume and the seaward-side slope of the dike. However, similar success was not achieved in finding a suitable empirical relationship for the best-fit values of theWeibull shape factor, b. However, it was noted that the values of the best-fit Weibull shape factors were distributed about a peak value in the vicinity of b = 2, which is the shape factor for the related Rayleigh version of the Weibull equations. Consequently, it is proposed that the time-varying discharge per unit dike length (Eq. 10) and the time-varying cumulative volume per unit dike length (Eq. 11) use a shape factor of b = 2, along with the scale factor, a, given by Eq. (22). Assessment of the root-mean-square errors between predictions and measurements indicated the one-parameter Rayleigh versions of the equations provided reasonable estimates of the time-varying discharge, and an empirical equation provided good predictions of the maximum discharge in an individual overtopping wave. The new equations presented in this paper strictly apply at the seaward edge of the dike crest on dikes having planar seaward-side slopes ranging between 1-on-3 to 1-on-6 (vertical-on-horizontal). These equations may prove useful for additional refinements to the science of full-scale wave overtopping simulation with the goal of providing even more realistic replication of full-scale wave overtopping by better representing the time-varying discharge at the seaward edge of the dike crest. The new formulations can also be applied in the cumulative excess work methodology for assessing the erosional resiliency of earthen dike landward-side slopes subjected to wave overtopping. Finally, it would be possible to use the developments in this paper to provide estimates of the time variation of shear stress acting on levee and dike crests for individual waves, or to evaluate risk to people or infrastructure due to overtopping waves. List of symbols.