Question

Explain the embankment in mathematics near a well and what is formula of volume of embankment

Answer 1

Answer:

The prediction and calculation of the peak outflow discharge resulting from embankment dam breach due to overtopping is fundamental (Hooshyaripor et al., 2015, Mohamed and El-Ghorab, 2016, Singh, 1998, Singh, 1996, Singh, 1982, Tabrizi et al., 2015). Predicting such flow provides a perfect tool in drawing the rescue scenario to safeguard against loss of life and property damage due to resulting hazards (Baker et al., 1999). Empirical, physically based models are widely used by many researchers to predict the peak outflow discharge due to embankment dam breach by overtopping flow (ASCE/EWRI, 2011). These models are simple models and can be developed by employing certain equations that relate the breach outflow discharge hydrograph to the breach parameters using regression analysis technique and case study data. The breach parameters include the embankment dam height, reservoir storage volume, or a combination of these two parameters (Ali and Tarkan, 2014).

Zhao (2016) listed and discussed most of the regression equations that are used to predict the peak flow discharge due to embankment dam breach experienced overtopping flow. Saberi and Zenz (2015) developed a regression based relationship that relates the peak flow discharge with the height and volume of water in the reservoir upstream of the embankment dam. Wahl (2004) improved the accuracy of the overtopping breach peak outflow discharge equation by incorporating a parameter that expresses the role of soil erodibility. Thornton et al. (2011) added other parameters, such as the length and width of the embankment for improving the performance of predicting the peak flow discharge by regression equation. Gupta and Singh (2012) summed up both the length and width variables of the embankment in conjunction with the embankment height and volume of reservoir water upstream of the embankment to reduce the prediction error and improve the prediction accuracy. Pierce et al. (2009) reviewed the published regression equations in the literature and came up with a new developed expression that relating peak outflow discharge as a function of the height and/or volume of reservoir water upstream of the embankment dam at failure. The developed equation gives an encouragement for practical applications where a best estimate of the peak-breach flow discharge is desired.

The volume of water behind the embankment dam is a dominant variable in most of the regression equations that are used to predict the peak breach flow discharge (Evans, 1986, Hagen, 1982, Pierce et al., 2009, Zhao, 2016). However, the previously developed equations for the peak breach flow discharge due to overtopping assumed that the whole reservoir volume of water becomes empty during the failure time which is not true especially for embankment dam constructed from cohesive soil materials. As for cohesive soil embankment dam, the failure is not complete; a remaining vertical head-cut wall in the upstream side exists. This remaining vertical head-cut averts part of the reservoir volume of water to be spelled from the embankment dam breach. Also, to find the area under the outflow hydrograph curve, earlier researchers approximated this area by dividing the curve into simple geometric shapes that are easy to be calculated (e.g., a rectangle and two equal triangles) which might not be applicable to all the embankment dams. The area under the outflow hydrograph curve represents the total volume of spelled water out of the embankment dam breach.

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