Paired embankment geometries from height, truncation ratio and slope

Usage

buildGeometry(Hs, lo, s)

Arguments

Hs: Positive heights in metres.
lo: Truncation ratios strictly between 0 and 1, aligned with Hs.
s: Positive horizontal-to-vertical slopes, aligned with Hs.

Value

A data.table with IDg, b, bmax, s, Hs and beta.

Mathematics

The truncation ratio of the shear beam is \(\lambda = b / (2 H_s s + b)\) for a berm width \(b\), height \(H_s\) and horizontal-to-vertical slope \(s\); inverting it gives \(b = 2 H_s s / (1/\lambda - 1)\). The base width is \(b + 2 H_s s\) and the slope angle \(\beta = \arctan(1/s)\) in degrees. Widths and heights are rounded to metres and slopes to two decimals, as in newmark 1.7.1; the identifier IDg is S followed by the rounded height.

Examples

buildGeometry(Hs = c(10, 120), lo = c(0.35, 0.075), s = c(2.5, 3.5))
#>       IDg     b  bmax     s    Hs     beta
#>    <char> <num> <num> <num> <num>    <num>
#> 1:    S10    27    77   2.5    10 21.80141
#> 2:   S120    68   908   3.5   120 15.94540