Yield-acceleration grid of a displacement scenario

Builds the log-spaced yield accelerations at which the displacement curves of one scenario are evaluated, from the calibration ranges of the displacement models and the mean peak ground acceleration of the scenario.

Usage

buildKyGrid(PGA, n)

Arguments

PGA

One finite positive mean peak ground acceleration of the scenario in g.

n

Number of grid points, one positive integer (the displacement products use 30).

Value

A numeric vector of n increasing yield accelerations in g.

Mathematics

For \(n > 1\), $$k_{y,i} = \exp\left(\ln 0.01 + \frac{i - 1}{n - 1} \left[\ln \max(\overline{PGA}, 0.80) - \ln 0.01\right]\right), \quad i = 1, \dots, n$$ in g. For \(n = 1\) the grid is the lower bound alone, \(k_{y,1} = \exp(\ln 0.01)\), whatever the PGA. The lower bound 0.01 g is the lowest calibration point of BM17; the upper bound is the mean peak ground acceleration of the scenario, beyond which a rigid block does not slide, extended to the 0.80 g calibration ceiling of BM17 for low-intensity scenarios. The displacement products take \(\overline{PGA}\) as the mixture mean \(\sum_k w_k e^{\mu_k + \sigma_k^2/2}\) at zero period of an analytic spectrum, or the "mean" row at the smallest period of a quantile spectrum.

Examples

buildKyGrid(PGA = 0.5, n = 30)
#>  [1] 0.01000000 0.01163118 0.01352844 0.01573517 0.01830186 0.02128722
#>  [7] 0.02475955 0.02879828 0.03349580 0.03895957 0.04531458 0.05270620
#> [13] 0.06130353 0.07130325 0.08293409 0.09646214 0.11219685 0.13049819
#> [19] 0.15178479 0.17654363 0.20534109 0.23883592 0.27779437 0.32310764
#> [25] 0.37581233 0.43711410 0.50841530 0.59134701 0.68780637 0.80000000