Getting started with newmark

Overview

newmark implements a four-workflow pipeline for probabilistic seismic performance analysis of slopes and embankments:

Dynamic Site Response — compute the fundamental period Ts and site-amplified UHS from the soil profile (getSiteProperties, getCylinderRoots, fitSaF).
Hazard import — import PSHA output from OpenQuake (buildGMDP).
Displacement curves — Monte Carlo Newmark ensemble Dn(ky) (getDnKy, fitDnCurve).
Seismic coefficient — invert ensemble draws to kmax(d*) (invertDnDraws).

This vignette demonstrates Workflows 3 and 4 using the bundled example dataset. For the full pipeline see the pipeline vignette (vignette("pipeline", package = "newmark")).

Example dataset

uhs.csv is a site-amplified uniform-hazard spectrum included with the package: NBCC hazard model, Vs30 = 560 m/s, TR = 10 000 yr, with quantile levels 0.05–0.95 and mean (Mode B input).

library(newmark)
library(data.table)
#> 
#> Attaching package: 'data.table'
#> The following object is masked from 'package:base':
#> 
#>     %notin%

uhs <- fread(system.file("extdata", "uhs.csv", package = "newmark"))
uhs[p %in% c("0.16", "mean", "0.84") & Tn <= 0.2, .(Tn, p, Sa)]
#>        Tn      p      Sa
#>     <num> <char>   <num>
#>  1: 0.000   0.16 0.12513
#>  2: 0.000   0.84 0.21655
#>  3: 0.000   mean 0.18228
#>  4: 0.050   0.16 0.39859
#>  5: 0.050   0.84 0.69551
#>  6: 0.050   mean 0.54639
#>  7: 0.075   0.16 0.43086
#>  8: 0.075   0.84 0.73093
#>  9: 0.075   mean 0.57871
#> 10: 0.100   0.16 0.41504
#> 11: 0.100   0.84 0.72926
#> 12: 0.100   mean 0.56767
#> 13: 0.120   0.16 0.39547
#> 14: 0.120   0.84 0.67237
#> 15: 0.120   mean 0.53474
#> 16: 0.150   0.16 0.36396
#> 17: 0.150   0.84 0.61739
#> 18: 0.150   mean 0.49354
#> 19: 0.180   0.16 0.32485
#> 20: 0.180   0.84 0.54772
#> 21: 0.180   mean 0.44060
#> 22: 0.200   0.16 0.29781
#> 23: 0.200   0.84 0.49987
#> 24: 0.200   mean 0.41868
#>        Tn      p      Sa
#>     <num> <char>   <num>

Parameters

# Ts: fundamental period of the sliding mass (s).
# In production, derived from getSiteProperties() + getCylinderRoots()
# using the soil USCS profile and slope geometry (Ishihara 1996,
# Gazetas & Dakoulas 1985). Here set to a representative value.
Ts <- 0.60

# Mw: moment magnitude from PSHA disaggregation.
Mw <- 6.8

# Ensemble weights (0 = model inactive).
weights <- c(AM88 = 1, JB07 = 0, BT07 = 1, SR08 = 1, BM17 = 0, BM19 = 1)

# Displacement targets (cm).
Da <- c(0.5, 2.5, 5.0, 25.0)

Workflow 3 — Displacement curve Dn(ky)

ky     <- getDnKy(uhs, Ts = Ts)
result <- fitDnCurve(
  uhs     = uhs,
  ky      = ky,
  Ts      = Ts,
  Mw      = Mw,
  NS      = 200,
  weights = weights
)

result$curve[IDn == "ensemble" & p == "mean", .(ky, Dn)]
#>             ky           Dn
#>          <num>        <num>
#>  1: 0.01000000 1.004869e+02
#>  2: 0.01163118 8.682039e+01
#>  3: 0.01352844 7.452751e+01
#>  4: 0.01573517 6.349283e+01
#>  5: 0.01830186 5.362009e+01
#>  6: 0.02128722 4.482754e+01
#>  7: 0.02475955 3.704470e+01
#>  8: 0.02879828 3.020985e+01
#>  9: 0.03349580 2.426759e+01
#> 10: 0.03895957 1.916588e+01
#> 11: 0.04531458 1.485252e+01
#> 12: 0.05270620 1.127147e+01
#> 13: 0.06130353 8.360034e+00
#> 14: 0.07130325 6.047943e+00
#> 15: 0.08293409 4.259055e+00
#> 16: 0.09646214 2.914419e+00
#> 17: 0.11219685 1.933913e+00
#> 18: 0.13049819 1.242371e+00
#> 19: 0.15178479 7.765737e-01
#> 20: 0.17654363 4.811288e-01
#> 21: 0.20534109 3.038794e-01
#> 22: 0.23883592 1.976599e-01
#> 23: 0.27779437 1.316048e-01
#> 24: 0.32310764 8.820158e-02
#> 25: 0.37581233 5.853126e-02
#> 26: 0.43711410 3.841309e-02
#> 27: 0.50841530 2.493600e-02
#> 28: 0.59134701 1.601435e-02
#> 29: 0.68780637 1.017661e-02
#> 30: 0.80000000 6.400033e-03
#>             ky           Dn
#>          <num>        <num>

Workflow 4 — Seismic coefficient kmax(d*)

kmax <- invertDnDraws(result$draws, Da = Da, weights = weights)
kmax[p %in% c("0.16", "mean", "0.84")]
#>        Da      p       kmax
#>     <num> <char>      <num>
#>  1:   0.5   mean 0.15764430
#>  2:   0.5   0.16 0.10892312
#>  3:   0.5   0.84 0.21525185
#>  4:   2.5   mean 0.09069962
#>  5:   2.5   0.16 0.05822390
#>  6:   2.5   0.84 0.12932144
#>  7:   5.0   mean 0.06823023
#>  8:   5.0   0.16 0.04167541
#>  9:   5.0   0.84 0.09906638
#> 10:  25.0   mean 0.02848082
#> 11:  25.0   0.16 0.01382170
#> 12:  25.0   0.84 0.04613801

kmax is in g. The normalised pseudostatic coefficient is Kh = kmax / PGA_rock x 100 %.

Next steps

vignette("dynamic-site-response", package = "newmark") — soil profile to fundamental period and site amplification (getSiteProperties, geSiteTable, getCylinderRoots, fitModel.Ts, fitSaF).
vignette("ensemble-formulation", package = "newmark") — mathematical derivation of the probabilistic propagation.
vignette("pipeline", package = "newmark") — the four-workflow overview at function level.
Function reference: ?fitSaF, ?getDnKy, ?fitDnCurve, ?invertDnDraws, ?getSiteProperties, ?getCylinderRoots, ?buildGMDP.