Characterize one evaluated soil column

Reduces the layers of one column to the profile quantities used by the shear-beam vibration and site-response calculations: the travel-time velocity of the upper 30 m, its site class, the fitted power law of the stiffness profile, the basal velocity, the constant-density Rayleigh estimate of the site period and the thickness composition.

Usage

characterizeProfile(layers, Hs, Vref)

Arguments

layers

The result of evaluateSoilLayers(), or a table with columns USCS, hs, zm, gsat, Gm and VSm.

Hs

One positive column height in metres.

Vref

One positive reference velocity in m/s completing the upper 30 m when the column is shallower; see estimateVS30().

Value

A one-row data.table: NL (layers), Go (MPa), mo, VSo and VS30 (m/s), SID, TrRayleigh (s, the Rayleigh estimate of the site period with constant density of estimateRayleighPeriod(), as newmark 1.7.1 computed it per realization), Gravels, Sands, Fines, Clays, Silts, Organic (percent of thickness), USCS (sorted classes present, joined by .), fitSigma and fitLayers. Every value is a conditional evaluation of the supplied layers.

Mathematics

The stiffness profile is fitted by least squares in logarithmic coordinates over the layers with positive modulus, $$\log G_m = \log G_o + m_o \log (z_m / H_s),$$ so that \(G_o\) is the modulus at the base \(z = H_s\) and \(m_o\) the exponent of a profile whose origin is the crest, \(z\) being the depth below it. evaluateBeamPeriod() uses \(m_o\) with the roots of the truncated shear beam, whose profile has its origin at the apex of the extended slopes, as an approximation. The basal velocity uses the saturated unit weight of the deepest layer, \(V_{So} = \sqrt{9.81 \cdot 1000 G_o / \gamma_{sat,N_L}}\). The composition columns are thickness percentages.

No value is rounded: every quantity is returned at the precision of its calculation. The rounding of newmark 1.7.1, its basal velocity derived from a rounded modulus and its threshold depth ratios Z500 and Z1000 belong to the compatibility route of buildShearTable(). fitSigma is the residual standard error of the stiffness fit in log units, a numerical diagnostic separate from any physical dispersion.

Examples

set.seed(1)
Layers <- evaluateSoilLayers(sampleSoilLayers(Hs = 10, USCS = c("ML", "MH"), h = 1),
                             Hs = 10, water = 0, POP = 100)
characterizeProfile(Layers, Hs = 10, Vref = 760)
#>       NL       Go        mo      VSo     VS30    SID TrRayleigh Gravels Sands
#>    <int>    <num>     <num>    <num>    <num> <char>      <num>   <num> <num>
#> 1:    10 71.37685 0.4409324 197.0563 324.8741     CD   0.229461       0     0
#>    Fines Clays Silts Organic   USCS  fitSigma fitLayers
#>    <num> <num> <num>   <num> <char>     <num>     <int>
#> 1:   100     0   100       0  MH.ML 0.1600874        10