Package 'newmark'

Highcharts-style cubic spline interpolation

Description

Drop-in replacement for stats::approx. Uses the Catmull-Rom spline (with the same smoothing parameter as Highcharts type = "spline") instead of straight-line segments. The call signature and return value are identical to stats::approx, so it can be substituted transparently.

Usage

approx.spline(
  x,
  y = NULL,
  xout = NULL,
  n = 50,
  rule = 1,
  log = FALSE,
  smoothing = 1.5,
  ...
)

Arguments

x	Numeric vector of abscissa values.
y	Numeric vector of ordinate values, same length as x.
xout	Optional numeric vector of points where the spline is evaluated. If NULL, a regular grid of length n is used.
n	Integer. Number of points to generate when xout is NULL. Default is 50.
rule	Handling of points outside the range of x. 1 returns NA; 2 repeats the nearest endpoint value. Matches the semantics of stats::approx.
log	Logical. If TRUE, interpolation is performed in log-log space. Default is FALSE.
smoothing	Numeric tension parameter used in the Catmull-Rom to Bezier conversion. Default is 1.5 (Highcharts default).
...	Additional arguments ignored; present only for full signature compatibility with stats::approx.

Value

A list with components x and y, just like stats::approx.

See Also

approx

Examples

x <- c(0.05, 0.10, 0.20, 0.30, 0.50, 1.0, 2.0, 3.0)
y <- exp(-x)
Td <- seq(0.05, 3.0, length.out = 100)
approx.spline(x, y, xout = Td, log = TRUE)$y

---

Build Ground-Motion Design Parameters (GMDP)

Description

Assembles an annual-exceedance-probability (AEP) table, uniform-hazard-spectrum (UHS) table, and–where available–a magnitude-distance disaggregation table, using OpenQuake or user-supplied hazard files.

Usage

buildGMDP(
  path,
  IDo = "GEM",
  engine = "openquake",
  vref = 760,
  TRo = c(100, 200, 500, 1000, 2000, 2500, 5000, 10000)
)

Arguments

path	Character. Directory with hazard data files.
IDo	Character. Identifier for the GMDP. Default "gmdp".
engine	Character. "openquake" (default) or "user".
vref	Numeric. Reference Vs30 (m/s). Default 760.
TRo	Numeric vector. Target return periods (years).

Value

A named list with AEPTable, UHSTable, and RMwTable (NULL if disaggregation is unavailable).

Examples

## Not run: 
# Requires an 'OpenQuake' Engine output directory containing classical
# PSHA + disaggregation ZIPs; not bundled with the package.
out <- buildGMDP(path = "path/to/openquake/output", vref = 760)

## End(Not run)

---

Build a monotone quantile spline Q(u) for ln(Sa)

Description

Build a monotone quantile spline Q(u) for ln(Sa)

Usage

buildQSpline(SaTable)

Arguments

SaTable

data.table with probability column p (0-1 or "mean") and spectral-acceleration column Sa.

Value

A closure Q(u) returning ln(Sa) for any u in[0,1].

Examples

tbl <- data.table::data.table(p = c(0.16, 0.50, 0.84), Sa = c(0.3, 0.5, 0.8))
Q <- buildQSpline(tbl)
Q(0.5)   # median ln(Sa)

---

Check monotonicity and duplicates in UHSTable

Description

Ensures that, for every combination TR, Vs30, Vref, ID, Tn, there is exactly one row per probability p and that Sa(p) is non‑decreasing.

Usage

checkUHS(UHSTable, epsMonot = 1e-06)

Arguments

UHSTable	data.table with columns TR, Vs30, Vref, ID, Tn, p, Sa.
epsMonot	numeric tolerance (default 1e-6).

Value

invisibly TRUE; stops on error.

Examples

## Not run: 
# Requires a fully populated UHSTable produced by buildGMDP() or an
# equivalent upstream pipeline (must include the ID column that
# disaggregates per-quantile rows). Not bundled with the package.
checkUHS(UHSTable)

## End(Not run)

---

Cylinder Roots Data

Description

This dataset contains cylinder roots.

Usage

data(CylinderRoots)

Format

A data frame with 307124 rows and 4 variables:

n

Integer: Root number (1-10)

m

Double: Inhomogeneity ratio (0-0.95)

l

Double: Aspect Ratio (0-0.4950)

an

Double: Cylinder roots

---

MCER / Design elastic spectrum for a Vs30/Vref slice (ASCE 7-22)

Description

The input UHS slice must contain at least Tn and SaF. Typical usage passes a single TR and p == "mean".

Usage

designUHS(UHS, TL = 8, spectrum = c("MCER", "DESIGN"))

Arguments

UHS	data.table slice from UHSTable (single TR, p == "mean").
TL	numeric, long-period transition (seconds). Default 8.
spectrum	character, "MCER" (default) or "DESIGN" (2/3 * MCER).

Value

data.table with columns ⁠Tn, SaF⁠.

Examples

uhs <- data.table::data.table(Tn = c(0, 0.2, 0.5, 1, 2), SaF = c(0.4, 1.0, 0.9, 0.6, 0.3))
designUHS(uhs)

---

Ambraseys & Menu (1988) rigid sliding-block model

Description

Ambraseys & Menu (1988) rigid sliding-block model

Usage

Dn_AM88(PGA, ky)

Arguments

PGA	Peak ground acceleration (g).
ky	Yield acceleration (g).

Value

data.table(muLnD, sdLnD, ID = "AM88")

Examples

Dn_AM88(PGA = 0.5, ky = 0.1)

---

Bray & Macedo (2017) - subduction/interface events

Description

Bray & Macedo (2017) - subduction/interface events

Usage

Dn_BM17(ky, Sa, Ts, Mw = 7.5)

Arguments

ky	Yield acceleration (g).
Sa	Spectral acceleration at 1.5 * Ts (g).
Ts	Fundamental period (s).
Mw	Moment magnitude (default 7.5).

Value

data.table(muLnD, sdLnD, ID = "BM17")

Examples

Dn_BM17(ky = 0.1, Sa = 0.8, Ts = 0.3, Mw = 8.0)

---

Bray & Macedo (2019, corrected 2023) - shallow-crustal events

Description

Multi-equation structure per BM23 (Soil Dynamics and Earthquake Engineering 168, 107835, DOI 10.1016/j.soildyn.2023.107835): Eq (10): ordinary motions, PGV <= 115 cm/s Eq (6): D100 max-component, PGV > 115 cm/s Eq (7): D50 median-component, PGV > 115 cm/s with a sub-regime split at PGV = 150 cm/s within Eqs (6) and (7).

Usage

Dn_BM19(ky, Ts, Sa, PGA, PGV, Mw = 6.5, NFC = "D100")

Arguments

ky	Yield acceleration (g).
Ts	Fundamental period (s).
Sa	Spectral acceleration at 1.3 * Ts (g).
PGA	Peak ground acceleration (g).
PGV	Peak ground velocity (cm/s).
Mw	Moment magnitude (default 6.5).
NFC	Near-fault component: "D100" (default; max-component, slope within 45 deg of fault-normal) or "D50" (median-component, other orientations). Used only when PGV > 115 cm/s.

Value

data.table(muLnD, sdLnD, ID = "BM19")

Examples

Dn_BM19(ky = 0.1, Ts = 0.3, Sa = 0.8, PGA = 0.5, PGV = 80, Mw = 7.0)

---

Bray & Travasarou (2007) flexible sliding-block model

Description

Bray & Travasarou (2007) flexible sliding-block model

Usage

Dn_BT07(ky, Sa, Ts, Mw = 6.5)

Arguments

ky	Yield acceleration (g).
Sa	Spectral acceleration at 1.5 * Ts (g).
Ts	Fundamental period (s).
Mw	Moment magnitude.

Value

data.table(muLnD, sdLnD, ID = "BT07")

Examples

Dn_BT07(ky = 0.1, Sa = 0.8, Ts = 0.3, Mw = 7.0)

---

Jibson (2007) empirical model

Description

Jibson (2007) empirical model

Usage

Dn_JB07(PGA, ky, AI = NULL)

Arguments

PGA	Peak ground acceleration (g).
ky	Yield acceleration (g).
AI	Arias Intensity (m/s); if NULL, back-calculated from PGA.

Value

data.table(muLnD, sdLnD, ID = "JB07")

Examples

Dn_JB07(PGA = 0.5, ky = 0.1)

---

Saygili & Rathje (2008) model

Description

Saygili & Rathje (2008) model

Usage

Dn_SR08(PGA, ky, AI = NULL)

Arguments

PGA	Peak ground acceleration (g).
ky	Yield acceleration (g).
AI	Arias Intensity (m/s); if NULL, back-calculated from PGA.

Value

data.table(muLnD, sdLnD, ID = "SR08")

Examples

Dn_SR08(PGA = 0.5, ky = 0.1)

---

Non-linear site amplification factor F_ST17

Description

Implements the period-dependent, Vs30-dependent model of Seyhan & Stewart (2014) for the natural-log mean and standard deviation of the amplification factor $F(T_n,PGA,V_{s30})$.

Usage

F_ST17(PGA, Tn, vs30, vref = 760, Vl = 200, Vu = 2000)

Arguments

PGA	numeric vector – peak ground acceleration (in g).
Tn	numeric scalar – oscillator period (s).
vs30	numeric scalar – time-averaged shear-wave velocity to 30 m (m/s).
vref	numeric scalar – reference velocity (760 m/s or 3000 m/s), default 760.
Vl	numeric scalar – lower Vs30 bound for NL sigma interpolation (default 200).
Vu	numeric scalar – upper Vs30 bound for NL sigma interpolation (default 2000).

Details

If vs30 == vref, the site factor equals 1 deterministically, so the function returns muLnF = 0 and sdLnF = 0 (zero dispersion; rnorm(n, 0, 0) returns zeros and ln F = 0).

Value

A data.table with columns:

muLnF

natural-log mean of $F$

sdLnF

natural-log standard deviation of $F$ (set to 0 when vs30 == vref)

ID

character string "ST17"

References

Stewart, J.P. & Seyhan, E. (2017) “Semi-empirical nonlinear site amplification model for global application.” Earthquake Spectra 33(1).

---

Newmark displacement curve Dn(ky) for one scenario

Description

Evaluates ensemble and per-submodel Dn over a vector of ky values. The scenario is sampled once and the same epsilon is reused across all ky so that each realisation s represents a coherent physical curve Dn_s(ky).

Usage

fitDnCurve(uhs, ky, Ts, Mw = 6.5, NS = 30L, Rrup = 100, weights, NFC = "D100")

Arguments

uhs	data.table with columns Tn, p, Sa (one scenario)
ky	numeric vector, yield accelerations (g)
Ts	numeric scalar, fundamental period (s)
Mw	numeric scalar, moment magnitude
NS	integer, Monte Carlo samples for curve quantiles and per-realisation draws.
Rrup	numeric scalar, rupture distance (km)
weights	named numeric vector, ensemble weights by IDn
NFC	character, near-fault component selector for model BM19: "D100" (maximum component, default) or "D50". Ignored by all other submodels.

Value

list(curve, draws). curve = data.table(ky, p, Dn, IDn, w). draws = data.table(ky, s, Dn, IDn) — always populated (possibly empty when no model produces output). Dn in cm.

Examples

## Not run: 
uhs <- data.table::fread(
  system.file("extdata", "uhs.csv", package = "newmark"))
out <- fitDnCurve(uhs, ky = getDnKy(uhs, Ts = 0.3), Ts = 0.3, Mw = 7.5,
                  NS = 100, weights = c(AM88=1, BT07=1, SR08=1, BM17=1))

## End(Not run)

---

Newmark displacement for a single submodel and scenario

Description

Newmark displacement for a single submodel and scenario

Usage

fitDnModel(uhs, ky, Ts, Mw = 6.5, NS = 30L, Rrup = 100, IDn, NFC = "D100")

Arguments

uhs	data.table with columns Tn, p, Sa (one scenario)
ky	numeric scalar, yield acceleration (g)
Ts	numeric scalar, fundamental period (s)
Mw	numeric scalar, moment magnitude
NS	integer, Monte Carlo samples
Rrup	numeric scalar, rupture distance (km)
IDn	character, submodel identifier
NFC	character, near-fault component selector for model BM19: "D100" (maximum component, default) or "D50". Ignored by all other submodels.

Value

data.table with columns p, Dn, IDn. Dn in cm.

Examples

## Not run: 
uhs <- data.table::fread(
  system.file("extdata", "uhs.csv", package = "newmark"))
fitDnModel(uhs, ky = 0.1, Ts = 0.3, Mw = 7.5, NS = 100, IDn = "AM88")

## End(Not run)

---

Site's Fundamental Period

Description

Site's Fundamental Period

Usage

fitModel.Ts(VSm, hs, zm)

Arguments

VSm	Vector. Shear Wave Velocity profile in m/s (vector)
hs	Vector. Layer Thickness profile in m (vector)
zm	Vector. Layer Coordinates profile in m (vector)

Value

Double. Site's fundamental period Ts in seconds

---

Site-amplified AUXtral acceleration (Seyhan & Stewart 2014)

Description

Computes site-amplified AUXtral acceleration using two modes: (A) If the input UHS contains only p == "mean", rock Sa is treated as deterministic and the dispersion in SaF comes solely from F_ST17 (sdLnF), sampled on the natural-log scale. (B) If the input UHS contains numeric quantiles (e.g., "0.10", "0.50", ...), ln Sa(Tn) is sampled from those quantiles using an empirical inverse quantile function (buildQSpline). Dependence between PGA and Sa(Tn) is represented by a Gaussian "star" copula (Baker & Jayaram, 2009) with correlation rhoBJ(Tn, T0 = 0, Rrup). For each Monte Carlo draw, F_ST17 is evaluated with the paired PGA draw, and ln SaF = ln Sa + ln F with ln F ~ Normal(muLnF, sdLnF). Independence between ln Sa and ln F is assumed.

Usage

fitSaF(
  uhs,
  vs30,
  vref = 760,
  ns = 1000,
  models = "ST17",
  Rrup = 100,
  p_TARGET = c(0.05, 0.1, 0.16, 0.5, 0.84, 0.9, 0.95)
)

Arguments

uhs	data.table with columns Tn, p, Sa.
vs30	target Vs30 (m/s).
vref	reference Vs30 (m/s), default 760.
ns	Monte Carlo size (default 1000).
models	character. Site-response model id. Currently the only implemented model is "ST17"; reserved for future site-response models.
Rrup	rupture distance (km) for rhoBJ() in the quantile case (default 100).
p_TARGET	probabilities to report when only 'mean' is provided, default c(0.05, 0.10, 0.16, 0.50, 0.84, 0.90, 0.95).

Details

Requirements:

• The input table must have columns Tn, p, Sa.

• It must include exactly one row (Tn == 0, p == "mean") providing PGA on rock.

Output columns: Tn, p, Sa, SaF, AF, where AF = SaF / Sa. In mode (B), the same numeric p values found in the input are returned plus "mean". In mode (A), the set of p values is taken from p_TARGET plus "mean".

Value

data.table with columns Tn, p, Sa, SaF, AF.

Examples

## Not run: 
uhs <- data.table::fread(
  system.file("extdata", "uhs.csv", package = "newmark"))
fitSaF(uhs, vs30 = 360, vref = 760, ns = 500)

## End(Not run)

---

Single-realisation synthetic soil profile and site properties

Description

Builds one Monte Carlo realisation of a layered soil column from a total height Hs and a USCS classification, samples random geotechnical properties (void ratio, unit weight, plasticity, shear modulus parameters), computes the fundamental period Ts via Rayleigh's method (fitModel.Ts) and the Vs30-equivalent shear-wave velocity. getSiteProperties calls this function repeatedly to assemble the Monte Carlo ensemble; call directly when one realisation suffices.

Usage

geSiteTable(
  Hs,
  Water = 0,
  USCS,
  Group = NULL,
  h = 0.5,
  DrID = NULL,
  Vref = 760,
  UniformDistribution = TRUE,
  POP = 100,
  IgnoreModelIntervals = TRUE,
  getSiteLayers = FALSE
)

Arguments

Hs	Numeric scalar. Total height to hard ground (m).
Water	Numeric scalar. Water-table depth as fraction of Hs: zw = Hs - Water * Hs.
USCS	Character vector. Unified Soil Classification System codes (e.g. c("GC", "CL", "ML")).
Group	Character vector or NULL. Soil groups, c("Gravels","Fines","Sands"); if NULL, derived from USCS.
h	Numeric scalar. Layer thickness in the discretisation (m). Default 0.50.
DrID	Character or NULL. Relative-density label, c("Very Dense","Dense","Compact","Loose","Very Loose"); NULL samples relative density from the standard prior.
Vref	Numeric. Reference shear-wave velocity (m/s) for the site-class assignment. Default 760.
UniformDistribution	Logical. If TRUE (default), sample soil properties from uniform distributions; if FALSE, use normal distributions.
POP	Numeric. Pre-consolidation pressure (kPa); enters the over-consolidation ratio OCR = (pm + POP) / pm. Default 100.
IgnoreModelIntervals	Logical. If TRUE (default), ignore model-specific layer-thickness intervals and use h as the discretisation step.
getSiteLayers	Logical. If TRUE, return the per-layer detail in addition to the per-site summary.

Value

data.table with one row per (Hs, POP, Hw, sample) combination and columns Hs, Hw, NL, Z500, Z1000, SID, Go, mo, Ts, VSo, VS30, plus USCS-fraction columns.

---

Characteristic root of an inhomogeneous truncated shear beam

Description

Returns the eigenvalue an of mode no for a Gazetas & Dakoulas (1985) inhomogeneous truncated shear beam parameterised by inhomogeneity ratio mo and truncation ratio lo. The value is interpolated from the precomputed CylinderRoots table using the requested model (linear glm, non-linear glm, decision tree, or random forest).

Usage

getCylinderRoots(mo, lo, no = 1, model = "nlm", extrapolate = TRUE, OSF = 0.1)

Arguments

mo	Double. Inhomogeneity ratio of the shear-modulus profile. mo = 0 is a homogeneous column. Range 0 to 0.95.
lo	Double. Truncation ratio (top-radius / bottom-radius); lo = 0 is a fully truncated cone. Range 0 to 0.495.
no	Integer. Mode number, 1..8. Default 1 (fundamental).
model	Character. Interpolation model: "lm" (linear GLM), "nlm" (non-linear GLM with interactions, default), "dt" (decision tree), or "rf" (random forest).
extrapolate	Logical. If TRUE (default), allow mo/lo outside the table support and warn; if FALSE, clamp to the table maxima.
OSF	Double. Outlier scale factor used by the random-forest model to shrink the training set around the query point. Default 0.10.

Value

Double. Characteristic root an for the requested mode and parameters.

Examples

getCylinderRoots(mo = 0.45, lo = 0.20, no = 1, model = "nlm")

---

Build a log-spaced ky grid for one scenario

Description

Derives the effective intensities PGA, Sa(1.3Ts), Sa(1.5Ts) from the scenario UHS and constructs a log-spaced ky grid covering the calibrated range of the displacement models.

Usage

getDnKy(uhs, Ts, kyN = 30L, pRef = "mean")

Arguments

uhs	data.table with columns Tn, p, Sa (one scenario)
Ts	numeric scalar, fundamental period (s)
kyN	integer, number of grid points (default 30)
pRef	character, probability level for intensity anchor (default "mean")

Details

Default bounds come from the calibration ranges of the models in the ensemble:

• lower: 0.01g (BM17 lowest calibration point)

• upper: max(PGA, 0.80g). The physical limit is ky < PGA (no slip below the yield acceleration); the 0.80g floor extends the grid for low-PGA scenarios up to BM17's calibration ceiling.

Value

numeric vector of ky values (log-spaced)

Examples

uhs <- data.table::data.table(Tn = 0, p = "mean", Sa = 0.5)
getDnKy(uhs, Ts = 0.3)

---

Get calibrated ky range for each displacement model

Description

Returns the ky bounds within which each model's regression is calibrated. For rigid models (AM88, SR08) the bounds are relative to PGA. For flexible models the bounds are absolute.

Usage

getKyLimits(PGA)

Arguments

PGA	numeric scalar, peak ground acceleration (g). Required for rigid model limits.

Value

data.table with columns IDn, ky.lo, ky.hi

Examples

getKyLimits(PGA = 0.5)

---

Monte Carlo site properties from synthetic soil profiles

Description

Generates NR realisations of synthetic soil profiles for a given total height Hs and USCS classification, then summarises the resulting Ts, mo, Go, VSo and VS30 by user-requested quantile levels (and/or the mean). Each realisation is built by geSiteTable().

Usage

getSiteProperties(
  Hs,
  USCS,
  POP = 100,
  Water = 0,
  NR = 1,
  h = 1,
  levels = c(0.05, 0.5, "mean", 0.95),
  Vref = 760
)

Arguments

Hs	Numeric vector. Total height(s) to hard ground (m).
USCS	Character vector. USCS soil classification codes (e.g. c("GC", "CL", "ML")).
POP	Numeric. Pre-consolidation pressure (kPa). Default 100.
Water	Numeric. Water-table depth as fraction of Hs. Default 0 (no water).
NR	Integer. Number of Monte Carlo realisations. Default 1.
h	Numeric. Layer thickness (m) in the discretisation. Default 1.00.
levels	Vector. Quantile levels to report; entries can be numeric in (0, 1) and/or the literal "mean". Default c(0.05, 0.5, "mean", 0.95).
Vref	Numeric. Reference shear-wave velocity (m/s) for site-class assignment. Default 760.

Value

data.table with one row per (Hs, POP, Hw, level) combination and columns USCS, Go, mo, Ts, VSo, VS30, Z500, Z1000, level. Numeric properties are rounded for readability.

Examples

getSiteProperties(
  Hs   = 30,
  USCS = c("GC", "CL", "ML"),
  NR   = 50,
  levels = c(0.16, "mean", 0.84)
)

---

Interpolate Sa(p) at arbitrary period using log-log interpolation

Description

Interpolate Sa(p) at arbitrary period using log-log interpolation

Usage

interpolateSaTable(uhs, Tn)

Arguments

uhs	data.table with columns Tn, p, Sa.
Tn	numeric scalar — target period for interpolation.

Value

data.table with interpolated Tn, p, Sa

Examples

uhs <- data.table::data.table(
  Tn = c(0.2, 0.5, 1.0, 0.2, 0.5, 1.0),
  p  = c("0.16", "0.16", "0.16", "0.84", "0.84", "0.84"),
  Sa = c(0.8, 0.6, 0.3, 1.2, 0.9, 0.5)
)
interpolateSaTable(uhs, Tn = 0.3)

---

Invert Dn draws to kmax(Da)

Description

For each realisation s, inverts each model's Dn(ky) curve to kmax(Da), builds weighted ensemble mean, then averages over realisations.

Usage

invertDnDraws(draws, Da, weights, p = c(0.05, 0.1, 0.16, 0.84, 0.9, 0.95))

Arguments

draws	data.table(ky, s, Dn, IDn) — Dn in cm
Da	numeric vector — displacement targets in cm
weights	named numeric vector, ensemble weights by IDn
p	numeric quantiles in (0,1) to report alongside the mean. Default c(0.05, 0.10, 0.16, 0.84, 0.90, 0.95). The output always includes the ensemble mean as the first p row.

Details

Log-log linear extrapolation is used when Da falls outside the support of the computed Dn(ky) curve. No calibration-range clamping is applied — the natural support of the curve bounds the inversion.

All inputs must be in the same displacement units (cm).

Value

data.table(Da, p, kmax). Column p is character: "mean" or the numeric quantile formatted as "0.84", "0.90", etc.

Examples

## Not run: 
uhs <- data.table::fread(
  system.file("extdata", "uhs.csv", package = "newmark"))
out <- fitDnCurve(uhs, ky = getDnKy(uhs, Ts = 0.3), Ts = 0.3, Mw = 7.5,
                  NS = 100,
                  weights = c(AM88=1, BT07=1, SR08=1, BM17=1))
invertDnDraws(out$draws, Da = c(2.5, 5, 10),
              weights = c(AM88=1, BT07=1, SR08=1, BM17=1))

## End(Not run)

---

Baker and Jayaram (2008) inter-period correlation model

Description

Computes the Pearson correlation coefficient between the residuals of ln(Sa) at two oscillator periods, using the canonical predictive equation of Baker and Jayaram (2008), Earthquake Spectra 24(1), 299-317 (DOI 10.1193/1.2857544), Eqs. 5 and 6 verbatim.

Usage

rhoBJ(Tn, T0 = 0.01, Rrup = 100)

Arguments

Tn	Numeric scalar. Target spectral period in seconds.
T0	Numeric scalar. Reference period in seconds. Default 0.01 (used as a numerical proxy for PGA). Values <= 0 are silently converted to 0.01.
Rrup	Numeric scalar. Not used; retained for backward compatibility.

Details

The model has no dependence on rupture distance or magnitude. Rrup is retained for signature compatibility and is silently ignored. Periods of zero are treated as 0.01 s (standard PGA proxy in B&J 2008).

Form (Eqs. 5-6 of B&J 2008): C1 = 1 - cos(pi/2 - 0.366 * ln(Tmax / max(Tmin, 0.109))) C2 = (1 - 0.105 * (1 - 1/(1 + exp(100*Tmax - 5))) * (Tmax-Tmin)/(Tmax-0.0099)) if Tmax < 0.2; else 0 C3 = C2 if Tmax < 0.109; else C1 C4 = C1 + 0.5 * (sqrt(C3) - C3) * (1 + cos(pi * Tmin / 0.109))

rho = C2 if Tmax < 0.109 = C1 else if Tmin > 0.109 = min(C2, C4) else if Tmax < 0.2 = C4 otherwise

Validity: 0.01 <= T1, T2 <= 10 s.

Value

Numeric scalar correlation coefficient rho(T0, Tn).

References

Baker, J. W. & Jayaram, N. (2008). Correlation of Spectral Acceleration Values from NGA Ground Motion Models. Earthquake Spectra, 24(1), 299-317. DOI: 10.1193/1.2857544.

Examples

rhoBJ(Tn = 0.3, T0 = 0.01)   # rho(PGA, 0.3 s)
rhoBJ(Tn = 1.0, T0 = 0.5)

---

Site-amplified spectral acceleration using Seyhan & Stewart (2014)

Description

Computes site-amplified spectral acceleration Sa_F using the Seyhan & Stewart (2014) non-linear site factor model. This is the canonical implementation that calls the underlying F_ST17() function.

Usage

SaF_ST17(Sa, pga, Tn, vs30, vref = 760)

Arguments

Sa	numeric vector - rock spectral accelerations at period Tn (g)
pga	numeric vector - peak ground acceleration on rock (g), same length as Sa
Tn	numeric scalar - oscillator period (s)
vs30	numeric scalar - time-averaged shear-wave velocity to 30 m (m/s)
vref	numeric scalar - reference velocity (m/s), default 760

Value

A data.table with columns:

muLnSaF

natural-log mean of amplified Sa

sdLnSaF

natural-log standard deviation of amplified Sa

ID

character string "ST17"

References

Seyhan, E. & Stewart, J.P. (2014) "Semi-empirical nonlinear site amplification from NGA-West2 data and simulations." Earthquake Spectra 30(3):1241–1256. doi:10.1193/063013EQS181M

See Also

F_ST17 for the underlying site factor model

fitSaF for Monte-Carlo site amplification analysis

Examples

library(data.table)

# Site amplification for soft soil site
Sa_rock <- c(0.1, 0.2, 0.3, 0.4)
PGA_rock <- c(0.1, 0.1, 0.1, 0.1)

result <- SaF_ST17(
  Sa = Sa_rock,
  pga = PGA_rock,
  Tn = 0.5,      # 0.5s period
  vs30 = 300,    # Soft soil
  vref = 760     # Rock reference
)

print(result)

---

Draw a correlated sample of spectral accelerations

Description

Draw a correlated sample of spectral accelerations

Usage

sampleSaCorr(uhs, Tn, rho, NS)

Arguments

uhs	data.table with columns Tn, p, Sa (must include p == "mean").
Tn	numeric vector; the first element is the reference period Tn[1], e.g., 0.01 or 0.00. It does not have to be sorted.
rho	numeric vector of length length(Tn) - 1; correlations between the reference period Tn[1] and each remaining period.
NS	integer, Monte Carlo sample size.

Value

matrix of dimension NS x length(Tn) with Sa draws (g).

Examples

## Not run: 
uhs <- data.table::data.table(
  Tn = c(0, 0, 0, 1, 1, 1),
  p  = c("0.16", "mean", "0.84", "0.16", "mean", "0.84"),
  Sa = c(0.3, 0.5, 0.7, 0.1, 0.2, 0.3)
)
rho <- rhoBJ(Tn = 1.0, T0 = 0.01)
mat <- sampleSaCorr(uhs, Tn = c(0, 1), rho = rho, NS = 100)

## End(Not run)

---

ShearModelParameters

Description

This dataset contains hear Model Parameters from Ishihara (1996)

Usage

data(ShearModelParameters)

Format

A data frame with 20 rows and 10 variables:

ModelID

Character: Model ID

GroupID

Character: Group ID

NameID

Character: NameID

AuthorID

Character: AuthorID

emin

Double: Min Void Ratio

emax

Double: Max Void Ratio

A

Double: A

Ce

Double: Ce

n

Double: Ce

UN

Character: Go Units

---

Convert Site Class to Vs30 in m/s

Description

Convert Site Class to Vs30 in m/s

Usage

SIDtoVs30(SID = NULL)

Arguments

SID	Site Class

Value

Vs30 in m/s

Examples

SIDtoVs30("A")

SIDtoVs30("AB")

SIDtoVs30(c("BC","C","CD","D"))

---

Site Class Data

Description

This dataset contains Site Class data from ASCE 7-22

Usage

data(SiteClass)

Format

A data frame with 9 rows and 4 variables:

SC

Character: Site Class

Description

Character: Category description

Vs30 (m/s)

Character: Vs30 in m/s

Vs30 (ft/s)

Character: Vs30 in ft/s

---

SiteTable Data

Description

This dataset contains simulations of different site conditions

Usage

data(SiteTable)

Format

A data frame with 255614 rows and 38 variables:

Hs

Double: Height in m.

Hw

Double: Water Table in m.

NL

Integer: Number of Layers

Z500

Double: Depth to 500 m/s in m.

Z1000

Double: Depth to 1000 m/s in m.

SID

String: Site ID

Go

Double: Shear Modulus in kPa.

mo

Double: Shear Modulus Exponent.

Ts

Double: Fundamental Period in s.

VSo

Double: Shear Wave Velocity in m/s.

VS30

Double: Shear Wave Velocity at 30 m in m/s.

UID

String: USCS ID

Gravels

Double: Percentage of Gravels.

Sands

Double: Percentage of Sands.

Fines

Double: Percentage of Fines.

Clays

Double: Percentage of Clays.

Silts

Double: Percentage of Silts.

Organic

Double: Percentage of Organic.

Water

Double: Percentage of Water.

GP

Double: GP Fraction.

GM

Double: GM Fraction.

GC

Double: GC Fraction.

GW

Double: GW Fraction.

SP

Double: SP Fraction.

SM

Double: SM Fraction.

SC

Double: SC Fraction.

SW

Double: SW Fraction.

CL

Double: CL Fraction.

ML

Double: ML Fraction.

OL

Double: OL Fraction.

PT

Double: PT Fraction.

OH

Double: OH Fraction.

MH

Double: MH Fraction.

CH

Double: CH Fraction.

POP

Double: Overpressure in Kpa.

POP_Units

String: Overpressure Units.

Go_Units

String: Shear Modulus Units.

Vs_Units

String: Shear Wave Velocity Units.

---

Convert Vs30 (m/s) to Site Class Identifier

Description

Given one or more Vs30 values (in m/s), returns a character vector of site class designations ("A", "B", "BC", "C", "CD", "D", "DE", "E"). The classification thresholds are:

• A: Vs30 >= 1500

• B: 900 <= Vs30 < 1500

• BC: 640 <= Vs30 < 900

• C: 440 <= Vs30 < 640

• CD: 300 <= Vs30 < 440

• D: 210 <= Vs30 < 300

• DE: 150 <= Vs30 < 210

• E: 0 <= Vs30 < 150

Usage

Vs30toSID(Vs30)

Arguments

Vs30	Numeric vector. One or more Vs30 values in m/s.

Value

A character vector of the same length as Vs30, with site class designations.

Examples

Vs30toSID(1500)  # returns "A"
Vs30toSID(c(120, 790, 3000, 455))

---