cons: Consolidation Process in a Homogeneous Cohesive Soil Layer

In gek: Gradient-Enhanced Kriging

Consolidation Process in a Homogeneous Cohesive Soil Layer

Description

Computer experiments and variational sensitivities of a consolidation process in a homogeneous cohesive soil layer with an inhomogeneous permeability distribution.

Usage

consTPM
consVSA

Format

The data.frame consTPM contains 50 observations of 5 variables:

[, 1]	disp	solid vertical displacement \rm u_{S2} in \rm m
[, 2]	stiff	oedometric stiffness \rm E_{oed} in \rm MPa
[, 3]	poisson	Poisson's ratio \nu
[, 4]	mass	reference mass density \rho_{\rm 0S}^{\rm SR} in \rm kg/m^3
[, 5]	volume	reference solid volume fraction \rm n_{0S}^S

The data.frame consVSA contains 50 observations of 4 variables:

[, 1]	stiff	sensitivity for oedometric stiffness \rm E_{oed}
[, 2]	poisson	sensitivity for Poisson's ratio \nu
[, 3]	mass	sensitivity for reference mass density \rho_{\rm 0S}^{\rm SR}
[, 4]	volume	sensitivity for reference solid volume fraction \rm n_{0S}^S

Details

The data sets provided here contain computer experiments and variational sensitivities for a specific example of a settlement calculation.

The data.frame consTMP consists of computer experiments obtained by a deterministic simulator that models a consolidation process in a homogeneous cohesive soil layer as a result of the filling of a railroad dam. Calculations are preformed using the finite element method, whereby the underlying partial differential equations used to describe the soil characteristics are based on the theory of porous media. The response analyzed here is the solid vertical displacement disp after 20 days in the middle node at the top of the soil layer, which depends on four uncertain material parameters, namely the oedometer stiffness stiff, Poisson's ratio poisson, reference mass density mass, and reference solid volume fraction volume. The inputs are based on a Latin hypercube sample that has been transformed componentwise to the domains below. For uncertainty quantification, the following distributions of the inputs can be assumed.

Input	Domain	Distribution
\rm E_{oed}	[20, 30]	\mathcal{LN}(3.198, 0.05211)
\nu	[0.25 0.30]	\mathcal{U}(0.25 0.30)
\rho_{\rm 0S}^{\rm SR}	[2000, 2500]	\mathcal{LN}(7.712, 0.02868)
\rm n_{0S}^S	[0.50, 0.65]	\mathcal{U}(0.50, 0.65)

Note, \mathcal{LN}(\mu, \sigma) is the log-normal distribution with mean \mu and standard deviation \sigma of the logarithm and \mathcal{U}(a,b) denotes the continuous uniform distribution over the interval [a,b].

The data.frame consVSA contains the variational sensitivities, i.e. the partial derivatives of the solid vertical displacement at the inputs in consTPM. These were determined using the variational sensitivity analysis.

Source

Both data sets were generated by Carla Henning as part of her dissertation. She has granted permission to publish the data.

References

Henning, C. (2025). Analytical Development of the Variational Sensitivity Analysis for the Theory of Porous Media as Extension for a Gradient-Enhanced Gaussian Process Regression. Ph.D. thesis, Institute of Structural Mechanics and Dynamics in Aerospace Engineering, University of Stuttgart. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18419/opus-16260")}.

See Also

gekm for fitting (gradient-enhanced) Kriging models.

plot.gekm for plotting the results of a leave-one-out cross-validation.

Examples

# Structure of the data frames
str(consTPM)
str(consVSA)

# Summary of the data frames
summary(consTPM)
summary(consVSA)

# Fit a gradient-enhanced Kriging model for the solid vertical displacement 
# with Matérn 3/2 correlation function and first-order polynomial trend.
# Note that 'ncalls = 3' is set for illustrative purposes only. 
# In practice, it is advisable to choose a higher value for 'ncalls' or
# to retain the default value.
mod <- gekm(disp ~ ., data = consTPM, deriv = consVSA, covtype = "matern3_2", ncalls = 3)

# Model summary
summary(mod)

# Plot leave-one-out cross-validation results
plot(mod, add.interval = TRUE, col = 4, pch = 16, panel.first = {grid(); abline(0, 1)})

gek documentation built on Jan. 31, 2026, 1:07 a.m.