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@PHDTHESIS{Liang:1012294,
author = {Liang, Rui},
othercontributors = {Schüttrumpf, Holger and Reicherter, Klaus},
title = {{A} universal mathematical model for porosity prediction of
fluvial sediments},
school = {Rheinisch-Westfälische Technische Hochschule Aachen},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2025-04980},
pages = {1 Online-Ressource : Illustrationen},
year = {2025},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, Rheinisch-Westfälische Technische
Hochschule Aachen, 2025},
abstract = {The porosity of riverbed is a key structural property
arising from the packs of fluvial sediments in varied sizes
and shapes, which is defined as the ratio of pore volume to
total volume. It is significant to nearly every
investigation related to riverbed. For instance,
morphologically, porosity determines the sediment
concentration in the river bed and hence the rate of bed
level changes. Ecologically, porosity governs the
interstitial space of the hyporheic zone for aquatic
habitats. Geologically, porosity dominates the exploitable
reserve of oil, gas, and groundwater stored in the voids of
fluvial deposits. Despite its important role, information
regarding the spatial variations in porosity is rarely
available in riverbed. Instead, porosity is often simply
assumed to be spatially constant, which could cause a
systematic error in morphological, ecological, and
geological studies. The reason for this is partly due to the
costly and arduous effort for in-situ measurements on
porosity. As an alternative, mathematical porosity
predictors turn out to be an effective way to estimate
porosity based on porosity-controlling factors, such as
grain size, grain shape and packing state. However, so far,
no such a model can provide satisfactory results in terms of
universality, accuracy, and efficiency. Regression-based
models, while simple to use, is often insufficient when
utilized in regions outside the original dataset. On the
other hand, existing analytical models despite their general
usefulness, are complex to compute and have been found to
systematically underestimate porosity due to their intrinsic
assumptions.In this thesis, the objective was to develop a
novel mathematical porosity predictor that is general,
accurate, and simple to apply. As a first step, the grain
size effect on porosity was explored by assuming sediment
shape as spherical. Unlike traditional analytical models
that are typically derived from the analysis of binary
mixtures of spheres, and then extended into complex models
for arbitrary spherical packings, this study reverses such
process by conceptualizing arbitrary spherical packings into
a binary spherical mixture. This was achieved based on a
newly proposed binary-unit concept, which states that any
multi-sized (or continuous) spherical mixture can be
transformed into an equivalent binary-unit mixture of
spheres through the link of identical grain size statistics
of mean, standard deviation and skewness. The obtained
binary mixture is actually the most elementary spherical
packing unit that can equivalently represent the diversity
of intraparticle interactions in the original spherical
mixtures, i.e., the mixing and unmixing effects. With this
concept, the model, namely the binary-unit conceptual (BUC)
packing model, can be readily implemented to estimate the
porosity of complex spherical packings solely by leveraging
models capable of predicting the porosity of a binary
spherical packing. The Westman-equation model is recommended
for this purpose. Validation against 85 digital riverbeds of
spheres generated through a validated non-smooth granular
dynamics (NSGD) algorithm suggested that the BUC packing
model is able to provide very accurate porosity predictions,
producing a root-mean-square error (RMSE) of 0.01. Next, the
non-spherical grain shape effect was integrated into the BUC
packing model in order to fully resolve the porosity of
fluvial sediments. Initially, an ideal regular shape was
employed to simplify the complex grain shapes of fluvial
sediments. 241 of sediment particles were scanned in high
quality, and then compared to four candidate regular shapes:
cuboid, elliptic disk, truncated octahedron, and ellipsoid.
And it was found that the ellipsoid renders the best shape
similarity to fluvial sediments, allowing it as a reasonable
surrogate. Following the concept of equivalent packing
diameter, a non-spherical (ellipsoid) sediment mixture can
then be converted into a spherical packing with an
equivalent size effect on porosity that can be well handled
by the BUC model, alongside an initial porosity capturing
the isolated non-spherical shape effect at a specific
packing stage. The three theoretical transformations, i.e.,
from sediment to ellipsoid packing, from ellipsoid to
spherical packing, and from spherical to binary-unit
spherical packing, form the foundation of the integrated BUC
(IBUC) packing model. As a result, the IBUC packing model
requires only two inputs: the grain size distribution (GSD)
of the transformed spherical packing, and the initial
porosity. It demonstrated that the GSD of the spherical
packing can be well approximated with the measured GSD of
the original sediment packing. For practical purposes, the
use of a measured mean initial porosity has been proposed as
a general representation for a local site being
investigated. Despite this simplification, the IBUC packing
model still achieved accurate porosity predictions with RMSE
of 0.03, when validated against 138 porosity measurement
data across four diverse riverbeds: the Rhine, Bès,
Galabre, and Kuqa. Overall, the generality, simplicity, and
prediction performance of the IBUC packing model positions
itself as a state-of-the-art tool for investigating the
spatial variability in riverbed porosity. In addition, as a
key component of the IBUC model, the binary-unit concept is
expected to go beyond porosity estimation, as intraparticle
interactions impact a range of other factors. The potential
applications involve estimation of permeability in sediment
mixtures, determination of the cut-off grain size for
morphological alterations, and even prediction of the
incipience of sediment transport.},
cin = {314410},
ddc = {624},
cid = {$I:(DE-82)314410_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2025-04980},
url = {https://publications.rwth-aachen.de/record/1012294},
}
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