Thesis-2011-Zheng.pdf (2.7 MB)
Mathematical modeling of soil erosion by rainfall and shallow overland flow
thesis
posted on 2011-11-28, 14:08 authored by Tingting ZhengNew analytical and numerical solutions are developed to both the kinematic
approximation to the St Venant equations and the Hairsine-Rose (HR) soil erosion
model in order to gain a better physical understanding of soil erosion and
sediment transport in shallow overland flow. The HR model is unique amongst
physically based erosion models in that it is the only one that: considers the entire
distribution of the soil s sediment size classes, considers the development of
a layer of deposited non-cohesive sediment having different characteristics to the
original underlying cohesive soil and considers separately the erosion processes of
rainfall detachment, runoff entrainment and gravitational deposition.
The method of characteristics and the method of lines were used to develop
both the analytical and numerical solutions respectively. These solutions were
obtained for boundary and initial conditions typical of those used in laboratory
flume experiments along with physically realistic constant and time dependent
excess rainfall rates. Depending on the boundary and initial conditions, interesting
new solutions of the kinematic wave equation containing expansion waves,
travelling shocks as well as solutions which split into an upslope and downslope
drying profiles were found.
Numerical solutions of the HR model were applied to the experimental flume
data of Polyakov and Nearing (2003) obtained under flow conditions which periodically
cycled between net erosion and net deposition conditions. While excellent
agreement was found with suspended sediment data, the analysis suggested that
an additional transport mechanisms, traditionally not included in soil erosion
models, was occurring. While the inclusion of bed-load transport improved the
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overall model prediction, it was still not sufficient. Subsequent asymptotic analysis
then showed that the interaction of the flow with an evolving bed morphology
was in fact far more important than bed load transport. A very interesting finding
from this work showed that the traditional criterion of validating sediment
transport model based solely on suspended sediment data was not sufficient as reliable
predictions could be obtained even when important transport mechanisms
were neglected.
Experimental plots of sediment discharge or suspended sediment concentration
against water discharge in overland flow have been shown to contain significant
hysteresis between the falling and rising limbs of the discharge hydrograph.
In the final Chapter, the numerical solution developed for the complete system of
soil erosion and kinematic flow was used to show that it was possible for the HR
model to simulate three of the four hysteresis loops identified in the literature.
Counter clock-wise loops, clock-wise loops and figure 8 loops could all be produced
as a result of starting with different initial conditions, being mi(x; 0) = 0,
mi(x; 0) = pimt and mi(x; 0) = 0:5pimt respectively. This is the first time that
these types of hysteresis loops have been produced by any erosion model. The
generation of these hysteresis loops are physically explainable in terms of sediment
availability and is consistent with data obtained on the field scale.
History
School
- Architecture, Building and Civil Engineering
Publisher
© Tingting ZhengPublication date
2011Notes
A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.EThOS Persistent ID
uk.bl.ethos.554137Language
- en