ABSTRACT
Failures
of water boreholes that have impeded the performance and operation of boreholes
have been recorded in recent times. To help solve some of the problems, the
role of contact and seepage forces on the failure of water boreholes was
explored. This study is important as the scouring of the particles collected at
the wall of the transport pipe could damage pumps and result in huge financial
loss to owners of boreholes. Combined finite-discrete element method was used
to generate model expression from contact and seepage forces considered to be the
major forces contributing to the flow of fluid through soil mass and boiling or
quick sand effect. Mathematical model was developed for calculating the
critical hydraulic head causing critical seepage given as
=
while
an expression for the safe hydraulic head during well pumping was developed and
given as
=
,
the ability of the model to predict result was verified using result of test
conducted in the laboratory. Correlation coefficient result has shown that
there is strong agreement between model result and the laboratory result which
has shown a perfect correlation of 1.00 and 0.99 for the critical state
condition and equilibrium state condition respectively. For safe pumping and
corresponding yield in the borehole system, inter-granular force between
granular particles should equal the seepage force and this is achieved by
ensuring that the deduced model expression is used to determine the safe
hydraulic head. Finally, irrespective of the fact that an increase in hydraulic
head increases discharge, the system should be operated at a head safe for the
performance of the well and as long as the model hydraulic head expression
deduced is used under the above conditions, safe pumping can be achieved.
TABLE OF CONTENTS
Title
page
Table
of contents
Notations
List
of Tables
List
of Figures
Abstract
CHAPTER ONE: INTRODUCTION
1.1 Statement of the Problem
1.2 Aim and Objectives
1.3 Significance of Study
1.4 Scope and Limitation of Study
CHAPTER TWO: FINITE-DISTINCT
ELEMENT MODELING
2.1 Distinct Element Method
2.2 Finite Element Method
2.3 Combined Finite Distinct Element Method
2.4 Combined Continua-Discountnua Problem
2.5 Transient Hydrodynamic Condition
2.6 Algorithmic and Computational Challenge
of the Combined FDEM
2.7 Contact Force in Aquifer
2.8 Groundwater Flow in Aquifer
2.8.1 Governing Flow continuity Equation
2.8.2 Seepage under Critical Hydraulic
Conductivity
2.9 Failure Criterion
2.10 Discussion of parameters
CHAPTER THREE: MATERIALS AND
METHODS
3.1 Numerical Implementation and Formulation
3.1.1 Formulation of Problem Equations
3.1.2 Contact Force Modeling
3.1.3 Seepage force Modeling
3.1.4 Equilibrium Condition Equation
3.2 Assumptions and Simplifications
3.3 Solution of Problem Equations
3.3.1 Contact Force Model Solution
3.3.2 Seepage force Model Solution
3.3.3 Equilibrium Condition of Flow Region or
Studied Region
3.4 Laboratory Implementation
3.4.1 Sample Collection
3.4.2 Description of Fundamental Equations
3.4.3 Laboratory set-up, test and analysis
CHAPTER FOUR: RESULTS AND
DISCUSSION
4.1 Results
4.1.1 Laboratory Results
4.1.2 Mathematical Model Data Collection
4.2 Simulation Results Discussion
4.2.1 Seepage Force Simulation Results
4.2.2 Equilibrium Condition of Flow Region
4.2.3 Model verification and Validation Tests
CHAPTER FIVE: CONCLUSION AND
RECOMMENDATION
REFERENCES
CHAPTER ONE
INTRODUCTION
Nigeria
has a total land mass of 932,768 sq. km falling between latitude 4011 and 13091N and longitudes 2021 and 14031W and a population,
currently of about 120 million people (Eduvie, 2006). The total replenishable water
resource in Nigeria is estimated at 319 billion cubic meters, while the ground
water component is estimated at 52 billion cubic meters. Water shortages are
acute in some major centers and in numerous rural communities due to a variety
of factors including variation in climatic conditions, drought increasing
demands, distribution system losses and breakdown of works and facilities
(Eduvie 2006). Ground water is the water stored in an aquifer in pore spaces or
fractures in rocks or sediments. Groundwater is generally a readily available
source of water throughout populated Africa but the construction costs for
sustainable supplies are high. The reason why groundwater is preferred to
surface water includes:
(i)
Its relative low costs compared to surface water
(ii)
Availability in most areas
(iii)
Potable without treatment
(iv)
Employs low cost technologies
(v)
The frequent drought problems enforce the use of groundwater source as many
small intermittent rivers and streams dry out during the dry seasons. Nigeria
is geologically covered by two broad and distinct formations: the basement
crystalline rocks and sedimentary rocks. The basement rocks have underlain
about 50% of the total surface area of the country, while the sedimentary rocks
covered the remaining areas (Eduvie 2006). The basement rocks are found in four
broad segments, in the northwest, southwest, northeast and southeast segments.
Groundwater which can be extracted by boreholes and hand-dug wells occurs in
permeable geological formations known as aquifers which have properties that
allow storage and movement of water through them. The geological structure of
Nigeria gave rise to two types of groundwater pore-type water in sedimentary
cover and fissure-type water found in crystalline rocks. There are the
following aquifer types in Nigeria according to (Eduvie, 2006)
1. Fissure
type water in Precambrian crystalline rocks
2. Pore-type
water in sedimentary deposits
3. Pore-type
water in superficial deposits
The
availability of groundwater in areas underlain by crystalline basement rocks
depends on the development of thick soil overburden (overburden aquifer) or the
presence of groundwater is confined to fractures and fissures in the weathered
zone of igneous, metamorphic and volcanic rocks, (Eduvie 2006). Sholes, clays,
limestone are generally poor aquifers due to their argillaceous nature. There
is little groundwater in them while in the basement complex terrain,
groundwater occurs in the weathered regolith and in fracture in the fresh
crystalline rocks; where thick weathered zones or fracture in fresh rocks
occur, wells and boreholes tap the groundwater for water supply (Eduvie, 2006).
The establishment of the Nigerian geological survey in 1817 has as one of its
major objectives to search for groundwater in the semiarid areas of the former
northern Nigeria. These activities of the authorities of the Nigerian
geological survey culminated in the commencement in 1928 of systematic
investigations of towns and villages for the digging of hand dug wells. In
1938, a water drilling section of the geological survey was setup and by 1947;
the engineering aspects of the water supply section were handed over to the
public works Department, which is the forerunner of Nigeria’s today’s ministry
of works while the geological survey maintained the exploration department. The
aim of studying borehole failures is to identify the factors responsible for
borehole engineering solutions. According to (Eduvie 2006), the most plausible
causes of these borehole failures can be attributed to
(i)
Design and construction
(ii)
Groundwater potential/hydro geological
consideration and
(iii)
Operational and maintenance failures.
With
the foregoing, Eduvie has failed to recognize the purely engineering factors
that could cause the failure of boreholes and this has stimulated the present
research work to establish those factors that cause failure or operational
inefficiency of water boreholes. Consequently, seepage and contact force
(intergranular force) are the two major opposing physical factors that fell within
the scope of the present work for study.
A
water borehole is a cylindrical hole usually vertical, excavated in the earth
for bringing ground water to the surface for use (Chukwurah, 1992). An
estimated 91% of total fresh water available to humanity is found as ground water
which occurs in aquifers (Chukwurah, 1992). Observation by (Baars, 1996)
reveals that several years after the drilling of a borehole, sand particles and
small sandstone particles start to break away from the borehole surface. The quantity
of particles which are transported by the fluid (water) can block and damage
the transport pipes, well casings and other equipment by the scouring of these
particles (Baars, 1996). Remedial measures range from the replacement of the
electro pump (submersible pump) to drilling of a new borehole, which is
especially a huge financial loss (Baars, 1996). This study is aimed at solving some
of the challenges facing water borehole drilling, operation and performance in
the developing countries. The problems include borehole surface soil failure,
which leads to the failure of boreholes soon after drilling and commissioning
for use. The major objective of the present research work is to investigate
seepage force which is a volume force as the fundamental physical disturbing
force that sets in motion all other secondary factors causing the homogeneous
mass of the flow region to dislodge particle by particle and also to study the
restoring effects of the contact force or the inter-granular force to the opposing
force.
The
problem will be addressed through the simulation of borehole behaviour with the
Combined Finite-Discrete Element Method of numerical study. This will be done
at both the micro and macro levels. The present research work concerns itself
with the seepage force as a disturbing force and contact force or
inter-granular force as the restoring force. The later being the force that
binds the discontinuous mass of distinct particles together by contact and the
former being the force that sets the breaking of the distinct particles into
motion and their consequent displacement. By convention the present work
assumes the fact that the restoring force i.e. the contact force
(inter-granular force) is a positive force while the disturbing force, i.e. the
seepage force is negative.
However,
for there to be failure of the walls of the borehole, the disturbing force must
exceed the restoring force which is the case with the number of boreholes that
have failed.
Moreover,
the use of the combined FDEM was necessitated by the combined continuum and
discontinuum nature of the problem area.
1.1 Statement
of the Problem
Identification
and establishment of the factors that cause the failure of boreholes is one of
the main targets of this research work. The medium under study is a
solid-liquid medium with the liquid (fluid) migrating through the voids of the
solid (granular soil) to where it is pumped for use. During this process,
whereby the fluid moves from areas of high potential to that of low potentials
there is the introduction of forces acting both on the fluid and the granular
material causing dislodgment and displacement of the particles to be collected
at the walls of the well casing. These collected particles also block the well
casing perforations or screens making the well casing inefficient to
transmitting the collected fluid into the well for pumping (Durlofsky and Aziz,
2004; Shun-cai et al, 2015; Soon et al, 2015; Zheng, 2015)......
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