## MODELLING THE EFFECT OF CONTACT AND SEEPAGE FORCES ON THE FAILURE OF WATER BOREHOLE

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.

Title page
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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