Modelling the Effect of Contact and Seepage Forces on the Failure of Water Borehole

Modelling the Effect of Contact and Seepage Forces on the Failure of Water Borehole

CHAPTER ONE

Aim and Objectives of Study

The aim of the study will be achieved through the following objectives:

To determine the force that causes the dislodgement of the particles and their consequent displacement.
To determine the interaction pattern between soil particles, the magnitude and direction of the contact force between grains of soil.
To determine the effect of the transient hydraulic dynamics of the fluid on the soil particles.
To determine the continuum and Discontinuum principles are involved in the present work.
And to determine the geotechnical engineering measures to adopt to accommodate the failure of boreholes.

By proffering solution and answers to the above objectives by restoring equilibrium between the disturbing force (seepage force) and restoring force (contact force) applying computational and numerical methods on physical fundamental laws, the present work would be arriving at the thesis of the work.

CHAPTER TWO

FINITE-DISCRETE ELEMENT MODELING

Discrete Element Method

The Discrete Element Method (DEM) was first introduced in 1979 by Cundall and Strack (Cundal and Strack 1979). It has always been developed in the manner that it simulates the complex physical features of various materials using more advanced model with higher-accuracy. The main methodology is widely adopted into many theoretical investigations and practical applications, and has particularly been proved to be adequate for the modeling of granular materials such as adhesive clays, cohesionless sands, loose or dense soil and rigid gravels (Wan, 2011; Zhang et al, 2015; Limin et al, 2015). Distinct element modeling which is also called discrete element modeling is in fact a type of finite element modeling. Every element represents one grain. The main difference from the normal finite element modeling is that due to deformation, some contacts between the grains can be lost and new contacts can be made. This causes softening and hardening respectively of the structure. Because of this, the global stiffness matrix of the complete structure has to be rebuilt constantly (Baars 1996; Sergio et al, 2015; Manne and Neelima, 2015). For non-cohesive materials there is also a second reasons why this matrix has to be updated, the behaviour of the contacts both in the normal and the shear directions is not linear, which means that the stiffness K_n and K_s of these contacts, have to be recalculated continuously. If the boundary condition of the structure: forces or displacements are changed, then this will affect every grain (Zhu & Yu, 2006). All grains will be displaced then in such a way that new force equilibrium is created. For the present system under consideration, the case in hand goes beyond the dislodgment of the discrete elements of the soil material and their consequent displacement to the wall of the well casing, there is considerable failure and deformation of these elements (Ferdowsi & Shafipour, 2009; Manne and Neelima, 2015).

CHAPTER THREE

MATERIALS AND METHODS

Numerical Implementation And Formulation

Formulation of Problem Equations

Contact force (inter-granular force) and seepage force are two fundamental physical phenomena under serious study in the present work because of their pronounced effect on the failure of the walls of water boreholes. They are two opposing forces i.e. disturbing and restoring forces and therefore deserve keen attention and study. The basic principle involved in the formulation is the combined FDEM because of the continuum and discontinuum nature of the studied region. From the foregoing, the problem of contact force (intergranular force) existing within the region of the soil mass or volume is a discontinuum problem. Using the discrete element method in the formulation of the matrix contact force equation, where every particle that make up the soil mass is considered a discrete element. Similarly, the problem of volume force or seepage force is a continuum problem and employs the finite element method in its formulation (Pan et al, 2014a; Pan et al, 2014^b; Yulin and HuaLong, 2014; Hui et al, 2013).

CHAPTER FOUR

RESULTS AND DISCUSSION

Results

Laboratory Results

The result of geophysical study carried out on the study sample is presented

CHAPTER FIVE

CONCLUSION AND RECOMMENDATIONS

Conclusions

Interestingly, the following conclusions can be drawn from the study;

The modelling of the effect of contact and seepage forces on the failure of water boreholes has yielded validated results as shown by graphs and equations. An expression has been deduced from the model as shown in equations (120) and (140) to compute critical hydraulic head causing quicksand effect and the hydraulic head at which safe pumping is restored in boreholes across Umuahia and other south eastern urban and suburban dwellings 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.
Irrespective of the fact that an increase in hydraulic head resulted in increases in discharge, the system should be operated at a head safe for the performance of the well.
And from the correlation analysis carried out on the model and the observed values, the critical state condition has shown a perfect correlation of 1.00 while that of the equilibrium state correlation has also shown a near perfect correlation of 0.99.
Finally, so long as the model hydraulic head expression generated is used under the specified conditions, safe pumping can be achieved.

Recommendations for Further Research

We recommend further research into the cause of the failure of boreholes considering other factors thus underground flow factors and some chemical factors within and outside Eastern Nigeria.

REFERENCES

Abia State Ministry of Environment (2014), Geological Data of Umuahia, Abia State.
Agunwamba, J.C. (2007), Engineering Mathematical Analysis, De-Adroit Innovation, Enugu.
Alaneme, G (2014), Properties of granular soil and its relevance to civil engineering works, Unpublished B.Eng Project, Department of Civil Engineering, Michael Okpara University of Agriculture, Umudike.
American Society for Testing Materilas, (2007), Annual Book of ASTM Standards, Part 19, Soil and Rock, Philadelphia.
Amorin, R. and Broni-Bediako, K. (2010), Application of Minimum Curvature Method to Wellpath calculations, International Journal of Engineering and Mathematical Intelligence, 1(3); 69-80.
Baars, S. (1996), Discrete Element Analysis of Granular Materials, TROISS, Netherland.

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