Continuum and discontinuum problems were considered in the solid-liquid medium under study. The necessitated the use of combined finite-discrete element method to generate model expressions from contact force and seepage force considered to be the major forces contributing to the flow of fluid through soil mass and boiling or quicksand effect when seepage force becomes more in effect under critical hydraulic gradient and / or critical hydraulic head. The equilibrium model has deduced an expression for the safe hydraulic head during well pumping as = and this has been verified using a laboratory check; prototype well failure test. It has been established that there is strong agreement between model result and the laboratory check at 1.8m flow distance and the correlation analysis carried out has also shown a perfect correlation of 0.989879999701. Note, a perfect correlation lies between -1 (perfect negative) and 1 (perfect positive) (Agunwamba, 2007; Inyama and Iheagwam, 1995).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. For the system under study, the safe hydraulic head must be maintained. Finally, as long as the model hydraulic head expression deduced is used under the above conditions, safe pumping can be achieved at any voltage between 150volts and 240volts.
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