Assessment of Granular Soil Failure at the Water Borehole Depth in South Eastern Nigeria by Discrete and Finite Element Methods

Abstract

Failures of water boreholes that have impeded the performance and operation of boreholes have been recorded in recent times across the world and mostly in developing countries and within the south eastern Nigeria. 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. The 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$$ {\text{h}}_{{\left({\text{x}} \right)}} \, = \,0.000524{\text{r}}^{2} [{\text{X}}_{5} (5 - (2*{\text{SF}}_{{{\text{x}}_{2} }} ))] $$ while an expression for the safe hydraulic head during well pumping was developed and given as$$ {\text{H}}_{{\left({\text{x}} \right)}} = 0.0065814.{\text{r}}^{4} {\text{X}}_{5} \aleph_{{{\text{x}}_{2} }} $$. The ability of the model to predict results was verified using the results of the 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.