The interaction between drainage from the variably saturated zone above the water table, and the response of an unconfined aquifer to pumping has been the source of debate for many decades. While various field tests (Nwankwor et al., 1992 and Moench et al., 2001) have supported the concept that variably saturated flow processes delay drainage above a falling water table, Neuman (1972, 1974, 1975), has asserted that the impact is minimal, delay in response of the water table is due to elastic storage effects, and instantaneous yield above the water table is a reasonable assumption in unconfined aquifer analysis. This assumption results in exceedingly low estimates of specific yield in comparison to other analysis techniques (Neuman, 1987). A 7-day pumping test by Bevan et al. (2005) in the unconfined aquifer at Canadian Forces Base Borden has highlighted the complexity in drainage from above the water table during pumping, as the tension saturated zone was found to increase in thickness as a function of both proximity to the pumping well, and elapsed pumping time. This extended thickness persisted for the 7-day pumping duration. Analytical analysis of the test by Endres et al. (2007) resulted in significant underestimates of specific yield in comparison to laboratory values for most solutions. Narasimham (2007) suggested that the use of numerical simulators which include variably saturated flow may provide the most accurate representation of the test results. An attempt to replicate test results using a numerical simulation of variably saturated flow by Moench (2008) could not provide a complete physical mechanism for the extension observed by Bevan et al. (2005). This study provides a detailed investigation on the effect of heterogeneity, hysteresis, and entrapped air on drainage during unconfined pumping tests using numerical simulations, field experiments, and laboratory observations. The results of the Bevan et al. (2005) pumping test are used as a standard for comparison. Three variably-saturated groundwater flow numerical codes were evaluated for their ability to replicate the variations in soil moisture content observed during pumping by Bevan et al. (2005). Results of the numerical simulations were also analyzed for their similarity to the peak and subsequent decrease in vertical gradients observed during pumping in the Borden aquifer. While the models generated vertical gradients through the capillary fringe during pumping, these gradients dissipated significantly before 1000 min. of pumping. No gradients in the saturated zone generated by the numerical model would be capable of shifting the pressure head sufficiently to cause an apparent capillary fringe extension following the first few hours of pumping. Significant gradients were persistent throughout the test at locations where saturation was less than 85%. Accounting for the formation of vertical gradients, no simulation was able to replicate the soil moisture distributions observed by Bevan et al. (2005). Based on these results, heterogeneity, hysteresis, and entrapped air were proposed as processes with the potential to significantly affect drainage from above the water table during pumping, as their investigation may provide the physical mechanism for the observed capillary fringe extension. Compaction of the aquifer material was dismissed as a potential mechanism based on the results of a proctor test. The effect of heterogeneity on drainage from the Borden aquifer during pumping was investigated numerically using geostatistical methods. A log-normal saturated hydraulic conductivity distribution was used to represent the Borden aquifer. Brooks and Corey parameters were used to describe the pressure-saturation-relative conductivity relationships. The air-entry pressure parameter was scaled to the saturated conductivity using the scaling relationship for Borden sand proposed by Keuper and Frind (1991). The Brooks and Corey lambda parameter was kept constant. A Monte Carlo analysis was performed on the results. While several realizations of the hydraulic conductivity distribution resulted in the formation of perched water during drainage, the ensemble capillary fringe thickness was unchanged from the thickness generated using a homogeneous conceptual aquifer model. No single realization produced a capillary fringe extension in which the magnitude was a function of elapsed pumping time, or distance from the pumping well. Approximation of the effect of air-entry barriers on drainage did not increase the estimated capillary fringe thickness. The presence and location of finer grained layers appeared to have a much greater impact on the thickness of the capillary fringe than the drawdown induced by pumping. Ensemble results for the hydraulic head drawdown provided improved matches to the field observations in comparison to the homogeneous numerical model during intermediate and late times in the pumping test. A mild degree of heterogeneity appears to have sufficient effect on drainage from above the water table during pumping to impact hydraulic drawdown. The effect would be magnified with the greater degree of heterogeneity that is more typical of natural aquifer systems. A 24-hour pumping test was conducted at CFB Borden to gain a better understanding of the nature of drainage during a pumping test. Due to the wet site conditions prior to the test, the moisture profile during pumping was significantly influenced by hysteresis. The hydraulic head drawdown generated during the test was insufficient to generate any drainage due to the lowering of the top of the saturated zone, and the formation of perched lenses could not occur. Hysteresis in the moisture profile was a controlling factor in this result. Although there was no significant drainage initiated due to the lowering of the top of the saturated zone, an inflection point was still apparent in the time-drawdown curve for the four monitoring wells observed. Vertical gradients measured throughout the saturated zone, including the capillary fringe, remained low throughout the duration of pumping, and no significant increase was apparent in the transition from saturated to tension-saturated conditions. Hysteresis has the potential to increase the delay in drainage as the water table falls during pumping. A laboratory tank apparatus was used to determine the effect of entrapped air, grain size distribution, and horizontal gradient on drainage in a primarily horizontal flow regime. The tank was packed on three separate occasions, once with a coarse well sorted silica sand, and twice with sand from the Borden aquifer. For each packing, the tank was drained twice, using two different horizontal gradient magnitudes. Results show that horizontal gradient magnitude has no impact on soil moisture distributions during drainage. Air-entry pressure was elevated in comparison to gravity drainage derived pressure head – saturation curves. This elevation was not transient, nor dependant on gradient or grain size distribution. The increase in air-entry pressure does not appear to be due to insufficient equilibration time between water level drops or flow redistribution around the TDR Rods. Results of this study support a conceptual model of unconfined aquifer response in which drainage from above the water table is a complex and time dependant process. Individually, heterogeneity and hysteresis have been shown to cause a time delay between the lowering of the water table and the subsequent drainage of the tension saturated zone during intermediate to late pumping times. The magnitude and duration of this delay varies by process and is a function of the degree of heterogeneity, moisture conditions in the aquifer prior to pumping, and the drawdown rate of the water table. While no individual process tested could produce the capillary fringe extension observed by Bevan et al. (2005), the investigation of each has led to an improved conceptual understanding of the response to pumping in unconfined aquifers. Due to the complex interaction of these processes it is unlikely that pumping test results, even those which include moisture content observations, could be used to accurately predict unsaturated flow parameters. Storage parameter (i.e. specific yield) estimates made using analytical solutions may not be appropriate unless delayed drainage from above the water table is properly accounted for.

The interaction between drainage from the variably saturated zone above the water table, and the response of an unconfined aquifer to pumping has been the source of debate for many decades. While various field tests (Nwankwor et al., 1992 and Moench et al., 2001) have supported the concept that variably saturated flow processes delay drainage above a falling water table, Neuman (1972, 1974, 1975), has asserted that the impact is minimal, delay in response of the water table is due to elastic storage effects, and instantaneous yield above the water table is a reasonable assumption in unconfined aquifer analysis. This assumption results in exceedingly low estimates of specific yield in comparison to other analysis techniques (Neuman, 1987). A 7-day pumping test by Bevan et al. (2005) in the unconfined aquifer at Canadian Forces Base Borden has highlighted the complexity in drainage from above the water table during pumping, as the tension saturated zone was found to increase in thickness as a function of both proximity to the pumping well, and elapsed pumping time. This extended thickness persisted for the 7-day pumping duration. Analytical analysis of the test by Endres et al. (2007) resulted in significant underestimates of specific yield in comparison to laboratory values for most solutions. Narasimham (2007) suggested that the use of numerical simulators which include variably saturated flow may provide the most accurate representation of the test results. An attempt to replicate test results using a numerical simulation of variably saturated flow by Moench (2008) could not provide a complete physical mechanism for the extension observed by Bevan et al. (2005). This study provides a detailed investigation on the effect of heterogeneity, hysteresis, and entrapped air on drainage during unconfined pumping tests using numerical simulations, field experiments, and laboratory observations. The results of the Bevan et al. (2005) pumping test are used as a standard for comparison. Three variably-saturated groundwater flow numerical codes were evaluated for their ability to replicate the variations in soil moisture content observed during pumping by Bevan et al. (2005). Results of the numerical simulations were also analyzed for their similarity to the peak and subsequent decrease in vertical gradients observed during pumping in the Borden aquifer. While the models generated vertical gradients through the capillary fringe during pumping, these gradients dissipated significantly before 1000 min. of pumping. No gradients in the saturated zone generated by the numerical model would be capable of shifting the pressure head sufficiently to cause an apparent capillary fringe extension following the first few hours of pumping. Significant gradients were persistent throughout the test at locations where saturation was less than 85%. Accounting for the formation of vertical gradients, no simulation was able to replicate the soil moisture distributions observed by Bevan et al. (2005). Based on these results, heterogeneity, hysteresis, and entrapped air were proposed as processes with the potential to significantly affect drainage from above the water table during pumping, as their investigation may provide the physical mechanism for the observed capillary fringe extension. Compaction of the aquifer material was dismissed as a potential mechanism based on the results of a proctor test. The effect of heterogeneity on drainage from the Borden aquifer during pumping was investigated numerically using geostatistical methods. A log-normal saturated hydraulic conductivity distribution was used to represent the Borden aquifer. Brooks and Corey parameters were used to describe the pressure-saturation-relative conductivity relationships. The air-entry pressure parameter was scaled to the saturated conductivity using the scaling relationship for Borden sand proposed by Keuper and Frind (1991). The Brooks and Corey lambda parameter was kept constant. A Monte Carlo analysis was performed on the results. While several realizations of the hydraulic conductivity distribution resulted in the formation of perched water during drainage, the ensemble capillary fringe thickness was unchanged from the thickness generated using a homogeneous conceptual aquifer model. No single realization produced a capillary fringe extension in which the magnitude was a function of elapsed pumping time, or distance from the pumping well. Approximation of the effect of air-entry barriers on drainage did not increase the estimated capillary fringe thickness. The presence and location of finer grained layers appeared to have a much greater impact on the thickness of the capillary fringe than the drawdown induced by pumping. Ensemble results for the hydraulic head drawdown provided improved matches to the field observations in comparison to the homogeneous numerical model during intermediate and late times in the pumping test. A mild degree of heterogeneity appears to have sufficient effect on drainage from above the water table during pumping to impact hydraulic drawdown. The effect would be magnified with the greater degree of heterogeneity that is more typical of natural aquifer systems. A 24-hour pumping test was conducted at CFB Borden to gain a better understanding of the nature of drainage during a pumping test. Due to the wet site conditions prior to the test, the moisture profile during pumping was significantly influenced by hysteresis. The hydraulic head drawdown generated during the test was insufficient to generate any drainage due to the lowering of the top of the saturated zone, and the formation of perched lenses could not occur. Hysteresis in the moisture profile was a controlling factor in this result. Although there was no significant drainage initiated due to the lowering of the top of the saturated zone, an inflection point was still apparent in the time-drawdown curve for the four monitoring wells observed. Vertical gradients measured throughout the saturated zone, including the capillary fringe, remained low throughout the duration of pumping, and no significant increase was apparent in the transition from saturated to tension-saturated conditions. Hysteresis has the potential to increase the delay in drainage as the water table falls during pumping. A laboratory tank apparatus was used to determine the effect of entrapped air, grain size distribution, and horizontal gradient on drainage in a primarily horizontal flow regime. The tank was packed on three separate occasions, once with a coarse well sorted silica sand, and twice with sand from the Borden aquifer. For each packing, the tank was drained twice, using two different horizontal gradient magnitudes. Results show that horizontal gradient magnitude has no impact on soil moisture distributions during drainage. Air-entry pressure was elevated in comparison to gravity drainage derived pressure head – saturation curves. This elevation was not transient, nor dependant on gradient or grain size distribution. The increase in air-entry pressure does not appear to be due to insufficient equilibration time between water level drops or flow redistribution around the TDR Rods. Results of this study support a conceptual model of unconfined aquifer response in which drainage from above the water table is a complex and time dependant process. Individually, heterogeneity and hysteresis have been shown to cause a time delay between the lowering of the water table and the subsequent drainage of the tension saturated zone during intermediate to late pumping times. The magnitude and duration of this delay varies by process and is a function of the degree of heterogeneity, moisture conditions in the aquifer prior to pumping, and the drawdown rate of the water table. While no individual process tested could produce the capillary fringe extension observed by Bevan et al. (2005), the investigation of each has led to an improved conceptual understanding of the response to pumping in unconfined aquifers. Due to the complex interaction of these processes it is unlikely that pumping test results, even those which include moisture content observations, could be used to accurately predict unsaturated flow parameters. Storage parameter (i.e. specific yield) estimates made using analytical solutions may not be appropriate unless delayed drainage from above the water table is properly accounted for.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第15034号 / 工博第3183号 / 新制||工||1479(附属図書館) / 27495 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 関口 秀雄, 教授 間瀬 肇, 教授 後藤 仁志 / 学位規則第4条第1項該当

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This study discusses the mathematical modeling of groundwater flows, and the bases for the development of a numerical model that simulates the flow in unconfined aquifers, affected by singularities like wells and interconnected streams. The main application of the model is directed to urban areas with water wells. Numerical approximations are used to estimate changes of the piezometric levels, groundwater drawdowns and water flow rates in the aquifer caused by simultaneous pumping from multiple wells. In this study, we used the finite differences method for the numerical treatment of the differential governing equation. In this context, all spatial derivatives were discretized by central differences of the second order. Two explicit schemes were used for the treatment of the temporal derivative: the first order Euler scheme, and the fourth order Adams-Bashforth scheme. Two schemes were also used to model the sinks, that is the extraction of water by the wells. The results of these two schemes are compared with a hybrid model that uses analytical solutions in small areas within the radius of influence of the wells, a numerical solution in the remaining area. As a case study, the model is applied to our area situated in the urban fabric of the city of Araguari (MG), in the area of the Bauru aquifer. The model has the potential to help future guidelines for the management of the free aquifers underlying urban areas, intending its best use, and indicating possible saturation places of exploitation. / O presente trabalho aborda a modelagem matemática do escoamento de águas subterrâneas. E os fundamentos para elaboração de um modelo numérico que simule o escoamento em aquíferos não confinados, submetidos a singularidades como poços e córregos interconectados. O modelo visa à aplicação preferencial em zonas urbanas que apresentam poços tubulares distribuídos na sua área. São utilizadas aproximações numéricas com o objetivo de estimar as mudanças nas cotas piezométricas, os rebaixamentos do lençol freático e as velocidades de escoamento da água no aquífero, ocasionadas pelo bombeamento simultâneo de múltiplos poços. Neste trabalho, utilizou-se o método de diferenças finitas para tratamento numérico da equação diferencial governante. Neste contexto, todas as derivadas espaciais foram discretizadas por diferenças centrais de segunda ordem. Dois esquemas explícitos foram utilizados para o tratamento da derivada temporal: o esquema de Euler, de primeira ordem, e o esquema de Adams- Bashforth, de quarta ordem. Também foram utilizadas duas alternativas para modelação do termo sumidouro, que representa a extração de água pelos poços. Os resultados desses dois esquemas são comparados com um modelo híbrido que utiliza soluções analíticas em áreas pequenas, dentro do raio de influência dos poços e, nas outras áreas, uma solução numérica por diferenças finitas. A área de aplicação do modelo situa-se sob a malha urbana da cidade de Araguari (MG), nos domínios do aquífero Bauru. O modelo tem potencial de auxiliar as futuras diretrizes para a gestão de aquíferos livres sotopostos a zonas urbanas, para seu melhor aproveitamento, indicando possíveis lugares de saturação de explotação. / Mestre em Engenharia Civil