100 SUBSURFACE DRAINAGE

18. Schilfgaarde, J. (1965). Transient design of drainage systems. Amer. Soc. Civil Eng. Proc. 91(IR3): 9–22.

19. Moody, W.T. (1966). Nonlinear differential equation of drain spacing. Journal of Irrigation and Drainage Division, ASCE 92(IR2): 1–9.

20. Pandey, R.S. and Gupta, S.K. (1990). Drainage design equation with simultaneous evaporation from soil surface. ICID Bulletin 39(1): 19–25.

21. Singh, K.M., Singh, O.P., Ram, S., and Chauhan, H.S. (1992). Modified steady state drainage equations for transient condi- tions in subsurface drainage. Agricultural Water Management 20(4): 329–339.

22. Singh, K.M., Singh, O.P., Chauhan, H.S., and Ram, S. (1996). Comparison of subsurface drainage theories for drainage of waterlogged saline soils of Haryana state, India. Applied Engineering in Agriculture 8(5): 653–657.

23. Nikam, P.J., Chauhan, H.S., Gupta, S.K., and Ram, S. (1992). Water table behaviour in drained lands: effect of evapotran- spiration from the water table. Agricultural Water Manage- ment 20: 313–328.

24. De Boer, D.W. and Chu, S.T. (1975). Bi-level subsurface drainage theory. Transactions of the American Society of Agricultural Engineers 18(4): 664–667.

25. Bouwer, H. and Van Schilfgaarde, J. (1963). Simplified method of predicting fall of water table in drained lands. Transactions of the American Society of Agricultural Engineers 6(4): 228–291,296.

26. Chu, S.T. and DeBoer, D.W. (1976). Field and laboratory evaluation of bi-level drainage theory. Transactions of the American Society of Agricultural Engineers 19(3): 478–481. 27. Sabti, N.A. (1989). Linear and nonlinear solution of the

Boussinesq equation for the bi-level drainage problem. Agricultural Water Management 16: 269–278.

28. Verma, A.K., Gupta, S.K., Singh, K.K., and Chauhan, H.S. (1998). An analytical solution for design of bi-level drainage systems. Agricultural Water Management 37: 75–92. 29. Upadhyaya, A. and Chauhan, H.S. (2000). An analytical

solution for bi-level drainage design in the presence of evapotranspiration. Agricultural Water Management 45: 167–184.

30. Kraijenhoff Van de Leur, D.A. (1958). A study of non-steady ground water flow with special reference to a reservoir coefficient. De Ingenieur 70: 87–94.

31. Maasland, M. (1959). Water table fluctuations induced by intermittent recharge. Journal of Geophysical Research 64(5): 549–559.

32. Dass, P. and Morel-Seytoux, H.J. (1974). Subsurface drainage solutions by Galerkin’s method. Journal of Irrigation and Drainage Division 100(IR1): 1–15.

33. Marino, M.A. (1974). Water table fluctuation in response to recharge. Journal of Irrigation Drainage Division, ASCE 100: 117–125.

34. Singh, S.R. and Jacob, C.M. (1976). Numerical solution of Boussinesq equation. Journal of the Engineering Mechanics Division, Proceedings of ASCE 102(EM5): 807–823. 35. Singh, R.N. and Rai, S.N. (1989). A solution for the nonlinear

Boussinesq equation for phreatic flow using an integral balance approach. Journal of Hydrology 109(3/4): 319–323. 36. Skaggs, R.W. (1991). Modelling water table response to

subirrigation and drainage. Transactions of the American Society of Agricultural Engineers 34(1): 169–175.

37. Pandey, R.S., Bhattacharya, A.K., Singh, O.P., and Gupta, S.K. (1992). Drawdown solutions with variable drainable

porosity. Journal of Irrigation and Drainage Engineering 118(3): 382–396.

38. Pandey, R.S., Bhattacharya, A.K., Singh, O.P., and Gupta, S.K. (1997). Water table drawdown during drainage with evaporation/evapotranspiration. Agricultural Water Manage- ment 35: 61–73.

39. Ram, S., Jaiswal, C.S., and Chauhan, H.S. (1994). Transient water table rise with canal seepage and recharge. Journal of Hydrology 163: 197–202.

40. Werner, P.W. (1957). Some problems in non-artesian ground water flow. Transactions American Geophysical Union 38(4): 511–518.

41. Schmid, P.A. and Luthin, J.N. (1964). The drainage of sloping lands. Journal of Geophysical Research 69: 1525–1529. 42. Wooding, R.A. and Chapman, T.G. (1966). Groundwater flow

over a sloping impermeable layer, 1. Application of the Dupuit-Forchheimer assumptions. J. Geophys. Res. 71: 2895–2902.

43. Luthin, J.N. and Guitjens, J.C. (1967). Transient solutions for drainage of sloping land. Journal of the Irrigation and Drainage Division, Proceedings of American Society of Civil Engineers 93(IR3): 43–51.

44. Chauhan, H.S., Schwab, G.O., and Hamdy, M.Y. (1968). Analytical and computer solution of transient water table for drainage of sloping land. Water Resources Research 4(3): 673–679.

45. Childs, E.C. (1971). Drainage of ground water resting on sloping bed. Water Resources Research 7(3): 1256–1263. 46. Jaiswal, C.S. and Chauhan, H.S. (1975). A Hele-Shaw model

study of steady state flow in an unconfined aquifers resting on a sloping bed. Water Resources Research II(4): 596–600. 47. Ram, S. and Chauhan, H.S. (1987). Analytical and experi-

mental solutions for drainage of sloping lands with time varying recharge. Water Resources Research. American Geo- physical Union 23(6): 1090–1096.

48. Upadhyaya, A. and Chauhan, H.S. (2001). Falling water tables in a horizontal/sloping aquifer. Journal of Irrigation and Drainage Engg. ASCE 127(6): 376–384.

49. Kidder, E.H. and Lytle, W.F. (1994). Drainage investigation in plastic till soils of Northeastern Illinois. Agr. Eng. 39: 384–386.

50. Neal, J.H. (1934). Proper spacing and depth of tile drains determined by the physical properties of the soil. Minnesota Agr. Exp. Sta. Tech. Bull. 101.

51. De Ridder, N.A. (1973). Drainage by means of pumping from wells pp. 223–237; Theories of Field Drainage and Watershed Runoff. Vol. II. Drainage Principles and Applications; ILRI. Wageningen, the Netherlands.

52. Attia, F.A.R. and Twinhof, A. (1989). Feasibility of tube well drainage in nile valley. pp. 303–326 Chapter 13 Land Drainage in Egypt. M.H. Amer and de Ridder (Eds.). Cairo, p. 377.

53. Awan, N.M. (1991). Salinity control and reclamation project, a case study in ‘Approaches to Integrated Water Resource Management in Humid Tropics Arid and Semi Arid Zones in Developing Countries’ compiled by Maynara. M. Hufschmidt, Janusz, Kindler.

54. Smedema, B. and Zimmer, D. (1994). Vertical drainage and conjunctive use. GRID ISSN. 1021-268X, pp. 7–8.

55. Smedema, B. (Dec. 1997). Biological drainage myth or opportunity? GRID Iptrid Network Magazine, p. 9.

56. Smedema, L.K. (2000). Global needs and challenges, the role of Drainage in today’s world. Proc. 8th ICID International Drainage Workshop, 31st Jan–4th Feb, New Delhi, Vol. 1–1.

DRAWDOWN 101

DRAWDOWN

JOHNE. MOORE USGS (Retired) Denver, Colorado

According to Wilson and Moore (1), drawdown is the lowering of the water level in a well as a result of withdrawal. Drawdown data are collected to evaluate the performance of the well and to determine the aquifer’s hydraulic character (transmissivity). Drawdown measurements also provide information on the well efficiency and performance. For example, measurements can be used with well discharge data to detect deterioration of the well screen.

The drawdown in a pumping well is the sum of head loss factors (2). Some of the factors are natural processes, head loss in the aquifer, loss in the damage zone (well drilling), well development, and turbulent loss in the filter zone. The damage zone consists of drilling debris, filter cake, and drilling fluid.

When water is withdrawn from a well, the initial discharge is from casing storage and from aquifer storage near the well bore. As withdrawal continues, water is withdrawn at greater distances from the well. The cone depression or drawdown expands and deepens more slowly with time because an increasing amount of stored water is available from each foot of expansion of the cone (3). The cone of depression will continue to enlarge until the following conditions are met (4):

1. It intercepts a body of water (stream, lake, or wetland) that supplies enough water to equal the pumping rate.

2. Enough recharge from precipitation occurs within the cone of depression’s influence to equal the pumping rate.

3. Leakage occurs from overlying or underlying aquifers to equal the pumping rate.

The cone of depression around a well is controlled by the transmissivity of the aquifer. In aquifers of a low transmissivity (10,000 gpd/ft2), the cone is deep and

has steep sides and a small radius. In aquifers of high transmissivity (100,000 gpd/ft2), the cone is shallow and

has a large radius

Slichter in 1899, Thiem in 1906, and Theis in 1935 (5) introduced the equations to predict drawdown. The transmissivity of the aquifer determines the shape of the drawdown curve.

The following is a list of key terms associated with well drawdown (6):

Static level— water level of a well that is not affected by the withdrawal of ground water.

Pumping level— the level of water in the well during pumping.

Well yield— the discharge of a well or rate at which a well yields water either by pumping or free flow.

Specific capacity— an expression of the productivity of a well obtained by dividing the rate of discharge by the drawdown in the well. It should be described on the basis of the number of hours of pumping prior to the time the measurement is made because it generally decreases with time as drawdown increases.

Well efficiency (well hydraulics)— defined as the ratio of actual specific capacity to theoretical specific capacity. Actual specific capacity is related to drawdown in the well and theoretical specific capacity. Well efficiency is determined by a step drawdown test.

Step drawdown test— In this test, the well is pumped at several (three or more) successively higher pumping rates, and the drawdown at each rate is recorded. The test is usually conducted during 1 day. The discharge is kept constant through each step.

Getting access to the well to take drawdown measure- ments is sometimes difficult. Ideally, you can gain access through a pipe intended for measurements. Measurements of drawdown in wells can be obtained by one of the follow- ing methods (7):

1. wetted steel tape

2. air-line submergence method 3. electrical tape

4. pressure transducer Wetted Steel Tape

Before the 1960s, most water level measurements were made with a steel tape (most likely a 100- or 200- foot Lufkin tape). It is typically used for depths up to 90 feet. Electrical methods and pressure transducers in part have replaced tapes. However, the steel tape still has applications today, for example, to calibrate pressure transducers. To use the wetted tape method, the hydrologist will need a steel measuring tape, a weight, and carpenter’s chalk. Before the tape is lowered down the well, the lower 1 to 2 feet or so of the tape is coated with carpenter’s chalk. Problems that may be encountered using this method are moisture on the well casing, cascading water, and oil (leaking from pump lubrication). In some cases, this method can be very inaccurate. For example, if the water level is below the well screen, water flowing into the well can wash the chalk off the tape. Electrical Tape

Most electrical tapes are marked every one-tenth foot. An electrical probe is lowered into the water, which completes an electrical circuit, and this sounds a buzzer or light. Pressure Transducer

The transducer probe measures the column of water above the probe. It is very useful in aquifer tests where the water level changes rapidly with time.