Installation — business terrible  1 part
September 8th, 2015
a. General.
(1) Design. Design of a dewatering system requires the determination of the number, size, spacing, and penetration of wells or wellpoints and the rate at which water must be removed from the pervious strata to achieve the required groundwater lowering or pressure relief. The size and capacity of pumps and collectors also depend on the required discharge and drawdown. The fundamental relations between well and wellpoint discharge and corresponding drawdown are presented in paragraphs 42, 43, and 44. The equations presented assume that the flow is laminar, the pervious stratum is homogeneous and isotropic, the water draining into the system is pumped out at a constant rate, and flow conditions have stabilized. Procedures for transferring an anisotropic aquifer, with respect to permeability, to an isotropic section are presented in appendix E.
(2) Equations for flow and dmwdown to drainage slots and wells. The equations referenced in paragraphs 42, 43, and 44 are in two groups: flow and drawdown to slots (b below and fig. 41 through 49) and flow and drawdown to wells (c below and fig. 410 through 422). Equations for slots are applicable to



















DRAWDOWN
L[D2(ho + hs)2] L° ~2DH – D2 (h + h f
0 s
COMBINED ARTESIANGRAVITY FLOW
(Modified from “Foundation Engineering,” G. A. Leonards, ed.,1962, McGrawHill Book Company.
Used with permission of McGrawHill Book Company.)
Figure 41. Flow and head for fully penetrating line slot; singleline source; artesian, gravity, and combined flows,
flow to trenches, French drains, and similar drainage systems. They may also be used where the drainage system consists of closely spaced wells or wellpoints. Assuming a well system equivalent to a slot usually simplifies the analysis; however, corrections must be made to consider that the drainage system consists of wells or wellpoints rather than the more efficient slot. These corrections are given with the well formulas discussed in c below. When the well system cannot be simulated with a slot, well equations must be used. The figures in which equations for flow to slots and wells appear are indexed in table 41. The equations
for slots and wells do not consider the effects of hydraulic head losses Hw in wells or wellpoints; procedures for accounting for these effects are presented separately.
(3) Radius of influence R. Equations for flow to drainage systems from a circular seepage source are based on the assumption that the system is centered on an island of radius R. Generally, R is the radius of influence that is defined as the radius of a circle beyond which pumping of a dewatering system has no significant effect on the original groundwater level or piezometric surface. The value of R can be estimated







ARTESIAN FLOW
(Modified from “Foundation Engineering," G. A. Leonards, ed., 1962, McGrawHill Book Company. Used with permission of McGrawHill Book Company.)
Figure 43. Flow and head for partially penetrating line slot; singleline source; artesian, gravity, and combined flows.
FULLY PENETRATING SLOT
THE FLOW TO A FULLY PENETRATING SLOT FROM TWO LINE SOURCES, BpTH OF INFINITE LENGTH (AND PARALLEL), IS THE SUM OF THE FLOW FROM EACH SOURCE, WITH REGARD TO THE APPROPRIATE FLOW BOUNDARY CONDITIONS, AS DETERMINED FROM THE FLOW EQUATIONS IN FIG. 41. LIKEWISE, THE DRAWDOWN FROM EACH SOURCE CAN BE COMPUTED FROM THE DRAWDOWN EQUATIONS IN FIG. 41 AS IF ONLY ONE SOURCE EXISTED.
PARTIALLY PENETRATING SLOT
ARTESIAN FLOW
NOTE: WIDTH OF SLOT, b, ASSUMEO – 0.
t WITHIN THIS DISTANCE (1.3D) THE
PIEZOMETRIC SURFACE IS NONLINEAR DUE TO CONVERGING FLOW.
(o)
FLOW
t ORAWOOWN WHENyC 1.30 CAN BE ESTIMATEO BYDRAWING A FREEHAND CURVE FROM h TANGENTTOTHE SLOPE OF THE LINEARPARTATySl,3D. *
G R Avityflow
FLOW
APPROXIMATELY, BUT SOMEWHAT LESS THAN, TWICE THAT COMPUTED FROM A SINGLE SOURCE, EQ3, FIG. 43,
DRAWDOWN
APPROXIMATELY THAT COMPUTED FROM A SINGLE SOURCE, EQ 4, FIG. 41.
(Modified from “Foundation Engineering, " G. A, Leonards, ed., 1962, McGrawHill
Book Company. Used with permission of McGrawHill Book Company.)
















FLOW
FLOW TO EACH SLOT APPROXIMATELY THAT ONE SLOT WITH ONE LINE SOURCE, EQ 3, FIG. 43.
WHERE C, AND Cj ARE OBTAINED FROM FIG.(C) AND (d) ABOVE
GRAVITY FLOW
t MAXIMUM RESIDUAL HEAO MIDWAY BETWEEN THE TWO SLOTS
(Modified from “Foundation Engineering," G. A. Leonards, ed., 1962, McGrawHill Book Company. Used with permission of McGrawHill Book Company.)










(b)
U. S. Army Corps of Engineers
Figure 46. Flow and head for fully andpartiullypenetratingcircular slots; circular source ; artesian flow
from the equation and plots in figure 423. Where there is little or no recharge to an aquifer, the radius of influence will become greater with pumping time and with increased drawdown in the area being clewaterecl. Generally, R is greater for coarse, very pervious sands than for finer soils. If the value of R is large relative to the size of the excavation, a reasonably good approximation of R will serve adequately for design because flow and drawdown for such a condition are not especially sensitive to the actual value of R. As it is usually impossible to determine R accurately, the value should
be selectd conservatively from pumping test data or, if necessary, from figure 423.
(4) Wetted screen. There should always be sufficient well and screen length below the required draw – dom in a well in the formation being dewatered so that the design or required pumping rate does not produce a gradient at the interface of the formation and the well filter (or screen) or at the screen and filter that starts to cause the flow to become turbulent. Therefore, the design of a clewatering system should always be checked to see that the well or wellpoints have ade










FLOW. QT, OR DRAWDOWN, H – he. CAN BE E5TI MATED FROM
QT = (H – he)kD $ (1)
WHEREJ)I5 OBTAINED FROM PLOTS SHOWN BELOW AND PERCENT PENETRATION =WDx100
NOTE HEAD ALONG LINE AA WITHIN THE ARRAY, h, ISOBTAINED FROM FIG 49





U. S. Army Corps of Engineers
Figure 48. Flow and drawdown at slotfor fully and partially penetrating rectangular slots; circular source; artesian flow.
quate “wetted screen length hws or submergence to pass the maximum computed flow. The limiting flow qc into a filter or well screen is approximately equal to
2тіг*/Е 7.48 gallons per minute clc = і Qy x per foot of filter or screen
where
rw = radius of filter or screen к = coefficient of permeability of filter or aquifer sand, feet per minute
(5) Hydraulic head loss Hw. The equations in fig
ures 41 through 422 do not consider hydraulic head losses that occur in the filter, screen, collector pipes, etc. These losses cannot be neglected, however, and must be accounted for separately. The hydraulic head loss through a filter and screen will depend upon the diameter of the screen, slot width, and opening per foot of screen, permeability and thickness of the filter; any clogging of the filter or screen by incrustation, drilling fluid, or bacteria; migration of soil or sand particles into the filter; and rate of flow per foot of screen. Graphs for estimating hydraulic head losses in pipes, wells, and screens are shown in figures 424 and 425.

h= h + (h — h )
p e p e
U. S. Army Corps of Engineers
HYDRAULIC HEAD LOSS, IS OBTAINED FROM FIG. 42 4
RADIUS о f INFLUENCE, R, IS OBTAINED FROM FIG. 423
(a)
2ffkD (H – h)
DRAWDOWN, H ■
WHERE G IS EQUAL TO THE RATIOOF FLOW FRO,., A PARTIALLY PENETRATING WELL, Qwp, TO THAT FOR A FULLY P enetrAting WELL fO r THE SAME DRAWDOWN, Hhw, AT THEPERIPHERY OF THEWELLS.
DRAWDOWN
2. COMPUTE llh w FROM EQ 2 FOR A FULLY PENETRATING. w E L L FORA DISCHARGE OF Qwp (20N (O).
3. PLOT DRAWDOWN FOR FULLY PENETRATING WELL VS
POINT В IN I L L U S T R A T I О N – FOR THEPARTIALLY PENE
THEDRAWDOWNCURVE FORA PARTIALLY
(Modified from “Foundation EngineeringG. A. Leonards, ed., 1962, McGraw,Hill Book Company.
Used with permission of McGrawHill Book Company.)





















(Modified from “Foundation Engineering, " C. A. Leonards, ed., 1962, McGrawFIill Book Company. Used with permission of McGrawHill Book Company.)
FLOW, Q CAN BE COMPUTED FROM
ffk (2DH – d2 –
w" In (R/r )
4 w’
DRAWDOWN, H – h, CAN BE COMPUTED AT ANY DISTANCE FROM
R, DISTANCE FROM WELL AT WHICH FLOW CHANGES FROM GRAVITY TO ARTESIAN CAN BE COMPUTED FROM
R IS DETERMINED CROMFIG. 423.
EQUATIONS 1 AND 2 ARE BASED ON THE ASSUMPTION THAT THE HEAD h AT THE WELL IS AT
w
THE SAME ELEVATION AS THE WATER SURFACE IN THE WELL. THIS WILL NOT BE TRUE WHERE THE DRAWDOWN IS RELATIVELY LARGE. IN THE LATTER CASE, THE HEAD AT AND IN THE CLOSE VICINITY OF THE WELL CAN BE COMPUTED FROM EQ 4 THROUGH 9 (FIG. 4111. IN THESE EQUATIONS THE VALUE OF Q
USED IS THAT COMPUTED FROM EQ 1, ASSUMING hw EQUAL TO THE HEIGHT OF WATER IN THE WELL,
AND THE VALUE OF R COMPUTED FROM EQ 3 IS USED IN LIEU OF R.
(Modified from “Foundation Engineering,” G. A. Leonards, ed., 1962, McGrawHill Book Company. Used with permission of McGrawHill Book Company.)
Hw IS OBTAINED FROM FIG. 424
(Ы ARTESIAN FLOW ( c) GRAVITY FLOW
ARTESIAN FLOW
DRAWDOWN (H – hp) AT ANY POINT P
t DRAWDOWN FACTORS, F, FOR SEVERAL COMMON WELL ARRAYS ARE GIVEN IN FIG. 414 t FOR RELATIVELY SMALL DEWATERING SYSTEMS AND WHERE NO UNUSUAL BOUNDARY C ONDITIONS EXIST, THE RADIUS OF INFLUENCE FOR ALL WELLS CAN BE ASSUMED CONSTANT AS IN (a) ABOVE. SEE FIG. 423 FOR DETERMINING THE VALUE OF R.
(Modified from “Foundation Engineering," G. A. Leonards, ed., 1962, McGrawHill Book Company. Used with permission of McGrawHill Book Company.)
ALL WELLS ARE FULLY PENETRATING WITH A CIRCULAR SOURCE. THE FLOW, Ow, FROM ALL WELLS IS EQUAL. F = DRAWDOWN FACTOR FORANYWELL IN THE ARRAY. F = DRAWDOWN FACTOR FOR CENTER OF THEARRAY.
ARRAY 1. CIRCULAR ARRAY OF EQUALLY SPACED WELLS
DRAWDOWNAT POINTS p And c FOR ARTESIAN FLOW CANBE COMPUTED FRO M
WHERE = WELL NUMBER AS SHOWN IN THE ARRAY ABOVE.
NOTE THAT THE LOCATION OF M IS MIDWAY BETWEEN THE LINES OF WELLS AND CENTERED BETWEEN
THE END TWO WELLS OF THE LINE. THIS POINT CORRESPONDS TO THE LOCATION OF THE MINIMUM DRAWDOWN WITHIN THE ARRAY.
VALUES DETERMINED FOR F, F.AND F ARE SUBSTITUTED FOR F IN EQ 1 AN D 3 (FIG.413)To COMPUTE
w c m
DRAWDOWNAT THE RESPECTIVE POINTS.
(Modified from “Foundation Engineering, ” G. A. Leonards, ed., 1962, McGrawHill Book Company. Used with permission of McGrow – Hill Book Company.)
FULLY PENETRATING WELL


HEAD INCREASE MIDWAY BETWEEN WELLS
(Hh ) $
e y
2/ГГ
DRAWDOWN MIDWAY BETWEEN WELLS HEAD INCREASE IN CENTER OF A RING OF WELLS, Ah IS EQUAL D TO Ah and can be computed FROM EQ 1.drawdown at the w CENTER OF THE RING OF WELLS, H — h D, IS EQUAL TO H – h ^A h ^ 
OR Hh AND, CONSEQUENTLY, CAN BE COMPUTED FROM EQ 1 ( FIG. 46). e
FOR EQ 1 THROUGH 4:
FLOWS FROM ALL WELLS ARE EQUAL
SHAPE FACTOR § IS OBTAINED FROM FIG 46c.
COEFFICIENT OF PERMEABILITY
all Other terms are e XP LaIned In a, b, and c
U. S. Army Corps of Engineers
Figure 415. Flow and drawdown for fully penetrating circular well arrays; circular source; artesian flow