Installation — business terrible  1 part
September 8th, 2015
(a) Most of the equations and graphs presented in this manual for flow and drawdown to slots or well systems were basically derived for fully penetrating drainage slots or wells. Equations and graphs for partially penetrating slots or wells are generally based on those for fully penetrating drainage systems modified by model studies and, in some instances, mathematical derivations. The amount or percent of screen penetration required for effective pressure reduction or interception of seepage depends upon many factors, such as
thickness of the aquifer, distance to the effective source of seepage, well or wellpoint radius, stratification, required “wetted screen length,” type and size of excavation, and whether or not the excavation penetrates alternating pervious and impervious strata or the bottom is underlain at a shallow depth by a less pervious stratum of soil or rock. Where asizeable open excavation or tunnel is underlain by a fairly deep stratum of sand and wells are spaced rather widely, the well screens should penetrate at least 25 percent of the thickness of the aquifer to be dewatered below the
SEE FIG. 415, a, b, AND c for explanation of terms NOT DEFINED in this figure.
DRAWDOWN, Hhe, PRODUCED BY PUMPING A FLOW OF Qy FROM AN EQUIVALENT SLOT, IS COMPUTED FROM EQ 1 (FIG. 46) FOR CIRCULAR SLOT AND EQKFIG.48) FOR RECTANGULAR SLOT.
HEAD LOSS DUE TO CONVERGING FLOW AT WELL
(1)
TOTAL DRAWDOWN AT WELL (NEGLECTING H^)
(2)
HEAD INCREASE MIDWAY BETWEEN WELLS
DRAWDOWN MIDWAY BETWEEN WELLS
H – h = H – h – Ah = – Д IJ + – (6 – 6L)
m w " kD и 11 mJ
HEAD INCREASE IN CENTER OF A RING OF VfELLS. All.., IS EQUAL TO Ah AND CAN BE COMPUTED
D W
FROM EQ 1.
DRAWDOWN AT THE CENTER OF A RING OF WELLS, H – hQ, IS EQUAL TO H – hw – Ahw OR H — h^ AND, CONSEQUENTLY, can BE COMPUTED FROM EQ 1 (FIG. 46).
FOR EQ 1 THROUGH 4: = + Ah^
FLDWS FROM ALL WELLS ARE EQUAL.
в AND в are DRAWDOWN FACTORS OBTAINED FROM FIG. 421 (a AND b. RESPECTIVELY).
o m
0 FROM FIG. 46 AND 40.
U. S. Army Corps of Engineer?
Figure 416. Flow and dmwdown for partially penetrating circular and rectangular well arrays; circular source; artesian flow.
bottom of the excavation and more preferably 50 to 100 percent. Where the aquifer(s) to be dewatered is stratified, the drainage slots or well screens should fully penetrate all the strata to be dewatered. If the bottom of an excavation in a pervious formation is underlain at a shallow depth by an impervious formation and the amount of “wetted screen length” avail
able is limited, the drainage trench or well screen should penetrate to the top of the underlying less pervious stratum. The hydraulic head loss through various sixes and types of header or discharge pipe, and for certain well screens and (clean) filters, as determined from laboratory and field tests, are given in figures
4 24 and 425.
EQUATIONS FOR FLOW AND DRAWDOWN FOR a fully PENETRATING WELL WITH Д LINE SOURCE OF INFINITE LENGTH WERE DEVELOPED UTILIZING THE METHOD OF IMAGE WELLS. THE IMAGE well IS CONSTRUCTED AS SHOWN IN (a) BELOW.
IN THE EQUATIONS ABOVE, THE DISTANCE TO THE LINE SOURCE MUST BE COMPARED TO THE CIRCULAR RADIUS OF INFLUENCE, R, FOR THE WELL. IF 2L IS GREATER THAN R, THE WELL WILL PERFORM AS IF SUPPLIED BY A CIRCULAR SOURCE OF SEEPAGE, AND SOLUTIONS FOR A LINE SOURCE OF SEEPAGE ARE NOT APPLICABLE.
SEE FIG. 423 FOR DETERMINING THE VALUE OF R.
SEE FIG. 424 FOR DETERMINING THE VALUE OF Hw.
(Modified from “Foundation Engineering," G. A, Leonards, ed. ,1962, McGrawHill Book Company. Used with permission of McGrawHill Book Company.)
WHERE
and Qw = flow from WELL і
r, S DISTANCE FROM WELL і TO POINT P
GRAVITY FLOW
DRAWDOWN (н2 – Нр)дт ANY POINT P
WHERE F’t’S COMPUTED FROM EQ 2. P
ARTESIAN OR GRAVITY FLOW
DRAWDOWN AT ANY WELL, j, FOR ARTESIAN OR GRAVITY FLOW CAN BE COMPUTED FROM EQ 1 OR 3, RESPECTIVELY, SUBSTITUTING F ‘ FOR FI
2L. i>n S..
Fw = Qwj ІП— + £ Qi
J rwj 12 lj
Г. * DISTANCE FROM EACH WELL TO WELL j
у
t DRAWDOWN FACTORS, F*. FOR SEVERAL COMMON WELL ARRAYS A R E G IVE N I N FIG. 419
(Modified from “Foundation Engineering," G. A. Leonards, ed., 1962, McGrawHill Book Company, Used with permission of McGrawHill Book Company.)
H— L
V
ARRAY 2
= DRAWDOWN FACTOR FOR CENTER OF ARRAY.
F’ "DRAWDOWN FACTOR FORANYWELLOFARRAY
w
FB – DRAWDOWN FACTOR FOR MIDWAY BETWEEN LAST TWO WELLS (ARRAY 2). J
VALUES DETERMINED FOR DRAWDOWN FACTORS ARE SUBSTITUTED INTO EQ 1 OR 3 (FIG. 418).
ALL WELLS ARE FULLY PENETRATING. FLOWS FROM ALL WELLS ARE EQUAL.
SEE FIG. 418 FOR EXPLANATION OF TERMS NOT DEFINED IN THIS FIGURE.
ARRAY 1 CIRCULAR ARRAY OF EQUALLY SPACED WELLS



ARRAY 2 – SINGLE LINE OF EQUALLY SPACED WELLS



WHERE noo USE EQUATIONS GIVEN IN FIG. 420.421, AND 422.
ARRAY 3“ TWO PARALLEL LINES OF EQUALLY SPACED WELLS

ARRAY 4 – RECTANGULAR ARRAY OF EQUALLY SPACEDWELLS
APPROXIMATE METHOD. COMPUTE F’ANDF’ FROM EQ 1 OR 2 AND 3 RESPECTIVELY, WHERE A IS
SUBSTITUTED FOR A AND
EXACT METHOD. COMPUTE AND from EQ 2 An D 4 ( FIG. 418), RESPECT IVELY.
(Modified from “Foundation Engineering, " G. A. Leonards, ed., 1962, McGrawHill Book Company. Used with permission of McGrawHill Book Company.)
Figure 419. Drawdown factors for fully penetrating circular, line, twoline, and rectangular well arrays; line source; artesian and gravity flows.
























HEAD INCREASE Ah0 DOWNSTREAM OF WELLS IS EQUAL TO Ah,.„ EQ 1 .
DRAWDOWN H – hD DOWNSTREAM OF WELLS IS EQUAL TOHhw* Ahw OR Hh{AND, CONSEQUENTLY, CAN BE COMPUTED FRO" EQ 1 (FIG. 41), W H E R E 7j, AND Q = QwHhD CAN ALSO BE COMPUTED FROM
h – h
D *
(o/2wL)(lne/2Wr„)
(Modified from "Foundation Engineering, " G. A. Leonards, ed., 1962, McGrawHZ Book Company. Used with permission of McGraw – Hill Book Company.)
SEE DRAWINGS IN FIG. 46 AND FIGURES la) AND ( b) BELOW FOR DEFINITIONS OF TERMS IN EQUATIONS.
DRAWDOWN, H – h, PRODUCED BY PUMPING FROM AN EQUIVALENT CONTINUOUS
SLOT IS COMPUTED FROM EQ1 ( FIG.43).
HEAD LOSS DUE TO CONVERGING FLOW AT WELL
Q в
Л I W a
Ah = —j——
w к d
TOTAL DRAWDOWN AT WELL (NEGLECTING Hw>
HEAD INCREASE MIDWAY BETWEEN WELLS
Q в
A I W П
A hm = —:——
m к D
HEAD INCREASE AhQ DOWNSTREAM OF WELLS IS EQUAL TO Ahw_EQ1. DRAWDOWN H – h DOWNSTREAM OF WELLS IS EQUAL TO H h – Ah OR H – h
D W W Є
AND, CONSEQUENTLY, CAN BE COMPUTED F ROM EQ 1 (fig. 43).
(Modified from “Foundation Engineering, " G. A. Leonards, ed.,1962, McGrawHill Book Company. Used with permissior of McGrawHill Book Company.)
Figure 421. Flow and drawdown for fully and partially penetrating infinite line of wells; line source; artesian flow.
HEAD INCREASE AH DOWNSTREAM OF WELLS IS EQUAL TO ДЬ (EQ 1
D W
DRAWDOWN H2 – h2 DOWNSTREAM OF WELLS IS EQUAL TO
D
Ы – h2
V—.—ТГ
— In—
2nL 2m
(Modified from “Foundation Engineering, "G. A. Leonards, ed., 1962, McGrawHill
Book Company. Used with permission of McGrawHill Book Company,)
RADIUS OF INFLUENCE, R, CAN BE ESTIMATED FOR BOTH ARTESIAN AND GRAVITY FLOWS BY
R=C(Hhw)Vk
WHERE R, H, AND h ARE DEFINED PREVIOUSLY w
AND EXPRESSED IN FEET. COEFFICIENT OF PERMEABILITY, k, IS EXPRESSED IN 10’4 CM/SEC.
AND C=3 FOR ARTESIAN AND GRAVITY FLOWS
TO A WELL.
C = 1.5 TO 2.0 FOR A SINGLE LINE OF WELLPOINTS.
THEVALUEOF R FOR (h – hj = 10 FT CAN BE DETERMINED FROM THE PLOT HEREIN WHEN EITHER THE D10 SIZE OR PERMEABILITY OF THE MATERIAL IS KNOWN. THE VALUE OF R WHEN (H Ю
CAN BE DETERMINED BY MULTIPLYING THE R VALUE OBTAINED FROM THE PLOT BY THE RATIO OF THE ACTUAL VALUE OF (H – h ) TO 10 FT.
A DISCUSSION ON THE DETERMINATION OF R FROM EQ 1 AND PUMPING TESTS IS CONTAINED IN PARAGRAPH 42a(3) OF THE TEXT.
(Modified from “Foundation Engineering, " G. A. Leonards, ed„ 1962, McGrawHill
Book Company. Used with permission of McGrawHill Book Company.)
Figure 423. Approximate radius of influence R.
(b) Head losses in the screened section of a well Hs are calculated from figure 424b. This head loss is based on equal inflow per unit of screen surface and turbulent flow inside the well and is equivalent to the entire well flow passing through onehalf the screen length. Other head losses can be determined directly from figure 424. Hydraulic head loss within a well – point system can be estimated from figure 425. As stated in a(4) above, flow into a well can be impeded by the lack of “wetted screen length,” in addition to hydraulic head losses in the filter or through the screens and/or chemical or mechanical clogging of the aquifer and filter.