# Well or screen репе tration W/D

(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. 4-15, a, b, AND c for explanation of terms NOT DEFINED in this figure.

DRAWDOWN, H-he, PRODUCED BY PUMPING A FLOW OF Qy FROM AN EQUIVALENT SLOT, IS COMPUTED FROM EQ 1 (FIG. 4-6) FOR CIRCULAR SLOT AND EQKFIG.4-8) FOR RECTANGULAR SLOT.

HEAD LOSS DUE TO CONVERGING FLOW AT WELL

(1)

TOTAL DRAWDOWN AT WELL (NEGLECTING H^)

(2)

DRAWDOWN MIDWAY BETWEEN WELLS

H – h = H – h – Ah = – Д I-J- + – (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. 4-6).

FOR EQ 1 THROUGH 4: = + Ah^

FLDWS FROM ALL WELLS ARE EQUAL.

в AND в are DRAWDOWN FACTORS OBTAINED FROM FIG. 4-21 (a AND b. RESPECTIVELY).

o m

0 FROM FIG. 4-6 AND 4-0.

U. S. Army Corps of Engineer?

Figure 4-16. 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 4-25.

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. 4-23 FOR DETERMINING THE VALUE OF R.

SEE FIG. 4-24 FOR DETERMINING THE VALUE OF Hw.

(Modified from “Foundation Engineering," G. A, Leonards, ed. ,1962, McGraw-Hill Book Company. Used with permission of McGraw-Hill 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— + £ Q-i

J rwj 1-2 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. 4-19

(Modified from “Foundation Engineering," G. A. Leonards, ed., 1962, McGraw-Hill Book Company, Used with permission of McGraw-Hill 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. 4-18).

ALL WELLS ARE FULLY PENETRATING. FLOWS FROM ALL WELLS ARE EQUAL.

SEE FIG. 4-18 FOR EXPLANATION OF TERMS NOT DEFINED IN THIS FIGURE.

ARRAY 1 -CIRCULAR ARRAY OF EQUALLY SPACED WELLS

 И)

 (2)

ARRAY 2 – SINGLE LINE OF EQUALLY SPACED WELLS

 (4)

 (5)

WHERE n-oo USE EQUATIONS GIVEN IN FIG. 4-20.4-21, AND 4-22.

ARRAY 3“ TWO PARALLEL LINES OF EQUALLY SPACED WELLS

 (6)

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. 4-18), RESPECT IVELY.

(Modified from “Foundation Engineering, " G. A. Leonards, ed., 1962, McGraw-Hill Book Company. Used with permission of McGraw-Hill Book Company.)

Figure 4-19. Drawdown factors for fully penetrating circular, line, two-line, and rectangular well arrays; line source; artesian and gravity flows.

 77777х}т77777777Я77ІЇ7777?7777777777777Я. HYDRAULIC HEAD LOSS, H IS OBTAINED FRO’

 B-B (c)

 (b)

 к Do

 DRAWDOWN, H – h. , PRODUCED BY PUMPING Q FROM AN EQUIVALENT CONTINUOUS SLOT IS COMPUTED FROM

 HEAD LOSS DUE TO CONVERGING FLOW AT WELL

 ДЬ = —In—5- W 2ff kD 277 7

 (U

 TOTAL DRAWDOWN AT WELL (NEGLECTING HYDRAULIC HEAD LOSS, Hw> Q L Q „ н-h =H-h + Ah = t— + —rr In—— w e w hDa 277 kD 2777 HEADINCREASEMIDWAY BETWEEN WELLS

 (3)

 Ah = —r— In – m 277 kD 7

 (4)

HEAD INCREASE Ah0 DOWNSTREAM OF WELLS IS EQUAL TO Ah,.„ EQ 1 .

DRAWDOWN H – hD DOWNSTREAM OF WELLS IS EQUAL TOH-hw* Ahw OR H-h{AND, CONSEQUENTLY, CAN BE COMPUTED FRO" EQ 1 (FIG. 4-1), W H E R E |7j, AND Q = Qw-H-hD CAN ALSO BE COMPUTED FROM

h – h

D *

(o/2wL)(lne/2Wr„)

(Modified from "Foundation Engineering, " G. A. Leonards, ed., 1962, McGraw-HZ Book Company. Used with permission of McGraw – Hill Book Company.)

SEE DRAWINGS IN FIG. 4-6 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.4-3).

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>

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. 4-3).

(Modified from “Foundation Engineering, " G. A. Leonards, ed.,1962, McGraw-Hill Book Company. Used with permissior of McGraw-Hill Book Company.)

Figure 4-21. 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, McGraw-Hill

Book Company. Used with permission of McGraw-Hill Book Company,)

RADIUS OF INFLUENCE, R, CAN BE ESTIMATED FOR BOTH ARTESIAN AND GRAVITY FLOWS BY

R=C(H-hw)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 4-2a(3) OF THE TEXT.

(Modified from “Foundation Engineering, " G. A. Leonards, ed„ 1962, McGraw-Hill

Book Company. Used with permission of McGraw-Hill Book Company.)

Figure 4-23. Approximate radius of influence R.

(b) Head losses in the screened section of a well Hs are calculated from figure 4-24b. 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 one-half the screen length. Other head losses can be determined directly from figure 4-24. Hydraulic head loss within a well – point system can be estimated from figure 4-25. 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.