Subsurface Hydraulics in the 

Area of the Gila River 

Phreatophyte Project, 

Graham County, Arizona

GEOLOGICAL SURVEY PROFESSIONAL PAPER 655-F

Subsurface Hydraulics in the 

Area of the Gila River 

Phreatophyte Project, 

Graham County, Arizona

By RONALD L. HANSON

fTith a section on AQUIFER TESTS

By S. G. BROWN

GILA RIVER PHREATOPHYTE PROJECT

GEOLOGICAL SURVEY PROFESSIONAL PAPER 655-F

An evaluation of the aquifer constants and 

ground-water movement in the alluvial and 

has in-fill deposits of the Gila River 

Phreatophyte Project area

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1972
UNITED STATES DEPARTMENT OF THE INTERIOR 

ROGERS G. B. MORTON, Secretary

GEOLOGICAL SURVEY 

V. E. McKelvey, Director

Library of Congress catalog-card No. 78-187308

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 - Price 40 cents (paper cover)

Stock Number 2401-2051
CONTENTS

Page

Abstract ....._.._._.._-.___-...._._...--_..._._._. Fl 

Introduction ---______-_____-__________-__---.__-_-__ 1

Description of study area and water-bearing deposits _ _ 1 

Determination of aquifer constants _______-_-_--__--_ 4

Storage coefficient --_______-__.--.--__--_-____-- 4

Aquifer tests of the alluvium and basin fill . _ _ - _ _ _ 6 

Alluvium ---_____----------------------_-_- 6

Aquifer test at section 1, by S. G.

Brown _____-__-_--____-__--_-_---_-- 6

Flood-wave propagation analysis ____._.__ 10

Analysis of cyclic fluctuations of water 

levels ______------------__-----_------ 14

Pag-;

Determination of aquifer constants Continued 

Alluvium Continued

Constant-head drain-function analysis _. _ _ F14 

Slugtests ------------------------------ 16

Basin fill ---------------------------------- 17

Aquifer tests at wells 0531 and 0532 ------ 17

Analysis of water-level recessions -------- 17

Geothermal tests at wells 1141 and 

1756 ---__-----_--.------------------ 22

Evaluation of results _..._.--__----____--_-_--___--- 23

Ground-water movement _-___-_-___-_.-_---__------- 2r~

Conclusions ---------------------------------------- 2i~

References cited ------------------------------------ 27

ILLUSTRATIONS

Pag?

FIGURE 1. Map of project area, showing location of cross sections, data-collection sites, boundaries of saturated

alluvium, and the contact between the basin fill and igneous and metamorphic rock ..-.--_.-_--_.__ FZ

2. Geologic section across the study area ___-_____-_-__------.----------------------------------------- 4

3. Profiles of soil-moisture content at well 1958, showing increase in water level and change in moisture content in the capillary zone --------------------------------------------------------------- 5

4. Semilogarithmic graphs of drawdown in observation wells near well C-l, showing results of the

modified Theis type analysis --_-____________-___----____-------------_-------------------------- 8

5. Schematic map showing position of terrace, flood-plain, and river wells, and their designation when

used as reference and observation wells in the flood-wave propagation analysis ---------------- _.__. 11

6. Observed and computed hydrographs at observation well 0307, July 16-September 24, 1967 ------------ 12

7. Graph showing relation between flood amplitude at the reference wells and computed diffusivity at

the observation wells ___-___-__________________-___.________-_______-___--__---_--_---____-_-__ 13

8. Graph showing frequency distribution of diffusivity derived from the flood-wave propagation analysis, using the combination of river and terrace wells at eight sites during the 1968 flood period _ .. _ 13

9. Graph showing relation between stage ratio, sr/2s0, and distance from the river to the well for nine 

wells in the flood plain, where sr/2s0 is an average of four flood cycles during July and August 

1964 ....-_----_........_....._....._._.._...__......................._............_....._.... 15

10. Plots of af/t versus s, for the left-bank and right-bank wells in section 5, at t = 2.4 days, following a rise in river stage on July 17, 1967 --__ .-__--.-...._----____---_---------_-_-_---_.---_.__- 16

11. Time-drawdown plot and the matching nonleaky type curve for aquifer test of basin fill at well

0532 --------------___-----_.___-____-__._-_._---_--_- 18

12. Time-recovery plot of aquifer test in basin fill at well 0532 _-_---__-------_-..---_--___.----_---- - - - - 19

13. Semilog plots of seasonal water-level recessions in five basin-fill wells and straight lines averaging

their slopes for obtaining the time interval per log cycle of water-level change ------------------ 20

14. Graphs of average water-table profiles in the basin fill near cross-section 9 during the periods June

2 to August 8, 1966, and January 17 to March 19, 1969 ____------_-------------_----------------- 22

15. Graphs of /3 type curves and temperature profiles in the basin fill at wells 1141 and 1756 ------------ 24

16. Schematic block diagram showing ground-water-flow pattern in alluvium and basin fill -__----__---._.--- 26

ra
IV CONTENTS

TABLES

Page

TABLE 1. Comparison of storage-coefficient determinations before and after clearing phreatophytes from the

flood plain __----_--_-._---_._____-_._____..___.___.._____._______.._-_.___---_-_.-___-----__-_ F5

2. Average storage coefficient, number of determinations of S per well, and standard deviation of St per

well for 34 wells in the flood plain of study area -__---_-___--__-___-------------------------- _ _ _ _ 5

3. Summary of transmissivities and storage coefficients at observation wells used in the aquifer tests at

section 1 ___--______-___________.___.___________._____-___-__________-----------_---------_-_-- 10

4. Diffusivities at the sites of selected wells in the alluvium _--_____---__--_-----------------_---------- 11

5. Summary of alluvium diffusivities derived from flood-wave propagation analysis, using various combinations of river, flood-plain, and terrace wells _._ --____--___-_-_------------------------------ 13

6. Example of tabulations used to define the average period of flood-stage fluctuation and the average

stage ratio at well 0105 for four flood cycles during July and August 1964 .____---__----------_--- 14

7. Diffusivities for five wells at sections 1 and 5, derived from constant-head drain-function analysis ___-__-. 16

8. Description of basin-fill wells used in water-level-recession analysis _________----_---------------------- 19

9. Diffusivities at five wells in basin fill computed from selected water-level recessions, using equation 9 ------ 19

10. Water-level heads, water-level changes, distances between wells, time increments, and corresponding 

diffusivities, computed from equation 10 using water-level recessions at wells 0730, 0731, and 

0729 during 1966 and 1969 ...-.._...__.__.-..-..__-_-___-_-------..---------------------------- 22

11. Water-temperature observations in wells 1141 and 1756, from the geothermal test __----__---_---------- 23

12. Summary of diffusivities and transmissivities for the alluvium and basin fill ___-___---------------------- 25

13. Hydraulic head, distance between well and outflow boundary, width of basin fill, and corresponding 

basin-flll flow computed from equation 14 for five wells on the right bank and six wells on the 

left bank _-__._-.-_.______._..__...____.._..._.___._._._._-_.-...---.---------------.---------- 26
GILA RIVER PHREATOPHYTE PROJECT

SUBSURFACE HYDRAULICS IN THE AREA OF

THE GILA RIVER PHREATOPHYTE PROJECT,

GRAHAM COUNTY, ARIZONA

By RONALD L. HANSON

ABSTRACT

Along a 15-mile reach of the Gila River valley upstream 

from the San Carlos Reservoir in south-central Arizona, the 

flood plain and its adjacent terraces are underlain by basin 

fill and alluvial deposits. The basin fill consists of silt, sand, 

and clay and is estimated to be more than 1,000 feet thick. 

The alluvium consists of as much as 60 feet of gravel, sand, 

and silt and fills a 6,000-foot-wide valley incised in the 

basin fill.

Results obtained by using several analytical techniques indicate that the average storage coefficients for the basin fill 

and alluvium are 0.0005 and 0.15, respectively. The average 

transmissivities for the basin fill and alluvium are 15 cubic 

feet per day per foot (110 gallons per day per foot) and 

28,000 cubic feet per day per foot (210,000 gallons per day 

per foot), respectively. Estimates of hydraulic conductivity 

are 0.015 foot per day (0.11 gallon per day per square foot) 

for the basin fill and 695 feet per day (5,200 gallons per 

day per square foot) for the alluvium.

Downvalley ground-water flow through the alluvium averages 5.1 acre-feet per day. Estimates of flow from the basin 

fill into the overlying alluvium range from 0.14 to 2.4 acrefeet per day per mile of valley length.

INTRODUCTION

The primary objective of the Gila River Phreatophyte Project is to evaluate evapotranspiration from 

an analysis of all the significant components comprising the hydrologic system (Culler and others, 

1970). Because ground water is a principal component in the hydrologic system, a relatively accurate 

evaluation of its amount and rate of movement 

through the project area is a prerequisite to making 

reliable estimates of evapotranspiration.

This ground-water flow is a function of the hydraulic properties of the water-bearing material 

underlying the flood plain and terraces. The two

principal hydraulic properties evaluated in this study 

are the storage coefficient and the transmissivity for 

both the basin fill and the overlying alluvium. Included in this investigation are estimates of (1) tin 

areal extent of the saturated alluvium, (2) tin 

spacial variability of the storage coefficient, transmissivity, and diffusivity of the alluvium and basin 

fill, (3) the upward vertical velocity of ground water 

from the basin fill to the overlying alluvium, and (4) 

the rate of ground-water movement in the alluvium 

and basin fill. Where sufficient data were available, 

estimates were also made of the accuracy of thes°. 

determinations. Only the basic equations used in tin 

solutions and the significant constraints unique to 

each method are presented. A more detailed discussion of the development of each method is available 

in the indicated references. All equations are expressed in a general form, hence; they are applicable where consistent units are used.

DESCRIPTION OF STUDY AREA AND WATERBEARING DEPOSITS

The project area covers a 15-mile reach of tin 

Gila River valley immediately above the San Carlos 

Reservoir in south-central Arizona (fig. 1). Tin 

oldest rock units in the area are igneous and metsmorphic and are exposed only in the adjoining 

mountains. In the valley these units are overlain 

by a fine-grained material of low permeability referred to as basin fill. This material, which consists 

primarily of clay, silt, and sand, is more than 1,00^ 

feet thick and 10 miles wide (Davidson, 1961).

Alluvial deposits with relatively high permeability 

fill a valley incised in the basin fill. These deposits, as 

much as 60 feet thick and averaging 6,000 feet in

Fl
F2 GILA RIVER PHREATOPHYTE PROJECT

460.000 FT

33°15' -

810.000 FT -

Igneous and 

metamorphic rock

Igneous and metamorphic rock

FIGURE 1. Location of cross sections, data-collection sites, boundaries of saturated alluvium,
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA F3

Igneous and 

metamorphic rock

Igneous and metamorphic rock

Geology by E. S. Davidson, 1970; hydrology by R. L. Hanson, 1970

EXPLANATION

Contact

Between basin-fill deposits and igneous 

and metamorphic rocks

Contact

Between basin-fill deposits and 

saturated alluvium

Cross section and number

Wells

Well numbers (0926) given only for 

wells discussed in this report 

00106

Observation well and soil-moisture 

access pipe in cross section 

00522

Observation well at 

miscellaneous site

Observation well used in aquifer 

test at cross section 1

and the contact between basin fill and igneous and metamorphic rock in the project area.
F4 GILA RIVER PHREATOPHYTE PROJECT

width, form the flood plain and lower terraces of the 

study area. They consist of lenticular gravel, sand, 

and silt beds. The present Gila River flows across the 

alluvium in a channel 100 to 400 feet wide and 5 to 

8 feet deep.

Figure 2 shows a typical geologic section through 

the flood plain and lower terraces near the middle of 

the study area. A more detailed description of the 

geology of the area was discussed by Weist (1971).

To study ground-water movement in the area, a 

program was initiated in 1963 to record groundwater levels in 164 wells and soil-moisture contents 

at 77 access tubes. The locations of these sites are 

shown in figure 1. Well numbers are indicated on 

the map for only those wells discussed in this report.

During most of the year the average depth to 

ground water in the alluvium ranges from 5 to 8 

feet below land surface near the river and from 15 

to 20 feet below land surface near the outer boundaries of the flood plain. On the terraces adjacent to 

the flood plain, however, the depth to water ranges 

from 20 to 40 feet below land surface. Ground-water 

levels in the basin-fill wells 2 to 4 miles distant from 

the flood plain range from 100 to more than 300 feet 

below land surface.

Wells on the flood plain which penetrate through 

the alluvium into the underlying basin fill indicate 

that the ground water in the basin fill is under artesian head. Water levels in this unit at well 0105 

(fig. 1) were observed to be 6.1 feet higher than 

those in the alluvium, indicating flow from the basin 

fill to the overlying alluvium.

An estimate of the areal extent of saturated alluvium in the flood plain was made by Weist (1971, 

pi. 2). Additional ground-water-level data, well-log 

information, and field investigations of the surface 

contact between the basin fill and alluvium were 

used to define the revised saturated-alluvium bounds

3000' ,

2500'-

2000'

aries, as shown in figure 1. The average widtr of the 

alluvium between these boundaries at the water 

table is about 5,500 feet, and the average saturated 

thickness of the alluvium is about 40 feet.

DETERMINATION OF AQUIFER CONSTANTS 

STORAGE COEFFICIENT

"Storage coefficient [S] is defined as the volume 

of water that an aquifier releases from or tal~es into 

storage per unit surface area of aquifer p-^r unit 

change in the component of head normal to that 

surface" (Todd, 1963, p. 31). For an unconfined 

aquifer, estimates of S may be obtained from the 

ratio AC/A/I, where Ac is the change in soil-moisture 

content resulting from a ground-water altitude 

change, A/I (Stallman, 1967, p. 183).

Figure 3 shows moisture-content profiles s.nd corresponding ground-water levels at well 1958 for 

October 26, 1964, and April 13, 1965. The change in 

moisture content (AC) for this period, indicated by 

the shaded area in figure 3, includes only that change 

in the zone arbitrarily selected to represent the 

capillary zone. This zone extends from about 2 feet 

above the top of the maximum-recorded water table 

to about 1 foot below the minimum-recorded water 

table. Soil moisture above the capillary zone is assumed to be unaffected by changes in water level 

and, therefore, is not included in the storagecoefficient computation. Any change in soil-moisture 

content below the minimum water table, as indicated 

in figure 3, is due to errors in measurement of the 

moisture content. Studies by this writer indicate 

that measurement errors of moisture content in the 

capillary zone are generally less than 5 percent of 

the total moisture content of the zone.

The storage coefficient is generally considered to 

reflect soil-moisture change due to gravity drainage 

alone. In areas of phreatophyte cover, however, the

Flood-plain and C§ 

terrace alluvium _o

Basin fill " ' Basin fill "-

2000

VERTICAL EXAGGERATION X4 

DATUM IS MEAN SEA LEVEL

4000 FEET Geology by E. S. Davidson, 1964

FIGURE 2. Geologic section across the study area.
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA F5

10

- 15

20

Change in moisture content

in capillary zone

(Ae)=0.59 ft

-Waterjfrtjie.

:" J'""""": pP" Afe=3.55ft 

Water table A

10 20 30 40 50

SOIL-MOISTURE CONTENT, IN PERCENT BY VOLUME

FIGURE 3. Profiles of soil-moisture content at well 1958, 

showing increase in water level (A/0 and change in moisture content (Ac) in the capillary zone.

soil-moisture change results not only from gravity 

drainage, but also from transpiration.

In an attempt to evaluate the effect of transpiration on the storage-coefficient determination, values 

of S determined from soil-moisture and water-level 

data obtained before clearing phreatophytes from 

the area were compared with those values from data 

obtained after the phreatophytes had been cleared.

Table 1 shows calculated S values at eight wells in 

sections 1 through 7 for "before-clearing" conditions 

during the winter of the 1965 water year, and for 

"after-clearing" conditions during the winter of the 

1969 water year. The average storage coefficient 

value, S, for these wells decreased from 0.34 before 

phreatophyte clearing to 0.19 after clearing. This 

change in S suggests that transpiration by phreatophytes accounts for about 45 percent of the soilsome of the soil-moisture change in the cleared areas 

is caused by evaporation from bare ground and by 

transpiration from deep-rooted grasses that have 

replaced the phreatophytes.

An analysis of the spacial variability of S throughout the study area was made by determining an rverage storage coefficient,^, at each of 34 well sites 

in the flood plain. Each St value was computed from 

the arithmetic average of the storage coefficierts 

determined from n selected periods of water-ler^el 

and corresponding moisture-content change. In orc^r 

to analyze several periods without introducing the 

variability caused by phreatophyte clearing, the analysis was confined to the period, before clearing 

during water years 1964-67. Values of Afo and Ac 

were selected from relatively long periods (40 days 

or more) because the measurement error of those 

parameters is frequently a significant part of their 

total change for shorter periods.

Table 2 lists the average storage coefficient, (Si), 

number of determinations of S per site, (n), and 

standard deviation of Si, (a), for each of the 34 sites 

analyzed. The weighted-average storage coefficient, 

(Stv ), was computed from the relation

The weighted-average storage coefficient for these 

34 sites is 0.30 with a standard deviation of ±0.07, 

indicating that the spacial variability in S over the 

area is about 25 percent.

The pooled standard deviation of Si is ±0.10, inTABLE 2. Average storage coefficient (SO at each well, 

number of determinations of S per well (n), and standard deviation of Si per well (<r), for 34 wells in the fltod 

plain of study area

moisture change in those regions having phreatoof the alluvium is probably less than 0.19 because

TABLE 1. Comparison of storage-coefficient determinations 

before and after clearing phreatophytes from the flood 

plain 

[S, storage coefficient; S, average storage coefficient]

Before clearing; 1965 water year After clearing; 1969 water year Well 

No. Period S Period S

0102---.--NOV. 10-Feb. 23 0.36 Nov. 11-Feb. 3 0.15 01 03- -.-..Nov. 10-Feb. 24 .25 Nov. 11-Feb. 3 .08

0308-.- .--Nov. 10-Feb. 23 .39 Nov. 11-Feb. 3 .21

0311-.- .--Nov. 9-Feb. 23 .34 Nov. 12-Feb. 3 .27

0514- --.-.Nov. 10-Feb. 23 .37 Nov. 12-Feb. 4 .07 0517-.--.-Nov. 9-Feb. 23 .36 Nov. 13-Feb. 4 .30

0720__-_..Nov. 10-Feb. 24 .28 Nov. 12-Feb. 4 .15

0723--. ...Dec. 3-Mar. 17 .36 Nov. 13-Feb. 4 .27

S = 0.34 S 0.19

Well 

No.

AQAI7

no no

0309-

0311-

noi o

0514-

0517-

0721.

A.7OQ

0926-

1131.

1132-

1133-

Si

.-_-- .20

on

_____ .36

_.-_- .37

___-. .36

1 Q

-_--_ .46

_--.. .31

_____ .26

_-_._ .12

QA

._.__ .29

_____ .26

_-..- .27

__..- .43

-.... .38

n

6 

5 

2 

9 

2

5 

2

4 

4

7 

2

8

7

2 

5 

2 

5

a

0.10 

.10

.is

.10

.01 

.12

.07

".09 

.09

"08 

.12

Weighted -average storage 

Standard deviation of S» 

Confidence interval S» at 

Pooled standard deviation

Well 

No.

1274

1277--.

1337---

1338.--

1340-.-

1341---

1544---

1750--.

1753--.

1956--.

1957---

1958--.

1959--.

1960---

2162---

2163--.

2164.--

of Si ----------

St

.--0.30

._- .33

.-- .26

--. .26

-.- .25

-_. .27

--. .31

_.- .32

--. .33

--. .24

.-- .20

-.. .18

-.- .32

-.. .34

... .42

.-- .32

--. .26

n

2 

4 

2 

4 

5

5 

5 

6 

3

6 

4 

7 

6

4 

3 

2 

2

a

o~i9

".10 

.03

.03 

.08 

.18 

.06

.05 

.07 

.04 

.10

.10 

.15

0.30 

-K07 

-K02

-«-io
F6 GILA RIVER PHREATOPHYTE PROJECT

dicating that two-thirds of the storage coefficient 

determinations at a particular site range Jrorn 0.20 

to 0.40. However, by assuming that the Si in table 

2 defines a t distribution, one can say with 95-percent confidence that the true weighted-average storage coefficient lies between 0.28 and 0.32. The season 

of the year, location of the wells in relation to the 

river, and the hysteretic effect, due to a rising versus 

a falling water table, do not appear to explain the 

relatively high standard deviation in <S>. Much of this 

variability may be real, however, because of the 

heterogeneity of these alluvial deposits.

Estimates of S were also obtained from relatively 

short term aquifer tests in the alluvium and basin 

fill. Analysis of a constant-discharge aquifer test in 

the alluvium near well 0105 (inset in fig. 1) gave a 

storage coefficient of 0.16. A similar test of shorter 

duration in the basin fill at well 0532 gave a storage 

coefficient of 0.0005. Discussion of the analytical 

techniques used to derive these values is presented 

in the next section.

On the basis of the preceding analysis, an average 

storage coefficient for the zone of water-level change 

of 0.30 is considered to be representative for the 

alluvium with phreatophyte cover. This value should 

be reduced to about 0.20 for alluvium after clearing. 

A storage coefficient of 0.15 is considered to be a 

reasonable value for the total thickness of saturated 

alluvium and should be used when predicting the 

behavior of wells or drains in the alluvium.

The single storage-coefficient determination of 

0.0005 for the basin fill may differ substantially at 

other sites and is here considered to be only an approximate value.

AQUIFER TESTS OF THE ALLUVIUM AND BASIN FILL

Transmissivity (T) is defined as the volume rate 

of flow of water through a vertical strip of aquifer 

of unit width extending the full saturated thickness 

of the aquifer under a hydraulic gradient of 1 :1. 

Diffusivity (D) is defined as the ratio T/S. Hydraulic conductivity (K) is defined as the volume rate of 

flow of water through a unit cross-sectional area 

under a hydraulic gradient of 1:1. The relation 

between transmissivity and hydraulic conductivity is 

T Km, where m is the saturated thickness of the 

aquifer.

These aquifer constants are commonly derived 

from an analysis of the drawdown and recovery of 

water levels in a pumped well and adjacent observation wells. This method is restrictive, however, in 

that it defines these constants for only the region in 

which drawdown and recovery occurs. Furthermore,

this technique is time consuming and expensive to 

perform. Various other techniques for determining 

aquifer constants have been developed which consider natural or suddenly induced changes in 

ground-water levels. Some of these techniques were 

employed in this analysis in an attempt to verify the 

aquifer constants derived from drawdown and recovery tests and to evaluate the areal variation in 

these constants.

Most of these analytical techniques assume that 

the aquifer is homogeneous and isotropic, and that 

the observation wells fully penetrate the p.quifer. 

These assumptions, along with those constraints 

unique to each method, limit their application in the 

field and reduce the reliability of the results*. However, where different methods give consistent results based on different sets of data, the results are 

considered to be representative.

The following sections discuss the various aquifer 

tests used to determine transmissivity, diffusivity, 

hydraulic conductivity, and storage coefficient. Determinations for the alluvium are presented first, 

followed by those for the basin fill.

ALLUVIUM

The aquifer constants of the alluvium were determined by analyzing the following aquifer conditions :

1. Drawdown and recovery in the aquifer due to 

constant discharge from a well penetrating the 

aquifer.

2. Propagation of a flood wave through the aquifer 

in response to fluctuations in river ste^e.

3. Cyclic fluctuations of ground-water levels due to 

sequential flood stages in the adjacent stream.

4. Decline in artesian head of a well using the 

constant-head "drain function."

5. Response of a well following an instantaneous 

charge of water (slug test).

AQUIFER TEST AT SECTION 1

By S. G. BROWN

Estimates of transmissivity and storage coefficient 

were obtained from analysis of an aquifer test of 

the alluvium on the right bank of the Gila Piver at 

section 1.

Well C-l, the pumped well, was drilled near observation well 0105, and 16 other observation wells 

were drilled nearby. (See inset in fig. 1.) Well C-l 

was 161 feet deep and 8 inches in diameter. It completely penetrated the flood-plain alluvium and 110 

feet of the underlying basin-fill unit. The flood-plain
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA

alluvium at well C-l is 51 feet thick and consists of 

sand, gravel, and some silt. The basin-fill unit that 

underlies the flood-plain alluvium consists mainly of 

silt and clay and some thin layers of fine to very 

fine sand. The water level is 12 feet below the land 

surface in observation wells that were completed in 

the alluvium near well C-l. Initially, casing in well 

C-l was set to a depth of 81 feet, which is about 30 

feet below the base of the alluvium. The well then 

tapped only water in the basin fill, causing the 

water level in the well to rise to about 6 feet higher 

than the water level in nearby wells that tapped only 

water in the alluvium.

A wire-wrapped well screen 6 inches in diameter 

and 30 feet long with slot openings of 0.060 inch 

was set in the well with the bottom of the screen 

49V2 feet below the land surface and about 2 feet 

above the alluvium-basin-fill contact. A neoprene 

packer at the top of the screen fit snugly inside the 

8-inch-diameter casing. Below the alluvium-basin-fill 

contact, the well was filled with sand, gravel, and 

silt and was capped with five sacks of quick-setting 

cement. The cement was allowed to harden, and the 

bottom of the 6-inch-diameter screen was set on the 

concrete. The 8-inch-diameter casing was withdrawn 

until about 1 foot extended below the packer at the 

top of the screen. The well was treated with a dispersing agent to aid the removal of clay-size particles from the aquifer during development, and the 

well was developed by bailing and surging with a 

surge block and, later, by surging with a pump. As 

the fine material was removed from the aquifer 

materials surrounding the screen during the development process, the rate of pumping was increased 

slowly until the well was discharging 0.50 cfs 

(cubic feet per second) or 225 gpm (gallons per 

minute). At this maximum rate of pumping, very 

fine sand and silt were drawn into the well; however, 

when the discharge of the well was regulated to 0.35 

cfs (160 gpm), the sand problem was eliminated. 

The aquifer test was therefore made at a regulated 

discharge of 0.34 cfs (152 gpm).

The test was begun on April 16, 1964, at 2 p.m. 

and was continued until 1:41 a.m. on April 20, 1964, 

when the test was unintentionally terminated during 

an attempt to repair a leaky fuel line. The length of 

the pumping test was 5,021 minutes or 3.487 days.

Depth to water was measured systematically in 18 

wells, including the pumped well. Nine observation 

wells were equipped with digital recorders. Of the 

nine wells, six were equipped with a 5-minute punch 

interval, and three were equipped with a 1-minute 

punch interval. Water levels in eight observation

wells were measured frequently with a chalked ste^l 

tape, and the water level in the pumped well was 

measured with a mercury manometer.

Well discharge was regulated by a gate valv^, 

measured with a 6-inch throat Parshall-type flume, 

and carried to the Gila River, about 1,500 feet to tl e 

south. Leakage from the plastic-film-lined ditch was 

negligible.

The data were analyzed by use of the modified 

nonequilibrium equation (Ferris and others, 1962, p. 

100), in which

2.3Q T =

47TAS

(1)

where 

T transmissivity, in cubic feet per day per

foot of width of aquifer; 

Q = rate of discharge of the pumped well, in

cubic feet per day; and 

AS = change in the drawdown .over one log

cycle of time, in feet.

2.25 T h.

.r2

(B)

where T is as previously defined, and

S = storage coefficient (dimensionless); 

t0 = time intercept, in days, where the plotted 

straight line intersects the zer> 

drawdown axis; and 

r = distance, in feet, from the pumped well

to the observation well.

In general, this modification of the Theis nonequilibrium equation is valid when the value u is <0.01 

(Todd, 1963, p. 94), in which

u = 4,Tt (8) ' 

where

t = the time, in days, since pumping began;

and r, S, and T are as previously defined. 

Figure 4 and table 3 summarize the results of tM 

analysis of the aquifer test for all observation wells 

in which u is <0.01 within the 3.5-day test period.

In all instances the calculated value of the storage 

coefficient fell well within the range of values characteristic of nonartesian, water-table conditions. 

The average transmissivity, calculated by eliminating data from all wells at which u was greater thrn 

0.01, was somewhat lower and the storage coefficient 

somewhat higher than if the data for all wells had 

been used. The rate of drawdown per log cycle for 

wells where u was equal to or less than 0.01 is somewhat steeper than that for wells farther away with 

a u value greater than 0.01. Therefore, the calculated 

storage coefficient is greater for the observation wells
F8 GILA RIVER PHREATOPHYTE PROJECT

10 100 1000 

TIME SINCE PUMPING BEGAN ft), IN MINUTES

10,000

FIGURE 4. Drawdown in observation wells near well C-1,
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA F9

10 100 1000 

TIME SINCE PUMPING BEGAN (t), IN MINUTES

10,000

showing results of the modified Theis type analysis.
F10 GILA RIVER PHREATOPHYTE PROJECT

TABLE 3. Summary of transmissivities (T) and storage 

coefficients (S) at observation wells used in the aquifer 

tests at section 1

Well 

No.

Distance from

pumped well

(ft) (cu ft per day per ft)

N-l N-a

N-3

C-3

0105

E-l

E-2

S-l

S-2

S-3

W-l

W-2

W-3

_______ 34

_______ 70

....... 100

___._. 7

..... 31

______ 41

. __ . 100

37

74

.. . . 99

... . . 30

60

90

Mean

Maximum _ _ _ _ . . _ Minimum _____

10,700

10,700

10,700

9,200

9,200

9,200

9,200

9,900

9,900

9,900

9,800

9,800

9,800

9,800

10,700

9,200

0.12

.09

.12

.23

.36

.09

.12

.15

.16

.11

.31

.15

.05

0.16

.36

.05

near the pumped well because the aquifer had been 

draining for a longer time.

The range of T determined at this site from 

10,700 cu ft per day per ft (cubic feet per day per 

foot) (80,000 gpd per ft (gallons per day per foot)) 

to 9,200 cu ft per day per ft (69,000 gpd per ft) is 

reasonable and probably can be accounted for by 

local variations within the aquifer. The range of <S 

0.36 to 0.05 is much greater in relation to the average S, but is characteristic of water-table (nonartesian) conditions. The <S calculation is sensitive to 

to, which depends on the slope and placement of the 

straight line through the drawdown data. Some variation can be expected because of lithologic variations 

within the aquifer.

The mean transmissivity of 9,800 cu ft per day 

per ft (73,000 gpd per ft) and the mean storage 

coefficient of 0.16 can be used with confidence to calculate ground-water underflow and change in 

ground-water storage in the area sampled by the 

aquifer test.

FLOOD-WAVE-PROPAGATION ANALYSIS

A comprehensive investigation of the diffusivity 

(D) of the alluvial material underlying the flood 

plain and lower terrace was made by using a technique that describes the response of an aquifer to 

the propagation through it of a flood wave originating from a hydraulically connected stream. Finder, 

Bredehoeft, and Cooper (1969) developed the technique based on the theory of heat flow and adapted 

it to the digital computer. The computer calculates 

a synthetic flood hydrograph (type curve) of groundwater heads at a distance x0 from the river, using

as input: (1) the "reference hydrograph" of groundwater heads at a distance x t from the river, where 

#r < #0 ; (2) the aquifer width, defined as the distance between the point of the reference hydrograph 

and the boundary of saturated alluvium; anc1 (3) an 

assumed diffusivity for the aquifer. A visual comparison between the computed hydrograph r.nd corresponding observed hydrograph is provided by a 

plotting routine included in the computer program. 

Additional hydrographs are generated for selected 

diffusivities until a reasonable match is obtained 

between the computed and observed hydrographs.

The assumptions underlying this technique are 

that the aquifer is confined, homogeneous, and isotropic and is bounded on one side by impevmeable 

material and on the other side by a hydraulically 

connected straight stream which fully penetrates the 

aquifer.

Diffusivity determinations were made at sections 

1, 3, 5, 7, 9, 11, and 13. (See fig. 1.) There are three 

wells on each side of the river at each section. Except for those in section 1, the wells in these sections 

are in a line approximately normal to the river. All 

wells extend below the water table, but only a few 

penetrate the full thickness of the alluvium. The 

wells were cased with 4i/£-inch-diameter lightweight 

steel tubing into which a 41,4-inch-diameter plastic 

liner was inserted. The casings were not perforated, 

but were left open at the bottom. Digital recorders 

recorded water levels at 1-hour intervals at each 

well.

At each section the well adjacent to the river is 

designated "river well," the outermost well is designated "terrace well," and the middle well, between 

the river and terrace wells, is designated "floodplain well," as indicated in figure 5. Diffusivity was 

determined by using one of the three combinations 

of reference and observation wells.

Figure 6 compares two computed hydrographs 

with the observed hydrograph of the July 16 to September 24, 1967, flood period for observation well 

0307 (terrace well), using well 0308 as a reference 

well (flood-plain well). The diffusivity corresponding to the computed hydrograph of best fit in figure 

6 is 122,000 cu ft per day per ft (916,000 gpd per 

ft).

Seldom could the computed hydrograph be 

matched exactly with the observed one. At several 

well sites, large changes in the diffusivity (^termination changed the computed hydrograph only 

slightly. Occasionally, a reasonable match of the 

computed with the observed hydrograph could be 

obtained by changing the aquifer width. No reason-
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA Fll

2000 FEET

APPROXIMATE SCALE

FIGURE 5. Position of terrace, flood-plain, and river wells, 

and their designation when used as reference and observation wells in the flood-wave propagation analysis.

able match was obtained at a few sites, regardless 

of the aquifer width or diffusivity used.

An attempt to verify the diffusivity determinations was made by analyzing two or three different 

flood peaks at each site. For several sites, however, 

water-level data were available for only one flood 

peak. The flood periods analyzed included August 1 

to September 30, 1963; March 8 to April 21, 1966; 

July 16 to September 24, 1967; and December 16, 

1967, to February 10, 1968. Table 4 summarizes the 

results of this analysis and groups the data according to the combination of terrace, flood-plain, and 

river wells used.

The diffusivities in table 4 are consistent and of a 

reasonable magnitude at some sites, but are unrealistically low or high at others. The large discrepancy 

in D values at a given site may be attributed to (1) 

slow response of the reference well or observation 

well, as a result of partial plugging; (2) a change 

of diffusivity, due to a change in saturated thickness; and (3) use of a partial-penetrating standpipe 

as a piezometer. In some instances, those values obtained by using the river well as a reference well 

may reflect vertical-flow components and, thus, represent erroneous results.

The extreme variability in D values between sites

TABLE

Reference

well

4. Diffusivities at the sites

Observation

well

alluvium

of selected

Water year Flood amplitude at 

of flood reference well (ft)

wells in the

Diffusi'ity 

(cu ft per

day per ft)

River-flood-plain wells

0103-.

0104.-

0309 . .

0310.-

0515 ._

0516.-

0721 _

0928 -.

1133--

1339 --

--0102

--0105

--0308

-.0311

--0514

-.1517

_ 0720

_ 0929

--1132

--1338

1963

1967

1963

1968

1966

1967

1968

1963

1967

1968

1963

1967

1968

1963

1963

1968

1963

1966

1966

2.95

6.60

2.75

2.95

4.30

6.00

6.40

1.90

5.30

6.55

3.10

5.90

5.46

3.15

2.65 '4.5

3.10

3.90

5.30

26,700

2,251,000

21,400

147,000

245,000

338,000

245,000

96,200

9,625,000

9,625,000

40,000

250,000

444,000

78,600

17,100

107,000

719,000

722,000

225,000

River-terrace wells

0103

0104 -

0309 -

»

0310

» 0515 _

0516 -

0721 .

0722 _

0927 _

0928

1133.-

1339 _

. 0101

..0106

_ 0307

. 0312

_ 0513

. 0518

. 0719

_ 0724

- 0926

. 0930

1131

1337

1963

1967

1968

1963

1968

1966

1967

1968

1963

1967

1968

1963

1967

1968

1963

1963

1968

1968

1966

1963

1967

1968

1966

1966

2.95

6.60

3.75

2.75

2.95

4.30

6.00

6.40

1.90

5.30

6.55

3.10

5.90

5.45

3.15

2.65 '4.5

'4.5

3.90

3.10

6.70

4.90

3.90

5.30

44,400

379,000

327,000

89,800

561,000

305,000

197,000

197,000

57,700

497,000

230,000

44,400

73,800

88,200

103,000

1,070

107

5,880

17,600

123,000

1,361,000

766,000

112,000

64,200

Flood-plain terrace wells

0102 .

0308 .

0514 .

0517 .

0723 -

1132

1338 .

- 0101

-0307

_ 0513

- 0518

. 0724

. 1131

1337

1967

1967

1968

1967

1968

1967

1968

1968

1966

1966

6.85

4.95

5.70

5.15

4.70

5.40

4.60

2.00

4.00

4.10

94,600

122,000

245,000

81,800

62,600

358,000

160,000

36,900

40,100

64,200

1 Estimated.

may be due to the above-mentioned problems and 

may reflect the effect of using incorrect aquifer 

widths. Some of this variability probably reflects 

the true areal distribution of D throughout the area; 

however, a wide variation in the values at a given 

site precludes the use of these results to evaluate 

their distribution.
F12 GILA RIVER PHREATOPHYTE PROJECT

Computed | #= 218>°00 cu ft per day per ft , 

^ | D= 122,000 cu ft per day per ft -. \

I

5*

 "*sr<>».

200 400 600 800 1000 

ELAPSED TIME, IN HOURS

1200 1400 1600

FIGURE 6. Observed and computed hydrographs at observation well 0307, July 16 to September 24, 1967. Computed graphs 

were derived from flood-wave propagation analysis, using well 0308 as reference well.

Figure 7 shows a plot of flood amplitude at the 

reference well versus the corresponding diffusivity 

at the obervation well. The plot indicates a slight 

direct correlation that may reflect a change in 

diffusivity, due to a corresponding change in saturated thickness.

An estimate of the median diffusivity for each 

combination of wells listed in table 4 was made by 

plotting a frequency distribution of diffusivities corresponding to a given combination of wells and flood 

period. All diffusivities for a given well combination 

were delineated by flood period and assigned probabilities by using the relation

where Dm is the wth largest diffusivity value, and n 

is the total number of values. The largest diffusivity 

was, therefore, assigned m = 1 ; the second largest, 

m = 2, and so forth. A log-normal probability plot 

with Dm on the logarithmic scale against P(Dm ) on 

the probability scale was then made, as illustrated in 

figure 8. The diffusivity at the 50-percent probability

level was selected from the line averaging the data 

points on this plot. (Outlying points were rot considered in drawing this line.) Similar plots were prepared for each of the three combinations of wells for 

each of the four flood periods. The diffusivities corresponding to the 50-percent probability level for 

each of these plots is given in table 5.

The weighted-mean diffusivity, D50 , was computed 

for each well combination from the relation:

#50 =

K

£

i = 1

hi D50, i

(5)

£«,*,

where k is the number of flood periods, nt is t*ie number of diffusivity determinations used to define the 

frequency distribution plot for the tth flood period, 

hi is the average change in water level at th^ observation wells associated with the tth flood period, and 

DBO ,i is the 50-percent-diffusivity value selected from
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA F13

10,000

1000

100

10

EXPLANATION

o River to ftood plain 

A Flood plain to terrace 

 River to terrace

1234567 

FLOOD AMPLITUDE AT REFERENCE WELL. IN FEET

FIGURE 7. Relation between flood amplitude at the reference 

wells and computed diffusivity at the observation wells. 

(Data are from table 4.)

the frequency distribution plot for the ith flood 

period. This relation gives the greatest weight to 

those median diffusivities derived from the greatest 

number of determinations and highest flood peaks.

Table 5 shows that the weighted-mean diffusivity 

is greater for the combination of river and floodplain wells than for the flood-plain and terrace wells, 

which suggests that D decreases with the increase 

in distance from the_river.

Selection of that D50 value in table 5 which best 

represents the alluvium is questionable because none 

of the wells used in the analysis fully meet the wellconstruction requirements desired for this type of 

test that is, wells that penetrate the full depth of 

the alluvium and that are screened. An observation 

well slow to respond because of partial plugging will 

result in a low estimate of D. Conversely, a reference 

well slow to respond will give an estimate of D which 

is too high. Some of the shallow river wells may respond too rapidly because of vertical-flow components, and the resulting estimates of D are, thus, too 

low. Despite Jhese problems, the magnitude and 

range of the D50 values in table 5 are thought to be 

reasonable.

The weighted-mean diffusivity of 185,000 cu ft

1000

500

100

50

10

.D50,i = 166,000 cu ft 

per day per ft

Z>=108 cu ft per day per ft

\\ r i i i i

98 95 90 80 70 60 50 40 30 20 10 5 

PROBABILITY, IN PERCENT

FIGURE 8. Frequency distribution of diffusivity, D, derived 

from the flood-wave propagation analysis by using tl^ 

combination of river and terrace wells at eight sites during the 1968 flood period. (Data from table 4.)

TABLE 5. Summary of alluvium diffusivities derived fro'm 

flood-wave propagation analysis, using various combination $ 

of river, flood-plain, and terrace wells

Flood 

period

1963

1966

1967

1968

1963

1966 

1967

1968

1963 

1966 

1967 

1968

Number of Average flood 

diffusivity amplitude at 

determinations observation 

well 

(n) (ft, in ft)

River-flood-plain wells

............ 7 1.5

....-...._. 3 3.9

........ 5 4.8

........... 6 4.2

Weighted-mean diffusivity, D5o

Flood-plain terrace wells

___________ 2 1.8 

............. 4 3.4

............ 4 3.0

River terrace wells

............ 7 1.0

... . 4 2.1 

.......... 5 3.6 

............ 8 3.0

Mffusivity at 50-pcrEent probability level D X 103 

(cu ft per day 

per ft)

42.8

34.2

337

112

__ 215

50.3 

134

96.3

._ 108

64.2 

80.2 

305 

166

.. 185

per day per ft derived from the combination of river 

and terrace wells is considered to be representative 

of the total width of saturated alluvium. If the stor-
F14 GILA RIVER PHREATOPHYTE PROJECT

age coefficient is 0.15, the corresponding weightedmean transmissivity is 28,000 cu ft per day per ft 

(210,000 gpd per ft).

These results are considered to be significant because they were derived from different flood periods 

and from several observation sites dispersed over a 

large part of the study area.

ANALYSIS OF CYCLIC FLUCTUATIONS OF WATER LEVELS

Estimates of diffusivity at several sites in the 

project area were obtained by analyzing the cyclic 

fluctuation of water levels in response to sinusoidal 

changes in stage of the Gila River. Ferris (Ferris 

and others, 1962, p. 132-135) showed that diffusivity 

may be determined from the relation

D (6)

where D is diffusivity, t0 is the average period of 

stage fluctuation, and A# is the distance corresponding to one log cycle of a plot of the stage ratio, 

sr/2s0 , on logarithmic coordinates versus distance, x, 

between the river and a given well on rectangular 

coordinates. The values, sr and s0 are the total range 

of the ground-water stage and one-half the range of 

the surface-water stage, respectively. (See inset in 

fig. 9.)

This solution assumes an isotropic semi-infinite 

artesian aquifer of uniform thickness. A change in 

water storage within the aquifer is assumed to occur 

instantaneously with a change in pressure in the 

aquifer. Further, the bounding stream is assumed 

to fully penetrate the aquifer. Because the saturated 

alluvium of the study area is not under artesian conditions and the Gila River only partially penetrates 

the aquifer, application of this technique is limited 

to those observation wells sufficiently distant from 

the stream to be unaffected by vertical components 

of flow within the aquifer. Also, the cyclic fluctuations in the observation wells must be of fairly uniform duration, and their amplitude must be small 

relative to the saturated thickness of the alluvium.

Figure 9 shows a plot of x versus the average 

stage ratio, sr/2s0 , for nine flood-plain wells. The 

average stage ratio for each well is based on four 

flood cycles that occurred sequentially from July 14 

to August 10, 1964. Table 6 shows an example of 

the tabulations used to determine the average stage 

ratio and average period of flood-stage fluctuation 

for well 0105. The average stage ratio of 0.047 is an 

average of the rise and fall over the four flood cycles 

and the average period of flood-stage fluctuation of 

7 days is the average duration of each of these four 

flood cycles. This average £ of 7 days also applies

TABLE 6. Example of tabulations used to define the average 

period of flood-stage fluctuation, to, and the average stage 

ratio, sr/2so, at well 0105 for four flood cycles during July 

and August 1964

1964 flood cycles 

July 14-20 July 20-24 July 24-30 July 30-Augr. 10

Rise Fall Rise Fall Rise Fall P'*e Fall

8r---

2v8,-/28

(ft) ..

-(ft) -.

*

0.14

3.16

.044

0.04

2.80

.014

0.03

1.06

.028

0.06

1.04

.058

0.07

2.16

.032

0.05

1.90

.026

C.26

£.80

.092

0.23

2.90

.080

tot-.(days) .. 11

*Average «r/2s0 = 0.047. 

f Average t0 = 7 days.

to the other wells in this analysis because these same 

flood cycles were used in determining their stage 

ratios. The straight line averaging the points in 

figure 9 gives a A# value of 1,460 feet per log cycle 

of the stage ratio. The resulting diffusivity, computed by using equation 6, is 179,000 cu ft per day 

per ft. If the storage coefficient of the alluvium is 

0.15, the transmissivity is 27,000 cu ft per day per 

ft (200,000 gpd per ft).

These results compare favorably with those obtained using the river wells in the flood-wave propagation analysis, but are considered as only approximate because of the fairly wide scatter cf points 

in the plot of figure 9. The fact that the flood cycles 

used in this analysis are not of uniform duration 

and magnitude and that vertical-flow components 

may exist at some of the wells near the river probably accounts for much of this scatter.

CONSTANT-HEAD DRAIN-FUNCTION ANALYSES

Stallman (Ferris and others, 1962, p. 126-131) 

showed that when a change in artesian head occurs 

as a result of a sudden change in river stage, diffusivity, D, can be estimated from the r^ation

x2

D = (7)

where x is the distance between the river and a point 

at which the decline in the head of the aquifer, s, 

is observed; t is the time from a sudden cl'ange in 

the river stage; and u = x2S/4Tt, where S and T 

are as previously defined. Equation 7 assumes that:

1. The aquifer is confined, homogeneous, isotropic, 

and semi-infinite in extent and is bounded on 

one side by a straight stream which fully penetrates the aquifer,

2. The head in the stream suddenly changes at time 

t - 0,

3. The direction of ground-water flow is perpendicular to the direction of streamflow,

4. The change in the rate of discharge from the
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA PI 5

1500

1400 -

1300 

0.02 0.03 0.04 0.05 0.06 0.08 0.10

STAGE RATIO (s r/2s0 )

0.20 0.30 0.40 050

FIGURE 9. Relation between stage ratio, s,/2s0, and distance, x, from the river to the well for nine wells in the flood plain, 

where Sr/8s0, is an average of four flood cycles during July and August 1964.
F16 GILA RIVER PHREATOPHYTE PROJECT

aquifer is derived from changes in storage by 

drainage after t = 0.

A solution for equation 7 is obtained by first 

matching the drain-function type curve of the relation between $ (u)j, and u2 (Ferris and others, 1962, 

fig. 31) to a logarithmic data plot of x2 /t versus s. 

Any value of uz (usually u2 = 1.0 is selected for 

convenience of computation) from the type curve 

and corresponding value of x2 /t from the data plot 

may then be substituted in equation 7 to solve for D.

Figure 10 shows data plots of x2 /t versus s for 

the left-bank and right-bank wells in section 5 of 

the Gila River, at t = 2.4 days following a fairly 

sudden rise in river stage on July 17, 1967. Included 

in the figure are the drain-function type curves adjusted to the position that best fits the data points, 

the corresponding match-point values of u2 and xz/t, 

and computed diffusivities. If the storage coefficient 

is 0.15, the corresponding transmissivities are 16,000 

cu ft per day per ft (120,000 gpd per ft) for the 

left bank and 56,000 cu ft per day per ft (420,000 

gpd per ft) for the right bank in section 5.

A check on these results was made by applying 

this same analysis to the recovery of five wells in 

sections 1 and 5 following the fairly rapid rises in 

river stage. For each well, a plot was made of s 

versus l/t defined by the ground-water recessions 

following selected river rises. As before, the drainfunction type curve was matched to each plot, values 

of u2 and corresponding t selected from each plot,

and substituted in equation 7 to solve for D. The results of these determinations are listed in table 7.

The diffusivities in table 7 give a median value of 

16,000 cu ft per day per ft when their frequency 

distribution is plotted on log-normal probability 

paper. For a storage coefficient of 0.15, the corresponding transmissivity is 2,400 cu ft per day per ft 

(18,000 gpd per ft).

The wide range in diffusivities in table 7 makes 

these results questionable. The assumptions of a 

semi-infinite artesian aquifer, an instantaneous 

change in river stage, and a river which penetrates 

the entire thickness of the alluvium are not fully 

satisfied in this problem. The particularly low diffusivities for those wells near the river (we^s 0103 

and 0104) may not be representative because of 

possible vertical flow in that region of the alluvium.

SLUG TESTS

Slug tests described by Cooper, Bredehoeft, and 

Papadopulos (1967), which induce a sudden change

TABLE 7. Diffusivities for five wells at sections 1 and 5 

derived from constant-head drain-function analysis

Well 

No.

0103 _.......

0104 ________

0105 __.-____

0105 ________

0514 ________

0514 ________ 

0517 ________

Distance from 

stream to well 

(ft)

81

61

890

890

280

280 

744

Flood 

period

July 1964

July 1964

July 1964

Sept. 1966

July 1964

July 1967 

July 1964

Diffusivity 

(cu ft per 

day per ft)

4,500

3,420

23,900

103,000

11,600

7,490 

1E5,000

1.00

- O l 1 1 1 MM

_ 0516

 Well number

-

_

-

I

_

1 1 1 1 1 1 1 1

1 1 1 1 M 1 1

^0515

1 1 1 1 M 1 1

1 1 1 1 1 1 1 1

Right bank

~~ - - .

0514 """"-> -^

M ' = 1.0

1 1 1 1 1 1 II 1 1 1-

_

M2 =1.0 ~

a: 2 /«=1.5 X 106 sq ft per day ~ 

- - X)0517 D =375,000 cu ft per day per ft -

Drain function ^\

type curves N.

>N\ \

X

\

\ Match 

\ / point

/\

jc 2 /t=OA2 X 106 sq ft per day \ 

D= 104,000 cu ft per day per ft \

1 1 1 1 1 1 1 1

\

0513^

\

1 1 1 1 1 1 1 l\

s

\

^^ 

\ C518 ~

°\ =

_

i r i

0.10

0.01

100 1000 10,000 100,000

x 2/t, IN SQUARE FEET PER DAY

FIGURE 10. Plots of nc2/t versus s, for the left-bank and right-bank wells in section 5, at t

river stage on July 17, 1967.

1,000,000

2.4 days following a rise in
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA F17

in the water level of the aquifer, were performed on 

eight wells in the alluvium in a further attempt to 

define the approximate magnitude of transmissivity 

and its variation throughout the study area. Transmissivities were determined from an analysis of the 

recovery of the wells following instantaneous submergence or removal of a mass (slug) of known 

volume. The resulting transmissivities ranged from 

0.4 to 150 cu ft per day per ft (3 to 1,100 gpd per 

ft).

These transmissivities are substantially lower than 

those values determined by the other methods previously discussed. The wells used in this analysis are 

cased to the bottom of the hole with no screening or 

perforations in the well casing. As a result, only a 

relatively small volume of the aquifer is stressed 

during these short-term tests, and movement of 

water into and out of the well is primarily vertical 

rather than horizontal. Therefore, these determinations are not considered to be representative, and 

this method of analysis is probably not applicable to 

most wells in the study area.

BASIN FILL

Estimates of the transmissivity and the storage 

coefficient of the basin fill were obtained from an 

analysis of the drawdown and recovery of the 

ground-water level following a constant discharge 

from the aquifer. Estimates of diffusivity were obtained from an analysis of the seasonal groundwater-level recessions. Estimates of the upward 

vertical flow from the basin fill to the overlying 

alluvium were obtained from an analysis of geothermal gradients in the basin fill.

AQUIFER TESTS AT WELLS 0531 AND 0532

An estimate of transmissivity and storage coefficient for the basin fill was obtained from an aquifer test performed at wells 0531 and 0532 in the 

basin fill outside the boundaries of the alluvium. 

(See fig. 1.) The pumped well (0531) is 6 inches in 

diameter and about 200 feet deep. The observation 

well (0532), 62 feet away from the pumped well, 

is 16 inches in diameter and 160 feet deep. Whether 

the bottom of these wells are perforated, finished 

with a screen, or are open ended is unknown, as 

they were drilled for stock and domestic purposes 

before inception of this study.

Figure 11 shows a time-drawdown plot of the 

water level in observation well 0532 during 24 hours 

of pumping at an average rate of Q = 0.0194 cfs 

(8.7 gpm). An estimate of transmissivity was made 

from this data plot by using Theis' nonequilibrium 

equation (Theis, 1935), in which

Q

47TS

W(u), (8)

where T and Q, are as defined in equation 1, * is tlv» 

drawdown in the observation well, and W(u) is tH 

well function for constant discharge (or recharge) 

of the aquifer without vertical leakage. A type curve 

of the relation W(u) versus u (Ferris and others, 

1962, fig. 23) was matched to the data points in figure 11, and match-point values for u from the type 

curve and s from the data plot were substituted in 

equation 8 to give a transmissivity of 15.5 cu ft 

per day per ft (116 gpd per ft). Equation 3 was 

used to compute a storage coefficient of S = 0.00048 

for the basin fill.

Discharge from the pumped well during this test 

varied by about 6 percent. This is the probable caire 

for the deviation of data points from the type currre 

in figure 11.

A check on this estimate of T was made by appl-'- 

ing equation 1 to the data points defining the rate of 

recovery of the water level in observation well 05f 2. 

A convenient procedure for obtaining As in equation 

1 is to plot recovery, s', on rectangular coordinates 

against t/t' on logarithmic coordinates, where t is 

the time since pumping started, and t' is the time 

since pumping stopped. After t' becomes sufficiently 

large, the data points approach a straight line, and 

AS' may be selected over one log cycle of t/t'.

Figure 12 shows a data plot of the recovery of 

well 0532. A straight-line projection of the dsta 

points over one log cycle of t/t' defines AS' = 23 fe^t. 

The resulting transmissivity computed from equation 1 is 13.4 cu ft per day per ft (100 gpd per f';).

The relatively close agreement between the drawdown and recovery determinations of transmissivity 

at this well (16-percent difference) suggests that a 

value of about 15 cu ft per day per ft (110 gpd per 

ft) may be representative for the basin fill at tHs 

test site.

ANALYSIS OF WATER-LEVEL RECESSIONS

Rorabaugh (1960) described a method for determining diffusivity from the seasonal recession of ihe 

water table. This method of analysis is applicable 

when sufficient time has elapsed following recharge 

to the aquifer for the ground-water profile to reach 

a stable condition. The profile is considered to be 

stable when the water table falls exponentially w'th 

time. For this condition, diffusivity, D, may be expressed as

D = 4-^-2.3 logf-M / (t, - t,}, (9)

7T \ '6-' /

where a is the distance from the ground-water di-
F18 GILA RIVER PHREATOPHYTE PROJECT

50.0

10.0

t =43 min 

a = 8.6 ft

1.0

Match point

Type curve

0.1

10 100 1000

TIME SINCE PUMPING BEGAN (t), IN MINUTES

FIGURE 11. Time-drawdown plot and matching nonleaky type curve for aquifer test of basin fill at well 0532.
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA F19

J.£.

13

IW 14 LJ 

U.

* 15

C\f 

00in

o 16

_i _i

LJ

$ 17 ! 18

jg 19

w ffl 

o

I 20

S 21

o:

u 22

0 

O

£ 23

24 

25

'\ "

-\

- \

- \

\

-

IMI

1 1 1 1 1 1 1 1

0

\

V\.

\

\°

\ °

\ °

\ °0

\ "»

\ °o

\ 

\ 1 \ 1 1 1 1 1 1 1

-

-

-

-

-

-

D 0 0 0 0

10 50 100 200

tit'

FIGURE 12. Time-recovery plot of aquifer test in basin fill 

at well 0532.

vide to the discharge boundary, and h^ and h« are 

the water-table heads at any point in the aquifer at 

times ti and t>, respectively, following a sudden recharge at time t = 0. Equation 9 assumes that the 

water table is horizontal prior to recharge and that 

the water-table heads represent the rise in water 

above this initial horizontal level.

To obtain a solution for D, a semilog plot is made 

of the water-level recession at any given well, and 

the time interval (t> tj, in days, over one log 

cycle of head is selected from the straight-line portion of the recession. This time interval may then be 

substituted for (t, - £i)/log (/ti//t2 ) in equation 9.

For this analysis, a was taken as the width of the 

basin fill between its contact with the saturated 

alluvium, near the edge of the flood plain, and its 

contact with the igneous and metamorphic rock, approximately 5 miles from the flood plain. (See fig. 

1.)

Equation 9 was used to compute diffusivity from 

selected water-level recessions at each of five wells 

located in the basin fill. A description of these wells 

is summarized in table 8. Figure 13 shows graphs of 

the recessions for each well. The resulting diffusivities computed for each recession are listed in table 

9. The median diffusivity for these five wells, obTABLE 8. Description of basin-fill wells used in water-leve 1- 

recession anc

Well 

No.

0524 * ...

0530 1 ...

0725 ---_

0730 1 ...

0731 > ...

Total 

depth 

(ft)

.. 300

66

.. 92

.. 226

.. 340

Depth 

cased Diameter Type of 

(ft) (in.) finish

Unknown 

.. .do. ......

44 

226

Unknown

8 

16 

1 

6

6

Unknown. 

Do. 

Well point. 

Casing perforated 

in lower 50 ft. 

Unknown.

1 Occasional pumping for stock use.

TABLE 9. Diffusivities at five wells in the basin fill compute* 

from selected water-level recessions, using equation 9

Basin-fill Time interval Diffusivif^

Well width Recession period per log cycle (cu ft per

No. (ft) (days) dayperfl}

0524-

0530.

0530 _

0725.

0725-

0730_

0731.

. - __. 27,000

-. ---24,000

_. _--24,000

.. ..-24,000

_. .. .24,000

-. --.27,000

_. ---28,000

Aug. 1967-May 1968 1

Apr. 1966-Oct 1965 1

Apr. 1969-Aug. 1969 1

June 1968-Nov. 1968

Feb. 1969-May 1969

Oct. 1968-June 1969 1

Sept. 1966-June 1967 »

425

425

565

385

450

470

1,370

1,600,000

1 * 1,070,000

.

V 2 1,280,000

1,440,0<P

535,000

------ 1,200,000

1 Affected by periodic pumping.

2 Average of two recession periods.

tained from a log-normal probability plot of th°. 

values in the table, is 1.2 x 106 cu ft per day per ft 

(9.0 x 106 gpd per ft). If the storage coefficient of 

the basin fill is 0.0005, then the transmissivity is 600 

cu ft per day per ft (4,500 gpd per ft).

Rorabaugh (1960, p. 315) stated that the period 

required for the water-table profile to stabilize following recharge to the aquifer may be approximated 

by t = 0.15 a2 /D). Assuming a = 25,000 feet and 

D = 1.2 X 106 cu ft per day per ft, then t = 78 days, 

Thus, the water-table profile in the basin fill would 

not be expected to stabilize until about 2^ month"51 

after it had been recharged. Most of the recession"51 

used in this analysis define a continuous water-level 

decline for at least 6 months and, therefore, should 

satisfy this criteria. The range in diffusivities shown 

in table 9 may indicate actual variability over th<? 

study area, but it may also reflect erroneous estimates of the basin-fill width. All the wells, except 

well 0725, may define recessions that are too steep 

because of periodic pumping; resulting D valuer 

would then be too high. The assumptions of an initial 

horizontal water table and an instantaneous recharge to the aquifer are not satisfied in this problem, and their effect on the results is unknown. 

These determinations are also dependent on th<? 

altitude of the water table prior to recharge, which 

is questionable in this analysis. However, the standard deviation of the computed diffusivities in table
F20 GILA RIVER PHREATOPHYTE PROJECT

I I I I I I I I I

I I I I I I I I I I I I

I I I I I I

III I I I I

FIGURE 13. Seasonal water-level recessions in five basin-fill wells, and straight lines averaging their slopes for obtaining the

time interval per log cycle of water-level change.
SUBSUEFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA F21

i i i i I i I I I ill

MAMJ JASON ONDJFMAMJJAS 

1968 1969

1

0.9

0.8

0.7

0.6

0.5

I I I I I I I I I 1 I I I I I

Well 0725

I I I I I I I I 'I

MAMJ JASON 

1968

FMAMJJAS 

1969

FIGURE 13. Continued.

9 is relatively small (±31 percent), considering the 

numerous limitations and unknowns associated with 

this analysis.

Rorabaugh (1960) also described a method of estimating diffusivity from the decline in the groundwater profile during a recession period, using three 

wells in a line normal to the flood plain. The recession period is assumed to represent steady-state conditions, so that the shape of the profile is stable 

throughout its decline. An expression for diffusivity 

in this instance is

A/I D = (10)

where Afe is the drop in the water-table profile during the period A£ ; a and b are the differences in the 

head of the profile between the upper and middle 

wells, and between the middle and lower wells, respectively; and c and d are the horizontal distances 

between these respective wells.

Three wells (0730, 0731, and 0729), on the right 

bank of the Gila River approximately on a line perpendicular to the flood plain near section 9 (fig. 1) 

were used to estimate diffusivity of the basin fill by 

this method. Wells 0730 and 0731 are in the basin 

fill and are described in table 8. Well 0729 is in th* 

flood plain; it was angered to a depth of 42 feet, 

cased with a 1-inch-diameter pipe to a depth of 3? 

feet, and finished with a 2!/2-foot well point. 

Whether this well penetrates the basin fill is questionable.

Computations were made for two recession periods June 2 to August 8, 1966, and January 17 to 

March 19, 1969. Wells 0730 and 0731 may have been 

pumped occasionally during these two periods, but 

drawdown does not appear to have been significant, 

judging from the shape of their water-level hydrographs. Average water-table profiles for these recession periods are shown in figure 14. The data 

obtained from these profiles and used in equation 10 

to compute diffusivity are listed in table 10. The 

resulting diffusivities are 516,000 cu ft per day per 

ft for the 1966 profile and 62,900 cu ft per day per
F22 GILA RIVER PHREATOPHYTE PROJECT

ft for the 1969 profile. If the storage coefficient of 

the basin fill is 0.0005, the transmissivities for these 

two profiles are 258 cu ft per day per ft (1,930 gpd 

per ft) and 31.5 cu ft per day per ft (235 gpd per 

ft). The large discrepancy between these two determinations suggests that these profiles are not sufficiently stable for this method to be applicable. This 

is apparent from the change in shape of the profiles 

during each recession period (indicated by the range 

in A/z. values between wells) and from the change in 

shape between each recession period. The water 

levels in wells 0730 and 0731 may also be affected by 

periodic pumping and well 0729 may reflect water 

levels in the alluvium, rather than in the basin fill. 

These results are therefore considered to be unreliable.

GEOTHERMAL TESTS AT WELLS 1141 AND 1756

Bredehoeft and Papadopulos (1965) described a 

technique for determining the vertical velocity of 

ground water in a fully saturated porous medium 

from observations of the temperature profile in the 

medium. By assuming that the aquifer is isotropic 

and homogeneous, the vertical steady movement of 

ground water may be expressed as

v. = Jj-_, (ID

where vg is the apparent vertical velocity, k is the 

thermal conductivity of the water-mass complex, cn 

is the specific heat of water, Po is the density of 

water, L is the vertical distance over which the tern2900 -

Z 2800 -

2700 -

2600 -

2500 -

DISTANCE FROM RIVER, IN THOUSANDS OF FEET

FIGURE 14. Average water-table profiles in the basin fill 

near cross-section 9 during the periods June 2 to August 

8, 1966, and January 17 to March 19, 1969.

TABLE 10. Water-level heads (a and b), water-lev il changes 

(Ah), distances between wells (c and d), time increments 

(At), and corresponding diffusivities (D), competed from 

equation 10 using water-level recessions at wvlls 0780, 

0731, and 0729 during 1966 and 1969

[See fig. 14]

Period (ft)

D

bed Average __* (cu ft

(ft) (ft) (ft) Afe (<Jays) per day

(ft) per ft)

June 2-Aug. 8, 1966 ... 168.80 182.94 10,500 10,800 

Jan. 17-Mar. 19, 1969 _- 152.45 181.98 10,500 10,800

2.8 

0.84

 7 

fl

516,000

62,900

perature profile is measured, and /? is a dimensionless parameter obtained from type curves used to 

match the measured temperature profile. Velocities 

computed from equation 11 account for the porosity 

of the medium, and, therefore, represent the "apparent" velocity through the gross cross-sectional area 

of flow. The corresponding velocity through the pore 

spaces is vp = vx /a, where vp is the pore velocity, 

and a is the porosity of the medium.

The values for c0 and PO in equation 11 are 1 cal/ 

g-°C (calorie per gram per degree Celsius) and 1 

g/cm3 (gram per cubic centimeter), respectively. 

Birch (Birch and others, 1942, p. 259) gave values 

of k for various soils ranging from 0.8 X 10~3 cal/ 

cm-sec-°C (calorie per centimeter per second per degree Celsius) for muck soil at 40-percent moisture 

by weight to 5.5 x 10~3 cal/cm-sec-°C for fine sandy 

loam at 21-percent moisture by weight. A k of 3 X 

10~3 cal/cm-sec-°C is considered to be a reasonable 

value for the basin fill deposits of saturated sand, 

silt, and clay.

A solution for equation 11 is obtained by first plotting the measured temperature profile of the saturated medium in the nondimensional form (z/L) - 

(Te -T0 )/(TL - To) versus z/L (Stallman, 1967, p. 

185), where

Tg - temperature at any depth, z, fc^low the 

uppermost temperature measurement;

To = temperature at the top of the measured 

profile (z = 0); and

TL - temperature at the bottom of the measured profile (z = L).

This plot is then compared with type curves of 

z/L - f(p) versus z/L prepared from tabulated 

values in Bredehoeft and Papadopulos (If^S, table 

1, p. 327) and the /8 value associated with the type 

curve which best fits the data points on tH plot is 

substituted in equation 11 to obtain v,.

R. W. Stallman applied this technique in estimating the rate of upward flow from the basin fill 

to the overlying alluvium at wells 1141 r.nd 1756.
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA F23

(See fig. 1.) Both wells were drilled 120 feet deep, 

and the upper 50 feet in each was cased with an 

8-inch-diameter pipe. The total depth in each was 

then cased with a 2-inch-diameter pipe placed inside 

the 8-inch-diameter casing. A temperature-measuring device sensitive to small temperature changes 

was lowered into the 2-inch-diameter pipes, and 

water-temperature readings were obtained at intermittent depths. Table 11 lists these readings for 

both wells.

Well-log data indicate that the basin-fill deposits 

occur 50 feet below land surface at well 1141 and 

60 feet below land surface at well 1756. The temperature profile for well 1756 indicates a downward 

movement of water above the 80-foot depth. To insure that the velocity determinations were representative of the region of upward movement in the 

basin fill, the analysis considered only that part of 

the temperature profile below 60 feet at well 1141 

and below 85 feet at well 1756. The temperature 

measurements at the bottom of each well (120-ft 

depth) were also omitted because of possible adverse effects that might result from the temperature 

sensor being buried in silt and clay.

Figure 15 shows the measured-temperature profiles for both wells and the type curves with their 

corresponding ft values. The ft values for the type 

curves which provide the best fit to the data plots 

are -0.2 for well 1141 and -0.7 for well 1756. The 

computed velocities corresponding to these ft values 

are 0.4 foot per year for well 1141 and 2.4 feet per 

year for well 1756.

TABLE 11. Water-temperature observations in 

wells mi and 1756 from the geothermal test

[--__, No observation]

Depth below

point 1 (ft)

40 --__---...__

45 ------ _

50 ..__.._.-..

55 ...........

60 ._._.._.___

65 ....-....._

70 _._-_._____

75 .... ----__

80 _________

85 . ... ....

90 .--_-__..._

95 ....._...._

100 .........

105 -_ .-.-_._.

110 __..__...._

115 .. ..._.__

120 ...__.._....

Water tempers

Well 1141

17.36

17.43

17.55

17.72

17.96

18.19

18.48

18.72

18.90

18.92

iture (°C)

Well 1756

20.62

20.68

20.74

20.81

20.88

20.93

21.00

21.04

21.10

21.15

21.22

21.27

21.32

21.38

21.43

1 Measuring point 1 ft above land surface for well 1141, 

and 2 ft above land surface for well 1756.

A brief discussion of this test by Weist (1971) indicates apparent velocities of 0.8 foot per year at 

well 1141 and 1.1 feet per year at well 1756. TT« 

revised values presented in this report result from 

a slightly different interpretation of the temperature 

profiles and a reevaluation of the value for k.

Thermal instability within the aquifer caused t^e 

turnover of water within the observation wells, r*- 

.sulting in temperature readings at any given depth 

to vary about ±0.01°C. However, the rate of change 

in temperature with depth an indicator of vertical 

flow was generally greater than this measurement 

variation. Similar tests by Edwin P. Weeks (wr'tten commun., 1970) suggest that the metal well essing may act as a thermal short circuit and distort the 

thermal gradient. Thus, the actual temperature profiles may depart from the measured profiles. T ?. 

value of k for the basin fill is also questionable and 

undoubtedly varies with depth. Because the trie 

average of k may range from 1 x 10~3 to 5 x 10-3 

cal/cm-sec-°C, the corresponding value computed for 

vz would accordingly range from 0.1 to 4.1 feet p^r 

year.

Because of these uncertainties, the vertical velocities derived in this analysis are considered as orly 

approximate. The results do indicate, however, that 

the movement of water from the basin fill into the 

overlying alluvium is very small and may average 

about 1.5 feet per year, or 0.004 foot per day.

EVALUATON OF RESULTS

The average storage coefficient, S, for the full 

saturated thickness of alluvium was estimated to be 

0.15. The S for the alluvium in the zone of watertable fluctuations with phreatophyte cover is O.PO. 

The pooled standard deviation of these estimates is 

33 percent, whereas the areal variability in the storage coefficient throughout the alluvium is about 25 

percent.

The S for the basin fill has been estimated as 

0.0005. Insufficient data are available to evaluate the 

error in this estimate or define the areal variation of 

the storage coefficient.

Several analytical techniques were employed in 

this analysis to determine the diffusivity and transmissivity of the alluvium and basin fill. Table 12 

summarizes the results of these determinations. 

Where more than one determination was made for a 

particular location, the indicated diffusivity and the 

transmissivity represent median values taken from 

their probability distribution. The table indicator a 

wide range in values for both the alluvium and the 

basin fill, which may, in part, reflect the true areal
F24 GILA RIVER PHREATOPHYTE PROJECT

i.o

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1 -

z =0 ft at 60-ft depth 

L = 55 ft at 115-ft depth

0 

-0.05 -0.04 -0.03 -0.02 -0.01 

z/L--

115

110

105

100

95

90

85

80

75

70

65

60

115

0.01 0.02

T-T

z =0 ft at 85-ft depth 

= 30 ft at 115-ft depth

-0.10 -0.08 -0.06 -0.04 -0.02

z/L1L ~ TO

A. Well 1141 B. Well 1756

FIGURE 15. /3 type curves and temperature profiles in the basin fill at wells 1141 and 1756.

variation in the water-carrying capacity of each of 

these aquifers. Some of these values are questionable, however, because the assumptions underlying 

their solution may not have been sufficiently satisfied. In general, those values derived from several 

determinations at one site or from data at several 

wells are considered to be the most representative.

Of the methods used in this study, the drawdownrecovery tests are considered to give the best estimate of transmissivity at a particular site, while the 

flood-wave propagation analysis is considered to give 

the best estimate of the average diffusivity for the 

area.

On the basis of these criteria, the best estimate of 

transmissivity for the alluvium at a particular site 

is 9,800 cu ft per day per ft (73,000 gpd per ft) 

obtained from the drawdown-recovery test at section 

1. Assuming the saturated thickness of alluvium, m, 

is 40 feet, the corresponding hydraulic conductivity, 

K, is 245 ft per day (1,830 gpd per sq ft). The 

storage coefficient at this site was computed as 0.16.

A representative average value of diffusrdty for 

the alluvium is 185,000 cu ft per day per ft, as obtained from the flood-wave propagation analysis. If 

the average storage coefficient is 0.15, the corresponding average transmissivity for the study area 

is 27,800 cu ft per day per ft (208,000 gpd per ft). 

Assuming m = 40 feet, the corresponding average 

K is 695 feet per day (5,200 gpd per sq ft). This 

value of K would classify the alluvium as a good 

aquifer consisting of mixtures of clean sands and 

gravels (Todd, 1963, figure 3.4).

The drawdown-recovery tests at wells 0531 and 

0532 were used to obtain an average transmissivity 

for the basin fill of 15 cu ft per day per ft (110 gpd 

per ft). The significantly higher transmissiv'ties obtained from the ground-water recession analysis in 

the basin fill are considered to be less reliable because of the effect that periodic pumping may have 

had on the recessions.

Assuming that the basin fill is 1,000 feet thick, 

the corresponding horizontal hydraulic conductivity
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA F25

TABLE 12. Summary of diffusivities and transmissivities for the alluvium and basin fill

[Asterisk (*) indicates value has been calculated from its indicated storage-coefficient value]

Location

Number Number 

of of deterwells minations

Storage 

coefficient

Diffusivity 

(cu ft per 

day per ft)

Transmissivity

Cubic feet 

per day 

per foot

Gallons 

per day 

per foot

Method of 

analysis

Alluvium

Section 1, right bank _______ _ 

River and flood plain wells _ _

Flood-plain and terrace wells

River and terrace wells _

Sections 1, 9, and 17 _________

Section 5, left bank _ _ _ _ _

Section 5, right bank

Sections 1 and 5 ________________

13 

21 

10 

24 

9 

3 

3 

5

13 

21 

10

24 

1 

1 

1

7

0.16 

.15 

.15 

.15 

.15

.15 

.15 

.15

*61,300 

215,000 

108,000 

185,000 

179,000 

104,000 

375,000 

16,000

9,800 

*32,200 

*16,200 

*27,800 

*26,800 

* 16,000 

* 56,000 

*2,400

73,000 

*241,000 

*121,000 

*208,000 

*201,000 

* 120,000 

*420,000 

* 18,000

Drawdown-recovery. 

Flood-wave propagation. 

Do. 

Do. 

Cyclic fluctuation. 

Constant- head drain function 

Do. 

Do.

Basin fill

Wells 0531 and 0532 ________

Basin-fill wells, sections 5-7 _ Wells 0729, 0730, and 0731 _

Do---.----.--..............

2

5 

3 

3

2

7 

1 

1

0.0005 

.0005 

.0005 

.0005

*27,000 

1,185,000 

516,000 

62,900

15 

*600 

*258 

*31.5

110 

*4,500 

*1,930 *235

Drawdown-recovery. 

Ground-water recession. 

Ground-water recession. 

Do.

is K = 0.015 foot per day (0.11 gpd per sq ft). This 

K value classifies the basin fill as a poor aquifer, consisting of sand, silt,-and clay (Todd, 1963, fig. 3.4). 

The upward vertical velocity determinations of 

0.4 foot per year at well 1141 and 2.4 feet per year 

at well 1756, based on the geothermal tests in the 

basin fill, are questionable, but are considered to be 

reasonable estimates of vertical movement of water 

from the basin fill into the overlying alluvium.

GROUND-WATER MOVEMENT

The aquifer constants derived in this analysis may 

be used to compute ground-water movement in the 

study area. Two components of flow are considered 

here downvalley flow through the alluvium, and 

basin-fill flow into the overlying alluvium. Figure 16 

illustrates the direction of both of these groundwater-flow components.

Downvalley flow through the alluvium is computed 

from

q = Tiw, (12)

where q is the downvalley flow, T is the transmissivity of the alluvium, i is the downvalley hydraulic gradient, and w is the alluvium width. By 

substituting in equation 12 the representative average values of T = 28,000 cu ft per day per ft, i = 

0.0016, and w = 5,000 feet, the average downvalley 

flow through the alluvium is computed to be 224,000 

cu ft per day (5.1 acre-ft per day).

Virtually all ground water flowing from the basin 

fill into the alluvium moves vertically upward, as 

indicated in figure 16. The contribution to the alluvium may be computed from

(13)

where qb is the total vertical upward flow through 

an area of alluvium of width w and length L, and vz 

is the apparent upward vertical velocity through the 

basin fill, as defined in equation 11. Assuming that 

w = 5,000 feet, L = 5,280 feet, and vg = 0.004 foot 

per day, equation 13 gives a vertical upward flow of 

106,000 cu ft per day per mile of valley length (2.4 

acre-ft per day per mile).

Rorabaugh (1964) showed that basin-fill flow irto 

the alluvium may be computed from

qb = 2Tha/x(2a-x), (14)

where qb is the flow per unit strip of aquifer normal 

to the downstream direction, T is the transmissivity 

of the basin fill, a is the width of the basin fill between its contact with an impermeable boundary 

(ground-water divide) and its contact with the saturated alluvium, and h is the hydraulic head in the 

basin fill at a distance, x, from the basin-fill-alluvium 

contact. This relation assumes that recharge to the 

basin fill is under steady state conditions and is considered applicable where the water-level fluctuations 

are small compared to the hydraulic head. If the 

basin fill is recharged at a constant rate over a prolonged period, equation 14 gives an upper limit of 

discharge.

Equation 14 was used to compute qb at five well 

sites on the right bank (north bank) and six well 

sites on the left bank (south bank) of the study 

reach of the Gila River. A transmissivity of 15 cu 

ft per day per ft (110 gpd per ft) was assumed for 

use in all computations. Table 13 lists the values of 

h, x, a, and corresponding qb for each site.

The median flows in table 13 are 0.42 cu ft per 

day per foot of valley length on the right bank, rnd
F26 GILA RIVER PHREATOPHYTE PROJECT

wwa

^ ^. ^ ...-^s^ Basin fi.ll

Not to scale

FIGURE 16. Ground-water-flow pattern (arrows) in the alluvium and the basin fill.

0.72 cu ft per day per foot of valley length on the 

left bank. The total average flow from the basin fill 

into the alluvium is, therefore, 1.14 cu ft per day 

per foot of valley length or 0.14 acre-ft per day per 

mile of valley length.

TABLE 13. Hydraulic head (h), distance between well and 

outflow boundary (x), width of basin fill (a), and corresponding basin-fill flow (qb ) computed from equation 14 for 

five wells on the right bank and six wells on the left bank

Well No.

0524 

0730 _ . 

0731 

1761 --_-. 

1762

Median q*

0522 

0531 

0732 . .- .- 

1343 .- . - 

2169 

2373

Median q*

h (ft)

325 

329 

181 

16 

451

423 

25 

460 

34 

416 

822

X

(ft)

Right bank

14,000 

17,000 

7,500 

1,000 

26,000

Left bank

9,200 

500 

13,700 

2,400 

18,800 

27,500

a 

(ft)

26,000 

24,500 

27,500 

21,500 

26,000

21,200 

23,300 

21,700 

22,400 

33,800 

36,500

(cu ft per 

day per ft)

0.47 

.45 

.42 

.24 

.52

0.42

0.89 

.76 

.74 

.22 

.46 

.72

_ _ 0.72

If virtually all this water moves vertically upward 

into the overlying alluvium, having a width of 5,000 

feet, the corresponding apparent vertical velocity is 

vz = 1.14/5,000 = 0.0002 foot per day. This velocity 

is 6 percent of the average apparent velocity of 

0.004 foot per day obtained from the gee thermal 

test. (See p. F23.) Additional aquifer tests in the 

basin fill would be required to explain the large discrepancy between these two average value-* of v,. 

However, these determinations do provide an estimate of the possible magnitude of basin-fill f ow into 

the overlying alluvium.

CONCLUSIONS

Various analytical techniques were used to evaluate the aquifer characteristics of the alluvium and 

basin fill. Extensive use was made of existing soilmoisture, ground-water, and streamflow dat-\ in applying these techniques.

The reliability of the resulting determinations of 

storage coefficient, diffusivity, transmissiv'ty, hydraulic conductivity, and vertical velocity of ground 

water is questionable in many of the determinations 

because of the constraints and assumptions associ-
SUBSURFACE HYDRAULICS, GRAHAM COUNTY, ARIZONA F27

ated with the techniques used in the analysis. However, where relatively consistent aquifer constants 

were obtained by using different methods of analysis 

or different sets of data, the results are considered to 

be representative.

This study indicates that the average storage coefficient is 0.15 for the alluvium and 0.0005 for the 

underlying basin fill. The average transmissivity is 

28,000 cu ft per day per ft (210,000 gpd per ft) for 

the alluvium and 15 cu ft per day per ft (110 gpd 

per ft) for the basin fill. The corresponding average 

horizontal hydraulic conductivity of the alluvium is 

695 feet per day (5,200 gpd per sq ft). The horizontal hydraulic conductivity in the basin fill is estimated at about 0.015 foot per day (0.11 gpd per sq 

ft). Geothermal measurements of the upward vertical flow of water from the basin fill to the overlying alluvium average 1.5 feet per year per square 

foot of area. Because of the wide range in determinations of storage coefficient and transmissivity at 

any given site, no attempt has been made to define 

their spacial distribution. These aquifer constants 

will be used, however, in analog and digital groundwater models to test their reliability and approximate their spacial distribution.

The aquifer constants derived in this analysis indicate that the average downvalley ground-water 

flow through the alluvium is 5.1 acre-feet per day. 

Estimates of flow from the basin fill into the overlying alluvium range from 0.14 to 2.4 acre-feet per 

day per mile of valley length.

REFERENCES CITED

Birch, A. F., Schairer, J. F., and Spicer, H. C., eds., 1942, 

Handbook of physical constants: Geol. Soc. America 

Spec. Paper 36, 325 p.

Bredehoeft, J. D., Papadopulos, I. S., 1965, Rates of vertical 

ground-water movement estimated from the earth's thermal profile: Water Resources Research, v. 1, no. 2, p. 

325-328.

Cooper, H.H., Bredehoeft, J. D., and Papadopulos, I. S., 1967, 

Response of a finite-diameter well to an instantaneoir 

charge of water: Water Resources Research, v. 3, no. 1, 

p. 263-269.

Culler, R. C., and others, 1970, Objectives, methods, and environment Gila River Phreatophyte Project, Graham 

County, Arizona: U.S. Geol. Survey Prof. Paper 655-A, 

25 p.

Davidson, E. S., 1961, Facies distribution and hydrology of 

intermontane basin fill, Safford basin, Arizona, in Short 

papers in the geologic and hydrologic sciences: U.S. 

Geol. Survey Prof. Paper 424-C, p. C151-C153.

Ferris, J. G., Knowles, D. B., Brown, R. H., and Stallmair, 

R. W., 1962, Theory of aquifer tests: U.S. Geol. Survey 

Water-Supply Paper 1536-E, p. 69-174.

Finder, G. F., Bredehoeft, J. D., and Cooper, H. H., 1968, 

Determination of aquifer diffusivity from aquifer response to fluctuations in river stage: Water Resource.'' 

Research, v. 5, no. 4, p. 850-858.

Rorabaugh, M. I., 1960, Use of water levels in estimating 

aquifer constants in a finite aquifer: Internat. Assoc. 

Sci. Hydrology, Pub. 52, p. 314-323.

 1964, Estimating changes in bank storage and groundwater contribution to streamflow: Internat. Assoc. Sci. 

Hydrology, Pub. 63, p. 432-441.

Stallman, R. W., 1967, Flow in the zone of aeration, in Ver 

Te Chow, ed., Advances in hydroscience: New York, 

Academic Press, v. 4, 428 p.

Theis, C. V., 1935, Relation between the lowering of the 

piezometric surface and the rate and duration of discharge of a well using ground-water storage: Am. 

Geophys. Union Trans., v. 16, pt. 2, p. 519-524.

Todd, D. K., 1963, Ground water hydrology: New York, John 

Wiley & Sons, Inc., 336 p.

Weist, W. G., Jr., 1971, Geology and the ground-water system in the Gila River Phreatophyte Project area, Graham County, Arizona: U.S. Geol. Survey Prof. Paper 

655-D (in press).

 fr U.S. GOVERNMENT PRINTING OFFICE: 1972 0 446-437