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Prof.Dr.Ir. Sunjoto Dip.HE, DEA-Hydrology of Groundwater-Post Graduate Program JTSL-FT-UGM-2014 1

SUBSURFACE HYDROLOGY

By: Prof.Dr.Ir. Sunjoto Dip.HE,DEA

Lecture note:

Post Graduate ProgramDepartment of Civil and Environmental Engineering

Faculty of Engineering Gadjah Mada University

Yogyakarta, 2014


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I. INTRODUCTION

1. EtymologyHydrogeology (eng) Geohydrologie (fr) Geohidrologi (id)

Geohydrology (eng) Hydrogeologie (fr) Hidrogeologi (id)

2. Hydrology

a. Water cycle

Fig. 1.1. Hydrological cycle

THE WATER CYCLE

Water storagein ice and snow

Water storage in oceans

Evaporation

Groundwater discharge

Infiltration

Precipitation

Sublimation

Water storage in the atmosphere

Evapotranspiration

SpringFresh water storage

Groundwater storage

Surface runoff

Snowmelt runoff to stream Condensation

SUN


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b. Water Balance

Water balance on the ground surface is:

Fig 1.2. Water balance on the ground surface

Fig 1.3. Water balance of the storage

Acccording to Lee R. (1980): P + Ev annual 5 .105 km3/y, equal the depth 973

mm to cover the earth and needs 28 ceturies to evaporate by atmosphericdestilation.

I OS

I - O = S

I : InflowO : OutflowS : Storage

P E

I

RP E = R + I

P : PrecipitationE : Evapotranspiration

R : RunoffI : Infiltration


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c. Water Quantity in the Earth (Volume dimension x10 6 Km3 )

Table 1.1. Water distribution in the earth (Todd, 1970)Items Volume x10 6 Percentage

Ocean location Saline Water 1,320 Km3 97.300 % Continents location

Lake fresh water 0.125 Km3 0.0090 % Lake saline water 0.104 Km3 0.0080 % Rivers 0.00125 Km3 0.0001 % Soil moisture 0.067 Km3 0.0050 % Groundwater (above 4000 m) 8.350 Km3 0.6100 % Eternal ice and snow 29.200 Km3 2.1400 %

Total volume 37.800 Km3

2.800 %Atmosphere location:

Vapor 0.013 Km3 0.001 %Total water 1,360 Km3 100.000 %

Table 1.2. Water distribution in the earth (Nace, 1971)Items Volume x10 6 Percentage

Saline water 1,370 Km3 94.000 %

Ice & snow 30 Km3

2.000 % Vapor 0.010 % Groundwater 60 Km3 4.000 % Surface water 0.040 % Total water 100.000 %

Table 1.3. Water distribution in the earth (Huissman, 1978)Items Volume x10 6 Percentage

Free water, consist of:1,370 Km3

Saline water 97.200 % Ice & snow 2.100 % Vapor 0.001 % Fresh water, consist of: 0.600 %

Groundwater 98.80 % Surface water 1.20 %

Total water 100.000 %


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Table 1.4. Water distribution in the earth (Baumgartner and Reichel, 1975)Items Volume Percentage

Solid 2.782 .107 Km3 2.010 % Liquid 1.356 .109 Km3 97.989 %

Oceans 1.348 .109

Km3

97.390 % Continent; groundwater 8.062 .106 Km3 0.583 % Continent; surface water 2.250 .105 Km3 0.016 %

Vapor 1.300 .104 Km3 0.001 % Total (all forms) 1.384 .109 Km3 100.000 %

Saline water 1.348 .109 Km3 97.938 % Fresh water 3.602 .107 Km3 2.202 %

Table 1.5. Fresh water distribution in the earth (Baumgartner and Reichel, 1975)Items Volume PercentageSolid 2.782 .107 Km3 77.23 % Liquid 8.187 .106 Km3 22.73 %

Groundwater 7.996 .106 Km3 22.20 % Soil moisture 6.123 .104 Km3 0.17 % Lakes 1.261 .105 Km3 0.35 % Rivers, organic 3.602 .103 Km3 0.01 %

Vapor 1.300 .104 Km3 0.04 %

Total (all forms) 3.602 .107 Km3 100.00 %

Table 1.6. Annual average water balance components for the earth (Fig. 1.4) Item Continent Ocean Earth

Area (106 km2)Volume (103 km3)

Precipitation Evaporation Discharge

Avererage depth (mm) Precipitation Evaporation Discharge

148.90

+111 -71 -40

+745 -477 -269

361.10

+385 -425 +40

+1066 -1177 +111

510.00

+496 -496

0

+973 -973

0 Source: (Baumgartner & Reichel, 1975 in Lee R., 1980)


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Fig. 1.4. Earth water balance components, in 103 km3 (Baumgartner & Reichel, 1975 inLee R., 1980)

d. Management of Groundwater

1). Advantages and Disadvantages of Groundwater

Table 1.7. Conjunctive use of Surface and Groundwater ResourcesAdvantages Disadvantages

1. Greater water conservation 2. Smaller surface storage 3. Smaller surface distribution system 4. Smaller drainage system 5. Reduced canal lining 6. Greater flood control 7. Ready integration with existing

development 8. Stage development facilitated

9. Smaller evapotranspiration losses 10. Greater control over flow 11. Improvement of power load 12. Less danger than dam failure 13. Reduction in weed seed distribution 14. Better timing of water distribution 15. Almost good quality of water resources

1. Less hydroelectric power 2. Greater power consumption 3. Decreased pumping efficiency 4. Greater water salination 5. More complex project operation 6. More difficult cost allocation 7. Artificial recharge is required 8. Danger of land subsidence

Source: Clendenen in Todd, 1980.

P=385

=40 P=111

E=425Q=40

E=71

CONTINENT

OCEAN

ATMOSPHER

Water balance:P + E + Q = 0


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Table 1.8. Advantages and Disadvantages of subsurface and Surface Reservoir s (USBR) Subsurface Reservoirs Surface Reservoirs

Advantages 1. Many large-capacity site available 2. Slight to no evaporation loss

3. Require little land area 4. Slight to no danger of catastrophic

structural failure 5. Uniform water temperature 6. High biological purity 7. Safe from immediate radio active fallout

8. Serve as conveyance systems-canals orpipeline across land of othersunnecessary

Disadvantages 1. Water must be pumped 2. Storage and conveyance use only 3. Water maybe mineralized

4. Minor flood control value 5. Limited flow at any point 6. Power head usually not available 7. Difficult and costly to evaluate,

investigate and manage 8. Recharge opportunity usually dependent

of surplus of surface flows 9. Recharge water maybe require expensive

treatment 10. Continues expensive maintenance of

recharge area or wells

Disadvantages 1. Few new site available 2. High evaporation loss even in humid

climate 3. Require large land area 4. Ever-present danger of catastrophic

failure 5. Fluctuating water temperature 6. Easily contaminated 7. Easily contaminated radio active fallout

8. Water must be conveyed

Advantages 1. Water maybe available by gravity flow 2. Multiple use 3. Water generally of relatively low mineral

content

4. Maximum flood control value 5. Large flows

6. Power head available 7. Relatively to evaluate, investigate and

manage 8. Recharge dependent o annual

precipitation 9. No treatment require recharge of

recharge water 10. Little maintenance required of

facilities


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Table 1.9. Attributes of GroundwaterThere is more ground water than surface water

Ground water is less expensive and economic resource.

Ground water is sustainable and reliable source of water supply.

Ground water is relatively less vulnerable to pollution

Ground water is usually of high bacteriological purity.

Ground water is free of pathogenic organisms.

Ground water needs little treatment before use.

Ground water has no turbidity and color.

Ground water has distinct health advantage as art alternative for lower sanitary

quality surface water. Ground water is usually universally available.

Ground water resource can be instantly developed and used.

There is no conveyance losses in ground water based supplies.

Ground water has low vulnerability to drought.

Ground water is key to life in arid and semi-arid regions.

Ground water is source of dry weather flow in rivers and streams.

Source: http://www.tn.gov.in/dtp/rainwater.htm

e. Data collection1). Topographic data2). Geologic data3). Hydrologic data

(a). Surface inflow and outflow

(b). Imported and exported water(c). Precipitation(d). Consumptive use(e). Changes in surface storage(f). Changes in soil moisture(g). Changes in groundwater storage(h). Subsurface inflow and outflow
http://www.tn.gov.in/dtp/rainwater.htmhttp://www.tn.gov.in/dtp/rainwater.htmhttp://www.tn.gov.in/dtp/rainwater.htmhttp://www.tn.gov.in/dtp/rainwater.htm


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3. History

a. Dug well

Fig. 1.5. A crude dug well in Shinyanga Region of Tanzania. (after DHV Con. Eng.,in Todd, 1980)

The simplest dug well is crude dug well where the people go down to draw a water

directly. Then brick or masonry casing dug well which were build before century. The

dug well with casing equipped by bucket, rope and wheel to draw water.


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Fig. 1.6. Sketch of crude dug well cross section as the first generation of step well.

Fig. 1.7. A modern domestic dug well with rock curb, concrete seal and hand pump.(after Todd, 1980)


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Fig 1.8. Communal dug well equipped by recharge systems surraunding the well.

Fig 1.9. Traditional step well in India it is called baollis or vavadi were built from8th to 15th century (Source: Nainshree G. Sukhmani A. Design of WaterConservation System Through Rain Water Harvesting; An Excel Sheet Approach)


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b. Qanat

Qanat is a system of water exploitation which providing of irrigation water in Central

East. Qanat is a method to get clean water by digging horizontal gallery across the

slope surface of ground till reach groundwater table of the aquifer. From this aquiferwater flow with smaller slope than original slope of groundwater table of impervious

canal go in the direction of irrigation area (Fig. 1.10.). According to Todd (1980), the

total gallery length of qanats in this area, reach thousands of miles. Iran has the

greatest concentration of qanats , here some 22,000 qanats are supplying 75% of all

water used in the country. Lengths of qanats extend up to 30 km but most are less

than 5 km. The depth of qanats mother well is normally less than 50 m but instancesof depth exceeding 250 m. Discharges of qanants vary seasonally with water table

fluctuation and seldom exceed 100 m 3/h. The longest qanat near Zarand, Iran is 29

km with a mother well depth of 96 m with 966 shafts along its length and the total

volume of material excavated is estimated at 75,400 m 3.

Fig. 1.10. Vertical cross section along a qanat (after Beaumont, in Todd, 1980)


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Fig 1.11. Roman aquaducts as water coveyance were built before century

Fig 1.12. Roman city water system provider from ground water resources to the city.

Note:1. Infiltration gallery/qanat2. Steep chute in this case dropshafts3. Settling tank4. Tunnel and shafts5. Covered trench

6. Aquaduct bridge7. Siphon8. Substruction9. Arcade10. Distribution basin11. Water distribution (pipes)
http://www.romanaqueducts.info/aquasite/foto/P5300081.jpg


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c. Crush Bore Well (Cable tool)

Crush Bore Well is a well which is build to provide drinking water by crush or impact

of a sharp cylindrical metal using cable tool to rise on the certain height and then be

released and fall down to the ground and create a hole which reach ground watertable. In Egypt this system was implemented since 3000 BC, in Rome near the first

century and in a small town in south French Artois, which well had a hydraulic

pressure and it created an artesian well due to the water squirt out from the well

(Fig.1.13.).

Fig. 1.13. Schematic cross section illustrating unconfined and confined aquifer (afterTodd, 1980)

d.

Rotary Bore WellRotary bore well was implemented since 1890 in USA to draw gas and oil and the hole

reach 2,000 meter depth. Nowadays, the rotary bore well reach 7,000 meter depth.


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e. Springs

Spring is an outflow of ground water to the ground surface due to hydraulic head or

gravitational force (Fig. 1.14). This technique had been implanted since before

century like in Greek or Roman Kingdom. Spring water as a drinking water is usually beconveyed by network of pipes or canals to the town. Like in Trowulan as capital of

Majapahit Kingdom it was implemented since 12nd century that on the site of spring

was built a temple is now called Tikus Temple. Nowadays from this temple still flowing

water even though with small discharge and this building installed by inflow-outflow

and overflow system and conveyance pipes to Segaran Pond with the area are more

than 6 ha.

Fig. 1.14. Diagrams that illustrating types of gravity springs. (a). Depression spring. (b).Contact springs. (c). Fracture artesian spring. (d). Solution tabular spring (after Bryan,in Todd, 1980)


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Above:Fig 1.15. Kaptering or springwater catcher of MajapahitKingdom in Java was build in 12century recently its called TikusTemple (personal photocollection=pc).

Left:Fig 1.16. Water pipes system withdiameter about 60 cm, convey thewater to the pond and housing ofthe Kingdom(Photo: Prof. Hardjoso P.)


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Left:Fig 1.17. Distribution pipesto the housing(Photo: Prof. Hardjoso P.)

Left:Fig 1.18. Fontains ofTrwulan city(Photo: Prof. Hardjoso P.)


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Fig 1.20. Water pond with brick structure which is called Segaran Pond (pcp).

4. Qualitative Theorya. Early Greek Philosophers

Homer, Thales (624-546 BC) and Plato (428-347 BC) hypothesized that springs were

formed by sea water conducted through subterranean channels below the mountains,

then purified and raised to the surface.

Left:Fig 1.19. Ancient dug wellcased by bricks in thehousing of the Kingdom(Photo: Prof. Hardjoso P.)


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b. Aristoteles (384-322 BC

Water is every day carried up and is dissolved into vapor and rises to the upper

region, where it is condensed again by the cold and so returns to the earth.

c. Marcus Vitruvius (15 BC)

Theory of the hydrologic cycle, in which precipitation falling in the mountains

infiltrated the Earth's surface and led to streams and springs in the lowlands.

d. Early Roman Philosophers

Lucius Annaeus Seneca (1 BC AD 65) and Pliny clarify theory of Aristoteles is

precipitation fall down in the mountain, a part of water infiltrate to the ground as a

storage water and then flow out as springs.

e. Bernard Palissy (1509-1589)

He described more clearly about hydrological cycle from evaporation in the sea till

water come back again to the sea in his book: Des eaux et fontaines .

f. Johannes Kepler (1571-1630)

The earth as a big monster whose suck water from the sea, be digested and flow out

as fresh water in springs.

g. Athanasius Kircher (1602-1680)

Interaction with magma heat which causes heated water to rise through fissures and

tidal and surface wind pressure on the ocean surface which forces ocean water into

undersea.

5. Quantitative Theory

a. Pierre Perrault (1608-1690)

He observed rainfall and stream flow in the Seine River basin, confirming Palissy's

hunch and thus began the study of modern scientific hydrology. He said that the

depth of precipitation in the Seine river, France was 520 mm/y


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b. Edme Mariotte (1620-1684)

In his book Des mouvements des eaux Seine River: Discharge Q = 200.000 ft 3/min,

local flow is 1/6 part, evaporation is 1/3 part and infiltration is 1/3 part.

c. Edmund Halley (16561742)

He developed the equation of balance : I O = S

d. Daniel Bernoulli (1700-1782)

He stated that, in a steady flow, the sum of all forms of mechanical energy in a fluid

along a streamline is the same at all points on that streamline.

e. Jean Leonard Marie Poiseuille (1797-1869).The original derivation of the relations governing the laminar flow of water through a

capillary tube was made by him in the early of 19 th century.

f. Reynold (1883)

The Reynolds number NR is a dimensionless number that gives a measure of

the ratio of inertial forces V2/L to viscous forces V/L2 and consequently quantifies

the relative importance of these two types of forces for given flow conditions.

g. Henry Philibert Gaspard Darcy (June 10, 1803 January 3, 1858)

On his books Les fontaines publiques de Dijon (1856), he developed mathematical

equation for flow in porous media.

h. Badon Gabon (1888) and Herzberg (1901)

They developed equilibrium theory of fresh water and saline water in the circular

island with porous soil.
http://en.wikipedia.org/wiki/Edme_Mariottehttp://en.wikipedia.org/wiki/Streamlines,_streaklines,_and_pathlineshttp://en.wikipedia.org/wiki/Dimensionless_numberhttp://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Inertial_forcehttp://en.wikipedia.org/wiki/Viscoushttp://en.wikipedia.org/wiki/Viscoushttp://en.wikipedia.org/wiki/Inertial_forcehttp://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Dimensionless_numberhttp://en.wikipedia.org/wiki/Streamlines,_streaklines,_and_pathlineshttp://en.wikipedia.org/wiki/Edme_Mariotte


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i. Jules Dupuit (1863)

In his book: Estudes Thoriques et Pratiques sur le mouvement des Eaux dans les

canaux dcouverts et travers les terrains permables , Dupuit developed the

formulas for groundwater flow from trench to trench with definite distance, radialflow in unconfined and confined aquifer with definite distance.

j. Adolph Thiem (1870)

a German engineer who developed equation for the flow toward well and infiltration

galleries.

k. Gunther Thiem (1907)

In 1906, he continued Dupuit principle and his father research he developed steady

stage equation for the circular flow, using two test wells and drawdown data, and the

formula is nowaday called Dupuit-Thiem.

l. Lugeon (1930)

Lugeon developed the double packers bore hole inflow test made at constant head.

Lugeon is a measure of transmissivity in rocks, determined by pressurized injection

of water through a bore hole driven through the rock.

m. Theis (1936)

The Theis equation was developed to determine transmissivity of storage coefficient

by drawdown measuring at any given radius from the well in form exponential integral.

Due to the equations are difficult to compute so the graphic solutions are needed.

n. Expansion of Theis

Cooper-Jacob simplified the Theis formula by negligible after the first two terms.

The same manner it was expanded to by Chow (1952) and Todd (1980) but all

together still need graphic solution.
http://en.wikipedia.org/w/index.php?title=Lugeon&action=edithttp://en.wikipedia.org/w/index.php?title=Lugeon&action=edit


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o. Forchheimer (1930)

He developed the flow equation of steady state radial flow in borehole using new

parameter is shape factor and neglected data of observation well.

p. Expansion of Forchheimer

Development of formulas of shape factors by Samsioe (1931), Dachler (1936), Taylor

(1948), Hvorslev (1951), Aravin (1965), Wilkinson (1968), Al-Dahir & Morgenstern

(1969), Luthian & Kirkham (1949), Kirkham & van Bavel (1948), Raymond & Azzouz

(1969), Smiles & Young (1965) and Sunjoto (1988-2008).

q. Taylor (1940)

Certain guiding principles are necessary such as the requirement that the formation

of the flownet is only proper when it is composed of curvilinear squares.

r. Sunjoto (1988)

Base on Forchheimer (1930) principle, Sunjoto (1988) developed an unsteady state

radial flow equation for well which was derived by integration solution and shape

factors of the tip of the well. In 2008 he developed too the formula of unsteady

state condition of recharge trench and its shape factors.

6. Interest of Research

a. Russian Groundwater in ice region

b. Dutch Groundwater in sand dunes

c. Japanese Hot groundwater

d. Indonesian Recharge Systems


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7. Dimension and Unit

a. Georgy System (mks)

Table 1.8. Dimension and Unit

Description Dimension Unitmass length time

m l t

gram meter second

Force

Energy

Power

Pressure

mlt-2

ml2t -2

ml2t -3

ml-1t -2

N (Newton) = kgm.s-2

J (Joule) = N.m

W (Watt) = N.m.s-1

N.m-2

b. Metric prefixes

Table 1.9. Metric preficesPrefix Symbol Factor Prefix Symbol Factor

tera T 1012 centi c 10-2

giga G 109 milli m 10-3

mega M 106 micro 10-6

kilo k 103 nano n 10-9

hecto h 102 pico p 10-12

deca da 101 femto f 10-15

deci d 10-1 atto a 10-18


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c. Conversion of unit

Table 1.10. ConversionDescription Unit mks NoteForce

Energy

Power

1 kg

1 kg.m

1 kg.ms-1

g.N

g.J

g.W

1 N = 105 dynes

g = 9.78 m.s-2 = 32.3 ft.s -2

1 HP = 75.g.W = 734 W

d. Metric-English equivalents

Table 1.11. Metric-English equivqlent1). Length

1 cm = 0.3937 in

1 m = 3.281 ft

1 km = 0.6214 mi

2). Area

1 cm2 = 0.1550 in2

1 m2 = 10.76 ft 2

1 ha = 2.471 acre

1 km2 = 0.3861 mi2

3). Volume

1 cm3 = 0.06102 in3

1 l = 0.2642 gal = 0.03531 ft 3

1m3 = 264.2 gal = 35.31 ft 3

= 8.106 .10-4 acre.ft

4). Mass 1 g = 2.205 .10-3 lb (mass)

1 kg = 2.205 lb (mass)

= 9.842 .10-4 long ton

5). Velocity

1 m/s = 3.281 ft/s

= 2.237 mi/hr

1 km/hr = 0.9113 ft/s

= 0.6214 mi/hr

6). Temperature o C = K 273.15

= (o F 32)/1.8

7). Pressure

1 Pa = 9.8692 .10-6 atm

= 10-5 bar

= 10-2 millibar

= 10 dyne/cm2

= 3.346 .10-4 ft H 2O (4o C)

= 2.953 .10-4 in Hg ( 0o C) = 0.0075 mm Hg

= 0.1020 kg (force)/m 2

= 0.02089 lb (force)/ft 2


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8). Flow rate

1 l/s = 15.85 gpm

= 0.02282 mgd = 0.03531 cfs

1 m3

/s = 1.585 .104

gpm = 22.82 mgd = 35.31 cfs

1 m3/d = 0.1834 gpm

= 2.642 .10-4 mgd = 4.087 .10-4 cfs

9). Force

1 N = 105 dyne

= 0.1020 kg (force)

= 0.2248 lb (force) 10). Power

1 W = 9.478 .10-4 BTU/s

= 0.2388 cal/s

= 0.7376 ft.lb (force)/s

11). Water quality

1 mg/l = 1 ppm = 0.0584 grain/gal

12). Hydraulic conductivity

1 m/d = 24.54 gpd/ft 2

= 1.198 darcy (water 20 o C)

1 cm/s = 2.121 .104 gpd/ft 2

= 1035 darcy (water 20 o C)

13). Viscosity

1 Pa.

s = 103

centistoke= 10 poise = 0.02089 lb (force) .s/ft 2

1 m2/s = 106 centistoke = 10.76 ft 2/s

14). Gravitational acceleration, g

9.807 m/s 2 = 32.2 ft/s 2 (std., free fall)

15). Heat

1 J/m2

= 8.806 .10-5

BTU/ft2

= 2.390 .10-5 cal/cm2

1 J/kg = 4.299 .10 -4 BTU/lb (mass)

= 2.388 .10-4 cal/g

16). Density of water,

1000 kgmass/m3 = 1.94 slugs/ft 3

(when 50o F/10o C)

17). Specific weight of water,

9.807 .103 N/m3 = 62.4 lb/ft 3 (50oF/10oC)

18). Dynamic viscosity of water,

1.30 .10-3 Pa.s=2.73 .10-5lb.s/ft 2(50o/10oC)

10-3 Pa.s = 2.05 .10-5 lb.s/ft 2 (68o F/20 o C)

19). Kinematic viscosity of water,

1.30.10-6m2/s=1.41 .10=5 ft 2/s(50 o F/10oC)

10-6 m2/s = 1.06 .10-5 ft 2/s (68 o F/20 o C)

20). Atmospheric pressure, p (std)

1.013 .105 Pa = 14.70 psia

21). Energy

1 J = 9.478 .10 -4 BTU

= 0.2388 cal

= 0.7376 ft.lb (force) = 2.788 .10-7 kw.hr


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e. Legends

1). Density

Symbol :

Dimension : ml-3 Unit : kgmass.m-3 or slug.ft -3

Detail:

1 slug = 14.60 kgmass

1 feet = 0.305 m

1 slug.ft -3 = 514.580 kgmass.m-3

In practical use: pure water = 1,000 kgmass.m-3 = 1.94 slug.ft-3

sea water = 1,026 kgmass.m-3 = 1.99 slug.ft-3

Table 1.12. Density of pure water in kg mass.m-3 dependent temperature t o Ct t t t 0

2 4

6

8

999.8679

999.9267 1000.0000

999.9081

999.8762

10

12 14

16

18

999.7277

999.5247 999.2712

998.9701

998.6232

20

22 24

26

28

998.2323

997.7993 997.3256

996.8128

996.2623

30

32 34

36

38

995.6756

995.0542 994.3991

993.7110

992.9936

2). Specific weight

Symbol : = .g Dimension : ml-2t -2

Unit : N.m-3 atau lbs.ft -3


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3). Specific Gravity

Symbol : s s = / w = / w

Dimension : -

Unit : -

4). Viscosity

(a). Dynamic viscosity

Symbol :

Dimension : ml-1t -1

Unit : N.s.m-2

1 N.s.m-2 = 10 poise; 478 poise = 1 lbs.ft -2

Table 1.13. Dynamic viscosity of water in 10-2 poisses dependent temperature t o Ct t t t

0

2

4 6

8

1.7921

1.6728

1.5674 1.4728

1.3860

10

12

14 16

18

1.3077

1.2363

1.1709 1.1111

1.0559

20

22

24 26

28

1.0050

0.9579

0.9142 0.8737

0.8360

30

32

34 36

38

0.8007

0.7679

0.7371 0.7085

0.6814

(b). Cinematic viscocity

Symbol :

Dimension : l2t -1

Unit : m2s-1 or stokes

1 m2s-1 = 10-4 stokes

1 ft 2s-1 = 929 stokes

= /


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5). Surface Tension

Symbol :

Dimension : mt-2

Unit : N.m-1 water/air = 0.074 N.m-1

Table 1.14. Relationship of , and of watert = 10o C; p = atm t = 60o F; p = atm

Water Air Unit Water Air Unit

1000

1.3 .10-2

1.3 .10-6

1.37

1.8 .10-4

1.3 .10-5

kgmass.m-3

poise

m2s-1

1.94

2.3 .10-5

1.2 .10-5

2.37 .10-3

3.7 .10-7

1.6 .10-4

slug.ft -3

lbs.s.ft -2

ft 2s-1


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II. GENERAL DESCRIPTION

1. Terminologya. Aquifer

The origin of aqua is water and ferre is contain.

b. Aquiclude

The origin of claudere is to shut.

c. Aquifuge

The origin of fugere is to expel.d. Aquitard

The origin of tard is late.

2. Vertical Distribution

Fig. 2.1. Diagram of zones in permeable soil

Ground surface

Soil water zone

Intermediatevadoze

zone

Capillary zone

Saturated zone

ZONE OFAERATION

ZONE OFSATURATION

VADOZEWATER

GROUND /PHREATICWATER

Groundwater table

Impermeable

P

e

r

m

e

a

b

le


30/137


a. Zone of Aeration

This zone divided into:

Soil water zone

Intermediate vadose zone

Capillary zone

2 = 2 = 2 (2.1)

Fig. 2.2. Schematic of capillary rise

hc

2r

=0.15

hc : height of capillary zone : surface tension (dynes/cm) : specific weight of waterr : radius of tube : contact angle of water and wa ll

When pure water in clean glass, = 0and temperature at 20 o C so value ofs = 75 dyne/cm= 0.076 g/cm and,


31/137


Table 2.1. Capillary rise in samples of unconsolidated materials (after Lohman inTodd, 1980)

Soils Type Grain size (mm) Height of capillary (cm)

Fine gravel

Very coarse sand

Coarse sand

Medium sand

Fine sand

Silt

Silt

5 - 2

2 - 1

1 0.5

0.5 0.2

0.2 0.1

0.1 0.05

0.05 0.002

2.50

6.50

1.50

24.60

42.80

105.50

200.00

Table 2.3. Capillary rice of some soils type (Murthy, 1977)Soils Type Size of particles (mm) Capillary rise (cm)

Sand, coarse

Sand, medium

Sand, fine

Silt

Clay, coarse

Clay, colloid

2.00 - 0,60

0.60 0.20

0.20 0.06

0.06 0.002

0.002 0.0002

< 0.0002

1.50 5

5 15

15 - 50

50 - 1,500

1,500 15,000

>15,000


32/137


b. Zone of Saturation

1). Specific retention (Sr)

= (2.2)

Wr : the rest water volume after drainage

V : total volume of soil

2). Specific yield (Sy)

= (2.3)

W y : volume of water which be drained

= Sr + S y

c. Solid Liquid and Air System

Solid phase : geometricly difficult be soluble

Liquid phase : solution organic & unorganic

Air phase : vapor

Fig. 2.3. Diagram of solid, water and air relationship

V

Vv

Va

Vw

Vs

Wa

Ww

Ws

1

air

water

solid


33/137


1). Void ratio (e)

The ratio of the volume of voids (Vv) to the volume of solids (Vs), is defined as

void ratio, and:

= (2.4)

2). Porosity (n)

The ratio of the volume of voids (Vv) to the total volume (V), is defined as

porosity, so:

= 100% (2.5)

3). Degree of saturation (S)

The ratio of volume of water (Vw) to the volume of voids (Vv) sis defined as

degree of saturation so:

= 100% (2.6)

4). Water content (w)

The ratio of weight of water (Ww) in the voids to the weight of solids so:

= 100% (2.7)

5). Unit Weight

a). Unit weight of water ( w)


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The ratio of weight of water to the volume of water in the same

temperature ( w) and (o) is designated as unit weight of water at 4 o C.

= 1

3

= 1

3

= 1

3

= 1000

3

b). Total unit weight of soil mass ( t )

The ratio of the weight of the mass (W) to the volume of the mass (V) so:

= (2.8)

c). Dry unit weight mass (d)

The ratio of the weight of solids (Ws) to the total volume (V)

= (2.9)

d). Ratio of the saturated weight of the mass ( sat )

Saturated unit weight soil mass (when S = 100%) to the total volume (V).

= (2.10)

e). Unit weight of solid (s)

The ratio of the weight of solids (Ws) to the volume of solids (Vs)

= (2.11)

f). Specific gravity (Gm)

Specific gravity of a substance is the ratio of its weight in air to the weight

of an equal volume of water at reference temperature 4 o C.

The specific gravity of mass of soil including air, water and solid:


35/137


=

=

= = (2.12)

The specific gravity of mass of soil excluding air, water and solid:

=

=

= = (2.13)


36/137


3. Type of Aquifer

gs

gwt

gwt

H

e. Suspended aquifer

Note:gs : ground surfaceps : piezometric surface

gwt : groundwater tablegwt : groundwater table ofperched water

D : thickness of aquiferH : depth of groundwaterK : coefficient of permeability

Note: Compare to Todd (1980) page 44 about leaky aquifer, which the elevation ofgwt is higher than ps.

Fig. 2.4. Types of aquifers

gs

gwt

K=0

gs

gwt

KD H

ps

D=H K

psK 1


37/137


III. BASIC PARAMETERS

1. Law of Groundwater Flow

a. Poiseuilles Law

=2

8 = (3.1)

whereva : average velocityw : unit weight of waterR : radius of tube : viscosity of fluidi : hydraulic gradientA : areaQa : average dischargeZ = w.R2/8

This equation is the proof of Poiseuilles Law which states that the velocity in

laminar flow is proportional to the first power of the hydraulic gradient i.

b. Darcys Law (1856),

1). Equation

= = (3.2) General equation can be written as a vector form:

= (3.3) Substitute to the Laplace Equation:

= + + (3.4) Consider on x direction only so:


38/137


= 0 & = 0 The equation becomes:

=

= + = + = + = + = (3.5)

The essential point of above equation is that the flow through the soils is also

proportional to the first power of the hydraulic gradient i as propounded by

Posseuilles Law. And the discharge is by Darcys equation is:

= = (3.6) where,Q : dischargeK : coefficient of permeabilityA : section area of aquiferdh : difference water elevationdl : length of aquifer

i = dh/dl

c. Based on Dupuit (1863), according to Castany (1967):

= . i = sin = 2 + 2 =

2 + 2

=

1 +

2

dx

dy

2 + 2 : = 2 + 2

=1

1 + 2


39/137


Due to the assumption of vertical velocity is so small, (dy/dx) 2 can be neglected so:

1 +

2

= 1

=

(3.7)

2). Similar equations

Fouriers Law on heat transfer {Jean Baptiste Joseph Fourier (1768

1830)}:

= = (3.8) where,

H : rate of heat flowk : thermal conductivityA : cross section areadT : temperature differencedx : thicknessi = dT/dx

Ohms Law on electrical current flow { George Simon Ohm (1787 - 1854)}:

= = (3.9) where,

I : currentC : coefficient of conductivitya : sectional area of conductordv : drop in voltagedl : length of conductor


40/137


i : dv/dl

3). Va lidity of Darcy Law

= (3.10)

It can be written in other equation as:

=

(3.11)

where,NR : Reynolds Number D : diameter of pipe : density of water : flow velocity : viscosity of fluid : unit weight of fluidg : acceleration of gravity

Experiments show that Darcys law is valid for NR < 1 and does not depart seriously

up to NR = 10, and this value represents an upper limit to the validity of Darcys law

(Todd, 1980).

Note:

Nr defines that flow is in laminar, transition or turbulent condition

Re defines that flow is in subcritical, critical or supercritical condition


41/137


Figure 3.1.a. Diagram of development of groundwater science

DUPUIT(1863)

FORCHHEIMER(1930)

LUGEON(1930)

SichardtCambefortChoultseKoussakineCastanyKozenBogomolov

DARCY (1856)

POISEUILLE (1797-1869) Qa=Z.i.A

FOURIER (1768-1830) H= K.i.A

OHM (1789 -1854 I=C.i..a

THEIS (1936)

Samsioe (1931), Dahler(1936), Taylor (1948),Hvorslev (1951), Aravin(1965), Wilkinson (1968), Al-Dahir & Morgenstern (1969),Luthian & Kirkham (1949),Kirkham & van Bavel (1948),Raymond & Azzouz (1969),Smiles & Young (),Sunjoto(1988; 2002)

Cooper-Jacob(1946)Chow (1952)

Todd (1980)

Ehrenberger (1928),Vodgeo Institut (1954),Iokutaro Kano (1939),Vibert (1949) ,Castany (1967)

Mikel & Klaer (1956),Spiridonoff &Hantush (1964),Nasjono (2002), Das,Saha, Rao &Uththmanthan (2009)Sriyono (2010)

F

Q, K

Castany (1967)Murthy (1977)Suharjadi

S & T

SUNJOTO

(1988-2010)

H, Q, K

Q

Q, K K Q, K , s S & T

hR i

Note:V : velocity Q : discharge h : drawdown correction S :K : permeability F : shape factor s : drawdown T : transmissivityI : hydraulic head H : hydraulic head R i : radius of depletion

V= K.i.A

Glover (1966)s


42/137


2. Permeability of soils

a. Factors that affect permeability Void ratio

Grain size Temperature Structure and stratificationInterrelated of grain size and void ratio will affect permeability of soils.Smaller grain size, smaller void ratio which leads to reduce size of flowchannels and lower permeability.

1). Void ratioThe ratio of the volume of voids (Vv) to the volume of solids (Vs), is defined as

void ratio, and:

= (3.12)

= . 1 + (3.13) The relationship between real pore channels to the idealized pore channel is:

=

(3.14)

where,L : length of idealized channela : area of idealized channelL : length of real channela : area of real channel

2). Grain size

If the cross section of a tube is circular, the flow in the tube as per Poiseui llesLaw is:

= 2

8 (3.15)

The average velocity flow in the tube:


43/137


= = 2

8 =

2

32 . (3.16)

3). Temperature

The coefficient of permeability K is product of k which is dependent ontemperature and a function of the void ratio e, and the value of k is expressed :

= 1,16 22 . = (3.17) Where, C is constant which is independent of temperature and the expressionof K may now be as below and K varies asw/ .

=

. . ( ) .

(3.18)

4). Structure and stratification

Fig 3.2. Diagram of soil layers structure

a). Flow in the Horizontal Direction ( Fig 3.2.)

Q = V.A = V. Z = K.i.Z

Q = (V1.Z1 + V2.Z2 + + Vn-1.Zn-1 + Vn.Zn)

Q = (K1.i.Z1 + K2.i.Z2 + + Kn-1.i.Zn-1 + Kn.i.Zn)

= ( + + + ) (3.19)

K 1

K 2

K n-1

K n

Z

Z2

Zn-1

Zn

Z

K v

K h

V1.i.K 1

V2.i.K 2

Vn-1 .i.K n-i

Vn.i.K n


44/137


b). Flow in the Vertical Direction ( Fig 3.2.)

The hydraulic gradient is h/Z and:

=

=

1 1

=

2 2

=

If h1, h 2 hn are the loss of heads in each of the layers, therefore:

H = h1 + h2 + hnor,

H = Z1h1 + Z2H2+ ..ZnHn

Substitution:

=+ ++

(3.20)

b. Method of Determination

1). Laboratory Method

a). Constant head permeability method

The coefficient of permeability K is computed:

= (3.21) =

(3.22) b). Falling head permeability method

The coefficient of permeability K can be determined on the basis of drop in

head (h o- h 1 ) and the elapse time ( t 1 - t o).

= = .. (3.23) = ( ) (3.24)

when A = a the equation be:


45/137


=( ) (3.25)

where:

K : coefficient of permeabilityL : length of sampleA : cross section area of samplea : cross section area stand pipeho h1 : head of water in observation well 1 and 2 respectivelyt o t 1 : duration of flow in observation well 1 and 2 respectively

c). Computation from consolidation test data

In the case of materials of very low permeability with K less than 10-6

cm/sconsolidation test apparatus with permeability attachment may be used. The

coefficient of permeability K of sample can be computed from equation:

=

. . (3.26) where,

K : coefficient of permeability

L : length of sampleA : cross section area of sampleQ : discharge in certain time th : average headt : duration of flow

d). Computation from grain size distribution

On the basis of Poiseuilles Law the coefficient of permeability can be

computed:

= 2 (3.41) According to Allen Hazen (1911) in Murthy (1977) the empirical equation can becomputed as:

= 102 (3.27)


46/137


where,K : coefficient of permeability (cm/s)C : a factor (100


47/137


IV. RADIAL FLOW

Assumptions for the equations are (Dupuit-Thiem):

The soils surrounding the well is assumed homogeneous The flow towards the well is assumed as steady, laminar, radial and

horizontal

The horizontal velocity is independent of depth

The ground water table is assumed as horizontal in all direction The hydraulic gradient at any point on the drawdown is equal to the slope of

the tangent at the point. According to Castany G. (1967) that value is sinus at the point.

1. Unconfined aquifer

a. Dupuit (1863)

Fig. 4.1. Circular unconfined aquifer

Let h be the depth of water at radial distance r . The area of the vertical

cylindrical surface of radius r and depth h through which water flow is (Fig. 4.1.):

= 2 (4.1)

r w r

R

hw

h H


48/137


The hydraulic gradient is:

=

(4.2)

Discharge of inflow when the water levels in the well remain stationary (DarcysLaw)

= (4.3) = (4.4)

Substituting for Eqn (4.1) and (4.2) for (4.3), the rate inflow across thecylindrical surface is:

=

2

(4.5)

The equation for discharge outflow from pumping is:

= ( ) (4.6) The equation for permeability of soil is:

=( ) (4.7)

where,H : depth of water outside of aquifer layerhw : depth of water at face of pumping wellR : radius of outside of aquifer layer

rw : radius of pumped well


49/137


b. Dupuit-Thiem

1). According to UNESCO (1967),

G. Thiem (1906) based on Dupuit and Darcy principle developed a formula

of pumping and the formula is called Dupuit-Thiem.

Let h be the depth of water at radial distance r (Fig. 4.2.). The area ofthe vertical cylindrical surface of radius r and depth h through whichwater flow is:

Fig. 4.2. Pumping in unconfined aquifer

Area of cylinder of piezometric h and radi us r: A = 2rh

The hydraulic gradient is: =

Darcys Law: V = Ki and Q = KiA

Substituting, so the rate inflow across the cylindrical surface is:

= 2 (4.8) Rearranging the terms, so:

r 1 r

r 2

h1 hh2


50/137


=2

The equation for permeability of soil is:

= (4.9) The equation for discharge outflow from pumping is (Fig, 5.2):

Dupuit-Thiem Formula for the full penetration well in free aquifer:

= (4.10) where,

Q : discharge of pumpingK : coefficient of permeabilityD : thickness of aquifer layerr1 r 2 : distance from well to observation well 1 and 2 respectively

h1 h2 : head of water in observation well 1 and 2 respectively

2). According to Castany (1967)G. Thiem (1906) based on Dupuit principle developed a formula ofpumping in unconfined aquifer and the formula is called Dupuit-Thiem(Fig. 4.3.).

Darcys law:

= 2

(4.11)

= (4.12)

= 2 . tg (4.13)


51/137



tg= 1 2r 2 r1 (4.14) For first permanent regime:

= 2 11 . tg (4.15) For second permanent regime:

= 2 111 . tg1 (4.16)

Dupuit-Thiem equation for the full penetration well in free aquifer:

= ( + )( ) (4.17)=

( + )(

)

(4.18)

where:

Q : discharge of pumpingK : coefficient of permeabilityr1 r 2 : distance from well to observation well 1 and 2 respectively

r 1 r 2

h1

h2

2 1

w

hw

r w

R i

H


52/137


1 2 : drawdown in observation well 1 and 2 respectively

3). According to Murthy V.N.S. (1977)

Murthy developed the formula for unconfined aquifer by otherparameters and can be found as (Fig.4.3.):

=( ) (4.19)

=(

)

(4.20)

If we write hw = (H - w) where w is the depth of maximum drawdown inthe test well or pumped well so (Castany, 1967):

= = ( ) (4.21) = ( ) (4.22)

where:

Q : discharge of pumpingK : coefficient of permeabilityRi : radius of influencerw : radius of pumped wellH : depth of water before pumpingw : maximum drawdown (on well)


53/137


2. Confined aquifera. Dupuit (1863)


= = . = 2 = 2 ] = 2 ]

Dupuit (1863) formula for full penetration well on confined aquifer (Fig.

4.4.):

= (4.23) =

( ) (4.24) where,

Q : discharge of pumping

K : coefficient of permeabilityD : thickness of aquiferR : radius of influencerw : radius of pumped wellH : depth of water outside of aquifer layerhw : depth of water at face of pumping well

hw

H

D

r w R


54/137


b. Dupuit-Thiem (1906)

1). According to UNESCO (1967)

Fig. 4.5. Circular unconfined embankment

= Dupuit-Thiem formula for full penetration well on confined aquifer (Fig.4.5.):

= (4.25) =

( ) (4.26) where,

Q : discharge of pumpingK : coefficient of permeabilityD : thickness of aquiferr1 r 2 : distance from well to observation well 1 and 2 respectivelyh1 h2 : head of water in observation well 1 and 2 respectively

h1 h2 D

rr 2


55/137


2). According to Castany (1967)


Dupuit-Thiem equation for the full penetration well in confined aquifer (Fig. 4.6.):

= ( ) (4.27) = ( )

(4.28)

where:Q : discharge of pumpingK : coefficient of permeabilityD : thickness of aquifer layerr1 r 2 : distance from well to observation well 1 and 2 respectively1 2 : drawdown in observation well 1 and 2 respectively

r 1

r 2

h2

2 1

h1

D


56/137


3. Alternate equations of the Dupuit-Thiem principle

1). Pumping in circular aquifer

a). Unconfined aquifer:

o Without observation well and with piezometric head data:

=( ) (4.29)

o Without observation well and with drawdown data:

= ( ) (4.30) b). Confined aquifer:


= ( ) (4.31)

2). Pumping in unlimited aquifer

a). Unconfined aquifer:


= ( ) (4.32)

o Without observation well and with drawdown data:


57/137


= ( ) (4.33) o With one observation well and with piezometric head data:

= (4.34) o With one observation well and with drawdown data:

=

(

)

(4.35)

=( + )( ) (4.36 )

o With two observation wells data and piezometric head data:

= (4.37) o With two observation wells and drawdown data:

=( + )() (4.38)

b). Confined aquifer:

o Without observation well and with piezometric head data:=

( ) = . (4.39) o With one observation well and with piezometric head data:


58/137


=( ) (4.40)

o With one observation well and with drawdown data:

= (

) (4.41)

o With two observations well and piezometric head data:

=( ) (4.42)

o With two observations well and drawdown data:

= (

) (4.43)

= ( ) (4.44) c). Special case of confined aquifer

According to Murthy (1977) , f igure below (Fig. 4.7.) shows that a confinedaquifer with the test well and two observation wells. The elevation of water in theobservation wells rises above the top of the aquifer due to artesian pressure.

When pumping at steady flow condition from artesian well two cases might foundthey are:

Case 1 : The water level in the test well might remain above the roof level (h w >D)

Case 2 : The water level in the test well might fall below the roof level (h w < D)


59/137



Case 1: (hw > D)

= (4.45) =

( ) (4.46) This equation is like mention above.

Case 2 : (hw < D)

=( ) (4.47)

=( ) (4.48)

r w r 1

R i

Dhw

h1 h

r

H

Case 1

Case 2


60/137


4. Correction to flow line


a. Castany (1967) implemented Dupuit (1868) equation (Fig. 4.8.):

For the lateral flow:

= 2(+) 22

(

) = [

(

) ] (4.49)

For the free aquifer and parallel flow:

= 2(+) 2 ( ) = [ ( ) ] (4.50)

b. Ehrenberger (1928)

= , ( ) (4.51)

Real curve

Theoretic curve

h h+h

H


61/137


a. Vodgeo Institut (1954)

=

, (

) , (4.52)

b. Iokutaro Kano (1939)

= (4.53) 0,324 < C < 1,60

c. Vibert (1949)

= , + (4.54)


62/137


5. Radius of depletion

According to many researchers, the radius of depletion depends on the depressioncone because the drawdown of pumping:

a. W.Sichardt (in Castany, 1967)

= ( ) (4.55) where,Ri : radius of depletion (m)H h : drawdown (m)K : permeability (m/s)

b. H.Cambefort (in Castany, 1967)

= (4.56) where,Ri : radius of depletion (m)H : drawdown (m)Ki : permeability (m/s)

c. I. Choultse (in Castany, 1967)

= (4.57) where,

me : porosity of soilT : duration of pumping (s or h)H : drawdown (m)K : permeability (m/s or m/h)Ri : radius of depletion (m)


63/137


d. I.P. Koussakine (in Castany, 1967)

=

(4.58)

where,

K : permeability (m/s)T : duration of pumping (hour)

e. Dupuit1). Lateral flow :

1). Dupuit (in Castany, 1967)

= (4.59) 2). Castany (1967)

=

(4.60)

2). Radial flow (in Castany, 1967):

Using Darcys Law, Castany (1967) proposed an equation:

=( 2 2 ) + (4.61)

Sunjoto tried to improve above formula as:

=( ) +

= ( )


64/137


= .( ) (4.62 )

where,

Ri : radius of depletion (m)r : radius of observation well location (m)Q : discharge (m 3/h)H : drawdown (m)K : permeability (m/h)h : height of water on observation well (m)

f. Some authors (in Castany, 1967)

= (4.63) where,Ri : radius of influence (L)Q : rate of pumping (L/T 3)I : precipitation intensity (debit/L 2/T)

g. Kozen (in Bogomolov et Silin-Bektchoutine (1955)

= (4.64)


65/137


h. G.V. Bogomolov (in Castany, 1967)

Table 5.1. Coefficient of permeability and Radius of depletionAquifer material Granulometric

fraction(mm)

Coefficient ofPermeability

(m/day)

Welldischarge(m3/hour)

Radius ofDepletion

(m)

Clay sand 0,01-0,05 0,500-1,000 0,100-0,300 65Fine sand 0,01-0,05 1,500-5,000 0,200-0,400 65Clay sand in smallgrains

0,10-0,25 10,00-15,00 0,500-0,800 75

Sand in small grains 0,10-0,25 20,00-25,00 0,800-1,700 75Clay sand in mediumgrains

0,25-0,50 20,00-25,00 1,600-10,00 100

Sand in medium grains 0,25-0,50 35,00-50,00 15,00-20,00 100Clay sand in big grains 0,50-1,00 35,00-40,00 20,00-25,00 100

Sand in big grains 0,50-1,00 60,00-75,00 40,00-50,00 125Gravels - 100,0-125,0 75,00-100,0 150

Note: drawdown 5-6 meter


66/137


V. FIELD TEST OF SOIL PERMEABILITY

Field test of soils permeabilityThe pumping test method is equal to the method of computing discharge from

the well using equation of Dupuit or Dupuit-Thiem for confined and unconfined

aquifer as mentioned in above article. That is why that pumping theory can be

implemented for the computation of permeability of soils.

a). Casing bore hole test

1). Murthy (1977)

According to Murthy (1977), hydraulic gradient of the some conditions are (Fig.

5.1.):

(a). Without pressure and end casing above groundwater table

= (5.1) (b). Without pressure and end casing below groundwater table

= (5.2) (c). With pressure and end casing above groundwater table= + (5.3)

(d). With pressure and end casing below groundwater table

= + (5.4) The coefficient of permeability is calculated by making use of formula:

=0.18

(5.5)

where:Q : discharge (L 3/T)


67/137


K : coefficient of permeability (L/T)H : hydraulic head (L) Fig. 3.2.

Fig 5.1. Bore hole in some conditions

Note:Compare to Forchheimer (1930) that Q= FKH and to Harza (1935), Taylor (1948)

and Hvorslev (1951) that F = 5,5 r. And Sunjoto (2002) developed the formula for

the same condition that F = 2r.

2). Forchheimer (1930)

Forchheimer (1930) proposed to find a coefficient of permeability (K) by bore

hole with certain diameter and depth.

=( ) (5.6) where:

K : coefficient of permeability (L/T)R : radius of well (L)F : shape factor (L) (F = 4 R, Forchheimer, 1930)

Q Q Q & h p Q & h p

hw

hw

hw

hw

(2). H=h w (3). H=h w+ hp (4). H=h w+ hp

H b

Hg


68/137


t 1 t 2 : time of the measurement respectively (T)h1 h2 : height of water of the measurement respectively (L)

As : cross section area of well (L 2 , As = R2)

b). Partial permeable casing bore hole test Suharyadi (1984)

There are two conditions of hydraulic head (Fig. 3.3) as:

The hole is submerged in groundwater:

H = difference of groundwater table to the water elevation test

The hole above the groundwater table:

H = Depth of water test on the hole minus half of permeable hole length

Fig. 3.3. Hydraulic head dimension on bore hole test according to Suharyadi

(1984)

The coefficient of permeability can be computed by:

=2.302 = 2 (5.7)

Q

Q

(2). The hole test above groundwater table

L L

2R 2R

gwtHw

Hw

(1). The hole test below groundwater table

gwt

(H=H w) H=H c+ / 2L


69/137


where,

K : coefficient of permeabilityL : length of permeable partH : Hydraulic head (L R)R : radius of casing

c). Uncasing bore hole test

1). Pecker test

Suharyadi (1984)

=. = (5.8)

= + (5.9)

Fig. 3.6. Hydraulic head dimension on packer test (after Suharyadi, 1984)

2). Boast and Kirkham (in Todd, 1980)

= . (5.10)


70/137


Fig. 3.7. Diagram of auger hole and dimensions for determining coefficient ofpermeability (after Boast and Kirkham, in Todd, 1980)

Table 3.1. Value of C after Boast and Kirkham (in Todd, 1980)Lw/r w

y/Lw

(H-L w)/Lw for Impermeable Layer H-Lw (H-L w)/Lw for InfinitelyImpermeable Layer

0 0.05 0.1 0.2 0.5 1 2 5 5 2 1 0.5

1 1.00 447 423 404 375 323 286 264 255 254 252 241 213 1660.75 469 450 434 408 360 324 303 292 291 289 278 248 1980.50 555 537 522 497 449 411 386 380 379 377 359 324 264

2 1.00 186 176 167 154 134 123 118 116 115 115 113 106 910.75 196 187 180 168 149 138 133 131 131 130 128 121 1060.50 234 225 218 207 188 175 169 167 167 166 164 156 139

5 1.00 51.9 48.6 46.2 42.8 38.7 36.9 36.1 35.8 35.5 34.6 32.40.75 54.8 52.0 49.9 46.8 42.8 41.0 40.2 40.0 39.6 38.6 36.30.50 66.1 63.4 61.3 58.1 53.9 51.9 51.0 50.7 40.3 49.2 466

10 1.00 18.1 16.9 16.1 15.1 14.1 13.6 13.4 13.4 13.3 13.1 12.60.75 19.1 18.1 17.4 16.5 15.5 15.0 14.8 14.8 14.7 14.5 14.00.50 23.3 22.3 21.5 20.6 19.5 19.0 18.8 18.7 18.6 18.4 17.8

20 1.00 59.1 55.3 53.0 50.6 48.1 47.0 46.6 46.4 46.2 45.8 44.6

0.75 62.7 59.4 57.3 55.0 52.5 51.5 51.0 50.8 50.7 50.2 48.90.50 76.7 73.4 71.2 68.8 66.0 64.8 64.3 64.1 63.9 63.4 61.9

50 1.00 1.25 1.28 1.14 1.11 1.07 1.05 1.04 1.03 1.020.75 1.33 1.27 1.23 1.20 1.16 1.14 1.13 1.12 1.110.50 1.64 1.57 1.54 1.50 1.46 1.44 1.43 1.42 1.39

100 1.00 0.37 0.35 0.34 0.34 0.33 0.32 0.32 0.32 0.310.75 0.40 0.38 0.37 0.36 0.35 0.35 0.35 0.34 0.34

Lw y

2r w H


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0.50 0.49 0.47 0.46 0.45 0.44 0.44 0.44 0.43 0.43

Table 3.2. Coefficient of Permeability of some Soils (Casagrande and Fadum)

K (cm/sec) Soils type DrainageCondition

Recommended method ofdetermining K

101 - 102 Clean gravels Good Pumping Test

101 Clean sand Good Constant head or Pumping test

10-1 10-4 Clean sand and gravel

mixtures

Good Constant head, Falling head

or Pumping test

10-5 Very fine sand Poor Falling head

10-6 Silt Poor Falling head

10-7 10-9 Clay soils Practicallyimpervious

Consolidation test

d). Constant discharge test by Sunjoto (1988)

= 1 2 (5.11 ) where: H : depth of hollow well (L)

F : shape factor (L)K : coefficient of permeability (L/T)Q : inflow discharge (L3/T)

When steady flow condition (5.11) become F =Q/KH, it means that the H isconstant, so the permeability of soil can be computed by:

= (5.12)


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e. Lugeon Test

The Lugeon test, extensively used in Europe, is a special case of double packer borehole

inflow test made at constant head. Lugeon is a measure of transmissivity in rocks,

determined by pressurized injection of water through a bore hole driven through the rock.One Lugeon (LU) is equal to one liter of water per minute injected into 1 meter length of

borehole at an injection pressure of 10 bars. The three successive test runs, each of 5

minutes duration on constant pressures enable a rough assessment of the water behavior.

The Lugeon unit is not strictly a measure of hydraulic conductivity but it is a good

approximation for grouting purposes and 1 (one) Lugeon is approximately equivalent to

1x10-5 cm/s or 1x10 -7 m/s.

Lugeon is a measure of transmissivity in rocks, determined by pressurized

injection of water through a bore hole driven through the rock.

o One Lugeon (LU) is equal to one liter of water per minute injected into 1 meter

length of borehole at an injection pressure of 10 bars.

o 1 Lugeon Unit = a water take of 1 liter per meter per minute at a pressure of 10

bars.o Lugeon value : water take (liter/m/min) x 10 bars/test pressure (in bars)

The Lugeon unit is not strictly a measure of hydraulic conductivity but it is a

good approximation for grouting purposes and 1 Lugeon is approximately equivalent

to 1x10 -5 cm/s or 1x10 -7 m/s.

The three successive test runs, each of 5 minutes duration enable a rough

assessment of the water behavior.

b. Flow on the Well

1). Darcys law
http://en.wikipedia.org/w/index.php?title=Lugeon&action=edithttp://en.wikipedia.org/w/index.php?title=Lugeon&action=edithttp://en.wikipedia.org/w/index.php?title=Lugeon&action=edithttp://en.wikipedia.org/w/index.php?title=Lugeon&action=edit


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The basic formula on groundwater flow is Darcys law (1856) which is very appropriate to

solve complex mathematical problem for example on single or multiphase condition. But for

the practical solution it has always difficulty on direct computation due to the formula

consist of hydraulic gradient ( i ) parameter and this formula depend on the two knownelevations of water table in certain distance (h o & h1) and for radial flow the formula as:

= ; = ; = 2 = = 2 = 2

= 2 ( 1 ) (

1 ) =

= 2 ( 5.13) 2). Forhheimers formula

Forchheimer (1930) formula have breakthrough by simplification solution

especially for radial flow to computes the coefficient of permeability for the

casing hole test with zero inflow discharge (Q=0) on steady state flow condition.

The outflow discharge on the hole (Q o) is equal to shape factor of tip of casing (F)

multiplied by coefficient of permeability of soils (K), multiplied by hydraulic head

(h) as:

= (5.14) where:

Qo : outflow discharge (L3/T) (L3/T)K : coefficient of permeability (L/T)h : hydraulic head (L)F : shape factor (L)

3). Sunjotos formula


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Based on Forchheimers formula, Sunjoto (1988) developed the formula to

compute hydraulic head for the recharging system. Sunjotos formula computes

hydraulic head or depth of water on the well ( H ) on unsteady state flow condition

with the parameters are inflow discharge ( Q ), shape factor of tip of casing (F),

coefficient of permeability of soils ( K ), duration of flow ( T ) and the derivation of

formula as follows:

a). Assume that inflow discharge ( Q ) to the well is constant and Q 0 .

b). Ouflow discharge (Qo) is equal to shape factor of tip of casing (F) multiplied by

coefficient of permeability of soils ( K ), multiplied by hydraulic head (h ) or Q o =FKh

(Forchheimer, 1930).

Fig. 1. Flow scheme of well (Sunjoto, 1988)

Storage volume of water on the well is difference of inflow discharge and outflow

discharge multiplied by duration of flow {Eq.(4)}. In other side that storage volume

is equal to the cross section area of well multiplied by depth of water {Eq.(5)}, so:

= ( ) = ( ) (5.15) = (5.16)

Those above Eq.(4)=Eq.(5) and solved by integration computation:


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= ( ) = Solved by manipulation that the value is divided by FK/FK , so:

= = =

With cross section area A s=r2 and according to Sunjoto (1988) formula for the

hollow well becomes:

= 1 2 (5.17) When Q=Qo and T=, the formula Eq. (6) is steady state condition of flow and the

equation becomes:

= = (5.18) where:

h/H : hydraulic head (L)t/T : flow duration (T)Q : inflow discharge (L3/T)Qo : outflow discharge (L3/T)F : shape factor (L)K : conductivity (L/T)r : radius of hole (L/T)V : storage volume (L3/T)As : cross section area of hole (L 2)

Formula Eq. (6) is similar and equal to Eq. (2), the difference is that Forchheimers

formula has only outflow discharge and it means that hydraulic head depends on

t ime or duration of flow. The contrary, Sunjotos formula has inflow and outflow


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discharge and when they are equal value, it means that the flow in steady state

condition and the hydraulic head will be constant.

ANALYSIS:

a. Shape Factor

1). Dachler (1936)

Forchheimer (1930), Dachler (1936) and Aravin & Numerov (1965) with difference ways

derived mathematically a formula of well condition shape factor as figure Fig. 2a. and they

had one conclusion that the value was:

= 4 (5.19)

Fig.2. Sketch of well condition.

Beside of the above formula, Dachler (1936) developed analytically, a formula of shape

factor of well as be presented on Fig.2b. as:

=2

+ 2 + 1 (5.20) From the figure (Fig.2b.) when L=0, the condition the well is equal to the figure (Fig.2a.) so

the value of shape factor of condition Eq. (8) should be equal to the Eq. (7), that is F=4r .

But when L=0 of the figure (Fig.2b.) the value of shape factor of formula Eq. (8) has un-

definite value. For this reason based on Darcys Law (1856), Sunjoto (2002) developed a

correction formula for condition (Fig.2b.) which was derived analytically using the concept

of ellipse equation.

a b


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2). Sunjotos formula

When the base of hole is permeable Dachler (1936) assumed that it was

impermeable so that is why the value L=L (Fig. 3.). According to Sunjoto (2002),

even-though the base of hole is impermeable, the real vertical flow still exist and

should be replaced theoretically by horizontal flow as depth as rln2 , so he

determined that L= L rln , so:

Fig. 3. Sketch of assumption of flow on ellipse concept.

For the condition as presented on Fig. 3. The condition:

= 12 ; = 12 ; =

: 2 +

2 =

2 so:

0 12

2=

12

2+ 2

2 12 + = 2 + 2 = ( + 2 ) + 2 + 2 (5.21)

Substitute Eq. (9) to Eq. (1) and the equation becomes:

=2 ( +

2)

( + 2 ) +

2 + 2

=2 ( + 2)

+ 2+ 1 + 2


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According to Forchheimer (1930) that

= : =

2 + 2 2

( + 2 ) +

2

+ 1

(5.22)

Based on formula Eq. (10), it can be developed analytically the similar formula which

flow only through the wall side of hole and has not flow to the base and top of hole due to

it was shut by the packers and according of condition of rack layers as a presented on

figure Fig.4. the equations become:

1). Condition of well (a) Fig. 4a.:

Fig. 4. Sketch of aquifer layers and packers location.

=2

2( + 2 ) + 2

2

+ 1

(15.23)

2). Condition of well (b) Fig. 4b.:

=2

( + 2 )+ 2 + 1 (5.24)


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3). Condition of well (c) Fig. 4c.:

=2

( + ) + 2 2 + 1 (5.25) b). Conductivity

For the comparison of the conductivity parameters test, that Thiem (1906) had

taken into account the value of diameter of hole but Lugeon didnt and the formula

was:

=

2

(5.26)

where:

H : hydraulic head (m)

Q : inflow discharge

Ri : radius of influence

r : radius of hole

T r : transmissivityLugeon test carried out by measuring of discharge on constant head, it means

that flow in steady state condition. That is why, to compute the value of

conductivity can be developed formula by substitution of Eq. (11, 12 & 13) to Eq (6)

and for each condition are:

1). Rock tested (aquifer) is in between two impermeable layers or condition of well

(a) Fig. 4a.:

=

2( + 2 ) + 2 2 + 12

(5.27)


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2). Rock tested (aquifer) is in the border between impermeable layer or condition

of well (b) Fig. 4b.:

=

( + 2 )+

2

+ 1

2 (5.28)

3). Rock tested (aquifer) is thick permeable layer or condition of well (c) Fig. 4c.:

=

( + 2 )2 + 2 2 + 1

2 (5.29)

3. Data for Computation

Computation will be carried out to find value of conductivity with the data of

the standard parameters of Lugeon Unit as:

Hydraulic head : H = 10 bar = 102 m

Discharge: Q = 1 l/min = 1.66667 .10-05 m3/s

Length of hole : L = 1 m

The three successive test runs, each of 5 minutes duration in constant discharge

Hole diameter using outside standard drill size are (Table 1.):

Table 1. Drill size

Size type Diameter (mm)

Hole (outside) Core (inside)

AQ 48.0 27.0

BQ 60.0 36.5

NQ 75.7 47.6

HQ 96.0 63.5PQ 122.6 85.0

CHD 76 75.7 43.5

CHD 101 101.3 63.5

CHD 134 134.0 85.0


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DISCUSSION

With above data of the standard parameters of Lugeon Unit and using formula

Eq. (15), (16) and (17) the value of conductivity can be computed and the result as

presented on Table 2. The smallest rock conductivity value computed by proposed

formulas is K=0.7209x10-7 m/s for the drill type CHD 134 and the biggest value is

K=1.336x10-7 m/s for the drill type AQ show that the result are closed to the

approximation value of is 1x10-7 m/s with deviation is about 30% above and below

Lugeon Unit value.

Table 2. Result of computation

No.

Size type Diameter(mm)

Conductivity of each drill diameter and aquiferlayer condition

Ka (10-7 m/s) Kb (10-7 m/s) Kc (10-7 m/s)1. AQ 48.0 1.3366 1.1564 0.97622. BQ 60.0 1.2801 1.0999 0.91983. NQ 75.7 1.2216 1.0414 0.86144. HQ 96.0 1.1624 0.9822 0.80245. PQ 122.6 1.1021 0.9220 0.74246. CHD 76 75.7 1.2216 1.0414 0.86147. CHD 101 101.3 1.1491 0.9689 0.78918. CHD 134 134.0 1.0804 0.9003 0.7209

Average 89.16 1.9142 1.1041 0. 8342


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Prof.Dr.Ir. Sunjoto Dip.HE, DEA-Subsurface Hydrology-Post Graduate Program JTSL-FT-UGM=2012 82

VI. FRESH AND SALINE WATER BALANCE

1. Basic equation

Badon Ghyben (1888) and Herzberg (1901),

Fig. 6.1. Schematic of cross section circular homogenous, isotropic and porous island.

=

(6.1)

Normal condition:

Sea water s = 1.025 tmass/m3 = 1,025 kgmass/m3 } so: = Fresh water f = 1.00 tmass/m3 = 1,000 kgmass/m3

hf hs

A

h

precipitation

ground surface

groundwater surface

sea level

fresh water boundary area of salinewater and fresh water

saline water


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2. Shape of the Fresh-Salt Water interface

Fig. 6.2. Flow pattern of fresh water in an unconfined coastal aquifer

The exact shape of the interface is (Glover in Todd, 1927):

2 =2

+

2

(6.2)

The corresponding shape for the water table is given by:

= 2( + )1 2 (6.3)

The width xo of the submarine zone through which fresh water dischargesinto the sea can be obtained for z=0,

= 2 (6.4)

Sea

Saline water

Fresh water

Ground surface

Water table

Interface

xo

zo


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The depth of the interface beneath the shoreline z o, occurs where x = 0 sothat:

=

(6.5)

3. Upconing

Upconing is phenomenon that occurs when an aquifer contains an underlying of

saline water and is pumped by a well penetrating only the upper freshwater

portion of the aquifer, a local rise of the interface bellow the well occurs.

Fig. 6.2. Diagram of upconing of underlying saline water to a pumping well(after Schmorak and Mercado ini Todd, 1980)


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According to Todd (1980) using Dupuit assumption and Ghyben-Herzberg relation, theupconing is:

=(

)

(6.6)

Comment:

Compare 2d of this equation to the shape factor of Sunjoto (2002) F = 2R

Base on Forchheimer (1930) principle, Sunjoto proposes that the upconing is:

=

(6.7)

Usually:o Sea water s = 1,000 kgmass/m3 = 1.00 tmass/m3 o Fresh water f = 1,000 kgmass/m3 = 1.00 tmass/m3

And for the security take z/d < 0.50


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4. Drawdown versus Built upa. Theory of Dupuit-Thiem

Fig.6.3. Schematic of pumping

Discharge (Dupuit-Thiem) base on Darcys Law:

=

(6.8)

Problem: Solution of this equation needed minimum two dependent unknown (h2 & r2)so this formula is difficult for predicting computation.

From the above legends and schematic (Fig. 6.3) so the Power:

= ( + ) (6.9)

pump axis level

gsH

S

Q

gwl

r 1

r 2

h1 h

= ( +

)

=( )

Drawdown due to pumping

where,P : power (kN.m/s = kW)Q : discharge (m 3/s)

: specific weight of water(9.81 kN/m3)

H : gap of groundwater level to pump axis (m)S : drawdown m

: pump efficiency K : coefficient of permeability (m/s)h1 : piezometric of observation well 1h2 : piezometric of observation well 2

r1 : radius of observation well 1r2 : radius of observation well 2


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b. Theory of Forhheimer (1930)

Fig.6.4. Theory of Forchheimer (1936)

According to Forchheimer (1930) discharge (Q) on the hole with casing is hydraulichead (H) multiplied by coefficient of permeability (K) multiplied by shape factor (F),and for the hole with casing F = 4 R.

On his auger test with Q = 0, or water was poured instantly and then be measured therelationship between duration (t) and height of water on hole (h), he derivedmathematically the equation to compute coefficient of permeability:

=( ) (6.10)

where,K : coefficient of permeabilityR : radius of holeF : shape factor (F=4R)h1 : depth of water in the beginningh2 : depth of water in the end

t 1 : time in the beginningt 2 : time in the end

=

=( )

t2

t1 h1

h2

2R


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c. Theory of Sunjoto (1988)

Fig.6.5. Theory of recharge well and anti-drawdown (Sunjoto, 1988)

1). Discharge

Base on the steady flow condition theory of Forchheimer (1930), Sunjoto (1988)developed the equation of discharge through the hole with continue discharge flow tothe hole which was derived mathematically by integration and the result is unsteadyflow condition:

Forchheimer (1936) formula:

= (6.11) Sunjoto (1988) formula:

= = (6.12) This formula (6.14) when duration T is infinite so the equation will become Q = FKH

(see Fig. 6.5)

H

T

Q/FK

= 0

Built up due torecharging

Q

K

H

=

Relationship between H an T


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2). Drawdown - Built up value

Drawdown due to pumping (S) will occur in discharge system by pumping (Fig. 6.3) andthe reverse side the built up (anti-drawdown) due to recharging (H) will occur (Fig.6.5) for the recharge system. For the equal condition and equal parameters the both

value drawdown and anti-drawdown are equal with opposite direction.

a). Steady flow condition= = (6.13)

b). Unsteady flow condition

= = (6.14) (negative sign means that the direction is opposite and in this case downward)

where,S : drawdown (m)H : depth of water on the hole/well (m)Q : discharge through the well (m 3/s)F : shape factor (m)K : coefficient of permeability (m/s)T : duration of flow (s)R : radius of pipe/well (m)


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EXAMPLE:Pumping system with discharge Q = 0.1667 m3/s, distance between pumping axis tothe groundwater level H = 6.50 m, coefficient of permeability K = 0.00047 m/s,length of screen casing or perforated pipe L = 18 m and diameter of casing is 45 cm,fresh water: f = 1,000 kg/m3 or f = 9.81 kN/m3 and saline water: s = 1,025 kg/m3 or

s = 10.552 kN/m3. Tip of the well in -28 m and the pumps are installed on the sandycostal which beneath of the pump in -160.00 m laid the boundary of fresh and saline

water.Compute:Power needed and how is the pumping system related to salt water intrusion.

Fig.6.6. Pumping data

Shape factor installed:

=2 18 + 2 0.225 2

18 + 2 0.2252 0.225 + 182 0.225 2 + 1 = 25.95

K=4.70*10 -4

S

5.00 m

Q=0.1667 m 3/s

6.50 m

23.00 m

18.00 m

+1.5

-5.00

-28.00


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The drawdown of 1 pump installed:

= =0.1667

25.95 0.00047= 13.667

To decrease of drawdown value S is by increasing value of F value, in this case be

installed 4 wells with same dimension and each well equipped by P = 4.30 KW.

The drawdown of 4 pumps installed:

=0.1667

4 25.95 0.00047= .

The pumps are installed on the sandy costal which beneath of them laid down the

boundary of fresh and saline water in 200,00 m.Upconing:

According to Sunjoto Eq.(6.9) is:

=3.41

1,025 1,0001,000 = 136,40 Power needed:

P = 0.1667 m3/s x 9.81 kN/m 3 x (6.50+3.41) m/ 0.60 = 27 kN.m/s = 27 kW

Conclusion:

The level of boundary will move upward to 200 + 136.40 = 63.60 m and due to thetip of the well level is 28 m so the saline water will not flow into tip of pipe so thereis not sea water intrusion.

Recommendation:

To avoid saline water intrusion to the pump so the shape factor F d should beincreased by enlarging the diameter of well or/and adding the length of porous well.


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5. Saline water pumping

Since the last three decades, the cultivation of fish in coastal area speedy increasedue to the demand of fish consumption increases. The fishpond in fresh water andbrackish water had been developed largely in Indonesia and then the fish cultivation

in seawater is now its beginning to be developed. A seawater fishpond in sandycoastal area which was equipped by geo-membrane had been developed in YogyakartaSpecial Province with 7.20 ha area, 60 cm depth. One third of water should bereplaced by seawater. The needed pumping system for hydraulic head H = 7.50 mand coefficient of

aatoutline2014s2

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