Gradation Design of Sand Gravel Filters USDA Neh633-Ch26

8/3/2019 Gradation Design of Sand Gravel Filters USDA Neh633-Ch26

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(210-viNEH, October 1994) 261

Chapter 26 Gradation Design of Sand and

Gravel Filte rs

Part 633

National Engineering HandbookUnited StatesDepartment ofAgriculture

NaturalResourcesConservationService

Part 633NationalEngineeringHandbook

Chapter 26 Gradation Designof Sand and GravelFilters


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262 (210-viNEH, October 1994)


Gravel Filte rs

Part 633

National Engineering Handbook

Issued October 1994

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National Engineering HandbookPreface

26i

Most of the criteria in this document was originally issued in Soil Mechan-

ics Note 1, revised January 1986. This revision of Soil Mechanics Note 1 and

any future revisions of other Soil Mechanics Notes will be placed in theNational Engineering Handbook , Part 633, Soil Engineering. This mater ial is

Chapter 26, Gradation Design of Sand and Gravel Filters.


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26ii

Acknowledgments

The criteria in this document are based on the results of an extensive labo-

ratory filter study carr ied out by the Soil Conservation Service (SCS) at the

Soil Mechanics Laboratory in Lincoln, Nebraska, from 1980 to 1985. Theprincipals involved in this study were Lorn P. Dunnigan, SCS (retired),

James R. Talbot , SCS (retired), and James L. Sherard, consultant

(deceased).

Revisions were developed in 1993 by Danny K. McCook, assistant head,

Soil Mechanics Laboratory, SCS, Fort Worth , Texas; Charles H. McElroy,

head of the Soil Mechanics Laboratory, SCS, Fort Worth, Texas; and James

R. Talbo t , national soils engineer, SCS, Washington , DC (re tired) . Danny

McCook developed the example problems.

Special recognition is given to the following Soil Conservation Service

engineers for their many helpful comments during the review process:

Philip N. Jone s , Lincoln, Nebraska; Christ ine M. Portillo , Fort Worth,

Texas; William G. Hughey, Chester, Pennsylvania; and Clifton E. Deal,

Portland, Oregon.

Special thanks also t o the following persons in the Technical Publishing

Section of the National Cartography and GIS Staff, SCS, Fort Worth, Texas:

Wendy Pierce for the graphic illustrations, Suzi Selffor desktop publish-

ing, and Mary Matt inso n for her ed itorial contributions.


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National Engineering HandbookChapter 26 Gradation Design of Sandand Grave l Filters

633.2600 Purpose 261

633.2601 Basic purpose of filters and drains 261

633.2602 Permeability and capacity 262

633.2603 Determining filter gradation limits 262

633.2604 Definitions 2637

633.2605 References 2637

63 3.26 06 Appe ndix esAppendix 26A Steps in Filter Design ........................................................ 26A1

Appendix 26B Standard ASTM Aggregate Specifications ...................... 26B1

Tables Table 261 Regraded gradation curve data 263

Table 262 Filtering criteria Maximum D15 263

Table 263 Permeability criteria 263

Table 264 Other filter design criteria 263

Table 265 Maximum and minimum particle size criteria 264

Table 266 Segregation criteria 265

Table 267 Cr it er ia for filt er s use d adjac ent to p erfor at ed 265

collector pipe

Table 268 Design specification gradation for example 261 soil 268

Table 269 Design specification gradation for example 262 soil 2613

Table 2610 Design specification gradation for example 2616

262A soil

Table 2611 Design specification limits for clayey gravel base soil 2621

Table 2612 The final selected design filt er band gradat ion 2625

for silty sand base soil

Contents:

26iii


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Table 2613 Data for designed filter band 2629

Table 2614 Des ign filt er band dat a for exa mple 266 soil 2634

Table 26B1 Selected standard aggregate gradations 2641

Figure s Figure 261 Grain size distribution curve for fine clay base soil 269

Figure 262 Grain s ize dis tr ibut ion curve for silty sand with 2614

gravel base soilCategory 3

Figure 262A Grain s ize dis tr ibut ion curve for silty sand with 2617

gravel base soil where p rimary function is filter

Figure 262B Grain size distribution curve for silty sand 2618

with gravel base soil

Figure 263 Grain size dis tr ibut ion curve fo r c layey grave l 2622

base soil

Figure 264 Grain size distribution curve for silty sand base soil 2626

Figure 265 Gravel filter band design 2630

Figure 265A Gravel filter band design using an extended 2631

coars e filter limit

Figure 266 Grain s ize dis tr ibut ion curve fo r very fine c lay 2636

base soil

Figure 26B1 Standard aggregate gradations 2643

26iv


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Examples Example 261 Fine clay base soilCategory 1 267

Example 262 Silty sand with grave l base soilCategory 3 2611

Example 262A Silty sand with grave l base soilCategory 3 2615

Example 263 Clayey gravel base soilCategory 2 2619

Example 264 Silty sand base soilCategory 4 2623

Example 265 Design of a coarse filter to be compatible 2627

with a previously designed fine filter an d used

around a perforated pipe

Example 266 Very fine clay base soilCategory 1 2633

26v


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6 3 3 .2 6 0 0 P u r p o s e

Chapter 26 presents c riteria for determining the grain-

size d istribution (gradat ion) of san d and gravel filters

needed to prevent internal erosion or piping of soil in

embankments or foundations of hydraulic structu res.

These criteria are based on results of an extensive

laboratory filter s tudy carried out by the Soil Conser-

vation Service at the Soil Mechanics Laboratory in

Lincoln, Nebraska, from 1980 to 1985. (See Section

633.2605, References, for published repo rts .)

Refer to section 633.2604 for definitions used in this

chapter.

6 33 .2 6 01 B a s ic p u r po s e o f

f i l te r s a n d d r a i n s

Filters ar e placed in embankment zones, foundations,

or other areas of hydraulic structures for two pur-

poses:

To intercept water flowing through cracks or

openings in a base soil and block the move-

ment of eroding soil particles into the filter.

Soil particles are caught at the filter face,

reducing the flow of water through cracks or

openings and preventing further e rosion and

enlargement of the cracks or openings.

To intercept water flowing through the pores

of the base soil, allowing passage of the water

while preventing movement of base soil par-

ticles. Without filters , piping of susceptible

base soils can occur when seepage gradients

or pressures are high enough to produce

erosive discharge velocities in t he base so il.

The filter zone is generally placed upstream of

the discharge point where sufficient confine-

ment prevents u plift or blow-out of the filter.

Drains consist of sand, gravel, or a sand an d gravelmixture placed in embankments, foundations, and

backfill of hydraulic structures, or in other locations to

reduce seepage pressure. A drains most important

design feature is its capacity to collect and carry water

to a safe outlet at a low gradient or without pressure

build-up. Drains are often used downstream of or in

addition to a filter to provide outlet capacity.

Combined filters and d rains are commonly used. The

filter is designed to function as a filter and as a drain.

Chapter 26 Gradation Design of Sand andGravel Filters


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6 33 .2 60 2 P er me ab i l i ty an d

c a p a c i t y

The laboratory filter study clearly demonstrat ed that

graded filters designed in accordance with these

criteria will seal a crack. The sealing begins wh en

water flows through a crack or opening and carries

soil particles erod ed from the sides o f the openings.

Eroding soil particles collect on the face of the filter

and seal the crack at the interface. Any subsequent

flow is through the p ores of the soil. If filters are

designed to intercept c racks, the pe rmeability required

in the filter zone should be based on the ste ady stateseepage flow through the pores of the base soil alone.

The hydraulic capa city of any cracks n eed not be

considered in designing the filter because the cracks

have been shown to se al.

Where saturate d steady-state seepage flow will not

develop, for instance in dry dams for flood control

having a normal drawdown time of 10 days or less,

filter capacity need only be nominal. Filters designed

either to protect against steady state seepage or inter-

nal erosion through cracks are to be thick enough to

compensate for potential segregation and contamina-

tion of the filter zones d uring construction. They must

also be thick enough that cracks cannot extend

through the filter zone during any possible differential

movements.

A zone of coarser materials immediately downstream

or below th e filter, or both , provides additional capac-

ity to collect and convey seepage to a controlled

outlet. In some cases a strip drain is used, and in

others a perforated collector pipe is employed to

outlet the collected seepa ge. To prevent movement of

the filter materials into the coarse drain materials, the

coarse drain materials must be designed for the propergradation using procedures in this subchapter. Perfo-

rations in collector pipes must a lso be sized properly

to prevent movement of the coarse drain materials

into the perforations.

6 33 .2 60 3 De te rm in i n g f i l -

t e r g r a d a t i o n l i m i t s

Determine filter gradation limits using the following

steps:

Step 1: Plot the gradation curve ( grain-size

distribution) of the base s oil material. Use enough

samples to de fine the r ange of grain sizes for the ba se

soil or soils. Design the filter u sing the base soil that

requires the smallest D15 size for filtering purposes.

Base the design for drainage purposes on th e base so il

that has the largest D15 size.

Step 2: Proceed to step 4 if the base soil contains

no gravel ( material larger than No. 4 sieve) .

Step 3: Prepare adjusted gradation curves for

base s oils that have particles larger than the

No. 4 (4.75 mm) sieve.

Obtain a correction factor by dividing 100 by

the pe rcent passing the No. 4 (4.75 mm) sieve.

Multiply the percentage passing each sieve

size of the b ase soil smaller than No. 4 (4.75

mm) sieve by the correction factor deter-

mined above.

Plot these adjusted percentages to obtain a

new gradation curve.

Use the adjusted curve to determine the per-

cen tage pa ssing the No. 200 (0.075 mm) sieve

in step 4.

Step 4: Place the base soi l in a category deter-

mined by the percent passing the No. 200 ( 0.075

mm) sieve from the regraded gradation curve

data according to table 26 1.

Step 5: To satisfy filtration requirements, dete r-mine the maximum allowable D15 size for the

filter in accordance with the table 262.

If desired, the maximum D15 may be adjusted for

certa in noncritical uses of filters where significant

hydraulic gradients are not predicted, such as bedding

beneath riprap and concret e slabs. For fine clay base

soil that has d85 sizes between 0.03 and 0.1 mm, a maxi-

mum D15 of 0.5 mm is still conservative. For fine-

grained silt that has low sand content, plotting below the

"A" line, a maximum D15 of 0.3 mm may be used.


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Step 6: If permeability is a requirement (see

section 633.2602), determine the minimum allow-

able D15 in accordance with t able 263. Note: Thepermeability requirement is determined from the d15size of the base soil gradation be fore regrading.

Step 7: The width of the allowable filter design

band must be kept relatively narrow to prevent

the use of pos sibly gap-graded filte rs. Adjust the

maximum and minimum D15 sizes for the filter

band dete rmined in steps 5 and 6 so that t he

ratio is 5 or less at any given percentage passing

of 60 or less. Criteria are summarized in table 264.

Table 261 Regraded gradation cur ve data

Base % finer than Basesoil No. 200 sieve soilcategory (0.075 mm) description

(after regrading,where applicable)

1 > 85 Fine silt and clays

2 40 85 Sands, silts, clays, and silty

& clayey sands

3 15 39 Silty & clayey sands and

gravel

4 < 15 Sands and gravel

Table 262 Filtering criteria Maximum D15

Ba se soil F ilte ring c rite riacategory

1 9 x d85 but not less than 0.2 mm

2 0.7 mm

3

( ) [ ] +40

40 154 0 7 0 785

Ad mm mm. .

A = % passing #200 sieve after regrad ing

(If 4 x d85 is less th an 0.7 mm, use 0.7

mm)

4 4 x d85 of base soil after regrading

This ste p is required to avoid the use of gap-graded

filters. The use of a broad ran ge of particle sizes to

specify a filter gradation could result in allowing theuse of gap-graded ( skip-graded) materials. These

mater ials have a grain size distribution curve with

sharp breaks or other undesirable characteristics.

Materials that have a broad range of particle sizes may

also be susceptible to segregation during placement.

The requirements of step 9 should prevent segregation,

but other steps are needed to eliminate the use of any

gap-graded filters.

Gap-graded ma terials generally can be recognized by

simply looking at their grain size distribution curve.

However, for specification purposes, more prec ise

controls ar e needed. In designing an acceptable filter

band us ing the preliminary control points obt ained in

steps 1 through 6, the following additional require-

ments should be followed to decrease the probability

of using a gap-graded filter.

Table 263 Permeability criteria

Base soil category Minimum D15

All categor ies 4 x d15 of the base soil before

regrading, but not less than 0.1 mm

Table 264 Other filter design criteria

Design element Criteria

To prevent The width of the designe d filter

gap-graded band should be such that the ratio

filters of the maximum diameter to the

minimum diameter at any given

percen t pass ing value 60% is 5.

F ilt er band Coarse and fin e limits of a filt er

limits band should each have a coefficient

of uniformity of 6 or less .


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First, calculate the ratio of the max imum D15 to the

minimum D15 sizes determined in steps 5 and 6. If this

ratio is greater than 5, adjust the values of these con-trol points so that the ra tio of the maximum D15 to the

minimum D15 is no greater than 5. If the ra tio is 5 or

less, no adjustments a re necessary. Label the maxi-

mum D15 size as Control point 1 and the minimum D15size as Control point 2. Proceed to s tep 8.

The decision on where t o locate the final D15 sizes

within the range established with previous criteria

should be based on one of the following consider-

ations:

1. Locate the design filter band at the maximum

D15 side of the range if the filter will be re-

quired to transmit large quantities of water

(serve as a dra in as well as a filter). With the

maximum D15 size as the control point, estab-

lish a new minimum D15 size by dividing the

maximum D15 size by 5, and locate a new

minimum D15 size. Label the maximum D15 size

Control point 1 and the minimum D15 size

Control point 2.

2. Locate the band at the minimum D15 side of

the range if it is probable there are finer base

mater ials than those sampled and filtering isthe mo st important function of the zone. With

the minimum D15 size as the cont rol point,

establish a new maximum D15 size by multiply-

ing the minimum D15 size by 5, and locate a

new maximum D15 size. Label the maximum

D15 size Control point 1 and th e minimum D15size Control point 2.

3. The most important consideration may be to

locate the maximum and minimum D15 sizes,

within the acceptable range of sizes deter -

mined in steps 5 and 6, so that a standard

gradation available from a commerc ial sourceor other gradations from a natural source near

the site would fall within the limits. Locate a

new maximum D15 and minimum D15 within

the permissible range to coincide with the

readily available mate rial. Ensure that the ratio

of these s izes is 5 or less. Label the maximum

D15 size Control point 1 and th e minimum D15size Control point 2.

Step 8: The designed filter band must not have

an ex tremely broad range of particle sizes to

prevent the use of poss ibly gap-graded filters.Adjust the limits of the de sign filter band so that

the coarse and fine sides have a coe fficient o f

uniformity of 6 o r less. The width of the filte r

band should be such that the ratio of maximum

to minimum diamete rs is less than or equal to 5

for all percent passing values of 60 or less.

Other filte r design criteria in st ep 8To prevent gap-graded fi ltersBoth sides of the

design filter band will have a coefficient of uniformity,

defined as:

CUD

D= 60

10

6

Initial design filter bands by this step will have CU

values of 6. For final design, filter bands may be ad-

justed to a steeper configuration, with CU values less

than 6, if needed. This is acceptable so long as other

filter and permeability criteria are satisfied.

Calculate a maximum D10 value equal to the maximum

D15 size divided by 1.2. (This factor of 1.2 is based on

the assu mption that the slope of the line connecting

D15 and D10 should be on a coefficient of uniformity ofabout 6.) Calculate t he maximum permissible D60 size

by multiplying the maximum D10 value by 6. Label this

Control point 3.

Determine the minimum allowable D60 size for the fine

side of the ban d by dividing the dete rmined maximum

D60 size by 5. Label this Contro l point 4.

Step 9: Determine the minimum D5 and maxi-

mum D10 0 sizes o f the filter according to table

265. Label as Control points 5 and 6, respectively.

Table 265 Maximum and minimum particle size criteria*

Base soil cat ego ry Maximum D100

Minimum D5, mm

All categor ies 3 inches 0.075 mm

(75 mm) (No. 200 sieve)

* The minus No. 40 (.425 mm) material for all filters must benonplastic as determined in accordance with ASTM D4318.


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Ste p 10: To minimize se gregation during con-

struction, the relationship betwe en the maximum

D90 and the minimum D10 of the filter is impor-tant . Calculate a preliminary minimum D10 size

by dividing the minimum D15 size by 1.2. ( This

factor of 1.2 is based on the assumption that the

slope of the line conne cting D15 and D10 should

be on a coe fficient of uniformity of about 6.)

Dete rmine the maximum D90 using table 266.

Label this as Control point 7.

Sand filters that have a D90 less than about 20 mm

generally do not require special adjustments for the

broadness of the filter band. For coarse r filters and

gravel zones that serve both as filters and drains, the

ratio of D90/D10 should decrease rapidly with increas-

ing D10 sizes.

Ste p 11: Connect Control points 4, 2, and 5 to

form a partial design for the fine side o f the

filter band. Connect Control points 6, 7, 3, and 1

to form a design for the coarse side o f the filter

band. This resu lts in a preliminary design fo r a

filter band. Complete the de sign by ext rapolating

the coarse and fine curves t o the 100 pe rcent

finer value. For purpose s o f writing specifica-

tions, se lect appropriate sie ves and correspond-ing percent finer values that be st recons truct the

design band and tabulate t he values.

Table 266 Segregation criteria

Ba se so il c at ego ry If D10

is : Then maximum D90

is:

(mm) (mm)

All categories < 0.5 20

0.5 1.0 25

1.0 2.0 30

2.0 5.0 40

5.0 10 50

> 10 60

Ste p 12: Design filters adjacent to perforated

pipe to have a D85 size no smaller than shown in

table 267. For critical structure drains where rapidgradient reversal (surging) is probable, it is reco m-

mended that the D15 size of the material surrounding

the pipe be no smaller than the pe rforation size.

Additional des ign considerations: Note that these

steps provide a filter band design that is as well graded

as p ossible and st ill meets criteria. This generally

provides the most desirable filter characteristics.

However, in some cases a more poorly graded filter

band ma y be preferable; for example, if more readily

available standard gradations are needed or where

onsite filters ar e used for economy.

The design filter band obtained in st eps 1 through 12

may be adjusted to a steeper configuration in such

cases . The width of the filter band should be main-

tained so that the ratio of the maximum diameters to

the minimum diameters at a given percent finer is no

greater th an 5 below the 60 percent finer value.

Only the por tion of the d esign filter band above the

previously established minimum and maximum D15sizes should be adjusted. The des ign band may be

adjusted so that t he coefficients of uniformity of both

the coar se and fine sides of the design band are lessthan 6, but not less than 2, to prevent use of very

poorly graded filters.

Table 267 Criteria for filters u sed adjacent to perforatedcollector pipe

Noncritical drains The filter D85 must be greater

where surging or than or equal to thegrad ient reversal is perforation s ize

not anticipated

Crit ical drains where The filter D15 must be greater

surging or grad ient than o r equa l t o t he

reversal is anticipated perforation size.


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Note that the requirement s for coefficient of unifor-

mity apply only to the coarse and fine limits of the

design filter band. It is possible that an individual,accep table filter whose gradation plots completely

within the specified limits could have a coefficient of

uniformity greate r than 6 and still be perfectly accept-

able. The design step s of this procedure will prevent

accep tance of gap-graded filters, which is the main

concern associated with filters having a high coeffi-

cient of uniformity, and it is not necessary to closely

examine the co efficient of uniformity of a part icular

filter as long as it plots within the design filter band.

Illustrations of these filter design steps a re in the

following examples. The steps in the filter design

process are summarized in appendix 26A. The sum-mary is useful to follow as th e examp le problems are

reviewed.


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Given: The most important function of the filter

being designed is to a ct as a filter.

Step 1: Plot the gradation curve of the base soil

material.

Refer to figure 261 for the plott ed grain size dist ribu-

tion curve for this e xample clay base soil, labeled Base

soil. The plotted curve is from the following data:

Sieve size % passing

No 10 100

No. 200 90

0.05 mm 80

0.02 mm 60

0.005 mm 40

0.002 mm 32

Step 2: Proceed to step 4 if the base soil contains no

gravel (mate rial larger t han the No. 4 sieve).

The example base s oil has 100 percen t finer than the

No. 4 sieve, and the grain size distribution curve does

not need to be regraded. Proceed to ste p 4.

Step 3: Not applicable because the base soil con-

tains no par ticles larger than the No. 4 sieve

Step 4: Place the base soil in a category determined

by the pe rcent passing the No. 200 (0.075 mm) sieve

from the regraded gradation curve data according to

tab le 261.

The example soil has 90 percent finer than the No. 200

sieve. From table 261, the so il is in category 1.

Step 5: To satisfy filtration requirements, d etermine

the maximum a llowable D15 size for the filter accord-

ing to table 262.

The filtering criteria for base soil category 1 is (table

262): The maximum D15 of the filter will be less than

or equal to 9 times the d85 of the base soil, but not less

than 0.2 mm.

The d85 size of the base soil is 0.06 mm. Thus, the

maximum D15 of the filter is

9 x 0.06 = 0.54 mm (not < 0.2 mm)

This is labeled as Maximum D15 in figure 261.

Step 6: If permeability is a requirement (section

633.2602), dete rmine the minimum allowable D15according to table 263. Note: The permeability re-

quirement is dete rmined from the d15 size of the base

soil gradation before regrading.

The permeability criterion for all categories of base

soils is that the filter will have a minimum D15 of no

less than 4 times the d15 of the base soil (before any

regrading of the base soil), but will not be less than 0.1

mm in any case.

The example 261 base soil does not have a meaning-

ful d15 size. The data show that the base soil has 32

percen t finer than 0.002 mm, the smallest commonly

determined particle size. Therefore, use t he default

value of 0.1 mm for the minimum D15 of the filter . This

value is the preliminary value for minimum D15. Pro-ceed to step 7 for any needed adjustments.

Step 7: The width of the allowable filter design band

must be kept relatively narrow to prevent the use of

possibly gap-graded filters. Adjust the maximum and

minimum D15 sizes for the filter ba nd dete rmined in

previous steps 5 and 6 so that t he ratio is 5 or less, at

any given percent passing of 60 or less. Adjustments

may be required based on the following consider-

ations.

For exa mple 261, the rat io of the maximum D15 to the

minimum D15 sizes is equal to 0.54 / 0.1 = 5.4. Because

the value is slightly greater than 5, a slight adjustment

is needed in this step. The minimum D15 is the control

because filtering is stated as the most important pu r-

pose. Label this as Control point 2. Determine an

adjusted maximum D15 size for the final des ign filter

band as equal to the minimum D15 size, 0.10 x 5 = 0.50

mm. This is the final Contro l point 1 labeled in figure

261. Go to step 8.

Ex am p l e 2 6 1 Fi n e c la y b a s e s o i lCa te g o r y 1


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Step 8: The designed filter band mus t not have an

extremely broad range of particle sizes to prevent

using possibly gap-graded filters. Adjust the limits ofthe des ign filter band so th at coarse and fine sides of

the filter band have a coefficient o f uniformity of 6 or

less . Width of the filter band should be such that the

ratio of maximum to minimum diameters is less than or

equal to 5 for all percen t passing values of 60 or less.

For example 261, calculate a value for maximum D10by dividing the maximum D15 size of 0.5 mm (deter-

mined in st ep 7) by 1.2 = 0.42 mm. Determine the value

for the maximum D60 size by multiplying the value of

D10 by 6 = 0.42 x 6 = 2.5 mm. Label this as Control

point 3.

Determine the minimum allowable D60 size for the fine

side of the band by dividing the dete rmined maximum

D60 size by 5:

D 60

5

2 5

50 50= =

..

Label this Control point 4.

Step 9: Determine the minimum D5 and maximum

D100 sizes of the filter according to table 265.

This table shows that filters mu st have a D5 greater

than or equal to 0.075 mm, equal to t he No. 200 sieve

size. Label this value as Control point 5 in figure 261.

It also shows that filters must h ave a D100 of less than

or equal to 3 inches. Label this value as Control point 6

in figure 261.

Step 10: To minimize segregation during construc -

tion, the relationship between the maximum D90 and

the minimum D10 of the filter is important. Calculate a

preliminary minimum D10 size by dividing the mini-

mum D15 size by 1.2. Determine the maximum D90using tab le 266. Label this as Contro l point 7.

Calculate t he minimum D10 size of the pre liminary

filter band as equal to the minimum D15 value of 0.1

mm (obtained in step 6) divided by 1.2:

0.10 / 1.2 = 0.083 mm

Table 266 lists maximum D90 sizes for filters for a

range of D10 sizes. Because the D10 value is less than

0.5 mm, the maximum D90 size is 20 mm. Label this

value as Control po int 7 in figure 261.

Step 11: Connect Control points 4, 2, and 5 to form a

partial design for the fine side of the filter band. Con-

nect Control points 6, 7, 3, and 1 to form a partialdesign for the c oarse s ide of the filter band.

Complete the design of the filter ba nd by extrapolating

the coarse and fine curves to t he 100 percent finer

value. For purposes of writing specifications, select

appropriate sieves and corresponding percent finer

values that bes t reconstruct the design band and

tabulate the values.

Refer to figure 261 for an illustration of the complete

filter design. Note that adjustments have been made in

straight line portions of the design band to intercept

even values for percent pass ing at standard sieve sizes

and to prevent the use of very broadly graded filters.

The final design specified gradation is shown in table

268.

Step 12: Design filters a djacent to perforated pipe to

have a D85 size no smaller than the per foration size.

For critical structure dra ins where rapid gradient

reversal (surging) is probable, it is recommended that

the D15 size of the material surrounding the pipe be no

smaller than the perforation size.

For this example, the filter will not be used around aperforated collector pipe, so step 12 is not applicable.

Additional design considerations: For thisexample, ASTM C-33 concre te sand falls well within

the design band. Because this is a fairly standard ,

readily available gradation, no adjustments in the

design band appear warranted. Selected ASTM Aggre-

gate Specifications are given in appendix 26B.

Table 268 Design specification gradation for example261 soil


1 inch 100

3/4 inch 90100

No. 4 70100

No. 10 52100

No. 20 3075

No. 60 040

No. 140 015

No. 200 05


16/47



Gravel Filte rs

Part 633


Figure 261 Grain size distribution curve for fine clay base soil

MATERIALS

TESTING REPORT

U.S. DEPARTMENT of AGRICULTURE

SOIL CONSERVATION SERVICE DRAIN MATERIALS

DATEBYDESIGNED AT

PROJECT and STATE

Form SCS 130

12-93

COBBLES

GRAVELS

SANDS

FINES

REMARKS

GRAIN

SIZE

IN

MILLIM

ETERS

100

90

85

80

70

60

40

30

20

15

1 0 0

50

100

90

85

80

70

60

40

30

20

15

1 0 0

50

PERCENTFINERBYDRYWEIGHT

0.001

0.002

0.005

0.01

0.02

0.03

0.04

0.05

0.1

0.2

0.3

0.4

0.5

1.0

2.0

3.0

4.0

5.0

10

20

30

40

50

100

200

300

400

USDA-SCS FORT WORTH, TEXAS 1993

(9.525)

(12.7)

(19.05)

(25.4)

(38.1)

(50.8)

(76.2)

(152.4)

(304.8)

SIEVE

OPENING,(mm)

U.S.STANDARD

SIEVES

IZE

#200

#140

#100

#60#50

#40

#.30

#20

#16

#10#8

#4

3/8"

1/2"

3/4"

1"

11/2"

2"

3"

6"

12"

(0.075)

(0.105)

(0.149)

(0.250)(0.297)

(0.42)

(0.59)

(0.84)

(1.19)

(2.0)(2.38)

(4.76)

Example 1 Fine Clay Base Soil Cat egory 1

6

1

2

5

4

DesignFilt

erBand

Base

Soil

d85

=0.06

mm

Max

D15

1-0.54mm

2-0.108

mm

3

-2.7mm

4-0.54

5-.075mm

6

-3"

7-20

mm

3

7

6

4

2

5

MinD

15

Preliminarydesign

band

Preliminarydesign

band


17/47



Gravel Filte rs

Part 633


Ex am pl e 2 62 Si l ty s an d w i th g r a ve l b as e s o i l

Ca t e g o r y 3


being designed in this example is to act as a drain.


material.

Refer to figure 262 for the plotted grain size distribu-

tion curve for this example silty sand with gravel base

soil. The plotted curve is from the following data:


3 inch 100

1 inch 90

3/8 inch 82

No 4 78

No. 10 72

No. 20 66

No. 40 54

No. 100 32

No. 200 200.005 mm 4

0.002 mm 2


gravel (material larger th an the No. 4 sieve).

The examp le 262 base soil has particles larger than

the No. 4 sieve, so the grain size distribution curve

should be regrade d on the No. 4 sieve. Proceed to ste p

3:

Step 3: Prepare adjusted gradation curves for base

soils with particles larger than the No. 4 (4.75 mm)

sieve.

Determine the regrading factor by dividing the value

100 by the percent passing the No. 4 (4.75 mm) sieve

size. The regrading factor is:

100

781 28

%

%.=

Using the original gradation analysis, plot a regraded

curve for 100 percent passing the No. 4 (4.75 mm)

sieve. The regraded percent pass ing values are equal

to the or iginal percent pass ing values times th e regrad-

ing factor.

Sieve size Original % Regraded %passing passing

3 inch 100

1 inch 90

3/8 inch 82

No 4 78 100

No. 10 72 92

No. 20 66 85

No. 40 54 69

No. 100 32 41

No. 200 20 26

0.005 mm 4 5

0.002 mm 2 3


by the p ercent passing the No. 200 (0.075 mm) sieve


table

261.

The example soil after regrading has 26 percent finer

than the No. 200 sieve. From table 261, the soil is in

category 3.

Step 5: To satisfy filtration requirements, determine

the max imum allowable D15 size for the filter accord-

ing to t able 262.

The filtering criteria for base soil category 3 is (table

262): The maximum D15 of the filter will be less than

or equal that given b y the following expression:

DA

d mm mm15 85

40

40 154 0 7 0 7

( )( )

( )( ) [ ] +. .


18/47



Gravel Filte rs

Part 633


Determine from the gradation curve of the regraded

base soil that the d85 size is 0.84 mm. From the re-

graded curve, the value of A is 26 percent. Then themaximum D15 of the filter by the equation above is:

D mm mm

mm

15

40 26

40 154 0 84 0 7 0 7

2 2

( )( )

( )( ) [ ] +

. . .

.

This is labeled as Maximum D15 in figure 262.



quirement is dete rmined from the d15

size of the base



soils is that the filter ha ve a minimum D15 of no less

than 4 times the d15 of the base soil (before any regrad-

ing of the base soil), but not be less than 0.1 mm in any

case.

The example 262 base soil has a d 15 size o f 0.032

before regrading. The minimum D15 of the filter is 4 x

0.032 = 0.128 (accep tab le because it is larger than 0.1

mm). Label this value as Minimum D15 in figure 262.


must be kep t relatively narrow to prevent the use of


minimum D15 sizes for the filter band dete rmined in

previous steps 5 and 6 so that th e ratio is 5 or less at

any given pe rcent passing of 60 or less . Adjustments

may be required based on the following considerations:

Determine the ratio of the maximum D15 size to the

minimum D15 sizes determined in previous steps. This

ratio is:

2 2

0 1316 9

.

..

mm

mm =

Because this ratio exceeds the criterion ratio of 5,

adjustments ar e required in the values.

It was given that the most important function of the

filter is to serve as a drain, so the maximum D15 is

selected as t he con trol point, equal to 2.2 mm. Label

this value as Control point 1. To satisfy criteria, deter-

mine that the minimum D15 value is 1/5 of this value.

The minimum D15 value is th en:

2 2

5 0 44

.

.

mm

mm=

Label this as Control point 2 in figure 262.

Step 8: The designed filter band must not have an

extremely broad range of particle sizes to prevent the

use of possibly gap-graded filters. Adjust the limits of

the design filter band so that t he coarse and fine sides

of the filter band have a coefficient of uniformity of 6

or less. The width of the filter band shou ld be such

that the r atio of maximum to minimum diameter s is

less than or equal to 5 for all percent passing values of

60 or less .

The value for max imum D10 is calculated to be the

maximum D15 size dete rmine in s tep 7, divided by 1.2:

Dmm

15

1 2

2 2

1 21 83

.

.

..= =

Calculate a value for the maximum D60. The maximum

D10 size times 6 is 1.83 x 6 = 11 mm. Label the maxi-

mum D60 size as Control point 3.

The minimum allowable D60 size is equal to the maxi-

mum D60 size divided by 5.11

52 2= . mm



D100 sizes of the filter according to table 26.5.

This table re quires filters to have a D5 greater than or

equal to 0.075 mm, equal to the No. 200 sieve size.

Label this value as Control po int 5 in figure 262.

It also shows that filters must h ave a D100 of less than

or equal to 3 inches. Label this value as Control point 6

in figure 262.





mum D15 size by 1.2. Determine the maximum D90using tab le 266. Label this as Control po int 7.


19/47



Gravel Filte rs

Part 633


Determine that the minimum D10 size is equal to the

minimum D15 size (det ermined in step 7) of 0.44 di-

vided by 1.2:0 44

1 20 37

.

..= mm

Because t he value of minimum D10 size is less t han

0.5 mm, the maximum D90 size is 20 mm ( tab le 266).

Label this value as Control po int 7 in figure 264.

Step 11: Connect control points 4, 2, and 5 to form a

partial design for the fine side of th e filter b and. Con-

nect control points 6, 7, 3, and 1 to form a design for

the coar se side of the filter band.

Complete the design of the filter band by extrapolating

the coarse an d fine curves to the 100 percent finer


appropriate s ieves and cor responding percent finer

values that best reconst ruct the design band and


Refer to figure 262 for the completed filter band

design. Table 269 gives the final design specified

gradation. Note that all the control points are co nsid-

ered and tha t sieve sizes and corresponding percent

finer values are se lected to bes t fit the design band.

Step 12: Design filters adjacent to perforated pipe to






It is not given tha t this filter is to be used around a

collector pipe, so this criterion is not applicable.

Additional design cons iderations: The des ign filter

band does not coincide with standard, readily avail-

able aggregate gradations. Probably, a blend of stan-

dard aggregate gradations would be required to meet

this design. Adjustments to the filter according to this

step would not improve the availability. See following

examples where this adjustment would be applicable.

Using the design filter band, prepare the following

tabular listing of the design.

Table 269 Design specification gradation for example262 soil


3 inch 100

3/4 inch 90100

1/2 inch 75100

No. 4 40100

No. 10 1055

No. 20 030

No. 40 015

No. 100 09No. 200 05


20/47



Gravel Filte rs

Part 633


Figure 262 Grain size distribution cur ve for silty sand with gravel base soilCategory 3

MATERIALS

TESTING REPORT



DATEBYDESIGNED AT

PROJECT and STATE

Form SCS 130

12-93

C

OBBLES

GRAVELS

SANDS

FINES

REMARKS

GRAIN

SIZE

IN

MILL

IMETERS

100

90

85

80

70

60

40

30

20

15

1 0 0

50

100

90

85

80

70

60

40

30

20

15

1 0 0

50


0.001

0.002

0.005

0.01

0.02

0.03

0.04

0.05

0.1

0.2

0.3

0.4

0.5

1.0

2.0

3.0

4.0

5.0

10

20

30

40

50

100

200

300

400


(9.525)

(12.7)

(19.05)

(25.4)

(38.1)

(50.8)

(76.2)

(152.4)

(304.8)

SIEVE

OPENING,(mm

)

U.S.STANDARD

SIEVE

SIZE

#200

#140

#100

#60#50

#40

#.30

#20

#16

#10#8

#4

3/8"

1/2"

3/4"

1"

11/2"

2"

3"

6"

12"

(0.074)

(0.105)

(0.149)

(0.250)(0.297)

(0.42)

(0.59)

(0.84)

(1.19)

(2.0)(2.38)

(4.76)

1-2.2

mm

2-0.4

4

mm

3-11mm

4-2.2

mm

5-0.0

75mm

6

-3"

7-20mm

MaxD

15

=2.2

mm

MinD

15=

0.1

3

mm

MinD

15

Example 2 - Silt y sand wit h gravel base soil - Cat egory 3

5

2

1

MaxD

15

3

7

6

Preliminarydesignband

4

d15

=0.0

32mm


d85

=0.8

4mm

Re-gra

dedbas

esoil

Base

soil

Final

design

filterba

nd


21/47



Gravel Filte rs

Part 633


Ex am pl e 2 62 A Si l ty s an d w i th g r a ve l b as e s o i l

Ca t e g o r y 3


must be kept relatively narrow to p revent the use of


minimum D15 sizes for the filter band de termined in

steps 5 and 6 so tha t the ra tio is 5 or less at any given

percen t passing of 60 or less. Adjustment s may be

required based on the following considerations.

Determine the ratio of the maximum D15 size to the

minimum D15 sizes determined in previous steps:2 2

0 1316 9

.

..

mm

mm=

Because this ratio exceeds the criterion ratio of 5,

adjustments a re required in the values.

The most important function of the filter is to serve as

a filter, so the minimum D15 is selected as the control

point, equal to 0.13 mm. Label this Control point 2. To

satisfy criteria, determine that the maximum D15 value

is 5 times this value. The maximum D15 value is:

0.13 x 5 = 0.65 mm

Label this as Contro l point 1 in figure 262A.

Step 8: The designed filter band mus t not have an


use of possibly gap-graded filters. Adjust the limits o f

the design filter band so that the coarse and fine sides

of the filter band ha ve a coefficient of uniformity of 6

or less . The width of the filter band should be such that

the ratio of maximum to minimum diameters is less than

or equal to 5 for all percent passing values of 60 or less.

A value for maximum D10 is calculat ed by dividing the

maximum D15 size (determine in step 7) by 1.2.

0 65

1 20 54

.

..= mm

Calculate a value for the maximum D60 by multiplying

the maximum D10 size times 6:

0.54 x 6 = 3.24 mm

Label the maximum D60 size as Control point 3.

This exa m ple uses the sam e base soil as that i n

example 262. It is assum ed that the most im portant

function of the filter bein g designed i s to act as a

filter. Exam ple 262 assum ed the m ost im portant

function was to act as a drain . Note the differences

in the design steps.

Step 1: Plot the gradation curve of the base soil mate-

rial. This step is the same as that in example 262. Refer

to figure 262A for the plotted grain size distr ibutioncurve for this example silty sand with gravel base soil.


gravel (material larger th an the No. 4 sieve). Because

the example 262 base soil has par ticles larger tha n

the No. 4 sieve, the grain size distribution curve should

be regraded on the No. 4 sieve. Proceed to st ep 3.



sieve. This step is th e same as that for example 262.

Refer to that example and see figure 262A.


by the p ercent passing the No. 200 (0.075 mm) sieve


table 261. This step is the same as tha t for example

262. The soil is in category 3.


the maximum allowable D15 size for the filter acco rd-

ing to table 262. This step is the same as th at for

example 262. The maximum D15 size is 2.2 mm. This

is labeled as Maximum D15 in figure 262A.



quirement is dete rmined from the d15 size of the base


The example 262A base soil has a d15 size o f 0.032

mm before regrading. The value of minimum D15 of the

filter is 4 x 0.032 = 0.128 mm (acceptab le because it is

larger than 0.1 mm). Label this value as Minimum D15in figure 262A.


22/47



Gravel Filte rs

Part 633


The minimum allowable D60 size is equal to the maxi-

mum D60 size divided by 5:

3 24

50 65

..= mm

Label this as Cont rol point 4 in figure 262A.



This table shows that filters must have a D5 greater

than or equal to 0.075 mm, equal to the No. 200 sieve

size. Label this value as Control point 5 in figure 262A.

It also shows that filters must h ave a D100 of less th anor equal to 3 inches. Label this value as Control point 6

in figure 262A.

Step 10: To minimize segregation during constru c-




mum D15 size by 1.2. Determine the maximum D90using table 266. Label this as Control po int 7.

This table lists maximum D90 sizes for filters for a

range of D10 sizes. Calculate the minimum D10 size as

equal to the minimum D15 size (determined in step 7)

of 0.13 mm divided by 1.2:

0 13

1 20 11

.

..= mm

Because the value is less th an 0.5 mm, the maximum

D90 size is 20 mm (table 266). Label this value as

Control point 7 in figure 262A.

Step 11: Connect cont rol points 4, 2, and 5 to form a

partial design for the fine side of the filter band. Con-

nect control points 6, 7, 3, and 1 to form a design for

the coarse side of the filter band.

Complete the des ign of the filter band by extrapolating

the coar se and fine curves to the 100 percent finer


appropriate sieves and corresponding percent finer

values that best r econstruct the design band and


Refer to figure 262A for the c ompleted filter band

design. The design is also tabulated in table 2610.

Note that the control points are considered and tha t

relatively even percent finer values are selected for

standard sieve sizes for ease in wr iting specifications.



For critical structure drains where rapid gradient




It is not given tha t this filter is to be used aroun d a


Additional des ign considerations: The des ign filter

band c oincides fairly well with a standard, readily

available aggregate gradation, ASTM C-33 fine aggre-

gate for concre te. However, a slight adjustment in the

filter design would make it more comp atible with this

standard gradation. The filter band can be adjusted to

a more poorly graded configuration, a CU value of less

than 6. Note tha t this is accomp lished without violat-

ing other filtering or permeability criteria. Figure 26

2B shows how the or iginal filter band de sign shown in

figure 262A could be slightly altere d to a s teeper

sloping band for the filter limits without violating any

of the c riteria previously covered.

The final filter design specification limits selected for

example 262A, before and after possible adjustment ,

are shown in table 2610.

Table 2610 Design specification gradation forexample 262A soil

Sieve size Fig. 262A before Fig. 262B afteradjustment adjustment(% passing) (% passing)

3 inch 100

3/4 inch 90100

1/2 inch 85100 100

No. 4 70100 80100

No. 10 45100 60100

No. 20 2065 20100

No. 40 045 060

No. 60 030 035

No. 100 017 017

No. 200 05 05


23/47



Gravel Filte rs

Part 633


Figure 262A Grain size distribution curve for silty sand with gravel base soil where primary function is filter

MATERIALS

TESTING REPORT



DATEBYDESIGNED AT

PROJECT and STATE

Form SCS 130

12-93

C

OBBLES

GRAVELS

SANDS

FINES

REMARKS

GRAIN

SIZE

IN

MILL

IMETERS

100

90

85

80

70

60

40

30

20

15

1 0 0

50

100

90

85

80

70

60

40

30

20

15

1 0 0

50


0.001

0.002

0.005

0.01

0.02

0.03

0.04

0.05

0.1

0.2

0.3

0.4

0.5

1.0

2.0

3.0

4.0

5.0

10

20

30

40

50

100

200

300

400


(9.525)

(12.7)

(19.05)

(25.4)

(38.1)

(50.8)

(76.2)

(152.4)

(304.8)

SIEVE

OPENING,(mm

)

U.S.STANDARD

SIEVE

SIZE

#200

#140

#100

#60#50

#40

#.30

#20

#16

#10#8

#4

3/8"

1/2"

3/4"

1"

11/2"

2"

3"

6"

12"

(0.074)

(0.105)

(0.149)

(0.250)(0.297)

(0.42)

(0.59)

(0.84)

(1.19)

(2.0)(2.38)

(4.76)

Example 2A - Silt y sand wit h gravel base soil - Cat egory 3

2

1-0.6

5m

m

2-0.1

3m

m

3-3.2

4m

m

4-0.6

5

5-.0

75mm

6

-3"

7-20

mm

MaxD

15

=2

.2mm

Min

D15

=0

.13mm

MinD

15

5

1

MaxD

15

3

4

d85

=0.8

4mm

6

7

d15

=0.0

32mm

Preliminarydesign

band


Re-gra

dedbas

esoil Ba

seso

il Final

design

filterband


24/47



Gravel Filte rs

Part 633


Figure 262B Grain size distribution cur ve for silty sand with gravel base soil (adjusting limits)

ASTM

C-33Concretesa

ndwillplotinfinaldesignband

Example 2 - Adjust ing filt er design t o suit available st andard gradat ion

Figure B-3

MATERIALS

TESTING REPORT



DATEBYDESIGNED AT

PROJECT and STATE

Form SCS 13012-93

CO

BBLES

GRAVELS

SANDS

FINES

REMARKS

GRAIN

SIZE

IN

MILLIMETERS

100

90

85

80

70

60

40

30

20

15

1 0 0

50

100

90

85

80

70

60

40

30

20

15

1 0 0

50


0.001

0.002

0.005

0.01

0.02

0.03

0.04

0.05

0.1

0.2

0.3

0.4

0.5

1.0

2.0

3.0

4.0

5.0

10

20

30

40

50

100

200

300

400


(9.525)

(12.7)

(19.05)

(25.4)

(38.1)

(50.8)

(76.2)

(152.4)

(304.8)

SIEVE

OPENING,(mm)

U.S.STANDARD

SIEVE

SIZE

#200

#140

#100

#60#50

#40

#.30

#20

#16

#10#8

#4

3/8"

1/2"

3/4"

1"

11/2"

2"

3"

6"

12"

(0.074)

(0.105)

(0.149)

(0.250)(0.297)

(0.42)

(0.59)

(0.84)

(1.19)

(2.0)(2.38)

(4.76)

Curvesshiftedtosteeper

configurationbymoving

D60

valuesequallyto

left

Finaldesign

Finaldesign

Originalde

sign


25/47



Gravel Filte rs

Part 633



being designed is to act a s a filter.


material.


tion curve for th is example c layey gravel base soil,

labeled Base soil. The plotted curve is from the follow-

ing data:


3 inch 100

1 inch 73

3/4 inch 66

1/2 inch 59

No. 4 47

No. 40 34

No. 60 31

No. 200 28

0.05 mm 26

0.02 mm 250.005 mm 18

0.002 mm 13



Because t he exam ple 263 base soil has par ticles

larger than the No. 4 sieve, the grain size distribution

curve should be regraded on the No. 4 sieve. Proceed

to step 3.



sieve.

Determine the regrading factor by dividing the value

100 by the percent passing the No. 4 (4.75 mm) sieve

size. The regrading factor is

100

472 13

%

%.=

Using the original gradation analysis, plot a regraded

curve for 100 percent passing the No. 4 (4.75 mm)

sieve. The regraded percent pass ing values are equal

to the or iginal percent pass ing values times th e regrad-

ing factor.

Sieve size Original Regraded% passing % passing

3 inch 100

1 inch 73 3/4 inch 66

1/2 inch 59

No. 4 47 100

No. 40 34 72

No. 60 31 66

No. 200 28 60

0.05 mm 26 55

0.02 mm 25 53

0.005 mm 18 38

0.002 mm 13 28




table 261.

The example 263 base soil after regrading has 60

percent finer than the No. 200 sieve. From table 261,

the soil is in category 2.



ing to t able 262.

This table sh ows the filtering criteria for base soil

category 2 as follows. The maximum D15 of the filter

will be less than or equal to 0.7 mm. This is labeled as

Maximum D15 in figure 263.



quirement is determined from the d15 size of the base


Ex a mp l e 2 6 3 Cl a ye y g r ave l b a se s o i l Ca te g o r y 2


26/47



Gravel Filte rs

Part 633



soils is that the filter ha ve a minimum D15 of no less

than 4 times the d15 of the base soil (before any regrad-ing of the base soil), but will not be less than

0.1 mm in any case .

The example 263 base soil has a d 15 size of about

0.0028 mm before regrading. Using the crite rion, the

minimum D15 of the filter would be 4 x 0.0028 = 0.011

mm. However, table 263 also shows that the mini-

mum D15 is 0.1 mm. Label this value as minimum D15 in

figure 263.


must be kep t relatively narrow to prevent the use of


minimum D15 sizes for the filter band dete rmined in

steps 5 and 6 so that the ra tio is 5 or less at any given

percent passing of 60 or less. Adjustments may be

required based on the following considerations:

Determine the ratio of the maximum D15 to the mini-

mum D15 sizes:

0 7

0 17

.

.

mm

mm=

Because this value exceeds the criterion of 5, adjust-

ment in the values is required. The most important

function of this design filter is to act as a filter, so the

minimum D15 value becomes controlling and is un-

chan ged. Label this value Contro l point 2 in figure

263. Then, the maximum D15 value is 5 times this, or

5 x 0.1 mm = 0.5 mm. Label this as Control po int 1 in

figure 263.

Step 8: The designed filter ban d must not have an


use of possibly gap-graded filters. Adjust th e limits of

the design filter band so t hat the coarse and fine sides

of the filter band have a coefficient of uniformity of 6or less. The width of the filter band should be such

that the ra tio of maximum to minimum diameters is


60 or less

Calculate a value for the maximum D10 size as equal to

the maximum D15 size determined in Step 7 divided by

1.2:

0 5

1 20 42

.

..= mm

The value for the maximum D60 is calculated using the

maximum D10 size times 6:

0.42 x 6 = 2.52 mm


The minimum allowable D60 size is then :

Dmm

60

5

2 52

50 50= =

..




This table shows that filters mu st have a D5 greater


size. Label this value as Control point 5 in figure 263.

Table 265 also sh ows that filters must have a D100 of

less than or equal to 3 inches. Label this value as

Contro l point 6 in figure 263.




preliminary minimum D10

size by dividing the mini-



range of D10 sizes. Calculate a value for minimum D10size by dividing the minimum D15 size determined in

Step 7 by 1.2:

0 1

1 20 083

.

..= mm

Because t he value is less than 0.5 mm, the maximum

D90

size is 20 mm (table 266). Label this value as




nect Control points 6, 7, 3, and 1 to form a des ign for

the coarse side of the filter band. Complete the design

of the filter band by extrapolating the coa rse and fine

curves to the 100 percent finer value. For purposes of

writing specifications, select appro priate sieves and

corresponding percent finer values that bes t recon-

struct the d esign band and tabulate the values.


27/47



Gravel Filte rs

Part 633


See figure 263 for the final filter band design.

Step 12: Design filters adjacent to perforated pipe tohave a D85 size no smaller than the per foration size.





It is not given tha t this filter is to be used aroun d a


Additional des ign considerations: Standard Con-

cre te Sand, ASTM C33, plots within th is final des ign

band, so one may consider the des ign acceptable with

no further modifications. If onsite sand or o ther

cheaper filters could be located, some modification

could be considered. Poss ible specification limits a re

shown in table 2611.

Table 2611 Design specification limits for clayeygravel base soil

Sieve size % passing (1)

3 inch 100

3/4 inch 90100

No. 4 70100

No. 10 55100

No. 20 3075

No. 40 1055

No. 50 045

No. 100 025

No. 200 05


28/47



Gravel Filte rs

Part 633


Figure 263 Grain size distribution curve for clayey gravel base soil

MATERIALS

TESTING REPORT



DATEBYDESIGNED AT

PROJECT and STATE

Form SCS 130

12-93

C

OBBLES

GRAVELS

SANDS

FINES

REMARKS

GRAIN

SIZE

IN

MILL

IMETERS

100

90

85

80

70

60

40

30

20

15

1 0 0

50

100

90

85

80

70

60

40

30

20

15

1 0 0

50


0.001

0.002

0.005

0.01

0.02

0.03

0.04

0.05

0.1

0.2

0.3

0.4

0.5

1.0

2.0

3.0

4.0

5.0

10

20

30

40

50

100

200

300

400


(9.525)

(12.7)

(19.05)

(25.4)

(38.1)

(50.8)

(76.2)

(152.4)

(304.8)

SIEVE

OPENING,(mm

)

U.S.STANDARD

SIEVE

SIZE

#200

#140

#100

#60#50

#40

#.30

#20

#16

#10#8

#4

3/8"

1/2"

3/4"

1"

11/2"

2"

3"

6"

12"

(0.074)

(0.105)

(0.149)

(0.250)(0.297)

(0.42)

(0.59)

(0.84)

(1.19)

(2.0)(2.38)

(4.76)

1-0.5

m

m

2-0.1

mm

3-2.5

m

m

4-0.5

mm

5-0.0

75mm

6

-3"

7-20mm

MaxD

15

=0.7

mm

MinD

15=

0.1

mm

Example 3 - Clayey gravel base soil - Cat egory 2

1

M

axD

15

2

MinD

15

5

4

3

Re-gra

ded

basesoil

P

reliminarydesign

b

and

7

6

Finald

esign

filte

rban

d

Bas

eso

il



29/47



Gravel Filte rs

Part 633



being designed is to act a s a filter.


material.


tion curve for th is example s ilty sand b ase soil, labeled

Base soil. The plotted curve is from th e following data.


No. 20 100

No. 40 94

No. 60 44

No. 140 14

0.05 mm 12

0.02 mm 10

0.005 mm 7

0.002 mm 4

Step 2: Proceed to Step 4 if the base soil contains nogravel (material larger th an the No. 4 sieve).

Because t he example 264 base s oil has 100 percent of

its particles finer than the No. 20 sieve, it has no pa r-

ticles larger than the No. 4 sieve. Therefore, the grain

size distribution curve does not h ave to be regraded .

Proceed to step 4.

Step 3: This step is not applicable because the base

soil contains no part icles larger than the No. 4 sieve.

Go to step 4.




table 261.

The example 264 base soil has 13 percent finer th an

the No. 200 sieve, determined from examination of the

plotted grain size distribu tion curve in figure 264.

From table 261, the soil is in category 4.



ing to t able 262.

The filtering criterion for base soil category 4 (table

262) is that the maximum D15 of the filter will be less

than or e qual to 4 times the d 85 of the base soil.

The d85 of the base soil from the plotted grain size

distribut ion curve in figure 264 is 0.39 mm. The

maximum D15 is:

4 x 0.39 mm = 1.56 mm

Label th is as Maximum D15 in figure 264.



quirement is determined from the d15 size of the base



soils is that the filter have a minimum D15 of no less

than 4 times the d15 of the base s oil (before any regrad-ing of the base soil), but not be less than 0.1 mm in any

case.

The example 264 base soil has a d15 size of 0.12 mm

before r egrading. Using the criterion, the minimum D15of the filter would be 4 x 0.12 = 0.48. This is greater

than the minimum required D15 of 0.1 mm, so it is

acceptable. Label this value as Minimum D15 in figure

264.


must be kept relatively narrow to p revent the use of


minimum D15 sizes for the filter band de termined in

steps 5 and 6 so tha t the ra tio is 5 or less at any given

percen t passing of 60 or less. Adjustment s may be

required based on the following considerations.

The ratio of the maximum D15 to the minimum D15 is:

1 56

0 483 3

.

..=

Ex a m pl e 2 6 4 Si l ty s an d b a s e s o i lCa te g o r y 4


30/47



Gravel Filte rs

Part 633


Because this value is less than the cr iterion value of 5,

no adjustment is necessary. Label the max imum D15

and minimum D15 sizes as Control points 1 an d 2,respec tively, and proceed to th e next cons ideration.

Step 8: The designed filter ban d must not have an


use of possibly gap-graded filters. Adjust th e limits of

the design filter band so t hat the coarse and fine sides

of the filter band have a coefficient of uniformity of 6

or less. The width of the filter band should be such

that the ra tio of maximum to minimum diameters is


60 or less .

Calculate a value for the maximum D10 size as equal to

the maximum D15 size (determined in Step 7) divided

by 1.2:

1 56

1 21 3

.

..= mm

Calculate a value for the maximum D60 by multiplying

the maximum D10 size times 6:

1.3 x 6 = 7.8 mm


The minimum allowable D60 size is:

7 8

51 56

..= mm

Label this as Cont rol point 4 in figure 264.



This table shows that filters must have a D5 greater


size. Label this value as Contro l point 5 in figure 264.

The table also shows tha t filters must have a D100 of

less than or equal to 3 inches. Label this value as

Control p oint 6 in figure 264.



the minimum D10 of the filter is important. Calculate apreliminary minimum D10 size by dividing the mini-



range of D10 sizes. Calculate a value for minimum D10size by dividing the minimum D15 size determined in

step 7 by 1.2:

0 48

1 20 40

.

..= mm

Because the D10 size is less than 0.5 mm, the maximumD90 size is 20 mm (table 266). Label this value as




nect Control points 6, 7, 3, and 1 to form a des ign for

the coarse side of the filter band. Complete the design

of the filter band by extrapolating the coa rse and fine

curves to the 100 percent finer value. For purposes of

writing specifications, select appro priate sieves and

corresponding percent finer values that bes t recon-

struct the d esign band and tabulate the values.

Refer to figure 264 for the selected filter band drawn.

Table 2612 lists the sieve/percent finer values se-

lected.



For critical structure drains where rapid gradient




The filter is not being used adjacent to a collectorpipe, so this step is not applicable.


31/47



Gravel Filte rs

Part 633


Additional des ign considerations: The specified

filter band does not meet standard aggregate grada-

tions. The band is more coar se than C33 concret esand, and it is finer than the sta ndard gravel gradations

(see appendix 26B). Possibly, the required filter grada-

tion could be met by blending standard available

gradations.

Consider adjustments in the steepn ess of the final

design filter band shown in figure 264 if these adjust-

ments wo uld allow the use o f such blends or other

readily available gradations. The filter band may be

adjusted to a steeper configuration, with a coefficient

of uniformity of less than 6, but all the other criteria

must still be met. Example 262A illustrated such an

adjustment in the design filter band.

Table 2612 The final selected design filter bandgradation for silty sand bas e soil


3 inch 100

3/4 inch 90100

No. 4 50100

No. 10 2570

No. 20 035

No. 40 014

No. 60 010

No. 200 05


32/47



Gravel Filte rs

Part 633


Figure 264 Grain size distribution curve for silty sand base soil

MATERIALS

TESTING REPORT



DATEBYDESIGNED AT

PROJECT and STATE

Form SCS 130

12-93

C

OBBLES

GRAVELS

SANDS

FINES

REMARKS

GRAIN

SIZE

IN

MILL

IMETERS

100

90

85

80

70

60

40

30

20

15

1 0 0

50

100

90

85

80

70

60

40

30

20

15

1 0 0

50


0.001

0.002

0.005

0.01

0.02

0.03

0.04

0.05

0.1

0.2

0.3

0.4

0.5

1.0

2.0

3.0

4.0

5.0

10

20

30

40

50

100

200

300

400


(9.525)

(12.7)

(19.05)

(25.4)

(38.1)

(50.8)

(76.2)

(152.4)

(304.8)

SIEVE

OPENING,(mm

)

U.S.STANDARD

SIEVE

SIZE

#200

#140

#100

#60#50

#40

#.30

#20

#16

#10#8

#4

3/8"

1/2"

3/4"

1"

11/2"

2"

3"

6"

12"

(0.074)

(0.105)

(0.149)

(0.250)(0.297)

(0.42)

(0.59)

(0.84)

(1.19)

(2.0)(2.38)

(4.76)

1-1.56m

m

2-0.4

8

mm

3-7.8

mm

4-1.56

mm

5-0.0

75mm

6

-3"

7-20

mm

MaxD

15=

1.56

mm

MinD

15=

0.4

8

mm

Example 4 - Silt y sand base soil - Cat egory 4

5

4

3

7

6

d85

=0.3

9

mm


Preliminary

designband

d15=

0.1

2mm

MinD

15

MaxD

15

1

2Baseso

il

Finalde

signfilte

rband


33/47



Gravel Filte rs

Part 633


The base soil for this example is the filter band ob-

tained in the design for example 261. The base soil in

this case is actually a band of soil gradations specify-

ing a suitable sand filter. The sand filter was designed

to prot ect a silty clay base soil.

Example 265 illustrates how to design a gravel filter

band to b e compatible with the finer sand filter previ-

ously designed. In the first pa rt of this example it is

understood that the gravel filter will not be used

around perforate d collector pipe, but some other type

of outlet of seepage is employed. The second part of

this example illustrates how the design of a coar se

filter is changed if perforated pipe is used.


material. In example 265, the base soil is actually a

band o f possible filter gradations. The filter ba nd that

was o btained in example 261 is used. Refer to the

plotted grain size distribution curve for this example,

labeled F ine filter in figure 265. The plotted band isfrom the following data:


1 inch 100

3/4 inch 90100

No. 4 70100

No. 10 52100

No. 20 3075

No. 60 040

No. 140 015

No. 200 05



Only the fine side of the specified filter band n eed be

considered for this step because th e finest base so il

controls the filter criteria. Because the fine side of the

filter band ha s no pa rticles larger than the No. 4 sieve,

step 3 is skipped. Proceed to s tep 4.

Step 3: Not applicable because the base soil con-

tains no particles larger than the No. 4 Sieve.




table 261.

Examp le 265 base filter band has from 0 to 5 percentfiner t han th e No. 200 sieve, determined from ex ami-

nation of the plotted grain size distribution curve in

figure 265. From table 261, the soil is in category 4.



ing to t able 262.

This table st ates the filtering criteria for base so il

category 4 as: The maximum D15 of the filter will be

less than or equal 4 times the d 85 of the base soil.

The finest gradat ion from the range of gradations

given by the base filter band will be controlling under

this criterion. The d85 of the fine side of the base filter

band fr

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Gradation Design of Sand Gravel Filters USDA Neh633-Ch26

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