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SIGNIFICANCE OF COEFFICIENTOF UNIFORMITY OF BASES ONTHEIR FILTER DESIGNM. A. Lone aa Civil Engineering Departemnt , National Institute ofTechnology , Srinagar , J & KPublished online: 07 Jun 2012.

To cite this article: M. A. Lone (2007) SIGNIFICANCE OF COEFFICIENT OF UNIFORMITYOF BASES ON THEIR FILTER DESIGN, ISH Journal of Hydraulic Engineering, 13:2, 31-40,DOI: 10.1080/09715010.2007.10514869

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VOL. 13. (2)

THE INDIAN SOCIETY FOR HYDRAULICS JOURNAL OF HYDRAULIC ENGINEERING

SIGNIFICANCE OF COEFFICIENT OF UNIFORMITY OF BASES ON THEIR FILTER DESIGN

by

M.A. Lone1

ABSTRACT

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Filter tests for the bases of various gradations were carried out to study the effect of Coefficient of Uniformity of bases (Cu) on their filter design. Filters usually designed on the basis of dx

5(85% finer size of the base material) of a base prove conservative in

most of the cases. The present study indicates that the filters designed on the basis of some other representative size d* of the base result in Jess conservative and more economical design of filters for a particular base. This sized*, which has been termed as design controlling usually size in the present study, does not only depend on dxs size of the base but also on the coefficient of uniformity Cu of the base material, thereby taking into account almost overall gradation of the base material for filter design.

KEYWORDS : Bases, Coefficient of uniformity, Filters, Filter materials, Filter design, Gradation, Laboratory filter tests, Permeability, Piping, Washout.

INTRODUCTION

The literature review concerning filter design criteria indicates that since 1922 till-date, most of the work is guided by empirical relations evolved by a number of researchers (Terzaghi-1922, Betram-1940, Karpoff-1955, Kawakami et al.-1961, Sherard-1979, Sherard et al. 1984 etc.). The design criteria developed for protecting a particular base from being washed out and allowing free passage of seepage water is based on designing the filter mass for preventing a particular base size in the first instance, for the self filtration phenomenon at the base-filter interface (Fig.l ). This size has been, in most of the case, taken as dss of the base and related to the 0

15 (15%

finer size) of the filter. The ratio of these sues of filler and base i.e. 01/ d

85, termed

as piping criterion, has been suggested a value range of 4 to 9 by various researchers and for permeability criterion of D

1/d

15 a value of 5 to 40 has been proposed. As far

I. Assistant Professor, Civil Engineering Departemnt, National Institute of Technology,

Srinagar, J & K

Note : Written discussion of this paper will be open until 31st December 2007.

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VOL. 13. (2)

as the piping criterion is concerned, the retention of dx5

size of any base by a filter mass should result in the stability of the system, as per the existing criterion.

In the present study a number of bases of different gradations were tested on filters designed on the basis of the Controlling Constriction Size of the filter mass (Lone, et al. 2005) and it was observed that the filters designed only on the bases of dx~ size of base is not adequate, as the filters designed on this basis result conservative in most of the cases, as has been indicated by other researchers also, (Sherard, 1984a).The filters designed on the basis of dK

5 of has been found to retain even Y2 of

the size of the base i.e. required for the self filtration phenomenon, as per piping criterion of 'DI5(filter)/dx~(base)=5'. Instead some other sized* has been found more effective for designing the filter, which not only depends on dK~ but also on the Coefficient of Uniformity of the base, thereby involving almost the overall gradation of the base in deciding its filter. Filters designed on the basis of this size have shown satisfactory performance from the piping criterion points of view and also the permeability ratio remained well within the limits.

LABORATORY INVESTIGATIONS

For ascertaining the effect of base gradation on filter design, as discussed above, the laboratory investigations were carried out. These investigations supported the above concept of significance of Coefficient of Uniformity on filter design, for which otherwise only dK~ has been considered in most of the studies.

The Experimental Set-up, materials used and procedure adopted are described in the following sections.

Experimental Set-up

The experimental set-up used for the study is shown in Fig. 2. The set-up consisted of a cylindrical container of 250 mm diameter and 600 mm length with a hopper type base of 80 mm diameter. A grid of rods at 5 em interval was provided at the end of the cylindrical container for supporting the wire mesh of different opening sizes varying form 25 mm to 80 mm (for preventing the filter material movemer1t). A pressure gauge and two air vents were provided at the top of the filter apparatus and a stopcock at the inlet for regulating the supply. Piezometer taps with geo-textiles to prevent soil infiltration were provided at intervals along the surface ofthe cylinder and connected to manometer I piezometer boards to measure the intermediate heads.

Materials

The river gravel used as filter materials was grouped into following standard sizes: 63.0,50.0,31.5, 25.0,20.0,16.0,12.5,1 0.0,6.3, 4.75,4.0,3.55, 2.818, 2.411, 2.032, 1.767, 1.405, I .20, I .00, 0.853 and so on. The particle shape of the material ranged from

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VOL. 13. (2) SIGNIFICANCE OF COEFFICIENT OF UNIFORMITY OF BASES ON THEIR FILTER DESIGN

I I

gravel 11le~ t 1-- ba sand

Lstable Filler Zone some base intrudes into gravel making a stable filter zone

FIG. 1 PROCESS OF SELF-FILTRATION LAYER MAKING

ide material (coarser than base sand & finer than filter)

_..--tt--0.075 mm sieve for collection of washout

FIG. 2 MAIN BODY OF EXPERIMENTAL SET-UP

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spherical to ellipsoidal. The shape parameters of these materials are presented in Table I. For base materials river sand of various gradations were procured and six base materials of different gradations were selected for various filter tests. The particle size of bases ranged from 0.075 mm to 4.75 mm with negligible percentage of silt size material. The main gradation features of these materials are given in Table 2. The specific gravity of the material was 2.65 and its average density was 1.7 gm/cm1

.

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TABLE-t

VOL. 13. C2l

SHAPE PARAMETERS OF THE FILTER MATERIAL

Size b/a da Flatness Shape factor Sphericity (mm) Ratio dvab (Particle vQIDm~}m

63.0

50.0

40.0

31.0

25.0

20.0

16.0

12.5

10.0

06.3

(a+b)/2c

0.801 0.875 1.445 0.743

0.780 0.855 1.417 0.732

0.779 0.647 1.394 0.733

0.765 0.625 1.440 0.714

0.735 0.642 1.371 0.747

0.576 0.472 1.75 0.621

0.557 0.443 1.845 0.592

0.553 0.399 2.046 0.536

0.585 0.419 1.977 0.533

0.520 0.395 2.063 0.542

where, a = Major axis of the particle b = Intermediate axis of the particle c = Minor axis of the particle

TABLE-2

{(n/6 )a3} 113

0.815

0.804

0.812

0.802

0.789

0.647

0.602

0.590

0.573

0.533

MAIN GRADATION FEATURES OF DIFFERENT BASE MATERIALS

Base Percentage material finer passing in(mm) Cu Remarks

diU d·~ d541 dB! d'l5

81 0.155 0.16 0.445 0.98 1.45 3.19 W.G.'

82 0.34 0.41 0.71 1.56 2.25 2.79 Not so W.G.

83 0.19 0.23 1.00 2.33 3.35 6.29 W.G.

84 0.37 0.45 0.96 1.60 1.90 3.1 I W.G.

85 0.25 0.30 0.74 1.65 2.50 4.00 W.G.

86 1.10 1.23 1.65 2.00 2.25 1.68 U.G.2

Cu = Coefficient of Uniformity of Base 1W.G. = Well Graded 2 U.G. = Uniformly Graded

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VOL. 13, (2)

PROCEDURE

SIGNIFICANCE OF COEFFICIENT OF UNIFORMITY OF BASES ON THEIR FILTER DESIGN

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A permeability test was conducted on the filter material prior to placing the base material. A relatively low hydraulic gradient was applied across the filter material, and piezometer heads along the filter, rate of flow through the specimen and water temperature were measured. The hydraulic gradient was then increased and the measurements were repeated. This sequence was continued until the maximum hydraulic gradient was obtained. The purpose of permeability test was not to document a property of the soil but rather was to compare the relative permeability of the filter and the base.

Following the completion of the permeability test on the filter material, the filter specimen was drained slowly. The top plate of the test device was removed along with the pea gravel and the base material was placed on the top of the filter material using a small scoop, without any compaction. The thickness of the base was usually taken as 10.5 to 10.7 em. The base material was placed a few centimetres below the top of the cy I inder. An average density of I. 7 gm/cm3 and a void ratio of 0.51 were maintained in case of the base. At the top of the base, a wire mesh of 2.5 mm openings was placed, over which pea gravel was placed for preventing the base from any damage due to the direct impact of incoming water. Side material, coarser than the base but finer than the filter material was placed along the periphery for the top 7 to 8 em top height of the filter mass (as shown in Fig. 1) to prevent the washout of the base material through the wider pores formed between the filter material and the cylinder periphery. The cylinder was then closed tightly.

Initially a relatively low hydraulic gradient was applied across the base material. Before taking any head measurements, air valves were opened for removing the air from the specimen and then closed. To start with piezometer heads along the base and filter specimen, rate of flow through the specimen and water temperature were measured. A number of readings were taken for a particular hydraulic gradient till the rate of flow became relatively constant with time. The washouts, if any. were collected at the intervals of time which were later on weighed after drying. The procedure was continued until the maximum available hydraulic gradient (44) was employed for the test. After the completion of the test, the top surface of the base was examined for any damage and deformation etc. The base was then removed in two layers and after drying the gradation analysis was carried out for both these layers to assess the change in gradation of the top and bottom base layers due to migration of the particles from the base into the filter mass and also due to the washout, if any. After the removal of the base, the extent to which the base had migrated into the filter at the interface was determined directly. The filter material was then removed and the test for the next base-filter combination was carried out in the same way. Several tests were conducted for a particular base with different filter masses till the failure occurred. The test runs were repeated in the same way for other base till their failure.

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VOL. 13. t21

Failure of the base was indicated by the significant quantity of base material passing through the filter in the first 3 to 5 minutes and its continuation afterwards also. Moreover there was significant base migration into the filter and deformation of the base like depressions, piping etc. Borderline success cases were indicated where no significant quantity of base material passed through the filter under flow i.e. the washout remained less than I to 1.5% and the base deformation was negligible.

RESULTS AND DISCUSSIONS

Failure of a filter may occur because of significant quantity of base material passing through the filter and migration of base into the filter. Some migration of base is needed to develop filter action(Fig.l ), the required thickness of which as given by Sherard( 1981) is:

t: 2(dK/0.)5) (I)

where t =required base migmtion for development of filter action, and dK~ = size of base material at 85% passing

During the present study the actual migration of base into the filter was determined directly after removing the base material at the end of the test. Table 3 presents the comparison between the observed and calculated values of conformity with calculated value. The permeability criterion 'D 15(filter)/d 1 ~ (base) = 5' (Terzaghi,l922), for ensuring a permeability ratio (k/k

8) of 16 to 25 between the filter and base was also

studied in the present investigations. This ratio was also found quite satisfactory. The test results with respect to filter-base permeability ratio(k/k

8), washouts, base

migration for borderline successful cases of various bases are presented in Table 4.

TABLE-3 BASE MIGRATION FOR DESIGN BORDERLINE SUCCESS TESTS

Base Base Migration (em)

Observed Calculated

a. 1.50 1.31

B2 2.25 2.08

B3 2.00 3.09

B4 2.00 2.13

B~ 2.50 2.20

B~ 2.50 2.67

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TABLE-4 SUMMARY OF DESIGN BORDERLINE SUCCESSFUL

TESTS RESULTS FOR BASES Bl TO B6

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Base Filter Washout Bas Permeability Primary size (gm) Migration

(mm) (em) k~B

Bl 25.0,20.0, 12.5 30 1.50 255

B, 25.0,25.0,25.0 23 2.25 50

B, 50.0,31.5.16.0 123 2.00 155

84 63.0,31.5, 16.0 30 2.00 30

B~ 25.0.25.0,25.0 78 2.50 120

8(1 40.0,40.0,40.0 25 2.50 43

kF= Permeability of filter material and k8 = Permeability of base material

Inferences Drawn from the Filter Tests on Bases Bl to B6

Limits have been imposed to the nature of materials gradation by various researchers which impeded the development of a general procedure for filter design. For instance according to Terzaghi ( 1929), the coefficient of uniformity for the materials should not exceed 2 and the gradation curves of base and filter materials should be parallel. The significance of the material gradation and coefficient of uniformity has been recognized by most of the researchers but very limited work has been done to correlate the gradation parameters with filter behaviour. With this end in view, the six bases with different values of the design controlling sized* i.e. size which is to be retained at the base-filter interface before the formation of self-filtration layer. which usually is being taken as dx~ as per the existing criteria. The design controlling size d* with respect to coefficient of uniformity Cu and dx~ for different bases have been presented in Table 5 and a plot of dx/d* versus Cu is shown in Fig. 3. The plot indicates a linear variation of Cu with dx/d*. This linear curve can be represented by the following equations:

or

Cu = 8.00(dK/d*)-4.72

d* = 8.00 x dK/( Cu + 4.72)

Coefficient of Correlation 'Cr'=0.99159

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7•5

1·0

6·5

6·0

s·s

S·O

4-5

4·0

::J J-5 u

J-()

2-5

X>

1·5

1·0 0 o-2

SIGNIFICANCE OF COEFFICIENT OF UNIFORMITY OF BASES ON THEIR FILTER DESIGN

0·4 Q-6

• ~ 85/d

FIG. 3 CURVE SHOWING RELATION BETWEEN Cu AND d./d*

TABLE-S

VOL. 13. (2)

DESIGN CONTROLLING SIZEd* WITH RESPECT TO Cu AND d85 OF BASEBl TOB6

Base d* dl5 d./d* Cu (mm) (mm)

B, 1.090 0.98 0.90 3.19

B, 1.575 1.56 0.99 2.79

B, 1.710 2.33 1.36 6.29

B~ 1.710 1.60 0.94 3.11

B~ 1.500 1.65 1.10 4.00

Bt. 2.500 1.97 0.79 1.68

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CONCLUSION

SIGNIFICANCE OF COEFFICIENT OF UNIFORMITY OF BASES ON THEIR FILTER DESIGN

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Inspite of the fact that a number of cases tested were exceeding Terzaghi's piping criterion for D./ dx~· yet these filters, on the bases of the proposed concept of design controlling size d*, worked successfully. The permeability criterion of D./d 1 ~ was found significantly higher than the Terzaghi's minimum required value of 5. The parallelism of filter and base gradation curves were found no longer necessary, as also indicated by some other researchers earlier (USCE, 1987). By employing the Eq. (3), one can workout the value of design controlling sized* for a particular base from its gradation curve. With the help of this d* the filter mass can be designed on the basis of the model referred earlier (i.e. Lone et al. 2005).

REFERENCES

Bertram, G. E. ( 1940). An Experimental Investigation of Protective Filters. Soil Mechanics Series No, Graduate School of Engg. Harvard University.

Hussain, B. (1981). A Physical Model for Rock Fill Behaviour. Proc., Vol. I, Con f. Geomech- 1981, Hyderabad.

Karpoff, K. P. ( 1955). The Usage of Laboratory Tests to Develop Design Criteria for Protective Filters. Proc., ASTM, 55, pp. 1183-1198.

Kawakamy and Esashi ( 1961) On Drainage Filters for Earth Structures. Abstract of Papers 16th Annu. Meet, Jap. Soc. Civil Engrg.

Lone, M. A. ( 1995) Design Criteria and Physical Behaviour of Protective Filters. Ph.D. Thesis, Faculty of Engineering, University of Kashmir, Sri nagar, India.

Lone, M. A., Hussain, B. and Asawa, G. L. (1996). Effect of Base Gradation on Filter Design. Proc., International Seminar on Civil Engineering Practices in 21 '' Century, Roorkee, pp. 1633-1642.

Lone, M.A., Hussain, B. and Asawa, G. L. (2005). Filter Design Criteria for Graded Cohesionless Bases. Jr. of Geotechnical and Geoenvironmental Engineering, ASCE, 131(2), pp. 251-259.

Sherard. J. L. ( l919).Sinkholes in Dams ofCoar.'ie. Brocully Graded Soils. Transactions 13'11 Conf. on large dams. New Delhi, Vol. 2.

Sherard, J. L., Dunnigan, L. P. and Talbot, J. P. ( 1984a). Basic Properties of Sand and Gravel Filters. J.Geotech. Engg; ASCE 110 (6), pp. 684-700.

Terzaghi, K. and Peck, R. B. ( 1961 ). Soil Mechanics in Engineering Practice. Fourth edition, Asia Publishing House, New Delhi.

Terzaghi, K. (1929). Effects of Minor Geological Details on the Safety of Dams. Technical publication 215, AIME.

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USCE (1987). Laboratory Tests on Granular Filters for Embankment Dams. Tech. Report GL-87-22, US Army Waterways Experiment Station, Vicksburg, Miss.

NOTATIONS

Cu = coefficient of uniformity of base d* = design controlling size

dK5 = 85% finer size of the base material

015 = 15% finer size of the filter material a = major axis of the particle b = intermediate axis of the particle c = minor axis of the particle W.G. = Well Graded U.G. = Uniformly Graded

= required base migration for development of filter action,

kf = permeability of filter material

kB = permeability of base material

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