USSD_2014 Sangho Lee

United States Society on Dams

Dams and Extreme Events —Reducing Risk of Aging

Infrastructure under ExtremeLoading Conditions

34th Annual USSD Conference

San Francisco, California, April 7-11, 2014

Probabilistic Constriction Size Application 395

PROBABILISTIC CONSTRICTION SIZE APPLICATION FOR EARTH DAM/LEVEE FILTER DESIGN

Sangho Lee, Ph.D., P.E.1Samuel S. Lee, Ph.D.2

ABSTRACT

Authors introduced a probabilistic model to relate filter/base soil grain size distribution (GSD) and relative density with the filter/base soil constriction size distribution (CSD) in ICOLD 2013. The maximum fine particle size susceptible to piping (backward erosion) was probabilistically assessed from given GSD of base soil, also minimum conduit size of filter, deciding whether the eroded fine particles to be retained within or migrate through the filter was assessed with the probabilistic model. This paper will guide and demonstrate how the probabilistically estimated CSD of base soil and filter can be utilized in selection of filter GSD to achieve better earth dam/levee filter performance in view of both retention and drainage purposes. Percentage of fines erodible from base soil, clogging potential of chimney filter and optimum constriction size of filter were evaluated and compared with exemplary base soil and filter material appeared on FEMA dam filter design manual (2011).

INTRODUCTION

The internal stability of granular soil structure has been investigated in depth by Kenney and Lau (1985) and Lafleur et al (1990). Their research focused on developing criteria for the internal stability of soil when seepage or vibration is applied. According to Kenney and Lau (1985), non-cohesive soils are internally stable if their GSD is such that H>1.3 FD, where FD is the cumulative weight fraction relative to a particle size, D, and H=F4D–FD. The reason of using H=F4D–FD as the characteristic particle size interval was that, in a stable granular soil, predominant constrictions of the void network are approximately four times smaller than the small particles (Kenney et al, 1985). The resulting granular filter design criterion, D5 < 4 d50 or D15 < 5 d50 for soils with Cu < 6 is more conservative than Terzaghi’s (1922) suggestion using a base soil size of d85 instead of d50 on the granular filter.

In connection with granular filter design for broadly graded soils Lafleur et al (1990) took into account the bridging effect (i.e. self-filtration) which may exist also in this case. As the screen test results indicated that the thickness of the self-filtration zone was proportional to the constriction size (Dc) of the granular filter, the authors suggested the granular filter constriction size should be between d50 and d80 for linearly graded base soil, and within the gap range in the case of gap-graded soil. It was also noted that, in absence of vibration, particle interlocking might contribute to limiting the loss of fines.

1 Senior Engineer, GESTRA Engineering Inc., Milwaukee, WI, Tel) 414-933-7444, Fax) 414-933-7844, e-mail: [email protected] 2 Civil Engineer F.E.R.C., Dam Safety and Inspections, San Francisco, CA, Tel) 1-415-369-3393, e-mail: [email protected]

396 Dams and Extreme Events

Particle size uniformity (as represented, for instance, by the coefficient of uniformity Cu=D60/D10) can affect soil retention. This property plays a role in filter design through the ratio Of/Dl where Of is the largest constriction size of the filter and Dl is the largest size of particle retained. Watson and John (1999) studied the effect of Cu on particle bridging (or filter cake). They investigated which were the largest constriction sizes compatible with stable granular bridging structures, for different cases of particle size gradation. They assumed a spherical particle shape and tested their model on the basis of the ratio, O90/D90. They found that the uniformity coefficient (Cu) influences the smallest size of the particles that can form the granular bridging structure, and that particles smaller than 0.228 Of are not associated with bridging formations regardless of the soil grain size uniformity. In general, as Cu increases, the ratio O90/D90 decreases. In practice, to prevent piping within earth dam structure, the largest constriction size of filter, Of,should be reduced when the soil is better graded. Giroud (1996) considered the selection of Of*/D85 should take into account the soil uniformity coefficient (Cu) and state of compaction. Three different density states of bridging granular structure were considered: hyperstable (Cu*=3), mesostable (Cu*=6.5) and hypostable (Cu*=13), where Cu* are the coefficients of uniformity, characteristic values related to soil internal stability. The relationship between Of and the finest size of bridging particles was derived for the cases where, Cu > Cu* and Cu ≤ Cu*. Both approaches outlined above show similar trends such as relatively high values of Of*/D85 obtained in dense conditions and relatively low values in loose conditions. However, neither model was based on consideration of actual particle size distributions. Instead, idealized linearly graded soils were assumed.

The effect of particle shape on soil retention performance had been investigated, but without clear, quantitative conclusions being reached. Aberg (1992) accounted for the particle shape in his investigation of void ratio for the various GSD types of soils. His experiments led to a linear relationship between the void ratio and the particle angularity.He also observed in compacted samples that the small grains were more angular than the large ones because, during sample preparation, compaction work had produced particle breakage. Lafleur et al (1990) suggested that the angularity of fines particles in soil contributes to making the thicker - granular bridge formation in successful filtration cases. In connection with this idea, when actual soil was tested in comparison with glass beads, the later yielded lower critical ratio, O95/D85, and amount of piping which was more sensitive to the filter constriction size when the ratio is close to its critical value (Bhatia and Huang, 1995).

METHODOLOGY AND ANALYSIS APPROACH

Filter and base soil constriction sizes were reasonably evaluated based on soil/filter grain size distribution and its compaction degree using a proposed probabilistic approach as the detail derivation process was described at the same author’s paper in ICOLD 2013. Piping potential of fine particle size was also evaluated using a renormalization technique. In the paper, the fine particles, smaller than 28.2 % of cumulative constriction distribution (CSD) of base soil, are susceptible to internal backward erosion or piping by associate seepage flow. After the fine particle internal erosion, grain size distribution of the base soil will change from the original shape by loss of the eroded fine particles.


Figure 1 presents the grain size distribution (GSD) change of an internally unstable soil which can be differentiated by initial compaction degree. Therefore, grain size distribution of unstable soils can easily change by small vibration under gravity due to the nature of self-segregation process. Beside the soil internal stability, the fine particle erosion can be driven by underlying filter material constriction size. In the case, all fine particles smaller than a constriction size of 0.282 cumulative filter CSD will be migrated through the filter material. This soil GSD change adjacent to filter material will produce the CSD change of base soil retained above filter, which will impact on the subsequent fine particle migration process of upper soils at up-gradient.

Figure.1 (a) Relationship between Forward Passing Probability, F(p) versus Passing Probability for a Particle Size, p derived from Renormalization Method (b) Soil CSD Estimated from an Unstable Soil GSD with a Model Parameter (R.D.) Presenting Soil

Relative Density and Associated GSD Changes after Segregation.

A simulation model capable of tracing the subsequent changes of grain and constriction size distribution from the fine particle migration associated with opening size of wire screen or constriction size distribution of granular filter can be proposed. The simulation model also can trace the percentage net gain or loss of fine particle weight relative to original base soil unit weight at each sub-layer.

Figure 2 Typical Cross Section of Successful Self-filtration Soil Structure


Figure 2 shows a typical cross section of established self-filtration structure (alternatively called a filter cake) and Figure 3 shows a flow chart, describing the internal calculation process of the simulation model.

Figure 3 Flow Chart of Soil Self-filtration Process Simulation Model

Total weight, W of fine particles eroded from base soil can be calculated with following formula. Basic principle presumed the initial weight fraction of largest particle is invariant throughout the soil sub-layer during fine particle migration.

−==

m

i

kkk jmGjmGjiGjiGjW1

00 ),()),(/),((),()( )()()()()( (1)

where G(k)(i,j) is the weight fraction of volume based GSD for the i th particle size range at the j th layer above the filter interface in the k th infiltration stage based on the largest particle size range, m.

Total weight of eroded fine particles is directly related to filter opening or constriction size, relative density of base soil and site hydraulic gradient condition. Pore space of filter material should be sufficient to prevent these fine particles eroded from the base soil from blocking the pore space until upper fines erosion is suppressed by the self-filtration structure, generally established above or within filter interface. The limited accessibility of filter material openings, reduced by entrapment of the eroded fines can deter drainage function of filter material which prevents the seepage inside embankment from raising groundwater level. Thus, weight fraction of base soil fine particles, corresponding to


constriction size range of 0.282 to 1.0 of filter CSD can be related to the fines entrapped inside filter and the filter drainage performance after the partial clogging.

PROBABILISTIC FILTER DESIGN EXAMPLES

Federal Emergency Management Agency (FEMA) published “Filters for Embankment Dams, Best Practice for Design and Construction” in 2011. This manual contains useful information of effective filter design to minimize piping potential of existing or new earth dam, embankment or levee, consisted of variously graded core and down-stream shell material under different site conditions (hydraulic condition, foundation soil type and treatment, toe drain system equipment and etc.). As detailed process of current filter design is conceptually well explained in the document, this paper will more focus on demonstrating how estimated constriction sizes of base soil and filter can contribute to improve the existing filter design.

EXAMPLE CASE I – EVALUATION OF SELF-FILTRATION POTENTIAL

Figure 4 presents a base soil gradation after regarding below #4 sieve (which is from the example problem used in FEMA manual (Pabst et al, 2011).

Figure 4 Filter Grain Size Distributions Compared to Example 1 Base Soil (after FEMA, 2011)

Two filter gradations, satisfying both retention and permeability criteria, can be suggested for a well graded base soil presented in Figure 4. As current filter design is purely based on 15% particle size of base soil passing #4 sieve, various filter gradation is still allowed as long as it meets a uniformity criterion (Cu = D60/D10 < 6) to avoid particle segregation during filter installation. However, we don’t know yet what mechanism exists behind different filter performances expected from the various gradations of filter. Probabilistic model, proposed in ICOLD 2013 can examine variation of GSD within the base soil in response to filter constriction size.


Internal stability of base soil can impact its GSD change even under a low hydraulic gradient or small vibration because fine particles of the base soil are prone to migrate through the larger constrictions available in well graded or gap graded soil. The internal stability of compacted base soil could be evaluated with a graphical method, suggested by Kenney and Lau (1985). If a relationship between F and H (F4D-FD) of based soil GSD is located below H=1.3F line until F=0.2, the base soil can be classified as internally unstable. Internally stable soil produced relatively small amount of fine particle migration, and internally unstable soil produced relative large amount of fine particle migration even the base soils were sufficiently compacted (Kenney and Lau, 1985). Authors applied this graphical method to check internal stability of Example 1 base soil as shown in Figure 5 (a) so that we can conclude Example 1 soil is classified as internally unstable soil even if initially compacted.

A probabilistic model also can examine this internal stability check with setting up no particle migration allowed through the base layer which will produce self-filtered or self-segregated GSD, evaluated at each sub-layer number (a higher number indicates upper soil layer from the base at down-gradient), which can be indirectly identified with net weight gain or loss at each sub-layer using Equation (1) as shown in Figure 5 (b). Authors used the probabilistic model to estimate the internal stability of Example 1 base soil assumed with different initial compaction degrees. Figure 5 (b) indicates internal stability of base soil is significantly influenced by the initial compaction degree beside the shape of base soil GSD as more severe fine particle migration was predicted at each sub-layer in a low relative density (R.D.=0.1) compared to a high relative density case (R.D.=0.9).

Figure 5 (a) Examination of Internal Stability of Example 1 Base Soil Using Graphical Method Proposed by Kenney and Lau (1985) (b) Self-segregation Prediction of Example

1 Base Soil, Differentiated by Initial Compaction Degree Parameter of Probabilistic Model


Figure 6 indicates calculated CSDs of Filters 1 and 2, the GSD of which are presented in Figure 4 and compare with GSD of Example 1 base soil. Using a constriction size corresponding to 0.282 CSD of Filters 1 and 2 as the estimation was graphically described in Figure 1, base soil GSD change, resulted from fine particle migration through filter could be assessed.

Figure 6 Comparison of Example 1 Base Soil GSD and Filter 1 and 2 CSDs and GSD Change at Filter Interface after 1st Migration of Fine Soil through Filter

Figure 7 Simulated Fine Particle Migration in Example 1 Base Soil and Associated GSD changes at Each Sub-layer by (a) Filter 1 and (b) Filter 2 (lower sub-layer number indicates closer to filter layer) with a Different Initial Compaction Degree of Base Soil


In Figure 7, different behaviors of fine particle migration within Example 1 base soil were predicted by application of two candidate filter GSDs even both of them satisfy all filter design criteria (retention, permeability and a uniform gradation) required in FEMA manual (2011). Even up and down stream shell material were fully compacted, the compacted base soil can be loosened from arching effect near dam abutment and post-settlement at underlying foundation soil. For a well compacted base soil (R.D.=0.9), both Filters 1 and 2 produced a GSD close to original base soil GSD at the upper most sub-layer 5 even though significant fine particle loss predicted at the sub-layer 1 closest to filter interface. However, Filters 1 and 2 produced a very different performance in filter retention function to suppress fine particle migration through the base soil for the loosened shell condition (R.D.=0.1). Filter 1 successfully produced a filter cake within the base soil to suppress migrating fines effectively whereas Filter 2 seems incapable of producing the self-filtration process within the loosened base soil which is clearly compared in Figure 8.

Figure 8 Simulated Fine Particle Migration at Different Sub-layer Level (lower number indicating closer to filter layer) and (a) Successful Filter Cake Formation versus (b)

Persistent Fines Erosion within Example 1 Base Soil after Filter 1 and Filter 2 Application, Respectively.


In consideration of the filter CSD and GSD change at the interface layer in Figure 6, Filter 1 CSD seems likely to produce a more internal migration of fine particles within the base soil due to the larger constriction sizes compared to Filter 2. However, in order to prevent potential piping or backward erosion within base soil, internally unstable soil like Example 1 base soil needs selection of Filter 1, consisting of constriction size greater than Filter 2, which failed to form a filter cake within Example 1 base soil from probabilistic model as shown in Figures 7 and 8. Therefore, the proposed probabilistic model using filter and base soil CSD can contribute in selection of the best optimized filter gradation especially for loosened dam base soil among candidate filter GSDs satisfying current FEMA filter design criteria (Pabst et al, 2011).

EXAMPLE CASE II– EVALUATION OF FILTER CLOGGING POTENTIAL

FEMA filter manual (2011) suggests using double filter layer in case well graded single filter cannot be installed in embankment chimney or toe trench to prevent self-segregation potential during the filter installation or for other subsurface underdrain system structurally and hydro-geologically feasible. Most of double filter design are applied to fine soils or well graded soils showing a broad particle size distribution range.

Figure 9 GSD Comparison between Example 2 Base Soil and a Common Filter C33 and Aggregate No. 467 Selected for a Double Filter Layer System (after FEMA, 2011)


As both filters C33 and No. 467 have a uniform soil gradation, we can anticipate a self-healing process within the filter media which is not susceptible to any internal crack or ceiling cap generation or prompt to recover to original pore state if any damage is generated. In case of using this double filter/drainage layer, commonly applied for fine soils, retention performance of fine particles shall not be an issue because of fore-mentioned reasons but rather drainage performance or clogging potential of the filter media due to consistent fine particle introduction will be more applicable for the long term serviceability of filter.

The probabilistic model also predicted each filter layer helps facilitate self-filtration process within Example 2 base soil and C33 filter, which promptly suppress fine particle intrusion from the base soil at up-gradient. Figures10 and 11 present the GSD changes of the base soil and C33, above each the finer filter (C33) and the coarser filter (No. 467) and associated weight loss pattern at each sub-layer.

Figure 10 Fine Particle Migration Behavior of Example 2 Base Soil with Filter C33

Figure 11 Coarse Particle Migration Behavior of Filter C33 with Filter No. 467


The probabilistic model also can provide an analysis tool to estimate the long term drainage performance of filter in view of base soil GSD and filter CSD. Our previous study showed soil particles corresponding to 0.282 CSD of base soil or filter media is susceptible for piping through the coarser constrictions of base soil or filter. Filter C33 or No. 467 has no chance of self-erosion because no small particle is available below the 0.282 CSD of the uniformly graded filters. Thus, CSD of these internally stable filter media will not change from the self-erosion during service life but will be influenced by accumulation of fine particles within filter, transferred from the base soil at up-gradient.

Simulation result indicates small particles up to 72%wt. of Example 2 base soil are susceptible to migration through C33 constrictions as shown in Figure 12 (a). Fine particles smaller than 0.282 CSD of C33, introduced from the base soil at up-gradient will be persistently eroded through filter C33, total erosion of which can be up to 30%wt. of initial base soil unless the self-filtration or filter cake is generated within the base soil. Thus, a mass fraction up to 42 %wt. of Example 2 base soil corresponding to CSD range from 28.2% to 100% can be retained in filter C33 depending upon site hydraulic condition and actual compaction degree of base soil and filter. Figure 10 indicates self-filtration process is expected within Example 2 base soil if filtered with C33, and the erosion will be limited up to 40%wt. of the base soil. Therefore, long term drainage performance or clogging potential of C33 with respect to Example 2 base soil is considered relatively low based on above simulation results. Figure 12 (b) indicates no C33 particle intrusion is predicted within No. 467 since the particle size of C33 corresponding to 0.282 CSD of No. 467 is the largest matching to 100%wt of C33 GSD. This means all C33 particles are prone to migrate through No. 467 constrictions unless self-filtration process occurs within C33 which is also estimated in simulation result of Figure 11. Therefore, long term drainage performance of No. 467 is considered having a very low clogging potential by soils eroded from the base soil and filter C33.

Figure 12 Evaluation of Long Term Drainage Performance of (a) Filter C33 and (b) Filter No. 467 by Comparison of Mass Fractions of Base Soil Susceptible to Persistent Erosion

through Filter and Retention within Filter


CONCLUSION

Many possible gradations of dam filters can be designed especially for complicated base soil type, such as well graded soil or internally unstable soils even FEMA manual (2011) specifies three different categories of embankment filter design criteria (retention, drainage and segregation proof). Probabilistic model suggested by authors can envision internal process of filter cake formation within base soil related to filter retention performance and internal clogging process within filter related to filter drainage performance which are essential components of filter design on the problematic soils. Follow-up study in conjunction with additional laboratory or pilot scale test is still required to evaluate more accurate filter performance.

ACKNOWLEDGEMENTS

This research was performed as addendum part of the first author’s Ph.D. research titled “Filter Performance and Design for Highway Underdrain” published by FHWA/IN/JTRP 2005/1, May, 2006.

REFERENCES

Aberg, B. (1992) Void ratio of non-cohesive soils and similar materials, Journal of Geotechnical Engineering, ASCE, Vol. 11, No. 9, 1315-1334

Bhatia, S. K. and Huang, Q. (1995) Geotextile filters for internally stable/ unstable soils, Geosynthetics International, Vol. 2, No.3, 537-565

Giroud, J. P. (1996) Granular filters and geotextile filters, Geofilters ’96 Conference,Montreal, 565-680

Kenney, T. C., Chahal, R., Chiu, E., Ofoegbu, G. I., Omange, G. N., and Ume, C. A. (1985) Controlling constriction sizes of granular filters, Canadian Geotechnical Journal,22, 32-43

Kenney, T. C. and Lau, D. (1985) Internal stability of granular filters, CanadianGeotechnical Journal, 22, 215-225

Lafleur, J., Mlynarek, J. and Rollin, A.L. (1990) Filtration of broadly graded cohesionless soils, Journal of Geotechnical Engineering, Vol.115, No.12, 1747-1767

Pabst, M., McCook, D., Talbot, J., Hammer, D., Vroman, N. and Lee, L. (2011) Filters for Embankment Dams, Best Practice for Design and Construction, FEMA

Watson, P.D.J. and John, N.W.M. (1999) Geotextile filtration design and simulated bridge formation at the soil-geotextile interface, Geotextiles and Geomembranes,Elsevier, 17, 265-280

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