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Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils
Soils and Foundations ]]]];](]):]]]–]]]
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Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils Yousif A.H. Dalloa, Yuan Wangb,n a
Hohai University, College of Water Conservancy & Hydropower Engineering, 1 Xikang Rd, Nanjing 210098, Jiangsu, PR China b Professor, College of Civil and Transportation Engineering, Hohai University, 1 Xikang Rd, Nanjing, PR China Received 25 February 2015; received in revised form 16 November 2015; accepted 18 December 2015
Abstract Internal instability is associated with geotechnical structures such as earth dams and dikes, and involves movement of fine loose particles through the voids of the main soil skeleton. In this study, some methods to determine the delimiting particle size (DPS) were critically reviewed. The accurate determination of the values of DPS and the diameter of the controlling constriction size (d cont: ) is essential for internal stability assessment. Here, a relationship is derived from the capillary tube model in order to determine the controlling constriction size, knowing that the diameter of the controlling constriction size should be smaller than the diameter of the loose fine particles to ensure the safety against internal stability. This derived relationship was verified with a large amount of data and it gave more accurate prediction than other methods. & 2016 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.
Keywords: Controlling constriction size; Capillary tube model; Internal stability; Granular soils
1. Introduction Internal instability problems are important issues in geotechnical engineering structures such as earth dams and dikes. They can lead to the improper functioning of the structures as a result of settlement or excessive seepage or even collapse of the engineering structures. Internal stability problems are associated with widely graded or gap-graded soils, where the soils are expected to have a bimodal structure. That is, the soil has a primary skeleton composed of the coarse soil particles, and among the voids of these particles, there are finer loose particles. The main soil particles can be distinguished from the loose particles by knowing the delimiting particle size DPS, which is the particle diameter at which the n Corresponding author. Peer review under responsibility of The Japanese Geotechnical Society.
grain size distribution curve (GSD) is split in to two components, primary the skeleton and fine loose particles. The loose particles are expected to wash out under the seepage forces if their diameter is less than the “controlling constriction size”, Kenney et al. (1985), which is the predominant constriction size among the soil particles, and it is correlated to the maximum particle size that can pass through a filter. Kenney et al. (1985) obtained some relationships to determine the controlling constriction size from experimental tests. Indraratna et al. (2007) suggested the controlling constriction size as Dc35, which is the diameter of constriction corresponding to finer ¼ 35%. Dallo et al. (2013) developed some relations to determine the controlling constriction size based on statistical analysis. Many methods are available to assess the internal stability of granular soils, among these are Kezdi (1979) and Kenney and Lau (1985, 1986). In the method developed by Kezdi (1979)
http://dx.doi.org/10.1016/j.sandf.2016.02.013 0038-0806/& 2016 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.
Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013
Y.A.H. Dallo, Y. Wang / Soils and Foundations ] (]]]]) ]]]–]]]
solid material intersected by a series of tubes. The average pore diameter, d 0 , of those tubes can be computed as d0 ¼ 4
n Dh ; 1 n αD
where n is the porosity of the soil; αD is a shape coefficient (αD ¼ 6 for rounded particles, αD ¼ 8 for angular particles); Dh is the Kozeny’s effective grain diameter, which can be computed as 1 Dh ¼ P F i ;
The capillary tube model, suggested by Kovacs (1981), envisioned the soil material and the voids among them as a
ð2Þ
Di
where F i is finer the percentage of particle Di . 3. Critical review of Li and Fannin (2013) method 3.1. Using Kenney and Lau method to determine delimiting particle size The KL method was originally suggested to assess the internal stability of cohesionless soils using the H/F ratio, which has a physical meaning related to the possibility that the small particles could be washed out (suffused) through the coarse skeleton of the soil. It seems that using the KL method to determine the delimiting particle size at the minimum H/F, as suggested by Li and Fannin (2013), has no clear physical meaning. Nevertheless, this suggestion requires comparison with some experimental tests to check its applicability and accuracy. An experimental test was provided by Binner et al. (2010) for the soil shown in Fig. 1. They found that the delimiting particle size is 4 mm at a fines percent of 23.5%. The delimiting particle size from the Li and Fannin's suggested method is 1.005 mm at F ¼ 16.2% as shown in Fig. 1. It is clear that there is a considerable difference between the computed value and the actual one. A reasonable method to determine the delimiting particle size was mathematically derived by Aberg (1992): R1 y R 1 dy 2c ya xðyÞ dy ya ya xðyÞ xa ¼ ; ð3Þ R 2c þ 1 þ 2d 1 dy 2 ya xðyÞ 4.0
100 90 80
3.0
70 60
H/F
50
GSD
2.0
40 30
actual F=23.5%
1.0
20 computed F=16.2%
10
computed delimiting size=1.005mm
0 0.1
2. Capillary tube model
ð1Þ
H/F
the grain size distribution curve (GSD) is divided by an arbitrary diameter to coarser and finer components. The coarser component acts as a filter and the finer component behave as a base material. Hence, the criterion D15 =d85 ¼ 4 proposed by Terzaghi (1939) could be employed to assess the stability. D15 is the diameter of the coarser component corresponding to 15% and d 85 is the diameter of the finer component corresponding to 85%. By the next step, another arbitrary diameter will be selected and the calculations are repeated. The soil is considered internally stable if Terzaghi’s criterion is fulfilled for the whole range of selected diameters. Kenney and Lau (1985, 1986) suggested a method (the KL method) to assess the internal stability based on the shape of the GSD curves of cohesionless soils. In this method, by determining the fines percent (F) corresponding to an arbitrary particle diameter (D), and the fines percent corresponding to the particle diameter (4D), the value of (H) can be easily calculated as the difference of the fines percent between D and 4D. The internal stability is determined by calculating the H/F ratios in the range of F r 20% for widely-graded soils, and by F r 30% for narrowly-graded soils. The soil is considered unstable if the ratio (H/F) lies below the stability boundary (H/ F ¼ 1.0). The method assumes that the maximum possible fines content (i.e. erodible particles) for the widely graded soils (with Cu 4 3) is 20% and for the narrowly graded soils (with Cu o 3) is 30%. For this reason the analysis is performed in the range of F o 20% or F o 30%. Li (2008) found out that the method of Kenney and Lau assesses the stability of “unstable gradations” correctly, while it provides a wrong assessment of some “stable gradations”. Accordingly, the method is conservative in evaluating the potential for internal stability. Li and Fannin (2013) suggested using the KL method to determine the delimiting particle size followed by using the capillary tube model, as suggested by Kovacs (1981), to determine the average pore size of the primary skeleton. The later value is to be compared with the diameter corresponding to finer¼ 85% of the fine loose particles, ́d85 , to assess the internal stability. Based on their results they suggested modifying the threshold boundary between stable and unstable soils. In this study, the method of Li and Fannin (2013) was critically discussed and it was found that the KL method produced unreliable results when determining the delimiting particle size. Also, it was shown that the threshold boundary between stable and unstable gradations based on the average pore diameter is questionable. In the light of this discussion, a new procedure of analysis was suggested to use the controlling constriction size rather than the average pore diameter. A new relationship for use in determining the controlling constriction size was developed from Kovacs model and the threshold boundary between internally stable and unstable soils. The latter relationship can be used to assess the internal stability of granular soils against suffusion.
Finer (%)
2
actual delimiting size=4mm
1.0
10.0
0.0 100.0
diameter (mm)
Fig.1. Grain size distribution of the soil tested by Binner et al. (2010), with the actual delimiting particle size and computed one according to the Li and Fannin method.
Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013
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where xa is the delimiting particle size with finer percent “ya”; c is a coefficient equal to 0.75 for sands and gravels; and d is a constant depending on the relative density “Rd” (d ¼ 0.18, for minimum relative density Rd ¼ 0 while d ¼ 0 for maximum relative Rd ¼ 1.0. For any other density d can be computed from interpolation as d ¼ 0.18*(1 Rd)). y is the percentage finer corresponding to a particle diameter x(y). Eq. (3) can be solved by a trial and error process. First, an arbitrary diameter xa1 is selected and its corresponding finer percent ya1 is obtained from the GSD curve. Second, the value of ya1 is substituted into Eq. (3) to obtain xa. If the difference between xa1 (the actual value) and xa (the computed value) is less than, say, 1% then the calculation process is stopped and the value of xa1 is considered as the delimiting particles size, otherwise another arbitrary diameter will be chosen and the above procedure is repeated. By applying Aberg’s method to the soil tested by Binner et al. (2010), we can obtain F¼ 22.2% which is very close to the actual value. The data from the experimental tests published by Burenkova (1993) were analyzed and the DPS were determined according to the Aberg method and the Li and Fannin method. A comparison between this data and the actual DPS is shown in Fig. 2. It can be seen that the Aberg method is a remarkably accurate predictor of the DPS, while the DPS values are underestimated when the Li and Fannin method is employed.
4. A New analysis procedure Based on the above discussion, we suggest a new analysis procedure, where a database of 32 soil gradations were reanalyzed, namely Kenney and Lau (1985), Skempton and Brogan (1994), Honjo et al. (1996), Moffat (2005), and Li (2008). The internal stability of the granular soils can be characterized in the laboratory by measuring the weight of the eroded fine soil particles, measuring the changes in their permeability, and measuring the changes in the grain size distribution curves before and after the experiments. Aberg’s method was employed to determine the delimiting particle size, then the average pore size of the main soil skeleton was determined using Kovacs (1981) equation [Eq. (1)], which is drawn against d 085 of the fines particles. The results are shown in Fig. 4. It is clear that all the internally stable and unstable soils are above the boundary threshold, suggesting to the authors that the value of d 085 of the fines soil must not be compared with the “average” pore diameter, but with the “controlling constriction size”. From inspection of Fig. 4, it can be seen that the values of d0 must be divided by some factor so that the data points will be around the internal stability threshold suggested by Kovacs. From a trial and error process it is found that if the values of d0 are divided by 2.75 then the internally stable and unstable soils will be located below and above the threshold boundary, respectively. Hence, the controlling constriction size d cont: can be expressed as dcont: ¼ d 0 =2:75;
3.2. The threshold boundary between stable and unstable gradations Li and Fannin (2013) found out that the threshold boundary between stable and unstable soils should be d0 ¼ 2:3d085 . This relation tells us that the average pore diameter must equal 2.3 times the d 085 of the fine particles to allow suffusion, see Fig. 3a. It seems that it is not a reasonable relationship. If a particle is being suffused out a filter, it must have a diameter less than the tube diameter, i.e. (d 0 =d085 4 1) as suggested by Kovacs (1981), see Fig. 3b.
3
ð4aÞ
or dcont: ¼ 1:4545
nc Dch 1 nc αD
ð4bÞ
where nc is the porosity of the coarse component and Dch is the Kozeny’s effective grain diameter of the coarse component. Fig. 5 shows the relationship between the controlling constriction size and d085 of the fines soil. It can be concluded that Eq. (4) is accurate. The internal stability assessment of 32 soils gave only two wrong predictions, and accuracy is approximately 94%.
100.0 according to Aberg method
5. Verification of the new procedure
Predicted DPS (mm)
according to Li and Fannin method
5.1. Controlling constriction size relation 10.0
To check the accuracy of Eq. (4), it is compared with some published relationships, namely, Kenney et al. (1985) and Dallo et al. (2013). Kenney et al. (1985) suggested two relations ((Eqs. (5) and 6)) to compute the controlling constriction size (dKenney cont: ) as
1.0
dKenney cont: ¼ 0:20 D15 ;
ð5Þ
or 0.1 0.1
1
10 Actual DPS (mm)
Fig. 2. The actual and the predicted values of DPS.
100
dKenney cont: ¼ 0:25 D5;
ð6Þ
where D5 and D15 are obtained from the GSD curve as the particles diameters corresponding to 5 and 15 finer percent,
Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013
Y.A.H. Dallo, Y. Wang / Soils and Foundations ] (]]]]) ]]]–]]]
4
Base soil particle
Solid material Capillary tube
100
average pore size (mm)
10
Unstable zone
K&L (Unstable)
1
K&L (Stable) Li (Unstable)
Li (Stable) Moffat (Unstable)
0.1
S&B (Unstable)
Stable zone
S&B (Stable) Honjo (Unstable) Honjo (Stable)
0.01 0.001
0.01
0.1
1
10
100
Grain size d' 85 (mm)
Fig. 4. Average pore size against d085 .
Controlling constriction size (mm)
100
10
1
0.1
0.01
Dallo et al. (2013) Kenny et al [Eq.(5)] Kenney et al [Eq.(6)]
0.001 0.1 1 0.001 0.01 10 Controlling constriction size (mm) [other methods]
and
K&L (Unstable) K&L (Stable)
dcont:ðLoosestÞ ¼ 0:437 D10 þ 0:114 D15 þ 0:008 D30 0:007 D60 0:015 D75 þ 0:007 D95 0:012:
Li (Unstable) Li (Stable) Moffat (Unstable)
0.1
S&B (Unstable)
Stable zone
S&B (Stable) Honjo (Unstable) Honjo (Stable)
0.01
10
Fig. 6. Comparison between Eq. (4) and Kenney et al. (1985) and Dallo et al. (2013) methods.
Unstable zone
1
0.01 0.001
Controlling constriction size (mm) [Eq.(4)]
Fig. 3. Suffused fine particle through the capillary tube (a) Li and Fannin (2013) (b) Kovacs (1981) criteria.
0.1
1
10
100
ð8Þ
Comparisons between Eq. (4) and the relation suggested by Kenney et al. (1985) and Dallo et al. (2013) are shown in Fig. 6 from which we can conclude that Eq. (4) is reasonable.
Grain size d'85 (mm)
5.2. Assessing the internal stability
Fig. 5. Controlling constriction size against d 085 of the finer soil.
respectively. Dx denotes the particle diameter corresponding to X finer percent. Dallo et al. (2013) suggested two relations ((Eqs.(7) and 8)) to compute the controlling constriction size at the densest state, dcont:ðDensestÞ and the loosest state, d cont:ðloosestÞ , as dcont:ðDensestÞ ¼ 0:177 D10 þ 0:007 D15 þ 0:003 D30 0:008 D60 þ 0:003 D95 þ 0:003;
ð7Þ
Fig. 5 can be used to assess the internal stability of granular soils. The boundary threshold between stable and unstable soils can be mathematically expressed as dcont: =d085 ¼ 1. For the purpose of comparison, the data base of 32 soil gradations were also assessed using the methods of Kezdi (1979), Kenney and Lau (1985), and Li and Fannin (2013). The results are shown in Table 1. In the case of Kezdi’s method, there are 9 incorrect predictions, whereas there are 5 wrong predictions in the case of Kenney and Lau’s method.
Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013
Y.A.H. Dallo, Y. Wang / Soils and Foundations ] (]]]]) ]]]–]]]
5
Table 1 Assessment of the internal stability employing Kezdi (1979), Kenney and Lau (1985), Li and Fannin (2013) and the new suggested method. ID
Reference
Gradation
d cont: =d085
Kezdi
Kenney and Lau
Li and Fannin
Current method
Laboratory assessment
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Skempton and Brogan (1994)
A B C D FR7 FR8 HF01 HF03 HF05 HF10 A As X Y Ys Ds 1 2 3 20 21 23 G1-a G1-b G3-a G3-b G4-a G4-b C-20 C-30 T-5 T-0
2.48 1.14 0.99 0.93 1.70 1.81 1.87 2.97 1.45 1.45 1.41 0.98 1.17 1.05 1.34 0.59 0.60 0.77 1.05 0.81 0.68 0.03 0.72 0.86 1.17 1.37 1.38 1.98 182.13 198.97 5.65 5.91
U U U U U U U U U U S S U U U S U U U S S S U U U U U U U U U U
U T S S U U U U U S T T U U U S S S S S S S T T U U U U U U U U
U U U S U U U U U U U U U U U U S S S S S S S S U U U U U U U U
U U S S U U U U U U U S U U U S S S U S S S S S U U U U U U U U
U U S S U U U U U S U S U U U S S S S S S S S S U U U U U U U U
Li (2008)
Kenny and Lau (1985,1986)
Honjo et al. (1996)
Moffat (2005)
(1) U ¼Unstable, S¼ Stable, and T ¼Transition.
When the Li and Fannin (2013) method was used, there are 4 wrong predictions. The new suggested method has only 2 wrong predictions. It can be seen that the new method is more accurate than the other methods. Soils that are predicted as unstable using the current method are expected to show signs of internal instability in the field also, such as the excessive seepage of water due to increments in permeability, and the formation of cavities due to the loss of fines soil particles. Eventually, this may result in the partial or complete failure of the structures.
6. Summary and conclusions
Using the KL method to determine the delimiting particle size is not very accurate. The controlling constriction size can be obtained from the capillary tube model, Eq. (4). The results of the new relation are reasonable when they are compared with the predictions of the other methods. The internal stability threshold for cohesionless soils should be expressed as dcont: =́d 85 ¼ 1. In other words, the predominant constriction (controlling constriction size) should
be smaller than the diameter of the loose fine particles to ensure the safety against internal instability. Internal stability can be assessed, with good accuracy, based on the internal stability threshold and the suggested relation to determine the controlling constriction size.
Acknowledgment The research was supported by the National Natural Science Foundation of China (no. 51179060), 973 Program (no. 2013CB036003), the Education Ministry Foundation of China (no. 20110094130002), and in part, supported by the Program for Changjiang Scholars and Innovative Research Team in University (no. IRT1125), the 111 Project (no. B13024) of China. References Aberg, B., 1992. Void ratio of noncohesive soils and similar materials. J. Geotech. Eng. 118 (9), 1315–1333. Binner, R., Homberg, U., Prohaska, S., Kalbe, U., Witt, K.J., 2010. Identification of Descriptive Parameters of the Soil Pore Structure using Experiments and CT Data. In: Proceedings of the Fifth International Conference on Scour and Erosion, American Society of Civil Engineers. pp. 397–407.
Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013
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Y.A.H. Dallo, Y. Wang / Soils and Foundations ] (]]]]) ]]]–]]]
Burenkova, V.V., 1993. Assessment of Suffosion in Non-cohesive and Graded Soils. Filters in Geotechnical and Hydraulic Engineering. Balkema, Rotterdam357–360. Dallo, Y.A.H., Wang, Y., Ahmed, O.Y., 2013. Assessment of the internal stability of granular soils against suffusion. Eur. J. Environ. Civil Eng. http://dxdoi.org/10.1080/19648189.2013.770613. Honjo, Y., Haque, M.A., Tsai, K.A., 1996. In: Geofilters’96, J., Lafleur, Rollin, A. (Eds.), Self-Filtration Behavior of Broadly and Gap-Graded Cohesionless Soils. Bitech Publications, Montreal. Indraratna, B., Raut, A.K., Khabbaz, H., 2007. Constriction-based retention criterion for granular filter design. J. Geotech. Geoenviron. Eng. 133 (3), 266–276. Kenney, T., Chahal, R., Chiu, E., Ofoegbu, G., Omange, G., Ume, C., 1985. Controlling constriction sizes of granular filters. Can. Geotech. J. 22 (1), 32–43. Kenney, T.C., Lau, D., 1985. Internal stability of granular filters. Can. Geotech. J. 22 (2), 215–225. Kenney, T.C., Lau, D., 1986. Internal stability of granular filters: Reply. Can. Geotech. J. 23 (3), 420–423. Kezdi, A., 1979. Soil Physics. Elsevier Scientific, Amsterdam, The Netherlands.
Kovacs, G., 1981. Seepage Hydraulics. Elsevier Scientific, Amsterdam, Netherlands. Li, M., 2008. Seepage induced instability in widely graded soils (Ph.D. thesis). Department of Civil Engineering, The University of British Columbia, Vancouver. Li, M., Fannin, R., 2013. Capillary tube model for internal stability of cohesionless soil. J. Geotech. Geoenviron. Eng. 139 (5), 831–834. Moffat, R., 2005. Experiments on the internal stability of widely graded cohesionless soils (Ph.D. thesis). Department of Civil Engineering, The University of British Columbia, Vancouver. Skempton, A.W., Brogan, J.M., 1994. Experiments on piping in sandy gravels. Geotechniqué 44 (3), 449–460. Terzaghi, K., 1939. Soil mechanics: a new chapter in engineering science. J. Inst. Civ. Eng. 12, 106–141.
Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013
HOSTED BY
The Japanese Geotechnical Society
Soils and Foundations www.sciencedirect.com journal homepage: www.elsevier.com/locate/sandf
Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils Yousif A.H. Dalloa, Yuan Wangb,n a
Hohai University, College of Water Conservancy & Hydropower Engineering, 1 Xikang Rd, Nanjing 210098, Jiangsu, PR China b Professor, College of Civil and Transportation Engineering, Hohai University, 1 Xikang Rd, Nanjing, PR China Received 25 February 2015; received in revised form 16 November 2015; accepted 18 December 2015
Abstract Internal instability is associated with geotechnical structures such as earth dams and dikes, and involves movement of fine loose particles through the voids of the main soil skeleton. In this study, some methods to determine the delimiting particle size (DPS) were critically reviewed. The accurate determination of the values of DPS and the diameter of the controlling constriction size (d cont: ) is essential for internal stability assessment. Here, a relationship is derived from the capillary tube model in order to determine the controlling constriction size, knowing that the diameter of the controlling constriction size should be smaller than the diameter of the loose fine particles to ensure the safety against internal stability. This derived relationship was verified with a large amount of data and it gave more accurate prediction than other methods. & 2016 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.
Keywords: Controlling constriction size; Capillary tube model; Internal stability; Granular soils
1. Introduction Internal instability problems are important issues in geotechnical engineering structures such as earth dams and dikes. They can lead to the improper functioning of the structures as a result of settlement or excessive seepage or even collapse of the engineering structures. Internal stability problems are associated with widely graded or gap-graded soils, where the soils are expected to have a bimodal structure. That is, the soil has a primary skeleton composed of the coarse soil particles, and among the voids of these particles, there are finer loose particles. The main soil particles can be distinguished from the loose particles by knowing the delimiting particle size DPS, which is the particle diameter at which the n Corresponding author. Peer review under responsibility of The Japanese Geotechnical Society.
grain size distribution curve (GSD) is split in to two components, primary the skeleton and fine loose particles. The loose particles are expected to wash out under the seepage forces if their diameter is less than the “controlling constriction size”, Kenney et al. (1985), which is the predominant constriction size among the soil particles, and it is correlated to the maximum particle size that can pass through a filter. Kenney et al. (1985) obtained some relationships to determine the controlling constriction size from experimental tests. Indraratna et al. (2007) suggested the controlling constriction size as Dc35, which is the diameter of constriction corresponding to finer ¼ 35%. Dallo et al. (2013) developed some relations to determine the controlling constriction size based on statistical analysis. Many methods are available to assess the internal stability of granular soils, among these are Kezdi (1979) and Kenney and Lau (1985, 1986). In the method developed by Kezdi (1979)
http://dx.doi.org/10.1016/j.sandf.2016.02.013 0038-0806/& 2016 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.
Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013
Y.A.H. Dallo, Y. Wang / Soils and Foundations ] (]]]]) ]]]–]]]
solid material intersected by a series of tubes. The average pore diameter, d 0 , of those tubes can be computed as d0 ¼ 4
n Dh ; 1 n αD
where n is the porosity of the soil; αD is a shape coefficient (αD ¼ 6 for rounded particles, αD ¼ 8 for angular particles); Dh is the Kozeny’s effective grain diameter, which can be computed as 1 Dh ¼ P F i ;
The capillary tube model, suggested by Kovacs (1981), envisioned the soil material and the voids among them as a
ð2Þ
Di
where F i is finer the percentage of particle Di . 3. Critical review of Li and Fannin (2013) method 3.1. Using Kenney and Lau method to determine delimiting particle size The KL method was originally suggested to assess the internal stability of cohesionless soils using the H/F ratio, which has a physical meaning related to the possibility that the small particles could be washed out (suffused) through the coarse skeleton of the soil. It seems that using the KL method to determine the delimiting particle size at the minimum H/F, as suggested by Li and Fannin (2013), has no clear physical meaning. Nevertheless, this suggestion requires comparison with some experimental tests to check its applicability and accuracy. An experimental test was provided by Binner et al. (2010) for the soil shown in Fig. 1. They found that the delimiting particle size is 4 mm at a fines percent of 23.5%. The delimiting particle size from the Li and Fannin's suggested method is 1.005 mm at F ¼ 16.2% as shown in Fig. 1. It is clear that there is a considerable difference between the computed value and the actual one. A reasonable method to determine the delimiting particle size was mathematically derived by Aberg (1992): R1 y R 1 dy 2c ya xðyÞ dy ya ya xðyÞ xa ¼ ; ð3Þ R 2c þ 1 þ 2d 1 dy 2 ya xðyÞ 4.0
100 90 80
3.0
70 60
H/F
50
GSD
2.0
40 30
actual F=23.5%
1.0
20 computed F=16.2%
10
computed delimiting size=1.005mm
0 0.1
2. Capillary tube model
ð1Þ
H/F
the grain size distribution curve (GSD) is divided by an arbitrary diameter to coarser and finer components. The coarser component acts as a filter and the finer component behave as a base material. Hence, the criterion D15 =d85 ¼ 4 proposed by Terzaghi (1939) could be employed to assess the stability. D15 is the diameter of the coarser component corresponding to 15% and d 85 is the diameter of the finer component corresponding to 85%. By the next step, another arbitrary diameter will be selected and the calculations are repeated. The soil is considered internally stable if Terzaghi’s criterion is fulfilled for the whole range of selected diameters. Kenney and Lau (1985, 1986) suggested a method (the KL method) to assess the internal stability based on the shape of the GSD curves of cohesionless soils. In this method, by determining the fines percent (F) corresponding to an arbitrary particle diameter (D), and the fines percent corresponding to the particle diameter (4D), the value of (H) can be easily calculated as the difference of the fines percent between D and 4D. The internal stability is determined by calculating the H/F ratios in the range of F r 20% for widely-graded soils, and by F r 30% for narrowly-graded soils. The soil is considered unstable if the ratio (H/F) lies below the stability boundary (H/ F ¼ 1.0). The method assumes that the maximum possible fines content (i.e. erodible particles) for the widely graded soils (with Cu 4 3) is 20% and for the narrowly graded soils (with Cu o 3) is 30%. For this reason the analysis is performed in the range of F o 20% or F o 30%. Li (2008) found out that the method of Kenney and Lau assesses the stability of “unstable gradations” correctly, while it provides a wrong assessment of some “stable gradations”. Accordingly, the method is conservative in evaluating the potential for internal stability. Li and Fannin (2013) suggested using the KL method to determine the delimiting particle size followed by using the capillary tube model, as suggested by Kovacs (1981), to determine the average pore size of the primary skeleton. The later value is to be compared with the diameter corresponding to finer¼ 85% of the fine loose particles, ́d85 , to assess the internal stability. Based on their results they suggested modifying the threshold boundary between stable and unstable soils. In this study, the method of Li and Fannin (2013) was critically discussed and it was found that the KL method produced unreliable results when determining the delimiting particle size. Also, it was shown that the threshold boundary between stable and unstable gradations based on the average pore diameter is questionable. In the light of this discussion, a new procedure of analysis was suggested to use the controlling constriction size rather than the average pore diameter. A new relationship for use in determining the controlling constriction size was developed from Kovacs model and the threshold boundary between internally stable and unstable soils. The latter relationship can be used to assess the internal stability of granular soils against suffusion.
Finer (%)
2
actual delimiting size=4mm
1.0
10.0
0.0 100.0
diameter (mm)
Fig.1. Grain size distribution of the soil tested by Binner et al. (2010), with the actual delimiting particle size and computed one according to the Li and Fannin method.
Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013
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where xa is the delimiting particle size with finer percent “ya”; c is a coefficient equal to 0.75 for sands and gravels; and d is a constant depending on the relative density “Rd” (d ¼ 0.18, for minimum relative density Rd ¼ 0 while d ¼ 0 for maximum relative Rd ¼ 1.0. For any other density d can be computed from interpolation as d ¼ 0.18*(1 Rd)). y is the percentage finer corresponding to a particle diameter x(y). Eq. (3) can be solved by a trial and error process. First, an arbitrary diameter xa1 is selected and its corresponding finer percent ya1 is obtained from the GSD curve. Second, the value of ya1 is substituted into Eq. (3) to obtain xa. If the difference between xa1 (the actual value) and xa (the computed value) is less than, say, 1% then the calculation process is stopped and the value of xa1 is considered as the delimiting particles size, otherwise another arbitrary diameter will be chosen and the above procedure is repeated. By applying Aberg’s method to the soil tested by Binner et al. (2010), we can obtain F¼ 22.2% which is very close to the actual value. The data from the experimental tests published by Burenkova (1993) were analyzed and the DPS were determined according to the Aberg method and the Li and Fannin method. A comparison between this data and the actual DPS is shown in Fig. 2. It can be seen that the Aberg method is a remarkably accurate predictor of the DPS, while the DPS values are underestimated when the Li and Fannin method is employed.
4. A New analysis procedure Based on the above discussion, we suggest a new analysis procedure, where a database of 32 soil gradations were reanalyzed, namely Kenney and Lau (1985), Skempton and Brogan (1994), Honjo et al. (1996), Moffat (2005), and Li (2008). The internal stability of the granular soils can be characterized in the laboratory by measuring the weight of the eroded fine soil particles, measuring the changes in their permeability, and measuring the changes in the grain size distribution curves before and after the experiments. Aberg’s method was employed to determine the delimiting particle size, then the average pore size of the main soil skeleton was determined using Kovacs (1981) equation [Eq. (1)], which is drawn against d 085 of the fines particles. The results are shown in Fig. 4. It is clear that all the internally stable and unstable soils are above the boundary threshold, suggesting to the authors that the value of d 085 of the fines soil must not be compared with the “average” pore diameter, but with the “controlling constriction size”. From inspection of Fig. 4, it can be seen that the values of d0 must be divided by some factor so that the data points will be around the internal stability threshold suggested by Kovacs. From a trial and error process it is found that if the values of d0 are divided by 2.75 then the internally stable and unstable soils will be located below and above the threshold boundary, respectively. Hence, the controlling constriction size d cont: can be expressed as dcont: ¼ d 0 =2:75;
3.2. The threshold boundary between stable and unstable gradations Li and Fannin (2013) found out that the threshold boundary between stable and unstable soils should be d0 ¼ 2:3d085 . This relation tells us that the average pore diameter must equal 2.3 times the d 085 of the fine particles to allow suffusion, see Fig. 3a. It seems that it is not a reasonable relationship. If a particle is being suffused out a filter, it must have a diameter less than the tube diameter, i.e. (d 0 =d085 4 1) as suggested by Kovacs (1981), see Fig. 3b.
3
ð4aÞ
or dcont: ¼ 1:4545
nc Dch 1 nc αD
ð4bÞ
where nc is the porosity of the coarse component and Dch is the Kozeny’s effective grain diameter of the coarse component. Fig. 5 shows the relationship between the controlling constriction size and d085 of the fines soil. It can be concluded that Eq. (4) is accurate. The internal stability assessment of 32 soils gave only two wrong predictions, and accuracy is approximately 94%.
100.0 according to Aberg method
5. Verification of the new procedure
Predicted DPS (mm)
according to Li and Fannin method
5.1. Controlling constriction size relation 10.0
To check the accuracy of Eq. (4), it is compared with some published relationships, namely, Kenney et al. (1985) and Dallo et al. (2013). Kenney et al. (1985) suggested two relations ((Eqs. (5) and 6)) to compute the controlling constriction size (dKenney cont: ) as
1.0
dKenney cont: ¼ 0:20 D15 ;
ð5Þ
or 0.1 0.1
1
10 Actual DPS (mm)
Fig. 2. The actual and the predicted values of DPS.
100
dKenney cont: ¼ 0:25 D5;
ð6Þ
where D5 and D15 are obtained from the GSD curve as the particles diameters corresponding to 5 and 15 finer percent,
Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013
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4
Base soil particle
Solid material Capillary tube
100
average pore size (mm)
10
Unstable zone
K&L (Unstable)
1
K&L (Stable) Li (Unstable)
Li (Stable) Moffat (Unstable)
0.1
S&B (Unstable)
Stable zone
S&B (Stable) Honjo (Unstable) Honjo (Stable)
0.01 0.001
0.01
0.1
1
10
100
Grain size d' 85 (mm)
Fig. 4. Average pore size against d085 .
Controlling constriction size (mm)
100
10
1
0.1
0.01
Dallo et al. (2013) Kenny et al [Eq.(5)] Kenney et al [Eq.(6)]
0.001 0.1 1 0.001 0.01 10 Controlling constriction size (mm) [other methods]
and
K&L (Unstable) K&L (Stable)
dcont:ðLoosestÞ ¼ 0:437 D10 þ 0:114 D15 þ 0:008 D30 0:007 D60 0:015 D75 þ 0:007 D95 0:012:
Li (Unstable) Li (Stable) Moffat (Unstable)
0.1
S&B (Unstable)
Stable zone
S&B (Stable) Honjo (Unstable) Honjo (Stable)
0.01
10
Fig. 6. Comparison between Eq. (4) and Kenney et al. (1985) and Dallo et al. (2013) methods.
Unstable zone
1
0.01 0.001
Controlling constriction size (mm) [Eq.(4)]
Fig. 3. Suffused fine particle through the capillary tube (a) Li and Fannin (2013) (b) Kovacs (1981) criteria.
0.1
1
10
100
ð8Þ
Comparisons between Eq. (4) and the relation suggested by Kenney et al. (1985) and Dallo et al. (2013) are shown in Fig. 6 from which we can conclude that Eq. (4) is reasonable.
Grain size d'85 (mm)
5.2. Assessing the internal stability
Fig. 5. Controlling constriction size against d 085 of the finer soil.
respectively. Dx denotes the particle diameter corresponding to X finer percent. Dallo et al. (2013) suggested two relations ((Eqs.(7) and 8)) to compute the controlling constriction size at the densest state, dcont:ðDensestÞ and the loosest state, d cont:ðloosestÞ , as dcont:ðDensestÞ ¼ 0:177 D10 þ 0:007 D15 þ 0:003 D30 0:008 D60 þ 0:003 D95 þ 0:003;
ð7Þ
Fig. 5 can be used to assess the internal stability of granular soils. The boundary threshold between stable and unstable soils can be mathematically expressed as dcont: =d085 ¼ 1. For the purpose of comparison, the data base of 32 soil gradations were also assessed using the methods of Kezdi (1979), Kenney and Lau (1985), and Li and Fannin (2013). The results are shown in Table 1. In the case of Kezdi’s method, there are 9 incorrect predictions, whereas there are 5 wrong predictions in the case of Kenney and Lau’s method.
Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013
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5
Table 1 Assessment of the internal stability employing Kezdi (1979), Kenney and Lau (1985), Li and Fannin (2013) and the new suggested method. ID
Reference
Gradation
d cont: =d085
Kezdi
Kenney and Lau
Li and Fannin
Current method
Laboratory assessment
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Skempton and Brogan (1994)
A B C D FR7 FR8 HF01 HF03 HF05 HF10 A As X Y Ys Ds 1 2 3 20 21 23 G1-a G1-b G3-a G3-b G4-a G4-b C-20 C-30 T-5 T-0
2.48 1.14 0.99 0.93 1.70 1.81 1.87 2.97 1.45 1.45 1.41 0.98 1.17 1.05 1.34 0.59 0.60 0.77 1.05 0.81 0.68 0.03 0.72 0.86 1.17 1.37 1.38 1.98 182.13 198.97 5.65 5.91
U U U U U U U U U U S S U U U S U U U S S S U U U U U U U U U U
U T S S U U U U U S T T U U U S S S S S S S T T U U U U U U U U
U U U S U U U U U U U U U U U U S S S S S S S S U U U U U U U U
U U S S U U U U U U U S U U U S S S U S S S S S U U U U U U U U
U U S S U U U U U S U S U U U S S S S S S S S S U U U U U U U U
Li (2008)
Kenny and Lau (1985,1986)
Honjo et al. (1996)
Moffat (2005)
(1) U ¼Unstable, S¼ Stable, and T ¼Transition.
When the Li and Fannin (2013) method was used, there are 4 wrong predictions. The new suggested method has only 2 wrong predictions. It can be seen that the new method is more accurate than the other methods. Soils that are predicted as unstable using the current method are expected to show signs of internal instability in the field also, such as the excessive seepage of water due to increments in permeability, and the formation of cavities due to the loss of fines soil particles. Eventually, this may result in the partial or complete failure of the structures.
6. Summary and conclusions
Using the KL method to determine the delimiting particle size is not very accurate. The controlling constriction size can be obtained from the capillary tube model, Eq. (4). The results of the new relation are reasonable when they are compared with the predictions of the other methods. The internal stability threshold for cohesionless soils should be expressed as dcont: =́d 85 ¼ 1. In other words, the predominant constriction (controlling constriction size) should
be smaller than the diameter of the loose fine particles to ensure the safety against internal instability. Internal stability can be assessed, with good accuracy, based on the internal stability threshold and the suggested relation to determine the controlling constriction size.
Acknowledgment The research was supported by the National Natural Science Foundation of China (no. 51179060), 973 Program (no. 2013CB036003), the Education Ministry Foundation of China (no. 20110094130002), and in part, supported by the Program for Changjiang Scholars and Innovative Research Team in University (no. IRT1125), the 111 Project (no. B13024) of China. References Aberg, B., 1992. Void ratio of noncohesive soils and similar materials. J. Geotech. Eng. 118 (9), 1315–1333. Binner, R., Homberg, U., Prohaska, S., Kalbe, U., Witt, K.J., 2010. Identification of Descriptive Parameters of the Soil Pore Structure using Experiments and CT Data. In: Proceedings of the Fifth International Conference on Scour and Erosion, American Society of Civil Engineers. pp. 397–407.
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Burenkova, V.V., 1993. Assessment of Suffosion in Non-cohesive and Graded Soils. Filters in Geotechnical and Hydraulic Engineering. Balkema, Rotterdam357–360. Dallo, Y.A.H., Wang, Y., Ahmed, O.Y., 2013. Assessment of the internal stability of granular soils against suffusion. Eur. J. Environ. Civil Eng. http://dxdoi.org/10.1080/19648189.2013.770613. Honjo, Y., Haque, M.A., Tsai, K.A., 1996. In: Geofilters’96, J., Lafleur, Rollin, A. (Eds.), Self-Filtration Behavior of Broadly and Gap-Graded Cohesionless Soils. Bitech Publications, Montreal. Indraratna, B., Raut, A.K., Khabbaz, H., 2007. Constriction-based retention criterion for granular filter design. J. Geotech. Geoenviron. Eng. 133 (3), 266–276. Kenney, T., Chahal, R., Chiu, E., Ofoegbu, G., Omange, G., Ume, C., 1985. Controlling constriction sizes of granular filters. Can. Geotech. J. 22 (1), 32–43. Kenney, T.C., Lau, D., 1985. Internal stability of granular filters. Can. Geotech. J. 22 (2), 215–225. Kenney, T.C., Lau, D., 1986. Internal stability of granular filters: Reply. Can. Geotech. J. 23 (3), 420–423. Kezdi, A., 1979. Soil Physics. Elsevier Scientific, Amsterdam, The Netherlands.
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Please cite this article as: Dallo, Y.A.H., Wang, Y., Determination of controlling constriction size from capillary tube model for internal stability assessment of granular soils. Soils and Foundations (2016), http://dx.doi.org/10.1016/j.sandf.2016.02.013