Stability of non-cohesive Soils with respect to Internal Erosion

Stability of non-cohesive Soils with respect to Internal Erosion ICSE6-17 M.F. AHLINHAN 1, M. ACHMUS 2, S. HOOG 1, E. K. WOUYA 3 1 IMPaC Offshore Engineering, Hamburg, Germany, Hohe Bleichen 5, 2354 Hamburg, e-mail: marx.ferdinand.ahlinhan@impac.de; sven.hoog@impac.de 2 Institute for Geotechnical Engineering, Leibniz University Hannover, Germany, Appelstr. 9A, 3167 Hannover, e-mail: achmus@igth.uni-hannover.de 3 University of Lokossa, Benin, e-mail: woukesta@yahoo.fr Finer grains can pass through the pores of the coarse soil matrix due to seepage flow in non-cohesive soil. This phenomenon called internal instability or suffusion can occur in or under dams, dikes or barrages. To assess whether suffusion is possible, in general the composition of the soil and the geometry of the pore channels have to be considered. Internal erosion is only possible if the grains of the fine soil can migrate through the pores of the coarse soil matrix. Since the pore channel geometry cannot be exactly measured, the assessment is based on the grain size distribution only. If the geometric criterion yields the result that suffusion is possible, i.e. the soil is potentially unstable, the minimum hydraulic gradient necessary to cause erosion and to transport the fine soil grains has to be assessed by a hydraulic criterion. Kezdi (1979) proposed splitting up the grain size distribution of a soil into two distributions of the fine and coarse parts, and assessing the stability by Terzaghi s well-known contact erosion criterion applied to the two distributions. However, it is not clear at which point the grain size distribution curve should be split up. In the present paper an analytical approach to assess the critical split-off point is proposed. The results of experimental investigations regarding internal instability depending on the grain size distribution, the initial relative density of the sample and the seepage flow direction are presented and discussed. A clear dependence on an instability index derived from the grain size distribution of the soils is obtained. Finally, a combined geometric-hydraulic criterion regarding the design with respect to internal instability in noncohesive soils is suggested. Key words Internal erosion, stability, instability index, sand, suffusion. I INTRODUCTION Non-cohesive soils under the influence of seepage flow can exhibit a behavior in which grains of finer fraction pass through the pores of the coarse soil matrix. The phenomenon is termed internal instability, internal erosion or suffusion and can occur in natural soil deposits and also in geotechnical structures such as dams or barrages. Whether internal instability is geometrically possible, depends on the distribution of constriction sizes in the soil matrix. Practically the determination of constriction size distributions is not possible. Instead, the grain size distribution is used for the assessment, since the constriction sizes correlate with the grain sizes. Instability criteria basing only on the grain size distribution are termed geometric criteria. In case that according to geometric criteria suffusion is potentially possible, hydraulic criteria are used to assess whether suffusion actually occurs under the hydraulic gradients acting on the soil. For instance, the criterion of Istomina cited in Busch et al. (1993) gives critical hydraulic gradients for vertical upward seepage flow depending on the coefficient of uniformity of the soil. In practical design, usually keeping the geometrical criteria is desired in order to avoid any risk of suffusion processes. Kenney and Lau (1985) proposed transforming the ordinary grain size distribution curve to a F-H diagram. Here F is the mass percentage of grains with diameters less than a particular grain diameter d and H is the mass percentage of grains with diameters between d and 4d. Poorly graded soils with 329

the minimum value of H/F 1. for F.3 and well graded soils with the minimum value of H/F 1. for F.2 are assumed as stable (Kenney and Lau 1986). Kezdi (1979) proposed splitting up the grain size distribution of a soil into two distributions of the fine and coarse parts, and assessing the stability by Terzaghi s well-known filter criterion applied to the two distributions: d d (1) c, 15 4 f,85 with d c,15 = grain diameter for which 15% of the grains by weight of the coarse soil are smaller and d f,85 = grain diameter for which 85% of the grains by weight of the fine soil are smaller. A question with respect to the Kezdi criterion is at which point the grain size distribution should be split up. II APPROACH TO ASSESS THE SPLIT-UP POINT OF THE GRADING CURVE Theoretical considerations were made in order to define the point at which the split-up of the grain size distribution should be carried out. In general, the grain size distribution might be splitted up at several points. For the illustration of the splitting up approach in Fig. 1 two points T 1 and T 2 have been exemplary considered. The steeper the grading curve, the smaller is the distance b between fine and coarse fraction obtained from the splitting up of the grain size distribution curve at a point T (Fig. 1). A maximum distance b represents the worst case for the geometric stability of the soil. The slope β between a horizontal axis and the grading curve at the split-off point T can be expressed with the Equation 2. H tan β = (2) log 4d log d Here d is the particle diameter at the split-off point T, F the mass fraction of particles smaller than d and H the mass fraction of particles between d and 4d. H and F are the parameters used in the Kenney and Lau criterion. If b is maximal, β is minimal, and then H also becomes minimal. Therefore, it is proposed to use T at (H/F) min as the split-up point. The associated filter quotient is denoted as a modified filter or instability index (d 15f /d 85b ) mod. The point (H/F) min represents a "weak point" for the soils and is therefore relevant for the assessment of its geometric stability. The newly defined instability index was used in the evaluation of experiments regarding internal stability of non-cohesive soils. Figure 1: Illustration of the splitting up approach. III EXPERIMENTS Five different non-cohesive soils (Fig. 2) were tested in a specially developed test device under vertical upward seepage flow (Fig. 3) and under horizontal seepage (Fig. 4). The hydraulic gradient was increased slowly and gradually in order to identify the critical gradient at which erosion begins. The initial relative density of the soils was varied in the tests. Details regarding soil properties, sample preparation, execution and evaluation of the tests can be found in Ahlinhan and Achmus (21, 211) and Ahlinhan (211). 33

Figure 2: Grain size distributions of the soils used in the experiments. Figure 3: Test device for vertical upward seepage flow. Figure 4: Test device for horizontal seepage flow. 331

The experimentally determined hydraulic gradients for vertical upward flow and horizontal flow are given in Fig. 5, depending on the initial relative density and the instability index of the soil samples. The relative density is defined here with respect to the porosity of the soil: nmax n D = (3) n n max min Here n max and n min are the porosities at the loosest and the densest states, respectively, determined in the respective laboratory tests. For poorly graded soils suffusion is not an issue. Instead, hydraulic failure might occur under vertical upward seepage flow. According to Terzaghi (see e.g. Terzaghi and Peck 1961), the respective critical gradient is i crit v γ ', = (4) γ W with γ = submerged unit weight of the soil and γ W = unit weight of water. For the poorly graded soil A1 the obtained critical vertical gradients agree quite well with the theoretical values according to Equation 4. In fact, slightly lower values were found with a maximum deviation of about 1%, which might be a result of unavoidable heterogeneities of the samples. For the clearly gap graded soils E2 and E3 suffusion occurred at very small critical vertical gradients between.18 and.23. There is only a small dependence on the relative density of the sample. The comparison between the critical vertical gradient and the critical horizontal gradient shows that the critical horizontal gradient is always smaller than the critical vertical gradient at the same relative density of the sample, probably due to the effect of gravity. However, the greater the instability index (d 15f /d 85b ) mod, the lower is the discrepancy between the critical vertical and horizontal gradients. For the investigated soils, the critical horizontal gradient is about 6% up to 9% of the critical vertical gradient. In Fig. 5 three zones can be distinguished, the stable zone, in which no transportation of particles occurs, the unstable zone and the transition zone. In the latter, it depends on the relative density of the soil whether erosion occurs or not. The hydraulic criterion after Istomina for non-uniform soils (uniformity index U>25) is also plotted in Fig 5. It can be seen, that the limit line of Istomina s criterion lies in the transition zone, possibly due to the use of the uniformity index only without considering the relative density. Critical hydraulic gradient i crit [1] 1..8 A1 D=.75.6 D=.58 D=.5.4.2 D=.92 D=.75 D=.5 unstable D=.25 E1 D=.7 D=.85 D=.59 D=.45 D=.4 stable D=.6 D=.5 E2 D=.6 D=.85 D=.31 D=.41 vertical tests horizontal tests Transition zone for stable soils Transition zone for unstable soils Limit for U > 25 after Istomina (1957) E5 D=.85 D=.95 D=.75 D=.76 4 8 12 16 2 Instability index (d /d ) [1] 15f 85b mod Figure 5: Dependence of the critical hydraulic gradient on the instability index (d 15f /d 85b ) mod. The geometric criteria after Kézdi (1979) and Kenney and Lau (1985) are depicted in Fig. 6 and our own test results and the test results of several authors regarding the internal stability of soils are presented. Fig. 6 shows that all soils with points lying above the Kenney and Lau (1986) line are stable and all soils with points lying below the Kezdi line are unstable. Soils with points lying in the transition zone (H > F <.15 and.15 < H < F) can obviously be either stable or unstable. 332

H Mass fraction of particles between d and 4d [1].5.4.3.2.1 (c) (a) stable E1 A1 A2.83.71 Kenney et Lau (1986) H = F Kezdi (1979) H =.15 (b) unstable E2 E5.1.2.3.4.5 F Mass fraction of particles smaller than d [1] Figure 6: Compilation of the test results in combined Kezdi (1979) and Kenney and Lau (1986) criterion. (d) stable unstable Author Own tests Adel (1988) Kenney and Lau (1985) Burenkova (1993) Honjo et al. (1996) Skempton (1994) Moffat et al. (26) Li and Fannin (28) Lafleur (1984) Wan and Fell (28) IV SUGGESTION OF A COMBINED GEOMETRIC-HYDRAULIC CRITERION Internal stability depends on geometric conditions (resistance side), i.e. on the composition of the soil matrix, and also if erosion is geometrically possible on hydraulic conditions (effect side). Thus, the use of combined geometrical and hydraulic criteria may be appropriate to assess the stability of non-cohesive soils with respect to internal erosion. Such a combined approach is useful, because potentially unstable soils are often used in practice for economic reasons. Therefore a combined geometric-hydraulic criterion for non-cohesive soils presented in Figs. 7 and 8 based on our own tests and on the experimental data of several authors is proposed for practical use. In fact, the diagrams are derived by combining the Figs. 5 and 6 shown before. The basis of the combination of the two graphs is that H=.15 for (d 15f /d 85b ) mod = 4, the other values of H have been calculated to match with (d 15f /d 85b ) mod. The use of the diagrams shall be elucidated by two examples: Example 1 (see Fig. 7): For the fine sand A1 the instability index (d 15f /d 85b ) mod = 1.31 and (H/F) min = 5.93 with F =.14, H =.83. By plotting the H and F values in Figure 7 it is found that the fine sand A1 lies in the stable zone, so the material can be considered as geometrically stable. To determine the critical vertical gradient for A1, the representative point in the F-H graph and the ordinate (d 15f /d 85b ) mod = 1.31 are connected by means of a straight line. Depending on the relative density D, the critical vertical gradient i crit,v is found by normal projection on the horizontal axis. For instance, assuming a relative density D =.25 the critical vertical gradient is i crit,v =.7, which agrees well with the experimental results. Example 2 (see Fig. 8): The instability index (d 15f /d 85b ) mod for soil E2 is.2 and (H/F) min is 7.2 (where H =.15 and F =.3). The plotting in the H-F graph shows that soil E2 lies in the unstable zone and is therefore to be considered as unstable. To estimate the vertical hydraulic gradient under which erosion of the fine grains of soil E2 is to be expected, the representative point for E2 in the H-F-graph and the ordinate (d 15f /d 85b ) mod = 7.2 are connected by a straight line (see Fig. 8). Then the vertical hydraulic gradient i crit,v =.18 at relative density D =.4 is obtained, which again agrees well with the experimental results. 333

H Mass fraction of particles between d and 4d [1] 1..8.6.4.2 A1 A2 (a) stable (c) Kenney et Lau (1986) H = F Kezdi (1979) H =.15 Critical vertical gradient i crit,v [1] i crit,v =.7 1.2.8.4 A2 A1 D =.25 D =.5 D =.75 D =.95 (c) (b) unstable stable unstable Author Own tests.2.4.6.8 1. Adel (1988) F Mass fraction of particles smaller Kenney et Lau(1985) than d [1] Burenkova (1993) Honjo et al. (1996) Skempton (1994) Moffat et al. (26) Li et Fannin (28) Lafleur (1984) Wan et Fell (28) Figure 7: Combined geometric-hydraulic criterion for poorly graded non-cohesive soils. 1 1.31 2 3 4 Instability index (d 15f /d 85b ) mod [1] H Mass fraction of particles between d and 4d [1].6.5.4.3.2 A1 A2.83.71 (a) stable Kenney et Lau (1986) H = F (b) unstable Kezdi (1979).1 E1 H =.15,3 E2 E5.1.2.3.4.5.15 F Mass fraction of particles smaller than d [1] stable unstable Critical vertical gradient i crit,v [1] i crit,v =.18.6.4.2 E1 D =.7 lower limit Author Own tests Adel (1988) Kenney et Lau(1985) Burenkova (1993) Honjo et al. (1996) Skempton (1994) Moffat et al. (26) Li et Fannin (28) Lafleur (1984) Wan et Fell (28) upper limit E2 D =.4 E5 D =.95 4 7,2 8 12 16 Instability index (d 15f /d 85b ) mod [1] Figure 8: Combined geometric-hydraulic criterion for well graded and gap graded non-cohesive soils. 334

V CONCLUSIONS The assessment of soils with respect to stability against internal erosion is still a difficult task. A number of geometric criteria exist and might be used. However, for certain soils different results can be obtained. A new value (d 15f /d 85b ) mod derived from the H-F-presentation and the split-up of a grain size distribution to distinguish the fine and the coarse portions is proposed to be used in the assessment of potential instability. Experimental tests and also tests reported in literature show that this value is suitable for use to distinguish stable and unstable soils. The test results also show that in a transition zone the hydraulic gradients leading to erosion are strongly depending on the relative density of the soil. The tests reported here show that for clearly unstable soil, i.e. with values (d 15f /d 85b ) mod >4, the critical hydraulic gradient for vertical upward flow lies around.2 with only a slight influence of the initial relative density. Also the critical horizontal gradient is about 6% up to 9% of the vertical one at the same initial relative density. New design charts, which combine geometric and hydraulic criteria, are derived from the experimental results. By these charts, an assessment whether a soil is potentially unstable and an estimation of the critical hydraulic gradient for the onset of erosion is obtained. In that, the H-F representation of the grain size distribution and the newly defined value (d 15f /d 85b ) mod are applied. The approach gives good agreement with the own experimental findings. However, more investigations are needed to refine this combined geometric and hydraulic criterion. At the time being, it should only be used for soils similar to the soils investigated here. VI ACKNOWLEDGMENTS This research was partially supported by the German Ministry of Education and Research through IPSWaT (International Postgraduate Studies in Water Technologies). This support is gratefully acknowledged. VII REFERENCES AND CITATIONS Ahlinhan, M.F. (211) - Untersuchungen zur inneren Erosionsstabilität nichtbindiger Böden. Mitteilungen des Instituts für Geotechnik, Leibniz Universität Hannover, Heft 72 (in German). Ahlinhan M. F. and Achmus, M. (211) - Discrete Element Modeling of Stress Condition in Unstable Soils, 2 nd International Symposium on Computational Geomechanics, Croatia, 27-29 April, pp. 262-271. Ahlinhan M. F. and Achmus, M. (21) - Experimental Investigation of Critical Hydraulic Gradients of Unstable Soils, Proceedings of the Fifth International Conference on Scour and Erosion, San Francisco, USA, pp. 599-68. Adel, H. den, Bakker, K.J. and Breteler, M.K. (1988) - Internal stability of minestone, Proc. Int. Symp. Modelling Soil-Water-Structure Interaction, pp.225-231. Rotterdam, Balkema. BAW (1989) - Bundesanstalt für Wasserbau Merkblatt Anwendung von Kornfiltern an Wasserstraßen (MAK), Ausgabe 1989 (in German). Burenkova, V.V. (1993) - Assessment of suffusion in non-cohesive and graded soils, Filters in Geotechnical and Hydraulic Engineering, ed. Brauns, Heibaum and Schuler, pp. 357-36. Busch, K.-F., Luckner, L. and Tiemer, K. (1993) - Geohydraulik: Lehrbuch der Hydrologie, 3rd ed., Gebrüder Borntraeger, Berlin / Stuttgart (in German). Honjo, Y., Haque, M.A. and Tsai, K.A. (1996) - Self-filtration behavior of broadly and gap graded cohesionless soils. Geofilters 96, Montreal/Canada. Kenney, T.C. and Lau, D. (1985) - Internal stability of granular filters, Canadian Geotechnical Journal, Vol. 22, pp. 215 225. Kenney, T.C. and Lau, D. (1986) - Internal stability of granular filters: Reply, Canadian Geotechnical Journal, Vol. 23, pp. 42-423. Kezdi, A. (1979) - Soil physics. Elsevier Scientific Publishing Company, Amsterdam. 335

Lafleur, J. (1984) - Filter testing of broadly graded cohesionless tills, Canadian Geotechnical Journal, Vol. 21, pp. 634-643. Li, M. and Fannin, R.J. (28) - Comparison of two criteria for internal stability of granular soil, Canadian Geotechnical Journal, Vol. 45, pp. 133 139. Moffat, R.A. and Fannin, R.J. (26) - A large permeameter for study of internal stability in cohesionless soils, Geotechnical Testing Journal, Vol. 29. No.4, pp. 273-279. Skempton, W. and Brogan, J.M. (1994) - Experiments on piping in sandy gravels, Géotechnique No. 3, pp. 449 46. Terzaghi, K. and Peck, R.B. (1961) - Die Bodenmechanik in der Baupraxis, Springer Verlag, Berlin, 1961 (in German). Wan, C.F. and Fell, R. (28) - Assessing the potential of internal instability and suffusion in embankment dams and their foundations, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 134, No. 3, pp. 41-47. 336