Paper Number XXX

DEFICIENCIES IN THE USE OF POST-LIQUEFACTION STRENGTH

Jian Chu School of Civil and Environmental Engineering, Nanyang Technological University, Singapore

Dariusz Wanatowski Nottingham Centre for Geomechanics, University of Nottingham, United Kingdom

ABSTRACT:

Loose sand can liquefy under either dynamic or static load. Liquefaction of sand or tailings leads to the failure of granular slopes or tailings dams. One of the design approaches adopted for granular slopes or tailings dams is to use the so-called post-liquefaction undrained shear strength. However, this post-liquefaction strength cannot be determined properly by laboratory tests. This leads to questions on the validity of the design approach using the post-liquefaction strength. In this paper, the deficiencies associated with the post-liquefaction strength approach for granular slopes or tailings dams are identified. An alternative approach using the conditions for instability is suggested.

1 INTRODUCTION

Flow failures in the form of a sudden loss of strength followed by a very rapid development of large deformations can occur for granular soil slopes or tailings dams. The effects of flow failure are often much more dramatic and devastating than other types of landslides as the failure can occur with little warning. Examples of such flow failures include Fort Peck Dam (Casagrande 1965), Helsinki Harbour (Andresen and Bjerrum 1976), Nerlerk berm (Sladen et al. 1985), Wachusett Dam (Olson et al. 2000), West Guide Bund failure in Bangladesh (Hight et al. 1999), and the failures of some tailings dams such as the Gypsum Tailings Impoundment at East Texas (Kleiner 1976) or the Merriespruit Tailings Dam in South Africa (Fourie et al. 2001). Most of these failures are often considered to be triggered by static liquefaction or instability of granular soils occurring under undrained conditions. Here, static liquefaction refers to a phenomenon in which loose sand loses a large percentage of its shear resistance and flows in a liquid manner when it is subjected to undrained monotonic loading and instability a behaviour in which large plastic strains are generated rapidly due to the inability of a soil element to sustain a given stress.

Liquefaction of sand is often described using the behaviour of loose sand under undrained conditions as shown in Fig. 1 (Davies et al. 2002). For the design of granular soil slopes or tailings dams, two ap-proaches, the effective stress analysis (ESA) and the undrained strength analysis (USA), have been adopted in practice. According to Martin and McRoberts (1998), in the ESA method, effective stresses during shear are assumed unchanged from those that existed immediately prior to the onset of shear. In other words, failure is calculated as the failure shear stress corresponds to the in-situ effective stresses using the effective failure envelope, at point F, as marked in Fig. 1a. This method may be applicable to dense, dilative soil where the excess pore pressure generated during shear is very small or negative. However, for loose, contractive soil where positive excess pore pressure is generated, this method is unconservative, as failure occurs at point P, not at point F, as shown in Fig. 1a. In the USA method, the undrained shear strength is defined as the residual strength, or the steady state strength, or the post-liquefaction strength, Sus, as shown in Fig. 1a. This approach is also called the steady state method (Poulos et al. 1985). As elaborated by Martin and McRoberts (1998), for contractive materials, design analyses must include both undrained strength analysis (USA) and effective stress analysis (ESA),

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with design controlled by the analysis type giving the lowest factor of safety. For dilative or fully drained materials, only ESA is required.

(a) (b)

Figure 1 Response of loose, saturated cohesionless tailings under monotonic and cyclic loading (after Davies et al. 2002)

However, the use of post-liquefaction strength as the residual strength is problematic. In this paper, the deficiencies related to the use of post-liquefaction strength are discussed. An alternative approach using the stress ratio of instability line that defines the instability condition for loose sand under both drained and undrained conditions or the peak strength ratio are suggested.

2. WHAT IS POST-LIQUEFACTION STRENGTH

Most of the studies on liquefaction of soil in the past are based on laboratory triaxial tests. When con-ducting a triaxial test, the axial load can be applied either in a load controlled or deformation con-trolled mode. The different loading mode may lead to different post-peak behaviour as explained in detail by Chu and Leong (2002). For the testing of very loose sand under undrained conditions, strain-softening occurs if the test is conducted under a deformation controlled loading mode, whereas insta-bility takes place if the test is conducted under a load controlled loading mode. The Sus should be measured from a test where the soil liquefies. By definition, liquefaction is a type of instability. There-fore, the tests to study post-liquefaction behaviour should be conducted under a load controlled load-ing modes. However, once a soil liquefies, the specimen collapses suddenly from the point where liq-uefaction is initiated, e.g., from the peak point P in Fig. 1a. Thus the stresses and strains in the post-peak region cannot be measured properly. The so-called post-liquefaction strength as illustrated in Fig. 1a is, in fact, measured as the post-peak strain softening behaviour for a test conducted under a defor-mation controlled loading mode, where the specimen does not collapse, but the shear stress is reduced gradually. Although the strength measured at the end of the test is taken as the residual or the “post-liquefaction strength”, liquefaction does not occur in this test. It has been demonstrated experimentally by Chu and Leong (2001) and Wanatowski and Chu (2007) that the post-peak behavior during strain softening and instability (or liquefaction) is quite different. Therefore, the Sus obtained from tests with strain softening may not be relevant to soil or tailings that liquefy. After liquefaction, a soil has com-pletely changed in terms of void ratio, stress histories, soil structures and fabrics. Thus the post-liquefaction strength can only be measured by testing liquefied soil, not on soil that has not liquefied before test.

The differences between the post-peak liquefaction and strain softening behaviour are further ex-plained in Fig. 2 where a comparison of two undrained plane-strain tests on two nearly identical loose sand specimens, but one conducted under load-controlled and another deformation-controlled loading mode is shown. It can be seen that after liquefaction occurred at the peak for Test U05L, the pore pres-sure increased suddenly and more than 15% strain developed within minutes. The specimen had col-

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lapsed and distorted. Therefore, the stress and strain measured after the specimen had collapsed did not represent an element behavior anymore. Hence, the post-liquefaction strength obtained from the load-controlled test is no longer meaningful. Even if a “strength” value is obtained, it is different from that determined from the deformation-controlled test. Therefore, the post-liquefaction strength ob-tained from a test exhibiting strain soften does not represent the “strength” of the soil after liquefac-tion. Thus, the post-liquefaction strength cannot be measured properly.

Figure 2 Behavior of undrained plane-strain tests on loose sand conducted under deformation con-trolled and load-controlled loading conditions.

The same conclusion can also be made from undrained triaxial tests. One example is given in Fig. 3 where the results of two undrained tests on loose sand are compared. It can be seen that the residual strength obtained for the deformation controlled loading test (where strain softening occurred) is dif-ferent from that under load controlled loading test (where liquefaction occurs).

3. DEFICIENCIES

The data and discussion presented in the preceding section have revealed several deficiencies in the post-liquefaction strength approach.

Firstly, the post-liquefaction strength cannot be determined properly or the value cannot be uniquely obtained. Therefore, the post-liquefaction strength will not be able to be used consistently in the de-sign. Fig. 1a shows that the post-liquefaction strength is on the CSL or the steady state line. The data shown in Fig. 2 have indicated further that the CSL obtained for axisymmetric conditions is different

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0 50 100 150 200 250Mean Effective Stress, p' (kPa)

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CSL (ηcs = 1.16)

Instability Line (ηIL = 0.89)

● Peak state

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from that under plane-strain conditions. Therefore, the post-liquefaction strength determined using tri-axial tests will not be able to be applied directly to slope stability design which are under plane-strain or three-dimensional conditions, even if a post-liquefaction strength is obtained.

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Figure 3 Behaviour of undrained triaxial tests on loose sand conducted under deformation controlled and load-controlled loading conditions (after Leong 2003).

Secondly, for granular soil or tailings with relatively large permeability, the assumption of “undrained” under static loading conditions may not be reasonable. There are cases where instability or static liquefaction occurred under essentially drained conditions. In a recent reanalysis of the Wa-chusett Dam failure in 1907, Olson et al. (2000) concluded that the failure was mainly triggered by static liquefaction that occurred under completely drained conditions. Through laboratory model tests, Eckersley (1990) observed that the pore water pressure increase in the gentle granular soil slope was a result, rather than the cause of flowslide. In other words, the flowslide took place under a drained con-dition. In these cases, failures appear to be triggered by a mechanism similar to static liquefaction al-though the drainage condition prior to failure is not undrained. In this case, the undrained post-liquefaction strength will no longer be relevant.

Experimentally, it has been shown by Chu et al. (2003) that instability can occur under drained condi-tion. One example on loose sand is shown in Fig. 4. When a specimen is sheared along a constant shear stress path with reduction in the mean stress under a drained condition, the specimen becomes unstable at point B (Fig. 4a) where the axial strain and axial strain rate increases rapidly (Fig. 4b and 4d). It should be noted that the instability occurs at a stress state far below the CSL. Therefore, the use of critical friction angle or the effective stress ratio at the steady state to the design of granular slope can be unconservative. It should be noticed that there is not any post-liquefaction strength as a result of drained instability because this test is conducted under a load controlled loading mode and the specimen becomes unstable rather than going through strain softening.

Thirdly, it has been demonstrated experimentally that instability or liquefaction of sand can occur under non-undrained, i.e., other than undrained conditions (Chu et al. 1993; Chu and Leong 2001). Failure mechanisms related to a redistribution of void ratio within a globally undrained sand layer (Fig. 5a) and spreading of excess pore pressure with global volume changes (Fig. 5b) have been envisaged by NRC (1985) as Mechanisms B and C, respectively. The possibility of dilating behaviour of soil masses prior to slope collapse is also observed in several case studies. Been et al. (1987) argued that the Nerlerk berm failure case might have occurred for dilative sand which lies below the steady state line. Several other cases of flow slide failure in dilative sand have also been presented by Been et al. (1988).

Load controlled

Deformation

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Figure 4 Instability of loose sand along a CSD path: (a) effective stress paths; (b) confining stress, ax-ial strain, and volumetric strain versus time curves; (c) axial and volumetric strains versus mean effec-

tive stress curves; and (d) strain rate versus time curve.

(a) (b)

Figure 5 Failure mechanisms identified by NRC (1985): (a). Mechanism B for the situation where void redistributes within a globally undrained sand layer; (b). Mechanism C for the situation where failure

is induced by spreading of excess pore pressure with global volume changes.

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4. INSTABILITY CONDITIONS

It is well established that when a loose sand specimen is sheared along an undrained path, an effective stress path as typically shown in Fig. 6 will be obtained. Point A is the peak of effective stress path. If the test is conducted under a deformation-controlled condition, strain-softening behaviour which is characterized by a reduction in deviator stress will manifest. On the other hand, if the test is conducted under a load-controlled condition, the specimen will become unstable at point A. The unstable behav-iour should be referred to as static liquefaction, not the strain-softening behaviour. The line connecting the top of the effective stress paths is termed as the instability line. The zone between the instability line and the failure line (or the critical state line) is called the zone of potential instability, as shown in Fig. 6 (Chu et al. 2003).

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a) CU21

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ec CU21 0.864 CU26 0.888 CU20 0.916 CU44 0.972 INS3 1.014

CU26

The instability line is not unique, but varies with the void ratio of sand and the applied effective mean stress. Fig. 7 shows the effective stress paths obtained from a series of isotropic consolidated undrained (CIU) tests conducted on specimens with different consolidation void ratios, ec, but under the same mean effective stress. It can be seen from Fig. 7 that the smaller the ec, the higher the insta-bility line. Fig. 7 also shows that the deviator stress in Tests CU26, CU20 and CU44 approached zero. Therefore, the post-liquefaction strength cannot be defined from these tests. For Test CU21, the post-liquefaction strength is as high as the peak. Note that the void ratio differences in Test CU26 and CU21 is only 0.024. Therefore, the post-liquefaction strength is very sensitive to the void ratio of the tested specimen. Hence, it is difficult to determine the post-liquefaction strength reliably even if it can be defined properly. This is another deficiency of the post-liquefaction strength approach.

Based on Fig. 7, a relationship between the slope of instability line and the consolidated void ratio of sand ec (which is equivalent to the in-situ void ratio for a slope) can be established as shown in Fig. 8 (Chu and Leong 2002). This relationship can be replotted into Fig. 9 using the state parameter Ψ to take the effect of stress level into consideration. In Fig. 9, the same relationship established under plane-strain conditions is also shown (Wanatowski and Chu 2007) for comparison. This relationship can be used to assess the stability of granular soil slopes or tailing dams. However, as the relationship established under axisymmetric conditions is different from that under plane-strain, the relationship established using triaxial tests will have to be converted before it can be used for plane-strain problems (Wanatowski and Chu 2007).

It should be pointed out that the relationships established in Figs. 8 or 9 are also applicable to instabil-ity under drained conditions, as discussed in detail by Chu et al. (2003). Therefore, these relationships can be used in slope stability analysis without specifying the drained or undrained conditions if the

A

Failure point from drained test

Zone of potential instability Critical state

line

Instability line

Figure 6. Instability line defined us-ing undrained tests.

Figure 7. Variation of instability line with void ratio

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mean stresses in the slope are reducing. For slopes under rain water infiltration or experiencing a re-duction in lateral stresses, the effective stress path can be idealized into a constant shear stress path (Chu et al. 2003). Knowing the state parameter of a soil element, the stress ratio or the slope of insta-bility line, ηIL, can be determined using Fig. 8. The ηIL can be converted into an effective stress friction angle. For example, for ψ = 0.1, ηIL = 0.63 under plane-strain conditions. This corresponds to a friction angle of 170, which can be considered as the liquefaction friction angle. As an approximation, the slope can then be designed with reference to this liquefaction friction angle. It should be noted that the liquefaction friction angle is smaller than the critical state friction angle.

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0.85 0.90 0.95 1.00Void Ratio, ec

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ine,

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Plane-strainTriaxial

5. CONCLUSIONS

Post-liquefaction undrained shear strength defined as the residual strength of an undrained test on loose sand, Sus, has been used for the design of granular soil slopes or tailings dams. However, this ap-proach is problematic as explained in the paper. The main deficiencies include that the Sus value can-not be determined properly and the assumption of an undrained condition is questionable for sand or tailings with relatively high permeability. An alternative method using the instability condition is sug-gested in which liquefaction friction angle is defined based on instability conditions. These conditions are applicable to liquefaction occurring under both drained and undrained conditions.

REFERENCES:

Andresen, A. and Bjerrum, L. 1976. Slides in subaqueous slopes in loose sand and silt. Proc. International Research Conference on Marine Geotechnique. University of Illinois Press, Chicago, 221-237.

Been, K., Conlin, B. H., Crooks, J. H. A., Fitzpatrick, S. W., Jefferies, M. G., Rogers, B. T. and Shinde, S. 1987. Back analysis of the Nerlerk berm liquefaction slides: Discussion. Can. Geotech. J., 24, 170-179.

Been, K., Crooks, J. H. A., Colin, B. H. and Horsfield, D. 1988. Liquefaction of hydraulically placed sand fills. Conference on Hydraulic Fill Structures, ASCE Geotechnical Special Publication 21, 330-345.

Casagrande, A. 1965. Role of calculated risk in earthwork and foundation engineering. J. Soil Mech. Found. Div., ASCE, 91(SM4), 1-40.

Chu, J. and Leong, W. K. 2001. Pre-failure strain softening and pre-failure instability of sand: a comparative study. Geotechnique, 51(4), 311-321.

Chu J. and Leong W. K. 2002. Effect of fines on instability behaviour of loose sand. Geotechnique, 52(10), 751-755.

Chu, J. Lo, S-C. R. and Lee, I. K. 1993. Instability of granular soils under strain path testing. J. Geotech. Eng., ASCE, 119(5), 874-892.

Chu, J., Leroueil, S. and Leong, W. K. 2003. Unstable behaviour of sand and its implications for slope instability. Can. Geotech. J., 40, 873-885.

Figure 8. Relationship between the slope of instability line and the void ratio of sand

Figure 9. Relationship between the slope of in-stability line and the state parameter

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Davies, M, McRoberts, E. C. and Martin, T. E. 2002. Static liquefaction of tailings – fundamentals and case histories. Proc. Tailings Dams 2002, ASDSO/USCOLD, Las Vegas.

Eckersley, J. D. 1990. Instrumented laboratory flowslides. Geotechnique, 40(3), 489-502.

Hight, D. W., Geogiannou, V. N., Martin, P. L. and Mundegar, A. K. 1999. Flow slides in micaceous sands, Problematic Soils, Yanagisawa, Moroto and Mitachi (eds), Balkema, Rotterdam, 945-958.

Kleiner, D.E. 1976. Design and construction of an embankment dam to impound gypsum wastes. In Proc. International Commission on Large Dams, 235-249.

Leong, W. K. (2003). Instability behavior of granular fill material. Ph.D. Thesis, Nanyang Technological University, Singapore.

Martin, T. E. and McRoberts, E. C. 1998. Some considerations in the stability analysis of upstream tailings dams, Tailings and Mine Waste ’99, Fort Collins, Colorado, 287-302.

National Research Council 1985. Liquefaction of soils during earthquakes. Committee on Earthquake Engineer-ing, Commission on Engineering and Technical Systems, USA.

Olson, S. M., Stark, T. D., Walton, W. H. and Castro, G. 2000. 1907 static liquefaction flow failure of the north dike of Wachusett dam, J. Geotech. Geoenv. Eng., ASCE, 126(12), 1184-1193.

Poulos, S. J., Castro, G. and France, J. W. 1985. Liquefaction evaluation procedure. J. Geotech. Eng., ASCE, 111(GT6), 772-792.

Sladen, J. A., D’Hollander, R. D., Krahn, J. and Mitchell, D. E. 1985. Back analysis of the Nerlerk berm liquefaction slides. Can. Geotech. J., 22, 579-588.

Wanatowski, D. 2005. Strain softening and instability of sand under plane-strain conditions. Ph.D. Thesis, Nanyang Technological University, Singapore.

Wanatowski, D. and Chu, J. 2007. Static liquefaction of sand in plane-strain. Can. Geotech. J. 44, 299-313.