Undrained shear strength of clean sands to trigger flow liquefaction

Transcription

1 891 Undrained shear strength of clean sands to trigger flow liquefaction M. Yoshimine, P.K. Robertson, and C.E. (Fear) Wride Abstract: This paper attempts to evaluate the undrained shear strength of sand during flow failures, based on both laboratory testing and field observations. In the laboratory, the minimum shear resistance during monotonic loading was taken as the undrained strength, based on the criterion of stability. Triaxial compression, triaxial extension, and simple shear test data on clean sand were examined and it was revealed that the undrained shear strength ratio could be related to the relative density of the material provided that the initial stress, p i, was less than 500 kpa. Three previous flow failures involving sand layers with relatively low fines contents and reliable cone penetration test (CPT) data were studied. Using existing calibration chamber test results, the Toyoura sand specimen densities in the laboratory tests were converted to equivalent values of CPT penetration resistance. The undrained shear strengths measured in the laboratory for Toyoura sand were compared with those from the case studies. It was found that the behaviour of sand in simple shear in the laboratory was consistent with the field performance observations. Triaxial compression tests overestimated the undrained strengths, and triaxial extension tests underestimated the undrained strengths. From both the simple shear test result and the CPT field data, the threshold value of clean sand equivalent cone resistance for flow failure was detected. Based on these observations, a CPT-based guideline for evaluating the potential for flow failure of a clean sand deposit is proposed. Key words: liquefaction, flow, laboratory testing, in situ test, case histories. Résumé : Cet article tente d évaluer la résistance au cisaillement du sable durant les ruptures par écoulement en se basant tant sur des essais en laboratoire que sur des observations en nature. Dans le laboratoire, la résistance au cisaillement minimum durant le chargement monotone a été prise comme étant la résistance au cisaillement non drainé, en partant du critère de stabilité. Les données d essais de compression et d extension triaxiales et d essais de cisaillement simple sur du sable propre ont été examinées et il est apparu que le rapport de résistance au cisaillement non drainé pouvait être relié à la densité relative du matériau à la condition que la contrainte initiale p i soit inférieure à 500 kpa. L on a étudié trois coulées antérieures impliquant des couches de sable ayant des teneurs en particules fines relativement faibles et comportant des données de CPT fiables. En utilisant les résultats disponibles d essais en chambre de calibrage, les densités de spécimens du sable de Tayoura dans des essais en laboratoire ont été converties en valeurs équivalentes de résistance à la pénétration au CPT. Les résistances au cisaillement non drainé mesurées en laboratoire pour le sable de Tayoura ont été comparées avec les études de cas. L on a trouvé que le comportement du sable en cisaillement simple en laboratoire était consistant avec les observations de performance en nature. Les essais de compression triaxiale ont surestimé les résistances non drainées, et les essais triaxiaux en extension ont sous-estimé les résistances non drainées. En partant du résultat de l essai en cisaillement simple et des données de CPT de terrain, l on a identifié une valeur limite de résistance équivalente au cône pour la rupture par écoulement du sable propre. En se basant sur ces observations, l on a proposé des règles pour évaluer au moyen du CPT le potentiel de coulée d un dépôt de sable propre. Mots clés : liquéfaction, écoulement, essai en laboratoire, essais in situ, histoires de cas. [Traduit par la Rédaction] Yoshimine et al. 906 Introduction Received April 27, Accepted March 25, M. Yoshimine. 1 Department of Civil Engineering, Tokyo Metropolitan University, Mimani-Osawa 1-1, Hchioji, Tokyo, Japan. P.K. Robertson. Geotechnical Group, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB T6G 2G7, Canada. C.E. Wride. AGRA Earth & Environmental Ltd., th Street Southeast, Calgary, AB T2E 6J5, Canada. 1 Author to whom all correspondence should be addressed ( yoshimine-mitsutoshi@c.metro-u.ac.jp). Can. Geotech. J. 36: (1999) If a natural slope or manmade earth structure is composed of a sufficient quantity of loose material that is strain softening, and if the in situ gravitational shear stress is larger than the undrained strength of the material at large deformation, a sudden flow failure can be triggered due to any minor disturbance, such as cyclic loading during an earthquake. Hazen (1920, p ) described the mechanism of flow failure of an embankment as follows: If the pressure of the water in the pores is great enough to carry all the load, it will have the effect of holding the particles apart and of producing a condition that is practically equivalent to that of quick-

2 892 Can. Geotech. J. Vol. 36, 1999 sand... the initial movement of some part of the material might result in accumulating pressure, first on one point, and then on another, successively, as the early points of concentration were liquefied. In the assessment and prediction of such flow failures, the key factor is the evaluation of the undrained strength of the material that is reduced by the porewater pressure development due to internal deformation of the material itself. For evaluation of the undrained strength of sandy materials, two different methodologies have traditionally been used: one is based on steady-state concepts using laboratory testing, and the other on case studies using field testing, such as the standard (SPT) or cone (CPT) penetration tests, at sites of previous flow failures. Laboratory shear strength In the laboratory, undrained monotonic loading shear tests, mainly triaxial compression tests, have been used for evaluating flow deformation of sandy material. Castro (1969) reported that when loose sands were sheared undrained in triaxial compression, a unique stress condition was achieved at large deformation, irrespective of the initial stress conditions, but dependent on only the density of the sand. This final and steady stress condition was called steady state by Poulos (1981) and will be called ultimate steady state in this study based on the work by Poorooshasb (1989) and Poorooshasb and Consoli (1991). The shear resistance at ultimate steady state has been considered as the undrained shear strength of the material for a flow failure, because once undrained shear deformation was initiated and if the driving force was higher than the ultimate steady state strength, the deformation could continue infinitely. Although many studies have been done based on steady-state concepts in the past few decades, general relationships between the density of sands and the undrained strength in flow failures have not been established, even approximately. The main reason for the difficulty might arise from the fact that in triaxial compression tests, especially when the initial confining stress is not very high, sand tends to dilate at large deformations and the observed resistance at the ultimate steady state becomes considerably higher than what is expected from field experience. As a result, very conservative interpretations of the test results were required. It was not until 1990 that the importance of shear mode in laboratory testing for evaluating flow failures of sandy materials was recognized (Vaid et al. 1990). Recently, laboratory testing with various shear directions using hollow cylinder torsional shear devices has revealed that the anisotropic characteristics of the soil dilatancy can seriously affect the undrained behaviour (Nakata et al. 1995, 1998; Uthayakumar 1996; Uthayakumar and Vaid 1998; Yoshimine 1996; Yoshimine et al. 1998). Based on such new knowledge, a reevaluation of flow failures of sand is needed because the deformation mode of failure in the field may not be the same as triaxial compression, and other modes such as simple shear may be more relevant. Another difficulty of using laboratory testing for flow-failure evaluation is that the observed undrained behaviour of the material is sensitive to factors such as grain characteristics, soil fabric, and soil density. Fines content, in particular, can affect the undrained behaviour significantly, as explained in the following sections. To avoid the complexity of fines content, only laboratory test results on clean sand and clean sand equivalent cone resistance of sands with low fines contents in the field will be considered in this study. CPT- and SPT-based shear strength correlation Correlating the back-calculated undrained shear strength from case studies of flow failure to penetration resistance of the failed material in terms of the SPT or CPT is an alternative approach to laboratory testing. Seed (1987), Seed and Harder (1990), and Stark and Mesri (1992) have presented charts for predicting residual strength of soils from the (N 1 ) 60 value from the SPT. Ishihara (1993) plotted residual strength versus normalized penetration resistance, q c1, from the CPT. In both cases, there is large scatter in the data. A major reason for the scatter may be attributed to the uncertainty in evaluating the penetration resistance. In many cases, the in situ measurements were carried out using nonstandard equipment, or the resistance was converted from different kinds of in situ tests such as the Swedish penetration test (Ishihara et al. 1991, 1993). In other cases, no in situ measurement was available and the penetration resistance was estimated only by the judgment of the investigator (Seed 1987). The uncertainties of the correlation using the SPT are described in detail by Wride et al. (1999). Correction of the SPT and CPT data to account for the fines content of the material is another major source of the scatter. Although the penetration resistances described in the above studies were corrected to the clean sand equivalent values, the corrections were only approximate and tentative as emphasized by Ishihara et al. (1993). Especially in the case of the CPT, the evaluation of the fines content itself involved considerable uncertainties. In one case study of a flow failure of a slope analyzed by Ishihara et al. (1991, 1993), the estimated fines content was up to 80% and the corrected cone resistance was as much as 10 times larger than the measured value. The objective of this paper The objective of this paper is to develop a methodology for evaluating undrained strength of sand, which governs the initiation of flow failures of a natural slope or earth structure, based on both laboratory and field testing. To reduce the uncertainties of field test data described above as much as possible, only well-documented data acquired by a standardized cone penetrometer (CPT) will be adopted in this study. SPT blow counts will not be used because they are less sensitive in the authors opinion and not reliable for loose materials compared with the CPT. Furthermore, to minimize errors due to the correction for fines content, only case histories involving relatively clean sand layers have been studied. Undrained strength of sand from laboratory testing Triaxial and torsional shear tests An extensive number of undrained monotonic loading shear tests on saturated sands has been performed at the University of Tokyo (Ishihara 1993; Verdugo and Ishihara 1996; Yoshimine et al. 1998; Yoshimine and Ishihara 1998). Verdugo (1992) conducted triaxial compression (TC) tests

3 Yoshimine et al. 893 Table 1. Physical properties of materials tested in the laboratory. Specific gravity ρ s (g/cm 3 ) Fines content FC (%) Mean diameter D 50 (mm) Max. void ratio e max Min. void ratio e min Toyoura Kawagishi-cho Mobara No Mobara No Sekiyado Kushiro-cho Ohgata Fig. 1. Phase transformation for Toyoura sand (initial effective mean principal stress p i = 100 kpa) (after Yoshimine et al. 1998). SS, simple shear; TC, triaxial compression; TE, triaxial extension. Fig. 2. Definition of ultimate steady state, quasi steady state, and critical steady state. on Toyoura sand, which was reconstituted using moist tamping to a wide range of initial void ratios and initial confining stresses (p i = kpa, where p i is the initial effective mean principal stress). Uehara (1994), Itoh (1996), Uchida (1996), and Yoshimine (1996) conducted TC, triaxial extension (TE), and simple shear (SS) tests on Toyoura sand. In these tests, the samples were reconstituted using dry deposition and consolidated to relatively low initial stress levels (p i = kpa). In simple shear tests, a hollow cylinder torsional shear apparatus with flexible lateral boundary was used (Yoshimine et al. 1998). In addition to Toyoura sand, natural sandy materials with various fines contents, FC (1 12%), were obtained from the field and tested using the triaxial apparatus (Tsuda 1994; Uehara 1994; Matsuzaki 1995; Yoshimine 1996). In these tests, samples that were reconstituted using both dry deposition and water sedimentation methods were examined. Undisturbed samples obtained by lowering the water table and block sampling at each site were also examined. The physical properties of the tested materials are listed in Table 1. All of the tested materials consisted of subangular to subrounded particles. Details of the different types of apparatus, sample preparation methods, and testing procedures are described in Ishihara (1993), Verdugo and Ishihara (1996), and Yoshimine et al. (1998). In Fig. 1, the states of phase transformation (the point of minimum p value, where p is the mean effective stress) during undrained shearing on Toyoura sand from an initial isotropic stress state of p i = 100 kpa are shown. In this figure, the test data in the TC and TE modes using the hollow cylinder torsional device are consistent with the measurements using the conventional triaxial apparatus. This indicates that

4 894 Can. Geotech. J. Vol. 36, 1999 Fig. 3. Ultimate steady state lines (USSL) and initial dividing lines (IDL) for Toyoura sand (based on test data from Verdugo 1992 and Yoshimine 1996). Fig. 4. Undrained shear behaviour of Toyoura sand in triaxial compression, triaxial extension, and simple shear. the test results from these two different devices can be compared directly. Definition of undrained strength If steady state is simply defined as the state of deformation without any increment of stress components, then it may appear at two stages during undrained monotonic loading tests on loose sand under relatively low initial confining stress levels (Fig. 2). The first is quasi steady state (QSS) following unstable deformation after peak stress state, and the second is ultimate steady state (USS) at the final stage of shear deformation. Quasi steady state appears at the state of phase transformation, which is the state of minimum effective mean stress during undrained shear. At quasi steady state not only mean stress but also shear stress components are minimum. When initial effective confining stresses are large enough, no hardening will develop after the reduction in strength and the minimum stress state becomes ultimate steady state. This state is called critical steady state (Yoshimine and Ishihara 1998). Figure 2 defines phase transformation, quasi steady state, critical steady state, and ultimate steady state. If shearing results in critical steady state, the shear resistance at this state can be taken as the undrained strength, but if it results in quasi steady state and then ultimate steady state occurs following hardening, a question arises as to which state should be used for the definition of undrained strength for evaluating flow failures. If the static driving shear stresses are larger than the minimum strength of the soil (i.e., QSS), and if enough excess pore-water pressure is developed due to some trigger mechanism, instability (i.e., softening) of the soil mass may result due to the brittleness of the initial response. In this sense, it may be more suitable to take the minimum shear resistance at quasi steady state as the undrained strength for evaluating the initiation of failure. On the other hand, ultimate steady state following hardening is a fully stable condition with higher resistance, which is less related to the initiation of flow deformation. Furthermore, once stability is lost and deformation starts in the field, the behaviour may become dynamic and turbulent due to inertia effects, and it is unknown if hardening is possible in such conditions. In Fig. 3, the ultimate steady state lines (USSLs) of Toyoura sand in TC, TE, and SS are plotted on the relative density mean effective stress (D r p ) plane. The positions of the USSLs for TE and SS were estimated as the upper boundaries of phase transformation points by Yoshimine et al. (1998). In the same figure, the initial dividing lines (IDLs), which divide initial states resulting in contractive behaviour with a quasi steady state from initial states resulting in fully dilative behaviour without instability, are presented based on the same test results. The IDL was introduced by Ishihara (1993) and is the same as the P line defined by Castro (1969). Although the USSL and IDL for TC are close to each other, the IDLs for SS and TE are much below the USSLs. In such cases, an initial state significantly below the USSL can result in strain softening to QSS, and the classical steady-state theory which refers to only the USSL may not work well for adequate evaluation of such softening behaviour. Based on the considerations outlined above, the shear resistance at quasi steady state or critical steady state will be adopted as the undrained strength for flow failures in the fol-

5 Yoshimine et al. 895 Fig. 5. Brittleness index plotted against relative density. DD, dry deposition; WS, water sedimentation. Fig. 6. Contour lines of undrained strength S u on D r p i plane (based on test data from Verdugo 1992 and Yoshimine 1996). lowing analysis. The undrained strength, S u, is calculated using the following formula: 1 [1] S u = 1s 3s s 2 ( σ σ )cosφ where σ 1s, σ 3s, and φ s are the quasi steady state or critical steady state values of the maximum and minimum principal stresses and the mobilized friction angle, respectively. This definition of undrained strength is based on the stability criteria and is not related to the magnitude of resultant deformation. This strength controls the initiation of undrained flow failure but is not necessarily equal to the residual shear resistance of the material during flow deformation. Effects of the mode of shear The effects of the mode of shear on the undrained shear behaviour of sand were described by Yamada and Ishihara (1985), Symes et al. (1985), Nakata et al. (1995, 1998), Uthayakumar and Vaid (1998), Yoshimine et al. (1998), and Yoshimine and Ishihara (1998). Generally, larger inclinations of the maximum principal stress from the vertical to the deposition plane and larger intermediate principal stresses make the behaviour more contractive. Figures 1 and 3 clearly show the importance of the mode of shear during undrained shearing of sand. Another example which shows the effect of the mode of shear is demonstrated in Fig. 4, in which the results of TC, SS, and TE tests on samples of Toyoura sand with relative densities of 33 36% are plotted. Despite the fact that the TC samples had the lowest relative density, the TC and TE tests resulted in the most dilative and the most contractive behaviour, respectively, whereas the behaviour in SS was intermediate. Figure 5 shows the relationship between brittleness index I B and relative density for clean Toyoura and Kawagishi-cho sands. The brittleness index (Bishop 1967) is an index of the collapsibility of a strain-softening sand when sheared undrained and is defined as follows: [2] I B S = S peak S peak u where S u is the undrained strength defined by eq. [1], and S peak is the peak shear resistance prior to quasi steady state or critical steady state during monotonic undrained shearing. I B = 1 indicates zero residual strength. If shearing results in only dilative behaviour and no strain softening is observed,

6 896 Can. Geotech. J. Vol. 36, 1999 Table 2. Undrained triaxial compression test results on wettamped Toyoura sand (Verdugo 1992). D r (%) p i (kpa) S u (kpa) S u /p i I B Table 2. (concluded). D r (%) p i (kpa) S u (kpa) S u /p i I B Note: IfI B = 0, shear resistance at phase transformation without softening was denoted. then I B is defined as zero. In the field, a more brittle response may result in higher acceleration of the sliding mass. Figure 5 shows that clean sands with D r = 30% exhibit a brittleness of nearly zero in triaxial compression, whereas the same material could exhibit almost zero strength with I B = 1 in triaxial extension or simple shear. In triaxial extension, clean sands with relative densities as high as 60 80% could have some brittleness (i.e., show some strain-softening response). Since the discrepancies in undrained shear response are so large, it is important to take these effects into account when evaluating the undrained strength of sand. It should be noted that the undrained triaxial compression test, which is the test most commonly performed in the laboratory, gives the highest undrained strength and lowest brittleness for a given relative density, resulting in the most unconservative judgement for flow liquefaction problems. A similar influence of direction of shear is observed in clays (Bjerrum 1972), for which the undrained shear strength is generally larger in TC than in TE. The difference is larger for clays of low plasticity (Jamiolkowski et al. 1985). Effects of the initial consolidation stress level If undrained strength is related to relative density, the strength should be normalized by the initial confining stress in the form S [3] u = fd ( n r) ( p i ) where n is a normalization exponent between 0 and 1.0. Generally, n is also a function of p i and D r. Figure 6 shows contour lines of undrained strength (S u )of Toyoura sand on the D r p i plane for different modes of shear. These contour lines were drawn based on 75 TC tests on wet-tamped Toyoura sand (Verdugo 1992) and 37 TE tests (Uehara 1994; Itoh 1996; Yoshimine 1996), and 34 SS

7 Yoshimine et al. 897 Table 3. Undrained triaxial extension test results on drydeposited Toyoura sand. D r (%) p i (kpa) S u (kpa) S u /p i I B Note: IfI B = 0, shear resistance at phase transformation without softening was denoted. tests on dry-deposited Toyoura sand (Uchida 1996; Yoshimine 1996) listed in Tables 2 4. Because they were few in number, the data from triaxial compression tests on dry-deposited sand were not used in Fig. 6. If dry-deposited sand and wet-tamped sand are compared, the latter is somewhat stiffer, as shown in Figs. 3 and 5. The broken lines in Fig. 3 are extrapolations of the contour lines using the undrained strength at phase transformation for strain hardening (without drop of shear stress, i.e., I B = 0), and assuming that the undrained strength has an upper limit equal to the drained strength when the material is very dense. From Fig. 6a for triaxial compression, it can be seen that when the initial confining stress is sufficiently high, critical steady state develops (Yoshimine and Ishihara 1998) and the undrained strength (S u ) is uniquely related to density, irrespective of the initial confining stress level. In this case, the n Table 4. Undrained simple shear test results on dry-deposited Toyoura sand. D r (%) p i (kpa) S u (kpa) S u /p i I B value in eq. [3] is equal to zero. For smaller stress levels, the undrained strength is a function of the initial confining stress. For a given relative density, smaller initial stresses result in smaller undrained strengths, and larger n values should be used for the normalization. The L line (Castro 1969) divides the initial states resulting in critical steady state being reached from the initial states resulting in quasi steady state being reached. The original steady-state approach that assumes n = 0 can be used only when the initial state exists above the L line. In Fig. 6b for simple shear and Fig. 6c for triaxial extension, although the contour lines of S u appear to become almost horizontal at stresses beyond around p i = 300 and 500 kpa, respectively, critical steady state was not achieved fully at these confining stress levels and shear strain levels up to 15%. The contour lines may have some inclination if they are plotted over a wider range of p i, and the L lines may be located at higher stresses. Figure 7 shows contour lines of the undrained strength ratio, S u /p i,onthed r p i plane for different modes of shear. In

8 898 Can. Geotech. J. Vol. 36, 1999 Fig. 7. Contour lines of undrained strength ratio S u /p i on D r p i plane (based on test data from Verdugo 1992 and Yoshimine 1996). Fig. 8. Density undrained strength relationship for clean sands (p i < 500 kpa). n value (eq. [3]) equal to one is suitable if p i is lower than 500 kpa. Based on the considerations outlined above, the undrained strength ratio, S u /p i, will be related to the relative density of the material or in situ penetration resistance with the limitation that the initial stress levels are less than or equal to 500 kpa. In Fig. 8, the undrained strength ratios (S u /p i )of Toyoura and Kawagishi-cho sands are plotted against relative density. In addition to these data, the undrained strengths of intact samples of Fraser River sand from Vaid et al. (1996) are also plotted. Note that the plot is limited to clean sands that resulted in strain softening with initial effective stresses, p i, less than 500 kpa. Shear tests on Ohgata sand and Sekiyado sand at the densities tested resulted in only strain hardening, so they are not included in the figure. Figure 8 shows a reasonably consistent set of responses regardless of the mode of deposition, with the undrained strength ratio being significantly larger in triaxial compression than in triaxial extension. If the stress levels are higher, the relationship in Fig. 8 overestimates the S u /p i values. In higher stress ranges, the relationship may also be affected by progressive crushing of the particles, even though the material is limited to essentially clean sand, as suggested by the higher slopes of the USSLs shown in Fig. 9a in the higher stress ranges. As a result, it may be impossible to establish a general relationship between undrained strength and the relative density of a sand at high stress levels. the same manner as in Fig. 6, the broken lines denote contour lines of stress ratio at phase transformation without softening. These contour lines are equivalent to the flow potential lines defined by Yoshimine and Ishihara (1998). It can be seen that S u /p i is nearly uniquely related with relative density if p i is lower than 500 kpa, especially for lower strengths. If p i is higher than 500 kpa, higher p i values result in lower strength ratios. This fact indicates that taking a Effect of fines content of the material Ultimate steady state lines from undrained triaxial compression tests on sands with fines (i.e., FC > 5%) are plotted in Fig. 9b, which shows that the vertical position of the ultimate steady state lines is affected by fines content. As fines content increases, the USSL moves down, as pointed out by Poulos et al. (1985) and Zlatovi and Ishihara (1995). Although enough data for evaluating the minimum strength were not obtained for these silty materials, the maximum density that results in essentially zero residual strength with I B = 1 during triaxial compression can be estimated from the position of the ultimate steady state lines at p = 0 and plot-

9 Yoshimine et al. 899 Table 5. Case studies of submarine flow failures. Jamuna Bridge Fraser River delta Nerlerk berm Fines content, FC (%) (mainly <5) Mean grain size, D 50 (mm) Slope angle before failure, β 1 ( ) Slope angle after failure, β 2 ( ) Undrained shear strength ratio, S u / σ vi =(γ/γ ) tanβ Clean sand equivalent normalized cone resistance, (q c1n ) cs * * Mean value minus one standard deviation. Fig. 9. Ultimate steady state lines for various sandy soils. FC, fines content. Fig. 10. Relative density for essentially zero residual strength plotted as a function of fines content. ted as a function of fines content, as illustrated in Fig. 10. The D r at I B = 1 for triaxial extension and simple shear on Toyoura sand can also be estimated from the ultimate steady state lines (Fig. 3) or brittleness plot (Fig. 5) for each stress condition. In addition to Toyoura sand, triaxial extension tests were conducted on Kawagishi-cho sand and Kushirocho sand. Although zero residual strength with I B = 1 was not observed for both sands, D r at I B = 1 in triaxial extension on Kawagishi-cho sand may be almost the same as that for Toyoura sand, as Fig. 5 suggests. Kushiro-cho sand with D r = 50% exhibited only dilative behaviour (i.e., I B =0)and no looser samples were tested in triaxial extension. These facts are also plotted in Fig. 10, from which it can be said that in triaxial compression a sand with D r = 40% and a fines content of 10% could be equivalent to a clean sand with D r = 12%. Lade and Yamamuro (1997), Yamamuro and Lade (1998), and Thevanayagam (1998) reported a similar effect of fines content. Such a high sensitivity to fines content makes it very difficult to evaluate the undrained behaviour of sandy materials, in general. The effect of type of fines was not examined in this study. To avoid the complexity of fines content, only clean sand will be included in this study. If only clean sand or a clean sand equivalent parameter is examined and the undrained strength characteristics are not significantly affected by the fabric of the sand (see Fig. 8), the relationship between D r and S u /p i might be applied, in general, to a sand deposit with subangular to subrounded particles when p i 500 kpa. Evaluation of undrained strength of sands from case studies Clean sand equivalent normalized cone resistance The three case studies listed below are shallow submarine flow failures of deposits involving sand layers with relatively low fines contents under initial effective stresses (p i ) less than 300 kpa. A summary of the details for each case history is given in Table 5. At each site, reliable CPT data

10 900 Can. Geotech. J. Vol. 36, 1999 Fig. 11. Normalization and correction of CPT data (after Robertson and Wride 1998). F, normalized sleeve friction; I c, soil behaviour type index; K c, grain characteristics correction factor; P a, reference pressure. 0.8 MPa had the same residual undrained strength as clean sands with q c1 = 2 MPa, i.e., K c = 2.5 for FC = 30%. This correction factor is approximately the same as those used in this study. Since weak zones within a deposit control instability of a slope, the representative cone resistance of the failed material should be smaller than the mean value. However, the minimum value of cone resistance may be too small for a representative value, because the failed layer should be continuous to some extent, both laterally and vertically. In this paper, at any given depth the mean minus one standard deviation of the (q c1n ) cs values was taken as the representative cone resistance of the failed material. Popescu et al. (1997) found that the 80th percentile of soil strength was a good characteristic value to be used in deterministic dynamic analyses if the effects of spatial variability of soil properties were taken into account. The mean minus one standard deviation value is approximately the same as the 80th percentile if a standard distribution of the data is assumed. Estimate of undrained strength The undrained strengths of the submerged failed materials in the three case studies were estimated from the slope inclinations, β, using the following formula: [4] S u σ vi γ = sinβ cos β γ acquired by standard cone penetrometers were available. The measured tip resistance (q c ) was normalized for overburden pressure at the site (q c1n ) and corrected for the grain characteristics of the material ((q c1n ) cs ) using the method proposed by Robertson and Wride (1998). The process of normalization and correction is shown in Fig. 11. For calculating overburden pressure, the gross unit weight and submerged unit weight of the soils were assumed as γ = 18.6 kn/m 3 and γ = 8.8 kn/m 3, respectively. The grain characteristics correction factor, K c (= (q c1n ) cs /q c1n ), in this process was originally proposed for initial liquefaction during cyclic loading. Although the K c value for flow failures is unknown, the K c value for cyclic liquefaction, as proposed by Robertson and Wride (1998), was used without any modification in this study. Since the fines contents of the materials in the three case studies being considered are relatively small, any resultant error in the calculation of equivalent clean sand normalized cone penetration resistance, (q c1n ) cs, due to the uncertainty of the correction factor is likely small. If the fines content is less than or equal to 5%, the correction factor is equal to 1.0. The correction factor K c is equal to 1.17, 1.40, 1.74, and 2.69 for apparent fines contents equal to 10, 15, 20, and 30%, respectively. Ishihara et al. (1993) indicated that sands with FC = 30% and q c1 = where σ vi is the vertical effective stress at the initial state. If the slope inclination before failure, β 1, is used in eq. [4], the calculated strength ratio is larger than the true value because the shear stress induced by the slope inclination before failure should be larger than the undrained shear strength of the material to initiate unstable flow deformation. If the slope inclination after failure, β 2, is used, the calculated strength ratio may be smaller than the true value due to the effects of inertia of the sliding mass (Davis et al. 1988). It is also possible that the calculated strength using β 2 is larger than the actual minimum undrained strength, S u, because of the dissipation of pore pressure and the effects of strain hardening during deformation. Furthermore, if the flow deformation is turbulent in nature, the failed material may act as a viscous fluid rather than as a frictional material, and the resultant slope angle may be less related to the undrained strength that controlled by the initiation of the flow failure. Although conventional estimates of the undrained strength have many uncertainties, as described above, the undrained strength ratio calculated by eq. [4] using the slope inclination after failure, β 2, will be adopted in this study. It should be noted that the estimated strength is only approximate and tentative. Jamuna Bridge site Over 30 submarine flow slides occurred along the West Guide Bund of the Jamuna Bridge in Bangladesh. The Guide Bund slopes were formed in very young (< 200 years) sandy sediments deposited by the Jamuna River. The sand involved in the flow slides was a normally consolidated fine to medium micaceous sand. The mica content ranged from about 15 to 30% by weight. The percent passing the 0.06 mm grain size was approximately 2 10%, and the mean grain

11 Yoshimine et al. 901 Fig. 12. Cross section of the failed slope at the Jamuna Bridge site (modified from Ishihara 1996). Fig. 13. CPT data from the Jamuna Bridge site. Fig. 14. CPT data from the Fraser River site.

12 902 Can. Geotech. J. Vol. 36, 1999 Fig. 15. CPT data for selected sandy layers at the Fraser River site. Fig. 16. Histogram of fines content for Nerlerk sand (after Rogers et al. 1990). size was approximately mm. The slides occurred on relatively gentle slopes (1:5 and 1:3.5, i.e., β 1 = ), involved large volumes of soil, and resulted in very flat final slopes (approx. 1:8 to 1:20, i.e., β 2 = ). A typical cross section of a slope before and after a failure is shown in Fig. 12. Details of the flow failures are described in reports by Fugro Engineers B.V. (1995a), Robertson (1996), and Ishihara (1996). Twenty-two CPTs were conducted along the shoulder of the slope (Fugro Engineers B.V. 1995b), predominantly in Jamuna River sand. The minimum, maximum, and mean values and the mean plus and minus one standard deviation of the measured CPT tip resistance (q c ) and the normalized sleeve friction ratio (F) are shown in Fig. 13. Figure 13 also shows the grain characteristic correction factor (K c ) and normalized clean sand equivalent tip resistance, (q c1n ) cs, calculated using the method proposed by Robertson and Wride (1998). A very uniform loose sand deposit exists at an elevation of about 12 m to +6 m where F < 1.0%. Since the lower part of this layer is slightly more dense than the upper part, the material between an elevation of about 7 m and the elevation of the water table (+8 m) was considered to have caused the flow failures. The calculated average apparent fines content of this failure zone based on the CPTs was less than 15%, slightly higher than the value based on soil sampling. This may be due to the high mica content of the material. The resultant average correction factor based on grain characteristics was 1.4. The mean minus one standard deviation of the clean sand equivalent cone resistance, (q c1n ) cs, within the target elevations ( 7 m to +8 m), was approximately 40 55, as indicated by the shaded area in Fig. 13. Using eq. [4], the corresponding residual strength ratio was calculated as ranging from 0.11 to Fraser River delta Five large-scale failures on the Fraser River delta front near Sand Heads, British Columbia, have been detected by comparing successive bathymetric surveys between 1970 and 1986 (McKenna et al. 1992). The largest mass-wasting event occurred in June During this slope failure, over m 3 of delta-front sediments were removed. The removed soil mass had a thickness of around m and the slope angle after the event was about 1 5 at the lower part of the gully (Chillarige et al. 1997). The angle of the front slope before the failure event ranged between 20 and 23. Five cone penetration tests (FD93CPT1, FD93CPT2, FD93RCPT3, FD93SCPT4, and FD94SCPT1) and a borehole log test (FD93S2) were conducted in the seabed of delta sediments approximately 1 km south of the failure and m inside the front slope (Christian et al. 1997). The borehole log showed that the sediments consisted of loose fine sand with sandy silt to clayey silt layers. Although the silty layers had fines contents of 30 80%, the fine to medium sand layers had fines contents of 3 15%. The results of the five CPTs are shown in Fig. 14. Since the number of CPTs is limited, the mean, maximum, and minimum values and one standard deviation of the clean sand equivalent cone resistance were examined for a moving 0.6 m thick interval, as indicated in Fig. 14. Boulanger et al. (1997) stated that this averaging interval is reasonable because continuous layers of this thickness can be a source of significant deformations in liquefaction problems. Figure 14 shows that the mean minus one standard deviation of normalized clean sand equivalent cone resistance of the deposit was between 35 and 45. Figure 14 shows that the grain characteristics correction factors used in this case study were very large, i.e., K c =3 10, on average, with a maximum value of 30. In this case, the accuracy of the correction factor becomes important and the accuracy of the calculated clean sand equivalent cone resistance could be questioned. To examine this aspect, the CPT profiles were reanalyzed using only the data points in relatively clean sand layers which had K c values less than

13 Yoshimine et al. 903 Fig. 17. CPT data from the Nerlerk berm site. Fig. 18. D r (q c1n ) cs relationships from calibration-chamber testing. 2.5, as shown in Fig. 15. The data are plotted in Fig. 15 for depths up to only 25 m, because only one CPT (test FD93CPT1) detected sandy layers with K c < 2.5 below 25 m. The average K c value of the selected layers was about Although the profile of the resultant (q c1n ) cs values has larger scatter due to the much smaller number of data points, the range of the mean minus one standard deviation of (q c1n ) cs values for the sandy layers is Thus, the representative range (q c1n ) cs = 35 to 45 from the first analysis (see Fig. 14) is still applicable. This indicates that there appears to be no bias in the process of grain characteristics normalization, as presented in Fig. 11, and any errors in the K c values are small, provided it is assumed that the sandy layers and the siltier layers had almost the same resistance to flow failures. Nerlerk berm site The Nerlerk berm is a hydraulically placed submarine sand berm constructed as a hydrocarbon exploration platform in the Canadian Beaufort Sea. During construction of the berm, five large-scale failures occurred. Details of the failures are described by Sladen et al. (1985). According to Sladen et al., the berm consisted of hopper-placed Ukalerk sand overlaid by pipeline-placed Nerlerk sand. The depths of the failures varied between 5 and 12 m, and the failed mass involved only Nerlerk sand, which had a mean grain size of 0.22 mm and a fines content of about 2 15%. On the other hand, Rogers et al. (1990) reported that Nerlerk sand sampled directly from the borrow sources had a mean grain size of about 0.28 mm and that most of the samples had fines contents of less than 5% (see Fig. 16). The prefailure slope gradients were typically between 10 and 12 and the postfailure gradients were as flat as 1 to 2 (Sladen et al. 1985). Twenty-six CPTs were carried out before the failures. From the spatial distribution of material deduced from construction records, Sladen et al. (1985) separated the Nerlerk sand penetration resistance data from those of the Ukalerk sand. Only measured penetration resistance data for Nerlerk sand are used in this study. Since records of sleeve friction from the CPTs were not available and it is likely that most of the failed material had a fines content less than 5% as shown in Fig. 16, this study assumed that all layers of Nerlerk sand had a fines content less than 5% (i.e., K c = 1.0) and normalized clean sand equivalent tip resistance values were calculated, as indicated in Fig. 17. The values of mean minus one standard deviation for (q c1n ) cs in the failed mass (depths of less than 12 m) are approximately Using eq. [4], the residual undrained strength ratio of Nerlerk sand is estimated to range from about 0.04 to 0.08 based on the postfailure gradients of the slopes. A summary of the main features of the three case studies is given in Table 5. Link between laboratory and field responses For the purpose of comparing laboratory data with field observations, the densities of the specimens of Toyoura sand in the laboratory tests need to be converted to equivalent values of cone penetration resistance. Iwasaki et al. (1988) and Tatsuoka et al. (1990) conducted calibration-chamber testing using the CPT in normally consolidated Toyoura sand. In most of the tests air-dried sand was examined. They used a standard cone penetrometer with a diameter of 36 mm and a calibration chamber with a diameter of 790 mm. The test results are plotted in Fig. 18. For the calibration tests with constant-volume conditions, the vertical stress during penetration (not the initial value) was used for calculating the normalized cone resistance. The effect of chamber size was not taken into account, although it would have had some effect when the density of sand was relatively higher. Based on this calibration-chamber testing, Tatsuoka et al. proposed the following equation for normally consolidated clean Toyoura sand:

14 904 Can. Geotech. J. Vol. 36, 1999 Fig. 19. Undrained strength ratio versus clean sand equivalent normalized cone resistance. [5] D r = 85+76log 10 (q c1n ) cs On the other hand, Jamiolkowski et al. (1985) proposed the following average relationship based on calibration-chamber tests on five different normally consolidated clean sands: [6] D r = 65+66log 10 (q c1n ) cs The correlation denoted by eqs. [5] and [6] is also shown in Fig. 18. In addition, the possible range in the relationship proposed by Jamiolkowski et al. is shown. For the same cone penetration resistance, eq. [5] gives a slightly smaller relative density than eq. [6] when (q c1n ) cs is less than about 100. In this study, Tatsuoka s correlation as given in eq. [5] will be used to calculate equivalent (q c1n ) cs values from the densities of Toyoura sand samples tested in the laboratory. Although there are no calibration-chamber test data on other sands, Figs. 5, 8, and 9 and the similarity of eqs. [5] and [6] suggest that Toyoura sand can be representative of clean sands when confining stress is not so high. The D r S u /p i data for Toyoura sand based on TC, TE, and SS tests plotted in Fig. 8 were converted to (q c1n ) cs S u / σ vi data using eq. [5] and are shown in Fig. 19. In the conversion it was assumed that σ vi = 1.5p i (i.e., the coefficient of lateral earth pressure at rest K 0 = 0.5). Figure 19 also presents the (q c1n ) cs S u / σ vi data obtained from the three case studies (see Table 5) and shows that the undrained-strength characteristics observed for the case studies are, in general, consistent with the measured undrainedstrength characteristics of Toyoura sand when tested in simple shear (SS) in the laboratory. Triaxial extension tests appear to exhibit much lower strengths, and triaxial compression tests appear to result in higher strengths. Thus it appears that simple shear was likely the predominant mode of shear in the failed material in the field. The broken line in Fig. 19 represents the approximate relationship between the undrained-strength ratio and the clean sand equivalent resistance based on the case studies and the simple shear test data. Figures 8 or 19 show that the undrained strength of clean sand is very sensitive to relative density or cone penetration resistance; therefore, it is almost impossible to predict the exact undrained strength. Inversely, relatively clear boundaries of relative density or cone penetration resistance for estimating the potential for flow failures can be detected. Based on Fig. 19, it appears that (q c1n ) cs = 50 is the approximate boundary for the possibility of flow failures, although the number of case records is limited. If (q c1n ) cs is less than 40, the undrained-strength ratio of the material could be very small. On the other hand, if (q c1n ) cs is greater than 60, only dilative behaviour in simple shear or triaxial compression is expected and flow failures are unlikely. This (q c1n ) cs boundary for flow failure is similar to the boundaries proposed in prior studies, e.g., Sladen and Hewitt (1989), Robertson et al. (1992), and Ishihara (1993). Fear and Robertson (1995, 1996) and Konrad and Watts (1995) also reported similar boundaries in terms of shear wave velocity, SPT blow count, or CPT penetration resistance. Although the estimated strength from case studies has much uncertainty as discussed earlier, the (q c1n ) cs boundary may not be greatly affected by the uncertainty, as suggested by Fig. 19. Conclusions Undrained shear strengths of clean sand during flow failures were calculated based on both laboratory testing and field observations. From laboratory testing on seven sandy materials, it was shown that fines content can have a large effect on the undrained shear behaviour of a sandy soil. To avoid this complexity, only laboratory results for clean sands (mainly Toyoura sand) were used in this study. Also, only case studies in which the failed material had a relatively low fines content were selected to minimize uncertainty associated with the estimated normalized clean sand equivalent cone penetration resistance, (q c1n ) cs. From the laboratory undrained shear testing, it was observed that sands generally dilated and strain hardened at large deformations following quasi steady state. Based on stability considerations, the minimum undrained shear resistance at quasi steady state was used as the undrained strength (S u ) for flow failures. For clean sands under relatively low initial confining stress levels, it was shown that the ratio of the minimum undrained shear strength to the initial confining stress (S u /p i ) could be related to relative density. This relationship was shown to be strongly affected by the mode of shear. Triaxial compression tests exhibited the highest resistance, whereas triaxial extension tests resulted in the lowest resistance. Simple shear tests exhibited intermediate behaviour. Three case studies of submarine flow failures in sand deposits with low fines contents and with reliable CPT data were examined. Due to the low fines contents, any error in the correction of measured cone resistance to clean sand equivalent normalized cone resistance, (q c1n ) cs, could be minimized. Since looser but continuous layers control flow failures of slopes, the mean value of cone resistance may be too high but the minimum value may be too low to be taken as representative. Thus the mean minus one standard deviation value of (q c1n ) cs was taken as the representative cone resistance of the failed material for each case study. The undrained shear strength ratio (S u / σ vi ) of the material at each site was estimated based on the gradient of the postfailure