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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, pi′, 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 pi’ 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]
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Introduction Received April 27, 1998. Accepted March 25, 1999. 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., 221 18th Street Southeast, Calgary, AB T2E 6J5, Canada. 1
Author to whom all correspondence should be addressed (e-mail:
[email protected]).
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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. 1740–1744) 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© 1999 NRC Canada
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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
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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 (N1)60 value from the SPT. Ishihara (1993) plotted residual strength versus normalized penetration resistance, qc1, 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 © 1999 NRC Canada
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Table 1. Physical properties of materials tested in the laboratory.
Toyoura Kawagishi-cho Mobara No. 1 Mobara No. 2 Sekiyado Kushiro-cho Ohgata
Specific gravity ρs (g/cm3)
Fines content FC (%)
Mean diameter D50 (mm)
Max. void ratio emax
Min. void ratio emin
2.650 2.664 2.672 2.663 2.747 2.589 2.694
0.0 1.4 8.3 11.6 1.8 5.9 0.8
0.20 0.32 0.14 0.14 0.28 0.28 0.28
0.977 1.054 1.274 1.442 1.180 1.267 1.039
0.597 0.793 0.772 0.859 0.752 0.767 0.655
Fig. 1. Phase transformation for Toyoura sand (initial effective mean principal stress pi′ = 100 kPa) (after Yoshimine et al. 1998). SS, simple shear; TC, triaxial compression; TE, triaxial extension.
on Toyoura sand, which was reconstituted using moist tamping to a wide range of initial void ratios and initial confining stresses (pi′ = 100–3000 kPa, where pi′ 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 (pi′ = 50–500 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,
Fig. 2. Definition of ultimate steady state, quasi steady state, and critical steady state.
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 pi′ = 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 © 1999 NRC Canada
894 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).
Can. Geotech. J. Vol. 36, 1999 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 (Dr – 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© 1999 NRC Canada
Yoshimine et al. Fig. 5. Brittleness index plotted against relative density. DD, dry deposition; WS, water sedimentation.
895 Fig. 6. Contour lines of undrained strength Su on Dr–pi′ plane (based on test data from Verdugo 1992 and Yoshimine 1996).
lowing analysis. The undrained strength, Su, is calculated using the following formula: [1]
Su =
1 (σ1s − σ3s) cos φs 2
where σ1s, σ3s, and φs 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 IB 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]
IB =
Speak − Su Speak
where Su is the undrained strength defined by eq. [1], and Speak is the peak shear resistance prior to quasi steady state or critical steady state during monotonic undrained shearing. IB = 1 indicates zero residual strength. If shearing results in only dilative behaviour and no strain softening is observed, © 1999 NRC Canada
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Table 2. Undrained triaxial compression test results on wettamped Toyoura sand (Verdugo 1992). Dr (%)
pi′ (kPa)
Su (kPa)
Su/pi′
IB
7.4 11.1 12.4 16.3 17.1 17.4 17.6 17.9 26.1 37.9 38.2 45.3 57.6 61.1 63.7 63.7 65.8 67.1 12.4 15.0 21.3 23.2 27.1 35.5 39.5 56.1 60.8 12.4 17.6 20.0 23.7 24.7 28.7 30.5 42.4 46.6 56.6 66.8 11.6 13.7 14.7 15.5 18.7 20.3 20.5 31.8 37.9 43.4 55.5 63.7 66.3 17.4 21.3 24.7 25.8 32.1
98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 294 294 294 294 294 294 294 294 294 490 490 490 490 490 490 490 490 490 490 490 981 981 981 981 981 981 981 981 981 981 981 981 981 1471 1471 1471 1471 1471
0.0 0.0 0.0 15.1 17.7 24.6 28.2 32.7 36.5 25.0 35.8 35.2 24.2 49.2
0.000 0.000 0.000 0.154 0.180 0.251 0.287 0.333 0.372 0.255 0.365 0.359 0.247 0.501
49.4
0.504
0.0 0.0 17.1 69.5 67.6 90.5 128.7 112.1 94.9 122.7 0.0 35.5 59.4 96.5 97.3 145.1 180.7 181.2 211.3 168.5 176.6 0.0 23.2 0.0 69.8 83.2 0.0 110.2 259.8 356.9 350.1 392.7 332.0 411.8 59.5 104.9 141.2 215.8 325.7
0.000 0.000 0.058 0.236 0.230 0.308 0.438 0.381 0.323 0.417 0.000 0.072 0.121 0.197 0.198 0.296 0.368 0.369 0.431 0.344 0.360 0.000 0.024 0.000 0.071 0.085 0.000 0.112 0.265 0.364 0.357 0.400 0.339 0.420 0.040 0.071 0.096 0.147 0.221
1.000 1.000 1.000 0.471 0.424 0.206 0.117 0.101 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.770 0.211 0.186 0.000 0.000 0.000 0.000 0.000 1.000 0.689 0.527 0.298 0.292 0.051 0.000 0.000 0.000 0.000 0.000 1.000 0.879 1.000 0.664 0.627 1.000 0.540 0.053 0.000 0.000 0.000 0.000 0.000 0.787 0.637 0.542 0.400 0.205
Table 2. (concluded). Dr (%) 35.5 38.2 40.8 55.3 18.2 35.3 37.9 61.6 63.7 22.9 25.8 28.2 31.6 37.9 38.9 50.0 62.9 63.7
pi′ (kPa) 1471 1471 1471 1471 1961 1961 1961 1961 1961 2942 2942 2942 2942 2942 2942 2942 2942 2942
Su (kPa) 392.2 437.4 456.4 566.6 77.0 419.5 483.4 771.6 793.1 148.8 168.5 187.2 269.8 522.1 503.5 868.5 1171.0 1100.0
Su/pi′ 0.267 0.297 0.310 0.385 0.039 0.214 0.246 0.393 0.404 0.051 0.057 0.064 0.092 0.177 0.171 0.295 0.398 0.374
IB 0.084 0.000 0.027 0.000 0.779 0.202 0.119 0.000 0.000 0.693 0.668 0.644 0.529 0.277 0.295 0.000 0.001 0.000
Note: If IB = 0, shear resistance at phase transformation without softening was denoted.
then IB 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 Dr = 30% exhibit a brittleness of nearly zero in triaxial compression, whereas the same material could exhibit almost zero strength with IB = 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 [3]
Su = f (Dr ) ( p′i ) n
where n is a normalization exponent between 0 and 1.0. Generally, n is also a function of pi′ and Dr. Figure 6 shows contour lines of undrained strength (Su) of Toyoura sand on the Dr–pi′ 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 © 1999 NRC Canada
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Table 3. Undrained triaxial extension test results on drydeposited Toyoura sand.
Table 4. Undrained simple shear test results on dry-deposited Toyoura sand.
Dr (%)
pi′ (kPa)
Su (kPa)
Su/pi′
IB
Dr (%)
pi′ (kPa)
Su (kPa)
Su/pi′
IB
23.4 30.5 42.1 46.8 56.8 63.4 73.2 26.6 27.9 32.6 33.9 36.6 39.2 42.4 49.5 57.4 65.8 79.2 34.5 44.7 51.1 57.6 66.1 29.2 31.8 42.9 31.1 32.6 38.7 46.1 53.7 60.0 67.4 76.1 30.8 38.4 46.1
50 50 50 50 50 50 50 100 100 100 100 100 100 100 100 100 100 100 200 200 200 200 200 300 300 300 400 400 400 400 400 400 400 400 500 500 500
0.0 3.0 1.7 5.5 10.4 13.3 16.6 1.1 2.2 3.6 4.6 3.0 2.7 6.0 8.0 17.6 24.7 33.2 1.9 18.3 24.3 39.7 50.9 0.8 2.5 15.5 7.5 11.9 25.9 35.7 54.5 76.2 81.1 121.3 9.2 10.1 35.5
0.001 0.059 0.034 0.109 0.208 0.266 0.331 0.011 0.022 0.036 0.046 0.030 0.027 0.060 0.080 0.176 0.247 0.332 0.009 0.091 0.122 0.199 0.255 0.003 0.008 0.052 0.019 0.030 0.065 0.089 0.136 0.191 0.203 0.303 0.018 0.020 0.071
0.991 0.592 0.831 0.358 0.157 0.000 0.000 0.907 0.860 0.787 0.752 0.832 0.839 0.688 0.510 0.223 0.000 0.000 0.937 0.522 0.393 0.113 0.000 0.979 0.936 0.645 0.880 0.798 0.626 0.501 0.294 0.113 0.000 0.000 0.865 0.849 0.539
27.6 31.3 35.0 39.5 50.8 83.4 23.4 26.1 26.6 27.1 28.9 30.0 30.5 32.1 35.0 35.8 35.8 36.1 36.1 37.4 38.2 39.7 41.8 42.4 45.5 22.1 31.1 31.6 34.7 36.6 40.0 24.2 28.9 34.7 36.6
50 50 50 50 50 50 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 200 200 200 200 200 200 300 300 300 300
0.5 0.3 14.5 17.9 18.8 1.0 0.5 9.0 4.1 9.3 2.9 11.8 5.7 13.8 20.4 26.5 7.3 23.6 9.6 25.5 19.4 34.9 31.8 32.5 38.2 12.8 32.9 40.6 33 48.2 64.9 19.3 29.8 46.4 65
0.957 0.974 0.000 0.000 0.000 0.000 0.974 0.605 0.821 0.611 0.872 0.524 0.744 0.434 0.269 0.000 0.693 0.129 0.562 0.079 0.276 0.000 0.000 0.000 0.000 0.726 0.347 0.188 0.298 0.000 0.000 0.697 0.545 0.336 0.170
0.010 0.006 0.290 0.358 0.376 0.020 0.005 0.090 0.041 0.093 0.029 0.118 0.057 0.138 0.204 0.265 0.073 0.236 0.096 0.255 0.194 0.349 0.318 0.325 0.382 0.064 0.165 0.203 0.165 0.241 0.325 0.064 0.099 0.155 0.217
Note: If IB = 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., IB = 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 (Su) is uniquely related to density, irrespective of the initial confining stress level. In this case, the n
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 Su appear to become almost horizontal at stresses beyond around pi′ = 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 pi′, and the L lines may be located at higher stresses. Figure 7 shows contour lines of the undrained strength ratio, Su/pi′, on the Dr–pi′ plane for different modes of shear. In © 1999 NRC Canada
898 Fig. 7. Contour lines of undrained strength ratio Su/pi′ on Dr–pi′ plane (based on test data from Verdugo 1992 and Yoshimine 1996).
Can. Geotech. J. Vol. 36, 1999 Fig. 8. Density – undrained strength relationship for clean sands (pi′ < 500 kPa).
n value (eq. [3]) equal to one is suitable if pi′ is lower than 500 kPa. Based on the considerations outlined above, the undrained strength ratio, Su/pi′, 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 (Su/pi′) 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, pi′, 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 Su/pi′ 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 Su/pi′ is nearly uniquely related with relative density if pi′ is lower than 500 kPa, especially for lower strengths. If pi′ is higher than 500 kPa, higher pi′ 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 IB = 1 during triaxial compression can be estimated from the position of the ultimate steady state lines at p′ = 0 and plot© 1999 NRC Canada
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Table 5. Case studies of submarine flow failures.
Fines content, FC (%) Mean grain size, D50 (mm) Slope angle before failure, β1 (°) Slope angle after failure, β 2 (°) Undrained shear strength ratio, Su/σ′vi = (γ/γ′) tan β 2 Clean sand equivalent normalized cone resistance, (qc1N)cs*
Jamuna Bridge
Fraser River delta
Nerlerk berm
2–10 0.1–0.2 11–16 3–7 0.11–0.26 40–55
3–15 0.25 20–23 1–5 0.04–0.18 30–45
2–15 (mainly
