Comparing liquefaction evaluation methods using penetration-VS relationships

Soil Dynamics and Earthquake Engineering 24 (2004) 713–721 www.elsevier.com/locate/soildyn

Comparing liquefaction evaluation methods using penetration-VS relationships Ronald D. Andrusa,*, Paramananthan Piratheepanb, Brian S. Ellisc, Jianfeng Zhanga, C. Hsein Juanga a

Department of Civil Engineering, Clemson University, Lowry Hall Box 340911, Clemson, SC 29634-0911, USA b URS Corporation, 915 Wilshire Boulevard, Suite 700, Los Angeles, CA 90017-3437, USA c US Air Force, 5th CES/CEO, Minot AFB, ND 58705-5000, USA

Abstract Three methods that follow the general format of the Seed-Idriss simplified procedure for evaluating liquefaction resistance of soils are compared in this paper. They are compared by constructing relationships between penetration resistance and small-strain shear – wave velocity ðVS Þ implied from cyclic resistance ratio (CRR) curves for the three methods, and by plotting penetration-VS data pairs. The penetration-VS data pairs are from 43 Holocene-age sand layers in California, South Carolina, Canada, and Japan. It is shown that the VS based CRR curve is more conservative than CRR curves based on the Standard Penetration Test (SPT) and Cone Penetration Test (CPT), for the compiled Holocene data. This result agrees with the findings of a recent probability study where the SPT-, CPT-, and VS -based CRR curves were characterized as curves with average probability of liquefaction of 31, 50, and 26%, respectively. New SPT- and CPT-based CRR equations are proposed that provide more consistent assessments of liquefaction potential for the Holocene sand layers considered. q 2004 Elsevier Ltd. All rights reserved. Keywords: Cone penetration test; Earthquake; Liquefaction; In situ tests; Probability; Shear– wave velocity; Standard penetration test

1. Introduction The occurrence of liquefaction in soils is often evaluated using the simplified procedure originally proposed by Seed and Idriss [1] based on the Standard Penetration Test (SPT). This procedure has undergone several revisions and updates since it was first proposed in 1971, including the development of methods based on the Cone Penetration Test (CPT), the Becker Penetration Test (BPT), and small-strain shear – wave velocity ðVS Þ measurements. Youd et al. [2] provide a recent review of the Seed-Idriss simplified procedure and the in situ test methods commonly used to evaluate liquefaction resistance of soils. In situ VS measurements provide a promising alternative to the penetration tests, which may be unreliable in some soils, such as gravelly soils, or may not be feasible at some sites, such as capped landfills. In addition, VS is an engineering property, directly related to small-strain shear modulus, and required for dynamic soil response analyses. On the other hand, some factors that affect VS may not * Corresponding author. Tel.: þ 1-864-656-0488; fax: þ1-864-656-2670. E-mail address: [email protected] (R.D. Andrus). 0267-7261/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2004.06.001

equally affect resistance to liquefaction, which is a mediumto large-strain event. Also, VS testing usually does not produce samples for classification or may not be conducted with sufficient detail to detect thin liquefiable strata. Youd et al. [2] and Andrus et al. [3] provide further discussion on the advantages and disadvantages of the VS - and penetration-based liquefaction evaluation methods. The purpose of this paper is to compare the VS liquefaction evaluation method, or curves, proposed by Andrus and Stokoe [4] and updated in Andrus et al. [3,5] with the SPT and CPT curves summarized in Youd et al. [2] using relationships between penetration resistance and VS : The approach of using penetration-VS relationships to compare curves was applied earlier by Andrus et al. [6] with data from 25 Holocene-age (, 10,000 years) sands with , 10% fines (particles , 0.075 mm). In this paper, the SPT-VS and CPT-VS databases are expanded to include 18 additional sand data pairs. Regression analyses are performed on the expanded databases and the resulting penetration-VS relationships are used to develop new, more consistent liquefaction evaluation curves.

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2. Review of liquefaction evaluation methods

b ¼ 1:0

The Seed-Idriss simplified procedure for evaluating liquefaction resistance basically involves the calculation of two parameters: (1) the level of cyclic loading on the soil caused by the earthquake, expressed as a cyclic stress ratio; and (2) the resistance of the soil to liquefaction, expressed as a cyclic resistance ratio. The cyclic stress ratio, CSR, at a particular depth in a level soil deposit is calculated from (Seed and Idriss [1]):

b ¼ ½0:99 þ FC1:5 =1000

CSR ¼ 0:65ðamax =gÞðsv =s0v Þrd

ð1Þ

where amax ; peak horizontal ground surface acceleration, g, acceleration of gravity, sv ; total vertical (overburden) stress at the depth in question, s0v ; effective overburden stress at the same depth, and rd ; a shear stress reduction coefficient. Three methods, or curves, for determining the cyclic resistance ratio, CRR, are shown in Fig. 1a – c. In Fig. 1a, the curve for determining CRR from energy- and overburden stress-corrected SPT blow count, ðN1 Þ60; by Seed et al. [7] and modified by Youd et al. [2] is shown. This curve is for earthquakes with moment magnitude, Mw ; of 7.5 and sands with fines content, FC, # 5%. To apply the curve to soils with FC . 5%, I. M. Idriss with the assistance of R. B. Seed developed the following correction of ðN1 Þ60 to an equivalent clean sand value [2]: ðN1 Þ60cs ¼ a þ bðN1 Þ60

ð2Þ

where ðN1 Þ60cs , equivalent clean sand value of ðN1 Þ60 ; and a and b; coefficients determined using the following relationships:

a ¼ 0:0

2

a ¼ exp½1:76 2 190=FC  a ¼ 5:0

ð3aÞ

for FC # 5%

for FC $ 35%

for 5% , FC , 35%

ð3bÞ ð3cÞ

b ¼ 1:2

ð4aÞ

for FC # 5% for 5% , FC , 35%

for FC $ 35%

ð4bÞ ð4cÞ

Eqs. (3) and (4) are suggested for routine liquefaction resistance calculations [2]. In Fig. 1b, the curve for determining CRR from overburden stress-corrected CPT tip resistance, qc1N ; by Robertson and Wride [8] is shown. This curve is for earthquakes with Mw of 7.5, and sands with FC # 5% and median grain size, D50 ; of 0.25 –2.0 mm. To apply the curve to soils with FC . 5%; Robertson and Wride [8] developed the following correction of qc1N to an equivalent clean sand value: ðqc1N Þcs ¼ Kc qc1N

ð5Þ

where ðqc1N Þcs ; equivalent clean sand value of qc1N ; and Kc ; a correction factor for grain characteristics determined using the following relationships: Kc ¼ 1:0

for Ic # 1:64

ð6aÞ

Kc ¼ 2 0:403Ic4 þ 5:581Ic3 2 21:63Ic2 þ 33:75Ic 2 17:88 for Ic # 1:64 ð6bÞ where Ic ; soil behavior type index, defined by: Ic ¼ ½ð3:47 2 log QÞ2 þ ð1:22 þ log FÞ2 0:5

ð7Þ

where Q ¼ ½ðqc 2 sv Þ=Pa ½Pa =s0v n

ð8Þ

and F ¼ ½fs =ðqc 2 sv Þ100%

ð9Þ

where qc ; measured cone tip resistance, fs ; measured cone sleeve resistance, Pa ; a reference stress of 100 kPa (or 1 atm), and n; an exponent that depends on soil type. The values of qc ; fs ; Pa ; sv ; and s0v are all in the same units. The value of n ranges from 0.5 for clean sands to 1.0 for

Fig. 1. Liquefaction resistance curves based on SPT by Seed et al. [7], CPT by Robertson and Wride [8], and VS by Andrus and Stokoe [4].

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Fig. 2. Relationships between ðVS1 Þcs and ðN1 Þ60cs for uncemented, Holocene sands.

Fig. 4. Relationships between ðN1 Þ60cs and ðqc1N Þcs for uncemented, Holocene sands.

clays [9], and can be approximated through an iterative approach [8]. In Fig. 1c, the curve for determining CRR from overburden stress-corrected shear – wave velocity, VS1 ; by Andrus and Stokoe [4] is shown. This curve is for earthquakes with Mw of 7.5 and young, uncemented sands and gravels with FC #5%. To apply the curve to soils with FC . 5% and/or older soils, VS1 can be corrected to an equivalent young, clean soil value by:

estimating Kcs :

ðVS1 Þcsa1 ¼ Ka1 ðVS1 Þcs ¼ Ka1 Kcs VS1

ð10Þ

where ðVS1 Þcsa1 ; equivalent young clean soil value of VS1 ; ðVS1 Þcs ; equivalent clean soil value not corrected for age, Kcs ; a fines content correction factor, and Ka1 ; an age factor to correct for high VS1 values caused by aging. Juang et al. [10] suggested the following relationships for

Kcs ¼ 1:0

for FC # 5%

Kcs ¼ 1 þ ðFC 2 5ÞT Kcs ¼ 1 þ 30T

for 5% , FC , 35%

for FC $ 35%

ð11aÞ ð11bÞ ð11cÞ

where T ¼ 0:009 2 0:0109ðVS1 =100Þ þ 0:0038ðVS1 =100Þ2

ð12Þ

Andrus and Stokoe [4] assumed Ka1 ¼ 1:0 for all Holocene-age soils. Because the three CRR curves shown in Fig. 1 are all for Mw ¼ 7:5 earthquakes and sands with FC # 5%; they imply relationships between SPT, CPT and VS : One can obtain these relationships by plotting values of ðN1 Þ60cs ; ðqc1N Þcs and ðVS1 Þcsa1 with the same CRR values. The implied ðN1 Þ60cs 2 ðVS1 Þcsa1 ; ðqc1N Þcs 2 ðVS1 Þcsa1 and ðqc1N Þcs 2 ðN1 Þ60cs relationships are presented in Figs. 2 – 4, respectively. One advantage of studying penetration-VS relationships is they provide comparisons of the liquefaction evaluation methods without needing to calculate CSR. Thus, data from sites not shaken by earthquakes can also be used to validate the consistency between liquefaction evaluation methods.

3. Holocene sand data

Fig. 3. Relationships between ðVS1 Þcs and ðqc1N Þcs for uncemented, Holocene sands.

Data from 43 Holocene-age sand layers with FC # 20% or Ic # 2:25 are also plotted in Figs. 2 –4. The data are summarized in Table 1. They are from California, South Carolina, Canada, and Japan, and are based on measurements performed by various investigators [11 – 22] at both liquefaction and no liquefaction sites. The data were originally compiled by Andrus et al. [6], Piratheepan [23], and Ellis [24]. Four of their compiled Holocene sand data

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Table 1 Data from Holocene soil deposits with FC , 20% or Ic , 2:25 Site name

Depth (m)

USCS soil type

D50 (mm)

FCa (%)

VS test typeb

VS1cs (m/s)

ðN1 Þ60cs

Ic

qc1Ncs

Source

California, USA Bay Bridge, SFOBB1 Bay Bridge, SFOBB1 Bay Farm Island-dike Heber Road, point bar Port of Oakland, P007-2 Port of Oakland, P007-2 Port of Oakland, P007-2 Sandholt Road, UC-4 State Beach, UC-15 State Beach, UC-15 State Beach, UC-15 State Beach, UC-16 State Beach, UC-16 State Beach, UC-16 Treasure Island, B1-B3 Treasure Island, B1-B3 Treasure Island, UM-05 Treasure Island, UM-05 Treasure Island, UM-06 Treasure Island, UM-06 Treasure Island, UM-09 USGS Alameda, ALC026

5.4–7.2 8.0–9.9 3.7–7.8 1.8–4.2 3.0–5.1 5.3–6.8 6.8–9.1 6.3–10.1 2.0–3.8 3.8–5.5 5.6–8.7 2.4–4.6 4.6–6.7 6.7–8.6 2.2–4.0 9.0–11.5 3.3–5.7 5.8–8.3 2.2–5.0 5.0–10.4 2.7–6.3 4.0–10.0

SP-SM SP-SM SP-SM SM SP-SM SP-SM SP-SM SP SP SP SP SP SP SP SP-SM SM SP SP-SC SP SP SP-SC na

0.26 0.27 0.25 0.11 0.29 0.30 0.30 1.11 0.28 0.38 1.68 0.43 0.57 0.57 0.21 0.21 0.33 0.33 nac 1.41 0.15 na

12 8 11 18 7 6 3 3 2 1 2 2 1 1 7 14 4 7 3 3 11 7d

CH CH CH CH CH/SCPT CH/SCPT CH/SCPT SCPT SCPT SCPT SCPT SCPT SCPT SCPT CH CH SCPT SCPT SCPT SCPT SCPT SCPT

152 151 237 233 183 172 167 216 137 156 231 192 175 197 162 183 170 188 175 193 161 233

7 20 50 51 22 13 16 43 7 9 39 22 17 30 21 17 14 18 12 21 9 na

2.15 1.90 1.85 2.00 1.50 1.88 1.71 1.19 1.90 1.73 1.32 1.47 1.40 1.32 1.87 2.11 1.82 1.88 2.10 1.82 2.04 1.73

67 77 230 319 173 73 112 332 67 76 204 171 166 201 85 64 79 72 44 73 68 237

[11] [11] [11] [12,13] [11] [11] [11] [14] [14] [14] [14] [14] [14] [14] [15] [15] [16] [16] [16] [16] [16] [17]

South Carolina, USA WPC 2000-344, SC2 WPC 2000-344, SC3 WPC 2000-344, SC5A WPC 2000-344, SC5B WPC 2000-344, SC10 WPC 2000-344, SC15 WPC 2001-211, SCPT4

6.4–10.4 4.5–8.5 3.8–8.8 3.8–10.8 7.4–10.4 6.4–10.4 1.7–4.7

na na SM SM na na na

na na 0.13 na na na na

6d 6d 29 7d 20d 6d 9d

SCPT SCPT SCPT SCPT SCPT SCPT SCPT

193 160 224 210 247 198 253

na na 29 na na na na

1.67 1.72 1.61 1.77 2.24 1.68 1.85

108 118 130 105 229 105 158

[18] [18] [18] [18] [18] [18] [18]

12.0–17.0 8.0–13.0 6.0–10.0 8.0–12.0 3.0–7.0 27.0–37.0

SP SP SP-SM SP-SM SM SP-SM

0.20 0.20 0.25 0.25 0.17 0.16

,5 ,5 8 10 15 10

SCPT SCPT SCPT SCPT SCPT SCPT

177 168 154 142 129 157

13 10 5 6 6 19

68 53 43 52 28 87

[19] [19] [19] [19] [19] [19]

2.5–5.5 8.5–11.4 3.5–8.4 6.5–11.8 3.5–5.5 5.5–7.5 3.8–8.0 8.0–12.0

SM SP-SM SP-SM SM SP-SM SP-SM SP-SM SP-SM

0.13 0.24 0.29 0.08 0.17 0.19 na na

31 7 8 39 7 8 6 6

SL SL SL SL SL SL DH DH

163 149 171 152 196 298 208 212

14 7 7 24 25 56 29 28

60 62 60 85 na na na na

[20] [20] [20] [20] [21] [21] [22] [22]

Canada Fraser River Delta, Kidd Fraser River Delta, Massey HVC Mine, LL Dam HVC Mine, Highmont Dam Syncrude, J-Pit Syncrude, Mildred Lake Japan Hakodate Port No. 1 Hakodate Port No. 1 Hakodate Port No. 2 Hakodate Port No. 3 Kushiro Port, No. 2 (PB-1) Kushiro Port, No. 2 (PB-1) Port Island, Common Factory Port Island, Common Factory a b c d

,1.64d ,1.64d 1.79d 1.88d 2.07d 1.88d 1.95 1.99 1.83 1.85 na na na na

FC, fines content (silt and clay). CH, crosshole; SCPT, seismic CPT; SL, suspension logger; DH, downhole. na, not available. Estimated fines content or Ic from: FC ¼ 1.75 Ic 3.25 2 3.7 for 1:26 # Ic # 3:5 (Robertson and Wride [8]).

(Coyote Creek with depth of 3.6 – 6.0 m; Bay Bridge Toll Plaza, SFOBB1 with depth of 10.0 –12.8 m; Sandholt Road, UC-4 with depth of 2.1 – 3.5 m, and WPC 2000-344, SC1 with depth of 3.8 –6.8 m) are not considered in this paper, because penetration or VS measurements are not consistent with the data plotted in Figs. 2– 4.

The reason for selecting sands with FC # 20% or Ic # 2:25 is so that a significant number of data points are available for regression analysis, while limiting the FC or Ic corrections. According to a relationship proposed by Robertson and Wride [8], sands with Ic # 2:25 typically have values of FC # 20%: Average values of D50 for

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the sand layers listed in Table 1 range from 0.08 to 1.68 mm. These sands classify as SP, SP-SM, SP-SC, and SM by the Unified Soil Classification System. The general criteria used for selecting the penetration and VS measurements are as follows: (1) Measurements are from below the ground-water table where reasonable estimates of effective stress can be easily made. (2) Measurements are from thick, uniform soil layers identified primarily using CPT measurements. When no CPT measurements are available, exceptions to Criterion 2 are allowed if there are several SPT and VS measurements within the layer that follow a consistent trend. (3) Penetration test locations are within 6 m of the VS test locations. (4) At least two VS measurements, and the corresponding test intervals, are within the uniform layer. (5) Time history records used for VS determination exhibit easy-to-pick shear wave arrivals. Thus, values of VS determined from difficult-to-pick shear – wave arrivals are not used. When the time history records are not available, exceptions to Criterion 5 are allowed if there are at least 3 VS measurements within the selected layer. The 43 Holoceneage sand layers range in depth from 1.7 to 13.0 m. Of the 43 selected sand layers, 26 were tested by seismic cone, 6 by crosshole, 3 by both seismic cone and crosshole, 6 by suspension logger, and 2 by downhole techniques. Values of ðVS1 Þcs are calculated using average FC values. Where no FC information is available, an apparent FC value is calculated using the Ic value and the relationship suggested by Robertson and Wride [8], where FC < 1:75Ic3 2 3:7 for 1:26 # Ic , 3:5: Calculated ðVS1 Þcs values are 0 –7% higher than values of VS1 : SPT blow counts are available for 36 of the 43 selected sand layers. Values of ðN1 Þ60 are determined from measured SPT blow counts using reported test equipment and procedure information. Where no energy measurements are available, average corrections recommended by Youd et al. [2] are assumed based on the type of hammer used. Calculated ðN1 Þ60cs values are 0% to 76% higher than values of ðN1 Þ60 : CPT resistances are available for 39 of the 43 selected layers. All of the CPT measurements are believed to be from 10-cm2 cones. Values of qc1N and Ic are averaged over the interval of the selected VS measurements. They are calculated using the electronic CPT data files, when available. When the electronic files are not available, average values are determined from the reported graphical profiles. Because values of Ic are not available for the six sand layers in Canada, they are approximated using Robertson and Wride’s [8] Ic 2 FC relationship. Calculated (qc1N)cs values are 0 –77% higher than values of qc1N :

4. Regression analysis Average equations are determined for the Holocene sand data from nonlinear regression analysis by power curve

717

fitting. The decision to use power curve fitting is based primarily on results of earlier studies. The regression equation developed for 36 ðN1 Þ60cs 2 ðVS1 Þcs data pairs is expressed as: ðVS1 Þcs ¼ B1 ½ðN1 Þ60cs B2

ð13Þ

where B1 ¼ 87:8 ^ 14:0 (95% confidence interval) and B2 ¼ 0:253 ^ 0:052; with ðVS1 Þcs in m/s and ðN1 Þ60cs in blows/0.3 m. These values of B1 and B2 are most similar to values obtained in earlier SPT-VS regression studies by Yoshida et al. [25] for fine sand, Fear and Robertson [26] for Ottawa sand, and Andrus and Stokoe [4] for uncemented, Holocene-age sands. The coefficient of multiple regression, R2 ; and standard deviation of the residuals (or errors), s; associated with this regression are 0.738 and 18 m/s, respectively. The equation developed for 39 ðqc1N Þcs 2 ðVS1 Þcs data pairs is expressed as: ðVS1 Þcs ¼ B1 ½ðqc1N Þcs B2

ð14Þ

where B1 ¼ 62:6 ^ 17:8 and B2 ¼ 0:231 ^ 0:060; with ðVS1 Þcs in m/s and ðqc1N Þcs is dimensionless. These values of B1 and B2 are most similar to values obtained in earlier CPT-VS regression studies by Robertson et al. [27] for mainly quartz sands and Hegazy and Mayne [28] for various sands. Values of R2 and s associated with this regression are 0.619 and 20 m/s, respectively. The equation developed for 32 ðqc1N Þcs 2 ðN1 Þ60cs data pairs is expressed as: ðN1 Þ60cs ¼ B1 ½ðqc1N Þcs B2

ð15Þ

where B1 ¼ 0:356 ^ 0:296 and B2 ¼ 0:851 ^ 0:160 with ðN1 Þ60cs in blows/0.3 m and ðqc1N Þcs is dimensionless. It should be noted that similar B1 and B2 values (0.263 and 0.913, respectively) are obtained when Eqs. (13) and (14) are set equal to each other and solved for ðN1 Þ60cs ; indicating that the three equations are in general agreement. For this regression, R2 ¼ 0:798 and s ¼ 6 blows/0.3 m. This high s value of 6 blows/0.3 m associated with Eq. (15) is not likely the result of grain size characteristics. Robertson and Campanella [29] and Seed and de Alba [30] developed relationships between median grain size, D50 ; and the ratio of CPT tip resistance to energy-corrected SPT blow count. Their relationships exhibit penetration ratios increasing from about 2.5 at D50 ¼ 0:01 mm to about 5.5 –8 at D50 ¼ 1 mm. This increasing trend is not seen in the energy-, overburden-, and fines content-corrected penetration resistances listed in Table 1. Presented in Fig. 5 are the ratios of corrected penetration resistances compiled for this study versus corresponding values of D50 : Because there is little or no increasing trend in the plotted ðqc1N Þcs =ðN1 Þ60cs values with D50 ; it appears that the fines content correction accounted for most, if not all, of the effects of grain size characteristics. Eqs. (13) – (15) are also plotted in Figs. 2 – 4, respectively. Although somewhat better fits of the plotted

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Fig. 5. Relationships between corrected penetration ratio and median grain size for uncemented, Holocene sands.

data can be obtained using more complex regression models, these equations appear to be adequate for the comparison of liquefaction evaluation methods.

5. Comparison of evaluation methods As explained by Andrus and Stokoe [4], both the SPT and VS evaluation methods provide similar predictions of liquefaction resistance when the data point lies on the implied curve in Fig. 2. When the data point plots below the implied curve, the VS method provides the more conservative prediction. When the data point plots above the implied curve, the SPT method provides the more conservative prediction. Because most of the data points plot below the implied curve, the VS method provides an overall more conservative prediction of liquefaction resistance than does the SPT method below ðN1 Þ60cs of 26 for the plotted Holocene sand data. Above ðN1 Þ60cs of 26, both methods appear to provide similar predictions on average. This finding agrees with the probability assessment of Juang et al. [10], where the SPT-based CRR curve (see Fig. 1a) and the VS -based CRR curve (see Fig. 1c) are characterized with average probability of liquefaction, PL ; of 31 and 26%, respectively. In Fig. 3, both the CPT and VS evaluation methods provide similar predictions of liquefaction resistance when the data point lies on the implied curve. When the data point plots below the implied curve, the VS method provides the more conservative prediction. When the data point plots above the implied curve, the CPT method provides the more conservative prediction. Because the majority of the data points lie below the implied curve, the VS method provides an overall more conservative prediction of liquefaction resistance than does the CPT method for the plotted data.

This finding also agrees with the assessment of Juang et al. [10], where the CPT-based CRR curve (see Fig. 1b) is characterized with average PL of 50%. The flatter slope exhibited by the implied curves below ðN1 Þ60cs of 6 in Fig. 2 and ðqc1N Þcs of 30 in Fig. 3 can be explained by different assumed minimal values of CRR. A minimum CRR value of 0.05 is assumed for the SPT and CPT liquefaction resistance curves, whereas 0.033 is assumed for the VS liquefaction resistance curve for the lowest VS1 value (100 m/s) of most soils with FC # 5%: More liquefaction and no liquefaction case histories are needed at these lower values of CSR, ðN1 Þ60cs ; ðqc1N Þcs ; and ðVS1 Þcs to fully assess these assumptions. In Fig. 4, both the CPT and SPT methods provide the same predictions of liquefaction resistance, when the data point lies on the implied curve. When the data point plots below the implied curve, the SPT method provides the more conservative prediction. When the data point plots above the implied curve, the CPT method provides the more conservative prediction. Because more of the data points between ðqc1N Þcs of 40 and 120 plot above the implied curve, the CPT method provides more conservative predictions of liquefaction resistance than does the SPT method in this range. Above ðqc1N Þcs of about 120, the mean curve for the data points plots below the implied curve, indicating the SPT method is more conservative in that range. Liquefaction resistance curves that are consistent, on average, may be obtained using Eqs. (13) and (14) and the VS -based CRR curve defined by [4]:     ðVS1 Þcsa1 2 1 1 þ2:8 2 CRR7:5cs ¼ 0:022 2152ðVS1 Þcsa1 215 100 ð16Þ Substituting Eqs. (13) and (14) into Eq. (16) leads to the following relationships: CRR7:5cs ¼ 0:017½ðN1 Þ60cs 0:506   1 1 þ2:8 2 215287:8½ðN1 Þ60cs 0:253 215 CRR7:5cs ¼ 0:0086½ðqc1N Þcs 0:462   1 1 þ2:8 2 215262:6½ðqc1N Þcs 0:213 215

ð17Þ

ð18Þ

Eqs. (16) –(18) are compared with the original CRR curves in Fig. 6a –c, respectively. The ranges where the VS -based CRR curve is more conservative than the SPTand CPT-based CRR curves can be clearly seen in Fig. 6a and b, respectively. It should be noted that the dashed curves in Fig. 6a and b are developed from comparative analyses of data from both sands layers where liquefaction did and did not occur. These analyses incorporate corrected SPT penetration resistances as great as 50 and corrected CPT penetration resistances as high as 330. The solid curves were developed

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Fig. 6. Comparison of liquefaction resistance curves by Seed et al. [7], Robertson and Wride [8], and Andrus and Stokoe [4] with curves derived from penetration-VS equations.

by visually drawing curves to bound most of the liquefaction case histories available at that time. The following discussion provides additional support for the use of the dashed curves in Fig. 6a and b. Because Eq. (16) is characterized with PL ¼ 26% [10] and the penetration-VS data pairs compiled for this paper are from young sand deposits, Eqs. (17) and (18) should also define curves of similar PL : To verify this assumption, results of various probability studies are plotted in Fig. 7a – c. In Fig. 7a, Eq. (17) is compared with six PL ¼ 26% curves determined from SPT-based liquefaction case histories. The curves by Liao et al. [31], Youd and Noble [32], Toprak et al. [34], and Juang et al. [10] Model 1 are derived from logistic regression analysis. The curves by Cetin et al. [34] and Juang et al. [10] Model 2 are derived from Bayesian analysis. Five of the PL ¼ 26% curves suggest upper bounds for liquefaction occurrence greater than ðN1 Þ60cs of 30, the value traditionally assumed as the limiting upper bound [7]. These larger upper bound values could be real, or they could be the result of the model assumed. Nevertheless, the agreement is remarkable given the fact that Eq. (17) is derived from VS -based liquefaction case histories and the SPT-VS regression equation. In Fig. 7b, Eq. (18) is compared with three PL ¼ 26% curves determined from CPT-based liquefaction case

histories. The curves by Toprak et al. [33] and Juang et al. [10] Model 1 are derived from logistic regression analysis. The Model 2 curve by Juang et al. [10] is derived from Bayesian analysis. It can be seen that Eq. (18) generally agrees with all three curves below ðqc1N Þcs of 100. Above ðqc1N Þcs of 100, each curve suggests a different limiting upper bound value of ðqc1N Þcs for liquefaction occurrence. Eq. (18) and the Juang et al. [10] Model 1 curve both suggest upper bounds for liquefaction occurrence greater than ðqc1N Þcs of 160, the value traditionally assumed as the limiting upper bound [8]. These results support I. M. Idriss’ suggestion [2, page 821] that the limiting upper value of 160 be increase by 10– 15%. In Fig. 7c, Eq. (16) is compared with three PL ¼ 26% curves determined by Juang et al. [10]. Model 1 is derived from logistic regression analysis using a model similar in form to the logistic model equation assumed in the SPT and CPT probability studies [31 –33]. Model 2 in Fig. 7c is also derived from logistic regression analysis, but is different from the Model 1 equation by an additional term. Model 3 is the Andrus and Stokoe [4] curve and is characterized as a PL ¼ 26% curve from Bayesian analysis. It can be seen that all three curves are in general agreement below ðVS1 Þcsa1 of 210 m/s. The high limiting upper ðVS1 Þcsa1 value of 235 m/s suggested by Model 1 is believed to be the result of the form

Fig. 7. Comparison of liquefaction resistance curves derived from the VS -based CRR curve by Andrus and Stokoe [4] and penetration-VS equations with PL ¼ 26% curves developed by various investigators.

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of the assumed logistic model equation, and not a true limiting upper value for young, uncemented sands.

6. Recommendations for design evaluations The Building Seismic Safety Council (BSSC) [35] suggests a factor of safety of 1.2 –1.5 is appropriate when applying the SPT-based CRR curve by Seed et al. [7] in engineering design evaluations, where factor of safety, FS ; is defined as CRR/CSR Traditionally, liquefaction is predicted to occur when FS # 1; and not occur with FS . 1: Juang et al. [10] characterize the Seed et al. [7] curve as a PL ¼ 31% curve, and interpret FS of 1.2 – 1.5 as corresponding to PL of 20– 10%, respectively. The SPT-, CPT-, and VS -based CRR curves defined by Eqs. (16) – (18), respectively, are shown earlier in this paper to be approximately PL ¼ 26% curves. When applying these equations in engineering practice, the appropriate range of FS values that correspond to the BSSC’s [35] suggested range is 1.1 to 1.4 [10]. Greater care should be exercised when applying the VS -based CRR curves to soils older than Holocene age. Preliminary values of Ka1 for Pleistocene-age (10,000 – 1.8 million years) sands are given in Andrus and Stokoe [4] and Andrus et al. [3]. Until better age correction factors are developed, these values of Ka1 should be used when applying the VS -based CRR curves to Pleistocene sands. Work is under way to develop a continuous relationship between age and Ka1 ; which will be presented in another paper.

7. Conclusions Regression analyses were performed on penetration and VS data pairs from Holocene sands, and the resulting equations were compared with relationships implied by CRR curves for three liquefaction evaluation methods. Based on the comparisons, the following conclusions can be made: For the compiled Holocene sand data, the SPT-based CRR curve [7] between ðN1 Þ60cs values of 8 –20 was shown to be less conservative, on average, than the VS - and CPT-based CRR curves [4,8]. The CPT-based CRR curve above a ðqc1N Þcs value of about 120 was shown to be less conservative than the SPT- and VS -based CRR curves. These results are in general agreement with a recent probability study [10]. New equations were developed for estimating CRR from ðN1 Þ60cs and ðqc1N Þcs by substituting the developed regression equations into the equation defining the VS - based CRR curve. Because the VS -based CRR curve has been characterized with PL of about 26% [10] and the penetration-VS data pairs were from young sand deposits, these new equations should correspond to a similar PL value. This conclusion was supported by nine

PL ¼ 26% curves developed by various investigators using SPT and CPT liquefaction case histories. More high-quality penetration-VS data are needed from other deposit and soil types to further compare the liquefaction evaluation methods. One advantage of studying penetration-VS relationships is that they provide comparisons of the liquefaction evaluation methods without needing to calculate CSR. Thus, data from sites not shaken by strong earthquakes, which have been largely ignored in the past, can be used in the comparisons.

Acknowledgements This work was funded in part by the US Geological Survey, Department of the Interior under USGS award number 01HQGR0007; and by the South Carolina Department of Transportation (SCDOT) and the Federal Highway Administration under SCDOT Research Project No. 623. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the US Government or the State of South Carolina. The authors acknowledge the insights shared by K.H. Stokoe, II of The University of Texas at Austin during earlier collaborative studies and by T.L. Holzer of USGS during parts of this work. The authors also express their sincere thanks to the many individuals who generously assisted with data compilation. In particular, T. L. Holzer, M.J. Bennett, J.C. Tinsley, III, and T.E. Noce of USGS, S. Iai of the Port and Harbour Research Institute in Japan, R. Boulanger of the University of California at Davis, and T.J. Casey and W.B. Wright of Wright Padgett Christopher, Inc.

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