Semi-empirical procedures for evaluating liquefaction potential during earthquakes

Transcription

1 Soil Dynamics and Earthquake Engineering 26 (26) Semi-empirical procedures for evaluating liquefaction potential during earthquakes I.M. Idriss, R.W. Boulanger* Department of Civil and Environmental Engineering, University of California, Davis, CA, USA Received 5 April 24; revised October 24; accepted November 24 Abstract Semi-empirical procedures for evaluating the liquefaction potential of saturated cohesionless soils during earthquakes are re-examined and revised relations for use in practice are recommended. The stress reduction factor (r d ), earthquake magnitude scaling factor for cyclic stress ratios (MSF), overburden correction factor for cyclic stress ratios (K s ), and the overburden normalization factor for penetration resistances (C N ) are discussed and recently modified relations are presented. These modified relations are used in re-evaluations of the SPT and CPT case history databases. Based on these re-evaluations, revised SPT- and CPT-based liquefaction correlations are recommended for use in practice. In addition, shear wave velocity based procedures are briefly discussed. q 25 Elsevier Ltd. All rights reserved. Keywords: ; SPT; CPT; Earthquakes. Introduction Semi-empirical field-based procedures for evaluating liquefaction potential during earthquakes have two essential components: () the development of an analytical framework to organize past case history experiences, and (2) the development of a suitable in situ index to represent soil liquefaction characteristics. The original simplified procedure by Seed and Idriss [] for estimating earthquake-induced cyclic shear stresses continues to be an essential component of the analysis framework, although there have been a number of refinements to the various components of this framework. In situ penetration tests have continued to prove useful for representing soil liquefaction characteristics because they not only provide an indication of denseness, but also reflect other important characteristics such as fabric, gradation, cementation, age, and stress history, as was articulated by Seed [2]. Overall, the major developments in the past thirty years have included improvements in * Corresponding author. Tel.: C ; fax: C address: rwboulanger@ucdavis.edu (R.W. Boulanger) /$ - see front matter q 25 Elsevier Ltd. All rights reserved. doi:.6/j.soildyn the in situ index tests (e.g. SPT, CPT, BPT, shear wave velocity), the refinements in the analysis framework, and the continued collection of liquefaction/no-liquefaction case histories. The strength of the semi-empirical approach is the use of theoretical considerations and experimental findings to establish the framework of the analysis procedure and its components. Sound theory provides the ability to make sense out of the field observations, tying them together, and thereby having more confidence in the validity of the approach as it is used to interpolate or extrapolate to areas with insufficient field data to constrain a purely empirical solution. Purely empirical interpretations of the field case histories, without any physics-based framework, would leave unclear the conditions for which the empirical relations truly are applicable. For example, the purely empirical derivations of individual factors of the analysis method (e.g. an MSF, r d,ork s relation) are complicated by their dependence on other components of the analysis method, and thus a purely empirical derivation is often not well constrained by the available case history data. This paper provides an update on the semi-empirical field-based procedures for evaluating liquefaction potential of cohesionless soils during earthquakes. This update

2 6 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) 5 3 includes recommended relations for each part of the analytical framework, including the: stress reduction coefficient r d, magnitude scaling factor MSF, overburden correction factor K s for cyclic stress ratios, and overburden correction factor C N for penetration resistances. For each of these parameters, the emphasis has been on developing relations that capture the essential physics while being as simplified as possible. These updated relations were then used in re-evaluations of the field case histories to derive revised deterministic SPT-based and CPT-based liquefaction correlations. Lastly, shear wave velocity (V S ) based liquefaction correlations are discussed briefly. 2. Overview of the framework used for semi-empirical liquefaction procedures A brief overview is provided for the framework that is used as the basis for most semi-empirical procedures for evaluating liquefaction potential of cohesionless soils during earthquakes. This overview provides the context in which the r d, MSF, K s, and C N relations are derived and used. Each of these factors is then revisited in subsequent sections. 2.. The simplified procedure for estimating cyclic shear stress ratios induced by earthquake ground motions The Seed Idriss [] simplified procedure is used to estimate the cyclic shear stress ratios (CSR) induced by earthquake ground motions, at a depth z below the ground surface, using the following expression: CSR Z :65 s voa max s vo r d () in which a max is the maximum horizontal acceleration at the ground surface in g s, s vo is the total vertical stress and s vo is the effective vertical stress at depth z. The parameter r d is a stress reduction coefficient that accounts for the flexibility of the soil column (e.g. r d Z corresponds to rigid body behavior) as illustrated in Fig.. The factor of 5 is used to convert the peak cyclic shear stress ratio to a cyclic stress ratio that is representative of the most significant cycles over the full duration of loading Adjustment for the equivalent number of stress cycles in different magnitude earthquakes The values of CSR calculated using Eq. () pertain to the equivalent uniform shear stress induced by the earthquake ground motions generated by an earthquake having a moment magnitude M. It has been customary to adjust the values of CSR calculated by Eq. () so that the adjusted values of CSR would pertain to the equivalent uniform shear stress induced by the earthquake ground motions generated by an earthquake having a moment magnitude MZ7 2, i.e. (CSR) MZ7.5. Accordingly, the values of (CSR) MZ7.5 are given by: ðcsrþ MZ7:5 Z CSR MSF Z :65 s voa max rd svo MSF 2.3. Use of the SPT blow count and CPT tip resistance as indices for soil liquefaction characteristics The effective use of SPT blow count and CPT tip resistance as indices for soil liquefaction characteristics require that the effects of soil density and effective confining stress on penetration resistance be separated. Consequently, Seed et al. [3] included the normalization of penetration resistances in sand to an equivalent svo of one atmosphere (P a Z.6 tsfz kpa) as part of the semi-empirical procedure. This normalization currently (2) a max Maximum Shear Stress r d = (τ max ) d /(τ max ) r h γh Depth (τ max ) r = γha max (τ max ) r (τ max ) d Fig.. Schematic for determining maximum shear stress, t max, and the stress reduction coefficient, r d.

3 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) takes the form: ðn Þ 6 Z C N ðnþ 6 (3) q C Z C N q C (4) in which the (N) 6 value corresponds to the SPT N value after correction to an equivalent 6% hammer efficiency [4,5], and q C is the cone tip resistance. In addition, q C is conveniently normalized by P a to obtain a dimensionless quantity (i.e. q CN Zq C /P a ), as suggested by Robertson and Wride [6]. The purpose of the overburden normalization is to obtain quantities that are independent of svo and thus more uniquely relate to the sand s relative density, D R. The correlation of the cyclic stress ratio required to cause liquefaction (which will be designated as CRR to distinguish it from the cyclic stress ratio CSR induced by the earthquake ground motions) to normalized penetration resistance is thus directly affected by the choice of the C N relation, as will be illustrated later in this paper Adjustment of cyclic resistance for the effects of overburden stress and sloping ground conditions The cyclic resistance ratio (CRR) of cohesionless soil varies with effective confining stress and is affected by the presence of static driving shear stresses such as exist beneath slopes. Note that CRR is the cyclic stress ratio that causes liquefaction for a MZ7 2 earthquake as obtained from the case-history-based semi-empirical correlations. Since the semi-empirical liquefaction correlations are based primarily on data for level ground conditions and effective overburden stresses in the range of G kpa, Seed [7] recommended that the CRR be corrected for these effects using the following expression: CRR Z CRR sz;az K s K a (5) in which K s is the overburden correction factor and K s is the static shear stress correction factor. Revised K s relations are described in more detail by Boulanger [8] and by Idriss and Boulanger [9,], and are not reviewed herein. 3. Stress reduction coefficient, r d Seed and Idriss [] introduced the stress reduction coefficient r d as a parameter describing the ratio of cyclic stresses for a flexible soil column to the cyclic stresses for a rigid soil column, as illustrated in Fig.. They obtained values of r d for a range of earthquake ground motions and soil profiles having sand in the upper 5Gm (z5 ft) and suggested an average curve for use as a function of depth. The average curve, which was extended only to a depth of about 2 m (z4 ft), was intended for all earthquake magnitudes and for all profiles. The shear stresses induced at any point in a level soil deposit during an earthquake are primarily due to the vertical propagation of shear waves in the deposit. These stresses can be calculated using analytical procedures and are particularly dependent on the earthquake ground motion characteristics (e.g. intensity and frequency content), the shear wave velocity profile of the site, and the dynamic soil properties. Idriss [], in extending the work of Golesorkhi [2], performed several hundred parametric site response analyses and concluded that for the conditions of most practical interest, the parameter r d could be adequately expressed as a function of depth and earthquake magnitude (M). The following relation was derived using those results: Lnðr d Þ Z aðzþ CbðzÞM (6a) z aðzþ ZK:2 K:26 sin :73 C5:33 (6b) z bðzþ Z :6 C:8 sin :28 C5:42 (6c) in which z is depth in meters and M is moment magnitude. These equations are applicable to a depth z%34 m, whereas the following expression is applicable for zo34: r d Z :2 expð:22mþ (6d) The uncertainty in r d increases with increasing depth such that Eq. (6) should only be applied for depths less than about 2G m. evaluations at greater depths often involve special conditions for which more detailed analyses can be justified. For these reasons, it is recommended that CSR (or equivalent r d values) at depths greater than about 2 m should be based on site response studies, providing, however, that a high quality response calculation can be completed for the site. Plots of r d calculated using Eq. (6) for MZ5.5, 6.5, 7.5 and 8 are presented in Fig. 2. Also shown in this figure is the average of the range published by Seed and Idriss []. Depth Below Ground Surface - m Stress Reduction Coefficient, r d Average of Range Published by Seed & Idriss (97) Magnitude: M = 5½ M = 6½ M = 7½ M = 8 Fig. 2. Variations of stress reduction coefficient with depth and earthquake magnitude (from Idriss []).

4 8 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) 5 3 The information in Fig. 2 indicates that the average of the range published by Seed and Idriss is comparable to the curve calculated using Eq. (6) with MZ8 for depths shallower than about 4 m and is comparable to the curve calculated using Eq. (6) with MZ7 2 for depths greater than about 8 m. Seed et al. [3] proposed the use of r d values that are not only a function of depth and earthquake magnitude, but also of the level of shaking and the average shear wave velocity over the top 4 ft (z2 m) of the site. It is believed that this adds another degree of complication and implied accuracy that is not warranted at this time. Therefore, it is suggested that the use of Eq. (6) would provide a sufficient degree of accuracy for engineering applications and it is recommended that these equations be used in lieu of the figure originally published by Seed and Idriss [] or any of the equations that have been derived over the past 3 or so years based on that figure. 4. Magnitude scaling factor, MSF The magnitude scaling factor, MSF, has been used to adjust the induced CSR during earthquake magnitude M to an equivalent CSR for an earthquake magnitude, MZ7 2. The MSF is thus defined as: MSF Z CSR M =CSR MZ7:5 (7) Thus, MSF provides an approximate representation of the effects of shaking duration or equivalent number of stress cycles. Values of magnitude scaling factors were derived by combining: () correlations of the number of equivalent uniform cycles versus earthquake magnitude, and (2) laboratory-based relations between the cyclic stress ratio required to cause liquefaction and the number of uniform stress cycles. These two relations are interdependent, as described below, and thus must be developed in parallel to maintain compatibility. Methods for converting an irregular time series to equivalent uniform cycles involve similar concepts to those used in fatigue studies. The relation between CSR required to cause liquefaction (i.e. CRR) and number of uniform stress cycles (N), such as shown in Fig. 3, provides the means to convert the irregular stress time series into an equivalent number of uniform stress cycles. For example, the data for Niigata sand in Fig. 3 indicate that uniform cycles at CRRZ4 would cause liquefaction, while it would take 4 uniform cycles at CRRZ8 to cause liquefaction. Thus, if an irregular stress time series consists of two cycles, one cycle with a peak of 4 and the other cycle having a peak of 8, the irregular time series can be converted to an equivalent uniform stress time series having.25 (i.e. C/4) cycles with a peak of 4, or 5 (i.e. C4/) cycles with a peak of 8. Cyclic Stress Ratio Relative Density = 78% Relative Density = 54% (Adjusted by the ratio of 78/54)..9 This process can be carried out for any given irregular time series to represent it by an equivalent number of stress cycles each having the same peak stress. A unique conversion is obtained when CRR is related to N by a power relationship of the following form: CRR Z A o ðnþ Kb (8) where b is the slope of the CRR versus N line on a log log plot. Accordingly, the numbers of cycles to cause failure at two different CSR are related as follows: N A N B Z Test results on frozen samples from Niigata (after Yoshimi et al 989) Test results by Yoshimi et al (984) on frozen samples Number of Cycles, N Fig. 3. Cyclic stress ratio to cause liquefaction versus number of uniform loading cycles for frozen samples tested by Yoshimi et al. [2,34]. CSR =b B (9) CSR A The number of equivalent uniform cycles determined for any given irregular stress time series, therefore, depends on the value of b in Eqs. (8) and (9). Idriss [] re-evaluated the MSF derivation, as summarized in Figs. 3 through 6. Results of cyclic tests on high quality samples obtained by frozen sampling techniques were used to define the variation in CRR with the number of uniform loading cycles, as shown in Fig. 3. The two sets of test results shown in Fig. 3 have essentially the same slope on the log(crr) versus log(n) plot (i.e. bz.337), and therefore will produce comparable estimates for the equivalent number of uniform cycles produced by earthquakes of different magnitudes, and thus comparable MSF relations. In comparison, the original Seed and Idriss [4] MSF values were based on data for reconstituted sands that had significantly lower cyclic strengths than for these field samples and a different slope on a log(crr) versus log(n) plot. Despite these differences, the re-evaluated relation for the number of equivalent uniform stress cycles versus earthquake magnitude turned out to be only slightly different from the Seed et al. [5] results, as shown in Fig. 4. The relations in Figs. 3 and 4 were then used to derive the curve in Fig. 5, wherein CRR was further normalized by the CRR value for 5 uniform stress cycles, which is the number of cycles obtained for MZ7 2 as shown in Fig. 4.

5 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) Number of Equivalent Stress Cycles The MSF relation produced by this re-evaluation was then expressed by Idriss [] as: MSF Z 6:9 exp KM K :58 (a) 4 MSF% :8 (b) The values of MSF obtained using Eq. () are presented in Fig. 6, together with those proposed by others. The re-evaluated MSF values are somewhat greater than those originally proposed by Seed and Idriss [4] and to those more recently derived by Cetin et al. [6] and summarized in Seed et al. [3,7]. The relations by Ambraseys [8], and Arango [9] give significantly larger MSF values for earthquake magnitudes M!7, but these differences are partly attributable to differences in the assumed r d relations, as described below. MSF and r d relations are inter-related through their dependence on earthquake magnitude. For example, CRR at N Cycles / CRR at N = Earthquake Magnitude, M Seed & Idriss (982) Idriss (999) Fig. 4. Number of equivalent stress cycles versus earthquake magnitude. Magnitude = 5½.69 Magnitude = 6½.3. Number of Cycles Required to Reach r u = % or 5% DA Strain Fig. 5. Derivation of MSF for various earthquake magnitudes based on laboratory cyclic test data on frozen samples. Magnitude = 7½. Magnitude = 8½.77 Magnitude Scaling Factor, MSF Earthquake Magnitude, M Seed & Idriss (982) Tokimatsu & Yoshimi (983) Ambraseys (988) Arango (996) Seed et al (23) Idriss (999) M MSF = 6.9 exp.58 4 Fig. 6. Magnitude scaling factor, MSF, values proposed by various investigators. smaller earthquake magnitudes result in smaller r d values and larger MSF values. Consequently, empirical derivations of MSF that rely on magnitude-independent r d relations (e.g. [8,9]) are lumping both effects of earthquake magnitude into the MSF parameter alone. For this reason, it is essential that r d and MSF relations be used in the same combination in which they were derived. However, even if the MSF relationships by Ambraseys [8] or Arango [9] are used with their corresponding magnitude-independent stress reduction coefficients, it is believed that they will produce unconservative results for shallow depths during small magnitude earthquakes (say, M%6 2 ). The MSF relation by Idriss [] is limited to a maximum value of.8 at small earthquake magnitudes (M%5 4 ). This limit arises from consideration of the effects of one single peak in the cyclic shear stress time series. For an earthquake dominated by one single strong cycle of shaking, the equivalent uniform cyclic loading can be no smaller than 2 cycle at the peak cyclic stress. Taking this limiting case to consist of 3 4 of a cycle at the peak stress, the equivalent number of uniform loading cycles at 5 times the peak stress can be computed from Eq. (9) as: N min Z : =:337 3 :65 4 cycles Z 2:69 cycles () This minimum value for N applies for all M%5 4,as shown on Fig. 4. The corresponding maximum value of the MSF at M%5 4 can then be computed using Eqs. (7) and (9) rearranged as: MSF Z CSR M Z N b MZ7:5 (2a) CSR MZ7:5 N M MSF Z 5 :337 Z :8 (2b) 2:69

6 2 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) 5 3 Thus, the maximum MSF value, expressed in Eq. () and shown in Fig. 6, derives from the fact that the minimum duration of small magnitude earthquakes would correspond to about 3 4 of a cycle at the peak stress. The r d and MSF relations described in Eqs. (6) and () are recommended for use in practice because they incorporate the primary features of behavior identified by analytical and experimental studies, without becoming too complex or implying undue accuracy. The actual behavior is considerably more complicated, including the observations by Liu et al. [2] regarding the dependence of MSF on distance from the rupture source, the earlier work of Yoshimi et al. [2] showing a dependence of MSF on D R, and the recent work by Seed et al. [3,7] indicating the influence of the level of shaking and stiffness of the profile on r d. Nonetheless, it is believed that incorporating these refinements into the semi-empirical procedure introduces more complexity than is warranted at this time. 5. Overburden correction factor, K s The effect of overburden stress on CRR was recently reevaluated in some detail by Boulanger [22] and Boulanger and Idriss [23]. This re-evaluation used a critical state framework in which a relative state parameter index (x R ), as defined in Fig. 7, was introduced by Boulanger [8] as a practical means to inter-relate the combined effects of D R and s vo on CRR. As shown in Fig. 7, x R is the difference between the current D R and the critical state D R (denoted D R,CS ) for the same mean effective normal stress. The empirical critical state line in Fig. 7 was derived from Bolton s [24] relative dilatancy index (I RD ), which is an empirical index that embodies critical state concepts. The parameter Q determines the stress at which the critical state line curves sharply downwards, indicating the onset of Relative density, D R % % Critical state line from I RD relation (Bolton 986) with Q =.. Mean effective normal stress, p / P a Fig. 7. Definition of the relative state parameter index (after Boulanger [8]). significant particle crushing, and its value depends on grain type, with Qz for quartz and feldspar [24]. The resulting x R parameter enables the incorporation of critical state concepts into the analytical framework that is used to evaluate liquefaction potential. Boulanger [22] showed that CRR could be expressed as a unique function of x R, and Idriss and Boulanger [9] showed that x R could be expressed in terms of SPT or CPT penetration resistance. The studies described above showed that overburden stress effects on CRR could be represented in either of two ways: () through the additional normalization of penetration resistances for relative state, thereby producing the quantities (N x ) 6 and q Cx, or (2) through a K s factor. In the first approach, the normalization for relative state is in addition to the conventional normalization for overburden stress [Eqs. (3) and (4)] and it eliminates the need for a K s factor. The first approach has several technical advantages, while the second approach has been the standard approach since 983. More details regarding the use of either approach are given in Boulanger and Idriss [23], and are not repeated here. Instead, only the resulting relations for K s are summarized because they can more easily be compared to the methods currently in use. The recommended K s relations, as expressed by Boulanger and Idriss [23], are: K s Z KC s ln s Vo P a %: (3a) C s Z %:3 (3b) 8:9 K7:3D R Idriss and Boulanger [9] re-evaluated correlations between (N ) 6, q CN and D R for the purpose of liquefaction evaluations, and recommended the following expressions for clean sands: rffiffiffiffiffiffiffiffiffiffiffiffiffi ðn D R Z Þ 6 (4) 46 D R Z :478ðq CN Þ :264 K:63 (5) Boulanger and Idriss [23] subsequently expressed the coefficient C s in terms of (N ) 6 or q CN as: C s Z p 8:9 K2:55 ffiffiffiffiffiffiffiffiffiffiffiffi (6) ðn Þ 6 C s Z 37:3 K8:27ðq cn Þ :264 (7) with (N ) 6 and q CN limited to maximum values of 37 and 2, respectively, in these expressions (i.e. keeping C s %.3). The resulting K s curves, calculated using Eqs. (3), (6) and (7), are shown in Fig. 8 for a range of (N ) 6 and q CN. Although it is recommended that K s be restricted to % for use with the liquefaction evaluation procedures developed

7 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) K σ (N ) 6 =,q cn =8 (N ) 6 =2,q cn =3 (N ) 6 =4,q cn =5 (N ) 6 =3,q cn = Vertical effective stress, σ v / P a Fig. 8. K s relations derived from x R relations (from Boulanger and Idriss [23]). herein [Eq. (3)], the K s curves are shown without this restriction in Figs. 8 and 9. The recommended K s relations provide significantly higher K s values at s vo=p a O and lower K s values at s vo=p a! in comparison to the K s curves developed by Hynes and Olsen [25] and recommended in Youd et al. [26], as shown in Fig. 9. The K s values were restricted to % [Eq. (3)] for the re-evaluation of the SPT and CPT liquefaction correlations presented later, although conceptually the K s values should be allowed to exceed. when s vo=p a is less than unity. The reasons for imposing this restriction on K s are as follows. First, the primary purpose of the K s relation is for the extrapolation of the semi-empirical correlations to depths K σ D R =4% D R =6% D R =8% Hynes & Olsen (998) This study D R =4% D R =6% D R =8% Vertical effective stress, σ v / P a Fig. 9. Comparison of derived K s relations to those recommended by Hynes and Olsen [25] (from Boulanger and Idriss [23]). beyond which the empirical data are available, and thus the K s relations were derived to most closely match the x R - based analysis results for!s vo=p a! [23]. A consequence of this focus on higher confining stresses was that the derived K s relations slightly overestimate the x R -based K s values at s vo=p a! for the relative densities of most interest. For example, for D R Z5% and s vo=p a Z.5, the x R -based K s value is.5 while Eq. (3) gives.7. In contrast, the Hynes and Olsen [25] relations give K s Z.9 and the empirical relation by Seed et al. [7] gives K s Z.2 for this case. In effect, the x R -based analyses show that K s only slightly exceeds. at s vo=p a! because the critical state line is relatively flat at low confining stresses (Fig. 7). In addition, it was subsequently found that letting K s exceed. [using Eq. (3) but without an upper limit of unity], caused four data points for the clean sands from shallower depths to fall somewhat below the recommended CRRK(N ) 6 curve. These points were not far below the curve, and would have been closer to the curve if the x R -based K s values had been used. Since the effect of K s at s vo=p a! is generally only a few percent, and since it was desirable for the curve not to be controlled by these few points from shallower depths, it was decided to maintain the simple limit of K s %, for both re-evaluating the case histories and for use in practical applications. 6. Normalization of penetration resistances SPT and CPT penetration resistances are routinely normalized to an equivalent svoz atm to obtain quantities that more uniquely relate to the relative density, D R, of sand (i.e. they no longer depend on svo). One of the most commonly used expressions for the overburden correction (or normalization) factor in Eqs. (3) and (4) was proposed by Liao and Whitman [27], viz: C N Z P :5 a (8) s vo Boulanger [22] recently re-evaluated C N relations based on theoretical and experimental data for the CPT and experimental data for the SPT. The C N relation for the CPT is quite well constrained by both the theoretical solutions and the calibration chamber test data against which the theoretical solutions have been calibrated. The resulting C N relation for the CPT was accurately expressed in the form: C N Z P m a (9) s vo where the exponent m was linearly dependent on D R,as m Z :784 K:52D R (2) For the SPT, Boulanger [22] re-evaluated the calibration chamber test data by Marcuson and Bieganousky [28,29]

8 22 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) 5 3 (a) Vertical effective stress (atm) N value , 54, D R =9% Platte River sand (b) N value , 5, D R =96% Standard concrete sand (c) N value Rotating rainer (with tamping at DR=73%) 3, 46, D R =73% Reid Bedford model sand Fig.. Re-examination of the calibration chamber SPT data by Marcuson and Bieganousky [28,29] showing variation in SPT N values with vertical effective stress and relative density for three sands. using a least squares, weighted, nonlinear regression that assumed the functional form provided by Eq. (9). The resulting relations are compared in Fig. to the SPT calibration chamber test data for the three sands studied, after adjusting each bin of SPT data to equivalent constant D R values. This adjustment for slight variations in D R among different SPT tests was based on the regressed D R - versus-(n ) 6 relation for the individual sand. The results of these SPT regression analyses are summarized in Fig. showing the exponent m versus D R for the three sands. The SPT results are consistent with the CPT relation provided by Eq. (2) and plotted in Fig. for comparison. In fact, Eq. (2) provides an adequate description of both the CPT and SPT data over the range of D R values most relevant to practice. Boulanger and Idriss [23] subsequently used the relations in Eqs. (4) and (5) to obtain the following expressions for determining C N : C N Z P a p a %:7 a Z :784 K:768 s vo ffiffiffiffiffiffiffiffiffiffiffiffi ðn Þ 6 C N Z P b a %:7 b Z :338 K:249ðq CNÞ :264 s vo (2) (22) with (N ) 6 limited to a maximum value of 46 and q CN limited to a maximum value of 254 in these C N expressions. Extrapolating the above expressions for C N to very shallow depths (i.e. s vo values smaller than the values for which C N was calibrated) gives C N /N as s vo/. Therefore, a limit must be imposed on the maximum value of C N because of uncertainties in Eqs. (2) and (22) at shallow depths. The NCEER/NSF workshop in 996/98 [3] recommended that C N %2. Considering the range of s vo and (N ) 6 for the case histories of observed surface evidence of liquefaction /no-liquefaction, it would appear more reasonable to limit the value of C N to.7 as noted in Eqs. (2) and (22). The resulting C N curves are plotted in Fig. 2 showing the increasing importance of D R with increasing depth (with D R represented by (N ) 6 and q CN values in this figure). Solving for C N requires iteration because (N ) 6 depends on C N and C N depends on (N ) 6 (and similarly for q CN ). As suggested by Boulanger and Idriss [23], this iteration can be easily accomplished in most software; e.g. in Excel, use a circular reference with the Iteration option activated under the Tools/Options/Calculation tab. Exponent m.8 Platte river sand Standard concrete sand Reid Bedford model sand.76 SPT: m =.37D R CPT: m = D R.8 Relative density, D R Fig.. Overburden normalization exponent m obtained by Boulanger [22] from nonlinear regression on SPT calibration chamber test data by Marcuson and Bieganousky [28,29] and from CPT penetration theory and calibration chamber test data.

9 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) Vertical effective stress, σ v /P a C N.5.5 (N ) 6 =4, q cn =223 (N ) 6 =3, q cn =77 (N ) 6 =2, q cn =3 (N ) 6 =, q cn =8 (N ) 6 =4, q cn =5 Fig. 2. Overburden normalization factor C N calculated using equations (2) or (22) (Boulanger and Idriss [23]). 7. SPT-based procedure for evaluating liquefaction potential of cohesionless soils Semi-empirical procedures for liquefaction evaluations originally were developed using the Standard Penetration Test (SPT), beginning with efforts in Japan to differentiate between liquefiable and nonliquefiable conditions in the 964 Niigata earthquake (e.g. [3]). Subsequent developments have included contributions from many researchers, especially in the investigations of individual case histories where surface evidence of liquefaction was or was not observed. The procedures recommended by Seed et al. [4,5] to obtain and adjust the SPT blow count and to obtain the values of CRR are particularly note worthy as they have set the standard for almost two decades of subsequent engineering practice. The NCEER/NSF workshop in 996/98 resulted in a number of suggested revisions to the SPT-based procedure but with only minor adjustments to the CRRK(N ) 6 curve for clean sands put forth by Seed et al. [4]. Cetin et al. [6] re-examined and expanded the SPT case history database. The data set by Seed et al. [4] had some 25 cases of liquefaction/no-liquefaction in 9 earthquakes, of which 65 cases pertain to sands with fines content FC%5%, 46 cases had 6%%FC%34%, and 4 cases had FCR35%. Cetin et al. [6] included an additional 67 cases of liquefaction/no-liquefaction in 2 earthquakes, of which 23 cases pertain to sands with FC%5%, 32 cases had 6%%FC%34%, and 2 cases had FCR35%. Cetin et al. [6] used their expanded data set and site response calculations for estimating CSR to develop revised deterministic and probabilistic liquefaction relationships. The results of Cetin et al. [6] were also summarized in Seed et al. [3]. The re-evaluation of the SPT-based procedures that is presented herein incorporates several different adjustments and parameter revisions. The CSR and (N ) 6 values were re-calculated using the revised r d, MSF, K s, and C N relations recommended herein. The C N and K s relations for silty sands were computed using the equivalent clean sand (N ) 6 values (the specific relation for this correction is described later in this section), which appears to be a reasonable approximation pending better experimental definition of how fines content affects these relations. For case histories where strong motion recordings showed that liquefaction occurred early in shaking, CSR were adjusted to reflect the number of equivalent cycles that had occurred up to the time when liquefaction was triggered [32]. Experimental data and theoretical considerations that provide guidance on the shape of the CRRK(N ) 6 curve at high (N ) 6 values (where there is very limited case history data) were re-examined. In particular, the SPT and CPT correlations were developed in parallel to maintain consistency between the two procedures. A few additional comments on some of these aspects are provided below. The revised r d [Eq. (6)] relation was used to estimate CSR for each case history, as opposed to using site response studies. The main reason is that, except for a few cases, the available information for the liquefaction/no-liquefaction case histories is insufficient to have confidence that detailed site response analyses would be more accurate. The K s factor is normally applied to the capacity side of the analysis during design [Eq. (5)], but it must also be used to convert the site CSR to a common svo value for the empirical derivation of a CRRK(N ) 6 curve. This is accomplished as: ðcsrþ MZ7:5; sz Z :65 s voa max rd svo MSF K s (23) such that the values of CSR correspond to an equivalent svo of atm, and thus the liquefaction correlation also corresponds to an equivalent svo of atm. Since K s has been restricted to % [Eq. (3)], this only affects a few of the case history points. Note that in applying the liquefaction correlation in design, the K s factor is still applied to the capacity side as indicated in Eq. (5). The shape of the CRRK(N ) 6 curve at the higher range of (N ) 6 values is guided by experimental and theoretical considerations because there is insufficient case history data to constrain the curve in this range. In 982, Seed and Idriss [4] set the CRRK(N ) 6 curve asymptotic to vertical at (N ) 6 z35 because the shake table results of De Alba et al. [33] indicated that the slope of the CRRKD R relation would increase substantially at high values of D R. Seed et al. [4] similarly kept the CRRK(N ) 6 curve asymptotic to vertical, but at (N ) 6 z3. In the work presented herein, the CRRK(N ) 6 relation was assigned a very steep, but non-vertical, slope based on a re-evaluation of experimental results for high quality field samples obtained by frozen sampling techniques (e.g. Yoshimi et al. [2,34]) and judgments based on the conceptual relations between D R

10 24 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) 5 3 (which relates to (N ) 6 values), effective confining stress (which changes with applied shear stresses), and CRR as derived through the x R framework (Fig. 7). In this regard, the application of probabilistic methods to the development of liquefaction correlations has often suffered from not including experimental and theoretical constraints on the liquefaction correlations at high CRR and (N ) 6 values. Consequently, such probabilistic methods often predict probabilities of liquefaction at high (N ) 6 values that are unreasonably high. It is believed that including experimental and theoretical findings in the development of probabilistic relations would improve the results in the upper range of CRR and (N ) 6 values. The SPT and CPT data were utilized together in developing a consistent pair of liquefaction correlations for the cases with FC%5%. The consistency between the two in situ test types was achieved through a common CRRKx R relation [23] as opposed to a constant q CN /N 6 ratio as had been used in some past studies. Maintaining a common CRRKx R relation results in a q CN /N 6 ratio that is dependent on D R. The corresponding q CN /(N ) 6 ratio (in lieu of q CN /N 6 ratio) can be determined using Eqs. (4) and (5) to obtain: q CN Z ð2:92d R C2:224Þ 3:788 ðn Þ 6 46ðD R Þ 2 (24) The q CN /(N ) 6 ratios calculated using Eq. (24) are plotted versus (N ) 6 in Fig. 3, which shows values that range from greater than in very loose sands to about 5.5 in very dense sands. In the range of particular interest, which is approximately %(N ) 6 %25, the calculated q CN /(N ) 6 ratio ranges from 6 to 8. The variation of the q CN /(N ) 6 ratio with D R is consistent with the expected differences in drainage conditions for these two in situ tests. The CPT is a quasistatic test that is largely drained or partially drained, depending on the grain size distribution of the cohesionless q CN /(N ) q CN /(N ) 6 ratio based on : D R = [(N) 6 /46].5 D R = 78(q CN ) (N ) 6 Fig. 3. Ratio of CPT and SPT penetration resistances based on adopted correlations to relative density. Cyclic Stress Ratio (CSR).5.3. NCEER/NSF Workshop (997) Recommended Curve FC 5% Marginal No Modified Standard Penetration - (N ) 6 - Blows/ft Fig. 4. SPT case histories of clean sands with the curve proposed by the NCEER Workshop [3] and the recommended curve for MZ7 2 and s voz atm (z tsf). soils, whereas the SPT is a dynamic test that is largely undrained. Thus, it would be expected that for SPT tests, loose sand would develop positive excess pore pressures while dense sand would more likely develop negative excess pore pressures. This difference in drainage conditions can explain, at least in part, the trend depicted in Fig. 3. Revised CRRK(N ) 6 relations, derived incorporating the above considerations, are presented in Figs. 4 through 9. The cases for cohesionless soils having FC%5% are plotted in Fig. 4 along with the curve agreed to at the NCEER/NSF workshop. Also shown in Fig. 4 is the new curve proposed herein. The individual cases are those from Seed et al. [4] and Cetin et al. [6] subject to the previously described adjustments. The proposed changes to the CRRK(N ) 6 relation are relatively modest. For (N ) 6 values between 8 and 25, the maximum difference in CRR is about 5% at (N ) 6 z2. The revised relation for FC%5% is further compared to other published relations in Fig. 5, Cyclic Stress Ratio (CSR).5.3. Curves derived by Seed (979) 2 Seed & Idriss (982) 3 Seed et al (984)/NCEER Workshop (997) 4 Seed et al (2) 5 Recommended Curve FC 5% Marginal No Modified Standard Penetration - (N ) 6 - Blows/ft Fig. 5. Curves relating CRR to (N ) 6 published over the past 24 years for clean sands and the recommended curve for MZ7 2 and svoz atm (z tsf).

11 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) Cyclic Stress Ratio (CSR).5.3. Fines Content (FC) NCEER (997) (FC 35%) 43 Derived Curve (FC = 35%) Derived Curve (FC 5%) Revised Values for Cases Published in 984 Revised Values for Cases Published in 2 No Modified Standard Penetration - (N ) 6 - Blows/ft Fig. 6. SPT case histories of cohesionless soils with FCR35% and the NCEER Workshop [3] curve and the recommended curves for both clean sand and for FCZ35% for MZ7 2 and s voz atm (z tsf). including relations from early in their development (i.e. Seed [2]) to a very recent relation by Cetin et al. [6] that is summarized in Seed et al. [3]. Note that the curves and the data points for the liquefaction/no-liquefaction case histories pertain to magnitude MZ7 2 earthquakes and an effective vertical stress s voz atm (z tsf). The cases for cohesionless soils with FCR35% are plotted in Fig. 6 along with the applicable curve agreed to at the NCEER/NSF workshop and the new curve proposed herein. Several case history points fall well below the FCR35% boundary curve agreed to at the NCEER/NSF workshop, and these points control the position of the revised curve. The FCZ5% boundary curve that was recommended at the NCEER/NSF workshop and the revised FCZ5% boundary curve proposed herein are compared in Figs. 7 and 8. Fig. 7 shows the case history points for Cyclic Stress Ratio (CSR).5.3. Fines Content (FC) Revised Values for Cases Published in 984 Revised Values for Cases Published in 2 Derived Curve (FC = 5%) Derived Curve (FC 5%) Marginal No Modified Standard Penetration - (N ) 6 - Blows/ft Fig. 7. SPT case histories of cohesionless soils with 5%!FC!5% and the recommended curves for both clean sands and for FCZ5% for MZ7 2 and s voz atm (z tsf). Cyclic Stress Ratio (CSR) NCEER/NSF (997) (FC = 5%) Fines Content (FC) Modified Standard Penetration - (N ) 6 - Blows/ft cohesionless soils with 5%!FC!5%, while Fig. 8 shows the cases for 5%%FC!35%. The revised curve is lower than the curve recommended at the NCEER/NSF workshop, reflecting the influence of the revised case history data set compiled by Cetin et al. [6]. The revised boundary curves proposed herein for cohesionless soils can be expressed using the following equations. First, the SPT penetration resistance is adjusted to an equivalent clean sand value as: ðn Þ 6cs Z ðn Þ 6 CDðN Þ 6 (25) DðN Þ 6 Z exp :63 C 9:7 FC C: K 5:7 2 FC C: 8 Derived Curve (FC = 5%) (26) The variation of D(N ) 6 with FC (in percent), calculated using the Eq. (26), is presented in Fig. 9. The value of CRR for a magnitude MZ7 2 earthquake and an effective vertical stress s voz atm (z tsf) can be calculated based on Revised Values for Cases Published in 984 Revised Values for Cases Published in 2 No Fig. 8. SPT case histories of cohesionless soils with 5%%FC!35% and the NCEER Workshop [3] curve and the recommended curve for FCZ 5% for MZ7 2 and s voz atm (z tsf). (N ) Fines Content, FC - percent Fig. 9. Variation of D(N ) 6 with fines content.

12 26 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) 5 3 (N ) 6cs using the following expression: CRR Z exp ðn Þ 6cs 4: C ðn 2 Þ 6cs 26 K ðn 3 Þ 6cs C ðn 4 Þ 6cs K2:8 ð27þ 23:6 25:4 The use of these equations provides a convenient means for evaluating the cyclic stress ratio required to cause liquefaction for a cohesionless soils with any fines content. The plasticity of the fines is a key parameter affecting both the cyclic behavior of a soil and the choice of procedures for evaluating that cyclic behavior. For fine-grained soils, Idriss and Boulanger [35] suggested that a PI of 5G was indicative of the transition from essentially cohesionless (sand-like) soil behavior to essentially cohesive (clay-like) soil behavior. Boulanger and Idriss [36] have since recommended new procedures for evaluating the cyclic failure potential of cohesive fine-grained soils and recommended that a PI of 7 be used for distinguishing between cohesionless and cohesive soils unless site-specific laboratory testing indicates an adjustment to this criterion is warranted. These issues are beyond the scope of this paper, other than to conclude that the above SPT-based procedures are considered applicable to soils with fines that are nonplastic or of very low plasticity (PI!7) and that the use of the Chinese Criteria or their variants for identifying liquefiable soils should be discontinued. It must be stressed that the quality of the site characterization work is extremely important for the reliable evaluation of liquefaction potential. With regard to SPT testing, it is vital that the testing procedures carefully adhere to established standards (as summarized at the NCEER Workshop [26]) and that, regardless of the test procedures, SPT tests can produce misleading (N ) 6 values near contacts between soils of greatly differing penetration resistances (e.g. sand overlying soft clay) and can miss relatively thin critical strata. Such difficulties have been reported in many cases (e.g. Boulanger et al. [37,38]) and are generally recognized as requiring careful diligence in the field investigations. In this regard, companion CPT soundings are extremely valuable, whenever possible, for identifying SPT (N ) 6 values that might have been adversely affected by overlying or underlying strata, and for enabling a more reliable characterization of thin liquefiable strata (e.g. Robertson and Wride [6], Moss [39]). 8. CPT-based procedure for evaluating liquefaction potential of cohesionless soils The cone penetration test (CPT) has proven to be a valuable tool in characterizing subsurface conditions and in assessing various soil properties, including estimating the potential for liquefaction at a particular site. The main advantages of using the CPT are that it provides a continuous record of the penetration resistance and is less vulnerable to operator error than is the SPT test, whereas its main disadvantage is the unavailability of a sample. Zhou [4] used observations from the 978 Tangshan earthquake to propose the first liquefaction correlation based directly on CPT case histories. Seed and Idriss [4] as well as Douglas et al. [42] proposed the use of correlations between the SPT and CPT to convert the then available SPT-based charts for use with the CPT. In recent years, the expanding data-base for field case histories has produced several CPT-based correlations (e.g. Shibata and Teparaksa [43]; Stark and Olson [44]; Suzuki et al. [45,46]; Robertson and Wride [6,47]; Olsen [48]; Moss [39]; Seed et al. [7]). The CPT-based liquefaction correlation was re-evaluated using case history data compiled by Shibata and Teparaksa [43], Kayen et al. [49], Boulanger et al. [37,38], Stark and Olson [44], Suzuki et al. [46], and Moss [39]. The work of Moss [39] was particularly valuable in providing the most comprehensive compilation of field data and associated interpretations. This re-evaluation of the CPT-based procedures incorporated adjustments and parameter revisions that are similar to those previously described for the SPT re-evaluation. For case histories where strong motion recordings showed that liquefaction occurred early in shaking, CSR were adjusted to reflect the number of equivalent cycles that had occurred up to the time when liquefaction was triggered. All CSR and q CN values were re-calculated using the revised r d, MSF, K s, and C N relations summarized above. The shape of the CRRKq CN curve at high q CN values was re-examined, and the CPT and SPT correlations were developed in parallel to maintain consistency between these procedures. The revised CRRKq CN relation, derived using the above considerations, is shown in Fig. 2 with the case Cyclic Stress Ratio (CSR).5.3 Recommended Relationship. Clean Sands No Earthquake Magnitude, M = 7½; σ' vo = atm Normalized Corrected CPT Tip Resistance, q cn Fig. 2. CPT-based case histories and recommended relation for clean sands for MZ7 2 and s voz atm (z tsf).

13 I.M. Idriss, R.W. Boulanger / Soil Dynamics and Earthquake Engineering 26 (26) Cyclic Stress Ratio (CSR).5.3. Shibata & Teparaksa (988) Robertson & Wride (997) Suzuki et al (997) Moss (23) - 5% Probability Earthquake Magnitude, M = 7½; σ' vo = atm Recommended Relationship Clean Sands No Normalized Corrected CPT Tip Resistance, q c N Fig. 2. CPT-based case histories and recommended relation for clean sands with relations proposed by others. CRR.5.3. CPT correlation Clean sand (FC 5%) 5 D 5 (mm) 2. M = 7.5 SPT correlation.8 Relative state parameter index, ξr history points for cohesionless soils having FC%5%. The derived relation can be conveniently expressed as: CRR Z exp q cn 54 C q cn 2 q K cn 3 q C cn 4 K (28) This CRRKq CN relation is compared in Fig. 2 to those by Shibata and Teparaksa [43], Robertson and Wride [6], Suzuki et al. [46], and the 5% probability curve by Moss [39] as summarized in Seed et al. [7]. The derived relation [Eq. (28)] is comparable to the curve proposed by Suzuki et al. [46] for clean sands. It is more conservative than the corresponding curves by Robertson and Wride [6] and by Seed et al. [7] for almost the entire range of q CN.The curve proposed by Shibata and Teparaksa [43] is less conservative than the derived relation except for q CN greater than about 65. Note that these relations and the plotted data pertain to magnitude MZ7 2 earthquakes and an effective vertical stress svoz atm (z tsf). As previously mentioned, the CPT and SPT liquefaction correlations were developed in parallel to maintain consistency in terms of their implied CRRKx R relations for clean cohesionless soils. The relative state parameter index (x R ) for a given q CN or (N ) 6 can be estimated using Eqs. (4) or (5) to estimate D R, after which x R can be calculated using the expressions in Fig. 7. Following this approach, the CRRKx R relations produced for the SPT and CPT liquefaction correlations are compared in Fig. 22. As intended, the two relations are basically identical. The effect of fines content on the CRRKq CN relation is still being re-evaluated. This issue includes the actual effect of fines content and the most reliable means of incorporating this effect into CPT-based procedures. While revised procedures are not provided herein, a few comments regarding this issue are warranted. Robertson and Wride [6] and Suzuki et al. [46] suggested the use of the soil behavior type index, I c (Jefferies Fig. 22. Field CRRKx R relations derived from liquefaction correlations for SPT and CPT. and Davies [5]), which is a function of the tip resistance (q C ) and sleeve friction ratio (R f ), to estimate the values of CRR for cohesionless soils with high fines content. The curve recommended by Robertson and Wride [6] relating CRRKq CN at I c Z2.59 (defined by Robertson and Wride as corresponding to an apparent fines content FCZ35%) is presented in Fig. 23. Also shown in this figure are the CPT-based data points for the cases examined by Moss [39] for cohesionless soils with FCR35%. As can be seen in the figure, the curve recommended by Robertson and Wride [6] is unconservative. Similarly, the relations by Suzuki et al. [46] for cohesionless soils with high fines content are unconservative. The recent work by Moss [39] using friction ratio R f in lieu of the parameter I c as a proxy for fines content appears promising, but does require further scrutiny before it is adopted. Cyclic Stress Ratio (CSR).5.3. Robertson & Wride (997) I c = 2.59; FC = 35% Fines Content, FC [data points from Moss (23)] Earthquake Magnitude, M = 7½; σ' vo = atm Recommended Relationship for Clean Sands Clean Sands No Normalized Corrected CPT Tip Resistance, q c N Fig. 23. Comparison of field case histories for cohesionless soils with high fines content and curve proposed by Robertson and Wride [47] for soils with I c Z2.59 (apparent FCZ35%).