Return Period of Soil Liquefaction Steven L. Kramer, M.ASCE1; and Roy T. Mayfield2 Abstract: The paper describes a performance-based approach to the evaluation of liquefaction potential, and shows how it can be used to account for the entire range of potential ground shaking. The result is a direct estimate of the return period of liquefaction, rather than a factor of safety or probability of liquefaction conditional upon ground shaking with some specified return period. As such, the performance-based approach can be considered to produce a more complete and consistent indication of the actual likelihood of lique- faction at a given location than conventional procedures. In this paper, the performance-based procedure is introduced and used to compare likelihoods of the initiation of liquefaction at identical sites located in areas of different seismicity. The results indicate that the likelihood of liquefaction depends on the position and slope of the peak acceleration hazard curve, and on the distribution of earthquake magnitudes contributing to the ground motion hazard. The results also show that the consistent use of conventional procedures for the evaluation of liquefaction potential produces inconsistent actual likelihoods of liquefaction. DOI: 10.1061/͑ASCE͒1090-0241͑2007͒133:7͑802͒ CE Database subject headings: Earthquakes; Liquefaction; Sand; Penetration tests; Hazards. Introduction probability of liquefaction conditional upon ground shaking with some specified return period. As such, the performance-based Liquefaction of soil has been a topic of considerable interest to approach can be considered to produce a more complete and geotechnical engineers since its devastating effects were widely consistent indication of the likelihood of liquefaction at a given observed following 1964 earthquakes in Niigata, Japan and location than conventional procedures. In this paper, the Alaska. Since that time, a great deal of research on soil liquefac- performance-based procedure is introduced and then used to com- tion has been completed in many countries that are exposed to pare the actual likelihoods of liquefaction at identical sites located this important seismic hazard. This work has resulted in the de- in areas of different seismicity; the results show that the consis- velopment of useful empirical procedures that allow the determin- tent use of conventional procedures for evaluation of liquefaction potential produces inconsistent actual likelihoods of liquefaction. istic and probabilistic evaluation of liquefaction potential for a specified level of ground shaking. In practice, the level of ground shaking is usually obtained from the results of a probabilistic seismic hazard analysis Liquefaction Potential ͑PSHA͒; although that ground shaking model is determined Liquefaction potential is generally evaluated by comparing con- probabilistically, a single level of ground shaking is selected and sistent measures of earthquake loading and liquefaction resis- used within the liquefaction potential evaluation. In reality, tance. It has become common to base the comparison on cyclic though, a given site may be subjected to a wide range of ground shear stress amplitude, usually normalized by initial vertical ef- shaking levels ranging from low levels that occur relatively fre- fective stress and expressed in the form of a cyclic stress ratio, quently to very high levels that occur only rarely, each with dif- CSR, for loading and a cyclic resistance ratio, CRR, for resis- ferent potential for triggering liquefaction. tance. The potential for liquefaction is then described in terms of This paper shows how the entire range of potential ground a factor of safety against liquefaction, FS =CRR/CSR. shaking can be considered in a fully probabilistic liquefaction L potential evaluation using a performance-based earthquake engi- neering ͑PBEE͒ framework. The result is a direct estimate of the Characterization of Earthquake Loading return period of liquefaction, rather than a factor of safety or The CSR is most commonly evaluated using the “simplified method” first described by Seed and Idriss ͑1971͒, which can be 1Professor, Dept. of Civil and Environmental Engineering, Univ. of expressed as Washington, Seattle, WA 98195-2700. E-mail: [email protected] 2Consulting Engineer, Kirkland, WA 98034; formerly, Graduate Re- ␴ amax vo rd search Assistant, Dept. of Civil and Environmental Engineering, Univ. of CSR = 0.65 · · ͑1͒ ␴Ј Washington. E-mail: roy@mayfield.name g vo MSF Note. Discussion open until December 1, 2007. Separate discussions where amax =peak ground surface acceleration; g=acceleration of must be submitted for individual papers. To extend the closing date by ͑ ͒ ␴ gravity in same units as amax ; vo =initial vertical total stress; one month, a written request must be filed with the ASCE Managing ␴Ј Editor. The manuscript for this paper was submitted for review and pos- vo =initial vertical effective stress; rd =depth reduction factor; sible publication on April 4, 2006; approved on July 20, 2006. This paper and MSF=magnitude scaling factor, which is a function of earth- is part of the Journal of Geotechnical and Geoenvironmental Engineer- quake magnitude. The depth reduction factor accounts for com- ing, Vol. 133, No. 7, July 1, 2007. ©ASCE, ISSN 1090-0241/2007/7- pliance of a typical soil profile, and the MSF acts as a proxy for 802–813/$25.00. the number of significant cycles, which is related to the ground 802 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / JULY 2007 Fig. 1. ͑a͒ Deterministic cyclic resistance curves proposed by Youd et al. 2001, ASCE; ͑b͒ cyclic resistance curves of constant probability of liquefaction with measurement/estimation errors by Cetin et al. 2004, ASCE. motion duration. It should be noted that two pieces of loading Research 1997͒. The liquefaction evaluation procedure described information—amax and earthquake magnitude—are required for by Youd et al. ͑2001͒ will be referred to hereafter as the NCEER estimation of the CSR. procedure. The NCEER procedure has been shown to produce reasonable predictions of liquefaction potential ͑i.e., few cases of ͒ Characterization of Liquefaction Resistance nonprediction for sites at which liquefaction was observed in past earthquakes, and is widely used in contemporary geotechni- The CRR is generally obtained by correlation to in situ test re- cal engineering practice. For the purposes of this paper, a conven- ͑ ͒ ͑ ͒ sults, usually standard penetration SPT , cone penetration CPT , tionally liquefaction-resistant site will be considered to be one for ͑ ͒ or shear wave velocity Vs tests. Of these, the SPT has been most which FS ജ1.2 for a 475-year ground motion using the NCEER commonly used and will be used in the remainder of this paper. A L procedure. This standard is consistent with that recommended by number of SPT-based procedures for deterministic ͑Seed and Martin and Lew ͑1999͒, for example, and is considered represen- Idriss 1971; Seed et al. 1985; Youd et al. 2001; Idriss and Bou- tative of those commonly used in current practice. langer 2004͒ and probabilistic ͑Liao et al. 1988; Toprak et al. 1999; Youd and Noble 1997; Juang and Jiang 2000; Cetin et al. Probabilistic Approach 2004͒ estimation of liquefaction resistance have been proposed. Recently, a detailed review and careful reinterpretation of lique- Deterministic Approach faction case histories ͑Cetin 2000; Cetin et al. 2004͒ was used to Fig. 1͑a͒ illustrates the widely used liquefaction resistance curves develop new probabilistic procedures for the evaluation of lique- recommended by Youd et al. ͑2001͒, which are based on discus- faction potential. The probabilistic implementation of the Cetin et ͑ ͒ sions at a National Center for Earthquake Engineering Research al. 2004 procedure produces a probability of liquefaction, PL, ͑NCEER͒ workshop ͑National Center for Earthquake Engineering which can be expressed as ͑N ͒ ͑1+␪ FC͒ − ␪ ln CSR − ␪ ln M − ␪ ln͑␴Ј /p ͒ + ␪ FC + ␪ ⌽ͫ 1 60 1 2 eq 3 w 4 vo a 5 6 ͬ ͑ ͒ PL = − 2 ␴␧ where ⌽=standard normal cumulative distribution function; faction includes both loading terms ͑again, peak acceleration, as ͑ ͒ ͑ ͒ ͒ ͑ N1 60 =corrected SPT resistance; FC=fines content in percent ; reflected in the CSR, and magnitude and resistance terms SPT ͓ ͑ ͒ ͔ ͒ CSReq =cyclic stress ratio Eq. 1 without MSF ; Mw =moment resistance, FC, and vertical effective stress . Mean values of the ␴Ј magnitude; vo =initial vertical effective stress, pa is atmospheric model coefficients are presented for two conditions in Table 1—a ␴Ј ␴ pressure in same units as vo; ␧ =measure of the estimated model case in which the uncertainty includes parameter measurement/ ␪ ␪ and parameter uncertainty; and 1– 6 are model coefficients ob- estimation errors and a case in which the effects of measurement/ tained by regression. As Eq. ͑2͒ shows, the probability of lique- estimation errors have been removed. The former would corre- JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / JULY 2007 / 803 Table 1. Cetin et al. ͑2004͒ Model Coefficients with and without Measurement/Estimation Errors ͑Adapted from Cetin et al. 2002͒ ␪ ␪ ␪ ␪ ␪ ␪ ␴ Case Measurement/estimation errors 1 2 3 4 5 6 ␧ I Included 0.004 13.79 29.06 3.82 0.06 15.25 4.21 II Removed 0.004 13.32 29.53 3.70 0.05 16.85 2.70 spond to uncertainties that exist for a site investigated with a found that the average effective stress for their critical layers were normal level of detail and the latter to a “perfect” investigation at lower effective stresses ͑ϳ0.65 atm͒ instead of the standard 1 ͓i.e., no uncertainty in any of the variables on the right-side of atm, and made allowances for those differences. Also, the basic ͑ ͔͒ ͑ ͒ Eq. 2 . Fig. 1 b shows contours of equal PL for conditions in shapes of the cyclic resistance curves are different—the Cetin which measurement/estimation errors are included; the et al. ͑2004͒ curves ͑Fig. 3͒ have a smoothly changing curvature measurement/estimation errors have only a slight influence on the while the Youd et al.