AN INVESTIGATION INTO WHY LIQUEFACTION CHARTS WORK: A NECESSARY STEP TOWARD INTEGRATING THE STATES OF ART AND PRACTICE

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1 AN INVESTIGATION INTO WHY LIQUEFACTION CHARTS WORK: A NECESSARY STEP TOWARD INTEGRATING THE STATES OF ART AND PRACTICE by Ricardo Dobry Tarek Abdoun Department of Civil and Environmental Engineering Rensselaer Polytechnic Institute Troy, NY, USA ISHIHARA LECTURE Proceedings of the 5 th Int l Conf. on Earthquake Geotechnical Engineering, pp , January 10-13, 2011 Chilean Geotechnical Society

2 AN INVESTIGATION INTO WHY LIQUEFACTION CHARTS WORK: A NECESSARY STEP TOWARD INTEGRATING THE STATES OF ART AND PRACTICE Ricardo Dobry 1, Tarek Abdoun 2 ABSTRACT This paper is a systematic effort to clarify why field liquefaction charts based on Seed and Idriss Simplified Procedure work so well. This is a necessary step toward integrating the states of the art (SOA) and practice (SOP) for evaluating liquefaction and its effects. The SOA relies mostly on laboratory measurements and correlations with void ratio and relative density of the sand. The SOP is based on field measurements of penetration resistance and shear wave velocity coupled with empirical or semi-empirical correlations. This gap slows down further progress in both SOP and SOA. The paper accomplishes its objective through: a literature review of relevant aspects of the SOA including factors influencing threshold shear strain and pore pressure buildup during cyclic strain-controlled tests; a discussion of factors influencing field penetration resistance and shear wave velocity; and a discussion of the meaning of the curves in the liquefaction charts separating liquefaction from no liquefaction, helped by recent fullscale and centrifuge results. It is concluded that the charts are curves of constant cyclic strain at the lower end (V s1 < 160 m/s), with this strain being about 0.03 to 0.05% for earthquake magnitude, M w 7. It is also concluded, in a more speculative way, that the curves at the upper end probably correspond to a variable increasing cyclic strain and K o, with this upper end controlled by overconsolidated and preshaken sands, and with cyclic strains needed to cause liquefaction being as high as 0.1 to 0.3%. These conclusions are validated by application to case histories corresponding to M w 7, mostly in the San Francisco Bay Area of California during the 1989 Loma Prieta earthquake. Keywords: Liquefaction, Simplified Procedure, empirical correlations, cyclic strains. INTRODUCTION A large amount of research has been conducted in the last years on liquefaction and its effects in the free field. The research has significantly developed the state-of-the-art (SOA), producing a huge amount of information, a number of important models, and basic insights on the mechanics of pore pressure buildup, liquefaction and ground deformation due to earthquake-like shaking. Despite these advances, the current state-of-practice (SOP) continues to be largely empirical, or semi-empirical, using field charts or correlations based on earthquake case histories or, at most, simplified analyses calibrated with case histories (Seed and Idriss, 1971; Seed et al., 1983; Seed and Harder, 1990; Bartlett and Youd, 1995; Robertson and Wride, 1998; Andrus and Stokoe, 2000; Youd et al., 2001; 2002; Idriss and Boulanger, 2004, 2007, 2008; Moss et al., 2006; Olson and Johnson, 2008). In a number of these SOP methods, and especially in the popular charts used to evaluate liquefaction potential in the field, the 1 Institute Professor of Engineering, Department of Civil & Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA. 2 Iovino Chair Professor, Department of Civil & Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA. 13

3 resistance of the soil is characterized by the penetration resistance (Standard Penetration Test, SPT, or Cone Penetration Test, CPT), rather than by any kind of laboratory parameter. More recently, liquefaction charts based on field measurements of shear wave velocity, V s, have also been developed. Penetration resistance, shear wave velocity and liquefaction resistance, all depend in complex ways on a number of factors, of which relative density (or void ratio) is only one. As a result, there is currently poor understanding of the reasons why the field liquefaction charts work. A significant gap exists between the SOP, based largely on field measurements of penetration resistance or shear wave velocity, and the SOA, which tends to rely on laboratory measurements of various soil properties and correlates them to the void ratio or relative density of the sand. Closing the gap requires first a better understanding of why the field charts work, as well as a better integration between the laboratory and the field. This paper develops a methodology aimed at achieving such understanding and integration and applies it to clean sands subjected to earthquakes of magnitude, M w 7. THE SEED AND IDRISS SIMPLIFIED PROCEDURE The liquefaction potential charts are based on the Simplified Procedure originally proposed by Seed and Idriss (1971). The soil was characterized by the standard penetration resistance of the sand normalized to a vertical effective overburden pressure of one atmosphere, N 1 (later refined to (N 1 ) 60 ), obtained from field SPT measurements, and the method was successfully calibrated with actual case histories during earthquakes. The procedure has been modified and improved periodically with more case histories, with the latest version shown in Fig. 1 (Youd et al., 2001). Similar charts have also been calibrated using the normalized static cone penetration resistance, q c1n (Robertson and Wride, 1998), obtained from field CPT measurements. The latest version of these CPT charts for clean sands is shown in Fig. 2 (Idriss and Boulanger, 2004, 2008), while Fig. 3 includes a similar chart for both clean and silty sands using a probabilistic approach to predict the occurrence of liquefaction (Moss et al., 2006). Figure 1. Liquefaction chart for earthquakes of magnitude 7.5, based on standard penetration tests, SPT (Youd et al., 2001; modified from Seed et al., 1985). 14

4 Figure 2. Liquefaction chart for clean sands based on point resistance measured during static cone penetration tests, CPT (Idriss and Boulanger, 2004, 2008). Figure 3. Probabilistic contours for liquefaction of sands during earthquakes of magnitude 7.5 using static cone penetration tests, CPT (Moss et al., 2006). 15

5 More recently, liquefaction charts have been developed using the same simplified procedure framework, but now based on the normalized shear wave velocity, V s1, of the sand to measure the liquefaction resistance of the soil. This was originally motivated by the strain approach to liquefaction (Dobry et al., 1981b, 1982), and subsequently compared with liquefaction performance at sites subjected to the Imperial Valley earthquakes in Southern California by Bierschwale and Stokoe (1984). A V s -based liquefaction chart, calibrated with a few case histories of liquefaction, was proposed by Robertson et al. (1992), and subsequent developments, in addition to many other case histories, culminated in the Andrus and Stokoe (2000) chart of Fig. 4. The sites that have experienced liquefaction are well-bounded by this chart, and thus, it has also been added to the arsenal of tools available to practitioners (Youd et al., 2001; Idriss and Boulanger, 2008). Figure 4. Liquefaction chart based on measured shear wave velocity (Andrus and Stokoe, 2000). The SPT, CPT and V s charts all use the same basic approach and share important characteristics. These charts have stood the test of time by showing again and again their predictive power when earthquakes occur. As a result, they define the state-of-practice of seismic liquefaction evaluation of saturated sand sites (Youd et al., 2001; Idriss and Boulanger, 2008). Figure 5 sketches some aspects of this common approach, which includes the following features for deterministic charts like those in Figs. 1, 2 and 4: (i) the chart corresponds to an earthquake of moment magnitude, M w = 7.5, with other magnitudes considered through the use of a Magnitude Scaling Factor, MSF; (ii) every chart contains a curve of Cyclic Resistance Ratio, CRR, versus a normalized soil liquefaction resistance parameter (based on SPT, CPT, or V s ), which separates sites where liquefaction has been observed from those where liquefaction did not occur; (iii) these curves have been calibrated by case histories of liquefaction or no liquefaction during actual earthquakes (data points in Figs. 1-4), for which a Cyclic Stress Ratio, CSR, is calculated and used to plot the data point; and (iv) for a new site where future liquefaction is being evaluated, this same CSR is first calculated for a given design earthquake magnitude and peak ground surface acceleration, a max, then the CSR is corrected as needed by the MSF to bring it to M w = 7.5, and the corrected CSR is plotted on the chart as a new data point. In principle, if this data point is above the curve, liquefaction is predicted, while below the curve the site is safe against liquefaction. Therefore, 16

6 CSR measures the earthquake demand, while CRR is the resistance of the soil against liquefaction, and CSR > CRR is the necessary condition for liquefaction to occur. A key aspect of the procedure is the calculation of CSR for either historic or future site liquefaction in Fig. 5, using Eq. (1): where, a max = maximum horizontal acceleration at the ground surface; τ max = maximum horizontal shear stress in the liquefiable layer; σ v0 and σ v0 = total and effective vertical normal stress before the shaking, respectively; and r d = stress reduction coefficient, which accounts for the flexibility of the soil profile, with r d = 1.0 at the ground surface and, typically, r d < 1.0 below the ground surface. As shown in Fig. 5, the procedure offers two alternatives to obtain CSR for a site: (i) from the value of a max estimated at the ground surface; or (ii) directly from τ max calculated with a site amplification program such as SHAKE (Schnabel et al., 1972). Implicit in Eq. (1) is the assumption that τ max = (a max /g) σ v0 r d. It is also assumed that the values of τ max and a max are not affected by pore pressure buildup during the earthquake shaking. The two expressions included in Eq. (1) are associated with actual earthquake loadings consisting of widely different cycles of acceleration and stress. The factor 0.65 has been historically used in charts such as Figs. 1-4, as a way to facilitate comparison between field observations of liquefaction associated with time histories of unequal cyclic amplitude and laboratory undrained cyclic tests applying uniform stress cycles. That is, the assumption is that the non-uniform cyclic shear stresses acting on the layer during an earthquake can be replaced by an equivalent number of cycles of uniform stress, τ c 0.65 τ max 0.65 (a max /g) σ v0 r d (Fig. 5). The equivalent number of cycles or duration is related to M w (Fig. 6). The parameter τ c is typically not used in the development and use of the charts, playing a role only when trying to relate the chart to laboratory tests involving uniform loading cycles. (1) Figure 5. Calculation of the Cyclic Stress Ratio, CSR, in the Seed and Idriss Simplified Procedure. 17

7 Figure 6. Number of equivalent cycles versus earthquake magnitude (Idriss and Boulanger, 2008). An extremely important feature of the charts in Figs. 1-4 is that the expression CSR = 0.65 (a max /g) (σ v0 / σ v0 ) r d has been consistently used to calculate the data points of case histories, with a max estimated from either available strong motion recordings nearby, site response analyses, or attenuation relations (e.g., see Youd et al., 2001; Moss, 2003). A consequence of this - as explicitly stated by Youd et al. (2001) and illustrated in Fig. 5 - is that the values of τ max and a max used with the liquefaction charts, neglect the effect of pore pressure buildup and liquefaction in softening the soil, while incorporating the influence of site amplification. This is a very significant assumption, which is equivalent to characterizing the liquefiable soil by the nonrealistic, fictitious property that the cyclic stress-strain behavior, characterized by stressstrain (or backbone) curves of τ vs. shear strain, γ, or by shear modulus reduction G/G max vs. γ curves, are unaffected by the pore pressure buildup, and as such, are the same before, during and after liquefaction! This is manifestly untrue: practically every cyclic undrained test, shaking table, or centrifuge test involving sand and significant pore pressure buildup shows either: (i) significant decreases in τ c and G for a constant cyclic strain, γ c, in strain-controlled tests; (ii) significant increases in γ c for a constant τ c in stress-controlled tests; or (iii) decreases in τ max and a max for a given uniform base shaking (e.g., Ishihara, 1985; Whitman, 1985; Vucetic and Dobry, 1988; Idriss and Boulanger, 2008; Sharp et al., 2010). Therefore, the values of CSR calculated for sites that plot high above the CRR curve in Figs. 1-4, that is cases of CSR >> CRR, bear no relation to the actual a max and τ max experienced by the liquefying layer at the site. The calculated values of CSR, τ max, and a max are realistic only for cases in which CSR < CRR, or perhaps also CSR CRR, that is for points below the curve, or on the curve itself, which do not experience enough pore pressure buildup to affect the shear stress-strain response of the soil. Recognition of this lack of realism of CSR for points well above the curve in the charts does not constitute criticism of the method, as there does not seem to be any simple way to realistically estimate a max or τ max of sites that have liquefied in the past or may liquefy in the future. It is not even clear that such an estimate would serve a useful purpose in the context of a simplified procedure, as accelerations and stresses of liquefied soils tend to be either very small, or characterized by high frequency spikes linked to the undrained dilative stress-strain response of the sand. The assumption has kept the Simplified Procedure appropriately simple, allowing development of the corresponding field databases and of the very successful liquefaction charts of Figs However, clarification of this aspect of the procedure has several implications for cases where CSR >> CRR. First, as in this case CSR is an index parameter without physical reality, CSR, and derived τ max and a max, should not be compared with shear stresses and accelerations measured in the field, centrifuge, or laboratory tests when high pore pressure buildup or liquefaction are taking place. Second, and again for the case where CSR >> CRR: CSR from the 18

8 liquefaction charts (or derived τ max and a max ) may be compared with the results of a site response analysis, such as SHAKE, where the curve of G/G max versus γ is kept constant throughout the shaking; but CSR should not be compared with results of nonlinear site response analyses which use an effective stress approach and allow the G/G max, or backbone curve, to degrade as the pore pressure increases (unless this option of the program is turned off). And third, this assumption, that the curve of G/G max vs. γ of the sand is unaffected by pore pressure buildup or liquefaction, allows the use of alternative approaches to the development of liquefaction charts, as discussed later in this article. Several authors have correlated penetration resistance with shear wave velocity at potentially liquefiable sand sites (Andrus and Stokoe, 2000; Youd et al., 2001; Andrus et al., 2004; Brandenberg et al., 2010). Figure 7 shows one of these correlations, which illustrates a general shape characterized by a significant flattening of the curve at high values of penetration resistance. This is consistent with the sharper rise of the curve at the higher end in the V s chart of Fig. 4, compared with a smoother rise in the CPT chart of Fig. 2, and seems to be associated with the larger sensitivity of penetration resistance to the greater horizontal stresses present in overconsolidated and preshaken sites (Dobry, 2010). Figure 7. Field relationships between equivalent clean sand values of q c1n and V s1 for uncemented, Holocene sands (Andrus et al., 2004). THRESHOLD STRAIN, CYCLIC STRAINING AND PORE PRESSURE BUILDUP There are two aspects of the SOA which are directly relevant to the question of why field liquefaction charts work. One is the existence in sands of a volumetric threshold shear strain, γ tv, typically on the order of 10-2 %, below which there is no volumetric strain accumulation in dry sand during cyclic straining, or pore pressure buildup if the sand is saturated. The other is the rate at which pore pressure builds up during undrained shear straining in cyclic strain-controlled tests when the cyclic shear strain, γ c > γ tv. The parameter γ tv was called threshold strain and given the symbol γ t in the original publications, but has been since renamed volumetric threshold strain, γ tv, to avoid confusion with other threshold levels present in sands (Hsu and Vucetic, 2004). While the more correct symbol γ tv is used in this paper, the shorter and more convenient name threshold strain has been preserved. 19

9 Table 1. Volumetric Threshold Shear Strain, γ tv, Dry and Saturated Sands SOIL Testing Technique γ tv (%) Reference(s) Dry Ottawa sand Resonant column 1 x 10-2 Drnevich and Richart (1970) Dry Crystal Silica sand Cyclic simple shear 2 x10-2 Silver and Seed (1971) Dry and saturated Ottawa Cyclic simple 1 x10-2 Youd (1972) sand shear (drained) Dry Monterey sand Cyclic simple shear Shaking Table 1 x 10-2 Pyke (1973) Saturated nonplastic silt Cyclic triaxial (0.5 to 0.6) x10-2 Stoll and Kald (1977) Saturated Monterey sand (normally and over consolidated Cyclic triaxial 1.2 x10-2 (OCR=1) 2.9 x 10-2 (OCR=8) Dobry et al. (1981a) Saturated Monterey Sand Cyclic triaxial 1.1 X 10-2 Dobry et al. (1982) Saturated Banding Sand Cyclic triaxial (0.8 to 0.9) x10-2 Dyvik et al. (1984) Saturated Heber Road fine sand Cyclic triaxial 1 x10-2 Ladd (1982) Stokoe et al. (1982) Several saturated sands Cyclic triaxial 1 x10-2 Dobry (1985) Whitman (1985) Saturated Monterey sand Resonant column 1.2 x10-2 Chung et al. (1984) Saturated Monterey sand Cyclic triaxial (1 to 2) x10-2 Hynes (1988) Saturated Folsom gravel: Cyclic triaxial Hynes (1988) normally consolidated overconsolidated (0.3 to 0.6) x10-2 (OCR=1) (γ tv ) OCR=2 = (4 to 5)x(γ tv ) OCR=1 Dry Nevada sand Cyclic simple shear (1.3 to 1.7) x10-2 Hsu and Vucetic (2004) Partially saturated La Cienaga silty sand (undisturbed sample) Cyclic simple shear (1.1 to 1.6) x10-2 Hsu and Vucetic (2004) Saturated clean aggregate sand fill deposited in a 1.2x1.2x1.2 m trench in the field Saturated Monterey sand Pore pressure generation by vertical vibration of circular foundation 3.3 m from trench Cyclic simple shear (0.5 to 1.0) x10-2 Chang et al. (2007) 1 x10-2 Hazirbaba and Rathje (2009) 20

10 As shown in Table 1, several observations of γ tv were made at the beginning of the 1970s during resonant column, cyclic simple shear, and shaking table tests. These tests involved either dry sand or saturated sand tested in drained condition. Drnevich and Richart (1970), Silver and Seed (1971), Youd (1972), and Pyke (1973), all reported that cyclic strains below about 10-2 % did not induce changes in density, modulus, or damping, even when a large number of cycles were applied to the soil. Stoll and Kald (1977) summarized these observations, conducted additional undrained cyclic testing on a nonplastic silt to verify that pore pressure buildup could not happen below this threshold, and proposed that the existence of γ tv and its specific value around 10-2 % defined a fundamental property of granular soils related to the minimum level of strain needed to start gross sliding and rearrangement of the individual particles. Very precise cyclic undrained measurements on saturated Monterey sand were reported by Dobry et al. (1982) and Ladd et al. (1989), obtaining a value of γ tv = 1.1x10-2 % (Fig. 8). Calculations in the report by Dobry et al. (1982) using a simple cubic array of quartz spheres, confirmed Stoll and Kald s hypothesis about the fundamental meaning of γ tv in granular soils and provided computed values of γ tv close to the measured ones. Table 1 lists a number of determinations of γ tv over the last four decades in both dry and saturated sands. Hsu and Vucetic (2004) reported the measurements of Fig. 9 in a paper where they explored the implications of this threshold strain for evaluation of settlement under earthquakes and other cyclic loadings, and extended the threshold strain concept to clays. Figure 8. Determination of threshold strain, γ tv, using strain-controlled undrained cyclic triaxial tests (Dobry et al., 1982; Ladd et al., 1989) The most important conclusion from Table 1 is that the value of γ tv in normally consolidated sand is very stable for a wide range of soils and testing conditions, including undisturbed samples of silty sand tested by Hsu and Vucetic (2004), and field measurements of pore pressure buildup induced by ground vibration, as reported by Chang et al. (2007). Essentially all values of γ tv for normally consolidated sand lie in the range between 0.5x10-2 % and 2x10-2 %, with the majority grouping around a representative γ tv 1x10 2 %. While some of the authors listed in Table 1 did measure small amounts of excess pore pressure at smaller strains, they all concluded that those could be neglected for practical purposes, with larger pore pressures only starting in the vicinity of 10-2 %. This threshold value is notably independent of sand type, deposition method (fabric), effective confining pressure, density or relative density, and prior shear straining at levels lower than the threshold. 21

11 Figure 9. Cyclic settlement of dry sand in direct simple shear strain-controlled tests (Hsu and Vucetic, 2004). On the other hand, as documented in Table 1 and Fig. 10, γ tv in sand is very sensitive to overconsolidation (Dobry et al., 1981a), with γ tv almost doubling when the overconsolidation ratio, OCR, equals 2, and reaching a value of almost 3x10-2 % for OCR = 8. This tendency for γ tv to increase rapidly with overconsolidation has also been found in gravel (Hynes, 1988; see Table 1). Figure 10. Influence of Overconsolidation Ratio on threshold strain (Dobry et al., 1981a). Based on the existence of γ tv for the initiation of excess pore pressures, Dobry et al. (1981b, 1982) developed the concept of a minimum ground surface threshold acceleration, a t, for a given site and liquefiable layer. The value of a t can be calculated from the γ tv of the layer and other conditions of the site. 22

12 If the maximum ground surface acceleration induced by the earthquake is below a t, there is no pore pressure buildup and liquefaction is not possible. For the representative value of γ tv = 10-2 %, associated with normally consolidated sand, and combined with typical values of V s, Dobry et al. (1981b, 1982) and Hynes (1988) calculated typical a t significantly below 0.10g, in agreement with field observations of liquefaction. Measurements of acceleration and pore pressure in a downhole array at Owi Island in Japan during small earthquakes (Ishihara, 1981), and the centrifuge tests illustrated in Figs. 11 and 12, have experimentally confirmed these small values of predicted a t < 0.10g for normally consolidated sand. On the other hand, the greater values of γ tv associated with overconsolidated sand, in conjunction with the increased V s due to higher lateral stresses, may double or triple the value of a t. The results of centrifuge tests reported by Adalier and Elgamal (2005) and summarized in Fig. 12, illustrate this increase. In these experiments, the measured threshold base acceleration of about 0.04g in the normally consolidated sand more than doubles to 0.09g for OCR = 2 and more than triples to 0.14g for OCR = 4. These are significant increases that have practical implications for the evaluation of liquefaction potential in the field. Furthermore, the calculated a t reaches even higher levels in excess of 0.2g when large γ tv due to overconsolidation, are combined with very large V s of the soil in the field due to high relative density, high K o and other effects (Dobry et al., 1981a). Figure 11. Determination of threshold acceleration of sand in centrifuge tests (Arulanandan et al., 1983). Figure 12. Influence of Overconsolidation Ratio on threshold base acceleration in centrifuge tests (modified after Adalier and Elgamal, 2005). 23

13 Figure 13 includes pore pressure buildup after ten cycles measured in strain-controlled cyclic triaxial tests on several normally consolidated sands (Dobry, 1985; Whitman, 1985). The figure shows clearly the threshold at around 10-2 %, with the pore pressure increasing as the cyclic strain of the test, γ c, increases beyond γ tv. The results are remarkably consistent, despite the fact that the graph includes fifty tests conducted on eight loose and dense sands at three laboratories, using a wide range of effective confining pressures and both undisturbed specimens and specimens remolded with various deposition methods. This is in contrast with the results of stress-controlled cyclic tests in sands, which are very sensitive to relative density and deposition method (Seed, 1979; Dobry et al., 1982). Bhatia (1980) presented similar results to those in Fig. 13 for several normally consolidated sands and relative densities, measured in cyclic direct simple shear tests. The corresponding band of pore pressures after ten cycles in these simple shear experiments (not presented here), is reasonably consistent with that in Fig. 13, suggesting that the rate of pore pressure buildup versus γ c > γ tv 10-2 % is not much affected by the testing technique. Figure 14 presents results for strain-controlled cyclic simple shear tests for both normally consolidated and overconsolidated Ottawa sand, reported by Bhatia (1980), Finn and Bhatia (1980), and Finn (1981). The graph shows a significant reduction in pore pressure at a given γ c when the sand is overconsolidated. This is consistent with the increase in threshold strain induced by overconsolidation, previously discussed, and also with many other tests in the literature, both strain- and stress-controlled, showing lower pore pressure buildup and higher cyclic strength when the sand is overconsolidated (Seed and Peacock, 1971; Ishihara and Takatsu, 1979; Dobry et al., 1981a; Stamatopoulos et al., 1999). The effect of overconsolidation in reducing pore pressure buildup has also been observed in centrifuge tests (Sharp et al., 2003; Adalier and Elgamal, 2005). Figure 13. Summary of results of strain-controlled undrained cyclic triaxial tests on several sands using different specimen preparation techniques (Dobry, 1985; Whitman, 1985). Figure 14. Influence of Overconsolidation Ratio on pore pressure buildup during cyclic straincontrolled direct simple shear tests (data from Bhatia, 1980; Finn, 1981) 24

14 It is also important to mention the effect of preshaking or prestraining in reducing pore pressure buildup and increasing cyclic strength. From the available evidence, preshaking/prestraining in a drained condition, or mild preshaking/prestraining in an undrained condition with subsequent pore pressure dissipation and densification, seems to play a role similar to that of overconsolidation. Both phenomena cause a rapid increase in the lateral stress and K o acting on the soil (Fig. 15). During cyclic straincontrolled tests in the lab, both overconsolidation and prestraining decrease the additional changes in void ratio or pore pressure buildup developed in subsequent cyclic straining, with a corresponding increase in measured liquefaction resistance of preshaken compared to virgin sand (Finn et al., 1970; Martin et al., 1975; Seed et al., 1977; Seed, 1979; Bhatia, 1980; Finn, 1981). The effect of preshaking in decreasing pore pressure buildup and increasing liquefaction resistance has also been detected in centrifuge tests (Sharp et al., 2010). Figure 15. Coefficient of lateral stress, K o, of dry sand during cyclic strain-controlled testing (Youd and Craven, 1975). WHAT DO FIELD PENETRATION AND V s MEASURE? Originally, it was believed that liquefaction resistance was mainly controlled by either void ratio, e, or relative density, D r. In that context, it was also thought that penetration resistance was correlated mainly, or exclusively with D r. However, first research by Finn et al. (1970), and then several other laboratory cyclic loading studies summarized by Seed (1979) and Finn (1981), showed that a number of other factors could be as important as D r or e in determining liquefaction resistance. This caused a decisive switch in engineering practice, away from the laboratory and toward the use of liquefaction charts based on penetration resistance. In his 1979 paper, Seed proposed, as an explanation for the success of penetrationbased charts, the hypothesis that the factors tending to increase the resistance to cyclic mobility or liquefaction also tend to increase the penetration resistance of sand. He listed these factors as relative density, the soil structure or fabric (method of sand deposition), the length of time the sand is subjected to sustained pressure, overconsolidation, and the value of the coefficient of lateral stress at rest, K o, and seismic prestraining. Table 2 reproduces the original table contained in Seed s 1979 paper. 25

15 Table 2. Factors Affecting Cyclic Mobility or Soil Liquefaction Characteristics and Penetration Resistance (Seed, 1979) Factor (1) Increased relative density Increased stability of structure Increase in time under pressure Increase in K o Prior seismic strains Effect on stress ratio required to cause cyclic mobility (2) Increases stress ratio for cyclic mobility or liquefaction Increases stress ratio for cyclic mobility or liquefaction Increases stress ratio for cyclic mobility or liquefaction Increases stress ratio for cyclic mobility or liquefaction Increases stress ratio for cyclic mobility or liquefaction Effect on penetration resistance (3) Increases penetration resistance Increases penetration resistance Probably increases penetration resistance Increases penetration resistance Probably increases penetration resistance Research after 1979 has generally confirmed Seed s general explanation summarized in Table 2, while eliminating some of the complexities of laboratory results as listed in the second column of Table 2. This simplification occurs when pore pressure buildup is evaluated using cyclic strain-controlled rather than stress-controlled tests in the laboratory, in the context of a cyclic strain approach that provides a more fundamental basis to liquefaction evaluation (Seed et al., 1983). Specifically, as shown in the previous section, the threshold strain of sands, as well as the rate of pore pressure buildup for strains above the threshold, is quite independent of two of the factors listed in Table 2: relative density and sand structure (fabric). On the other hand, these same strain-controlled tests have confirmed the beneficial effects of overconsolidation and a higher K o (Table 1, Figs. 10, 12, 14). More indirect but still powerful laboratory evidence has also confirmed the great beneficial effect of preshaking or prestraining, another of the factors listed in Table 2 (Fig. 15, see also Martin et al., 1975; Sharp et al., 2010). While there is considerable field evidence that geologic age increases liquefaction resistance, time under pressure seems to be only one of several contributing factors (Youd and Hoose, 1977; Hayati et al., 2008). Research after 1979 has also generally confirmed and reinforced Seed s explanation of the effect on penetration resistance of the factors as listed in the third column of Table 2. While the table at the time was only referring to SPT, the effects are generally the same on the CPT point resistance, so it is reasonable to consider together the evidence on both types of penetration. There is overwhelming evidence and general consensus that for recently deposited, normally consolidated, and non preshaken sands, normalized penetration resistance values such as (N 1 ) 60 and q c1n are strongly correlated to the value of D r of that sand. However, even for this restricted set of conditions the correlations are not unique, being affected by deposition method (fabric) when only one sand is considered, and by grain compressibility, specifically the presence of nonquartz particles such as mica, broken shells and calcite fragments when a number of sands or sites are considered (Jamiolkowski et al., 1985; Lee et al., 1999; Dobry et al., 2011). Overconsolidation and associated increases in lateral stress and K o increase dramatically the values of CPT point resistance and q c1n (Alperstein and Leifer, 1976; Baldi et al., 1981; Lunne and Kleven, 1981; Schmertmann, 1973, 1978; Sharp et al., 2010). This is illustrated by the chamber tests results on dry sand from Baldi et al. (1981), reproduced in Figs More limited evidence also indicates that q c1n may double when the sand is preshaken with small change in D r (Sharp et al., 2010). All of this points to a 26

16 general picture where relative density, fabric, and grain compressibility jointly control the value of the CPT at the lower end of the liquefaction chart in Fig. 2 (q c1n 15 to 80); and relative density, overconsolidation, and preshaking (and perhaps also geologic age), jointly control the value of CPT at the higher end of the liquefaction chart in Fig. 2 (q c1n > 80). One important corollary of this picture is that, while generally it is possible to state with some confidence that a sand is loose solely from a low measured penetration resistance, no similar statement is possible about the sand being dense solely from a high penetration value. For example, in the centrifuge results reported by Sharp et al. (2010), a high measured q c1n = 160 in Nevada sand could correspond to three very different states: normally consolidated/non preshaken with D r 75%, heavily overconsolidated with D r 50%, and mildly preshaken with D r 50%. Figure 16. Relationship between Over-consolidation Ratio and K o in dry sand, calibration chamber tests (Baldi et al., 1981). The next question is the effect of the factors listed in the first column of Table 2 on the value of the normalized shear wave velocity, V s1, used in the liquefaction chart of Fig. 4. A related question is the relationship between the shapes of the curves in the various charts included in Figs. 1-4, with the help of field correlations between penetration resistance and shear wave velocity, such as Fig. 7. The first author (Dobry, 2010) recently discussed these issues. The value of V s1 increases with lower void ratio, higher effective confining pressure, and increased K o. This is illustrated by Fig. 18, which reflects mostly laboratory results on dry pluviated clean sand. The shear wave velocity also increases with time under pressure (Richart et al., 1977; Anderson and Stokoe, 1978). The available evidence about the influence of fabric (method of sand deposition) is conflicting. Tatsuoka et al. (1979) conducted a systematic study on the effect of deposition method on V s and concluded that it is not significant. On the other hand, a recent comparison between dry pluviated and hydraulically-filled Ottawa sand showed a significant increase 27

17 Figure 17. Increase in point cone penetration resistance due to overconsolidation in dry sand, calibration chamber tests (Baldi et al., 1981) for the dry pluviated soil (Gonzalez, 2008; Abdoun et al., 2010). The disconnect between the lowest values of V s1 predicted by the laboratory results in Fig. 18, on the order of V s1 150 m/s, and those measured in clean sands in the field that may be as low as V s1 100 m/s (Fig. 4), also strongly suggests that the laboratory evidence, mainly based on dry pluviated specimens, may not be fully reflecting lower wave velocities of hydraulic fills in the field. The effect of overconsolidation on V s1 occurs through the increase in value of K o and is depicted in Fig. 18. The effect of preshaking seems to occur mainly through the increase in K o ; otherwise, the available evidence suggests that preshaking has little effect on V s1, producing at most very modest increases after straining for thousands of cycles (Drenevich and Richart, 1970; Witchmann and Triantafyllidis, 2004). At the lower end of the liquefaction chart of Fig. 4 (V s1 < m/s), the value of V s1 seems to be determined by the same factors that control q c1n in this range (relative density, fabric). As a result, the shapes of the curves in Figs. 2 and 4 are similar. However, at the higher end of Fig. 4 (V s1 > 170 m/s), where the curve is again controlled by the same factors previously discussed for the CPT in the corresponding range (relative density, overconsolidation, preshaking, age), the curve in Fig. 4 rises much more sharply than in Fig. 2. The reason seems to be the much lower sensitivity of V s1 to increased K o, illustrated by Fig. 18, which is also consistent with the flattening of the curve of Fig. 7 at high values of q c1n. 28

18 Figure 18. Normalized shear wave velocity of saturated clean sand, V s1, predicted from the Hardin and Drnevich (1972) laboratory correlation (Dobry, 2010). WHY DO LIQUEFACTION CHARTS WORK? Seed et al. (1983) and Dobry (1989) addressed the issue of why penetration liquefaction charts work so well in separating sites that have and have not liquefied in earthquakes. They linked it to the existence of the threshold strain in sands, γ tv 10-2 %, already discussed in a previous section. In this explanation, at the lower end of the charts, the curve that separates liquefaction from no liquefaction is a line of constant minimum cyclic strain, (γ c ) min, that must be exceeded for liquefaction to occur. Both publications also agreed that (γ c ) min should be only a few times the value of γ tv, and that (γ c ) min should be higher for small earthquake magnitudes, decreasing and approaching γ tv 0.01% as the magnitude and duration of the earthquake increases. In those publications, Seed et al. and Dobry provided various estimates of (γ c ) min ranging from 0.03% to 0.06% for large magnitude earthquakes of M w = 7 to 8. On the basis of similar considerations, the form of the equation selected by Andrus and Stokoe (2000) for the V s -based curve in Fig. 4 assumes a constant (γ c ) min in the beginning part of the curve, which after calibration with the field case histories corresponds to (γ c ) min 0.03 to 0.05% for M w = 7 (see also Andrus et al., 1999). However, these estimates by Seed et al. (1983) and the first author (Dobry, 1989) of a (γ c ) min needed to cause liquefaction in the field were based on very simplified calculations and the issue was not pursued further. Also, these estimates are limited to the lower end of the curves. In his 1989 paper, the first author speculated that the much faster rise of the SPT curve in Fig. 1 at the upper end may be correlated to the rapid decrease in sand compressibility and much lower amount of water expelled by the soil after liquefaction at high values of penetration resistance. The rest of this section revisits the issue of what controls the field liquefaction curves in Figs. 1-4 with the help of a recent series of full-scale and centrifuge liquefaction tests involving various levels of shaking intensity (see Abdoun et al., 2010 for more details). Figure 19 shows a photo of the inclined laminar box at the University at Buffalo used to conduct fullscale Test SG-1. The box is 6 m in height, and the soil model was constructed with hydraulic filling of 29

19 saturated fine Ottawa sand, simulating a loose clean sand deposit with the groundwater level at the ground surface. As a result of the hydraulic filling, this deposit simulates the fabric of many of the loosest and most liquefiable sands found in the field. This was confirmed by field property measurements of the deposit that provided the low values of D r 40%, q c1n 50, and V s1 114 m/s. These q c1n and V s1 are located at the very low ends of the charts in Figs. 2 and 4. The laminar box was inclined 2 0 in order to simulate a mild infinite slope and lateral spreading, and it was shaken at the base by horizontal actuators connected to a strong wall. Additional details on the laminar box and Test SG-1 are presented by Thevanayagam et al. (2009), Dobry et al. (2011) and Medina et al. (2011). Figure 19. Full-scale liquefaction and lateral spreading Test SG-1: (a) laminar box before shaking; (b) setup and instrumentation; and (c) input displacement and acceleration time histories (Dobry et. al., 2011). As shown in Figs. 19(c) and 20, the base of the box was excited by ten cycles of a very small acceleration of about 0.01g at a frequency of 2Hz, followed by stronger shaking that liquefied the deposit very fast and generated about 30 cm of lateral spreading. Only the first ten cycles, corresponding to the first 5s of shaking, are of interest here. The main results are presented in Fig. 20 for these first ten cycles; they generated some excess pore pressures and a couple of centimeters of lateral spreading, but did not cause liquefaction in the deposit. The maximum excess pore pressure ratio at the end of the ten cycles, measured near the ground surface, was r u = 0.7. As documented by Gonzalez (2008) and Abdoun et al. (2010), two centrifuge tests were conducted at Rensselaer Polytechnic Institute with the specific purpose of simulating this full-scale Test SG-1. In both centrifuge experiments, the prototype height, laminar box inclination, and base input shaking were 30

20 essentially the same as in Test SG-1. The soil was deposited by dry pluviation in both tests, and comparisons of the centrifuge results with those of the full-scale experiment are shown in Fig. 20. Figure 20. Comparison of results between full-scale Test SG-1 and two centrifuge tests (Gonzalez, 2008; Abdoun et al., 2010). The first centrifuge experiment, FF-V1, used the same Ottawa sand deposited at the same void ratio and D R 40% of the full-scale experiment. Because the test was conducted at 25g centrifugal acceleration, the sand was saturated with a viscous fluid having twenty-five times the viscosity of water, in order to correctly simulate the permeability of the deposit in Test SG-1. Due to the different fabric of the Ottawa sand in this centrifuge Test FF-V1 (dry pluviation versus hydraulic filling in Test SG-1), the centrifuge model soil had a normalized shear wave velocity, V s1 174 m/s, much greater than the V s1 114 m/s in the full-scale test. The great significance of this difference in V s1 values due to fabric for the same normally consolidated sand placed at the same D r may be appreciated by looking at the chart in Fig. 4; the two values cover almost the whole range of liquefiable sands in the field. As shown by Fig. 20, the results of centrifuge Test FF-V1 are in poor agreement with those of full-scale Test SG-1. Specifically, no excess pore pressures and no lateral spreading were developed in the centrifuge at any depth in the first ten cycles, compared with excess pore pressure ratios, r u 0.1 and 0.7, at mid-depth and near the ground surface, respectively, in Test SG-1. The second centrifuge experiment, FF-P2, followed a different testing strategy. Instead of utilizing the same soil of Test SG-1, a different soil labeled scaled sand was used in this centrifuge model, particularly designed to simulate the prototype Ottawa sand by matching both its permeability and stiffness. This scaled sand was a silty sand, obtained by mixing a finer Ottawa sand with nonplastic silt, so that: (i) the two grain distribution curves in the centrifuge and full-scale deposits were more or less parallel, and (ii) the permeability of this scaled sand was about 25 times that of the original Ottawa sand at 1g. In this way, after depositing the scaled sand by dry pluviation in the centrifuge and saturating it with water, it matched 31

21 correctly, at 25g, the permeability of the sand in the prototype. Finally, the scaled sand was deposited very loose in order to match as well as possible the V s1 114 m/s of the hydraulically filled Ottawa sand in the prototype. This was successfully accomplished, with V s1 135 m/s measured in the saturated scaled sand at 25g. While these two values of V s1 are not identical, they are close, with both located at the lower end of the field liquefaction chart of Fig. 4. Figure 20 also includes the results of this centrifuge Test FF-P2, and the agreement with the results of full-scale Test SG-1 is now much better. At mid-depth and at the end of 5s, r u 0.05 compared with 0.10 in full scale (and r u = 0.4 near the ground surface compared with 0.7 in full scale). Both centrifuge and full-scale deposits also developed a couple of centimeters of lateral spreading. Other response measurements at the end of the ten cycles in centrifuge Test FF-P2, not shown here, all confirm the generally good agreement with full-scale Test SG-1, much better than the performance of centrifuge Test FF-V1. It is reasonable to assume that this better agreement between FF-P2 and SG-1 than between FF-V1 and SG-1, is related to the much higher value of V s1 = 174 m/s in FF-V1, compared with V s1 = m/s for FF-P2 and SG-1. This was verified by treating the measured responses of the three experiments during the first ten cycles of shaking as field case histories, and by plotting them as data points of CSR versus V s1 in the Andrus and Stokoe liquefaction chart of Fig. 4. This is done in Fig. 21, where the Andrus and Stokoe curve for clean sands and M w = 7 is used, in order to avoid the need for a magnitude correction factor, and taking advantage of the fact that M w = 7 corresponds approximately to the first ten cycles of shaking used in the three full-scale and centrifuge tests (Fig. 6). The three data points are plotted as vertically elongated ellipses in Fig. 21 to cover the uncertainty of the calculated CSR, with the top of each ellipse being an upper bound and the bottom a lower bound. An open ellipse, like Test FF-V1, means no pore pressure buildup, while a half-full ellipse means some pore pressure buildup but no liquefaction (Tests SG-1 and FF-P2). A full ellipse (none in Fig. 21) would represent full liquefaction, with r u = 1.0. Figure 21. Comparison of full-scale and centrifuge tests of Fig. 20, with Andrus and Stokoe (2000) liquefaction chart for clean sand (Abdoun et al., 2010). The locations of the three data points in Fig. 21 are fully consistent with the predictions of the Andrus- Stokoe chart. Test FF-V1 plots significantly below the curve, consistent with the fact that no excess pore 32

22 pressures developed in this test. Tests SG-1 and FF-P2 are located on the curve itself, separating liquefaction from no liquefaction, and some pore pressure buildup short of liquefaction was observed in both full-scale and centrifuge experiments. Figure 21 clearly constitutes a big step forward in the effort to integrate field and laboratory, a main purpose of this paper. It both explains qualitatively the pore pressure responses of the three experiments, and increases the confidence in both the testing and the liquefaction chart. It provides a clear first order explanation for the difference in liquefaction responses between Tests SG-1 and FF-V1, despite the fact that both used the same sand and void ratio, with the effect of void ratio (and D r ) being, in this case, completely overridden by the different fabrics of the two deposits as reflected in their different values of V s1. Additional full-scale and centrifuge experiments, involving ten cycles of shaking, were conducted as part of this series, using the same Ottawa and scaled sands discussed before (Abdoun et al., 2010). The corresponding ellipses, including the three tests of Fig , are plotted in Fig. 22, which confirms the consistency of the proposed presentation of results. That is, Fig. 22 shows that the location of the data points, representing each of these ten case histories, predicts well the pore pressure response of the corresponding centrifuge or full-scale test, with the Andrus and Stokoe field-based curve efficiently separating cases of liquefaction and no liquefaction. The authors extracted, for these ten case histories, the maximum value of seismic shear strain, γ max, calculated with the help of computer program SHAKE during the ten cycles at any depth within the deposit, and the results are summarized in Fig. 22. In those cases where no pore pressure or limited pore pressure buildup occurred in the test, the SHAKE calculations of γ max were supplemented by γ max extracted from the measured soil accelerations using a system identification technique (Zeghal et al., 1995). The data points in Fig. 22 are divided in three groups: two experiments that did not build up any pore pressure and γ max = to 0.01%; six experiments where there was generally some pore pressure buildup short of liquefaction and γ max = 0.02 to 0.04%; and two deposits that liquefied and γ max = 0.3 to more than 1%. This is very consistent with the explanations offered by Seed and Dobry and discussed earlier in this paper, that the boundary curve between field liquefaction and no liquefaction (at least at the lower end of the charts) may be explained by the earthquake developing a shear strain, (γ c ) min, a few times the threshold strain of normally consolidated sand, γ tv 0.01%, with this explanation now supported by substantial field evidence as well as by fullscale and centrifuge laboratory tests. Figure 22. Maximum seismic shear strains in the soil determined by computer Program SHAKE and system identification techniques, for the ten full-scale and centrifuge case histories reported by Abdoun et al. (2010). 33

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