Dobry-and-Abdoun-2011 (1).pdf

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 5th

Int’l Conf. on Earthquake Geotechnical Engineering, pp. 13-45

Santiago, Chile, January 10-13, 2011

Chilean Geotechnical Society

5th International Conference on Earthquake Geotechnical Engineering January 2011, 10-13

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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 full-

scale and centrifuge results. It is concluded that the charts are curves of constant cyclic strain at the lower

end (Vs1 < 160 m/s), with this strain being about 0.03 to 0.05% for earthquake magnitude, Mw ≈ 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 Ko, 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 Mw ≈ 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 40-50 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.


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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, Vs, 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, Mw ≈ 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, N1 (later refined to (N1)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, qc1N (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).


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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).


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More recently, liquefaction charts have been developed using the same simplified procedure framework, but now based on the normalized shear wave velocity, Vs1, 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 Vs-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 Vs 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, Mw = 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 Vs), 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, amax, then the CSR is corrected as needed by the MSF to bring it to Mw = 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,


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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):

(1)

where, amax = maximum horizontal acceleration at the ground surface; τmax = maximum horizontal shear

stress in the liquefiable layer; σv0 and σ’v0 = total and effective vertical normal stress before the shaking,

respectively; and rd = stress reduction coefficient, which accounts for the flexibility of the soil profile, with rd = 1.0 at the ground surface and, typically, rd < 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 amax estimated at the

ground surface; or (ii) directly from τmax calculated with a site amplification program such as SHAKE

(Schnabel et al., 1972). Implicit in Eq. (1) is the assumption that τmax = (amax/g) σv0 rd. It is also assumed

that the values of τmax and amax 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, τc ≈ 0.65 τmax ≈ 0.65

(amax/g) σv0 rd (Fig. 5). The equivalent number of cycles or duration is related to Mw (Fig. 6). The parameter τc 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.

Figure 5. Calculation of the Cyclic Stress Ratio, CSR, in the Seed and Idriss Simplified Procedure.


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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 (amax/g) (σv0 /

σ’v0) rd has been consistently used to calculate the data points of case histories, with amax 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 τmax and amax 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 stress-

strain (or backbone) curves of τ vs. shear strain, γ, or by shear modulus reduction G/Gmax 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 τc and G for

a constant cyclic strain, γc, in strain-controlled tests; (ii) significant increases in γc for a constant τc in

stress-controlled tests; or (iii) decreases in τmax and amax 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 amax and τmax experienced by the liquefying layer at the site. The calculated values of CSR, τmax, and amax 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

amax or τmax 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. 1-4. 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 τmax and amax, 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


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liquefaction charts (or derived τmax and amax) may be compared with the results of a site response analysis, such as SHAKE, where the curve of G/Gmax 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/Gmax, 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/Gmax 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 Vs 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 qc1N and Vs1 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, γtv, 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, γc

> γtv. The parameter γtv was called “threshold strain” and given the symbol γt in the original publications,

but has been since renamed “volumetric threshold strain,” γtv, to avoid confusion with other threshold

levels present in sands (Hsu and Vucetic, 2004). While the more correct symbol γtv is used in this paper,

the shorter and more convenient name “threshold strain” has been preserved.


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Table 1. Volumetric Threshold Shear Strain, γtv, Dry and Saturated Sands

SOIL Testing

Technique γtv (%) 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 sand

Cyclic simple shear (drained)

1 x10-2

Youd (1972)

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:

normally consolidated

overconsolidated

Cyclic triaxial

(0.3 to 0.6) x10-2

(OCR=1)

(γtv)OCR=2 = (4 to 5)x(γtv)OCR=1

Hynes (1988)

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

Pore pressure

generation by vertical vibration

of circular

foundation 3.3 m from trench

(0.5 to 1.0) x10-2 Chang et al. (2007)

Saturated Monterey sand Cyclic simple

shear

1 x10-2

Hazirbaba and Rathje

(2009)


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As shown in Table 1, several observations of γtv 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 γtv 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 γtv = 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 γtv in granular soils and provided computed values of γtv close to the measured

ones. Table 1 lists a number of determinations of γtv 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, γtv, 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 γtv 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 γtv for normally consolidated sand

lie in the range between 0.5x10-2

% and 2x10-2

%, with the majority grouping around a representative γtv ≈

1x102%. 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.


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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, γtv in sand is very sensitive to overconsolidation

(Dobry et al., 1981a), with γtv almost doubling when the overconsolidation ratio, OCR, equals 2, and

reaching a value of almost 3x10-2

% for OCR = 8. This tendency for γtv 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 γtv for the initiation of excess pore pressures, Dobry et al. (1981b, 1982) developed the concept of a minimum ground surface threshold acceleration, at, for a given site and

liquefiable layer. The value of at can be calculated from the γtv of the layer and other conditions of the site.


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If the maximum ground surface acceleration induced by the earthquake is below at, there is no pore pressure buildup and liquefaction is not possible. For the representative value of γtv = 10

-2%, associated

with normally consolidated sand, and combined with typical values of Vs, Dobry et al. (1981b, 1982) and

Hynes (1988) calculated typical at 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 at < 0.10g for normally consolidated sand. On the other hand, the greater values of γtv associated with overconsolidated sand, in conjunction with the

increased Vs 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 at reaches even higher levels in excess of 0.2g when large γtv due to overconsolidation, are combined with very large Vs of the soil in the field due to high relative density,

high Ko 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).


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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, γc, increases

beyond γtv. 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 γc > γtv ≈ 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 γc 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 strain-

controlled direct simple shear tests (data from Bhatia, 1980; Finn, 1981)


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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 Ko acting on the soil (Fig. 15). During cyclic strain-

controlled 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, Ko, of dry sand during cyclic strain-controlled testing (Youd

and Craven, 1975).

WHAT DO FIELD PENETRATION AND Vs MEASURE?

Originally, it was believed that liquefaction resistance was mainly controlled by either void ratio, e, or relative density, Dr. In that context, it was also thought that penetration resistance was correlated mainly,

or exclusively with Dr. 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 Dr 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 penetration-

based 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, Ko, and seismic prestraining. Table 2 reproduces the original table contained in Seed’s 1979 paper.


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Table 2. Factors Affecting Cyclic Mobility or Soil Liquefaction Characteristics and Penetration

Resistance

(Seed, 1979)

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 Ko (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 (N1)60 and qc1N are strongly correlated to the value of Dr 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 Ko increase dramatically the values of

CPT point resistance and qc1N (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. 16-17. More limited evidence also indicates that qc1N may

double when the sand is preshaken with small change in Dr (Sharp et al., 2010). All of this points to a

Factor

(1)

Effect on stress ratio required

to cause cyclic mobility

(2)

Effect on penetration

resistance

(3)

Increased relative density Increases stress ratio for cyclic

mobility or liquefaction

Increases penetration

resistance

Increased stability of structure Increases stress ratio for cyclic



resistance

Increase in time under pressure Increases stress ratio for cyclic


Probably increases

penetration resistance

Increase in Ko Increases stress ratio for cyclic



resistance

Prior seismic strains Increases stress ratio for cyclic


Probably increases

penetration resistance


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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 (qc1N ≈ 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 (qc1N > 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 qc1N = 160 in Nevada sand could correspond to three very different states: normally

consolidated/non preshaken with Dr ≈ 75%, heavily overconsolidated with Dr ≈ 50%, and mildly

preshaken with Dr ≈ 50%.

Figure 16. Relationship between Over-consolidation Ratio and Ko 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, Vs1, 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 Vs1 increases with lower void ratio, higher

effective confining pressure, and increased Ko. 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 Vs 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


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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 Vs1 predicted by the laboratory results in Fig. 18, on the order of Vs1 ≈ 150 m/s, and those measured in clean sands in the field that may be as low as Vs1 ≈ 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 Vs1 occurs through the increase in value of Ko and is depicted in Fig. 18. The effect of preshaking seems to occur mainly through

the increase in Ko; otherwise, the available evidence suggests that preshaking has little effect on Vs1,

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 (Vs1 < 160-170 m/s), the value of Vs1 seems to be

determined by the same factors that control qc1N 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 (Vs1 > 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 Vs1 to increased Ko,

illustrated by Fig. 18, which is also consistent with the flattening of the curve of Fig. 7 at high values of

qc1N.


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Figure 18. Normalized shear wave velocity of saturated clean sand, Vs1, 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, γtv ≈ 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, (γc)min, that must be exceeded for liquefaction to occur. Both publications also

agreed that (γc)min should be only a few times the value of γtv, and that (γc)min should be higher for small

earthquake magnitudes, decreasing and approaching γtv ≈ 0.01% as the magnitude and duration of the earthquake increases. In those publications, Seed et al. and Dobry provided various estimates of (γc)min

ranging from 0.03% to 0.06% for large magnitude earthquakes of Mw = 7 to 8. On the basis of similar

considerations, the form of the equation selected by Andrus and Stokoe (2000) for the Vs-based curve in Fig. 4 assumes a constant (γc)min in the beginning part of the curve, which after calibration with the field

case histories corresponds to (γc)min ≈ 0.03 to 0.05% for Mw = 7 (see also Andrus et al., 1999).

However, these estimates by Seed et al. (1983) and the first author (Dobry, 1989) of a (γc)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 full-scale Test SG-1. The box is 6 m in height, and the soil model was constructed with hydraulic filling of


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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 Dr ≈ 40%, qc1N ≈ 50, and Vs1 ≈ 114 m/s. These qc1N and Vs1 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 ru = 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


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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

DR ≈ 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, Vs1 ≈ 174 m/s, much greater than the Vs1 ≈ 114 m/s in the full-scale test. The great significance of this difference in Vs1 values due to fabric for the same

normally consolidated sand placed at the same Dr 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, ru ≈ 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


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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 Vs1 ≈ 114 m/s of the hydraulically filled Ottawa sand

in the prototype. This was successfully accomplished, with Vs1 ≈ 135 m/s measured in the saturated

scaled sand at 25g. While these two values of Vs1 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, ru ≈ 0.05 compared with 0.10 in full scale (and ru = 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 Vs1 = 174 m/s in FF-V1, compared with Vs1= 114-135 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 Vs1

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 Mw = 7 is used, in order to avoid the need for a magnitude correction factor, and taking advantage of the fact that Mw = 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 ru = 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


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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 Dr) being, in this case, completely overridden by the different fabrics of the two deposits as reflected

in their different values of Vs1.

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. 20-21, 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, γmax, 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 γmax were supplemented by γmax 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 γmax = 0.005 to 0.01%; six

experiments where there was generally some pore pressure buildup short of liquefaction and γmax = 0.02 to 0.04%; and two deposits that liquefied and γmax = 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, (γc)min, a few times the threshold strain of normally consolidated sand, γtv ≈ 0.01%, with this explanation now supported by substantial field evidence as well as by full-

scale 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).


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PROPOSED EXPLANATION OF WHOLE CURVE

Based on the previous discussions in this paper, the authors propose the explanation summarized in Figs.

23-24 for the CSR versus Vs1 liquefaction chart of Andrus and Stokoe. Similar to the previous section, an earthquake magnitude, Mw, equal to 7 was selected in these figures, but the arguments for other

magnitudes are similar. Also, as the boundary curves separating liquefaction from no liquefaction

represent the same sites and sands irrespective of the chart being based on Vs or penetration resistance, if the explanation is valid for the Vs1 chart, it should also be valid for the other charts.

Figure 23. Relationship between Andrus and Stokoe (2000) clean sand liquefaction curve for Mw ≈ 7

and lines of constant cyclic shear strain, γc.

Figure 24. Speculative explanation of Andrus and Stokoe (2000) clean sand liquefaction curve for

Mw = 7 by zones of increasing cyclic strain, γc.


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Figure 23 includes several curves of constant cyclic shear strain, γc, calculated using the expression:

(2)

where σ’vo is in kPa and Vs1 is in m/s. Equation (2) was obtained by assuming a constant mass density of the liquefiable sand, ρ = 1.92 Mg/m

3. The curves in Fig. 23 were calculated using the expressions

proposed by Darendelli (2001) to represent G/Gmax versus γc in clean sand. As these equations include a

dependence on isotropic confining pressure, σ’o, and σ’o = (1+2Ko)/3 for field conditions, the curves in

Fig. 23 depend both on σ’vo and Ko in addition to their basic dependence on γc. A value of σ’vo = 50 kPa, representative of many of the field sites included in the Andrus et al. (1999) database, was used for all

curves in Fig. 23.

It is important to note that the use in Eq. (2) of standard G/Gmax versus γc curves for sand that do not

change even if the soil liquefies, is made possible by the basic assumption of the Simplified Procedure, of

ignoring the effect of excess pore pressure in softening the stress-strain response of the soil. This was discussed in a previous section (see Fig. 5). Therefore, values of γc for the curves in Fig. 23 are realistic

only when they are below or close to the field curve; but they are not realistic and provide only an index

value of γc for points much above the field curve. This is consistent with the previous conclusion that the

values of CSR, and derived shear stresses and ground accelerations, are only realistic when below or around the field curve.

As expected, the curve corresponding to the threshold strain, γc = 0.01%, plots below the field curve separating liquefaction from no liquefaction. Also as expected, the curves corresponding to γc = 0.03-

0.05% (and Ko = 0.5 for these normally consolidated sites), represent extremely well the lower end of the

Andrus-Stokoe field curve up to about Vs1 = 160 m/s. Above this Vs1, the field curve rises much more sharply than the γc = 0.03-0.05% curves. Therefore, for this lower end of the field liquefaction chart up to

Vs1 ≈ 160 m/s, the proposed explanation is essentially the same formulated by Seed et al. (1983) and

Dobry (1989) more than 20 years ago: for Mw = 7 the field curve corresponds to a constant γc = (γc)min =

0.03-0.05%.

For Vs1 > 160 m/s, that is for the upper end of the field curve, the situation is more complicated. In a

recent publication, the first author (Dobry, 2010) arrived at the conclusion that this upper end is likely controlled by overconsolidated and preshaken sites having high values of Ko. As discussed in a previous

section, the laboratory evidence shows that for a given γc and number of cycles, the pore pressure buildup

is much smaller when the soil is overconsolidated or preshaken. Therefore, significantly greater values of

γc should be required at these overconsolidated or preshaken sites to generate the high excess pore pressures needed for liquefaction. Curves of increasingly higher Ko and higher γc have been plotted in Fig.

23 to reflect this preliminary conclusion. The curves of constant γc intersect the field curve at increasingly

higher values of Vs1 and CSR as expected. Therefore, the authors propose that this upper end of the field liquefaction chart is explained by a variable value of (γc)min as Vs1 increases. While for Vs1 < 160 m/s,

(γc)min ≈ 0.03-0.05%, for Vs1 ≈ 200 m/s the value would increase to (γc)min ≈ 0.2 or 0.3%. In both cases, the

necessary condition for liquefaction is γc > (γc)min, but with vast differences in the values of (γc)min at the lower and upper ends of the chart.

Figure 24 sketches this explanation in a very preliminary and speculative way by just taking the points of

intersection between the constant γc curves and the field curve and arbitrarily assigning stages around these intersection points associated with increasing γc = (γc)min (as well as increasing Ko).

CSR=0.191


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APPLICATION TO EARTHQUAKE MAGNITUDE Mw = 7

In order to provide initial validation to the explanation of field liquefaction charts proposed in the

previous section, the authors selected, from the Andrus et al. (1999) database, those sites which correspond to earthquake magnitudes, Mw ≈ 7, and clean sands with fines content, FC ≤ 12%. Magnitude

7 was selected because it has by far the largest number of clean sand case histories of the database. Also,

magnitude 7 was used before in this paper for comparison with laboratory experiments (Figs. 21-22). As there is evidence that gravels have a threshold strain lower than sands (Hynes, 1988; see Table 1), gravels

and gravelly sands were not considered. This resulted in 34 case histories of liquefaction and no

liquefaction, which are plotted the traditional way in Fig. 25. The vertical effective confining pressures of

these case histories range between 37 and 195 kPa, with a representative value of about σ’vo = 75 kPa. As can be seen in Fig. 25, the curve proposed by Andrus et al. (1999) and Andrus and Stokoe (2000) for this

earthquake magnitude and clean sands separates very well the cases of liquefaction and no liquefaction.

Figure 25. Andrus and Stokoe (2000) clean sand sites and corresponding liquefaction chart for Mw

≈ 7 (data points from database in Andrus et al., 1999).

Thirty two out of the thirty four case histories in Fig. 25 correspond to the 1989 Loma Prieta earthquake

in Northern California, which had a Mw = 7.0. (The other two are data points of sites that liquefied and

had CSR > 0.4, far above the curve in Fig. 25, corresponding to the Mw = 6.9 Kobe, Japan earthquake.)

Figure 26 includes only the case histories corresponding to artificial fills, deposited by various methods,

including dumping and hydraulic filling. These sites share two important characteristics: (i) they were not

compacted or otherwise improved after placement; and (ii) they have been in place for a relatively short period of time and thus have not experienced much the effects of age and seismic activity. Therefore, the

low values of Ko = 0.5 and (γc)min = 0.03-0.05% previously used in Fig. 23 for these kinds of soils appear

reasonable. The corresponding curves of constant γc are plotted in Fig. 26, and they constitute an excellent lower boundary for liquefaction of these unimproved young fills.


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Figure 26. Loose artificial clean sand fills, mostly in the San Francisco Bay Area, liquefied by

earthquake magnitudes, Mw ≈ 7, explained by γc = (γc)min = 0.03 to 0.05% (data points from Fig. 25

and Andrus et al., 1999).

The rest of the thirty four case histories, corresponding to either natural soil deposits or improved fills, are

included in Fig. 27. The natural soils correspond to the specific geologic and seismic environment of the

San Francisco Bay Area, characterized by a high frequency of earthquake occurrence. This is important, because it suggests that the natural soil sites included in Fig. 25, typically of Recent (< 500 years) or

Holocene (< 10,000 years) geologic ages, have been subjected many times to earthquake shaking, with

their current liquefaction response reflecting the effect of this preshaking. Based on the discussion in the previous section, higher values of Ko and (γc)min should characterize such natural sites. The data points in

Fig. 27 also include six case histories of artificial fills that had been improved and did not liquefy during

the 1989 Loma Prieta earthquake, all having values of Vs1 > 200 m/s. These six sites were densified with vibratory methods (Andrus et al., 1998), which thus induced preshaking, and presumably also an

increased value of Ko compared to the uncompacted fills. The graph in Fig. 27 indicates that, as expected,

curves calculated with large values of (γc)min = 0.1-0.2% (combined with high Ko), separate well the cases

of liquefaction and no liquefaction, for Mw ≈ 7 and either improved clean sand fills or natural deposits subjected for hundreds or thousands of years to frequent earthquakes.

Figures 26 and 27 show that the proposed alternative way of plotting curves of constant γc to separate liquefaction from no liquefaction in field liquefaction charts, may do as well as the traditional way (Fig.

25). While the proposed alternative may require additional information about the geologic or seismic

environment of natural soil deposits, it has some significant advantages, including: (i) it provides additional insight into the meaning of the boundary curve with a clear interpretation in terms of laboratory

tests and existing knowledge (constant γc); and (ii) it allows new conclusions and refinement of

liquefaction potential evaluations (for example, it had been concluded previously on the basis of Fig. 4

that no site could liquefy if Vs1 is greater than about 200-215 m/s, while Fig. 27 suggests that such liquefaction may be possible for a very high value of CSR even if Vs1 approaches 250 m/s). Furthermore,

it has been known qualitatively for a long time that geologic setting and age have a profound effect on

liquefaction susceptibility (Youd and Hoose, 1977; Youd and Perkins, 1978); curves such as Figs. 26-27 allow making this qualitative knowledge more quantitative and precise.


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Figure 27. Liquefaction and no liquefaction of clean sand improved artificial fills and natural

deposits in the San Francisco Bay Area during the Mw = 7 Loma Prieta earthquake, explained by γc

= (γc)min = 0.1 to 0.2% (data points from Fig. 25 and Andrus et al., 1999).

DISCUSSION AND CONCLUSIONS

This paper constitutes a systematic effort to clarify why field liquefaction charts based on Seed and Idriss’ Simplified Procedure work so well. The authors believe 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 of sand properties and correlates them to void ratio or relative density. On the other hand, the SOP is based on field measurements of penetration resistance and shear

wave velocity, coupled with empirical or semi-empirical correlations calibrated with actual case histories

during earthquakes. This gap slows down further progress in both SOP and SOA. The paper accomplishes

its objective through: a review of the main features of the Simplified Procedure; a literature review of relevant aspects of the SOA including the factors influencing threshold shear strain and pore pressure

buildup during cyclic strain-controlled tests in sands; a discussion of the factors influencing penetration

resistance and shear wave velocity in the field; and a discussion of the meaning of the curves in the liquefaction charts separating liquefaction from no liquefaction, helped by a recent series of full-scale and

centrifuge tests. It is concluded with reasonably strong certainty that these are curves of constant cyclic

shear strain at the lower end of the charts (Vs1 < 160 m/s), with this strain being about 0.03 to 0.05% for

earthquake magnitude, Mw ≈ 7. That is, the cyclic strain needed to cause liquefaction at this lower end is only slightly larger than the threshold strain in normally consolidated sand, γtv ≈ 1x10

-2%. It is also

concluded, in a more speculative way, that the upper end of the charts probably correspond to a variable

increasing cyclic strain as well as increasing Ko, as this upper end seems to be controlled by overconsolidated and preshaken sands, with cyclic strains needed to cause liquefaction being as high as

0.1 to 0.2%. These conclusions are validated by application to case histories corresponding to Mw ≈ 7,

mostly in the San Francisco Bay Area of California, USA, during the 1989 Loma Prieta earthquake. The validation shows that larger cyclic shear strains of about 0.1-0.2% were necessary in this earthquake to


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liquefy improved fills as well as natural deposits preshaken by the frequent seismic activity in the area, while small strains on the order of only 0.03-0.05% were enough to liquefy the loose artificial fills.

While the paper makes significant progress in clarifying the issues and answering some key questions, it

is only a first step which raises other questions. This becomes clear when looking at the various sections of the paper reviewing relevant aspects of existing knowledge. There is overwhelming evidence that

overconsolidation increases Ko in sand and the effect has been thoroughly quantified; however, the

evidence of preshaking doing the same is less compelling and has not been quantified to the same extent. There is also less direct quantitative evidence about the effects of preshaking on threshold strain and rate

of pore pressure buildup during undrained cyclic straining. As a result, the linking established by the

authors between overconsolidation and preshaking when analyzing why the liquefactions chart work,

while consistent with the available evidence, intuitively strong, and well validated by case histories in Figs. 26-27, is a preliminary conclusion that requires confirmation through further research. This is one

example where additional research is necessary. Another area of needed research is the influence of soil

fabric on penetration resistance and shear wave velocity, where there seems to be a disconnect between the lowest values predicted by laboratory results on dry pluviated sands (Vs1 ≈ 150 m/s), and the very low

values approaching 100 m/s that have been measured in the field and in at least one full-scale hydraulic

fill test. While strong circumstantial evidence does indeed suggest that the upper end of the liquefaction

charts are controlled by overconsolidated and preshaken sites, additional research is also needed here, including thorough review of the databases supporting the existing charts based on penetration resistance.

Finally, even the results where the concept works well, as validated by the case histories in Figs. 26-27,

are limited to the liquefaction chart based on shear wave velocity, to one earthquake magnitude, and to a specific geologic and seismic environment (the San Francisco Bay Area of California). There is a need to

extend the concept to other magnitudes and environments as well as to charts based on penetration

resistance. As this paper is largely restricted to clean sands without gravels, the possibilities and limitations of the approach need to be explored for silty sands, clayey sands, and gravels, as well as for

gravelly sands. Finally, there is a need to link systematically the levels of cyclic strain causing

liquefaction in the field to those observed in laboratory cyclic tests.

The issue of the effects of liquefaction can also be looked at in a different way now, based on the results presented in this paper. The cyclic strains needed to trigger liquefaction in the field in a large magnitude

earthquake seem to be at most on the order of 0.3% (Fig. 27). This is considered a small strain in most

laboratory tests and in geotechnical engineering practice, explaining why shear wave velocity – which is a small strain measurement – can be used successfully to construct a liquefaction chart, as done by Andrus

and Stokoe (2000). However, once the soil has liquefied, its response in the free field and its interaction

with structural elements, may reach much larger strains where the shear wave velocity of the nonliquefied soil may become irrelevant. This is linked with the basic assumption of the Simplified Procedure,

reviewed in the paper that results in calculated values of CSR, τ, and γ that have no clear physical

meaning once the sand liquefies. Therefore, clarification of the fact that the curves separating liquefaction

from no liquefaction in the charts, correspond to small strains and thus have little predictive power in regards to the effects of liquefaction, suggests that future research on these effects should be separated

from the research on the curves themselves. In other words, while shear wave velocity and the factors

controlling it have great significance for the triggering of liquefaction, the SOA suggests that completely different factors may influence the response of already liquefied soil.

In summary, the authors hope that this paper, besides providing clarification on some issues, may help

point to the research needed for the solution of other important issues in an effort to close the existing gap

between states of the art and practice. The objective should be to have both SOA and SOP develop in a more integrated manner, toward better analysis and design procedures for the mitigation of liquefaction

and its effects.


Santiago, Chile

40

ACKNOWLEDGEMENTS

Some of the key results and conclusions presented were obtained over an extended period of time, with

the help of many colleagues who are just too numerous to mention by name, but who are still most

gratefully acknowledged. In the immediate past, the authors are deeply grateful to a number of colleagues, researchers and students for providing precious laboratory and field data and analyses, illuminating issues

through insightful discussions, contributing directly to the paper and reviewing it. These more recent

collaborators include: the staffs at the U. at Buffalo and RPI NEES Experimental Sites; graduate students at RPI and U. at Buffalo; Drs. R. Andrus, V. Bennett, S. Bhatia; A. Elgamal, M.E. Hynes, M. Gonzalez, I.

Sasanakul, M. Sharp, S. Thevanayagam, and M. Zeghal; Messrs. H. El Ganainy and V. Mercado; and Ms.

Meghan Hatton. All this help is cheerfully acknowledged. Important parts of the paper are based on work

supported by the National Science Foundation of the U.S. under NEESR-SG Grant No. 0529995; this support is also gratefully acknowledged.

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