Assessment of Liquefaction Potential during ...

ASSESSMENT OF LIQUEFACTION POTENTIAL DURING EARTHQUAKES BY ARIAS INTENSITY

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By Robert E. Kayen; Member, ASCE, and James K. Mitchell,z Honorary Member, ASCE ABSTRACT: An Arias intensity approach to assess the liquefaction potential of soil deposits during earthquakes is proposed, using an energy-based measure of the severity of earthquake-shaking recorded on seismograms of the two horizontal components of ground motion. Values representing the severity of strong motion at depth in the soil column are associated with the liquefaction resistance of that layer, as measured by in situ penetration testing (SPT, CPT). This association results in a magnitude-independent boundary that envelopes initial liquefaction of soil in Arias intensity-normalized penetration resistance space. The Arias intensity approach is simple to apply and has proven to be highly reliable in assessing liquefaction potential. The advantages of using Arias intensity as a measure of earthquake-shaking severity in liquefaction assessment are: Arias intensity is derived from integration of the entire seismogram wave form, incorporating both the amplitude and duration elements of ground motion; all frequencies of recorded motion are considered; and Arias intensity is an appropriate measure to use when evaluating field penetration test methodologies that are inherently energy-based. Predictor equations describing the attenuation of Arias intensity as a function of earthquake magnitude and source distance are presented for rock, deep-stiff alluvium, and soft soil sites.

INTRODUCTION Liquefaction of saturated cohesionless soil has been extensively investigated using laboratory and field methods over the past 30 years. During seismic loading, initial liquefaction occurs when excess pore water pressure has increased to a level equal to the prior effective confining stress. A procedure based on field penetration resistance and cyclic stress was developed by Seed and his colleagues (1967, 1971, 1983, 1984) based on the use of peak ground acceleration (PGA) to assess the initial liquefaction of soil, and is now in standard use around the world. This study evaluates the applicability of an energybased measure of earthquake shaking severity, Arias intensity, to field assessment of the initial-liquefaction potential of soil. Recently, several laboratory studies related pore water pressure rise to cumulative strain energy during shear testing (Davis and Berrill 1978; Figueroa and Dahisarla 1991; Law et al. 1990; Cao and Law 1991; Liang et al. 1995). These studies have demonstrated that the cumulative energy per unit volume absorbed by a laboratory soil sample has two componentshysteretic damping and a plastic deformation. In contrast with such studies, this paper investigates a field approach that uses the energy content of ground motion recorded as seismograms. Arias intensity, calculated by integrating processed accelerogram records, can be used as a measure of the severity of earthquake motions at a point on or below the surface of the earth. That such an approach might be useful was shown by Egan and Rosidi (1991), who used surface-measured Arias intensity to assess liquefaction for a limited set of earthquakes in California, though with only moderate success. This paper describes an approach for relating the Arias intensity at depth in the soil column to field-based measures of liquefaction resistance and applies this approach to a number of sites in the United States and Japan. Generalized profiles for a depth-reduction factor for Arias intensity are developed through a parametric study of synthetic seismograms. Predic'Res. Civ. Engr., U.S. Geological Survey, 345 Middlefield Rd., Menlo Park, CA 94025. 2University Distinguished Prof.• Virginia Tech. 109B Patton Hall. Blacksburg. VA 24061-0105. Note. Discussion open until May 1. 1998. To extend the closing date one month. a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on August 20. 1996. This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering. Vol. 123. No. 12. December 1997. ©ASCE. ISSN 1090-0241/97/0012-1162-1174/$4.00 + $.50 per page. Paper No. 13983.

tive models for the relation of Arias intensity to source-distance from an earthquake rupture plane are developed to estimate the intensity of ground motion for site investigations. All of these considerations are combined to formulate a new methodology for assessing liquefaction potential during earthquakes.

METHODS A quantitative measure of earthquake-shaking intensity, often termed Arias intensity, is used to represent the total energy per unit weight absorbed by an idealized set of oscillators during earthquake motion (Arias 1970). The Arias intensity measure (also termed accelerogram energy) is the sum of the energy absorbed by a population of simple oscillators evenly spaced in frequency. For a single component of motion in a given direction, Arias (1970) demonstrated that the cumulative energy-per-unit weight absorbed by a set of single degree of freedom oscillators at a site can be expressed as ra(V)

arccos v = gyl-lr ~ ~

'O 2 ait) dt

L

(1)

0

where Ixx(v) = viscous damping-dependent intensity measured in x-direction in response to transient motions in x-direction; v = damping ratio of oscillators; g = acceleration due to gravity; to = duration of earthquake-shaking; and ait) - transient acceleration. The damping factor arccos v/(gVl - v 2 ) is largely insensitive to variations in the structural-damping ratios of the oscillators. Though structural- and soil-damping characteristics are different, the damping characteristics of a given nonliquefied soil deposit do not significantly affect the calculated Arias intensity. For the case where the damping ratio approaches zero, (1) reduces to 'o 2 'IT (2) IxiO) = 2" ait) dt g

i

0

Because of the additive nature of scalar energy measures, one can calculate the two-component horizontal Arias intensity as Ih

=I

xx

+

Iyy

'IT =-2g

i

0

'O

2

ax(t) dt

+ -'IT

2g

i'o

2

ay(t) dt

(3)

0

The parameter I h represents the sum of the two-component energy per unit weight stored in a population of undamped linear oscillators evenly distributed in frequency, at the end of earthquake-shaking. The Arias intensity integral is given in dimensional units of length/time.

1162/ JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / DECEMBER 1997

J. Geotech. Geoenviron. Eng., 1997, 123(12): 1162-1174

Accelerograms 0.2

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0.1

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10

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20

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a rJJ

::YBI. (rol\O\ :::::::t:::::::::::::t:::::::::::EAstWEST::::: \U--'\1.' : : : : :

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Time (sec)

Time (sec)

Franciscan Fnn. FIG. 1. Time-Histories of Acceleration and Arias Intensity for Treasure Island (TI) and Yerba Buena Island (YBI) Recorded during Loma Prieta Earthquake, October 17,1989

For initial liquefaction assessment, the advantages of using Arias intensity over peak ground acceleration (PGA) which is used in the cyclic-stress approach, are: (1) Arias intensity is derived from the entire acceleration records of both horizontal components of motion, whereas PGA uses a single, arbitrarily selected value; and (2) Arias intensity incorporates the intensity of motions over the full range of recorded frequency, whereas PGA is often associated with high-frequency motion. Furthermore, the breakdown of soil structure that results in liquefaction is fundamentally more dependent on input energy than on a single level of acceleration (Liang et al. 1995). This study correlates the two-component horizontal Arias intensity with liquefaction field performance data. It disregards the vertical component of motion in the calculation of Arias intensity because transient vertical motions tend to be dominated by P-waves that cause little change to the effective stresses carried by the soil grains or the residual pore water pressures (Martin et al. 1975). Fig. 1 presents an example of the build-up of single-component Arias intensity for the eastwest (090°) Treasure Island (TI) and Yerba Buena Island (YBI) accelerograms, recorded during the Loma Prieta earthquake of October 17, 1989. Both Arias intensity time-histories and acceleration histories are shown. The TJ station is on a thick section of fill, fine-grained estuarine, and stiff alluvial deposits, and the YBI station is on a Franciscan rock outcrop; both are approximately 85 km northwest of the fault rupture plane and separated by approximately 1 km. The PGA for the TI and YBI sites were 0.16 g and 0.068 g, respectively. The twocomponent Arias intensity at the end of earthquake-shaking was lh = 0.54 mls for TI and lh = 0.059 mls for YBI. Amplification of motions at the soil site (TI) resulted in the elevation of lh nearly an order of magnitude over the nearby bedrock site (YBI). The Arias intensity of earthquake-shaking was associated

with the liquefaction resistance of soil, as measured by the field penetration tests (SPT, CPT). The guidelines of Seed and his colleagues (1983, 1984) were followed in calculating the effective stress-normalized, 60% energy-efficiency standard penetration resistance, (N 1)60' The procedures for the SPT test involve dropping a 63.6 kg (140 lb.) weight 0.762 m (30 in.) onto the drill-rod, imparting some portion of the 48.4 m-kg (4,200 in.-lb) of energy-per-blow to the soil. Some energy is lost in the test system during the hammer drop, and much effort has gone into standardizing the energy efficiency of the SPT test (Seed et al. 1984; ASTM D 4633-86; Farrar 1991, unpublished master's thesis). The parameter (N')60 is an appropriate field measure of liquefaction resistance to associate with Arias intensity because the SPT blow count represents a quantity of energy imparted to the soil by the hammer to break down the soil structure. Other destructive tests (e.g., CPT, DMT) impart work to the soil and would also be appropriate for such an association. CPT measurements made at Loma Prieta and Niigata, Japan, test sites are used to develop an association with Arias intensity values, and preliminary boundary curves are proposed based on these field data and on SPT-CPT correlations. VARIATION OF ARIAS INTENSITY WITHIN SOIL COLUMN: FIELD DATA AND ANALYSIS OF SYNTHETIC SEISMOGRAMS A study of the depth dependency of lh was done primarily through a parametric analysis of synthetic seismograms, although limited field data indicate that Arias intensity diminishes with depth below the ground surface. Empirical data from instrument recordings at the USGS Wildlife liquefaction array test site in Southern California during the Elmore Ranch and Superstition Hills earthquakes of November 23 and 24,

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / DECEMBER 1997/1163



1987, indicate that the Arias intensity at the ground surface is greater than that measured at depth within the soil column (Holzer et al. 1989; Kayen et al. 1994). The Wildlife liquefaction instrument array was established on the flood plain of the Alamo River in Imperial Valley astride the southernmost segment of the San Andreas Fault. The array has strong motion accelerometers at the surface and at 7.5 m depth as well as downhole piezometers (Bennett et al. 1984; Holzer et al. 1989). The Elmore Ranch earthquake (M = 6.2) struck on November 23, 1987, triggering the recording instrumentation, which logged earthquake motions but did not register elevated pore water pressures. The following day, the Superstition Hills earthquake (M = 6.6) also triggered recording instruments at the Wildlife site, which suffered extensive soil liquefaction. The cumulative horizontal Arias intensity at depth was calculated from the triaxial accelerograms and the value was normalized by the surface Arias intensity for each event [Fig. 2(b)]. In this way, the Arias intensity depth-of-burial reduction parameter, rb, is defined as the ratio of buried to surface cumulative Arias intensity.

(4) The rb parameter is analogous to the shear-stress depth reduction factor, rd, of Seed and Idriss (1971). The depth reduction parameter, rb' can be calculated from either a one- or twocomponent horizontal Arias intensity. The rb responses at the Wildlife site instrument array to the Elmore Ranch and Superstition Hills earthquakes are presented in Fig. 2(b) as the right and left limbs, respectively, of the shaded triangle that diminishes from rb = 1.0 at the surface to rb < 0.5 at 7.5 m depth. For more detail, see Kayen et al. (1994). Because of the dearth of available downhole field data, it was necessary to evaluate the variation of Arias intensity with depth of burial in the soil column through an analysis of synthetic seismograms. Synthetic seismograms were generated for the surface and depth nodes of soil column input files with the ground-response computer-program SHAKE (a modified version of the program presented by Schnabel et al. 1972). Then rb profiles were constructed by normalizing the synthetic Arias intensity at depth with the calculated surface Arias intensity, in the same manner as the field measurements at the Wildlife liquefaction array. SHAKE was used to propagate strong motion records from eight recorded earthquakes through four soil columns representing: (I) medium-loose sand (Dr = 45%); (2) medium-dense sand (Dr = 75%); (3) loose fill overlying a cohesive soil with a monotonically increasing shear modulus profile with depth; and (4) loose fill overlying overconsolidated cohesive soil with a monotonically increasing shear modulus profile (Kayen 1993, unpublished PhD dissertation). Soil column models representing sand at relative densities of 45% and 75% were constructed using shear modulus relationships presented by Hardin and Drnevich (1972) and Seed et al. (1984). For soil columns with loose sandy fill overlying cohesive deposits, shear wave velocity profiles at San Francisco Bay shore sites were used (Sun et al. 1989; Golesorkhi 1989). The representative soil column profiles were truncated at three different total soil thicknesses: 30.5 m (100'), 61 m (200'), and 91.5 m (300'). Under each profile lay an elastic base-rock material with a shear wave velocity of 2500 m/s. The eight seismograms used in the SHAKE study are of rock motions recorded during strike-slip, and shallow reverse and thrust faulting events (San Francisco, M = 5.25, 3/22/57; Coyote Lake, M = 5.6, 8/6/79; Parkfield, M = 5.6, 6/27/66; Borrego Mountain, M = 6.5, 4/8/68; San Fernando, M = 6.5,2/9/71; Helena, M = 6.0, 10/31/35; Tabas, Iran, M = 7.4, 9/16/78; Kern County, M = 7.6, 7/21/52). Output synthetic acceleration-time histories

2

2a) Synthetic seismogram profiles

2b) SHAKE profile statistics and field data

10

4

6

20

I

a o"

€ -'=

8

15.

"

30 0 10 12

40

14

o

0.2

0.4

0.6

0.8

FIG. 2. (a) Normalized Arias Intensity Depth-Reduction Profiles Modeled Using Ground Response Program SHAKE; (b) Statistical Synthesis of Synthetic Siesmogram Profiles, along with Field Data from WLA Response during Elmore Ranch and Superstition Hills Earthquakes

were integrated to calculate the Arias intensity for layer nodes at depth in the model soil profiles and then normalized by the corresponding surface Arias intensity [Fig. 2(a)]. This normalization process allows researchers to evaluate the depthdependency of I h over a broad range of earthquake magnitudes and site geologic conditions by collapsing the profiles to a common reference point at the ground surface. Modeling the depth-variation of rb using an equivalent-linear model like SHAKE is appropriate for assessment of initial liquefaction potential, but cannot account for the degradation in shear modulus and shear strength after pore pressure rise. Postliquefaction rb profiles are likely to be noticeably different from the profiles leading to initial liquefaction, as was observed at the Wildlife site during the Superstition Hills earthquake (Kayen et al. 1994). The mean and ± 10' responses calculated from the set of SHAKE runs are plotted in Fig. 2(b), along with the field results of the Wildlife study. The mean and standard deviation profiles were determined by evaluating each soil-layer nodecluster of Arias intensity data points generated in the SHAKE program runs (1,080 seismograms in all). The mean attenuation profile of rb fell somewhat linearly from 1.0 to 0.58 at 6 m depth, then decreased to 0.46 at 10 m. The value of rb remained relatively constant at depths below 10 m (30.5 ft). The field data from the Wildlife liquefaction array site are consistent with the results of the parametric study. The calculated rb of the Elmore Ranch event is slightly less than the mean-response curve of the SHAKE study, and the calculated rb of the Superstition Hills event is slightly less than the -10' curve.

CASE HISTORIES OF SOIL LIQUEFACTION DURING EARTHQUAKES The historic performance of liquefaction test sites near recording accelerometer stations in Japan and the western United States was evaluated by relating the documented field penetration resistance to the estimated Arias intensity at depth in the soil column (Table 1). At most sites it is possible to calculate the surface intensities (Ih ) only from acceleration records and so in this study the below-ground intensity was determined by using the mean rb profile presented in Fig. 2(b). For the Wildlife liquefaction array site in Imperial Valley, California, subsurface motions are known and an interpolated rb profile for the liquefied layers could be estimated from field data. For either condition, the Arias intensity at depth in the soil column, I hb , can be calculated as follows




TABLE 1. Case Reports from Liquefaction Site Investigations in the United States and Japan

Earthquake (1 )

c....

o

C :II Z

» r o "T1

G>

§ ~

I Z

o» r

»z

Cl

G>

m

o m z S

:II

o Z

s::

m

z

~ r m

z G> Z

m m

:II

Z

G>

...... Cl

m

(')

m

s::

Site (2)

CALIFORNIA Superstition HilIs (1987) Elmore Ranch (1987) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989)

Wildlife Liquefaction Array Wildlife Liquefaction Array SF-Oakland Bay Bridge1 SF-Oakland Bay Bridge2 SF-Oakland Bay Bridge3 SF-Oakland Bay Bridge4 SF-Oakland Bay Bridge5 Treasure Island

Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989)

Port of Oakland, 7th St.-l Port of Oakland, 7th St.-2 Port of Oakland, 7th St.-3 Port of Oakland, 7th St.-4 Port of Oakland, 7th St.-5 Port of Oakland, 7th St.-6 Bay Farm IslandLagoon Bay Farm IslandSo. Loop Rd. Bay Farm Islandhnproved Dike Oakland Int'l Airport, Site 3 Oakland InCI Airport, Site 4 Oakland InCI Airport, Site 7 Coyote Creek

Lorna Prieta (1989) Lorna Prieta (1989) Lorna Prieta (1989)

Downtown Santa Cruz, Site 2 Downtown Santa Cruz, Site 2 Downtown Santa Cruz, Site 2

Case Number (3)

Seismogram (4)

1

Wildlife Surface

2

Wildlife Surface

3 4 5 6 7 71 8

Oakland Outer Harbor Oakland Outer Harbor Oakland Outer Harbor Oakland Outer Harbor Oakland Outer Harbor Treasure Island

I. (mls) (5)

Depth (m) (6)

IIIb (mls)

(N')60

(N'.",)60

(7)

(8)

(9)

(MPa) (10)

Fines Content (%) (11 )

1.97 (1.37)

4.9

0.92

10

16.5

5

33

Yes

0.44

4.9

0.30

10

16.5

5

33

No

1.71

7

0.99

10

11.2

8

10

Yes

1.71

7.5

0.96

12

13.2

11

10

Yes

1.71

7

0.99

9

10

Yes

1.71

7

0.99

5

10

Yes

1.71

7

0.99

10

11.2

9

10

Yes

0.54

6

0.34

5

5.0

5

Yes

1.71

6.5

1.03

12

5

Yes

1.71

6

1.00

15

15.0

9

2

Yes

1.71

6.5

0.99

18

18.0

7

2

Yes

1.71

9

0.88

37

37.0

17

5

No

1.71

5

1.15

12

5

Yes

10

5

Yes

QC1

Liquefaction (12)

94)

'4) '94)

1.71

5.5

1.10

14

Oakland Outer Harbor Oakland Outer Harbor Oakland Outer Harbor Oakland Outer Harbor Oakland Outer Harbor Oakland Outer Harbor Alameda NAS

0.8

4

0.60

16.9

16.9

7

2

Yes

15

Alameda NAS

0.8

4

0.60

15

15.0

12

5

Yes

16

Alameda NAS

0.8

3

0.60

38

38.0

35

5

No

17

Alameda NAS

0.8

4

0.58

3

3.0

10

5

Yes

18

Alameda NAS

0.8

4

0.58

9

9.0

5

5

Yes

19

Alameda NAS

0.8

4

0.58

12

12.0

10

5

Yes

72

Milpitias

0.69

7

0.38

10

12.3

15

No

20

UCSClCapitola

4.71

3

3.69

27

34.0

40

Possible

21

UCSC/Capitola

4.71

4.6

3.25

20

24.2

23

Yes

22

UCSC/Capitola

4.71

9.2

2.40

12

14.3

15

Yes

9

10 11 12 13

:II ~

0.25 mm and D so < 0.15 mm, as shown in Fig. 5.

RELATION OF ARIAS INTENSITY TO EARTHQUAKE MAGNITUDE AND SOURCE DISTANCE The attenuation of Arias intensity from a fault rupture plane was investigated in its relation to earthquake magnitude, source distance, and local site geology. The basis of the attenuation model of Arias intensity is the assumption of a loglinear relation between Arias intensity (lh) and moment magnitude (M). Wilson (1993) used the Brune seismic source model (1970, 1971), the Hanks and McGuire source model (1981), and Hanks and Kanamori's (1979) moment magnitude relation to relate Arias intensity to moment magnitude, M, as follows: loge/h) = M - 2 10g(R) - 3.990 5

+

0.365P

(8)

The probit, P, is the exceedance probability of Arias intensity in terms of standard deviation about the mean (P = ± 1 for ± la), and R is the source distance in kilometers. Working with a data set for California earthquakes, Wilson (1993) uses the closest distance to the surface projection of the fault plane and the regressed "best-fit" source depth, h, to calculate the Pythagorean source-distance R that gave the lowest probit coefficient. In the present study, published values of earthquake focal depth, d, were used for the vertical depth measure. That is, the source-distance, r*, was defined as the Pythagorean distance between a seismometer site and the closest distance to the fault rupture plane at the earthquake focal depth, d. (9) In a manner similar to that in Wilson's (1993) study, earthquake motion and site characteristics data were tabulated for 66 earthquake records in the western United States, primarily from California (Kayen 1993), and the sites were segregated into three representative profiles-rock, alluvium, and soft soil-to regress the following relations between two-component Arias intensity, moment magnitude, and source distance: Rock sites: log /h

=M

- 4.0 - 2 log r*

0.63P

(10)

Alluvium sites: log /h = M - 3.8 - 2 log r* + 0.61P

(11)

Soft soil sites (insufficient number of samples to determine P): (12)

log /h = M - 3.4 - 2 log r*

The relation for rock sites in this study is similar to Wilson's (1993) Eq. (8), although the use of focal depths in this study increased the variance of the data set. For alluvium and soft soil sites the regressed value of Arias intensity is higher than for rock sites because of local soil amplification. The increase in Arias intensity is due, in part, to the longer duration of earthquake motion associated with soft soil sites relative to nearby rock sites (Dobry et aI. 1978). Liquefiable soil conditions are often found in coastal harbor developments, reclaimed land, and the coastal plain, where fill and native sands cover overly soft, low-velocity native soils. At these sites, amplification of Arias intensity might be expected. Based on the equations above, Fig. 6 presents the predicted mean intensity 1000 ...---_....-..,...,._.....,.-_-

"....,..,....,..,....-r;-r;-r;""T

+

....--_ _,

•.•.•.•• Predicted Mean Surface-Arias Intensity (m/s) •••••• for Focal Depth of 10 km. 100

10

0m .!!2 E

---

o

.n ..c

Ih (m/s)

--- ........

1'------:=

............

0.1

0.Q1

0.001

NO LIQUEFACTION

•••••• , Soft Soil Alluvium - - Rock

0.1

o

5

10

15

20

Qc1 (MPa) FIG. 5. Ihb versus qc1 for Sites in Table 1. Boundary Curves for 0 50 > 0.25 mm and 0 50 < 0.15 mm Are Based on Field Data and qc· NRelations

Surface Distance to Fault-Rupture Plane, (km) FIG. 6. Ih for 50th Percentile (P = 0) Earthquake Response Plotted as Function of Surface Distance to Fault Rupture; r; Moment Magnitude, M; and Site Material Properties of Rock, Allu· vium, and Soft Soil, Based on 10 km Earthquake Focal Depth



(P == 0) for rock, alluvium, and soft soil sites versus the horizontal (surface) distance to the fault rupture plane in kilometers, based on an earthquake focal depth of 10 km. It should be noted that the use of focal depth as a substitute for vertical depth to the centroid of energy release may lead to unconservative values of Arias intensity at short source-distances for ruptures that propagate upward toward the surface.


APPLICATION OF ARIAS INTENSITY METHOD TO TWO SITES IN NIIGATA, JAPAN To demonstrate of the applicability of the Arias intensity method, two extensively documented sites in Niigata, Japan, were chosen near the apartments at Kawagishi-cho. The Kawagishi-cho site is located on the western bank of the Shinano River and founded on deltaic deposits of clean sand (Kawasumi 1968). During the earthquake of June 16, 1964, the ground beneath several multistory apartment buildings suffered extensive liquefaction, resulting in massive bearing failures of some structures. An accelerometer located on the bottom floor of apartment building no. 2 (which did not suffer bearing-support failure) recorded strong surface motions during the earthquake. The two horizontal components of motion, along with the cumulative Arias intensity time-histories (total surface I h = 0.82 mls) absorbed at the site are presented in Fig. 3. A second site, on the south bank of the Shinano River approximately 100 m west of Showa Bridge and 1 km east of the Kawagishi-cho apartment site, had no surface manifesta-

tions of liquefaction damage, although the northern piers beneath Showa Bridge collapsed in bearing failure (Ishihara and Koga 1981). Soil at the southern bank of the Shinano River is texturally similar to the Kawagishi-cho site, but has higher liquefaction resistance, as measured by penetration resistance values. Investigations of the Kawagishi-cho and Showa Bridge sites were presented by Seed and Idriss (1967), Ishihara and Koga (1981), and Hamada (1992). Data from Niigata were used to compare the Arias intensity method with Seed et al.'s (1984) field liquefaction evaluation procedure and Ishihara and Koga's (1981) laboratory results. Profiles of N60 for the two sites are presented in Fig. 7(a) and (d). Fig. 7(b) and (e) present the estimated Niigata earthquakeinduced Arias intensity profiles, Ihb,eq. The SPT values for the two sites were converted into equivalent liquefaction threshold values, Ihb,l' That is, Fig. 7(b) and (e) present profiles for I hb .1> the Arias intensity at the liquefaction boundary curve, determined by using Fig. 4 and the (N1)60 profiles. The cyclic stress ratio at liquefaction (CSR 1) was determined using boundary curve defined by the cyclic stress ratio and (N 1)60 [Seed et al. (1983)]. The threshold shaking intensity function required to cause liquefaction (lhb.1 or CSR j ) and the corresponding earthquake-induced intensity function (lhb.eq or CSReq) were used to determine profiles of the factor of safety against liquefaction. The Arias intensity-based factor of safety F1hb against initial-liquefaction occurrence is defined as the Arias intensity required to cause liquefaction normalized by the Arias intensity induced by the earthquake. This definition of factor of

Kawagishi-cho Site 0

0 10 20 30 0

a)

.

5

g

1

0

b)

2

0

c) 5

:--Ihb,l : ._.-_.Ihb, eq

..s::::

0- 10

g

-F1hb -••-•• F CSR

10-50.. (l)

(l)

Cl

Cl

15 No Evaluation Below 15m

20

Showa Bridge Site

0

0

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d)

f)

e)

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..1'.........

i

5

wt=O.5m

Liquefied Layer?

No Tests Below5m.

g Non-Liquefiable Silt & Peat

.£0.. 10

.·1 • • • 11 • • • • • • •

Liquefied Layer?

(l)

Cl

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........ § ......... 10-5 0.. (l)

Cl

. . . . . . . . . . . . . . . . . 11 • • • • • • •

,I...........................

15 --Ihb,l -•••-. Ihb , eq

2°0 10 20 30 0

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0.8

--F1hb

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Ihb (m/s)

IhbMethod, CSRMethod

••-._. F CSR

1

15

Ishihara & Koga Laboratory Study (1981)

2

20

Factor of Safety

FIG. 7. Comparison of Arias Intensity Method, Field Cyclic Stress Method (SPT-CSR; Seed and Idriss, 1982), and Laboratory Study of Ishihara and Koga for Kawagishi-cho and Showa Bridge Sites JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / DECEMBER 1997/1171


safety is similar to that by Seed and his colleagues based on cyclic stress, but represents relative safety against liquefaction in terms of Arias intensity.


(13)

Fig. 7(c) and (f) plot the factor of safety profiles based on both Arias intensity and cyclic stress approaches. For the Kawagishi-cho apartment site, the Arias intensity approach and CSR field method predict liquefaction from 1.5 to 14 m, except for a thin unit at 11 m depth that resists liquefaction. A second unit resisting liquefaction is predicted to occur between 15 and 16 m, and another liquefiable layer is predicted between 17 and 19 m (Fig. 7). Ishihara and Koga's (1981) laboratory results for large-diameter and Osterberg samples taken to a depth of IS m indicate a zone of liquefaction between 2.5 and 13.5 m. Ishihara and Koga did not sample below 15 m and therefore could not evaluate the deeper unit. An evaluation for the Showa Bridge site, using the Arias intensity, field cyclic-stress, and laboratory approaches, predicted possible liquefaction for only a thin soil layer at 4.5 m depth. For both these sites, the results of the Arias intensity method and the field and laboratory cyclic-stress approaches agreed in delineating the liquefaction potential of specific soil layers. Similar agreement was found between the Arias intensity method and the CSR field method at 42 sites in Niigata (Kayen 1993, unpublished PhD dissertation) and for 10 test sites near San Francisco Bay influenced by the Loma Prieta earthquake (Kayen and Egan 1995; Kayen et aI., in press; Kayen and Mitchell, in press). SUMMARY The Niigata study site was used to demonstrate the efficacy of the Arias intensity approach. The general procedural steps for assessing liquefaction potential during earthquakes using the Arias intensity method follow:

1. Characterization of the soil column using field penetration testing methods. The standard penetration test (SPT) and cone penetration test (CPT) are used to develop an association between Arias intensity and in situ field measurements of liquefaction resistancy. The SPT method and correction procedures for overburden stress, short sampling rod length, and SPT hammer efficiency should be performed using the methodology outlined by Seed et al. (1984). Fines content corrected values for equivalent clean sand can be determined by calculating an appropriate aNI' Guidelines for the standardized use of the cone penetration test to measure qc are presented in ASTM D 3441-86. The correction factor, Cq , for effective stress was presented by Mitchell and Tseng (1990), Kayen et al. (1992), and Kayen et al. (in press). 2. Estimation or calculation of the earthquake-induced surface Arias intensity. Seismogram records should be selected from recording stations situated near the investigated liquefaction test site and should reflect the geology and source-distance characteristics of the test site. For design purposes, the surface Arias intensity can be estimated from: (1) the history of Arias intensity response at the seismometer site during previous earthquakes; (2) the Arias intensity predictor equations (10)-(12), which are based on the site soil characteristics, the minimum source-distances to nearby fault segments, and the design basis earthquake moment magnitudes estimated for the fault segments; or (3) earthquake site response modeled using numerical computation methods. Design criteria for determination of a minimum penetration resistance

value required to resist liquefaction can be met using the Arias intensity predictor equations with the mean intensity condition (P = 0) for ground-supporting normal structures, and with the + 1(J' intensity condition (P = 1) for ground-supporting critical structures. 3. Estimation of Arias intensity within the soil column during earthquake-shaking. The Arias intensity at a given depth can be estimated by multiplying the surface intensity by the reduction factor for Arias intensity presented in Fig. 2(b). If the shear modulus stratigraphy of the site is known, the depth reduction factor can be computed from synthetic seismograms using a computational ground-response program. 4. Determination of the factor of safety against liquefaction occurrence. The associated penetration resistance and Arias intensity measures should be plotted and compared with the boundary line that envelopes the liquefaction occurrence field (Figs. 4 and 5). The boundary line defines the threshold level of Arias intensity required to cause initial liquefaction. Compute the Arias intensitybased factor of safety against liquefaction occurrence by taking the ratio of the Arias intensity required to cause liquefaction to the Arias intensity estimated from the earthquake motion. Initial liquefaction during the earthquake-shaking-the rise of pore-water pressure to a level equal to the prior effective overburden stress-is predicted if the factor of safety falls below 1.0. CONCLUSIONS An Arias intensity method for assessment of the initial-liquefaction potential of soil deposits during earthquakes is described. The method has been shown to almost completely segregate the field penetration data of liquefaction test sites into zones of liquefaction and nonliquefaction on one plot for earthquakes ranging from magnitude 6.1 to 7.9, and it is relatively simple to apply. The Arias intensity approach has the following advantages over the cyclic-stress method: • Arias intensity incorporates the entire seismogram record; that is, it incorporates all data points, frequencies, and the duration of recorded motion. Since energy measures are scalar quantities, the cumulative Arias intensity (damage potential) can be summed from both orthogonal-horizontal components of motion. Because Arias intensity incorporates both amplitude and duration of earthquake motion, it leads to one magnitude-independent boundary curve for the assessment of initial-liquefaction potential. Therefore, the Arias intensity approach does not require arbitrary magnitude correction factors. • Arias intensity is appropriately compatible with energybased penetration tests, such as the SPT, and appears to be compatible with other destructive penetration tests, such as the CPT, that impart work to the soil. • Arias intensity is insensitive to minor fluctuations in the water table. • The separation of liquefaction and nonliquefaction points across the boundary curve, shown in Fig. 4(b), is nearly complete. The nearly dichotomous zones of liquefaction and nonliquefaction points across a magnitude-independent boundary indicate that Arias intensity is a robust and empirically reliable measure of earthquake-shaking severity in the field and that penetration resistance values capture the in situ liquefaction susceptibility of soil. The excellent separation of points can be attributed to these factors.



ACKNOWLEDGMENTS The writers wish to thank Thomas Holzer, William Joyner, and Homa Lee, of the USGS, for their thoughtful reviews of the manuscript. Shin'ya Nishio (Shimizu Corp.) and the Railway Technical Research Institute (RTRI) of Japan are thanked for assisting the writers in locating numerous strong motion records in Japan.


APPEND~.

REFERENCES

Arias, A. (1970). "A measure of earthquake intensity." R. J. Hansen, ed. Seismic design for nuclear power plants, MIT Press, Cambridge, Mass. Bennett, M. J., McLaughlin, P. V., Sarmiento, J. S., and Youd, T. L. (1984). "Geotechnical investigation of liquefaction sites, Imperial Valley, California." USGS Open-File Report 84-252, U.S. Geological Survey, Menlo Park. Calif. Brune, J. N. (1970). "Tectonic stress and the spectra of seismic shear waves from earthquakes." J. Geophys. Res., 75, 4997-5009. Brune, J. N. (1971). [Correction.] J. Geophys. Res., 76, 5002. Cao, Y. L., and Law, K. Y. (1991). "Energy approach for liquefaction of sandy and clayey silts. Paper No. 3.38." Proc., 2nd Int. Con! on Recent Adv. in Geotech. Earthquake Engrg. and Soil Dyn., Univ. of Missouri, Rolla, Mo. Davis, R. 0., and Berrill, J. B. (1978). "Energy dissipation and seismic liquefaction in sands." Earthquake Engrg. and Struct. Dyn., 10, 5968. Dobry, R., Idriss, I. M., and Ng, E. (1978). "Duration characteristics of horizontal components of strong-motion earthquake records." Bull. Seismology Soc. Am., 68(5), 1487 -1520. Egan, J. A., and Rosidi, D. (1991). "Assessment of earthquake-induced liquefaction using ground-motion energy characteristics." Proc., Pacific Corif'. on Earthquake Engrg., New Zealand. Figueroa, J. L., and Dahisaria, N. (1991). "An energy approach in defining liquefaction." Proc., 2nd Int. Con! Recent Advances on Geotech. Earthquake Engrg. and Soil Dyn., St. Louis, Mo, 407-410. Golesorkhi, R. (1989). "Factors influencing the computational determination of earthquake-induced shear stresses in sandy soils," PhD thesis, Dept. of Civ. Engrg., Univ. of California at Berkeley. Hamada, M. (1992). "Large ground deformations and their effects on lifelines: 1964 Niigata earthquake." Case studies of liquefaction and lifeline performance during past earthquakes. Vol. I: Japanese Case Studies, M. Hamada and T. D. O'Rourke, eds., Tech. Rep. NCEER-920001, Buffalo, N.Y. Hanks, T. C., and Kanamori, H. (1979). "A moment magnitude scale." J. Geophysical Res., 84(B5), 2349-2350. Hanks, T. C., and McGuire (1981). "The character of high-frequency strong ground motion." Bull. Seis. Soc. Amer., 71, 2071-2095. Hardin, B. 0., and Drnevich, V. P. (1972). "Shear modulus and damping in soils: Measurement and parameter effects." J. Soil Mech. and Found. Div., ASCE, 98(6), 603-624. Holzer, T. L., Youd, T. L., and Hanks, T. C. (1989). "Dynamics of liquefaction during the 1987 Superstition Hills California earthquake." Sci., 244, 56-59. Ishihara, K., and Koga, Y. (1981). "Case studies of liquefaction in the 1964 Niigata earthquake." Soils and Foundations, 21(3), 35-52. Ishihara, K., Silver, M. L., and Kitagawa, H. (1979). "Cyclic strength of undisturbed sands obtained by a piston sampler." Soils and Foundations, 19(3), 61-76. Ishihara, K., and Koga, Y. (1981). "Case studies of liquefaction in the 1964 Niigata earthquake." Soils and Foundations, Tokyo, Japan, 21(3), 35-52. Ishihara, K., Shimizu, K., and Yamada, Y. (1981). "Pore pressures measured in sand deposit during an earthquake." Soils and Foundations, Tokyo, Japan, 21(4). Iwasaki, T., Tatsuoka, F., Tokida, K. I., and Yasuda, S. (1978). "A practical method for assessing soil liquefaction potential based on case studies at various sites in Japan." Proc., 2nd Int. Con! Microzonation for Safer Construction: Research and Application, Earthquake Engineering Research Institute, Oakland, Calif., Vol. II, 885-896. Kawasumi, H., Morimoto, R., Oakamoto, S., Umemura, H., and Kubo, K. (eds.). (1968). General report on the Niigata earthquake. Tokyo Electric Engineering College Press, Tokyo, Japan. Kayen, R. E., and Egan, J. A. (1995). "Energy characteristics of ground motion recorded at sites of historic soil liquefaction along the east-side of San Francisco Bay, California, during the Lorna Prieta earthquake, 17 October 1989." Proc., 1995 Pacific Section Convention, AAPGI SEPM, San Francisco, Calif. Kayen, R. E., and Mitchell, J. K. (in press). "Arias intensity assessment of liquefaction on the east side of San Francisco Bay during the Lorna Prieta, California, earthquake of 17 October 1989." Natural Hazards.

Kayen, R. E., Mitchell, J. K., Seed, R. B., Lodge, A., Nishio, S., and Coutinho, R. (1992). "Evaluation of SPT-, CPT-, and shear wave-based methods for liquefaction potential assessment using Lorna Prieta data. Tech. Rep. NCEER-92-0019." Proc., 4th Japan-U.S. Wkshp. earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, Buffalo, N.Y., Vol. I, 177-204. Kayen, R. E., Mitchell, J. K., and Holzer, T. L. (1994). "Ground motion characteristics and their relation to soil liquefaction at the Wildlife liquefaction array, Imperial Valley, California." Proc., 5th U.S. -Japan Wkshp. Earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, T. D. O'Rourke and M. Hamada, eds., NCEER-94-0026, Buffalo, N.Y., 267-284. Kayen, R. E., Mitchell, J. K., Seed, R. B., and Nishio, S. (in press). "Soil liquefaction in the east bay during the earthquake. " Loma Prieta earthquake of October 17,1989: U.S. Geological Survey Professional Paper 1551-B, T. L. Holzer (ed.), USGS, Menlo Park, Calif. Kishida, H. (1966). "Damage to reinforced concrete buildings in Niigata city with special reference to foundation engineering." Soil and Found., Tokyo, Japan, 7(1). Koizumi, Y. (1966). "Change in density of sand subsoil caused by the Niigata earthquake." Soil and Found., Tokyo, Japan, 8(2). Kropp, A., and Thomas, M. (1991). "Ground failure in downtown Santa Cruz." Loma Prieta earthquake: Engineering geologic perspectives, J. Baldwin II and N. Sitar, Eds. Assn. of Engineering Geologists, Sudbury, Mass., Special Publication No. 1, 61-74. Law, K. T., Cao, Y. L., and He, G. N. (1990). "An energy approach for assessing seismic liquefaction potential." Can. Geotechnical J. , 27(3), 320-329. Liang, L., Figueroa, J. L., and Saada, A. S. (1995). "Liquefaction under random loading: unit energy approach." J. Geotech. Engrg., ASCE, 121(11), 776-781. Martin, G. R., Finn, W. D. L., and Seed, H. B. (1975). "Fundamentals of liquefaction under cyclic loading." J. Geotech. Engrg. Div., ASCE, 101 (5), 423 -438. Mitchell, J. K., Lodge, A. L., Coutinho, R. Q., Kayen, R. E., Seed, R. B., Nishio, S., and Stokoe, K. H. II (1994). "In situ test results from four Lorna Prieta earthquake liquefaction sites: SPT, CPT, DMT and shear wave velocity." Report No. UCB/EERC-94/04, Earthquake Engrg. Res. Ctr., Univ. of California, Berkeley, Calif., 179. Mitchell, J. K., and Tseng, D.-J. (1990). "Assessment of liquefaction potential by cone penetration resistance." J. Duncan, ed., Proc., H. Bolton Seed Memorial Symp., Vol. 2, Bitech Publishers, Ltd., Vancouver, B.C., Canada, 335-350. Ohsaki, Y. (1966). "Niigata earthquakes, 1964 building damage and condition." Soil and Foundation, Tokyo, Japan, 7(12). Robertson, R. K., and Campanella, R. G. (1985). "Liquefaction of sands using the CPT." J. Geotech. Engrg., ASCE, 111(3), 384-403. Schnabel, P., Lysmer, J., and Seed, H. B. (1972). "SHAKE: A computer program for earthquake ground response." Report No. UCB/EERC-7212, Earthquake Engrg. Res. Ctr., Univ. of California, Berkeley, Calif. Seed, H. B. (1986). "Design problems in soil liquefaction." J. Geotech. Engrg. Div., ASCE, 113(8),827-845. Seed, H. B., and Idriss, I. M. (1967). "Analysis of soil liquefaction: Niigata earthquake." J. Soil Mech. and Found. Div., ASCE, 93(3), 83-108. Seed, H. B., and Idriss, 1. M. (1971). "Simplified procedure for evaluating soil liquefaction potential." J. Soil Mech. and Found. Div., ASCE, 97(9), 1249-1273. Seed, H. B., and Idriss, I. M. (1982). Ground Motions and Soil Liquefaction During Eathquakes, Earthquake Engineering Research Insitute, Berkeley, California, 134. Seed, H. B., Idriss, I. M., and Arango, I. (1983). "Evaluation of liquefaction potential using field performance data." J. Geotech. Engrg. Div., ASCE, 109(3),458-482. Seed, H. B., Tokimatsu, K., Harder, L. F., and Chung, R. M. (1984). "Influence of SPT procedures in soil liquefaction resistance evaluation." Rep. No. UCB/EERC-84/15, Earthquake Engrg. Res. Ctr., Univ. of California, Berkeley, Calif. Seed, R. B., Dickenson, R. B., Reimer, M. F., Bray, J. D., Sitar, N., Mitchell, J. K., Idriss, I. M., Kayen, R. E., Kropp, A., Harder, L. F. Jr., and Power, M. S. (1990). "Preliminary geotechnical aspects of the October 17, 1989, Lorna Prieta earthquake." Rep. No. UCB/EERC-90/ 05, Earthquake Engrg. Res. Ctr., Univ. of California, Berkeley, Calif. "Standard test method for deep, quasi-static, cone and friction-cone penetration tests of soil." (1986). D 3441-86, ASTM, Philadelphia, Pa. "Standard test method for stress wave energy measurement for dynamic penetrometer systems." (1986). D 4633-86, ASTM, Philadelphia, Pa. Stark, T. D., and Olson, S. M. (1995). "Liquefaction resistance using CPT and field case histories." J. Geotech. Engrg. Div., ASCE, 121(12), 856-869.

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING 1 DECEMBER 1997/1173



Sun, J. I., Golesorkhi, R., and Seed, H. B. (1988). "Dynamic moduli and damping ratios for cohesive soils." Rep. No. UCB/EERC-88115, Earthquake Engrg. Res. Ctr., Univ. of California, Berkeley, Calif. Suwa, A. (1971). "The Tokachi-oki earthquake of 1968 and seismic history of the region." Z. Suzuki, ed., General report on the Tokachi-Oki earthquake of 1968, Keigaku Publishing Co., Ltd., Tokyo, Japan. Suzuki, Z. (ed.). (1971). General report on the Tokachi-Oki earthquake of 1968. Keigaku Publishing Co., Ltd., Tokyo, Japan. Tohno, I., and Yasuda, S. (1981). "Liquefaction of the ground during the 1978 Miyagiken-Oki earthquake." Soils and Found., Tokyo, Japan, 21(3). Wentworth, C. M. (1978). Seismicity and geologic setting, reconnaissance report: Miyagi-Ken-Oki, Japan, earthquake. P. I. Yanev, ed., Earthquake Engrg. Res. Inst., Oakland, Calif. Wilson, R. C. (1993). "Relation of Arias Intensity to Magnitude and Distance in California." USGS Open-File Rep. 93-556, U.S. Geological Survey. Xie, J. (1979). "Empirical criteria for sand liquefaction." Proc., 2nd U.S. Nat. Con! Earthquake Engrg., EERI, Oakland, Calif.

fc = fines content (weight, in percent, of particles > 63 /-Lm);

g fa

fh f hb lhb.eq lhb,t

lxx,lyy

M N (N t )60

P

PGA qc qc1

APPENDIX II.

NOTATION

R

The following symbols are used in this paper: alt), ay(t) CPT CSR CSReq CSR I Cq D~o

Dr F 1hb F CSR

= horizontal acceleration in the x- and y-directions; = Cone Penetration Test;

= cyclic stress ratio; = cyclic stress ratio induced by earthquake;

= threshold cyclic stress ratio to induce liquefaction; = correction factor to normalize qc values to ITSF; = mean particle diameter; = relative density;

= Arias-intensity-based factor of safety; = cyclic-stress-based factor of safety;

r r* rb rd

SPT Vs ~

WI v 11

rr

= acceleration due to gravity; single component Arias intensity; = two-component horizontal Arias intensity at surface; two-component horizontal Arias intensity at depth of burial; = Arias intensity at depth induced by earthquake; = threshold arias intensity to initiate liquefaction; = x- and y-component Arias intensity; = moment magnitude; = uncorrected standard penetration test value; = SPT blow counts normalized to ITSF and 60% hammer efficiency; = probit (deviation from mean-standard deviation); = peak ground acceleration; = cone penetration resistance; = cone penetration resistance normalized to 1TSF effective stress; = Pythagorean source distance to "best fit" depth (Wilson 1993); = closest surface distance to fault rupture plane; = Pythagorean distance to earthquake focal depth, ~; = Arias intensity depth-of-burial reduction factor; = shear stress depth-reduction factor; = standard penetration test; = shear wave velocity; = earthquake focal depth; = fines content correction factor for Nt = damping ratio; = viscosity; and = standard deviation.

