ASSESSMENT OF LIQUEFACTION POTENTIAL DURING EARTHQUAKES BY
ARIAS INTENSITY
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 lique-
faction 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.
(3)
(1)
(2)
INTRODUCTION
Liquefaction of saturated cohesionless soil has been exten-
sively investigated using laboratory and field methods over the
past 30 years. During seismic loading, initial liquefaction oc-
curs 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 energy-
based measure of earthquake shaking severity, Arias intensity,
to field assessment of the initial-liquefaction potential of soil.
Recently, several laboratory studies related pore water pres-
sure rise to cumulative strain energy during shear testing (Da-
vis 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 components-
hysteretic damping and a plastic deformation.
In contrast with such studies, this paper investigates a field
approach that uses the energy content of ground motion re-
corded as seismograms. Arias intensity, calculated by inte-
grating processed accelerogram records, can be used as a mea-
sure 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 in-
tensity 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-dis-
tance from an earthquake rupture plane are developed to es-
timate the intensity of ground motion for site investigations.
All of these considerations are combined to formulate a new
methodology for assessing liquefaction potential during earth-
quakes.
METHODS
A quantitative measure of earthquake-shaking intensity, of-
ten termed Arias intensity, is used to represent the total energy
per unit weight absorbed by an idealized set of oscillators dur-
ing earthquake motion (Arias 1970). The Arias intensity mea-
sure (also termed accelerogram energy) is the sum of the en-
ergy 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
L
'O
arccos v 2
ra(V) = ait) dt
gyl-lr 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 grav-
ity; 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 ra-
tios 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 ra-
tio approaches zero, (1) reduces to
i
'o
'IT 2
IxiO) =2" ait) dt
g 0
Because of the additive nature of scalar energy measures, one
can calculate the two-component horizontal Arias intensity as
i
'O i'o 'IT 2 'IT 2
I
h
= I
xx
+ I yy =- ax(t) dt +- ay(t) dt
2g 0 2g 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
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