Coseismic ground motion, water-level change and liquefaction in sedimentary basins
- Field-based relation from the 1999 Chi-Chi (Mw=7.5) earthquake, Taiwan
Chi-yuen Wang1, Douglas S. Dreger1, Chung-Ho Wang2, Daniel Mayeri1
1
Department of Earth and Planetary Science, University of California, Berkeley, CA 94720
2
Institute of Earth Sciences, Academia Sinica, Nankang, Taiwan, ROC
Abstract
Examination of the ground motion, water-level change and liquefaction in sedimentary
basins during the 1999 (Mw=7.5) Chi-Chi earthquake, Taiwan, reveals a field-based, basin-wide
relation among these processes, which may be useful for predicting pore-pressure increase and
liquefaction potential in sedimentary basins in earthquakes. In the upper aquifer, a threshold of
~1.5 m/s appeared in the spectral velocity (Sv) at ~1 Hz, below which the coseismic water-level
change (Cw) was insignificant; above this, Cw (m) increased with Sv as Cw = 1.74 (Sv - 1.5)2;
coseismic liquefaction occurred in the upper aquifer where Cw  ~ 3 m and Sv  ~2.8 m/s.
Introduction
Bounded by active faults, sedimentary basins around the world are often shaken by
severe earthquakes that led to some of the worst loss in human life and property damage (1).
Liquefaction, manifested by a loss of strength and stiffness as a result of rising pore pressure in
soils and sediments, commonly occurs during or immediately following earthquakes and is one of
the most destructive seismic hazards in sedimentary basins (2). As a consequence, the assessment
of the liquefaction potential of sedimentary basins has always been a key task in any earthquakehazard mitigation programs (2). Fundamental understanding of the relationship between dynamic
loading, pore-pressure change and liquefaction has been largely based upon laboratory studies
since the 1960's on sediments and soils subjected to cyclic loading (3). Significant differences,
however, exist between the field and the laboratory conditions, both in the soil condition and in
the loading and boundary conditions. Thus a field-based relationship between seismic loading,
pore pressure change and liquefaction in sedimentary basins would be useful to improve our
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understanding of the seismic hazards in sedimentary basins and to verify the field applicability of
laboratory results (4). A critical obstacle to advance in this direction has been the scarcity of
adequate field data for both the ground response and the water-level change in the same
sedimentary basin during the same earthquake. Holzer et al. (5) measured coseismic ground
motion and increase of pore-pressure at a site in the Imperial Valley, California, during the 1987
Superstition Hills earthquake. Basin-wide study of coseismic ground motion, pore-pressure
increase and liquefaction, however, has been lacking. The 1999 Chi-Chi earthquake in Taiwan
created a watershed of data for the study of these processes, as reported here.
Taiwan is a young mountain belt formed by the oblique collision between the Luzon arc
on the Philippine Sea plate and the continental margin of the Eurasian plate (Figure 1a) since 5
Ma. The 1999 Chi-Chi (Mw=7.5) earthquake, the largest to hit Taiwan in the last century, ruptured
the crust along a ~80 km segment of the Chelungpu fault (6). Widespread liquefaction occurred
during the earthquake in two sedimentary basins near the ruptured fault (Figure 1b), causing
extensive property damage (7). The occurrence of liquefaction is not particularly surprising in
view of the magnitude of the earthquake and the geology of the affected area (Holocene
sedimentary basins). However, what is noteworthy about the liquefaction in this earthquake is the
enormous data resource available that may be useful for investigating the mechanisms of porepressure increase and liquefaction in sedimentary basins under seismic loading. A network of 60
broadband strong-motion stations in the study area (Figure 1b) recovered an unprecedented
amount of near-field ground-motion data for the Chi-Chi earthquake (8). At the same time, 70
evenly distributed hydrologic stations (Figure 1b), with 188 monitoring wells and hourly digital
recording of the water-level at a precision of 0.1 cm, documented widespread coseismic changes
in water-level across a large sedimentary basin in the Chi-Chi earthquake (9). The close
proximity to a large earthquake, the dense distribution of the hydrological and strong-motion
stations, and the availability of high-quality seismic, pore-pressure and well-log data in the same
sedimentary basin, provided a unique and rare opportunity for studying how seismic loading
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affects pore pressure and causes liquefaction. The synthesis of these data has revealed a fieldbased, basin-wide relationship between these processes.
Spectral velocity and liquefaction
Sixty strong-motion seismometers in the study area functioned normally during the ChiChi earthquake and captured the coseismic ground response (8). The broadband characteristics
(nominal DC to 50 Hz) and the high sampling rate (200 Hz) make the recorded acceleration traces
ready for numerical integration into particle velocity and displacement time-histories, once the
effect of instrument drift due to ground motion and the ensuing numerical problems are dealt with
(10, 11). The most commonly used parameter is the spectral acceleration (Sa), obtained at discrete
periods, which is the maximum of the response acceleration of a single-degree-of-freedom
damped harmonic-oscillator (12). The corresponding spectral velocity (Sv) and displacement (Sd)
responses may also be determined from these records. Boore (11) showed that the response
spectra are largely unaffected by the baseline corrections for periods less than ~20 s.
Liquefaction in the form of sand blow, mud volcanoe and differential settlement during
and immediately following the Chi-Chi earthquake were reported at numerous locations in two
Holocene sedimentary basins (i.e., the Choshui River fan and the Taichung Basin) bounding the
Pakuashan anticline (7). Since these basins are densely populated, and since the local population
responded closely to the call by the Central Geological Survey immediately following the
earthquake to report liquefaction occurrences, the published occurrences (7) are likely to be fairly
complete. The distribution of the liquefaction sites was highly uneven (Figure 2a, b). Most of the
75 reported liquefaction sites occurred within a distance of ~30 km from the ruptured Chelungpu
fault north of the Choshui River. Three sites occurring at greater distances were along the coast in
artificial fills. No liquefaction occurred on the uplifted Pleistocene ridges where rocks are
exposed.
In search of a relationship between the coseismic liquefaction occurrence and seismic
loading, we compiled the distributions of Sa and Sv over a wide range of seismic frequencies. The
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distribution of Sv at 1 Hz with zero damping is plotted in Figure 2a, together with the distribution
of the liquefaction sites. As expected, Sv generally decreased in magnitude with distance from the
ruptured fault; but its distribution was complex in details. Comparison of this distribution with the
liquefaction occurrence shows a strong correlation between the two: Among a total of 75 reported
liquefaction sites, 71 sites occurred in the areas where Sv  ~2.8 m/s. At frequencies far from ~1
Hz, the spatial distribution of Sv has distinctly different patterns (not shown) that do not exhibit
any relationship with the liquefaction occurrence, suggesting that the sediment response to
seismic loading may be frequency-dependent and most sensitive to loading at ~1 Hz.
Coseismic water-level change and liquefaction
The hydrologic monitoring stations are located on the Choshui River fan (9) - a Holocene
alluvial fan on the west of the uplifted Pleistocene Pakuashan anticline. More than 50 stations
registered stepwise co-seismic water-level changes (Cw) in different aquifers that showed no
correlation with earth tides, precipitation or changes in barometric pressure (9). In the upper
aquifer, the focus of this study, Cw was less than 0.5 m over most part of the Choshui River fan;
but in an area of ~100 km2 west of the Pakuashan anticline (Figure 2b), Cw exceeded 3 m. No
monitoring wells were installed in the Taichung Basin on the east of the Pakuashan anticline; thus
no Cw data is available in this basin.
The occurrence of liquefaction on the Choshui River fan is closely correlated with
elevated Cw in the upper aquifer: Out of a total of 13 reported liquefaction sites on the Choshui
River fan, 9 sites occurred in the ~100 km2 area where Cw > 3 m in the upper aquifer. This
corresponds to ~10-1 site/km2, as compared with an average of ~10-3 site/km2 over the rest of the
Choishui River fan. Since no Cw data is available for the Taichung Basin, a similar correlation
cannot be made. The patterns of Cw in the lower aquifers were discussed in earlier studies (9).
They were distinctly different from that in the upper aquifer and showed no correlation with the
occurrence of liquefaction, suggesting that liquefaction occurred only in the upper aquifer. This is
consistent with the fact that sediments in the upper aquifer are the youngest and least compacted,
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and thus most responsive to coseismic consolidation and liquefaction.
An important question is how the initial condition at the hydrological stations might have
affected the above observations. We plot in Figure 3 the distribution of pore pressure 1 hour prior
to the earthquake at a common depth (say, 10 m beneath the surface), normalized by the sediment
overburden at that depth. Comparison between this and the distribution of the liquefaction sites
(Figure 3) shows no correlation between the liquefaction sites and the initial pore pressure. Thus
we can rule out the effect of the initial condition on liquefaction in the region; and the localization
of liquefaction must therefore be due to localized seismic shaking and the coseismic porepressure increase.
Coseismic water-level change and seismic energy
Since both Cw and Sv show a spatial correlation with liquefaction, we may expect a spatial
correlation between Cw and Sv. To test this hypothesis we interpolated the Sv-values at the 20
hydrologic stations that lie within the spatial coverage of the strong-motion stations on the
Choshui River fan. The interpolated Sv is plotted against the corresponding Cw in the upper
aquifer (Figure 4). Since Cw is dependent on several other factors, i.e., the spatial variations in the
permeability and the thickness of the upper aquifer, and the thickness of the confining layer above
the upper aquifer (13), which are not represented in this diagram, we may expect some scatter in
the data points on this diagram. In spite of the scatter, however, a relationship between Cw and Sv
appears evident in this diagram.
The Cw ~ Sv relationship in Figure 4 suggests that there is a lower threshold in Sv, below
which the coseismic water level was insignificant. We choose this threshold to be 1.5 + 0.5 m/s,
acknowledging the fact that the scatter in the data prevents a clear choice; i.e.,
Cw ~ 0, if Sv  1.5 + 0.5 m/s.
Above this threshold, we fit the data with a simple function:
Cw (m) = 1.74 (Sv - 1.5)2,
The goodness of this fit is given by the square of the correlation coefficient, 0.97; the standard
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error is 0.1 m.
Discussion
The correlation between the coseismic liquefaction with high Sv may be expected because
Sv is related to the seismic energy per unit mass (Sv2/2) that supplies the required energy to break
up the bonds between the sediment grains and to allow relative movements among grains promoting coseismic consolidation, pore-pressure increase and liquefaction. What is noteworthy
about Figure 2a is that it provides for the first time a field-based, basin-wide relation between
coseismic liquefaction and elevated Sv at ~1 Hz. Coupled with recent advances in strong-motion
modeling, this relation may provide an additional means for predicting coseismic pore-pressure
increase and liquefaction in sedimentary basins.
The correlation between the coseismic liquefaction and elevated Cw may also be expected
because rising pore pressure in sediments under seismic loading is widely believed to be the
precursor for the coseismic liquefaction (2). It should be noted, however, that pore pressure in the
aquifers is not always equal to the water pressure in wells (13) and that liquefaction may not
occur at the same depth as that where water pressure was measured. Thus the coseismic increase
in pore pressure in the liquefied layer may not be the same as the recorded value. There is good
reason to believe, however, that the recorded water level at the Yuanlin station may indeed
represent the coseismic pore-pressure increase in the liquefied layer: At this station, two wells
were drilled to the upper aquifer, but screened at different depths; in spite of the depth difference,
the recorded coseismic water-level changes in the two wells were identical (6.55 m). The depth of
liquefaction may be estimated on the basis of the effective-stress principle that the effective stress
at the liquefaction depth should be equal to the increase in pore pressure (14). Thus a coseismic
water-level increase at the Yuanlin station implies an effective stress of 6550 Pa and a
liquefaction depth of 4 - 7 m, depending on the thickness of the saturated column above the
liqefied layer. This estimate of liquefaction depth is in substantial agreement with that determined
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from boring at the liquefied site by Hwang and Yang (15) shortly following the Chi-Chi
earthquake.
Holzer et al. (5) made simultaneous measurements of the ground acceleration and
coseismic pore-pressure change at a single site in southern California, which was undergoing
liquefaction during the 1987 Superstition Hills earthquake. They showed that pore pressure did
not change until the peak ground acceleration (PGA) reached 0.21 g. To compare this result with
the pore-pressure change on the Choshui River fan during the Chi-Chi earthquake, we determine
the PGA from the acceleration records and plot the interpolated PGA at the 20 hydrologic stations
that lie within the spatial coverage of the strong-motion stations on the Choshui River fan against
the corresponding Cw at the hydrological stations (Figure 5a). No relationship between Cw and
PGA is evident. On the other hand, plotting the interpolated Sa (1 Hz) against Cw reveals a strong
correlation between Cw and Sa (Figure 5b):
Cw = 0, if Sa< 1.0 g
Cw (m) = -3.02 + 1.07 exp [Sa (g)], if Sa > 1.0 g
The goodness of this fit is given by the square of the correlation coefficient, 0.98; the standard
error is 0.06 m.
Laboratory data for soils under cyclic loading (16) shows there is a threshold in the shearstrain amplitude below which loading does not cause a buildup of excess pore pressure, but above
which increasing strain amplitude causes rapid increase in pore pressure. For different sands this
threshold is on the order of 10-4 (16). Following (17), we estimate the dynamic strain in the ChiChi earthquake by dividing Sv with the average shear-wave velocity (~400 m/s) estimated for the
top soft layers in the Taichung Basin (18), while acknowledging the uncertainty from using an
average shear velocity. The thresholds in Sv for initiating pore-pressure increase and liquefaction
thus imply strain thresholds, respectively, of ~4x10-3 and ~7x10-3. Thus, while the field-based
estimate of the lower threshold in strain amplitude for initiating pore-pressure increase is more
than an order of magnitude greater than that estimated from the laboratory data for different sands
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(16), there is substantial agreement between the field and the laboratory results in the strain
amplitude required for initiating liquefaction. We interpret the discrepancy in the threshold for
initiating pore-pressure increase as due to the different conditions of the sediments in the field
and in the laboratory: While cohesionless sands are used in most laboratory experiments (16), the
sediments in the Choshui River fan are lightly cemented by secondary minerals precipitated from
groundwater, which imparted a cohesion to the sediments, which in turn may have raised the
threshold in the strain amplitude required for coseismic consolidation and pore-pressure increase
to occur in the field, beyond that determined in the laboratory. Once this initial resistance is
overcome, sediments in the field would consolidate to cause pore-pressure increase in the same
manner as that in the laboratory. At liquefaction, the sedimentary grains in the field and in the
laboratory are fully mobilized such that whatever mechanism (e.g., cementation) that caused the
differences between the threshold strains for initiating pore-pressure increase in the field and in
the laboratory, may no longer be active at the strain amplitude that initiates the liquefaction.
Manga et al. (17) calculated the pore pressure and the particle velocity in a watershed at
Sespe Creek, CA, induced by several large earthquakes. From these they estimated a threshold of
5 - 20 cm/s for the particle velocity to initiate pore-pressure increase, which is an order of
magnitude lower than that estimated in this study (1.5 m/s). It is difficult to explain the difference
between the two studies, but we suspect it may partly be due to the different tectonic settings in
the two areas, i.e., strike-slip setting at Sespe Creek versus foreland setting in Taiwan, and partly
be due to the different approaches in the two studies, i.e., model calculation in (17) versus data
analysis in this study.
Summary
In spite of some scatter in the data, a field-based, basin-wide relation appears to exist
between the coseismic water-level changes, ground motion and liquefaction in the Chi-Chi
earthquake. The large difference between the laboratory-based and the field-based results in the
lower threshold in the dynamic strain for pore-pressure increase calls for caution in transferring
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laboratory results to the field applications. The similarity in the strain amplitude for initiating
liquefaction in the field and in the laboratory suggests that whatever mechanism(s) that caused the
difference between the threshold strains that initiated pore-pressure increase in the field and in the
laboratory, was no longer active at the strain amplitude that initiated the liquefaction.
Acknowledgements. This work was partly funded by NSF grants EAR-0106802 and EAR0125548, and partly by NSC grant NSC91-2116-M-001-017. We thank Michael Manga for
discussion and for calling to our attention the references listed in (11); we also thank Emily
Brodsky, James Kirchner and Lorraine Wolf for discussion.
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References
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Figure captions
Figure 1. (a) Location map of the study area. (b) Topographic map showing the locations of the
sedimentary basins, strong-motion seismic stations (solid triangles) and hydrological
monitoring wells (cycles with crosses) in the study area. Taichung Basin is on the east of
the Pakuashan anticline; the Choshui River fan is west of Pakuashan and related ridges.
The epicenter of the Chi-Chi earthquake is marked by a red star; the ruptured Chelungpu
fault is also marked in red.
Figure 2. (a) Contour map of the coseismic water-level changes in the Chi-Chi
earthquake,together with the locations of liquefaction sites. Note that most liquefaction
sites in the Choshui River alluvial fan occurred in the area where the coseismic waterlevel change is greater than ~3 m. (b) Contour map of the spectral velocity at 1 Hz in the
Chi-Chi earthquake, together with the locations of liquefaction sites. Note that most
liquefaction sites occurred in the basins where the seismic energy is greater than 2.8 m/s.
Figure 3. Contour map of the normalized pore pressure an hour prior to the Chi-Chi earthquake,
showing no correlation between the initial pore pressure and the distribution of the
liquefaction sites.
Figure 4. Diagram showing coseismic water-level change versus the spectral velocity at 1 Hz.
Note that, at Sv  ~1.5 m/s, most data show little coseismic change in water-level; at Sv
 ~1.5 m/s, on the other hand, the coseismic change in water-level increases rapidly with
the spectral velocity.
Figure 5. (A) Diagram showing coseismic water-level change plotted against PGA. No
relationship between the two variables is evident. (B) Diagram showing coseismic waterlevel change plotted against the spectral acceleration at 1 Hz. A strong correlation
between the two variables is evident. Note that only data at Sa > 1.0 g is shown; data at Sa
< 1.0 g (not shown) are not associated with significant coseismic water-level change.
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