Coseismic Ground Motion, Water-Level Change and Liquefaction in Sedimentary Basins

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

1Department of Earth and Planetary Science, University of California, Berkeley, CA 94720

2Institute 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

2 change (Cw) was insignificant; above this, Cw (m) increased with Sv as Cw = 1.74 (Sv - 1.5) ; 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 earthquake- hazard 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

C-1 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 pore- pressure 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

C-2 affects pore pressure and causes liquefaction. The synthesis of these data has revealed a field- based, basin-wide relationship between these processes.

Spectral velocity and liquefaction

Sixty strong-motion seismometers in the study area functioned normally during the Chi-

Chi 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

C-3 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;

2 but in an area of ~100 km 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

2 River fan, 9 sites occurred in the ~100 km 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,

C-4 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 pore- pressure 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:

2 Cw (m) = 1.74 (Sv - 1.5) ,

The goodness of this fit is given by the square of the correlation coefficient, 0.97; the standard

C-5 error is 0.1 m.

Discussion

The correlation between the coseismic liquefaction with high Sv may be expected because

2 Sv is related to the seismic energy per unit mass (Sv /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

C-6 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 shear- strain 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 Chi-

Chi 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

C-7 (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

C-8 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 EAR-

0125548, 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.

C-9 References

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earthquake, 10th European Conference on Earthquake Engineering, Ed. Duma, Balkema,

Rotterdam, 229-234.

(11) Boore, 2001, Effect of baseline corrections on displacements and response spectra for

several recordings of the 1999 Chi-Chi, Taiwan, earthquake, Bull. Seism. Soc. Am., 91,

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(12) Jennings, P.C., 1983, Engineering seismology, in Earthquakes: Observation, Theory and

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(15) Hwang, J.-H., and Yang, C.-W., 2001, Verification of critical cyclic strength curve by

Taiwan Chi-Chi earthquake data, Soil Dynamics Earthquake Engrg., 21, 237-257.

(16) Dobry, R., R.S. Ladd, F.Y. Yokel, R.M. Chung and D. Powell, Prediction of pore water

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C-12 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 water-

level 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 water-

level 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.

C-13 C-14