Liquefaction

Abstract

Liquefaction of the ground during earthquakes has long been documented and has drawn much attention from earthquake engineers because of its devastation to engineered structures. In this chapter we review a few of the best studied field cases and summarize insights from extensive experimental data critical for understanding the interaction between earthquakes and liquefaction. Despite the progress made in the last few decades, several outstanding problems remain unanswered. One is the mechanism for liquefaction beyond the near field, which has been abundantly documented in the field. This is not well understood because, according to laboratory data, liquefaction should occur only in the near field where the seismic energy density is great enough to cause undrained consolidation leading up to liquefaction. Another outstanding question is the dependence of liquefaction on the frequency of the seismic waves, where the current results from the field and laboratory studies are in conflict. Finally, while in most cases the liquefied sediments are sand or silty sand, well-graded gravel has increasingly been witnessed to liquefy during earthquakes and is not simply the result of entrainment by liquified sand. It is challenging to explain how pore pressure could build up in gravely soils and be maintained at a level high enough to cause liquefaction.

11.1 Introduction

In 373/2 BC, Helice, a coastal town in ancient Greece, disappeared entirely under the sea after being leveled by a great earthquake. In 1861, the same place was hit by another earthquake, though with less damage. Schmidt (1875) studied the affected area and documented the extensive lateral spreading and subsidence of land along the coast (Fig. 11.1).

Fig. 11.1

(from Marinatos 1960)

Drawing shows the affected area of Helice after the earthquake of 1861. In the foreground, the remaining part of the land was broken into a collage of many irregular pieces separated by a patchwork of extensional fractures, covered sparingly by sand-craters. Off the coast in the Gulf of Corinth, tree tops mark part of the submerged coastal plain

One of the best studied regions for liquefaction features occurs in the New Madrid Seismic Zone of the central United States (Fig. 11.2), where widespread liquefaction was induced by nearby historic and prehistoric earthquakes. Liquefaction features, mapped over several thousand square kilometers (Obermeir 1989), are present in various shapes, sizes, and ages. Many surficial vented deposits, or sand blows, are 1.0–1.5 m in thickness and 10–30 m in diameter and are still easy to identify on the ground surface, on aerial photographs and even on satellite images, despite years of modification by active agricultural activities (Tuttle and Schweig 1996). Sand dikes, which represent the conduits for escaping pore water and sediments from the liquefied layers below the sand blows, are also abundant. Most of these features are thought to have formed during the 1810–1811 M8 New Madrid earthquakes, even though many may be prehistoric in age (Tuttle and Schweig 1996).

Fig. 11.2

(from Tuttle and Schweig 1996)

Location map showing the liquefaction sites within the New Madrid seismic zone. Shaded area represents the area where >1% of the ground surface is covered by sand-blow deposits (Obermeir 1989). Seismicity (1974–1991), shown by crosses, defines the New Madrid Seismic Zone. Symbols and letters refer to sites of previous liquefaction and paleo-liquefaction studies

Two earthquakes in 1964 are particularly important in bringing liquefaction phenomena and their devastating effects to the attention of engineers and seismologists. These earthquakes inspired a great amount of research during the past 60 years in an effort to better understand liquefaction and to mitigate its damage.

The 1964 M9.2 Alaska earthquake occurred at a depth of approximately 30 km beneath Prince William Sound; the rupture extended laterally for 800 km parallel to the Aleutian trench and uplifted about 520,000 km² of the crust. Many landslides occurred; the most spectacular slide took place in the Turnagain Heights area of Anchorage, caused by liquefaction of the underlying soft clay and sands. The slide extended ∼2800 m laterally along a bluff and continued inland for an average distance of ∼300 m, resulting in 130 acres of land sliding toward the ocean (Seed 1968). Within the slide area the ground was broken into blocks that collapsed and tilted at all angles forming a chaotic collage of ridges and depressions. In the depressed areas, the ground dropped an average of 12 m during the sliding. Houses in the area, some of which moved laterally as much as 150 or 180 m, were completely destroyed.

During the 1964 M7.5 Nigata Earthquake, Japan, dramatic damage was caused by liquefaction of the sand deposits in the low-lying areas of Nigata City (Fig. 11.3). The soils in and around this city consist of recently reclaimed land and young sedimentary deposits having low density and a shallow ground water table. About 2000 houses in the City of Nigata were totally destroyed; more than 200 reinforced concrete buildings tilted rigidly without appreciable damage to the structure.

Fig. 11.3

(from the Earthquake Engineering Research Center Library, University of California at Berkeley)

Tilted apartment buildings after the 1964 Nigata earthquake. Despite the extreme tilting, the building themselves suffered remarkably little structural damage

A more recent liquefaction event happened in New Zealand where widespread liquefaction occurred during both the 2010 Mw7.1 Darfield and the 2011 Mw6.2 Christchurch earthquakes. Greatest damage was induced by the second earthquake because, while smaller, it occurred close to the population center of a major city. The majority of the ~3000 buildings in the central business district of the city and tens of thousands of residential buildings and properties were destroyed for all practical purposes (e.g., Fig. 11.4; van Ballegooy et al. 2014). Structures near river banks or the coast suffered the most liquefaction damage.

Fig. 11.4

(modified from van Ballegooy et al. 2014)

Liquefaction-induced land damage and dwelling foundation damage due to Christchurch earthquakes: a extensive liquefaction in low-lying suburbs; b suburban Christchurch street covered with liquefaction ejecta; c pavement buried by liquefaction ejecta and ponded water after liquefaction; d Uplifted and cracked concrete floor inside house covered with liquefaction ejecta

Another recent liquefaction event occurred in a densely populated area during the Mw7.9 Wenchuan earthquake, China. Various liquefaction-related processes were directly witnessed and left marks on structures. Based on a survey of observations, together with borehole investigation, Liu-Zeng et al. (2017) found that the liquefied layers are in general <8 m deep, where the lithology is dominated by coarse-grained alluvial gravel in a sandy matrix and capped by clayey to silty overbank deposits. They also found that anomalously high water ejections (>2.0 m; Fig. 11.5) and coarse ejected material are more common along the NE–SW trending surface projection of the Range Front blind thrust and its splay faults, suggesting that liquefaction intensity may have increased near these faults.

Fig. 11.5

(from Liu-Zeng et al. 2017)

Contour map showing variations in water ejection heights (m) following the 2008 Wenchuan earthquake. Circles show the locations of ejection height measurements. Red lines show the earthquake ruptured faults; black lines show the surface projections of known faults in the basin

11.2 Sediment Consolidation and Liquefaction in Cyclic Loading

In addition to being a significant hydrogeologic process, liquefaction has drawn much attention from engineers because it can create great damage to engineered structures. Since the 1960s, earthquake engineers have carried out a great amount of research to study liquefaction and to predict its occurrence. Their works are summarized in several special volumes (e.g., National Research Council 1985, 2016; Pitilakis 2007) and will not be repeated here. We thus summarize only some fundamental  results critical to the understanding of the interaction between earthquakes and water.

Engineering practice has relied on two complementary approaches to study liquefaction. One approach is based on field data from various penetration tests (National Research Council 2016). Interpretations of these tests, however, are empirical and often do not offer physical insight. A second approach is based on controlled laboratory experiments. The results of the laboratory experiments have been variously applied to evaluate the liquefaction potential of field sites, either using a threshold stress (e.g., Seed and Idriss 1967; Youd 1972), strain (Fig. 3.9; Dobry et al. 1982; Vucetic 1994; Hsu and Vucetic 2004), or dissipated energy (Nemat-Nasser and Shokooh 1979; Berrill and Davis 1985; Law et al. 1990; Figueroa et al. 1994; Liang et al. 1995; Dief 2000; Green and Mitchell 2004) as criteria.

The effective stress principle (Sect. 3.2.2), first proposed in the early twentieth century (Terzaghi 1925), laid the foundation for soil mechanics and earthquake engineering. The mechanical integrity of sediments, which allows the sediments to carry weight, is mainly maintained through grain-to-grain contacts (Fig. 11.6a; see also Sect. 11.3). Seismic shaking may break the frictional contact and the load of the overburden is then transferred from the soil particles to the pore water (Fig. 11.6b). Since the duration of seismic shaking, normally tens of seconds, is short compared to the time required to dissipate pore pressure in the sediment, the process occurs in an ‘undrained’ state (Chap. 2), and pore pressure builds up. As a result, the ‘effective stress’ supported by the sediments decreases correspondingly. When pore pressure becomes high enough to support the overburden, the effectives stress is reduced to zero, and sediments become fluid-like, i.e., liquefy, which is often manifested on the surface by the ejection of sand-water mixtures to many meters high with the subsequent formation of sand-craters. Following the dissipation of pore pressure, sediments then settle under gravity into a more densely packed configuration (Fig. 11.6c), either by diffusion before liquefaction or by expulsion of pressurized water with liquefaction.

Fig. 11.6

(from National Research Council 2016)

Idealized schematic of pore-pressure change in soils during earthquakes. a Before an earthquake, individual soil grains are held in place by frictional or adhesive contact forces, creating a solid soil structure with water filling the spaces between the grains. Note the grain-to-grain contact. b After seismic shaking, particle rearrange with no change in volume (e.g., a lateral shift of a half diameter of every other row of particles in the figure), causing the particles to lose contact and go into suspension, and increased pore pressure as gravity load is transferred from the soil skeleton to the pore water. c As water flows out of the soil, pore pressure decreases, the soil particles settle into a denser configuration, and the soil skeleton once again carries the load

Different experimental designs have been used to document pore-pressure buildup during cyclic deformation in undrained conditions, e.g.,  cyclic torsional shearing of cylinders in a triaxial loading apparatus (e.g., Liang et al. 1995) and shake tables designed to operate in large centrifuge machines (e.g., Dief 2000). Some results were presented in Chap. 3 (Sect. 3.4) and are summarized in Fig. 11.7. Here the deformation behavior of a saturated soil under cyclic shear stress of constant amplitude is illustrated. Figure 11.7a shows the stress versus strain relation at increasing number of stress cycles. At relatively low number of stress cycles (below 15), the stress-strain relations are nearly linear; at higher numbers of stress cycles, however, the stress-strain relations become increasingly non-linear, with the shear strain increasing greatly at the same amplitude of cyclic stress, indicating the occurrence of liquefaction. Figure 11.7b shows that the normalized vertical effective stress decreases with increasing number of stress cycles at constant shear strain amplitude. Figure 11.7c and d are similar to Fig. 11.7a and b but show, instead, the increases of shear strain and decreases of the normalized effective normal stress, respectively, with increasing stress cycles.

Fig. 11.7

Behavior of a saturated soil under cyclic shear stress of constant amplitude. Numbers shows the cycle number. a Stress-strain behavior of an initially stiff soil. Shear strain increases with more cycles. b Effective normal stress decreases with more cycles. c Shear strain increases with more cycles. d Effective normal stress decreases with more cycles (National Research Council 2016)

The dissipated energy criterion is most useful in the study of the interaction between seismic waves and sediment response because seismic energy may be directly measured at the field site. Nemat-Nasser and Shokooh (1979) introduced the concept of dissipated energy for the analysis of densification and liquefaction of sediments. Berrill and Davis (1985), Law et al. (1990) and Figueroa et al. (1994) established relations between pore pressure development and the dissipated energy during cyclic loading to explore the use of energy density in the evaluation of the liquefaction potential of sediments. Liang et al. (1995) conducted torsional triaxial experiments on hollowed cylinders of sand to examine the effect of relative density, initial confining pressure and shear-strain magnitude and determined the energy per unit volume (i.e., dissipated energy density) accumulated up to liquefaction; they showed that the dissipated energy density required to induce liquefaction is a function of the relative density of the sediment and the confining pressure. Dief (2000) carried out shake table experiments in a centrifuge with scaled models under a wide range of physical conditions. Dief (2000) also determined the energy density accumulated up to the point of liquefaction.

Given the experimental time-histories of shear stress and strain (e.g., Figures 3.12 and 11.7a), the cumulative dissipated energy density required to initiate liquefaction by undrained consolidation may be determined by performing the following integral (Berrill and Davis 1985):

$$e = \int\limits_{0}^{t} {\tau \left( t \right)d\gamma }$$

(11.1)

where τ is the shear stress, γ the shear strain, and the integration extends from the beginning of the cyclic loading to the onset of liquefaction (i.e., time = t). Since the stress-strain relation varies with each loading cycle when deformation is nonlinear, the integral can only be evaluated by numerical integration of the experimental stress and strain time histories.

Through such integration, Liang et al. (1995) estimated a dissipated energy density for liquefaction ranging from 290 to 2700 J/m³ for sediments with relative densities ranging from 51 to 71% subjected to confining pressures ranging from 41 to 124 kPa; Dief (2000) estimated a dissipated energy density ranging from 470 to 1700 J/m³ for relative densities ranging from 50 to 75% subjected to an equivalent confining pressures of ∼30 kPa; and Green and Mitchell (2004) obtained a dissipated energy density ranging from 30 to 192 J/m³ for clean sand at an effective confining pressure of 100 kPa. Thus, there is a wide range in the dissipated energy density required to induce liquefaction for the studied ranges of sediment type, relative density and confining pressure. The large differences among the studies may be expected in view that sediments vary widely in their hydromechanical properties and the wide range of experimental conditions. Assuming that the sediment types, the relative density, and confining pressures in these studies are representative for the field conditions relevant to liquefaction, we may take the low value 30 J/m³, as determined by Green and Mitchell (2004) for clean sand, as the lower bound for the dissipated energy density required to induce liquefaction in the field. This lower bound imposes a threshold seismic energy density required to initiate consolidation-induced liquefaction in the field, which, in turn, sets a maximum distance from the earthquake source, beyond which consolidation-induced liquefaction may not be expected. The maximum distance so estimated may then be compared with the actual occurrence of liquefaction in the field to verify the hypothesis of undrained consolidation.

11.3 Liquefaction Beyond the Near Field

Figure 11.8 shows a plot of a global compilation of liquefaction data on a diagram of earthquake magnitude M versus the logarithm of the hypocentral distance of the documented liquefaction (Wang 2007) updated with data during the 2010–2011 Canterbury earthquake sequence (Simon Cox, personal communication). We use the earthquake magnitude M and the hypocentral distance r to characterize the liquefaction occurrence because the majority of reported (many historical) liquefactions are documented with these two parameters. The style of faulting, the directivity of fault rupture, and the distance to the ruptured fault are not available for most of these data, even though these factors may significantly affect liquefaction occurrence. Neither do most of the current data for liquefaction consider the difference between different magnitude scales. Refinement of the liquefaction data with these considerations is needed.

Fig. 11.8

Global data of documented liquefaction (black circles; Wang 2007) plotted on a diagram of earthquake magnitude versus the hypocentral distance, updated with data for the Canterbury earthquake sequence (2010–2011, red squares) and Fiordland (2003, green circle) compiled by Simon Cox (personal communication). Green line marks the liquefaction limit; blue line marks the contour for constant seismic energy density of 30 J/m³—the minimum dissipated energy density required to initiate consolidation in sensitive sediments (see text for explanation), which is approximately the boundary of the near field. Abundant liquefactions occurred at distances beyond the near field up to distances where the seismic energy density is ~0.1 J/m³

Several authors (Kuribayashi and Tatsuoka 1975; Ambraseys 1988; Papadopoulos and Lefkopulos 1993; Galli 2000; Wang et al. 2006; Wang 2007) showed that the occurrence of liquefaction at a given M is delimited by a maximum distance—the liquefaction limit. Since the susceptibility of sediments to liquefaction varies significantly with sediment type and grain size (Seed and Lee 1966; National Research Council 1985, 2016; Dobry et al. 1982; Hsu and Vucetic 2004), sediments that liquefy at the liquefaction limit are likely those with the least resistance.

The threshold strain required to initiate undrained consolidation in the field may be the same as that in the laboratory (Hazirbaba and Rathje 2004). It may thus be justified to compare the seismic energy density in the field with the laboratory-based dissipated energy required to initiate liquefaction. Given the discussion in the last section on the laboratory-determined dissipated energy required to initiate liquefaction, we may associate the maximum distance of liquefaction occurrence due to undrained consolidation with the contour of e = 30 J/m³.

In Chap. 6 (Sect. 6.4.3) we derived an empirical relation among the epicentral distance (r), the earthquake magnitude (M) and the seismic energy density (e) of an idealized point-source earthquake (Eq. 6.23; Wang et al. 2006; Wang 2007)

$${ \log }_{10} e = - 3 { \log }_{10} r + 1.44 {\rm M} - 4.62,$$

(11.2)

where r is in km. As noted in Chap. 6, this relation shows that contours of constant seismic energy density appear as straight lines on a diagram of log  versus M, such as the straight lines on Fig. 11.8. A seismic energy density of 30 J/m³ is associated with the blue line in this diagram, which also marks approximately the epicentral distance equal to 1 ruptured fault length (Wells and Coppersmith 1994). The diagram shows that a large number of liquefactions occurred beyond the near field at distances where the seismic energy density decreased to ~0.1 J/m³ (Wang 2007). Thus, undrained consolidation alone may not account for all occurrences of liquefaction.

The mechanism for liquefaction beyond the near field is not fully understood. We may invoke the hypothesis that, even though the seismic energy density in the intermediate field is not large enough to induce sediment liquefaction by undrained consolidation, the cyclic stresses from seismic waves nonetheless may move the mechanical state of the sediments towards a critical state so that they may liquefy if an additional increment of pore pressure becomes available to push the sediments over the liquefaction limit. Another viable mechanism is the spreading of pore pressure from a nearby high-pressure source that occurs when permeability is enhanced by earthquake (Roeloffs 1998; Brodsky et al. 2003; Wang 2007; Cox et al. 2021) which may push some critically stressed sediments over the critical state to become liquefied.

Finally, we note that the seismic energy density at the liquefaction limit is minute (∼0.1 J/m³). What are the micromechanisms that trigger liquefaction at such small seismic energies? More detailed laboratory and field studies are needed to resolve this problem.

11.4 Experiment at Wildlife Liquefaction Array, California

The Wildlife Liquefaction Array was a field experimental established in 1982 on a flood plain in southern California, about 10 km southeast of the Salton Sea (Fig. 11.9a), and designed specifically to study liquefaction processes. The array (Fig. 11.9b) consisted of two 3-component accelerometers, one placed on the surface and the other in a cased borehole at a depth of ∼7 m, and six pore-pressure transducers placed around the accelerometers at various depths up to 12 m. Both the M6.2 Elmore earthquake and the M6.6 Superstition Hills earthquake triggered the accelerometers, but only the latter earthquake triggered liquefaction at the array, which caused sand boils with eruptions of water and sediments. Extensive ground cracking implied lateral spreading at the array (Holzer et al. 1989).

Fig. 11.9

(modified from Holzer and Youd 2007)

a Location map of the Wildlife Liquefaction Array (filled circle) and earthquake epicenters (stars). M6.6 is the 1987 Superstition Hills earthquake, M6.2 is the 1987 Elmore Ranch earthquake, and M5.9 is the 1981 Westmorland earthquake. b Stratigraphic cross-section of array and schematic of instrument deployment. In plan view, pore-pressure transducers (denoted by p) are equally spaced on the perimeter of a circle with a diameter of 9.1 m. Accelerometers (sm1 and sm2) are near the center of the circle

Many investigators have studied the Wildlife Liquefaction Array data (e.g., Zeghal and Elgamal 1994; Youd and Carter 2005; Holzer and Youd 2007). The in situ time histories of pore pressure and acceleration (Fig. 11.10) during and following the Superstition Hills earthquake reveal a complex interaction among ground shaking, pore pressure buildup and liquefaction. For the convenience of description, Zeghal and Elgamal (1994) divided the recorded time histories of ground shaking during the Superstition Hills earthquake into four stages: Stage 1 (0.0–13.7 s): Ground acceleration was below ∼0.1 g and pore water pressure buildup was small. Stage 2 (13.7–20.6 s): Strongest shaking occurred, with peak accelerations of 0.21 and 0.17 g at the surface and downhole instruments, respectively. Pore-water pressure increased rapidly, with small instantaneous drops. Stage 3 (20.6–40.0 s): Accelerations declined and stayed below 0.06 g. Pore-water pressure continued to increase at a high rate. Stage 4 (40.0–96.0 s): Ground acceleration was very low (∼0.01 g), but excess pore pressure continued to rise, though at a slower rate, reaching the maximum pore pressure at 96 s.

Fig. 11.10

(from Holzer and Youd 2007)

Time histories of a north-south surface accelerations, b north-south downhole accelerations, and c excess pore pressure ratio recorded by piezometer P5 during and following the Superstition Hills earthquake. The downward spikes show rapid and transient decreases in pore-pressure. Ratio was calculated by dividing recorded values by the value at 97 s

Zeghal and Elgamal (1994) also demonstrated that the buildup of pore pressure was accompanied by a progressive softening of the sediments. Double-integrating the surface and downhole acceleration records leads to the time histories of displacements at the surface and downhole. The acceleration and displacement records may then be used to calculate the time histories of shear stress and the average shear strain (Zeghal and Elgamal 1994). Holzer and Youd (2007) recalculated the displacement history as displayed in Fig. 11.11. An interesting result is that large amplitude (up to ∼2%) long period (∼5.5 s) cyclic shear strains continued to affect the sediments long after the high-frequency acceleration had abated. It shows that the sediments had softened so much that they underwent large shear deformations at very small shear stresses. Thus a large portion of the excess pore pressure at the Wildlife Reserve Array developed after the stronger high-frequency ground motion had abated, and liquefaction did not occur until the earthquake was almost over (Holzer et al. 1989).

Fig. 11.11

(from Holzer and Youd 2007)

Time histories of a north-south shear stress and b north-south shear strain at the Wildlife Reserve array during the Superstition Hills earthquake

The progressive softening of sediments is best demonstrated by plotting the time history of shear stress against that of shear strain (Fig. 11.12), recalling that the slope of the stress-strain curve may be identified as the ‘rigidity’ of the sediments. At the onset of rapid pore-pressure increase, i.e., at 13.6 s (Fig. 11.10), the stress-strain curve shows steep slopes (Fig. 11.12), i.e., high rigidity. With increasing time, the slopes of the stress-strain curves decrease rapidly, showing that the sediments softened. Near the strain extremes, however, the slopes increase suddenly, showing that the sediments stiffened once more. This latter stiffening was attributed to strain-hardening (Zeghal and Elgamal 1994) and may be related to the rapid and transient decreases in pore pressure as recorded by the piezometers (Fig. 11.10; some of the decreases are labeled in Fig. 11.12), which, in turn, may be interpreted as a consequence of dilatancy in the strain-hardened sediments. With progressive softening, the activation of strain-hardening requires progressively greater shear strain. As a result, large deformation may be induced by very small disturbances and the sediments fluidize.

Fig. 11.12

(from Holzer and Youd 2007)

Four hysteresis curves between shear stress and shear strain at different time segments. The times of instantaneous drop of pore pressure as recorded by piezometer P5 (Fig. 11.9) are labeled on the hysteresis curves

It has been a challenge to explain why pore pressure continued to increase long after the ground acceleration had abated (e.g., Holzer et al. 1989; Holzer and Youd 2007). One explanation is offered by the discussion in the last section of this chapter. We note first that the distance between the Wildlife Liquefaction Array and the epicenter of the M6.6 Superstition Hills earthquake (31 km, Holzer et al. 1989) is beyond the near field of the earthquake (<20 km); thus the seismic energy density at the Wildlife Reserve Array at the time of the earthquake may be too small to induce undrained consolidation, even in the most sensitive sediments. Second, we note that the rise in pore pressure (Fig. 11.9c) was gradual and sustained, distinct from that caused by undrained consolidation which would have appeared as a step-like increase coincident with the strongest ground shaking (Roeloffs 1998; Wang and Chia 2008). The gradual and sustained change of pore pressure, however, can be readily explained by the diffusion of pore pressure from a nearby high-pressure source that connected to the Wildlife Liquefaction Array through earthquake-enhanced permeability, as discussed in the previous section. Under such conditions, the duration of the pore-pressure increase does not depend upon the duration of ground shaking, but rather on the distance between the pore-pressure source and the Wildlife Liquefaction Array as well as the permeability between the two locations, thus explaining the continued pore-pressure buildup long after the ground acceleration had diminished. A different explanation offered by Holzer and Youd (2007) is that the strong ground shaking had initiated consolidation and thus pore-pressure increase in the sediments, and consolidation may have continued afterwards under the action of the long-period surface waves that arrived after the ground shaking had abated. If so, the sediments at the Wildlife Liquefaction Array would have to be more sensitive than the most sensitive sediments so far tested in the laboratory. An interesting point of this model is the positive feedback between pore-pressure buildup and sediment weakening, i.e., sediments which have been progressively weakened by rising pore pressure during seismic loading may continue to consolidate and generate pore pressure at progressively lower stresses, which further weakens the sediments.

In summary, the Wildlife Liquefaction Array experiment demonstrated that the occurrence of liquefaction is the culmination of a complex sequence of interactions among ground shaking, sediment deformation and pore-pressure redistribution and/or buildup. An increase in pore pressure weakens the sediment framework; this leads to greater deformation of the sediments. Continued increase in pore pressure may occur due to enhanced permeability connecting the sediments to a nearby source, or possibly by continued consolidation. This process continues at low frequency and very small shear stresses until the sediments liquefy.

11.5 Dependence of Liquefaction on Seismic Frequency

The period of seismic waves recorded near some liquefaction sites ranges from less than a second to many tens of seconds, as illustrated by the seismic records at the Wildlife Liquefaction Array discussed in the last section. It is thus important to investigate whether the initiation of liquefaction depends on the frequency of seismic waves and, if so, how does it depend on the seismic frequency.

Established engineering methods frequently use the peak ground acceleration (PGA) as an index to predict liquefaction risk (Seed and Idriss 1971). This is because PGA is proportional to the maximum shear stress induced in the sediment (Terzaghi et al. 1996). Midorikawa and Wakamatsu (1988) calculated PGA and PGV at ∼130 liquefaction sites and found, however, that the occurrence of liquefaction is better correlated with the calculated PGV than with PGA. This result implies that liquefaction may be more sensitive to the low frequency components of the ground motion. This is because the integration of the acceleration records to calculate velocity ‘filters’ out higher frequencies, so PGV is more dominated by low frequencies than PGA. In the following we test these models by using the occurrence of liquefaction, groundwater-level changes, and strong-motion records from central Taiwan during the Chi-Chi earthquake (Wang et al. 2003; Wong and Wang 2007).

The 1999 M_w7.6 Chi-Chi earthquake (Fig. 11.13) caused widespread liquefaction on the Choshui Alluvial Fan (Fig. 11.13b). An extensive network of strong-motion seismographs and a similarly extensive network of clustered wells were installed on the fan (Fig. 11.13a) which captured both the ground motion and the concurrent groundwater level changes during and after the earthquake. These data provide a rare opportunity to investigate the field relationship among liquefaction, ground motion and groundwater level changes. Liquefaction sites on the Choshui River fan are closely associated with the largest coseismic rise of the groundwater level in the uppermost aquifer. At the same time, the distribution of liquefaction sites is entirely different from that of the highest pore pressure in the lower quifers (Fig. 6.4b and c), suggesting that liquefaction occurred only in the shallowest aquifer. No monitoring wells were installed in the basins east of the Choshui River fan; thus a similar comparison between pore pressure rise and the distribution of liquefaction cannot be made.

Fig. 11.13

(modified from Wang et al. 2006)

a Distribution of strong-motion stations (solid triangles) and hydrologic stations (open circles) on the Choshui alluvial fan (i.e., the flat fan-shaped area to the west of the hilly area) and nearby areas in western Taiwan. At each of the stations, there are one to five monitoring wells drilled to different depths up to 300 m. Red star marks the epicenter of the Chi-Chi earthquake, and red curve shows the ruptured fault in the earthquake. b Contours (in m) of the coseismic changes in groundwater level in the topmost aquifer in the Choshui alluvial fan. Open diamonds show sites of liquefaction. Note that, on the Choshui alluvial fan, most liquefaction sites occurred in an area where the rise in groundwater level was above 2 m

In order to test the frequency-dependence of pore-pressure development and liquefaction Wang et al. (2003) and Wong and Wang (2007) calculated the spectral acceleration, Sa, and spectral velocity, Sv, defined as the maximum response of a harmonic oscillator at 5% damping at each seismometer location. Contours for constant Sa and Sv were then interpolated from the calculated Sa and Sv values at the seismic stations (Fig. 11.14) using a kriging procedure. Visual inspection of the maps shows that there is a strong correlation between the liquefaction sites (filled diamonds) and Sa occurs at 0.7 and 1 Hz, but not at 2 Hz. A similar result occurs between the spatial distribution of Sv (not shown) and the liquefaction sites.

Fig. 11.14

(from Wong and Wang 2007)

Contours of spectral acceleration Sa at a 0.7 Hz, b 1 Hz, and c 2 Hz during the Chi-Chi earthquake, plotted together with the distribution of liquefaction sites in solid diamonds. Note the strong correlation between liquefaction sites and Sa at 0.7 Hz and the weak correlation at 2 Hz

A statistical test of the correlation of liquefaction with seismic wave frequency may be provided by plotting the t-values for the correlations of water level increase (i.e., pore pressure increase) with Sa and Sv over a range of frequencies. Calculations were made from ∼10⁻³ to ∼10² Hz, but only a section of this range is shown in Fig. 11.15 for clarity. In general, Sa and Sv below about 0.8 Hz are more strongly correlated with the water-level increase than those above 0.8 Hz. The strength of the correlation peaks at 0.3–0.4 Hz, but declines rapidly at lower frequencies (Wong and Wang 2007).

Fig. 11.15

(from Wong and Wang 2007)

t-values of the correlation of the water-level increase with Sa and Sv over a range of frequencies from 0.1 to 1.5 Hz, which pore pressure increases and liquefaction are typically attributed

Laboratory studies of the dependence of liquefaction on the frequency of the seismic loads are few. Yoshimi and Oh-Oka (1975) conducted a series of cyclic shear tests under undrained conditions to determine the conditions to induce liquefaction in saturated sands. Most specimens in their experiments had a relative density, i.e., the ratio of the density of a specimen to the average density of the solid grains, of approximately 40%, and the frequency of the cyclic shear stress ranged from 1 to 12 Hz. They found that liquefaction failure became imminent when the ratio of the peak shear stress to the vertical effective stress reached a certain critical value, but the condition to induce liquefaction was nearly independent of the frequency of the cyclic shear stress from 1 to 12 Hz.

Sumita and Manga (2008) measured the rheology of non-Brownian particle suspensions under oscillatory shear at frequencies ranging from 0.1 to 10 Hz. A rheological transition was found to occur at a shear strain threshold of 10⁻⁴, whereby the shear modulus of the viscoelastic suspension reduces sharply. This transition is in excellent correspondence with the threshold shear strain determined in geotechnical engineering experiments where excess pore pressure begins to develop and the shear modulus of the sediments begins to decline (Dobry et al. 1982; Vucetic 1994; Hsu and Vucetic 2004, 2006). Sumita and Manga (2008) found no dependence of the threshold shear strain on the frequency of shearing from 0.1 to 10 Hz.

The field and laboratory results on the dependence of liquefaction on frequency thus appear to be in conflict. On the one hand, existing laboratory results show little frequency-dependence of liquefaction; on the other hand, in situ studies of seismically instrumented liquefaction sites show an association of liquefaction with low-frequency ground motions.

Using dynamic numerical models with nonlinear constitutive relations for sediments, Popescu (2002) and Ghosh and Madabhushi (2003) showed that the association of liquefaction and low-frequency ground motion may be due to sediment softening induced by ground motions. They also suggest a spectra-dependent feedback loop for liquefying sediments: low frequency excitation causes ground softening and pore pressure increases more efficiently than for high frequency excitation. This softening in turn reduces the resonant frequency of the sediment column, amplifying low frequency motions and damping high frequency motions, leading to further softening and pore pressure increases, possibly leading to liquefaction.

Kostadinov and Towhata (2002) proposed a linearly elastic model of one dimensional wave propagation that suggests liquefaction may occur when the sediment column reaches a resonant state. Similarly, Bachrach et al. (2001) used a dynamic poroelastic model to simulate the effect of P-waves on pore-pressure buildup and liquefaction near the resonant frequency of sediment columns.

Further in situ, laboratory, and theoretical work are required to evaluate the dependence of pore-pressure buildup and liquefaction on the frequency of seismic waves. If the frequency dependence is due to resonance in the soil, as theoretical models suggest, local hydrologic and geologic conditions would affect ground motion frequencies.

Finally, to make predictions regarding liquefaction at particular sites, results must be integrated with site-specific geotechnical data. This requires the development of predictive theories of liquefaction that incorporate both the seismic spectral information of the ground motion, as well as geotechnical information such as SPT (Standard Penetration Test) and CPT (Cone Penetration Test). Such predictions should be verified with data from earthquake-affected sites where both geotechnical data and ground motion data are available. For more detailed discussions on the predictions of liquefaction at particular sites, the readers are referred to the volume of National Research Council (2016).

11.6 Concluding Remarks

Despite the tremendous progress made in the last ~60 years towards a better understanding of the processes of earthquake-induced liquefaction, several important problems remain not understood. Most of the past progress was made by earthquake engineers who based their approach on Terzaghi’s theory that liquefaction is caused by pore pressure buildup due to undrained consolidation of saturated sediments. Thus, a pre-requisite for this mechanism is the undrained consolidation of sediments which can occur only when the seismic energy density exceeds a threshold that, in turn, imposes a limit of liquefaction in the near field of an earthquake. Field studies, however, have documented liquefaction at epicentral distances far beyond the near field (Fig. 11.8; Wang 2007) where the seismic energy density may be too low to cause sediments to consolidate. The mechanism for the liquefaction beyond the near field is not understood and requires further study.

Another outstanding question is the dependence of liquefaction on the frequency of the seismic waves. As discussed in Sect. 11.5, the current results from the field and laboratory studies are in conflict and more work is needed to resolve these conflicts. In addition, the roles of different types of seismic waves in inducing liquefaction also needs to be better investigated.

Finally, while in most cases the liquefied sediments are sand or silty sand, well-graded gravel has increasingly been witnessed to liquefy during earthquakes. This occurred during the 1983 Borah Peak earthquake in Idaho (Youd et al. 1985), during the 1995 Hyogoken Nambu earthquake near Kobe, Japan (Kokusho 2007), and during the 2008 Wenchuan earthquake, China. With borehole investigations, Liu-Zeng et al. (2017) demonstrated that the ejected gravels during the Wenchuan earthquake were not simply the result of entrainment by liquified sand but was due to the liquefaction of gravely layers themselves at depth. As these authors pointed out, because gravels typically have high permeability that allows for rapid dissipation of pore pressure, it is challenging to understand how pore pressure is built up in gravely soils and maintained at a level high enough to cause liquefaction. Hence more investigation is required to understand the mechanism of the liquefaction of gravely soils.