Seismic base-isolation mechanism in liquefied sand in terms of energy

Soil Dynamics and Earthquake Engineering 63 (2014) 92–97

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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn

Seismic base-isolation mechanism in liquefied sand in terms of energy Takaji Kokusho Department of Civil & Environment Engineering, Chuo University, Japan

art ic l e i nf o

a b s t r a c t

Article history: Received 22 July 2013 Received in revised form 20 January 2014 Accepted 24 March 2014

Seismic base isolation effect in a liquefied sand layer was investigated based on soil properties measured in a series of undrained cyclic triaxial tests. Transmission of seismic wave in a soil model consisting of a liquefied surface layer and an underlying nonliquefied layer was analyzed in terms of energy, considering liquefaction-induced changes in S-wave velocity and internal damping. It was found that, between two different base-isolation mechanisms, a drastic increase in wave attenuation in the liquefied layer due to shortening wave length gives a greater impact on the base isolation with increasing thickness of the liquefied layer than the change of seismic impedance between the liquefied and nonliquefied layer. Also indicated was that cyclic mobility behavior in dilative clean sand tends to decrease the seismic isolation effect to a certain extent. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Liquefaction Seismic wave energy Base isolation Impedance ratio Wave attenuation

1. Introduction During past earthquakes triggering seismic liquefaction, a seismic base-isolation effect was sometimes observed on building structures resting on liquefied ground. One of the first cases was apartment buildings in Kawagishi-cho, Niigata city, during the 1964 Niigata earthquake. Four-story RC buildings resting on very loose liquefiable sand settled and tilted considerably because they were directly on shallow foundations. There were seismometers at the base and roof of one of the buildings recording the earthquake motions as shown in Fig. 1, which demonstrates very clear baseisolation in which only low-amplitude long-period motions sustained after some seconds of S-wave shaking [1]. The number of such seismic records reflecting the liquefactioninduced base-isolation has increased since then. Wildlife site records shown in Fig. 2 during the 1987 Imperial Valley in California, USA, consist of not only ground motions but also in situ excess pore-water pressure [2]. Horizontal acceleration time histories at the surface show a peculiar motion reflecting cyclic mobility of liquefying sand. Another cyclic-mobility type acceleration records were observed in a vertical array in Kushiro harbor, in Hokkaido, Japan during the 1993 Kushiro-Oki earthquake [3]. Kobe Port-Island records during the 1995 Kobe earthquake were down-hole array strong motions observed in a man-made island, where top reclaimed decomposed granite sand and gravel of about 16 m thick liquefied extensively. The records at 4 different levels in Fig.3 clearly demonstrate deamplification in horizontal acceleration

E-mail address: [email protected] http://dx.doi.org/10.1016/j.soildyn.2014.03.015 0267-7261/& 2014 Elsevier Ltd. All rights reserved.

in the liquefied layer [4]. The wave energy flow was calculated based on the down-hole records, indicating that considerable energy dissipation occurred in the liquefied layer [5]. The cyclicmobility type acceleration motion was also recorded at Kashiwazaki city during the 2007 Niigataken Chuetsu-oki earthquake [6]. During the 2011 Tohoku earthquake in Japan, quite a few records were obtained in liquefied sites, where long-lasting low acceleration motions by the M9.0 far-field subduction earthquake triggered liquefaction and cyclic-mobility type acceleration response in young-aged man-made soils e.g. [7]. The degree of base isolation in the above mentioned seismic records seems to differ from site to site, among which one in Kawagishi-cho during the 1964 earthquake seems to exhibit the most conspicuous base-isolation. Thus the manifestation of base-isolation seems to reflect the intensity of liquefaction associated with soil conditions and ground motions. The effect of base isolation was also demonstrated by clear reduction in seismic energy, influencing structural damage of buildings resting on liquefied ground. During the 1964 Niigata earthquake, the RC buildings in Kawagishi-cho, previously mentioned, stayed perfectly intact, suffering no structural damage such as wall cracks or window-glass breakage [8]. During the 1995 Kobe earthquake, a viaduct highway route running through coastal liquefied man-made land in Kobe experienced little damage in superstructures directly by shaking, while another similar highway structures passing through inland nonliquefied areas, only a few kilometer apart, suffered severe damage in concrete columns by strong shaking [9]. During the 1999 Kocaeli earthquake in Turkey, building damage in a heavily damaged city, Adapazari, could be classified into shaking damage and liquefaction damage and the areas of the two types of damage did not overlapped [10].

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geotechnical damage. In this paper, a uniform sand layer is considered as a simplified model to discuss the base-isolation mechanism under an idealized condition. In order to quantify liquefaction-induced variations of shear modulus and damping ratio, undrained cyclic triaxial test results are incorporated. Then, simple analyses based on a 1-dimesional wave propagation theory are conducted using the laboratory test results to evaluate the base-isolation effect in terms of energy in the liquefied layer.

2. Base-isolation mechanism

Fig. 1. Strong-motion records at Kawagishi-cho apartment building in Niigata city during 1964 Niigata earthquake [1].

0.2

NS directions

0 -0.2 0.2

EW directions

v‘

0 -0.2 100 50 0 0

Excess Pressureat GL 9 m 20

40

60

80

100

Time s Fig. 2. Time histories of surface accelerations and subsurface excess pore pressure at Wildlife site during 1987 Imperial Valley earthquake [2].

In order to evaluate liquefaction-induced base-isolation effect in a simple condition, let us consider a uniform fully-saturated sand layer shown in Fig. 4. It is assumed that, during an earthquake, liquefaction occurs in the upper portion with a thickness H but not in the lower part due to some reasons such as aging effect. Equivalent shear modulus and internal damping ratio corresponding to an induced strain amplitude before liquefaction are G1 and pffiffiffiffiffiffiffiffiffiffiffi D1. Accordingly, S-wave velocity is V s1 ¼ G1 =ρ, using the soil density ρ. In the liquefied portion, G1, D1 and Vs1 change to G, D pffiffiffiffiffiffiffiffi and V s ¼ G=ρ, whereas the properties in the nonliquefied part are assumed unchanged for simplicity, transforming the original uniform layer into a two-layer system of liquefied and nonliquefied layers as indicated in Fig. 4. The wave equations in the two-layer system can be written as follows: u1 ¼ A1 eiðωt  k

n

u2 ¼ A2 eiðωt  k1

zÞ

n

þB1 eiðωt þ k

zÞ

n

zÞ

þ B2 eiðωt þ k1

n

ð1Þ zÞ

ð2Þ

where u1, u2 ¼horizontal displacements in the liquefied and nonliquefied layers, respectively, t¼time, z¼vertical coordinate upward starting from the layer boundary and ω ¼ 2πf is angular frequency. The complex wave numbers kn ¼ω/Vns and kn1 ¼ω/Vns1 in the above equations are expressed by using the complex S-wave velocity, V s n ¼ ð1 þ 2iDÞ0:5 V s and V s1 n ¼ ð1 þ 2iD1 Þ0:5 V s1 in the liquefied and nonliquefied layers, respectively. Complex numbers A1 and B1 are amplitudes of upward and downward waves just above the boundary in the liquefied layer, respectively, and A2 and B2 are those just below the boundary in the nonliquefied layer. Using boundary conditions at the layer boundary (z¼0) and at the ground surface (z¼H), the amplitude ratio of A1 to A2 is expressed as A1 2 ¼ n A2 ð1 þ αn Þ þ ð1  αn Þe  2ik H

ð3Þ

where αn is a complex impedance ratio defined by the equation

Fig. 3. Kobe Port Island down-hole array records: EW-direction [4].

It was pointed out during the 2004 Niigataken Chuetsu earthquake in Japan that roof tiles of Japanese wooden houses serve as an indicator if their foundation ground liquefied or not; no damage if liquefied [11]. More recently, almost no damage by seismic inertia force in superstructures has been seen during the 2011 Tohoku earthquake in liquefied areas in the Kanto plain in Japan. Thus, the liquefaction-induced base-isolation is widely recognized not only in observed seismic records but also actual performance of structures. However, its basic mechanism has been discussed very scarcely, compared to liquefaction-induced

Fig. 4. 2-layer model of uniform sand transforming to upper liquefied and lower nonliquefied layers.

94

αn ¼

T. Kokusho / Soil Dynamics and Earthquake Engineering 63 (2014) 92–97

  ρV ns 1 þ 2iD 1=2 n ¼α 1 þ2iD1 ρ1 V s1

ð4Þ

using the impedance ratio α ¼ ρV s =ρ1 V s1 . The ratio of upward wave at the ground surface As to A1 is [12] n As ¼ e  ik H A1

ð5Þ

From Eqs. (3) and (5), the ratio of As to A2 becomes As 2 ¼ n n A2 ð1 þ αn Þeik H þ ð1  αn Þe  ik H

ð6Þ

Based on the above equations on wave amplitude ratios Eqs. (3), (4) and (6), the wave energy ratio can be written in the following forms because the energy is expressed as the square of velocity wave amplitude times impedance according to a definition of wave energy [13,14]:     2  Eu1  n A21   n 2  ð7Þ ¼ α 2  ¼ α  n Eu2  A2   ð1 þ αn Þ þ ð1  αn Þe  2ik H    A2    n  Es    ¼  s2  ¼ e  2ik H  Eu1 A1 

ð8Þ

   2   A2    Es 2     ¼ αn s2  ¼ αn  n n Eu2  A2   ð1 þ αn Þeik H þ ð1  αn Þe  ik H 

ð9Þ

where Es, Eu1 and Eu2 are the energies corresponding to As, A1 and A2, respectively. In the liquefied layer, S-wave velocity Vs or corresponding shear modulus G decreases considerably. During the 1995 Kobe earthquake, the Vs-value back-calculated from the Port-Island downhole array records decreased down to 20% (the G-value down to 4%) of the low-strain initial value and the damping ratio D increased at the same time [4,15]. It may well be expected that these property changes will considerably decrease the amplitude of the downward wave in the liquefied layer due to tremendous increase in energy dissipation. Thus, if B1 in the liquefied layer is assumed negligibly small in Eq. (1), then the next equation can be obtained in lieu of Eq. (7) for the energy transmission ratio at the boundary:   Eu1  n A21  4α ¼ α ð10Þ ¼ Eu2  A2  ð1 þ αÞ2 2

This equation also holds in a two-layer system with no surface boundary without reflecting downward wave in the upper layer [14]. It can easily be checked that the difference in replacing αn by α as in Eq. (10) (ignoring the effect of soil damping) is a few percent or less and almost negligible. In Eq. (10), unlike Eq. (7), Eu1/Eu2 does not depend on kn or frequency f but only on impedance ratio α. This indicates that Eq. (10) can be applicable not only to harmonic but also to any arbitrary waves, because any irregular wave can be expressed as a superposition of Fourier series, in which the amplitude for each frequency component satisfies Eq. (10). In order to examine the applicability of Eq. (10) to a liquefied layer, the energy ratio Eu1/Eu2 for a stationary response to harmonic excitation in Eq. (7) is calculated and depicted versus the impedance ratio α with a set of thin curves in Fig. 5 for various damping ratios D. The damping ratio is varied stepwise as D¼ 10%, 17.5%, and 25% in the liquefied layer and D1 ¼10% in the nonliquefied layer based on soil test results mentioned later. The exciting frequency f is parametrically changed as f/f1 ¼0.4–1.6, where f1 is the first resonant frequency of the two-layer system. In the resonance or near the resonance (f/f1 ¼1.0, 0.8 or 1,2) the energy ratio Eu1/Eu2 can be larger than unity for some α-values,

Fig. 5. Energy ratio versus impedance ratio at a boundary between liquefied and nonliquefied layers.

because the energy accumulates in the liquefied layer during the stationary harmonic excitation in spite of large energy dissipation. If the f/f1-value is off-resonance (f/f1 ¼0.4, 0.6, 1.4, 1.6), then Eu1/Eu2 becomes smaller than unity. A thick solid curve in Fig. 5 shows the Eu1/Eu2  α relationship calculated by Eq. (10). The off-resonance thin curves calculated by Eq. (7) show similar decreasing trends with decreasing α in Fig. 5. Because soil liquefaction is obviously strongly nonlinear behavior with soil properties always changing and earthquake motions are not harmonic but irregular, the resonance is very difficult to occur. Consequently, the energy flow in a liquefied layer is very similar to the off-resonance condition, which can be approximated by Eq. (10) ignoring the downward wave. The upward energy at the bottom of the liquefied layer Eu1 decreases down to Es at the ground surface. The ratio Es/Eu1 is expressed by Eq. (8), which is further approximated for the condition n D⪡1.0 by using k ¼ ω=V ns ¼ k=ð1 þ 2iDÞ0:5  kð1  2iDÞ0:5 as  n  Es  ¼ e  2ik H   e  2ðωD=V s ÞH ¼ e  2βH Eu1

ð11Þ

Here, β¼ωD/Vs is called a wave attenuation coefficient by internal damping, where damping ratio D is assumed hysteretic or nonviscous. Thus, the base-isolation mechanism in liquefied layer splits into the next two components (a) and (b), so that the energy transmission Es/Eu2 at the ground surface compared to the underlying nonliquefied layer is expressed as the product of the two energy ratios: Es =Eu2 ¼ Eu1 =Eu2  Es =Eu1

ð12Þ

(a) Due to the drastic drop of Vs in a liquefied layer, the impedance ratio α decreases considerably at the boundary. This results in reduction of the energy transmission ratio Eu1/Eu2 at the boundary as indicated in Eq. (10). In reality, the Vs-change may occur not only at the exact boundary but also at the neighboring depths because of gradual pore-pressure change. It is assumed though to concentrate at the boundary alone for simplicity. (b) Due to drastic changes in Vs and variations in D in a liquefied layer, the energy dissipates for the upward wave in propagating from the bottom to the surface in a liquefied layer by hysteretic soil damping, reducing the energy transmission ratio Es/Eu1 as indicated in Eq. (11). Here the energy dissipation

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As already explained, an originally uniform saturated sand layer transforms to a two-layer system consisting of an upper liquefied layer (thickness H) and lower nonliquefied layer. In the liquefied pffiffiffiffiffiffiffiffi layer, G1, D1 and Vs1 change to G, D and V s ¼ G=ρ cycle by cycle

of this mechanism is assumed to occur uniformly throughout the liquefied layer.

3. Soil property change during triaxial liquefaction tests A series of test results were reviewed to quantify the variation of material properties in liquefied sand with increasing induced strain during stress-controlled undrained cyclic triaxial tests. The specimens used were 100 mm in diameter and 200 mm in height and reconstituted using beach sand (D50 ¼0.2 mm, Uc ¼1.9), which consists of non-weathered sub-round particles. The results on medium dense to loose sands of nominal relative density Dr ¼50– 30% with or without low-plasticity fines (a plasticity index Ip E6) tested under isotropic confining stress s0c ¼ 98 kPa were used here. Test conditions and pertinent results used in this research are listed in Table 1. Further details of the tests are available in other literature [16]. In Fig. 6, a typical stress–strain relationship is shown; shear stress τ¼ 0.5sd versus shear strain γ ¼1.5ε, where sd andεare axial stress and axial strain in the triaxial test, respectively. The secant modulus calculated from a straight line connecting plus and minus peaks of τ–γ curve is denoted as G1 in the first cycle of loading and G in a given cycle. The damping ratio is calculated as D ¼ΔW/ (4πW) from the dissipated energy per one cycle ΔW (the area ABB'C) and corresponding strain energy W (the area OBB0 ). In Fig. 7, the values of G/G1 and D obtained from all the tests listed in Table 1 are plotted versus double amplitude strain γDA in the semi-log graph. Strains γDA cover the interval from about 0.1% in the first load cycle (almost identical irrespective of the differences in Dr and Fc) up to the maximum 20–50% in the last cycle. Plots of the same symbol are connected with thin dotted line to show the loading sequence for the same test specimen. Modulus ratios shown with solid symbols monotonically decrease from G/ G1 ¼1.0 to almost zero with increasing strain amplitude. Damping ratios with open symbols starts from D1 E 10% in the first cycle and tend to increase to a maximum D E25–30% at around γDA ¼1%, eventually converging to D E10–20%. For specimens Dr ¼50%, Fc ¼ 0, decreasing trends in damping ratio D after taking the maximum value are more conspicuous. This presumably reflects the cyclic mobility type stress–strain curve appearing in the latter part of cyclic loading (γDA E5% or larger) as typically shown in Fig. 6, due to dilative behavior of medium dense clean sands.

Fig. 6. Typical shear stress versus shear strain relationship in undrained cyclic triaxial test.

4. Calculation of base-isolation in liquefied layer Based on the triaxial test results, the base-isolation effect of a simplified model shown in Fig. 4 is calculated in terms of energy.

Fig. 7. Shear modulus ratio and damping ratio versus double-amplitude strain obtained from a series of liquefaction tests.

Table 1 Conditions and pertinent results of undrained cyclic triaxial tests used in this research. Nominal relative density Dr (%)

Fines content Fc (%)

Relative density before test Dr (%)

CSR sd =2s0c

CRR for Nc ¼ 20 RL

Number of cycles Nc εDA

30

0

50

0

50

0

50

0

27 36 51 52 53 48 49 49 54

0.118 0.124 0.146 0.157 0.150 0.096 0.123 0.082 0.103

Δu/sc0

εDA

20

Δu/sc0

2%

5%

10%

1.0

2%

5%

10%

1.0

32 16 34 17 12 33 10 37 7.6

32 16 34 17 12 33 10 37 7.6

32 17 34 18 13 33 10 37 7.6

33 17 35 18 13 34 10 38 8.5

0.122 0.122 0.157 0.154 0.140 0.105 0.109 0.090 0.089

0.122 0.122 0.157 0.154 0.140 0.105 0.108 0.090 0.089

0.122 0.123 0.158 0.155 0.141 0.105 0.109 0.090 0.089

0.123 0.122 0.158 0.155 0.141 0.106 0.108 0.092 0.089

96

T. Kokusho / Soil Dynamics and Earthquake Engineering 63 (2014) 92–97

due to undrained cyclic loading toward complete liquefaction, respectively. The shear modulus G1 or G was determined from the secant modulus measured in the triaxial tests under p0 ¼98 kPa by considering the effective confining stress s0c ¼ ð1 þ 2K 0 Þs0v =3 at the layer boundary or at the mid-depth of the liquefied layer in the model ground, where s0v ¼effective overburden stress and K0 ¼earth pressure coefficient at rest. Namely, low-strain shear modulus G0 under the initial confining stress s0c was first computed using the next empirical equation [17–19]: G0 =p0 ¼ 840

ð2:17  eÞ2 0 ðsc =p0 Þ0:5 1þe

ð13Þ

Then, the shear modulus at the first load cycle G1 was determined considering the induced strain amplitude γ (approximately 0.05%: a half of γDA E 0.1% for all the tests) and the reference strain γr according to Hardin–Drnevich [20]: G1 =G0 ¼ 1=ð1 þ γ=γ r Þ

ð14Þ

Here, the reference strain, normally assumed proportional to the square root of effective confining stress [20], was chosen as γ r ¼ 0:8  10  3  ðs0c =p0 Þ0:5 based on previous research on typical fine sands [21]. As for the damping ratio, the effect of the confining stress was relatively minor in the strain level concerned here, and the measured values in the triaxial tests were directly used in the calculation. The soil properties thus determined at the mid-depth of the liquefied layer and at the top of the nonliquefied layer were used as representative values to compute the energy transmission ratios at the boundary Eu1/Eu2 in Eq. (10) and through the liquefied layer Es/Eu1 in Eq. (11). In preparation to calculate Eqs. (10) and (11) associated with α ¼ ρVs=ρVs1 and βH ¼ ωDH=V s ¼ 2πDf H=ðG=ρÞ0:5 , some pertinent parameters have to be determined. Considering a typical liquefaction problem, the thickness of liquefied layer H ¼10 m and representative frequency f ¼1.0 Hz are chosen here. In Fig. 8, the two energy ratios, Eu1/Eu2 and Es/Eu1, thus calculated are plotted versus double amplitude shear strain γDA in a semi-log diagram. For the calculation of Es/Eu1, Eq. (8) was used actually, because values approximated by Eq. (11) are always larger than exact values with an error mostly less than a few percent, but more than 20% larger for those corresponding to cyclic mobility in particular. Although the liquefaction process may vary due to irregularity of earthquake motions, a constant amplitude stress cycle is assumed here to act on soil elements to simplify the problem. Thus, the stresscontrolled cyclic triaxial test results in terms of G and D are directly applied cycle by cycle to evaluate variations in the energy transmission ratio in the liquefied layer with increasing double amplitude

Fig. 8. Energy ratios Eu1/Eu2, and Es/Eu1 versus double amplitude strain γDA calculated for various soil conditions (thickness of liquefied layer: H¼ 10 m).

shear strain, while the properties, G1 and D1, in the nonliquefied layer are assumed unchanged. The plots with identical symbols in Fig. 8 are connected with thin dotted lines to show the sequential variation of the two energy ratios, Eu1/Eu2 and Es/Eu1, with increasing γDA. As approximated by thick solid and dashed curves in the figure, almost unique strain-dependent energy ratios hold both for Eu1/Eu2 and Es/Eu1 despite the differences in Dr and Fc. For Es/Eu1, some plots tend to diverge from the thick approximation curve at some value of γDA. The most conspicuous are open triangle symbols corresponding to specimens of Dr ¼50% and Fc ¼ 0%, which seem to reflect a previously mentioned cyclic-mobility response due to positive dilatancy of clean sand. Except for this diverging trend, Es/Eu1 is smaller (the base-isolation effect is greater) than Eu1/Eu2 for all values of γDA, indicating that the base-isolation mechanism (b) due to wave attenuation in the liquefied layer is more dominant than the mechanism (a) due to impedance ratio at the boundary under the condition of H¼10 m and f¼1.0 Hz. The damping ratio D does not change so much with increasing γDA as shown in Fig. 7. Hence, the mechanism (b) may be mostly attributed to the increase of wave attenuation coefficient β ¼ ωD=V s ¼ 2πD=λ in Eq. (11), mainly because the wave length λ¼Vs/f is very much shortened with decreasing Vs as liquefaction develops. In Fig. 9, the global base isolation effect calculated in Eq. (12) is plotted versus γDA. Again, the trend does not differ so much according to different soil conditions and may be approximated by a thick solid curve. It starts from Es/Eu2 E0.8–0.9 due to the wave attenuation in the pre-liquefaction sand layer, and drastically reduces with increasing γDA to almost zero for contractive soils containing low-plasticity fines. For dilative clean sand, the curve tends to converge to a slightly higher value (Es/Eu2 ¼0.05–0.1). Thus, perfect base-isolation may be difficult to occur in a dilative clean sand compared to contractive sand containing low-plasticity fines, and some minor energy tends to arrive at the ground surface even during very extensive liquefaction. In the above, the thickness of liquefied layer was assumed H ¼10 m. In Fig. 10, the energy ratios calculated for H ¼2.5, 5 and 10 m are shown for the test results Dr ¼50% and Fc ¼ 10% shown in Fig. 7. As mentioned before, the effective confining stresses at the top of the nonliquefied layer and at the mid-depth of the liquefied layer are used in calculating the energy ratio. The energy ratio Es/Eu1 tends to increase (the base isolation effect tends to reduce) with decreasing thickness H, and become comparable with Eu1/Eu2 for H ¼2.5 m if γDA E7.5% (at the onset of liquefaction in normal design practice), though for a liquefied layer thicker than H ¼5 m, the base isolation by Es/Eu1 tends to dominate that by Eu1/Eu2. The

Fig. 9. Global energy ratio Es/Eu2 (ground surface/top of nonliquefied layer) versus double amplitude shear strain for various soil conditions.

T. Kokusho / Soil Dynamics and Earthquake Engineering 63 (2014) 92–97

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97

propagation distance in the liquefied layer, where wave attenuation coefficient increases considerably mainly because the wave length is very much shortened with decreasing Vs as liquefaction becomes severer. (4) In dilative clean sand, perfect base-isolation may be more difficult to occur than in a contractive sand containing lowplasticity fines even under very large induced strain, because some minor energy tends to arrive at the ground surface. Thus a base-isolation mechanism in a liquefied deposit has been basically captured in terms of energy by an idealized twolayer model, using soil properties from laboratory tests. Considering that actual liquefaction in the field is much more complex in terms of spatial/time-dependent variations of soil properties as well as seismic inputs, analytical studies under more realistic field conditions are certainly needed to quantitatively apply baseisolation effects in structural design.

Fig. 10. Energy ratios Eu1/Eu2, and Es/Eu1 versus double amplitude shear strain γDA calculated for various thickness of liquefied layer: H¼ 2.5, 5, 10 m (soil condition: Dr ¼ 50%, Fc ¼10%).

References mechanism (a) due to the impedance ratio acts at the boundary only, while the mechanism (b) due to the wave attenuation works all through the wave propagation distance in a liquefied layer. Hence the base-isolation effect by (b) gets greater as the liquefied layer becomes thicker. As for the representative input frequency for irregular seismic motions, if it is assumed higher than the value f ¼1 Hz employed here, the effect of Es/Eu1 tends be more dominant with shortening wave length in the liquefied layer, while the effect of Eu1/Eu2 at the boundary is unchanged. Thus, in major liquefaction cases, the wave attenuation effect in the liquefied layer seems to be more dominant than the impedance effect at the layer boundary. However, an exception of this trend may potentially occur when very loose layered sand liquefies and continuous horizontal water films are formed beneath low-permeable silt layers by void-redistribution, which may be suspected to have occurred during the 1964 Niigata earthquake [22,23]. If this happens, the energy transmission of the SH-wave is impossible at the water films, realizing almost perfect base-isolation by that mechanism as shown in the Kawagishi-cho seismic records [1].

5. Summary A basic mechanism of liquefaction-induced base-isolation was investigated in a simplified uniform sand layer based on a 1dimesional wave propagation theory. Variations of shear modulus and damping ratio with increasing shear strain measured on sand specimens during undrained cyclic triaxial tests were incorporated to evaluate the base-isolation effect in terms of energy, yielding the following major findings: (1) In a simplified two-layer model of liquefied and underlying nonliquefied layers, the downward wave in the liquefied layer may be ignorable. In this condition, the base-isolation mechanism for arbitrary earthquake motions can be expressed as the products of the two components: the mechanism (a) due to the impedance ratio at the layer boundary and the mechanism (b) due to the wave attenuation in the liquefied layer. (2) The base isolation mechanism (b) is found to become more dominant than the mechanism (a) in a liquefied layer with increasing thickness H of a liquefied layer. (3) This is because the mechanism (a) works at the boundary only, while the mechanism (b) works all along the wave

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