Ground response at liquefied sites: seismic isolation or amplification?

Soil Dynamics and Earthquake Engineering xx (xxxx) xxxx–xxxx

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

Ground response at liquefied sites: seismic isolation or amplification? ⁎

George D. Bouckovalasa, Yannis Z. Tsiapasa, , Alexandros I. Theocharisb, Yannis K. Chaloulosa a b

Geotechnical Department, School of Civil Engineering, NTUA, Greece Department of Mechanics, School of Applied Mathematics and Physical Sciences, NTUA, Greece

A R T I C L E I N F O

A BS T RAC T

Keywords: Seismic response Liquefaction Base isolation Site amplification

The seismic response of liquefied ground is parametrically investigated via analytical visco-elastic wave propagation theory, as well as nonlinear, effective stress, numerical analyses. It is found that a minimum liquefied layer thickness is required in order to ensure seismic isolation effects, i.e. significant attenuation of the seismic motion at the ground surface relative to that at the base, while for thinner layers attenuation of the seismic motion becomes marginal and may even turn into amplification. For harmonic excitations, the limiting thickness for seismic isolation and for seismic amplification are expressed as fractions of the corresponding wave length in the liquefied layer, and are also correlated to the thickness of the non-liquefiable soil crust reduced relative to that of the underlying liquefied layer. For a given soil profile, the above criteria may be inversely utilized in order to identify the harmonic excitation components that will be eventually filtered out and those that will be amplified. Application examples verify the validity of the proposed criteria for site and excitation conditions of engineering interest.

1. Introduction Among the various design issues related to earthquake-induced liquefaction, the free-field response is probably the least considered by the research community today. One possible reason is that the current practice is overwhelmingly in favor of pile foundations, which transfer the structure loads to deeper non-liquefiable strata, combined with soil improvement over the entire liquefaction depth aimed to minimize the lateral loads applied upon the piles. However, this practice has been challenged in recent years (e.g. [1–6]), in the light of new evidence that the existence of a shear resistant non-liquefiable crust, either natural (e.g. clay or dense gravel) or artificial (e.g. stone-column densified sand), on top of the liquefied soil layers may moderate liquefaction effects so that performance criteria for the structures are satisfied even for shallow foundations (e.g. [7–10]). An additional benefit from this alternative design approach may result from the liquefaction-induced reduction of the inertia loads on the superstructure, since it is widely acknowledged that liquefaction may soften the site characteristics and consequently act as a form of “natural seismic isolation”. In that sense, liquefaction of the subsoil may also provide an extra protection shield to the superstructure in the accidental case when the design seismic intensity is exceeded. Kokusho [11] provides a comprehensive review of cases studies from past earthquakes where damage reduction was observed to structures resting on liquefied ground, due to the afore-

mentioned base-isolation effect. Within the above research and design initiatives, this paper refers to the capacity of liquefied soil layers to effectively attenuate the seismic motion, providing thus natural isolation of the seismic ground motion, as well as to the conditions which may lead to opposite results, i.e. detrimental amplification effects. These tasks are first explored analytically, with the aid of visco-elastic harmonic wave propagation theory in a stratified soil column. Nonlinear, effective stress, numerical analyses are used in the sequel in order to verify the analytical findings and provide quantitative criteria for the liquefied ground response. It is important to clarify that this study refers to the site response at a liquefied state, i.e. after complete over depth liquefaction of a given subsoil layer. Furthermore, the emphasis is given to the soil and excitation conditions required in order to obtain significant attenuation of the seismic ground motion and those required in order to avoid its amplification. The exact amount of the anticipated attenuation and/or amplification of the seismic motion should be assessed independently, from site-specific response analyses which have been specifically developed for liquefiable ground conditions and take consistently into account the initial (pre-liquefaction) segment of the seismic excitation [12]. It is fortunate that, apart from advanced numerical methodologies, such as those that are used in the following, this task may be also accomplished approximately by a number of practice-oriented simplified methodologies, such as those proposed by Miwa and Ikeda [13],

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Corresponding author. E-mail addresses: [email protected] (G.D. Bouckovalas), [email protected] (Y.Z. Tsiapas), [email protected] (A.I. Theocharis), [email protected] (Y.K. Chaloulos). http://dx.doi.org/10.1016/j.soildyn.2016.09.028 Received 25 January 2016; Received in revised form 19 September 2016; Accepted 23 September 2016 Available online xxxx 0267-7261/ © 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: Bouckovalas, G.D., Soil Dynamics and Earthquake Engineering (2016), http://dx.doi.org/10.1016/j.soildyn.2016.09.028

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over the entire period range, except for medium periods between 0.2 s and 0.5 s, where the site effects are marginal. The ratio of surface to base elastic response spectra, shown in the second row of Fig. 3a and b, suggests that the average attenuation factor in the PIDA recordings and the respective amplification factor in the WLA recordings is of the order of two. The distinctly different response demonstrated in Figs. 2 and 3 may be attributed to the aforementioned difference in liquefied soil thickness at the PIDA (13 m) and the WLA (4.5 m) sites, suggesting that thick liquefied layers tend to attenuate the seismic motion, while relatively thin layers may amplify it. Furthermore, the results from the PIDA recordings show that, apart from the liquefied soil thickness, the excitation period may also affect the associated ground response. Similar conclusions with regard to the conditional attenuation or amplification effects of liquefied soil layers are drawn from the results of centrifuge tests T3-30 and T3-50-SILT of Dashti et al. [19], presented in Fig. 4a. These tests were performed for a relatively thin (3 m thick) liquefiable sand layer at two relative densities Dr = 30% and Dr = 50%. In the second test, a very thin silica flower layer was placed on top of the liquefiable sand layer in order to delay excess pore pressure drainage to the free ground surface. The base of the test models was subjected to the N-S Kobe (1995) PIDA recording scaled down to peak acceleration equal to about 0.18g. Reported excess pore pressure time-histories indicate that soil softening and liquefaction in both tests were triggered very early during shaking, and hence it may be safely assumed that, except possibly from the low period range T < 0.5 s, the presented response spectra reflect the liquefied soil response. Observe that the seismic motion is moderately attenuated for the very loose liquefiable layer (Dr = 30%) and considerably amplified for the medium dense (Dr = 50%) layer, identifying the relative density as one more factor affecting the liquefied ground response. It is further noteworthy that the amplification response of the medium dense sand layer is overall consistent with that obtained from the Superstition Hills recording at WLA (Fig. 3b), where the liquefied layer was also thin (4.5 m thick) and the estimated in situ relative density varied between Dr ≈ 40% and 60%. The effect of excitation period Texc on the liquefied ground response seen in Fig. 3a is also indirectly suggested by the study of Kramer et al. [14], which is based on results from a very large number of numerical seismic response analyses of liquefiable sites, for nine soil profiles with different liquefiable layer thickness and density, as well as 139 input motions with different frequency content and intensity. Each analysis was performed once using nonlinear, effective stress analysis with excess pore pressure buildup and once using nonlinear, total stress analysis. The resulting spectral accelerations were then divided in order to compute the response spectral ratio RSR(T) which is a measure of excess pore pressure effects on seismic ground motion. Fig. 4b shows the variation of RSR with excitation period for cases of intense liquefaction, with average factors of safety FSL = 0.50−0.55. The Authors admit that the large scatter of the data points masks the identification of any detailed effects of soil liquefaction on seismic ground motion. It is still of interest to observe that, similar to the PIDA

Fig. 1. Kawagishi-cho (E-W) seismic recordings of the Niigata, 1964 earthquake [15].

Kramer et al. [14], Kokusho [11] and Bouckovalas et al. [12]. 2. Overview of liquefied ground response Based on a number of seismic motion recordings at liquefied sites, such as the ones from Niigata, Japan Mw = 7.5 earthquake shown in Fig. 1 [15], it is a widespread belief among geotechnical and earthquake engineers today that the only beneficial effect of soil liquefaction is the drastic attenuation of the seismic motion of the free ground surface. Nevertheless, more recent studies suggest that this belief may not be unconditionally true. For instance, observe the seismic recordings in Figs. 2 and 3, obtained at the Port Island downhole array (PIDA) in Japan and at the Wildlife Liquefaction Array (WLA) in USA, during the Kobe (1995, Mw = 6.9) and the Superstition Hills (1987, Mw = 6.6) earthquakes respectively [16,17]. Each figure summarizes recorded acceleration time-histories and elastic response spectra at the ground surface and at the base of the liquefied layer. There are at least two distinct differences with respect to the recordings in Figs. 2 and 3, which should be considered for interpreting the observed trends. The first difference is that the liquefied layer is 13 m thick at PIDA and only 4.5 m thick at WLA. The second difference is that the average factor of safety against liquefaction was much lower during the Kobe (FSL = 0.4) than during the Superstition Hills (FSL = 0.8) earthquake and consequently the onset of liquefaction occurred very early during shaking in the first case and late during shaking in the second one. This is demonstrated in Fig. 2a and b, where recorded acceleration time-histories at the base of the liquefied layers and at the ground surface are plotted in parallel using a common time origin. It is thus observed that the incoherence between the two motions, indicating soil softening due to excess pore pressure buildup, becomes significant after about 8.3 s in the PIDA recording and after about 13.6 s in the WLA recording [18]. To isolate the effects of the pre-liquefaction seismic shaking, and focus upon the response of the liquefied ground, Fig. 3a and b compare the elastic response spectra corresponding to the segments of excitation and ground surface recordings that follow the onset of excess pore pressure induced soil softening. Observe that spectral accelerations for the PIDA recordings are drastically attenuated for periods up to T ≈ 1.0 s, while they are marginally affected thereafter. On the contrary, spectral accelerations for the WLA recordings are practically amplified

Fig. 2. Acceleration time-histories recorded at the ground surface and at the base of the liquefied layer (a) at Port Island seismic array during the Kobe, 1995 earthquake and (b) at Wildlife Liquefaction Array during the Superstition Hills, 1987 earthquake.

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Fig. 3. Elastic response spectra at the ground surface and at the base of the liquefied layer, following the onset of soil softening (a) at Port Island downhole array during the Kobe, 1995 earthquake and (b) at Wildlife Liquefaction Array during the Superstition Hills, 1987 earthquake.

Fig. 4. Liquefaction-induced attenuation and amplification effects on elastic response spectra from (a) centrifuge experiments by Dashti et al. [19] and (b) parametric numerical analyses by Kramer et al. [14].

analysis of PIDA and WLA recordings during Kobe and Superstition Hills earthquakes presented above, while the second conclusion is in line with the findings regarding the effect of sand density on the liquefied ground response deduced from the centrifuge study of Dashti et al. [19]. Concluding this selective review of previous studies with relevance to liquefied ground response, it is noted that evidence of seismic isolation is also provided in a number of additional centrifuge experiments (e.g. [20,21]) and numerical studies (e.g. [22,23]). Furthermore, marginal amplification effects are also evident in the field case studies presented by Youd and Carter [18], for the Loma Prieta (1989, Mw = 6.8) earthquake recordings at “Treasure Island” and “Alameda Naval Air Station” sites, in San Francisco, USA, where the liquefied layers were relatively thin, with 4.5 m and 5 m thickness respectively.

recording of Kobe earthquake analysed in Fig. 3a, the average (black line) relation in this figure shows attenuation of the seismic motion up to excitation periods Texc ≈ 1.0 s followed by amplification at higher periods. Kokusho [11] analysed the seismic isolation capacity of a liquefied layer resting on a non-liquefied base in terms of transmitted energy, considering: (a) the liquefaction-induced reduction in shear wave velocity and the associated shear wave length, as well as the corresponding increase in hysteretic damping, and (b) the change in seismic impedance between the liquefied layer and the non-liquefied base. It was thus found that the first mechanism (i.e. seismic isolation) generally dominates the latter (i.e. change in seismic impedance), the significance of which is gradually diminished with increasing thickness of the liquefied layer. As a result, seismic isolation effects become more pronounced as the thickness of the liquefied layer increases, while they are hindered to a certain extent in dilative clean sands due to the cyclic mobility τ–γ behaviour and the associated internal damping reduction. It is noteworthy that, although from an entirely different point of view, the first of these conclusions is consistent with the comparative 3

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Table 1 VS,L/VS,o ratios proposed by Miwa and Ikeda [13]. FSL VS,L/VS,o

0.3−0.6 0.10 − 0.14

0.6−0.9 0.12 − 0.16

0.9−1.0 0.14 − 0.19

ratio to increase with the factor of safety against liquefaction FSL (Table 1). As for the corresponding hysteretic damping ratio, the inverse analyses of Pease and O’Rourke [26] suggest that it is equal to ξL = 20−30%, while experimental data from cyclic triaxial tests [11] indicate that it may rise to a maximum of ξL = 25−30% at double amplitude strain γDA ≈ 1% and eventually stabilize to ξL = 10−20% at much larger strains. For m ≡ c, Eq. (1) should satisfy the free ground surface condition (point A in Fig. 5), namely that the shear stress and, consequently, the shear strain at zc = 0 should remain equal to zero during shaking, i.e.:

γ (z c = 0, t ) =

∂uc (z c = 0, t ) =0 ∂z

(4)

In addition, the continuity of displacements and shear stresses at the interface between the two layers (point B in Fig. 5) requires that: (5)

uc (z c = Hc, t ) = uL (zL = 0, t )

Fig. 5. Two-layer soil profile of uniform liquefied sand covered by a non-liquefied clay crust.

and (6a)

τ (z c = Hc, t ) = τ (zL = 0, t )

3. Visco-elastic wave propagation analysis of liquefied ground response

or

∂uc (z c = Hc, t ) ∂u (z = 0, t ) = GL* L L ∂z ∂z

3.1. Analytical formulation

Gc*

As a first step, the seismic response of liquefied sand layers was simulated based on harmonic wave propagation theory for the twolayer visco-elastic soil profile shown in Fig. 5, i.e. a non-liquefied crust overlying liquefied sand. It is clarified that the purpose of this simplified approach is primarily to explore the mechanisms which control the observed response of liquefied sites and also to identify the soil and excitation parameters which may have a significant quantitative effect on the site response. The findings from this initial investigation will be quantitatively verified in the sequel, based on more realistic time-domain, elasto-plastic, numerical analyses with a wide range of harmonic as well as recorded seismic motions.. In general terms, the horizontal displacement along the soil column of Fig. 5 is expressed as:

When combined, Eqs. (1) and (4) - (6b) lead to the following expression for the ratio of ground motion amplitudes at the top (point B) and at the base (point C) of the liquefied sand layer:

u m (zm , t ) = (Am eikm* zm + Bm e−ikm* zm ) eiωt

F (ω ) =

(1)

(2)

where ω = 2π/Τexc is the circular excitation frequency and VS*, m is the complex shear wave velocity of layer m:

VS*, m = VS, m (1 + iξm ) =

Gm (1 + iξm ) ρm

1 ⎛ H ⎞ cos ⎜2π λ*L ⎟ − L⎠ ⎝

ρc VS*, c ρL VS*, L

⎛ H⎞ ⎛ H ⎞ tan ⎜2π λ *c ⎟ sin ⎜2π λ*L ⎟ c⎠ L⎠ ⎝ ⎝

(7)

where λ m* = VS*, m Τexc (m ≡ c, L) denote the harmonic wave lengths in the surface crust and in the underlying liquefied sand. It should be clarified that Eq. (7) was derived under the assumption of “rigid rock” conditions at the base of the two-layer profile of Fig. 5. Nevertheless, this assumption should not be interpreted as a limitation of the present study, as the exact base conditions (i.e. “rigid” or “elastic” rock) are indifferent when there is a marked difference in elastic properties and moderate to large motions are considered, associated with high levels of strains and a substantial amount of internal damping in the soil (e.g. [28]). This is true indeed in the examined case, where liquefaction-induced softening reduces the initial shear wave velocity of the sand by 75−90% and thus creates a high impedance contrast at the interface between the sand and the underlying non-liquefied soil layers. On parallel, the internal damping of the liquefied sand layer is really high, in the order of 20−30%. In addition to the above, the use of “elastic rock” base was avoided for one more reason: it would unnecessarily complicate the interpretation of the analytical and the numerical analyses by increasing the number of problem variables that should be considered (i.e. by introducing the elastic rock characteristics). Fig. 6 shows the variation of the norm of F in terms of the thickness ratio HL/λL of the liquefied layer, for a typical case with HL/Hc = 3, VS,L/VS,c = 0.15, ρL/ρc = 1.0, ξc = 10% and ξL = 25%. Although the result of a simplified analytical solution, Fig. 6 verifies the trends of the actual recordings, discussed in the previous section. In particular, it shows that a liquefied soil layer would either amplify or attenuate the seismic motion depending on its thickness HL, the shear wave velocity upon liquefaction VS,L and the seismic excitation period Texc. The effect of the last two parameters is jointly expressed through the wave

where subscript m ≡ c for the top non-liquefied crust and m ≡ L for the liquefied sand. Furthermore, Am and Bm are the amplitudes of the waves travelling upwards and downwards respectively and km* is the complex, in terms of the hysteretic damping ratio ξm, wave number:

k m* = ω / VS*, m

u (zL = 0, t ) = u (zL = HL , t )

(6b)

(3)

while Gm, ρm and ξm (m ≡ c, L) denote the constant values of shear modulus, mass density and hysteretic damping ratio of each layer. It is important to notice that the shear wave velocity VS,L and the hysteretic damping ratio ξL of the underlying layer correspond to a liquefied state and consequently they differ significantly from the conventional values assigned to natural soils. Namely, inverse analyses of actual seismic recordings at liquefied sites [13,24–27] have shown that the shear wave velocity of liquefied sands and silts VS,L is reduced to 10−25% of the initial value VS,o, with a tendency of the VS,L/VS,o 4

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Fig. 6. Typical analytical predictions for the norm of F versus HL/λL.

length λL. In more detail, the following three distinct modes of response are observed, depending on the thickness ratio HL/λL: (a) Amplification (i.e. |F| > 1.00) at small thickness ratios (i.e. HL/λL < 0.3). (b) Rapid attenuation (i.e. de-amplification) from |F| ≈ 1.00 to |F| ≈ 0.20−0.30 for intermediate thickness ratios (i.e. HL/λL ≈ 0.3−0.8). (c) Marginal further attenuation of |F| for larger thickness ratios (i.e. HL/λL > 0.75−0.85).

Fig. 7. Effect of (a) damping ratio ξc, (b) damping ratio ξL, (c) density ratio ρL/ρc and (d) velocity ratio VS,L/VS,c on |F|.

The bounds between these modes are denoted as (HL/λL)ampl for seismic motion amplification (i.e. when |F| ≥ 1.00) and (HL/λL)iso for seismic motion isolation (i.e. when |F| ≤ 0.20−0.30).

3.2. Parameter Identification The second valuable information that is derived from the analytical solution (i.e. Εq. (7)) is that, except from HL/λL, the amplitude ratio | F| depends on the following independent site variables: thickness ratio HL/Hc, velocity ratio VS,L/VS,c, density ratio ρL/ρc, and hysteretic damping ratios ξc and ξL. To evaluate the relative significance of these additional variables, Eq. (7) was applied parametrically for the following range of input values: VS,L/VS,c = 0.10−0.60, ρL/ρc = 0.85−1.15, ξc = 5−15%, ξL = 20−30% and HL/Hc = 0.1−6.0. The site characteristics used to obtain the plot of Fig. 6 represent the baseline case. It was thus found that VS,L/VS,c, ρL/ρc, ξc and ξL have a minor effect on |F| (Fig. 7), which can be practically ignored. On the contrary, the thickness ratio HL/Hc has a pronounced effect (Fig. 8), with the plot of |F| systematically shifting to larger HL/λL ratios, when the thickness of the liquefied layer increases relative to that of the non-liquefied crust. Ιn a more systematic way, Fig. 9 shows the variation with the relative thickness ratio HL/Hc of: (a) the limiting thickness ratios (HL/ λL)iso for seismic isolation, i.e. for |F| = 0.20−0.30, and (b) the limiting thickness ratios (HL/λL)ampl for seismic amplification, i.e. at |F| = 1.00. Observe that the analytical predictions for (HL/λL)iso form a narrow band indicating that, in the commonly encountered range of HL/Hc = 1−6, the minimum required thickness of the liquefied layer, in order to have seismic isolation, increases almost linearly from HL,iso ≈ 0.60λL to 1.10λL. A similar trend is observed for the variation of (HL/λL)ampl, although the corresponding values of the seismic amplification thickness HL,ampl are much lower, i.e. they amount only to (0.3−0.4)HL,iso.

Fig. 8. Effect of the thickness ratio HL/Hc on |F|.

Fig. 9. Variation of the limiting thickness ratios HL/λL for seismic isolation (i.e. |F| = 0.20–0.30) and seismic amplification (i.e. |F| = 1.00) with relative thickness ratio HL/ Hc.

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4. Numerical analysis of liquefied ground response 4.1. Methodology outline For a more systematic approach, the liquefied ground response was also examined with the aid of nonlinear, fully-coupled, dynamic, effective stress analyses which capture realistically the earthquakeinduced excess pore pressure buildup and the associated softening of the ground. Similar to the previous analytical solution, the soil profile consists of a non-liquefiable clay crust, over a liquefiable sand layer of variable thickness and an underlying non-liquefiable clay bed (Fig. 10). The analyses were performed with the finite difference code FLAC [29]. The NTUA-SAND critical state plasticity constitutive model [30,31] was employed to simulate the response of the liquefiable sand, while the simpler Ramberg and Osgood [32] constitutive model was selected to simulate the nonlinear hysteretic response of the crust and bed clay layers. The NTUA-SAND model was calibrated against static and cyclic tests on saturated fine Nevada Sand [20], while the Ramberg and Osgood [32] model was calibrated against the experimental modulus reduction and damping curves of Vucetic and Dobry [33] for low plasticity (PI = 30) clays. All parametric analyses were performed with the finite difference mesh shown in Fig. 10, i.e. a 14 m deep single column of elements with element zone size 1 m x 0.50 m (width×height). Free-field lateral boundaries were simulated with the “tied-node” technique, which imposes the same boundary displacements at grid points of the same elevation. The base of the soil column was shaken with a 15-cycle

Fig. 10. Soil profile, finite difference mesh and range of input parameters used in the parametric numerical analyses.

Fig. 11. Typical acceleration and excess pore pressure ratio time-histories, as well as stress paths for (a) HL = 10 m, (b) HL = 6 m and (c) HL = 2 m.

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liquefied sand layer, soil to excitation resonance, low stress shearinduced dilation of the sand) deserves further investigation, as the associated effects are coupled and their quantitative assessment becomes complex.

harmonic excitation, of variable maximum acceleration amax = 0.10−0.40g and frequency f = 2−10 Hz. The shear wave velocity of the clay crust and the clay bed layers was equal to VS = 100 m/s and 300 m/s respectively. The initial relative density of the sand varied from Dr = 40% to 75%, while the associated permeability coefficient was increased from k = 0–0.06 cm/s. The thickness of the clay crust and the liquefied sand layers varied at 2 m and 1 m increments respectively, in the range Hc = 2–6 m and HL = 1–12 m, while the thickness of the clay bed was properly adjusted so that the total height of the column was maintained constant. To reduce the numerical noise from the FLAC predictions, the pre- and the post-liquefaction segments of the predicted acceleration time-histories at the ground surface were filtered separately, using appropriate high frequency filtering criteria [12].

4.3. Interpretation of results In the sequel, the numerical predictions from all parametric analyses were used in order to verify the existence and quantitatively assess the limits of liquefied sand thickness HL,ampl and HL,iso, for amplification and isolation of the seismic base motion, predicted by the previous linear visco-elastic analysis. The minimum thickness HL,ampl required in order to avoid amplification of the seismic motion, was defined by direct comparison of the post-liquefaction acceleration timehistories at the top and at the base of liquefied sand layer, plotted in the top row of Fig. 11. However, this approach proved unreliable for the evaluation of the minimum isolation thickness HL,iso, as the corresponding amplitude of the seismic motion at the top of the liquefied sand becomes very small, making the direct comparison between two consecutive sand thicknesses uncertain. Hence, for greater accuracy, the comparison was alternatively performed on the basis of the corresponding elastic response spectra, where differences are more clearly visible. This is demonstrated in Fig. 12a, which shows the elastic response spectra at the top of the liquefied sand layer, computed for the soil and excitation parameters referenced above (i.e. amax = 0.3g, f = 3.3 Hz, Hc = 2 m, Dr = 60%, k = 0) and gradually increasing liquefied sand thickness from HL = 1–12 m. Observe that spectral accelerations initially decrease drastically with increasing HL, demonstrating the previously identified beneficial effects of liquefaction-induced soil softening. However, their values over a wide period range are subsequently stabilized at a minimum bound when HL exceeds a certain critical thickness, approximately equal to about 7 m for the specific set of parametric analyses. This last observation verifies essentially the existence of HL,iso and allows its quantitative evaluation based on the numerical predictions. The acceleration time-histories for HL,iso = 7 m, as well as for the previous and the next value of HL, are also plotted in Fig. 12b–d in order to demonstrate the transition of the acceleration response to the completely attenuated state.

4.2. Review of numerical predictions Fig. 11 shows typical numerical predictions, regarding the following aspects of site response which are of interest to the present study: the acceleration time-histories at the sand surface and base, the timehistory of excess pore pressure ratio ru = Δu/σ′v,o at mid-depth of the sand layer and the associated stress paths τ–σ′ν (Δu denotes the excess pore pressure, τ and σ′ν denote the applied shear and vertical effective stresses respectively, while subscript “o” indicates initial geostatic conditions). The predictions refer to frequently encountered site and excitation parameters (i.e. amax = 0.3g, f = 3.3 Hz, Hc = 2 m, Dr = 60%, k = 0) and three distinctly different with regard to thickness liquefiable sand layers: “thick” (HL = 10 m), “medium” (HL = 6 m) and “thin” (HL = 2 m). It is observed that effective isolation of the seismic motion is only exhibited by the “thick” sand layer (Fig. 11a), where the seismic motion at the top of the sand layer is completely attenuated upon liquefaction (i.e. ru ≈ 1). In parallel, shear stresses applied at the middle of the sand layer are drastically reduced and practically diminish when ru approaches unity. On the contrary, for the “thin” sand layer (Fig. 11c) the ground motion and the associated shear stresses remain practically unaltered during the entire shaking period, despite the fact that liquefaction (i.e. ru ≈ 1) has occurred very early during shaking. In addition, large dilation spikes accompany the post-liquefaction excess pore pressure time-history. Finally, the response of the “medium” layer (Fig. 11b) exhibits essentially a gradual transition from the “thin” to the “thick” sand layer response, as the predicted acceleration and shear strain amplitudes, as well as the excess pore pressure dilation spikes are significantly reduced after the first few loading cycles, but they do not completely vanish. It is speculated that the differences observed in Fig. 11 may be traced back to the effect of liquefaction on the natural period of vibration of the soil column. Namely, liquefaction of the “thick” sand layer reduces drastically the shear wave velocity of the sand, as explained in later sections of this paper, and shifts the natural period of the soil column far beyond the fundamental excitation period, leading thus to out-of-phase ground surface response and to the observed seismic isolation effects. On the other hand, the increase of the natural soil period in the case of the “thin” soil layer is marginal, mainly due to the small thickness of that layer, compared to the height of the column, and consequently it may lead to some amplification or attenuation of the seismic motion, depending on the initial value of the natural soil period relative to the excitation period. It is also interesting to observe that the sand response in the latter case becomes extremely dilative upon liquefaction, with the ru values in Fig. 11c ranging between ru = −0.80 and 1.00. It is thus possible that the degradation of the associated shear wave velocity is less than in the former case of the “thick” sand layer, restraining further the increase of the natural soil period and preventing the drastic attenuation of the seismic ground motion amplitude. It should be acknowledged that the interaction between the various mechanisms described above (i.e. softening of the

5. Effect of liquefied sand thickness and excitation period on seismic ground response 5.1. Estimation of shear wave length upon liquefaction, λL To correlate the limiting values of thickness HL,ampl and HL,iso with the corresponding wave length λL ≅ VS, L Texc , by analogy to the results of the previous linear visco-elastic analysis, it is necessary to first estimate the average shear wave velocity in the liquefied sand layer VS,L. This task was performed separately for each parametric numerical analysis using the “pulse method”, explained in Fig. 13a. More specifically, after the end of the seismic excitation, a single sine pulse was applied at the base of the soil column and the time lag Δt between the first arrival times of the pulse at the top and at the base of the liquefied sand layer was estimated. Thus, the average (over the liquefied sand thickness) VS,L was estimated as:

VS, L = HL / Δt

(8)

Note that a “quiet” period of 2−3 s was allowed between the end of shaking and the pulse triggering, so that the free vibration of the soil column ceases. Drainage of the excess pore water pressures was not allowed during that period, so that the sand remained at a liquefied state. Following parametric sensitivity analyses aiming to optimize identification of the first arrival time at the top of the liquefied layer, the maximum acceleration and the period of the sine pulse were set equal to amax = 0.03g and Texc = 0.5 s. First arrival times were 7

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Fig. 12. Effect of liquefied sand thickness HL on numerically predicted (a) elastic response spectra and (b)–(d) acceleration time-histories at the top of the sand layer.

conventionally determined as the time of first exceedance of the 0.01g level in the predicted acceleration time-histories at the top and at the base of the liquefied sand layer. The same procedure was also followed before application of the seismic excitation and led to the estimation of the average initial shear wave velocity of the sand layer VS,o. The post- to pre-shaking shear wave velocity ratios are plotted in Fig. 13b against the liquefied sand thickness. Observe that the bulk of the data vary in the more or less constant range VS,L/VS,o = 0.10−0.23, without a clearly pronounced effect from any specific site and excitation parameters. It is noteworthy that the numerical predictions of VS,L/VS,o are in fair agreement with results from the inverse analyses of actual seismic recordings at liquefied sites, referenced earlier in Section 2 [13,24–27] and shown as a shaded area in Fig. 13b.

in Fig. 14a and b. To compare with the numerical predictions, the range of analytical predictions is also shown in these figures in grey color. As a general observation, it should be acknowledged that the agreement between the two sets of data is remarkable, considering that they were obtained from widely different methodologies. Namely, the range of analytical predictions for (HL/λL)iso essentially coincides with the core of the numerical predictions (Fig. 14a), while the analytical predictions for (HL/λL)ampl form a consistent lower bound to the associated numerical results. From a practical standpoint, observe that the numerical predictions of both figures form a relatively narrow band of data points, which can be fitted with the following simple analytical expressions in terms of HL/Hc:

⎛ H ⎞0.35 ⎛ HL ⎞ ⎜ ⎟ = 0.55 ⎜ L ⎟ ⎝ λL ⎠iso ⎝ Hc ⎠

5.2. Effect of liquefied sand thickness

for HL / Hc ≥ 1

(9a)

and

⎛ H ⎞0.35 ⎛ HL ⎞ = 0.275 ⎜ L ⎟ ⎜ ⎟ ⎝ λL ⎠ampl ⎝ Hc ⎠

Numerically predicted values of limiting thicknesses HL,iso and HL,ampl are correlated to the liquefied wave length λL and the ratio of liquefied sand over the non-liquefied crust thickness HL/Hc, as shown

Fig. 13. Shear wave velocity evaluation of liquefied sand: (a) the “pulse” method for the numerical evaluation of VS,L and (b) range of predicted VS,L/VS,o values.

8

(9b)

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Table 2 Scaled seismic motion recordings used for the numerical analyses in Fig. 15a. Seismic motion

Kobe - TDO (1995) Loma Prieta - AND (1989) New Zealand (1987) Northridge - FLE (1994) San Fernado - PEL (1971) Average:

Mw

6.9 6.9 6.6 6.7 6.6

PGA (g) Strong

Weak

0.424 0.354 0.297 0.190 0.234 0.30

0.212 0.177 0.149 0.095 0.117 0.15

and

⎛ H ⎞−0.35 HL (≈ 2Tiso ) Tampl = 3.64 ⎜ L ⎟ ⎝ Hc ⎠ VS, L

To follow up with the application example of the previous section, it may be now assumed that a liquefied layer with thickness HL = 6 m is subjected to a real seismic excitation with a wide spectrum of harmonic components. On the basis of Eqs. (11a) and (11b), it is estimated that spectral accelerations will be drastically reduced for periods Texc ≤ Tiso ≈ 0.33 s and they may be amplified for periods Texc ≥ Tampl ≈ 0.66 s. Furthermore, to check the applicability of Eqs. (11a) and (11b) to real seismic excitations, the soil profile of Fig. 10 was subjected to a number of scaled seismic motion recordings, with a wide frequency spectrum. In particular, a suite of five Mw = 6.6−6.9 earthquake motions (Table 2) recorded at bedrock outcrop, has been selected and properly scaled so that the average spectrum fits the design spectrum of Eurocode EC-8 for soil type B (Fig. 15a), for two seismic scenarios: a “strong” motion with average peak ground acceleration PGA = 0.30g and a “weak” motion with PGA = 0.15g. A parametric study was then conducted for Dr = 40% and 60% and HL = 2−10 m (in 2 m increments). The crust thickness was fixed at Hc = 2 m and the bedrock was considered flexible with properties VS,b = 650 m/s, ρb = 2 Mg/m3 and ξb = 2%. Each soil profile was subjected to all aforementioned seismic motions, to give a total of 100 additional parametric numerical analyses. The ratio of elastic response spectra at the surface and at the base of the examined soil profile was subsequently computed for all numerical analyses and plotted in Fig. 15b. To eliminate the effect of the preliquefaction segment of the seismic excitation, the elastic response spectra were computed only for the post-liquefaction part of the acceleration record, i.e. after the onset of liquefaction at the ground surface. Furthermore, for a unified presentation, spectral acceleration ratios are plotted against structural periods normalized against Tiso, as computed for each case from Eq. (11a). The same procedure wass followed for the actual recordings from Kobe (1995) earthquake obtained at the Port Island downhole array (PIDA), also shown in Fig. 15b (in black line). It is observed that, for the vast majority of the results, spectral components are indeed drastically attenuated for T/ Tiso < 1. For greater T/Tiso ratios, spectral acceleration ratios increase steadily and, although significantly scattered, amplification effects become more and more pronounced as T/Tiso exceeds the limiting value of Tampl/Tiso ≈ 2, as predicted according to Eq. (11b). The average predicted spectral acceleration ratios, shown in thick (red) line in Fig. 15b, are equal to 0.20–0.25 for T/Tiso < 1.0, increase to 0.75 at T/Tiso = Tampl/Tiso ≈ 2 and become approximately greater than 1.0 for T/Tiso > 2.

Fig. 14. Numerically predicted variation of the limiting thickness ratios HL/λL with the relative thickness ratio HL/Hc, for (a) seismic isolation and (b) seismic amplification.

For harmonic excitation components of period Texc, Eqs. (9a) and (9b) can be solved for the thickness of the liquefied layer and give:

HL, iso = 0.40(VS, L Texc )1.54 /(Hc )0.54

for HL / Hc ≥ 1

(10a)

and

HL, ampl = 0.137(VS, L Texc )1.54 /(Hc )0.54

(10b)

To acquire a quantitative feeling of the previous findings, Eqs. (10a) and (10b) are applied for a typical soil profile with 2 m of non-liquefied crust over a liquefied sand layer with more or less uniform initial shear wave velocity VS,o = 170 m/s and a liquefaction-reduced shear wave velocity VS,L = 0.15·170 ≈ 25 m/s. Assuming further that the anticipated predominant excitation period may vary in the range Texc = 0.20−0.30 s, Eq. (10a) will predict that the maximum attenuation of the seismic motion will be obtained when HL ≥ HL,iso ≈ 3−6 m, whereas, according to Eq. (10b), amplification of the seismic motion may occur for HL ≤ HL,ampl ≈ 1–2 m. 5.3. Effect of excitation period In addition to the case examined so far, i.e. that of a given harmonic wave filtered through a liquefied sand layer with variable thickness, it is also of practical interest to examine the inverse case, when a real seismic excitation, with a wide spectrum of harmonics, is filtered through a liquefied layer with given thickness HL. In that case, Eqs. (10a) and (10b) can be solved for the excitation period Texc and give the limiting period values Tiso and Tampl associated with drastic attenuation (seismic isolation) or eventual amplification of the corresponding spectral amplitudes:

⎛ H ⎞−0.35 HL Tiso = 1.82 ⎜ L ⎟ ⎝ Hc ⎠ VS, L

(11b)

6. Summary and conclusions Field case studies and numerical analyses show that liquefied soil layers may amplify or attenuate (de-amplify) the seismic ground motion, depending on two main factors: the liquefied layer thickness

(11a) 9

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initial (pre-liquefaction) one, namely VS,L = (0.10−0.25)VS,o. The VS,L/VS,o ratio may increase with the factor of safety against liquefaction FSL (e.g. Table 1), but appears to be practically independent from any other individual soil or excitation parameter. e) The application examples presented in previous sections suggest that the predicted limiting values, of excitation period or liquefied sand thickness, for seismic amplification or isolation effects, do not represent any extreme and unrealistic conditions, but fall in the range of interest for ordinary engineering applications. Finally, it is important to acknowledge that the criteria presented in this paper refer to the response of the “liquefied” ground, i.e. the ground response after the onset of liquefaction. Hence, they apply in practice to cases of severe liquefaction and very low factors of safety (e.g. FSL < 0.30−0.40), when ground softening initiates prior to the strong motion part of the seismic excitation. In the opposite case, the pre-liquefaction segment of the seismic excitation may play a significant role in the seismic isolation or amplification potential of the site. These effects can be only evaluated with site- and excitation-specific analyses which take consistently into account the initial (pre-liquefaction) stage of shaking. In addition, it should be noted that the presented criteria refer to the “potential” of a given site to isolate or amplify a given seismic excitation. The accurate quantitative estimation of these effects on the seismic ground motion requires also separate site response analyses, as above. Acknowledgements This research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)-Research Funding Program: THALES. Investing in knowledge society through the European Social Fund.

Fig. 15. Parametric numerical analyses with actual (scaled) seismic motion recordings: (a) comparison of the average elastic response spectrum at bedrock outcrop with the design spectrum of Eurocode EC-8 for soil type B and the “strong” seismic excitation scenario, (b) surface-to-base spectral acceleration ratios.

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