Investigation of Vs – based liquefaction charts using a heavily preshaken silty sand centrifuge deposit

Soil Dynamics and Earthquake Engineering 122 (2019) 39–52

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Investigation of Vs – based liquefaction charts using a heavily preshaken silty sand centrifuge deposit

T

T. Abdouna,c, W. El-Sekellyb,c, , R. Dobrya ⁎

a

Dept. of Civil and Environmental Eng., Rensselaer Polytechnic Institute, 110 8th Street, JEC 4049, Troy, NY 12180, USA Dept. of Structural Engineering, Mansoura University, Mansoura 35516, Egypt c New York University Abu Dhabi, Abu Dhabi, UAE b

ABSTRACT

Preshaking by previous seismic activity can significantly affect the liquefaction resistance of saturated sands. Field evidence, cyclic laboratory testing and centrifuge modeling show that: (i) earthquake events that build up excess pore pressures short of liquefaction strengthen the soil; and (ii) liquefying earthquakes may weaken the soil. The paper presents the results of a centrifuge test (Experiment 2), where a 6 m saturated loose silty sand deposit was subjected to 52 successive base shakings. Three types of shakings were used: preshaking Events A, with a shaking duration of 5 cycles, and stronger Events B and C having a duration of 15 cycles, with Events C having the largest input accelerations. A total of 35 Events A, 9 Events B, and 8 Events C were applied at the base of the model in an alternating sequence. All Events C liquefied the deposit, with the Events B inducing liquefaction at the beginning but not at the end of Experiment 2. Events A generally induced excess pore pressures but not liquefaction. In addition to the pore pressures, horizontal accelerations, settlement and densification, and the soil shear wave velocity, Vs, were also monitored during the test. The results were compared with those of Experiment 1, reported in a previous publication, where a similar 6 m deposit of the same silty sand was subjected to a different sequence of shakings A and B which did not include any Event C. Conclusions are drawn on the effect of the strong Events C on the deposit's response. Events A, B and C of Experiment 2 are plotted on existing Vs –based liquefaction charts. The charts predict well the liquefaction response of the deposit at the beginning of Experiment 2. On the other hand, for shakings near the end of the test, the charts predict liquefaction for the Events B, which by this time have stopped liquefying the deposit due to the previous history of shakings. This result is consistent with the field evidence including the presence of a number of “false positives” in the charts for silty sand sites in the Imperial Valley of California, an area of intense seismic activity.

1. Introduction Soil liquefaction during earthquakes can result in severe damage. Several researchers have studied the effects of liquefaction, most recently in Haiti [1,2], Chile [3], Japan [4], and New Zealand [5,6]. The estimation of the liquefaction potential of a sandy soil deposit is commonly based on field liquefaction triggering charts based on the Seed and Idriss [7] simplified procedure. This method, originally developed using the blow count from the SPT, is represented by the cyclic stress ratio (CSR). In most applications, CSR is estimated from the expression:

CSR = 0.65

amax g

v0 v0

rd

(1)

where amax = peak horizontal ground surface acceleration; g = acceleration of gravity; σv0 = total vertical overburden pressure at the same depth as σ’v0 which is the effective vertical overburden pressure and rd = shear stress reduction coefficient, which is unity at the ground surface and decreases with the depth of the layer. The application of Eq. (1) is equivalent to assuming that the value of the representative cyclic shear stress amplitude, τc, is 65% of the maximum cyclic shear stress in ⁎

the same layer, τmax = (amax / g) σv0 rd A number of liquefaction charts have been proposed relating CRR to field tests such as the Standard Penetration Test (SPT), Cone Penetration Test (CPT), and Shear Wave Velocity (Vs). Fig. 1 shows the Vs-based chart developed by [8], normalized to an earthquake of moment magnitude, Mw = 7.5. The normalized shear wave velocity (Vs1) in Fig. 1 is defined as:

Vs1 = Vs

100

0.25

v0

(2)

where Vs1, Vs are in m/s and σ’v0 is in kPa. All charts have been empirically calibrated by field case histories of liquefaction and no liquefaction cases, which makes them a very reliable tool. On the other hand, several authors have pointed out some limitations of these SPT, CPT and Vs charts, including: (i) the deterministic charts provide a lower bound for the occurrence of liquefaction and therefore are conservative; and (ii) they do not account for the geologic age and shaking history of the sand layer [9–13]. Points (i) and (ii) above are related. [13,14] showed that the Andrus and Stokoe clean sand curve of Fig. 1 (labeled “ < 5% fines” in the

Corresponding author at: Dept. of Structural Engineering, Mansoura University, Mansoura 35516, Egypt. E-mail address: [email protected] (W. El-Sekelly).

https://doi.org/10.1016/j.soildyn.2019.03.030 Received 16 October 2018; Received in revised form 28 January 2019; Accepted 19 March 2019 0267-7261/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. Liquefaction chart for sands, silts and gravels based on field shear wave velocity, 225 case histories [8].

Fig. 2. Vs-based liquefaction charts and natural soil case histories (modified after [13]).

figure), provides a reasonable boundary separating liquefaction from no liquefaction for recent uncompacted sandy fills. On the other hand, the same curve tends to be too conservative for natural sandy soils located in some highly seismic areas. This is consistent with the higher resistance of some natural sand sites in California and Japan compared with recent fills of similar SPT, reported respectively by [15,9]. The paper inspects the effect of preshaking on the liquefaction resistance of sandy soils using a long centrifuge experiment on silty sand (Experiment 2). Experiment 2 is related to Experiment 1 presented by [16]; both tests are comparable in terms of the initial deposits’ characteristics but differ in their shaking sequences. Specifically, Experiment 2 corresponds to a stronger seismic environment than Experiment 1, as discussed in detail later in the paper. While this paper focuses on Experiment 2, the results of Experiment 1 are also summarized and compared to those of Experiment 2, in order to gain a better understanding of the liquefaction behavior of silty sand deposits subjected to different seismic environments. Experiments 1 and 2 are in turn part of a wider series of centrifuge and large scale preshaking experiments performed by the authors on clean and silty sands. More details about the four experiments can be found in [17].

Further examination of these “false positives” by [13], revealed that almost all of them (eleven out of thirteen) correspond to geologically young (deposited less than 200–500 years ago) alluvial/fluvial layers of silty sand, located in the very highly seismic Imperial Valley of Southern California, with all sites located within 40 km of each other. Therefore, the most probable explanation of the higher liquefaction resistance exhibited by these silty sand sites in the Imperial Valley is preshaking by previous earthquakes, which have shaken the sites dozens of times since deposition. [13] thoroughly investigated the possibilities that lack of full saturation and/or existence of a thick nonliquefiable shallow layer were the explanation for the lack of surface manifestations of liquefaction for these eleven “false positives” in the Imperial Valley. It was concluded that these were indeed cases of no liquefaction and were fully saturated, thus supporting the conclusion that the silty sand sites in the Imperial Valley have an increased liquefaction resistance. Previous work by [14] on the liquefaction of recent uncompacted fills during the 1989 Loma Prieta earthquake had shown that: (i) the Andrus and Stokoe clean sand curve of Figs. 1 and 2 provides a realistic boundary for those uncompacted clean and silty sands, separating well liquefaction from no liquefaction; and (ii) centrifuge testing with base shaking produced realistic results in agreement with the 1989 field liquefaction response of these recent uncompacted fills.

2. Effect of preshaking by previous earthquakes Fig. 2 shows again the same clean sand curve proposed by [8] from Fig. 1, along with the more recent curve proposed by [18] from their probabilistic study. It must be noted that the Andrus-Stokoe curve in Fig. 2 was originally proposed for clean sands, but subsequent evaluations indicate that the two curves in Fig. 2 can be used for both clean and silty sands, see [13,18]. Specifically, only the 15% probability curve from [18] was included herein, as this is what they recommended for use as the single deterministic boundary for Vs1-based liquefaction evaluation. Fig. 2 also includes data points compiled by [13], corresponding to all field case histories of liquefaction and no liquefaction in the original [8] database, which are naturally deposited clean and silty sands having a non-plastic fines content, FC ≤ 34%. The figure clearly illustrates the over-conservatism of the [8] curve, already mentioned, and to a lesser extent also of the [18] curve, for many natural sand sites as opposed to uncompacted artificial fills. Essentially all thirteen data points which are above the Andrus-Stokoe curve up to CSR ≈ 0.10–0.13 in Fig. 2, are “false positives,” that is natural soil layers that were predicted to liquefy but did not experience liquefaction.

3. Previous preshaking centrifuge test (Experiment 1, [16]) In order to investigate the effect of preshaking in increasing the liquefaction resistance of silty sands – such as that may have taken place in the Imperial Valley of California – the authors conducted a centrifuge experiment with a sequence of base shakings similar to that extracted from the seismic history of the Wildlife site, located in the Imperial Valley. That centrifuge test, reported in detail by [16], is labeled here Experiment 1, while the main test discussed herein is labeled Experiment 2. Both experiments modeled the same deposit having the same soil characteristics, but subjected to two different sequences of base shakings. Figs. S1 and S2 of Appendix S1, respectively, show the setup and instrumentation as well as the grain size distribution of the silty sand used in both Experiments 1 and 2. That is, Figs. S1 and S2 are common to Experiments 1 and 2. Fig. 3 summarizes the sequence of shakings and 40

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As expected, the first Event B (S1) liquefied the deposit, while the Events A mostly preshook it. If the value of (ru)max is taken to measure the resistance to liquefaction of the soil to the corresponding event, the following conclusions are obtained for liquefaction resistance, shear wave velocity, and relative density based on the measured data in Fig. 3c, d and e, respectively: ● There was a significant increase in the liquefaction resistance of the silty sand as the deposit was exposed to an increasing number of earthquakes, with the excess pore pressure generation decreasing for both Events A and B (Fig. 3c). ● The occurrence of an Event B tended to decrease the liquefaction resistance of the deposit to the immediately subsequent Event A (e.g., compare S11 and S13 in Fig. 3c). However, it took only two to three additional Events A to undo the damage done by the Event B and bring the liquefaction resistance of the deposit back up to where it was before the Event B occurred. Furthermore, this detrimental effect of Events B gradually faded away as the total number of earthquakes increased. The net effect after the 66 shakings was a significant increase in liquefaction resistance to both Events A and B (Fig. 3c). ● This increase in liquefaction resistance with the number of earthquakes was not reflected in a significant increase of the normalized shear wave velocity of the soil, Vs1 - measured by bender elements throughout the experiment - with Vs1 changing less than 10% between the beginning and the end of Experiment 1 (Fig. 3d). ● There was a consistent and steady densification of the deposit, from Dr = 38% at the beginning to Dr = 50% at the end of Experiment 1 (Fig. 3e). The results above for Experiment 1, in conjunction with the centrifuge study presented by [14] for uncompacted recent fills, are used here as a starting point for the interpretation of Experiment 2. The comparison of results between Experiments 1 and 2, conducted at the end of the paper herein, serve to further explore the evolution of liquefaction resistance and other relevant parameters in the same silty sand deposit subjected to two different seismic environments. The databases generated by both Experiments 1 and 2 are available in digital form through a Database paper [19]).

Fig. 3. Key Results of Experiment 1 reported by El-Sekelly et al. [13]: (a) shaking sequence of 66 shaking events showing the peak base acceleration, apb, of each Event A or B; (b) sequence of 66 shaking events showing the measured peak shallow acceleration, aps, of each Event A or B (0.75 m below surface); (c) maximum pore pressure ratio measured for the whole deposit in each shaking; (d) values of Vs1 measured at three elevations by bender elements before each shaking, and average Vs1 for the deposit; and (e) value of relative density, Dr, obtained from the initial Dr and subsequent vertical LVDT measurements.

4. Centrifuge Experiment 2

some key results of Experiment 1. As mentioned before, this sequence of shakings in Experiment 1 was approximately tailored to simulate in a crude way the earthquake history felt by the liquefiable layer at the Wildlife site since deposition (estimated to be about a century). The sequence shown in Fig. 3a consists of 66 shakings of alternating Events A and B. The more numerous Events A in Fig. 3a, consisting of 5 cycles of a base acceleration of amplitude, apb ≈ 0.03–0.04 g, represent actual local earthquakes of low magnitude and short duration that usually do not liquefy the Wildlife layer but induce some excess pore pressures which should have a beneficial preshaking effect on the soil. The less numerous Events B, consisting of 15 cycles of base acceleration, apb ≈ 0.04–0.05 g represent larger magnitude earthquakes that may liquefy (and in some cases, have liquefied) the layer at the Wildlife site, partially or totally canceling the beneficial effects of the preshaking. As shown in Fig. 3a, the ratio used in Experiment 1 was ten Events A for each Event B, with a regular pattern that is repeated several times between shakings S1 (Event B) and S66 (Event A). Enough time was always allowed between any two successive shakings to allow for full dissipation of excess pore pressures in the soil, which was monitored at all times while the experiment was running. Fig. 3b shows the measured peak accelerations at a shallow elevation (about 0.75 m below the surface). Fig. 3c shows a consistent but not straightforward pattern of evolution of the measured maximum pore pressure ratio, (ru)max, for each of the 66 shakings, where (ru)max invariably happens at a shallow depth.

Experiment 2 presented herein was conducted at a centrifuge acceleration of 25g in a 2-D laminar container at Rensselaer Polytechnic Institute's (RPI) centrifuge facility. More details about the container, soil and sensors used in Experiment 2 discussed herein are included in Figs. S1 and S2 of Appendix S1 in the Supplemental material. The centrifuge model was instrumented with pore pressure transducers, accelerometers, vertical LVDTs, and bender elements. An important parameter which was monitored throughout the experiment was the Vs, and the corresponding normalized Vs1, obtained with Eq. (2). The value of Vs1 for the whole deposit is necessary to characterize it and locate any shaking on the CSR-Vs1 liquefaction field graph of Fig. 2, as well as to monitor the effect of the various shakings on Vs1. Due to this importance of Vs1, the shear wave velocity of the soil was obtained in Experiment 2 using two different methods: (i) direct measurements with bender elements, which were conducted before each of the shakings; and (ii) indirect measurements via backfiguring Vs and Vs1 from the accelerometer records obtained during weak shakings conducted specifically for this purpose before certain shakings in the sequence, and using an established System Identification (SI) technique, see [20–22]. The results of these two sets of measurements are discussed later herein. The direct measurements using bender elements were used as the primary source of information for Vs1, with the SI method utilized for independent verification. The bender element technique was described in detail by [23,24]. It 41

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uses shear waves propagating in the horizontal direction and polarized in the vertical direction, with measurements conducted at three different elevations within the model deposit. At each of these elevations, two bender elements were placed at an actual (model) horizontal distance, d = 15 cm, playing the roles of sender and receiver sensors. Predefined mechanical shear waves were sent from the sender bender element and detected by the corresponding receiver bender element. In all cases, the sender bender element was excited with one sine wave cycle having a frequency of 7000 Hz [25]. The first arrival time of the wave was defined and used to calculate the time, t, needed for the wave to propagate between the two bender elements. The wave velocity at that elevation, Vs, was then calculated using the relation VS = d / t . Fig. S2 in Appendix S1 in the Supplemental material shows the grain size distribution of the silty sand used to construct the centrifuge model in Experiment 2. It is the same soil successfully used by [26] for some of their centrifuge tests, and it is also the same soil used in Experiment 1 discussed in the previous section. The sand was used to construct a uniform saturated model deposit 24 cm deep representing a prototype depth of about 6 m at a 25g centrifuge acceleration, having an initial target relative density of 35%. The actual relative density after model construction was 38% for Experiment 1% and 30% for Experiment 2. The preparation procedure of the centrifuge models in Experiments 1 and 2 followed the standard technology used for saturated tests in the geotechnical centrifuge facility at Rensselaer Polytechnic Institute as follows: a)the sand and silt were dry-mixed together using concrete mixers to ensure uniformity, b) a funnel was used to deposit the mix into the container slowly with very low drop height to avoid segregation and loss of fines, c) the required density was achieved by applying pressure on the silty sand layers every 2 cm, d) the shear wave velocity was measured at multiple locations using bender elements to ensure uniformity. Random checks were also performed throughout the process before and after the experiment to ensure no significant changes in soil characteristics, and e) carbon dioxide is then introduced to the model in order to replace the air; and, finally, water is introduced by percolation for 12 h under vacuum to fully saturate the sand deposit. Therefore, in every respect, the sand deposit used herein for Experiment 2 was very similar to that used by [16] for Experiment 1, already discussed.

surface). Target Event A is defined as 5 sinusoidal cycles of a peak base acceleration, apb = 0.035g in prototype units, and is consistent with the way an Event A was defined before for Experiment 1. Event B is defined as 15 sinusoidal cycles of a peak base acceleration, apb = 0.04g in prototype units, again consistent with the Event B for Experiment 1. On the other hand, Event C in Fig. 4, defined as 15 sinusoidal cycles of a larger peak base acceleration, apb = 0.1g in prototype units for Experiment 2, had no counterpart in Experiment 1. That is, Experiment 2 discussed herein includes several Event C shakings, which are much stronger than any event used in Experiment 1 reported by [16]. This means that, in addition to the different shaking sequences between the two centrifuge tests, Experiment 2 corresponds to a significantly stronger seismic environment than that of Experiment 1. The prototype frequency in all cases in Experiment 2 was 2 Hz, so the prototype durations of the two records in Fig. 4 are about 7.5–8.0 s for Events B and C, and 2.5–3.0 s for Events A (unless otherwise specified, all parameters in the rest of this paper are specified in prototype units). The 15-cycle duration of the Events B and C corresponds approximately to earthquakes of moment magnitude, Mw ≈ 7.5; while the 5-cycle duration of the Events A corresponds to Mw ≈ 6 [27]. These three event types were applied in the 52-event sequence shown in Fig. 5a, which is substantially different from the sequence for Experiment 1, described by [16] and reproduced in Fig. 3a. The first applied base shaking in Fig. 5a (S1) was the Event B of Fig. 4b, followed by shaking S2, corresponding to the Event C of Fig. 4c, followed by S3, corresponding to the Event A of Fig. 4a. In fact, the three acceleration time histories included in Fig. 4 are the actual accelerograms applied to the deposit in these shakings S1, S2 and S3 of Experiment 2. The five subsequent shakings, S3 to S7 in Fig. 5a, were all Events A, followed by S8 which was an Event B. This sequence of one Event B, then one Event C, followed by five Events A, was then repeated, as shown by Fig. 5a until the last three shakings, which were an Event B followed by an Event C followed by the final shaking, another Event B. As in Experiment 1, enough time was always allowed in Experiment 2 between any two successive shakings to allow for full dissipation of excess pore pressures in the soil, which was monitored at all times while the experiment was running. It was decided to start the sequence in Fig. 5a with an Event B (S1), in order to provide a baseline for the liquefaction response of the deposit to Events B. That is, S1 was intended to measure the response and liquefaction resistance of the virgin, just deposited silty sand, with S1 expected to induce liquefaction of a deposit which was at this point indistinguishable from a recent uncompacted fill. It must be noted that the sequence shown in Fig. 5a for Experiment

5. Types and sequence of shakings in Experiment 2 Fig. 4 shows the three basic acceleration times histories applied at the base of the model deposit in Experiment 2, as well as the accelerations recorded at a shallow elevation (about 0.75 m below the

Fig. 4. Base and shallow (0.75 m below surface) acceleration time histories for the first Event A, first Event B, and first Event C in Experiment 2. 42

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Fig. 5. Key Results of Experiment 2: (a) shaking sequence of 52 shaking events showing the peak base acceleration, apb, of each Event A, B or C; (b) maximum pore pressure ratio measured for the whole deposit in each shaking; (c) values of Vs1 measured at three elevations by bender elements before each of the shakings, and average Vs1 for the deposit; and (d) value of relative density, Dr, obtained from the initial Dr and subsequent vertical LVDT measurements.

2 does not correspond to any specific field site or location. This is unlike Experiment 1, which explicitly tried to approach in a crude way the actual seismic history experienced by the liquefiable layer at the Wildlife site since deposition [16]. In addition to the sequence of 52 Events A, B and C shown in Fig. 5a, six weak shakings having much smaller peak accelerations, apb = 0.014–0.017 g, labeled I to VI, were also applied to the base of the model before some specific shakings, as listed in Table 1. The purpose was to provide an independent set of measurements of Vs1 using System Identification (SI), throughout the experiment that could be compared with the Vs1 measured by the bender elements. Each one of these weak shakings consisted of 5 cycles of a prototype frequency of 2 Hz. A value of Vs1 was backfigured for each one of these six weak shakings from the measured horizontal acceleration response at different depths using the System Identification (SI) procedure developed by [20–22]. In this

method, the cyclic shear stress-strain loops are first estimated from the accelerations, and then each of these loops is used to estimate an average secant shear modulus, G. Finally, this secant modulus is converted into the small strain modulus, Gmax, using an appropriate shear modulus reduction curve [23]. The shear wave velocity, Vs, is calculated with VS = Gmax / , As shown by Table 1, while the six weak shakings were originally meant to be nondestructive (ND), some of them did in fact cause a limited pore pressure buildup, so they did contribute to the preshaking of the deposit. This is especially true for Shaking I which generated an (ru)max = 0.22 before the first Event B. Therefore, that first Event B (S1) was in fact applied to a deposit that had been preshaken once. A value of Vs1 = 89 m/s was measured initially by weak Shaking I, which gradually increased to Vs1 = 117 m/s for weak Shaking VI. These values are similar (within 10%), to the corresponding bender element

Table 1 Characteristics of six very weak shakings preceding selected Events A, B and C in Experiment 2. Shaking #

Before Shaking #

apb (g)

(ru)max

Vs1 (m/s)

I II III IV V VI

S1 (B) S3 (A) S10 (A) S36 (B) S50 (B) S52 (B)

0.014 0.015 0.016 0.016 0.017 0.017

0.22 0.16 0.1 0 0 0.01

89 96 101 110 113 117

43

(from SI)

Vs1 (m/s) 94 97 99 104 106 110

(from Bender elements)

(CSR)7.5 0.028 0.03 0.032 0.032 0.033 0.033

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Table 2 Events A immediately following a sequence of Events B and C in centrifuge Experiment 2 (see Fig. 8). Shaking #

apb (g)

Maximum Excess Pore Pressure Recorded at Shallowest and Deepest Piezometers (ru)max

3 10 17 24 31 38 45

0.035 0.037 0.038 0.033 0.033 0.033 0.033

@ 0.8 m

0.86 0.75 0.63 0.2 0.15 0.12 0.12

(ru)max

Liquef-ied?

Δεv (%)

Vs1 (m/s) before event

Dr (%) before event

(CSR)7.5

Yes Yes No No No No No

0.130 0.082 0.063 0.024 0.019 0.012 0.008

97 99 101 103 105 107 108

42 47 50 53 55 56 57

0.06 0.064 0.065 0.057 0.058 0.058 0.058

Liquefied?

Δεv (%)

Vs1 (m/s) before event

Dr (%) before event

(CSR)7.5

Yes Yes Yes Yes Yes? No No No No

1.15 0.09 0.13 0.12 0.09 0.02 0.01 0.008 0.013

94 96 96 98 100 104 105 106 110

30 43 48 51 53 55 56 57 58

0.14 0.13 0.13 0.14 0.12 0.11 0.11 0.11 0.11

@ 5.38 m

0.12 0.095 0.08 0.04 0.03 0.02 0.013

Table 3 Events B in centrifuge Experiment 2 (see Fig. 10). Shaking #

apb (g)

Maximum Excess Pore Pressure Recorded at Shallowest and Deepest Piezometers (ru)max

1 8 15 22 29 36 43 50 52

0.048 0.045 0.046 0.048 0.04 0.036 0.035 0.034 0.035

@ 0.8 m

0.965 0.925 0.9 0.835 0.81 0.2 0.15 0.1 0.15

(ru)max

@ 5.38 m

0.4 0.2 0.14 0.1 0.085 0.035 0.02 0.013 0.02

measurements of Vs1, which increased from 94 m/s to 110 m/s at the times of the same six weak events (Table 1).

in the corresponding Event A is affected by an immediately preceding 2shaking sequence consisting of stronger Events B and C.

6. Results of Experiment 2

6.1. Soil densification and evolution of Vs1

This section presents the results of the measurements in the centrifuge test before, during and after the 52 shakings of Experiment 2. The data -always in prototype units- are displayed in Tables 2–4 and Figs. 5–11. The first trends examined are the evolution in the value of the Vs1 measured by the bender elements with successive Events A, B and C, as well as the relation between Vs1 and the densification of the deposit caused by the successive shakings. After this, most of the attention focuses on the piezometric readings, including comparative discussions of pore pressure buildup and liquefaction/no liquefaction occurrence caused by similar Events A, similar Events B, or similar Events C after an increasing degree of preshaking by previous events. In this context, again, a smaller pore pressure buildup caused by the same type of Event - and especially a switch from liquefaction to no liquefaction - is interpreted to mean an increased liquefaction resistance of the soil deposit. Attention is also paid to how the pore pressure buildup

Fig. 5d shows the evolution of the overall relative density (Dr) of the deposit throughout the experiment. The density of the model was calculated by dividing the mass of the soil by the volume which it occupies in the container. While the mass remained constant throughout the experiment, the volume changed due to the settlement (S) corresponding to each shaking event. The initial prototype value of H ≈ 6 m was reduced in this calculation throughout the test as the deposit densified. The value of Dr increased fast with the first two strong Events B and C (from 30% to 42%), and then kept increasing more slowly. Overall the deposit experienced significant densification, from Dr = 30% at the beginning to Dr = 58% at the end of Experiment 2. Fig. 5c shows the evolution of the normalized shear wave velocity (Vs1) measured by bender elements and normalized using Eq. (2) throughout the experiment at different depths, as well as the average Vs1 for all depths. It is seen in Fig. 5c that the upper layers of the deposit

Table 4 Events C in centrifuge Experiment 2 (see Fig. 9). Shaking #

apb (g)

Maximum Excess Pore Pressure Recorded at Shallowest and Deepest Piezometers (ru)max

2 9 16 23 30 37 44 51

0.092 0.094 0.094 0.093 0.095 0.1 0.096 0.094

0.95 0.95 0.94 1 1 1 0.9 0.85

@ 0.8 m

(ru)max

Liquefied?

Δεv (%)

Vs1 (m/s) before event

Dr (%) before event

(CSR)7.5

Yes Yes Yes Yes Yes Yes Yes Yes

1.862 0.799 0.504 0.413 0.308 0.319 0.221 0.205

94 97 96 100 101 104 104 105

35 44 48 51 53 55 56 57

0.24 0.25 0.25 0.24 0.25 0.27 0.25 0.25

@ 5.38 m

0.9 0.6 0.5 0.5 0.46 0.42 0.28 0.28

44

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6.3. Maximum pore pressure profiles for Events A, B and C throughout Experiment 2 Fig. 7a-c shows the maximum excess pore pressure profiles induced by the various Events A, B and C throughout the experiment. Fig. 7a includes the response of all Events A happening immediately after a two-shaking sequence of Events B and C. The figure shows that S3 and S10 caused liquefaction of the top 0.5–1 m of the deposit. However, the rest of Events A do not seem to have caused liquefaction anywhere in the deposit (see also Table 2). Fig. 7b shows the response of all Events B that occurred immediately before an Event C (that is, all Events B except for S52). The figure indicates that S1 liquefied about 2–2.5 m of the deposit. Gradually, the liquefaction depth decreased as the model was subjected to an increasing number of shaking events, until the sequence reached Event B S36, which did not cause liquefaction anywhere (see also Table 3). Fig. 7c shows the response of all eight Events C, which invariably took place immediately after an Event B in the shaking sequence. The figure shows that all Events C liquefied at least part of the deposit, with the liquefaction depth gradually decreasing as the model was subjected to more and more shakings (the depth of liquefaction was reduced from 5 m in S2 to about 1 m in S51 (see also Table 4). Fig. 7d-f present the measured peak acceleration profiles for different Events A, B and C. The profiles in Figs. 6 and 7 suggest that the maximum pore pressure ratio of the whole profile, (ru)max, which shows how close to liquefaction was the deposit for a given shaking, tended to occur at shallow depths. These values of (ru)max are plotted versus shaking number in Fig. 5b. Detailed inspection of the piezometric records revealed that for all Events A, (ru)max was invariably recorded by the shallowest piezometer, located at a depth, z = 0.8 m. Therefore, for the Events A listed in Table 2, (ru)max = (ru)max @ 0.8 m. This was also true for almost all Events C, with (ru)max = (ru)max @ 0.8 m. In one Event B and a few Events C which reached liquefaction, (ru)max occurred at depths which were still shallow, 0.8 m ≤ z ≤ 2 m, with (ru)max @ 0.8 m being close to, but slightly smaller than (ru)max. More details about the pore pressure and settlement responses of the deposit to shaking Events A, B and C are provided under the next two headings.

Fig. 6. (a) Maximum excess pore pressure profiles recorded in the first Event B (S1), first Event C (S2), and first Event A (S3), Experiment 2; (b) Maximum excess pore pressure profiles recorded in the first Event B (S1) and first Event A (S2), Experiment 1 [16].

6.4. Events A and C throughout Experiment 2

tend to stiffen somewhat more than the lower layers, as the value of Vs1 for the top layer increases at a slightly higher rate, deviating from the average value. Fig. 5c shows that the overall Vs1 of the deposit increased 10–15% throughout the experiment, starting at 93–95 m/s and ending at 110 m/s. This overall increase in stiffness is consistent with the increase in relative density already mentioned. All these changes in Vs1, both within a sequence of preshaking Events A, and throughout the experiment, are small, with the total range 93–110 m/s still clearly located at the very low end of the Andrus & Stokoe and Kayen et al. liquefaction charts (Figs. 1 and 2).

This heading presents an additional discussion of the trends shown by all Events A and C, based on Figs. 8 and 9 and Tables 2, 4. Figs. 8 and 9 plot the following parameters versus shaking number (S1 to S52):

• Figs. 8c and 9c: (r ) •

6.2. Pore pressure profiles for initial Events B, C and A (S1, S2 and S3) Fig. 6a compares the profiles of maximum excess pore pressure measured in shaking S1 (Event B), the subsequent shaking S2 (Event C), and the following shaking S3 (Event A). Fig. 6a also includes the line of initial vertical effective stress, which indicates if liquefaction has been reached at a given depth. As expected, the excess pore pressures caused by Event A are smaller than those induced by Event B, which are in turn smaller than those caused by Event C. This is consistent with the smaller base acceleration and shorter duration of Event A, as compared to Events B and C. Also, although Events B and C have the same duration, the Events B have about half the base acceleration amplitude of the Events C. The pore pressure profiles in Fig. 6a suggest that S1 liquefied the deposit down to about 2–2.5 m, S2 liquefied the deposit down to about 5 m, and S3 liquefied only the top 1 m of the deposit.

u max @ 5.38 m, which is the maximum pore water pressure ratio recorded by the deepest sensor in the deposit, located at a depth, z = 5.38 m. Figs. 8b and 9b: Δεv, which is the permanent vertical strain for the whole deposit caused by the corresponding Event A or C. This Δϵv = (S/H) x 100% was calculated from the settlement S measured by the vertical LVDT at the ground surface, and from the distance H between the LVDT and the base of the deposit. The initial prototype value of H ≈ 6 m was reduced in this calculation throughout the test as the deposit densified.

The following trends are clear in Figs. 8 and 9:

• In Fig. 8c, (r )

u max @ 5.38 m decreases within each 5-Event A sequence, but jumps up for the next Event A after each 2-shaking sequence of Liquefying Events B and C, with a net tendency for (ru)max @ 5.38 m to decrease over time, so that while this parameter is in the range 0.065–0.12 for Events A at the beginning of Experiment 2, it is only 0.002–0.013 at the end of the test. This suggests that the liquefaction resistance of the deposit increased over time despite the

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Fig. 7. Profiles of (a-c) maximum excess pore pressure; and (d-f) maximum acceleration for selected shaking Events A, B and C, Experiment 2.

• •

periodic decrease in liquefaction resistance that occurred after the liquefaction produced by an Event C. In Fig. 8b, Δεv shows essentially the same trends as those just discussed for (ru)max @ 5.38 m for the same Events A. That is, Δεv decreases within each 5-Event A sequence, jumps immediately after Events B and C, and decreases significantly between the beginning and end of the test. In Fig. 9b-c, both (ru)max @ 5.38 m and Δεv decrease monotonically over time for Events C, indicating again that the net effect of the particular shaking sequence used in Experiment 2, involving at the two extremes both liquefaction (C) and preshaking (A) events, was to increase the liquefaction resistance of the deposit. This increase in liquefaction resistance over time is also reflected in a decrease in depth of liquefaction during Events C, as noted previously in this paper. This is clear in Fig. 7c, which includes the maximum pore pressure profiles of all Events C. For shaking S2, which is the first Event C in Fig. 7c, the depth of liquefaction was about 5 m, while for the last Event C, S51, the depth of liquefaction was less than 1 m. This overall increase in liquefaction resistance of the deposit over time is consistent with the significant increase in relative density with time, from 30% at the beginning to 58% at the end of Experiment 2.

6.5. Events B throughout Experiment 2 This heading presents a discussion of the trends shown by Events B, similar to the discussion of Events A and C presented in the previous sub-section. This discussion of Events B is based on Fig. 10 and Table 3. It is important to note that the actual intensity of the base excitation of Events B decreased somewhat during the experiment, as follows:

• Shakings S1 to S22: 15 cycles of maximum base acceleration, a ≈ 0.045–0.048 g • Shakings S29 to S52: 15 cycles of maximum base acceleration, a ≈ 0.034–0.04 g

pb pb

Fig. 10 plots the following parameters versus shaking number for all Events B: , which is the maximum pore water pressure • Fig. 10c: (r ) ratio recorded by the deepest sensor in the deposit. • Fig. 10b: Δε , which is, again, the permanent vertical strain calcuu max @ 5.38 m v

lated the same way already discussed for Figs. 8b and 9b. The following trends are clear in Fig. 10:

• Shakings S1 to S22 have more or less the same a 46

pb

≈ 0.045–0.048 g.

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Fig. 8. Histories of permanent vertical strain for the whole deposit measured by the vertical LVDT at the ground surface and maximum excess pore pressure ratios measured in Events A throughout centrifuge Experiment 2: (a) shaking sequence; (b) measured ∆εv; and (c) measured maximum pore pressure ratio at a depth of 5.38 m, (ru)max @ 5.38 m.

Fig. 9. Histories of permanent vertical strain for the whole deposit measured by the vertical LVDT at the ground surface and maximum excess pore pressure ratios measured in Events C throughout centrifuge Experiment 2: (a) shaking sequence; (b) measured ∆εv; and (c) measured maximum pore pressure ratio at a depth of 5.38 m, (ru)max @ 5.38 m.

Both (ru)max @ 5.38 m and Δεv decrease monotonically with shaking number, in a way similar to that shown in Fig. 9 for Events C. This similarity between the trends for Events B and C is consistent with the similar behavior shown by the corresponding profiles of excess pore pressure versus depth for these two types of events in Fig. 7; in both cases there is a systematic decrease in the depth of liquefaction. Shaking S29: In this Event B, for which there is a decrease in the intensity of the base shaking to apb = 0.040 g (from apb = 0.045–0.048 in the previous Events B), the monotonic decrease of (ru)max @ 5.38 m and Δεv noted in the previous bullet continues. Shakings S36 to S50: In these shakings taken as a group (which can be done because in all of them the base excitation has decreased to the narrow range of accelerations, apb = 0.034–0.036 g), (ru)max @ 5.38 m and Δεv decrease even faster compared to the trend in the previous Events B (S1 to S29). Furthermore, as shown by Table 3, for the shallowest piezometer located at z = 0.8 m, the measured value of (ru)max @ 0.8 m, which had shown values close to 1.0 for Events B until then, suddenly drops to less than 0.2 for Events B S36-S50. It is also noticed from Table 3 that the value of Vs1 increases systematically with each successive Event B, being about 94 m/s before shaking S1 and about 106 m/s before Event S50. This 13% increase in Vs1 is not very important in practical terms, as both 94 and 106 m/s are still small values corresponding to the very flat part of the curve in the Andrus and Stokoe and Kayen et al. charts of Fig. 2. Shakings S50 and S52: It is important also to perform a one-to-one comparison between S50 and S52, which are both Events B. These two Events B are special in that no preshaking takes place between the two (no Event A between S50 and S52, see Fig. 10). The only thing that happens between these two Events B is Event C S51, which liquefied the top 1 m or so of the deposit. So, as the base

shaking intensity is very similar for S50 and S52 (apb = 0.034 g), any dramatic difference in response (for example, a change from nonliquefaction to liquefaction), could be attributed mostly to intervening Event C S51. While Δϵv, (ru)max @ 5.38 m and (ru)max @ 0.8 m increase due to this Event C S51 in Fig. 10b-c and Table 3, they all continue to be small after the change, certainly not big enough to convert the Event B back from a nonliquefaction to a liquefaction event. This can probably be attributed to the fact that Event C S51 only induced liquefaction at shallow depths (Fig. 7c), not causing much of a disturbance at deeper elevations.

• •

•

6.6. Relation between densification and pore pressure ratio for Experiment 2 Inspection of the variation of (ru)max @ 5.38 m and Δϵv throughout Experiment 2 for Events A, C and B in Figs. 8, 9 and 10, respectively, reveals that the two parameters follow very similar patterns. That is, both (ru)max @ 5.38 m and the overall Δϵv of the deposit: (i) decrease monotonically with each new Event C; (ii) decrease monotonically with each new Event B; (iii) decrease monotonically with each new Event A within each 5-Event A sequence; (iv) both (ru)max and Δϵv jump to a higher value for the Event A immediately after a 2-shaking sequence of Events B and C, with the Event C invariably causing liquefaction; and (v) these jumps in (ru)max @ 5.38 m and Δϵv after the Event C are rapidly cancelled by the subsequent Events A, with the net result being a significant decrease in both (ru)max @ 5.38 m and Δϵv for Events A between beginning and end of the 52-shaking experiment. While Figs. 8–10 plotted the (ru)max @ 5.38 m measured at a depth of 5.38 m, any other depth could have been used with similar results. It was decided to correlate Δϵv with (ru)max, where (ru)max is the absolute maximum pore pressure ratio of the whole deposit plotted in Fig. 5b, 47

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above 0.8, the slope drastically decreases showing rapidly increasing values of Δϵv as the soil approaches liquefaction. The consistency between the (ru)max and Δϵv results in Fig. 11, obtained independently from piezometric and LVDT readings, further increase the confidence on the key results obtained in centrifuge Experiment 2. These parallel trends between (ru)max (or (ru)max @ 5.38 m), and Δϵv, shown by Figs. 8–10 and confirmed by the correlation of Fig. 11, are most probably due to the combination of two phenomena: i. If one makes the reasonable assumption that (ru)max represents well the level of maximum pore pressures generated by the corresponding event, with the shape of the maximum pore pressure profile versus depth being similar for different events and thus with this shape playing a minor role, then (ru)max is a measure of the total increase in effective vertical pressure, ∆σ’v, that takes place when the soil reconsolidates and those excess pore pressures are dissipated at the end of the test. It should be expected that ∆σ’v - and thus also (ru)max – should be closely related to Δϵv, absent significant changes during the experiment in the overall compressibility of the sand deposit. ii. An increased value of the settlement of the deposit for a given shaking, and thus also of Δϵv = S/H, results in an increased amount of the pore water volume that must be expelled from the soil. Typically this consolidation process in liquefied soils starts with water being expelled in the lower part of the deposit which is dissipated upward. This results in an upward flow of water, with the corresponding upward hydraulic gradient causing an increased excess pore water pressure in the top part of the deposit, where (ru)max typically occurs. This is another explanation of why the (ru)max should be closely related to Δϵv.

Fig. 10. Histories of permanent vertical strain for the whole deposit measured by the vertical LVDT at the ground surface and maximum excess pore pressure ratios measured in Events B throughout centrifuge Experiment 2: (a) shaking sequence; (b) measured ∆εv; and (c) measured maximum pore pressure ratio at a depth of 5.38 m, (ru)max @ 5.38 m.

In other words, in the phenomenon (i), Δϵv is the result of (ru)max, while in the phenomenon (ii), Δϵv is one of the causes of (ru)max. Inspection of the settlement time history of individual shakings reveals that part of the settlement and of Δϵv occurs before (ru)max is reached, with the remaining Δϵv happening afterwards. This supports the previous speculation that the parallel trends between (ru)max and Δϵv are most probably due to a combination of the two phenomena (i) and (ii) listed above. 7. Comparison of results between Experiments 1 and 2 The purpose of this section is to compare the general behavior of the soil deposits in Experiment 1 (presented by [16]) and Experiment 2 (discussed in this paper). 7.1. Similarity between the two deposits In a first step, it is necessary to verify that the two deposits had indeed similar characteristics and liquefaction resistances at the beginning of the two experiments. This is done through the following comparisons:

• The initial relative densities were in the range, D = 30–38%, with the deposit in Experiment 2 being slightly looser (Figs. 3e and 5d). • The initial normalized shear wave velocities for the whole deposit r

Fig. 11. Correlation between measured maximum pore pressure ratio for the whole deposit, (ru)max, and the permanent vertical strain, ∆εv measured in the same event, all 52 shakings, Experiment 2. The two curves are the least square best fit for the data points of Experiments 1 and 2.

•

which as discussed earlier occurred invariably at a shallow depth. The soundness of this line of reasoning is illustrated by Fig. 11, which shows the relation between (ru)max - representing the excess pore pressure ratios at shallow depths - and Δϵv for all 52 shaking events, be them Events A, B or C. A single curve has been fitted to the data points which show little scatter, with the relation being linear up to (ru)max ≈ 0.8 (labeled Best fit, Experiment 2). As (ru)max increases to values 48

were the same, Vs1 = 94 m/s, with this Vs1 being about the same at different depths showing that both were homogeneous deposits (Figs. 3d and 5c). The pore pressure responses of both deposits to the initial Events B and A were very similar (Figs. 6a and 6b). The similarity in maximum pore pressure profiles for initial Events B in Fig. 6a-b is especially striking, with both deposits liquefying down to z = 2–2.5 m and with excess pore pressures at larger depths being essentially the same (20–23 kPa). The profiles for Events A in Figs. 6a and 6b are also similar, with both shakings liquefying the

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•

deposit to z < 1 m, and with excess pore pressures at larger depths in the range 5–10 kPa. This similar pore pressure responses to initial Events A and B was accompanied by very similar settlements (Δϵv = 0.09–0.13% for the two Events A, and Δϵv = 0.99–1.15% for the two Events B).

These comparisons demonstrate that the two model deposits in Experiments 1 and 2 were initially very similar, with the differences throughout the two tests in pore pressure responses and values of Δϵv, Dr and Vs1 caused mainly by the two different shaking sequences. 7.2. Differences in shaking sequence As discussed before and depicted in Figs. 3a and 5a, the main differences between the two shaking sequences are:

• The presence of strong shaking Events C in Experiment 2 which are absent in Experiment 1. • The lower relative number of Events A compared to Events B in •

Experiment 2 (5:1 ratio in Experiment 2, 10:1 ratio in Experiment 1). The occurrence of two strong Events B and C before the next Event A in Experiment 2, compared to only a strong Event B in Experiment 1.

Fig. 12. Approximately unique correlation between the relative density before the shaking, Dr, and the maximum pore pressure ratio for the whole profile, (ru)max, generated by the 5th Event A after a strong Event B (Experiment 1), or the 5th Event A after two strong Events B & C (Experiment 2), see Figs. 3 and 5.

deposited by Dry Pluviation. Significantly different lines relating Δϵv and (ru)max were obtained by [17] for a different soil, a clean sand deposited both by Dry Pluviation and Hydraulic Filling, confirming that curves such as those in Fig. 11 reflect the overall compressibility of the soil deposit.

7.3. Comparison of results The summary results of Experiment 1 and 2 are shown in Figs. 3 and 5. Figs. 3c and 5b show the absolute recorded maximum pore pressure ratio, (ru)max associated with each shaking of the sequence. The trend in both experiments is generally similar. That is, the (ru)max of Events A and B decrease with time and are characterized by a jump for an Event A immediately after an Event B (or after a sequence of Events B and C). Events C in Experiment 2 always liquefied the deposit. A main difference between Experiments 1 and 2 is associated with the rate of reduction of (ru)max for Events A within each preshaking sequence. This rate of reduction of (ru)max is much higher in Experiment 2 (e.g., compare (ru)max for the 5 Events A S13-S17 in Fig. 3c, with the similar 5 Events A S10-S14 in Fig. 5b). This faster effect of preshaking on Events A is probably due to the presence of strong Events C in Experiment 2 but not in Experiment 1. The very large drop in Fig. 5b of the (ru)max of Event B S36 compared to previous Event B S29 in Experiment 2, was influenced by the fact that there was a significant reduction in maximum base acceleration, apb, between the two shakings (Table 3). Therefore, this drop cannot be used for comparison of similar Events B in Experiment 2, or to draw any inference between Experiments 1 and 2. Figs. 3d and 5c show the change in Vs1 throughout Experiments 1 and 2. Again, the trend is generally the same and is characterized by a slight increase in Vs1 with time. The occurrence of Events C in Experiment 2 makes the deposit more heterogeneous, with Vs1 increasing faster at shallow depths (Fig. 5c). This effect is not present in Experiment 1 where the Events C do not exist, with the sand deposit continuing to be quite homogeneous throughout the test (Fig. 3d). Figs. 3e and 5d show the change in relative density, Dr, throughout each experiment. Again, the rate of increase in Dr is much higher in Experiment 2, probably due to a combination of effects associated with: (i) the presence of strong shaking Events C in Experiment 2; and (ii) the fact that the deposit was slightly looser at the beginning of Experiment 2. The unique relationship between Δϵv and (ru)max for all shakings of Experiment 2, is presented in Fig. 11 and was previously discussed. A similar unique relation between Δϵv and (ru)max, also valid for all shakings, had been found by [16] in Experiment 1, and is reproduced here as the curve labeled “Best fit, Experiment 1” in Fig. 11. The two lines for Experiments 1 and 2 are essentially identical up to (ru)max ≈ 0.8, again confirming that the two deposits were very similar in every respect. These two deposits consisted of the same silty sand

7.4. Correlation between Dr and (ru)max As mentioned above, the faster reduction of (ru)max for Events A in Experiment 2, is probably due to the presence of Events C in this test. Similarly, it was noted that there is faster densification in Experiment 2, probably also due to these Events C. This suggests the possibility of using the value of Dr in both Experiments 1 and 2, as a predictor of (ru)max for a given Event A, other things being equal. In this hypothesis, (ru)max would be uniquely related to Dr for both tests, as both parameters are affected in a similar way by the presence or absence of strong Events C in Experiments 1 and 2. Fig. 12 shows (ru)max versus Dr, for all shakings in Experiments 1 and 2 corresponding to the 5th Event A after a strong Event B in Experiment 1, or for a similarly located 5th Event A after two strong Events B and C in Experiment 2. Fig. 12 confirms that the correlation between Dr and (ru)max is unique in first approximation for Experiments 1 and 2. As Dr is a parameter that in principle can be measured in the field, this correlation points to the possibility of developing practical prediction methods for the pore pressure buildup in future earthquakes, in silty sand layers located in areas of high seismicity such as the Imperial Valley. 8. Calculation of normalized cyclic stress ratio (CSR)7.5 for Experiment 2 A main objective of this paper is to plot the pore pressure response of the deposit to the various shakings during Experiment 2, as data points of “liquefaction” or “no liquefaction” on the Vs –based liquefaction graph of Fig. 2 which includes both the [8,18] charts. As shown by [13,14]: (i) the [8] chart does an excellent job in separating liquefaction and no liquefaction of recent uncompacted clean and silty sandy fills; and (ii) this same chart separates also well liquefaction from no liquefaction of clean and silty model sand deposits tested in the centrifuge. In addition, [13] showed that for the silty sands in the Imperial Valley of California – which have developed an increased liquefaction resistance after being subjected to dozens of earthquakes – the [8] chart 49

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is too conservative (see Fig. 2). Therefore, it should be expected that the first few shakings in Experiment 2, corresponding to a silty sand deposit that has not yet been preshaken or has been minimally preshaken, should plot well on the graph of Fig. 2, with the chart(s) doing a good job of predicting if the corresponding Event A, B or C (or any of the weak shakings listed in Table 1), liquefied or not the deposit. Plotting the response of the same Events A, B or C after substantial preshaking, that is in the middle or near the end of Experiment 2, should provide additional information on the effect of this preshaking on liquefaction resistance, especially in the light of the field experience provided by the Imperial Valley and reflected in the “false positives” of Fig. 2. The values of Vs1 for the deposit just before the various shakings in Experiment 2, were obtained from the bender element measurements, as listed in Tables 1–4. In order to be able to plot each shaking of Experiment 2 on the (CSR)7.5 versus Vs1 graph of Fig. 2, it is necessary also to establish the value of (CSR)7.5 for the shaking. This was done by the authors following the same procedures for centrifuge tests used by [26,14], as described in detail in Appendix S1 in the Supplemental material. The values of (CSR)7.5 obtained in Appendix S1 for the weak shakings as well as for Events A, B and C are also listed in Table 1. It must be noted that for Events B and C, having a duration of shaking of 15 cycles, the CSR was not corrected for magnitude, as these 15 cycles are assumed to correspond already to a moment magnitude, Mw = 7.5. On the other hand, for both the weak shakings and for Events A, having a duration of 5 cycles assumed to correspond to Mw = 6, the value of CSR obtained from analysis of the Event A was corrected by the Magnitude Scaling Factor, MSF [27]:

(CSR)7.5 = CSR/MSF

(3)

where the expression used for MSF in Appendix S1 in the Supplemental material is the same proposed by [8] and used for their case histories plotted in Figs. 1 and 2. This expression is MSF = (Mw /7.5)−2.56, That is, for the weak shakings and the Events A, Mw = 6.0, MSF = (6/ 7.5)−2.56 = 1.77, and (CSR)7.5 = CSR/1.77. 9. Andrus and Stokoe [8] and Kayen et al. [18] field liquefaction charts The objective of this section is to locate for Experiment 2 the Events A, B and C of Tables 2–4, as well as the weak shakings of Table 1, on the Vs-based liquefaction charts shown in Fig. 2 and repeated in Fig. 13. In order to locate a shaking on the chart, both Vs1 and (CSR)7.5 are needed. The Vs1 used herein is the same average Vs1 plotted in Fig. 5c and listed in Tables 1–4, while (CSR)7.5, also listed in Tables 1–4, was calculated as described in the previous section. Fig. 13 is divided into six plots (Fig. 13a-f), with each of the six graphs including the curves proposed by [8,18] from Fig. 2. Each plot includes three data points that correspond to immediately subsequent Events B, C, and A. That is, shakings S1, S2 and S3 (Fig. 13a), shakings S8, S9 and S10 (Fig. 13b), etc. Also included in Fig. 13a-f are data points for all six weak shakings of Experiment 2, using the data listed in Table 1, labeled SI shakings in Fig. 13a-f. In the graphs of Fig. 13, full data points correspond to shakings that liquefied the soil at any depth, and open data points correspond to shakings when liquefaction did not happen anywhere in the deposit. The plots in Fig. 13 show that all SI shakings are located almost exactly on the Andrus and Stokoe curve and below the Kayen et al.

Fig. 13. Location of shaking events of Experiment 2 relative to the Andrus and Stokoe [8] and Kayen et al. [18] field liquefaction charts. 50

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curve, with none of them causing significant excess pore pressures, certainly not enough to liquefy any part of the deposit (Table 1). Events A in Fig. 13 are generally located on or slightly below the Kayen et al. curve and above the Andrus and Stokoe curve, with the exact location changing slightly with shaking number. The behavior of Events A is interesting, as this Event liquefied the deposit for the first two events plotted in Fig. 13a-b (S3 and S10), but did not liquefy the deposit in any of the subsequent appearances of Event A (S17…. S45), plotted in Fig. 13c-f. This behavior illustrates the effect of preshaking by Events A in increasing the liquefaction resistance of the deposit to the same Events A, but does not provide a definite conclusion about the performance of the two liquefaction curves proposed by Andrus-Stokoe and Kayen et al., because of the close proximity of the data points in Fig. 13 to both curves. In this respect, the behavior of the deposit during Events B is much more interesting. Events B are all located far above both the Andrus-Stokoe and the Kayen et al. curves in Fig. 13, with the location of the point changing slightly with shaking number. Fig. 13 shows that Events B liquefied the deposit the first four times they occurred, in shakings S1, S8, S15 and S22 (Fig. 13a-d), as predicted by the two charts. It is not very clear if the fifth Event B (S29) liquefied the deposit or not (S29 is not included in Fig. 13). However, the subsequent Events B after S29 clearly did not liquefy the deposit (and induced very low excess pore pressures, (ru)max @ 0.8 m ≤ 0.2 in Table 3), as illustrated by the corresponding data points for S36 and S43 in Fig. 13e-f). That is, in these shakings S36 and S43 (as well as in subsequent Events B S50 and S52, not included in Fig. 13). Events B did not liquefy the soil starting with S36, despite both [8,18] field charts clearly predicting liquefaction. These Events B “false positives” starting with S36 are similar to the Imperial Valley “false positives” in Fig. 2, showing that centrifuge modeling mimics well -at least qualitatively- the effect of preshaking in increasing liquefaction resistance of silty sands that has been observed in the field. The behavior of Events B in Fig. 13 is also consistent with the field evidence in the Imperial Valley, that this increased liquefaction resistance by preshaking, develops without a large increase in the value of Vs1, with the data point for similar earthquake events not moving much on the liquefaction chart as the soil is subjected to successive earthquakes [16]. The location of Events C is further above the liquefaction curves in Fig. 13 than Events B. All Events C in Experiment 2 caused liquefaction, as correctly predicted by both the Andrus-Stokoe and Kayen et al. liquefaction charts. However, an aspect of these Events C that is not reflected in the comparisons in Fig. 13, is that, as Experiment 2 proceeded, the depth of liquefaction soil steadily decreased (see Fig. 7c). This decreased liquefaction depth – from about 5 m to less than 1 m, occurred with very little change in the value of Vs1 and with essentially no change in the location of the data point on the liquefaction charts of Fig. 13.

● There was a significant increase in the liquefaction resistance of the silty sand deposit to liquefaction when subjected to Events A, B and C as the deposit was exposed to an increasing degree of preshaking. This was reflected in the facts that Events B liquefied the soil at the beginning but not at the end of the test, and the depth of liquefaction induced by Events C decreased between the beginning and end of the test (Fig. 7b-c). ● The occurrence of a strong Event C -which invariably liquefied the deposit- tended to decrease its liquefaction resistance, as measured by the response to a subsequent Event A. However, it took only two to three additional Events A to undo the damage done by the Event C and bring the liquefaction resistance of the deposit to where it was before the Event C occurred. Furthermore, this effect gradually faded away as the total number of earthquakes increased (Fig. 5b). ● This increase in liquefaction resistance with the number of earthquakes was reflected insignificant densification of the deposit, as measured by its relative density. However, the corresponding increase in the shear wave velocity of the soil, measured by bender elements, was slight, with Vs1 changing less than 10–15% between the beginning and the end of the test (Fig. 5c). ● As a result of this small change in Vs1, the increased liquefaction resistance due to preshaking was not reflected in the Vs-based liquefaction charts, consistent with the presence of a number of false positives in the [8] chart and the fact that most of these false positives are case histories from silty sand sites subjected to intense preshaking in the Imperial Valley of California (Figs. 2 and 13). ● The Andrus and Stokoe [8] and Kayen et al. [18] field liquefaction charts seem to be able to separate well liquefaction from non-liquefaction events in the case of newly deposited uncompacted fills ([13], Fig. 13a), but may be too conservative in the case of heavily preshaken silty sand deposits (Figs. 2 and 13e-f). ● These general trends in Experiment 2 are generally similar to those of Experiment 1, with some differences attributed mainly to the presence of strong Events C in Experiment 2 but not Experiment 1 (Figs. 3 and 5). ● Two approximately unique correlations were found for the silty sand deposit in Experiments 1 and 2. The first was between maximum excess pore pressure ratio and settlement generated by the same Event up to (ru)max ≈ 0.8, valid for all shakings (Fig. 11). This correlation reflects the overall compressibility of the deposit. The second correlation was between (ru)max and relative density, Dr, valid for all Events A similarly located within the shaking sequence, with this correlation being potentially useful for practical field predictions (Fig. 12) Acknowledgments The authors wish to thank the RPI geotechnical centrifuge technical staff for their help in the project and the preparation of this paper. Prof. Mourad Zeghal helped with the system identification of records from the centrifuge experiment, which is most appreciated. The research was supported by the National Science Foundation under NES-SG Grant No. 0529995; this support is gratefully acknowledged.

10. Summary and conclusions The paper investigates the influence of preshaking on the liquefaction resistance of silty sands, using centrifuge testing in conjunction with Vs-based field liquefaction charts. Centrifuge Experiment 2 was conducted on a 6 m homogeneous deposit of loose saturated silty sand subjected to 52 base shakings. Three types of shakings were applied: a strong 15-cycle shaking (Event C), a mildly strong 15-cycle shaking (Event B), and a mild 5-cycle shaking (Event A). The 52 shakings consisted mainly of seven sequences of an Event B followed by an Event C followed by five Events A. The results of Experiment 2 are compared with the field charts as well as with centrifuge Experiment 1, reported previously by [16] and conducted on a similar deposit using a different sequence of shakings. The following main conclusions are reached from the examination of the results of Experiment 2 and comparison with both Experiment 1 and the field charts:

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