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Evaluation of reliquefaction resistance using shaking table tests
Soil Dynamics and Earthquake Engineering 31 (2011) 682–691
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Evaluation of reliquefaction resistance using shaking table tests Ik-Soo Ha a, Scott M. Olson b, Min-Woo Seo c,n, Myoung-Mo Kim d a
Korea Water Resources Corporation, Daejeon, Korea Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Samsung C&T, Seoul, Korea d Department of Civil and Environmental Engineering, Seoul National University, Korea b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 July 2009 Received in revised form 1 August 2010 Accepted 3 December 2010 Available online 3 January 2011
Cases of modern and prehistoric liquefaction illustrate that sand deposits can be liquefied again (or ‘‘reliquefied’’) by a subsequent earthquake after initially liquefying during seismic shaking. In order to test the validity of two postulates regarding reliquefaction mechanisms and to examine the role of gradational characteristics on reliquefaction resistance, 1 g shaking table tests were performed using five sands with differing gradation characteristics. The test results demonstrate that the number of cycles required to reliquefy each sand decreased significantly following the 1st liquefaction event as a result of destroying the ‘‘aged’’ sand fabric developed prior to the 1st shaking event via secondary compression of the initially loose sands. Reliquefaction resistance correlated reasonably well with a proxy for cv (pD210D2.8 r ), illustrating that both the permeability and compressibility of the sand play significant roles in the post-liquefaction fabric (and hence reliquefaction resistance) formed by a sand. While the initial decrease in reliquefaction resistance supports both the Oda et al. [8] and the Olson et al. [5] reliquefaction postulates, only the Olson et al. [5] postulate reasonably explains the subsequent, large increase in reliquefaction resistance observed during the 3rd through 5th shaking events. These tests suggest that the or D10/CU) may be a useful tool coefficient of consolidation, cv ¼ kv/gwmv (or proxy values such as D210D2.8 r for evaluating reliquefaction potential in forward and inverse (i.e., paleoliquefaction) analysis. & 2010 Elsevier Ltd. All rights reserved.
1. Introduction Cases of modern and prehistoric liquefaction illustrate that after initially liquefying in response to cyclic or seismic loading, sand deposits can be liquefied again (or ‘‘reliquefied’’) by a subsequent smaller cyclic or seismic load [1–3]. As a result, understanding the liquefaction resistance of previously liquefied sites is important for both forward and inverse (i.e., paleoliquefaction) geotechnical analysis. The process of liquefaction can be simplified into three phases: (1) destruction of pre-earthquake soil structure during undrained monotonic or cyclic loading, leading to porewater pressure increase and loss of strength and stiffness in very loose to medium dense soils; (2) post-liquefaction reconsolidation and densification; and (3) post-consolidation aging [4]. Despite the increase in density associated with post-liquefaction consolidation, Olson et al. [4] argued that this process may not lead to a post-event increase in liquefaction resistance.
n
Corresponding author. Tel.: +82 2 2145 6107; fax: 82 2 2145 6630. E-mail addresses: [email protected], [email protected] (M.-W. Seo).
0267-7261/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2010.12.008
At least three postulates (which are not mutually exclusive) are available to explain this phenomenon. Olson et al. [4,5] proposed one, as follows. Thomann and Hryciw [6] suggested that liquefaction causes ‘‘effectively infinite’’ shear straining at particle contacts. This straining completely destroys the pre-existing (aged) soil structure that had developed through mechanisms such as secondary compression, preshearing, and cementation, all of which improve interlocking at particle contacts and increase liquefaction resistance. As a result of the large shear straining associated with liquefaction, the liquefied soil essentially becomes freshly deposited following post-liquefaction reconsolidation. Thus, the postevent liquefaction resistance may be lower than the pre-event liquefaction resistance because of the loss of particle interlocking [4,5]. However, Olson et al. [4,5] also argue that after sufficiently large density changes occur as the result of shaking-induced settlement and post-liquefaction reconsolidation, post-event liquefaction resistance should increase. Based on data compiled by Mesri et al. [7] from ground improvement projects, liquefaction resistance may increase after the relative density increases on the order of 20% to 30% (from originally loose to medium dense states). Prior to Olson et al. [4,5], Oda et al. [8] proposed that deposits undergoing liquefaction experience large shear strains (exceeding 2% to 3%), and this straining changes the soil fabric from a random
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Fig. 1. Schematic illustration of changes to sand fabric resulting from large strains associated with liquefaction (Oda et al. [8]): (a) initial state; and (b) following liquefaction and reconsolidation.
or slightly anisotropic grain structure into a highly anisotropic structure that consists of column-like grain structures separated by large connected voids (Fig. 1; [8,9]). This type of anisotropy is very unstable, and as a result, subsequent undrained monotonic or cyclic loading (applied perpendicular to the major principal stress direction) can cause this column-like grain structure to collapse and reliquefy the soil more readily [8]. Ha et al. [10] concluded that the extent of anisotropic fabric change and resulting hydraulic conductivity variation depend on the gradational characteristics of the soil. The third postulate involves the formation of a loosened zone of soil immediately below a lower permeability surface soil layer (e.g., clay cap) as a result of impeded water flow resulting from liquefactioninduced reconsolidation. This process is termed void redistribution [11–13]. Loosened zones immediately below a clay cap (resulting from void redistribution) may be more than 1 m thick when liquefaction is severe (S.F. Obermeier, 2008, personal communication based on observations in the New Madrid seismic zone), and exhibit significantly smaller liquefaction resistance than the densified sand below the loosened zone. As a result, reliquefaction during subsequent loading events may initiate predominantly within this loosened zone. In this study, 1 g shaking table tests were performed using five sands with differing gradation characteristics (effective grain size (D10)¼0.11–0.40 mm, and coefficient of uniformity (Cu)¼ 1.53–2.57) to test the validity of the first two postulates and to examine the role of gradational characteristics on reliquefaction resistance. As the shaking table tests were performed for profiles consisting of uniformly deposited sand, significant void redistribution was not likely to occur, and we did not explore the role of void redistribution on reliquefaction resistance. During the tests, excess pore pressures (ux) at various depths and surface settlements were measured to define the triggering of levelground cyclic liquefaction and to estimate the change in density associated with liquefaction-induced reconsolidation, respectively. Multiple shaking events (with adequate time between shakes to allow for porewater pressure dissipation and reconsolidation) were used to simulate multiple earthquakes closely spaced in time.
2. Testing program Five sands locally available in Korea were used for the shaking table tests: Jumunjin, Youngjong, Incheon1, Incheon2, and Han River sand. All test sands were passed through a 2-mm sieve to remove impurities and large particles, and the resulting soil was washed (using water) on a U.S. Standard #200 sieve to remove fines. Fig. 2 presents the grain size distribution curves for the test sands after preparation, and Table 1 presents their index properties. Fig. 2 includes the range of the gradations reported to be ‘‘most liquefiable’’ by Tsuchida [14], and all of the test sands fall within this range.
Fig. 2. Grain size distributions of the five sands used in this study.
Table 1 Index properties of the test sands. Test sand
Jumunjin Youngjong Incheon1 Incheon2 Han River
Grain sizes (mm) D10
D50
0.40 0.11 0.24 0.23 0.21
0.57 0.16 0.34 0.50 0.50
Coefficient of uniformity, Cu
Specific gravity, Gs
Dry unit weight (kN/m3), (void ratio) Max.
1.5 2.0 1.7 2.5 2.6
2.64 2.64 2.57 2.67 2.61
15.68 15.88 16.27 17.35 17.05
Min. (0.65) (0.63) (0.55) (0.51) (0.50)
13.72 13.23 14.11 14.90 14.11
(0.89) (0.96) (0.78) (0.76) (0.81)
A 40-cm thick, saturated sand layer was prepared by water pluviation in a model box with dimensions of 192 cm 44 cm (in plan) 60 cm high. A 5-cm thick sponge was attached to each of the shorter-dimension sidewalls (perpendicular to the direction of shaking) to reduce the development of reflected waves by the rigid walls. Water sedimentation was used to prepare the soil models in order to simulate offshore reclamation and fluvial deposition. The pluviation process involved the following steps: (1) the model box was filled with water to a depth of about 50 cm (leaving 10 cm freeboard); (2) a wire screen with 2 mm spacing was placed at the water surface in the soil box; and (3) sand saturated with water was carefully poured onto the screen and allowed to fall through the net and into the water by gravity. As a result of the pluviation process, the soil at the bottom of the tank may have been slightly denser than the soil near the surface of the box as a result of different settling heights and velocities. Each shaking table model was instrumented with eight porewater pressure transducers, five uniaxial accelerometers, and two linear variable differential transformers (LVDTs) as shown in Fig. 3. The extension rod tip of each LVDT was connected to a perforated square wooden plate (10 cm 10 cm 0.5 cm thick) to prevent the tip from plunging into the liquefied ground. LVDT measurements were used to estimate average density changes of the sand during and after shaking. The input acceleration consisted of 20 sinusoidal cycles of 0.15 g amplitude (4 Hz wave with a 5-s duration), similar to the loading conditions used in previous shaking table test studies (e.g., Koga and Matsu [15]). As discussed subsequently, porewater pressure records clearly illustrated that this loading frequency was sufficient to induce liquefaction during the 1st shaking event. After the 1st shaking event was completed and excess porewater pressure generated by the 1st shaking event had entirely dissipated, all test sands were subjected sequentially to four additional (and identical) shaking events to evaluate reliquefaction resistance.
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3. Test results and analysis 3.1. Acceleration, vertical strain, and porewater pressure response Fig. 4 presents acceleration time histories measured during the 1st shaking event on Incheon2 sand. As illustrated in the figure, the input motion reached its full amplitude after the first cycle and continued for 5 s. The motions were significantly altered after the first cycle at a distance of 30 cm above the base (3/4H), after the third cycle 20 cm above the base (2/4H), and after the seventh cycle 10 cm above the base (1/4H). There also was a slight phase shift starting in the first few cycles throughout the soil column. The
Fig. 3. Schematic model and instrumentation layout. (Instruments were installed along the longitudinal centerline of the soil box.)
alteration of the motion involved two distinct stages: (1) a significant increase in frequency and slight to moderate amplification (peak amplification ratios ranging from 1.3 to 2.5); followed by (2) a substantial attenuation of the acceleration amplitudes and decrease in frequency. The substantial attenuation in the second stage occurred predominately in the upper half of the soil column (i.e., 3/4H and 2/4H), while only minor attenuation occurred at 1/4H. These trends are consistent with limited available field downhole accelerometer array data [16]. It is also apparent that some trapped and reflected waves were measured in the rigid soil container, despite efforts to minimize these effects. However, these reflected waves had little influence on the soil response early during shaking, and did not affect our interpretation as we were primarily interested in ux, which increased during the early part of shaking. Furthermore, these waves rapidly attenuated (after about 2 cycles) after the input motion ceased. These results were similar for tests performed on the other sands. Fig. 4 includes the settlement time histories measured at LVDT1 and LVDT2. Overall, the measured settlements at LVDT1 and LVDT2 were similar, both during shaking and during reconsolidation. Net vertical strains (ev) of approximately 3% to 3.5% were measured as a result of the 1st shaking event on Incheon2 sand. Interestingly, approximately half of the vertical strains occurred during shaking (1% to 2.3%), with the remainder occurring during reconsolidation following shaking. These magnitudes of net vertical strains are consistent with strains measured at field sites of level ground liquefaction, as well as measured in laboratory element tests [17,18]. Similar results were measured for the other test sands. Interestingly, these results indicate that local drainage occurs during earthquake shaking, leading to void redistribution and
Fig. 4. Settlement and acceleration time histories measured during 1st shaking event on Incheon2 sand.
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settlement while positive excess porewater pressures are still being generated. Fig. 5 presents excess porewater pressure time histories for each of the five shaking events for Incheon1 sand. As illustrated in Fig. 5(a), during the 1st shaking event ux increased with increase in the cycles of shaking at a relatively linear rate throughout the entire sand profile until liquefaction was triggered at each depth. Liquefaction triggering was defined when ux first equaled the initial vertical effective stress (s0 vo), and the arrows in Fig. 5 are used to illustrate the instant of triggering. The fairly linear rate of increase in ux resulted in liquefaction occurring first in the upper portion of the profile, as anticipated from the cyclic stress method [19–21], and progressing downward through the profile. In contrast to the 1st shaking event, ux increased sharply early in the 2nd shaking event, with liquefaction occurring almost simultaneously throughout the entire profile. In the 3rd and subsequent shaking events, ux increased rapidly; however, the porewater pressures generated during these events generally were lower than during the 2nd event. 3.2. Characteristics of liquefaction/reliquefaction resistance Table 2 reports the average relative density (Dr,avg) prior to each shaking event, the number of cycles required to trigger liquefaction (NL), the maximum excess porewater pressure ratio (ru ¼ux/s’vo)
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measured for each shaking event at each level in the sand profile, as well as the number of cycles required to trigger liquefaction (or reliquefy the sand; NR) at each level in the sand profile during the 2nd and subsequent shaking events. Fig. 6 summarizes these data graphically. As illustrated in Fig. 6, liquefaction resistance increases with depth during the 1st shaking event for all sands, although the rate of porewater pressure increase is essentially constant with depth. We attribute these observations to the small increases in effective confining stress and relative density with depth. This combination likely results nearly in a constant state parameter with depth (where state parameter is defined as the difference in void ratio between the consolidation void ratio and critical state void ratio, as defined by Been and Jefferies [22]). Fig. 6 also demonstrates that the number of cycles required to trigger liquefaction during the 1st shaking event (at any depth) was considerably larger than that required to trigger liquefaction during the 2nd event (i.e., reliquefaction) for all five sands. Furthermore, in contrast to the 1st shaking event, the number of cycles required to trigger liquefaction during the 2nd shaking event was nearly constant (or only slightly increasing with depth) for each sand. These results suggest that each sand was at a uniform density and had a fairly homogeneous fabric because the effective ‘‘drop height’’ was essentially zero throughout the liquefied sand during post-liquefaction reconsolidation. The greater rate of porewater pressure increase during the
Fig. 5. Excess porewater pressure generation during shaking table test on Incheon1 sand. (a) 1st shaking event (i.e., initial liquefaction test); (b) 2nd shaking event (i.e., reliquefaction test); (c) 3rd shaking event (i.e., reliquefaction test); (d) 4th shaking event (i.e., reliquefaction test); (e) 5th shaking event (i.e., reliquefaction test). (ru ¼ ratio of excess porewater pressure to initial vertical effective stress¼ ux/s0 vo; Dr,i ¼initial relative density.)
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Table 2 Number of cycles required to trigger liquefaction during each of five shaking events. Test sand
Dist. above base
1st shaking event
2nd shaking event
3rd shaking event
4th shaking event
5th shaking event
Dr,avg (%)
NL
Dr,avg (%)
NR
Dr,avg (%)
NR
Dr,avg (%)
NR
Dr,avg (%)
NR
Jumunjin sand
3/4H 2/4H 1/4H
30
1.0 2.0 3.0
50
0.4 0.4 0.4
59
0.2 ru ¼ 0.87 ru ¼ 0.58
61
ru ¼ 0.50 ru ¼ 0.21 ru ¼ 0.02
62
ru ¼ 0.13 ru ¼ 0.05 ru ¼ 0.00
Youngjong sand
3/4H 2/4H 1/4H
20
1.3 2.3 2.8
40
1.1 1.5 1.5
48
0.8 0.8 1.1
54
1.1 1.1 1.5
60
0.9 0.9 1.4
Incheon1 sand
3/4H 2/4H 1/4H
21
2.0 6.0 10.5
43
0.6 0.8 1.0
57
0.8 0.8 ru ¼ 0.91
59
0.8 ru ¼ 0.69 ru ¼ 0.55
59
ru ¼ 0.43 ru ¼ 0.14 ru ¼ 0.07
Incheon2 sand
3/4H 2/4H 1/4H
23
1.5 3.0 5.9
45
0.6 1.0 1.5
57
1.0 1.5 ru ¼ 0.67
57
1.0 ru ¼ 0.41 ru ¼ 0.24
59
ru ¼ 0.25 ru ¼ 0.08 ru ¼ 0.05
Han River sand
3/4H 2/4H 1/4H
19
1.0 3.5 4.5
40
0.8 1.3 1.5
50
1.0 1.5 ru ¼ 0.89
52
1.0 ru ¼ 0.90 ru ¼ 0.60
52
ru ¼ 0.89 ru ¼ 0.62 ru ¼ 0.30
H: height of sand deposit; Dr,avg: relative denstity (%); NL and NR: number of cycles required to liquefaction and reliquefaction, respectively; ru: ratio of excess pore pressure to effective stress. Note: if the soil is not liquefied, the resistance is presented as a ratio of excess pore pressure to vertical effective stress (ru).
2nd shaking event also supports our assertion that the initial sand fabric was destroyed by liquefaction during the 1st shaking event. During the 3rd (and subsequent) shaking events, the test sands (with the exception of Youngjong sand) did not develop excess porewater pressures large enough to liquefy the sands at all depths. At depths where liquefaction was triggered, the number of cycles required to trigger liquefaction generally increased slightly during each subsequent shaking event. By the 5th shaking event, the test sands (excluding Youngjong sand) did not liquefy at any depth after 20 cycles of shaking. 3.3. Effect of density on liquefaction resistance Fig. 7 illustrates the initial relative density and void ratio for each test sand prior to the each shaking event. Initial relative densities for the test sands prior to the 1st shaking event ranged from about 20% to 30%, and the dissipation of excess porewater pressures induced by shaking led to reconsolidation settlements and an increase in relative density to values of about 40% to 50% after the 1st shaking event. During subsequent shaking events, each sand experienced a much smaller increase in relative density. Similarly, void ratios decreased following each shaking event as shown in Fig. 7(b), with the largest decreases in void ratio occurring following the 1st shaking event, and each subsequent event inducing smaller decreases in void ratio. In Fig. 7, solid symbols represent the occurrence of liquefaction throughout the sand profile, while open symbols represent conditions where liquefaction either did not occur throughout the entire profile or did not occur at all. These data, combined with the data from Fig. 6, illustrate that despite the significant increase in density resulting from shaking and liquefaction-induced reconsolidation after the 1st shaking event, liquefaction resistance decreased substantially in each of the sands. This result illustrates that the sand fabric is dramatically altered by liquefaction and reconsolidation, and is consistent with previous field and laboratory data [1–3] that suggest that liquefaction resistance initially decreases following the occurrence of liquefaction. However, following the 2nd shaking event, each sand (excluding Youngjong sand) had densified sufficiently to preclude liquefaction in at least some portion of the soil column. Where liquefaction occurred at limited depths, it occurred near the top of the sand profile where the excess porewater pressures that developed may have been augmented
by: (1) water pressures diffusing from the bottom of the profile as a result of upward flow during shaking and reconsolidation in the lower portion of the profile (as illustrated in Fig. 5, porewater pressure dissipation occurred concurrently with shaking as during the 3rd and 4th shaking events on Incheon1 sand); and (2) slight amplification in the ground motions observed near the top of the profile. Overall, consistent with past research, initial density (in terms of either relative density or void ratio) is not an adequate indicator of liquefaction resistance. Soil fabric and possible aging effects significantly influence initial liquefaction resistance. However, once the initial soil fabric is destroyed by liquefaction, void ratio became a good indicator of reliquefaction resistance for all of the test sands, and relative density was appropriate for all of the test sands excluding Youngjong sand. In contrast to the other four test sands, Youngjong sand liquefied throughout its entire profile during all five shaking events, despite the increase in density resulting from shaking and reconsolidation. As illustrated in Fig. 7(a), the relative density of Youngjong sand was on the low end of measured relative densities during the first four shaking events; however, by the end of the 4th event, the relative density of Youngjong sand had increased to approximately 60%, yet the entire profile still liquefied during the 5th shaking event. In terms of void ratio though, the global void ratio of Youngjong sand remained larger than that of the other four test sands during each shaking event. As reported in Table 1, the maximum void ratio is larger than that of the other four test sands, the minimum void ratio is the second largest, and Youngjong sand is finer than the other sands. These observations indicate that grain characteristics such as gradation, particle shape, and uniformity significantly influences excess porewater pressure generation, as suggested by Seed and Idriss [23].
3.4. Effect of grain characteristics on liquefaction resistance In order to compare liquefaction resistance from profiles that liquefied in a specific number of cycles with profiles that developed excess porewater pressures without liquefying (i.e., ru o1), we defined a simple capacity to demand ratio as follows: 8 NL NR Capacity C < 20 cycles or 20 cycles for ru ¼ 1 ¼ 1 Demand D : ru for ru o 1
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Fig. 6. Variation of liquefaction resistance with successive shaking events (H¼model height; DNL¼ did not liquefy; ru ¼ratio of excess porewater pressure to initial vertical effective stress ¼ux/s0 vo).
Fig. 8 presents C/D ratios for each of the five test sands during each shaking event with respect to several sand gradational characteristics: D10, D50, and CU. The plots in Fig. 8 only include
the C/D ratios for the mid-depth of the profile (i.e., 2/4H) for clarity and because this depth provided a reasonable average response for the entire profile during each shaking event. In addition, Fig. 8 also
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reasonable trend with C/D, with liquefaction resistance increasing as D210D2.8 increases. r Fig. 9 presents the ratio of NR (2nd event)/NL (1st event; e.g., refer to Table 3) for each of the test sands with respect to D210D2.8 r (computed prior to the 1st shaking event) as well as D10/CU as proposed by Ha et al. [10]. The latter parameter also is crudely related to cv, as D10 is proportional to k0.5 v for cohesionless sands [24] and CU is inversely proportional to permeability and compressibility for cohesionless sands ([24] and [27], respectively); however, the value of CU does not vary greatly among the test sands and the effect of D10 dominates the correlation. As shown in Fig. 9, the ratio of NR (2nd event)/NL (1st event) linearly decreased as both D210D2.8 and D10/CU increased, but r remained constant as about 0.20–0.25 (i.e., 20–25% of the initial liquefaction resistance) for values of D210D2.8 and D10/CU greater than r about 4 102 mm2 (for Dr in percent) and 0.12 mm, respectively. These combined gradational parameters reasonably describe the decrease in liquefaction resistance observed following initial liquefaction for the test sands.
4. Evaluation of liquefaction and reliquefaction resistance mechanisms
Fig. 7. Variation of pre-event average relative density and average void ratio with successive shaking events.
shows the number of cycles required to trigger liquefaction with respect to (D10)2(Dr)2.8. This parameter can be empirically related to the coefficient of consolidation, cv, as follows cv ¼
kv
gw mv
cD210
1:4 w 1:7=N 60
g
cD210
gw 1:7=½ða þ bsuv ÞD2r 1:4
‘cv pD210 D2:8 r
ð1Þ
ð2Þ conductivityEcD210
for cohesionwhere kv is the vertical hydraulic less sands [22]; gw is the unit weight of water; mv is the coefficient 1:4 of volume change, dev =dsuv 1:7=N60 , for cohesionless sands and gravels [25]; ev is the vertical strain; su is the vertical effective stress; N 60 is the average energy-corrected standard penetration test blow countE(a +bs0 v)D2r [26]; and a, b, and c are constants. As illustrated in Fig. 8, neither initial liquefaction resistance nor reliquefaction resistance (in terms of C/D) appear to be related to D50, D10, and CU, although D10 may exhibit a weak correlation with liquefaction resistance because it is related to hydraulic conductivity. The lack of correlation observed in these plots suggests that while grain characteristics influence initial liquefaction resistance (as noted above), no individual grain characteristic examined in Fig. 8 is sufficient to define trends of liquefaction and reliquefaction resistance. However, the proxy for cv (pD210D2.8 r ) shows a
Fig. 6 illustrates that the liquefaction resistance of each of the test sands decreases significantly from the 1st to the 2nd shaking event, despite the increase in Dr. This decrease in liquefaction resistance immediately followed by an initial liquefaction event supports the liquefaction and reliquefaction resistance mechanism postulates proposed by both Oda et al. [8] and Olson et al. [5]. In particular, the number of cycles required to reliquefy Youngjong sand decreased after the 1st shaking event, and remained essentially constant during subsequent shaking events (Fig. 6b). These data support the Oda et al. [8] postulate that suggest that the large shear strain experienced during liquefaction (42–3%) creates a highly anisotropic, column-like structure with connected voids that is highly unstable when stressed in a direction perpendicular to the elongation direction (i.e., mainly the major principal stress direction). However, in contrast to Youngjong sand, Fig. 6(a), (c), (d) and (e) illustrates that while the liquefaction resistance decreased considerably after the 1st shaking event for these four test sands, liquefaction resistance generally increased following the 2nd event. In fact, liquefaction was not achieved in at least a portion of each sand model profile during the 3rd shaking events, and during the 5th event, none of the model profile liquefied in these four test sands. The large increase in liquefaction resistance following the 2nd shaking event observed for these four sands could not be reasonably explained by the Oda et al. [8] postulate. Presumably, if a column-like structure is formed following the 1st occurrence of liquefaction, this column-like structure should re-form after each occurrence of liquefaction. However, if a column-like structure re-forms after each event, presumably the relative density and liquefaction resistance should remain relatively constant following the first liquefaction occurrence. Therefore, Oda et al.’s [8] postulate appears to hold following the 1st shaking event. However, this postulate does not directly account for the density increase observed during subsequent shaking events for four of the five test sands. The Olson et al. [4,5] postulate suggests that liquefaction resistance may decrease following the 1st shaking event as a result of destruction of the pre-existing ‘‘aged’’ soil structure. In the case of the test sands, each of the sands were ‘‘aged’’ for approximately 1 h prior to the 1st shaking event; as the specimen was prepared, instruments were connected to the data acquisition system and initialized, etc. Consolidation following the final lift placement during initial deposition in the specimen box occurred in approximately 20–30 s for Youngjong sand and about 10–15 s for the other four sands. Therefore, the approximately one hour required to
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Fig. 8. Liquefaction capacity to demand ratio (C/D) with respect to grain characteristics at the mid-depth of the profile (i.e., 2/4H).
Fig. 9. Ratio of reliquefaction resistance during the 2nd shaking event to the initial liquefaction resistance, NR (2nd)/NL, with respect to gradational parameter D210D2.8 and r D10/Cu.
Table 3 Ratio of initial liquefaction resistance to reliquefaction resistance for each shaking event. Test sand
Dist. above base
NR (2nd event)/NL
NR (3rd event)/NL
NR (4th event)/NL
NR (5th event)/NL
Jumunjin sand
3/4H 2/4H 1/4H
0.40 0.20 0.13
0.20 No liq. No liq.
No liq. No liq. No liq.
No liq. No liq. No liq.
Youngjong sand
3/4H 2/4H 1/4H
0.85 0.65 0.54
0.62 0.35 0.39
0.85 0.48 0.54
0.70 0.39 0.50
Incheon1 sand
3/4H 2/4H 1/4H
0.30 0.13 0.10
0.40 0.13 No liq.
0.40 No liq. No liq.
No liq. No liq. No liq.
Incheon2 sand
3/4H 2/4H 1/4H
0.40 0.33 0.25
0.67 0.50 No liq.
0.67 No liq. No liq.
No liq. No liq. No liq.
Han River sand
3/4H 2/4H 1/4H
0.80 0.37 0.33
1.0 0.43 No liq.
1.0 No liq. No liq.
No liq. No liq. No liq.
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prepare for the 1st shaking event represents about two to three log cycles of time for secondary compression to occur. Secondary compression is the time-dependent process of minor grain adjustments into a more stable configuration under constant vertical effective stress [7,25,28], and it significantly improves particle interlocking and liquefaction resistance. In addition, more secondary compression occurs per log cycle of time in more compressible soils, as the secondary compression index (Ca ¼ De/D log t) is proportional to the compression index (Cc ¼ De/ D log s0 v), i.e., Ca/Cc ¼ constant for a given soil [25,28]. In sands, compressibility is inversely proportional to relative density; therefore, looser sands will exhibit larger values of Cc (as illustrated by the void ratio changes in Fig. 7), and in turn, larger values of Ca. Thus, secondary compression of the initially loose sand column, in conjunction with the anisotropic sand fabric, provided relatively high initial liquefaction resistance despite the initially low relative densities. Liquefaction during the 1st shaking event destroyed the ‘‘aged’’ soil fabric, and the sand reconsolidates as a young, normally consolidated sand. Again, less than about one hour of time elapsed following each shaking event to allow for downloading data, rechecking instruments, etc. Therefore, about two log cycles of time elapsed following reconsolidation, allowing secondary compression to occur. However, the factor of two increase in relative density following the 1st event results in a significant decrease in compressibility (i.e., mvpDr 2.8), and in turn, results in a significant decrease in Ca. Therefore, despite having almost the same time for secondary compression to occur, significantly less secondary compression occurred following the 2nd shaking event because of the large decrease in Ca. This decrease in secondary compression, in conjunction with the destruction of the anisotropic soil fabric, results in a sizeable reduction in reliquefaction resistance following the 1st shaking event despite the increase in relative density, consistent with the Olson et al. [4,5] postulate. Following the 2nd shaking event, additional reconsolidation occurs, although the increase in Dr is much less than that following the 1st shaking event (see Fig. 7). Following the 3rd and subsequent events, even smaller increases in Dr occur for each of the sands. As Dr increases, the opportunity for secondary compression to influence the sand fabric decreases. However, for the Jumunjin, Incheon1, and Incheon2 sands, the combination of relatively high hydraulic conductivity (larger D10 grain sizes) and medium dense to dense relative density (Dr Z 60%) prevented the generation of large excess porewater pressure and reliquefaction resistance increases. These increases in relative density and corresponding increases in liquefaction resistance are reasonably consistent with prior observations [4,5,7]. For the Han River and Youngjong sands, the combination of lower hydraulic conductivity (smaller D10 grain sizes) and medium dense relative densities (Dr 50%) allows excess porewater pressures to be generated and maintained. The combination of hydraulic conductivity and compressibility is captured by cv. As discussed previously, cvpD210D2.8 r , and Fig. 8 illustrates that reliquefaction resistance increases significantly when this parameter exceeds about 104 mm2 (for D10 in mm and Dr in percent). For the level of cyclic demand employed in these tests, sands 4 2 with D210D2.8 r 4 10 mm become nonliquefiable. Given this observation, with additional study it may be possible to extend this concept to other values of seismic or cyclic demand and identify values of cv (or its more readily estimated proxy, D210D2.8 r ) above which liquefaction or significant generation of porewater pressure does not occur.
5. Conclusions In this study, 1 g shaking table tests were performed using five sands with differing gradation characteristics [effective grain size (D10) ¼0.11 to 0.40 mm, and coefficient of uniformity
(Cu)¼1.53–2.57] to test the validity of two postulates regarding reliquefaction mechanism and to examine the role of gradational characteristics on reliquefaction resistance. Test results demonstrate that the number of cycles required to trigger liquefaction during the 1st shaking event (at any depth) is considerably larger than that required to trigger liquefaction during the 2nd event (i.e., reliquefaction), likely as a result of the ‘‘aged’’ sand fabric developed during secondary compression of the initially loose sands and the initially anistropic sand fabric resulting from initial deposition. During the 3rd (and subsequent) shaking events, only Youngjong sand with the smallest effective grain size liquefied at all depths in the profile. The test results illustrate that liquefaction and reliquefaction resistances do not correlate well to relative density or void ratio, D10, D50, or CU. While no single index property or grain characteristic is sufficient to define trends of liquefaction and reliquefaction resistance, the proxy for coefficient of consolidation (cv ¼kv/gwmvpD210D2.8 r ) shows reasonable correlation with liquefaction and reliquefaction resistance. Similarly, liquefaction and reliquefaction resistance correlate reasonably well with D10/CU, which also is crudely related to cv. 4 2 That is, as D210D2.8 r increased above a value of about 10 mm (for Dr in percent), reliquefaction resistance increased significantly. The observation that liquefaction resistance decreases following the first occurrence of liquefaction supports both the Oda et al. [8] and the Olson et al. [4,5] postulates. However, the subsequent increase in liquefaction resistance following the 2nd shaking event for four of the five test sands is not consistent with the Oda et al. postulate that the sand forms a column-like structure following liquefaction. In contrast, the increasing density following each shaking event and increases in liquefaction resistance following the 2nd shaking event is reasonably consistent with the Olson et al. postulate. Based on our observations, the coefficient of consolidation, cv, or proxy values such as D210D2.8 or D10/CU correlate reasonably well r with reliquefaction resistance and, with additional study, may be a useful tool for evaluating reliquefaction potential.
References [1] Kuribayshi E, Tatsuoka F. Brief review of liquefaction during earthquakes in Japan. Soils Found 1975;15(4):81–91. [2] Yasuda S, Tohno I. Sites of reliquefaction caused by the 1983 Nihonkai-Chubu earthquake. Soils Found 1988;28(2):61–72. [3] Sims JD, Garvin CD. Recurrent liquefaction induced by the 1989 Loma Prieta earthquake and 1990 and 1991 aftershocks: implications for pleoseismicity studies. B Seismol Soc Am 1995;85(1):51–65. [4] Olson SM, Obermeier SF, Stark TD. Interpretation of penetration resistance for back-analysis at sites of previous liquefaction. Seismol Res Lett 2001; 72(1):46–59. [5] Olson SM, Green RA, Obermeier SF. Geotechnical analysis of paleoseismic shaking using liquefaction effects: a major updating. Eng Geol 2005;76: 235–61. [6] Thomann TG, Hryciw RD. Discussion of ‘‘Postdensification penetration resistance of clean sands’’ by Mesri G, Feng TW, Benak JM. J Geotech Eng 1992;118: 508–611. [7] Mesri G, Feng TW, Benak JM. Postdensification penetration resistance of clean sands. J Geotech Eng 1990;116(GT7):1095–115. [8] Oda M, Kawamoto K, Fujimori H, Sato M. Microstructural interpretation on reliquefaction of saturated granular soils under cyclic loading. J Geotech Geoenviron Eng 2001;127(5):416–23. [9] Oda M. The mechanism of fabric changes during compressional deformation of sand. Soils Found 1972;12(2):416–23. [10] Ha IS, Park YH, Kim MM. Dissipation pattern of excess pore pressure after liquefaction in saturated sand deposits. Transportation Research Record 1821, TRB, National Research Council, Washington, D.C., 2003, p. 59–67. [11] NRC (National Research Council). Liquefaction of soils during earthquake: committee on earthquake engineering commission on engineering and technical systems, NRC, National Academy Press, Washington, D.C., 1985. [12] Seed HB. Design problems in soil liquefaction. J Geotech Eng 1987;113:827–45. [13] Boulanger RW, Truman SP. Void redistribution in sand under post-earthquake loading. Can Geotech J 1996;33:829–34. [14] Tsuchida H. Prediction and countermeans against the liquefaction in sand deposits. Abstract of the Seminar in the Port and Harbor Research Institute, Yokohama, Japan, 3.1–3.33, 1970.
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[15] Koga Y, Matsuo O. Shaking table tests of embankments resting on liquefiable sandy ground. Soils Found 1990;30(4):162–74. [16] Youd TL, Carter BL. Influence of soil softening and liquefaction on spectral acceleration. J Geotech Geoenviron Eng 2005;131(7):811–25. [17] Tokimatsu K, Seed HB. Evaluation of settlements in sands due to earthquake shaking. J Geotech Eng 1987;113(GT8):861–78. [18] Ishihara K, Yoshimine M. Evaluation of settlements in sands following liquefaction during earthquakes. Soils Found 1996;32(1):173–88. [19] Seed HB, Tokimatsu K, Harder LF, Chung RL. Influence of SPT procedures in soil liquefaction resistance evaluations. J Geotech Eng 1985;111(12):1425–45. [20] Youd TL, et al. Liquefaction resistance of soils: summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils. J Geotech Geoenviron Eng 2001;127(4):297–313. [21] Green RA. Energy-based evaluation and remediation of liquefiable soils. PhD thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, 2001.
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[22] Been K, Jefferies MG. A state parameter for sands. Geotechnique 1985; 35(2):99–112. [23] Seed HB, Idriss IM. Simplified procedure for evaluating soil liquefaction potential. J Geotech Eng 1971;SM9:1249–73. [24] Hazen A. Physical properties of sands and gravels with reference to their use in filtration. Report to the Massachusetts State Board of Health, 1892, p. 539. [25] Terzaghi K, Peck RB, Mesri G. Soil mechanics in engineering practice. John Wiley & Sons, Inc.; 1996. [26] Skempton AW. Standard penetration test procedures and the effects in sands of overburden pressure, relative density, particle size, ageing, and overconsolidation. Geotechnique 1986;36(3):425–47. [27] Burmister DM. Physical, stress–strain, and strength responses of granular soils. In: Proceedings of the symposium on field testing of soils STP 322 ASTM, Philadelphia, PA, 1962, p. 67–97. [28] Mesri G, Godlewski PM. Time- and stress-compressibility interrelationship. J Geotech Eng 1977;103(GT5):417–30.
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Evaluation of reliquefaction resistance using shaking table tests Ik-Soo Ha a, Scott M. Olson b, Min-Woo Seo c,n, Myoung-Mo Kim d a
Korea Water Resources Corporation, Daejeon, Korea Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Samsung C&T, Seoul, Korea d Department of Civil and Environmental Engineering, Seoul National University, Korea b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 July 2009 Received in revised form 1 August 2010 Accepted 3 December 2010 Available online 3 January 2011
Cases of modern and prehistoric liquefaction illustrate that sand deposits can be liquefied again (or ‘‘reliquefied’’) by a subsequent earthquake after initially liquefying during seismic shaking. In order to test the validity of two postulates regarding reliquefaction mechanisms and to examine the role of gradational characteristics on reliquefaction resistance, 1 g shaking table tests were performed using five sands with differing gradation characteristics. The test results demonstrate that the number of cycles required to reliquefy each sand decreased significantly following the 1st liquefaction event as a result of destroying the ‘‘aged’’ sand fabric developed prior to the 1st shaking event via secondary compression of the initially loose sands. Reliquefaction resistance correlated reasonably well with a proxy for cv (pD210D2.8 r ), illustrating that both the permeability and compressibility of the sand play significant roles in the post-liquefaction fabric (and hence reliquefaction resistance) formed by a sand. While the initial decrease in reliquefaction resistance supports both the Oda et al. [8] and the Olson et al. [5] reliquefaction postulates, only the Olson et al. [5] postulate reasonably explains the subsequent, large increase in reliquefaction resistance observed during the 3rd through 5th shaking events. These tests suggest that the or D10/CU) may be a useful tool coefficient of consolidation, cv ¼ kv/gwmv (or proxy values such as D210D2.8 r for evaluating reliquefaction potential in forward and inverse (i.e., paleoliquefaction) analysis. & 2010 Elsevier Ltd. All rights reserved.
1. Introduction Cases of modern and prehistoric liquefaction illustrate that after initially liquefying in response to cyclic or seismic loading, sand deposits can be liquefied again (or ‘‘reliquefied’’) by a subsequent smaller cyclic or seismic load [1–3]. As a result, understanding the liquefaction resistance of previously liquefied sites is important for both forward and inverse (i.e., paleoliquefaction) geotechnical analysis. The process of liquefaction can be simplified into three phases: (1) destruction of pre-earthquake soil structure during undrained monotonic or cyclic loading, leading to porewater pressure increase and loss of strength and stiffness in very loose to medium dense soils; (2) post-liquefaction reconsolidation and densification; and (3) post-consolidation aging [4]. Despite the increase in density associated with post-liquefaction consolidation, Olson et al. [4] argued that this process may not lead to a post-event increase in liquefaction resistance.
n
Corresponding author. Tel.: +82 2 2145 6107; fax: 82 2 2145 6630. E-mail addresses: [email protected], [email protected] (M.-W. Seo).
0267-7261/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2010.12.008
At least three postulates (which are not mutually exclusive) are available to explain this phenomenon. Olson et al. [4,5] proposed one, as follows. Thomann and Hryciw [6] suggested that liquefaction causes ‘‘effectively infinite’’ shear straining at particle contacts. This straining completely destroys the pre-existing (aged) soil structure that had developed through mechanisms such as secondary compression, preshearing, and cementation, all of which improve interlocking at particle contacts and increase liquefaction resistance. As a result of the large shear straining associated with liquefaction, the liquefied soil essentially becomes freshly deposited following post-liquefaction reconsolidation. Thus, the postevent liquefaction resistance may be lower than the pre-event liquefaction resistance because of the loss of particle interlocking [4,5]. However, Olson et al. [4,5] also argue that after sufficiently large density changes occur as the result of shaking-induced settlement and post-liquefaction reconsolidation, post-event liquefaction resistance should increase. Based on data compiled by Mesri et al. [7] from ground improvement projects, liquefaction resistance may increase after the relative density increases on the order of 20% to 30% (from originally loose to medium dense states). Prior to Olson et al. [4,5], Oda et al. [8] proposed that deposits undergoing liquefaction experience large shear strains (exceeding 2% to 3%), and this straining changes the soil fabric from a random
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Fig. 1. Schematic illustration of changes to sand fabric resulting from large strains associated with liquefaction (Oda et al. [8]): (a) initial state; and (b) following liquefaction and reconsolidation.
or slightly anisotropic grain structure into a highly anisotropic structure that consists of column-like grain structures separated by large connected voids (Fig. 1; [8,9]). This type of anisotropy is very unstable, and as a result, subsequent undrained monotonic or cyclic loading (applied perpendicular to the major principal stress direction) can cause this column-like grain structure to collapse and reliquefy the soil more readily [8]. Ha et al. [10] concluded that the extent of anisotropic fabric change and resulting hydraulic conductivity variation depend on the gradational characteristics of the soil. The third postulate involves the formation of a loosened zone of soil immediately below a lower permeability surface soil layer (e.g., clay cap) as a result of impeded water flow resulting from liquefactioninduced reconsolidation. This process is termed void redistribution [11–13]. Loosened zones immediately below a clay cap (resulting from void redistribution) may be more than 1 m thick when liquefaction is severe (S.F. Obermeier, 2008, personal communication based on observations in the New Madrid seismic zone), and exhibit significantly smaller liquefaction resistance than the densified sand below the loosened zone. As a result, reliquefaction during subsequent loading events may initiate predominantly within this loosened zone. In this study, 1 g shaking table tests were performed using five sands with differing gradation characteristics (effective grain size (D10)¼0.11–0.40 mm, and coefficient of uniformity (Cu)¼ 1.53–2.57) to test the validity of the first two postulates and to examine the role of gradational characteristics on reliquefaction resistance. As the shaking table tests were performed for profiles consisting of uniformly deposited sand, significant void redistribution was not likely to occur, and we did not explore the role of void redistribution on reliquefaction resistance. During the tests, excess pore pressures (ux) at various depths and surface settlements were measured to define the triggering of levelground cyclic liquefaction and to estimate the change in density associated with liquefaction-induced reconsolidation, respectively. Multiple shaking events (with adequate time between shakes to allow for porewater pressure dissipation and reconsolidation) were used to simulate multiple earthquakes closely spaced in time.
2. Testing program Five sands locally available in Korea were used for the shaking table tests: Jumunjin, Youngjong, Incheon1, Incheon2, and Han River sand. All test sands were passed through a 2-mm sieve to remove impurities and large particles, and the resulting soil was washed (using water) on a U.S. Standard #200 sieve to remove fines. Fig. 2 presents the grain size distribution curves for the test sands after preparation, and Table 1 presents their index properties. Fig. 2 includes the range of the gradations reported to be ‘‘most liquefiable’’ by Tsuchida [14], and all of the test sands fall within this range.
Fig. 2. Grain size distributions of the five sands used in this study.
Table 1 Index properties of the test sands. Test sand
Jumunjin Youngjong Incheon1 Incheon2 Han River
Grain sizes (mm) D10
D50
0.40 0.11 0.24 0.23 0.21
0.57 0.16 0.34 0.50 0.50
Coefficient of uniformity, Cu
Specific gravity, Gs
Dry unit weight (kN/m3), (void ratio) Max.
1.5 2.0 1.7 2.5 2.6
2.64 2.64 2.57 2.67 2.61
15.68 15.88 16.27 17.35 17.05
Min. (0.65) (0.63) (0.55) (0.51) (0.50)
13.72 13.23 14.11 14.90 14.11
(0.89) (0.96) (0.78) (0.76) (0.81)
A 40-cm thick, saturated sand layer was prepared by water pluviation in a model box with dimensions of 192 cm 44 cm (in plan) 60 cm high. A 5-cm thick sponge was attached to each of the shorter-dimension sidewalls (perpendicular to the direction of shaking) to reduce the development of reflected waves by the rigid walls. Water sedimentation was used to prepare the soil models in order to simulate offshore reclamation and fluvial deposition. The pluviation process involved the following steps: (1) the model box was filled with water to a depth of about 50 cm (leaving 10 cm freeboard); (2) a wire screen with 2 mm spacing was placed at the water surface in the soil box; and (3) sand saturated with water was carefully poured onto the screen and allowed to fall through the net and into the water by gravity. As a result of the pluviation process, the soil at the bottom of the tank may have been slightly denser than the soil near the surface of the box as a result of different settling heights and velocities. Each shaking table model was instrumented with eight porewater pressure transducers, five uniaxial accelerometers, and two linear variable differential transformers (LVDTs) as shown in Fig. 3. The extension rod tip of each LVDT was connected to a perforated square wooden plate (10 cm 10 cm 0.5 cm thick) to prevent the tip from plunging into the liquefied ground. LVDT measurements were used to estimate average density changes of the sand during and after shaking. The input acceleration consisted of 20 sinusoidal cycles of 0.15 g amplitude (4 Hz wave with a 5-s duration), similar to the loading conditions used in previous shaking table test studies (e.g., Koga and Matsu [15]). As discussed subsequently, porewater pressure records clearly illustrated that this loading frequency was sufficient to induce liquefaction during the 1st shaking event. After the 1st shaking event was completed and excess porewater pressure generated by the 1st shaking event had entirely dissipated, all test sands were subjected sequentially to four additional (and identical) shaking events to evaluate reliquefaction resistance.
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3. Test results and analysis 3.1. Acceleration, vertical strain, and porewater pressure response Fig. 4 presents acceleration time histories measured during the 1st shaking event on Incheon2 sand. As illustrated in the figure, the input motion reached its full amplitude after the first cycle and continued for 5 s. The motions were significantly altered after the first cycle at a distance of 30 cm above the base (3/4H), after the third cycle 20 cm above the base (2/4H), and after the seventh cycle 10 cm above the base (1/4H). There also was a slight phase shift starting in the first few cycles throughout the soil column. The
Fig. 3. Schematic model and instrumentation layout. (Instruments were installed along the longitudinal centerline of the soil box.)
alteration of the motion involved two distinct stages: (1) a significant increase in frequency and slight to moderate amplification (peak amplification ratios ranging from 1.3 to 2.5); followed by (2) a substantial attenuation of the acceleration amplitudes and decrease in frequency. The substantial attenuation in the second stage occurred predominately in the upper half of the soil column (i.e., 3/4H and 2/4H), while only minor attenuation occurred at 1/4H. These trends are consistent with limited available field downhole accelerometer array data [16]. It is also apparent that some trapped and reflected waves were measured in the rigid soil container, despite efforts to minimize these effects. However, these reflected waves had little influence on the soil response early during shaking, and did not affect our interpretation as we were primarily interested in ux, which increased during the early part of shaking. Furthermore, these waves rapidly attenuated (after about 2 cycles) after the input motion ceased. These results were similar for tests performed on the other sands. Fig. 4 includes the settlement time histories measured at LVDT1 and LVDT2. Overall, the measured settlements at LVDT1 and LVDT2 were similar, both during shaking and during reconsolidation. Net vertical strains (ev) of approximately 3% to 3.5% were measured as a result of the 1st shaking event on Incheon2 sand. Interestingly, approximately half of the vertical strains occurred during shaking (1% to 2.3%), with the remainder occurring during reconsolidation following shaking. These magnitudes of net vertical strains are consistent with strains measured at field sites of level ground liquefaction, as well as measured in laboratory element tests [17,18]. Similar results were measured for the other test sands. Interestingly, these results indicate that local drainage occurs during earthquake shaking, leading to void redistribution and
Fig. 4. Settlement and acceleration time histories measured during 1st shaking event on Incheon2 sand.
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settlement while positive excess porewater pressures are still being generated. Fig. 5 presents excess porewater pressure time histories for each of the five shaking events for Incheon1 sand. As illustrated in Fig. 5(a), during the 1st shaking event ux increased with increase in the cycles of shaking at a relatively linear rate throughout the entire sand profile until liquefaction was triggered at each depth. Liquefaction triggering was defined when ux first equaled the initial vertical effective stress (s0 vo), and the arrows in Fig. 5 are used to illustrate the instant of triggering. The fairly linear rate of increase in ux resulted in liquefaction occurring first in the upper portion of the profile, as anticipated from the cyclic stress method [19–21], and progressing downward through the profile. In contrast to the 1st shaking event, ux increased sharply early in the 2nd shaking event, with liquefaction occurring almost simultaneously throughout the entire profile. In the 3rd and subsequent shaking events, ux increased rapidly; however, the porewater pressures generated during these events generally were lower than during the 2nd event. 3.2. Characteristics of liquefaction/reliquefaction resistance Table 2 reports the average relative density (Dr,avg) prior to each shaking event, the number of cycles required to trigger liquefaction (NL), the maximum excess porewater pressure ratio (ru ¼ux/s’vo)
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measured for each shaking event at each level in the sand profile, as well as the number of cycles required to trigger liquefaction (or reliquefy the sand; NR) at each level in the sand profile during the 2nd and subsequent shaking events. Fig. 6 summarizes these data graphically. As illustrated in Fig. 6, liquefaction resistance increases with depth during the 1st shaking event for all sands, although the rate of porewater pressure increase is essentially constant with depth. We attribute these observations to the small increases in effective confining stress and relative density with depth. This combination likely results nearly in a constant state parameter with depth (where state parameter is defined as the difference in void ratio between the consolidation void ratio and critical state void ratio, as defined by Been and Jefferies [22]). Fig. 6 also demonstrates that the number of cycles required to trigger liquefaction during the 1st shaking event (at any depth) was considerably larger than that required to trigger liquefaction during the 2nd event (i.e., reliquefaction) for all five sands. Furthermore, in contrast to the 1st shaking event, the number of cycles required to trigger liquefaction during the 2nd shaking event was nearly constant (or only slightly increasing with depth) for each sand. These results suggest that each sand was at a uniform density and had a fairly homogeneous fabric because the effective ‘‘drop height’’ was essentially zero throughout the liquefied sand during post-liquefaction reconsolidation. The greater rate of porewater pressure increase during the
Fig. 5. Excess porewater pressure generation during shaking table test on Incheon1 sand. (a) 1st shaking event (i.e., initial liquefaction test); (b) 2nd shaking event (i.e., reliquefaction test); (c) 3rd shaking event (i.e., reliquefaction test); (d) 4th shaking event (i.e., reliquefaction test); (e) 5th shaking event (i.e., reliquefaction test). (ru ¼ ratio of excess porewater pressure to initial vertical effective stress¼ ux/s0 vo; Dr,i ¼initial relative density.)
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Table 2 Number of cycles required to trigger liquefaction during each of five shaking events. Test sand
Dist. above base
1st shaking event
2nd shaking event
3rd shaking event
4th shaking event
5th shaking event
Dr,avg (%)
NL
Dr,avg (%)
NR
Dr,avg (%)
NR
Dr,avg (%)
NR
Dr,avg (%)
NR
Jumunjin sand
3/4H 2/4H 1/4H
30
1.0 2.0 3.0
50
0.4 0.4 0.4
59
0.2 ru ¼ 0.87 ru ¼ 0.58
61
ru ¼ 0.50 ru ¼ 0.21 ru ¼ 0.02
62
ru ¼ 0.13 ru ¼ 0.05 ru ¼ 0.00
Youngjong sand
3/4H 2/4H 1/4H
20
1.3 2.3 2.8
40
1.1 1.5 1.5
48
0.8 0.8 1.1
54
1.1 1.1 1.5
60
0.9 0.9 1.4
Incheon1 sand
3/4H 2/4H 1/4H
21
2.0 6.0 10.5
43
0.6 0.8 1.0
57
0.8 0.8 ru ¼ 0.91
59
0.8 ru ¼ 0.69 ru ¼ 0.55
59
ru ¼ 0.43 ru ¼ 0.14 ru ¼ 0.07
Incheon2 sand
3/4H 2/4H 1/4H
23
1.5 3.0 5.9
45
0.6 1.0 1.5
57
1.0 1.5 ru ¼ 0.67
57
1.0 ru ¼ 0.41 ru ¼ 0.24
59
ru ¼ 0.25 ru ¼ 0.08 ru ¼ 0.05
Han River sand
3/4H 2/4H 1/4H
19
1.0 3.5 4.5
40
0.8 1.3 1.5
50
1.0 1.5 ru ¼ 0.89
52
1.0 ru ¼ 0.90 ru ¼ 0.60
52
ru ¼ 0.89 ru ¼ 0.62 ru ¼ 0.30
H: height of sand deposit; Dr,avg: relative denstity (%); NL and NR: number of cycles required to liquefaction and reliquefaction, respectively; ru: ratio of excess pore pressure to effective stress. Note: if the soil is not liquefied, the resistance is presented as a ratio of excess pore pressure to vertical effective stress (ru).
2nd shaking event also supports our assertion that the initial sand fabric was destroyed by liquefaction during the 1st shaking event. During the 3rd (and subsequent) shaking events, the test sands (with the exception of Youngjong sand) did not develop excess porewater pressures large enough to liquefy the sands at all depths. At depths where liquefaction was triggered, the number of cycles required to trigger liquefaction generally increased slightly during each subsequent shaking event. By the 5th shaking event, the test sands (excluding Youngjong sand) did not liquefy at any depth after 20 cycles of shaking. 3.3. Effect of density on liquefaction resistance Fig. 7 illustrates the initial relative density and void ratio for each test sand prior to the each shaking event. Initial relative densities for the test sands prior to the 1st shaking event ranged from about 20% to 30%, and the dissipation of excess porewater pressures induced by shaking led to reconsolidation settlements and an increase in relative density to values of about 40% to 50% after the 1st shaking event. During subsequent shaking events, each sand experienced a much smaller increase in relative density. Similarly, void ratios decreased following each shaking event as shown in Fig. 7(b), with the largest decreases in void ratio occurring following the 1st shaking event, and each subsequent event inducing smaller decreases in void ratio. In Fig. 7, solid symbols represent the occurrence of liquefaction throughout the sand profile, while open symbols represent conditions where liquefaction either did not occur throughout the entire profile or did not occur at all. These data, combined with the data from Fig. 6, illustrate that despite the significant increase in density resulting from shaking and liquefaction-induced reconsolidation after the 1st shaking event, liquefaction resistance decreased substantially in each of the sands. This result illustrates that the sand fabric is dramatically altered by liquefaction and reconsolidation, and is consistent with previous field and laboratory data [1–3] that suggest that liquefaction resistance initially decreases following the occurrence of liquefaction. However, following the 2nd shaking event, each sand (excluding Youngjong sand) had densified sufficiently to preclude liquefaction in at least some portion of the soil column. Where liquefaction occurred at limited depths, it occurred near the top of the sand profile where the excess porewater pressures that developed may have been augmented
by: (1) water pressures diffusing from the bottom of the profile as a result of upward flow during shaking and reconsolidation in the lower portion of the profile (as illustrated in Fig. 5, porewater pressure dissipation occurred concurrently with shaking as during the 3rd and 4th shaking events on Incheon1 sand); and (2) slight amplification in the ground motions observed near the top of the profile. Overall, consistent with past research, initial density (in terms of either relative density or void ratio) is not an adequate indicator of liquefaction resistance. Soil fabric and possible aging effects significantly influence initial liquefaction resistance. However, once the initial soil fabric is destroyed by liquefaction, void ratio became a good indicator of reliquefaction resistance for all of the test sands, and relative density was appropriate for all of the test sands excluding Youngjong sand. In contrast to the other four test sands, Youngjong sand liquefied throughout its entire profile during all five shaking events, despite the increase in density resulting from shaking and reconsolidation. As illustrated in Fig. 7(a), the relative density of Youngjong sand was on the low end of measured relative densities during the first four shaking events; however, by the end of the 4th event, the relative density of Youngjong sand had increased to approximately 60%, yet the entire profile still liquefied during the 5th shaking event. In terms of void ratio though, the global void ratio of Youngjong sand remained larger than that of the other four test sands during each shaking event. As reported in Table 1, the maximum void ratio is larger than that of the other four test sands, the minimum void ratio is the second largest, and Youngjong sand is finer than the other sands. These observations indicate that grain characteristics such as gradation, particle shape, and uniformity significantly influences excess porewater pressure generation, as suggested by Seed and Idriss [23].
3.4. Effect of grain characteristics on liquefaction resistance In order to compare liquefaction resistance from profiles that liquefied in a specific number of cycles with profiles that developed excess porewater pressures without liquefying (i.e., ru o1), we defined a simple capacity to demand ratio as follows: 8 NL NR Capacity C < 20 cycles or 20 cycles for ru ¼ 1 ¼ 1 Demand D : ru for ru o 1
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Fig. 6. Variation of liquefaction resistance with successive shaking events (H¼model height; DNL¼ did not liquefy; ru ¼ratio of excess porewater pressure to initial vertical effective stress ¼ux/s0 vo).
Fig. 8 presents C/D ratios for each of the five test sands during each shaking event with respect to several sand gradational characteristics: D10, D50, and CU. The plots in Fig. 8 only include
the C/D ratios for the mid-depth of the profile (i.e., 2/4H) for clarity and because this depth provided a reasonable average response for the entire profile during each shaking event. In addition, Fig. 8 also
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reasonable trend with C/D, with liquefaction resistance increasing as D210D2.8 increases. r Fig. 9 presents the ratio of NR (2nd event)/NL (1st event; e.g., refer to Table 3) for each of the test sands with respect to D210D2.8 r (computed prior to the 1st shaking event) as well as D10/CU as proposed by Ha et al. [10]. The latter parameter also is crudely related to cv, as D10 is proportional to k0.5 v for cohesionless sands [24] and CU is inversely proportional to permeability and compressibility for cohesionless sands ([24] and [27], respectively); however, the value of CU does not vary greatly among the test sands and the effect of D10 dominates the correlation. As shown in Fig. 9, the ratio of NR (2nd event)/NL (1st event) linearly decreased as both D210D2.8 and D10/CU increased, but r remained constant as about 0.20–0.25 (i.e., 20–25% of the initial liquefaction resistance) for values of D210D2.8 and D10/CU greater than r about 4 102 mm2 (for Dr in percent) and 0.12 mm, respectively. These combined gradational parameters reasonably describe the decrease in liquefaction resistance observed following initial liquefaction for the test sands.
4. Evaluation of liquefaction and reliquefaction resistance mechanisms
Fig. 7. Variation of pre-event average relative density and average void ratio with successive shaking events.
shows the number of cycles required to trigger liquefaction with respect to (D10)2(Dr)2.8. This parameter can be empirically related to the coefficient of consolidation, cv, as follows cv ¼
kv
gw mv
cD210
1:4 w 1:7=N 60
g
cD210
gw 1:7=½ða þ bsuv ÞD2r 1:4
‘cv pD210 D2:8 r
ð1Þ
ð2Þ conductivityEcD210
for cohesionwhere kv is the vertical hydraulic less sands [22]; gw is the unit weight of water; mv is the coefficient 1:4 of volume change, dev =dsuv 1:7=N60 , for cohesionless sands and gravels [25]; ev is the vertical strain; su is the vertical effective stress; N 60 is the average energy-corrected standard penetration test blow countE(a +bs0 v)D2r [26]; and a, b, and c are constants. As illustrated in Fig. 8, neither initial liquefaction resistance nor reliquefaction resistance (in terms of C/D) appear to be related to D50, D10, and CU, although D10 may exhibit a weak correlation with liquefaction resistance because it is related to hydraulic conductivity. The lack of correlation observed in these plots suggests that while grain characteristics influence initial liquefaction resistance (as noted above), no individual grain characteristic examined in Fig. 8 is sufficient to define trends of liquefaction and reliquefaction resistance. However, the proxy for cv (pD210D2.8 r ) shows a
Fig. 6 illustrates that the liquefaction resistance of each of the test sands decreases significantly from the 1st to the 2nd shaking event, despite the increase in Dr. This decrease in liquefaction resistance immediately followed by an initial liquefaction event supports the liquefaction and reliquefaction resistance mechanism postulates proposed by both Oda et al. [8] and Olson et al. [5]. In particular, the number of cycles required to reliquefy Youngjong sand decreased after the 1st shaking event, and remained essentially constant during subsequent shaking events (Fig. 6b). These data support the Oda et al. [8] postulate that suggest that the large shear strain experienced during liquefaction (42–3%) creates a highly anisotropic, column-like structure with connected voids that is highly unstable when stressed in a direction perpendicular to the elongation direction (i.e., mainly the major principal stress direction). However, in contrast to Youngjong sand, Fig. 6(a), (c), (d) and (e) illustrates that while the liquefaction resistance decreased considerably after the 1st shaking event for these four test sands, liquefaction resistance generally increased following the 2nd event. In fact, liquefaction was not achieved in at least a portion of each sand model profile during the 3rd shaking events, and during the 5th event, none of the model profile liquefied in these four test sands. The large increase in liquefaction resistance following the 2nd shaking event observed for these four sands could not be reasonably explained by the Oda et al. [8] postulate. Presumably, if a column-like structure is formed following the 1st occurrence of liquefaction, this column-like structure should re-form after each occurrence of liquefaction. However, if a column-like structure re-forms after each event, presumably the relative density and liquefaction resistance should remain relatively constant following the first liquefaction occurrence. Therefore, Oda et al.’s [8] postulate appears to hold following the 1st shaking event. However, this postulate does not directly account for the density increase observed during subsequent shaking events for four of the five test sands. The Olson et al. [4,5] postulate suggests that liquefaction resistance may decrease following the 1st shaking event as a result of destruction of the pre-existing ‘‘aged’’ soil structure. In the case of the test sands, each of the sands were ‘‘aged’’ for approximately 1 h prior to the 1st shaking event; as the specimen was prepared, instruments were connected to the data acquisition system and initialized, etc. Consolidation following the final lift placement during initial deposition in the specimen box occurred in approximately 20–30 s for Youngjong sand and about 10–15 s for the other four sands. Therefore, the approximately one hour required to
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Fig. 8. Liquefaction capacity to demand ratio (C/D) with respect to grain characteristics at the mid-depth of the profile (i.e., 2/4H).
Fig. 9. Ratio of reliquefaction resistance during the 2nd shaking event to the initial liquefaction resistance, NR (2nd)/NL, with respect to gradational parameter D210D2.8 and r D10/Cu.
Table 3 Ratio of initial liquefaction resistance to reliquefaction resistance for each shaking event. Test sand
Dist. above base
NR (2nd event)/NL
NR (3rd event)/NL
NR (4th event)/NL
NR (5th event)/NL
Jumunjin sand
3/4H 2/4H 1/4H
0.40 0.20 0.13
0.20 No liq. No liq.
No liq. No liq. No liq.
No liq. No liq. No liq.
Youngjong sand
3/4H 2/4H 1/4H
0.85 0.65 0.54
0.62 0.35 0.39
0.85 0.48 0.54
0.70 0.39 0.50
Incheon1 sand
3/4H 2/4H 1/4H
0.30 0.13 0.10
0.40 0.13 No liq.
0.40 No liq. No liq.
No liq. No liq. No liq.
Incheon2 sand
3/4H 2/4H 1/4H
0.40 0.33 0.25
0.67 0.50 No liq.
0.67 No liq. No liq.
No liq. No liq. No liq.
Han River sand
3/4H 2/4H 1/4H
0.80 0.37 0.33
1.0 0.43 No liq.
1.0 No liq. No liq.
No liq. No liq. No liq.
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prepare for the 1st shaking event represents about two to three log cycles of time for secondary compression to occur. Secondary compression is the time-dependent process of minor grain adjustments into a more stable configuration under constant vertical effective stress [7,25,28], and it significantly improves particle interlocking and liquefaction resistance. In addition, more secondary compression occurs per log cycle of time in more compressible soils, as the secondary compression index (Ca ¼ De/D log t) is proportional to the compression index (Cc ¼ De/ D log s0 v), i.e., Ca/Cc ¼ constant for a given soil [25,28]. In sands, compressibility is inversely proportional to relative density; therefore, looser sands will exhibit larger values of Cc (as illustrated by the void ratio changes in Fig. 7), and in turn, larger values of Ca. Thus, secondary compression of the initially loose sand column, in conjunction with the anisotropic sand fabric, provided relatively high initial liquefaction resistance despite the initially low relative densities. Liquefaction during the 1st shaking event destroyed the ‘‘aged’’ soil fabric, and the sand reconsolidates as a young, normally consolidated sand. Again, less than about one hour of time elapsed following each shaking event to allow for downloading data, rechecking instruments, etc. Therefore, about two log cycles of time elapsed following reconsolidation, allowing secondary compression to occur. However, the factor of two increase in relative density following the 1st event results in a significant decrease in compressibility (i.e., mvpDr 2.8), and in turn, results in a significant decrease in Ca. Therefore, despite having almost the same time for secondary compression to occur, significantly less secondary compression occurred following the 2nd shaking event because of the large decrease in Ca. This decrease in secondary compression, in conjunction with the destruction of the anisotropic soil fabric, results in a sizeable reduction in reliquefaction resistance following the 1st shaking event despite the increase in relative density, consistent with the Olson et al. [4,5] postulate. Following the 2nd shaking event, additional reconsolidation occurs, although the increase in Dr is much less than that following the 1st shaking event (see Fig. 7). Following the 3rd and subsequent events, even smaller increases in Dr occur for each of the sands. As Dr increases, the opportunity for secondary compression to influence the sand fabric decreases. However, for the Jumunjin, Incheon1, and Incheon2 sands, the combination of relatively high hydraulic conductivity (larger D10 grain sizes) and medium dense to dense relative density (Dr Z 60%) prevented the generation of large excess porewater pressure and reliquefaction resistance increases. These increases in relative density and corresponding increases in liquefaction resistance are reasonably consistent with prior observations [4,5,7]. For the Han River and Youngjong sands, the combination of lower hydraulic conductivity (smaller D10 grain sizes) and medium dense relative densities (Dr 50%) allows excess porewater pressures to be generated and maintained. The combination of hydraulic conductivity and compressibility is captured by cv. As discussed previously, cvpD210D2.8 r , and Fig. 8 illustrates that reliquefaction resistance increases significantly when this parameter exceeds about 104 mm2 (for D10 in mm and Dr in percent). For the level of cyclic demand employed in these tests, sands 4 2 with D210D2.8 r 4 10 mm become nonliquefiable. Given this observation, with additional study it may be possible to extend this concept to other values of seismic or cyclic demand and identify values of cv (or its more readily estimated proxy, D210D2.8 r ) above which liquefaction or significant generation of porewater pressure does not occur.
5. Conclusions In this study, 1 g shaking table tests were performed using five sands with differing gradation characteristics [effective grain size (D10) ¼0.11 to 0.40 mm, and coefficient of uniformity
(Cu)¼1.53–2.57] to test the validity of two postulates regarding reliquefaction mechanism and to examine the role of gradational characteristics on reliquefaction resistance. Test results demonstrate that the number of cycles required to trigger liquefaction during the 1st shaking event (at any depth) is considerably larger than that required to trigger liquefaction during the 2nd event (i.e., reliquefaction), likely as a result of the ‘‘aged’’ sand fabric developed during secondary compression of the initially loose sands and the initially anistropic sand fabric resulting from initial deposition. During the 3rd (and subsequent) shaking events, only Youngjong sand with the smallest effective grain size liquefied at all depths in the profile. The test results illustrate that liquefaction and reliquefaction resistances do not correlate well to relative density or void ratio, D10, D50, or CU. While no single index property or grain characteristic is sufficient to define trends of liquefaction and reliquefaction resistance, the proxy for coefficient of consolidation (cv ¼kv/gwmvpD210D2.8 r ) shows reasonable correlation with liquefaction and reliquefaction resistance. Similarly, liquefaction and reliquefaction resistance correlate reasonably well with D10/CU, which also is crudely related to cv. 4 2 That is, as D210D2.8 r increased above a value of about 10 mm (for Dr in percent), reliquefaction resistance increased significantly. The observation that liquefaction resistance decreases following the first occurrence of liquefaction supports both the Oda et al. [8] and the Olson et al. [4,5] postulates. However, the subsequent increase in liquefaction resistance following the 2nd shaking event for four of the five test sands is not consistent with the Oda et al. postulate that the sand forms a column-like structure following liquefaction. In contrast, the increasing density following each shaking event and increases in liquefaction resistance following the 2nd shaking event is reasonably consistent with the Olson et al. postulate. Based on our observations, the coefficient of consolidation, cv, or proxy values such as D210D2.8 or D10/CU correlate reasonably well r with reliquefaction resistance and, with additional study, may be a useful tool for evaluating reliquefaction potential.
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