Keywords

1 Introduction

When loose saturated sand deposits are subjected to shaking during an earthquake, there is reduction of mean effective stress (p′) due to the buildup of excess pore water pressure (∆u) subsequently leading to liquefaction under undrained boundary conditions. Understanding the phenomenon of liquefaction and the methods to mitigate its effects has received considerable attention for the past few decades. The post-liquefaction mechanical behavior of soils is as important as liquefaction. Awareness about the post-liquefaction reconsolidation and stress–strain behavior of soils susceptible to liquefaction is necessary to estimate the earthquake-induced settlements and to evaluate the bearing capacity of the liquefied soil deposits [7, 27]. The effect of previous seismic stress–strain history (cyclic pre-shearing) is important in evaluating the undrained response of liquefied soil deposits. In addition to the induced shear strains (γ), pore pressure (∆u) and degree of post-liquefaction reconsolidation, undrained mechanical behavior of liquefied soils deposits is governed by the same factors that govern the liquefaction behavior of soils, viz, density, fines content, nature of fines, mode of loading, initial effective consolidation pressure (p′c), and loading history. Initially, till early 1990s minimal work was carried out to understand the post-liquefaction behavior of sands [5, 24]. However, more recently various researchers [4, 10, 15, 17, 18, 23, 25] studied the post-liquefaction undrained shear behavior of sandy soils. Olson and Stark [12, 13] suggested a detailed procedure based on a well-documented large database of case histories to evaluate the liquefied strength and post-liquefaction stability of soil deposits susceptible to liquefaction.

Earthquake-induced ground settlements have two components: one resulting during the process of shear deformation of the soil (liquefaction) and the other due to reconsolidation of the liquefied deposits. Settlements resulting from post-liquefaction reconsolidation were reported to be directly related to the maximum induced γ and Δu; which developed during liquefaction [8]. A strong relationship between the post-liquefaction volumetric strains and the factor of safety against liquefaction was reported. Post-liquefaction reconsolidation behavior of the liquefied saturated sandy soils was explored by analyzing pore pressure dissipation curves using solidification and consolidation theory [20, 21]. The increased permeability after liquefaction (~5 times of the initial value) was also observed to facilitate larger settlements during reconsolidation stage of the liquefied deposits [3].

The post-liquefaction undrained monotonic shear behavior of liquefied soils was reported by many researchers [2, 4, 15, 17, 18, 24, 25]. If excess pore water pressure at the end of cyclic loading was allowed to dissipate, the post-liquefaction undrained monotonic stress–strain response was observed to be strongly dependent on relative density including the insignificant influence of amplitude of axial strain and initial confining pressure [18]. Amini and Trandafir [2] reported that the liquefied soil deposits would exhibit dilative post-liquefaction shear strength response, which would be strongly dependent on initial effective consolidation stress (p′c). Wang et al. [26] observed that post-liquefaction shear strength and stiffness increased with the increase in the degree of reconsolidation both at small and large deformations. The mentioned research also studied the post-liquefaction undrained monotonic behavior of soils considering the effect of degree of reconsolidation, relative density, initial effective confining pressure (p′c), fines content, nature of fines, and shear strain amplitude. Robertson [16] presented cone penetration test (CPT)-based relationships to evaluate liquefied shear strength for a wide range of soils based on well-documented case histories. The case histories indicated that young, loose, nonplastic, or low-plastic soils would tend to be more susceptible to significant and rapid strength loss than older, denser and more plastic soils.

A number of investigators also explored liquefaction characteristics of previously liquefied soils under triaxial or simple shear testing conditions [5, 9]. The studies confirmed that liquefaction resistance of previously liquefied specimen could exhibit a marked increase or decrease in its response depending on the level of induced shear strain (γ), excess pore water pressure (Δu), and the initial relative density (Dr) of the specimens. It might be due to the elimination of local instabilities and creation of a nonuniform structure [5]. Oda et al. [14] provided microstructural interpretation of liquefaction mechanism of liquefied granular soils under cyclic loading. Influence of cyclic pre-shearing on undrained cyclic behavior of cohesionless soils was studied by Porcino et al. [15] and Sriskandakumar et al. [17]. The findings revealed that the cyclic response of pre-sheared specimens would depend on the degree of Δu and level of γ reached during the previous cyclic loading. Current study is focused on the evaluation of reconsolidation and liquefaction response of previously liquefied silty-sand specimens under multilevel undrained cyclic triaxial conditions. The research work was carried out to understand the reconsolidation and liquefaction response of already liquefied specimens to simulate the behavior under earthquake aftershocks and other cyclic loading conditions in high seismicity region. The response of reconsolidated specimens under four levels of cyclic loading after initial liquefaction was explored. The material studied consists of medium dense silty-sand collected from Chang dam of Kucth region Gujarat, India. The soil had experienced severe liquefaction during the 2001 Bhuj earthquake resulting in significant damage to the dam [19].

2 Experimental Program

2.1 Material Properties and Specimen Preparation

In the present study, the soil was collected from downstream toe of Chang dam at a depth of 0.5 m. The soil consists of 82% sand, 15% silt, and 1% clay and classified as medium dense silty-sand (SM). Basic geotechnical properties of the Chang dam soil are presented in Table 1. The grain size distribution (GSD) of the soil is illustrated in Fig. 1. Solid cylindrical specimens of 50 mm diameter and 100 mm height were prepared using moist tamping method at in situ dry density and water content of 1.6 g/cm3 and 8%, respectively.

Table 1 Basic properties of test material
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Fig. 1
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Grain size distribution of Chang dam soil

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2.2 Testing Procedure

The post-liquefaction reconsolidation and undrained cyclic behavior of medium dense silty-sand of Chang dam was investigated by conducting a series of isotropically consolidated undrained cyclic triaxial tests under strain-controlled conditions. In post cyclic loading, the liquefied specimens were subjects to four rounds of reconsolidation and undrained cyclic loading to evaluate the post-liquefaction cyclic behavior of the specimens. A schematic representation of the testing procedure along with drainage conditions is mentioned in Fig. 2. The prepared soil specimens were mounted on the loading frame of cyclic cum static triaxial testing machine and were saturated in three steps: CO2 saturation, water flushing, and back pressure saturation. Specimens were flushed with CO2 for 45 min at very low pressure (~5 kPa) while maintaining a cell pressure of 20 kPa [11]. After CO2 flushing, water flushing was conducted by pushing water inside the specimen equal to 2–3 times the volume of the specimen. Back pressure was then applied in increments of 40 kPa (every 2 h) to acquire B (Skempton’s pore pressure parameter) values greater than 0.98. During the saturation stage, the effective confining stress (p′) was maintained at 20 kPa. After saturation, the specimens were isotropically consolidated to respective effective confining pressure (p′c) of 100, 200, and 300 kPa. The consolidated specimens were further subjected to first round (C0) of undrained (constant volume) harmonically varying cyclic axial loading of amplitude (A) 0.4 mm and frequency (f) 0.1 Hz for 50 number of cycles (N). The liquefied specimens were then allowed to reconsolidate and further subjected to second round (C1) of cyclic loading, (A = 0.4 mm, f = 0.1 Hz, and N = 35). The process was repeated three more times to arrive at the fourth round (C4) of cyclic loading, as shown in Fig. 2. The number of cycles was restricted to 50 and 35 as the specimens exhibited liquefaction within 10 cycles during C0.

Fig. 2
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Procedure adopted for repeated multilevel reconsolidation and cyclic loading

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3 Results and Discussion

Loose silty-sands are most susceptible to liquefaction owing to the large compressibility and small-undrained shear strength. These soils undersaturated and undrained conditions undergo liquefaction, even under moderate seismic/earthquake events. Due to their large susceptibility to liquefaction, the post-liquefaction cyclic behavior of such soils becomes essential to evaluate the settlements that will result from reconsolidation and further cyclic loading (aftershocks and other cyclic loads). The current study evaluates the cyclic, post-liquefaction reconsolidation, and undrained behavior of medium dense silty-sand of Chang dam under multilevel cyclic loading.

Chang soil exhibited low liquefaction resistance under first round (C0) of the applied strain control loading of amplitude (A) and frequency (f) to be 0.4 mm and 0.1 Hz, respectively. Figure 3 illustrates the stress–strain and excess pore water pressure (Δu) response of the soil at the three initial confining pressures (p′c) of 100, 200, and 300 kPa. The specimens exhibited initial liquefaction within five cycles with ∆u attaining values nearly equal to initial confining pressure (p′c). Figure 4 shows the effective stress path and evolution of cyclic stress ratio (CSR) and excess pore water pressure ratio (ru) with the number of loading cycles (N) for the specimens at the three p′c. It was observed that CSR exhibited values as low as 0.003 at N equal to 10. The corresponding ru values were evaluated to be higher than 0.97, indicating nearly initial liquefaction (Fig. 3b).

Fig. 3
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Response of Chang dam soil during C0. a Stress–strain, b excess pore water pressure

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Fig. 4
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Response of Chang dam soil during C0. a Effective stress path, b evolution of CSR and ru

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3.1 Post-Liquefaction Reconsolidation Behavior Under Repeated Multilevel Cyclic Loading

After C0, the developed ∆u was allowed to dissipate (reconsolidation) resulting in decreased void ratio. Subsequent cyclic loading after each level (round) is illustrated in Fig. 2. Reduction in void ratios due to reconsolidation at the end of four rounds of cyclic loading are presented in Table 2. The specimens exhibited significant decrease in void ratios with the increase in p′c and with the subsequent levels of cyclic loading. The decrease in void ratio during reconsolidation after a particular round of loading was observed to increase with p′c. At given p′c, the reduction in void ratio decreased with the subsequent rounds of cyclic loading (Δe during reconsolidation decreased as the loading progressed from level C0 to C3), as mentioned in Table 2. The reduced void ratio led to lower compressibility, which resulted in suppressed contractive behavior and increased resistance to liquefaction on subsequent repeated cyclic loading. The reconsolidation volumetric strains could be directly transformed to the maximum shear strain amplitudes that might result during a seismic event [8].

Table 2 Reduction in void ratio during reconsolidation after each level of cyclic loading
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3.2 Post-liquefaction Undrained Stress–Strain and Pore Pressure Behavior Under Repeated Multilevel Cyclic Loading

Specimens reconsolidated after C0 was subjected to the second round (C1) of cyclic loading (A = 0.4 mm and f = 0.1 Hz for N = 35). Figure 5a illustrates the response of specimens subjected to C1. During C1, qmax for each cycle was observed to be higher as compared to C0 except for the first cycle. The lower value of qmax during first cycle might be due to the weakening of the soil fabric resulting from excessively high levels of ru [17]. Although the immediate peak deviatoric stress was observed to be lower as compared to C0, the reconsolidated specimens exhibited higher liquefaction resistance to further cyclic loading. This could be attributed due to the reduced void ratio resulting in more compact packing of the soil particles. Evolution of CSR and ru with number of loading cycles (N) exhibited continuous decrease and increase, respectively for both C0 and C1. However, the respective values for C1 were lower for ru and higher for CSR as compared to C0. Peak parameters evaluated at the end of loading cycles 1, 5, 10, and 35 are presented in Table 3.

Fig. 5
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Stress–strain behavior (A) and pore pressure response (B) of Chang dam soil subjected to repeated multilevel cyclic loading. a C1, b C2, c C3, d C4

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Table 3 Summary of the test results of repeated multilevel reconsolidation and cyclic loading
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After C1, the specimens were allowed to reconsolidate and further subjected to C2. Figure 5b illustrates the stress–strain and pore pressure response of the soil specimens subjected to C2. Both CSR and ru evolved at a slower rate during C2 as compared to C1 and C0. The specimens exhibited significant improvement in liquefaction resistance and were reflected in CSR and ru evaluated at the end of cycles 1, 5, 10, and 35 (Table 3).

After C2, specimens were subjected to two more rounds of reconsolidation and cyclic loading (C3 and C4). Figures 5c, d illustrate the stress–strain and pore pressure response of Chang dam soil subjected to C3 and C4. The results indicated further increase in liquefaction resistance as compared to previous round of cyclic loading. This was reflected in the increasing CSR and decreasing ru for each cycle of subsequent loading rounds, as mentioned in Table 3. The ru at the end of a particular cycle was found to be lower in subsequent levels of cyclic loading. A significant increase in deviatoric stress as compared to ru was observed under repeated cyclic loading. This could be attributed due to the reduced void ratio thereby shifting the state of soil specimens lower and closer to the critical state line (CSL). The closeness of the state of specimen to the CSL increased upon subsequent levels of loading and hence the higher deviatoric stress was observed. This effect was found to increase with the increasing p′c. For C4 and p′c equal to 300 kPa, qmax and p′ at the end of 35 cycles were evaluated to be 51.3 kPa and 25 kPa, respectively, which indicated the strength degradation rather than initial liquefaction. Stress–strain response of specimens showed increased stiffness as compared to previous loading round (Fig. 5). During C4, CSR at the end of 35 cycles was nearly 20 times as that of during C0, however, the increase was a little lower during early stages of cyclic loading (Table 3). The increased resistance to liquefaction could be attributed due to the denser configuration of soil particles that resulted from reconsolidation after each round of cyclic loading. The difference in qmax, CSR and ru at given number of cycles during subsequent loading levels increased with p′c (Table 3) and could be attributed to the increased volumetric strains exhibited during the reconsolidation process (Table 2). The pore pressure response at the end of 35 cycles was found to exhibit ru values of around 0.99 and 0.93 for C0 and C4, respectively, implying increased liquefaction resistance.

The excess pore pressure evolution (Δu) under four repeated rounds of cyclic loading is shown in Fig. 5. Excess pore water pressure evolution (Δu) during the subsequent levels of loading showed prominent maximum and minimum Δu within each cycle of loading. This was addressed as transient or oscillatory excess pore water pressure by Zen and Yamazaki [28]. The zone bounded by maximum and minimum Δu widened as the loading progressed from C1 to C4. This behavior exhibited the increased liquefaction resistance under the subsequent repeated multilevel cyclic loading. Anbazhagan [1] reported similar findings for soils with higher liquefaction resistance as they exhibited larger and wider oscillatory pore pressure response as compared to soils with lower liquefaction resistance. Seed and Rahman [22] reported that oscillatory response was most common in marine sediments except for non-cohesive sediments of loose to medium density. In the current study, the soil behavior shifted to more liquefaction resistant soil behavior on subsequent levels of cyclic loading.

3.3 Effective Stress Path Behavior Under Repeated Multilevel Cyclic Loading

The variations in deviatoric stress (q) and mean effective pressure (p′) during the applied repeated cyclic loading were evaluated by following Cambridge soil mechanics group’s definition of p′ − q; where p′ and q were evaluated to be (σ′1 + 2 * σ′3)/3 and (σ1 − σ3), respectively. Figure 4a illustrates the cyclic effective stress path behavior of Chang dam soil subjected to C0. The stress path at three initial confining pressures evolved with rapid reduction in p′ due to large evolution of ru subsequently leading to initial liquefaction within 10 cycles of the applied cyclic loading. The stress paths reached the instability line established from isotropically consolidated undrained triaxial compression tests [6] during the second cycle of loading at all the three p′c.

Figure 6 illustrates the effective stress path response of Chang dam soil under repeated cyclic loading; C1, C2, C3, and C4. It could be observed that subsequent loading in soil mass exhibited higher mobilization of deviatoric stress, therefore, higher liquefaction resistance. On subsequent loading rounds, the slope of the qmax envelope, which coincided with the slope of the instability line during C0, became steeper. The stress states (p′ − q) at the end of 35 cycles of loading were observed to move gradually away from the stress origin indicating significant presence of mean effective confining pressure (p′) at the end of cyclic loading. Thus, the increase in liquefaction resistance increased with exposure to more levels of cyclic loading, which was further enhanced at higher initial confining pressures (p′c). This supports the fact that the probability of liquefaction of a soil deposit during a future earthquake is greatly reduced for the soil, which has experienced liquefaction due to a similar magnitude earthquake.

Fig. 6
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Evolution of effective stress path under repeated multilevel cyclic loading. a C1, b C2, c C3, d C4

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The evolution of effective stress path under initial and repeated cyclic loading revealed strong impact of pre-shearing on the cyclic behavior of soil. The increase in the liquefaction resistance after cyclic pre-shearing was observed to be higher when level of pre-shearing was lower: low γmax and lower ru [15, 17]. With repeated cyclic shearing, the effective stress path moved away from the origin. The positive effect on the rate of excess pore water pressure development and effective stress path pattern could be helpful in mitigating the liquefaction, provided the initial pre-shear stress levels should remain below critical value and should not induce intolerable residual deformations. The effect of pre-shear repeated cyclic loading is effective only when the soil mass is allowed to reconsolidate after each level of loading.

4 Conclusions

This paper evaluated the reconsolidation and liquefaction behavior of previously liquefied medium dense silty-sand of Chang dam under multilevel cyclic loading. The experiments were conducted under cyclic triaxial conditions and the results were analyzed in the context of reconsolidation volumetric strains, cyclic stress–strain behavior, excess pore water evolution and effective stress path response. In summary, the post-liquefaction reconsolidation and liquefaction behavior under multilevel cyclic loading revealed the followings:

  • Chang dam soil inherently has very low liquefaction resistance with excess pore water pressure (Δu) nearly reaching to initial effective confining pressure (p′c) within 10 cycles of applied dynamic loading. Interestingly, the specimens consolidated to 300 kPa besides 100 kPa and 200 kPa also exhibited liquefaction within 10 cycles indicating very high susceptibility to liquefaction even at greater depths (~30 m).

  • During reconsolidation, large volumetric strains as high as 6% were measured leading to reduction in void ratio by 0.052. The volumetric strains were found to increase with the increase in initial effective confining pressure (p′c) but decreased with the subsequent levels of cyclic loading.

  • The peak stress (qmax) during the first cycle of first level (C1) of loading was observed to be lower as compared to the corresponding value of C0 and could be attributed to the weakening of the soil fabric due to development of excessively high excess pore water pressure during C0. During subsequent rounds of cyclic loading, the qmax was found to be higher than the previous level owing to the increased relative density due to the reconsolidation. The excess pore water pressure during each cycle of subsequent level of loading was found to be lower as compared to the corresponding value during the previous level of loading.

  • Effective stress path response exhibited significant increase in mean effective confining pressure (p′) at the end of each level of cyclic loading as compared to previous level of loading. The value of p′ was found to be strongly dependent on the initial effective confining pressure (p′c).

  • Cyclic stress ratio (CSR) at the end of 35 cycles of fourth repeated loading (C4) was found to be nearly 20 times as compared to C0. It showed large increase in liquefaction resistance of Chang dam soil after five levels of each cyclic loading and reconsolidation.