Journal of the Korean Geotechnical Society. 30 June 2024. 65-75



  • 1. Introduction

  • 2. Experimental Program

  •   2.1 Cyclic Direct Simple Shear Device

  •   2.2 Test Material

  •   2.3 Test Procedure

  • 3. Test Results

  •   3.1 Cyclic Shear Strain

  •   3.2 Reconsolidation Volumetric Strain

  • 4. Conclusions

1. Introduction

Seismically active regions are often characterized by the susceptibility of saturated soil to liquefaction, a phenomenon with implications for infrastructure and community resilience. Historic earthquakes, such as the Niigata event in 1964 and more recent occurrences in Tohoku and Christchurch in 2011, have demonstrated the destructive potential of liquefaction-induced settlement (Cubrinovski et al., 2011; van Ballegooy et al., 2014; Kazama et al., 2012). When subjected to cyclic loading during seismic events, shear strain is accumulated during each cycle, leading to the development of excess pore water pressure, which subsequently reduces the soil’s stiffness and can result in liquefaction if the effective stress decreases to lower levels. The seismic event can cause the liquefaction of the soil which will be followed by settlement as the excess pore water pressure dissipates and the soil particles rearrange.

The evaluation of liquefaction has been the focus of extensive research, with different adaptations from the simplified procedure by Seed and Idriss (1971). However, conventional approaches are based on the cyclic shear stress ratio imposed by seismic loadings, while the generation of excess pore water pressure is more uniquely related to cyclic shear strain (Dobry and Abdoun, 2015; Cox, 2006). Studies have highlighted the independence of volumetric strain from cyclic stresses, emphasizing the critical role of shear strain in influencing post-liquefaction behavior (Silver and Seed, 1971; Martin et al., 1975).

The evaluation of soil deformations after cyclic loadings relies on a simplified approach correlating the simplified procedure’s factor of safety with the maximum shear strain (γmax) parameter (Ishihara and Yoshimine, 1992). The maximum shear strain shows a strong correlation and influences the behavior of the volumetric strain response (Tatsuoka, 1984). However, limitations arise, particularly under conditions of lower and constant cyclic loading amplitudes but prolonged durations enhance pore water pressure buildup and subsequent liquefaction. The accumulated shear strain (γacm) is a more reliable parameter that can continuously evaluate the soil behavior during the cyclic loading and account for the shear strains developed after a maximum shear strain has been presented (Sento et al., 2004).

As mentioned above, cyclic shear stress-based models are commonly used to describe the soil’s behavior under cyclic loading and its further settlement. However, stress-controlled tests are highly sensitive to frequency content and will present different behaviors under harmonic loadings simulated at the laboratory (Kamil Bekir, 2019). Stress-strain response of sands undergoing post-liquefaction volumetric strains remains not fully understood and further investigation is needed to clarify the factor controlling the strain accumulation.

This study aims to contribute to the understanding of liquefaction-induced settlement by conducting a series of strain-controlled tests using the cyclic direct simple shear (CDSS) device on clean sand specimens. Specifically, we examine soil deformation under seismic loading in terms of γacm, to assess the effects of soil density, cyclic wave shape, and sample preparation method. Through rigorous experimentation, our research aims to enhance insights into liquefaction-induced settlement mechanisms and inform more accurate predictive models and mitigation strategies in seismic risk management.

2. Experimental Program

2.1 Cyclic Direct Simple Shear Device

Testing was performed using an automated Cyclic Direct Simple Shear (CDSS) NGI-type (Norwegian Geotechnical Institute) design developed by Geocomp. This device comprises a ShearTrac-II system to allow the input of uniform shear deformations. One load cell is positioned above the sample in the vertical direction to measure normal stress, while another load cell is installed in the horizontal direction to measure shear stress. Additionally, a series of linear variable deformation transformers (LVDTs) were integrated to continuously monitor vertical and horizontal displacements throughout the testing process. LVDT is a position-to-electrical sensor whose output is proportional to the position of a movable magnetic core which assures an accurate and reliable method for measuring linear distances. To perform a test in undrained conditions, vertical displacements are restrained to prevent any change in height and create a constant volume condition, facilitating the measurement of changes in vertical effective stress, which corresponded to variations in excess pore water pressure (Dyvik et al., 1987; Finn, 1985). To confine the cylindrical specimen laterally and prevent horizontal deformations to create a K0 condition, a stack of rings was employed, this will simulate a pure shear plus rotation (Bjerrum and Landva, 1966).
Fig. 1

Cyclic direct simple shear device

2.2 Test Material

The test material was Jumunjin sand, a standardized clean uniform sand in Korea. It contains sub-angular particles and is classified as poorly graded (SP) according to the USCS and the particle size distribution is shown in Fig. 2. Table 1 lists the soil properties of Jumunjin sand. The maximum and minimum void ratios are 0.992 and 0.626, respectively. The minimum and maximum dry unit weights are 13.3 and 16.3 kN/m3, respectively and the specific gravity is 2.65.
Fig. 2

Soil particle distribution curve

Table 1.

Soil properties

Soil Jumunjin sand
D50 (mm) 0.61
Specific gravity 2.65
Max. dry unit weight (kN/m3) 16.3
Min. dry unit weight (kN/m3) 13.3

The Jumunjin soil specimen was reconstituted to a size of 63.5 mm in diameter and 20 mm in height. The target relative density of soil specimens was 40% (loose), 60% (medium), and 80% (dense), and each was divided and compacted into five layers to ensure homogeneity. Previous studies highlight the significance of soil fabric, which can be influenced by the reconstitution method (Whitman and Lambe, 1985). The moist tamping (MT) technique is widely used in the critical state approach because of its capacity to reconstitute samples under loose or very loose conditions, tending to show a contractive behavior. Air pluviation results in a more contractive response and enhanced reverse behavior than wet reconstitution methods, however, cannot be applied to every type of soil to reach lower densities. This study adopts two sample preparation techniques to investigate their impact on soil behavior. Samples were prepared under dry and moist conditions using the undercompaction technique by Ladd (1978). MT samples will initially be mixed with water to achieve water contents of w = 5%-6%, allowing for preparation at lower densities. On the other hand, dry samples will be remolded using the AP technique. Each prepared soil specimen was covered with a membrane and mounted on the testing device for the CDSS tests.

2.3 Test Procedure

The procedure encompasses three steps (1 to 3), consolidation, cyclic loading, and reconsolidation. During the consolidation step (step 1), a vertical stress (σv) of 100 kPa is applied and continuously monitored until vertical displacement stabilizes. The relative density after consolidation Drc is measured as a function of the change in height during loading, given the small height-to-diameter ratio in the CDSS, the Drc significantly increased compared to initial conditions.

Recent seismic events have highlighted the effects of magnitude and duration where the accumulations of strains with each loading increase constantly and can affect the response of the soil and its post-liquefaction settlement. Therefore, cyclic loading (step 2) was applied using events of different magnitudes by a sinusoidal wave with constant shear strain amplitude and frequencies. Fig. 3 illustrates an example of one of the applied sinusoidal waves. Waveshape was examined varying the frequency from 0.1 Hz to 0.74 Hz and the shear strain amplitude from 0.1% to 2.5%. The number of cycles is determined by the target accumulated shear strain (γacm) eq. 1, where higher γacm, will account for longer and stronger seismic events Measurements are continuously recorded throughout each cycle. The γacm is defined by Sento et al. (2004) as:
Fig. 3

Example of the input wave


where γ˙t denotes the shear strain rate at time t. Loading history can be denoted by the accumulated shear strain that represents the soil damage (Kanatani et al., 1994) and works as an index to analyze the volumetric strains as the excess pore water pressure dissipates (Kim et al., 2017). Table 2 expresses the waveshape for each test, in terms of amplitude, frequency, and accumulated shear strain for each test.

Table 2.

Test cases

CDSS ID Drc (%) γacm (%) γ (%) f (Hz) P. M.
1-72-80-0.1-0.33 72 80 0.1 0.33 AP
2-72-80-0.35-0.5 72 80 0.35 0.5 AP
3-70-80-1-0.33 70 80 1 0.33 AP
4-71-80-1.5-0.5 71 80 1.5 0.5 AP
5-87-20-0.5-0.1 87 20 0.5 0.1 AP
6-86-40-0.5-0.1 86 40 0.5 0.1 AP
7-86-60-0.5-0.1 86 60 0.5 0.1 AP
8-86-80-0.5-0.1 86 80 0.5 0.1 AP
9-85-100-0.5-0.1 85 100 0.5 0.1 AP
10-86-150-0.5-0.1 86 150 0.5 0.1 AP
11-87-200-0.5-0.1 87 200 0.5 0.1 AP
12-77-20-0.5-0.1 77 20 0.5 0.1 AP
13-75-40-0.5-0.1 75 40 0.5 0.1 AP
14-75-60-0.5-0.1 75 60 0.5 0.1 AP
15-74-80-0.5-0.1 74 80 0.5 0.1 AP
16-76-100-0.5-0.1 76 100 0.5 0.1 AP
17-75-150-0.5-0.1 75 150 0.5 0.1 AP
18-75-200-0.5-0.1 75 200 0.5 0.1 AP
19-69-200-0.5-0.1 69 200 0.5 0.1 AP
20-67-300-0.5-0.1 67 300 0.5 0.1 AP
21-70-20-0.5-0.33 70 20 0.5 0.33 AP
22-70-40-0.5-0.33 70 40 0.5 0.33 AP
23-67-60-0.5-0.33 67 60 0.5 0.33 AP
24-68-80-0.5-0.33 68 80 0.5 0.33 AP
25-67-100-0.5-0.33 67 100 0.5 0.33 AP
26-69-150-0.5-0.33 69 150 0.5 0.33 AP
27-68-200-0.5-0.33 68 200 0.5 0.33 AP
28-68-100-0.5-0.74 68 100 0.5 0.74 AP
29-67-200-0.5-0.74 67 200 0.5 0.74 AP
30-47-20-0.5-0.1 47 20 0.5 0.1 MT
31-46-40-0.5-0.1 46 40 0.5 0.1 MT
32-47-60-0.5-0.1 47 60 0.5 0.1 MT
33-48-80-0.5-0.1 48 80 0.5 0.1 MT
34-50-100-0.5-0.1 50 100 0.5 0.1 MT
35-47-150-0.5-0.1 47 150 0.5 0.1 MT
36-48-200-0.5-0.1 48 200 0.5 0.1 MT
37-66-500-2.5-0.1 66 500 2.5 0.1 MT
38-69-1000-2.5-0.1 69 1000 2.5 0.1 MT
39-68-1500-2.5-0.1 68 1500 2.5 0.1 MT
40-66-100-2.5-0.1 66 100 2.5 0.1 MT
41-65-300-2.5-0.1 65 300 2.5 0.1 MT

Note: ID: (Test no.-Drcacm-γ-f); Drc = relative density after consolidation, γacm = accumulated shear strain, γ = shear strain amplitude, f = frequency, P.M. = preparation method, MT = moist tamping, AP = air pluviation

Reconsolidation (step 3) was performed by applying a confining stress equal to the initial stress reached during consolidation (100 kPa) and displacements were measured to obtain the residual volumetric strain.

3. Test Results

3.1 Cyclic Shear Strain

Strain-controlled CDSS tests were conducted on specimens following consolidation, with typical results depicted in Fig. 4. Each test was subjected to specific strain amplitudes, frequencies, and accumulated shear strains. Fig. 4(a) shows the stress degradation with each loading until it reaches a state of low stresses or residual stress after the occurrence of liquefaction. Denser samples (dense specimens) tend to lose their strength at a smaller pace than looser samples (medium specimens) where stress decreased in the first 10 cycles. Fig. 4(b) is a representation of the hysteresis loops of the test where the reduction of stress in each cycle validates a decrease in the stiffness of the specimen. Fig. 4(c) shows the progressive increase in excess pore water pressure (EPWP) throughout the tests, indicating a gradual trend until it reaches the initial confining stress and a liquefaction state. In dry-dense samples (Drc > 80%), the EPWP reached the initial confining stress after 30 cycles, contrasting with medium samples where this occurred within the initial 10 cycles. Fig. 4(d) shows the gradual loss of vertical stress until it reaches the state of liquefaction and sways at low stresses. Medium samples require fewer cycles to achieve the liquefaction state compared to denser samples. These results agree with different studies presented by many researchers (Ishihara, 1996; Dobry and Abdoun, 2015).
Fig. 4

Typical results from the CDSS test for Dense and Medium samples (shear strain amplitude of 0.5%)

Illustrated in Fig. 5(a), the stress degradation is shown, and the residual stress can be identified. Notably, residual stresses are larger in MT samples compared to the AP samples. This suggests that the water content within the sample may induce some apparent cohesion at the state of low stiffness and confining stress. Conversely, in medium specimens (Drc = 69%) prepared by the MT technique, the EPWP reached the initial confining stress at higher γacm, requiring more cycles, as illustrated in Fig. 5(b).
Fig. 5

CDSS showing stress degradation and residual stress and excess pore water buildup under two different sample preparation techniques; moist-tamped (MT) and air pluviation (AP)

3.2 Reconsolidation Volumetric Strain

Reconsolidation after cyclic loading is reached by applying a confining pressure equal to the initial conditions, 100 kPa. To discover the dependencies with the accumulated shear strain, soil density, waveshape, and sample preparation the volumetric strain, after reconsolidation, is analyzed with the basis of the work proposed by Sento et al. (2004), where the volumetric strain is a parameter of the shear strain history during the cyclic loading. In the following paragraphs an analysis of each factor is evaluated:

3.2.1 Effects of Accumulated Shear Strain, γacm

Volumetric strain measurements are obtained at various levels of γacm, showing a plateau in the volumetric strain after values higher than 200% this behavior aligns with studies presented by previous researchers (Sento et al., 2004; Kim et al., 2021). The correlation suggests a threshold value after exceeding higher shear strain accumulations. This observation is validated at higher γacm of 500%, 1000%, and 1500% where the volumetric strain was 1.52%, 1.59%, and 1.45%, as depicted in Figure 6. Supporting the hypothesis of a maximum volumetric strain with further shear strain loadings.
Fig. 6

Effect of shear strain accumulation on post-liquefaction volumetric strain

3.2.2 Effects of Relative Density

The state of the soil was assessed by conducting tests on samples with different relative densities for each preparation method. Dry-dense samples (Drc ≈ 90%), illustrated in Fig. 7, exhibit a lower volumetric strain than looser samples (Drc ≈ 70%) which exhibited higher volumetric strains after reconsolidation. Dense specimens exhibit minimal volumetric strains at low γacm and increase to approximately 1% at higher γacm (200%). Conversely, loose samples display a volumetric strain of over 1% at low γacm, which rises to nearly 2% at higher γacm (200%) after reconsolidation. This trend aligns with the findings proposed by Sento et al. (2004), indicating that as relative density decreases, volumetric strains tend to increase. The observed effect can be explained by the smaller volume of voids in the denser samples that restrict the rearrangement of particles during the reconsolidation. The trend persisted although moist samples generally exhibited lower volumetric strains, with dense samples contracting less than looser specimens.
Fig. 7

Effect of relative density on post-liquefaction volumetric strain. Dense samples (Drc ≈ 90%), and loose samples (Drc ≈ 70%)

3.2.3 Effects of the Input Wave

Fig. 8 illustrates the effect of the frequency of the wave during the cyclic loading, identifying a fluctuation within a narrow range of volumetric strains due to reconsolidation, despite the variation of the frequency level (f = 0.1 Hz to 0.75 Hz) during the cyclic loading there is no concurrence and the influence is neglectable as described by previous studies (Peacock and Seed, 1968; Polito, 1999; Zhu et al., 2021). This fluctuation is evident in tests conducted under the same γacm. Specifically, Fig. 8(a) depicts strains at 100% γacm, revealing lower responses compared to Fig. 8(b), where higher strains are observed at 200% of γacm. The overall behavior indicates an increase in volumetric strains with increasing the γacm. However, no strong correlation is observed between the frequency and the post-liquefaction volumetric strain at lower or higher γacm. The apparatus has limitations that constrain the use of higher frequencies. Therefore, it is advisable to select frequencies that are within the operational capacity of the device to ensure better control over the applied shear strains during each loading cycle.
Fig. 8

Effect of loading frequency on post-liquefaction volumetric strain at (a) 100% accumulated strain and (b) 200% accumulated strain

The amplitude of the wave was assessed by applying amplitudes ranging from 0.1% to 2.5% (single strain amplitude). Lower amplitudes were not considered in this study to avoid the elastic behavior of the soil (Vucetic and Mortezaie, 2015). The post-liquefaction volumetric strain depends on the γacm, indicating the effect of loading history gradually reduces and reaches a plateau (Sento et al., 2004; Kim et al., 2021). As depicted in Fig. 9 the samples subjected to higher amplitudes tend to exhibit higher volumetric strains. Dry and moist samples were evaluated to confirm this behavior producing higher volumetric strains when subjected to higher amplitudes. Volumetric strains increase as the amplitude of the wave increases even when the γacm has not reached the plateau as observed with amplitudes ranging from 0.1% to 1.5% with volumetric strain after reconsolidation of 1.72%, 1.88%, 2.03%, 2.16%, and 2.28%, respectively. With each cyclic loading, shear strain accumulates, and this behavior at each peak varies before and after reaching the phase of transformation, that is the point of instability where the magnitude of pore pressure is large (Ishihara et al., 1975; Kawai et al., 2019). Consequently, higher amplitudes are expected to reach the phase of transformation earlier, thereby increasing the volumetric strain response of the sample after reconsolidation.
Fig. 9

Effect of shear strain amplitude and sample preparation method on post-liquefaction volumetric strain

3.2.4 Effects of Sample Preparation Method

The sample preparation method impacted the development of EPWP, resulting in a slower build-up of EPWP and higher residual shear stresses in samples prepared using the MT technique as shown in Figure 5. Ishihara (1996) indicates that the sample preparation method changes the cyclic resistance of sand depending on the fabric structure created. This caused a reduction in volumetric strains, after reconsolidation, in the sample compared with samples with the same Drc and different preparation methods. Fig. 10 illustrates this trend where samples with Drc = 70% reconstituted with AP have a higher volumetric strain than the samples reconstituted using the MT technique. Test results imply that soil particles, with the presence of low percentages of water (5%-6%), exhibit cohesion among each other, which causes a vacuum effect that increases their resistance. Therefore, it is not recommended to conduct undrained tests using constant-volume conditions in moist samples.
Fig. 10

Reconsolidation test results under different remolding methods

Sento et al. (2004), which evaluated the volumetric strain at different γacm as a function of the Dr, described the same trend, with looser samples exhibiting higher volumetric strains. This study tends to underestimate the volumetric strains compared with those reported by Sento et al. (2004). However, denser samples (Drc ≈ 90%), that underestimate the response, are closer to the correlation, compared to looser samples where the difference is higher, as depicted in Fig. 11. Based on the preceding discussions, it can be inferred that the primary factors contributing to the underestimation of post-liquefaction volumetric strains are the amplitude of the input wave and the soil fabric of each specimen.
Fig. 11

Post-liquefaction volumetric strain against accumulated shear strain

4. Conclusions

Experimental results of a series of cyclic direct simple shear tests on clean sand under constant volume conditions are presented to evaluate the deformations of the soil under cyclic loading. Samples were reconstituted to different relative densities through moist tamping and air pluviation, using the undercompaction technique to achieve uniform specimens. During the cyclic loading, characterized by a shear strain-controlled wave, the soil exhibits a well-documented behavior involving the development of pore water pressure and loss of stiffness. Dense samples typically reach a liquefaction state and experience stiffness loss after a higher accumulation of shear strain cycles compared to looser samples, which achieve these states of “zero stresses” in the initial cycles. The reconsolidation test conducted in this study yielded four significant findings:

(1) The accumulated shear strain parameter shows a strong correlation with the development of volumetric strain after cyclic loading. The volumetric strain reaches a plateau at large γacm (≈200%). Higher γacm (500% to 1500%) shows that even after a large γacm the volumetric strain does not change substantially. This is consistent with previous findings that suggest that even if the samples continue to shear the volumetric strain will not suffer sustainable changes.

(2) The post-liquefaction volumetric strains were found to be dependent on the Dr to which they are compared. Samples with higher density (Drc ≈ 90%) tend to exhibit smaller volumetric strains compared to medium-density samples (Drc ≈ 70%). Hence, the framework describes the relationship between volumetric strains and γacm, effectively capturing variations in volumetric strains across different levels of Dr.

(3) Despite the frequency variation (0.1 Hz, 0.33 Hz, 0.5 Hz, and 0.74 Hz), the volumetric strains observed after reconsolidation were similar, while the wave amplitude influences the soil’s volumetric strain response. Higher amplitudes lead to higher volumetric strains. This phenomenon was observed in MT samples, exhibiting the same trend.

(4) The sample preparation method influences the response of the soil. Dry samples exhibit higher volumetric deformations after the cyclic loading, while moist tamped samples, that present higher residual stresses in the cyclic loading, showed lower volumetric deformations after the cyclic loading. This implies that the soil particles with the presence of low percentages of water (5%-6%) exhibit cohesion between each other, which causes a vacuum effect that will increase its resistance. Therefore, conducting undrained tests using constant-volume conditions in moist samples is not recommended.

The conclusions drawn in this study are based on experimental observation of a clean sand subjected to strain-controlled cyclic loadings. The duration and magnitude of seismic events were simulated by a sinusoidal wave with different accumulated shear strains, frequencies, and amplitudes to isolate its effects on the post-liquefaction volumetric strain. Further studies are needed to assess alternative loading modes (e.g., triaxial test, torsional test), fine content influence, and irregular loading (previous seismic loading histories).


Research for this paper was carried out under the KICT Research Program (project no. 20240104-001, Database construction for ground liquefaction assessment based on AI technology) funded by the Ministry of Science and ICT.



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