Keywords

1 Introduction

Due to its catastrophic consequences, soil liquefaction has been a matter of great concern to the engineering community; therefore, intensive research and development efforts have been dedicated to understand the phenomena and prevent future losses and damages. The development of liquefaction constitutive and numerical models in the last decades promoted an increase in its use for research and engineering practice purposes. However, as stated by Kutter et al. (2018b), there is still no practical generally accepted process for validation of capabilities of the numerical implementations; therefore, V&V exercises are required to enhance its reliability.

In this sense, LEAP (Liquefaction Experiments and Analysis Projects) was established as an international joint project that pursues the verification, validation, and uncertainty quantification of numerical liquefaction models, based on high-quality experimental data (e.g., centrifuge model tests). In the LEAP framework, three main exercises (“LEAP-GWU-2015,” “LEAP-UCD-2017,” and “LEAP-ASIA-2019”) were developed to investigate the dynamic behavior of a uniform, 4-m-deep, 5-degree slope sandy ground.

As part of the “LEAP-GWU-2015” exercise, the same 4-m-deep, 5° slope sandy ground model was repeated by six centrifuge facilities; Kutter et al. (2018a) found that despite variability, the experimental results were consistent with each other, lending credence to the approach for a next-generation validation database. In the subsequent “LEAP-UCD-2017” exercise, 9 centrifuge facilities developed 24 centrifuge models with the same geometry as the previous exercise, but with different combinations of relative density (Dr) and peak ground acceleration (PGA). Kutter et al. (2020b) found consistent results and clear trends among the experiments in this exercise.

Building on the consistency of these exercises, Tobita et al. (2023) conceived “LEAP-ASIA-2019” to use the same model geometry as the previous tests, with two main objectives: validating the “generalized scaling law” for centrifuge modeling (Iai et al., 2005) by developing two models (Model A and Model B) representing the same prototype model using conventional scaling laws and the generalized scaling laws, respectively, and filling gaps in the data from the “LEAP-UCD-2017” exercise in terms of combinations of Dr and PGA to extend, establish, and confirm observed trends.

As part of “LEAP-ASIA-2019” exercise, five centrifuge tests were developed in the 2.50 m radius and 24g-ton centrifuge of the Disaster Prevention Research Institute (DPRI) at Kyoto University; although a comprehensive review of the test findings has already been published (Vargas et al., 2021), this paper focuses on the details of the model preparation and presents the test results.

2 Test Specifications and Model Preparation

2.1 Description of the Model and Scaling Laws

As described by Tobita et al. (2023), a uniform-density, 20-m-long, 4-m-deep at center, and 5° sloping deposit inside a rigid container was specified for “LEAP-ASIA-2019”; since the model specifications established for “LEAP-UCD-2017” are applicable for this exercise, the models were built following the specifications established by Kutter et al. (2020a).

The dimensions of the rigid box used in the tests are presented in Fig. 10.1. The instrumentation consisted of two horizontal (AH11 and AH12) and two vertical (AV1 and AV2) accelerometers placed outside the box to record the input motions. In addition, six horizontal accelerometers (AH1, AH2, AH3, AH4, AH6, and AH9) and eight pore pressure transducers (P1, P2, P3, P4, P6, P8, P9, and P10) were placed inside the ground to capture the soil response in the central array and the effects of the rigid boundaries.

Fig. 10.1
A front view and a section A-A of the model. The front view consists of a rigid container, a curved 5-degree slope, and six horizontal accelerometers with dimensions labeled. The section A -A depicts two vertical accelerometers and others with dimensions.

Dimensions and instrumentation of the models. (Vargas et al., 2021)

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The standard sand selected for the “LEAP-ASIA-2019” is Ottawa F-65, a clean, poorly graded, silica sand, with less than 0.5% fines by mass (Carey et al., 2020). In order to guarantee that all facilities use the same material, UC Davis delivered the sand to all the facilities prior to the tests.

As mentioned in the previous section, one of the goals of this exercise was the validation of the “generalized scaling law” for centrifuge modeling (Iai et al., 2005); this scaling law involves a two-stage scaling process in which physical model parameters are first scaled to a “virtual 1 g” field using the conventional centrifuge scaling factor, η, and then further scaled to the “prototype” field using scaling factors for 1g tests, μ. The scaling relationships are presented in Table 10.1.

Table 10.1 Generalized scaling relationships
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For this exercise, five models were developed in the geotechnical centrifuge of the Disaster Prevention Research Institute at Kyoto University; Table 10.2 shows the scaling factors used for each model.

Table 10.2 Tests developed at Kyoto University and its scaling factors
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As seen in Table 10.2, all models have the same dimensions in prototype scale (i.e., the same “generalized scaling factor”); however, different scaling factors were used. In order to study the validity of the generalized scaling law, and for comparative purposes, two groups of models were generated, aiming to achieve a similar relative density (Dr) and effective peak ground acceleration “PGAeff” (Kutter et al., 2020b) in each of them.

2.2 Model Preparation

As specified, the air pluviation method was used for sand placement; the constant air pluviation height was defined following a calibration process (definition of a height-density relationship), prior to each experiment. It was found that the height-density relationship was slightly different for each experiment; although it seems that the difference could be attributable to environmental conditions (such as humidity, temperature, etc.), further research would be required for confirmation.

Density measurements were conducted at three different stages during sand placement for each model; less than 5% (in terms of relative density) of difference between layers was found. Table 10.3 shows the target and achieved dry densities, and these densities were obtained through mass and volume estimations.

Table 10.3 Target and achieved dry densities for the five models
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Since the centrifuge facility at Kyoto University is equipped with a shaking table in the circumferential direction, to reduce the effects of variations in the radial gravity field, the surface was curved according to the geometry of the facility (i.e., a circumference with 2.50 m radius), so all points in the surface would have the same slope relative to the gravity field and may represent ground with a constant, 5° slope angle in the prototype scale (Tobita et al., 2018). The procedure for curving the surface was described by Vargas et al. (2020). Figure 10.2 shows Model KyU_A_A1_1, before and after curving the surface.

Fig. 10.2
Two photos exhibit Model K y U underscore A underscore A1 underscore 1, with one image capturing the surface in its initial state and the second image displaying the surface after the curving process.

Model KyU_A_A1_1. (a) Before curving the surface. (b) After curving the surface. (Vargas et al., 2021)

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2.3 Saturation Process

After curving the surface, the rigid container containing the model was placed in a vacuum chamber. Initially, vacuum pressure of around −0.1 MPa was applied to facilitate the dissolution of gas bubbles, and CO2 was gradually flooded until reaching atmospheric pressure values. Vacuum pressure was then reapplied and maintained until the end of the saturation process.

Following the vacuum application, the sample was saturated from the top, using a de-aired solution of de-ionized water and methylcellulose (SM-100, Shin-Etsu Chemical Co., Ltd.); the mixing rate was iteratively adjusted to achieve the target viscosity determined by the scaling laws.

Since the viscosity experiences significant variations along with changes in temperature, the amount of methylcellulose was properly adjusted to achieve the required viscosity at temperatures closer to the ones expected in the test. Figure 10.3 shows the viscosity-temperature curve for Model KyU_A_B2_1, measured using a “tuning fork vibration viscometer” (Izumo, 2006).

Fig. 10.3
A line graph plots viscosity versus temperature. The line starts at (7, 70), decreases, and drops at approximately (23.9, 39).

Viscosity-temperature curve – Model KyU_A_B2_1

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After depositing the viscous mixture, the applied vacuum was gradually removed until achieving the atmospheric pressure.

The degree of saturation of the model was estimated using Okamura’s method (Okamura & Inoue, 2012), which relates the degree of saturation with small variations of the water surface caused by pressure changes. In specific, a piece of polystyrene was placed floating over the model’s “water” surface (methylcellulose solution), and “small” amounts of vacuum (−0.02 ~ −0.03 MPa) were induced in the vacuum chamber. The vacuum-induced variations in the “water” surface height were measured using laser sensors, assuming that the variations of the floating polystyrene’s height correspond to variations of the “water” surface.

After confirming that the saturation of the model was higher than 99%, the model was transported by means of a crane from the vacuum chamber to a scale, to confirm the actual weight prior to testing. Figure 10.4 shows the model after the saturation process.

Fig. 10.4
A photograph of a model after saturation depicts its appearance or condition following the saturation process.

Model after saturation

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2.4 Model Testing

The testing procedure included a shake sequence of three “destructive” input motions, and each motion consists of a ramped sinusoidal 1 Hz wave (as seen in Fig. 10.5).

Fig. 10.5
A line graph plots acceleration versus time commencing at 0 seconds, transforming into a sinusoidal wave, and subsequently converging into a narrower pattern.

Specified ramped sine wave. (Vargas et al., 2021)

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Due to the presence of high-frequency vibrations in the achieved motions, and taking into account that higher-frequency components have some but relatively small effect on the behavior of the model, this project (as a first approximation) used the effective PGA (Kutter et al., 2020b).

$$ {\mathrm{PGA}}_{\mathrm{effective}}={\mathrm{PGA}}_{1\mathrm{Hz}}+{0.5}^{\ast }{\mathrm{PGA}}_{\mathrm{hf}} $$

where “PGA1Hz” represents the PGA of the 1 Hz component of the achieved motion and “PGAhf” represents the higher-frequency components of the ground motion.

2.5 Cone Penetration Tests (CPTs) and Measurement of Surface Displacement

As a parameter to better estimate the density and ground uniformity, cone penetration tests (CPTs) were performed in each experiment; for each experiment, three CPTs were developed, one before each destructive motion, with a new 6 mm mini-CPT (Carey et al., 2018); this method, although providing an indirect measurement (i.e., tip resistance “qc”), has proven to be reliable in the estimation of the uniformity of the ground and its associated dry density (Kutter et al., 2020b). Due to the characteristics of the CPT apparatus, it was not possible to induce shaking while the apparatus was mounted; consequently, each time the CPT was performed, the centrifuge had to (1) be stopped to assemble the CPT, (2) increase the required g-level to perform the test, (3) stop again the facility to disassemble the CPT, and (4) increase the g-level for the shaking process.

Regarding the measurements of the displacements of the ground surface, the centrifuge was equipped with a high-speed camera (Nac Image Technology, Inc.; MEMRECAM fx RX-6G), which allowed the estimation (by means of image analysis) of the time history values of the relative displacement of the 3-D printed surface markers placed on the ground surface (see Fig. 10.6).

Fig. 10.6
A schematic detailing the geometry of surface markers, featuring a top length of 26 millimeters, bottom length of 20 millimeters, left breadth of 1.5 millimeters, and right breadth of 9 millimeters.

Geometry of surface markers

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3 Test Results (Prototype Scale)

3.1 Achieved Input Motions

To estimate the PGAeffective, the PGA1Hz values were calculated using a notched bandpass filter with corner frequencies between 0.9 and 1.1 times the predominant frequency. Table 10.4 shows the estimated values of PGA, PGA1Hz, and PGAeff of the first destructive motion.

Table 10.4 Target and estimated PGAeff values – prototype scale
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As shown in Table 10.4, the achieved PGAeff values were consistently maintained within each group’s tests (i.e., 0.25g for Group 1 and 0.12g for Group 2). To achieve this, the shaking table was calibrated before each test.

Figures 10.7 and 10.8 show a comparison between the target motion and the achieved input Motion 1 for each model.

Fig. 10.7
3 line graph plots acceleration versus time The lines are achieved motion and target motion commencing at 0 seconds, transforming into a sinusoidal wave, and subsequently converging into a narrower pattern.

Comparison among achieved and target input motions for Group 1 models

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Fig. 10.8
3 line graph plots acceleration versus time The lines are achieved motion and target motion commencing at 0 seconds, transforming into a sinusoidal wave, and subsequently converging into a narrower pattern.

Comparison among achieved and target input motions for Group 2 models

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3.2 Excess Pore Water

Nine excess pore water pressure transducers (EPWPT) were installed inside the ground to estimate the excess pore water pressure (Δu). The Δu values of the first destructive motion for all sensors and the excess pore water pressure ratio (ru) for the sensors located in the central array are shown in Figs. 10.9 and 10.10, respectively.

Fig. 10.9
3 multi-line graphs depict delta u versus time, with lines labeled P1 to P10. The graphs exhibit an initial increase, peak at 20 seconds, followed by a subsequent decrease. Additionally, a table presents data for models P1, P2, P3, and P4.

(a) Excess pore water pressure – Model KyU_A_A1_1. (b) Excess pore water pressure – Model KyU_A_B1_1. (c) Excess pore water pressure – Model KyU_A_B1_2. (d) ru max for sensors located in the central array – Group 1. (Vargas et al., 2021)

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Fig. 10.10
2 multi-line graphs depict delta u versus time, with lines labeled P1 to P10. The graphs exhibit an initial increase, peaking at 10 to 15 seconds, followed by a subsequent decrease. The peak formed by plot 2 is higher compared to plot 1. Additionally, a table presents data for models P 1, P 2, P 3, and P 4.

(a) Excess pore water pressure – Model KyU_A_A2_1. (b) Excess pore water pressure – Model KyU_A_B2_1. (c) ru max for sensors located in the central array – Group 2. (Vargas et al., 2021)

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Figure 10.9 shows that small variations in Δu values (and thus in ru max values) were observed among the models in Group 1. These variations were found to be associated with the achieved PGA values (PGAKyU_A_A1_1 < PGAKyU_A_B1_2 < PGAKyU_A_B1_1). Despite the differences and variations, the models in Group 1 exhibited similar excess pore water pressure behavior even when different scaling laws (i.e., conventional scaling laws and generalized scaling laws) are used to represent the same prototype scale.

Regarding Group 2 models, as seen in Fig. 10.10, important differences among models were found; nevertheless, as with Group 1 models, this difference was found to be correlated with the achieved PGA values. It is worth noting that, for “small” PGA levels at a “low” gravity level, a significant increase in the high-frequency components of the input acceleration (expressed as a percentage of the PGA value) was observed. This resulted in significant differences in the PGA value, even though the PGAeff values were intended to be kept almost constant. Thus, for “large” values of high-frequency content, PGAeff (as previously defined) may not be an appropriate parameter to represent the demand, and further research is needed to clarify this point.

3.3 Ground Motion Accelerations

Figures 10.11 and 10.12 show the response time histories for all accelerometers located inside the deposit for the first destructive motion. As shown in these figures, no significant amplification or distortion of the motion is recorded prior to the development of significant EPWP. However, after significant EPWP development, the motion considerably changed, developing sharp spikes, which are typical characteristics of the dilative behavior of liquefied sand. It is noteworthy that the distortion in the acceleration starts in the shallow zones of the deposit and becomes more pronounced as the ru value increases more rapidly in these regions.

Fig. 10.11
A set of 18 line graphs illustrates acceleration over time for various models, displaying a fluctuating trend with an oscillating pattern.

(a) Ground motion accelerations for Model KyU_A_A1_1. (b) Ground motion accelerations for Model KyU_A_B1_1. (c) Ground motion accelerations for Model KyU_A_B1_2. (Vargas et al., 2021)

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Fig. 10.12
A set of 12 line graphs illustrates acceleration over time for various models, displaying a fluctuating trend with an oscillating pattern.

(a) Ground motion accelerations for Model KyU_A_A2_1. (b) Ground motion accelerations for Model KyU_A_B2_1. (Vargas et al., 2021)

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Figure 10.11 shows that all Group 1 models exhibited similar response acceleration behaviors, both before and after the distortion caused by significant EPWP development. Although some slight differences may be noticeable, as in the case of EPWP values (Sect. 10.3.2), these were found to be correlated with the achieved PGA values. Therefore, it can be concluded that Group 1 models, including those using either conventional scaling laws (KyU_A_A1_1) or generalized scaling laws (KyU_A_B1_1 and KyU_A_B1_2), show comparable behaviors in terms of ground response acceleration.

Regarding Group 2 models, Fig. 10.12 shows that only sensor AH4 exhibited significant distortions in the ground response acceleration, which is consistent with the EPWP values reported in Fig. 10.10. Despite the differences in PGA values, the ground response acceleration behavior appears to be reasonably similar between the two Group 2 models (KyU_A_A2_1 and KyU_A_B2_1).

Also, it is worth noting that, as mentioned in the previous section, Model KyU_A_B2_1 exhibited a significant increase in high-frequency components for “small” PGA levels at a “low” gravity level; and, in addition to the increment of the high-frequency components, additional cycles of vibration (from t = 18.5 s) were recorded.

3.4 Cone Penetration Tests

As specified, in-flight cone penetration tests “CPTs” (Carey et al., 2018) were carried out prior to each destructive motion. Specifically, CPT1, CPT2, and CPT3 were conducted before Motions 1, 2, and 3, respectively.

Kutter et al. (2020b) found that the tip resistance at the mid-depth (i.e., at 2.0 m) is well correlated with the initial relative density of the ground, so this parameter (qc2.0 at CPT1) can be used for comparisons among the tests.

Figures 10.13 and 10.14 show the CPT results for Group 1 and Group 2 models, respectively. The uniformity of the ground was confirmed by the absence of abrupt changes in any of the profiles. Regarding the qc2.0 value at CPT1, a good agreement was found for tests with μ ≤ 2, suggesting that further experiments are needed to determine the suitability of the generalized scaling laws for μ > 2.

Fig. 10.13
3 multi line graph plots q c versus depth for different models. The lines are C P T 1, C P T 2, and C P T 3. In each graph, the lines exhibit a consistent increasing trend.

(a) CPT for Model KyU_A_A1_1. (b) CPT for Model KyU_A_B1_1. (c) CPT for Model KyU_A_B1_2. (Vargas et al., 2021)

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Fig. 10.14
2 multi-line graph plots q c versus depth for different models. The lines are C P T 1, C P T 2, and C P T 3. In each graph, the lines consistently display an initial increasing trend followed by a sharp decrease.

(a) CPT for Model KyU_A_A2_1. (b) CPT for Model KyU_A_B2_1. (Vargas et al., 2021)

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As for the re-liquefaction process, despite that the global relative density of the model increased after each liquefaction process, no clear trend of increase nor decrease was observed in the qc value recorded before and after each process (i.e., comparison between CPT1–CPT2 and CPT2–CPT3); so, for subsequent processes of liquefaction, additional parameters (such as strain history, induced anisotropy, changes in fabric, etc.) need to be taken into account for the determination of the relative density.

3.5 Surface Displacements

As part of the previous exercise (LEAP-UCD-2017), Kutter et al. (2020b) stated that the use of high-speed cameras for measuring lateral displacements of ground surface during lateral spreading proved to be particularly valuable. In this regard, as discussed in Sect. 10.2.4, a high-speed camera was installed in the centrifuge to capture the behavior of the ground surface during and after the motion. An image analysis procedure was employed using the commercial software DIPP-Motion V to obtain the surface displacement based on the recorded images. It is worth noting that the deformation of some markers could not be tracked due to light reflection issues.

Figure 10.15 shows that the displacements of Group 1 models follow a similar trend to that found in the EPWP and the ground response acceleration measurements; the small differences among the tests can be correlated with the achieved PGA values.

Fig. 10.15
3 graph plots Y coordinate versus X coordinate for displacements of different models. The data points fall within the range of negative 4 to 4, with arrows pointing to the right in a horizontal line at each data point.

(a) Surface ground displacements – Model KyU_A_A1_1. (b) Surface ground displacements – Model KyU_A_B1_1. (c) Surface ground displacements – Model KyU_A_B1_2 (magnification of deformation – 15 times). (Vargas et al., 2021)

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In contrast, Fig. 10.16 shows significant differences between the measured displacements of the Group 2 models. As described in Sect. 10.3.3, the differences can be explained by the fact that significant differences in the input motion (an increase in high-frequency components and additional vibration cycles) are recorded, resulting in an increased seismic demand in Model KyU_A_B2_1.

Fig. 10.16
2 graph plots Y coordinate versus X coordinate for displacements of different models. The data points fall within the range of negative 4 to 4, with arrows pointing to the right in a horizontal line at each data point.

(a) Surface ground displacements – Model KyU_A_A2_1. (b) Surface ground displacements – Model KyU_A_B2_1 (magnification of deformation – 15 times)

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4 Conclusions

LEAP (Liquefaction Experiments and Analysis Projects) is a joint exercise that pursues the verification, validation, and uncertainty quantification of numerical liquefaction models. “LEAP-ASIA-2019” is one of the LEAP’s exercises, whose main objectives are to validate the “generalized scaling law” for lateral spreading and to fill the gaps of experiments to complete the dataset obtained as part of the “LEAP-UCD-2017.”

This paper presents the centrifuge tests developed in the geotechnical centrifuge of the Disaster Prevention Research Institute (DPRI) at Kyoto University, for “LEAP-ASIA-2019.”

  • Five models were tested under different centrifugal accelerations, keeping the same geometry in prototype scale (by changing the scaling laws); for comparison purposes, tests were divided into two groups. For Group 1 (Dr ≈ 75% and PGAeff ≈ 0.25g), three models were developed at 44.4g, 22.2g, and 11.1g; as for Group 2 (Dr ≈ 55% and PGAeff ≈ 0.12g), two models were developed at 44.4g and 22.2g.

  • Image analysis was used to estimate the ground displacements as a result of each experiment; the final displacements were estimated by image analysis.

  • The applicability of the generalized scaling law (for μ ≤ 4) was confirmed for generation of EPWP, ground motion response acceleration, and surface ground displacement.

  • As for the CPTs, the applicability of the generalized scaling law was confirmed for μ ≤ 2 values.

  • It has been found that for “large” values of high-frequency contents, the PGAeff (as defined in the LEAP-UCD-2017 exercise) does not seem to be a suitable parameter to represent the seismic demand.

  • As for the re-liquefaction process, no clear trend of increase nor decrease was observed in the qc value recorded before and after each process; so, for the estimation of the relative density in grounds with prior history of liquefaction events, additional parameters need to be taken into account.