LEAP-ASIA-2019 Centrifuge Tests at University of Cambridge

Abstract

Two dynamic centrifuge tests were conducted on a 5° liquefiable slope with a slope depth of 4 m at the centre line, as part of LEAP-ASIA-2019 at the Schofield Centre, University of Cambridge. The main purpose of these tests was to investigate the suitability of the generalised scaling laws proposed by Iai et al. (Geotechnique, 55(5):355–362, 2005). The two tests were carried out at two drastically different g levels, CU Model B at 80 g and CU Model B1 at 1 g, with corresponding virtual scaling factors of 0.5 and 40, respectively. Following the principles of generalised scaling, results from both tests should be representative of the same slope profile with a slope depth of 4 m previously tested as part of LEAP-UCD-2017. CU Model B exhibited typical liquefaction behaviour with substantial reduction in acceleration transmission along the depth of the slope coupled with considerable excess pore pressure build-up during shaking. For a similar input motion, the slope in CU Model B1 at 1 g showed little deformations. Intensity of the input motion had to be increased by nearly twofolds to trigger slope movements that can be measured by PIV.

1 Introduction

Numerical analysis related to geotechnical research has been widely performed during the last decades as it presents benefits in time and cost optimisation. However, reliable experimental data related to earthquake effects such as liquefaction phenomena is still required in order to validate numerical procedures. Liquefaction Experiments and Analysis Projects (LEAP) was commissioned to develop a database of centrifuge data on the liquefaction of slopes from tests performed at different institutions. The LEAP-ASIA-2019 is a sub-programme of LEAP, which aims to investigate the suitability of the generalised scaling laws proposed by Iai et al. (2005) at different g levels and virtual scaling factors. In this paper, two dynamic high gravity tests were carried out on a 5° liquefiable slope subjected to a 1 Hz ramped sine wave input motion. The two tests were conducted at two drastically different g levels “η” of 80 g and 1 g, with virtual 1 g scaling factors “μ” of 0.5 and 40, respectively. Following the principles of generalised scaling laws, these two tests would represent the same slope geometry at prototype. The models have been prepared following the procedures stated in LEAP-GWU-2015 (Madabhushi et al., 2018) and LEAP-UCD-2017 (Madabhushi et al., 2019). All results presented in this paper are scaled to prototype using Iai et al. (2005) unless otherwise stated.

2 Experiment Setup

Two tests were performed, one at 80 g (CU Model B) and one at 1 g (CU Model B1), using the centrifuge testing facilities at the Schofield Centre, University of Cambridge. The model represents a 5-degree slope in Ottawa sand, with a length of 20 m and a central depth of 4 m at prototype scale, which was the same prototype slope profile used during LEAP-UCD-2017. The general schematic layout of the slope profile and instrumentation used in the tests is shown in Fig. 5.1.

Fig. 5.1

Centrifuge model schematic showing instrument positions

2.1 Sand Pouring

Ottawa sand was poured by air pluviation using the automated spot pluviator (Madabhushi et al., 2006). The sand density was achieved by controlling the flow rate with a nozzle of 5 mm and a drop height of 810 mm. These parameters were obtained by pre-test pouring calibrations to achieve a target density of 1640 kg/m³.

During pouring, the strong window box was placed on a scale in order to obtain the mass of sand poured after each pluviation pass. Height of poured sand was measured using a digital calliper. The readings were recorded along a grid of 20 points at specific poured layers. Figure 5.2 shows the grid pattern adopted for the sand depth measurements. Results of the sand density achieved for the different layers are presented in Fig. 5.3.

Fig. 5.2

Digital calliper grid for surface measurements

Fig. 5.3

Bulk density measurements inferred from calliper and scale measurements at each layer: (a) CU Model B and (b) CU Model B1

2.2 Saturation

The saturation was conducted using the CAM-SAT system that regulates mass influx of fluid into sand models following Stringer and Madabhushi (2009). The mass rate was set to 0.4 kg/h in order to prevent sand boiling. The model was flushed with CO₂ in three cycles before the saturation stage in order to enhance the acquired vacuum. Figure 5.4 shows the saturation setup used in these two tests.

Fig. 5.4

Model saturation

2.3 Viscosity Measurement

The model saturation required the use of hydroxypropyl methylcellulose (HPMC) solution in order to increase the fluid viscosity and to meet the generalised scaling laws proposed by Iai et al. (2005). Prior to initiating saturation, viscosity of the fluid was measured using a viscometer to ensure compliance with the generalised scaling factor for viscosity: 47.6 cSt for CU Model B and 15.9 cSt for CU Model B1.

2.4 Slope Cutting

Once saturation was complete, the flat bed of sand was cut into the required logarithmic spiral profile using cutting plate guides running along the length of the container as shown in Fig. 5.5. Before cutting, the saturated model was partially drained to lower the methylcellulose level in the sand. This procedure relies on capillary suction between individual grains to increase effective stresses in the sand to facilitate cutting (Madabhushi et al., 2018). To compensate for the 1 g gravitational component acting on the model, a 1:80 slope was also cut along the transverse direction of the container for CU Model B.

Fig. 5.5

Use of cutting guide plates to achieve the desired slope profile

2.5 CPT

In both tests, an in-flight CPT was mounted on the package to obtain a soil strength profile before and after shaking. Although this device differs from the CPT used in UC Davis, previous centrifuge tests have verified the equivalence between both instruments (Carey et al., 2018; Madabhushi et al., 2019).

2.6 Scaling Laws

The scaling laws proposed by Iai et al. (2005) for CU Model B and CU Model B1 are summarised in Table 5.1 and Table 5.2, where η is the centrifuge scaling factor and μ is the virtual 1 g scaling factor. The generalised scaling factor λ is then the product of μ × η.

Table 5.1 Generalised scaling laws for CU Model B

Table 5.2 Generalised scaling laws for CU Model B1

3 Results

3.1 Destructive Motions

The target input motion set for CU Model B and CU Model B1 was a ramped 1 Hz sine wave with a peak ground acceleration of 0.25 g. Figure 5.6 shows the recorded base accelerations for the two tests conducted. The recorded signals are decomposed into the main 1 Hz driving frequency component superimposed with higher harmonics introduced by the mechanical response of the servo-shaker. A prototype PGA of 0.29 g was recorded for CU Model B and 0.57 g for CU Model B1. Prior to firing the 0.57 g earthquake in CU Model B1, two weaker input motions were triggered. The observed slope displacements for these two motions were negligible, which warranted an increase in the intensity of input motion to 0.57 g to trigger measurable slope movements. Consequently, only data from the stronger ramped input motion is presented for CU Model B1.

Fig. 5.6

Isolated input signal and high-frequency components of input motion

It is worth mentioning that the intensity of the higher harmonics is more prominent in the input signal for CU Model B1 at 1 g than it is for CU Model B at 80 g. It is believed that the higher g level provides better coupling between the shaking table and driving actuator in the servo-shaker and mitigates any tendency for rocking, resulting in lower-intensity high-frequency harmonics.

3.2 Excess Pore Pressure

Excess pore pressure time histories for both tests of the central arrays are presented in Figs. 5.7, 5.8 and 5.9. For CU Model B, considerable excess pore pressures were recorded after the fourth cycle of the shaking. Soil along the depth of the slope reaches complete liquefaction. In CU Model B1, after multiplying pore pressure transducer results by 40 (i.e. the generalised scaling factor for pore pressure), the build-up of excess pore pressures between CU Model B and CU Model B1 is comparable. Nevertheless, the cyclic response of excess pore pressures between the two tests is different. As shown in Fig. 5.8, excess pore pressures nearer to the crest of the slope record much larger suction spikes during the earthquake at 1 g compared to the results at 80 g. During the earthquake, sand within the slope is subjected to cyclic shear stresses, which, in the case of 1 g test on CU Model B1, cause the sand to dilate strongly owing to the low confining stresses. This results in sharp negative excess pore pressure spikes. The higher intensity of the input motion harmonics for CU Model B1 may have also contributed to this observation. However, it is felt that the scaling up of the measured excess pore pressures by a factor of “40” as prescribed by the generalised scaling laws meant that the oscillations in the excess pore pressures are amplified by a large factor.

Fig. 5.7

Excess pore pressures recorded by the central PPT array

Fig. 5.8

Excess pore pressures recorded by the left PPT array

Fig. 5.9

Excess pore pressures recorded by the right PPT array

3.3 Accelerations in the Soil

Acceleration time histories of the central array of piezoelectric accelerometers together with the input motion for CU Model B and CU Model B1 are presented in Fig. 5.10. In CU Model B, significant acceleration reductions are observed along the depth of the slope particularly close to the surface. This is a typical liquefaction phenomenon resulting from the softening of sand caused by excess pore pressure build-up and effective stress reduction. For CU Model B1, a similar reduction in accelerations is observed along the slope depth but not of the same intensity. The sand in the 1 g test continues to transmit some of the vertically propagating horizontal shear wave motion to the surface as complete liquefaction was not achieved. It is interesting to note the acceleration traces recorded from CU Model B, and the top surface of CU Model B1 shows distinctive spikes in acceleration, which can be attributed to strong dilation in the sand at low confining stresses.

Fig. 5.10

Soil accelerations recorded by central piezo array

3.4 CPT Strength Profiles

In-flight CPT testing was carried out before and after the 1 Hz ramped sine input motion for both CU Model B and CU Model B1. In Fig. 5.11, the soil depth below the slope surface is plotted on the y-axis, using the generalised scaling law for length. On the x-axis, the left-hand side plots show the cone-tip resistance in prototype scale using the generalised scaling laws. On the right-hand side plots, the x-axis is scaling using the normal centrifuge scaling laws for stress, which is unity. The effect of centrifugal acceleration on the strength and stiffness of the sand profile is very clear when comparing cone-tip resistance at model scale for CU Model B to that for CU Model B1. One would expect that if the generalised scaling laws hold well, then the two left-hand side plots should be similar. However, the peak cone-tip resistance before any shaking was applied, at a depth of 3.5 m, is approximately 2 MPa in the 80 g test and 4.6 MPa in the 1 g test. In contrast, using the normal centrifugal scaling laws, the cone-tip resistance at 3.5 m was 3.8 MPa in the 80 g test and only 0.12 MPa in the 1 g test. These latter results are consistent with the expectation that the strength of the soil will be much smaller in a 1 g test than in an 80 g test. Further, Madabhushi et al. (2019) also report a value of 1.8 MPa at a depth of 3.5 m in their 40 g centrifuge test carried out as part of the LEAP 2017 (with η = 40; μ = 1 for this test). While it is acknowledged that these are extreme examples in terms of the g levels, it is clear that the generalised scaling laws are over-predicting the strength of the soil in models with smaller η and larger μ factors.

Fig. 5.11

Cone-tip penetrometer results at model scale and scaled using generalised scaling laws

3.5 PIV Results

For plane strain condition problems, like the ones presented in this paper, PIV analyses can be employed to track the displacement of soil patches of a cross section of the system. Images of the cross-section view were taken using a fast digital camera placed on a gantry in front of the Perspex side of the container. Once the images were available, the displacement field of the soil was obtained employing the MATLAB-based software GeoPIV-RG (Stanier et al., 2015).

Figure 5.12 shows the layout of the instruments, the portion of the slope analysed and the position of four reference points A, B, C and D for the tests CU Model B and CU Model B1, respectively. Figure 5.13 shows the horizontal and vertical displacement of the four already mentioned reference points, as well as the input motion shaking the container, for the CU Model B. Figure 5.14 shows the displacement field and displacement contours of the slope in the CU Model B. During the shaking, the slope failed following a rotational pattern, with significant vertical settlement of the crest (reference point A) and vertical upward movement of the toe of the slope (reference point C). Significant horizontal displacement was observed in the middle of the slope (reference points B and D).

Fig. 5.12

Layout of the instruments, portion of slope analysed and position of four reference points A, B, C and D for CU Model B1 (top) and CU Model B (bottom)

Fig. 5.13

Horizontal and vertical displacement of reference points A, B, C and D and input motion shaking the container for CU Model B

Fig. 5.14

Horizontal and vertical displacement contours at prototype scale and displacement field for CU Model B

Figure 5.15 shows the horizontal and vertical displacement of the four previously mentioned reference points as well as the input motion shaking the container for CU Model B1. Figure 5.16 shows displacement contours of the slope in the CU Model B1. It is observable that the magnitude of displacement for this test was very small. In addition to this, the shape of the failing mechanism seems different from the previous test, with a uniform vertical settlement of all the four reference points.

Fig. 5.15

Horizontal and vertical displacement of reference points A, B, C and D and input motion shaking the container for CU Model B1 (prototype scale)

Fig. 5.16

Horizontal and vertical displacement contours at prototype scale and displacement field for CU Model B1

Figures 5.17 and 5.18 show a comparison between the slope before and after the earthquake, for the CU Model B and CU Model B1 (third earthquake), respectively. Again, it is observable that the magnitude of displacement for the CU Model B is significantly higher than CU Model B1, despite the larger amplitude of the input motion in the latter.

Fig. 5.17

Slope before and after the shaking for CU Model B

Fig. 5.18

Slope before and after the shaking for CU Model B1

4 Conclusions

The methodology and results from LEAP-ASIA-2019 tests performed at Cambridge are presented in this paper. The main purpose of these tests carried out at drastically different “g” levels of 80 g and 1 g was to evaluate the validity of the generalised scaling laws. The results from the two centrifuge tests CU Model B and CU Model B1 conducted at 80 g and 1 g, respectively, were quite different. This was despite scaling the model pore fluid to correct viscosities and frequency of shaking as prescribed by the generalised scaling laws.

The excess pore pressures seem to scale to similar values in both the models; however, the model tested at 1 g showed large dynamic oscillations with strong dilation-induced spikes. The accelerations in the slope showed attenuation with the build-up of excess pore pressures in the case of 80 g test, while those in the 1 g test showed large amplification due to the dilation in this model. The deformations in these centrifuge tests were obtained using PIV analyses. For the case of 80 g test, the slope deformations were as expected with large lateral movements being recorded at the mid-slope and an overall rotational motion of the slope with the top of the slope moving down and the base of the slope moving up. However, in the 1 g test, there were no observable slope movements when an equivalent base shaking was applied. In order to beget any observable movements of the slope, an earthquake that was nearly twofolds larger had to be applied to the slope.

In-flight cone penetration tests were conducted for the models at 80 g and 1 g before and after the ramped 1 Hz input motion. As expected, cone-tip resistance values along the depth of the slope scaled according to the centrifuge scaling law of stress (i.e. unity) showed significant discrepancies between the 80 g test and the 1 g test. This is due to the fundamentally different confining stresses in the soil body at these two different g levels. The application of the generalised scaling laws has predicted a much larger strength of the sand for the 1 g test; however, the cone-tip resistances between the 80 g test and the 40 g test conducted by previous researcher were comparable. This suggests that there is a limit on the values of virtual scaling factors μ that can be used in the generalised scaling laws.