Shaking table tests on deformation and failure mechanisms of seismic slope

2.1. Prototype slope

Fig. 1 illustrates a slope failure of relatively small size that occurred at Tazhiping in Dujiangyan City at the location (103.375_E, 31.629_N) in the Hongse village, Hongkou Town. It is evident that the slip plane is rather straight, suggesting that the weak materials at the surface fell under seismic excitation. There were many similar events associated with straight slip planes in the Wenchuan earthquake-hit region. The Tazhiping landslide was triggered by the main shock of Wenchuan earthquake and caused at least 1 fatality. The elevation of the landslide ranged from 1107 m to 1370 m. Its length was about 530 m, and the width was about 145 m. The landslide lithology was fragmentary rocks and the surface was covered by silty clay and gravel. The space distribution of slippery bodies was thick in the center and thin near the perimeter, and the estimated thickness of the sliding mass was 20 m to 25 m. The estimated volume of the landslide was about 116×104 m³. The landslide angle was around 32 degrees.

Fig. 1The Tazhiping landslide

To investigate the deformations and failure mechanisms of straight slopes, a series of tests was performed with different input amplitudes and frequencies of sinusoidal waves. Based on the measurements of the acceleration and displacement of different points in the slope model, the dynamic characteristics and responses of the straight model slope under earthquake, as well as the influence of ground motion parameters, are discussed.

2.2. Test set-up and instrumentation

The shaking table at the Geotechnical Engineering Laboratory, University of Tokyo, is 2 m wide and 3 m long, and is capable of applying bi-directional horizontal accelerations. The bearing capacity of the shaking table is 7 tons, and the maximum applied acceleration is 1,000 Gal (≈1 g) frequencies up to 50 Hz. Soil slope models were prepared in a soil container with 3 m in length, 0.4 m in width and 0.6 m in depth. This container was tightly fixed onto the shaking table so that there was no slippage between them. A total number of 14 accelerometers and 4 displacement gauges were installed to measure horizontal dynamic responses during the experiments (inclinometers were prepared by making a column of accelerometers) [14-16]. Fig. 2 shows that the accelerometers were installed in vertical arrays below the crest and the shoulder as well as along the slope to measure the distribution of accelerations inside the slope model. It is also seen that square grids with color were installed in the vertical glass wall to demonstrate visually the dynamically-induced deformation of the model.

Fig. 2Slope model with accelerometers and displacement gauges

2.3. Slope models in testing

Slope models consisted of uniform Toyoura sand with the mean grain size of 0.174 mm and the void ratio between $e_{min}=$ 0.605 and $e_{max}=$ 0.974. In the preparation of the slope models, the relative density of 32 %, the void ratio of 0.857, and the moisture content of 1 % were used. The effective stress in the small-scale 1-G model tests was around 1/500 of the prototype, and thus the density of sand was reduced so that similitude of dilatancy was maintained [17-19]. In line with this, the time scale in the model tests was made shorter than the prototype event in consideration of the reduced size of models by shaking all the models at, for example, 10 Hz, which was higher than the real earthquake events. Shaking at lower frequencies of 2 and 5 Hz was run as well. The duration of shaking was 30 seconds. The moisture content of 1 % was employed to provide a certain apparent cohesion to the sand to avoid failure at the very surface of the slope. The intensity of base shaking in the horizontal and longitudinal direction of models varied from 100 to 700 Gal.

3.1. Dynamic responses

Fig. 3 shows the dimensions of the straight-slope model. As in the aforementioned Tazhiping case, the slope angle of the model was 32 degrees.

Fig. 4 shows detailed acceleration time histories. Fig. 5 plots the ratio of maximum acceleration (amplitude) along the vertical array in the slope (A1 to A5 in Fig. 2) to the shaking table acceleration. The case of 500 Gal shaking under frequency of 10 Hz exhibits more remarkable amplification than others, as shown in Fig. 5(a). This is most probably due to the nonlinear stress-strain behavior of sand in that the elastic modulus decreases as the dynamic stress and shear strain increase, leading to varying natural periods in the model. This point is examined in more detail in Fig. 5(b), in which the variation of amplification with shaking frequency is plotted for base acceleration with input seismic wave of 500 Gal. Fig. 5(b) shows that the case of 10 Hz is probably closer to the resonance frequency of the model, exhibiting more remarkable amplification than the other cases.

Fig. 3The tested model slopes (unit: mm)

Fig. 4Time histories of acceleration along the slope

Fig. 5Distribution of acceleration inside a slope model

a) 10 Hz excitation

b) 500 Gal excitation

Fig. 6(a) shows the ratio of the maximum acceleration (i.e. amplitude) at the surface of the slope (AC1 to AC4 in Fig. 3) to that applied the base with amplitude up to 500 Gal. This allows study of the effects of nonlinearity of soils in greater detail. Actually, shaking at 700 Gal caused slope failure and thus the corresponding results are not included in Fig. 6. AC4 at the crest shows more significant amplification than the other cases. The amplification at the slope shoulder (AC3) is large as well but smaller than that at the crest (AC3$<$AC4). This is consistent with the findings after the Wenchuan earthquake that many cracks formed in the back scarp of the slope, although the main body of the slope was intact (Fig. 7). Fig. 6(b) illustrates that with increasing height (AC1 to AC4), the acceleration at the slope surface decreases and then increases at the mid-height of the slope.

Fig. 6Distribution of acceleration at the surface of the straight slope model

a) 10 Hz excitation

b) 300 Gal at base

Fig. 7Two cracks in the back scarp of the slope

3.2. Failure modes of straight slope models

Fig. 8 illustrates the failed shape after 700-Gal shaking at 10 Hz frequency. The square grids in the photo clearly indicate that shear failure or slippage took place at some depth below the surface, as expected by using 1 % moisture content. The linear shape of the shear plane was similar to the failure of the prototype slope as shown in Fig. 1.

Fig. 8Failed straight slope with 32-degree gradient subjected to shaking of 700 Gal and 10 Hz for 30 seconds

Fig. 9Acceleration response along the surface of a straight slope (32 degrees, 700 Gal, 10 Hz)

Fig. 10Time history of displacements derived from the measured accelerations

Fig. 9 compares the shape of the slope before and after shaking. The model slope, nearly intact under 500 Gal shaking, suddenly developed cracks and then slid at shallow depth below the slope under 700 Gal shaking. In the same figure, the time histories of horizontal acceleration along the slope surface are shown. The bias from zero is due to tilting of the transducer after slope failure. From the amplitude of acceleration at the slope surface, it is found that the shaking was weaker in the lower part of the slope (AC1 and AC2), and stronger in the upper half (AC3 and AC4). The increasing acceleration towards the top was caused by energy concentration at the narrower slope, as observed in reality. Moreover, the acceleration in the slope shoulder (C1) became less than that at the surface.

The recorded acceleration was integrated twice and the effects of tilting and other baseline errors from the acceleration were removed to obtain the time history of displacement, as shown in Fig. 10. Clearly, the displacement amplitude, which was closely related to the local shear strain amplitude, increased from the bottom (AC1) to the shoulder (AC3) and the crest of the slope (AC4), indicating more nonlinearity and extent of yielding of soils at higher elevations. The significant shear strain induced large deformation. The failure was initiated at AC4 at the crest and then proceeded to AC1 at the bottom of the slope. Fig. 11 traces the development of slope failure with time. The displacements in this photo are consistent with the findings in Fig. 10.

Fig. 11Development of slope failure

a) Before slope failure

b) After slope failure

3.3. Location and shape of sliding surface

The deformation of the slope subjected to seismic loads was further studied by the particle image velocimetry (PIV) [18]. Fig. 12 presents a digital cross-correlation analysis of double frame/single exposure records, in which the cross-correlation between two interrogation windows sampled from the image records is calculated [20] and the displacement of sand grains between photographs at two time points is detected. The PIV technology was applied to large-scale shaking table model tests of slope stability, and Fig. 13 indicates that the displacement and the velocity were greater above a plane known as the slip plane.

Fig. 12PIV process for tracking displacement vector [15]

The results show that the PIV technology could effectively measure the displacement of any point at any time with accuracy within the observation region. Furthermore, more information about the process of deformation development could be obtained, such as the formation of strain localization and the whole failure process of slopes under earthquake.

Fig. 13PIV analysis results with velocity vector boundary of slope