Earthquake-induced slope vibration and its relationship with material properties, slope height, and input wave frequency

Abstract

The relationship of the amplification of vibration on the surface with the slope geometry, earthquake input signal (mainly frequency of the wave) and the material property of the slope is studied using the finite difference program FLAC. A sinusoidal wave with acceleration of 1 m/s2 is applied for the duration of 0.25 sec. The influence of varying input frequency is investigated applying the frequencies in the range of 3 Hz to 15 Hz. The variation of amplification due to the change in shear modulus of the material in the slope and that due to slope height is also investigated.
 It is found that the crests of the higher slopes are amplified most by the lower input frequency and smaller slopes are amplified most by the higher input frequency. The overall magnitude of the amplification is maximum for smaller slopes when input signals of higher frequency are applied. The generation of standing waves at certain harmonic frequencies could be the reason behind such a high amplification. It is also seen that the amplification peaks of vibrations repeat at different slope heights, which is considered reflection of the harmonic effect. A clear resonance effect is seen when the amplification of vibration is plotted against the shear modulus. The peaks of such amplification also repeat periodically as a result of varying shear modulus. Present study provides some preliminary relationship of amplification with slope height and shear modulus of the material in the slope. The horizontal amplification of vibration as much as 17 (horizontal acceleration in the order of 1.7 g) is obtained at the crest of normal limestone slope with 20 m height when an input signal of 15 Hz frequency is applied. It is also revealed that for extremely lower values of shear modulus, there is mostly attenuation instead of amplification and for extremely high values of shear modulus, amplification is negligible as compared to the certain range of intermediate shear modulus. Maximum amplification in the order of 6.5 (horizontal acceleration of 0.66 g) is achieved for the shear modulus of 3000 MPa with slope height of 40 m when the input acceleration of 0.1 g is applied. This type of relationship is believed to have great importance for seismic microzonation study as the results might be used along with the digital elevation model for separating different zones of hazard levels. However, one should be aware that this result is for the slope with particular combination of material properties, geometry and earthquake input signals, and generalisation could lead to misleading results.