Simplified seismic soil classification: the Vfz matrix

Abstract

Site effect assessment studies aim at predicting the effect of seismic shaking on structures by modeling the subsoil as an oscillator coupled to another oscillator representing the construction. The resulting amplification functions and response spectra depend on so many strong assumptions and parameters that, in the standard engineering practice, simplified seismic classifications appear preferable to complex modeling procedures which can only offer an illusory better accuracy. Since stratigraphic seismic amplification is not properly related to the absolute rigidity of subsoil but to impedance contrasts, the standard simplified approaches based on the ‘average’ rigidity of subsoil in the first few meters (e.g. Vs30) can hardly be effective. Here it is proposed a simplified soil classification approach that takes into account the basic Physics of seismic amplification and its parameters, i.e. the average shear wave velocity of the cover layer, the resonance frequency and the impedance contrast between the cover and the bedrock, which we summarize as VfZ. A possible classification approach is illustrated through a set of examples.

Appendix

We have used the 1D equivalent linear (1D-EQL) analysis, which gives reasonable estimates of ground vibration under a seismic event (Idriss 1990) and is generally conservative over the results of nonlinear methods or real records from downhole acceleration arrays. In the second case, the difference between the 1D-EQL approach and experimental observations can be due to both non-linear behaviours but also to the fact that many input parameters of the models are measured on very small laboratory samples compared to the scale of the physical phenomenon. As a result, damping, stiffness versus shear strain curves and other parameters measured in the laboratory are usually conservative compared to what one would measure on the field, where the volume of investigation includes layering, fractures and many more heterogeneities than those existing at the laboratory scale.

It has been reported in the literature (Sugito et al. 1994; Yoshida et al. 2002; Kausel and Assimaki 2002) that at very low periods the 1D-EQL approach under predicts the motion as an effect of high-frequency overdamping and that results are unrealistic in the case of high shear strain levels ($>$0.1 %) induced by seismic excitation. On the contrary, Kwok et al. (2007) have shown that soil models with low modal frequency (approximately $<$1 Hz) are expected to result in lower amplification values.

Given such limits for the 1D-EQL approach, our models appear usable at strain levels approximately $<$0.1 %.

Additionally, as input motion for our models we used Ricker wavelets rather than real earthquake recordings. It is well known that the amplification transfer function depends strictly on the subsoil and not on the excitation function. This can clearly be seen in Fig. 18, where the amplification transfer function obtained by using a 1 Hz and a 0.5 Hz Ricker wavelet (red) is compared to the average $(\pm 2\sigma )$ transfer function obtained from 10 real accelerograms $(\hbox {PGA}_{0} = 0.35\,\hbox {g})$ on 3 ‘typical’ subsoil models, i.e.:

Fig. 18

Surface-to bedrock transfer functions obtained from a set of 10 real accelerograms (average $\pm$2 sigma interval in black, solid $\pm$ dashed lines) compared to the usage of 2 Ricker wavelets as input motion (1 and 0.5 Hz, respectively, in red). The subsoil is represented by (left) 30 m cover (Vs = 200 m/s) overlying the bedrock, (centre) 100 m cover (Vs = 200 m/s) overlying the bedrock, (right) 200 m cover (Vs = 500 m/s) overlying the bedrock. In all cases the bedrock is represented by a 800 m/s half space

• 1) Left: 30 m (Vs = 200 m/s, $\hbox {f}_{0}$ = 1.7 Hz) cover overlying the bedrock,

• 2) Centre: 100 m (Vs = 200 m/s, $\hbox {f}_{0}$ = 0.5 Hz) cover overlying the bedrock,

• 3) Right: 200 m (Vs = 500 m/s, $\hbox {f}_{0}$ = 0.6 Hz) cover overlying the bedrock.

In all cases the bedrock is characterized by Vs = 800 m/s and no difference is observed between the results produced by different input motions.

On the other hand, the response spectrum is mostly dependent on the input motion, so that when we use as excitation function a Ricker wavelet with a specific frequency, we expect to get the maximum of the response function more or less around that frequency. This can clearly be seen in Fig. 19 where we used 1 Hz (red) and 0.5 Hz (dashed red) Ricker wavelets as input motions and we had the maximum of the response spectrum at approximately 1 and 2 s. The subsoil specific properties certainly affect also this function but to a minor extent.

Fig. 19

Response spectra obtained from a set of 10 real accelerograms (average $\varvec{\pm }$ 2 sigma interval in black, solid $\pm$ dashed lines) compared to the usage of 2 Ricker wavelets as input motion (1 and 0.5 Hz, respectively, in solid and dashed red, respectively). The subsoil is represented by (left) 30 m cover (Vs = 200 m/s) overlying the bedrock, (centre) 100 m cover (Vs = 200 m/s) overlying the bedrock, (right) 200 m cover (Vs = 500 m/s) overlying the bedrock. In all cases the bedrock is represented by a 800 m/s half space

The models also suggest that the Ricker wavelet is a good proxy for the average response to real accelerograms for periods around the Ricker wavelet proper period. Therefore, under the linear elastic assumption, a Ricker wavelet with frequency 1 Hz is adequate to provide response spectra at periods $\le$1 s, a Ricker wavelet with frequency 0.5 Hz is adequate to provide response spectra at about 1.5–2.5 s etc.