Proceedings of Indian Geotechnical Conference December 13-15, 2012, Delhi
EFFECT OF UNCERTAINTIES IN SITE CHARACTERIZATION USING SURFACE WAVE TECHNIQUES Narayan Roy, Research Scholar, Dept. of Earthquake Engg., IIT Roorkee, India, Email:
[email protected] Ravi Sankar Jakka, Assistant. Professor, Dept. of Earthquake Engg., IIT Roorkee, India, Email:
[email protected] H.R. Wason, Professor, Dept. of Earthquake Engg., IIT Roorkee, India, Email:
[email protected]
ABSTRACT: In geophysical site characterization using surface wave techniques, inversion is the most important step. In the analysis, experimental dispersion curve which is generated from the field measurements is matched with theoretical dispersion curves to get shear wave velocity profiles. The main uncertainty associated with surface wave techniques is in the inversion process which can provide several equivalent profiles and consequently it leads to different local seismic responses. In this paper, the effect of uncertainty in one-dimensional ground response analysis is studied by using a realistic ground motion input. Equivalent shear wave velocity profiles are selected from inversion using neighbourhood algorithm on the basis of low misfit value with respect to target dispersion curve. Then these equivalent profiles are subjected to conventional onedimensional ground response analysis using software SHAKE2000 in the frequency range of engineering interest. Amplification and response spectra show significant difference and mean coefficient of variation of amplification spectra is as high as 20%.
uncertainty on seismic site response analysis using a realistic earthquake record for a low impedance contrast profile.
INTRODUCTION Surface wave method is used to geotechnical site characterization on the basis of shear-wave velocity profiles. Due to dispersive nature of Rayleigh wave, different frequency wave travel at different velocity in a layered medium and penetrates up to different soil thicknesses. As a result of the variation of the shear stiffness of the layers, waves with different wavelengths of frequency travel at different phase velocities. The applications of surface waves in engineering field started in the 1950s with the Steady State Rayleigh Method [1], but their revolution arrived only in the last two decades with the SASW method [2] and MASW [3].
SURFACE WAVE METHODS Different types of surface wave methods are used for constructing the dispersion curve. Active-source tests, in which waves are generated using a seismic source [11,3]. In passive-source tests, constant vibration of earth’s surface or microtremor [12,13] is used for the analysis. The main difference in active and passive-source tests is in frequency components which are directly related to the depth of investigation. Generally active-source tests are associated with high frequency components and in passive-source tests low frequency components are obtained. Sometimes both active-source and passivesource tests are used together for getting profile up to larger depths and better resolution at lower depth [14].
In surface wave methods, experimental dispersion curve is developed from field data using different processing techniques. This experimental dispersion curve is then used for inverse problem solution to get shear wave velocity profiles. The solution of the inverse problem is non-unique and provides several equivalent velocity profiles. Its final model strongly depends on the initial one. The surface wave data measurement uncertainty has been studied by different researchers [4-6]. Uncertainty in measured shear-wave velocity profile has also been investigated in some literature [7,6,8].
NEIGHBOURHOOD ALGORITHM IN SURFACE WAVE INVERSION The neighbourhood algorithm is a stochastic direct-search method for finding models of acceptable data fit inside a multidimensional parameter space [15]. A set of pseudorandom samples is generated after defining the variation of each model parameters (thickness and shear-wave velocity of each layer) in the parameter space. This set of samples is then processed to get the dispersion curves by using the forward problem algorithm for fundamental mode of Rayleigh wave propagation considering soil column as a stack of horizontal and homogeneous layers. Once the theoretical dispersion curve is developed from the random samples given by the neighbourhood algorithm, the misfit value is calculated. If the experimental dispersion curves
Some research has been carried out on the effect of the inversion uncertainty on the seismic ground response analysis. Foti et al. [9] showed that the effect of the surface-wave inversion uncertainty is not significant in seismic ground response analysis. Later this study was extended by Boaga et al. [10] for different impedance contrast and found out that the equivalent profiles as a results of surface wave inversion are not equivalent in terms of seismic ground response analysis. In this paper, an attempt has been made to study the effect of inversion
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Narayan Roy, Ravi Sankar Jakka & H.R. Wason are associated with an uncertainty estimate, the misfit is given by Eq. (1) as below Misfit =
selected (Fig. 2) for one-dimensional ground response analysis.
(1)
Table 1 Reference velocity profile Thickness Shear-wave velocity (m/s)
where is the theoretical and is the experimental phase velocity of the calculated curve at frequency fi, is the uncertainty of the frequency samples considered and is the number of frequency samples considered. If no uncertainty is provided, is replaced by in above equation. The details about the procedure are described in the literature [16]. As a result of the inversion process, we get a set of shear-wave velocity profiles based on the misfit value. Higher the value of misfit, higher will be the set of selected profiles.
5
180
7
240
12
300
Half-space
360
For shaking analysis, an earthquake record has been used as an input motion in the analysis. The earthquake data used, is taken from K-NET of magnitude 6.6 in Japan. The typical acceleration time history has shown in the Fig. 3.
SYNTHETIC ANALYSIS A synthetic study has been carried out to find out impact of non-uniqueness on seismic response of soil column using a realistic input motion. First we have taken a reference velocity profile consisting of three layers plus half-space with gradually increasing shear-wave velocity reported in Table 1. Theoretical dispersion curve is generated for the profile using the forward problem. Poisson ratio and unit weight are same for all layers (Poisson ratio- 0.33 and density-1950 kg/m3) because these parameters has a very little influence on Rayleigh wave dispersion. The neighbourhood of the dispersion curve is defined from previous study [6] so as to take an allowable range of standard deviation of the target dispersion curve. After the inversion 76 nos. of equivalent shear-wave velocity profiles are obtained (Fig. 1a). The dispersions curves developed from each equivalent profiles is shown in Fig. 1b which shows a good fit with the target dispersion curve. Within this 76 nos. of profiles, first 15 best fitting profiles having a misfit of less than 0.4 are
RESULTS
The result of ground response analysis shows significant differences in the amplification spectrum in terms of amplification as well as in peak frequency also (Fig. 4a). Amplification varies from 7.2 to 9.2 and peak frequency varies from 1.4 to 2.6 Hz. For soil condition, when shearwave velocity slowly increases with depth (i.e., low impedance contrast), it exhibits different ground response analysis. So, in this type of soil conditions, non-uniqueness of surface wave inversion may contribute significantly different ground motion. Large variation is also observed for response spectra (Fig. 4b). Variation in peak spectral acceleration is between 0.4g to 0.86g. Surface wave inversion uncertainty can ultimately lead to significant differences in the geotechnical site characterisation.
Fig. 1(a) Equivalent shear-wave velocity profiles (b) Equivalent dispersion curves with target dispersion curve (black)
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Effect of uncertainties in site characterization using surface wave techniques
Fig. 3 Input-motion (Magnitude: 6.6, Date: 2012/03/2720:00:00.00, Latitude-39.80N, Longitude-142.33E)
Fig. 2 First 15 best fitting shear-wave velocity profiles
Fig. 4(a) Comparison of amplification spectra from equivalent velocity profiles (b) Comparison of response spectra from equivalent velocity profiles
Fig. 5(a) Coefficient of variation of amplification spectra with respect to frequency (b) Coefficient of variation of response spectra with respect to frequency To quantify the uncertainty, a statistical study has been carried out to show the relative variation of different
spectra with frequency. Very high value of COV (mean 20%) is observed for the amplification spectrum (Fig. 5a)
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Narayan Roy, Ravi Sankar Jakka & H.R. Wason derived from best fitting 15 equivalent profiles and high data scatter is found out up to 10 Hz frequency. For response spectra, the COV observed (Fig. 5b) is little bit lower (Mean COV is 17%) and it also shows high data scatter up to 5Hz frequency.
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9.
DISCUSSION AND CONCLUSIONS Surface wave method becoming very much popular from geophysical and geotechnical point of view but a very few research has been carried out to find out the uncertainty associated with method. In this paper, an effort has been made to quantify the inversion uncertainty on site characterisation. The findings obtained from the entire study can be summarized as follows:
10.
11.
Equivalent profiles, results of surface wave inversion are not equivalent in terms of seismic ground response analysis. While the one recent study claim that amplification spectra shows variation in terms of peak frequency but our study shows significant variation is observed in amplification amplitude also. Statistical analysis shows very high value of mean of COV for amplification spectra (20%) and a little low values of mean COV (17%) is observed for response spectra. Surface wave inversion uncertainty has significant impact on site characterisation and it can mislead the calculation of design ground motion.
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