FORUM FOR THE PROMOTION OF SOIL DYNAMICS IN INDIA H.R.WASON, Emeritus Fellow, IIT Roorkee & President, Indian Society of Earthquake Technology 21 December, 2013 A presentation on IMPACT OF PARAMETER UNCERTAINTY IN GEOTECHNICAL EARTHQUAKE ENGINEERING

Capturing and translating uncertainty through any engineering analysis is necessary for resolving the mean or median response with any confidence, and for estimating the dispersion of possible results. Geotechnical earthquake engineering is a pseudo-empirical discipline where theory dictates the trends of the analytical models but data drives the shape, coefficients, and values of the numerical results.

Uncertainty in Geotechnical Earthquake Engineering can be conceptually lumped into two groups: 1.The inherent variability of geotechnical materials, i.e., the inherent variability of the underlying phenomena (Aleatory uncertainty), and 2.The stochastic nature of earthquake ground motions, i.e., uncertainty as a function of modeling, measuring, and other engineering machinations that are not part of the phenomena (Epistemic uncertainty). The relative contribution of Epistemic and Aleatory uncertainty in uncertainty propagation can be complex and there is little agreement as to how best separate the two (Helton, 2004). Recent advances in probabilistic methods have lead to improved uncertainty analysis in geotechnical earthquake engineering and related fields. These methods demonstrate how uncertainty is quantified and propagated through the analysis thereby providing a broader understanding of the problem at hand and the desired outcome.

The basis for error propagation is founded in the fundamentals of statistics and probability. Statistics is the means of quantifying past occurrences and probability the means of predicting future occurrences. Quantifying uncertainty can be accomplished through various statistical means if sufficient data exists, or By ascribing a probability distribution based on theory, assumptions, and/or expert solicitation. Propagating uncertainty involves “pushing” the uncertainty through the model, equation, or analysis to arrive at final results representative of the formulation and the contributing uncertainty. This can be accomplished by three methods: Exact methods if certain conditions are met (e.g. sum of normally distributed random variables), Approximate methods that can often give reasonable results (i.e. first order second moment approximation), and Simulation methods (e.g. Monte Carlo simulation).

Uncertainties in specifying the input soil properties required in a method of analysis Methods1D/2D(e.g., SHAKE, Quarter Wavelength, H/V Ratio) of response computation based on different idealizations Earthquake ground motions are affected by source, path, and local site response effects. Seismic hazard analyses typically use attenuation relations derived from strong motion recordings to define the probability density function for a ground motion parameter conditioned on the occurrence of an earthquake with a particular magnitude at a particular distance from the site. These relations are derived from statistical regression of observed ground motion parameters. Cont…

Insufficient and faulty validation of the theoretical results with limited recorded data There is a trade-off between site response effect and hanging wall and directivity effects, which are not all considered explicitly Focusing of seismic waves due to reflection from Moho discontinuity, basin effect or topography effect may not be modeled Neglecting the effect of the angle of incidence and azimuth For distant earthquakes there may be uncertainties in defining the path attenuation effects Measurement errors in surface wave methods and magnitude determinations etc.

Geotechnical earthquake engineering projects rely on engineering seismology models to define the loading for design. Many sources of uncertainty contribute to the overall uncertainty for a particular measure of seismic loading. Logic tree approach for uncertainty analysis in PSHA ( Joshi & Sharma,2011)

The studies by Moss(2008,2009) show a 10% reduction that can be achieved by evaluating the influence of V S30 measurement uncertainty on the overall uncertainty in a ground motion prediction equation. Cont…. Fig.1 The influence of V S30 measurement uncertainty on ground motion prediction equation is most pronounced at the longer periods. Here the Chiou and Youngs (2008) ground motion prediction equation is used as the basis to demonstrate a 10% reduction in one standard deviation for the 3.0 second period spectral ordinate when V S30 uncertainty is properly accounted for within the regression procedure (from Moss, 2009).

The argument made is that regression of a large database of ground motions from diverse regions that are questionably grouped together results in an artificially large dispersion. To control for site and travel path effects, Atkinson (2006) looked at the dispersion of a single site that experienced multiple earthquakes, near and far field. The results, based on the limited data set for this site, indicate that site effects alone contribute 10% of the uncertainty as measured by the standard deviation, and that travel path and site effects together can contribute 40% to the uncertainty.

(R.S.Jakka, Narayan Rao and H.R.Wason) Surface wave methods are used to measure the shear wave velocity variation with depth and are becoming popular in geotechnical engineering for in-situ dynamic site characterization. Multichannel Analysis of Surface Wave (MASW) method is being widely used for the site characterization as it provides the information in frequency bands of engineering interest. Surface-wave methods which suffer from data measurement uncertainty may result in variable ground motion as a result of 1D ground response analysis.

Model based uncertainty Data Measurement Uncertainty Noise present in the recorded signals Testing setup configuration Type of source used Subsurface soil profiles Uncertainty in Surface Wave Methods Error in seismic site responses Error in Shear wave velocity profiles

Two site specific case histories are presented to quantify the extent of data measurement uncertainty of surface- wave tests on 1D ground response analysis. Surface-wave data has been collected using 24 channel 2 Hz geophones with multiple repetitions keeping the same configuration. A wooden mallet weighing 10kg was used to generate the wave. For each shot statistical analysis is performed to generate the mean dispersion curve and associated standard deviation at each frequency.

Misfit = where X ti is the theoretical and X ei is the experimental phase velocity of the calculated curve at frequency f i, σ i is the uncertainty of the frequency samples and n is the number of frequency samples considered in the dispersion curve. If uncertainty is not provided, σ i is replaced by X ei in the equation.

Fig. 2 Bore-log data of the test sites (a) Lal Bahadur Shastri (LBS) ground (Site1) (b)Lecture Hall Complex (LHC) Area (Site2)

Table 1: Details of materials curves adopted in this study Soil TypeG/G max CurveDamping Curve Sandy Silt Soil PI=0 (Vucetic and Dobry, 1991) Soil PI=0 (Vucetic and Dobry, 1991) Silty Sand Sand Avg. (Seed & Idriss, 1970) Sand Avg., Damping for Sand (Seed & Idriss, 1970) Clayey Silt Soil PI=15 (Vucetic and Dobry, 1991) Soil PI=15 (Vucetic and Dobry, 1991) Fine Sand Sand Avg. (Seed & Idriss, 1970) Sand Avg., Damping for Sand (Seed & Idriss, 1970)

Fig.3 A sample recorded seismogram

Fig.4 Calculated mean curve with standard deviation for site1.

Fig. 5 Coefficient of variation of phase-velocity for site 1 Fig.6 Generated upper bound and lower bound curve

Fig.7(a) Dispersion curves selected after inversion with a maximum misfit value (b) Corresponding Vs profiles after inversion with a maximum misfit value 0.063

Fig.9 (a) Modulus Reduction Curves (b) Damping Curves used in the ground response analysis

Fig. 10 Comparison of (a) amplification spectrums and (b) response spectrums of the selected profiles

Fig. 11 COV plot of amplification and response spectrums.

Table 2: Comparison of different ground motion parameters at the two sites Parameters LBS Site (Site1)LHC Site (Site2) MeanStd.COV (%)MeanStd.COV (%) Peak Frequency (Hz) Peak Amplification Peak Spectral Acceleration (g) Peak Ground Acceleration (g)

The propagation of data measurement uncertainty associated with surface-wave tests on seismic site response is considerable. It may lead to erroneous estimate of seismic loading. The measured data uncertainty of phase-velocity shows two distinct regions in the COV plot. Above 25Hz frequency, phase- velocity is nearly constant with a low value of COV and below this a linear increase of COV is observed. Amplification spectra show remarkable variation in peak frequency and peak amplification. PGA and peak spectral acceleration also show significant variation at both the sites. Uncertainty in the shear wave velocity profiles further affects the seismic site responses which indirectly affect the design ground motion.

Formation of research groups for specific problem areas Preparation of National Atlas for local soil amplification factors. Establishment of a Data Bank for Geotechnical Information. Quantification of uncertainty in Ground Response Analysis/ Soil Investigations. Creating a website where general public or students can post their problems to get answers from experts. New pedagogical techniques /course material for outcome based learning in Geotechnical Earthquake Engineering. Start of a popular lecture series. Interaction with industry/ practicing professionals. Awareness about geotechnical hazards.

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