Experimental Validation of an Identification Procedure of Soil Profile Characteristics from Free Field Acceleration Records

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1 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 1 Experimental Validation of an Identification Procedure of Soil Profile Characteristics from Free Field Acceleration Records Z. Harichane, University of Chlef, Algeria H. Afra, CNERIB, Algeria R. Bahar, Université Mouloud Mammeri de Tizi-Ouzou, Algeria ABSTRACT In this paper, a new approach for soil profile characterization is validated. The soil characteristics are calculated by fitting the theoretical amplification functions to those obtained experimentally. The identified characteristics have been observed to agree well with those obtained by in situ and laboratory tests. This new approach uses system identification theory and free field records. It is based on formulation of theoretical soil amplification function for two sites in terms of the different parameters of the soil profile layers (thickness, damping ratio, shear wave velocity and unit weight). The theoretical function is smoothed according to the experimental data (spectral ratios) by means of the least squares minimization technique. The function parameters are determined by solving, numerically, a non linear optimization problem. In this approach, soil profile characteristics of two sites can be identified simultaneously, from only a single soil acceleration record at free surface of each site without need of bedrock or outcropping acceleration records. Strong ground motions data recorded during the Boumerdes earthquake (Algeria) of May 1, 003, are used for the validation. Keywords: Amplification Function, Boumerdes Earthquake, Experimental Validation, Free Field Records, Soil Profile Characteristics, Spectral Ratio, System Identification, INTRODUCTION The geotechnical and shallow surface seismic analyses are carried out by knowledge of the subsurface profile or stratigraphy of the site under study. An ideal identification of a soil profile for a seismic analysis must be extended to DOI: /jgee the rock, defined as material with a shear wave velocity greater than 700 m/s, and the physical properties of the soil between the ground surface and bedrock should be defined. Efficient geotechnical recognition and investigation of the subsurface require the exploration of the site under study. This begins generally with a thorough review of the available information about the site, viz. local geology, topographic

2 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 maps, faults maps, and depth-to-bedrock maps. These data can support inferences about subsurface conditions. Such inferences, however, are rarely sufficient for site-specific design or evaluation, and must be additionally confirmed. Subsurface investigations, accomplished by trenching, drilling and sampling and in situ testing, can provide quantitative information, frequently required in the evaluation of site responses. Logging and sampling should take place at sufficient intervals to detect weak zones or seams that could contribute to ground failure (Kramer & Stewart, 004). However, these classical techniques of investigation (drilling and sampling), in situ tests, or geophysical means are generally costly and needing heavy equipment and qualified personnel. To avoid these constraints, system identification and inverse problem analyses are used and offer ability to estimate soil properties without the measurement process disturbing the soil mass. Identification theory and inverse problem analyses have been largely documented by a number of published books and papers (Fletcher, 1980; Nelles, 001; Dahlquist, 1974; Ogunfunni, 007; Kozin & Nathe, 1986; Pearson, 004; Zentar et al., 001). System identification and inverse problem analyses play an important role in development, validation and calibration of soil models, as well as estimation of in situ properties and parameters, using experimental and recorded earthquake data. We are interested here on the role which they play on the characterization and modeling of geotechnical systems. Zeghal and Oskay (00) developed a system identification technique to identify local soil characteristics and properties of soilsystems using the acceleration records provided by local instrument arrays. They calibrated and evaluated an optimal model of soil response by minimizing discrepancies between recorded and computed accelerations. Tsai and Hashash (008) presented a review of inverse analysis techniques applied to downhole array data and developed an inverse analysis framework by using downhole array measurements to extract the underlying soil behavior and developed a neural network-based constitutive model of the soil. Oskay and Zeghal (011) have also summarized previous works on the identification technique used to estimate soil properties from strong motion records. Harichane et al. (005) and Harichane (005) proposed a new approach using system identification theory and free field records, for identifying simultaneously soil profile characteristics of two sites. The proposed new approach is based, firstly, on a formulation of a theoretical transfer function or soil amplification function for two sites in terms of the different parameters of the soil profile layers (thickness, damping ratio, shear wave velocity, and unit weight). The soil amplification function is formulated with the assumption of a vertical propagating shear wave through horizontally stratified soil layers of infinite side extent. One dimensional analyses of soil response are extensively used for their simplicity (Govinda Raju et al., 004). In other hand, transfer functions, or ratios of the Fourier amplitude spectra of input and output acceleration couples, have been widely used to estimate natural frequencies of vibration and associated wave propagation velocities of sites, earth dams, and other systems (Oskay & Zeghal, 011). In the new approach (Harichane et al., 005), the amplification function is smoothed with its analogous one obtained from experimental data (spectral ratios) by means of least squares minimization technique according to the Levenberg-Marquart algorithm. The identification of the parameters is performed by solving numerically a non linear optimisation problem. The numerical efficiency and the validity of this procedure have been demonstrated by Harichane et al. (005) for a single soil profile with experimental data recorded within the Garner Valley Downhole Array (GVDA) (Archuleta et al., 199) with selected acceleration records at free surface and m depth. The major objective of the present study is to provide an experimental validation of the approach by comparing numerical results with those obtained by in situ and laboratory tests. Strong ground motions data recorded during the 003 May 1, Boumerdes earthquake (Algeria) are used for the purpose.

3 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 3 IDENTIFICATION PROCEDURE Identification Method The present system identification method is based on the least squares minimization technique (Press et al., 199; Nelles, 001; Afra & Pecker, 00). The error function χ is minimized according to the parameters vector {γ} in the frequency domain as follows N P ω ({ } ) = ei ( ) di { } 0 i= 1 ( ) max χ γ, ω K Y ω Y γ, ω dω ({ } ) (1) ( ) is the measured Where Y di γ, ω is the frequency response of the model and Y ei w response on the N p considered point couples. ω max is the maximum circular frequency defining the measured function and K is a normalization factor defined by, N P w max K = Yei ( ) d w w 0 i= 1 1 The local minimum of χ γ, ω is obtained under two conditions: (1) the nil gradient condition and () the positive Hessien matrix condition (Harichane, 005; Afra, 1991), by using the Levenberg-Marquart algorithm which is an extension of the Gauss-Newton algorithm (Nelles, 001). Measured Function. ({ } ) The present identification method is based on simultaneous identification of soil profile characteristics of two sites from a single record at the free surface of each site. The frequency contents Y A ( w) and Y B ( w) of two records y A ( t) and y B ( t) at free surface of two sites S A and S B, respectively, can be obtained by using the Fast Fourier Transform (FFT) (Press et al., 199; Dahlquist & Bjorck, 1974). By assuming that the frequency content (or the seismic motion) is the same at the two bedrocks of sites S A and S B, Y Y BR ( ω) = α AR ( ω) where α is a coefficient which can be determined from the attenuation laws, the soil amplification functions corresponding to the two sites S A and S B are defined, assuming one dimensional model, by the following spectral ratios Y A ( w) Y B ( w) SRA ( w) = and SR Y B ( w) =, AR ( w) Y BR ( w) respectively. Considering the ratio between the two amplification functions, a measured function Y e (ω) can be defined for a couple of measured points A and B, as: Y ( ω) = e Y α Y A B ( ω) ( ω) Model Function and its Gradient () The soil deposit of each site S A or S B is assumed to be linear viscoelastic and horizontally stratified (Figure 1a) and the distance between the recording stations is about 9 kms which is assumed so long to satisfy the one dimensional model assumption. Assuming one dimensional (1D) vertical shear wave propagation (Figure 1a), the equation of motion in each layer of the non homogeneous soil deposit is: ρ j ( ) uj z j t uj ( z j t) uj z j t = Gj + η 3,, (, ) j t z z t (3) where G j, ρ j, η j, z j (0 z j h j ) and h j are, respectively, shear modulus, unit weight, viscosity, depth, and the thickness in each layer j (j = 1, N where N is the number of layers in the soil profile) (Figure 1a). The solution of the ordinary differential equation (3) in term of harmonic horizontal displacement is written as: i t j ( j ) = j ( j ) w (4) u z, t U z e

4 4 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 Figure 1. Schematization of soil profiles (a) one dimensional soil model of referential site, (b) lithology log with downhole test at experimental site U j (z j ) is the displacement amplitude which is written in the form of equation (5), with k j = ω/v Sj : ( ) = + ' U z A e A e j j j ikjz j ikj z j j (5) WhereVSj = Gj / r j is the shear wave velocity. The coefficients A j and A j are the incident and reflected wave amplitudes, respectively, in each layer j. These amplitudes are obtained from the boundary conditions: (1) nullity of shear stresses on the ground surface, () continuity of displacements at the interface of the layers j and j+1 and (3) continuity of shear stresses at the same interface (Figure 1a). By defining, simultaneously, transfer functions or soil amplification functions T A, R ({ γ A }, ω) and T B, R ({ γ B }, ω) for each site S A and S B as the ratio of the displacement amplitude at the free surface of the soil profile to the displacement amplitude at the interface between soil and bedrock (Roesset, 1977), both take the same form of the following equation: A1 T1, NS + 1 ({ γs }, ω ) = (6) ' AN AN + 1 Where N S is the layer number constituting the soil profile of the site S A (N S = N A ) or that of the site S B (N S =N B ) and { g S } is the parameters vector of the soil profile of the site S A ( { gs } = { ga} ) or that of the site S B ({ gs } = { gb } ). In order to clarify the vector {γ S }, the ' amplitudes A j and A j (j =, N S +1) are expressed in terms of the characteristics (thickness h j, damping ratio ξ j, shear wave velocity V Sj, and unit weight ρ j ) of each layer j of the soil profile (Figure 1a) and circular frequency ω. A recurrence relationship between the wave amplitudes in the j and j-1 layers of the multi layers soil profile is formulated (Harichane et al., 005; Harichane, 005). The effect of material damping is taken into account by introducing complex material properties in each l a y e r j : V * = V 1 + ix a n d ( ) Sj Sj j G * j = Gj 1 + ix j. ξ j denotes the ratio of the linear hysteretic damping of shear waves in the

5 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 5 j th layer (Wolf, 1985) and is related to the viscosity η j by the relation ( ωη = G ξ ). j j j ({ } ) The model function Y di γ, ω in the present case of simultaneous identification of two soil profiles at two sites, which is defined by the equation: Y di T ({ γ}, ω) = T A, R B, R ({ γa}, ω) ({ γ }, ω) is rewritten in the following form: Y di ({ γ}, ω) = T T 1, NA + 1 1, NB + 1 B ({ γa}, ω) ({ γ }, ω) B (7) (8) The parameters vector of the model is g defined as { g} = { } A. { g } B According to the Levenberg-Marquart algorithm, one needs to evaluate the gradient of the model function (equation 8), expressed in terms of the partial derivatives of the function Y di versus any parameter of the model γ j (j = 1, m A + m B, where m A and m B are the numbers of components in the vector {γ A } and {γ B }, respectively). The partial derivatives of the model function versus the parameters of the model are calculated in two steps (Harichane et al., 005). EXPERIMENTAL DATA Free Field Records In the present experimental validation of the identification procedure of soil profile characteristics, we have used strong ground motions data recorded during the destructive 6.8 magnitude earthquake that hit northern Algeria on May 1, 003, severely damaging the city of Boumerdes (about 50 km east of Algiers), the capital city of Algeria, and a number of small cities in Algiers - Boumerdes region (Figure ). These records were obtained by the Algerian s strong motion instrumentation network of the National Earthquake Engineering Research Centre (CGS) in and around the epicentral area. The E-W acceleration components corresponding to the city of Algiers (Figures 3 and 4), are used in the simultaneous identification of soil profile characteristics (layer thickness, damping ratio, shear wave velocity, and unit weight) of two sites by using the modulus of smoothed spectral ratios of two sites. The two recording stations A (Hussein Dey) and B (Dar Elbeida) (Figure ) are at 36 and 9 km from the epicenter, respectively (Bendimerad, 003; Laouami et al., 006). The E-W peak ground acceleration (PGA) corresponding to the two recording stations under study have reached 0.7g and 0.50g, respectively, which are relatively high for station B, due to site amplification (Laouami et al., 006; Maouche et al., 008; Harichane & Afra, 010). In Situ and Laboratory Results To validate the obtained numerical results, we select a site with available experimental data. The selected site, within an area of 4050 m is located at Bab-Ezzouar city, near the DarElbeida site (referential site S B ) (Figure ). As part of a complete geotechnical investigation program of this site, boring and sampling were realized during the period from November 005 to January 006 (Bahar, 006). The synthesis of boring results has revealed that under a filling layer of 1.0 to 6.0 m, the soil profile of the selected site is composed of alluvium deposit represented by gravely and silt clay in depth overlaying a horizon of sandstone and consolidated fine sand. The clayey formation is compact, generally with stiff consistency. On other hand, results of Dynamic Penetration Tests (DCPT), conducted as part of the investigation program of the same site, have confirmed hypothesis of lateral continuity of soil compactness, with respect to the one dimensional model, at the overall site (Bahar, 006). In fact, twenty six (6) tests of dynamic penetration were carried out in November

6 6 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 Figure. Epicentral area of May 1, 003 Boumerdes earthquake Figure 3. Accelerations recorded at free surface of site of Hussein Dey city Figure 4. Accelerations recorded at free surface of site of Dar Elbeida city

7 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 7 Figure 5. Dynamic resistance of point versus depth at the experimental site 005 using a Standardized Heavy Dynamic Penetrometer of type GEOTOOL LMSR-SPT/ Vk in accordance with standard AFNOR NF P (AFNOR, 1990) and XP P Norm (AFNOR, 000). The recorded values of the dynamic penetration resistance (R P in bars) are given in Figure 5. The obtained curves take similar forms, which mean a lateral continuity of compactness at all the site. Resistance R P varies between 3 and 100 bars from 1.0 to 7.0 m of depth and evolves in depth until reaching a marked refusal between 10.0 and 13.0m of depth. The profile of dynamic resistances of point clearly indicates two beds of clays of distinct resistances. The Down Hole test has been realized in December 005 (Bahar, 006) according to ASTM D448/D448M norm (ASTM, 005), nearness a boring, for vertically propagating waves. The obtained results in terms of shear wave velocity are: 300 m/s between 00.0 to 05.0 m 540 m/s between 05.0 to 14.0 m 1450 m/s between 14.0 to 0.0 m These velocities values are plotted versus depth H below the ground surface in Figure 6. Lithology of boring (Figure 1b) in which Down Hole test is realized is presented in Table 1. NUMERICAL RESULTS In order to validate the present approach, we compare the obtained results with experimental ones. Mono-Layer Soil Profiles For a minimal number of parameters to be identified, we consider an equivalent uniform soil layer for each referential site. To apply the identification method, initial guess for the model

8 8 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 Figure 6. Shear wave velocity profile at the experimental site Figure 7. Fourier spectrum amplitudes of ground accelerations at free surface of site of Hussein Dey city (referential site S A )

9 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 9 parameters of each site are adopted. Because the recording station sites selected in the present application are located in the eastern part of the coastal plain of Mitidja (Figure ), area of 1300 km (100km of long and 8 to 13 km of large), subsiding basin with continuous marl or clayey filling, we consider firm mono-layer soil profiles for the two sites. Initial estimates of model parameters are selected according to the Algerian seismic design code RPA99/003 (National Earthquake Engineering Research Centre, 003). Figures 7and 8 show the Fourier spectrum amplitudes of the ground accelerations recorded at free surfaces of sites of Hussein Dey city (referential site S A ) and Dar Elbeida city (referential site S B ), respectively. The spectral ratio between the two referential sites is depicted in Figure 9. The parameter α is assumed equal to unity (1.0). This assumption (α = 1) assumes bedrock motions (or frequency contents) at sites S A and S B the same. This assumption is valid when the two sites are relatively near, which is the case in our study (about 9 km). But this parameter can be determined from attenuation laws (which are not available for our study area) or can be considered as unknown parameter of the model function and then can be identified. The identification results of soil profile characteristics of the two referential sites are presented in Table. To check the accuracy of the identified soil profile amplification function, it is compared to the experimental one at the site of interest. For this purpose, we limit ourselves to the same identified depth (16.36 m) below ground surface to compute mean shear wave velocity of the equivalent uniform layer of the experimental site (Table 1) from shear wave velocity profile (Figure 6) with respect to the equation below (National Earthquake Engineering Research Centre, 003): V S N i = = 1 N i= 1 h i hi V Si (9) Where N is the layers number. The experimental amplification function is obtained by using the identified damping ratio value. The identified parameters are compared to the experimental ones in Table 3. The corresponding soil amplification functions are compared in Figure 10. Table 3 and Figure 10 show that identified characteristics and corresponding amplification functions are in a very good agreement with those obtained by in situ and laboratory tests. Multi-Layers Soil Profiles For more characterisation of sites, this example consists in the identification of a multi-layers soil profile of each referential site, simultaneously, by minimising between smoothed spectral ratio of the two sites (Figure 9) and their amplification function ratio. The two profiles are considered composed by four horizontal layers. Then, the number of parameters to be identified is 30, i.e., (x(4n-1), where N is the layers number of each soil profile). The identified parameters for the two referential sites are presented in Tables 4 and 5. To compare the identified soil characteristics with those obtained by in situ and laboratory tests at the experimental site, we should reconstitute an equivalent multilayers soil profile, from site lithology given in Table 1, where depths are taken equal to those identified; and then deduce the corresponding shear wave velocities and unit weights by using equation (9) and similar one, respectively. The identified parameters and those corresponding to the experimental site are compared in Table 6. Soil amplification functions corresponding to identified and experimental parameters are compared in Figure 11.

10 10 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 Table 1. Lithology of boring with down hole test Depth H(m) Layer designation Unit weight (kg/m 3 ) Filling Gravely brown clay Marley compact beige clay Reddish clayey silt Sandstone 15 Figure 8. Fourier spectrum amplitudes of ground accelerations at free surface of site of Dar Elbeida city (referential site S B ) Figure 9. Experimental spectral ratio between referential site S A and referential site S B

11 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June Table. Identified characteristics of uniform soil layers Site S A Site S B Parameter h(m) ξ(%) V S (m/s) ρ(kg/ m 3 ) h(m) ξ(%) V S (m/s) ρ(kg/ m 3 ) Soil layer Half-space Table 3. Comparison between identified and experimental characteristics of uniform soil layer Depth H(m) Identified Experimental Layer thickness h(m) Shear wave velocity V S (m/s) Ratio (h / V S ) Table 4. Soil profile characteristics of referential site S A Layers number Depth (m) Layer thickness (m) Damping (%) Shear wave velocity (m/s) Unit weight (kg/m 3 ) Half-space Table 5. Soil profile characteristics of referential site S B Layers number Depth (m) Layer thickness (m) Damping (%) Shear wave velocity (m/s) Unit weight (kg/m 3 ) Half-space

12 1 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 Table 6. Comparison between identified and experimental multi-layers soil profiles Layers number Depth (m) Layer thickness (m) Damping (%) Shear wave velocity (m/s) Unit weight (kg/m 3 ) Identified Experimental Identified Experimental Table 7. Uncertainties of individual parameters for monolayer profiles Parameter Identified parameter γ j Site S A h (m) ± ξ (%) ± V S (m/s) ± Site S B h (m) ± ξ (%) ± V S (m/s) ± δγ j From Table 6 and Figure 11 we conclude that identified parameters and corresponding soil amplification functions are in good agreement with those obtained experimentally. UNCERTAINTIES ON IDENTIFIED PARAMETERS The confidence interval and the accuracy with which the soil parameters are identified by the proposed method can be estimated through their covariance matrix. The experimental data are assumed to have a normal distribution of the error and its standard deviation is the same for the data. In this case, the approximate covariance matrix [C(γ*)] is given by (Press et al., 199): C * γ ({ }) σ S = [ 1 ] σ = χ ({γ*})/(l-m) where l is the number of experimental data, m is the number of identified parameters and χ (γ*) is the value of the optimal residual error function obtained for the optimal identified parameters {γ*}. Then, the uncertainty value for each parameter γ i is given by (Tables 7 and 8): δγ j ( ) * = C jj { γ } Tables 7 and 8 show that: The accuracy of the identified parameters for monolayer site is very acceptable and is better than for the multilayer site, The average uncertainty value for the thickness, velocity, damping and mass are respectively about %, 3%, 31% and 34% for site S A and about %, 6%, 30%, 33%, for site S B, which is relatively acceptable and means that the two first parameters are well identified than the two other parameters, Moreover, the effect of noise on the recorded seismic motions on the identified

13 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June Figure 10. Comparison between identified and experimental soil amplification functions, monolayer case Figure 11. Comparison between identified and experimental soil amplification functions, multilayers case parameters can be studied by corrupting the data with a given level of noise by using, for example, the Sohn and Law algorithm (Sohn, 000) and perform the identification. Nevertheless these uncertainties are assumed, in this study, as negligible since the recorded data have been processed with the Kinemetrics SWS software (Laouami et al., 006) and the sampling frequency has been set to 00 sps. In other hand, the Trifunac method (Trifunac, 1973), used for data processing, is based on three steps: (i) instrument correction, (ii) baseline correction of the acceleration data, and (iii) high-pass filtering of velocity and displacement, using an Ormsby filter. For instrument correction, the low-pass cut-off frequency of the Ormsby filter was set to 45 Hz, with a 3 Hz roll-off width. The corner frequency for both long-period baseline correction filtering and high-pass filtering of velocity and displacement depends mainly on the spectral signal-to-noise ratio of each component, and has been estimated in the Hz range with a roll-off width of 0.06 Hz. DISCUSSION In the identification procedure of soil profile characteristics and corresponding soil amplification functions, we have minimized between

14 14 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June 01 Table 8. Uncertainties of individual parameters of multilayer profiles Layer number Parameter Site S A Identified Identified δγ parameter γ j j parameter γ j Site S B h (m) ± ± ξ (%) ± ± V S (m/s) ± ± ρ (kg/m 3 ) ± ± h (m) ± ± ξ (%) ± ± V S (m/s) ± ± ρ (kg/m 3 ) ± ± h (m) ± ± 1.38 ξ (%) ± ± V S (m/s) ± ± ρ (kg/m 3 ) ± ± h (m) ± ± 0.77 ξ (%) ± ± V S (m/s) ± ± δγ j modulus of smoothed spectral ratio of two sites (measured function) and theoretical amplification function (model function) by using least squares minimization technique according to the Levenberg-Marquart algorithm. The great weakness of the Levenberg-Marquardt algorithm, which is a local optimization technique, is its sensitivity to the initial guesses. If these ones are far from the sought ones, optimization tends towards the nearest local peak but if the initial guesses are better selected, optimization leads to the global peak. So, the adjusting is more reliable if just a global estimation of the model is needed, i.e., nature of the site in the present case of identification, like as firm or soft site. This information can be obtained if the studied site is well documented. In fact, under assumption of firm site (i.e., mean value of shear wave velocity between 400 and 800 m/s over 30 m depth below ground surface, according to RPA99/003 (National Earthquake Engineering Research Centre, 003), uniquely, we have obtained concordant results with those obtained experimentally. Obviously, the present identification approach identifies well the ratio between thickness layer and shear wave velocity (h/v S ) for the different layers of the multilayer system and the corresponding amplification functions, in spite of its sensitivity to the high number of parameters (30 parameters in the second example) but the solution may not be unique. To illustrate this we optimized the error function χ according to the thickness (h) and shear wave velocity (V S ) of an elastic soil layer whose actual or required parameters are h = 0 m and V S = 00 m/s and we plot the surface shown on Figure 1. This figure shows that the line h/v S = 0.1 corresponds to the minimal values of χ which means that the obtained solutions are not unique and their validation is needed. On other hand, the equivalent shear wave velocities, calculated by equation (9) from identified values, are approximately 544 m/s and 470 m/s, respectively, which give equiva-

15 International Journal of Geotechnical Earthquake Engineering, 3(1), 1-17, January-June Figure 1. Schematization of the error function optimization in terms of thickness and shear wave velocity for a monolayer soil profile Figure 13. Base rock response spectrum at sites S A and S B lent fundamental frequencies equal to 9.34 Hz and 7.18 Hz, respectively. These two fundamental frequencies induce a spectral amplification coefficient equal to 1.36 and.49, respectively. This spectral amplification coefficient is determined from the response spectrum or normalized response spectrum curve of bedrock seismic motion at sites S A and S B (Figure 13). The normalized response spectrum can be interpreted as amplification factor of response and is obtained by dividing the pseudo spectral acceleration by peak ground acceleration (PGA) (Bakir et al., 007). The ratio between spectral amplification coefficients of sites S A and S B is equal to 1.83 which is in good agreement with the ratio between recorded free field motions. CONCLUSION In the present paper, an approach using system identification theory and free field records, for identifying soil profile characteristics of sites, is validated. The new approach allows identification of soil profile characteristics of two sites, simultaneously, from only a single soil acceleration record at free surface of each site. The validation is performed by comparing the identified model parameters, i.e., soil profile characteristics (thickness, damping ratio, shear

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