NDT.net • June 2006 • Vol. 11 No.6 
Estimating GMax & Field CBR of Soil Subgrade Using a Seismic MethodS.A. Rosyidi^{1}, K.A.M. Nayan^{2}, M.R. Taha^{3} & A. ISMAIL^{4}^{1}Lecturer, Division of Transportation Eng., Department of Civil Engineering Muhammadiyah University of Yogyakarta, Lingkar Barat, 55183, Yogyakarta, Indonesia email: atmaja_sri@umy.ac.id ^{2}Lecturer, ^{3}Professor, ^{4}Assoc.Prof., Department of Civil & Structural Engineering, Universiti Kebangsaan Malaysia. 43600, Bangi, Malaysia email: khairul@eng.ukm.my, drmrt@eng.ukm.my, abim@eng.ukm.my. ABSTRACTThe knowledge of the insitu strength and stiffness of the ground is normally required for the design monitoring and evaluation of highway pavement so as to ensure an adequate margin of safety. In order to estimate the stiffness of the pavement foundation a method called the spectral analysis of surface wave (SASW) has been developed. The method consists of generation, measurement and processing of the dispersive Rayleigh waves recorded from two vertical transducers. Subsequently, an inversion process is carried out to obtain the shear wave velocity versus depth profile of the site from the dispersive Rayleigh wave data. The results presented in this paper showed that the SASW method is able to determine reliably the shear modulus of the soil subgrade layer of the pavement profile. In situ subgrade bearing capacity test using the field CBR test was also carried out in the same location of SASW test. An empirical relationship between the CBR value and the dynamic soil stiffness from the SASW measurements was also established for practical applications for the purpose of pavement design and maintenance.Keywords: SASW, shear wave velocity, shear modulus, pavement subgrade layer INTRODUCTIONThe performance of pavement structures is strongly influenced by the stiffness of the soil subgrade layer. In order to establish the stiffness of subgrade structures of the existing roads, accurate information of the moduli of the various pavement layers is needed. The shear modulus parameter is used to calculate the bearing capacity and to characterize the mechanical behavior of the materials under different types of traffic loading in order to predict the performance, select and to design appropriate rehabilitation techniques. In order to effectively measure and evaluate the stiffness of soil subgrade layers, a nondestructive test (NDT) of the spectral analysis of surface wave (SASW) which is economic and fast is needed. The method is based on the dispersion of Rayleigh waves (R waves) to determine the shear wave velocity each layer of the pavement profile. The SASW method has been utilized in different applications over the past decade (Stokoe et al., 1994) after the advancement and improvement of the wellknown steadystate (Jones, 1958) technique. These applications include detection of soil profile, evaluation of concrete structures, detection of anomalies, detection of the structural layer of cement mortar, assessing compaction of fills and the evaluation of railway ballast. The purpose of this paper is to estimate the dynamic shear modulus of the soil subgrade layer measured from the SASW test and to derive the empirical correlation between the dynamic shear modulus parameter and the CBR values from different sites.LITERATURE REVIEWThe SASW method is based on the particles motion of R wave in heterogeneous media. The energy of R waves from the source propagates mechanically along the surface of media and their amplitude decrease rapidly with depth. Particle motions associated with R wave are composed of both vertical and horizontal components, which when combined, formed a retrogressive ellipse close to the surface. In homogenous, isotropic, elastic halfspace, R wave velocity does not vary with frequency. However, R wave velocity varies with frequency in layered medium where there is a variation of stiffness with depth (Stokoe et al., 1994). This phenomenon is termed dispersion where the frequency is dependent on R wave velocity. The ability to detect and evaluate the depth of the medium is influenced by the wavelength and the frequency generated. The shorter wavelength of high frequency penetrates the shallower zone of the near surface and the longer wavelength of lower frequency penetrates deeper into the medium.The range of wavelength to be used as a guide for the receiver spacing can be estimated from the shear wave velocities of the material anticipated at the site:
where f is the frequency and V_{S} is shear wave velocity. The higher and low frequency waves groups needed can be generated by various transient sources of different weights and shapes. Waves of low frequency for the base and subgrade layer could be generated from hammer weights of 3 to 5 kg (Rosyidi et al., 2005a, 2005b). The experimental dispersion curve of phase velocity and wavelength may be developed from phase information of the transfer function at the frequency range satisfying the coherence criterion. In addition, most of researchers apply the filtering criteria (Heisey et al., 1982) with a wavelength greater than ½ and less than 3 receiver spacings. The time of travel between the receivers for each frequency can be calculated by:
where f is the frequency, t(f) and ff are respectively the travel time and the phase difference in degrees at a given frequency. The distance of the receiver (d) is a known parameter. Therefore, R wave velocity, V_{R} or the phase velocity at a given frequency is simply obtained by:
and the corresponding wavelength of the R wave, L_{R} may be written as:
The actual shear wave velocity of the pavement profile is produced from the inversion of the composite experimental dispersion curve. In the inversion process, a profile of set of a homogeneous layer extending to infinity in the horizontal direction is assumed. The last layer is usually taken as a homogeneous halfspace. Based on the initial profile, a theoretical dispersion curve is then calculated using an automated forward modeling analysis of the dynamic stiffness matrix method (Kausel & Röesset, 1981). The theoretical dispersion curve is ultimately matched to the experimental dispersion curve of the lowest RMS error with an optimization technique. Finally, the profile from the bestfitting (lowest RMS) of the theoretical dispersion curve to the experimental dispersion curve is used that represents the most likely pavement profile of the site. The dynamic shear moduli of the materials can be easily obtained using the shear wave velocity parameter of SASW from the following equation (Yoder & Witczak, 1975):
where G is the dynamic shear modulus, VS the shear wave velocity, g the gravitational acceleration, ? the total unit weight of the material and µ the Poisson ratio. Nazarian & Stokoe (1986) explained that the shear modulus parameter of material obtained from the SASW test approaches to the maximum shear modulus at a strain below about 0.001 %. In this strain range, modulus of the subgrade materials is also taken as constant. METHODOLOGYExperimental Set Up An impact source on a pavement surface is used to generate R waves. These waves are detected using two accelerometers where the signals are recorded using an analog digital recorder and a notebook computer for post processing (Figure 1). Several configurations of the receiver and the source spacings are required in order to sample different depths. The best configuration in the SASW is the mid point receiver spacings (Heisey et al., 1982). In this study, the short receiver spacings of 5 and 10 cm with a high frequency source (ball bearing) are used to sample the AC layers while the long receiver spacings of 20, 40 cm and 80, 160 cm with a set of low frequencies sources (a set of hammers) are used to sample the base and subgrade layers, respectively. The SASW tests were carried out at two sites which include 30 test locations on the main road in the campus of Universiti Kebangsaan Malaysia in Bangi, Selangor, Malaysia and 20 test locations on the State Road of Prambanan to Pakem and Piyungan to Gading, Yogyakarta Province, Indonesia. Data were collected together with the field CBR tests conducted on the same SASW measured centre points.
Data Analysis All the data collected from the recorder are transformed using the Fast Fourier Transform (FFT) to frequency domain by the dBFA32 software resident in the notebook computer. Two functions in the frequency domain between the two receivers are of great importance: (1) the coherence function and (2) the phase information of the transfer function. The coherence function is used to visually inspect the quality of signals being recorded in the field and have a real value between zero and one in the range of frequencies being measured. The value of one indicates a high signaltonoise ratio (i.e., perfect correlation between the two signals) while values of zero represents no correlation between the two signals. The transfer function spectrum is used to obtain the relative phase shift between the two signals in the range of the frequencies being generated. Figure 2 shows a typical set of the coherence and the phase plot of the transfer function from the measurement of an 80 cm receiver spacing at the site of UKM's road. By unwrapping the data of the phase angle from the transfer function, a composite experimental dispersion curve of all the receiver spacings are generated. By repeating the procedure outlined above and using equation (2) through (4) for each frequency value, the R wave velocity corresponding to each wavelength is evaluated and the experimental dispersion curve is subsequently generated. Figure 3 shows the example of the composite experimental dispersion curve from measurements of all the receiver spacings.
RESULTS AND DISCUSSIONBy unwrapping data of the phase angle from the transfer function (Fig.2 for site 1), the composite experimental dispersion curve obtained is as shown in Figure 3. The figure shows the horizontal dash lines for wavelengths ranging from 0.8 to 3 m, the subgrade layer with the minimum phase velocity of 180 m/s to the maximum phase velocity of 230 m/s are obtained.In order to generate the actual shear wave velocity of the subgrade layer, an inversion process using 3 D forward modeling from the stiffness matrix method (Kausel & Röesset, 1981) and an optimization technique of the maximum likelihood method (Joh, 1996) were conducted. For developing the pavement profile from the inversion analysis, the starting model parameter is obtained from the cored road profile that was found to be consisting of an average asphalt concrete (AC) layer (70 mm thick), a base layer (400 mm thick) over a subgrade layer. Descriptions of model parameters and typical thickness of the pavement layers are shown in Figure 4.
The pavement profile obtained from inversion process is shown in Figure 5. The profile is an example of the SASW result from the first location (UKM, Malaysia). Core drilling was also conducted in the same location after the SASW measurement. There is a reasonable agreement of the profile depth between the results from the SASW measurement and the core drilling. The average of inverted shear wave velocity for UKM's road measuring points is 178.419 m/s with a range of 116.44 to 263.226 m/s. The dynamic shear modulus is then obtained from the shear wave velocity profile using the dynamic material equation (Equation 5). The average shear modulus of the subgrade material from the analysis is 69.779 MPa. Based on the shear modulus, the subgrade material maybe classified as a sandy soil material. The shear wave velocities and their corresponding shear modulus from this study were listed in Table 1 in comparison with the results of SASW testing obtained by other researchers such as Puri (1969) and Nazarian & Stokoe (1986). It is important to note that Puri (1969) obtained the dynamic properties of silty sand using the free vertical vibration stress waves measured at 1.0 x 10^{4} % strain level. The shear wave velocities from the SASW were then correlated to the CBR values for the evaluation of the bearing capacities of the subgrade materials. The relationship between the shear wave velocities and CBR values can also be derived as shown in Figure 6 for the subgrade layer.
Figure 6 also shows that the increased in the shear wave velocities correlates well with the increased in the CBR values. The coefficients of correlation obtained (Figure 6) indicate that the empirical equation derived between the shear wave velocities have significant correlations with the CBR value. The correlation coefficient, R^{2} of 0.938 was obtained for the subgrade layer. However, the empirical equations obtained only shows the best correlation of shear wave velocity to the CBR value that is not more than 400 m/s. Higher deviations obtained from Figure 6 for high values of CBR should be investigated. The derived equation of Vs and CBR can be written as: CBR = 0.0006 (V_{S}S)^{1.99} (6) where, CBR is the field California Bearing Ratio in % and VS is the shear wave velocity in m/s. Figure 7 shows the empirical correlation between the CBR values to the dynamic shear modulus from SASW for the subgrade layer. The result shows a good agreement between the dynamic shear modulus from the SASW test and the CBR value with a deviation range of ± 20 %. The empirical equations obtained were summarized as below : CBR = 0.266 (G)^{1.0027}, R^{2} = 0.947 (7) where G is an approach value of the maximum shear modulus in MPa obtained from the SASW analysis.
CONCLUSIONS1. Good agreements were obtained between the measured shear wave velocities and the corresponding dynamic shear modulus as compared to the work of Puri (1969) and Nazarian & Stokoe (1986). 2. This study has also managed to obtain good empirical correlations between the dynamic shear modulus and the field CBR values. 3. The SASW method is able to characterize the stiffness of the pavement subgrade layer in terms of shear wave velocity and its corresponding dynamic shear modulus satisfactorily for the propose of pavement design and evaluation.ACKNOWLEDGEMENTThe authors would like to give our sincere appreciation to the Ministry of Science, Technology and Environmental of Malaysia for supporting this research through the IRPA Grant No.0902020055EA151, and also to the Faculty of Engineering, Muhammadiyah University of Yogyakarta for supporting the study through Engineering Research Grant 2004. The authors also would like to thank Prof. Sung Ho Joh of the Chung Ang University, Korea for his assistance in using the WinSASW software in this study and Prof. Gucunski of Rutgers University, USA for his interested discussion.REFERENCES

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