than the Q L2, the ratios with the slope tangent method would suggest that the difference in failure load would only be reduced by about 10% on average. This reduction would clearly be insufficient to account for the observed differences in side resistance. Finally, differences in the shaft diameters in Tables 1 and 2 in the paper are generally very small and appear to be round-off errors or differences in the average diameter for the full shaft length versus the shaft segment in question. Likewise, differences in N values are generally due to reporting an average N value for the entire length of the shaft Table 1 versus a smaller section of the shaft under consideration Table 2 ; however, some reevaluations of appropriate N values used in the analysis were not updated in Table 1. The numbers in Table 2 will be more useful since they are for a given segment rather than for the entire shaft. Selection of appropriate average N values in gravelly soil is always a concern, but we believe the overall conclusions from the paper will not change based on differences in the selected N value. Alsamman, O. M. 1995. The use of CPT for calculating axial capacity of drilled shafts. Ph.D. dissertation, Univ. of Illinois, Urbana- Champaign. Bolton, M. D. 1986. The strength and dilatancy of sands. Geotechnique, 36 1, 65 78. Boulon, M., and Foray, P. 1986. Physical and numerical simulation of lateral shaft friction along offshore piles in sand. Proc., III Int. Conf. on Numerical Methods in Offshore Piling, Nantes, 127 147. Chen, J. R. 2004. Axial behavior of drilled shafts in gravelly soils. Ph.D. dissertation, Cornell Univ., Ithaca, N.Y. Harraz, A. M., Houston, W. N., Walsh, K. D., Perry, C. R., and Houston, S. L. 2005. Comparison of measured and predicted skin friction values for axially loaded drilled shaft foundations in gravelly soils. Advances in Deep Foundations, GSP 132, 12. Hirany, A., and Kulhawy, F. H. 2002. On the interpretation of drilled foundation load test results. Deep Foundations 2002, GSP116, Vol. 2, 1018 1028. Jamiolkowski, M. B. 2000. Axial load capacity of bored piles in sand and gravel. Proc., 3rd Symp. on Deep Foundations. Koerner, R. M. 1970. Effect of particle characteristics on soil strength. J. Soil Mech. and Found. Div., 96 4, 1221 1234. Kulhawy, F. H., and Hirany, A. 1989. Interpretation of load tests on drilled shafts. II: Axial uplift. Foundation Engineering. Current Principles and Practices, GSP, 22, 1150 1159. Kulhawy, F. H., and Mayne, P. W. 1990. Manual on estimating soil properties for foundation design. Rep. No. EPRI EL-6800, Electric Power Research Institute, Palo Alto, Calif., 2 25. Mayne, P. W., and Kemper, J. B. 1988. Profiling OCR in stiff clays by CPT and SPT. Geotech. Test. J., 11 2, 139 147. Menq, F.-Y. 2003. Dynamic properties of sandy and gravelly soils. Ph.D. dissertation, Univ. of Texas, Austin. O Neill, M. W., and Reese, L. C. 1999. Drilled shafts: Construction procedures and design methods. FHWA-IF-99-025, U.S. Department of Transportation, Washington, D.C., Vol. II, B-50 B-50. Rollins, K. M., Evans, M., Diehl, N., and Daily, W. 1998. Shear modulus and damping relationships for gravels. J. Geotech. Geoenviron. Eng., 124 5, 396 405. Turner, J. P., and Kulhawy, F. H. 1990. Drained uplift capacity of drilled shafts under repeated axial loading. J. Geotech. Engrg., 116 3, 470 491. U.S. Navy. 1982. Foundation and earth structures design manual 7.2, Department of the Navy, Naval Facilities Engineering Command, Alexandra, Va. Wernick, E. 1978. Skin friction of cylindrical anchors in non-cohesive soils. Proc., Soil Reinforcing and Stabilizing Techniques in Engineering Practice, 201 219. Discussion of Frequency-Dependent Amplification of Unsaturated Surface Soil Layer by J. Yang April 2006, Vol. 132, No. 4, pp. 526 531. DOI: 10.1061/ ASCE 1090-0241 2006 132:4 526 Jiewu Meng 1 1 Project Engineer, Fugro Consultants, Inc., Houston, TX 77081. E-mail: jmeng@fugro.com A proper characterization of dynamic soil behavior in ground motion analysis is of great importance in geotechnical earthquake engineering. The author provides an interesting demonstration of the significance of frequency-dependent site amplification of near-surface soils. The discusser offers the following remarks regarding the S-wave attenuation behavior of soils in the seismic frequency range, as presented in Fig. 3 of the paper. From the definition of the so-called characteristic frequency, f c =ng/2 k, and the assumed values as listed in Table 1, f c =7,022 Hz for the sands in the author s article can be determined accordingly. By using the characteristic frequency and the attenuation spectrum as shown in Fig. 3, S-wave attenuation is estimated to be approximately 0.0001 at 1 Hz and 10 times lower with the decrease of frequency per decade. On the one hand, body wave propagation in soils can be theoretically characterized with a closed-form solution under a one-dimensional wave propagation condition Biot 1956a,b. Basically, the computed dynamic soil parameters used by the author are in general agreement with the results obtained by Miura et al. 2001, who performed a thorough study of the dynamic properties of clays, silts, and sands by using Biot s equations. On the other hand, experimental studies have found little frequency effect on the dynamic properties of sands Bolton and Wilson 1989; Iwasaki et al. 1978 but observable frequency effect on soils with fine grains, as summarized in Fig. 1. The attenuation data were converted by using 1/Q=2D, where D is the damping ratio. It is apparent that attenuation of various soils is between 0.01 and 0.1 in the seismic frequency range and contradicts the pattern and the magnitude demonstrated in Fig. 3 of the original paper by the author and by Miura et al. 2001. Although still in debate, seismic-wave attenuation in soils appears to be a combination of viscoelastic losses i.e., the global-flow loss and the local-flow loss, fluid-solid surface physicochemical interaction loss, and scattering loss, along with other competing losses Li et al., 2001. The global-flow loss generally refers to the energy loss as characterized by the Biot equations 1956a,b. It is therefore very likely that the Fig. 3 attenuation modeled the global-flow loss, whereas the Fig. 1 attenuation reflects a more complete combination of energy losses. Of final note, it is plausible that the level of the Fig. 3 attenuation characterizes the behavior of the clean sands and may not compare well with that of the soils consisting of a certain amount of fine contents. However, the attenuation of dry sands is typically at a level of 0.02 e.g., Kim 1991, and the attenuation of sat- JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / OCTOBER 2007 / 1331
Closure to Frequency-Dependent Amplification of Unsaturated Surface Soil Layer by J. Yang April 2006, Vol. 132, No. 4, pp. 526 531. DOI: 10.1061/ ASCE 1090-0241 2006 132:4 526 J. Yang, M.ASCE 1 1 Dept. of Civil Engineering, Univ. of Hong Kong. E-mail: junyang@ hku.hk Fig. 1. S-wave attenuation of various soils in the seismic frequency range data from Kim 1991; Shibuya et al. 1999; Stokoe et al. 1999; d Onofrio et al. 1999; Meng 2003 rated or partially saturated sands is expected to be much higher than 0.0001 at 1 Hz, for example, as shown in Fig. 3. Biot, M. A. 1956a. Theory of propagation of elastic waves in a fluid saturated porous sand. I: Low-frequency rang. J. Acoust. Soc. Am., 28, 168 178. Biot, M. A. 1956b. Theory of propagation of elastic waves in a fluid saturated porous sand. II: High-frequency rang. J. Acoust. Soc. Am., 28, 179 191. Bolton, M. D., and Wilson, J. M. R. 1989. An experimental and theoretical comparison between static and dynamic torsional soil tests. Geotechnique, 39 4, 585 599. d Onofrio, A., Silvestri, F., and Vinale, F. 1999. Strain rate dependent behavior of a natural stiff clay. Soils Found., 39 2, 69 82. Iwasaki, T., Tatsuoka, F., and Takagi, Y. 1978. Shear modulus of sands under cyclic torsional shear loading. Soils Found., 18 1, 39 56. Kim, D.-S. 1991. Deformational characteristics of soils at small to intermediate strains from cyclic tests. Ph.D. thesis, The University of Texas, Austin, Tex., 341. Li, X., Zhong, L., and Pyrak-Nolte, L. J. 2001. Physics of partially saturated porous media: Residual saturation and seismic-wave propagation. Annu. Rev. Earth Planet Sci., 29, 419 460. Meng, J. 2003. The influence of loading frequency on dynamic soil properties. Ph.D. Thesis, Georgia Institute of Technology, Atlanta. Miura, K., Yoshida, N., and Kim, Y.-S. 2001. Frequency dependent property of waves in saturated soil. Soils Found., 41 2, 1 19. Shibuya, S., Mitachi, T., Fukuda, F., and Degoshi, T. 1995. Strain-rate effects on shear modulus and damping of normally consolidated clay. Geotech. Test. J., 18 3, 365 375. Stokoe, K. H. I., Darendeli, M. B., Andrus, R. D., and Brown, L. T. 1999. Dynamic soil properties: Laboratory, field, and correlation studies, 2nd Int. Conf. on Earthquake Geotechnical Engineering, Balkema, Rotterdam, The Netherlands, 811 845. The writer thanks the discusser for his interest in the paper. In his discussion, Meng raised the issue of the attenuation property of soils, for which the writer would like to provide the following comments. 1. The dynamic behavior of the soil, as indicated in the paper, was described by using Biot s theory Biot 1956. In other words, the soil was modeled by using the macroscopic laws of mechanics as a two-phase porous medium comprising the deformable solid skeleton and pore fluid. The solid skeleton was assumed to be elastic, and the flow of pore fluid was assumed to obey the generalized Darcy s law. The flow of fluid relative to the solid skeleton is responsible for the attenuation or damping characteristics shown in Fig. 3 of the original paper. The nature of the damping suggests that it may be largely influenced by factors that are associated with the fluid flow, such as permeability, porosity, and fluid viscosity For saturated soils, the fluid viscosity can be regarded as a constant, since the saturating fluid is groundwater. This damping mechanism is herein called flow damping. 2. To illustrate the effects of permeability and porosity on the flow damping, values of the attenuation Q 1 of the three body waves in a water-saturated soil are computed over a wide range of frequencies by varying the two factors. The results are presented in Figs. 1 and 2, along with the main soil parameters used in the computation. It is clear that the characteristic frequency, which gives the peak damping for the first P wave and S wave, will shift to the low-frequency end as the permeability increases or the porosity decreases. For typical values of permeability and porosity, the damping values of the first P wave and S wave are very small at frequencies of interest in earthquake engineering. As for the second P wave, it is generally not a true propagating wave but a diffusion process. A discussion on the roles of the two P waves in soil vibration can be found in Yang and Sato 2000, in which the response of a saturated soil column because of seismic cyclic loading was presented in terms of the individual contributions of the two waves. 3. The damping property of soils that is frequently referred to in the soil dynamics literature e.g., Ishihara 1996 is established mainly on the basis of such laboratory tests as the resonant column tests and the cyclic triaxial tests. The frequencies involved in the tests are generally between 0.1 and several Hz, and the soil specimens can either be in a saturated state or a dry state. For specimens in a dry state, the measured damping is considered as a result of energy loss 1332 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / OCTOBER 2007
Fig. 1. Effects of permeability on frequency-dependent attenuation n=0.45 G=40 MPa, G s =2.65 attributable mainly to the rearrangement of soil particles sliding, rolling, etc.. This damping is herein referred to as friction damping. For specimens in a saturated state, the mechanism of damping is even more complicated. The damping is thought to mainly comprise the friction damping and the flow damping; additional contribution to the energy dissipation may come from other microscopic interaction between the solid and fluid constituents e.g., Stoll 1989. The damping property shown by the discusser in Fig. 1 of the discussion appears to be the case of saturated soil samples. In this respect, it would be a reasonable observation that the values of damping in Fig. 1 are larger than those shown in Fig. 3 of the paper. 4. As far as the portion of the energy loss caused by the fluid flow is concerned, it appears to be an issue that has not yet been fully understood. For example, the resonant column tests by Hall and Richart 1963 showed that the difference in the damping values of similar saturated and dry specimens was remarkable, but the resonant column tests by Ellis et al. 2000 indicated an insignificant difference. The existing database for damping ratios of various saturated soils shows that the damping values at the strain amplitude of 10 4, which is approximately the upper threshold strain for elastic wave propagation and beyond which the plastic deformation occurs, typically vary between 0.02 and 0.05 Vucetic and Dobry 1991; Ishihara 1996. By comparison, the theoretically predicted values of flow damping at low frequencies appear to be much smaller Figs. 1 and 2, implying that the flow damping may be negligible. On the other hand, however, it should be noted from Figs. 1 and 2 that for soils whose permeability is extremely high e.g., coarse gravels with permeability of the order of 10 2 m/s, the contribution JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / OCTOBER 2007 / 1333
Fig. 2. Effects of porosity on frequency-dependent attenuation k=10 4 m/s; G=40 MPa; G s =2.65 of the flow damping to the total damping may not be simply disregarded. 5. Although the flow damping exhibits the frequency dependency in Biot s theory, the friction damping of soils does not appear to be significantly influenced by frequency, at least in the frequency range of earthquake loading Shibuya et al. 1995. Whether or not the soil damping is dependent on frequency is still a debatable issue. In this respect, care should be used in interpreting data for highly permeable soils or for the case when the test frequency is close to the characteristic frequency of the soil, because the flow damping may have a substantial contribution to the total damping in such cases and consequently, may lead to the observation that the damping is frequency-dependent. Over the past two decades, considerable effort has been made to investigate the strain dependency of shear modulus and damping. Experimental data for a variety of soil types have shown that the damping ratio can be as low as 0.01 at the strain amplitude of 10 5 and as high as 0.25 at the strain amplitude of 10 2. Despite the numerous test results, there still remains a question as to the reliability of damping values at small strains, particularly at strains lower than 10 5, because of difficulties associated with laboratory measurements. More precise measurement techniques are needed to help remove this question. Biot, M. A. 1956. Theory of propagation of elastic waves in a fluid saturated porous solid. J. Acoust. Soc. Am., 28, 168 191. 1334 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / OCTOBER 2007
Ellis, E. A., Soga, K., Bransby, M. F., and Sato, M. 2000. Resonant column testing of sands with different viscosity pore fluids. J. Geotech. Geoenviron. Eng., 126 1, 10 17. Hall, J. R., and Richart, F. E. 1963. Dissipation of elastic wave energy in granular soils. J. Soil Mech. and Found. Eng. Div, 89 SM6, 27 56. Ishihara, K. 1996. Soil behaviour in earthquake geotechnics, Clarendon Press, Oxford. Shibuya, S., Mitachi, T., Fukuda, F., and Degoshi, T. 1995. Strain rate effects on shear modulus and damping of normally consolidated clay. Geotech. Test. J., 18 3, 365 375. Stoll, R. D. 1989. Sediment acoustics. Lecture Notes in Earth Sci, 26, 1 4. Vucetic, M., and Dobry, R. 1991. Effect of soil plasticity on cyclic response. J. Geotech. Engrg., 117 1, 89 107. Yang, J., and Sato, T. 2000. Computation of individual contributions of two compression waves in vibration of water saturated soils. Comput. Geotech., 27 2, 79 100. JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / OCTOBER 2007 / 1335