FOTI S.

LANCELLOTTA R.

English

S. Foti

R. Lancellotta

Crossref

06 October 2021
POLITECNICO DI TORINO
Repository ISTITUZIONALE
Soil porosity from seismic velocities / FOTI S.; LANCELLOTTA R.. - In: GEOTECHNIQUE. - ISSN 0016-8505. - 54
(8)(2004), pp. 551-554.
Original
Soil porosity from seismic velocities
Publisher:
Published
DOI:
Terms of use:
openAccess
Publisher copyright
(Article begins on next page)
This article is made available under terms and conditions as specified in the  corresponding bibliographic description in
the repository
Availability:
This version is available at: 11583/1401818 since:
Foti, S. & Lancellotta, R. (2004). Géotechnique 54, No. 8, 551–554
551
TECHNICAL NOTE
Soil porosity from seismic velocities
S. FOTI

and R. LANCELLOTTA

INTRODUCTION
By analysing the wave propagation phenomenon in the
framework of porous media theory, it is possible to account
for the interaction between the soil skeleton and the pore
fluid, and to establish the dependence of seismic velocities
on elastic parameters of the two phases and on the soil
porosity (Foti et al., 2002).
Several empirical relationships have also been suggested
to correlate porosity and the velocity of propagation of
compressional wave in fluid-saturated porous media (Wyllie
et al., 1956; Raymer et al., 1980; Castagna et al., 1985; Han
et al., 1986; Ederhart-Phillips et al., 1989; Klimentos &
McCann, 1990; Krief et al., 1990). A good review on the
topic is provided by Berryman (1995), who also discusses
analytical approaches based on mixture theory.
Biot (1956a, 1956b) laid down the theory of seismic wave
propagation in saturated porous media, and his work is
widely recognised as a milestone in this field. Biot’s theory
is based on a macroscopic approach that models the binary
continuum as a superposition of a fluid and a solid phase
occupying simultaneously the same regions of space. In this
context, porosity can be seen as a parameter upscaling
information from micro to macro scale (Lancellotta, 2002).
Assuming an isotropic, linear elastic soil skeleton satu-
rated by a non-dissipative compressible fluid, Biot was able
to prove the existence of two different compressional waves,
namely of the first and second kind. The existence of the
compressional wave of the second kind, also known as the
Biot wave, has been proven by Plona (1980) and, more
recently, by Nakagawa et al. (1997). The Biot wave is very
difficult to observe experimentally because, as it is slower
than the compressional wave of the first kind, the first arrival
in seismic signals is always associated with the latter.
Considering the timescale of wave propagation and the
permeability of soils, the assumption that no relative motion
actually occurs between the solid and the fluid phases holds
for the low-frequency range (Santamarina et al., 2001).
Introducing the additional hypothesis of incompressible soil
grains, it is possible to obtain the following explicit relation-
ship for soil porosity n, as shown by Foti et al. (2002):
n ¼
rS
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rSð Þ2 4 rSrFð ÞKF= V 2P2 1SK)=(12SK
 
V 2S
  q
:
2 rSrFð Þ
(1)
where Vp and VS are the velocities of propagation of com-
pressional and shear waves respectively. The above relation-
ship is dependent only on properties that assume rather
standard values (grain density rS, water density rF, water
bulk modulus KF) and on the Poisson ratio of the soil
skeleton, SK. SK has a limited range of variability in soils
(0.1–0.4), and it can be shown to have negligible influence
on the estimated values of porosity (Foti et al., 2002).
Moreover, it is possible to show that the hypothesis of
incompressible soil grains can be removed with a relatively
small influence on the final results (Foti et al., 2002), even
if in this case the porosity evaluation requires the solution
of a more cumbersome mathematical inverse problem.
As already stated, the above solution is restricted to low-
frequency perturbations, because it assumes that there is no
relative motion between the soil skeleton and the fluid phase.
Indications about the range of validity of this assumption
can be found in Miura et al. (2001); it can be observed that
sources typically adopted for geophysical in-situ tests are
such that the predominant frequencies in the seismic signals
are well below the threshold value for all kind of soils (Foti
et al., 2002).
DESCRIPTION OF THE DATASET
Hunter (2003) recently reported a large dataset of seismic
velocities and porosity data from 12 boreholes in Canada. A
subset of his data is used in the present paper, referring only
to high-quality data (six boreholes) (Hunter, 2003, personal
communication). The porosity data of this subset have been
obtained from undisturbed samples, processed on the specia-
lised GSC laboratory on the same day as retrieval, except
for one case in which the data were analysed in the
laboratory of Carleton University. Great care was taken to
preserve the original water content during transportation of
the samples. A detailed description of the procedure and of
all the cautions taken to obtain reliable estimates is reported
in Hunter (2003).
Details of in-situ measurements of P and S wave velo-
cities, performed in down-hole tests, are also reported in
Hunter (2003).
Table 1 gives a description of the six boreholes. The
available data are typically for depths up to 60 m, except for
one borehole (JA01-4) for which data to a depth of 140 m
are available. Most of the data are related to clays, with the
exception of a few datapoints related to sands or tills.
Additional data have been collected in Italy, using cross-
hole tests for the seismic measurements and standard labora-
tory procedures for the determination of porosity (Jamiolk-
owski, 2003, personal communication). This dataset is
related to silty clays and clayey silts, with PI ranging
between 15% and 35%.
In order to have results relative to sandy soils, data from
laboratory tests, reported in the literature by Bates (1989)
and Tsukamoto et al. (2002), have also been considered.
MEASURED AND PREDICTED POROSITY
Using the available experimental results, porosity has been
estimated from the seismic velocities using equation (1). As
mentioned above, the Poisson ratio of the soil skeleton, SK,
has a very limited influence on the results; in the present
Manuscript received 27 February 2004; revised manuscript accepted
2 August 2004.
Discussion on this paper closes on 1 May 2005, for further details
see p. ii.
* Dipartimento di Ingegneria Strutturale e Geotecnica, Politecnico
di Torino, Italy.
work the estimate has been repeated considering different
values of SK ranging from 0.1 to 0.4, and the corresponding
results have been averaged to get a single estimate of
porosity. The following values have been considered for the
other parameters: rF ¼ 1.0 Mg/m3; KF ¼ 2.15 GPa; rS ¼
2.65 Mg/m3 for sands and 2.72 Mg/m3 for clays.
The results obtained for two representative boreholes from
the Canada dataset are reported in Figs 1 and 2, with
profiles showing:
(a) measured P-wave and S-wave velocities
(b) measured porosity (laboratory data) and predicted
porosity (from equation (1))
(c) the difference between measured and predicted porosity,
and the associated mean and median values.
The trends of the measured and predicted porosity values
with depth show defined similarities: in particular, borehole
JA01-4 is the only one in which very small values of
porosity (around 0.2) were measured in the laboratory for
samples retrieved at depth between 130 and 140 m. The
seismic velocities measured at this depth are consistently
larger than all the values measured at other depths and in
other boreholes (Vp higher than 2000 m/s and Vs around
800 m/s), and the predicted porosity is close to the measured
one. It is important to note also that these values of seismic
velocity and porosity are very consistent with the values for
dense sands and gravels reported by Foti et al. (2002).
Table 1. Results for the Canada dataset (experimental data by
Hunter, 2003)
Borehole ID Range of depth:
m
Difference between predicted and
measured soil porosity: %
Min Max Mean value Median value
AR93-1 11 50 10.9 7.8
LV96-1 4 31 13.4 8.8
LV96-2 17 36 10.0 5.7
JA-4 9 140 6.9 5.6
JA-5 4 35 13.2 13.6
JA-6 3 64 5.8 4.8
Difference: %
Calculated
Mean
Median
Porosity
Measured
Predicted
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
Velocity of propagation: m/s
D
e
p
th
: m
Vs
Vp
0 500 1000 1500 2000 2500 0 0·2 0·4 0·6 0·8 0 10 20 30 40
Fig. 1. Results for borehole JA01-4; experimental data from Hunter (2003)
Difference: %
Calculated
Mean
Median
Porosity
Measured
Predicted
0
10
20
30
40
50
60
Velocity of propagation: m/s
D
ep
th
: m
Vs
Vp
0 0·2 0·4 0·6 0·8 0 10 20 30 400 500 1000 1500
Fig. 2. Results for borehole JA01-6; experimental data from Hunter (2003)
552 FOTI AND LANCELLOTTA
A summary of the statistics of the difference between
measured and predicted porosity for the six boreholes is
reported in Table 1. On average, the difference between
measured and predicted porosity is less than 9%, but bore-
holes JA01-4 and JA01-6 are even better, with an average
difference of about 5%.
The same procedure has been applied to the other avail-
able datasets. A summary of the results is reported in Table
2. A reduced number of datapoints is available in these
datasets, but the quality of the estimate is supported, the
difference being on average of the order of 7%. The profiles
with experimental data and porosity predictions for the
Florence site are reported in Fig. 3.
Figure 4 reports the results obtained for the different
datasets. The predicted porosity on the basis of seismic
velocities is plotted against the measured porosity obtained
from undisturbed samples or from the properties of the
samples for laboratory testing.
CONCLUSIONS
Porosity is a state parameter that plays a relevant role for
many geotechnical applications because of its influence on
dilatancy and associated phenomena.
The use of seismic velocities for predicting soil porosity
on the basis of Biot’s theory is very promising. Estimation
of porosity for different independent datasets from both in-
situ and laboratory tests has given very encouraging results,
with average differences from direct measurements below
10%. Moreover, no systematic bias has been observed in the
predictions, and good results have been obtained over a wide
range of porosity, even if a limited number of points was
available for very dense and very loose materials.
A relevant advantage of the method is that by using high-
quality seismic measurements (preferably from cross-hole
tests) it is also possible to evaluate in detail the porosity
profile for coarse materials, which are still difficult to
sample.
One of the most relevant applications is related to the
evaluation of liquefaction susceptibility. Indeed the possibi-
lity of estimating soil porosity from non-destructive testing
can lead to substantial improvements compared with current
practice.
Table 2. Results for all datasets
Dataset Technique Number of
datapoints
Average difference:
%
Hunter Site (down-hole) 233 9.0
Florence Site (cross-hole) 13 8.3
Bates Laboratory 15 4.7
Tsukamoto Laboratory 5 6.6
Difference: %
Calculated
Mean
Median
Porosity
Measured
Predicted
0
10
20
30
40
50
Velocity of propagation: m/s
D
e
p
th
: m
Vs
Vp
0 500 1000 1500 2000 0 0·2 0·4 0·6 0·8 0 10 20 30 40
Fig. 3. Results for Florence site; experimental data from Jamiolkowski (2003, personal communication)
0
0·1
0·2
0·3
0·4
0·5
0·6
0·7
0·8
0·9
1·0
Measured porosity
P
re
di
ct
ed
po
ro
si
ty
Tsukamoto et al.
Hunter
Bates
Florence site
0 0·1 0·2 0·3 0·4 0·5 0·6 0·7 0·8 0·9 1·0
Fig. 4. Predicted against measured porosity for all datasets
SOIL POROSITY FROM SEISMIC VELOCITIES 553
ACKNOWLEDGEMENTS
The authors are very grateful to Dr James Hunter of
Geological Survey Canada, who very kindly made available
his large dataset of porosities and seismic velocities, and to
Professor Michele Jamiolkowski, who kindly provided the
results from the site in Florence, Italy.
REFERENCES
Bates, C. R. (1989). Dynamic soil property measurements during
triaxial testing. Géotechnique 39, No. 4, 721–726.
Berryman, J. G. (1995). Mixture theories for rock properties. In
Rock physics and phase relations: A handbook of physical
constants (ed. T. J. Ahrens), pp. 205–228. Washington: Amer-
ican Geophysical Union.
Biot, M. A. (1956a). Theory of propagation of elastic waves in a
fluid saturated porous solid. I: Low-frequency range. J. Acoust.
Soc. Am. 28, 168–178.
Biot M. A. (1956b). Theory of propagation of elastic waves in
a fluid saturated porous solid. II: Higher frequency range.
J. Acoust. Soc. Am. 28, 179–191.
Castagna, J. P., Batzle, M. L. & Eastwood, R. L. (1985). Relation-
ship between compressional-wave and shear-wave velocities in
clastic silicate rocks. Geophysics 50, 571–581.
Ederhart-Phillips, D., Han, D.-H. & Zoback, M. D. (1989). Empiri-
cal relationships among seismic velocities, effective pressure,
porosity, and clay content in sandstones. Geophysics 54, 82–89.
Foti, S., Lai, C. G. & Lancellotta, R. (2002). Porosity of fluid-
saturated porous media from measured seismic wave velocities.
Géotechnique 52, No. 5, 359–373.
Han, D.-H., Nur, A. & Morgan, D. (1986). Effects of porosity and
clay content on wave velocity in sandstones. Geophysics 51,
2093–2107.
Hunter, J. A. (2003). Some observations of Vp, Vs, depth and porosity
from boreholes in water-saturated unconsolidated sediments.
Proc. SAGEEP 2003, San Antonio, 650–661.
Klimentos, T. & McCann, C. (1990). Relationships between com-
pressional-wave attenuation, porosity clay content and per-
meability in sandstones. Geophysics 55, 998–1014.
Krief, M., Garat, J., Stellingwerff, J. & Ventre, J. (1990). A
petrophysical interpretation using the velocities of P and S
waves. The Log Analyst 31, 355–369.
Lancellotta, R. (2002). Coupling between the evolution of a
deformable porous medium and the motion of the fluids in
the connected porosity. In Porous media: Theory, experiments
and numerical applications (eds W. Ehlers and J. Bluhm), pp.
199–225. Berlin: Springer.
Miura, K., Yoshida, N. & Kim, Y. S. (2001). Frequency dependent
property of waves in saturated soil. Soils Found. 41, No. 2, 1–19.
Nakagawa, K., Soga, K. & Mitchell, J. K. (1997). Observation of
the Biot compression wave of the second kind in granular soils.
Géotechnique 47, No. 1, 133–147.
Plona, T. J. (1980). Observation of a second bulk compressional
wave in a porous medium at ultrasonic frequencies. Appl. Phys.
Lett. 36, 259–261.
Raymer, L. L., Hunt, E. R. & Gardner, J. S. (1980). An improved
sonic transit time-to-porosity transform. Trans. Soc. Prof. Well
Log Analysts, 21st Annual Logging Symposium, Paper P.
Santamarina, J. C., Klein, K. A. & Fam, M. A. (2001). Soils and
waves. New York: Wiley.
Tsukamoto, Y., Ishihara, K., Nakazawa, H., Kamada, K. & Huang,
Y. (2002). Resistance of partly saturated sand to liquefaction
with reference to longitudinal and shear wave velocities. Soils
Found. 42, No. 6, 93–104.
Wyllie, M. R., Gregory, A. R. & Gardner, G. H. F. (1956). Elastic
wave velocity in heterogeneous and porous media. Geophysics
21, 41–70.
554 FOTI AND LANCELLOTTA


Soil porosity from seismic velocities

FOTI, Sebastiano

LANCELLOTTA, RENATO

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

05 August 2020POLITECNICO DI TORINORepository ISTITUZIONALESoil porosity from seismic velocities / FOTI S.; LANCELLOTTA R.. - In: GEOTECHNIQUE. - ISSN 0016-8505. - 54(8)(2004), pp. 551-554.OriginalSoil porosity from seismic velocitiesPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/1401818 since:Foti, S. & Lancellotta, R. (2004). Ge´otechnique 54, No. 8, 551–554551TECHNICAL NOTESoil porosity from seismic velocitiesS. FOTIand R. LANCELLOTTAINTRODUCTIONBy analysing the wave propagation phenomenon in theframework of porous media theory, it is possible to accountfor the interaction between the soil skeleton and the porefluid, and to establish the dependence of seismic velocitieson elastic parameters of the two phases and on the soilporosity (Foti et al., 2002).Several empirical relationships have also been suggestedto correlate porosity and the velocity of propagation ofcompressional wave in fluid-saturated porous media (Wyllieet al., 1956; Raymer et al., 1980; Castagna et al., 1985; Hanet al., 1986; Ederhart-Phillips et al., 1989; Klimentos &McCann, 1990; Krief et al., 1990). A good review on thetopic is provided by Berryman (1995), who also discussesanalytical approaches based on mixture theory.Biot (1956a, 1956b) laid down the theory of seismic wavepropagation in saturated porous media, and his work iswidely recognised as a milestone in this field. Biot’s theoryis based on a macroscopic approach that models the binarycontinuum as a superposition of a fluid and a solid phaseoccupying simultaneously the same regions of space. In thiscontext, porosity can be seen as a parameter upscalinginformation from micro to macro scale (Lancellotta, 2002).Assuming an isotropic, linear elastic soil skeleton satu-rated by a non-dissipative compressible fluid, Biot was ableto prove the existence of two different compressional waves,namely of the first and second kind. The existence of thecompressional wave of the second kind, also known as theBiot wave, has been proven by Plona (1980) and, morerecently, by Nakagawa et al. (1997). The Biot wave is verydifficult to observe experimentally because, as it is slowerthan the compressional wave of the first kind, the first arrivalin seismic signals is always associated with the latter.Considering the timescale of wave propagation and thepermeability of soils, the assumption that no relative motionactually occurs between the solid and the fluid phases holdsfor the low-frequency range (Santamarina et al., 2001).Introducing the additional hypothesis of incompressible soilgrains, it is possible to obtain the following explicit relation-ship for soil porosity n, as shown by Foti et al. (2002):n ¼rSffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirSð Þ2 4 rSrFð ÞKF= V 2P2 1SK)=(12SK V 2S  q:2 rSrFð Þ(1)where Vp and VS are the velocities of propagation of com-pressional and shear waves respectively. The above relation-ship is dependent only on properties that assume ratherstandard values (grain density rS, water density rF, waterbulk modulus KF) and on the Poisson ratio of the soilskeleton, SK. SK has a limited range of variability in soils(0.1–0.4), and it can be shown to have negligible influenceon the estimated values of porosity (Foti et al., 2002).Moreover, it is possible to show that the hypothesis ofincompressible soil grains can be removed with a relativelysmall influence on the final results (Foti et al., 2002), evenif in this case the porosity evaluation requires the solutionof a more cumbersome mathematical inverse problem.As already stated, the above solution is restricted to low-frequency perturbations, because it assumes that there is norelative motion between the soil skeleton and the fluid phase.Indications about the range of validity of this assumptioncan be found in Miura et al. (2001); it can be observed thatsources typically adopted for geophysical in-situ tests aresuch that the predominant frequencies in the seismic signalsare well below the threshold value for all kind of soils (Fotiet al., 2002).DESCRIPTION OF THE DATASETHunter (2003) recently reported a large dataset of seismicvelocities and porosity data from 12 boreholes in Canada. Asubset of his data is used in the present paper, referring onlyto high-quality data (six boreholes) (Hunter, 2003, personalcommunication). The porosity data of this subset have beenobtained from undisturbed samples, processed on the specia-lised GSC laboratory on the same day as retrieval, exceptfor one case in which the data were analysed in thelaboratory of Carleton University. Great care was taken topreserve the original water content during transportation ofthe samples. A detailed description of the procedure and ofall the cautions taken to obtain reliable estimates is reportedin Hunter (2003).Details of in-situ measurements of P and S wave velo-cities, performed in down-hole tests, are also reported inHunter (2003).Table 1 gives a description of the six boreholes. Theavailable data are typically for depths up to 60 m, except forone borehole (JA01-4) for which data to a depth of 140 mare available. Most of the data are related to clays, with theexception of a few datapoints related to sands or tills.Additional data have been collected in Italy, using cross-hole tests for the seismic measurements and standard labora-tory procedures for the determination of porosity (Jamiolk-owski, 2003, personal communication). This dataset isrelated to silty clays and clayey silts, with PI rangingbetween 15% and 35%.In order to have results relative to sandy soils, data fromlaboratory tests, reported in the literature by Bates (1989)and Tsukamoto et al. (2002), have also been considered.MEASURED AND PREDICTED POROSITYUsing the available experimental results, porosity has beenestimated from the seismic velocities using equation (1). Asmentioned above, the Poisson ratio of the soil skeleton, SK,has a very limited influence on the results; in the presentManuscript received 27 February 2004; revised manuscript accepted2 August 2004.Discussion on this paper closes on 1 May 2005, for further detailssee p. ii.* Dipartimento di Ingegneria Strutturale e Geotecnica, Politecnicodi Torino, Italy.work the estimate has been repeated considering differentvalues of SK ranging from 0.1 to 0.4, and the correspondingresults have been averaged to get a single estimate ofporosity. The following values have been considered for theother parameters: rF ¼ 1.0 Mg/m3; KF ¼ 2.15 GPa; rS ¼2.65 Mg/m3 for sands and 2.72 Mg/m3 for clays.The results obtained for two representative boreholes fromthe Canada dataset are reported in Figs 1 and 2, withprofiles showing:(a) measured P-wave and S-wave velocities(b) measured porosity (laboratory data) and predictedporosity (from equation (1))(c) the difference between measured and predicted porosity,and the associated mean and median values.The trends of the measured and predicted porosity valueswith depth show defined similarities: in particular, boreholeJA01-4 is the only one in which very small values ofporosity (around 0.2) were measured in the laboratory forsamples retrieved at depth between 130 and 140 m. Theseismic velocities measured at this depth are consistentlylarger than all the values measured at other depths and inother boreholes (Vp higher than 2000 m/s and Vs around800 m/s), and the predicted porosity is close to the measuredone. It is important to note also that these values of seismicvelocity and porosity are very consistent with the values fordense sands and gravels reported by Foti et al. (2002).Table 1. Results for the Canada dataset (experimental data byHunter, 2003)Borehole ID Range of depth:mDifference between predicted andmeasured soil porosity: %Min Max Mean value Median valueAR93-1 11 50 10.9 7.8LV96-1 4 31 13.4 8.8LV96-2 17 36 10.0 5.7JA-4 9 140 6.9 5.6JA-5 4 35 13.2 13.6JA-6 3 64 5.8 4.8Difference: %CalculatedMeanMedianPorosityMeasuredPredicted0102030405060708090100110120130140150Velocity of propagation: m/sDepth: mVsVp0 500 1000 1500 2000 2500 0 0·2 0·4 0·6 0·8 0 10 20 30 40Fig. 1. Results for borehole JA01-4; experimental data from Hunter (2003)Difference: %CalculatedMeanMedianPorosityMeasuredPredicted0102030405060Velocity of propagation: m/sDepth: mVsVp0 0·2 0·4 0·6 0·8 0 10 20 30 400 500 1000 1500Fig. 2. Results for borehole JA01-6; experimental data from Hunter (2003)552 FOTI AND LANCELLOTTAA summary of the statistics of the difference betweenmeasured and predicted porosity for the six boreholes isreported in Table 1. On average, the difference betweenmeasured and predicted porosity is less than 9%, but bore-holes JA01-4 and JA01-6 are even better, with an averagedifference of about 5%.The same procedure has been applied to the other avail-able datasets. A summary of the results is reported in Table2. A reduced number of datapoints is available in thesedatasets, but the quality of the estimate is supported, thedifference being on average of the order of 7%. The profileswith experimental data and porosity predictions for theFlorence site are reported in Fig. 3.Figure 4 reports the results obtained for the differentdatasets. The predicted porosity on the basis of seismicvelocities is plotted against the measured porosity obtainedfrom undisturbed samples or from the properties of thesamples for laboratory testing.CONCLUSIONSPorosity is a state parameter that plays a relevant role formany geotechnical applications because of its influence ondilatancy and associated phenomena.The use of seismic velocities for predicting soil porosityon the basis of Biot’s theory is very promising. Estimationof porosity for different independent datasets from both in-situ and laboratory tests has given very encouraging results,with average differences from direct measurements below10%. Moreover, no systematic bias has been observed in thepredictions, and good results have been obtained over a widerange of porosity, even if a limited number of points wasavailable for very dense and very loose materials.A relevant advantage of the method is that by using high-quality seismic measurements (preferably from cross-holetests) it is also possible to evaluate in detail the porosityprofile for coarse materials, which are still difficult tosample.One of the most relevant applications is related to theevaluation of liquefaction susceptibility. Indeed the possibi-lity of estimating soil porosity from non-destructive testingcan lead to substantial improvements compared with currentpractice.Table 2. Results for all datasetsDataset Technique Number ofdatapointsAverage difference:%Hunter Site (down-hole) 233 9.0Florence Site (cross-hole) 13 8.3Bates Laboratory 15 4.7Tsukamoto Laboratory 5 6.6Difference: %CalculatedMeanMedianPorosityMeasuredPredicted01020304050Velocity of propagation: m/sDepth: mVsVp0 500 1000 1500 2000 0 0·2 0·4 0·6 0·8 0 10 20 30 40Fig. 3. Results for Florence site; experimental data from Jamiolkowski (2003, personal communication)00·10·20·30·40·50·60·70·80·91·0Measured porosityPredictedporosityTsukamoto et al.HunterBatesFlorence site0 0·1 0·2 0·3 0·4 0·5 0·6 0·7 0·8 0·9 1·0Fig. 4. Predicted against measured porosity for all datasetsSOIL POROSITY FROM SEISMIC VELOCITIES 553ACKNOWLEDGEMENTSThe authors are very grateful to Dr James Hunter ofGeological Survey Canada, who very kindly made availablehis large dataset of porosities and seismic velocities, and toProfessor Michele Jamiolkowski, who kindly provided theresults from the site in Florence, Italy.REFERENCESBates, C. R. (1989). Dynamic soil property measurements duringtriaxial testing. Ge´otechnique 39, No. 4, 721–726.Berryman, J. G. (1995). Mixture theories for rock properties. InRock physics and phase relations: A handbook of physicalconstants (ed. T. J. Ahrens), pp. 205–228. Washington: Amer-ican Geophysical Union.Biot, M. A. (1956a). Theory of propagation of elastic waves in afluid saturated porous solid. I: Low-frequency range. J. Acoust.Soc. Am. 28, 168–178.Biot M. A. (1956b). Theory of propagation of elastic waves ina fluid saturated porous solid. II: Higher frequency range.J. Acoust. Soc. 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Geophysics 55, 998–1014.Krief, M., Garat, J., Stellingwerff, J. & Ventre, J. (1990). Apetrophysical interpretation using the velocities of P and Swaves. The Log Analyst 31, 355–369.Lancellotta, R. (2002). Coupling between the evolution of adeformable porous medium and the motion of the fluids inthe connected porosity. In Porous media: Theory, experimentsand numerical applications (eds W. Ehlers and J. Bluhm), pp.199–225. Berlin: Springer.Miura, K., Yoshida, N. & Kim, Y. S. (2001). Frequency dependentproperty of waves in saturated soil. Soils Found. 41, No. 2, 1–19.Nakagawa, K., Soga, K. & Mitchell, J. K. (1997). Observation ofthe Biot compression wave of the second kind in granular soils.Ge´otechnique 47, No. 1, 133–147.Plona, T. J. (1980). Observation of a second bulk compressionalwave in a porous medium at ultrasonic frequencies. Appl. Phys.Lett. 36, 259–261.Raymer, L. L., Hunt, E. R. & Gardner, J. S. (1980). An improvedsonic transit time-to-porosity transform. Trans. Soc. Prof. WellLog Analysts, 21st Annual Logging Symposium, Paper P.Santamarina, J. C., Klein, K. A. & Fam, M. A. (2001). Soils andwaves. New York: Wiley.Tsukamoto, Y., Ishihara, K., Nakazawa, H., Kamada, K. & Huang,Y. (2002). Resistance of partly saturated sand to liquefactionwith reference to longitudinal and shear wave velocities. SoilsFound. 42, No. 6, 93–104.Wyllie, M. R., Gregory, A. R. & Gardner, G. H. F. (1956). Elasticwave velocity in heterogeneous and porous media. Geophysics21, 41–70.554 FOTI AND LANCELLOTTA

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Soil porosity from seismic velocities

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