2843
A new tool for the automated travel time analyses of bender element tests
Un nouvel outil pour les analyses automatisées du temps de déplacement des essais
« bender element »
Rees S., Le Compte A., Snelling K.
GDS Instruments, UK
ABSTRACT: Whilst bender elements are increasingly used in both academic and commercial laboratory test systems, there still
remains a lack of agreement when interpreting the shear wave travel time from these tests. Given such interpretation is often
subjective, a software tool was developed to automate the interpretation process using a number of analysis methods recommend in
the literature. The tool resulting from this development is accessed through two easy-to-use Microsoft Excel Add-Ins, allowing any
digital bender element data to be interpreted. Initial assessment of the tool was provided by a series of tests conducted on a triaxial
specimen of Leighton Buzzard sand at a mean effective stress of 100 kPa, with variation of the source element frequency. Travel
times estimated from a time-domain cross-correlation showed relatively low scatter, equal to ± 7 µs, across a frequency range of 3.3
kHz to 14.3 kHz, whilst times estimated from a frequency-domain cross-spectrum calculation produced much larger scatter, equal to ±
138 µs. Finally comparisons with subjective observational analyses performed by a geotechnical academic showed good agreement,
suggesting the tool can provide accurate, automated interpretation of bender element shear wave travel times.
RÉSUMÉ : Tandis que la technique des
Bender Elements
est de plus en plus utilisée dans les laboratoires commerciaux et de
recherche, il subsiste encore une carence dans l’interprétation du temps de parcours des ondes de cisaillement. Pour pallier ce manque,
un outil logiciel a été développé pour automatiser le processus en utilisant un certain nombre de méthodes d’analyses recommandées
dans la littérature. Cet outil est accessible par la simple utilisation de deux applications Microsoft Excel, permettant d’analyser
n’importe quelle donnée issue d’un essai de type
Bender Elements
. Les premiers tests de cet outil ont été effectués sur un échantillon
triaxial de sable « Leighton Buzzard » pour une contrainte effective moyenne de 100 kPa, avec une variation des fréquences de
l’élément source. Les temps de trajet estimés à partir d’une corrélation temporelle ont montré une dispersion relativement faible égale
à +/- 7 µs pour des fréquences de 3,3 kHz à 14,3 kHz, tandis que les temps calculés à partir d’une corrélation spectre-fréquence
indiquent une forte dispersion des résultats égale à +/- 138 µs. Enfin, les comparaisons réalisées avec des analyses classiques
effectuées par un laboratoire de géotechnique académique ont montré de bonnes similitudes, suggérant que cet outil peut
véritablement fournir des résultats précis et automatiques des temps de parcours des ondes de cisaillement.
KEYWORDS: bender elements, shear wave travel time, automated analysis, cross-correlation, cross-spectrum.
1 INTRODUCTION
Bender elements have seen increasing use in laboratory test
systems since their initial development in the 1970s (Shirley
and Hampton 1978), as they enable the small-strain shear
modulus,
G
0
, of a soil specimen to be estimated using a simple
methodology. This is achieved via determination of the shear
wave velocity,
V
S
, estimated from the time required for a shear
wave to propagate from one bender element (BE) to another.
V
S
can then be related to
G
0
as shown in Equation 1, wherein
ρ
=
bulk density of the soil,
L
= shear wave propagation distance,
and
t
= shear wave travel time.
)
(1)
/ (
2 2
2
0
tL V G
S
Primarily three different approaches have been identified for
determining the shear wave travel time,
t
: observation of the
source and received bender element signals, cross correlation of
the signals, and a cross-power spectrum calculation of the
signals (Yamashita et al. 2009). The two former approaches are
typically considered as techniques applied in the time-domain
(TD), with the latter viewed as a frequency-domain (FD)
method. Recommendations made by the Japanese Geotechnical
Society Technical Committee TC-29 suggest use of the two TD
methods is generally more appropriate, given the variability in
FD travel time estimates obtained from an international parallel
test. It is however important to note the suggested observational
techniques, which are the ‘start-to-start’ and ‘peak-to-peak’
methods, can be performed through visual analysis of the
bender element data by a test operator, and thus may produce
subjective travel time estimates. It is therefore considered useful
to automate the travel time estimation process to decrease the
subjectivity in such analyses.
Early studies demonstrated good agreement between
G
0
values obtained using bender elements and other small-strain
test systems such as the resonant column (Dyvik and Madshus
1986). A number of issues were however subsequently
identified that arise when interpreting bender element test
results, including the near field effect (Sánchez-Salinero et al.
1986) and subjectivity in determining arrival time of the
propagated shear wave (Jovičić et al. 1996). Such issues have
meant that despite bender element systems being well-
established within academic and commercial testing, there still
remains the lack of a satisfactory model or standard for test
interpretation (Viana da Fonseca et al. 2009, Alvarado and
Coop 2012). Therefore whilst it is understood that potential
errors in values of
ρ
,
L
, and
t
may each affect the estimated
value of
G
0
, this paper focuses on a principal issue in
interpreting bender element test data – the subjectivity in
determining the shear wave travel time,
t
.
1.1
Current recommendations for determining the shear wave
travel time
