





Effect of soil texture on the propagation
and attenuation of acoustic wave at unsaturated conditions WeiCheng Lo^{*}, ChaoLung Yeh, and
ChangTai Tsai Department of
Hydraulic and Ocean Engineering lowc@mail.ncku.edu.tw
Journal
of Hydrology, 338, 273284, 2007.




1.
RESEARCH OBJECTIVES
Over the past decades, the increasing
scientific focus on the mechanical behavior of a fluidcontaining
porous medium has generated great interest in connecting the
velocity and dissipation of acoustic waves to the hydrological
properties of the shallow subsurface, on which immense practical
applications to soil science, agriculture engineering, geomechamics,
resource engineering, and hydrogeology are being built. An
inverse issue is to use reflection and refraction seismology to
infer the spatial distribution of permeability, porosity, and
moisture content of sedimentary materials, as well as to detect the
type of pore immiscible fluids, the information of which is crucial
for improving the accurate description of water movement and
contaminant transport through the vadose zone and groundwater
aquifers. A forward problem is to predict the propagation
speed and attenuation coefficient of seismic waves, and induced
strains from the knowledge of hydrological and elastic data, by
which the dynamic response of partiallysaturated porous materials
to fluidpumped and earthquaketriggered pressure changes is capable
of being modeled. The success in implementing these two
problems requires a better understanding of the physics of elastic
wave propagation and attenuation through unconsolidated soils
containing two immiscible, compressible, viscous fluids.
As
opposed to the existence of only a single compressional wave and a
shear wave in a nonporous solid, three modes of acoustic
(dilatational, compressional) wave has been demonstrated to occur in
such a medium both theoretically and numerically. That denoted
by P1 has the highest magnitude of phase velocity, followed by P2
and P3 in descending order. The P1 wave for which the
displacements of fluid and solid are inphase is similar to the
ordinary dilatational wave in a nonporous medium. The P2 and
P3 waves exhibit a diffusion phenomenon and the latter (the P3 wave)
is related to the relationship between capillary pressure and
relative fluid saturation. The P3 wave thus disappears when
the pore space is saturated by a single fluid.
However,
despite numerous numerical calculations that have been performed to
study the dependence of elastic wave characteristics on water
saturation with excitation frequency for consolidated rocks, few
ones based on a physicallybased theory were conducted for
unconsolidated soils. In addition, little is known about the
influence of soil texture on acoustic wave motions at unsaturated
conditions. Thus, there remains a need to explore the effect
in a systematic manner. The present study systematically
investigates changes in two important acoustic wave signatures
(phase speed and attenuation coefficient) due to the influence of
fluid saturation and soil texture including sand, loamy sand, sandy
loam, loam, silt loam, sandy clay loam, clay loam, silty clay loam,
sandy clay, silty clay, and clay.
2. APPROACH
The coupled partial differential equations describing
dilatational wave propagation and attenuation through a
partiallysaturated porous medium were formulated by Lo et al.
[2005] using continuum mechanics of mixtures. Based on the
dispersion equation derived in the Lo et al. [2005] model for
depicting the relationship between excitation frequency and wave
number, the phase velocity and attenuation coefficient of three
different modes of acoustic wave were determined as a function of
water saturation for eleven different types of unconsolidated
soils. A renowned constitutive equation (the van Genuchten 
Mualem model) was applied to determine the capillary pressure –
saturation and relative permeability – saturation relations.
Then, so as to provide a more general result, the calculated phase
velocity and attenuation coefficient of the P1 and P2 waves for
different soil textures were normalized into a dimensionless form
using those obtained for sand. By doing so, these
dimensionless parameters were found to be independent of excitation
frequency up to 500 Hz, a critical frequency assuring that each
fluid flow is of the Darcy’s type under wave excitation for all soil
texture classes examined. The phase velocity and attenuation
coefficient of the P3 wave were not shown in the present study since
this wave has very high attenuation and low speed, thus making it
very difficult to observe.
3.
ACCOMPLISHMENTS
Our numerical studies show (Fig.1) that
the normalized phase velocity of the P1 wave remains a nearly
constant value at higher water saturations, but in the lower range
it increases with water saturation, decreasing after approaching a
maximum value, which occurs at water saturations between 0 and
0.2. The magnitude of this value is dependent on soil types,
which ranges from silty clay, clay, silty clay loam, sandy clay,
clay loam, silt loam, loam, sandy clay loam, sandy loam, to loamy
sand in descending order. A dimensionless ratio of effective
nonwetting fluid storativity factors associated with the capillary
pressure curve is found to be the controlling parameter responsible
for the occurrence of the maximum value. It has been also seen
that, when excitation frequency is lower, the phase velocity of the
P1 wave is equal to a characteristic wave speed, defined as the
square root of the ratio of the effective bulk modulus to the
effective density of the fluidfilled porous medium.
Figure 1 The normalized phase velocity of the P1 wave for
ten soil texture classes (loamy sand, sandy loam, loam, silt loam,
sandy clay loam, clay loam, silty clay loam, sandy clay, silty clay,
and clay) Figure 2 The normalized attenuation coefficient of the P1
wave for ten soil texture classes (loamy sand, sandy loam, loam,
silt loam, sandy clay loam, clay loam, silty clay loam, sandy clay,
silty clay, and clay)
As far as the
normalized attenuation coefficient of the P1 wave is concerned, we
see in Figure 2 that not only does it reveal a distinct
characteristic for soil textures, but it is also affected by the
degree of saturation. In addition, the normalized attenuation
coefficient of the P1 wave is found to be less than unity no matter
of water saturation for all soil textures, whereas that of the P2
wave is greater than unity (Fig. 4). This physically indicates
that sand has the highest attenuation coefficient for the P1 wave
and the lowest one for the P2 wave among eleven different types of
soils. Loamy sand has the second highest attenuation
coefficient for the P1 wave. Lastly, it is noted in Figures 3
and 4 that the normalized phase velocity and attenuation coefficient
of the P2 wave are closely related to the intrinsic
permeability. When a soil has a higher intrinsic permeability,
the normalized phase velocity of the P2 wave is greater while the
normalized attenuation coefficient of the P2 wave is smaller.
Two minor exceptions to this observation occur only at 0.99 water
saturation between silt loam and sandy clay loam, and at 0.99 and 1
water saturations between silty clay loam and sandy clay. This
proportional relation provides an informative indicator in linking
acoustic waves to the ability of soils in transporting fluid
flows.
Figure 3 The normalized phase velocity of the P2 wave for
ten soil texture classes (loamy sand, sandy loam, loam, silt loam,
sandy clay loam, clay loam, silty clay loam, sandy clay, silty clay,
and clay) Figure 4 The normalized attenuation coefficient of the P2
wave for ten soil texture classes (loamy sand, sandy loam, loam,
silt loam, sandy clay loam, clay loam, silty clay loam, sandy clay,
silty clay, and clay)
4. SIGNIFICANCE
OF FINDINGS
The combination of acoustic wave
characteristics obtained from our investigation concerning the
normalized phase velocity and attenuation coefficient of the P1 and
P2 waves should not only allow application of the results to other
cases without having to perform an entire set of numerical
simulations but can also serve as a basis for lowfrequency acoustic
wave methods used to measure the physical properties of soil, such
as moisture content, porosity, permeability, and material
density. One of the practical applications for environmental
remediation is to locate NAPL (nonaqueous phase liquid)contaminated
sites in groundwater aquifers by obtaining the distribution of
seismic wave velocity and
attenuation.
Reference Lo, W. C., G. Sposito, and
E. Majer, (2005), Wave propagation through elastic porous media
containing two immiscible fluids, Water Resources Research, 41,
W02025, (20 pp.)


  






