Transmission X-Ray and Computed Tomography Scan
5.10 INDIRECT METHODS FOR FABRIC CHARACTERIZATION
All physical properties of a soil depend in part on the fabric; therefore, the measurement of a property pro-vides indirect measure of the fabric. Some of the mea-surements that are particularly useful are listed in Table 5.3 and are discussed briefly in this section.
Elastic Wave Propagation
The propagation velocities of compression and shear waves through a soil depend on the density, confining
stress, and fabric of the soil. According to elastic the-ory, which is applicable to soils for the small defor-mations associated with wave propagation, the shear wave (S-wave) velocity Vs and the compression wave (P-wave) velocity Vp are related to the shear modulus G and the constrained modulus M by
Vs⫽ 兹G / (5.6)
and
Vp ⫽ 兹M / (5.7)
where is the mass density.
The constrained modulus M is related to the more familiar Young’s modulus according to
1⫺
M ⫽ E (5.8)
(1⫹ )(1⫺ 2)
in which is Poisson’s ratio. Young’s modulus and the shear modulus are related to each other by
E⫽ 2(1⫹ )G (5.9)
The moduli depend on the applied effective stresses, stress history, void ratio, and plasticity index. For co-hesionless soils the modulus varies approximately as the square root of the effective confining pressure. For cohesive soils the modulus varies as the effective con-fining pressure to a power between 0.5 and 1.0. The small strain shear modulus of soil depends on contact stiffness and fabric state. Therefore, the change in shear wave velocity with confining pressure provides
0 0.2 0.4 0.6 0.8 1
Figure 5.32 Variation in P- and S-wave velocities with B value in loose Toyoura sand under an isotropic compression stress of 98 kPa (after Tsukamoto et al., 2002).
insight on the pressure dependency of contact stiffness.
Equations (5.6) and (5.7) assume isotropic elasticity. If the material is viscoelastic, the wave velocities become frequency dependent. Solutions for various viscoelastic models are given by Santamarina et al. (2001).
If two samples of the same soil have the same mass density and are under the same effective confining pressure but have different fabrics, they will have dif-ferent modulus values. This difference will be reflected by differences in shear and compression wave veloci-ties. These velocities can be measured, and this pro-vides a means for assessing fabric. The shear wave velocity is the more useful of the two because shear waves are only transmitted through the solid grain structure of the soil mass, that is shear waves cannot be transmitted through water. Anisotropic soil structure and stress states can be detected on the basis of dif-ferent shear wave velocities in difdif-ferent directions. Fur-ther details of the relationships between small strain moduli and compositional and environmental factors are given in Chapter 11.
If the material is dry, the bulk modulus of the skel-eton can be derived using both shear wave and com-pression wave velocity measurements. If the material includes water, the P-wave velocity depends on the elastic properties of soil solids and water, saturation, and porosity. For fully saturated conditions, solutions are available for two-phase media (Biot, 1956a, 1956b;
Stoll, 1989; Mavko et al., 1998; Santamarina et al., 2001). The solutions show that there are two P-waves and one S-wave. The fast P-wave and S-wave are the standard waves and the velocities have weak depend-ency on frequdepend-ency. The slow P-wave (or Biot wave), which is associated with the diffusional process of wa-ter flow in deforming porous media, especially at low frequency, and is very difficult to detect (Plona, 1980;
Nakagawa et al., 1997). Hence, the fast P-wave and S-wave are commonly used to characterize the soil.
In fully saturated condition, the fast P-wave propa-gates with a velocity that is 10 to 15 percent faster than the velocity through water. This is because the stiffness of the soil skeleton contributes to increasing wave velocity. In very loose saturated soil, the P-wave velocity is essentially controlled by the bulk modulus of water and has a value of about 1500 m / s.
When air is introduced, P-wave velocity decreases.
Even with a small amount of air, the reduction is dra-matic due to a large decrease in bulk modulus of the fluid–air mixture. The effect of B-value (or water sat-uration ratio Sw) on P- and S-wave velocities of Toy-oura sand specimen (Dr⫽30 percent) is shown in Fig.
5.32 (Tsukamoto et al., 2002). The fast P-wave veloc-ity at B ⫽ 0.95 (Sw ⫽ 100 percent) is 1700 m / s,
whereas that at B ⫽ 0.05 (Sw ⫽ 90 percent) is only 500 m / s. The S-wave velocity, on the other hand, is independent of the water saturation. Kokusho (2000) derives the following relationship that relates the fast P-wave velocity to B value:
4 2(1 ⫺ b)
Vp ⫽ Vs冪3⫹ 3(1⫺ b)(1⫺ B) (5.10) where b is Poisson’s ratio of soil skeleton. Equation (5.10) is plotted in Fig. 5.32 for different b values.
There is a dramatic decrease in P-wave velocity with even a very small decrease in B value from fully sat-urated conditions.
Dielectric Dispersion and Electrical Conductivity The flow of electricity through a soil is a composite of (1) flow through the soil particles alone, which is small, because the solid phase is a poor conductor, (2) flow through the pore fluid alone, and (3) flow through both solid and pore fluid. The total electrical flow also depends on the porosity, tortuosity of flow paths, and conditions at the interfaces between the solid and liq-uid phases. These factors are, in turn, dependent on the particle arrangements and the density. Thus, a simple
INDIRECT METHODS FOR FABRIC CHARACTERIZATION 139
Figure 5.33 Dielectric and conductivity dispersion charac-teristics of saturated illite (Grundite) (from Arulanandan et al., 1973).
measurement of electrical conductivity would seem a rapid and reliable means for evaluation of soil fabric.
However, electrical measurements in soils are com-plicated by the fact that if direct current is used, then there will be electrokinetic coupling phenomena, such as electroosmosis, and electrochemical effects that can cause irreversible changes in the system, as discussed in Chapter 9. On the other hand, if alternating current (AC) is used, then the measured responses depend on frequency. Thus the application of electrical methods and interpretation of the data require careful consid-eration of how the measurement method may influence what is being measured. At the same time, however, measurement of the frequency dependence of electrical properties can be useful for evaluation of fabric and as an index for engineering properties.
The capacitance C and the resistance R can be mea-sured relatively easily. If electrical flow is in one di-mension only, then the electrical conductivity is given by
⫽ L/ (RA) (5.11)
where L is the sample length and A is the cross-sectional area.
The capacitance can be converted to the relative di-electric constant D (see Chapter 6) using
D⫽CL/ (A0) (5.12) where0is the permittivity of vacuum (8.8542⫻10⫺12 C2 J⫺1 m⫺1).
In fine-grained materials such as clays, the applica-tion of an AC field causes the electrical charges that are concentrated adjacent to particle surfaces to move back and forth with amplitude dependent on such fac-tors as type of charge, association of charge with sur-faces, particle arrangement, and strength and frequency of the field. These oscillating charges contribute to a polarization current that can be measured. The number of charges per unit volume times the average displace-ment is the polarizability. The magnitude of the po-larizability is determined by the composition and structure of the material and is reflected by the dielec-tric constant.
Phenomena contributing to polarization include di-pole rotation, accumulation of charges at interfaces be-tween particles and their suspending medium, ion atmosphere distortion, coupling of flows, and distortion of a molecular system. The extent to which polariza-tion can develop depends on ease of charge movement and time available for displacement. With increase in frequency the dielectric constant may decrease and the
conductivity may increase. These changes are termed anomalous dispersion. Several regions of anomalous dispersion may develop over the frequency range from zero to microwave (⬎1011 Hz). Different polarization mechanisms cease to be effective above different fre-quency values, thus accounting for the successive regions of anomalous dispersion. Electrolyte solutions alone do not exhibit dispersion effects at frequencies less than 108 Hz, but clays do in the radio frequency range. For example, the conductivity and dielectric dis-persion behavior of saturated illite are shown in Fig.
5.33.
The electrical response characteristics in the low-frequency range depend on particle size and size dis-tribution, water content, direction of current flow relative to the direction of preferred particle orienta-tion, type and concentration of electrolyte in the pore water, particle surface characteristics, and sample dis-turbance. Relationships between dielectric properties and compositional and state parameters such as poros-ity, particle shape, fabric anisotropy, and specific sur-face area are given by Arulanandan (1991). The theory is based on Maxwell’s (1881) relationship between po-rosity and the dielectric properties of a mixture of so-lution and spherical particles, and its extension to ellipsoidal particles that are all oriented in one direc-tion by Fricke (1953). Extensive discussion of electro-magnetic properties of soils is given in Santamarina et al. (2001).
The formation factor appears in the relationships used to describe soil properties and state in terms of electrical properties. The formation factor is the ratio of the electrical conductivity of the pore water to the electrical conductivity of the wet soil. It is a nondi-mensional parameter that depends on particle shape,
long axis orientation, porosity, and degree of satura-tion. If a soil has an anisotropic fabric, then the for-mation factor is different in different directions.
Thermal Conductivity
Heat transfer through soils is through soil grains, wa-ter, and pore air. As the thermal conductivity of soil minerals is about 2.9 W / (m C), and the values for water and air are 0.6 and 0.026 W / (m C), respec-tively, heat transfer is mainly through the soil particles.
Accordingly, the lower the void ratio, the greater the number and area of interparticle contacts and the higher the degree of saturation, the higher is the ther-mal conductivity. The therther-mal conductivity of a typical soil is likely to be in the range of 0.5 to 3.0 W / (m
C). This property is considered in more detail in Sec-tion 9.6.
Thermal conductivity can be determined using a rel-atively simple transient heat flow method in which a line heat source, called a thermal needle, is inserted into the soil. The needle contains both a heating wire and a temperature sensor. When heat is introduced into the needle at a constant rate, the temperatures T2 and T1at times t2 and t1are related to the thermal conduc-tivity k according to
4 ln(t )2 ⫺ ln(t )1
k ⫽ (5.13)
Q T2 ⫺ T1
where Q is the heat input between t1 and t2. This method and factors influencing the results are de-scribed by Mitchell and Kao (1978).
Differences in thermal conductivity in different di-rections provide a measure of soil anisotropy. For example, the ratios of thermal conductivity in the horizontal direction kh to that in the vertical direction kvfor three clays with preferred particle orientations in the horizontal direction were in the range of 1.05 to 1.70, depending on the clay type, consolidation pres-sure, and sample disturbance (Penner, 1963b). For the probe in the vertical position in a cross anisotropic fabric, the value of k determined from Eq. (5.13) is kh. For the probe in the horizontal direction, a value of ki
is measured that is related to kv and kh according to (Carlslaw and Jaeger, 1957)
k2i
kv⫽ (5.14)
kh
Thermal probe measurements can also be used to detect differences in density at different locations in the same material (Bellotti et al., 1991) and for eval-uation of changes in density, water content, and
struc-ture caused by mechanically and environmentally induced changes in state of the soil.
Mechanical Properties
The mechanical properties of soil, including stress–
deformation behavior, strength, compressibility, and permeability, depend on fabric in ways that are rea-sonably well understood, as considered in Chapter 8.
Therefore, information about fabric can be deduced from measurements of these properties and known in-terrelationships between properties and fabric.