**1. Introduction**

In many geoengineering design and analysis, the laboratory and field investigations are generally required to identify and classify geomaterials as well as to assess their engineering properties. One of the important engineering properties commonly used in geomechanical design and analysis is the stiffness of geomaterial. Such stiffness primarily describes the deformation characteristic of a geomaterial used to support engineered structures. Understanding the stiffness behaviour of geomaterials is therefore essential for improving design and analysis of structural behavior under varying loading and environmental conditions.

The importance of accurate stiffness measurements from small to large strains has gained increased recognition in both static and dynamic analyses over the past 20 years. In the static triaxial test, the local displacement transducer has been used to measure local axial strains (Goto et al. 1991). The resonant column and torsional shear devices have been widely used for many years to study cyclic and dynamic properties of geomaterials at strains ranging from 10=4 to 0.1% (Drnevich 1985, Saada 1988). The American Association of State Highway and Transportation Officials (AASHTO) has adopted the use of resilient modulus (MR) in pavement design, which is customarily used by the pavement community. The precise measurement of MR values of pavement materials is typically in the strain range from 10=2 to 0.1% (Kim and Stokoe 1992).

Based on the typical variation of shear moduli with shear strain levels shown in Fig. 1 (after Atkinson and Sallförs 1991, Mair 1993, Ishihara 1996, Sawangsuriya et al. 2005), three strain ranges are defined: (1) very small strain, (2) small strain, and (3) large strain. The very small strain range corresponds to the range of strain less than the elastic threshold strain (γet), approximately between 10-3% and 10-2%, depending on plasticity index (Ip) for plastic soils (Vucetic and Dobry 1991) and on confining pressure (σo) for non-plastic soils (Ishibashi and

© 2012 Sawangsuriya, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Zhang 1993). Within this very small strain region, the geomaterial exhibits linear-elastic behaviour and the shear modulus is independent of strain amplitude, approaching a nearly constant limiting value of the maximum shear modulus (Gmax). The small strain range starts from elastic threshold strain to 1% where the shear modulus is highly non-linear and straindependent. The large strain range corresponds to strain generally larger than 1%. In the large strains, the geomaterial is approaching failure and the shear modulus is substantially decreased. In many geoengineering applications, e.g. foundations, retaining walls, tunnels, pavements etc., the stress-strain behavior of geomaterial is highly non-linear, resulting in shear modulus degradation with strain by orders of magnitude. The variation of shear moduli and other properties of geomaterial with respect to shear strain levels for different geotechnical applications as measured by in situ and laboratory tests are also shown in Fig. 1.

Wave Propagation Methods for Determining Stiffness of Geomaterials 159

Shear modulus, Poisson's ratio, damping Angle of internal

Crack, differential

Elastic Elastic-plastic Failure

*Base Subbase*

Pavements

*Subgrade* Modulus

**Small Large**

10 0.1 10 -2 10-4 1

**Typical strain ranges**

Retaining walls

Foundations

Tunnels

friction, cohesion

settlement liquefaction Slide, compaction,

Shear strain, (%)

degradation curve

**Figure 1.** Variation in shear modulus with different shear strain levels for different geoengineering applications, in-situ tests, and laboratory tests (after Atkinson and Sallfors 1991, Mair 1993, Ishihara,

Wave propagation, vibration

10-3

Ranges of strain

**Very small**

Elastic threshold strain, et (depending on Ip and o)

2. Good agreement between stiffness measured in the laboratory and in the field is made when the laboratory specimens are at the same conditions as those in the field (Anderson and Woods 1976, Viggiani and Atkinson 1995a, Nazarian et al. 1999,

3. Load repetition, strain rate, and loading frequency have only minor influence in the small-strain range (Iwasaki et al. 1978, Ni 1987, Bolton and Wilson 1989, Tatsuoka and

Shibuya 1991, Jardine 1992, Shibuya et al. 1992, 1995, Ishihara 1996).

1996, Sawangsuriya et al. 2005).

ment Repeated loading test

Seismic wave method In situ vibration test

Shear modulus, G

Gmax

Wave propagation test Resonant column test

Repeated loading test

Phenomena Soil behavior Soil properties

Effect of load repetition Effect of loading frequency

In situ measurement

Laboratory measure-

Atkinson 2000).

Estimation of stiffness has traditionally been made in a triaxial apparatus using precise displacement transducers or resonant column devices (Lo Presti et al. 2001). Although several methods become commercially available to determine the stiffness of geomaterials both in the laboratory and in the field, the wave propagation techniques are widely accepted for their rapid, non-destructive, and low-cost evaluation methods. By knowing the elastic wave velocities as measured with the wave-based techniques and total mass density of the media, the stiffness of the geomaterials can be determined. In particular, a shear or S-wave velocity is a keystone for calculating the shear modulus of geomaterial. Such S-wave measurement has been researched extensively using shear plates (e.g. Lawrence 1963, 1965), resonant column tests (e.g. Hardin and Drnevich 1972), and bender elements (e.g. Shirley 1978, Shirley and Hampton 1978). The use of the shear plates is limited due to their large size and their need for a high excitation voltage (Ismail et al. 2005) while complexities and high cost of test equipments are disadvantages of resonant column tests. In contrast, bender elements have gained reputation particularly in research on geoengineering because of their smaller size, and lower voltage required leading to easier operation. Such method also provides cost-effectiveness and realistic design parameter which in turn becomes most valuable tool for mechanistic-based design and analysis, long-term performance monitoring, quality control process during construction etc.
