**4. Collection and interpretation of bender element measurement data in geomaterials**

Although S-wave measurements using bender elements are promising, the convenience of bender element tests is limited by subjectivity associated with identifying wave travel time arrivals. The effect of distances to boundaries and between source and receiver plays an important role in the evaluation of wave propagation test data. For example when S-waves are created in a bender element wave propagation test, reflection and refraction from boundaries may produce waves other than direct S-waves; near-field effect may obscure the S-wave arrival; or wave attenuation and dispersion may prevent the proper identification of multiple reflections (Sanchez-Salinero et al. 1986, Fratta and Santamarina 1996). Sawangsuriya et al. (2006) performed a series of experimental studies to explore and to establish the limits to minimize the boundary effects in the wave propagation experiments. The experimental results are presented as simple dimensionless ratios that can provide guidelines for the design and interpretation of the wave propagation experiments as the following:

Wave Propagation Methods for Determining Stiffness of Geomaterials 169

and Santamarina 2005). In 3-D arrangements of sources and receivers, the limiting separations can be expressed as a function of dimensionless ratios H/L and R/L and the Poisson's ratio as illustrated in Fig.8. Note that the normalized distances below the curves are the acceptable distances where the S-wave arrives earlier than the reflected P-wave. It is therefore important that depending on the Poisson's ratio of the geomaterial, the relative distance between sources and receivers and to the boundaries (H/L and R/L) must be limited

**Figure 7.** Near-field effects: (a) normalized receiver response (transverse particle motion) with increasing source-receiver separation (model parameters: Vp=288 m/s, Vs=175 m/s, damping D=0.01 – closed-form solution by Sanchez-Salinero et al. 1986), and (b) measured P- and S-waves travel times in Kaolinite specimens (Sawangsuriya et al. 2006). Note: M = constraint modulus, G = shear modulus, E =

As the separation between source and receiver increases, refracted waves may travel along rigid boundaries (having higher velocities) masking the S-wave arrivals. This phenomenon can be observed when the test specimen is confined within a rigid wall container. When monitoring S-waves, the velocity is calculated by an assumed straight ray travel length and the first arrival time. However, the presence of the rigid boundary may mask the arrival of the direct S-wave if a refracted wave arrives first. This phenomenon was observed by using specimens prepared inside the cylindrical rigid wall container where the source-receiver

to avoid possible P-wave reflection interferences.

Young's modulus, ρ = mass density.

**Boundary effects - refraction** 
