**9. Application of wave propagation methods in pavement design and analysis**

Wave Propagation Methods for Determining Stiffness of Geomaterials 189

exhibited by soils at large strains (above 10-2 %) must be established. Generally, strains in base and subbase courses vary from 0.01 to 1%, whereas those in subgrades may vary from 0.003 to 0.6% (see Fig. 1). Therefore, the pavement base, subbase, and subgrade layers involve strains at higher levels, i.e., typical strain range of 10-2 to 1%, and soil exhibits nonlinear properties. Fig. 1 also shows that the resilient modulus (MR) test operates within these strain range. However, the decay curve of measured soil moduli from the small-strain tests

must be evaluated and corrected to the modulus corresponding to these strain levels.

**Figure 24.** Go at a specified moisture equilibrium normalized with Go at optimum compaction

Degree of Saturation (%)

Stiffness of geomaterials is an important engineering property, commonly used in geomechanical design and analysis. The deformation performance of geomaterials used to support engineered structures depends primarily on their stiffness. Therefore, it is important that the laboratory and field investigation should be performed to identify and classify geomaterials as well as to assess their mechanical properties for the engineering design and analysis. This chapter summarizes the wave propagation methods that permit the determination of the stiffness of the geomaterials. By knowing the elastic wave velocities as measured with the wave propagation method and total mass density of the medium, the corresponding stiffness of the geomaterials can be determined. One of the wave propagation methods based on the S-wave measurement is called a bender element test. It is a rapid, non-destructive, and low cost method, which can provide a realistic engineering design parameter (e.g. shear modulus). Moreover, elastic waves permit monitoring the elastic (stiffness) and inertial (mass density) properties of geomaterials while evaluating other coupled processes, i.e., the changes in state of effective stresses, the stress-induced anisotropy, the generation of geo-structure in soft

0 20 40 60 80 100 120 140

condition vs. degree of saturation (Gupta et al. 2007).

**10. Summary** 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Go (unsat)/Go (compacted)

sediments, etc.

The new AASHTO 2002 highway design relies heavily on mechanistic pavement properties. Current mechanistic-empirical design procedures for structural design of flexible pavements consider the mechanical properties of pavement material such as stiffness and strength. Several countries are currently either implementing or favoring the development of performance-based specifications. To successfully implement a mechanistic-empirical design procedure and to move toward performance-based specifications, a cost-effective, reliable, and practical means to assess the stiffness and strength of highway materials is necessary since both stiffness and strength of pavement layers plays a key role on the overall quality and performance of pavements.

One of the potential approaches to directly assess stiffness of geomaterials both in the laboratory and in the field is to employ Go tests. Generally, Go of geomaterials is routinely measured in earthquake engineering. In highway engineering, the application of Go tests to assess the stiffness of highway materials and structural variability for pavement performance has increased dramatically (Kim and Stokoe 1992, Souto et al. 1994, Kim et al. 1997, Chen et al. 1999, Nazarian et al. 1999, Fiedler et al. 2000, Yesiller et al. 2000, Zeng et al. 2002, Nazarian et al. 2003). The key advantage of Go tests over conventional modulus tests is their ability to rapidly and non-destructively assess the shear modulus of highway materials at the surface or under a free-field condition (i.e., zero confining pressure). Laboratory test methods are also available for Go tests that can reproduce similar results to those measured in the field. Moreover in the field, the modulus changes in response to temporal variations in moisture content. The modulus changes in response to changes in moisture can be simply incorporated in Go test in order to provide a model to estimate changes in modulus due to changes in moisture content for the pavement design and analysis. The relationship can be quantified empirically using a modulus ratio defined as the ratio of Go at a specified moisture equilibrium to Go at optimum compaction conditions. An example of modulus ratio is plotted against the degree of saturation for types of geomaterials as illustrated in Fig. 24.

Typically, the associated strain levels corresponding to many proposed geotechnical engineering structures such as foundations, retaining walls, tunnels, and pavements are however much larger (Mair 1993, Sawangsuriya et al. 2005). For example, the strain levels of the bender element are below 5x10-3%, whereas the strain levels of the resilient modulus commonly used in the design of flexible pavement structures ranges from 0.01 to 0.1% (Sawangsuriya et al. 2005). In order to correct the small-strain modulus measurements to such relevant levels of strain amplitude imposed by the proposed structure, the modulusstrain relationship, or called strain-dependent modulus degradation curve, can be employed for a given operating stress level and soil type.

For pavement bases, subbases and subgrades, the stress-strain behaviour of soil is highly nonlinear and soil modulus may decay with strain by orders of magnitude. A relationship between the small-strain modulus (strains less than 10-2 %) and non-linear behaviour exhibited by soils at large strains (above 10-2 %) must be established. Generally, strains in base and subbase courses vary from 0.01 to 1%, whereas those in subgrades may vary from 0.003 to 0.6% (see Fig. 1). Therefore, the pavement base, subbase, and subgrade layers involve strains at higher levels, i.e., typical strain range of 10-2 to 1%, and soil exhibits nonlinear properties. Fig. 1 also shows that the resilient modulus (MR) test operates within these strain range. However, the decay curve of measured soil moduli from the small-strain tests must be evaluated and corrected to the modulus corresponding to these strain levels.

**Figure 24.** Go at a specified moisture equilibrium normalized with Go at optimum compaction condition vs. degree of saturation (Gupta et al. 2007).

## **10. Summary**

188 Wave Processes in Classical and New Solids

quality and performance of pavements.

geomaterials as illustrated in Fig. 24.

for a given operating stress level and soil type.

**analysis** 

**9. Application of wave propagation methods in pavement design and** 

The new AASHTO 2002 highway design relies heavily on mechanistic pavement properties. Current mechanistic-empirical design procedures for structural design of flexible pavements consider the mechanical properties of pavement material such as stiffness and strength. Several countries are currently either implementing or favoring the development of performance-based specifications. To successfully implement a mechanistic-empirical design procedure and to move toward performance-based specifications, a cost-effective, reliable, and practical means to assess the stiffness and strength of highway materials is necessary since both stiffness and strength of pavement layers plays a key role on the overall

One of the potential approaches to directly assess stiffness of geomaterials both in the laboratory and in the field is to employ Go tests. Generally, Go of geomaterials is routinely measured in earthquake engineering. In highway engineering, the application of Go tests to assess the stiffness of highway materials and structural variability for pavement performance has increased dramatically (Kim and Stokoe 1992, Souto et al. 1994, Kim et al. 1997, Chen et al. 1999, Nazarian et al. 1999, Fiedler et al. 2000, Yesiller et al. 2000, Zeng et al. 2002, Nazarian et al. 2003). The key advantage of Go tests over conventional modulus tests is their ability to rapidly and non-destructively assess the shear modulus of highway materials at the surface or under a free-field condition (i.e., zero confining pressure). Laboratory test methods are also available for Go tests that can reproduce similar results to those measured in the field. Moreover in the field, the modulus changes in response to temporal variations in moisture content. The modulus changes in response to changes in moisture can be simply incorporated in Go test in order to provide a model to estimate changes in modulus due to changes in moisture content for the pavement design and analysis. The relationship can be quantified empirically using a modulus ratio defined as the ratio of Go at a specified moisture equilibrium to Go at optimum compaction conditions. An example of modulus ratio is plotted against the degree of saturation for types of

Typically, the associated strain levels corresponding to many proposed geotechnical engineering structures such as foundations, retaining walls, tunnels, and pavements are however much larger (Mair 1993, Sawangsuriya et al. 2005). For example, the strain levels of the bender element are below 5x10-3%, whereas the strain levels of the resilient modulus commonly used in the design of flexible pavement structures ranges from 0.01 to 0.1% (Sawangsuriya et al. 2005). In order to correct the small-strain modulus measurements to such relevant levels of strain amplitude imposed by the proposed structure, the modulusstrain relationship, or called strain-dependent modulus degradation curve, can be employed

For pavement bases, subbases and subgrades, the stress-strain behaviour of soil is highly nonlinear and soil modulus may decay with strain by orders of magnitude. A relationship between the small-strain modulus (strains less than 10-2 %) and non-linear behaviour Stiffness of geomaterials is an important engineering property, commonly used in geomechanical design and analysis. The deformation performance of geomaterials used to support engineered structures depends primarily on their stiffness. Therefore, it is important that the laboratory and field investigation should be performed to identify and classify geomaterials as well as to assess their mechanical properties for the engineering design and analysis. This chapter summarizes the wave propagation methods that permit the determination of the stiffness of the geomaterials. By knowing the elastic wave velocities as measured with the wave propagation method and total mass density of the medium, the corresponding stiffness of the geomaterials can be determined. One of the wave propagation methods based on the S-wave measurement is called a bender element test. It is a rapid, non-destructive, and low cost method, which can provide a realistic engineering design parameter (e.g. shear modulus). Moreover, elastic waves permit monitoring the elastic (stiffness) and inertial (mass density) properties of geomaterials while evaluating other coupled processes, i.e., the changes in state of effective stresses, the stress-induced anisotropy, the generation of geo-structure in soft sediments, etc.

The use of bender elements to generate and receive shear waves in geomaterials has become a very robust technique in geoengineering design and analysis and has been widely adopted for determining and monitoring stiffness of geomaterials both in the laboratory and field. However as with any other wave propagation techniques, the interpretation of bender element-collected data is controlled by wave characteristics, boundary conditions, and properties of the medium. Guidelines for designing test geometries and interpretation measured data from the wave propagation experiments are summarized herein. A bender element test has been employed for a variety of geoengineering applications, i.e., the mechanistic based design development, the long-term performance monitoring as well as quality control process during construction.

Wave Propagation Methods for Determining Stiffness of Geomaterials 191

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