Seismic-based methods

1.2.1Principle

a - Measurement principle

The analysis of surface waves allows evaluating pavement shear moduli, and the layer thicknesses in multilayered structures, by taking advantage of the dispersive nature of the Rayleigh waves. Interpretation relies on three main scientific reviews. 1- shear waves velocity

in materials is directly linked to their stiffness ; 2- body shear wave velocities and phase velocities of surface Rayleigh waves are mathematically related ; and finally 3- Rayleigh waves are dispersive (their phase velocity VR depends on the frequency f) and their

penetration depth depends on the wavelength λ.

Waves are generated over the pavement surface and the propagation of surface waves is analyzed. Then dispersion curves giving shear waves velocity as a function of depth can be constructed based on the aforementioned reviews. Backcalculation of the material moduli use these dispersion curves.

b - Further developments related to functioning

In an elastic half-space a load impact generates two types of body waves: compression or primary (P) waves, shear or secondary (S) waves. Surface Rayleigh (R) waves result from the interaction between the two body waves types. Interest for the R-Waves in propagation analysis comes from their energy. In an isotropic homogeneous infinite half-space R waves represent 67% of the propagated energy, S-waves 26% and P-waves only 7% [Abraham et al., 1997]. But at surface, geometrical decrease in the body waves are proportional to 1/r2 _{(with r}

the distance to the source) and only 1 r for R waves. This explains why the R-waves are

easy to generate and measure.

The measurement principle consists (Fig. 0-9) in measuring the R-wave velocity using receivers positioned at several radial distances from the source. [Hildebrand, 2002] specifies that accelerometers are generally used for short distances and geophones far from the source. The following rule: λ / 4≤ d1 and λ / 16 ≤ d2-d1≤ λ, with λ the wavelength and d1 and d2 the

distances to the receivers, is recommended in [Abraham et al., 1997].

For a selected f frequency, relationship between the phase difference φ and elapsed time between receivers is provided by:

( ) ( )

f f f t π ϕ 2 = (0-1)

And the Rayleigh velocity by

( )

f t d d VR 1 2 − = (0-2)

Finally the wavelength is calculated writing:

f

V_R

=

λ (0-3)

Numerous relationship linking VRand VSare proposed in the literature.

[Roesset et al., 1990] and [Richart et al., 1970] respectively propose: - VS =

(

,1135−0,182ν

)

VR for ν ≥0,1

with ν the Poisson’s ratio of the material.

- VR VS is solution of the following equation :

(

24 16

)

16

(

1

)

0 8 4 2 2 2 6 _{− ⋅K + − ⋅α ⋅K − ⋅ α − =} K With ν ν α 2 2 2 1 − − = = P S V V (0-4) P

V being the P-waves velocity, and V_S = G ρ = E

(

2ρ

(

1+ν

))

,

ρ, E and G being respectively the material mass density, and the Young’s and shear elastic moduli.

Let then suppose that VS can be calculated in this manner for a f sampling of frequencies in a

given λ range. Two means are possible. Either harmonic vibrations or impulse loadings are used.

In the first case, experiment shall be reiterated for all expected λ values.

In the second case, like with the Spectral Analysis of Surface Waves (SASW) method [Roesset, 1990], the stress signal has to be transferred into the frequency domain. It is thus possible to obtain the dispersion curve defined as the velocity profile as a function of depth. This is made possible since the penetration depth (d) of the wave increases with its

wavelength (d≈λ). For instance for a wave whose wavelength is less than the first layer thickness, its velocity will be representative of the layer stiffness. For higher wavelengths, wave propagation is influenced by the stiffness of the different layers. Then it is possible using surface waves over a wide range of wavelengths to assess material properties over a broad range of depths.

A theoretical determination of the Young’s moduli value based on the wave equations

resolution is provided in [Yuan and Nazarian, 1993]. Some empirical relationships between d and λ are also available in the literature, allowing lighter inverse analyses.

A Young’s modulus profile is backcalculated (Fig. 0-10, right), so that the theoretical dispersion curve fits the experimental one (Fig. 0-10, left).

Fig. 0-10 Typical dispersion curve and corresponding modulus profile, after [Yuan et al., 1998]

1.2.2Main Devices

a - Goodman Vibratory

The first pavement testing device based on wave propagation techniques is the Goodman Vibratory [BL, 1968] developed in1961 by the Laboratoire des Ponts et Chaussées. This device was applying harmonic vibratory stresses over the pavement. A receiver was placed at the surface of the pavement near the source so that excitation and response were initially in phase. The receiver was then shift until the signals were again in phase. That meant that the receiver had been shift of one wave length. The same operation had to be performed with different frequencies.

Interpretation consisted in manually comparing the experimental dispersion curves to the theoretical data set. The time-consuming tests and the empirical manner to analyse results prevented the development of the method. Nowadays this device is not used any more.

b - Seismic Pavement Analyzer

[Nazarian et al., 1993] propose the so-called “seismic pavement analyser” (SPA) device. This device is trailermounted and enables to monitor the conditions associated to pavement

deterioration using several measurements methods. Actually, amongst other assessment techniques as the impact echo method [Simonin, 2005], ultrasonic-surface-wave-velocity or ultrasonic-body-wave-velocity analysis, the SPA also enables performing the Spectral Analysis of Surface Waves (SASW) of pavements.

1.2.3Advantages/Shortcomings

This method is recommended in [Hildebrand, 2002] as a potential supplement to the FWD method (see infra) for its ability to provide information on the stiffness of the asphalt surface layers, and layer thicknesses.

Nevertheless, the seismically determined moduli are moduli at small strain amplitudes and at high frequency with regard to the strains imparted to the pavement by an aircraft rolling wheel [Roesset et al., 1990].

It raises a double problem. First material behaviour (especially the untreated materials) may be affected by this large deviation (103 _{ratio) in the imparted strains. Fig. 0-11 after [Puech et}

al., 2004] shows the typical dependence of the normalized shear modulus Gs / Go with shear strain γ. Gs is the shear stress modulus and G0 is the dynamic shear modulus, obtained by the

seismic method. Note that design strain in untreated materials of an airfield structure is of the order of 10-3_{, what corresponds to a Gs / Go of about 0,45 for the considered material.}

Secondly, asphalt material behaviour depends on the stress frequency. Therefore the

backcalculated moduli values should be adjusted to be representative of the behaviour under real loadings.

Fig. 0-11 Typical variation of normalized shear modulus as a function of shear strain (blue curve), after [Puech et al., 2004]

Several methods have been proposed to correct the untreated material modulus with respect to the strain level. [Puech et al., 2004] propose the general following stress-strain relationship:

(

)

(

_γ bγ

)

S G a

G ₀ =1 1+ ⋅ ⋅ 1+10− (0-5)

where the coefficients a and b are soil type dependent.

In the absence of an empirical relation between GS and G0 [Kurtulus, 2006] proposes (Fig. 0-

12), to find GS, to use the laboratory trend.

(

Slab lab

)

field

field

S G G G

G _, = _{, 0,} × _0, (0-6)

where GS,fieldis the shear modulus at γ strain, G0,fieldthe seismically determined moduli, and

(

GS,lab G0,lab

)

the laboratory normalized shear modulus.

(0-6) is eventually corrected to take into account the uncertainty in the trend of the shear modulus reduction curve. The reference shear strain (shear strain at which GS/G0 is 0.5) is

thus adjusted using:

(

S field Slab

)

rlab field

r, V , V , γ ,

γ = × (0-7)

Laboratory values are obtained from Resonant Column tests (see appendix 1.1) for strains under 10-4_{, and using classical triaxial testings above this threshold.Laboratory results are}

necessarily affected by sample disturbance [Puech et al., 2004].

Fig. 0-12 Extrapolation of the field shear modulus from seismic determined shear modulus, after [Kustulus, 2006]

It can be observed in Fig. 0-12 that the laboratory G moduli are less than the in-situ values. [Puech et al., 2004] note that laboratory tests can underestimate the dynamic shear modulus by a ratio of 2 to 3.

As a conclusion, the strain level produced during the SASW tests is problematical.

Corrections are possible, but they necessitate information on the material and scientific know- how.

Besides, note that the method provides discrete measurements of the structural conditions.

In document Assessment of flexible airfield pavements using Heavy Weight Deflectometers (Page 47-53)