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Seismic solution Patrick Hooker of GDS Instruments looks at developments in seismic methods for stiffness measurement, and how these can be applied for monitoring ground improvement.

In many geotechnical engineering problems, evaluation of deformation properties of soils and rocks is required for the prediction of ground movements. Traditionally insitu loading tests and laboratory tests have been employed for this purpose.

During the past decade however, there have been important developments in the understanding of stress-strain behaviour of geomaterials which have closed the gap between static and very small strain dynamic measurements of stiffness. This has resulted in the increasing use of seismic methods to measure the shear modulus G as part of site investigations.

The use of seismic methods are attractive since they are not effected by sample disturbance or insertion effects and are capable of sampling a representative volume of the ground even in difficult materials such as fractured rock. These insitu non-destructive methods can be very usefully applied to the monitoring of soil improvements.

Stiffness in geotechnical engineeing The typical variation of shear or bulk stiffness with strain for most soils is given in figure 1. It is believed that most soils behave elastically at very small strains(ie 0.001%) giving rise to a constant stiffness. The strain induced by the propagation of seismic waves is within this range and hence provides a measure of the upper bound for stiffness (Emax or Gmax).It is also now generally accepted that ground strains associated with most soil-structure interaction problems are less than 0.1% and hence small strain stiffness values are required to make reasonable predictions of deformation (Jardine et al, 1986).

Numerical models used in geotechnical design now take account of the stiffness-strain relationship as well as kinematic yield surfaces. In most cases however, the data provided for such models are laboratory measured stiffness profiles at operational strain levels rather than upper bound stiffnesses. Current research into the stiffness-strain behaviour of geomaterials will eventually provide an accurate means of characterising the 'S' shaped curve of figure 1.

The upper bound stiffness is clearly a fundamental parameter in defining this curve and hence the use of insitu seismic measurements of stiffness will become even more important in the future. At the present time these measurements may be used in conjunction with laboratory measurements for soil and insitu loading test measurements in rock which provide a lower bound for stiffness. In the area of monitoring ground improve- ments, however, the seismic methods offer an immediate measure of a fundamental engineering parameter Gmax

Seismic methods for stiffness measurement

Seismic methods utilise the propagation of elastic waves through the ground. There are two categories of seismic wave: body waves, comprising compressional (P) and shear (S) waves, and surface waves, which include Rayleigh (R) waves. The modes of propagation of these wave types are well known and are described in most texts on seismic methods (eg Telford et al, 1990). The waves propagate at velocities which are a function of the density and elastic properties of the ground. The Rayleigh wave is a surface wave that travels parallel to the ground surface at a depth of approximately one wavelength. In an isotropic elastic medium the velocity of a shear wave, Vs, is:

where G is the shear modulus and INS the density. According to the theory of elasticty, Young's modulus E is related to G:

where INS is the Poisson's ratio. Thus G can be obtained from measurements of Vs alone.

Surface waves may also be used to determine shear stiffness in soils and rocks. Approximately two thirds of the energy from an impact source propagates away in the form of surface waves of the type first described by Rayleigh in 1885. These waves travel at speeds governed by the stiffness- depth profile of the near surface material. It can be shown from the theory of elasticity that the relationship between the characteristic velocity of shear waves Vs and Rayleigh waves Vr in an elastic medium is given by:

Vr = CVs (3)

where C is a function of Poisson's ratio . The range of C is from 0.911 to 0.955 for the range of Poisson's ratio associated with most soils and rocks if anisotropy is ignored. the maximum error in G arising from an erroneous value of C is therefore less than 10%.

The seismic methods employed to determine stiffness-depth profiles may be divided into subsurface and surface methods as shown schematically in Figure 2. Most of the subsurface methods require one or more boreholes which need to be cased with special plastic casing which adds to the cost of the survey.

These methods are most useful where the depth of investigation is greater than 15m and involve the measurement of the transit times of seismic waves over known distances. The seismic cone has the advantage of providing both strength and stiffness data and does not require a borehole since the cone is pushed into the ground. However, the depth of penetration is limited by the strength of the ground and any obstructions such as boulders, claystones or rock layers.

A simple and cost effective surface method makes use of surface waves. Surface-wave methods exploit the dispersive nature of Rayleigh waves. The speed of propagation of a Rayleigh wave travelling at the surface of inhomogeneous ground depends on its wavelength (or frequency) as well as the material properties of the ground. Measurements of phase velocity of Rayleigh waves of different frequencies (or wavelengths) can be used to determine a velocity-depth profile.

The surface wave method

Two distinct surface-wave methods are available. The Spectral Analysis of Surface Waves (SASW) method, which makes use of a hammer as an energy source. And the Continuous Surface-Wave (CSW) method, which makes use of a vibrator as an energy source. Both techniques are described in detail by Matthews et al (1996).

The SASW method relies on the frequency spectrum of the energy source used. In most cases a range of hammers of different mass are employed to achieve the necessary frequency range (3Hz-200Hz). It is inevitable, however, that certain frequencies will be missing from the spectra of these sources which may result in gaps in the stiffness profile data. This serious disadvantage may be overcome by replacing the hammers with a frequency controlled vibrator. This is the basis of the CSW method.

A typical CSW setup is shown in in figure 3 and the accompanying box which describes the basic procedure used.

The process of converting a field dispersion curve to a Rayleigh wave velocity-depth relationship is known as inversion. There are two principal ways of approaching this, either by the wavlength/depth method, or by using any of a number of finite element approaches.

The wavelength-depth method is the simplest, but least exact of the methods. It is of practical value because it offers a quick way of pocessing data on-site And so enables preliminary assessment. It also provides a useful initial estimate of the velocity-depth profile to input in the algorithms of the other approaches. In the wavelength/depth method the representative depth, D, is taken to be a fraction, z, of the wavelength, . This is known as the factored wavelength method for assigning depth. That is z is assumed ot be constant. Gazetas (1982) recommended that D=/4 is used at sites where the stiffness increases significantly with depth, and that D=/2 is suitable at more homogeneous sites. Gazetas also suggested that taking D=/3 is a reasonable compromise.

Typical shear modulus-depth profiles for a coastal alluvial site and a chalk site using the CSW method where depth is taken as D=/3 are given in figure 4.

Monitoring ground improvement

Seismic methods, particularly the methods based on surface waves, provide a good method for monitoring ground improvement works. In many types of ground improvement there is some uncertainty concerning the effectiveness of the improvement method.

In particular it is difficult to assess the degree of improvement brought about by dynamic compaction and vibroflotation while the ground is being treated. The result is either that too much work is carried out for little gain in ground stiffness after a certain point or that the improvement is insufficient and further remedial action is required.

In both cases extra costs are involved. Ideally a rapid and direct measure of improvement is required during the treatment process. Surface-wave geophysics can provide such a direct measurement. A survey of the site can be carried out prior to ground improvement to give a set of baseline stiffness profiles. During the improvement process further stiffness profiles can be obtained rapidly and compared directly with the baseline measurements. In this way the amount of improvement can be quantified in terms of stiffness. This has the added benefit that the effective depth of the improvement can be determined.

Cuellar (1997) discusses the use of surface-wave geophysics to assess the efficiency of some ground treat- ments such as grouted backfill and stone columns. In both examples the improvement in stiffness is clearly shown in the surface-wave data.

More recently GDS Instruments has carried out trials using the CSW technique to evaluate the effects of the use of stone columns inserted by vibro replacement.

A doubling of the average maximum shear modulus was observed in a test taking less than one hour to perform.

References

Jardine, RJ, Potts, DM, Fourie, AB and Burland, JB (1986).Studies of the influence of non-linear stress-strain characteristics

in soil-structure interaction. Gotechnique, 36(3), 377-396.

Telford, WM, Geldart, LP & Sheriff, RE (1990). Applied Geophysics. 2nd Edition, Cambridge University Press, Cambridge, 770pp.

Matthews, MC, Hope, VS & Clayton, CRI (1996). The use of surface waves in the determination of ground stiffness profiles. Proc Institution of Civil. Engineers Geotech. Engng 119, April, 84-95.

Gazetas, G (1982). Vibrational characteristics of soil deposits with variable velocity. Int. J. for Numerical and Analytical Methods in Geomechanics, 6, 1-20.

Cullar, V, Monte, JL and Valerio, J (1995) Characterisation of waste landfills using geophysical methods. Proc. 11th European Conf on Soil Mech and Found Engng, Copenhagen, Danish Geotechnical Society, Copenhagen, 2, 33-38.

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