SURFACE WAVE
SURVEYS LIMITED
Non-intrusive measurement
of ground stiffness
Website:
www.surfacewavesurveys.co.uk
E-mail:
info@surfacewavesurveys.co.uk
Idealised stiffness - strain behaviour
exhibited by most soils
The CSWS measures Gmax.
Gop/Gmax is 0.5 to 0.8 for soils and near unity
for sands and soft rocks.
Stiffness values can be converted to Young’s
Modulus (E) using Poisson’s ratio ()
E = 2(1+ )G
The different types of seismic wave
Energy
source
Ground
level
Boundary between
earth layers
Geophone
detector
Surface waves
Shallow
reflection
Refraction
Deep
reflection
Body waves: reflections and refractions
Two types:
P-waves (Pressure waves)
S-waves (Shear waves)
Surface waves
Two types: Love waves (A type of S-wave)
Rayleigh waves (Neither P- nor Swaves)
Seismic wave particle motion
P- Wave
Direction of propagation
Direction
of movement
S-Wave
Direction of propagation
Direction
of movement
(Or any other direction at right angles to the propagation
direction)
Rayleigh Wave
Direction of propagation
Direction
of movement
The surface wave method
Frequency controlled
vibrator
2Hz natural frequency geophones
Amplifier unit
Controller unit
Site recording 1
Site recording 2
Site recording 3
CSWS principle of operation (1)
 A range of frequencies is selected and the
vibrator, under computer control,
automatically shakes the ground at each
frequency throughout this range.
 For each frequency the surface waves are
detected by the geophones which send signals
representing the ground motion as a function
of time back to the controller.
 This data is Fourier transformed to give the
phase of the Rayleigh wave at each geophone
position.
CSWS principle of operation (2)
 The gradient of the phase-distance
relationship gives the wavelength of the
Rayleigh wave.
 The wavelength and frequency of the
Rayleigh wave give its velocity.
 Elastic theory is used to convert the Rayleigh
wave velocity to the shear wave velocity and
the shear wave velocity to the stiffness.
 The stiffness value is allocated to a depth
which is 1/3 of the Rayleigh wave
wavelength (/3 inversion).
Calculation of Rayleigh wave velocity
Frequency
d
=f
Distance between geophones = d

Phase difference
 = 2 - 1 = 
By proportion

= d
360

 = 360.d
Therefore



1
2
And
Rayleigh wave velocity V
R
=f
By knowing the frequency, f, and the
change in phase with distance from the
vibrator, d, we can determine the
Rayleigh wave velocity, VR.
Calculation of stiffness
From the theory of elasticity
VS = PVR
VS = Shear wave velocity
VR = Rayleigh wave velocity
P = f(Poisson’s ratio )
for  = 0.25, P = 1.09
for  = 0.50, P = 1.05
G = Shear modulus
 = Bulk density
G = VS2 = P2VR2
Chalk under shallow fill
0
1000
2000
3000
4000
0
5000
Fill
-5
Depth (m)
Dense chalk
-10
-15
-20
-25
-30
Gmax (MPa)
Stiffness inversion due to buried alluvium
0
50
100
150
200
0
250 300
Fill
Soft, grey, slightly sandy
silty clay [Alluvium]
Medium dense, subangular to sub-rounded
sandy fine to medium
flint gravel
Depth (m)
-5
-10
-15
Gmax (Mpa)
Sequence of clays
0
0
200
400
600
800
Weathered, sandy clay
-5
Silty clay
Depth (m)
-10
-15
Clay marl
-20
-25
-30
-35
Gmax (Mpa)
Example of using CSWS to measure
the degree of ground improvement
resulting from the insertion of vibro
stone columns
0
20 40 60 80 100 120 140 160 180
0
-2.00
-4.00
Depth (m)
-6.00
-8.00
-10.00
-12.00
-14.00
Gmax (Mpa)
Column diameter
500mm
Depth
6m
Triangular grid spacing
1500mm
By courtesy of Keller Ground Engineering
Dynamic compaction with
1.75m stone pillars
From Moxhay et al. (2001)
0
20
40
60
0
-1
Depth (m)
-2
-3
-4
-5
-6
-7
-8
Gmax (MPa)
Pre-treatment
Post-treatment
80
Vibro stone columns with surface
tamping – deep ash fill
From Moxhay et al. (2008)
0
20
40
60
0
-1
Depth (m)
-2
-3
-4
-5
-6
-7
Gmax (MPa)
Pre-treatment
Post-treatment
80
100
Stiffness increase after a temporary loss
during ground treatment
0
50
100
150
0
-1
-2
-3
Depth (m)
-4
-5
-6
-7
-8
-9
-10
Gmax (MPa)
Pre-treatment
Post-treatment
3 weeks post-treatment
200
Stiffness increase with time elapsed after
ground treatment
0
-0.5
-1
-1.5
Depth m
-2
-2.5
-3
-3.5
-4
-4.5
-5
0
10
20
30
40
50
60
70
Stiffness MPa
Pre-treatment
Two weeks post-treatment
Ten months post-treatment
Settlement prediction from CSW data
Required information: CSW stiffness/depth profile,
foundation shape, size, depth below ground and
load.
 The sub-surface is divided into layers and average Gmax
values are found for each.
 The initial value of Young’s Modulus E for each layer is
taken to be 2.5Gmax (average).
 The vertical stress at the centre of each layer is found
using the appropriate Boussinesq formula.
 Initial values of strain for each layer are found from the
vertical stress and initial E values.
 These strains will be too high to relate to the CSW Gmax
values. The E values are therefore revised using factors
from a standard curve of stiffness against strain (see
Moxhay at al. (2008) Appendix 2).
 The calculations are repeated to produce new strains.
 After repeating several times the new E values converge to
the previous ones.
 The settlement in each layer is calculated by multiplying
the final strain by the layer thickness.
 Addition of the settlements in each layer gives the total
settlement.
Vibro stone column site - example data
for settlement calculation
From Moxhay et al. (2008)
0
20
40
60
0
Depth (m)
-1
-2
-3
-4
-5
Gmax (MPa)
Pre-treatment
Post-treatment
80
100
Example settlement calculation
Z
E
Strain
Settlement
0.5
27.5889
0.144048
1.440479
1.5
26.85222
0.138098
1.380982
2.5
18.53303
0.168462
1.684624
3.5
22.26731
0.111213
1.112125
4.5
29.84521
0.06478
0.647796
6.266007
 Originally calculated settlement: 60mm.
 Settlements for whole site calculated from
CSW data varied between 6mm and 15mm,
average: 11mm.
 Observed settlement after four years: 10mm.
Phase difference
(Degrees)
Example of the effect on CSWS results of
a very hard raft of material near the
surface
0.00
500.00
0
400.00
20
40
60
80
100
300.00
-0.50
200.00
100.00
0.00
0
50
100
-1.00
150
Frequency (Hz)
Depth (m)
-1.50
-2.00
Wavelength (m)
-2.50
-3.00
12.00
10.00
8.00
6.00
4.00
2.00
0.00
-3.50
0
50
100
Frequency (Hz)
150
-4.00
Shear Modulus, Gmax (MPa)
120
Advanced processing of CSW data using
WinSASW2 software with PreCSW
 An experimental dispersion curve for input to
WinSASW2 is prepared from the field data
using PreCSW.
 A polynomial, called the representative
dispersion curve, is fitted to it. This
essentially produces a smoothed version of
the field data.
 An initial estimate of the earth model in terms
of layer thicknesses is made.
 The dispersion curve that would be produced
by this model is generated and superimposed
on the smoothed experimental one.
 Adjustments to the model are made to
produce a reasonable fit.
 The best-fit model is used as the starting point
for the main matrix inversion. Initially, layer
thicknesses are held constant and the
optimum velocities found by iteration.
 Thickness and velocity are then iterated
together to produce the final result.
Example WinSASW2 output - a steady
increase of stiffness with depth
0.00
0
10
20
30
40
-1.00
Depth (m)
-2.00
-3.00
-4.00
-5.00
-6.00
-7.00
Shear Modulus, Gmax (MPa)
By courtesy of ESG Pelorus Surveys
50
Example WinSASW2 output – a ‘hardlayer sandwich’
0.00
0
100
200
300
-1.00
Depth (m)
-2.00
-3.00
-4.00
-5.00
-6.00
Shear Modulus, Gmax (MPa)
400
Example WinSASW2 output – a stiffness
inversion
0.00
0
20
40
60
80
-1.00
-2.00
-3.00
Depth (m)
-4.00
-5.00
-6.00
-7.00
-8.00
-9.00
-10.00
Shear Modulus, Gmax (MPa)
By courtesy of ESG Pelorus Surveys
100
Example WinSASW2 quality control (1)
Criteria for a satisfactory result:
 The model is plausible.
 The dispersion curve for the model and the
representative dispersion curve are a good
match.
 The resolution of the shear wave velocity
does not fall below 0.1.
Example WinSASW2 quality control (2)
Index for the different dispersion curves:
Grey - Experimental
Blue - Representative
Red - Final model
By courtesy of ESG Pelorus Surveys
Advantages of the CSWS
 Non – invasive.
 Representative.
 Independent of soil type.
 Quick.
 Portable.
 Low – cost.
 Provides a direct route to settlement prediction.
Future development
 Processing software enhancement. The
Unbiased Short Array (USA)
Beamforming Technique, currently under
development by Professor Joh in South
Korea, will improve the results produced
by WinSASW2.