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SURFACE WAVE SURVEYS LIMITED
Non-intrusive measurement of ground stiffness
Website: www.surfacewavesurveys.co.ukE-mail: [email protected]
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
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 S- waves)
Geophonedetector
Ground
level
Boundary between
earth layers
Deep reflection
Refraction
Surface waves
Shallow reflection
Energy source
Seismic wave particle motion
Rayleigh Wave
Direction
of movement
S-Wave
P- Wave
(Or any other direction at right angles to the propagation direction)
Direction of propagation
Direction of propagation
Direction of propagation
Direction
of movement
Direction
of movement
Amplifier unit
Controller unit
Frequency controlledvibrator
2Hz natural frequency geophones
The surface wave method
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).
d
2
1
By knowing the frequency, f, and the change in phase with distance from the vibrator, d, we can determine the Rayleigh wave velocity, V .
Calculation of Rayleigh wave velocity
Frequency = f
Distance between geophones = d
Phase difference = 2 - 1 =
By proportion = d 360
Therefore = 360.d
And Rayleigh wave velocity V = f
R
R
Calculation of stiffness
From the theory of elasticity
VS = PVRVS = Shear wave velocityVR = Rayleigh wave velocityP = f(Poisson’s ratio )
for = 0.25, P = 1.09for = 0.50, P = 1.05
G = Shear modulus = Bulk density
G = VS2 = P2VR
2
-30
-25
-20
-15
-10
-5
01000 2000 3000 4000 5000
Gmax (MPa)
Fill
Dense chalk
Chalk under shallow fill
Dep
th (
m)
0
-15
-10
-5
050 100 150 200 250 300
Fill
Soft, grey, slightly sandysilty clay [Alluvium]
Medium dense, sub-angular to sub-rounded sandy fine to medium flint gravel
Stiffness inversion due to buried alluvium
Dep
th (
m)
Gmax (Mpa)
0
-35
-30
-25
-20
-15
-10
-5
0 200 400 600 800
Weathered, sandy clay
Silty clay
Clay marl
Sequence of clays
Dep
th (
m)
Gmax (Mpa)
0
Example of using CSWS to measure the degree of ground improvement resulting from the insertion of vibro
stone columns
-12.00
-10.00
-8.00
-6.00
-4.00
-2.00
20 40 60 80 100 120 140 160 180
Column diameter 500mm
Depth 6m
Triangular grid spacing 1500mm
By courtesy of Keller Ground Engineering
Dep
th (
m)
Gmax (Mpa)-14.00
00
Dynamic compaction with 1.75m stone pillars
From Moxhay et al. (2001)
-8
-7
-6
-5
-4
-3
-2
-1
0
0 20 40 60 80
Gmax (MPa)
Dep
th (
m)
Pre-treatment Post-treatment
Vibro stone columns with surface tamping – deep ash fill
From Moxhay et al. (2008)
-7
-6
-5
-4
-3
-2
-1
0
0 20 40 60 80 100
Gmax (MPa)
De
pth
(m
)
Pre-treatment Post-treatment
Stiffness increase after a temporary loss during ground treatment
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 50 100 150 200
Gmax (MPa)
De
pth
(m
)
Pre-treatment Post-treatment 3 weeks post-treatment
Stiffness increase with time elapsed after ground treatment
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0 10 20 30 40 50 60 70
Stiffness MPa
Dep
th m
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)
-5
-4
-3
-2
-1
0
0 20 40 60 80 100
Gmax (MPa)
De
pth
(m
)
Pre-treatment Post-treatment
Example settlement calculation
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.
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
Example of the effect on CSWS results of a very hard raft of material near the
surface
0.00
100.00
200.00
300.00
400.00
500.00
0 50 100 150
Frequency (Hz)
Pha
se d
iffer
ence
(D
egre
es)
0.002.004.006.008.00
10.0012.00
0 50 100 150
Frequency (Hz)
Wav
ele
ng
th (
m)
-4.00
-3.50
-3.00
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0 20 40 60 80 100 120
Shear Modulus, Gmax (MPa)
Dep
th (m
)
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
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
0 10 20 30 40 50
Shear Modulus, Gmax (MPa)
De
pth
(m
)
By courtesy of ESG Pelorus Surveys
Example WinSASW2 output – a ‘hard-layer sandwich’
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
0 100 200 300 400
Shear Modulus, Gmax (MPa)
De
pth
(m
)
Example WinSASW2 output – a stiffness inversion
-10.00
-9.00
-8.00
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
0 20 40 60 80 100
Shear Modulus, Gmax (MPa)
De
pth
(m
)
By courtesy of ESG Pelorus Surveys
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 - ExperimentalBlue - RepresentativeRed - 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.