Determination of rigidity index for a shallow
foundation on a carbonate clay till
Jesus Gonzalez-Hurtado, Tim Newson
Geotechnical Research Centre, Department of Civil
University of Western Ontario, London, Ontario, Canada.
Engineering,
Michelle Tyldesley
Golder Associates Ltd., Mississauga & London, Ontario, Canada.
ABSTRACT
Detailed investigation of the links between operational strain levels and site investigation techniques for foundations of
wind turbines have not been previously described in the literature. This paper reports on a study of an operating wind
turbine in Southern Ontario. It describes laboratory and field methods used to characterize the strength, stiffness and
rigidity index (ratio of shear modulus to undrained shear strength) of the carbonate clay till deposit underlying the large
shallow foundation. Various correlations between in-situ tests (geophysics, CPT and SPT) and laboratory results for the
stiffness and strength properties are compared. In particular, the operational strain levels for this specific geotechnical
problem are investigated and appropriate methods of determining rigidity index and stiffness parameters are discussed.
RÉSUMÉ
Enquête sur les liens entre les niveaux de souche opérationnelles et techniques d'investigation de site pour les
fondations de l'éolienne éoliennes n'ont pas été précédemment décrits dans la littérature en détail. Cet article présente
une étude d'une éolienne en fonctionnement dans le sud de l'Ontario. Il décrit des méthodes de laboratoire et de terrain
utilisés pour caractériser l'indice de résistance, de rigidité et de rigidité (rapport de module de cisaillement à la résistance
au cisaillement non drainé) de l'argile de carbonate jusqu'au dépôt qui sous-tendent la grande fondation superficielle.
Différentes corrélations entre essais in-situ (géophysique, CPT et SPT) et on a comparé les résultats de laboratoire pour
les propriétés de rigidité et résistance. En particulier, les niveaux de contrainte opérationnelle pour ce problème
spécifique géotechniques sont étudiés et on discute des méthodes appropriées pour déterminer les paramètres index et
rigidité de rigidité.
1
INTRODUCTION
Wind is a major source of renewable energy and is
projected to capture 11% of the energy generation
capacity for Ontario by 2018. Recent research output for
the foundations of offshore wind turbines has been
significant. In contrast, the literature for onshore
foundation systems is still relatively sparse. Consequently,
despite there being similar design issues for turbine
foundations across the industry, there is often a diverse
interpretation of design codes and understanding of the
behavior of these foundations. This can lead to quite
different foundation designs on similar wind farms, with
the same turbines and comparable geotechnical profiles.
This issue is exacerbated in Canada, since there is
currently no regional regulatory guidance for site
investigation and design specifically for wind turbine.
Faced with this situation, it is not surprising that varied
approaches to site investigation have developed across
the industry. In some cases, despite there being a range
of excellent techniques available, generic and relatively
crude site investigations can occur, leading to quite
conservative designs.
Design approaches for serviceability and ultimate
limit states for shallow wind turbine foundations are
typically based on European codes (e.g. DNV, 2010; IEC
61400-1, 2005). These involve the use of isotropic elastic
analyses of half-spaces (Borrowicka, 1943) and empirical
modifications of the standard bearing capacity equation
for surface founded shallow foundations (Meyerhof,
1953). For clay soils, analyses require accurate and
appropriate estimates of strength (su, undrained shear
strength) and elastic parameters (shear modulus, G and
Poisson’s ratio, ). These can be determined from site
investigation in a number of ways: empirical correlations,
laboratory tests, in-situ tests and geophysical tests. The
stress-strain response of soils is known to be complex
and non-linear, and is dependent on the mode of loading,
fabric anisotropy, rate and time effects, over-consolidation
ratio, stress state and strain history. Therefore
determining the appropriate test type (or group of
complementary tests) that will provide the relevant
stiffness and strength properties for specific geotechnical
problems can be difficult and is also dependent on the
funding available for the site investigation.
Researchers have previously developed calibrated
correlations of strength and stiffness between certain insitu and laboratory tests, and data from monitoring of fullscale geotechnical structures (e.g. Mair, 1983). The
operational stiffness moduli for structures have been of
particular interest and these are usually plotted on shear
degradation curves (see Figure 1). The small-strain
modulus (Go) is typically determined using shear wave
velocity methods and gives a limiting upper value; this is
the maximum soil stiffness for a specific void ratio and
stress state. Shear modulus (G) is found to decrease nonlinearly with shear strain () and this ‘shear degradation
curve’ is often shown in a normalized form, with G divided
by the maximum Gmax (or Go). The strain levels on this
curve have been divided previously into three zones
(Atkinson, 2000): very small strain, where stiffness is
constant and elastic, small strain, where stiffness varies
non-linearly with strain and large strain, where the soil
approaches failure and the stiffness is relatively low. The
majority of geotechnical structures operate within
intermediate strain levels from 10-5 to 10-2. Different
methods of determining the stiffness also provide a wide
range of applicable strain levels and hence stiffness
estimates, from very small strains to large strains, as
shown in Figure 1.
piles, etc. It is also a very useful parameter if only shear
strength data is available and/or disturbed samples
preclude accurate determination of stiffness moduli.
Although a range of different tests have been
proposed to determine rigidity index, the most commonly
reported benchmark results use standard triaxial
compression test data (e.g. Teh and Houlsby, 1991; Low
et al., 2011), with secant shear modulus at 50% (G50) of
the peak undrained shear strength (su). Values of rigidity
index have been found to range from 25 to 600 (Teh and
Houlsby, 1991; Schnaid et al. 1997). More common usage
of geophysical tests in the laboratory and in-situ test have
expanded the range of rigidity index measured and very
small strain rigidity index values (Go/su) for different soils
are now available in the literature and may span the range
200 to 3000 [e.g. Low et. al, 2011].
Many researchers have developed empirical
correlations to estimated Ir. As described by Mayne
(2001), a Cam-clay model was proposed by Kulhawy and
Mayne (1990), where Ir is dependent on the
overconsolidation ratio (OCR) and can be calculated from:
[1 + ln(OCR)]eo Λ
2
1 + eo
Ir = ( ) M (
) ln(10)
3
Cc
Λ(1 − Λ)OCRΛ
[1]
Figure 1. Stiffness degradation curve and strain range of
different structures and testing methods (After Atkinson,
2000 and Mayne, 2001)
Detailed investigation of the link between operational
strain levels and site investigation techniques for shallow
foundations of wind turbine foundations has not been
previously described in the literature. This paper reports
on a study of an operating wind turbine in Southern
Ontario (e.g. Tyldesley et al., 2013). Laboratory and site
investigation results for this site are discussed, and the
derivation of appropriate stiffness, strength and rigidity
index values are described. In particular, the applicable
strain levels for this specific geotechnical problem are
addressed and appropriate methods of determining
rigidity index and stiffness are discussed.
where M is the slope of the critical state line = (6sinφ')/(3sinφ'), Λ is the plastic volumetric strain ratio = 1 – Cs/Cc
(usually assumed to be 0.8); data compiled by Mayne and
Mitchell (1988) suggested that this value of Λ is
appropriate for many natural clays, and eo is the initial
void ratio.
Another empirical approach between Ir, OCR and
plastic index (PI) was proposed by Keaveny and Mitchell
(1986) on the basis of anisotropically consolidated
compression (CAUC) triaxial test data. Ir can be
approximated using:
Ir =
e[0.0435(137−PI)]
[1 + ln{1 + 0.385(OCR − 1)3.2 }]0.8
[2]
Mayne (2001) presented a further empirical solution to
estimate Ir using parameters measured in the CPT test:
[(
Ir = e
2
RIGIDITY INDEX
The rigidity index (Ir =G/su) was originally defined by Vesic
(1972), as the ratio of the shear modulus to the shear
strength. This provides a description of the compressibility
of the soil and was used by Vesic (1972) to distinguish
between different modes of failure for shallow
foundations. It has been shown to influence a large
number of geotechnical problems, from in-situ testing,
cavity expansion, tunneling, shallow foundations and
1.5
q − σvo
+ 2.925)( t
) − 2.925]
M
qt − u2
[3]
where M is the slope of the critical state line, q t is the tip
resistance, σvo is the initial vertical stress and u2 is the
pore pressure measured at the depth of interest. As this is
an exponential function, the derived values are particularly
sensitive to accurate CPT measurements and therefore
require proper saturations for the filter and cone assembly
to obtain u2 readings and correction of measured qc to
total qt (cone tip resistance).
Lu et al. (2004) obtained a relationship for use in insitu penetration testing, which can also be used for Ir:
Go = a. N1 b [tsf] , a = 143 and b = 0.71
[5]
40 m. The upper crust has very intense fissures and the
deposit becomes nearly unfissured below 4.5 m. The
upper crust zone of this deposit is weathered, mottled
brown-grey or brown-green with a stiff to very stiff
consistency. This weathered zone generally has higher
moisture contents due to the infiltration of surface water
into the fissures of the clay. The underlying lower crust is
prevalently brown in colour and has a very stiff
consistency and relatively lower natural moisture content.
At several locations, this layer has clayey silt, sandy clay
and silt seams. A soil colour change occurs from brown to
grey between 3 and 4 m below the ground surface. Below
the crust, the unweathered till extends beyond the
maximum depth of sampling. This zone is characterized
by a uniform grey appearance, a stiff to very stiff
consistency and relatively uniform moisture contents.
Overconsolidation throughout the whole stratum was
identified by field and laboratory tests and is considered to
be result from past lowering of the ground water level,
possible cementation from carbonates and other minerals
from weathering processes, and wetting and drying cycles
(Quigley and Ogunbadejo, 1976). Further geotechnical
parameter values for each layer are found in Table 1.
su = 4.85. N1 [kPa]
[6]
Table 1. Representative geotechnical properties for the till
N −3.4+1.9∆−1.3αc
( kt
)
1.6
Ir = e
[4]
Again this relationship is dependent on parameters
measured from the CPT test, Nkt is the cone factor =
qnet/su, Δ is the normalized in-situ deviator stress = σ’vo(1 –
Ko)/(2su). Ko is the earth pressure coefficient, which can
be estimated (Mayne and Kulhawy 1982) as Ko = (1 – sin
ϕ’) OCRsinϕ’. αc is the cone face roughness which varies
from 0 to 1 for perfectly smooth and rough interfaces.
Since stiffness parameters can be approximated
using different correlations, SPT data can be also used to
estimate Ir values, the following correlations were applied
to approximate the small strain shear modulus (Go) after
Ohsaki & Iwasaki (1973) and the undrained shear
strength (su) after Sivrikaya & Togrol (2002):
where N1 is the SPT blow count corrected for overburden
pressure.
3
3.1
FIELD AND LABORATORY TESTING
Wind farm site and foundation details
The octagonal shallow foundation that is the focus of this
study has a diameter of 19 m at 3 m depth. This serves as
a base for a 2.3 MW wind turbine with an 80 m hub height
and triple bladed rotors with a 93 m diameter. The site is
located in a simple geographical and environmental area
in the Great Lakes region of Southern Ontario. The area is
underlain by carbonate-rich clayey silt tills and is located
at the convergence of four major geological deposits.
These consist of the Port Stanley and Tavistock tills,
glaciolacustrine sand and gravel, and glaciolacustrine
clayey silt. These materials were laid down in the Port
Bruce Stade (c. 14,800 years bp.) during the re-advance
of the Laurentide Ice Sheet of the Late Wisconsin. These
subglacial lodgement tills are calcareous and fine-grained,
suggesting that the ice overrode and incorporated finegrained glaciolacustrine sediments deposited during the
previous Erie Interstade. This has created approximately
40 to 45 m thickness of clayey silt tills with interbedded
glaciolacustrine sediments. The bedrock is shale with
limestone-dolostone-shale interlayers.
3.2
Soil description and basic properties
The till deposit can be divided into three zones: a heavily
weathered oxidized upper crust from 0 to 1.5 m, a partially
weathered lower crust that transitions from an oxidized to
an unoxidized state between 1.5 and 4.5 m and an
unweathered clay till from 4.5 m to a depth greater than
Property
Natural Water
Content, (%)
Unit Weight,
(kN/m3)
Liquid Limit (%)
Plastic Limit (%)
Clay (%)
Silt (%)
Sand (%)
OCR
Go (MPa)
Undrained Shear
Strength (kPa)
3.3
Upper
Crust
Lower
Crust
Unweathered
Till
22-32
16-20
16-24
20.3
21
21.6
46
21
40
45
15
2-5
100-120
34
19
29
49
20
2-3
60-200
30
17
31
45
21
1-1.5
60-80
100-150
150-250
100-130
Overview of site investigation
A number of boreholes were drilled adjacent to the turbine
foundation to depths of twice the foundation diameter to
evaluate the soil profile, perform in situ tests and collect
high-quality samples for laboratory testing spaced at 3 m
to allow for later cross-hole geophysical testing. A trackmounted drill was used for the drilling activities. In situ
testing adjacent to the boreholes consisted of SPT, field
shear vane, cross-hole geophysics and seismic SCPTu,
and was conducted to depths of 30 m. Piezocone
dissipation tests [with a u2 (type 2 piezocone) filter
location] were also conducted by stopping the cone
penetration at certain depths and monitoring the decay of
excess pore pressures, typically until at least 50%
dissipation of the initial excess pore pressure. To
complement the in situ test results, a full suite of
laboratory tests were also conducted for soil classification
and geotechnical properties.
Typical field and laboratory data
A representative CPT profile of the till deposit from one of
the test locations is presented in Figure 2, showing total
cone tip resistance (qt), sleeve friction (qs), and friction
ratio (fr). Tip resistance readings clearly show fluctuations
between 1 MPa to 3 MPa for the first 1.5 m depth
reaching a peak value of 4.5 MPa at 0.5 m (upper crust).
Between 1.5 m and 2.5 m depth there is a steady
increase of qt from 2 MPa to 6 MPa and then a decrease
from 6 MPa to 2 MPa for the subsequent 1.5 m (lower
crust). For depths below 4.5 m, the tip resistance remains
around 2 MPa (unweathered till). The variations along the
first 4.5 m depth are likely related to localized weathering
and the presence of cracks and fissures. Sleeve friction
varies from 0 to 300 kPa for the first 3 m, decreasing for
the subsequent 7m to 25 kPa, where it remains constant
for the rest of the profile. Based on the fr and qt values it is
possible to characterize the soil deposit as a heavily over
consolidated silty clay (stiff to very stiff) between 0 to 1.5
m, heavily overconsolidated silty clay “crust” (hard)
between 1.5 to 4.5 m, and an overconsolidated silty clay
(stiff to very stiff) below 4.5 m depth.
the till deposit indicating a stiff consistency. Only a single
N1 value for the weathered till of 43 per 0.3 m of
penetration was recorded indicating a hard consistency.
The N1 values range from 11 to 20 per 0.3m of
penetration for the unweathered till indicating a firm to stiff
consistency.
Corrected SPT Blow Count (N1)
0
10
20
30
40
50
0
5
10
Depth (m)
3.4
15
20
25
30
35
Cone Tip Resistance
(MPa)
Sleeve Friction
(kPa)
Friction Ratio
(%)
40
Figure 3. Typical SPT profile of the till deposit
Depth (m)
Figure 4 shows the stiffness degradation curve
normalized by the undrained shear strength (s u) for the
material at 1D below the foundation (20 m). The blue line
is the stiffness degradation of the glacial till for the large
strain range from a cyclic triaxial test (Kiss et al., 2014).
The red dashed line is an empirical approximation of the
stiffness degradation curve of the till deposit, developed
with a method proposed by Vardanega and Bolton (2011).
The reference strain (γref) is used to normalize shear
strain values (γ) in relation to modulus reduction (G/Go).
The following empirical formulations were used for the
derivation of the curve:
G
Go
1
=
1+(
γ
γref
γref =
Figure 2. Typical CPT profile of the till deposit
A representative SPT profile of the till deposit from
one of the test locations is shown in Figure 3. The N1
values range from 14 to 15 per 0.3 m of penetration for
0.74
[8]
)
2.17.PI
1000
[9]
The maximum shear modulus (Go) at 20 m depth is
equal to 294 MPa (found from bender elements), the
undrained shear strength (su) is equal to 125 kPa (found
from triaxial compression), and the plasticity index (PI) is
equal to 15%. Taking these values it was possible to
approximate γref and hence G/Go, to produce the curve in
Figure 4.
Figure 6 shows a typical excess pore water pressure
fitting of a dissipation test (at 19.7 m) from the CPT is
shown. The horizontal coefficient of consolidation (c h) was
estimated from oedometer tests. Nine CPTU tests through
the soil profile were used to determine this curve.
2500
2000
Rigidity Index, Ir
G/su
1500
1
10
100
1000
10000
0
1000
Vardanega &
Bolton, 2011
500
Kiss et al., 2014
0
0.000001
0.0001
5
0.01
1
10
Shear Strain (%)
Figure 4. Normalized stiffness degradation curve for soil
at 20 m
To investigate the applicability of the various methods of
determining rigidity index for the chosen problem, different
approaches were used to derive the rigidity index (I r) with
depth. The majority of the methods are described in
Section 2 and they depend on parameters from in-situ
tests such as CPT and SPT (equations 3, 4, 5 and 6) and
laboratory classification and stress-strain tests (equations
1 and 2). These results are shown in Figure 5 along with
two other methods of deriving rigidity index. Small strain
Go values found from a seismic cone (SCPT) have been
normalized by dividing by undrained shear strength (s u)
from the CPT using equation [10] (Teh and Houlsby,
1991) and Nkt was taken between 11.8 to 12.1
su =
qt −σvo
30
35
SCPT
Equation 1
Equation 2
Equation 3
Equation 4
Equation 5 & 6
Equation 11 & 12
Figure 5. Summary of Ir values using different methods.
∆ui = (∆uoct )i + (∆ushear )i
[11]
(∆uoct )i = σ′vo (2M/3)(OCR/2)^ ln(Ir )
where
=
the
octahedral component during the penetration and
(∆ushear )i = σ′vo [1 − (OCR/2)Λ ] = is the shear induced
component. The pore water pressures at any time (t) are
obtained in terms of the modified time factor T* from:
1+50T∗
25
40
Nkt
(∆uoct )i
20
1D Below
Foundation
[10]
The last method uses a back analysis of a cylindrical
cavity expansion due to the insertion of the CPT. Burns
and Mayne (1998) developed a method to account for the
dilatory response of overconsolidated soils and equations
[11] and [12] were used to find Ir:
∆u =
Depth (m)
DETERMINATION OF RIGIDITY INDEX
(∆u
)
shear i
+ 1+5000T
∗
where 𝑇 ∗ = (𝑐ℎ . 𝑡)/(𝑎2 . 𝐼𝑟 0.75 ) and a = probe radius.
1000
900
800
Porewater u2 (kPa)
4
15
700
600
500
400
300
200
Measured Response
at 19.7 m
Approx. CE-CSSM
Method
Hydrostatic Pore
Water Pressure
100
[12]
0
0.01
1
100
10000
Log Time (min)
Figure 6. Typical measured and fitted dilatory response in
the hard overconsolidated clay (Depth: 19.70 m)
5
INTERPRETATION OF RESULTS
The results of the comparison of rigidity index (I r) with
depth show a wide range of estimates that are generally
uniform with depth. The majority of the results lie between
190 and 1000, and are representative of the errors in
measurement with different techniques, sample
disturbance, loading direction/shear mode, applicability of
the original database (in case of empirical relationships)
and the strain level of the tests. These values also span
the range from G50 to Go, with regard to the stiffness
component of the ratio and partly reflect the initial
intention of the originators of the methods. The biggest
difference between the estimates of Ir and the general
range is from equation 3 and this may be due to the
quality of the pore pressure measurement and the type of
cone used, or possibly some inherent issue with the
equation.
Given the wide range of estimates, it is informative to
compare these with the equivalent strain levels of the
material and the operating strains of the shallow
foundation subject to the soil-structure interaction due to
the wind loading on the turbine tower. Figure 7 shows a
portion of the normalized stiffness degradation curve (G/s u
vs. γ) along with estimates of rigidity index from the
different approaches.
1000
G/su
1
2
Operating
Strains
6
CONCLUSIONS
The links between operational strain levels and site
investigation techniques for a shallow foundation of an
operating wind turbine supported by a carbonate clay till
deposit in Southern Ontario were analyzed. Methods of
determining rigidity index and stiffness parameters for this
specific geotechnical problem were investigated and the
findings suggest that it is possible to correlate the
operating strains of the soil and different methods to
approximate the stiffness parameters (e.g. Go), which are
applicable across the range of normal operations to close
to the ultimate state conditions. By completing these types
of analyses it can lead engineering practice towards an
improved estimation of strain levels, resulting in a better
understanding of soil-structure interaction. This will help
with validation and calibration of state of design
approaches, leading to more efficient and economical
designs, and potentially extending the life-cycles and
investments made by wind turbine owners and operators.
ACKNOWLEDGEMENTS
100
The authors would like to acknowledge the help and
support of J.J. Davis, Paul Dawson and Golder
Associates. The financial support of NSERC for the first
and third authors is also acknowledged.
SCPT
Equation 1
Equation 2
Equation 3
Equation 4
Equation 5 & 6
Equation 11 & 12
10
0.001
typically associated with methods or responses for the
small strain stiffness (Go). The methods in box 2 are more
applicable to strain ranges associated with states
approaching the ultimate limit state.
According to DNV (2010), an appropriate stiffness
estimate can be made by determining Go from tests
applicable empirical methods, and then determining G/G o
ratio for the operating strain levels (10-3 according to the
code). This would correspond with a G/s u value of
approximately 600 and G/Go of 0.25, lying in the upper
range of values. Note that the strains below the
foundation will attenuate relatively quickly with distance
away from the foundation and that the strains represent
the extreme values in the soil profile.
0.01
0.1
Shear Strain (%)
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1
10
Figure 7. Ir values over the stiffness degradation curve
Also shown on the figure are the operating strains
from the base of the edge of the foundation found using
biaxial tiltmeters (Kiss et al., 2014). The range of strains
falls between 10-4 and 10-3 for the typical operating
conditions and would be in the vicinity of 10-2 close to the
ultimate limit state conditions. This would give an
applicable range of G/su of 100-1500, with the typical
operating values occurring towards the end of this range.
The methods more applicable to the operating range of
the foundation are shown in box 1 (in Figure 7) and are
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