Cone Penetration Testing 2022 – Gottardi & Tonni (eds)
© 2022 Copyright the Author(s), ISBN 978-1-032-31259-0
Open Access: www.taylorfrancis.com, CC BY-NC-ND 4.0 license
Estimation of constrained modulus from CPT measurements in case of
Zsombor Illés, István Kádár, Gábor Nagy, András Mahler & László Nagy
Budapest University of Technology and Economics, Budapest, Hungary
ABSTRACT: In case of major projects there are numerous measurements which provide a sufﬁcient set of
data to determine characteristic values based on statistical methods. In the current paper Cone Penetration Test
(CPT), oedometer and Flat Dilatometer Test (DMT) results are analyzed. Constrained or oedometric modulus
is one of the most important deformation parameters, which has a key role in settlement estimation. There are
various recommendations to derive E
from CPT tip resistance values. Three of these recommendations are
compared with the results of the oedometer tests and the correlation used in case of DMT measurements.
Keywords: Constrained modulus, CPT, Tip-resistance, DMT, Normally-consolidated layers
1.1 Measurements and methods
Several Cone Penetration Tests were conducted at
a site in South-Central Hungary near the Danube.
The probes penetrated until the depth of 20 - 40
meters. Altogether 32 CPTs were analyzed, penetrat-
ing at least to the depth of 25 – 26 m, until the
bottom of Holocene layers; clay, sand, and gravel.
Below that, over-consolidated late Miocene
(Pannon) layers were found.
Different methods are evaluated for estimating
constrained modulus from cone penetration resist-
ance of the CPT measurements in the article. These
three methods are the following: Sanglerat (1972),
Lunne and Christoffersen (1983) and Eslaamizaad
and Robertson (1996).
Furthermore, laboratory soil identiﬁcation and
oedometric tests were also carried out. In addition,
there is a possibility to compare Cone Penetration
and Flat Dilatometer Test (DMT) results.
1.2 Geology and stratigraphy of the site
The project site is located in South-Central Hun-
gary.Itusedtobe the ﬂood plain of the river
Danube until the construction of a dike system.
During the previous phases of the industrial com-
pound’s construction, the extracted soil was
placed on the current site as a backﬁll. The ﬁll
material consists of ﬁne sands, less often silty
sands, mostly grey-yellow silty clay and lean
clay, and medium sands. The landﬁll includes
construction waste as well. Its thickness varies
between 3.5-5.5 m.
Alluvial deposits are generated during periods of
high-water level when a predominantly suspended
ﬁne matter settles to the surface of the ﬂoodplain. It is
composed of lean clay mixed with ﬁrm-stiff organic
matter, and its thickness is approximately 0.7 m.
As described by Kádár and Nagy (2018), below
the alluvial deposit, there is eolian sand (transported
by wind). The rounded particles are in the size range
of silt and ﬁne sands; the layer has a thickness of
5.0 m. It is followed by ﬂuvial sand containing ﬁne,
medium, coarse and gravelly sands over a thickness
of 5.3 m. It abruptly turns into gravelly sands and
gravel; it forms a 10.0 m thick gravel terrace. Both
the in-situ measurements, CPT and DMT, and the
oedometric compressions, are evaluated up to the
base of the gravelly sand layer. In this study, the
eolian and ﬂuvial sands are treated as one layer.
2 SOIL CLASSIFICATION AND
2.1 Evaluation of CPT measurements
The CPT measurements were conducted according
to MSZ EN ISO 22476-1:2013.
The CPT-based soil behavior of the layers; land-
ﬁll, lean clay, silty sand and gravelly sand are pre-
sented in Figure 1. A CPT-based normalized soil
behavior chart was suggested by Robertson (1990)
and updated by Robertson (2009). The parameters
used are summarized in Robertson (2016).
The stratiﬁcation of the area was deﬁned accord-
ing to traditional geotechnical soil identiﬁcations and
CPT measurements. The layers appearing at the CPT
logs are presented in Figure 1. One dot is one layer
in one CPT. According to normalized cone resistance
) and normalized friction ratio (F
), the top layer,
landﬁll, is classiﬁed as silty sand and sand. The lean
clay is regarded as clay, silty clay and sandy silt.
This layer is not present in all the CPTs. The layers
of eolian and ﬂuvial sands (Kádár and Nagy, 2018)
are classiﬁed as silty sand and sand, while the last
normally consolidated layer is sand. The four layers
are not overconsolidated as they more or less fall in
the diagonal of the diagram.
Figure 1. Classiﬁcation of the layers according to Robert-
Each layers’ parameters obtained by CPT are
summarized in Tables 1-4, tip resistance (q
) and friction ratio (R
). To each of the
three parameters, minimum, maximum, average,
standard deviation and coefﬁcient of variation are
Table 1. CPT parameters of the landﬁll.
No. of samples
Table 2. CPT parameters of the lean clay.
No. of samples 26 26 26
Average 2.69 53.52 2.65
Min 0.29 1.60 0.90
Max 7.73 89.53 6.50
Std. 1.37 16.22 1.30
Co.V. 0.51 0.30 0.49
Table 3. CPT parameters of the silty sand.
No. of samples 32 32 32
Average 17.09 170.28 1.02
Min 8.77 74.22 0.52
Max 24.79 309.02 1.83
Std. 3.47 71.21 0.38
Co.V. 0.20 0.42 0.37
Table 4. CPT parameters of the gravelly sand.
No. of samples 33 33 33
Average 23.64 126.19 0.67
Min 16.76 68.75 0.27
Max 30.86 234.51 2.99
Std. 3.23 34.66 0.49
Co.V. 0.14 0.27 0.73
The landﬁll and the lean clay CPT parameters have
ahighercoefﬁcient of variation than the sandy layers.
2.2 Evaluation of DMT measurements
On the test site 11 DMT soundings penetrated to dif-
ferent depth. The ﬂat dilatometer was developed in
the 1980s by Silvano Marchetti. Shear strength
parameters of the soils such as undrained shear
). and friction angle (’). can be derived.
One of the most helpful information that DMT meas-
urements can derive is related to the soil layers’
stress history. Overconsolidation ratio (OCR), and
coefﬁcient of lateral earth pressure (K
) can be deter-
mined in the case of sands, in which sampling would
be difﬁcult (Marchetti et al. 2001).
In this paper. constrained modulus is estimated by
DMT measurements, which is the key parameter for
Two corrected readings (p
) are obtained
by the ﬂat dilatometer, from these, material index
), horizontal stress index (K
), and dilatometer
) are calculated. Vertical drained con-
strained modulus M
can be determined accord-
ing to Eq. (1) (Marchetti, 1980) as:
where RM is a correction primarily depending on
the stress history (K
2.3 Oedometer tests
To test the stress-strain relationship and the consoli-
dation parameters of each layer oedometer tests were
carried out according to MSZE CEN ISO/TS 17892-
5:2010 standard. Undisturbed samples were tested
with 0-100-200-400-600 kPa, it was a usual practice
to load, unload and reload the samples; a common
load path was 0-2-23-45-100-2-100-200-400 kPa.
A linear assumption was used between each load
step according to Eq. (2).
Figure 2. Different layers oedometric modulus and the
depth of the samples.
The results of the oedometric tests and the depth
from where the samples were extracted are presented
in Figure 2. the modulus is related to the stress state
as well as the depth.
In the case of the silty sand layer, the following
correlation can be derived between the depth and
While in case of the gravelly sand layer, a different
correlation can be made:
The linear correlations (Eq. 2.-3.) describe the con-
nection between depth and oedometric modulus well.
3 METHODS USED TO DERIVE THE
3.1 Sanglerat method
The Cone Penetration Testing (CPT) sounding was
developed in the Netherlands in the 1930s. It was
used to investigate the layers’ penetration resistance
for pile foundation design. A key parameter for
settlement calculation is the restrained modulus (M).
Buisman (1940) proposed the following correlation
between the tip resistance and oedometric modulus
in case of cohesionless soils (sands):
1.5 multiplier in Eq. (5) was replaced to αm by San-
The values for the coefﬁcient in the case of cohesive
soils were also deﬁned and presented by Sanglerat
(1972), later synthesized by Kumala Sari et al. (2017).
According to Figure 1. the landﬁll is classiﬁed as “silts
of low plasticity”, although it is very heterogenic, and
a high percentage of construction waste can be found
in it. According to Figure 1. and laboratory identiﬁca-
tion tests, the lean clay layer is considered a “clay of
low plasticity”, while the last two layers of silty sand
gravelly sand are regarded as “sands”.
3.2 Lunne and Christophersen method
Most correlations between CPT results and the
drained constrained modulus (M) refer to the tangent
modulus, as found from oedometer tests. The refer-
ence value of M is typically based on the effective
vertical stress (Lunne et al. 1997).
Lunne and Christoffersen (1983) reviewed the avail- The kM functions of different OCRs’ are esti-
able (at that time) calibration chamber test results and mated by digitalizing the ﬁgure in Lunne et al.
made the following recommendations to estimate M in (1997). The estimated functions are the following:
case of normally consolidated uncemented silica sands:
They also included overconsolidated sands in their
studies and made rough estimates for them as well.
3.3 Eslaamizaad and Robertson method
Based on the assessment of extensive calibration tests
on quartz sand (Baldi et al. 1986; Fioravante et al.
1991). Eslaamizaad and Robertson (1996) proposed
an alternative method to estimate M from CPT data.
The method presents a correlation incorporating
normalized cone resistance and normalized vertical
effective stress in the form of:
n: stress exponent equal to 0.200 for normally con-
solidated sands. and 0.128 for overconsolidated sands.
pa: atmospheric pressure. in the same units as ,
M and qc.
kM : is a dimensionless modulus number which
can be determined using Figure 3. based on normal-
ized cone penetration resistance and esti-
mated overconsolidation ratio (OCR).
Figure 3. Consolidation modulus number of sand as
a function of cone resistance and OCR (Eslaamizaad and
The method has the advantage that prior knowledge
of relative density is not required (Lunne et al.
1997). When Eslaamizaad and Robertson (1996)
compared the estimated values against the ones
measured in the calibration chamber, they were
between 75% and 125%. Later the M values are pro-
vided for each layer in Figure 5; the ones estimated
according to Eslaamizaad and Robertson (1996) are
divided by 1.25.
4 EVALUATION OF THE RESULTS
4.1 Vertical soil proﬁle
The 32 CPTs average. minimum and maximum tip
) are presented in a vertical proﬁle
(Figure 4). The average cone resistance (q
used for the calculation of restrained modulus (M)
by Sanglerat (1972), Lunne and Christoffersen
(1983) and Eslaamizaad and Robertson (1996)
There are lower and upper limits for cohesive
soils (landﬁll and lean clay). The eodometric moduli
of each layer measured on undisturbed samples in
the laboratory are also shown in Figure 4. Eodo-
) and constrained (M) modulus are the
same mechanical parameters. If it was measured in
the laboratory, the E
abbreviation is used, while if
it is estimated from ﬁeld measurements, CPT and
DMT, M is allocated.
The layers’ thickness in Figure 4. is just the aver-
age of the 32 CPTs. It happens that sometimes an
oedometric or DMT test falls below or above the
Figure 4. Soil strata with CPT values, estimated con-
strained (M), measured oedometric (E
In the upper two strata (landﬁll and lean clay) the
oedometric moduli measured in the laboratory seem
to agree with the minimum value estimated by San-
glerat (1972). In the top layer. constrained modulus
derived from DMT measurements are way higher.
than the results of other methods. The local inhomo-
geneity is probably also playing a part in the extreme
DMT results. The scatter of the measurements is not
really concerning as no foundation will be built in
landﬁll. The moduli estimated by DMT measurements
in lean clay spread between the other methods based
on CPT. In the lower two strata of silty sand and grav-
elly sand, the results of oedometer tests distribute
around the values estimated by the Sanglerat (1972)
method (Figure 4. Table 5.). However, the results of
the oedometric test vary with depth, Figure 2. Eq. 2-3.
Table 5. Constrained modulus of silty sand and gravelly
Silty sand Gravelly sand
In lower two strata the DMT measurements result
in a higher constrained modulus (Figure 4.) as the
methods proposed by Lunne and Christoffersen
(1983) and Eslaamizaad and Robertson (1996).
4.2 Different soil layers
The estimated constrained moduli by different methods
for each layer are summarized in Figure 5. From the
applied methods Lunne and Christoffersen (1983) and
Eslaamizaad and Robertson (1996) were calibrated
against tests of silica sand, their capability to estimate
soil parameters in cohesive soils is questionable. It is
assumed that DMT measurements give a better predic-
tion of constrained modulus as CPT measurements
(Marchetti, 2015) for two main reasons: (i) blades
cause penetration distortions lower than axy-cylindrical
probes, (ii) modulus by a mini load test relates better to
a modulus than a penetration resistance.
This is supported by many case studies such as
the Sunshine Skyway Bridge in Florida (Schmert-
mann, 1998), where the constrained modulus from
back calculation was closes by the DMT measure-
ments. It is also common to use the DMTs as
a calibration for CPT sounding, Jacksonville Power
Plant reported by Schmertmann (1998) and a project
in Bucharest (Poenaru et al., 2021).
The correlation between CPT and DMT data was
analyzed in the top layer of the silty-sand, regarded
as eolian sand, Figure 6.
Only 4 DMT and CPT test results for a single sub-
layer, 47 measurement pairs are analyzed. The CPT
data is averaged to be compared with a DMT meas-
value greater than 0.7 indicates that the
linear correlation describes the investigated param-
eters with sufﬁcient accuracy. The following equation
is on the border of the criteria, where: qc and the con-
stant is in MPa, so as the obtained M
Figure 5. Constrained modulus of the layers (landﬁll. lean clay. silty sand and gravelly sand).
According to Table 5. the constrained moduli esti-
mated by the Sanglerat (1972) method correlates
well with the measured ones in the laboratory by
The calculated oedometric modulus values have
a linear correlation with depth (Figure 2. and
The dilatometer disturbs the soil less than the
CPT, so more realistic constrained modulus can be
estimated, which is way higher than the results of
investigated correlations (Eslaamizaad and Robert-
son, 1996; Lunne and Christoffersen, 1983)
A simple linear connection (Eq. 17) is derived
between the cone resistance of CPT and the con-
strained modulus estimated by DMT in case of the
upper eolian layer of silty sand (Figure 6). It corres-
ponds to the mean value, in case of design the char-
acteristic value must be used.
Figure 6. Correlation between q
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