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Ŕ periodica polytechnica
Civil Engineering
53/2 (2009) 101–106
doi: 10.3311/pp.ci.2009-2.06
web: http://www.pp.bme.hu/ci
c
Periodica Polytechnica 2009
RESEARCH ARTICLE
Estimation of CPT resistance based on
DPH results
András Mahler /János Szendefy
Received 2009-02-27, revised 2009-03-24, accepted 2009-04-07
Abstract
Hungarian experience about the correlation of CPT and DPH
results is summarized. A historical review of CPT-DPH and
CPT-SPT correlations is presented, and the reliability of the
published CPT-DPH correlations is analyzed using recent data
from Hungarian geotechnical practice. Based on these data
the paper defines soil types where reliable correlation exists
and proposes formulas describing the relationships between the
CPT and DPH results, because in the case of hard state clays
and soils containing gravel an acceptable relationship cannot
be stated.
Keywords
CPT ·DPH ·tip resistance
András Mahler
Department of Geotechnics, BME, M˝uegyetem rkp. 3. Budapest, H-1521, Hun-
gary
e-mail: mahler@mail.bme.hu
János Szendefy
Department of Geotechnics, BME, M˝uegyetem rkp. 3. Budapest, H-1521, Hun-
gary
e-mail: szendefyjano@freemail.hu
1 Introduction
The two sorts of the indirect soil exploration methods widely
used in the Hungarian geotechnical practice are the dynamic
probing (heavy, DPH), and the cone penetration test or piezo-
cone test (CPTu). The dynamic probing has been a popular
method for a long time, therefore there is plenty of relationships
(local experience) regarding the soil’s condition and DPH re-
sults. The use of the CPTu has been growing rapidly in the past
decades in our country.
It would be useful to find a relationship between the results
from both probe types for the science and for engineers involved
in the engineering practice being familiar with the evaluation
methods for only one of the probe types and knowing less the
possibilities of the other type. As the dynamic probing is less
expensive, this will presumably come down to have a possibil-
ity to determine the approximate value of qc(CPTu cone resis-
tance) from dynamic probing. Although the reliability declines
this way, the numerous relationships elaborated for CPTu tests
become usable also for DPH results – the dynamic probes can
be used more widely thereby.
2 Overview of the results from earlier investigations
More investigations were carried out abroad earlier to con-
front the results from CPT and DPH, it is reasonable therefore
to overview and examine the relationships proposed by these
before the processing of the Hungarian data. We found dur-
ing searching in the literature that only few publications [6] can
be found about the correlation of the results from the in Hun-
gary most widely used dynamic probe (DPH - Dynamic Prob-
ing, Heavy) and the cone penetration test (CPTu). These re-
sults come mostly from German speaking countries, because
these probe types are widely used there. Far more (and more re-
cent) investigations can be found on the correlation of the results
from the in North-America widespread SPT (Standard Penetra-
tion Test) and of CPTu. As this problem is very similar to the
actual task (the relationship between the results from static and
dynamic probes), it is useful to study these works and utilize
their experience, too.
Estimation of CPT resistance based on DPH results 1012009 53 2
Tab. 1. Correlation between DPH and CPT (Biedermann, 1984)
Soil type qc/N10 qc/N20 Range of validity
poorly graded sand 0.7 0.35 6 <N20 <60
well graded sand 1.0 0.5 6 <N20 <60
sandy gravel 1.5 0.75 -
clay 1.0 0.5 6 <N20 <38
2.1 The correlation between CPTu and DPH
There has been carried out investigations since the begin-
ning of the dissemination of the cone penetration test, the 1960
decade. This is shown by a publication on this topic of 1968 [5],
which proposes for sands the following equation:
qc=4.708 ·N20,(1)
where qc=CPT cone resistance in M P a,N20 =number of
blows for 20 cm penetration of DPH.
This relationship gives a proposal only for sand soils; it tries
to describe the correlation between the results from both types
of probes by a single factor. We observed that this is valid only
for the so called Maihak type CPT, and the author experienced
different results from “Dutch” CPT. Although our approximate
calculations showed that this equation gives only a very inaccu-
rate approximation of the correlation, a summarizing research
report from 1975 [7] contains also this proposal.
A more detailed relationship is proposed by another research
report published in 1984 [2], where the author assigns different
qc/N10 ratios to the different soil types. These values and the
corresponding soil types are shown in the following table (1).
The table shows the ratios converted to N20and the range of va-
lidity for the calculation method, too.
We examined how exactly this relationship describes the cor-
relation between values for both CPT and DPH resistances mea-
sured in Hungary. For this reason we derived qcvalues from
DPH results, and represented it as a function of the empirical
“measured” resistance on a logarithmic scale (Fig. 1).
It can be seen that although the characteristic trend is readable
when using this relationship, the data are highly diffuse. This
method further-more overestimates qcfor clays in every case.
2.2 The correlation between CPTu and SPT
The most widespread relationships for the definition of the
correlation of the results from these probing methods are those
proposed by Robertson et al. (1983) as well as Kulhawy and
Mayne (1990). The authors of both methods point up the neces-
sity to correct the results gained from different types of standard
penetration tests (SPT). This is based on the fact that different
types of devices transmit the dynamic energy to a different ex-
tent (efficiency) toward the soil. Earlier measurements of this
type were based on the blow numbers pertaining to 60% effi-
ciency, the results from equipments having less or higher effi-
ciency must be corrected accordingly. This corrected blow num-
Fig. 1. Measured and derived CPT resistance values
ber is called N60 . This may be reasonable also in the Hungarian
practice of dynamic sounding, but we did not study this question
during our investigations because the analyzed DPH tests were
carried out using the same device.
Robertson uses in his work earlier already published data
gained from 16 locations. He states that the authors of these
earlier publications proposed ratios for the results gained from
both types of probes spreading a wide range, which seems to be
almost inconsistent. This fluctuation of the ratios becomes eas-
ily comprehensible nevertheless if their values are plotted as a
function of the mean grain size.
The measured qc/N60 ratios fit well for a curve if depicted in
a semilogarithmic system of coordinates.
Kulhawy and Mayne (1990) propose two relationships in their
work. On one hand they improve Robertson’s curve by process-
ing further data, on the other hand they propose a new relation-
ship for the qc/N60 ratio as a function of the fine content. These
two relationships are the followings:
qc/pa
N60
=5.44 ·d0.26
50 (2)
qc/pa
N60
=4.25 −FC
41.3(3)
where: pa=the reference pressure (equal to atmospherical pres-
sure =100 kPa), N60 =SPT blow numbers pertaining to 60 %
efficiency, d50 =the diameter in the grain size distribution curve
corresponding to 50 % [mm], F C =fine content [%].
There are lots of publications entertaining this subject besides
the ones described above. Their main goal was to analyze the
accuracy of the existing methods or to describe local experiences
[8].
3 The correlation between the results of CPTu and DPH
We utilized the data gained from 83 ground layers of 29 loca-
tions to process the Hungarian experiences. On every location
boring, CPT and DPH tests were carried out typically until 20 m
Per. Pol. Civil Eng.102 András Mahler /János Szendefy
depth. To filter out the influence of the formation boundaries and
interjacent layers we used to our investigations solely data from
homogeneous ground layers having the thickness of at least 2 m,
and did not take into account the influenced (descending or as-
cending) probe resistance values measured near the regions of
formation boundaries.
According to the preliminary calculations the values of the
qc/N20 ratios fluctuated within a wide range, but these varying
results can be properly separated for non-cohesive and cohesive
soils. This is why we studied these both soil types separately as
described in the followings.
3.1 Non-cohesive soils
As the qc/N20 ratios in question are diversified it is useful to
depict their values in any case as a function of a third variable
(soil parameter). We used for this purpose in case of grained
soils and for the SPT-CPT correlations the mean grain size (the
inflection point of the grain-size distribution curve) as proposed
by Robertson (1983) as well as Kulhawy and Mayne (1990),
and the values of the silt+clay content (d<0.02 mm according
to the Hungarian Standard MSZ 14043-2:1979). We attempted
to use also the uniformity coefficient, but this led to a far worse
correlation than using the other factors.
A relationship for each case silhouetted well, but the fluctua-
tion of the data was still to high. When examining the different
data it became unequivocal that these differences had a trend:
the ratios experienced in case of deeper ground layers were sit-
uated in the lower part of the set of points while those from
ground layers closer to the natural ground level in the upper part
of it. This is why we found necessary to correct (divide) the
DPH results (blow numbers) by the effective overburden stress,
thus the set of points “shrank” close to a curve – i.e. the fluctu-
ation decreased and the relationship became more accurate. In
order to get a dimensionless relationship we propose to divide
the addends having a pressure type dimension by a reference
pressure (according to the atmospherical pressure), thus a di-
mensionless (“normalized”) value, a Normalized CPT-DPH ra-
tio can be generated:
Normalized CPT-DPH ratio =qc/pa
N20
σ0
v/pa
(4)
where: qc=is the CPT cone resistance, pa=the reference pres-
sure (equal to atmospherical pressure =100 kPa), N20 =number
of blows for 20 cm penetration of DPH, σv’=effective overbur-
den stress
On the following figures we demonstrate the ratios between
the CPT cone resistance and the number of blows for 20 cm pen-
etration of DPH corrected by the effective overburden stress as a
function of the silt+clay content (Fig. 2) as well as of the mean
grain size (Fig. 3).
Fig. 2 shows that depicting the ratio of the probe resistance
as a function of the silt+clay content gives a curve that fits
well to the set of points, but the points fluctuate in a relatively
Fig. 2. Normalized CPT-DPH ratio as a function of silt+clay content
Fig. 3. Normalized CPT-DPH ratio as a function of mean grain size
broad zone, this is also shown by the lower correlation factor of
R2=0.63. We can observe furthermore that in case of the points
according to the silt+clay content =0% (these were typically
gravelly soils) the ratio varies in a wide range – in this case an
explicit relationship cannot be stated.
If we depict this normalized CPT-DPH ratio as a function of
the mean grain size, the points according to the dmea n<1-2 mm
grain size are situated in a very narrow zone, but the bigger mean
grain sizes lead to a higher fluctuation of the data here, too. In
our opinion the reason for this is that these soils (in the stud-
ied cases) contained bigger size gravels, too. The presence of
these gravels, the diameter of which exceeds ∼1/10 of the di-
ameter of the probe, reduces considerably the reliability (accu-
racy, repeatability) of the measurements for both probe types –
this means that the probe resistance varies in a wide range (“jig-
gles”) also in homogenous layers. Of course for these soils also
the relationship between the probe types can be determined only
with a higher uncertainty, it is useful therefore to handle the soils
containing a gravel size fraction (d>2 mm) separately.
On the following figure (Fig. 4) we marked differently the
Estimation of CPT resistance based on DPH results 1032009 53 2
Fig. 4. Normalized CPT-DPH ratio as a function of mean grain size #2
soils containing a gravel size fraction (triangle) and the ones not
containing it (circle). It shows obviously that for gravelly soils
it is not possible to determine a reliable relationship between
the ratio and the mean grain size (as well as in the case of the
silt+clay content). For the case of the soils not containing grains
larger than 2 mm (gravels) the points depicting the ratios fit well
to a straight line in a semilogarithmic system of coordinates;
this means that the relationship of the probe results can be well
described as a logarithmic function of the mean grain size.
We put the best fitting (best correlating) curves for the set of
points showed on the figures using the least squares method.
The following formula describes it as a function of silt+clay
content: qc/pa
N20
σ0
v/pa
= −2.3·log(S+C)+1.88 (5)
where (S+C)=the silt+clay content (d<0.02 mm) of the soil.
Because of the higher fluctuation of the data we propose to
use this relationship only for rough estimations.
A more accurate ratio value can be acquired by applying the
following relationship using the mean grain size:
qc/pa
N20
σ0
v/pa
=4.5·log dmea n +7.8(6)
where dmea n is the mean grain size used in the Hungarian prac-
tice („the point of inflection of grain size distribution curve”).
This relationship can be used exclusively for soils not contain-
ing grains of diameter d>2 mm (gravels). In this case also the
correlation coefficient is significantly better than for the former
relationship: R2=0.86.
3.2 Cohesive soils
In the case of cohesive soils the studied problem is more
complex and complicated than for non-cohesive soils. During
the processing of the results gained from DPH tests we experi-
enced that in homogeneous clay layers following the upper part
Fig. 5. Normalized CPT-DPH ratio as a function of plasticity index
of ∼1.0 m thickness giving approximately constant probe re-
sistance the blow numbers (N20 ) rose often (quasi) linearly as
a function of depth, although the type or condition of the soil
showed any change neither in the boring nor in the results of
the static probe. This phenomenon is caused likely by the fact
that because of the dynamic effect the pore-water pressure rises
in the clay, the soil does not have enough time to consolidate,
the probe “becomes springy” affected by the impacts. Because
of all these the blow numbers experienced in clay layers can be
hardly evaluated, the attenuation (correction) of the measured
values would be necessary in any case. In such cases we consid-
ered the upper, nearly constant probe resistance as characteristic
for the given layer.
A further problem is affected in the case of cohesive soils
by the fact that the excess pore-water pressures caused by both
static and dynamic loads are different. While in the case of the
static probe (CPTu) the effected pore-water pressure can be mea-
sured and therefore taken into account in the calculations, using
dynamic probes we haven’t any information about the magni-
tude of the pore-water pressure, which probably changes fur-
thermore during the process of the measurement.
Similarly to the non-cohesive soils we studied the normalized
CPT-DPH ratio as a function of a soil parameter also in this case.
For cohesive soils it is obvious to use the plasticity index (P I )
and the Liquidity index (L I ) for this purpose, thus the following
figures (Fig. 5 and Fig. 6) demonstrate the normalized CPT-DPH
ratio as a function of the plasticity index and the liquidity index.
The figures demonstrate that it is very difficult to find an ex-
act relationship between the values, also the low values of the
correlation coefficient underpin this (for P I R2=0.31, for L I
R2=0.48).
Besides these we can see a definite, broader and near linear
zone where the points are located. On the figure of the ratios
and the plasticity index (Fig. 5) there is a single point which is
Per. Pol. Civil Eng.104 András Mahler /János Szendefy
Fig. 6. Normalized CPT-DPH ratio as a function of liquidity index
Fig. 7. Experienced vs. calculated normalized CPT-DPH ratio
far out of this zone, this is however not a measuring error, but
represents a clay harder than the others (L I =-0.50) while for all
other locations L I ≥0.00). Also this underpins the statement
that the studied normalized CPT-DPH ratio rises when either the
plasticity index rise or the liquidity index decrease. To improve
the accuracy of the relationship it is necessary to create the for-
mula as a function of these both factors as follows:
qc/pa
N20
σ0
v/pa
=0.22 ·P I −12.2·L I +12.(7)
where P I =plasticity index (in %), L I =liquidity index.
To demonstrate the accuracy of the results we show on the
next figure (Fig. 7) the values of the normalized CPT-DPH ratio
both measured using the test results and calculated by the above
formula.
On this figure (Fig. 7) the cohesive soils having lower liquid-
ity index (LI) than 0.15 are represented by triangles, and those
with values L I ≥0.15 by circles. It is manifest that the cal-
culated ratio varies between 15 and 20 for stiffcohesive soils,
but the measured values spread a more wide range. Therefore
for such cohesive soils the proposed relationship is not able to
give a reliable result. For softer soils (L I ≥0.15) the points
are situated close to the straight 45◦line representing the exact
calculation, thus the proposed relationship gives a good approx-
imation for the ratio of the probe resistance. For such soils the
value of the correlation coefficient presented itself as R2=0.66,
and the experienced standard deviation as σ=2.45. This can
be considered as encouraging taking into account the complex
nature of the problem.
4 Conclusions
We processed the data gained from both CPT and DPH tests
of 83 ground layers on 29 locations. The following conclusions
can be drawn:
•In the case of soils containing a gravel size fraction (dmax >
2.0 mm) an acceptable relationship cannot be stated between
the probe resistance values. This is caused by the fact that
because of the higher grain size the results fluctuate in a very
wide range for both probe types, even in homogenous layers.
We could not find any relationship between the high standard
deviation CPT and DPH results capable for even rough esti-
mations.
•For harder state clays (L I ≤0.15) the conditions of the cohe-
sive soils can not be reliably characterized using DPH. While
the CPT resistance was approximately constant in such ho-
mogenous clay layers, the DPH blow numbers spread a wide
range.
•For the other soil types the relationship between the CPTu and
DPH results can be defined in case of grained soils with high
reliability, in case of cohesive soils with medium reliability.
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