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Predicting Geotechnical Parameters of Sands from CPT Measurements Using Neural Networks

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Computer-Aided Civil and Infrastructure Engineering
17
(2002) 31–42
Predicting Geotechnical Parameters of Sands fromCPT Measurements Using Neural Networks
C. Hsein Juang,* Ping C. Lu
Civil Engineering Department, Clemson University, Clemson,South Carolina 29634-0911, USA
&Caroline J. Chen
California Department of Transportation, Sacramento,California 95819, USA
Abstract:
Predicting sand parameters such as
D
r
,K
0
,and OCR from CPT measurements is an important and challenging task for the geotechnical engineer. In the present study, a system of neural networks is developed for predicting these parameters based on CPT measure-ments. The proposed system uses backpropagation neuralnetworks for function approximation and probabilistic neu-ral networks for classiﬁcation. By strategically combiningboth types of networks, the proposed system is able to predict accurately
D
r
,K
0
, and OCR of sands from CPT measurements and other soil parameters. Details on thedevelopment of the proposed system are presented, alongwith comparisons of the results obtained by this system withexisting methods.
1 INTRODUCTION
Over the past two decades, many empirical equations havebeen established for determining geotechnical parameterssuch as relative density (
D
r
), coefﬁcient of lateral earthpressure at rest (
K
0
), and overconsolidation ratio (OCR)of
sands
based on cone penetration test (CPT). These
*
To whom correspondence should be addressed. E-mail:
hsein@clemson.edu.
empirical equations (Robertson and Campanella, 1983;Jamiolkowski et al., 1985; Baldi et al., 1986; Kulhawyand Mayne, 1991) are mostly developed with CPT calibra-tion chamber test data using statistical regression methods.Indeed, good-quality chamber test data around the worldare now more abundant than ever. However, the accuracy of many existing empirical equations is often less than desir-able. It would be of interest to the geotechnical engineerto develop new methods that are more accurate than theexisting methods in light of the availability of more data of good quality and recent advance in the area of data analy-sis techniques.Statistical regression is a technique that the geotechnicalengineer has relied upon for establishing empirical equa-tions for many decades. There are, however, occasions thatthe statistical regression fails to produce empirical equa-tions with the desired accuracy. In such cases, an artiﬁcialneural network (ANN) approach may be preferred. Artiﬁ-cial neural networks, referred to herein simply as neuralnetworks or networks, can map input to output withoutprior knowledge of the underlying mathematical model.The use of ANN to approximate input–output or
cause– effect
relationships in geotechnical engineering has beenreported in recent years (Ghaboussi et al., 1991; Goh, 1994;Meier and Rix, 1994; Agrawal et al., 1995; Najjar et al.,
© 2002
Computer-Aided Civil and Infrastructure Engineering
. Published by Blackwell Publishers, 350 Main Street, Malden, MA 02148, USA,and 108 Cowley Road, Oxford OX4 1JF, UK.
32
Juang, Lu, & Chen
1996; Ni et al., 1996; Juang and Chen, 1999; Juang et al.,1999, 2000).In the present study, well-documented CPT calibrationchamber test data are used to establish a system for pre-dicting
D
r
, OCR, and
K
0
of sands. The proposed systemconsists of a series of neural networks, each performingsome task of function approximation or classiﬁcation. Forclassiﬁcation, a probabilistic neural network (Demuth andBeale, 1998) is employed, and for function approximation,backpropagation neural networks (Rumelhart et al., 1986)are used. Details of the development of various network models in the proposed system are presented, along withcomparisons of the network predictions with those obtainedfrom existing empirical equations.
2 EXISTING EMPIRICAL METHODS
Several empirical methods are available in the literature forestimating
D
r
. Robertson and Campanella (1983) presenteda chart that relates
D
r
to
q
c
and
σ
v
for normally consoli-dated sands. The inﬂuence of sand compressibility is alsoindicated in their chart, although no quantitative measureof the compressibility is speciﬁed. Juang et al. (1996) pre-sented a fuzzy-set-based method that uses sleeve friction(
f
s
) to account for sand compressibility. In their formula-tion,
D
r
is related to
q
c
,f
s
, and
σ
v
.Baldi et al. (1986) recommended the following formulasto estimate
D
r
:For normally consolidated sands:
D
r
=
1
C
2
ln
q
c
C
0
(σ
v
)
C
1
(1)For overconsolidated sands:
D
r
=
1
C
2
ln
q
c
C
0
(σ
m
)
C
1
(2)The constants in Equation (1) are as follows:
C
0
=
157,
C
1
=
0
.
55, and
C
2
=
2
.
41, while the constants in Equa-tion (2) are as follows:
C
0
=
181,
C
1
=
0
.
55, and
C
2
=
2
.
61. Note that in these equations, the units of thevariables
q
c
,
σ
v
, and
σ
m
are kPa. The parameter
σ
v
is thevertical effective stress, while the parameter
σ
m
is the meaneffective stress deﬁned as:
σ
m
=
(σ
v
+
2
σ
h
)/
3
=
(
1
+
2
K
0
)σ
v
/
3 (3)where the parameter
σ
h
is the horizontal effective stress.The ratio of
σ
h
to
σ
v
at the initial condition is, of course,
K
0
. The above empirical equations established by Baldiet al. (1986) imply that
q
c
is related to
D
r
,
K
0
, and
σ
v
.Jamiolkowski et al. (1985) published an empirical equa-tion similar to Equation (1) for normally consolidated,uncemented, and unaged sands, with a stress exponent (
C
1
)of 0.5. Olsen (1994), however, argued that the stress expo-nent, often reported to be in the range of 0.5 to 0.7, isvalid only for a particular sand type and relative density.He proposed a
stress focus theory
to explain the concept of “variable stress exponent.” However, the debate over stressexponent does not alter the implication of the above empir-ical equations that
q
c
is related to
D
r
,
K
0
, and
σ
v
.Kulhawy and Mayne (1991) proposed the followingequation for
D
r
that takes into account OCR and the effectsof compressibility and aging:
D
2
r
=
q
c
1
305
Q
c
Q
A
(OCR)
0
.
18
(4)where the compressibility factor
Q
c
is between 0.91 (forsands of low compressibility) and 1.09 (for sands of highcompressibility) with a mean of 1.0. The aging factor
Q
A
is a function of deposit time. For freshly deposited sand,
Q
A
is approximately equal to 1.0. The parameter
q
c
1
is thenormalized cone resistance deﬁned as:
q
c
1
=
q
c
p
a
σ
v
p
a
0
.
5
(5)where
p
a
is the atmosphere pressure (about 100 kPa).The above empirical equations established by Kulhawy andMayne (1991) imply that
q
c
is related to
D
r
, OCR, and
σ
v
. In general, the secondary factors,
Q
A
(aging factor)and
Q
C
(compressibility factor), are difﬁcult to assess,and for the calibration chamber data that are the basis of the present paper,
Q
A
may be assumed to be equal to 1.Juang et al (1996) suggest that sleeve friction (
f
s
) couldbe used to account for sand compressibility. Use of both
q
c
and
f
s
has been shown to be superior to use of
q
c
alonewhen attempting to correlate CPT data with engineeringproperties of sands such as drained shear strength (Chenand Juang, 1996) and cyclic liquefaction resistance (Olsen,1997; Robertson and Wride, 1998).The two groups of empirical equations by Baldi et al.(1986) and Kulhawy and Mayne (1991), summarizedabove, might be “cross-checked” by introducing the rela-tionship between OCR and
K
0
. To this end, the followingempirical equation established by Mayne (1991) may beused:
K
0
=
(p
a
/σ
v
)(q
c
/p
a
)
1
.
6
145exp
(q
c
/p
a
)/(σ
v
/p
a
)
0
.
5
12
.
2
(OCR)
0
.
18
0
.
5
(6)Equation (6) may be used for estimating
K
0
if OCR isgiven, or for estimating OCR if
K
0
is given. In many occa-sions, an iterative process may be required to determine
K
0
and OCR simultaneously.Notice that to use Equations (2), (4), or (6), all of whichdeal with overconsolidated sands, knowledge of either
K
0
Geotechnical parameters
33
or OCR of the sand is required. This knowledge is gener-ally not available from CPT measurements. In an attemptto overcome this problem, Mayne (1991) proposed an iter-ative method that involves an initial guess of
K
0
, followedby repeated updating of
K
0
based on an empirical cor-relation with OCR until converged results are obtained.However, this iterative method does not always yield satis-factory results. In fact, the method failed to yield convergedresults in many cases examined in this study. Thus, it is agreat challenge to geotechnical engineers to estimate OCRand
K
0
of sands from CPT measurements. This is the mainthrust behind the present study that attempts to resolve thisissue using neural networks.
3 DEVELOPMENT OF THEPROPOSED SYSTEM
The proposed system for predicting
D
r
,
K
0
, and OCR fromCPT measurements consists of several neural networks asillustrated in Figure 1. Details on the development of eachof these networks, along with sources of the data that areused in the development, are described below.
3.1 Source data used in the development of neural networks
The data used in the present study, which were compiledby Lunne et al. (1997), come from the results of calibra-tion chamber tests with Ticino and Hokksund sands. Thisdata set consists of calibration chamber tests that werecarried out by the following organizations: ENEL CRIS,Milan, Italy; ISMES, Bergamo, Italy; NGI, Oslo, Norway;and Southampton University, UK. Excluding those datathat did not have sleeve friction (
f
s
) measurements, whichincludes all of NGI data and a few others, a total of 339
Fig. 1.
Proposed system for determining
D
r
,K
0
, and OCRof sands.
data were selected. This data set includes 135 cases fromENEL CRIS, 145 cases from ISMES, and 59 cases fromSouthampton University. The data set, which is readilyavailable in the literature, is not listed in this paper to savespace. According to Lunne et al. (1997), these test resultsare of high quality and are consistent in every aspect of chamber testing except chamber size. In the present study,the listed
q
c
values are corrected for chamber size andboundary effects. This correction is carried out followingthe procedure proposed by Mayne and Kulhawy (1991).Each “data point” of the data set used in the presentstudy consists of the following information: dry unit weightof sand sample (
γ
d
), relative density of sample (
D
r
),applied vertical stress (
σ
v
), coefﬁcient of lateral earth pres-sure at rest (
K
0
), overconsolidation ratio (OCR), and mea-sured cone resistance (
q
c
) and sleeve friction (
f
s
) of sandsin the calibration chamber. Each data point is called an
instance
in the present study, and a total of 339 instanceswere used. In the present study, these data are separatedinto three subsets in the ratios of 6 : 3 : 1 for training, test-ing, and validation. Thus, 204 instances are used for train-ing neural networks, 101 instances are used for testing thetrained networks, and 34 instances are used for additionalvalidation. However, testing and validation subsets can becombined into one, because both serve the same purpose,that is, to verify the trained network.In the present study, every 3 data points taken from
eachdata source
for training was followed by 2 data points takenfor testing and validation. Thus, a ratio of 3 : 2 for thetraining subset and the testing (including validation) subsetwas maintained. No other effort was taken to keep track of soil properties (for examples, normally consolidated ver-sus overconsolidated; low
q
c
versus high
q
c
, and so on)in the sampling process. This sampling scheme is consid-ered appropriate. However, other sampling schemes are alsoinvestigated, and this is discussed later.Testing of the network generally is carried out after theentire training phase is completed. To facilitate the network development, network testing may be carried out right afterthe completion of each training epoch (note: one completepresentation of the entire training data set to the network is an epoch). With this approach, the testing subset is usedduring the training phase to gauge the anticipated perfor-mance of the trained network. However, this action doesnot affect the training results. The selection of ﬁnal net-work architecture and training parameters is based on theperformance of the trained network using the training sub-set. Updating of weights and biases during the training isbased solely on network error calculated with the trainingdata. Nevertheless, testing of the network during the train-ing phase allows for earlier detection of undesired network architectures. Thus, the testing subset and the validationsubset serve practically the same function, both for ver-ifying (or validating) the generalization capability of the
34
Juang, Lu, & Chen
trained network. The minor difference is that the testingsubset may be used during training, whereas the validationsubset is used after training.
3.2 Selection of input variables for variousnetwork models
Selection of input variables for a network model couldbe guided by the principles of soil mechanics. The exist-ing empirical equations, summarized previously, representa survey of various statistical regression attempts for corre-lations between CPT measurements and other geotechnicalparameters. Based on previous discussion of the existingempirical equations, relative density
D
r
is considered as afunction of
q
c
,
f
s
,
σ
v
, OCR, and
K
0
. However, OCR and
K
0
are generally unknown in a CPT test. In fact, they arethe parameters to be “predicted” from CPT in the presentstudy, and thus, should be excluded from the list of inputvariables for predicting
D
r
. Based on the above discus-sions, the following models for
D
r
are considered:Model 1:
D
r
=
f(q
c
,σ
v
)
Model 2:
D
r
=
f(q
c
,σ
v
,f
s
)
In addition, it would be of interest to investigate the effectof the addition of dry unit weight of sand (
γ
d
) to the list of input variables in Model 2. The combined effect of
σ
v
and
γ
d
is believed to be comparable to that of
σ
v
and
σ
v
(totalstress), which are often included in the models for predict-ing engineering behaviors of sands (Chen and Juang, 1996;Robertson and Wride, 1998). It is noted that relative density
D
r
is a function of
γ
d
by deﬁnition. In fact, if
γ
d
is given,
D
r
can be directly calculated once the minimum and max-imum dry unit weight,
(γ
d
)
min
and
(γ
d
)
max
, are determinedby laboratory testing of the sand samples. However, withCPT soundings, no samples are taken from the ﬁeld forlaboratory testing and thus such a direct calculation of
D
r
is not possible. Thus, the following model is investigated:Model 3:
D
r
=
f(q
c
,σ
v
,f
s
,γ
d
)
For Models 1, 2, and 3, backpropagation networks are con-sidered appropriate. A brief discussion of the issues relatedto backpropagation networks is presented later.For predicting OCR of sands, the following network models are explored based on the previous discussion of the existing empirical equations:Model 4: OCR
=
f(q
c
,f
s
,σ
v
,γ
d
)
Model 5: OCR
=
f(q
c
,f
s
,σ
v
,γ
d
,D
r
)
Model 6: OCR
=
f(q
c
,f
s
,σ
v
,γ
d
,K
0
)
Model 4 requires the same four parameters as inModel 3. Model 5 requires one additional parameter,
D
r
,which is inspired by the empirical equation establishedby Kulhawy and Mayne (1991). Model 6 uses
K
0
in lieuof
D
r
, which is inspired by the empirical equation estab-lished by Baldi et al. (1986). Backpropagation networks areattempted for these models.As is shown later, backpropaga-tion networks for OCR, based on Models 4 and 5, performpoorly, whereas the network based on Model 6 performssatisfactorily. However,
K
0
that is required in Model 6 isnot available from CPT measurements. Thus, it is of inter-est to investigate whether
K
0
can be predicted from thefour common parameters:Model 7:
K
0
=
f(q
c
,f
s
,σ
v
,γ
d
)
As is shown later, however, backpropagation networksbased on Model 7 perform poorly. To overcome this prob-lem, an indirect approach is taken, which is based on twopremises. The ﬁrst premise is that sands can be adequatelyclassiﬁed into different classes of OCR using the four com-mon parameters. Here, an indication of OCR, rather thanthe actual OCR value, is sought. This investigation is car-ried out by exploring the following model:Model 8:
OCR
class
=
f(q
c
,f
s
,σ
v
,γ
d
)
where
OCR class
is a class identiﬁcation, taking its valuesfrom the set
{
1
,
2
,
3
,
4
,
5
,
6
}
. With Model 8, classiﬁcationof sands in terms of
CRR class
is performed. This modelis explored to conﬁrm the ﬁrst premise stated previously.For this model, backpropagation neural networks are ﬁrstattempted, followed by probabilistic neural network (PNN).As is shown later, PNN based on Model 8 performs well,whereas backpropagation networks do not.The second premise is that an indication of OCR, interms of
OCR class
, is all that is required, in addition to thefour common parameters, to predict
K
0
. This necessitatesthe investigation of the following model for
K
0
:Model 9:
K
0
=
f(q
c
,f
s
,σ
v
,γ
d
,
OCR
class)
Model 9 is investigated to conﬁrm the second premise. Theidea is that if the neural network based on Model 9 per-forms well, we will be able to determine
K
0
from the fourcommon parameters, since
OCR class
can also be obtainedusing these parameters. To develop Model 9, the backprop-agation network is employed.In summary, the input variables for various network models are selected based on a thorough review of existingempirical equations that were established from statisticalregression analyses. Two types of networks are employedin the various models investigated; probabilistic neural net-works for classiﬁcation and backpropagation neural net-works for function approximation.
Geotechnical parameters
35
Fig. 2.
Architecture of the probabilistic neural network.
3.3 Network topology and training algorithm
In a backpropagation network, the objective of the network training is to determine the connection weights and biasesby minimizing the root-mean-square error (RMSE). In the-ory, an error goal is set before the network training, andif the network error during training becomes less than theerror goal, the training is stopped. In practice, the errorgoal is often experimented with initially and adjusted sub-sequently to accommodate the need of domain problemsand to avoid the scenario of over-training.In the present study, a software tool called DataEngine(1997) is used to implement the backpropagation trainingwith a momentum term and a small learning rate. Thelearning rate was set at 0.1, and the momentum term wasset at 0.9. The initial weights for the connections are ran-domly selected from the range of
−
0
.
1 to 0.1. Use of these training parameters yielded satisfactory results in thepresent study. It is noted that similar results were obtainedusing another software tool called Neural Networks Tool-box (Demuth and Beale, 1998).In each backpropagation network, the number of neuronsin the hidden layer is determined through a trial-and-errorprocess, as is normally done. The optimal number of hiddenneurons is often difﬁcult to deﬁne. However, the smallestnumber of neurons that are required to yield “satisfactory”results is usually preferred. In each model explored in thispaper, only the “best” network that can be obtained is pre-sented.For Model 8, a probabilistic neural network is attemptedafter exploring ﬁrst with a backpropagation network. Theprobabilistic neural network (PNN) provides a generaltechnique for solving pattern classiﬁcation problems. ThePNN uses the training data to develop distribution func-tions, which are then used to estimate the likelihood of aninput instance (called a vector) belonging to a given cate-gory. Figure 2 shows the network architecture of a PNN.It consists of an input layer, a radial-basis layer, and acompetitive layer. A brief outline of how the PNN worksis presented below.When an input vector is presented, the ﬁrst task in theradial-basis layer is to compute “distances” from the inputvector to each of the training vectors. This would producea distance vector whose elements indicate how close theinput vector is to each training vector. The training vectorsare stored in the radial-basis layer as a weight matrix,
W
R
(see Figure 2). The next task in the radial-basis layer isto adjust the computed distance with a bias and then topresent it to the transfer function. Use of the bias allows forthe sensitivity of the radial-basis network to be adjusted.The transfer function in the radial-basis layer is usuallya bell-shape function, which has a maximum value of 1when its input is 0. The output of the radial-basis layer is avector
a1
. Note that each element of the resulting
a1
vector(see Figure 2) is essentially a measure of the similaritybetween an input vector and each of the training vectorsstored in
W
R
.The next step is to add up the contributions of all trainingdata for each output class. This is done by feeding the
a1
vector to the competitive layer that has a weight matrix
W
C
to compute
n2
. The weight matrix
W
C
is formed by storingthe output portion of the training data. Each element of theresulting vector
n2
is a relative probability, the likelihoodof an input instance belonging to each of the six outputclasses.

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