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Accepted Manuscript
Discussion on: “Probabilistic transformation model for
preconsolidation stress based on clay index properties”
[Eng.Geo.226:33–43]
Karim Kootahi
PII:
DOI:
Reference:
S0013-7952(17)31168-7
doi:10.1016/j.enggeo.2017.10.017
ENGEO 4682
To appear in:
Engineering Geology
Received date:
Revised date:
Accepted date:
10 August 2017
14 October 2017
22 October 2017
Please cite this article as: Karim Kootahi , Discussion on: “Probabilistic transformation
model for preconsolidation stress based on clay index properties” [Eng.Geo.226:33–43].
The address for the corresponding author was captured as affiliation for all authors. Please
check if appropriate. Engeo(2017), doi:10.1016/j.enggeo.2017.10.017
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Discussion on: “Probabilistic transformation model for preconsolidation
stress based on clay index properties” [Eng.Geo.226:33-43]
Full-Time Instructor, Department of Civil Engineering, Saghez Branch, Islamic Azad
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Karim Kootahi*
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University, 6681973477 Saghez, Iran. E-mail: kootahi@iausaghez.ac.ir
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The authors (Ching and Wu 2017) present results from an interesting study to develop
probabilistic transformation models for predicting the preconsolidation stress (  'p ) of finegrained soils based on index properties. Simple empirical models that use index properties as
entry information for estimating  'p –whether deterministic or probabilistic– are of practical
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importance to geoengineers. This is because: (1) there always exist differences between the
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laboratory-determined values of  'p and in-situ  'p values (as sample disturbance is inevitable)
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and thus having simple empirical models to cross-check and validate laboratory-determined
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values of  'p would be helpful (Kootahi and Mayne 2017), (2) index properties, which are
readily and economically measurable on disturbed samples, are routinely determined in almost
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any geotechnical project that involves structures constructed on/in fine-grained soils and thus the
use of simple empirical models require no extra effort, and (3) in cases of encountering a thick
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deposit of fine-grained soil, in which cases the determination of complete  'p profile for the
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deposit would be quite time- and cost-consuming process, as suggested by Bowles (1996), a
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limited number of lab consolidation tests in combination with an empirical model can be used to
determine the complete profile of  'p .
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Three probabilistic transformation equations for clays with different stress histories were
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developed by the authors: one generic equation (Eq. 25) for both contractive and dilative clays
and two separate equations (Eqs. 28 and 31) for contractive and dilative clays. In the following,
these two models are referred to as the generic and split-up models, respectively. Like the work
by Kootahi and Mayne (2016), who choose overconsolidation ratio (OCR) of 3 as distinguishing
parameter between contractive and dilative behaviors, the authors used OCR = 3.
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The authors are to be commended for developing the first probabilistic transformation model for
 'p based on clay index properties. The discusser would like to add the following points as a
supplement of the paper.
1. The authors used
both external and
internal validation (k-fold cross-validation)
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techniques for the assessment of performance of both generic and split-up models. It is
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noted that model validation techniques are classified as external and internal, depending
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on the data that have been used in the building and validating the developed model. In
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external validation, two independent databases are employed. In internal validation, on
the other hand, only one database is used and it always involves some form of data re-use
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(Royston et al. 2010). Many studies (e.g., Snee 1977; Harrell et al. 1996; Royston et al.
2010) believe that external validation is the most stringent and unbiased test for the
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assessment of the performance of empirical models and internal validation can never be
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an adequate substitute for external validation (Royston et al. 2010). Moreover, As
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demonstrated by Kootahi and Mayne (2016) assessing the performance of an empirical
model on its building database (i.e., using internal validation) can only lead to an
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apparent validity (or optimistic validation) and performing validation studies using
external (independent) databases is needed to obtain realistic validations. This key issue
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has been somehow recognized by Ching and Phoon (2014), who suggested that it is
important to assess bias and uncertainty of transformation models with respect to global
databases (i.e., applying transformation models outside their range of calibration).
The authors well recognized the importance of the use of external validation. However,
the external database used by the authors to assess the performance of both generic and
split-up models is very limited; it is a “regional” clay database consisted of 216 data
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points from 24 different test sites in Finland. Apart from being validated with respect to
regional databases, it is better and important to validate global transformation models
with respect to global databases. The discusser has recently compiled a global clay
database (see Kootahi and Mayne 2017), which can be used to perform an external
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validation on the accuracy of transformation models developed by Ching and Wu (2017).
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However, this global database, which consisted of 1350 data points from 144 different
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sites, has few overlaps with the calibration database (CLAY/10/7490) used by Ching and
Wu (2017) and overlapped cases need to be excluded from the analyses in order to
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achieve a full external validation test. The resulting clay database (after excluding
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overlapped cases) consists of 1245 data points from 133 different test sites around the
world and includes wide variety of soil types (ranging from low to high plasticity,
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normally consolidated to heavily overconsolidated, insensitive to sensitive to quick clays,
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and fissured clays, as well as varved clays). The overconsolidation ratios of deposits
included in this database range from 0.8 to 40 (mostly 1.0~10, with 21 soil deposits in
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which OCRs > 10), which is wide enough for practical purposes. The geographical
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regions of these 133 test sites cover Alaska, Australia, Belgium, Canada, China, England,
Finland, Gulf of Mexico, Indian Ocean, Ireland, Italy, Japan, Macau, Malaysia,
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Netherlands, Norway, Pacific Ocean, Peru-Chile Continental Margin, Puerto Rico,
Singapore, South Korea, Sweden, Taiwan, Thailand, United States of America, and
Vietnam. Table 1 summarizes the statistics for main geotechnical characteristics of the
new validation database. Compared with Table 2 of Ching and Wu (2017), it is seen that
the parameter ranges for this validation database are even wider than those for Ching and
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Wu’s calibration database (CLAY/10/7490) and thus a conclusive validation test is
expected.
The preconsolidation stresses for the 1245 data points in the new validation database were
estimated using both the generic and split-up models. The performances of the generic
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and split-up models on the new validation database are presented graphically and
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quantitatively in Figure 1. Three quantitative measures were used to quantify the
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performance of each model. These measures are coefficient of determination (R2 ),
coefficient of efficiency (E), and mean absolute error (MAE). It may be seen from
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Figure 1 that acceptability of the performance of generic model is marginal. More
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specifically, the generic model can be evaluated as unsatisfactory because the generic
model exhibited a low E value of 0.24. This is in contradiction to the statement of Ching
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and Wu (2017), that “a generic model can accommodate both contractive and dilative
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clays”. On the other hand, as can be seen from Figure 1, the split-up model exhibited a
moderately high E value of 0.74 and thus its performance can be considered quite
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acceptable. There are, however, two issues regarding the spilt-up model: (1) application
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of the split-up model requires the knowledge of overconsolidation ratio (OCR) which is
indeed dependent on preconsolidation stress (OCR =  'p / 'vo ), and (2) the difference
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between measured values of preconsolidation stress with those estimated using the splitup model increases as values of OCR increase.
Regarding the first issue, since OCR depends on  'p , the decision on whether equation
(Eq. 28 or Eq. 31) is applicable to a specific depth in a soil deposit requires engineering
judgment and may lead to considerable confusion. Such predicaments can be overcome
by using the OCR classification scheme proposed by Kootahi and Mayne (2016), who
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developed an efficient classification scheme for discriminating between contractive clays
and dilative clays. As presented in Table 1 of Ching and Wu (2017), Kootahi and Mayne
(2016) found the following discriminant function (DF) for separating soils with OCR < 3
(contractive clays) versus soils with OCR ≥ 3 (dilative clays):
DS  5.152log vo pa   0.061LL  0.093PL  6.219e n
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(1)
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where DS = discriminant score;  'vo = effective overburden stress; pa = atmospheric
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pressure; LL= liquid limit; PL = plastic limit; and en = natural void ratio.
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The mean discriminant score (cut-off value) for this discriminant function is 1.123 and
dilative clay samples have DS < 1.123 and contractive clay samples have DS > 1.123.
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The discusser used the combination of Kootahi and Mayne’s (2016) classification scheme
and Ching and Wu’s (2017) spilt-up model to estimate the preconsolidation stresses for
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the 1245 data points in the new validation database. Figure 2 compares the measured  'p
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with the estimated  'p . Note that the discriminant function (Equation 1 of this discussion)
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correctly classified 1120 of the 1245 specimens, for a 90% correct classification rate. It
may be seen from Figure 2 that the performance of this model, which is the combination
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of Equation 1 of this discussion and Equations 28 and 31 of Ching and Wu (2017), is
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quite acceptable, albeit misclassification resulted in overestimations as high as 500% in a
few cases. It should be noted, however, that the number of misclassifications is quite
small (125 of the 1245 samples), which compared with number of soil deposits in the
validation database (i.e., 133), indicates that there is only one misclassification in each
soil deposit and it should not be a worrisome issue.
On the second issue, Figure 3 shows the performance of the split-up model as applied to
two groups of dilative clays (3 < OCR < 15 and 15 < OCR < 40) in the validation database.
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Note that in preparing Figure 3 the DF has not been used, in order to prevent any other
factor that may affect interpretations. It may be seen that the performance of the split-up
model degrades significantly as the OCR exceeds 15. The reason is perhaps that Ching
and Wu’s calibration database (CLAY/10/7490) is mostly consisted of soils with OCR ≤
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15. Indeed, according to Table 2 of Ching and Wu (2017), OCRs of soils included in
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Ching and Wu’s calibration database range from 0.46 to 20 (with an average value of
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2.47). The significant degradation of the split-up model at OCRs grater than 15 may
suggest either that at least one extra data splitting, at an OCR ≈ 15, is needed or that
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applicability of the split-up model should be limited to OCRs less than 15.
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2. The authors used two quantitative measures (namely, coefficient of determination R2 and
coefficient of efficiency E) to compare the overall accuracies of models employed in their
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study. However, the authors neither provided explanations/instructions on how these
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quantitative measures should be interpreted nor did they use these quantitative measures
efficiently. It is noted that the ranges of values of R2 and E lie respectively between 0 to 1
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and –∞ to 1. For both measures, a value of 1 indicates perfect agreement between
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estimated and observed values. Performance of models with E < 0 is judged unacceptable
because such models provide estimates that are worse than those estimated from either a
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one parameter 'no knowledge' model or a simple 'observed mean' model. Recent studies
indicate that E has several advantages over R2 (See e.g., Das and Sivakugan 2010;
Oommen and Baise 2010) and use of R2 as a measure to quantify and compare the
predictive accuracy of models could lead to misleading interpretations about forecasting
ability of models (Kootahi and Moradi 2017). Interestingly, Figure 3 of this discussion is
a case where use of R2 could result in serious misinterpretations. Figure 4 of this
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discussion shows the data from Figure 3 replotted using arithmetic scales and clearly
indicates the problem associated with the R2 ; as demonstrated by Willmott (1982) and
Kootahi and Moradi (2017), R2 only quantifies the dispersion around the data trend line
(not around the perfect prediction line) and models providing predictions that follow
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straight-line patterns would have values of R2 close to 1. This is in direct contradiction to
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the statement of Ching and Wu (2017), that “the prediction is effective if R2 is large.”
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Interpretations about the overall accuracies of models employed by Ching and Wu (2017)
can be made with the assistance of the instructions provided above. Figures 2a~2e of
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Ching and Wu (2017) show the performances of five traditional transformation models
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on CLAY/10/7490 database. Note that the CLAY/10/7490 database serves as external
(independent) database for traditional models because traditional models were not trained
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by the data points included in CLAY/10/7490 database. Figures 1 and 2 of this discussion
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show the performances of Ching and Wu’s generic and split-up models on the new
validation database, which, as discussed earlier, serves as external database for Ching and
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Wu’s probabilistic models. From Figures 2a~2e of Ching and Wu (2017), it is evident
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that the performances of four traditional transformation models (including those proposed
by Stas and Kulhawy 1984, Nagaraj and Srinivasa Murthy 1986, DeGroot et al. 1999, and
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Ching and Phoon 2012) are quite unacceptable, as their E-values range from – 28 to 0.07.
Furthermore, the performance of the model developed by Kootahi and Mayne (2016) is
acceptable because the model has a coefficient of efficiency (E) of 0.67.
With regard to Ching and Wu’s (2017) probabilistic models, the following can be
concluded from Figures 1 and 2 of this discussion: the performance of the generic model
(Equation 25 in Ching and Wu) is quite unacceptable; the performance of the split-up
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model (Equations 28 and 31 in Ching and Wu) is quite acceptable but the decision on
whether equation (Eq. 28 or Eq. 31) should be applied to a specific depth in a soil deposit
may result in considerable confusion; the performance of the model produced from
combining Kootahi and Mayne’s (2016) classification scheme and Ching and Wu’s
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(2017) spilt-up model is also quite acceptable.
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3. The authors stated that “in terms of amount of required information, Kootahi and
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Mayne’s (2016) model and probabilistic models developed by Ching and Wu (2017) are
not the most convenient models” (because these models need the most entry information,
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including  'vo , PL, LL, and wn ). It is also stated in the paper that “models developed by
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Stas and Kulhway (1984) and DeGroot et al. (1999) are more convenient because they
only require LI.” However, the discusser is concerned about these statements.
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Being convenient is a criterion for choosing among candidate models only when all
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candidate models contain most influential parameters that affect response variable.
Models developed by Stas and Kulhway (1984) and DeGroot et al. (1999) both lack the
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most influential parameter; the effective overburden stress ('vo ) is indeed the most
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influential parameter that affects preconsolidation stress. For example, Kootahi and
Mayne (2016) found 16 transformation equations for 'p that each depends strongly on
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the effective overburden stress and explained the strong dependence of 'p on 'vo as
being expected because stress changes, in most overconsolidated soils, are responsible for
being preconsolidated. Furthermore, Kootahi and Mayne (2017) showed that neither
liquidity index (LI) nor plasticity index (PI) can solely estimate 'p and any predictive
model of 'p should be a function of both the effective overburden stress ('vo ) and
liquidity index or plasticity index. This is consistent with the finding of Ching and Phoon
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(2012) that the updated coefficient of variation (COV) of 'p /pa is 0.934 when LI is the
only entry information for estimating 'p /pa but the updated COV of 'p /pa drops to 0.440
when both LI and 'vo /pa are the entry information. This is probably why almost all
attempts at developing robust predictive models for 'p without considering 'vo as a
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contributing (influential) parameter have failed (e.g., models developed by Stas and
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Kulhawy 1984, DeGroot et al. 1999, and Ching and Phoon 2012; as demonstrated
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earlier). Interestingly, it is seen from Figure 2d of Ching and Wu (2017) that applying
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Ching and Phoon (2012) model, which is a function of both LI and sensitivity (S t ), to
CLAY/10/7490 database resulted in a very low E value of 0.07 because the model lacks
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the most influential parameter (i.e., 'vo ). To provide further demonstration of the strong
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dependence of 'p on 'vo , Pearson's correlation matrix was calculated for logarithmic
values of measurements in the new validation database. Figure 5 and Table 2 show,
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respectively, scatter plots between all pairs of variables in the new validation database
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and the corresponding estimated correlation matrix (Note that each pair of variables
contains 1210 data points because only positive values of LI were considered). It may be
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seen from Figure 5 and Table 2 that the effective overburden stress ('vo ) is the most
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influential parameter that affects preconsolidation stress.
4. The authors implemented their approach to a Norway site (Onsφy site) and estimated 'p
profile based on the ('vo , PL, LL, wn ) profiles. Three scenarios were considered by the
authors: (a) there is no prior knowledge about the contractive/dilative behavior of the
clays; (b) there is prior knowledge that the clays are contractive; (c) there is prior
knowledge that the clays are dilative. In scenarios (b) and (c), the authors assumed the
soil profile at Onsφy site, respectively, as “a contractive clay deposit” and “a dilative clay
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deposit”. It is noted, however, that many soft normally consolidated as well as lightly
overconsilidated clay deposits have an overconsolidated crust (with an OCR as high as 30
or more) which overlies the main soil deposit. Examples of such deposits include Boston
Blue Clay in Massachusetts, USA (with OCRs < 11 in the desiccated crust) (Whittle
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1974), James Bay sensitive clay in Ontario, Canada (with OCRs < 15 in the weathered
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crust) (Ladd 1991), Haarajoki in Järvenpää, Finland (with OCRs < 20 in the dry crust)
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(Yildiz et al. 2009), and St. Clair clay in Ontario, Canada (with OCRs < 31 in the fissured
silty clay crust) (Lo and Becker 1979). It has been demonstrated that the properties of the
crust
significantly
affect
the
accuracy
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overconsolidated
of embankment
stability
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predictions (Graham 1979; Lefebvre et al. 1987) and consolidation settlement predictions
(Duncan et al. 1991). Therefore, soil deposit simplifications such as “a contractive clay
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deposit” or “a dilative clay deposit” are neither acceptable, nor would they be practical in
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many circumstances, of course, except when high-quality lab or in-situ tests as well as
knowledge of the geology of the site indicate the existence of such simple soil deposits.
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As discussed earlier, the OCR classification scheme proposed by Kootahi and Mayne
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(2016) may be used to determine which class (contractive or dilative) a particular sample
with known index properties (wn , LL, PL) and effective overburden stress ('vo ) belongs
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to, although fully successful outcomes are not guaranteed (as the approach has a correct
classification rate of about 90%).
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References
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Ching, J., Phoon, K. K., 2014. Transformations and correlations among some clay parameters —
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Ching, J., Wu, T. J., 2017. Probabilistic transformation model for preconsolidation stress based
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on clay index properties. Eng Geol 226, 33–43 doi: 10.1016/j.enggeo.2017.05.007.
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offshore clays. Proc., Intl. Conf. on Offshore and Nearshore Geotech. Engrg, Balkema,
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Rotterdam, 173–178.
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Duncan, J. M., Javete, D. F., Strak, T. D., 1991. The importance of a desiccated crust on clay
cettlements. Soils & Found 31, 77–90.
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Graham, J., 1979. Embankment stability on anisotropic soft clays. Can. Geotech. J. 16, 295–308.
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Harrell, F. E., Lee, K. L., Mark, D. B., 1996. Multivariable prognostic models: Issues in
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errors. J. Statist. Med. 15, 361–387.
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stress in clay deposits. J.
5606.0001519
Geotech. Geoenviron. Eng. 142, doi: 10.1061/(ASCE)GT.1943-
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Kootahi, K., Mayne, P. W., 2017. Closure to “Index test method for estimating the effective
preconsolidation stress in clay deposits”.
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Geotech. Geoenviron.
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crust. Can. Geotech. J. 24, 23–34.
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Lo, K. Y., Becker, D. E., 1979. Pore-pressure response beneath a ring foundation on clay. Can.
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Nagaraj, T. S., Srinivasa Murthy, B. R., 1986. Prediction of compressibility of overconsolidated
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Whittle, J. F., 1974. Consolidation behavior of an embankment on Boston Blue Clay, M.Sc
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of Haarajoki test embankment, Int. J. Geomech. 9, 153–168.
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Yildiz, A., Karstunen, M., Krenn, H., 2009. Effect of anisotropy and destructuration on behavior
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List of Tables
Table 1. Statistics for main geotechnical characteristics of the 1245 data points in the new
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validation database
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Table 2. Correlation matrix for logarithmic values of soil properties in the new validation
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AN
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database
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Table 1. Statistics for main geotechnical characteristics of the 1245 data points in the new
'p /p a
2.22
Standard
deviation
4.17
ln('p /p a)
0.23
0.94
-2.41
4.14
'vo /p a
1.22
3.20
0.01
56.82
ln('vo /p a)
-0.43
0.97
-4.61
PL
28.3
11.4
0.20
151.0
LL
67.8
31.3
16.0
232.0
wn
62.4
29.9
14.8
215.0
OCR
2.60
3.23
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validation database
0.80
40.05
Max
0.09
62.50
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Min
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Mean
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Clay Parameter
4.04
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Table 2. Correlation matrix for logarithmic values of soil properties in the new validation
database
LI
– 0.544
– 0.306
–
–
–
–
wn
– 0.636
– 0.402
0.381
–
–
–
LL
– 0.304
– 0.188
– 0.202
0.795
–
–
PL
– 0.337
– 0.221
– 0.038
0.767
0.823
–
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AN
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ED
PT
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PI
– 0.242
– 0.138
– 0.280
0.698
0.953
0.636
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'vo
0.752
–
–
–
–
–
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Soil Property
'p
'vo
LI
wn
LL
PL
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Figure Caption List
Fig. 1. Graphical and quantitative representation of the performance of Ching and Wu’s generic
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and split-up models on the new validation database
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Fig. 2. Graphical and quantitative representation of the performance of a model produced from
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the combination of Kootahi and Mayne’s (2016) classification scheme and Ching and Wu’s
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(2017) spilt-up model
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Fig. 3. Graphical and quantitative representation of the performance of split-up model as applied
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to two groups of dilative clays (3 < OCR < 15 and 15 < OCR < 40) in the new validation database
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Fig. 4. performance of split-up model as applied to groups of dilative clays (3 < OCR < 15 and 15
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< OCR < 40) in the new validation database (data from Figure 3 replotted using arithmetic scales)
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Fig. 5. Scatter plots between log-transformed values of the variables in the new validation
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database (Note: each pair of variables contains 1210 data points)
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and split-up models on the new validation database
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Fig. 1. Graphical and quantitative representation of the performance of Ching and Wu’s generic
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Fig. 2. Graphical and quantitative representation of the performance of a model produced from
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the combination of Kootahi and Mayne’s (2016) classification scheme and Ching and Wu’s
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PT
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(2017) spilt-up model
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Fig. 3. Graphical and quantitative representation of the performance of split-up model as applied
AC
CE
PT
ED
M
to two groups of dilative clays (3 < OCR < 15 and 15 < OCR < 40) in the new validation database
AN
US
CR
IP
T
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Fig. 4. performance of split-up model as applied to groups of dilative clays (3 < OCR < 15 and 15
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CE
PT
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< OCR < 40) in the new validation database (data from Figure 3 replotted using arithmetic scales)
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AN
US
CR
IP
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AC
Fig. 5. Scatter plots between log-transformed values of the variables in the new validation
database (Note: each pair of variables contains 1210 data points)
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Highlights
 Simple empirical models that use index properties as entry information for estimating the
preconsolidation stress are of practical importance to geoengineers.
A rigorous external validation using a database developed in discusser's previous studies
is performed.

The performances of most traditional transformation models are quite unsatisfactory.

The performance of the split-up model (Equations 28 and 31 in Ching and Wu 2017) is
quite acceptable, but the performance of the generic model (Equation 25 in Ching and
Wu 2017) is quite unsatisfactory.

The effective
stress is
the
most influential parameter
CR
overburden
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T

AC
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PT
ED
M
AN
US
preconsolidation stress.
that
affects
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