Abstract

The accuracy of the initial void ratio is vitally important to ensure the exact position of the normal compression line of remolded clay. In this article, a series of standard oedometer tests were performed on four different types of commercial clay in slurry state to analyze the error sources that affect the experimental accuracy of the initial void ratio. For remolded clay, it is found that the extra water at the end of the test has an unfavorable effect on the calculation accuracy. The precautions and steps for ensuring the experimental accuracy of initial void ratio in the oedometer test are detailed. According to the error propagation theory, the error estimation of five methods commonly used in the literature for calculating the initial void ratio is revealed. On this basis, a novel data fusion approach based on Bayesian inference is proposed to determine the initial void ratio of remolded clay, which fully considers the uncertainty of measurement error. The effectiveness of the proposed Bayesian data fusion approach has been validated by the data from mercury intrusion porosity testing, promoting the application of Bayesian theory in soil mechanics.

References

1.
ASTM International.
2010
.
Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils (Superseded)
. ASTM D4318-10. West Conshohocken, PA:
ASTM International
, approved January 15,
2010
. https://doi.org/10.1520/D4318-10
2.
ASTM International.
2011
.
Standard Test Methods for One-Dimensional Consolidation Properties of Soils Using Incremental Loading (Superseded)
. ASTM D2435/D2435M-11. West Conshohocken, PA:
ASTM International
, approved May 1,
2011
. https://doi.org/10.1520/D2435_D2435M-11
3.
ASTM International.
2017
.
Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System)
(Superseded). ASTM D2487-17e1. West Conshohocken, PA:
ASTM International
, approved December 15,
2017
. https://doi.org/10.1520/D2487-17E01
4.
ASTM International.
2023
.
Standard Test Methods for Specific Gravity of Soil Solids by the Water Displacement Method
. ASTM D854‐23. West Conshohocken, PA:
ASTM International
, approved November 1,
2023
. https://doi.org/10.1520/D0854-23
5.
Bayes
,
T.
1763
. “
LII. An Essay towards Solving a Problem in the Doctrine of Chances. By the Late Rev. Mr. Bayes, F. R. S Communicated by Mr. Price, in a Letter to John Canton, A. M. F. R. S
.”
Philosophical Transactions of the Royal Society of London
53
(December):
370
418
. https://doi.org/10.1098/rstl.1763.0053
6.
Bendat
,
J. S.
and
Piersol
A. G.
.
2010
.
Random Data: Analysis and Measurement Procedures
.
Hoboken, NJ
:
John Wiley & Sons
.
7.
Bergaya
,
F.
and
Lagaly
G.
, eds.
2013
.
Handbook of Clay Science
.
Amsterdam, the Netherlands
:
Elsevier
.
8.
Berrar
,
D.
2019
. “
Bayes’ Theorem and Naive Bayes Classifier
.” In
Encyclopedia of Bioinformatics and Computational Biology
,
403
412
. Amsterdam, the Netherlands:
Elsevier
. https://doi.org/10.1016/B978-0-12-809633-8.20473-1
9.
Box
,
G. E. P.
and
Tiao
G. C.
.
1992
.
Bayesian Inference in Statistical Analysis
.
Hoboken, NJ
:
John Wiley & Sons
.
10.
Brown
,
G.
and
Brindley
G. W.
.
1980
. “
X-ray Diffraction Procedures for Clay Mineral Identification
.” In
Crystal Structures of Clay Minerals and their X-ray Identification
,
342
358
. Hampton, UK:
The Mineralogical Society of Great Britain and Ireland
.
11.
Cai
,
Y.
,
Gu
C.
,
Wang
J.
,
Juang
C. H.
,
Xu
C.
, and
Hu
X.
.
2013
. “
One-Way Cyclic Triaxial Behavior of Saturated Clay: Comparison between Constant and Variable Confining Pressure
.”
Journal of Geotechnical and Geoenvironmental Engineering
139
, no. 
5
(May):
797
809
. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000760
12.
Cao
,
Z.-J.
,
Wang
Y.
, and
Li
D.-Q.
.
2016
. “
Site-Specific Characterization of Soil Properties Using Multiple Measurements from Different Test Procedures at Different Locations–A Bayesian Sequential Updating Approach
.”
Engineering Geology
211
:
150
161
. https://doi.org/10.1016/j.enggeo.2016.06.021
13.
Delage
,
P.
and
Lefebvre
G.
.
1984
. “
Study of the Structure of a Sensitive Champlain Clay and of Its Evolution during Consolidation
.”
Canadian Geotechnical Journal
21
, no. 
1
(February):
21
35
. https://doi.org/10.1139/t84-003
14.
Fuller
,
W. A.
1987
.
Measurement Error Models
.
Hoboken, NJ
:
John Wiley & Sons
.
15.
Ghorbany
,
S.
,
Yousefi
S.
, and
Noorzai
E.
.
2024
. “
Evaluating and Optimizing Performance of Public–Private Partnership Projects Using Copula Bayesian Network
.”
Engineering, Construction, and Architectural Management
31
, no. 
1
(January):
290
323
. https://doi.org/10.1108/ECAM-05-2022-0492
16.
Göksu
,
B.
,
Yüksel
O.
, and
Şakar
C.
.
2023
. “
Risk Assessment of the Ship Steering Gear Failures Using Fuzzy-Bayesian Networks
.”
Ocean Engineering
274
(April): 114064. https://doi.org/10.1016/j.oceaneng.2023.114064
17.
Guo
,
Y.
,
Sun
Y.
,
Li
L.
, and
Tang
X.
.
2019
. “
Reliability Assessment for Multi-source Data of Mechanical Parts of Civil Aircraft Based on the Model
.”
Journal of Mechanical Science and Technology
33
, no. 
7
(July):
3205
3211
. https://doi.org/10.1007/s12206-019-0615-4
18.
Holmes
,
D. T.
and
Buhr
K. A.
.
2007
. “
Error Propagation in Calculated Ratios
.”
Clinical Biochemistry
40
, nos. 
9–10
(June):
728
734
. https://doi.org/10.1016/j.clinbiochem.2006.12.014
19.
Jia
,
R.
,
Lei
H.
, and
Li
K.
.
2020
. “
Compressibility and Microstructure Evolution of Different Reconstituted Clays during 1D Compression
.”
International Journal of Geomechanics
20
, no. 
10
(October): 04020181. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001830
20.
Kedem
,
B.
,
de Oliveira
V.
, and
Sverchkov
M.
.
2017
.
Statistical Data Fusion
.
Singapore
:
World Scientific Publishing
.
21.
Kijima
,
M.
2013
.
Markov Processes for Stochastic Modeling
, 2nd ed.
Boca Raton, FL
:
CRC Press
.
22.
Ku
,
H. H.
1966
. “
Notes on the Use of Propagation of Error Formulas
.”
Journal of Research of the National Bureau of Standards
70C
, no. 
4
(October–December):
263
273
. https://doi.org/10.6028/jres.070C.025
23.
Li
,
J.
,
Hu
P.
,
Uzielli
M.
, and
Cassidy
M. J.
.
2018
. “
Bayesian Prediction of Peak Resistance of a Spudcan Penetrating Sand-Over-Clay
.”
Géotechnique
68
, no. 
10
(October):
905
917
. https://doi.org/10.1680/jgeot.17.P.154
24.
Li
,
J.
,
Wu
Z.
, and
Chen
J.
.
2022
. “
An Advanced Bayesian Parameter Estimation Methodology for Concrete Dams Combining an Improved Extraction Technique of Hydrostatic Component and Hybrid Response Surface Method
.”
Engineering Structures
267
: 114687. https://doi.org/10.1016/j.engstruct.2022.114687
25.
Martins
,
F. B.
,
Bressani
L. A.
,
Coop
M. R.
, and
Bica
A. V. D.
.
2001
. “
Some Aspects of the Compressibility Behaviour of a Clayey Sand
.”
Canadian Geotechnical Journal
38
, no. 
6
(December):
1177
1186
. https://doi.org/10.1139/t01-048
26.
Montgomery
,
D. C.
and
Runger
G. C.
.
2020
.
Applied Statistics and Probability for Engineers
.
Hoboken, NJ
:
John Wiley & Sons
.
27.
Phoon
,
K.-K.
,
Shuku
T.
, and
Ching
J.
, eds.
2023
.
Uncertainty, Modeling, and Decision Making in Geotechnics
.
Boca Raton, FL
:
CRC Press
.
28.
Rabinovich
,
S. G.
2005
.
Measurement Errors and Uncertainties: Theory and Practice
.
New York
:
Springer
.
29.
Rocchi
,
I.
and
Coop
M. R.
.
2014
. “
Experimental Accuracy of the Initial Specific Volume
.”
Geotechnical Testing Journal
37
, no. 
1
(January):
169
175
. https://doi.org/10.1520/GTJ20130047
30.
Roscoe
,
K. H.
,
Schofield
A.
, and
Thurairajah
A.
.
1963
. “
Yielding of Clays in States Wetter than Critical
.”
Géotechnique
13
, no. 
3
(September):
211
240
. https://doi.org/10.1680/geot.1963.13.3.211
31.
Roscoe
,
K. H.
and
Burland
J. B.
.
1968
.
On the Generalized Stress-Strain Behaviour of Wet Clay
.
Cambridge, UK
:
Cambridge University Press
.
32.
Shipton
,
B.
and
Coop
M. R.
.
2012
. “
On the Compression Behaviour of Reconstituted Soils
.”
Soils and Foundations
52
, no. 
4
(August):
668
681
. https://doi.org/10.1016/j.sandf.2012.07.008
33.
Skempton
,
A. W.
and
Sowa
V. A.
.
1963
. “
The Behaviour of Saturated Clays during Sampling and Testing
.”
Géotechnique
13
, no. 
4
(December):
269
290
. https://doi.org/10.1680/geot.1963.13.4.269
34.
Taylor
,
J. R.
1997
.
Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements
.
Melville, NY
:
University Science Books
.
35.
van de Schoot
,
R.
,
Depaoli
S.
,
King
R.
,
Kramer
B.
,
Märtens
K.
,
Tadesse
M. G.
,
Vannucci
M.
, et al.
2021
. “
Bayesian Statistics and Modelling
.”
Nature Reviews Methods Primers
1
: 1. https://doi.org/10.1038/s43586-020-00001-2
36.
Wu
,
Z.
,
Chen
C.
,
Zheng
Y.
,
Chen
J.
,
Bian
K.
, and
Li
J.
.
2024
. “
Analysis of Seepage Failure Probability for High Core Rockfill Dams during Rapid Drawdown of Reservoir Water Level
.”
Journal of Hydrology
633
(April): 131046. https://doi.org/10.1016/j.jhydrol.2024.131046
37.
Zhao
,
Z.
,
Congress
S. S. C.
,
Cai
G.
, and
Duan
W.
.
2022
. “
Bayesian Probabilistic Characterization of Consolidation Behavior of Clays Using CPTU Data
.”
Acta Geotechnica
17
, no. 
3
(March):
931
948
. https://doi.org/10.1007/s11440-021-01277-8
38.
Zheng
,
Y.
,
Baudet
B. A.
,
Delage
P.
,
Pereira
J. M.
, and
Sammonds
P.
.
2022
. “
Pore Changes in an Illitic Clay during One-Dimensional Compression
.”
Géotechnique
73
, no. 
10
(October):
917
932
. https://doi.org/10.1680/jgeot.21.00206
39.
Zheng
,
D.
,
Zhang
B.
, and
Chalaturnyk
R.
.
2025
. “
Quantifying Uncertainty of In-Situ Horizontal Stress and Geotechnical Parameters Using a Bayesian Inference Approach for Pressuremeter Tests
.”
Canadian Geotechnical Journal
62
(January):
1
23
. https://doi.org/10.1139/cgj-2023-0686
This content is only available via PDF.
You do not currently have access to this content.