Abstract

A new three-axis loading frame has been developed to enable real-time visualization of in-situ soil and rock structure interactions via X-ray tomography during small-scale model testing. The constructed frame is capable of performing a wide range of small-scale 1g tests and can accommodate monotonic and cyclic actuation under both load and displacement control. The compact size of the system enables remote multi-axis operation from within an X-ray cone-beam scanning bay, a capability which is owed to a comprehensive design process. Design and fabrication involved a blend of physical and numerical experiments to assess suitable construction materials and performance. In this scope, the new equipment is discussed and its capability is showcased.

References

1.
Abadie
,
C. N.
Cyclic Lateral Loading of Monopile Foundations in Cohesionless Soils
.” PhD diss.,
University of Oxford
,
2015
.
2.
Abadie
,
C. N.
,
Byrne
B. W.
, and
Houlsby
G. T.
.
2019
. “
Rigid Pile Response to Cyclic Lateral Loading: Laboratory Tests
.”
Géotechnique
69
, no. 
10
(October):
863
876
. https://doi.org/10.1680/jgeot.16.P.325
3.
Albiker
,
J.
,
Achmus
M.
,
Frick
D.
, and
Flindt
F.
.
2017
. “
1g Model Tests on the Displacement Accumulation of Large-Diameter Piles under Cyclic Lateral Loading
.”
Geotechnical Testing Journal
40
, no. 
2
(March):
173
184
. https://doi.org/10.1520/GTJ20160102
4.
Alia
,
M. A. K.
,
Younes
T. M.
, and
Subah
S. A.
.
2011
. “
A Design of a PID Self-Tuning Controller Using LabVIEW
.”
Journal of Software Engineering and Applications
4
, no. 
3
(March):
161
171
. https://doi.org/10.4236/jsea.2011.43018
5.
Alvarez-Borges
,
F.
,
Ahmed
S.
,
Madhusudhan
B. N.
, and
Richards
D.
.
2022
. “
Investigation of Pile Penetration in Calcareous Soft Rock Using X-ray Computed Tomography
.”
International Journal of Physical Modelling in Geotechnics
22
, no. 
1
(January):
38
52
. https://doi.org/10.1680/jphmg.20.00031
6.
Alvarez-Borges
,
F.
,
Burca
G.
,
Atwood
R.
,
James
A.
,
Wolstenholme
M.
, and
Ahmed
S.
.
2024
. “
Correlative Neutron and X-ray Tomography Imaging of Pile Installation in Chalk
.”
Géotechnique
74
, no. 
10
(September):
974
984
. https://doi.org/10.1680/jgeot.21.00318
7.
American Petroleum Institute.
2014
.
Geotechnical Foundation Design Considerations (Including Amendments to 2021), Technical Report API RP2 GEO
.
Washington, DC
:
American Petroleum Institute
.
8.
Arshad
,
M.
and
O’Kelly
B. C.
.
2014
. “
Development of a Rig to Study Model Pile Behaviour under Repeating Lateral Loads
.”
International Journal of Physical Modelling in Geotechnics
14
, no. 
3
(September):
54
66
. https://doi.org/10.1680/ijpmg.13.00015
9.
Arshad
,
M. I.
,
Tehrani
F. S.
,
Prezzi
M.
, and
Salgado
R.
.
2014
. “
Experimental Study of Cone Penetration in Silica Sand Using Digital Image Correlation
.”
Géotechnique
64
, no. 
7
(June):
551
569
. https://doi.org/10.1680/geot.13.P.179
10.
Åström
,
K.
and
Hägglund
T.
.
1995
.
PID Controllers: Theory, Design, and Tuning
, 2nd ed.
Research Triangle Park
,
NC
:
Instrument Society of America
.
11.
Autodesk.
2023
. “
Autodesk Fusion: More than CAD, It’s the Future of Design and Manufacturing
.”
Autodesk
. https://web.archive.org/web/20240514141427/https://www.autodesk.co.uk/products/fusion-360/overview.
12.
Bi
,
Z.
,
Gong
Q.
,
Guo
P.
, and
Cheng
Q.
.
2020
. “
Experimental Study of the Evolution of Soil Arching Effect under Cyclic Loading Based on Trapdoor Test and Particle Image Velocimetry
.”
Canadian Geotechnical Journal
57
, no. 
6
(June):
903
920
. https://doi.org/10.1139/cgj-2019-0205
13.
14.
Brecoflex
.
2023
. “
Products & Accessories
.” Brecoflex. https://web.archive.org/web/20240514141901/https://www.brecoflex.com/
15.
Buckley
,
R. M.
,
Jardine
R. J.
,
Kontoe
S.
,
Parker
D.
, and
Schroeder
F. C.
.
2018
. “
Ageing and Cyclic Behaviour of Axially Loaded Piles Driven in Chalk
.”
Géotechnique
68
, no. 
2
(February):
146
161
. https://doi.org/10.1680/jgeot.17.P.012
16.
Bull
,
D. J.
,
Smethurst
J. A.
,
Sinclair
I.
,
Pierron
F.
,
Roose
T.
,
Powrie
W.
, and
Bengough
A. G.
.
2020
. “
Mechanisms of Root Reinforcement in Soils: An Experimental Methodology Using Four-Dimensional X-ray Computed Tomography and Digital Volume Correlation
.”
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
476
, no. 
2237
(May): 20190838. https://doi.org/10.1098/rspa.2019.0838
17.
Canny
,
J.
1986
. “
A Computational Approach to Edge Detection
.”
IEEE Transactions on Pattern Analysis and Machine Intelligence
PAMI-8
, no. 
6
(November):
679
698
. https://doi.org/10.1109/TPAMI.1986.4767851
18.
Castellanza
,
R.
,
Parma
M.
,
Pescatore
V.
, and
Silvestro
G.
.
2009
. “
Model Footing Load Tests on Soft Rocks
.”
Geotechnical Testing Journal
32
, no. 
3
(May):
262
272
. https://doi.org/10.1520/GTJ101845
19.
Cerfontaine
,
B.
,
Ciantia
M. O.
,
Brown
M. J.
,
White
D. J.
, and
Sharif
Y. U.
.
2023
. “
DEM Study of Particle Scale Effect on Plain and Rotary Jacked Pile Behaviour in Granular Materials
.”
Computers and Geotechnics
161
: 105559. https://doi.org/10.1016/j.compgeo.2023.105559
20.
Cheng
,
Z.
,
Wang
J.
,
Coop
M. R.
, and
Ye
G.
.
2020
. “
A Miniature Triaxial Apparatus for Investigating the Micromechanics of Granular Soils with in Situ X-ray Micro-tomography Scanning
.”
Frontiers of Structural and Civil Engineering
14
, no. 
2
(April):
357
373
. https://doi.org/10.1007/s11709-019-0599-2
21.
Ciantia
,
M. O.
2022
. “
Installation Effects on Axial Performance of Monopiles in Chalk for Offshore Renewables
.” In
Proceedings of the Second Vietnam Symposium on Advances in Offshore Engineering: Sustainable Energy and Marine Planning
208
,
424
432
. Singapore: Springer. https://doi.org/10.1007/978-981-16-7735-9_47
22.
Ciantia
,
M. O.
,
Castellanza
R.
, and
Fernandez-Merodo
J. A.
.
2018
. “
A 3D Numerical Approach to Assess the Temporal Evolution of Settlement Damage to Buildings on Cavities Subject to Weathering
.”
Rock Mechanics and Rock Engineering
51
, no. 
9
(September):
2839
2862
. https://doi.org/10.1007/s00603-018-1468-3
23.
Ciantia
,
M. O.
,
Zheng
J.
,
Previtali
M.
, and
Knappett
J.
. n.d “
Simulation of Pile Installation in Chalk: Discrete and Continuum Approaches
.”
Paper presented at the XVIII European Conference on Soil Mechanics and Geotechnical Engineering
. Lisbon, Portugal, August 26–30,
2024
.
24.
Ciavaglia
,
F.
,
Carey
J.
, and
Diambra
A.
.
2017
. “
Monotonic and Cyclic Lateral Tests on Driven Piles in Chalk
.”
Proceedings of the Institution of Civil Engineers: Geotechnical Engineering
170
, no. 
4
(August):
353
366
. https://doi.org/10.1680/jgeen.16.00113
25.
Cnudde
,
V.
and
Boone
M. N.
.
2013
. “
High-Resolution X-ray Computed Tomography in Geosciences: A Review of the Current Technology and Applications
.”
Earth-Science Reviews
123
:
1
17
. https://doi.org/10.1016/j.earscirev.2013.04.003
26.
Dattola
,
G.
,
Ciantia
M. O.
,
Galli
A.
,
Blyth
L.
,
Zhang
X.
,
Knappet
J. A.
,
Castellanza
R.
,
Sala
C.
, and
Leung
K.
.
2020
. “
A Macroelement Approach for the Stability Assessment of Trees
.” In
Geotechnical Research for Land Protection and Development: Proceedings of CNRIG 2019
, vol.
40
,
417
426
. Cham, Switzerland:
Springer
. https://doi.org/10.1007/978-3-030-21359-6_44
27.
Davidson
,
C.
,
Brown
M. J.
,
Cerfontaine
B.
,
Al-Baghdadi
T.
,
Knappett
J.
,
Brennan
A.
,
Augarde
C.
, et al.
2022
. “
Physical Modelling to Demonstrate the Feasibility of Screw Piles for Offshore Jacket-Supported Wind Energy Structures
.”
Géotechnique
72
, no. 
2
(February):
108
126
. https://doi.org/10.1680/jgeot.18.P.311
28.
Desrues
,
J.
,
Andò
E.
,
Mevoli
F. A.
,
Debove
L.
, and
Viggiani
G.
.
2018
. “
How Does Strain Localise in Standard Triaxial Tests on Sand: Revisiting the Mechanism 20 Years on
.”
Mechanics Research Communications
92
:
142
146
. https://doi.org/10.1016/j.mechrescom.2018.08.007
29.
Doreau-Malioche
,
J.
,
Combe
G.
,
Viggiani
G.
, and
Toni
J. B.
.
2018
. “
Shaft Friction Changes for Cyclically Loaded Displacement Piles: An X-ray Investigation
.”
Géotechnique Letters
8
, no. 
1
(March):
66
72
. https://doi.org/10.1680/jgele.17.00141
30.
Ferreira
,
T. R.
,
Pires
L. F.
, and
Reichardt
K.
.
2022
. “
4D X-ray Computed Tomography in Soil Science: An Overview and Future Perspectives at Mogno/Sirius
.”
Brazilian Journal of Physics
52
, no. 
2
(April): 33. https://doi.org/10.1007/s13538-021-01043-x
31.
Gavin
,
K. G.
and
Lehane
B. M.
.
2003
. “
The Shaft Capacity of Pipe Piles in Sand
.”
Canadian Geotechnical Journal
40
, no. 
1
(February):
36
45
. https://doi.org/10.1139/t02-093
32.
Haiderali
,
A. E.
and
Madabhushi
G.
.
2016
. “
Evaluation of Curve Fitting Techniques in Deriving p–y Curves for Laterally Loaded Piles
.”
Geotechnical and Geological Engineering
34
, no. 
5
(October):
1453
1473
. https://doi.org/10.1007/s10706-016-0054-2
34.
Jardine
,
R. J.
,
Buckley
R. M.
,
Liu
T.
,
Andolfsson
T.
,
Byrne
B. W.
,
Kontoe
S.
,
Mcadam
R. A.
,
Schranz
F.
, and
Vinck
K.
.
2023
. “
The Axial Behaviour of Piles Driven in Chalk
.”
Géotechnique
74
, no. 
6
(May):
553
569
. https://doi.org/10.1680/jgeot.22.00041
35.
Karatza
,
Z.
,
Andò
E.
,
Papanicolopulos
S.-A.
,
Viggiani
G.
, and
Ooi
J. Y.
.
2019
. “
Effect of Particle Morphology and Contacts on Particle Breakage in a Granular Assembly Studied Using X-ray Tomography
.”
Granular Matter
21
, no. 
3
(August): 44. https://doi.org/10.1007/s10035-019-0898-2
36.
Khan
,
M. R.
,
Khan
A. A.
, and
Ghazali
U.
.
2015
. “
Speed Control of DC Motor under Varying Load Using PID Controller
.”
International Journal of Engineering (IJE)
9
, no. 
3
(August):
38
48
.
37.
Kikuchi
,
Y.
,
Morikawa
Y.
, and
Sato
T.
.
2008
. “
Plugging Mechanism in a Vertically Loaded Open-Ended Pile
.” In
Proceedings of the Second BGA International Conference on Foundations, ICOF 2008
,
169
180
. London:
IHS BRE Press
.
38.
Klinkvort
,
R. T.
Centrifuge Modelling of Drained Lateral Pile-Soil Response: Application for Offshore Wind Turbine Support Structures
.” PhD diss.,
Technical University of Denmark
,
2012
.
39.
Klinkvort
,
R. T.
,
Black
J. A.
,
Bayton
S. M.
,
Haigh
S. K.
,
Madabhushi
G. S. P.
,
Blanc
M.
,
Thorel
L.
,
Zania
V.
,
Bienen
B.
, and
Gaudin
C.
.
2018
. “
A Review of Modelling Effects in Centrifuge Monopile Testing in Sand
.” In
Physical Modelling in Geotechnics
, vol.
1
,
720
724
,
Boca Raton, FL
:
CRC Press
. https://doi.org/10.1201/9780429438660-108
40.
Larsson
,
E.
,
Gürsoy
D.
, and
Hall
S. A.
.
2023
. “
Kitchen-Based Light Tomography - A DIY Toolkit for Advancing Tomography - by and for the Tomography Community
.”
Tomography of Materials and Structures
1
: 100001. https://doi.org/10.1016/j.tmater.2022.100001
41.
Lauder
,
K. D.
,
Brown
M. J.
,
Bransby
M. F.
, and
Boyes
S.
.
2013
. “
The Influence of Incorporating a Forecutter on the Performance of Offshore Pipeline Ploughs
.”
Applied Ocean Research
39
:
121
130
. https://doi.org/10.1016/j.apor.2012.11.001
42.
LeBlanc
,
C.
,
Houlsby
G. T.
, and
Byrne
B. W.
.
2010
. “
Response of Stiff Piles in Sand to Long-Term Cyclic Lateral Loading
.”
Géotechnique
60
, no. 
2
(February):
79
90
. https://doi.org/10.1680/geot.7.00196
43.
Lehane
,
B. M.
and
Gavin
K. G.
.
2001
. “
Base Resistance of Jacked Pipe Piles in Sand
.”
Journal of Geotechnical and Geoenvironmental Engineering
127
, no. 
6
(June):
473
480
. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:6(473)
44.
Li
,
P.
,
Du
S.-J.
,
Shen
S.-L.
,
Wang
Y.-H.
, and
Zhao
H.-H.
.
2016
. “
Timoshenko Beam Solution for the Response of Existing Tunnels Because of Tunneling Underneath
.”
International Journal for Numerical and Analytical Methods in Geomechanics
40
, no. 
5
(April):
766
784
. https://doi.org/10.1002/nag.2426
45.
Liang
,
T.
Seismic Performance of Vegetated Slopes
.” PhD diss.
University of Dundee
,
2015
.
46.
Liu
,
C.
,
Tang
X.
,
Wei
H.
, and
Zhao
H.
.
2022
. “
Visualization Investigation of the Plugging Effect on Open-Ended Pipe Pile Jacked in Transparent Sand
.”
International Journal of Geomechanics
22
, no. 
10
(October): 04022176. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002455
47.
Liu
,
T.
,
Ahmadi-Naghadeh
R.
,
Vinck
K.
,
Jardine
R. J.
,
Kontoe
S.
,
Buckley
R. M.
, and
Byrne
B. W.
.
2022
. “
An Experimental Investigation into the Behaviour of Destructured Chalk under Cyclic Loading
.”
Géotechnique
74
, no. 
6
(May):
540
552
. https://doi.org/10.1680/jgeot.21.00199
48.
Marrazzo
,
G.
,
Ciantia
M.
,
Riccio
T.
,
Galli
A.
, and
Knappett
J.
.
2024
. “
Multi Axis Loading Tests on a Small Scale Tree Root Model
.” In
Fifth European Conference on Physical Modelling in Geotechnics
,
10. Delft, the Netherlands
:
ISSMGE
.
49.
Mayoral
,
J. M.
,
Pestana
J. M.
, and
Seed
R. B.
.
2016
. “
Multi-directional Cyclic p-y Curves for Soft Clays
.”
Ocean Engineering
115
:
1
18
. https://doi.org/10.1016/j.oceaneng.2016.01.033
50.
McCarel
,
S. C.
and
Beard
R.
1984
.
Laboratory Investigation on Piles in Calcareous Sediments, Report TN-1714
.
Port Hueneme, CA
:
Naval Civil Engineering Laboratory
.
51.
Monforte
,
L.
,
Arroyo
M.
,
Carbonell
J. M.
, and
Gens
A.
.
2022
. “
Large-Strain Analysis of Undrained Smooth Tube Sampling
.”
Géotechnique
72
, no. 
1
(January):
61
77
. https://doi.org/10.1680/jgeot.19.P.354
52.
Motors
MFA
.
2023
. “
Welcome to MFA Como Drills Website
.”
MFA/Como Drills
. https://web.archive.org/web/20240702202730/https://mfacomodrills.com/
53.
Muir Wood
,
D.
2004
.
Geotechnical Modelling
, 1st ed.
London
:
CRC Press
. https://doi.org/10.1201/9781315273556
54.
Murff
,
J. D.
1987
. “
Pile Capacity in Calcareous Sands: State if the Art
.”
Journal of Geotechnical Engineering
113
, no. 
5
(May):
490
507
, https://doi.org/10.1061/(ASCE)0733-9410(1987)113:5(490)
55.
National Instruments Corp.
2023
. “
What Is NI LabVIEW?” National Instruments
. https://web.archive.org/web/20240514141631/https://www.ni.com/en/shop/labview.html
56.
Nyquist
,
H.
1928
. “
Certain Topics in Telegraph Transmission Theory
.”
Transactions of the American Institute of Electrical Engineers
47
, no. 
2
(April):
617
644
. https://doi.org/10.1109/T-AIEE.1928.5055024
57.
Oliynyk
,
K.
,
Ciantia
M. O.
, and
Tamagnini
C.
.
2021
. “
A Finite Deformation Multiplicative Plasticity Model with Non–local Hardening for Bonded Geomaterials
.”
Computers and Geotechnics
137
: 104209. https://doi.org/10.1016/j.compgeo.2021.104209
58.
Omega.
2023
. “
Miniature Tension & Compression Stud-Mount Load Cells, ±10 to ± 5000 Newtons
.”
Omega
:
A DwyerOmega Brand
. https://web.archive.org/web/20240514140229/https://www.omega.co.uk/pptst/LCMFD.html
59.
Otani
,
J.
,
Pham
K.
, and
Sano
J.
.
2006
. “
Investigation of Failure Patterns in Sand Due to Laterally Loaded Pile Using X-ray XCT
.”
Soils and Foundations
46
, no. 
4
(August):
529
535
. https://doi.org/10.3208/sandf.46.529
60.
Paik
,
K.
,
Salgado
R.
,
Lee
J.
, and
Kim
B.
.
2003
. “
Behavior of Open- and Closed-Ended Piles Driven into Sands
.”
Journal of Geotechnical and Geoenvironmental Engineering
129
, no. 
4
(April):
296
306
. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:4(296)
61.
Peng
,
J. R.
,
Clarke
B. G.
, and
Rouainia
M.
.
2006
. “
A Device to Cyclic Lateral Loaded Model Piles
.”
Geotechnical Testing Journal
29
, no. 
4
(July):
341
347
. https://doi.org/10.1520/GTJ100226
62.
Perbawa
,
A.
,
Gramajo
E.
,
Finkbeiner
T.
, and
Santamarina
J. C.
. n.d “
Global vs Local Strain Measurements in Triaxial Tests – Implications
.”
Paper presented at the 53rd U.S. Rock Mechanics/Geomechanics Symposium
,
New York City
: June 2019.
63.
Phillips
,
D. H.
and
Lannutti
J. J.
.
1997
. “
Measuring Physical Density with X-ray Computed Tomography
.”
NDT & E International
30
, no. 
6
(December):
339
350
. https://doi.org/10.1016/S0963-8695(97)00020-0
64.
Poulos
,
H. G.
and
Hull
T. S.
.
1989
. “
The Role of Analytical Geomechanics in Foundation Engineering
.” In
Foundation Engineering: Current Principles and Practices
,
1578
1606
. New York:
American Society of Civil Engineers
.
65.
Previtali
,
M.
,
Ciantia
M. O.
, and
Riccio
T.
.
2023
. “
Numerical Installation Of OE Piles In Soft Rocks Within The GPFEM Framework
.” In
Proceedings of the 10th European Conference on Numerical Methods in Geotechnical Engineering
,
322
328
. London:
International Society for Soil Mechanics and Geotechnical Engineering
. https://doi.org/10.53243/NUMGE2023-322
66.
Riccio
,
T.
and
Ciantia
M.
.
2024
.
ICE-PICK Multi-axis Loading Frame Repository
.
Dundee, Scotland
:
University of Dundee
. https://doi.org/10.20933/100001306
67.
Riccio
,
T.
,
Previtali
M.
,
Ciantia
M. O.
, and
Brown
M. J.
.
2023
. “
P-Y Response in Porous Rock: Numerical Derivation with Experimental Validation
.” In
SUT OSIG 2023 Conference Proceedings
,
1357
1362
. London:
Society for Underwater Technology
.
68.
Riccio
,
T.
,
Previtali
M.
, and
Ciantia
M. O.
.
2024
. “
4D Model Tests of CPT Pile Design Performance in Chalk
.” In
Eurock 2024 - New Challenges in Rock Mechanics and Rock Engineering - An ISRM Regional Symposium
,
613
618
. Abingdon, UK:
CRC Press/Balkema
.
69.
Robinson
,
S.
,
Brown
M. J.
,
Matsui
H.
,
Brennan
A.
,
Augarde
C.
,
Coombs
W.
, and
Cortis
M.
.
2019
. “
Centrifuge Testing to Verify Scaling of Offshore Pipeline Ploughs
.”
International Journal of Physical Modelling in Geotechnics
19
, no. 
6
(November):
305
317
. https://doi.org/10.1680/jphmg.17.00075
70.
Sato
,
T.
,
Onda
K.
, and
Otani
J.
.
2018
. “
Development of a New Loading Test Apparatus for Microfocus X-ray XCT and Its Application to the Investigation of Soil Behavior Surrounding Driven Open-Section Piles
.”
Soils and Foundations
58
, no. 
3
(June):
776
785
. https://doi.org/10.1016/j.sandf.2018.03.004
71.
Schnaid
,
F.
and
Houlsby
G. T.
.
1991
. “
An Assessment of Chamber Size Effects in the Calibration of in Situ Tests in Sand
.”
Géotechnique
41
, no. 
3
(September):
437
445
. https://doi.org/10.1680/geot.1991.41.3.437
72.
Smith
,
J.
and
Augarde
C.
.
2015
. A Review of X-ray Computed Tomography in Geotechnical Research, Technical Report. Durham, UK: Durham University.
73.
Su
,
D.
2012
. “
Resistance of Short, Stiff Piles to Multidirectional Lateral Loadings
.”
Geotechnical Testing Journal
35
, no. 
2
(March):
313
329
. https://doi.org/10.1520/GTJ103840
74.
The Aluminum Association
.
2015
.
Aluminum Design Manual.
Arlington, VA
:
The Aluminum Association
.
75.
TE Connectivity.
2023
. “
TE Spring Pot Displacement Sensors
.”
TE Connectivity
. https://web.archive.org/web/20240514135551/https://www.te.com/en/product-SP1-12.html
76.
Timoshenko
,
S. P.
and
Goodier
J. N.
.
1970
.
Theory of Elasticity
.
New York
:
McGraw-Hill.
77.
Tudisco
,
E.
,
Andò
E.
,
Cailletaud
R.
, and
Hall
S. A.
.
2017
. “
TomoWarp2: A Local Digital Volume Correlation Code
.”
SoftwareX
6
:
267
270
. https://doi.org/10.1016/j.softx.2017.10.002
78.
Viggiani
,
G.
,
Andò
E.
,
Takano
D.
, and
Santamarina
J. C.
.
2015
. “
Laboratory X-ray Tomography: A Valuable Experimental Tool for Revealing Processes in Soils
.”
Geotechnical Testing Journal
38
, no. 
1
(January):
61
71
. https://doi.org/10.1520/GTJ20140060
79.
Wessolly
,
L.
and
Erb
M.
.
2016
.
Manual of Tree Statics and Tree Inspection
.
Berlin
:
Patzer Verlag
.
80.
White
,
D. J.
and
Bolton
M. D.
.
2004
. “
Displacement and Strain Paths during Plane-Strain Model Pile Installation in Sand
.”
Géotechnique
54
, no. 
6
(August):
375
397
. https://doi.org/10.1680/geot.2004.54.6.375
81.
Zhang
,
X.
,
Knappett
J. A.
,
Leung
A. K.
,
Ciantia
M. O.
,
Liang
T.
, and
Danjon
F.
.
2020
. “
Small-Scale Modelling of Root-Soil Interaction of Trees under Lateral Loads
.”
Plant and Soil
456
, nos. 
1–2
(November):
289
305
. https://doi.org/10.1007/s11104-020-04636-8
82.
Zhang
,
X.
,
Knappett
J. A.
,
Ciantia
M. O.
,
Leung
A. K.
,
Wang
H.
, and
Liang
T.
.
2024
.
"Root Size Effects on Transverse Root-Soil Interactions.”
Computers and Geotechnics
165
: 105860. https://doi.org/10.1016/j.compgeo.2023.105860.
83.
Zhao
,
T.
and
Wang
Y.
.
2018
. “
Interpretation of Pile Lateral Response from Deflection Measurement Data: A Compressive Sampling-Based Method
.”
Soils and Foundations
58
, no. 
4
(August):
957
971
. https://doi.org/10.1016/j.sandf.2018.05.002
84.
Zhao
,
T.
and
Wang
Y.
.
2020
. “
Differentiation of Discrete Data with Unequal Measurement Intervals and Quantification of Uncertainty in Differentiation Using Bayesian Compressive Sampling
.”
Computers and Geotechnics
122
: 103537. https://doi.org/10.1016/j.compgeo.2020.103537
85.
Zheng
,
J.-H.
,
Qi
C.-G.
,
Zhao
X.
,
Wang
X.-Q.
, and
Shan
Y.-L.
.
2020
. “
Experimental Simulation on Open-Ended Pipe Pile Penetration Using Transparent Granule
.”
KSCE Journal of Civil Engineering
24
, no. 
8
(August):
2281
2292
. https://doi.org/10.1007/s12205-020-1235-3
86.
Zheng
,
J.
,
Previtali
M.
,
Ciantia
M.
, and
Knappett
J.
.
2023
. “
Comparison of Continuum (PFEM) and Discrete (DEM) Approaches for Large Insertion BVPS in Soft Rocks
.” In
VIII International Conference on Particle-Based Methods
,
1
9
. Barcelona, Spain:
CIMNE
. https://doi.org/10.23967/c.particles.2023.037
87.
Zheng
,
J.
,
Previtali
M.
,
Knappett
J. A.
, and
Ciantia
M. O.
.
2022
. “
Coupled DEM-FDM Investigation of Centrifuge Acceleration on the Response of Shallow Foundations in Soft Rocks
.” In
Proceedings of the 10th International Conference on Physical Modelling in Geotechnics
,
264
267
. London:
ISSMGE
.
This content is only available via PDF.
You do not currently have access to this content.