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HP-TACO: A High-Pressure TriAxial COmpression Apparatus
HP-TACO: A High-Pressure TriAxial COmpression Apparatus for In-Situ
X-ray Measurements in Geomaterials
G. Shahin1and R.C. Hurley2
1)Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, MD USA
2)Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, MD USA
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD USA
(*Electronic mail: rhurley6@jhu.edu)
(Dated: 15 November 2022)
Triaxial compression experiments are commonly used to characterize the elastic and inelastic behavior of geomate-
rials. In-situ measurements of grain kinematics, particle breakage, stresses, and other microscopic phenomena have
seldom been made during such experiments, particularly at high pressures relevant to many geologic and man-made
processes, limiting our fundamental understanding. To address this issue, we developed a new triaxial compression
device called HP-TACO (High-Pressure TriAxial COmpression Apparatus). HP-TACO is a miniaturized conventional
triaxial compression apparatus permitting confining pressures up to 50 MPa and deviatoric straining of materials, while
also allowing in-situ x-ray measurements of grain-scale kinematics and stresses. Here, we present the design of and first
results from HP-TACO during its use in laboratory and synchrotron settings to study grain-scale kinematics and stresses
in triaxially-compressed sands subjected to 15 MPa and 30 MPa confining pressure. The data highlights the unique ca-
pabilities of HP-TACO for studying the high-pressure mechanical of sands, providing new insight into micromechanical
processes occurring during geologic and man-made processes.
I. INTRODUCTION
The mechanical behavior of soils and rocks in triaxial states
of stress governs their performance in man-made settings and
their contribution to geologic processes in the Earth’s up-
per crust. Laboratory studies employing conventional triaxial
stress experiments have been employed extensively to char-
acterize the mechanical behavior of geomaterials across pres-
sures regimes1,2. In such tests, two principal stresses are im-
posed on a sample. Specifically, imposing axial strain under a
constant pressure in the fluid surrounding the sample (which
is typically within a sealed membrane) induces a proportional
increase in the first and third principal stresses. Conventional
triaxial testing has revealed the peak strength of rocks and
soils, the strain localization patterns that develop after peak
strength, and the brittle-to-ductile transitions that frequently
occur as confining pressures are increased1–3.
In recent decades, in-situ x-ray imaging has been used to
monitor microscopic processes of rocks and soils during tri-
axial testing, revealing rich grain-scale kinematics and de-
formation patterns3–8. Such measurements play an important
role in our understanding of the micromechanics of strain lo-
calization and the local fluctuations in particle motion and
porosity during macroscopic soil testing. Prior triaxial test-
ing on sands with in-situ x-ray imaging has primarily been
limited to pressures below about 7 MPa6, below the level
relevant to many geologic and man-made processes. Other
in-situ measurements, such as acoustic emissions, have been
performed at higher pressures9. Recent testing on rocks
with in-situ imaging has employed confining pressures of
100 MPa and axial stresses of 200 MPa, providing access to
the brittle-to-ductile transition in some rocks, such as porous
limestone10–13. The more common low-pressure regimes (<7
MPa) are below those required to induce significant particle
fragmentation without deviatoric loading; such a pressure is
critical for anchoring the plastic yield surface to the hydro-
static axis in pressure-dependent plasticity models. Moreover,
testing has not typically employed measurements such as 3D
x-ray diffraction (3DXRD), which enables quantifying grain-
resolved stress tensors within individual grains14. We have
therefore developed a testing capability that provides access
to higher pressures and permits use with a variety of x-ray fa-
cilities and measurement modalities, thanks to a combination
of a unique design and light weight.
In this paper, we describe a new triaxial apparatus for test-
ing a variety of geomaterials in laboratory and synchrotron
x-ray facilities with confining pressures up to 50 MPa and ax-
ial stresses over 1 GPa in the smallest specimens. In Sec. II
we describe the apparatus design. In Sec. III we describe the
sample preparation procedures used in executing experiments
in HP-TACO. In Sec. IV we briefly describe two experiments
and preliminary results. In Sec. V we provide conclusions.
Technical drawings for reproduction of the instrument are pro-
vided in the supplementary materials.
II. LOAD FRAME DESIGN
The High-Pressure TriAxial COmpression Apparatus (HP-
TACO) described in this paper is a miniaturized version of
a conventional triaxial apparatus. It is not a true triaxial ap-
paratus but, as is conventional in soil and rock mechanics,
employs a pressurized fluid on the outside of a membrane
to constrain two of three principal stresses on samples. HP-
TACO was designed to: permit high-resolution laboratory-
based XRT imaging in an RX Solutions EasyTom 160; permit
high-resolution synchrotron-based XRT imaging and 3DXRD
measurements; permit lateral confining pressures up to 50
MPa on samples; permit axial compression of samples; ac-
commodate sample sizes ranging from 1.5 mm diameter for
synchrotron experiments to 15 mm diameter for laboratory ex-
HP-TACO: A High-Pressure TriAxial COmpression Apparatus 2
periments.
With these goals in mind, HP-TACO was designed and con-
structed with five critical subsystems: a light-weight chassis; a
fluid-control system for cell pressure; an axial loading system;
a sample environment system; a computerized control system.
Here, we briefly describe each subsystem. The subsystems are
visible in Fig. 1, which shows HP-TACO in operation within
a laboratory x-ray tomography machine (Fig. 1). The internal
features and HP-TACO components are also illustrated in Fig.
1. More technical details are provided in Table I and dimen-
sioned drawings are provided as supplementary material.
The load frame chassis was constructed primarily using
machinable Al-6061 and off-the-shelf T-slotted aluminum
framing. The chassis accommodates a dumbbell-shaped x-
ray translucent pressure cell (in the fluid system) and an axial
loading system. The chassis is lightweight, providing versatil-
ity for mounting in laboratory x-ray machines and at a variety
of synchrotron x-ray facilities where rotation stage weight re-
strictions are as low as 10 kg.
The fluid system contains and pressurizes the confining
fluid imposed on the exterior of membranes containing sam-
ples. As shown in Fig. 1, its critical features include:
a customized 20 mm diameter, 2 mm wall thickness Al-
6061 pressure cell which permits, with the low instrument
weight amenable for use on precision rotation stages, high-
resolution XRT and 3DXRD up to confining pressures of at
least 50 MPa; a Cetoni Nemesys 50 MPa syringe pump with
high-pressure stainless-steel tubing; an analog pressure gauge
to monitor the cell pressure during experiments; a quick-
disconnect feature for disconnecting the pump from the pres-
sure cell during measurements while maintaining the cham-
ber pressure in the cell. The dumbbell shape of the pressure
cell accommodates the approach of cone beam laboratory x-
ray sources close to the sample location to enhance geometric
magnification.
The axial loading system imposes axial stress on samples.
The system contains the following features, many of which
are visible in Fig. 1: a 1-inch stroke NEMA 34 linear stepper
motor actuator (Haydon Kerk Pittman) with 2500 counts-per-
revolution encoder and maximum load capacity of approxi-
mately 2250 N; a miniature 2225 N load cell (Futek LCM300)
for monitoring the axial load imposed on a sample; a drive
piston connected in line with the load cell and actuator and
featuring a hemispherical tip to impose axial sample loads.
The sample environment system maintains the intended ge-
ometry and environmental conditions of samples. A portion
of the system is visible in Fig. 1 and features: a support pis-
ton cylinder that remains fixed to the load frame base during
sample changes and features a central channel connected to a
suction port in the base; a quick-disconnect suction port in the
load frame base that can be used in conjunction with a hand-
operated vacuum pump to draw a light vacuum in the sample
environment; variable-diameter platens that can be bolted into
the top of the support piston to accommodate samples with di-
ameters of 1.5, 1.8, 5, 10, and 15 mm; variable-diameter neo-
prene membranes (Piercan USA) that can be placed around
platens and samples and sealed with vacuum grease and a vac-
uum drawn in the sample environment.
HP-TACO’s final subsystem is a computerized control and
monitoring system. The system contains the following fea-
tures: a Windows 10 laptop with appropriate Nemesys Qmix-
ELEMENTS (for the pump), LabView (for the load cell),
and IDEA Drive (for the actuator) software; an Ametek
PCM48026E IDEA Drive Stepper Motor Controller to which
the actuator connects and which connects to the laptop for
monitoring actuator extension; a high speed and resolution
USB encoder which connects to the load cell and computer
and aids in monitoring the axial load on the sample through
LabView; a 24 V 200 Amp power supply for the actuator.
In addition to the control system’s software and hardware,
HP-TACO also features variable-length cable arrays, ranging
from 5 m to 10 m. These arrays help to manage the ten wires
needed for connecting the actuator’s encoder and power input
to the stepper motor controller and power supply. The step-
per motor controller and power supply must be placed outside
of x-ray tomography machines, or must be located away from
sample environments in synchrotron x-ray hutches, necessi-
tating long cables for cable strain relief.
III. SAMPLE PREPARATION AND EXPERIMENT
PROCEDURE
The workflow of HP-TACO involves sample preparation,
experiment execution, and in-situ measurements. First, sam-
ples are prepared outside of HP-TACO. Membranes are placed
around the variable-diameter platens and sand is poured into
the membranes to a desired height, or a drilled and parallelised
rock sample is placed within the membrane. A small anvil is
inserted into the top of the membrane and the sample is sealed
with vacuum grease and bolted into the support piston. The
pressure cell is then screwed on the load frame base. A light
vacuum is optionally drawn in the sample environment using
a hand pump. The pressure cell is filled with tap water before
the axial loading system is placed on top and the pressure cell
is sealed.
Next, with the drive piston not in contact with the anvil,
the chamber pressure is gradually raised to a desired level at
10 kPa/s using the QmixELEMENTS software and the inter-
nal pressure monitor on the Cetoni Nemesys. For synchrotron
studies with small samples, the pump-tube connected to the
cell is then disconnected at the quick-disconnect feature which
maintains the chamber pressure. HP-TACO is then mounted
in the x-ray path so that the remaining steps of the prepara-
tion and experiment can proceed while monitoring the sample
with in-situ x-ray radiography. For laboratory studies with
larger samples, the pump remains connected during this stage
and a servo-control algorithm maintains the constant chamber
pressure during linear actuator extension. The drive piston
connected to the linear actuator is brought into grazing con-
tact with the anvil touching the top of the sample using the
IDEA Drive software. Axial loading proceeds by extending
the stepper motor by a desired distance. The distance is typ-
ically small and is dictated by the need to maintain strains of
2% or less between sequential XRT images for digital image
correlation or discrete particle tracking. The axial load mea-
HP-TACO: A High-Pressure TriAxial COmpression Apparatus 3
10
5
5
6
6
7
9
9
8
1
1
2
23
4
10
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x-ray
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FIG. 1. HP-TACO. (1) NEMA actuator, (2) plate, (3) Futek force-cell, (4) custom-built (CB) adapter, (5) CB plate, (6) CB piston, (7) CB pin,
(8) pressure gauge, (9) CB pressure cell, (10) Cetoni Nemesys 50 MPa syringe pump (11) Neoprene membrane (Piercan USA) containing a
sample, (12) CB anvil, (13) CB piston, (14) O-ring, (15) O-ring, (16) CB base plate, (18) high-pressure stainless steel tube, (19) high-pressure
quick disconnect system, and (20) high-pressure valve. The right figure shows HP-TACO in operation inside an X-ray tomography system.
TABLE I. HP-TACO components, manufacturer/supplier and model number. Numbers are linked to Figure 1. DW refers to drawings shared
as supplementary information. CB referes to custom-built.
Num Item Supplier Model Number
1 Actuator Haydon Kerk Pittman Size 34 Series 87000 Captive Lead-Screw Linear Actuator
2 Frame item CB DW8
3 Force cell Futek LCM 300
4 Frame item CB DW9
5 Frame item CB DW5
6 Frame item CB DW6
7 Frame item CB DW7
8 Pressure guage McMaster-Carr 3842K41
9 Frame item CB DW2
10 Pump Cetoni Nemesys 50 MPa
11 Neoprene membrane containing sample Piercan or CB
12 Frame item CB DW4
13 Frame item CB DW3
14 O-ring McMaster-Carr 9452K117
15 O-ring McMaster-Carr 9452K6
16 Frame item CB DW1
17 Air quick disconnect McMaster-Carr 5012K124
18 Tubes 1/16" McMaster-Carr 51755K36
19 Quick-disconnect McMaster-Carr 5220T17 3907N11
20 Valve McMaster-Carr 4715K11
sured by the load cell is monitored in LabView for any sig-
nificant stress drops indicative of sample failure or rearrange-
ment. The pump tube connected to the cell is then discon-
nected to allow the load frame to rotate freely in preparation
of acquiring x-ray measurements.
Between each increment of axial loading, in-situ XRT and
3DXRD (at synchrotron facilities) measurements are made.
These measurements involve rotating the entire HP-TACO ap-
paratus 180◦or 360◦for XRT measurements and then again
360◦for 3DXRD measurements. During the first rotation, be-
tween 1120 and 2881 x-ray radiographs are obtained for labo-
ratory and synchrotron XRT, respectively. During the second
HP-TACO: A High-Pressure TriAxial COmpression Apparatus 4
rotation, if performing 3DXRD, 3600 diffraction patterns are
obtained, each at 0.1◦angular increments of rotation.
After completing one x-ray scan, the pump is reconnected
to the pressure cell. The pump and the quick-disconnect fea-
ture are brought to a pressure equal to the pressure inside the
cell before the valve is opened to connect the pump fluid and
the cell fluid. The pump is set on a servo-control mode to
maintain the constant cell pressure while another loading in-
crement is being carried out.
IV. INITIAL EXPERIMENTS AND RESULTS
There were two initial experimental campaigns performed
with HP-TACO. The first campaign involved the compression
of Ottawa sand under confining pressures ranging from 10
MPa to 45 MPa with in-situ XRT at JHU. The goal of this
campaign was to quantify the micro- and meso-scale mecha-
nisms (grain breakage, deformation banding) of sand in sup-
port of developing a mechanism-based constitutive model15.
The second experimental campaign involved axial compres-
sion of single-crystal quartz grains under confining pres-
sures ranging from 25 MPa to 40 MPa with in-situ XRT and
3DXRD at APS. The goal of this campaign was to measure
particle-resolved stress and force evolution during deforma-
tion band development and progression. The remainder of this
section describes the initial experiments and results.
A. Definition of sample stresses
The axial load measured by the load cell minus to the load
after cell pressurization will be denoted n, the cell pressure
will be denoted pc, and the initial cross-sectional area of a
sample will be denoted a. Sample stress is given by
σi j =
n
a+pc0 0
0pc0
0 0 pc
.(1)
The mean, p, and the deviatoric stress, q, are given by
p=1
3σi jδi j ,and q=r3
2si jsi j ,(2)
where si j =σij −pδi j is the deviatoric stress tensor.
B. First experiments: Ottawa sand with XRT
Experiments were performed at JHU in an RX Solutions
EasyTom 160 MicroCT. Ottawa sand (Humboldt Co., d50 =
175 µm) was poured into a ≈5 mm Piercan neoprene mem-
brane (mounted onto a 5 mm diameter aluminum platen) to a
height of 10 mm. An aluminum platen was inserted into the
membrane on top of the sample and sample preparation pro-
ceeded as described in Sec. III. The fluid in the pressure cel
FIG. 2. Triaxial compression test on Ottawa sand. (a) Stress-strain
curve for test at 15 MPa confining pressure. Insets show XRT im-
ages at four strain levels indicated by numbers. (b) Horizontal slice
through XRT image at 0% strain. (c) Vertical slice through XRT im-
age at 14% axial strain. (d) Grain displacements found from dDIC
between three strain increments as described in text.
(outside of the membranes containing samples) were pressur-
ized to between 10-45 MPa with the goal of studying the mi-
cromechanics underlying the brittle-to-ductile transition. The
experiment featuring 15 MPa confining pressure is presented
in this paper as an example. Other tests will be described in a
dedicated publication elsewhere.
The specimen was deformed with XRT measurements
made at 2% axial strain increments. XRT measurements in-
volved acquiring radiographs at 1,120 angles (eight images
per angle) equally over 360◦rotation with an x-ray source
voltage of 100 kV and current of 70 W. The stress-strain curve
is shown in Fig. 3a. Stress drops observed in this curve reflect
the sample stress relaxation that occurs during XRT measure-
ments. The stress is quickly recovered upon further axial load-
ing. The stress-strain curve reflects sample strengthening.
XRT images were reconstructed using the X-Act software
provided by RX Solutions. Images featured a pixel size of
approximate (6 µm)3. A horizontal slice of an XRT image at
scan number 1 is shown in Fig. 2b showing ample solid-to-
void contrast for image segmentation16. A vertical slice of the
XRT image of scan number 7 is presented in Fig. 2c, showing
deformation patterns indicative of strain localization. XRT
images were processed to separate the grains from the void
space using a binarization operation that takes advantage of
Otsu’s method16. Individual grains were also labeled using
a watershed segmentation algorithm. After binarization and
segmentation, continuum digital image correlation (DIC) and
discrete digital image correlation (dDIC) were performed in
SPAM with the goal of quantifying the continuum strains and
the translation and rotation of individual particles16. Figure 2d
shows the result of displacement tracking using dDIC between
three incremental strain steps during the experiment. Strain
localization in an inclined shear band is evident, consistent
HP-TACO: A High-Pressure TriAxial COmpression Apparatus 5
with the dashed yellow lines in Fig. 2c. Additional results
will be provided in a separate publication.
C. First experiments: single crystal quartz with XRT and
3DXRD
Experiments on single crystal quartz were performed at
the APS beamline ID-1-E with in-situ XRT and 3DXRD,
the latter measurement to obtain the stress tensors within in-
dividual particles17. The grains used in these experiments
were single-crystal quartz, ball- and jet-milled from blocks of
hydrothermally-grown quartz (Sawyer Technical Materials),
as in our prior studies18. Grains were sieved to a size of ap-
proximately 106 - 150 µm before experiments.
Sample and HP-TACO preparation procedures were nearly
identical to those used in the experiments on Ottawa sand de-
scribed in Sec. IV B except samples were only 1.5 mm in
diameter and membranes were custom-made from a silicone
rubber material (AS40 Addition Cure Silicone Rubber from
Easy Composites UK). Samples were prepared to be approxi-
mately 2.5 mm in height before axial compression.
The experiment shown here involved pressurizing the sam-
ple to 30 MPa and then quasi-statically axially-compressing
the sample in displacement increments of 50 µm each. Be-
tween each displacement increment, XRT and 3DXRD mea-
surements were made by rotating the entire load frame 360◦
twice. During the first rotation, 2881 x-ray radiographs
were obtained at 0.125◦angular increments using a Retiga
4000DC CCD camera; XRT reconstructions were performed
in TomoPy19. During the second rotation, 3600 x-ray diffrac-
tion patterns were obtained at 0.1◦angular increments using a
GE-41RT area detector; 3DXRD analysis was performed us-
ing MIDAS20. The measurement and data analysis methods
will be described in more depth elsewhere.
A total of 12% axial strain was imposed on the sample com-
pressed to 30 MPa confining pressure. The chamber pressure
was monitored manually between x-ray measurements by in-
specting the analog pressure gauge (Fig. 1) and did not change
by more than 5% from its initial value throughout the duration
of any of the experiments.
Figure 3a shows a horizontal slice through the XRT image
obtained at zero sample strain, showing decent solid-to-void
contrast for image segmentation. Figure 3b shows the maxi-
mum intensity over all 3,600 diffraction patterns obtained dur-
ing diffraction measurements. Portions of this image highlight
the aluminum (Al) rings generated by pressure cell as well as
the SiO2rings from the sample. Clear diffraction peaks are
visible in individual diffraction images used to obtain Fig. 3b.
The analysis of these peaks for grain stresses and orientations
will be presented in-depth in a future publication. Figure 3c
shows the stress-strain curve for the experiment with insets
showing XRT images at two strain.
V. CONCLUSIONS
We developed a new triaxial compression apparatus for
subjecting sands and rocks to confining pressures up to 50
MPa. Our first results support our ability to reach desired
sample stress levels while also performing in-situ XRT and
3DXRD measurements. Ongoing experiments on sand and
sandstone are being performed: (1) to understand the kine-
matics and particle stress fluctuations associated with local re-
arrangements occurring within deformation bands; (2) to un-
derstand the microscale mechanisms of deformation during
triaxial compression of rocks.
SUPPLEMENTAL MATERIAL
See supplemental material for dimensioned drawings of all
custom-built components of the instrument described in this
paper.
ACKNOWLEDGMENTS
The authors gratefully acknowledge funding from the U.S.
NSF Award CBET-1942096 and the U.S. Defense Threat Re-
duction Agency (DTRA) Award #HDTRA-1-20-2-0001. The
content of the information does not necessarily reflect the po-
sition or the policy of the federal government, and no official
endorsement should be inferred. We acknowledge the APS
for synchrotron beamtime. Use of the APS, an Office of Sci-
ence User Facility operated for the US Department of Energy
(DOE) Office of Science by Argonne National Laboratory,
was supported by US DOE Contract DE-AC02-06CH11357.
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
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