ARTIGO DE GEOTECNIA I

Prévia do material em texto

Arshad, M. I. et al. (2014). Ge´otechnique 64, No. 7, 551–569 [http://dx.doi.org/10.1680/geot.13.P.179]
551
Experimental study of cone penetration in silica sand using digital
image correlation
M. I . ARSHAD�, F. S . TEHRANI�, M. PREZZI� and R. SALGADO�
The problem of cone penetration, particularly deep penetration, remains one of the most challenging
in geotechnical engineering. It involves large displacements, rotations and deformation of soil
elements in the path of the cone as well as complex response of the soil, including crushing and the
development of large mean stresses, to the displacements imposed by the penetration process. As a
result, rigorous theoretical solutions are not available for this problem, and experimental simulations
of penetration provide insights that would not otherwise be available. This paper presents the results
of a series of cone penetration tests performed in a half-circular chamber in sand samples prepared
with three silica sands with different crushability. Cone resistance was measured, and digital images of
the cone penetrating into the sand samples were acquired simultaneously during the entire penetration
process. The digital image correlation (DIC) technique was then used to process these images to
obtain the soil displacement field resulting from cone penetration. The results of DIC analyses and
measured cone resistance suggest that the soil displacement around an advancing cone depends on the
density and crushability of the sand, as well as the depth of penetration. Tests on silica sands with
different degrees of crushability show that, for shallow penetration, the displacement vectors near the
cone tip are essentially vertical for crushable sand, transitioning to subvertical for less crushable sands.
However, for deep penetration, the displacement vectors near the cone tip are mostly vertical below
the cone tip. Crushing was observed immediately below and around the cone tip for all sands tested.
After passage of the cone, the crushed particles form a thin, crushed particle band of thickness equal
to about 2.5D50 along the shaft, with a smaller percentage of crushed particles observed within an
outer band with thickness equal to 4D50.
KEYWORDS: model tests; particle crushing/crushability; piles; sands; soil/structure interaction
INTRODUCTION
The cone penetration test (CPT) has become a key tool in
site characterisation, partly owing to its simplicity, and partly
as a result of the development of cone resistance-based
correlations for shallow foundation design (Schmertmann,
1970; Mayne & Poulos, 1999; Lee & Salgado, 2002; Lee et
al., 2005; Foye et al., 2006; Lee et al., 2008; O’Loughlin &
Lehane, 2010), pile design (Lee & Salgado, 1999; Lee et
al., 2003; Jardine et al., 2005; Kolk et al., 2005; Xu et al.,
2008; Foye et al., 2009; Seo et al., 2009; Niazi & Mayne,
2013) and liquefaction resistance estimation (Seed & De
Alba, 1986; Stark & Olson, 1995; Salgado et al., 1997a;
Robertson & Wride, 1998; Carraro et al., 2003; Idriss &
Boulanger, 2006). The apparent simplicity of the CPT, how-
ever, hides considerably complex mechanics (Salgado,
2013). These include possible partial drainage during pene-
tration; particle size effects; the large displacements, rota-
tions, shear deformations and mean stresses that develop
around the cone; and the particle crushing that takes place
near the cone. This complexity leads to significant chal-
lenges in theoretical modelling of cone penetration. The
most applicable analyses for sand have been based on cavity
expansion analysis (Salgado et al., 1997b; Salgado & Ran-
dolph, 2001; Salgado & Prezzi, 2007).
The value of experimental modelling increases when the
target problem, cone penetration in the present case, is
difficult to solve theoretically. Even as attempts at a rigorous
theoretical solution of the cone penetration problem gain
sophistication, it will still be important to have companion
experimental results that can be used to validate theoretical
solutions.
Image-based analysis methods can be used in laboratory
investigations of the cone penetration process in particulate
media. X-ray film photogrammetry (Robinsky et al., 1964)
and, more recently, X-ray television (TV) imaging (Kobayashi
& Fukagawa, 2003) have been used for this purpose. These
techniques rely on embedded lead shot markers for tracking
motion within the soil (White, 2002), and metal marker
separation from the soil particles at large deformations affect
the precision of the observed displacements. Additionally, the
scanning time involved prevents the applicability of this tech-
nique to observation of continuous penetration in large-scale
models. The use of advanced non-destructive techniques, such
as X-ray computed tomography (CT), in geotechnical model-
ling has also been restricted to small-scale models (Otani,
2004; Morita et al., 2007; Ando` et al., 2012; Paniagua et al.,
2013). Stereo photogrammetry has been demonstrated for
planar displacement measurement using a false relief tech-
nique (Butterfield et al., 1970), but its accuracy is dependent
upon the grain size of the deforming medium and texture
contrast. Similarly, laser speckle interferometry (de Pater &
Nieuwenhuis, 1986) has been used to observe the displace-
ment field during cone penetration. This method relies on
formation of laser fringe patterns due to sand grain move-
ments and requires a minimum of 1 mm cone displacement
for pattern recognition. Optical analysis around penetrating
probes has also been employed (Allersma, 1987) for stress
visualisation in plane-strain conditions, and then extended to
displacement measurement by digital imaging of the same
observation plane (Dijkstra et al., 2006). Transparent soil
Manuscript received 27 October 2013; revised manuscript accepted
16 May 2014. Published online ahead of print 30 June 2014.
Discussion on this paper closes on 1 December 2014, for further
details see p. ii.� Purdue University, West Lafayette, USA.
particles have been used for measurement of displacement
during penetrometer/pile penetration (Iskander et al., 2002;
Liu, 2003; Lehane & Gill, 2004; Ni et al., 2010). In general,
the major limitations of these methods are their relatively low
resolution and accuracy in measuring displacements of gran-
ular materials and their reliance on photoelastic materials and
synthetic particles, which may not have properties similar to
those of real soils.
In the past decade, image correlation techniques, such as
particle image velocimetry (PIV) and digital image correla-
tion (DIC), have gained attention in experimental geomech-
anics. In the DIC technique, a transparent observation
window, located exactly where one of the symmetry planes
of a penetrating probe or model pile with a full cross section
would be (possible because the probe has a half cross
section), enables the observer to study the response of soil
during the penetration or loading process. After image
processing, the displacement field within the soil mass is
obtained at different stages of the penetration or loading
process.
In a pioneering work, White & Bolton (2004) used the
PIV technique to study the displacement of soil surrounding
a model ‘pile’ during penetration under plane-strain condi-
tions. In order to simulate three-dimensional (3D) penetra-
tion, Liu (2010) performed centrifuge CPTs under
axisymmetric conditions combined with PIV image analysis.
Centrifuge testing is similar to chamber testing with respect
to the PIV/DIC application, with the advantage of continu-
ous stress profiling. However, in most cases, deep penetra-
tion of the cone is accompanied by intrusion of sand
particles between the cone and the transparent observation
window, possibly reducing the accuracy of the analysis. To
reduce the sand intrusion problem at deep penetration in
axisymmetric models, a coarser sand is desirable; its usein
a centrifuge test may, however, affect the results because of
particle size effects, which can become significant at low
cone diameter-to-particle size ratios (Foray et al., 1998;
Loukidis & Salgado, 2008; Salgado, 2013).
This paper describes CPTs performed in a half-circular
DIC chamber to study the cone penetration process in silica
sand with uniform density. The DIC technique was used to
compute the soil displacement at shallow and deep penetra-
tion from images stored during penetration. The paper
examines the insights provided by the computed displace-
ment fields.
MATERIALS AND METHODS
Test equipment
The half-circular steel chamber used in the present re-
search has a diameter Dc of 1680 mm and a height of
1200 mm. Jacking and loading systems and a reaction frame
enabled penetration of the model cone penetrometer (see
Fig. 1) into the samples. The front wall of the half-circular
DIC chamber is a reinforced poly(methyl methacrylate)
(PMMA) sheet. The reinforcement comes from a steel frame
that contains three observation windows, which allow ima-
ging of the half-circular cone penetrometer and the sur-
rounding soil medium during the penetration process. A
clear, annealed glass sheet is fixed behind the PMMA to
prevent scratching of the PMMA by the sand particles
during testing.
Calibration chamber testing offers the advantage that the
initial state of the soil is known; however, for chambers of
small diameter, the effect of the chamber boundaries on
model piles or penetrating probes must be considered in the
interpretation of results (Ghionna & Jamiolkowski, 1991;
Salgado et al., 1998). The effect of chamber boundaries can
be minimised by choosing an appropriate chamber-to-cone
diameter ratio (Salgado, 2013). The diameter dc of the
model cone penetrometer is 31.75 mm. A ratio of Dc /dc
greater than 50 was considered sufficient to minimise the
effect of the chamber boundaries on the tests while allowing
preparation of samples that are not unmanageably large. The
cone diameter-to-D50 ratio of the test sands remained greater
than 20 to avoid scale effects (Gui & Bolton, 1998; Salgado,
2013). Fig. 2 shows the brass model cone penetrometer,
which consists of a half-circular rod section 915 mm long,
to which a half-section conical tip with a 608 apex angle is
attached. To measure the cone resistance qc during testing, a
compression load cell with 10 kN capacity was embedded
between the cone tip and the rod (see Fig. 2).
A removable jacking system with 50 kN capacity was
used to push the penetrometer into the sand at a penetration
(a)
Half-circular penetrometer
Jacking system
1200 mm
1680 mm
Observation
windows
Top lid
Sand discharge
valve
Soil sample
depth 1000 mm
(b)
Fig. 1. Schematic arrangement of the half-circular DIC chamber:
(a) front view; (b) side view
552 ARSHAD, TEHRANI, PREZZI AND SALGADO
rate of � 1 mm/s (0.83 mm/s). A 20 kN tension–compression
load cell embedded between the jack and the head of the
penetrometer measured the jacking load during penetration.
A roller assembly consisting of three cam followers and a
carefully aligned jacking system practically eliminated intru-
sion of sand between the penetrometer and the glass. Grease
on the penetrometer surface in direct contact with the glass
minimised friction.
A specially designed, half-circular, air–rubber bladder was
used to apply pressure on the top surface of the sample. A
half-circular steel plate was placed below the rubber bladder
to ensure uniform pressure application on the top of the
sample. A reaction steel lid was bolted on the top of the
chamber to constrain the air bladder.
Image and data acquisition system
The image acquisition system used to record the images
consists of three complementary metal-oxide-semiconductor
(CMOS), machine-vision digital cameras with 5 mega pixel
(MP) resolution. The cameras are equipped with compatible
high-resolution and low-distortion lenses of 12.5 mm fixed
focal length. A frame grabber with on-board memory was
used to record images during the penetration tests.
The sensors used for measuring the jacking force and
cone resistance during cone penetration were connected to a
separate data acquisition system. Base boundary effects were
monitored during testing by a load cell installed in the
sample at the base of the chamber along the cone penetra-
tion path. Lateral boundary effects were monitored by two
miniature pressure transducers installed at and near the
chamber boundary at sample mid-height.
Test sands
The main test sand was a coarse-grained, unground silica
sand (#2Q-ROK). This sand, which was mined from the
Oriskany sandstone deposits at Berkeley Springs in West
Virginia, has angular particles (Fig. 3(a)) and is composed
900
800
700
600
500
400
300
200
100
0
�100
�200
V
er
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 p
os
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 c
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�150 �100 �50 0 50 100 150
Horizontal position, : mmx
Cables
dc 31·75 mm�
20 kN in-line
tension/compression
load cell
Observation
window 2
Observation
window 3
10 kN compression
load cell
Fig. 2. Configuration of half-circular model penetrometer
100 mμ
(a)
100 mμ
(b)
50 mμ
(c)
Fig. 3. Microscopic images of the test sands: (a) #2Q-ROK;
(b) ASTM 20-30; (c) Ohio Gold Frac
CONE PENETRATION IN SILICA SAND USING DIGITAL IMAGE CORRELATION 553
mainly of quartz (silicon dioxide (SiO2) ¼ 99%), having
traces of calcite. For comparison purposes, additional tests
were performed with two other silica sands: ASTM-graded
20-30 Ottawa sand (SiO2 ¼ 99.8%), henceforth referred to
as ASTM 20-30, which has rounded particles (Fig. 3(b)),
and Ohio Gold Frac sand (SiO2 ¼ 99.7%), which has sub-
angular particles (Fig. 3(c)). These three sands are classified
as poorly graded (SP) according to the Unified Classification
System (ASTM D2487-11; ASTM, 2011). The maximum
and minimum densities of the sands were determined based
on ASTM D4253-00 (ASTM, 2006a) and ASTM D4254-00
(ASTM, 2006b). Table 1 provides the index properties of the
test sands.
During deep penetration, which induces large mean and
shear stresses below the cone tip, particle crushing is ob-
served in almost all sands (BCP Committee, 1971; White &
Bolton, 2004; Otani et al., 2005; Yang et al., 2010). White
& Bolton (2004) observed intense particle crushing ahead of
the tip of a plane-strain penetrometer monotonically jacked
into silica and carbonate sands. Yang et al. (2010) performed
cyclic loading tests on model, closed-ended steel piles
jacked into silica sand samples subjected to 150 kPa sur-
charge. Three distinct zones were identified near the pile
shaft that contained different percentages of crushed parti-
cles ranging in size from 20 �m to 100 �m.
In order to compare the crushability characteristics of the
test sands, one-dimensional (1D) compression tests were
performed on very dense samples (DR � 85%) with normal
stresses of up to 10 MPa (Fig. 4). The relative breakage
parameter Br, as defined by Hardin (1985), was then used to
provide an assessment of the crushability characteristics of
the test sands. From the results of the 1D compression tests,
the #2Q-ROK sand is the most crushable, with Br ¼ 10.51%;
Ohio Gold Frac sand is of intermediate crushability, with
Br ¼ 2.56%; and ASTM 20-30 sand is the least crushable of
the three silica sands, with Br ¼ 0.56%.
To assess the possible effect of sand–glass friction on the
observed displacements during cone penetration, sand–glass
interface direct shear tests were performed on #2Q-ROK
silica sand samples prepared at medium density (DR ¼ 65%)
for confining stresses of 25, 52 and 94 kPa. Fig. 5 shows the
shear stress plotted against horizontal displacement curves
obtained from the interface direct shear tests;the response is
almost rigid, perfectly plastic, with shear strength developing
at very small displacements (of the order of 0.15–0.2 mm).
The sand–glass interface friction angle is 8.58 for this silica
sand, which has angular particles; smaller interface friction
angles are expected for the other sands used in this study,
which have rounded and sub-angular particles. This value is
in line with previous work done by White (2002), who
reported a sand–glass interface friction angle of 118 based
on results of interface direct shear tests performed with
fraction-B Leighton Buzzard silica sand. The displacement
required for mobilisation of the interface friction is con-
siderably less than the displacement that occurs during cone
penetration. Thus, any interface friction is anticipated to
have minimum or negligible effect on the motion of the sand
particles near the cone and can be disregarded in the
interpretation of the displacement results. Only at locations
far from the penetrometer, where the displacements in the
absence of the glass would be very small, or possibly in
displacement reversals, would the drag from glass friction
potentially be non-negligible. So the displacements obtained
from the DIC technique are, in general, close estimates of
the displacements that would be observed in the real pro-
blem.
Table 1. Index properties of test sands
Sand Grain shape Silicon dioxide: % Specific gravity, Gs D50: mm Cu emax emin
#2 Q-ROK Angular 99.0 2.65 0.78 1.43 0.998 0.668
ASTM 20-30� Rounded 99.8 2.65 0.72 1.20 0.742 0.502
Ohio Gold Frac Sub-angular 99.7 2.65 0.65 1.37 0.853 0.537
� Data from Cho et al. (2006).
0·45
0·50
0·55
0·60
0·65
0·70
0·75
0·1 1 10
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oi
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ra
tio
, e
Normal stress, : MPaσ �n
#2Q-ROK
Ohio Gold Frac
ASTM 20-30
DR 85%�
Significant particle
crushing
Some particle crushing
Minimal particle crushing
Fig. 4. Change of void ratio in 1D compression tests
0
4
8
12
16
20
0 2 4 6 8
S
he
ar
 s
tr
es
s:
 k
P
a
Horizontal displacement: mm
DR 65%�
σ � �n 25 kPa
σ � �n 52 kPa
σ � �n 94 kPa
Fig. 5. Shear stress plotted against horizontal displacement for
direct shear tests performed on #2Q-ROK silica sand–glass
interface
554 ARSHAD, TEHRANI, PREZZI AND SALGADO
Digital image correlation fundamentals
The DIC technique involves obtaining a sequence of
digital images of a body or a structure in motion and then
processing these images using an image correlation scheme
to produce the displacements of material elements of the
body. Image correlation enables tracking of elements (groups
of particles) in time. There are two families of predefined
correlation criteria that are often used for this purpose (Pan
et al., 2009). The first group, referred to as the cross-
correlation (CC) criteria, seeks a maximum correlation of
grey level intensity of pixels across sequential images. The
second group, referred to as the sum-of-squared-differences
(SSD) criteria, seeks the minimum difference in grey-level
intensity of an image pattern (subset) in the reference and
deformed/displaced images. Both families of correlation
criteria are in essence complementary and can be deduced
from each other (Pan et al., 2009). The choice of the
matching criterion depends upon the experimental condi-
tions, nature of deformations, and the quality of the speckle
pattern or random texture. In general, as illustrated in Fig.
6(a), a DIC algorithm (Pan et al., 2009) involves
(a) defining a virtual grid on the initial image (reference
image)
(b) defining the subset size and search zone in the subsequent
image (deformed image)
(c) interpolating the discrete grey-level intensity of the
deformed image to form a continuous function
(d ) establishing the correlation between image sets using a
suitable criterion
Reference image
Subset size (L)0 x
y
Subset
spacing
f x y( , )i i
Reference subset
Correlation maximisation algorithm
Target subset
g x( ,�i y �i )
0 x
y
Deformed image
Displacement vector
(a)
ti ti�1 ti�2
ti n� �1
ti n�
(b)
Fig. 6. Digital image correlation: (a) procedure outline for one subset; (b) incremental correlation
CONE PENETRATION IN SILICA SAND USING DIGITAL IMAGE CORRELATION 555
(e) obtaining average displacements at the intersection of
measurement grids.
A fundamental assumption in the DIC technique is that
the image grey-level intensity pattern remains the same
before and after motion but for some Gaussian noise (Sutton
et al., 2009). In the case of large deformation problems,
such as the cone penetration problem, some soil particles
may disappear from the subset, resulting in loss of accuracy
due to a mismatch between the subsets of the deformed and
undeformed images. To avoid this problem, an incremental
correlation scheme was adopted in this study that involves
comparing an image at a given time ti with a subsequent
image at the next time step ti+1 (Fig. 6(b)). The accumulated
displacements at any given time were calculated by integrat-
ing the incremental displacement field obtained from the
incremental correlation. A disadvantage of the incremental
correlation scheme is that the systematic error associated
with the displacement obtained at any increment adds up. To
minimise the systematic error, instead of working with the
entire set of images, an optimum number of images were
selected for processing. In addition, other measures were
adopted to enhance the accuracy of the image correlation,
such as texture enhancement, use of a low-pass filter in the
analysis of the images, and use of improved correlation
algorithms accounting for subset deformation. Moreover, to
avoid variation in the lighting conditions during the test, a
matching criterion for image correlation based on a zero-
normalised sum of squared differences was employed (Sut-
ton et al., 2009). The commercial digital image correlation
software VIC-2D (Correlated Solutions, 2009) was used for
processing the images taken during cone penetration. Other
DIC parameters that affect the measurement accuracy of
displacements were optimised through a parametric study;
these factors include subset size, choice of correlation algo-
rithm, interpolation function for subset displacement and
image intensity interpolated function.
Camera calibration. The displacement field obtained from
image correlation is in pixels. To convert the pixel coordinates
to the object space coordinates, an image transformation
matrix is first obtained from camera calibration (White et al.,
2003). To obtain the camera calibration parameters, a set of
45 image control points were printed on a transparent
laminating film using a 1440 DPI printer. The calibration
target film covers the entire inner surface of the glass that is in
direct contact with the PMMA. The centroids of these control
points in image space were obtained using the Matlab
software geoCENTROID (White et al., 2003). These control
points were then used to establish the camera calibration
parameters using the camera calibration toolbox for Matlab
(Heikkila & Silven, 1997). A linear fit to the image-to-object
scale was chosen by minimising the standard deviation of the
projection error. This procedure was followed for all tests.
EXPERIMENTAL PROGRAMME
Test matrix
A series of ten CPTs was performed in the DIC chamber
in uniform sand samples (Table 2). In total, eight tests were
performed on the most crushable silica sand (#2Q-ROK) with
and without surcharge. Out of these eight tests, three tests
were performed without any surcharge to investigate the
development of the slip mechanism at shallow penetration
and the effect of stress level on the displacement field. Two
tests were performed on the other two sands, ASTM 20-30
sand and Ohio Gold Frac sand. The tests are identified by acode that specifies the sand density (L denotes ‘loose’, MD
denotes ‘medium dense’ and D denotes ‘dense’), surcharge
(0 or 50 kPa), test number (a number from 1 to 10) and sand
type (#2Q-ROK, ASTM 20-30 and Ohio Gold Frac). For
example, CPTL50-T4-#2Q-ROK identifies CPT number 4,
performed on a loose #2Q-ROK sand sample with a sur-
charge of 50 kPa.
Test procedure
The medium dense and dense sand samples were prepared
by air pluviation using a large pluviator (Lee et al., 2011)
placed above the DIC chamber at a fixed position such that
the sand drop height was always greater than the terminal
sand fall height of 500 mm, determined through the calibra-
tion procedure described by Rad & Tumay (1987). The
target sample densities were achieved by changing the flow
rate through addition or removal of a diffuser sieve. A
slightly different procedure was used for preparation of loose
sand samples. While carefully maintaining a drop height of
400 mm, a half-circular pluviator without diffuser sieves was
placed inside the DIC chamber and raised slowly as the
sample was prepared. For sample density and uniformity
verification, nine miniature thin tube samplers with diameter
equal to 2 in (5.08 cm) were placed at different heights
within the sand sample during sample preparation and were
used to determine density locally. The density variation in a
sample was determined to be within 2–3%. For the tests
performed with a surcharge of 50 kPa, the surcharge was
applied gradually on top of the sample by inflating the half-
circular, air–rubber bladder using a laboratory air-pressure
line. A special cross-hair alignment device was used to align
the cameras with the observation windows.
The penetrometer was subsequently jacked into the soil
sample at a rate of 1 mm/s (0.83 mm/s). Digital images were
acquired simultaneously from three cameras during the pene-
tration process at a constant frame rate of 2 frames/s. The
cone tip load Qc and the jacking force Qt were measured
Table 2. Test programme
Test code Surcharge: kPa Average relative density DR: % dc /D50 dc /Dc
CPTL0-T1-#2Q-ROK 0 45 41 53
CPTMD0-T2-#2Q-ROK 0 65
CPTD0-T3-#2Q-ROK 0 85
CPTL50-T4-#2Q-ROK 50 45
CPTL50-T5-#2Q-ROK 50 42
CPTMD50-T6-#2Q-ROK 50 63
CPTD50-T7-#2Q-ROK 50 85
CPTD50-T8-#2Q-ROK 50 82
CPTD50-T9-Ohio Gold Frac 50 87 59 53
CPTD50-T10-ASTM 20-30 50 85 43
556 ARSHAD, TEHRANI, PREZZI AND SALGADO
throughout each test. Feedback from the chamber base load
cell below the cone path was used to monitor base boundary
effects. Negligible chamber base boundary stresses were
measured for penetration depths up to 15 to 20 cone
diameters, depending on sand type and density.
CONE PENETRATION RESISTANCE
In addition to the digital images acquired during the
CPTs, cone resistance profiles were obtained from the meas-
urements made by the load cell embedded inside the cone
tip; these are illustrated in Fig. 7 and Fig. 8.
Figure 7(a) shows cone resistance profiles for the tests
performed in loose, medium dense and dense sand samples
without surcharge loading (CPTL0-T1-#2Q-ROK, CPTMD0-
T2-#2Q-ROK and CPTD0-T3-#2Q-ROK). Fig. 7(b) shows
the qc profiles for all the CPTs performed with a surcharge
of 50 kPa in the #2Q-ROK silica sand. Cone resistance
increases with increasing initial sample relative density in all
tests. In the loose and medium dense sand samples, cone tip
resistance tends to stabilise earlier than in the dense sand
sample. Fig. 8 shows the cone resistance profiles for the tests
performed in dense samples (DR ¼ 82%, 85% and 87%)
prepared with three different silica sands (#2Q-ROK, Ohio
Gold Frac and ASTM 20-30). These results clearly show the
effect of particle crushing on cone resistance, as the more
crushable sand (#2Q-ROK) offers less resistance to cone
penetration than the sand of intermediate crushability (Ohio
Gold Frac) and the sand of least crushability (ASTM 20-30).
DIC RESULTS
Presentation of the results
The DIC analyses of images stored for each test produced
(a) incremental displacement field resulting from each
0.415 mm increment of cone penetration between two
consecutive frames
(b) soil displacement paths
(c) post-penetration accumulated displacement field.
Figure 9 shows the coordinate reference system used to
report the DIC results. The cone penetration depth from the top
of the sample at any given time is denoted by h�. The vertical
distance of a point in the domain with respect to the cone tip is
h (h ¼ 0 at the cone tip, positive above the cone tip and
negative below it). Results are typically presented with h and
h� normalised by the cone radius (h/rc and h�/rc). The horizon-
tal distance from a point to the cone penetration axis is r,
whereas the vertical distance of the point to the sample surface
is z. Both r and z can be normalised with respect to the cone
radius (r/rc and z/rc).
Soil displacement pattern during cone penetration
The deformation pattern around an advancing cone has
historically been viewed through the prism of a slip mechan-
ism (Salgado & Prezzi, 2007). Such a slip mechanism can
be inferred from the observation of the soil displacement
field in the immediate neighbourhood of the cone tip for
small increments of cone penetration. Paniagua et al. (2013)
used 3D X-ray CT and 3D DIC algorithms to study displace-
ments and strains around a cone penetrometer pushed into
silt, and observed also that there was a pattern consistent
with the Salgado & Prezzi (2007) slip pattern. Fig. 10 and
Fig. 11 show the evolution of the slip mechanism during
incremental cone penetration. For each of the analyses
shown in Fig. 10 and Fig. 11, the incremental displacement
field was obtained for an incremental penetration of
2.075 mm (¼ 5 3 0.415 mm ¼ 2.075 mm increment of cone
penetration between images i and (i + 5)), which corre-
sponds to 0.13rc. The cone displacement in Fig. 10 and Fig.
11 is shown without magnification, but the displacement
vectors are magnified by a factor of 20 to allow better
visualisation of the displacement field. Fig. 10 illustrates the
evolution of the slip mechanism with increasing cone pene-
tration for the CPTD0-T3-#2Q-ROK test. A free surface
exists at the top of the sample since no surcharge was
applied in this test. Image pairs of the cone penetration at
three normalised penetration depths (h�/rc ¼ 2, 6 and 22)
were analysed to obtain the incremental displacement fields
at each of these normalised penetration depths. As the cone
600
400
200
0
0 1 2 3 4 5
qc: MPa
C
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tr
a
tio
n 
de
pt
h,
: m
m
z
CPTL0-T1-#2Q-ROK ( 45%)DR �
CPTMD0-T2-#2Q-ROK ( 65%)DR �
CPTD0-T3-#2Q-ROK ( 85%)DR �
600
400
200
0
0 5 10 15 20 25
qc: MPa
C
on
e 
pe
ne
tr
a
tio
n 
de
pt
h,
: m
m
z
(a)
(b)
CPTL50-T4-#2Q-ROK ( 45%)DR �
CPTL50-T5-#2Q-ROK ( 42%)DR �
CPTMD50-T6-#2Q-ROK ( 63%)DR �
CPTD50-T7-#2Q-ROK ( 85%)DR �
CPTD50-T8-#2Q-ROK ( 82%)DR �
Fig. 7. Cone resistance profiles for penetration tests in #2Q-ROK
silica sand: (a) tests without surcharge; (b) tests with a surcharge
of 50 kPa
CONE PENETRATION IN SILICA SAND USING DIGITAL IMAGE CORRELATION 557
first enters the sample, a shallow slip surface forms, with the
displacement vectors fanning out in a pattern similar to that
of ‘classical’ bearing capacity failure (Salgado, 2008), with
the conical tip acting as a rigid driving wedge.
Figure 11 compares the displacement field around
the cone during incremental penetration for three tests
performed on samples of three different sands (CPTD50-T8-
#2Q-ROK, CPTD50-T9-Ohio Gold Frac and CPTD50-T10-
ASTM 20-30) with approximately the same density (82%,
85% and 87%) subjected to the same surcharge (50 kPa).
The figure shows the incremental displacement fields for two
normalised depths, h�/rc ¼ 6 and h�/rc ¼ 20, correspondingto normalised depths just prior to and after the onset of
particle crushing in the soil zone below the cone (particle
crushing was visible to the naked eye through the observa-
tion window). The incremental displacement field for h�/
rc ¼ 6 (Figs 11(a)–11(c)) is such that, immediately below
the cone tip, the displacement vectors are nearly vertical,
while further away from it, the displacement vectors have a
larger radial component. A transition zone is observed where
the incremental displacement vectors rotate from the vertical
to the radial direction, as suggested by Salgado & Prezzi
(2007); this zone is more clearly observed for the least
crushable sand (ASTM 20-30), for which the degree of
incremental displacement vector rotation is more pro-
nounced. The incremental displacement field for h�/rc ¼ 20
500
400
300
200
100
0
0 6 12 18 24
qc: MPa
C
on
e 
pe
ne
tr
a
tio
n 
de
pt
h,
: m
m
z
CPTD50-T9-Ohio Gold Frac ( 87%)DR �
CPTD50-T10-ASTM 20-30 ( 85%)DR �
CPTD50-T7-#2Q-ROK ( 85%)DR �
CPTD50-T8-#2Q-ROK ( 82%)DR �
Fig. 8. Comparison of cone resistances for #2Q-ROK, Ohio Gold
Frac and ASTM 20-30 silica sands
0
10
20
30
N
or
m
al
is
ed
 d
ep
th
,
/
z
r c
10 5 0 5 10
Normalised radial position, / , relative to cone tipr rc
10
0
�10
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
,
/
, r
el
a
tiv
e 
to
 c
on
e 
tip
h
r c
r
z
h r*/ c
h r/ 0c �
h
h
h
r
* Cone penetration depth from top of sample
with time
Vertical position relative to cone top
( is positive above tip and negative below tip)
Cone radius
�
�
�c
Fig. 9. Coordinate reference system for DIC data reporting
8
6
4
2
0
6 4 2 0 2 4 6
N
or
m
al
is
ed
 d
ep
th
,
/z 
r c
Normalised radial position, / , relative to cone tip
(a)
r rc
σs R
c
0 kPa, 85%
* 2 , #2Q-ROK
� �
�
D
h r
Cone incremental displacement 0·13� rc
Scale for incremental displacement vectors:
0·063rc
12
10
8
6
4
6 4 2 0 2 4 6
N
or
m
al
is
ed
 d
ep
th
,
/z 
r c
Normalised radial position, / , relative to cone tip
(b)
r rc
σs R
c
0 kPa, 85%
* 6 , #2Q-ROK
� �
�
D
h r
Cone incremental displacement 0·13� rc
Scale for incremental displacement vectors:
0·063rc
28
26
24
22
20
6 4 2 0 2 4 6
N
or
m
al
is
ed
 d
ep
th
,
/z 
r c
Normalised radial position, / , relative to cone tip
(c)
r rc
σs R
c
0 kPa, 85%
* 22 , #2Q-ROK
� �
�
D
h r
Cone incremental displacement 0·13� rc
Scale for incremental displacement vectors:
0·063rc
Fig. 10. Evolution of slip pattern with penetration for test CPTD-
T3-#2Q-ROK (�s 0 kPa, DR 85%): (a) h�/rc 2; (b) h�/rc 6;
(c) h�/rc 22
558 ARSHAD, TEHRANI, PREZZI AND SALGADO
(Figs 11(d)–11(f)) illustrates that the overall incremental
displacement field becomes more vertical for all sands as the
cone penetrates to a depth at which the sand particles
surrounding the conical tip undergo crushing (i.e., incremen-
tal displacement rotation is less pronounced after particle
crushing becomes significant). In order to quantify the
degree of incremental displacement rotation within the tran-
sition zone, the direction of the average incremental
displacement vectors was calculated within a subdomain of
the soil domain obtained by revolution of the cross section
shown in Fig. 11. This subdomain is essentially a cylinder,
except for the conical space occupied by the penetrometer
tip, with radius 2dc and length extending from the cone
shoulder down to 1.25dc below the cone tip. The average
direction of the incremental displacement vectors is calcu-
lated using the product of the radius at which the displace-
ment is observed and the magnitude of the displacement as
a weight factor
Łave ¼
Pnel
i¼1 Łili2�ridrPnel
i¼1 li2�ridr
(1)
where
Łi ¼ tan�1 vi
ui
� �
(2)
12
10
8
6
4
6 4 2 0 2 4 6
N
or
m
al
is
ed
 d
ep
th
,
/z 
r c
Normalised radial position, / , relative to cone tip
(a)
r rc
σs R
c
50 kPa, 85%
* 6 , ASTM 20-30
� �
�
D
h r
Cone incremental displacement 0·13� rc
Scale for incremental displacement vectors:
0·063rc
12
10
8
6
4
6 4 2 0 2 4 6
N
or
m
al
is
ed
 d
ep
th
,
/z 
r c
Normalised radial position, / , relative to cone tip
(c)
r rc
σs R
c
50 kPa, 82%
* 6 , #2Q-ROK
� �
�
D
h r
Cone incremental displacement 0·13� rc
Scale for incremental displacement vectors:
0·063rc
Direction of average
displacement vector 13·2°�
12
10
8
6
4
6 4 2 0 2 4 6
N
or
m
al
is
ed
 d
ep
th
,
/z 
r c
Normalised radial position, / , relative to cone tip
(b)
r rc
σs R
c
50 kPa, 87%
* 6 , Ohio Gold Frac
� �
�
D
h r
Cone incremental displacement 0·13� rc
Scale for incremental displacement vectors:
0·063rc
Direction of average
displacement vector 33·2°�
Direction of average
displacement vector 31·5°�
Direction of average
displacement vector 33·0°�
26
24
22
20
18
6 4 2 0 2 4 6
N
or
m
al
is
ed
 d
ep
th
,
/z 
r c
Normalised radial position, / , relative to cone tip
(d)
r rc
σs R
c
50 kPa, 85%
* 20 , ASTM 20-30
� �
�
D
h r
Cone incremental displacement 0·13� rc
Scale for incremental displacement vectors:
0·063rc
Direction of average
displacement vector 40·1°�
26
24
22
20
18
6 4 2 0 2 4 6
N
or
m
al
is
ed
 d
ep
th
,
/z 
r c
Normalised radial position, / , relative to cone tip
(e)
r rc
σs R
c
50 kPa, 87%
* 20 , Ohio Gold Frac
� �
�
D
h r
Cone incremental displacement 0·13� rc
Scale for incremental displacement vectors:
0·063rc
Direction of average
displacement vector 36·8°�
26
24
22
20
18
6 4 2 0 2 4 6
N
or
m
al
is
ed
 d
ep
th
,
/z 
r c
Normalised radial position, / , relative to cone tip
(f)
r rc
σs R
c
50 kPa, 82%
* 20 , #2Q-ROK
� �
�
D
h r
Cone incremental displacement 0·13� rc
Scale for incremental displacement vectors:
0·063rc
Fig. 11. Soil displacement pattern for ASTM 20-30, Ohio Gold Frac and #2Q-ROK silica sands prior to (h�/rc 6) and after
particle crushing (h�/rc 20): (a) ASTM 20-30 at h�/rc 6; (b) Ohio Gold Frac at h�/rc 6; (c) #2Q-ROK at h�/rc 6; (d) ASTM
20-30 at h�/rc 20; (e) Ohio Gold Frac at h�/rc 20; (f) #2Q-ROK at h�/rc 20
CONE PENETRATION IN SILICA SAND USING DIGITAL IMAGE CORRELATION 559
li ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u2i þ v2i
q
(3)
and ui and vi are the radial and vertical displacements of
every soil element i within the averaging zone, respectively,
Łi is the direction of the displacement vector of element i
with respect to the horizontal, li is the magnitude of the
displacement vector for element i, nel is the number of soil
elements within the subdomain where the average is calcu-
lated, and ri is the radial distance between the centre of
element i and the cone axis.
Characterisation of displacement zones around the cone
Four zones providing a general, qualitative sense of the
displacement field and of processes taking place during cone
penetration were identified based on the displacement pat-
terns observed (Fig. 12(a)): zone I – a vertical compression
zone below the cone; zone II – a crushed particle band
along the surface of the cone tip and shaft; zone III – a
transition zone where the displacement vectors rotate from
the vertical/sub-vertical direction to the radial direction; and
zone IV – a zone in which the direction of the displace-
ments is approximately radial.
Figure 12(b) shows a vector plot of the incremental
displacementfield obtained when the cone tip moved down
from h� ¼ 6rc (initial position) to h� ¼ 7rc (final position)
for CPTD50-T8-#2Q-ROK. The four zones are sketched in
the same plot. In zone I, vertical compression of the soil
dominates, and the incremental displacement vectors are
mostly vertical. For small penetration increments, zone I
extends from the cone tip to h/rc � �3.8; for lower eleva-
tions, the incremental vertical displacement reduces to less
than 10% of the maximum incremental vertical displacement
observed in zone I. The maximum incremental vertical
displacement is observed along the cone surface at r/rc � 0.5
and h/rc ¼ 0.866.
Zone II forms due to intense shearing and particle crush-
ing that takes place below the cone. The particles crushed
below the cone are displaced laterally as the cone advances,
and stay roughly in the same place as the cone continues in
its advance. The finely crushed sand particles can be ob-
served coating the cone tip and the entire cone shaft in
close-up views of the images captured during penetration.
The maximum thickness of this zone, which was also ob-
served by White & Bolton (2004) and Yang et al. (2010), is
1.5–4 D50 at r/rc � 0.5 and h/rc ¼ 0.866.
Zone III exists immediately below the cone, where rota-
tion of the incremental displacement field from a mainly
vertical direction to the radial direction occurs, as can be
seen in Fig. 12(b). The inclination of the outer boundary of
the transition zone III depends on sand crushability: the
more crushable the sand, the less the boundary rotates
outward (away from the cone). In zone IV, the incremental
soil displacement field is purely radial, resembling the field
that would result from a cylindrical cavity expansion pro-
cess, with minimal vertical incremental displacement ob-
served.
Soil displacement in each of zones I though IV can be
better understood by observing the displacement paths of
key soil elements (labelled E1 through E6 in Fig. 12(a)).
Fig. 13 shows the evolution of the normalised vertical and
radial displacement increments ˜v/rc and ˜u/rc of elements
E1, E2, E3, E4, E5 and E6 shown in Fig. 12(a) due to a
penetration of approximately 1rc (¼ 1.05 rc) from a depth
h� ¼ 20rc. The incremental change in the displacement field
was deduced from the analysis of image sequences obtained
in tests CPTD50-T10-ASTM 20-30 and CPTD50-T8-#2Q-
ROK. Fig. 13(a) shows the displacement path of element
E1 located just below the cone tip in zone I. Element E1
experiences a maximum vertical displacement increment
˜v ¼ 0.68rc for the least crushable sand (ASTM 20-30)
and ˜v ¼ 0.49rc for the most crushable sand (#2Q-ROK).
The radial displacement change is negligible for both sands.
It is seen in Fig. 13(a) that particle tracking for element E1
ends before cone penetration equal to rc is achieved. For
element E2 next to the cone surface, maximum ˜v values
of 0.34rc and 0.48rc were observed for the least and most
crushable sand, respectively (Fig. 13(b)). The increase in
the normalised vertical displacement increment observed for
the most crushable silica sand #2Q-ROK is caused by the
intense particle crushing occurring just below the cone tip.
Element E2 undergoes a maximum radial displacement
increment equal to 0.17rc for the ASTM 20-30 sand and to
0.13rc for the #2Q-ROK sand. Element E3 (Fig. 13(c)),
located in the transition zone, experiences maximum radial
and vertical displacement increments of 0.12rc and 0.10rc
for ASTM 20-30 sand, and 0.12rc and 0.16rc for #2Q-ROK
sand. The displacement paths of elements E4, E5 and E6,
located on the transition line between zone III and zone IV,
indicate clearly that the radial component of the normalised
0 1 2 3 4 5
r r/ c
Symbol shows element location
(a)
2
1
0
�1
�2
�3
h
r/
c
Interface zone
Crushed particles band thickness 1·5–4� D50
II
E4
IV
Cavity expansion zone
(radial displacement
dominates)
E2 E3
E5
E6
III
Transition zone
(radial displacement
build-up)
E1
I
Axial compression zone
(vertical displacement
dominates)
Contour line corresponds
to displacement ratio ( / ) 1u v �
N
or
m
al
is
ed
 d
ep
th
,
/z 
r c
σs R
c
50 kPa, 82%
* 7 , #2Q-ROK
� �
�
D
h r
Normalised radial position, / , relative to cone tip
(b)
r rc
Zone II
5
7
9
11
13
6 4 2 0 2 4 6
Zone I
Zone III
Zone IV
0·2rc
Scale for incremental displacement vectors
Fig. 12. Characterisation of displacement zones near cone during
a penetration equal to rc: (a) displacement zones; (b) displacement
field change
560 ARSHAD, TEHRANI, PREZZI AND SALGADO
0
0·2
0·4
0·6
0·8
20·0 20·4 20·8 21·2
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t c
ha
ng
e,
/
an
d
/
Δ
Δ
u 
r
v 
r
c
c
Normalised penetration depth, */
(a)
h rc
σs
1 c
50 kPa
Element E : 0, 20·32
�
� �r z r
Radial (ASTM 20-30, 85%)DR �
Vertical (ASTM 20-30, 85%)DR �
Radial (#2Q-ROK, 82%)DR �
Vertical #2Q-ROK( ,
82%)DR �
σs
2 c c
50 kPa
Element E : 0·68 , 18·8
�
� �r r z r
Radial (ASTM 20-30, 85%)DR �
Vertical (ASTM 20-30, 85%)DR �
Radial (#2Q-ROK, 82%)DR �
Vertical #2Q-ROK( , 82%)DR �
0
0·1
0·2
0·3
0·4
0·5
20·0 20·4 20·8 21·2
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t c
ha
ng
e,
/
an
d
/
Δ
Δ
u 
r
v 
r
c
c
Normalised penetration depth, */
(b)
h rc
σs
3 c c
50 kPa
Element E : 1 , 19·2
�
� �r r z r
Radial (ASTM 20-30, 85%)DR �
Vertical (ASTM 20-30, 85%)DR �
Radial (#2Q-ROK, 82%)DR �
Vertical #2Q-ROK( , 82%)DR �
σs
4 c c
50 kPa
Element E : 1·12 , 18·2
�
� �r r z r
Radial (ASTM 20-30, 85%)DR �
Vertical (ASTM 20-30, 85%)DR �
Radial (#2Q-ROK, 82%)DR �
Vertical #2Q-ROK( , 82%)DR �
0
0·04
0·08
0·12
0·16
0·20
20·0 20·4 20·8 21·2
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t c
ha
ng
e,
/
an
d
/
Δ
Δ
u 
r
v 
r
c
c
Normalised penetration depth, */
(c)
h rc
0
0·02
0·04
0·06
0·08
20·0 20·4 20·8 21·2
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t c
ha
ng
e,
/
an
d
/
Δ
Δ
u 
r
v 
r
c
c
Normalised penetration depth, */
(d)
h rc
σs
5 c c
50 kPa
Element E : 2 , 19·2
�
� �r r z r
Radial (ASTM 20-30, 85%)DR �
Vertical (ASTM 20-30, 85%)DR �
Radial (#2Q-ROK, 82%)DR �
Vertical #2Q-ROK( , 82%)DR �
σs
6 c c
50 kPa
Element E : 2·7 , 20
�
� �r r z r
Radial (ASTM 20-30, 85%)DR �
Vertical (ASTM 20-30, 85%)DR �
Radial (#2Q-ROK, 82%)DR �
Vertical #2Q-ROK( , 82%)DR �
0
0·02
0·04
0·06
0·08
20·0 20·4 20·8 21·2
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t c
ha
ng
e,
/
an
d
/
Δ
Δ
u 
r
v 
r
c
c
Normalised penetration depth, */
(e)
h rc
0
0·01
0·02
0·03
20·0 20·4 20·8 21·2
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t c
ha
ng
e,
/
an
d
/
Δ
Δ
u 
r
v 
r
c
c
Normalised penetration depth, */
(f)
h rc
Fig. 13. Evolution of radial and vertical displacement change for 1rc penetration in the least crushable (CPTD50-T10-ASTM
20-30) and most crushable (CPTD50-T8-#2Q-ROK) silica sands
CONE PENETRATION IN SILICA SAND USING DIGITAL IMAGE CORRELATION 561
displacement increment dominates there for both sands (see
Figs 13(d)–13(f)). However, the values of the radial
displacement increment of elements located at larger radial
offsets from the cone tip (elements at positions E5 and E6)
are smaller for the most crushable silica sand than those
observed for the least crushable silica sand (0.036rc and
0.017rc, as opposed to 0.067rc and 0.02rc). These results
suggest that deformation gets more localised near the conein the most crushable sand.
Displacement paths during continuous penetration
Figure 14 shows the displacement paths of nine elements
located at different radial offsets from the cone penetration
axis (r/rc ¼ 0, 0.5, 1, 1.5, 2, 3, 4, 6 and 8) for test CPTD50-
T8-#2Q-ROK. The displacement paths follow the coordi-
nates of the centroid of each of the soil elements during
cone penetration from h� ¼ 0 to h� ¼ 30rc. The character-
istics of the displacement paths of each of these elements,
located initially at a depth z � 18rc, depend on their offset
position with respect to the cone penetrometer path. The
displacement paths for soil elements A, B, C, D and E
located at r/rc ¼ 0.5, 1, 1.5, 2 and 3 show that these
elements move away from the cone path, except near the
end of the displacement paths, when the soil elements move
slightly towards the cone shaft instead (see Fig. 15). For
elements F, G and H located at r/rc ¼ 4, 6 and 8, no inward
displacement is observed at the end of the displacement
paths. Vertical displacements, which accumulate below the
cone tip, decay sharply with increasing radial distance from
the cone penetration path. As can be seen in Fig. 14, the
soil displacement paths radiating from the cone tip are
inclined, with radial and vertical displacements decaying
with increasing radial distance from the cone tip. However,
the rate of decay of the radial displacement with increasing
distance from the cone path is lower than that of the vertical
displacement.
Figure 15 shows close-up views of the displacement paths
for elements C and H located at r/rc ¼ 1.5 and at r/rc ¼ 8,
respectively. For element C (Fig. 15(a)), the vertical compo-
nent of displacement dominates initially, but, on further cone
penetration, the displacement becomes more radial and,
immediately after the cone shoulder crosses the elevation of
element C, bends back towards the cone shaft. Fig. 15(b)
shows the displacement path of element H. The radial and
vertical displacements are of approximately the same magni-
tude, with no inward displacement towards the shaft taking
place as the cone penetrates beyond the elevation of this
element. As shown in Fig. 15(a), the motion of element C
undergoes a reversal, and its inward motion after this
reversal is significantly less than its outward displacement.
Given that the inward motion of element C is small, friction
between the glass and the sand particles may have somewhat
impeded the inward motion since the motion reversal is
300
290
280
270
�20 0 20 40 60 80 100 120 140
V
er
tic
al
 p
os
iti
on
: m
m
Horizontal position: mm
h r*/ 0c �
O A B C D E F G H
h r*/ 30c �
Thin crushed particle band 2·5� D50
End of
particle
tracking
C
on
e 
pe
ne
tr
a
tio
n 
pa
th
σs R50 kPa, 82%, #2Q-ROK� �D
Vertical shearing
Intense rotation Element A (0·5 )rc
Element B (1·0 )rc
Element C (1·5 )rc
Element D (2·0 )rc
Element E (3·0 )rc
Element O (0 )rc
Element E (4·0 )rc
Element F (6·0 )rc
Element G (8·0 )rc
Fig. 14. Displacement paths during cone penetration from h� 0rc to h� 30rc for soil elements O,
A, B, C, D, E, F, G and H
562 ARSHAD, TEHRANI, PREZZI AND SALGADO
linked to unloading, which is initially approximately elastic.
As mentioned earlier, the glass–soil stress–strain relationship
is a stiff, linear elastic curve, which makes it possible to
estimate any drag that may have been present. The inward
movement of element C and others like it reflect a decrease
in radial stress after the cone shoulder crosses the element
elevations, and this drop in radial stress, experienced on the
penetrometer shaft, implies a drop of shear stress.
Figure 16 and Fig. 17 show the evolution of the normal-
ised vertical and radial displacements of soil elements B, C,
D and E as the cone penetrates from h� ¼ 0 to 23 and 25rc,
respectively, for tests CPTL50-T4-#2Q-ROK and CPTD50-
T8-#2Q-ROK. Initially, the soil elements are located at
z ¼ 18rc for the loose sand sample and at z ¼ 18.5rc for the
dense sample and at radial offsets of 1rc (element B), 1.5rc
(element C), 2rc (element D) and 3rc (element E) from the
cone penetration axis.
Elements closer to the cone penetration path, such as
element B, are the first elements to sense the approaching
cone. This happens when the vertical distance from element
B to the cone tip is equal to approximately 15 to 16rc for
loose and dense sand samples, respectively. The normalised
radial displacement of soil element B increases sharply when
the cone tip reaches a distance of approximately 3–3.5rc
from soil element B and then moves closer to it. This build
up in radial stress is referred to in this paper as the cavity
expansion stage (Fig. 16(a)), the start of which is labelled as
point 2 in Fig. 16. Element B is displaced radially and
downward as the cone passes by it. If one chooses to view
the cone as stationary, then the element could be viewed as
flowing around the cone face. The normalised radial soil
displacement of element B peaks when the cone shoulder
starts to align with it at the end of the cavity expansion
process (see the peak in normalised displacements, identified
as point 3 in Fig. 16(a) and Fig. 17(a)). During the cavity
expansion process, particle crushing is observed near the
cone tip, with the crushed particle band starting to form
along the cone tip shoulder. A small reduction in normalised
radial and vertical displacements takes place after the cavity
expansion process (see points 3 and 4 in Fig. 16(a) and Fig.
17(a)). For the elements located farther away from the cone,
the peak in normalised radial displacement is either less
pronounced or no longer observed.
As the cone penetration continues, further vertical shear-
ing is observed above the cone only within the thin crushed
particle band (zone II) along the shaft. Particle movement is
very random within the crushed particle band. As observed
from close-up images of the cone penetration process, for
tests performed with no surcharge (such as CPTD0-T3-#2Q-
ROK), vertical particle movement is more pronounced in
loose sand than in dense sand prior to particle crushing. In
the case of the penetration tests performed in dense sand
with the 50 kPa surcharge (such as CPTD50-T8-#2Q-ROK),
noticeable particle crushing takes place below the cone tip.
Fig. 18 shows a close-up image of the soil in the zone
(1.25rc 3 1rc) immediately next to the cone shaft for
CPTD50-T8-#2Q-ROK. As shown in Fig. 18, a very thin
band of thickness equal to about 2.5D50 with highly crushed
particles is observed right next to the cone shaft. Next to
this thin band, there is a 4D50-thick band consisting of
moderately crushed sand particles.
Displacement paths below the cone tip
Figure 19 shows normalised radial and vertical displace-
ment paths below the cone tip for h�/rc � 20 for tests
performed on sand samples prepared with three different
initial densities (CPTL50-T4-#2Q-ROK, CPTMD50-T6-#2Q-
ROK and CPTD50-T8-#2Q-ROK). The normalised displace-
ment paths are given for soil elements located at r/rc � 1,
1.5, 2, 3, 5 and 8. Both the radial and vertical normalised
displacements decrease with increasing r. The maximum
value of the normalised radial displacement u/rc, which is
observed at an offset r/rc ¼ 1 along the shoulder of the cone
tip for dense and medium dense sand (Figs 19(a) and 19(c)),
is equal to 0.33, whereas u/rc ¼ 0.28 at 0.5rc below the cone
tip for loose sand (Fig. 19(e)). The normalised radial
displacement decays sharply with increasing vertical depth
below the cone tip, becoming negligible (u/rc � 1% of the
maximum normalised radial displacement observed) at h/rc
equal to �10, �12 and �14 for loose, medium and dense
sands, respectively (Figs 19(a), 19(c) and 19(e)). The oppo-
site trend is observed in the case of the maximum normal-
ised vertical displacement. The maximumnormalised
vertical displacement v/rc observed at r/rc ¼ 1 at h ¼ 0 is
equal to 0.8 for loose sand, as shown in Fig. 19(f), and to
approximately 0.6 for both the medium dense and dense
sands, as shown in Figs 19(b) and 19(d), respectively. At
larger r/rc (� 1.5, 2, 3, 5 and 8) from the cone tip, the rate
of decay of the normalised vertical displacement is greater
284
283
282
281
280
279
278
24 25 26 27 28 29 30
V
er
tic
al
 p
os
iti
on
: m
m
Horizontal position: mm
(a)
Cone shoulder aligns
with element
Inward motion
towards penetrometer
shaft
Element C (1·5 )rc
σs R50 kPa, 82%, #2Q-ROK� �D
279·0
278·8
278·6
278·4
278·2
278·0
277·8
127·0 127·2 127·4 127·6 127·8 128·0 128·2
V
er
tic
al
 p
os
iti
on
: m
m
Horizontal position: mm
(b)
Cone shoulder aligns
with element
No inward motion towards
penetrometer shaft
Element H (8 )rc
σs R50 kPa, 82%, #2Q-ROK� �D
Fig. 15. Displacement paths for: (a) element C and (b) element H
CONE PENETRATION IN SILICA SAND USING DIGITAL IMAGE CORRELATION 563
for the loose sand (v/rc � 0.30, 0.19, 0.13, 0.07 and 0.02)
than for the dense (v/rc � 0.34, 0.26, 0.18, 0.11 and 0.08)
and medium dense sands (v/rc � 0.32, 0.23, 0.16, 0.08 and
0.04). Fig. 19 also shows that the vertical distance from the
cone tip to the depth at which the normalised vertical
displacement is equal to � 1% of the maximum normalised
vertical displacement, is slightly greater for the dense sand
(h/rc � �14) than for the medium dense (h/rc � �12) and
loose sands (h/rc � �10).
Post-penetration displacement field
The complete displacement field at any instance of the
penetration process can be obtained by combining the
displacement data from all observation windows. Fig. 20
shows the normalised displacement fields obtained as the cone
moved from a normalised cone penetration depth h�/rc ¼ 0
to approximately 20 for tests CPTL50-T4-#2Q-ROK and
CPTD50-T8-#2Q-ROK. At h�/rc � 20, the cone tip was lo-
cated at a vertical distance of 40rc from the chamber base
boundary; at this position, there are no boundary effects on the
displacement field. The contour plots of normalised radial and
vertical displacements shown in Fig. 20 are approximately
symmetric. The radial displacement extends to larger offset
distances from the centre of the cone path in the dense sand
than in the loose sand. Sharp vertical displacements are ob-
served within a small zone in the vicinity of the cone shaft
(from r ¼ 0 to r/rc , 2) for all sands. Below the cone tip,
vertical displacement (v/rc) contours ranging from 0.8 to 0.05
extend vertically to h/rc � �8 and radially to r/rc � 5 for the
loose sand. For the dense sand, the vertical displacement
contour extends to h/rc � �12 vertically and to r/rc � 8 ra-
dially. The vertical displacement contours shown in Fig. 20 are
cut off at the bottom of the chart because they reach the cross
bar of the calibration chamber, which prevents visualisation of
displacements.
�0·2
0
0·2
0·4
0·6
0 10 20 30
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t, 
 /
an
d
/
u 
r
v 
r
c
c
Normalised penetration depth, */
(a)
h rc
#2Q-ROK
50 kPa, 45%σs R� �D
Element B: 1 , 18r r z r� �c c
Radial
Vertical
1: Start of axial compression
2: Start of cavity expansion
(radial displacement
build-up)
3: End of cavity expansion
4: End of motion
3
3
4
4
2
1
�0·1
0
0·1
0·2
0·3
0·4
0 10 20 30
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t, 
 /
an
d
/
u 
r
v 
r
c
c
Normalised penetration depth, */
(b)
h rc
#2Q-ROK
50 kPa, 45%σs R� �D
Element C: 1·5 , 18r r z r� �c c
Radial
Vertical
1: Start of axial compression
2: Start of cavity expansion
(radial displacement
build-up)
3: End of cavity expansion
4: End of motion
3
3
4
4
2
1
�0·1
0
0·1
0·2
0·3
0 10 20 30
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t, 
 /
an
d
/
u 
r
v 
r
c
c
Normalised penetration depth, */
(c)
h rc
�0·1
0
0·1
0·2
0·3
0 10 20 30
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t, 
 /
an
d
/
u 
r
v 
r
c
c
Normalised penetration depth, */
(d)
h rc
#2Q-ROK
50 kPa, 45%σs R� �D
Element D: 2 , 18r r z r� �c c
Radial
Vertical
1: Start of axial compression
2: Start of cavity expansion
(radial displacement
build-up)
3: End of cavity expansion
4: End of motion
3
3 4
4
2
1
#2Q-ROK
50 kPa, 45%σs R� �D
Element E: 3 , 18r r z r� �c c
Radial
Vertical
1: Start of axial compression
2: Start of cavity expansion
(radial displacement
build-up)
3: End of cavity expansion
4: End of motion
3
3
4
4
2
1
Fig. 16. Evolution of normalised radial and vertical displacements of soil elements at different locations during cone penetration from
h� 0 to 23rc for test CPTL50-T4-#2Q-ROK: (a) element B at r 1rc; (b) element C at r 1.5rc; (c) element D at r 2rc; (d) element E at
r 3rc
564 ARSHAD, TEHRANI, PREZZI AND SALGADO
SUMMARY AND CONCLUSIONS
This paper presents the results of a series of CPTs
performed in a half-circular chamber in sand samples with
uniform density. Three types of silica sands, with different
particle shape, size and crushability characteristics, were
used to prepare samples with different densities, which were
then subjected to a surcharge. Digital images of the cone
moving through the sand samples were acquired simultane-
ously from three cameras during the entire penetration
process. The DIC technique was then used to process these
images to obtain the soil displacement field resulting from
both shallow and deep cone penetration.
Four distinct zones were identified around the cone tip.
Immediately below the cone tip, the displacement vectors
were nearly vertical, while further away from it, the displace-
ment vectors had a larger radial component. This is largely
consistent with the coupling of a cavity expansion analysis
with a separate analysis to handle the intense stress rotation
observed around the cone to calculate cone resistances for a
given soil state. In the zone just below the cone, the
incremental displacement vectors were mostly sub-vertical
0
0·2
0·4
0·6
0 10 20 30
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t, 
 /
an
d
/
u 
r
v 
r
c
c
Normalised penetration depth, */
(a)
h rc
#2Q-ROK
50 kPa, 82%σs R� �D
Element B: 1 , 18·5r r z r� �c c
Radial
Vertical
1: Start of axial compression
2: Start of cavity expansion
(radial displacement
build-up)
3: End of cavity expansion
4: End of motion
3
3
4
4
2
1
�0·1
0
0·1
0·2
0·3
0·4
0 10 20 30
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t, 
 /
an
d
/
u 
r
v 
r
c
c
Normalised penetration depth, */
(b)
h rc
#2Q-ROK
50 kPa, 82%σs R� �D
Element C: 1·5 , 18·5r r z r� �c c
Radial
Vertical
1: Start of axial compression
2: Start of cavity expansion
(radial displacement
build-up)
3: End of cavity expansion
4: End of motion
3
3
4
2
1
0
0·1
0·2
0·3
0 10 20 30
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t, 
 /
an
d
/
u 
r
v 
r
c
c
Penetration depth, */
(c)
h rc
0
0·1
0·2
0·3
0 10 20 30
N
or
m
al
is
ed
 d
is
pl
ac
em
en
t, 
 /
an
d
/
u 
r
v 
r
c
c
Penetration depth, */
(d)
h rc
#2Q-ROK
50 kPa, 82%σs R� �D
Element D: 2 , 18·5r r z r� �c c
Radial
Vertical
1: Start of axial compression
2: Start of cavity expansion
(radial displacement
build-up)
3:End of cavity expansion
4: End of motion
3
3
4
4
2
1
#2Q-ROK
50 kPa, 82%σs R� �D
Element E: 3 , 18·5r r z r� �c c
Radial
Vertical
1: Start of axial compression
2: Start of cavity expansion
(radial displacement
build-up)
3: End of cavity expansion
4: End of motion
3
3
4
4
2
1
Fig. 17. Evolution of normalised radial and vertical displacements of soil elements at different locations during cone penetration from
h� 0 to h� 25rc for test CPTD50-T8-#2Q-ROK: (a) element B at r rc; (b) element C at r 1.5rc; (c) element D at r 2rc; (d) element
E at r 3rc
Highly crushed particles
Moderately crushed particles
1
(
16
 m
m
)
r c
�
1·25 ( 20 mm)rc �
σs c R50 kPa, 20 , 82%, #2Q-ROK� � �z r D
2·5
( 2 mm)
D50
�
4
( 3 mm)
D50
�
Fig. 18. Close-up view of the interface zone along the penetro-
meter shaft for CPTD50-T8-#2Q-ROK
CONE PENETRATION IN SILICA SAND USING DIGITAL IMAGE CORRELATION 565
�16
�12
�8
�4
0
4
0·4 0·3 0·2 0·1 0
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
, 
 /
, r
el
a
tiv
e 
to
 ti
p
h 
r c
Normalised radial displacement, /
(a)
u rc
h r*/ 20c �
σs R50 kPa, 82%
#2Q-ROK
� �D
r r/ 1c �
r r/ 1·5c �
r r/ 2c �
r r/ 3c �
r r/ 5c �
r r/ 8c �
h r*/ 20c �
σs R50 kPa, 82%
#2Q-ROK
� �D
r r/ 1c �
r r/ 1·5c �
r r/ 2c �
r r/ 3c �
r r/ 5c �
r r/ 8c �
�16
�12
�8
�4
0
4
0·8 0·6 0·4 0·2 0
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
, 
 /
, r
el
a
tiv
e 
to
 ti
p
h 
r c
Normalised vertical displacement, /
(b)
v rc
�12
�8
�4
0
4
8
0·4 0·3 0·2 0·1 0
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
, 
 /
, r
el
a
tiv
e 
to
 ti
p
h 
r c
Normalised radial displacement, /
(c)
u rc
�12
�8
�4
0
4
8
0·8 0·6 0·4 0·2 0
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
, 
 /
, r
el
a
tiv
e 
to
 ti
p
h 
r c
Normalised displacement, /
(d)
v rcvertical
h r*/ 20c �
σs R50 kPa, 65%
#2Q-ROK
� �D
r r/ 1c �
r r/ 1·5c �
r r/ 2c �
r r/ 3c �
r r/ 5c �
r r/ 8c �
h r*/ 20c �
σs R50 kPa, 65%
#2Q-ROK
� �D
r r/ 1c �
r r/ 1·5c �
r r/ 2c �
r r/ 3c �
r r/ 5c �
r r/ 8c �
�12
�8
�4
0
4
0·4 0·3 0·2 0·1 0
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
, 
 /
, r
el
a
tiv
e 
to
 ti
p
h 
r c
Normalised radial displacement, /
(e)
u rc
�12
�8
�4
0
4
0·8 0·6 0·4 0·2 0
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
, 
 /
, r
el
a
tiv
e 
to
 ti
p
h 
r c
Normalised displacement, /
(f)
v rcvertical
h r*/ 20c �
σs R50 kPa, 45%
#2Q-ROK
� �D
r r/ 1c �
r r/ 1·5c �
r r/ 2c �
r r/ 3c �
r r/ 5c �
r r/ 8c �
σs R50 kPa, 45%
#2Q-ROK
� �D
r r/ 1c �
r r/ 1·5c �
r r/ 2c �
r r/ 3c �
r r/ 5c �
r r/ 8c �
h r*/ 20c �
Fig. 19. Displacementpathsbelowthecone tipwhenthecone isath�/rc 20: (a) radialdisplacement
path for CPTD50-T8-#2Q-ROK; (b) vertical displacement path for CPTD50-T8-#2Q-ROK;
(c) radial displacement path for CPTMD50-T6-#2Q-ROK; (d) vertical displacement path for
CPTMD50-T6-#2Q-ROK; (e) radial displacement path for CPTL50-T4-#2Q-ROK; (f) vertical
displacement path for CPTL50-T4-#2Q-ROK
566 ARSHAD, TEHRANI, PREZZI AND SALGADO
for the least crushable sand, while they were mostly vertical
for the most crushable sand. A very thin, crushed particle
band of thickness equal to about 2.5D50 formed at the
interface with the cone surface due to intense shearing and
particle crushing below the cone. This thin particle band was
surrounded by a 4D50-thick band consisting of moderately
crushed sand particles. A transition zone, where the incre-
mental displacement vectors rotated from approximately
vertical to radial orientations, was also observed. A drop of
radial stress was observed for elements to the side of the
cone path after the cone moved down below the elevation of
the elements.
Crushability plays a clear role in the geometry of the
displacement field. Greater crushability causes steeper
displacement vectors near and below the cone and produces
sharper transitions to radial displacements in the outer zone
in the soil. The magnitude of the radial incremental
displacement vectors in this outer zone decreased, and that
�5
0
5
10
15
20
105 0 510
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
, 
 /
, r
el
a
tiv
e 
to
 c
on
e 
tip
h 
r c
Normalised radial position, / , relative to cone tip
(a)
r rc
σs R
c
50 kPa, 45%
* 20 , #2Q-ROK
� �
�
D
h r
u r/ c
0·05 0
·1
0·
15
0·2
0·
25
0·3
0·3
0·25
0·
2
0·
15
0·
1
0·
05
0·050·05
0·1
0·15
0·3
0·2
�5
0
5
10
15
20
105 0 510
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
, 
 /
, r
el
a
tiv
e 
to
 c
on
e 
tip
h 
r c
Normalised radial position, / , relative to cone tip
(b)
r rc
σs R
c
50 kPa, 45%
* 20 , #2Q-ROK
� �
�
D
h r
v r/ c
0·
05 0·
1 0·
2
0·5
0·
3 0·
3
0·
5
0·2 0·1
0·05
0·
05
0·05 0·1
0·3
0·5
0·2
�5
0
5
10
15
20
105 0 510
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
, 
 /
, r
el
a
tiv
e 
to
 c
on
e 
tip
h 
r c
Normalised radial position, / , relative to cone tip
(c)
r rc
σs R
c
50 kPa, 82%
* 20 , #2Q-ROK
� �
�
D
h r
u r/ c
0·
05
0·1
0·15
0·2
0·
25
0·35 0·
35
0·25
0·
2
0·
15
0·
1
0·
05
0·05
0·05
0·1 0·1
�5
0
5
10
15
20
105 0 510
N
or
m
al
is
ed
 v
er
tic
al
 p
os
iti
on
, 
 /
, r
el
a
tiv
e 
to
 c
on
e 
tip
h 
r c
Normalised radial position, / , relative to cone tip
(d)
r rc
σs R
c
50 kPa, 82%
* 20 , #2Q-ROK
� �
�
D
h r
v r/ c
0·
05
0·
1 0
·2
0·5
0·
3
0·3
0·5
0·2 0·1 0·05
0·
05
0·05
0·1
0·3
0·5
0·2
0·8
Fig. 20. Normalised radial andvertical displacement afterconepenetration to approximatelyh�/rc 20: (a) radial displacement for
CPTL50-T4-#2Q-ROK; (b) vertical displacement for CPTL50-T4-#2Q-ROK; (c) radial displacement for CPTD50-T8-#2Q-ROK;
(d) vertical displacement for CPTD50-T8-#2Q-ROK
CONE PENETRATION IN SILICA SAND USING DIGITAL IMAGE CORRELATION 567
of the vertical incremental displacement vectors near the
cone increased with increasing particle crushing. This sug-
gests that deformation becomes more localised near the cone
in crushable sand. At shallow penetration, these differences
are sharp for sands with different crushability; for deep
penetration, every sand crushes, and the differences are less
pronounced.
ACKNOWLEDGEMENT
This material is based upon work supported by the
National Science Foundation under grant no. 0969949. The
authors are very grateful for this support.
NOTATION
Br Hardin’s relative breakage parameter
Cu coefficient of uniformity
Dc diameter of DIC calibration chamber
DR relative density of the sand
D50 particle size larger than exactly 50% of soil particles (by
weight)
dc diameter of model cone penetrometer
emax maximum void ratio
emin minimum void ratio
Gs specific gravity
h vertical distance of point in domain with respect to cone tip
h� cone penetration depth measured from top of the sample
li magnitude of displacement vector for element i
nel number of soil elements within subdomain where average
direction of incremental displacement vectors is calculatedQc load measured at cone penetrometer tip
Qt jacking force
qc cone (tip) resistance
r horizontal distance from a point to the cone penetration axis
rc radius of cone penetrometer
ri radial distance from centre of element i to cone penetration
axis
ui radial displacement
vi vertical displacement
z vertical distance from surface of sample to a point
Łave average direction of incremental displacement vectors
Łi direction of displacement vector of element i
� 9n normal effective stress
�s applied surcharge
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