# Asphalt Concrete Characterization Using Digital Image Correlation: A
Systematic Review of Best Practices, Applications, and Future Vision

Siqi Wang, Ph.D  Zehui Zhu, Ph.D  Tao Ma, Ph.D  Jianwei Fan, Ph.D

###### Abstract

Digital Image Correlation (DIC) is an optical technique that measures
displacement and strain by tracking pattern movement in a sequence of captured
images during testing. DIC has gained recognition in asphalt pavement
engineering since the early 2000s. However, users often perceive the DIC
technique as an out-of-box tool and lack a thorough understanding of its
operational and measurement principles. This article presents a state-of-art
review of DIC as a crucial tool for laboratory testing of asphalt concrete
(AC), primarily focusing on the widely utilized 2D-DIC and 3D-DIC techniques.
To address frequently asked questions from users, the review thoroughly
examines the optimal methods for preparing speckle patterns, configuring
single-camera or dual-camera imaging systems, conducting DIC analyses, and
exploring various applications. Furthermore, emerging DIC methodologies such
as Digital Volume Correlation and deep-learning-based DIC are introduced,
highlighting their potential for future applications in pavement engineering.
The article also provides a comprehensive and reliable flowchart for
implementing DIC in AC characterization. Finally, critical directions for
future research are presented.

###### keywords:

Asphalt concrete , Digital image correlation , Fracture mechanics , Deep
learning , Digital volume correlation

††journal: Journal of Testing and Evaluation

[inst1]organization=Department of Road Engineering, School of Transportation,
Southeast University,addressline=Jiangning District, city=Nanjing,
state=Jiangsu, postcode=211189, country=China

[inst2]organization=Department of Civil and Environmental Engineering,
University of Illinois Urbana-Champaign,addressline=205 North Mathews Avenue,
city=Urbana, state=IL, postcode=61801, country=United States

††footnotetext: Accepted for publication in Journal of Testing and Evaluation.
DOI: 10.1520/JTE20230485.

##  1 Introduction

Digital Image Correlation (DIC) is an optical-based method used for measuring
displacements and strains in various materials. DIC functions by tracing
patterns across a sequence of surface images of the specimen during testing
[1]. This is achieved using subset-based matching, wherein gray value
correspondences are extracted by identifying their resemblances [2, 3]. In
1982, Peters and Ranson [4] introduced the concept of extracting local surface
deformations from single-camera images of planar specimens. A mathematical
framework was proposed to convert digitized 2-D images into full-field
displacement measurements, which is now known as two-dimensional digital image
correlation (2D-DIC). Professor Sutton further contributed to the field by
exploring implementation algorithms and applications [5, 6, 7]. However, it
became evident in the mid-1980s that 2D-DIC was limited to flat specimens and
single-plane deformations, which did not align with the requirements of most
engineering studies. Consequently, the necessity for stereovision systems
capable of capturing full-field three-dimensional displacement measurements on
surfaces emerged. In the early 1990s, Professors Chao and Sutton developed the
3D-DIC stereovision system and successfully conducted experiments using it [8,
9].

The accuracy and practicality of DIC have garnered attention within the
asphalt pavement engineering community since the early 2000s. In 2002, Seo et
al. [10] pioneered the application of 2D-DIC to analyze the stress-strain
behavior of the fracture process zone in monotonic and cyclic tests. Since
then, DIC has become a prominent tool for evaluating the material properties
of AC, validating experimental procedures, and verifying theoretical models
[11, 12, 13, 14, 15, 16, 17]. Figure 1 illustrates the number of scientific
papers retrieved from the Web of Science (Science Citation Index Expanded) by
using the search term _digital image correlation asphalt_ , covering the
period from 2002 to 2023. The increasing number of published articles
demonstrates the growing adoption of DIC in characterizing AC, particularly
after 2014. It is important to note that 2D-DIC has received considerably more
attention than 3D-DIC, primarily due to its simpler implementation (e.g.,
single-camera setup without the requirement of stereo camera calibration)
[18]. The dominance of 2D-DIC is evident as it accounts for over 95% of the
published articles in this field. Remarkably, the initial publication
employing 3D-DIC emerged as recently as 2017 [19].

Figure 1: Number of articles published using DIC in AC characterization.

Vendors commonly offer integrated software that enables users to obtain
displacement and strain measurements. Consequently, users often perceive the
DIC technique as an out-of-box tool and lack a thorough understanding of its
operational and measurement principles. However, the accuracy of displacement
and strain measurements obtained through DIC is significantly influenced by
the specific implementation details employed [1]. Common inquiries from users
encompass various aspects, such as the optimal preparation of specimen speckle
and imaging system set up to attain the highest accuracy, approaches for
assessing the precision of the DIC system, strategies for selecting user
inputs in DIC analysis, understanding the underlying algorithms used by the
DIC technique, and methods for post-processing and interpolating the measured
displacement or strain maps to characterize AC. Hence, performing a thorough
review of DIC can contribute to bolstering confidence in its usage and
fostering standardization within the pavement engineering community.

This article provides a comprehensive and in-depth review of DIC as a crucial
tool for laboratory testing of AC. The primary focus of this study centers
around the widely employed 2D-DIC and 3D-DIC techniques. The article
thoroughly examines the best practices pertaining to specimen speckle pattern
preparation, the configuration of single-camera or dual-camera imaging
systems, and the meticulous execution of DIC analyses. To enhance readers’
understanding of the utility of DIC in their own work, the article documents
experiences from over 100 publications spanning the past two decades, focusing
on applying DIC-measured full-field displacement and strain maps for AC
characterization. Furthermore, the article explores emerging DIC
methodologies, including Digital Volume Correlation (DVC) and deep-learning-
based DIC, which have not yet been adopted by the pavement engineering
community but exhibit significant potential for future applications. Lastly,
the article provides a flowchart intended to serve as a comprehensive and
reliable reference for future DIC implementation in AC characterization.

##  2 Specimen Preparation

A crucial factor for accurate DIC measurements is the quality of the speckle
pattern in use. The arrangement of speckles must possess specific attributes,
as highlighted by Dong et al. in their comprehensive analysis [20]. The term
”high contrast” refers to the necessity of observing variations in grayscale
intensities, resulting in significant intensity gradients among the speckles.
The condition of ”randomness” requires the absence of any repetitive or
periodic elements within the speckle configuration. This absence is vital for
achieving comprehensive displacement mapping across the entire field of view.
”Isotropy” mandates that the speckle arrangement remains unbiased in all
directions. Both the speckles and the spaces between them should maintain
consistent dimensions across various orientations, as noted by Reu [21]. To
prevent aliasing artifacts, it’s advisable to use speckle granules sized
around three to five pixels or slightly larger [22]. Lastly, the concept of
”stability” entails the firm adherence of the speckle pattern to the sample’s
surface. This adherence ensures that the pattern deforms coherently with the
sample, even during significant translations and deformations. This stability
should be upheld without causing noticeable changes in both geometric
arrangement and grayscale characteristics.

The ongoing scientific discourse pertains to whether the natural texture of AC
specimens meets the specified requirements. Xing et al. [23] proposed that the
natural texture of asphalt mixtures is suitable for DIC analysis, particularly
in the case of AC with a small normal maximum aggregate size (NMAS). This
perspective has received subsequent validation from various investigations,
including Guo et al. [24]. In contrast, Yuan et al. [25] conducted a
systematic comparison of DIC measurements using both artificially generated
patterns and natural textures. Their findings indicated that the natural
texture exhibited an error rate over three times greater than that of
artificially generated speckle patterns. Moreover, the broader DIC research
community tends to favor the generation of artificial speckle patterns to
enhance measurement reliability and consistency [1, 20]. Thus, the subsequent
discussion will center on best practices for creating artificial speckle
patterns.

###  2.1 Artificial Speckle Pattern Fabrication

citetdoll2015evaluation examined the performance of three commonly employed
methods in creating artificial speckle patterns for AC specimens. The
evaluation included a comprehensive analysis of the intensity histograms,
noise components, and measurement accuracy for simple motions involving rigid
body translation and rotation. The three speckle pattern fabrication
techniques assessed were as follows: 1) smoothing the sample surface using
sandpaper and an airbrush, followed by the application of several light layers
of white paint and a final layer of black paint [10]; 2) applying a black
paint layer to the surface and then generating the speckle pattern by spraying
white paint on top of it; and 3) applying a thin layer of plaster to the
specimen surface to fill in any holes (i.e., voids), followed by applying the
speckle pattern on the plaster layer.

The results showed that while there were no significant differences between
the two patterns where the paint was applied directly to the asphalt, the
pattern on plaster gave better results. However, using a coating can introduce
other drawbacks, as the material at the surface may not behave the same way as
the material underneath it, leading to inaccurate measurements. During
fracture experiments, the authors observed that the plaster coating did not
behave like the asphalt material, resulting in the peeling off of the plaster
and inaccurate measurements. Hence, the authors suggest using the direct
application of white and black paints without any coating, despite the
resulting increase in measurement error caused by surface irregularities, as
it enables accurate measurement of the material’s displacements [26].

LePage et al. [27] conducted an inquiry into whether superior results for DIC
are achieved with white-on-black or black-on-white painted speckle patterns.
Their findings identified the optimal speckle pattern composition as a white
paint basecoat overlaid with black speckles. The study highlighted that black
paint’s greater concealing capacity and white paint’s undertone due to
Rayleigh scattering contributed to heightened contrast of the black speckles.
Consequently, this increased contrast led to suggestions for reduced subset
sizes, narrower correlation confidence intervals, higher mean intensity
gradients, and ultimately more accurate displacement measurements (with a 24%
decrease in median normalized false displacement). As a result, the
recommended painted speckle pattern entails a thin white paint basecoat, equal
coverage for the basecoat and black speckles, and a speckle density of around
50% [27].

Regarding the fabrication of speckle patterns, both spray bottles and
airbrushes are commonly employed tools, as depicted in Figure 2. Nonetheless,
there exists a variation in the size of resulting speckle granules, with spray
bottle techniques generally yielding larger granules compared to airbrush
methods. To exemplify, in their work, Doll et al. [28] utilized an airbrush to
achieve an eight µm/pixel spatial resolution (i.e., the dimension of the pixel
size representing the area covered on the specimen), allowing differentiation
between strains in aggregate particles and the asphalt matrix regions between
particles. Conversely, for assessing far-field strain and displacement fields,
assuming homogeneous in-plane deformation, Doll et al. [29] utilized a spray
can, attaining an approximate spatial resolution of forty µm/pixel.

The dimensions of the nozzle, the gap between the nozzle and the specimen
surface, air pressure, and solution viscosity are all pivotal factors that may
impact the distribution of speckle sizes as well as the standard deviation of
this distribution [30]. Conducting preliminary trials is advisable to ensure
that speckle granules measure around three to five pixels in size or
marginally larger [22].

Figure 2: Schematic illustration of speckle pattern fabrication using a spray
can or airbrush.

###  2.2 Speckle Pattern Quality Assessment

Different operators using various techniques to fabricate speckle patterns may
result in different qualities, necessitating a quality assessment. Two
categories of parameters are used to assess speckle patterns: local and
global. Local parameters, such as subset entropy ($\delta$), sum of square of
subset intensity gradients (SSSIG), and mean subset fluctuation ($S_{f}$), are
designed to quantify individual subsets of the pattern and can assist with
selecting the optimal subset sizes. On the other hand, global parameters,
including mean intensity gradient (MIG) and Shannon entropy, quantify the
entire speckle pattern. SSSIG and MIG are the most cited local and global
metrics, respectively, owing to their solid theoretical foundations and
straightforwardnformulations [20, 31, 32, 33].

To calculate SSSIG, Equation 1 is used. The threshold of SSSIG can be
determined based on the desired level of accuracy. Further information can be
found in [31]. SSSIG is frequently employed to assist in selecting the optimal
subset size for DIC analysis, which will be discussed in a subsequent section.
It should be noted, however, that SSSIG cannot distinguish between random and
periodic speckle patterns as it only focuses on the local speckle pattern
within an individual subset.

$SSSIG=\sum_{i=1}^{N}\sum_{j=1}^{N}[f_{{x,y}}(\mathbf{x}_{ij})]$ (1)

where $f_{{x,y}}(\mathbf{x}_{ij})$ is the first derivative of the intensity
gray value at pixel $\mathbf{x}_{ij}$ in $x$\- or $y$\- direction; $N$ is the
subset size.

Equation 2 outlines the mathematical formula for calculating MIG. It is
essential to note that a high value of MIG indicates a good speckle pattern. A
recent study by Zhu and Al-Qadi [17] found that a minimum MIG value of 25
produced a small displacement error.

$MIG=\frac{\sum_{i=1}^{W}\sum_{j=1}^{H}|\nabla f(\mathbf{x}_{ij})|}{W\times
H}$ (2)

where $W$ and $H$ are image width and height in pixels, respectively; $|\nabla
f(\mathbf{x}_{ij})|=\sqrt{f_{x}^{2}(\mathbf{x}_{ij})+f_{y}^{2}(\mathbf{x}_{ij})}$;
$f_{x}(\mathbf{x}_{ij})$ and $f_{y}(\mathbf{x}_{ij})$ are the intensity
derivatives at pixel ${x}_{ij}$ at the $x$\- and $y$-direction, respectively.

##  3 2D-DIC

The 2D-DIC method is a popular optical measurement technology due to its
simple setup, minimal environmental prerequisites, and extensive sensitivity
and resolution capabilities. It has become the primary DIC technology used in
asphalt concrete characterization. However, limitations of the method include
in-plane deformation measurement only, the need for a randomly distributed
gray intensity on the object surface, and reliance on imaging system quality
[34]. This section will discuss best practices for 2D-DIC imaging system
setup, algorithms, and applications in asphalt concrete characterization.

###  3.1 Imaging System

A frequently employed 2D DIC setup comprises a camera, illumination system,
computer, and post-processing software. 2D-DIC requires high-quality images
and control of imaging parameters for accurate measurements.

First, to achieve optimal image quality and accurate measurement in 2D-DIC, it
is essential to determine the optimal camera-object distance by fitting the
Region-of-Interest (ROI) to the Field-of-View (FOV) as much as possible. The
pinhole camera model (Figure 3) can be used to calculate the optimal distance
between the camera and the object, given the selected lens.

Figure 3: Pinhole camera model.

For example, to measure the deformation of an AC specimen during a static
loading test, with a specimen size of approximately 50$\times$50 mm, a
standard 4 Megapixel camera with a sensor size of 2048$\times$2048 pixels and
a pixel size of 5 $\mu$m is used. The actual dimension is slightly increased
to ensure the object remains in view throughout the test. Using a 35 mm wide
lens, the optimal distance required to fit the ROI within the FOV can be
calculated (Equation 3):

$OD=\frac{wf}{S_{w}}+f=\frac{60\times 35}{2048\times\frac{5}{1000}}+35\approx
240mm$ (3)

where $OD$ is the optimal distance between the object and the sensor; $w$ is
the dimension of the AC specimen, in this case, its width; $S_{w}$ is the
corresponding dimension on the camera sensor, calculated as the number of
pixels multiplied by the size of a pixel on the sensor, which is typically
provided in the camera parameters; and $f$ is the focal length of the lens
[35].

Then, for precise 2D-DIC measurements, it’s essential for the camera’s CCD
sensor and the object’s surface to be aligned in parallel. Additionally, any
out-of-plane movement of the specimen during loading must be minimal, as
emphasized by Sutton et al. [36]. Therefore, careful adjustment and
positioning of the camera are essential, which can be challenging due to the
lack of proper tools.

A frequently employed method relies on the conventional computer vision camera
calibration process [37]. Initially, at least ten calibration images is
acquired using a standardized calibration plate. Subsequently, the calibration
plate is held against the specimen to ensure its parallel alignment with the
specimen. Next, a calibration procedure is executed, employing the final
captured image and readily accessible tools, such as the MATLAB Camera
Calibration Toolbox. Finally, iterative adjustments to the camera position are
made and the aforementioned steps are iteratively repeated until an acceptable
configuration is attained. It is essential to emphasize that this approach
yields accuracy within a tolerance of approximately $\pm$2∘ [38].

Wittevrongel et al. [38] developed a high-precision rotation stage (Figure 4)
using stepper engines to control the phi and theta angles, achieving precise
control with 200 steps per revolution. The Psi angle is omitted, as rotational
movements within the plane are permissible in 2D-DIC. The research findings
demonstrate that the camera can be positioned accurately with a perpendicular
precision of approximately $\pm$0.15∘.

Figure 4: Mechanical camera positioning tool (a) camera’s placement in
relation to the specimen’s surface; (b) diagram

.

Lastly, obtaining high-quality images involves adjusting the aperture, sensor
sensitivity (ISO), and exposure time (shutter speed) to achieve sharp, well-
illuminated images with minimal noise [39, 35]. These three parameters are
commonly referred to as the “exposure triangle” and are determined by the
properties of the lens and sensor. The relationship between these parameters
is illustrated in Figure 5.

Figure 5: Exposure triangle.

The ISO, or sensor sensitivity, is a property of the camera sensor. Increasing
the ISO makes the sensor more sensitive to light and increases the image
noise. To minimize noise, the ISO value should be kept at its factory default
(usually ISO 100) and not changed.

The aperture, a property of the lens, controls the amount of light that enters
the camera. A higher aperture allows more light to enter and narrows the depth
of field, which may cause the background to be blurred. For flat objects like
most AC specimens, positioned perpendicularly to the camera, narrow depths of
field are generally sufficient. However, more complex structures with curved
surfaces or different components may require a smaller aperture.

Moreover, to ensure a sharp image during a real experiment, the exposure time
must be shorter than the motion of the object being photographed. This is
crucial for accurate measurements. Increasing sensor sensitivity is not
recommended to avoid adding noise. Therefore, the solution is adding
artificial light to brighten the scene.

###  3.2 Algorithm

####  3.2.1 Fundamental Principles

DIC operates by monitoring pattern displacements in a series of images through
subset-based matching, which identifies gray value correlations by comparing
similarities. As depicted in Figure 7, when computing point $P$ displacements,
a square subset of pixels $((2M+1)\times(2M+1))$ is selected from the
reference image and matched with the deformed image. The subset size ($M$) is
a crucial parameter in DIC analysis as it directly affects measurement
accuracy. For dependable correlation analysis, the subset dimensions must
balance distinct intensity patterns and accurate approximation of deformations
using $1^{st}$ or $2^{nd}$-order subset shape functions. This balancing act
calls for a compromise between employing larger or smaller subset sizes, as
discussed by Pan et al. [31]. SSSIG, which assesses speckle pattern quality,
is commonly used to select the optimal subset size. Figure 6 illustrates a
flowchart outlining the process to identify the ideal subset size. This
involves commencing with a smaller subset size and progressively enlarging it
until the SSSIG surpasses the predefined threshold. The threshold can be
determined based on the desired level of accuracy following the procedures
presented in Pan et al. [31].

Figure 6: Flowchart of using SSSIG to select optimal subset size.

In the reference image, it’s essential to designate an ROI that is
subsequently partitioned into equidistant grids. The computation of
displacements at each grid point facilitates the derivation of the
displacement field.

The matching is attained by searching for a correlation coefficient extremum.
Equation 4 lists commonly used correlation criteria. Compared to cross-
correlation (CC) and sum-of-squared differences (SSD), the zero-normalized
cross-correlation (ZNCC) and zero-normalized sum-of-squared differences
(ZNSSD) offer better performance against noise. They are less insensitive to
lighting fluctuations (e.g., offset and linear scale) [34].

Figure 7: Area-based matching.

$\begin{aligned}
C_{SSD}&=\sum_{i=-M}^{M}\sum_{j=-M}^{M}[f(x_{i},y_{j})-g(x_{i}^{\prime},y_{j}^{\prime})]^{2}\\\
C_{ZNSSD}&=\sum_{i=-M}^{M}\sum_{j=-M}^{M}[\frac{f(x_{i},y_{j})-f_{m}}{\sqrt{\sum_{i=-M}^{M}\sum_{j=-M}^{M}[f(x_{i},y_{j})-f_{m}]^{2}}}-\frac{g(x_{i}^{\prime},y_{j}^{\prime})-g_{m}}{\sqrt{\sum_{i=-M}^{M}\sum_{j=-M}^{M}[g(x_{i}^{\prime},y_{j}^{\prime})-g_{m}]^{2}}}]^{2}\\\
C_{CC}&=\sum_{i=-M}^{M}\sum_{j=-M}^{M}f(x_{i},y_{j})g(x_{i}^{\prime},y_{j}^{\prime})\\\
C_{ZNCC}&=\frac{\sum_{i=-M}^{M}\sum_{j=-M}^{M}[f(x_{i},y_{j})-f_{m}]\times[g(x_{i}^{\prime},y_{j}^{\prime})-g_{m}]}{\sqrt{\sum_{i=-M}^{M}\sum_{j=-M}^{M}[f(x_{i},y_{j})-f_{m}]^{2}}\sqrt{\sum_{i=-M}^{M}\sum_{j=-M}^{M}[g(x_{i}^{\prime},y_{j}^{\prime})-g_{m}]^{2}}}\\\
\end{aligned}$

(4)

where $f(x_{i},y_{j})$ is gray value at $(x_{i},y_{j})$ in the reference
subset. $g(x_{i}^{\prime},y_{j}^{\prime})$ is gray value at
$(x_{i}^{\prime},y_{j}^{\prime})$ in the deformed subset. $f_{m}$ and $g_{m}$
are mean gray values of the reference and deformed subset, respectively.

A correlation coefficient or ZNSSD cost approaching zero indicates a favorable
match. ZNCC is directly related to ZNSSD. Equation 5 indicates that a
$C_{ZNCC}$ value of 1 signifies a perfect match, while a value of 0 denotes no
correlation.

$C_{ZNCC}=1-0.5C_{ZNSSD}$ (5)

In Equation 4, the reference point $(x_{i},y_{j})$ is associated with the
deformed point $g(x_{i}^{\prime},y_{j}^{\prime})$ through a mapping function.
This function can be either $1^{st}$-order (as in Equation 6) or
$2^{nd}$-order (as in Equation 7). The $2^{nd}$-order function has the ability
to approximate more intricate displacements compared to the $1^{st}$-order
one.

$\begin{bmatrix}x_{i}^{\prime}\\\
y_{j}^{\prime}\end{bmatrix}=\begin{bmatrix}x_{0}\\\
y_{0}\end{bmatrix}+\begin{bmatrix}1+u_{x}&u_{y}&u\\\
v_{x}&1+v_{y}&v\end{bmatrix}\begin{bmatrix}\Delta x\\\ \Delta y\\\
1\end{bmatrix}$ (6)

$\begin{bmatrix}x_{i}^{\prime}\\\
y_{j}^{\prime}\end{bmatrix}=\begin{bmatrix}x_{0}\\\
y_{0}\end{bmatrix}+\begin{bmatrix}1+u_{x}&u_{y}&\frac{1}{2}u_{xx}&\frac{1}{2}u_{yy}&u_{xy}&u\\\
v_{x}&1+v_{y}&\frac{1}{2}v_{xx}&\frac{1}{2}v_{yy}&v_{xy}&v\end{bmatrix}\begin{bmatrix}\Delta
x\\\ \Delta y\\\ \Delta x^{2}\\\ \Delta y^{2}\\\ \Delta x\Delta y\\\
1\end{bmatrix}$ (7)

Here, $u$ and $v$ represent the horizontal and vertical displacement
components for the subset center $(x_{0},y_{0})$, respectively. The quantities
$\Delta x=x_{i}-x_{0}$ and $\Delta y=y_{j}-y_{0}$ are defined. Additionally,
$u_{x}$, $u_{y}$, $v_{x}$, and $v_{y}$ signify the components of
$1^{st}$-order displacement gradients. Furthermore, $u_{xx}$, $u_{yy}$,
$u_{xy}$, $v_{xx}$, $v_{yy}$, and $v_{xy}$ denote the components of
$2^{nd}$-order displacement gradients. This paper employs the notation
$\mathbf{p}$ to represent the desired displacement vector, which consists of
either 6 or 12 unknown parameters.

Given the aforementioned definitions, it is evident that the computation of
$\mathbf{p}$ entails an optimization task involving a user-defined cost
function, such as Equation 4 and Equation 5. DIC employs the Newton–Raphson
(NR) iterative approach for optimization, as outlined in Equation 8.

$\mathbf{p}=\mathbf{p}_{0}-\frac{\nabla C(\mathbf{p}_{0})}{\nabla\nabla
C(\mathbf{p}_{0})}$ (8)

Here, $\mathbf{p}_{0}$ represents the initial estimation of the displacement
vector, while $\mathbf{p}$ denotes the subsequent iterative solution. The
symbol $\nabla C(\mathbf{p}_{0})$ corresponds to the $1^{st}$-order
derivatives of the cost function, and the term $\nabla\nabla
C(\mathbf{p}_{0})$ refers to the Hessian matrix [34].

####  3.2.2 RG-DIC

The preceding section exclusively delineated the process of computing
$\mathbf{p}$ for an individual point. To achieve full-field displacement
measurement, the reliability-guided digital image correlation (RG-DIC)
technique is widely employed [40]. This approach has been integrated into
open-source solutions such as Ncorr [40, 41].

The process commences with the determination of an initial displacement vector
estimate for a user-defined reference point. To achieve this, one might employ
normalized cross-correlation or the scale-invariant feature transform (SIFT)
technique for an informed initial estimation. Following this, the algorithm
computes $\mathbf{p}_{seed}$ and its associated correlation coefficient.
Subsequently, the algorithm computes the displacement vectors and correlation
coefficients for the four adjacent points of the seed point, utilizing
$\mathbf{p}_{seed}$ as the initial approximation. These computed correlation
coefficients are incorporated into a priority queue. The subsequent step
involves extracting the highest-correlation point from the queue and utilizing
its corresponding $\mathbf{p}$ as the starting point to compute displacements
for its neighboring points, if they are yet to be computed. This process
iterates until the priority queue becomes empty, signifying the calculation of
all points within the ROI.

Due to its incorporation of correlation analysis focused on points with the
highest correlation, the RG-DIC approach exhibits resilience to minor image
discontinuities. This attribute enhances its efficacy in analyzing images of
AC specimen surfaces, which often exhibit irregularities arising from factors
like air voids and diverse aggregate orientation.

The RG-DIC method may encounter challenges when dealing with substantial
discontinuities, such as cracks, within the deformed image. This issue
commonly arises during the analysis of deformed images obtained during the
post-peak load stage of AC testing. To mitigate the decorrelation problem, Zhu
and Al-Qadi [17] introduced the multi-seed incremental approach. In this
context, “multi-seed” entails manually placing seed points on all partitions
artificially created by the significant discontinuities, while “incremental
analysis” involves using an intermediate deformed image as an updated
reference image if the deformed image exhibits severe decorrelation with the
original reference image. When correctly implemented, the multi-seed
incremental RG-DIC analysis consistently attains high accuracy, even in the
presence of substantial discontinuities (such as cracks) in the deformed
image.

####  3.2.3 Compute of Strains

In the realm of AC characterization, complete strain distributions frequently
hold greater significance and desirability compared to displacement fields.
However, strains are more challenging to resolve than displacement fields due
to their sensitivity to noise caused by differentiation [34, 41]. Thus, it is
necessary to smooth displacement fields before calculating strain fields.

An illustration of this concept is the strain window technique introduced by
Pan et al. [42], wherein displacement gradients and Green-Lagrangian strains
are computed through a least squares plane fit applied to a subset of
displacement information. Subsequently, the algorithm resolves an excessive
system of equations to ascertain the strains, offering flexibility in
adjusting the size of the subset window. More details can be found elsewhere
[41, 42, 43].

Upon the parameter solution, they are employed for the computation of
$e_{xx}$, $e_{xy}$, and $e_{y}$ as per Equation 9. This procedure is then
extended across the entire displacement field to derive the corresponding
strain field.

$\displaystyle e_{xx}$ $\displaystyle=\frac{1}{2}(2\frac{\partial u}{\partial
x}+(\frac{\partial u}{\partial x})^{2}+(\frac{\partial v}{\partial x})^{2})$
(9) $\displaystyle e_{xy}$ $\displaystyle=\frac{1}{2}(\frac{\partial
u}{\partial y}+\frac{\partial v}{\partial x}+\frac{\partial u}{\partial
x}\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}\frac{\partial
v}{\partial y})$ $\displaystyle e_{yy}$
$\displaystyle=\frac{1}{2}(2\frac{\partial v}{\partial y}+(\frac{\partial
u}{\partial y})^{2}+(\frac{\partial v}{\partial y})^{2})$

It is vital to emphasize that achieving reliable and precise full-field strain
estimation necessitates the careful selection of an appropriate local strain
calculation window size. For uniform deformation, a larger window size for
strain calculation is preferable. However, when dealing with non-uniform
deformation, the choice of strain calculation window size should be
deliberate, considering the interplay between strain accuracy and smoothness.
A small window might not effectively mitigate displacement noise, whereas an
overly large window might yield an impractical linear deformation
approximation within the strain calculation window [34, 42, 44].

####  3.2.4 Software

The effective implementation of algorithms is crucial for 2D-DIC analysis.
Table 1 presents a compilation of presently accessible non-commercial 2D-DIC
software. It is essential to note that this list exclusively comprises
software with supporting peer-reviewed research papers, and there may be other
available choices.

Software | Authors | First Release | User Interface | Open Source | Free | Language | Citations (Oct 2023)
---|---|---|---|---|---|---|---
NCorr | Blaber et al. [41] | 2015 | Yes | Yes | Yes | Matlab | 1,629
DICe | Turner et al. [45] | 2015 | Yes | Yes | Yes | C++ | 12
$\mu$DIC | Olufsen et al. [46] | 2019 | No | Yes | Yes | Python | 36
OpenCorr | Jiang [47] | 2021 | No | Yes | Yes | C++ | 6
iCorrVision-2D | de Deus Filho et al. [48] | 2022 | Yes | Yes | Yes | Python | 7

Table 1: 2D-DIC Software.

###  3.3 Applications

The 2D-DIC technique is extensively used in the asphalt pavement field to
assess the material properties of AC. It is recognized as a practical and
robust method for quantifying the deformation of AC specimens in diverse
laboratory testing environments. A review of over 100 academic papers, with a
specific emphasis on publications from 2017 onwards, revealed that the semi-
circular bending (SCB) test, indirect tensile test (IDT), three-point bending
(3PB) test, and four-point bending (4PB) test were the most frequently
observed applications of the 2D-DIC technique. A limited number of studies
employed the single-edge notched bending (SENB) test, disk-shaped compact
tension (DCT) test, direct tension test (DTT), and triaxial repeated creep
test methodologies.

Table 2 summarizes the application of 2D-DIC in reviewed academic papers.
Broadly, the applications of 2D-DIC can be classified into three categories:
direct application of 2D-DIC-generated displacement or strain maps, derivation
of mechanistic parameters for AC material properties, and tracking of crack
propagation or damage evolution. The following sections provide detailed
discussions of these applications.

Type | Test | Applications | Articles
---|---|---|---
Fracture | SCB | Strain & Displacement | [49, 50, 51, 52, 19]
Mechanistic Parameters | [53, 54, 55, 56, 16, 57, 28, 29]
Crack Propagation | [53, 58, 59, 56, 54, 60, 55, 61, 62]
3PB | Strain & Displacement | [63, 64]
Crack Propagation | [65, 66, 67]
SENB | Strain & Displacement | [68]
Crack Propagation | [69]
DCT | Strain & Displacement | [70, 19, 64]
Fatigue | 4PB | Mechanistic Parameters | [71]
Crack Propagation | [72, 71, 73, 74, 75, 76, 77]
SCB | Strain & Displacement | [78, 50, 79, 80, 81, 82, 83]
Crack Propagation | [84, 79, 61, 15, 83, 62]
Flexural fatigue test | Crack Propagation | [85]
Strength | IDT | Strain & Displacement | [86, 87, 23, 88, 89, 90]
Damage Evolution | [56, 24, 91, 92]
Others | Pull-off adhesion test | Mechanistic Parameters | [93]
| DTT | Strain & Displacement | [94, 95, 96]
| Damage Evolution | [95, 97, 98]
| Freeze-thaw test | Strain & Displacement | [99]
| Light healing test | Strain & Displacement | [100]
| 2T3C HCA | Displacement | [101]

Table 2: Applications of 2D-DIC in AC laboratory tests.

####  3.3.1 Direct Application of Strain/Displacement Fields

The predominant focus in reviewed papers only involves the direct application
of DIC-measured strain or displacement maps. These applications can be broadly
categorized into two groups based on measurement scope: global, involving the
entire displacement or strain fields of the specimen, and local, focused
solely on the area of interest.

In global applications, researchers analyze chosen displacement or strain
components (e.g., horizontal, vertical) at various time points during specimen
loading to gain qualitative insights into material mechanical properties. This
includes identifying high-strain zones on the specimen surface often
associated with cracks or damage zones, which will be elaborated upon in the
subsequent section dedicated to crack propagation measurement via DIC [102,
91, 56, 103, 12]. Another significant application involves employing DIC as a
validation tool for numerical models or displacement/strain sensors. DIC-
measured displacement or strain fields serve as the ”ground truth” to validate
these models or sensors [104, 78, 105, 106, 107]. Additionally, DIC is
employed as a measurement tool for deformation assessment, such as quantifying
permanent deformations in repeated load uniaxial tests or cyclic uniaxial
compression tests and determining vertical deformations in AC specimens during
IDT [106, 108, 90].

In the context of local applications, researchers focus on specific regions
within DIC-derived displacement and strain maps. A prominent use case involves
the measurement of Crack Mouth Opening Displacement (CMOD) and the
investigation of aggregate crushing near the load point. CMOD serves to
characterize the displacement alteration perpendicular to the crack plane
within a fatigued-notched region of a specimen subjected to fracture toughness
testing [109]. CMOD measurements are taken along the loading axis or the
specimen’s surface, quantifying the difference between the initial and final
crack openings. Traditionally, this is done with a physical clip-on
displacement gauge attached to opposite sides of the crack mouth to generate a
load-CMOD curve for fracture energy calculation. The application of DIC for
measuring CMOD obviates the need for a physical gauge, replacing it with
virtual measurement points positioned on opposite sides of the specimen [64].
DIC-derived CMOD is a crucial metric for assessing AC’s fracture
characteristics and crack resistance. Specifically, fracture energy,
representing the energy required to generate a unit area of crack, is a
significant parameter in this context. It can be determined by calculating the
area under the load-CMOD curve and subsequently dividing it by the ligament
area, approximately equivalent to the product of the crack length and specimen
thickness [109, 64, 54, 103, 110, 111, 112].

Another crucial local application involves the investigation of potential
aggregate crushing near the load point. This is of paramount importance due to
the significant energy dissipation associated with such crushing, potentially
resulting in an overestimation of energy contributions to fracture or fatigue
crack formation. Such overestimations are undesirable when employing energy-
based parameters for material property comparisons. For example, Doll [26]
performed SCB tests, wherein strain fields in the vicinity of the loading
point were visually compared at multiple time points throughout the loading
procedure. Their observations revealed no substantial (i.e., order of
magnitude) differences, confirming the absence of significant aggregate
crushing. Similar investigation can be found in the work of Yang et al. [80].

####  3.3.2 Tracking Crack Propagation

Crack propagation monitoring in fracture or fatigue tests is a significant
application of DIC [113, 114, 115]. This application can be categorized into
four distinct approaches based on the underlying principles: visualization-
based, empirical-mechanistic-based, mechanistic-based, and computer-vision-
based.

Figure 8: Tracking crack propagation (a) visualization-based approach; (b)
strain thresholding approach; (c) deviation point assumption; (d) CTOD-based
mechanistic approach; (e) CrackPropNet.

In the visualization-based approach, researchers typically employ strain maps
to discern crack tips and boundaries [102, 91, 56, 103, 12]. High strains are
typically visually detected and categorized as zones of damage or cracks
(Figure 8 _(a)_). This method’s advantage lies in its simplicity, enabling
crack identification by a human expert without the need for subsequent
processing of DIC-derived strain fields. However, its drawback is its
subjective nature, leading to potential variations in crack propagation
assessment among different individuals. Additionally, domain expertise is
essential, as individuals lacking familiarity with the specific materials and
testing procedures may misinterpret crack identifications.

In the empirical mechanistic approach, researchers often make use of empirical
assumptions, such as strain thresholds or deviation points on relative
displacement curves, to define the initiation of cracking. For example,
Safavizadeh and Kim [75] employed a threshold of 9,000 $\mu\epsilon$ for
$e_{xx}$ and 6,000 $\mu\epsilon$ for $e_{yy}$ to detect vertical and
interfacial cracks in double-layer grid-reinforced asphalt concrete notched
beams under four-point bending fatigue loading (Figure 8 _(b)_). Buttlar et
al. [14] assumed that the deviation point on a relative displacement versus
number of cycles curve indicated failure at the layer interface in a double
shear test (Figure 8 _(c)_). The advantage of this approach is its minimal
post-processing requirements. However, it has the drawback of subjectivity and
a reliance on domain-specific knowledge. Furthermore, the empirical
assumptions are often challenging to validate or may remain unverifiable.

In the mechanics theory-based approach, researchers utilize fundamental
mechanics theory to identify cracks. For example, Zhu and Al-Qadi [17]
proposed employing the critical crack tip opening displacement (CTOD) to
define the onset of cleavage fracture (Figure 8 _(d)_). This proposed
threshold holds physical significance and can be readily determined from DIC
measurements. The advantage of this method lies in its reliance on well-
established fundamental theory, reduced dependence on user inputs, and a
higher likelihood of accurately representing actual cracks. However, it is
more complex to implement compared to previous approaches and is less amenable
to automation. It’s important to note that Zhu’s approach is specifically
applicable to fracture tests and has been validated only for mode I fracture.
Further research is recommended to develop methods suitable for fatigue tests
and other fracture modes.

In the context of low-level computer vision, researchers treat strain or
displacement maps as image data and apply classical computer vision techniques
such as thresholding, edge detection, and blob extraction to identify cracks
[116, 117, 118]. This approach primarily relies on detecting abrupt changes in
strain patterns, akin to sharp intensity changes in regular images. Its
advantages include reduced subjectivity compared to prior methods and the
potential for automation. However, a drawback lies in the necessity of using
thresholds, which lack physical meaning and cannot be explicitly validated for
their specific values. Another computer vision approach is based on optical
flow, which characterizes the apparent motion patterns of speckle patterns
[119]. Zhu and Al-Qadi [120] introduced CrackPropNet, a deep neural network
built upon optical flow principles (Figure 8 _(e)_). This network was trained
on a comprehensive image dataset encompassing various types of crack behavior
in AC. CrackPropNet takes a reference image and a deformed image as inputs,
producing a probability map representing crack edges as its output. Notably,
CrackPropNet achieves a high crack detection accuracy on AC specimen surfaces
while maintaining a rapid processing speed of 26 frames per second.

It is important to emphasize that after measuring crack propagation,
additional post-processing techniques can be employed to extract additional
insights. For instance, one can construct an R-curve, which plots the crack
growth resistance against the crack extension [109]. This R-curve-based
approach acknowledges the fact that the fracture resistance of AC may not
remain constant throughout the process of crack propagation [53, 121]. Crack
propagation measurement via DIC can also contribute to Paris’s law, a
prominent fatigue crack growth model that describes the connection between
crack growth rate and stress intensity factor for asphalt concrete, as
represented in Equation 10 [83, 102, 118].

$\frac{da}{dN}=A(\Delta K)^{n}$ (10)

where $a$ represents the crack length, $N$ is the loading cycle, and $A$ and
$n$ denote the material parameters in Paris’ law, while $\Delta K$ signifies
the stress intensity factor amplitude [122]. $A$ and $n$ find wide application
in various contexts, including the prediction of reflective cracking and the
design of asphalt overlays [123, 124].

####  3.3.3 Derivation of Mechanistic Parameters

DIC-measured displacement or strain maps facilitate the determination of
mechanistic parameters. These parameters can be categorized into two groups
based on their processing complexity: direct and secondary. Direct parameters,
such as CTOD, and fracture process zone (FPZ), require limited post-
processing. In contrast, secondary parameters, including strain energy
density, stress intensity factor (SIF) and J-integral, necessitate substantial
post-processing. Further elaboration on these parameters is provided in
subsequent sections.

Figure 9: Combining mechanistic theory and DIC (a) stress-strain curve; (b)
locate crack tip and select a pair of reference points for CTOD measurement;
(c) eFPZ; (d) line J-integral around a notch; (e) viscous and pseudo
displacement fields on a SCB specimen surface.

CTOD functions as a fracture mechanics parameter, particularly pertinent to
elastic-plastic materials, signifying the material’s resistance to crack
propagation through strain at the crack tip [125]. Physically measuring CTOD
is often challenging; nevertheless, it can be deduced using a conventional
plastic hinge model or a J-integral based model [126, 109, 127, 128].
Moreover, accurately measuring CTOD using DIC is widely recognized as
challenging due to the precise crack tip location and suitable reference point
selection difficulties [129]. Zhu and Al-Qadi [17] adopted a method proposed
by Vasco-Olmo et al. [129] for measuring CTOD using DIC-measured displacement
field data from a monotonic SCB test (Figure 9 _(b)_). This approach entails
two steps: first, locating the crack tip by plotting profiles of horizontal
displacement perpendicular to the crack plane and determining the crack tip
coordinates at the intersection of these profiles. Second, determining CTOD by
defining a pair of reference points after locating the crack tip. By plotting
relative displacements for various pairs of reference points, the appropriate
reference point can be identified by identifying a stable plateau region,
indicating the end of the strip-yield zone. It should be noted that this
approach has only been applied to mode I fracture tests.

The DIC-measured strain field enables the determination of the stress-strain
curve and the computation of strain energy density. The stress-strain curve
characterizes AC’s response to loading, offering information on its strength,
stiffness, ductility, and failure thresholds. Strain energy denotes the energy
stored within a deforming material, while strain energy density represents the
energy stored per unit volume and corresponds to the integral area under the
stress-strain curve, essentially encapsulating the area under the stress-
strain curve. Strain energy density has been employed for fracture toughness
prediction, fatigue damage characterization, and assessment of non-fracture-
related energy dissipation [29, 130, 131].

Asphalt concrete is a viscoelastic material, demonstrating both instantaneous
elastic behavior and time-dependent viscous properties. This implies the
presence of energy dissipation within the material when subjected to loading.
Furthermore, AC’s modulus is not constant, introducing complexity in deriving
a stress field from the DIC-measured strain field. In accordance with
established viscoelastic theory, the constitutive response of viscoelastic
media can be expressed using the convolution Equation 11 [132].

$\sigma_{ij}(\xi)=\int_{0}^{\xi}E_{ijkl}(\xi-\xi^{\prime})\frac{\partial\epsilon_{kl}(\xi^{\prime})}{\partial\xi^{\prime}}d\xi^{\prime}$
(11)

where $\sigma_{ij}$ and $\epsilon_{ij}$ represent stress and strain tensor
components, $E_{ijkl}$ denotes the stiffness modulus components that depend on
both time and temperature, and $\xi$ is a dimensionless time reduction
parameter. $\xi$ is defined for thermo-rheologically simple materials as
$\xi=t/a_{T}$, with $a_{T}$ representing a shift factor derived from the
Williams–Landel–Ferry equation [133, 134].

In a scenario where strain is directly determined as a function of applied
load using DIC, the stress history was determined by evaluating the
convolution integral described in Equation 11 at each load increment. To
employ Equation 11, it remains imperative to possess explicit knowledge of the
temperature and time-dependent modulus $E$, typically expressed as a Prony
series fit based on experimental data (Equation 12).

$E(t)=E_{e}+\sum_{n=1}^{N}E_{n}e^{-\frac{t}{\rho_{n}}}$ (12)

The equilibrium modulus, denoted as $E_{e}$, is a key parameter, while $E_{n}$
represents the Prony coefficients, and $\rho_{n}$ corresponds to the
relaxation times.

Following this, one can plot the stress-strain curve (Figure 9 _(a)_) and
compute the strain energy density using Equation 13.

$W=\int_{0}^{\epsilon}\sigma_{ij}d\epsilon_{ij}$ (13)

The DIC-measured strain field facilitates the study of the FPZ, a region near
the crack tip where material undergoes damage, even in the absence of complete
cracking. This damage may manifest as microcracks, void formation, significant
plastic deformation, or large-scale shearing (shear bands) [135]. For AC, a
strain-based approach inspired by Wu et al. [136]’s work on concrete is
considered effective. In this approach, the FPZ is defined as the zone where
strains surpass a specified threshold value known as the tensile strain
capacity, representing the maximum strain the material can endure before crack
formation [28]. As precise tensile strain capacity values for different AC
mixes are often unavailable, researchers commonly adopt a consistent, albeit
arbitrary, threshold for comparative purposes. Consequently, instead of
obtaining an absolute measurement of the FPZ extent for each mix, researchers
calculate an estimated Fracture Process Zone (eFPZ), allowing for meaningful
comparisons (Figure 9 _(c)_). Doll et al. [28] have proposed thresholds of
3000 $\mu\epsilon$ at 25∘C and 1500 $\mu\epsilon$ at -12∘C.

Furthermore, DIC measurements allow for the computation of classical fracture
parameters, including SIF and J-integral. In the context of linear elastic
fracture mechanics, SIF serves as a predictive tool for assessing stress
distributions near crack or notch tips induced by external loading or residual
stresses. This parameter is contingent upon specimen geometry and loading
conditions. For example, in mode I fracture, the onset of crack propagation is
posited to arise when the applied stress intensity factor, denoted as $K_{I}$,
surpasses a critical threshold known as fracture toughness ($K_{Ic}$) [109].
In experimental settings, DIC is employed to acquire displacement data,
assuming the material behaves elastically. Subsequently, a least squares
regression is executed using Equation 14 to calculate $K_{I}$. However, it is
important to note that asphalt material exhibits pronounced viscoelastic
behavior, in contrast to the assumptions underlying Equation 14 , which
pertain to purely elastic materials. In cases of viscoelasticity, a similar
approach can be adopted with the utilization of pseudo displacements as
defined in Equation 15 [137] (Figure 9 _(e)_). A least squares regression is
then applied to these pseudo displacements using Equation 14, yielding
$K_{IR}$ and accounting for rigid body motion. It is essential to acknowledge
that the aforementioned procedure assumes a constant modulus for the asphalt
material, which is erroneous in situations where the material exhibits high
viscosity [26].

$\begin{bmatrix}u_{x}\\\
u_{y}\end{bmatrix}=\frac{K_{I}}{2\mu}\sqrt{\frac{r}{2\pi}}\begin{bmatrix}\cos(\frac{\theta}{2})[\kappa-1+2\sin^{2}(\frac{\theta}{2})]\\\
\sin(\frac{\theta}{2})[\kappa+1-2\cos^{2}(\frac{\theta}{2})]\end{bmatrix}+\begin{bmatrix}u_{x0}-\theta_{0}y\\\
u_{y0}+\theta_{0}x\end{bmatrix}$ (14)

Here, $\nu$ represents the Poisson ratio, $\mu$ stands for the shear modulus,
$u_{x0}$ and $u_{y0}$ pertain to rigid translation, and $\theta_{0}$
represents rigid rotation. For plane strain, where $\kappa$ is defined as
$\kappa=3-4\nu$. For plane stress, $\kappa$ is defined as
$\kappa=\frac{3-\nu}{1+\nu}$.

$u_{i}^{R}=\frac{1}{E^{R}}\int_{0}^{t}E(t-t^{\prime})\frac{\partial
u_{i}}{\partial t^{\prime}}dt^{\prime}$ (15)

$E^{R}$ represents the reference modulus, which is typically selected as an
arbitrary value, often taken as the instantaneous modulus denoted by $E_{0}$,
while $E(t)$ signifies the relaxation function [138, 139].

The J-integral, unlike the SIF, is applicable to a broader range of material
behaviors, including linear elastic, non-linear elastic, and plastic materials
(under the condition of no unloading). It is valid for situations without body
forces and in the context of 2D deformation fields. Theoretically, three
primary methods exist for measuring the J-integral of a material. Firstly, the
J-integral can be determined by analyzing DIC-measured displacement and strain
fields (Figure 9 _(d)_). Secondly, it can be obtained through tests involving
multiple specimens with varied pre-crack (i.e., notch) lengths, while keeping
other test parameters controlled [140]. Thirdly, the J-integral can be
measured using a single specimen by directly measuring the crack length [141].
Since this section focuses on the application of DIC, the details of the first
approach will be presented. The J-integral exhibits path independence for
hyperelastic materials when subjected to monotonic loading conditions.
However, it loses this path-independence property if the material dissipates
energy within the bulk. Schapery [137] introduced an alternative formulation
known as the pseudo J-integral, which is suitable for viscoelastic-homogeneous
materials and is calculated along a line contour, which may pose numerical
challenges when dealing with displacement derivatives from discrete data, such
as those obtained from DIC measurements. An alternative expression (Equation
16) is derived using Green’s theorem (Divergence theorem) and is valid under
specific conditions, including the absence of thermal strain, body forces, and
traction along the crack faces [142, 26]. It is crucial to highlight that the
path independence of the J-integral relies on the assumption of material
homogeneity, whereas AC exhibits heterogeneity.

$J=\int_{A}[\sigma_{ij}u_{j,i}-W\delta_{ij}]q_{1,i}dA$ (16)

where $\sigma_{ij}$ is the stress component, $u_{j,i}$ is the displacement,
$W$ is the strain energy density of AC
($W=\int_{0}^{\epsilon}\sigma_{ij}d\epsilon_{ij}$). The expression involves
the parameter $q_{1}$, which takes a value of 1 along the inner contour and 0
along the outer contour [142].

##  4 3D-DIC

The 2D-DIC method has been extensively studied in the pavement engineering
community for characterizing asphalt concrete. However, it has specific
requirements regarding specimen deformation, loading devices, and measuring
systems. In cases where the surface of the specimen is not planar or
experiences three-dimensional deformation following loading, the application
of the 2D-DIC method is unfeasible [34]. In response to these constraints, the
3D-DIC method, often referred to as stereo-DIC, has emerged as a solution [8].
This technique entails the utilization of two synchronized cameras or a single
camera equipped with custom light-splitting apparatuses grounded in binocular
stereo vision principles. This section will discuss best practices for 3D-DIC
imaging system setup, algorithms, and applications in asphalt concrete
characterization.

###  4.1 Imaging System

A frequently employed 3D DIC setup comprises two synchronized cameras, an
illumination setup, a computer, and a post-processing software (see Figure
10). Notably, the recommendations and guidelines discussed in a previous
section regarding the setup of a 2D-DIC imaging system also apply to 3D-DIC.
In addition, this section presents additional techniques to effectively set up
a 3D-DIC imaging system.

Figure 10: 3D-DIC setup.

First, one essential requirement for 3D-DIC is the simultaneous acquisition of
stereo images. However, achieving precise synchronization with minimal delay
can be challenging. Generally, industrial cameras that support specific
digital interface standards, such as CoaXPress, which has a built-in
synchronization capability, are required to meet this demand [143].

Second, it is vital to determine the stereo angle ($\alpha$), which refers to
the angular difference between the two camera views (Figure 10). Typically,
narrower stereo angles (shorter baseline) enhance in-plane measurement
accuracy but increase uncertainty in out-of-plane measurements. In scenarios
emphasizing strain assessment, a narrower stereo angle is commonly favored.
However, for improved out-of-plane results, it is recommended to use a larger
stereo angle (longer baseline). When using a wide-angle lens, a stereo angle
of at least 25∘ is advisable [144].

###  4.2 Algorithm

####  4.2.1 Stereo Calibration

To ensure accurate and high-quality 3D-DIC measurements, precise calibration
of the two-camera unit used for simultaneous image capture, is crucial. Camera
calibration furnishes essential parameters for triangulation, encompassing
intrinsic details (such as center point, lens distortion coefficients, and
individual camera focal lengths) and extrinsic factors (including translation
and rotation between the dual cameras). A widely adopted and reliable method
for calibration was proposed by Zhang [37], which employs a 2D planar pattern.
This technique is known for its high accuracy and ease of use, and it has
become the standard method for calibration in most 3D-DIC techniques [1].

The calibration process involves utilizing the captured stereo pairs of the 2D
planar pattern. It is important to consider that the distortion-free
projection of a 3D point
$\widetilde{\mathbf{P}}_{w}=[x_{1}^{w},x_{2}^{w},x_{3}^{w},1]^{T}$ onto the
camera sensor $\widetilde{\mathbf{p}}_{c}=[x_{1}^{c},x_{2}^{c},1]^{T}$ can be
represented by Equation 17.

$\displaystyle s^{c}\widetilde{\mathbf{p}}_{c}$
$\displaystyle=\mathbf{K}_{c}[\mathbf{R}_{c}|\mathbf{t}_{c}]\widetilde{\mathbf{P}}_{w}$
(17) $\displaystyle=\begin{bmatrix}f_{1}^{c}&\gamma^{c}&c_{1}^{c}\\\
0&f_{2}^{c}&c_{2}^{c}\\\ 0&0&1\\\
\end{bmatrix}[\mathbf{R}_{c}|\mathbf{t}_{c}]\widetilde{\mathbf{P}}_{w}$

Here, the subscript and superscript $c$ are used to indicate the camera
indices. The symbol $s^{c}$ signifies a scaling factor, while $\mathbf{R}_{c}$
and $\mathbf{t}_{c}$ represent the rotation matrix and translation vector.
These parameters facilitate the transformation from the world coordinate
system to the camera coordinate system. $\mathbf{K}_{c}$ stands for the
camera’s intrinsic matrix, wherein $f_{1}^{c}$ and $f_{2}^{c}$ denote the
focal lengths in pixels, $c_{1}^{c}$ and $c_{2}^{c}$ represent the pixel
coordinates of the principal point (optical center), and $\gamma^{c}$
signifies the skew factor.

To achieve accurate calibration, it is essential to consider the non-linear
optical distortion caused by the lens. A widely employed distortion model
comprises radial and tangential distortions. These distortion coefficients are
specific to each camera and are thus included as part of the camera’s
intrinsic parameters.

Subsequently, the stereo extrinsic parameters ($\mathbf{R}$ and $\mathbf{t}$)
can be ascertained by evaluating the transformation equations connecting each
camera, as described in Equations 18 and 19.

$\mathbf{R}=\mathbf{R}_{r}\mathbf{R}_{l}^{-1}$ (18)

$\mathbf{t}=\mathbf{t}_{r}-\mathbf{R}_{r}\mathbf{R}_{l}^{-1}\mathbf{t}_{l}$
(19)

where subscripts $l$ and $r$ represent the left and right cameras,
respectively.

It is worth noting that stereo camera calibration can be conveniently
performed using available tools such as Matlab’s Stereo Camera Calibrator.

####  4.2.2 Stereo Correlation

The foundation of 3D-DIC lies in correlation algorithms to establish
correspondence between points within left and right images. This correlation
analysis comprises two key stages: stereo matching and temporal matching (or
tracking). Stereo matching’s primary goal is precise alignment of identical
physical points present in the left and right camera images. Meanwhile,
temporal matching tracks these identical points across successive images
captured by the same camera at different instances or conditions. For temporal
matching, the established subset-based 2D-DIC algorithm can be employed.
Stereo matching is notably more intricate due to substantial perspective
distortion between images captured by distinct cameras, rendering it the most
challenging aspect of stereo vision measurement. To guarantee accurate and
efficient 3D deformation measurements, crucial factors such as matching
strategy, correlation algorithm, shape function, and initial estimation need
careful consideration within the context of stereo matching [1].

In stereo matching, the non-linear perspective projection frequently leads to
substantial inaccuracies when employing first-order shape functions,
especially when dealing with large subset sizes and considerable stereo
angles. To tackle this issue, adopting $2^{nd}$-order shape functions in
stereo matching is advisable, as it can enhance accuracy. For instance, Gao et
al. [145] introduced the inverse compositional Gauss-Newton (IC-GN2)
algorithm, employing $2^{nd}$-order shape functions. Concerning temporal
matching, the IC-GN algorithm employing first-order shape functions is
typically favored due to its greater computational efficiency.

Subset-based matching algorithms face challenges in estimating an initial
guess when images from different cameras experience significant deformations
caused by a large stereo angle. To overcome this limitation, feature-based
matching techniques have been introduced. One such technique is the scale-
invariant feature transformation (SIFT) algorithm, which allows for fast and
accurate stereo matching in these scenarios [146, 147].

In the context of 3D-DIC, three prevalent matching strategies are employed.
The initial approach (depicted in Figure 11 _(a)_) entails matching the left
reference image with the right reference image (for the initial state), and
subsequently aligning all left and right deformed images to their
corresponding initial states (temporal matching). The second strategy (Figure
11 _(b)_) involves correlating all deformed left and right images with the
left reference image. The third strategy (Figure 11 _(c)_) compares the
deformed left images to the left reference image via temporal matching,
followed by matching each corresponding right image with the present left
image through stereo matching. Amid these strategies, the first one, which
conducts the computationally intensive stereo matching only once, is often
deemed the most effective choice for practical measurements [1].

Figure 11: Strategies for stereo-correlations in 3D-DIC.

####  4.2.3 Reconstruction

After the correlation process, each point in the image is now matched relative
to the reference image. By incorporating the calibrated parameters of the
stereo camera-unit, the classic triangulation method can be utilized to
recover the 3D coordinates of measurement points. Within the domain of 3D-DIC,
four prevalent techniques are utilized for 3D reconstruction: the least square
method, optimal method, mid-point method, and geometrical optimal method [148,
149, 150, 151]. A comparative analysis by Zhong et al. [152] established that
the least square method stands out for its superior computational efficiency
while maintaining measurement accuracy.

Figure 12: 3D reconstruction based on triangulation.

The least square method computation is straightforward. Initially, the world
coordinate system is established in alignment with the left camera coordinate
system. Illustrated in Figure 12, $\mathbf{R}_{L}$ corresponds to an identity
matrix, and $\mathbf{t}_{L}$ represents a zero vector.
$(\mathbf{R}_{R},\mathbf{t}_{R})$ is congruent to
$(\mathbf{R}_{C},\mathbf{t}_{C})$, as obtained through stereo calibration. The
point under computation is labeled as $Q$. Adopting the premise of a pinhole
camera model, the correlation between the left image coordinates
$(x_{l},y_{l})$ and the world coordinates $(X_{Q},Y_{Q},Z_{Q})$ is expressed
as elucidated in Equation 20.

$\begin{bmatrix}x_{l}\\\ y_{l}\\\
\end{bmatrix}=\begin{bmatrix}f_{x}^{L}&s_{L}&c_{x}^{L}\\\
0&f_{y}^{L}&c_{y}^{L}\\\ \end{bmatrix}\begin{bmatrix}X_{Q}/Z_{Q}\\\
Y_{Q}/Z_{Q}\\\ 1\\\ \end{bmatrix}$ (20)

Given, $\mathbf{R}_{c}=\begin{bmatrix}R_{11}&R_{12}&R_{13}\\\
R_{21}&R_{22}&R_{23}\\\ R_{31}&R_{32}&R_{33}\\\ \end{bmatrix}$ and
$\mathbf{t}_{c}=\begin{bmatrix}t_{x}\\\ t_{y}\\\ t_{z}\end{bmatrix}$. The
relationship between the right image coordinates $(x_{r},y_{r})$ and the world
coordinates $(X_{Q},Y_{Q},Z_{Q})$ can be described in Equation 21.

$\begin{bmatrix}x_{r}\\\ y_{r}\\\
\end{bmatrix}=\begin{bmatrix}f_{x}^{R}&s_{R}&c_{x}^{R}\\\
0&f_{y}^{R}&c_{y}^{R}\\\
\end{bmatrix}\begin{bmatrix}\frac{R_{11}X_{Q}+R_{12}Y_{Q}+R_{13}Z_{Q}+t_{x}}{R_{31}X_{Q}+R_{32}Y_{Q}+R_{33}Z_{Q}+t_{z}}\\\
\frac{R_{21}X_{Q}+R_{22}Y_{Q}+R_{23}Z_{Q}+t_{y}}{R_{31}X_{Q}+R_{32}Y_{Q}+R_{33}Z_{Q}+t_{z}}\\\
1\\\ \end{bmatrix}$ (21)

By integrating Equations 20 and 21, the world coordinates
$(X_{Q},Y_{Q},Z_{Q})$ can be reconstructed using Equation 22.

$\begin{bmatrix}X_{Q}&Y_{Q}&Z_{Q}\end{bmatrix}^{T}=(\mathbf{M}^{T}\mathbf{M})^{-1}\mathbf{M}^{T}\mathbf{b}$
(22)

$\mathbf{M}$ and $\mathbf{b}$ are given by Equations 23 and 24, respectively.
It is important to note that all the parameters in $\mathbf{M}$ and
$\mathbf{b}$ were obtained during the stereo calibration process.

$\mathbf{M}=\begin{bmatrix}f_{x}^{L}&s_{L}&c_{x}^{L}-x_{l}\\\
0&f_{y}^{L}&c_{y}^{L}-y_{l}\\\
R_{11}f_{x}^{R}+R_{21}s_{R}+R_{31}(c_{x}^{R}-x_{r})&R_{12}f_{x}^{R}+R_{22}s_{R}+R_{32}(c_{x}^{R}-x_{r})&R_{13}f_{x}^{R}+R_{23}s_{R}+R_{33}(c_{x}^{R}-x_{r})\\\
R_{21}f_{y}^{R}+R_{31}(c_{y}^{R}-y_{r})&R_{22}f_{y}^{R}+R_{32}(c_{y}^{R}-y_{r})&R_{23}f_{y}^{R}+R_{33}(c_{y}^{R}-y_{r})\end{bmatrix}$

(23)

$\mathbf{b}=\begin{bmatrix}0\\\ 0\\\
-(t_{x}f_{x}^{r}+t_{y}s_{R}+t_{z}(c_{x}^{R}-x_{r}))\\\
-(t_{y}f_{y}^{r}+t_{z}(c_{y}^{R}-y_{r}))\\\ \end{bmatrix}$ (24)

####  4.2.4 Compute of Displacements and Strains

The previously acquired 3D coordinates serve as the basis for constructing
complete displacement and strain maps. Displacements are individually computed
for each point, while for each triangular element, strains are determined
through the application of the Cosserat point element method [153, 154]. The
vertices’ positional vectors of each triangular element are employed to
calculate the deformation gradient tensor $\mathbf{F}$. Utilizing
$\mathbf{F}$, both the right and left Cauchy-Green deformation tensors
($\mathbf{C}=\mathbf{F}^{T}\mathbf{F}$ and
$\mathbf{B}=\mathbf{F}\mathbf{F}^{T}$) are derived, alongside the Green-
Lagrangian and Eulerian-Almansi strain tensors
($\mathbf{E}=0.5(\mathbf{C}-\mathbf{I})$ and
$\mathbf{e}=0.5(\mathbf{I}-\mathbf{B}^{-1})$, respectively). By analyzing
these tensors, principal components and directions are determined, leading to
the derivation of principal stretches ($\lambda_{i}$) and strains ($E_{i}$ and
$e_{i}$), as well as measures like equivalent (Von-Mises) strain, maximal
shear strain, and area change.

####  4.2.5 Software

The effective implementation of algorithms is crucial for 3D-DIC analysis.
Table 3 presents a compilation of presently accessible non-commercial 3D-DIC
software. It is essential to note that this list exclusively comprises
software with supporting peer-reviewed research papers, and there may be other
available choices.

Software | Authors | First Release | User Interface | Open Source | Free | Language | Citations (Oct 2023)
---|---|---|---|---|---|---|---
DICe | Turner et al. [45] | 2015 | Yes | Yes | Yes | C++ | 12
MultiDIC | Solav et al. [153] | 2018 | Yes | Yes | Yes | Matlab | 142
DuoDIC | Solav and Silverstein [154] | 2022 | Yes | Yes | Yes | Matlab | 4
iCorrVision-3D | Nunes et al. [155] | 2022 | Yes | Yes | Yes | Python | 2

Table 3: 3D-DIC Software.

###  4.3 Applications

The 3D-DIC technique offers advantages over the simpler 2D-DIC technique, as
it does not make assumptions about the planar surface of the specimen or
negligible out-of-plane displacement during testing. Yuan et al. [25]
investigated the out-of-plane deformation in both monotonic (fracture) and
cyclic (fatigue) SCB tests using 3D-DIC. The results showed that in the
fracture test, the out-of-plane displacement ranged from -0.45 mm to 0.45 mm,
while in the fatigue test, it fluctuated between -1 mm and 0.95 mm. In a
separate study, Cheng et al. [118] arrived at a similar conclusion. These
findings indicate that the widely accepted assumption of negligible out-of-
plane displacement in SCB tests may not be valid, further highlighting the
advantages of 3D-DIC.

However, the adoption of the 3D-DIC technique in characterizing AC has been
limited, with less than 5% of journal publications since 2002 utilizing this
technique. The first instance of such usage was reported in 2017 [19]. This
limited adoption can be primarily attributed to the requirement of two
synchronized cameras and a relatively complex camera calibration process [18].
Table 4 summarizes the applications of 3D-DIC in laboratory characterization
of AC. The current applications of 3D-DIC closely resemble those of the 2D
alternative, emphasizing the monitoring of displacement and strain map
evolution during testing and the tracking of crack propagation. Future
research may investigate the application of 3D-DIC in laboratory tests that
are not amenable to 2D-DIC. For example, the use of Linear Variable
Differential Transformers (LVDTs) is a common method for monitoring vertical
displacement in dynamic modulus (E*) tests on cylindrical specimens. However,
LVDTs require periodic calibration, labor-intensive installation, and
extensive training. Additionally, they provide only a limited number of
discrete measurement points on the specimen’s surface [156]. Conversely,
adopting 3D-DIC may allow for full-field displacement data acquisition,
potentially eliminating the need for LVDTs. Furthermore, it is crucial to
evaluate the validity of the assumption of negligible out-of-plane deformation
in tests other than the SCB.

Type | Test | Applications | Publications
---|---|---|---
Fracture | SCB | Strain & Displacement | [157, 118, 158, 25, 159]
Crack Propagation | [118]
Double cantilever beam (DCB) | Mechanistic Parameters | [160]
Fatigue | 4PB | Strain & Displacement | [161]
| Crack Propagation | [161]
SCB | Strain & Displacement | [25]
Strength | IDT | Strain & Displacement | [102]
Damage Evolution | [102]
Others | Repeated load uniaxial test | Displacement | [106]

Table 4: Applications of 3D-DIC in AC laboratory tests.

##  5 Emerging DIC Techniques

###  5.1 Digital Volume Correlation

2D-DIC and 3D-DIC are restricted to measuring surface displacements and
strains. However, the heterogeneous properties of AC can lead to inconclusive
results. This section discusses DVC, which enables displacement and strain
mapping within the interior of loaded samples [162, 163, 164]. Although the
asphalt pavement engineering community has not yet adopted the DVC technique,
the information presented here intends to promote future research in this
field.

Figure 13: The overall digital volume correlation process.

The initial stage in applying DVC involves acquiring 3D images of unloaded and
loaded specimens. X-ray computed tomography (CT) is the prevailing technique
used for imaging, where a series of 2D X-ray images are used to generate 3D
images of the specimens [164]. It is important to mention that CT has been
employed to investigate the internal structure of AC [165, 166, 167].
Additionally, other imaging techniques, such as magnetic resonance imaging
(MRI) and optical coherence tomography (OCT), can also be utilized [168, 169].

As depicted in Figure 13, the DVC process begins with the choice of an ROI
encompassing the points requiring displacement determination.

Next in line is the estimation of displacement vectors at each measurement
point. This is achieved through the correlation of a reference (unloaded)
image volume with a target (deformed) image volume. Like 2D- and 3D-DIC
methods, the calculation of displacement in DVC entails determining a
combination of transformations (e.g., translation, shear, rotation) that
minimizes a cost function, such as the sum-of-squares correlation coefficient
(SSCC) or normalized cross-correlation coefficient (NCCC) cost function [170,
171, 172].

In the last phase, strains are assessed at all measurement sites by analyzing
the deformation gradients within the neighboring vicinity. The strain tensor
at each point $\mathbf{p}$ is calculated by fitting a $2^{nd}$-order Taylor
series expansion of the displacement vector field using a group of nearby
points through a least squares approach [173, 171].

DVC presents promising solutions to common challenges in asphalt pavement
engineering, including the validation of surface strain maps’ representation
of strain distribution across the entire specimen and the assessment of the
correspondence between surface crack propagation measurements through DIC and
actual three-dimensional crack propagation. Additionally, DVC demonstrates
extensive prospective applications encompassing internal granular material
movement tracking, internal strain quantification, crack initiation and
fracture monitoring, computation of SIF along crack fronts, and analysis of
fatigue crack closure effects, among others. Nevertheless, it is important to
acknowledge that acquiring high-resolution 3D images capable of supporting DVC
can be particularly challenging, especially given the complex and
heterogeneous nature of AC [174].

###  5.2 Deep-Learning-Based DIC

DIC is an iterative optimization procedure that requires substantial
computational resources, resulting in extended calculation times. It also
involves user inputs, including ROI, seed locations, subset size, and strain
calculation window size, making it a non-automatic process. However, deep
learning presents a solution to these challenges, enabling faster and fully
automated DIC analysis, known as an end-to-end process.

To facilitate a comprehensive discussion on recent advancements in deep-
learning-based DIC, it is crucial to introduce the concept of optical flow.
Optical flow refers to the perceived displacement field derived from two views
of a scene. It arises from the relative motion between specimens and the
camera in the scene, encompassing movement and deformation [175]. Notably, DIC
and optical flow share common ground as both methodologies aim to determine
the movement of pixels or features across a sequence of images. Deep learning
techniques, including Convolutional Neural Networks (CNN), Recurrent Neural
Networks (RNN), and Transformers, have been widely employed by researchers for
optical flow estimation. Table 5 provides a concise overview of the most
influential works in this area. Furthermore, the table presents the average
endpoint error (AEPE) of these works on a well-known benchmark dataset, Sintel
[176].

Method | Year | Algorithm | AEPE (in pixels)
---|---|---|---
FlowNet [177] | 2015 | Supervised; CNN | S (8.43); C (8.81)
FlowNet2.0 [178] | 2017 | Supervised; CNN | 6.02
PWC-Net [179] | 2018 | Supervised; CNN | 5.04
UnFlow [180] | 2018 | Unsupervised; CNN | 10.22
RAFT [181] | 2020 | Supervised; RNN | 2.86
FlowFormer [182] | 2022 | Supervised; Transformer | 2.09

Table 5: Deep learning methods for optical flow estimation.

In 2021, Boukhtache et al. [183] introduced StrainNet, a deep-learning-based
DIC method, for accurately determining in-plane subpixel displacement fields
from pairs of reference and deformed speckle images. By fine-tuning FlowNet-S
using a synthetic speckle dataset, StrainNet achieved a high level of
accuracy, with a mean absolute error (MAE) of 0.0299 pixels. This accuracy is
comparable to conventional 2D-DIC methods while also significantly reducing
computation time. In a subsequent publication, the authors proposed a
lightweight version called StrainNet-l [184]. This version significantly
reduced the number of parameters from 38.68 million to 0.67 million while
maintaining a similar level of accuracy. StrainNet-l achieved an MAE of 0.0312
pixels, demonstrating that parameter reduction did not compromise its
performance. Wang and Zhao [185] made further advancements in improving the
accuracy of displacement field determination by training a CNN similar to
U-Net architecture. They utilized a synthetic dataset generated through the
application of the Hermite finite elements. The resulting network, named DIC-
Net, achieved an impressive MAE of 0.0130 pixels, indicating a significant
improvement in accuracy compared to previous methods. It is crucial to
emphasize that the aforementioned networks are designed exclusively for
retrieving displacement fields. To obtain strain maps, it is necessary to
convolve the displacement fields with suitable derivative filters. However,
Yang et al. [186] introduced an end-to-end network that directly measures
strain maps using a FlowNet-S-like architecture.

All the previously mentioned networks are applicable only to 2D-DIC, where a
reference image and a deformed image are used as input. However, Wang et al.
[187] developed a network called StrainNet-3D, designed explicitly for
displacement retrieval from stereo images, similar to 3D-DIC. This approach
incorporates an affine-transformation-based method for calculating disparities
and a lightweight CNN for subpixel correlation. To ascertain three-dimensional
displacement, the CNN-derived disparities and temporal optical flow are
employed, guided by principles from stereo vision. Additionally, an optional
refiner network can be employed to enhance the accuracy of the results
further. StrainNet-3D achieved comparable accuracy to conventional 3D-DIC,
with a mean absolute error (MAE) of 0.0146 pixels compared to 0.0110 pixels.
Notably, StrainNet-3D exhibited improved efficiency as it does not require
camera calibration and enables faster calculation.

Currently, deep-learning-based DIC methods utilizing RNN or transformer
architectures have not been observed in the literature. However, based on the
facts presented in Table 5, these architectures have the potential to enhance
the accuracy of deep-learning-based DIC approaches significantly.

Furthermore, it is worth noting that the pavement engineering community has
not yet adopted these recent advancements in DIC using deep learning.
Nevertheless, considering the advantages offered, such as improved
computational efficiency, full automation, and elimination of user inputs
compared to conventional DIC methods, it is recommended to initiate
investigations into the viability of employing these deep-learning-based DIC
methods for AC characterization.

##  6 Flowchart of DIC Implementation for AC Characterization

The presented flowchart (Figure 14) serves as a comprehensive and reliable
reference for implementing DIC in characterizing AC. It is based on a
synthesis of best practices derived from the literature discussed in this
paper. It is highly recommended to refer to the flowchart in conjunction with
the detailed explanations provided in the respective sections of this paper
for a thorough understanding of the implementation process.

Figure 14: Flowchart for DIC implementation in AC characterization: synthesis
of best practices from literature.

##  7 Summary and Recommendations for Future Research

This article presents a comprehensive review of DIC as a critical tool for
laboratory testing of AC. The focus is primarily on the widely used 2D-DIC and
3D-DIC techniques. The study thoroughly investigates best practices related to
speckle pattern preparation, configuration of single-camera or dual-camera
imaging systems, and meticulous execution of DIC analyses. Additionally,
emerging DIC methodologies, such as DVC and deep-learning-based DIC, are
introduced, highlighting their potential for future applications in pavement
engineering. Lastly, a flowchart is provided as a comprehensive and reliable
reference for implementing DIC in AC characterization.

The key takeaways are summarized as below:

  * 1.

_Speckle Pattern Preparation_. The optimal painted speckle pattern for AC
specimen consists of black speckles applied onto a thin white basecoat. The
speckle granules should ideally be 3-5 pixels or larger in size. SSSIG and MIG
serve as effective indices for assessing the quality of the speckle pattern.

  * 2.

_Imaging System Configuration_. The optimal camera-specimen distance can be
determined through mathematical calculations. To capture high-quality images
with minimal noise, the three parameters of the exposure triangle, namely
aperture, ISO, and shutter speed, need to be adjusted. Artificial lighting is
often required to enhance the brightness of the scene. In 2D-DIC, it is
advisable to employ a mechanical camera positioning tool to ensure parallel
alignment between the camera CCD sensor and the object surface. For 3D-DIC,
precise synchronization and stereo calibration of the dual-camera setup before
the experiment are essential to achieve accurate measurements. A narrower
stereo angle is preferable for in-plane measurement accuracy, while a larger
angle is preferred for improved out-of-plane results.

  * 3.

_Algorithm_. In 2D-DIC, subset-based matching is performed between reference
and deformed images. In parallel, 3D-DIC encompasses stereo matching, which
strives to precisely align corresponding physical points in the images of the
left and right cameras, and temporal matching, which monitors these identical
points across successive images taken by the same camera under varying
conditions or time frames. Open-source software options are readily accessible
for both 2D- and 3D-DIC analyses.

  * 4.

_Applications_. DIC has found extensive application in fracture, fatigue, and
strength tests. DIC has gained widespread utility in fracture, fatigue, and
strength testing, categorizable into three main groups: direct application of
DIC-generated displacement or strain maps, mechanistic parameter derivation,
and tracking of crack propagation or damage evolution.

The followings are recommended for future research:

  * 1.

A scientific discourse exists concerning whether the natural texture of AC
specimens aligns with prescribed criteria. In light of discrepant findings in
existing research, it is advisable to conduct further investigations into the
circumstances under which natural texture may be employed, considering factors
such as mixture characteristics, imaging system configuration, and precision
requirements.

  * 2.

Most of the reviewed articles primarily employed DIC for displacement and
strain measurement, with minimal post-processing. Nevertheless, it is crucial
to recognize that more meaningful and quantitative results, such as
mechanistic parameters and precise crack propagation paths, can be derived
through supplementary post-processing methods detailed in Section 3.3.

  * 3.

The prevailing approaches for tracking and quantifying crack propagation with
DIC predominantly rely on visual or empirical methodologies. It is advisable
to investigate the integration of fundamental mechanistic theories with DIC
for the measurement of cracks in mode II fracture, mixed-mode fracture, and
fatigue tests. Additionally, the combination of computer vision and
fundamental mechanistic theories appears promising for achieving both high
reliability and automation.

  * 4.

Present methods for computing pseudo SIF and J-integral using strain fields
obtained through DIC rely on the assumption of constant modulus and material
homogeneity, respectively. Nevertheless, under high viscosity, the constant
modulus assumption breaks down, and AC is inherently heterogeneous. Therefore,
it is recommended to investigate approaches for computing pseudo SIF and
J-integral under conditions where these assumptions do not hold.

  * 5.

The utilization of 3D-DIC in AC characterization remains limited, accounting
for less than 5% of published articles in the field. Future research efforts
could focus on implementing 3D-DIC in additional laboratory tests,
particularly those where 2D-DIC is not feasible. Moreover, it is crucial to
assess the validity of the assumption of negligible out-of-plane deformation
in tests other than the SCB test and establish distinct guidelines for
determining the appropriate use of 2D- or 3D-DIC in AC characterization.

  * 6.

A deficiency in the application of DIC in large- or full-scale tests of AC has
been observed. Cement concrete researchers have previously utilized DIC in
such assessments. Notable challenges that must be addressed include optimizing
the imaging system setup to minimize vibrations and achieve adequate spatial
resolution, preparing specimens suitable for large-scale testing, and
identifying the valuable insights attainable through DIC analysis.

  * 7.

Both 2D-DIC and 3D-DIC are limited to surface displacement and strain
measurements, which may yield inconclusive results due to the heterogeneous
nature of AC. To overcome this limitation, it is recommended to investigate
the potential of DVC as a tool for mapping displacement and strain within the
interior of loaded AC samples.

  * 8.

Deep-learning-based DIC methods have demonstrated enhanced computational
efficiency, full automation, and reduced dependence on user inputs when
compared to conventional DIC techniques. Therefore, it is recommended to
explore the viability of utilizing these deep-learning-based DIC methods for
characterizing AC.

## Acknowledgements

The authors extend their appreciation to the anonymous reviewers for their
valuable feedback, which significantly enhanced the quality of this paper.
This work received no external funding. Any commercial products mentioned in
this paper do not represent endorsements from the authors.

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