Abstract
Digital-image correlation (DIC) is a deformation-measurement technique used to determine rock and soil mechanics. We review DIC tests of rock and soil, with data categorized according to specimen shape, test type, and DIC method. A new three-dimensional-DIC system integrates a transparent triaxial-compression servo-control test system for rocks. The confining pressure cell is transparent and three groups of image-acquisition units, which can be controlled with loading cell at the same time, are adopted to obtain the maximum observed fields. The average magnification factors caused by the transparent cell and oil are 1.4430 and 1.0331 for the measured horizontal and vertical distances, respectively. A triaxial compressive test of rock is performed and the specimen’s surface-strain fields and crack propagation are discussed.
Keywords
Introduction
The damage evolution of rocks subjected to triaxial compression has proven important across many years in fields such as mining engineering and tunnel excavation. The mechanisms for damage to various kinds of rocks under triaxial compression have been widely investigated, and there are a rich variety of research results; however, failure processes and crack evolution still cannot be observed or analyzed directly during triaxial compression.
Digital image correlation (DIC) is a new experimental method widely used in mechanics, biology, medicine, architecture, and so on. A group at the University of South Carolina (Chu et al., 1985; Luo et al., 1993; Peters and Ranson, 1982; Sutton et al., 1983; 1986) firstly investigated the digital speckle-correlation method and developed software for deformation measurement. With the development of computers, the DIC method has achieved a higher accuracy and convenience. In the early stages, Sutton et al. (Sutton et al., 1983, 1986) showed an optimized digital-correlation method for planar-deformation analysis, and Luo et al. (1993) presented a three-dimensional-DIC (3D-DIC) method for the displacement measurement of bodies using a stereo pair of cameras. To date, the DIC method has been widely used in rock mechanics (e.g., uniaxial compression (Huang et al., 2013) and Brazilian tests (Stirling et al., 2013)). Moreover, this method can be used to investigate the damage and failure processes in rocks in terms of crack propagation (Xue et al., 2020). However, most investigations using the DIC method in rock mechanics are conducted in two dimensions and are applied for uniaxial or split tests. Application of the 3D-DIC method for triaxial compression of rocks is rare due to the limitations of the pressure cells made of metal.
In this paper, the applications of the DIC technique to rock and soil materials in previous studies are surveyed from the literature. Our survey shows that the application of the DIC method to rock mechanics has not been discussed in sufficient detail. Furthermore, a novel 3D-DIC system with six cameras is proposed and enacted in triaxial compression of rocks. The failure process and crack propagation of rock under triaxial compression are investigated by the system. Our results could help engineers to understand the in-situ deformation behaviors of rock structures.
Literature review of applications of the DIC technique to mechanical tests of geotechnical materials
Table 1 lists previous studies on the application of the DIC method to geotechnical materials. Materials, test types, specimen shapes, confining pressures, and DIC methods are all included.
Application of the DIC method to rock and soil mechanics tests.
UC: uniaxial compression; TC: triaxial compression; BT: Brazilian split; BD: bending; CUC: cycle uniaxial compression; CUT: cycle uniaxial tension; UT: uniaxial tension; CI: cyclic indentation.
In previous studies, the DIC method has been widely applied to many kinds of rock and soil materials. It is mainly used in uniaxial or Brazilian split tests for rock materials and occasionally in triaxial-compression tests for soil materials, because confining pressure is far smaller in soil-mechanics tests than that in rock-mechanics tests; therefore, the confining pressure cell can be transparent when using the DIC system in triaxial compression of rock. However, this topic has seldom been discussed in rock mechanics. Although the X-ray CT technique has been employed in a variety of geo-material testing applications, the CT-system is large and expensive to operate. To scan rock specimens in real time, special-purpose loading equipment must be installed on the CT machine, and testing can only be performed under a radiation-protected environment. Moreover, if the size of the specimens is large or the metal walls of the triaxial pressure chamber are thick, the applied radiation may be not strong enough to facilitate accurate scanning of the specimen.
Moreover, specimens are generally cuboid and disc-shaped, or cylindrical, with the observed face being planar and cambered, respectively. The use of 2D-DIC formed the basis for early applications of the proposed technique to deformation measurement and required the object to be planar or to possess only in-plane displacements. Another requirement of the technique was that the camera’s light path must be vertical and directly above the object’s plan surface. Thus, 2D-DIC was difficult to implement on cylindrical objects subjected to uniaxial- and/or triaxial-deformation tests. Table 1 shows that the 2D-DIC method is applied far more often than the 3D-DIC method in rock-mechanics investigations.
Moreover, the surface features of the specimen have mainly artificial speckle due to the DIC method requiring an irregular texture on the specimen surface. A popular method for creating such features is to spray white and black paint. Firstly, white matte paint was sprayed onto the specimen surface as an underpainting; then, black matte paint was used to create black speckles. The speckle pattern showed an irregular random distribution with high contrast (Tang et al., 2019).
Based on the above, we can see that deformation measurement of rock under triaxial compression should make use of a 3D-DIC method containing two cameras to obtain accurate results. Moreover, rock specimens usually experience shear failure under triaxial compression, and the failure plane cannot be predicted before the beginning of the test; therefore, it may not be possible to observe the failure plane using only two cameras. A new system should consider how to cover the maximum surface of the cylindrical specimen.
Set-up of the 3D-DIC system
3D-DIC instrumentation with the maximum observed field
Considering the randomness of shear failure of the rock specimens under triaxial compression, a large observation field is preferred. Therefore, cameras should be employed for image collection to the greatest extent possible. In this study, six cameras were adopted due to the pressure-cell structure limitation. The novel 3D-DIC system and transparent triaxial-compression system is shown as Figure 1(a).
Integration of the 3D-DIC and transparent triaxial-compression system.
Cameras with a resolution of 2,448 × 2,048 pixels were installed around the specimen at a perpendicular distance of about 50 cm, as shown in Figure 1(b). Each pair of cameras formed a three-dimensional acquisition unit together with an LED to provide sufficient light and the support devices to which the cameras were affixed. Three units were placed around the pressure cell to observe as much of the specimen as possible. Each acquisition unit was connected with the computer by a control box with eight data channels, of which six were used to collect image data from separate cameras and one acquired stress from the loading cell. All eight channels could be controlled simultaneously to assure synchronous digital-image and stress acquisition. The collected images from three units could be analyzed simultaneously by the 3D-DIC software and the stress–strain curve was shown in real time during the test. Following image analysis, the software could output the calculation results in excel or text format, as well as strain-contour test videos.
Pressure cell
Transparent pressure cells are essential for application of the 3D-DIC technique to triaxial compression of rock materials. The material and structure of the transparent cells used in this study are the same as those in Okubo et al. (2008), but they were manufactured using the latest technology without seams and bubbles, as shown in Figure 1(c). Due to the convexity of the transparent cell and the hydraulic oil within, the specimen will be magnified for easy observation of specimen deformation and observation of crack evolution by eyes and cameras during triaxial compression. The maximum confining pressure of the transparent cell is more than 55 MPa, and 10 MPa was the limit in daily use for safety reasons. Transparent heat-shrink tubing was used to cover the specimen to prevent the infiltration of oil. The use of a transparent pressure cell over traditional metal chambers offers the advantage of facilitating visual observation of the complete rock-specimen-deformation process during testing at high confined pressures using the 3D-DIC system.
There are three group-image acquisitions (six cameras) for deformation measurement on one specimen surface. It is necessary to calibrate the cameras to operate in the same coordinate system. On account of the transparent cell and oil, the distortion caused by light transmission must also be discussed, as presented in the next section.
Calibration and distortion
The calibration of cameras was undertaken using targets and software. The calibration steps are more complex than those of other DIC systems because six cameras must be calibrated in one coordinate system; then, specimen-surface deformation obtained by three units can be combined in three-dimensional space.
Three customized targets are used for calibration, as shown in Figure 2. Target A is rectangular and used to calibrate the three units one by one; this target was of a coded type with a size of 128 × 96 mm and was used to calibrate the light path and internal parameters of cameras. It was tilted or rotated eight times for one acquisition unit, while the calibration software captured an image and identified all codes in the target every time. Target B was a combination of three targets A; it was used to calibrate three units simultaneously to confirm the relative positions in the same coordinate system. Target C was much smaller and the same size as the test specimen. It can be placed in the transparent cell and used to calibrate the distortion of the cell and oil.
Calibration targets.
As described above, the transparent cell and oil have a magnification effect on specimen deformation. It can easily be seen that the lateral deformation had a larger magnification than the axial deformation due to the cell’s cylindrical shape. The calibration process for quantitative distortion is as follows:
(1) Number the marking points in target C as shown in Figure 2(d); (2) Place target C on the loading platform without a transparent cell or oil, then take the first picture; (3) Keep the target stable, install the transparent cell and fill it with oil. Then take the second picture; (4) Analyze the pictures obtained from steps (2) and (3) and calculate the horizontal and vertical point-to-point distances using the DIC method; (5) Rotate the target slightly and repeat steps (2) to (5).
The statistical results are shown in Tables 2 and 3. It can be seen that the average magnification factor (AVG) of the horizontal distance (Table 2) is 1.4430, the standard deviation (SD) is 0.0059, and the coefficient of variation (CV) is 0.0041. These values are larger than those for the vertical distance (Table 3): AVG: 1.0331; SD: 0.0040; CV: 0.0038. This indicates that the variation of image distortion was very small and magnification mainly occurred for horizontal deformation. Therefore, the measured DIC results can be easily corrected using the magnification factor.
Measured results of horizontal points.
Measured results of vertical points.
Example tests
Specimen
The sample rock was Ogino tuff obtained in Fukushima Prefecture, Japan. The rock is a fine tuff consisting of fine-grained volcanic glass and very small quantities of quartz, plagioclase, and mica. Rock cores without obvious fractures were selected and cut into cylinders with dimensions of φ25 × 50 mm. Sample surfaces were polished to ensure their conformance to flatness, verticality, and parallelism standards provided by ISRM. All specimens were air-dried in a laboratory for more than two weeks, then dried in an oven at 105 °C for more than 48 hours. Next all specimens were removed from the oven and put into a desiccator for 24 hours as “dried specimens”. The density of Ogino tuff is 1.81 g/cm3, the uniaxial compression strength is 27.35 MPa, the Young’s modulus is 4.02 MPa, and Poisson’s ratio is 0.31 (Tang et al., 2018).
Comprehensive test curve
The dried specimen placed under a confining pressure of 9 MPa is employed as an example according to which the strain field and crack propagation may be discussed. A typical stress–strain curve of Ogino tuff under loading rate (0.005 mm/s) is shown in Figure 3; the axial stress (σ1) was measured by a loading cell with simultaneous images. A confining pressure (σ3) was applied by the oil-hydraulic pump; the axial (ε1) and radial strain (ε3) were measured by 3D-DIC virtual extensometers (Munoz et al., 2016), the volume strain (εv) was calculated by ε1 + 2ε3 and consist of the elastic volumetric strain εve and the crack volumetric strain εvc, expressed by: εv = εve + εvc, where εve are calculated using the elastic modulus (E) and Poisson’s ratio (v) as follows (Martin and Chandler, 1994, Wen et al., 2018), to confirm the crack-stress thresholds (crack initiation, damage, and peak stress).
Axial stress–strain curve of Ogino tuff under triaxial compression.
Furthermore, the total absorbed energy (U), elastic energy (Ue), and dissipation energy (Ud) are also calculated with reference to Xie et al. (2009) and presented to describe crack evolution.
Figure 3 shows comprehensive information during rock-failure processes. In the figure,
Strain field and crack evolution
Figure 4 shows the major strain field obtained by three acquisition units (L1, L2, L3), respectively. Before the stress reaches point A indicating crack initiation, the strain field shows uniform increase in the measurements of L1, L2, and L3. During this stage, εv and εvc decrease to positive direction slightly, which indicates that the specimen experiences crack closure and linear elastic deformation, with no new cracks growing before point A. Ud shows no obvious increase and the absorption energy is mainly transformed to elastic energy and storage in the specimen, as presented in Figure 3.
Evolution of the major strain field of drying Ogino tuff. (a) L1, (b) L2 and (c) L3.
Between points A and B, Figure 3 shows εvc increasing to the negative direction and Ud increasing slightly, meaning that micro-cracks begin growing and stably extending in the specimen interior, while the curves of Ud and U also separate with each other from point A. However, the applied loading is insufficient for the crack to propagate to the external surface; therefore, the strain field at point B is also nearly homogenous, as shown in Figure 4.
When stress exceeds crack damage threshold to peak strength (Point C), Figure 3 shows εvc and Ud increasing quickly with the specimen exhibiting clear dilatation. Cracks grow unstable, connect with each other, and propagate gradually to the specimen surface. The strain field presented obvious strain localization in the observed region of L2; the red arrow indicates that the propagation direction of cracks is from the bottom right to the top left, as shown in Figure 4(b). In regions L1 and L3, the strain field shows a slight concentration with a wide area, as shown in Figures 4(a) and (c). Surface-strain localization is a warning indicating the locations of macro-cracks and specimen-failure modes.
When the stress reaches the post-peak region (Point D), stress and elastic energy rapidly increase and the absorbed energy is mainly transformed to dissipation energy, which contributes to crack growth, such that Ud and εvc increase very quickly, as shown in Figure 3. This indicates that the cracks propagated and connected with each other. The strain field increases progressively at different rates with a large deformation localized around the failure plane. Strain localizations appear in the observed regions L1, L2, and L3, reflecting the crack location and final fracture form. In Figure 4(a), the first localization band extends from left to right as the red-arrow direction, while the other extends from right to left. This indicates a shear crack-propagation direction. In Figure 4(b), there are two localization bands (shear cracks) located at the top and bottom of the observed region, with one significant shear band in the middle of the specimen.
In fact, all strain-localized bands in Figure 4 are parts of the specimen’s shear crack. Figure 5 shows the combination of strain fields obtained by three acquisition units, which also reflect the spatial distribution of macro-shear cracks. The damage was dominated by the main shear crack due to the restriction of confining pressure. Furthermore, other shear cracks, which were not cut-through, also contributed to rock failure and strength reduction.
Spatial distribution of the strain field measured by L1, L2, and L3.
Conclusions
In this study, a literature survey of the application of DIC methods to rock and soil was presented and a new three-dimensional DIC method covering most of the specimen’s surface was used to study the failure behavior of rock under triaxial compression with a transparent cell capable of supporting a higher confining pressure. The following conclusions have been drawn from this study.
(1) The authors collected published results concerning the application of DIC methods to geotechnical materials, which were categorized according to test type, specimen shape, confining pressure, and DIC method used. The DIC method can be seen to have wide utility for deformation measurement of rock and soil materials; however, it has seldom been applied to rocks under confining pressure, and the failure randomness of a cylindrical specimen under triaxial compression indicates that the observed fields of cameras should be as large as possible to comprehensively study the failure mechanism of rock. (2) A new 3D-DIC system with three groups of image-collection units (six cameras) is successful integrated with the compressive system using a transparent pressure cell. The new system can realize synchronous stress and image collection. The calibration of cameras and the distortion of measured results are discussed quantitatively. The proposed system can be further applied to investigate the fundamentals of rock-failure development.
A sample triaxial compressive test is implemented to study the progressive damage behavior of rock. The evolution of the specimen-strain fields is clarified corresponding to the stress–strain curves, stress thresholds, and energy transformation. Crack propagation is also discussed with strain localization. In the future, the damage mechanism of rock under triaxial compression can be comprehensively investigated using the new system.
Footnotes
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by the Natural Science Foundation of Chongqing, China (cstc2019jcyj-msxmX0488, cstc2021jcyj-msxm3199), the Chongqing university of arts and sciences Foundation (P2021TM09), and China Postdoctoral Science Foundation (2021M693751) for financial support.
