DSCM (digital speckle correlation method), also called as DIC (digital image correlation), is set as an optical, non-contact, speckle-based measurement for process displacement, strain and deformation of the material. In particular, 2D-DIC is widely applied to experimental research in the fields of geotechnical engineering, structure engineering, material research, etc. (Li et al., 2016; Szymczak et al., 2022). It relies on the correlation calculation of the selected subsets, where for each one in the reference image a best-fit subset is found in the target image (Li and Einstein, 2017). The criterion for judging the target subset is based on the correlation coefficient (CC). As depicted in Figure 1, each DIC subset appears as a block with a radius that can be adjusted. During the correlation analysis, the grey value f x , y is a key parameter in Equation 1. Here, k represents the subset radius, x , y indicates the coordinate of the central pixel, f 1 and f 2 are the grey values in the reference and target images respectively, and R 12 denotes the correlation coefficient. All subsets within the search range in the target image will be compared with the reference subset to derive the correlation coefficient. The subset with the highest R 12 value will be identified as the target subset, and the displacement can then be determined based on the coordinate data of the central pixels P i and P d (Li et al., 2022). R 12 = ∑ x = 1 2 k + 1 ∑ y = 1 2 k + 1 f 1 x , y × f 2 x , y ∑ x = 1 2 k + 1 ∑ y = 1 2 k + 1 f 1 x , y 2 × ∑ x = 1 2 k + 1 ∑ y = 1 2 k + 1 f 2 x , y 2 (1)

Cracks typically create discontinuous regions in digital images, which can interrupt surrounding subset blocks and potentially lead to correlation calculation errors when applying DIC to materials with cracks. To address this, one common approach is to reduce the subset radius, but this can increase image noise in the results. Balancing these factors requires manual adjustment of the subset radius to minimize noise interference. However, this process is complex and cannot completely eliminate the noise effect. To fix the issues of crack discontinuity and noise effects, a correlation calculation algorithm named OPFPM (one point with five pixel-block method) was developed (Li et al., 2022). This algorithm automatically adjusts the subset block around a crack. Figure 2 illustrates the calculation process of OPFPM, where a crack traverses the original subset block. When capturing images with a CCD camera, it is feasible to obtain images of newly formed cracks with minimal opening. As shown in Figure 2, the crack passes through the original block along with block 1, block 2, and block 3, but not block 4. This indicates that, provided the position point P is outside the crack area, it is possible to find a block with the position point in the corner that is least affected by the crack. OPFPM can be described as a block adjustment process. Initially, five subset blocks are generated around a position point in the target image, along with five corresponding CC values. Subsequently, the block set is determined based on the maximum CC value. This approach helps to mitigate the impact of cracks and noise, enhancing the accuracy of the correlation calculations. To conclude, the OPFPM helps to revise computational errors due to the generation of discontinuities without complex tests on the setting of DIC parameters.

The whole-field correlation calculation is mainly realised through software processing. PhotoInfor is a customized DIC software with a post-processing programme (user interface see Figure 3). Unlike software that relies on specific environments, PhotoInfor can be operated directly in Windows, making it user-friendly and highly functional. PhotoInfor has been widely used in DIC-related studies, and its measurement accuracy has been verified accordingly. PhotoInfor is particularly designed for geotechnical tests based on the deformation characteristics in terms of non-uniform deformation, large deformation, crack generation, etc. Besides the general correlation calculation function, specialized algorithms, i.e., OPFPM, are set in PhotoInfor which could largely improve the analysis speed and accuracy.

Rock-like material used in the experiment contains mixed liquor and plaster that are under a fixed mass ratio of 70%. Firstly, defoamer of 0.07% v/v was added to water and stirred thoroughly. Defoamer used here is to inhibit the phenomenon of inside bubbles when producing the plaster slurry. The mixture of plaster and liquor was performed later in an oscillator and then poured into a customized mould. A series of compression tests were conducted to obtain the material parameters, such as Young’s modulus, Poisson’s ratio, UCS, etc. Figure 4 depicts the uniaxial curves where a stress drop occurred after the peak of 8.01 MPa which indicates a fragile failure like the characteristics of practical rock. We prepared samples of dimensions 160 × 160 × 40 mm and a hole in the center with diameter of 30 mm (see Figure 5). Joints were realized through aluminium sheets with the same thickness of 0.6 mm and length of 160 mm, and the angles were set as 0, 45, 90°. As shown in Figure 5, a fixed confining boundary is applied by a pair of connected steel plates.

The purpose of this DIC-based experiment is to examine the role of boundary conditions on the mechanical behaviour and crack pattern of pre-holed jointed rock mass during a compressing period. As depicted in Figure 6, the experiment was conducted in MTS microcomputer control system which could reach a maximum of 300 kN and stabilizing the loading rate within ±1% deviation. In order to reach the crack generation moment, CCD camera (acA4024-8gc, Basler ace) was used for image capture, illuminated by two stepless dimming lights. Focal length of the camera was fixed during experiments. To better predict the crack moment, acoustic emission technology was applied either during the compressing by which the crack activity can be revealed in monitor data.

Firstly, in order to perform a precise DIC analysis which is based on the correlation calculation, sample surface needs a speckled dispose through colored paint before the tests. Multi-colored and scattered speckle patterns can normally induce a better effect. In this research, two boundary conditions were applied for comparison where one represents unconfined compression and another is set with displacement-fixed boundary. The fixation was realized through a couple of steel plates which were connected by four iron bolts. After the settlement of equipment, like image acquisition device and acoustic emission sensor, uniaxial compression was then conducted. The initial contact force was set at 200 N. The loading rate of the upper top was set as 0.12 mm per minute. Six cases, varied with boundary conditions and joint angles, were repeated for at least three times respectively to avoid experimental errors.

First, we present a case study on the revision of crack influence in DIC analysis by adopting the OPFPM mode. Figure 7a shows the measurement region as selected by the dashed line with a dimension of 150*200 pixels (1 pixel corresponds to 0.05 mm in reality). Here the searching radius in DIC is 15 pixels. Obviously to be observed that DIC analysis in conventional mode meets measurement error near the crack region while the adaptation of the OPFPM can perfectly revise the error which is simple and straightforward in the DIC. In what follows, the function of the OPFPM will be activated in the remaining analysis.

In DIC, the measurement quality of the deformation pattern is highly controlled by mesh density. Particularly, as for small-sized objects like cracks, it calls for denser mesh to realize the observation of crack boundary. Note here in addition to the acquisition of crack pattern, the mesh density should also be high enough to realize the crack thickness to be mesh-independent.

Figure 8 describes the volume stain of 4 mesh cases. First to be demonstrated, standard mesh mode in PhotoInfor is through square splitting and correspondingly the density is defined as the spacing between two neighbored subsets. Obviously to be observed, case (a) with a much dense mesh can capture the crack pattern while with much irrelevant information. Meanwhile, computation with large amounts of subsets can introduce huge time costs. As the density slightly decreased, case (b) can also present a clear pattern including the crack length and a general distribution mode. As for case (c) with subset interval size of 10 pixels, the crack pattern can be hardly captured and the thickness is fully mesh-dependent (thickness equals to mesh spacing). The results indicate that both calculations using a spacing of 5 pixels and 2 pixels can yield acceptable outcomes. However, taking into account the analysis speed, a mesh density of 5 pixels is recommended for this problem. Based on the above description, we propose a recommended criterion for mesh installation in DIC applications. Given that the average measured opening/thickness of the generated crack is 3 pixels, our analysis suggests that the mesh density (spacing) should be kept within twice the pattern size.

As for subset radius, it is generally related to noise effects. Image noise occurs irregularly during acquisition and signal transformation, and is hard to eliminate entirely. Published results indicate that the impact of noise on correlation calculations grows as the subset radius shrinks. Thus, it is predicted that there’s a subset radius threshold below which analysis errors occur. Additionally, an upper bound for subset radius exists, as overly large subsets can lead to loss of fine-scale patterns of interest. Therefore, it is crucial to conduct subset radius comparison considering both noise-based and pattern-based factors. Figure 9 presents a typical example of establishing an approximate radius range. Figure 9a with small size of subset radius shows evident computation error while the situation tends better for cases with larger size of subset. As the OPFPM mode is activated, the computation time is much longer in the case with subset radius as 25 pixels. In this experiment, the subset radius was set as 15 pixels for its identification of cracking pattern and its moderate magnitude with computation time and taken into account.

The joint angle and confining condition play significant roles in the change of mechanical behaviour of materials. Mechanical behaviour of samples with Three joint angles and two boundary conditions were compared as shown in Figure 10, and each case is repeated for three times. The strength of rock masses is highly dependent on the joint angle no matter in joint angle cases or boundary cases. In two boundary cases, 90° joint cases behave the highest strength. In uniaxial conditions, 90° jointed sample shows approximately 7.5 MPa, 0° jointed sample exhibits 4.75 MPa (the lowest strength), and 45° jointed sample behaves at a middle state of 5.05 MPa. In detail, for the horizontally jointed condition in the uniaxial case (where the joint angle is perpendicular to the main loading direction), the rock mass undergoes significant compaction at the initial stage of loading. This indicates that the perpendicular-jointed condition is highly unstable and prone to localized instability. As the loading progresses, the rock sample transitions from a dense state through a temporary elastic phase, ultimately reaching the peak of failure. When the angle is set at 45°, a comparable scenario is observed in uniaxial cases. Rock masses containing joints undergo a similar compression pattern from the initial stage to the peak point. Nevertheless, the post-peak behaviour differs significantly. The stress drop in the jointed condition is relatively more gradual compared to that in the zero-degree case. For 90° jointed rock mass, it behaves with the highest strength and brittle failure characteristics.

When the confining is applied, peak values in three jointed cases of loading pressure are overall enhanced while with different patterns in post peak stages. First, peak pressure of 0°, 45° and 90° jointed samples in confining condition shows approximately 5.85 MPa, 6.45 MPa and 7.85 MPa. Obviously to be observed, the confining boundary condition plays the most significant role in the 45° jointed cases due to its constraint on the sliding of rock mass. In comparison, another two cases embrace slight enhancement of the loading pressure. The reason lies on the displacement of rock mass upon loading. The deformation pattern will be further discussed in the latter through the analysis of DIC. The post-peak stress-strain relationship in three jointed cases subject to confining condition indicates ductile deformation which is different from the uniaxial results.

Drawing on the preceding analysis and integrating it with practical tunnel engineering scenarios, the following findings can be achieved. The presence of joints within the ground significantly impacts mechanical feedback, with the degree of influence varying according to the joint angle. Specifically, when joints are perpendicular to the loading direction, the primary effect is on the rock mass strength, while the rock mass continues to exhibit a brittle failure mode. In contrast, oblique joints tend to affect both the strength and the failure mode of the rock mass. Meanwhile, parallel joints have a relatively minor impact on mechanical characteristics, causing only a slight reduction in strength. The confining degree is associated with the buried depth. We further propose that the buried depth would also pose an influence on the strength of the rock in particular for oblique jointed case. Meanwhile, rock mass exhibits ductile failure in deep buried conditions. From these observations, it is evident that in jointed ground, tunnel engineering stability is influenced by joint angles and buried depth. Among these, the perpendicular-jointed condition poses the most significant risk in both shallow and deep-buried conditions. This is due to its relatively lower strength and the maintained brittle failure mode, which suggests that energy will be released abruptly upon failure. This abrupt energy release poses the greatest threat to the tunnel structure.

Acoustic emission technology relies on monitoring wave signals generated by internal structural changes within materials, such as cracking, fracture propagation, and dislocation displacement. However, it is important to note that stable defects like elastic strain do not produce acoustic signals. In the case of intact rock materials, AE activity is typically minimal at the beginning of the loading process but increases noticeably as the material approaches failure. This characteristic enables AE data particularly useful for predicting internal cracks and material failure, offering significant benefits for practical engineering applications.

Figure 11 presents AE count singles and the stress evolution upon the loading process for cases with various joint angles and boundary conditions. As depicted in Figures 11a,c,e, for free boundary samples, AE behaviour remains active firstly at the pre-compression stage. During this period, the entire rock mass is compressed and shows a plastic deformation mode. Specifically, 0° jointed rock tends to has a longer duration of pre-compression than other joint conditions. As the loading continues, 0° jointed mass will have a short period with mechanical behaviour like elastic performance. A similar period of 45° and 90° conditions is longer because 45° jointed rock mass has a lower starting point of elastic behaviour and 90° jointed mass is with a bigger yield limit. For cases with confining boundary as depicted in Figures 11b,d,f, AE singles remain active almost through the loading process in comparison with the free boundary cases, in particular in 0° and 45° joint cases, indicating more frequent internal cracks generated during the deformation. As indicated from AE behaviors in two boundary cases, more internal cracks may generate for deep-buried rock mass in comparison with shallow-buried ones which calls for effective monitoring.

Figure 12 further describes the volumetric strain pattern as measured by DIC for cases with various joint angles and confining conditions. Volumetric strain results indicate material cracking regions during the loading process. As described in above, 0° and 45° joint cases exhibit almost whole-stage AE activities in two boundary cases which corresponds to the closure of internal joints subject to the loading as measured by DIC. When it comes to the 90° joint case with joints parallel to the loading direction while with the highest strength than the other two cases, no evident joint closure can be detected. The overall failure of 90° joint behaves with a connected crack penetrating the central hole while another two cases show the connection of closed joints. There is no significant difference in failure pattern for cases with various confining conditions.