Experimental Investigation on Failure Characteristics of Pre-Holed Jointed Rock Mass Assisted with AE and DIC

Abstract

For jointed rock mass with anisotropy and discontinuity, the structure of the surrounding rock is constantly developing and changing during tunnel excavation. It is difficult to reasonably predict localized deformation of jointed rock mass by using the existing rock mechanics theory. In this paper, the failure characteristic of pre-holed jointed rock mass with three joint angles is experimentally investigated by adopting the digital image correlation and acoustic emission methods. To avoid the influence of measurement error on Digital Image Correlation (DIC) from discontinuous deformation, parametric studies and an optimized algorithm are also included in DIC tests. Results indicate that the perpendicular-jointed condition (0° joints) is the most dangerous situation because of its comparatively lower strength and brittle failure mode with a shift energy release. For rocks with different jointed angles, localized deformation emerges after the material enters the plasticity. Significant localization occurs after the failure with cracks surrounding the center hole and pre-existing joints.

1. Introduction

In the geotechnical engineering of hydropower, civil engineering, transportation and mining, engineers are often faced with the design and construction of rock mass engineering in rock mass [1,2]. Failure mechanism, as well as material strength of rock mass, plays significant roles in engineering design with adequate consideration of safe and economic factors [3,4,5]. In underground engineering, especially in tunnel or coal mine roadway engineering, people generally pay attention to the influence of joint fissures on the stability of surrounding rock. Excavation disturbance in discontinuous jointed rock mass often causes fracture, expansion and penetration of disjointed joints around caverns, which leads to instability and failure of surrounding rock [6,7]. Therefore, the analysis of the strength, deformation and fracture evolution process of the tunnel excavation model in the discontinuous jointed rock mass is helpful to deeply understand the deformation and failure mechanism of surrounding rock caused by tunnel excavation in the discontinuous jointed rock mass and provide a theoretical basis for proposing reasonable support countermeasures.

Since the jointed rock mass has obvious anisotropy and discontinuity, and the internal structure of surrounding rock is constantly developing and changing during tunnel or chamber excavation, it is difficult to reasonably predict the anisotropy and discontinuity of the jointed rock mass by using the existing rock mechanics theory, such as the elastic-plastic theory [8,9,10]. Currently, laboratory experiments [11,12] or numerical simulations [13,14] are often used for research, and most of these experiments are conducted using rock-like materials because natural rock samples containing irregular defects or joints are difficult to make. Lajtai et al. [15] studied the fracture evolution process around holes and defects under a pressure stress field through the gypsum simulated material test. It is shown that the evolution process includes the initiation of Primary tensile, Normal shear, Secondary tensile and Inclined shear cracks. Martin [16] observed that the cracks around the hole wall were divided into three categories: initial cracks, which formed in the tensile stress concentration area around the hole with the increase of applied load; A far-field crack, a crack that forms far away around a hole; Shear crack, a crack formed in the area of compressive stress concentration around the hole. Lin et al. [17] studied the mechanical characteristics and fracture mechanism of jointed rock mass containing holes and summarized the crack coalescence modes between joints and between holes and joints. Liu et al. [18] analyzed the stress–strain, contact force chain, vertical stress field and crack evolution characteristics of limestone samples with circular holes and persistent joints of different angles. Zhang et al. [19] studied the effects of weak inclusions on the fracture and fractal behavior of models containing joint sets and holes and proposed a cantilevering beam model to explain the initiation mechanism of tensile cracks around cavity filling. Chen et al. [20] studied the strain field and micro-fracture events of the jointed sample in real time, and the test results show that the joint inclination has a significant effect on the strength and failure mode of the sample. The above studies show that the failure mode and mechanical behavior depend on the geometry of the joints and the direction of the principal stress.

The development of the strain field of the sample is very important to reveal the fracture behavior mechanism of the sample under compression, which is difficult to obtain by the traditional monitoring method. Digital image correlation (DIC) is an optical non-contact deformation measurement technique that can be used to monitor the full-field strain evolution of the sample surface [21,22]. It has many advantages over traditional contact measurement techniques such as displacement extension meters, photoelastic coatings, and strain meters, such as DIC can capture the expansion of secondary cracks, which is difficult to observe with traditional methods because the secondary cracks remain closed after initiation. Therefore, DIC has been widely used in the fields of material testing, fracture mechanics investigation and engineering monitoring [23,24]. In rock mass engineering, DIC technology can be used to analyze the displacement and strain of rock mass and predict the stability of rock mass. It is very helpful to determine the construction scheme, safety measures and structural optimization of rock mass engineering. As for DIC improvement, from the author’s point of view, it can generally be summarized into two points: speed and accuracy. An important and frequently referred problem regarding accuracy is the discontinuity effect generated during DIC tests. Due to the working basis of DIC, inevitable discontinuity, like material cracking, will pose a risk to the computation error of correlation. This question has been raised for a long time, and there are some current ways to try to exclude or minimize this influence.

In this paper, we present experimental investigations on failure characteristics of pre-holed jointed rock mass. AE system incorporated with an improved DIC technology that can automatically revise the discontinuity error is also utilized for the measurement. The structure of the paper is organized as follows. Section 2 presents the mechanism and the optimized algorithm for the DIC. Details on the experimental setup are described in Section 3, followed by parametric studies for the DIC in Section 4. Experimental results on the evolution of mechanical properties and the characteristics of the failure modes are discussed in Section 5.

2. Deformation Measurement via the Geotechnical DIC System: PhotoInfor

2.1. Principle of the Digital Image Correlation

DIC is developed as an optical, non-contact, correlation-based method against the measurement of material deformation. In particular, 2D-DIC has been widely applied to experimental investigations in the field of geotechnics due to its efficiency. It relies on the subset network’s correlation coefficients throughout the deforming process for the displacement field and the strain [25].

The judgment process for monitoring moving subsets is based on the correlation coefficient (CC). As shown in Figure 1, each DIC subset is created as a block with an adjustable radius. As for correlation computation, grey value f(x, y) serves as the crucial variable in Equation (1), where k is the subset radius, (x, y) represents the coordinate of the center pixel, f₁ and f₂ refer to the grey value in reference and target images respectively, and R₁₂ hints the correlation coefficient. Each subset in the target image within the searching scope will be compared in groups with the ones in the reference, and the CC can be obtained accordingly. The subset with the highest value of CC will be viewed as the target one, and the displacement can, therefore, be calculated according to the coordinate data of central pixels P_i, P_d.

$$R_{12}={\displaystyle \frac{{\displaystyle {\sum }_{x=1}^{2k+1}{\displaystyle {\sum }_{y=1}^{2k+1}{f}_1(x,y)\times f_2(x,y)}}}{\sqrt{{\displaystyle {\sum }_{x=1}^{2k+1}{\displaystyle {\sum }_{y=1}^{2k+1}{f}_1{(x,y)}^2\times {\displaystyle {\sum }_{x=1}^{2k+1}{\displaystyle {\sum }_{y=1}^{2k+1}{f}_2{(x,y)}^2}}}}}}}$$

(1)

Figure 2 describes the monitor field marked by a mesh composed of the DIC subsets where an adjacent quadrangular grid surrounds each image point. Through a series of correlation calculations, the displacement of DIC subsets can be obtained first, and the point data can be achieved through interpolation. Equation (2) describes the interpolation calculation for the displacement of each point where u and v refer to the horizontal and vertical displacement, respectively, and N_i denotes the interpolation function according to the coordinate relationship. The displacements can then be transformed into the strain according to Equation (3), where ε_x, ε_y refer to the strain in horizontal and vertical direction, respectively, and γ_xy indicates shear strain.

$$\left\{\begin{array}{l}u={\displaystyle \sum _{i=1}^{4}uiNi}\\ v={\displaystyle \sum _{i=1}^{4}viNi}\end{array}\right.$$

(2)

$$\left\{\begin{array}{l}\epsilon x={\displaystyle \frac{\partial u}{\partial x}}={\displaystyle \sum _{i=1}^4\frac{\partial Ni}{\partial x}ui}\\ \epsilon y={\displaystyle \frac{\partial v}{\partial y}}={\displaystyle \sum _{i=1}^4\frac{\partial Ni}{\partial y}vi}\\ \gamma xy={\displaystyle \frac{\partial u}{\partial y}}+{\displaystyle \frac{\partial v}{\partial x}}={\displaystyle \sum _{i=1}^4\frac{\partial Ni}{\partial y}ui}+{\displaystyle \sum _{i=1}^4\frac{\partial Ni}{\partial x}vi}\end{array}\right.$$

(3)

2.2. DIC Software PhotoInfor: Designed for Geotechnical DIC-Analysis

Whole-field correlation calculation is normally realized via software processing. Specifically, PhotoInfor, adopted in the current study, is a DIC-cored software that includes a post-processing program in an auxiliary named PostViewer. Compared with other processing-environment-reliant software (or programs), PhotoInfor can be operated directly in the Windows system, which is easier to analyze and more functional. It has been widely applied in many DIC-related research [21,22,23,24,25], and accordingly, its measurement accuracy gets further verification. PhotoInfor is creatively designed for geotechnical tests with unique algorithms based on the deformation situation, including nonuniform characteristics, large deformation, and crack revision. Besides the general correlation calculation function, specialized algorithms, such as the One Point with Five Pixel-block Method (OPFPM) [26], are implemented in PhotoInfor, which could largely improve the speed and accuracy. Figure 3 depicts the software interface as well as its post-processing program.

2.3. Specialized Algorithm Equipped in PhotoInfor Regarding Discontinuity

No matter how maturely the DIC technique is utilized, deficiencies still exist in specific application fields that need to be solved. As for brittle-damage performance, cracks and/or openings normally bring with the material surface discontinuity, leading to localized computation error of correlation value. A typical solution is to increase the mesh density for a minimum error area while, unfortunately, bringing another problem referred to as image noise [25]. Meanwhile, additional but less necessary computation will be paid to realize a high-density meshed work, which is heavily inappropriate, especially for large field cases. Hence, to overcome the described drawbacks coming from the crack discontinuity, the OPFPM approach is designed with a full name of “one point with five pixel-block method” [26] to overwhelm/ minimize the discontinuity influence and to reach an optimized computation in terms of speed and noise.

Figure 4 describes the conceptualized model of OPFPM. As for the cracking event, capturing the generation moment via high-speed photography equipment is realizable, during which the crack exists as a small opening. In such a case, the crack region would influence the subset block in the conventional DIC. However, in the OPFPM case, due to the overall five blocks with the same radius generated for the subset, there exists at least one block (i.e., the block named “2” marked yellow in Figure 4b) out of the discontinuity influence as depicted in Figure 4. The core mechanism of the OPFPM lies in the generation of five neighbored blocks surrounding any selected coordinate points along with five CC values, followed by the auto-selection with the maximum one. It is easy to realize that the OPFPM works relying on automatic and effective computation for the fittest target position against the discontinuity error instead of the conventional meshwork.

3. Experimental Work

3.1. Material and Samples

The rock-like material used in this experiment is prepared with mixed liquor and plaster under a fixed mass ratio (70%). Firstly, a defoamer of 0.07% was added to pure water and then stirred thoroughly. Note that the defoamer used here inhibits the inner bubbles within the plaster liquid. The plaster and defoamer water mixture was performed later in an oscillator and then poured into a customized mold. We prepared samples of dimensions 160 × 160 × 40 mm with a hole in the center (diameter of 30 mm) (see Figure 5). Joints were realized by aluminum sheets with a thickness of 0.6 mm and a length of 160 mm. Finally, joint angles were prepared as 0°, 45° and 90°. Young’s modulus of 2.43 GPa and uniaxial compression strength (UCS) of 8.01 MPa are mechanical parameters. Figure 6 further depicts the uniaxial curves where a stress drop occurred after the peak strength, indicating a brittle failure performance.

3.2. Experimental Setup

The experiment aims to investigate the strength and deformation of pre-holed jointed rock mass. As described in Figure 7, experiments were conducted via the MTS microcomputer control system, which could reach a maximum loading of 300 kN and stabilize the rate deviation within ±1%. To capture the generation moment of cracking, a CCD camera (Manufacturer: Basler company registered in Germany, Mode: acA4024-8gc) was used for the monitor, illuminated by two step-less dimming lights. In the meantime, to synchronize the cracking process, an acoustic emission system was installed during the deformation through which the crack activity can be predicted from AE events.

3.3. Procedures

The sample surface needs a speckled treatment with paint to reach an effective DIC analysis, as shown in Figure 8. Notably, colorful and scattered speckle patterns can normally induce a better effect. Upon the settlement/adjustment of equipment, including the image acquisition system, AE sensor and loading framework, compression was then applied starting with a contact pressure of 200 N. Constant displacement mode is selected with the speed of 0.12 mm/min. Six cases, varied with boundary conditions and joint angles, were repeated at least three times to avoid experiment errors.

4. Confirmation of Conventional Parameters in the DIC for an Optimized Measurement

Appropriate selection of image resolution and wise setting of subset radius, searching radius, and subset interval (point density) contribute a lot to measurement accuracy in DIC (PhotoInfor, Version 2023). Several DIC software with customized functions, searching mode, correlation algorithms, sub-pixel division, etc., can also be adjusted for an optimal effect. Adjusting the DIC parameters according to experimental setup and requirements is essential to reach high-quality measurement results. As shown in Figure 9, the full image resolution is 2600 by 2600 pixels, and the testing area is selected around the center hole due to localized deformation with a dimension of 230 by 240 pixels. In what follows, we present the calibration work regarding the terms of subset radius and searching mode for further DIC process.

4.1. Subset Radius

As for the subset radius, it is normally linked to the noise effect. We know that image noise occurs irregularly during the process of acquisition and signal transformation, which is hard to suppress fully. Based on the published results [25], the impact of noise on the calculation of correlations grows as the subset radius decreases. A subset radius set below a certain threshold is expected to induce errors in the analysis. The upper bound of the subset radius meanwhile does exist that the over-sized subsets will induce the loss of tiny-scaled pattern with interest. Therefore, calibration corresponding to subset radius is essential to be conducted firstly against noise-based and pattern-based phenomena.

Figure 10 presents a representative example regarding determining an approximate radius range. Obviously, the 2-pixel case fails to measure the strain information due to noise error. It can be predicted that pixels influenced by noise constitute a significant portion of the subsets, which in turn exerts a substantial impact on the computation of the correlation value. As the subset radius expands, its ability to suppress noise becomes more pronounced, followed by the recognition of crack patterns. In this experiment, the subset radius was set as 10 pixels for the identification of a cracking pattern and its moderate magnitude.

4.2. Mesh Density

In DIC, a field pattern is observed based on the CC computation of each subset. Hence, the DIC quality should be highly controlled by mesh density. Particularly, small-sized objects like cracks call for denser mesh to observe the crack region in images. Note here that in addition to the acquisition of a crack pattern, the mesh density should also be high enough to realize the crack thickness mesh-independent.

Figure 11 describes volumetric stains in four mesh-density cases. First to be demonstrated, in the PhotoInfor, the standard mesh mode is achieved by dividing squares, and the mesh density is consequently determined by the distance between adjacent subsets. Clearly, case (a), characterized by a sparse mesh, is insufficient to effectively capture the crack pattern as it is barely observable, and the thickness is fully mesh-dependent (thickness equals mesh spacing). With an increase in density, case (b) is capable of depicting a more distinct pattern, encompassing the crack length and its overall distribution. Nevertheless, the thickness measurement is somewhat reliant on the mesh spacing, which is not entirely satisfactory. To address this, we conducted cases (c) and (d) with the aim of optimization for a more thorough comparison. The results indicate that computations with mesh spacings of 5 pixels and 2 pixels each yield satisfactory outcomes. Furthermore, to take into consideration the analysis speed, a mesh density of five pixels is suggested in this problem with respect to the DIC reorganization.

According to the discussion in the former, we aim to propose a recommended guideline for mesh placement in DIC studies. In this scenario, the average width/thickness of the cracks generated is gauged to be approximately 3 pixels. Hence, to be concluded from Figure 11, the mesh density (spacing) should be controlled within twice the pattern size. Nevertheless, employing a high-density mesh across the entire field can lead to substantial computational demands, a cost that, while significant, is unavoidable. Thus, localized treatment with high-density mesh could be an intelligent way. Fortunately, PhotoInfor provides an alternative solution to create mesh imported from third-party software, through which mesh density can be customized for any desired effect.

4.3. OPFPM Mode (Advanced Function in DIC)

The calibration work presented above can be viewed as a conventional process for a standard DIC test. In what follows, we are going to show an advanced treatment for the revision of discontinuity error, which is realized via the OPFPM algorithm as introduced in the former section.

As depicted in Figure 12, a crack in the target image generates the analysis error when the DIC is conducted through a conventional method. In this case, the subset radius is set as 10 pixels while the average opening value of cracks is measured as 4 pixels. Given the substantial size of the discontinuity, the extra color emanating from the crack could potentially lead to miscomputation in correlation analysis if it is included in the calculations of adjacent subsets. It is important to note that four subsets along the crack boundary encountered computational errors, resulting in an error rate of 21.1% among the 19 subsets that were distributed along the crack. As for case (c), the OPFPM scenario effectively mitigates the impact of cracks, leading to a refined calculation of the cracked region while leaving the rest of the area unchanged, aligning with the conventional solution. Last to be highlighted, due to the additional four blocks set for each subset, OPFPM mode takes at least five times the work to realize an optimized result. Hence, it should be activated thoughtfully based on specific needs.

Two superiorities are indicated for analysis with the OPFPM. The first one is the revision of the measurement error arising from discontinuities (i.e., cracks) in samples. Another advantage lies in the time cost when it comes to duplicated trial tests in DIC. We know that a trial test on DIC parameters (i.e., subset radius) is essential for a better revision of discontinuity influence in conventional DIC. The OPFPM helps to avoid parametric studies on error revision and saves time in analysis.

5. Results

5.1. Mechanical Properties

Mechanical properties, such as compression strength, elastic–plastic relationship, and hardening (or softening) characteristics, can be revealed from stress-strain curves. To investigate the above items, compression results are selected for comparison. As depicted in Figure 13, the deformation paths of the rock mass are quite different and varied with joint angles. As for the horizontally jointed condition whose joint angle is perpendicular to the main loading direction, rock mass compacts heavily at the beginning. The phenomenon demonstrates that this perpendicular-jointed condition is unstable and easy to induce localized instability. As the loading continues, the rock sample shows a dense state, undergoes a temporary period of elasticity, and finally reaches the failure’s peak. The peak strength of perpendicular-jointed rock mass is nearly 5.7 MPa, which decreases significantly compared with the UCS of intact rock. Turning to the 45° condition, there exists a similar situation in general: the rock mass with 45° joints experienced a similar compression mode from the beginning to the peak position, also with a peak strength of 5.7 MPa. However, the post-peak situation is different where the stress drop at 45° jointed condition is more moderate than that of the zero-degree case. For 90° jointed rock mass, the total stress-strain curve’s characteristic is basically the same as that of the intact rock. When continued loading is applied, rock mass enters into the elasticity status first and then undergoes plasticity after the yield point, and finally, failure happens when the stress reaches the strength value. The biggest difference lies in the failure mode of the rock mass with a 90° jointed case is significantly brittle, which shows that the process of energy release should be fiercer.

Based on the above description and practical tunnel engineering, we can obtain the following findings: If joints exist within the ground area, mechanical feedback will be greatly affected varied with the joint angle. Specifically, the perpendicular-jointed (0°) condition mainly affects the strength of the rock mass while the rock mass still maintains the brittle failure mode. Oblique-jointed (45°) condition normally produces the effect on both strength and failure mode. Parallel-jointed (90°) condition influences the mechanical characteristic a little, decreasing the strength slightly. Hence, we can conclude that if the tunnel is constructed in jointed ground, joint angles will affect engineering stability. In particular, the perpendicular-jointed condition is most dangerous because of its comparatively lower strength and the maintained brittle failure mode, which implies that energy will be released sharply upon failure and, therefore, threatens the tunnel structure the most.

5.2. Failure Behaviour

Acoustic emission technology works based on monitoring wave signals produced by the internal structure change, such as cracking, fracture propagation and dislocated displacement. In addition, stable defects such as elastic strain cannot generate acoustic signals, so cracking and failure activities can be revealed via AE signals. For an intact rock material, AE activities normally remain peaceful during a loading process and start to be active around and before the failure moment. Because of that, AE data can be used to predict material failure, which is also useful in practical engineering work. As for jointed rock mass, AE behavior differs from that of intact rock. As depicted in Figure 14a, AE behavior remains active first at the pre-compression stage. The entire rock mass is compressed during this period with a gradually enhanced stiffness. Specifically, $0^{°}$ jointed rock tends to have a longer pre-compression duration than other joint conditions due to its higher pre-compressibility. As the loading continues, 0° jointed mass will present a short period of elastic behavior during which a linear elastic deformation occurs, with comparatively milder AE signals. Obvious elastic behavior happens in the cases of $45°$ and 90° jointed angles while with a longer lasting period due to (with 90° jointed rock mass, for instance) a lower starting point of elastic behavior and a higher yield stress. There are no evident AE activities during this period, which is a common phenomenon in three joint conditions. Moreover, it can be found that when the rock mass turns into a yield surface, an isolated AE behavior will emerge, and clustered AE columns will appear before the failure.

Failure modes are recognized by the DIC measurement for three jointed cases, as depicted in Figure 14. As discussed earlier, four distinct regions are discovered as revealed in the stress evolution curves: region a of pre-compression, region b of elastic state, region c of sample yielding, and region d of post-yield process. Volumetric strain distribution measured by the DIC is attached for each region of respective cases. For three jointed cases, localized deformation emerges after the material comes into the plasticity, and significant localization occurs after the failure. With the 0° In a jointed case, for instance, cracks emerge near the center hole and tend to develop towards the exterior area as the compression continues. A similar situation can be found in the 90° jointed case with a higher degree of deformation (see Figure 14c). When it comes to the 45° jointed situation, localized deformation appears surrounding the pre-existed joints (see Figure 14b). According to the Mohr Column yield criterion, the joint angle of 45° is close to the failure plane, although for the sample with an internal hole. In such a case, localized deformation emerges from the joints and gets extended to the entire sample surface. A significant shear failure mode is distinguished in the 45° jointed case. It should also be noted that the 45°jointed case experiences a ductile failure mode after the peak strength and the localization develops with a longer duration and an extensive influenced area.

As described above, perpendicular-jointed condition (0° joints) is most dangerous because of its comparatively lower strength and brittle failure mode with a shift energy release. According to the characteristic of the AE behavior of respective jointed angle cases, it is instructive to predict jointed conditions based on AE signals for onsite situations. The unique distinction of the perpendicular-jointed condition is that there is no obvious calm stage of AE behaviors during the total period, which is evidence of its highest risk for sustained inner cracking.

6. Conclusions

In this study, the AE system incorporated with an improved DIC technology, which can automatically revise the discontinuity error, is utilized to investigate the failure process of jointed rock samples containing a hole in the center. The results help to enhance the understanding of jointed rock’s mechanical characteristics and failure behavior. The following conclusions can be drawn.

(1) At the material level, the jointed rock-like specimens containing holes were fabricated with plaster and defoamer water and then tested under uniaxial compression. The results show that the joint inclination significantly influences the mechanical characteristics and failure behavior of jointed samples containing holes;

(2) For an optimized measurement of cracks through the DIC, parametric studies are conducted with a suggested criterion to deal with the mesh installment for DIC. The mesh density (spacing) should be controlled within twice the pattern size. The OPFPM algorithm is suggested to reach the required deformation pattern while with a moderate computational load.

(3) For rocks with different jointed angles, localized deformation emerges after the material comes into the plasticity. Significant localization occurs after the failure with cracks surrounding the center hole and pre-existing joints;

(4) Results show that perpendicular-jointed condition ($0^{°}$ joints) is the most dangerous situation for its comparatively lower strength and brittle failure mode with a shift energy release. It is instructive to predict jointed conditions based on AE signals for onsite situations.