Quasistatic progressive crack propagation behavior of crystalline rocks based on SCB tests

To explore the influence of mineral grains on the mechanical strength and crack propagation behavior of rocks, this study investigates the quasi-static crack propagation characteristics in four types of granular structured rocks (three varieties of granite and one type of diabase rock) through a semi-circular bend three-point bending test. The implementation of a servo-controlled crack-opening displacement mechanism facilitated the realization of quasistatic crack propagation. The entire experimental procedure was documented on a camera. Subsequently, the quasistatic propagation and development of cracks in crystalline rocks were examined using digital image correlation, whereas the distribution of mineral grains and their relationship with the pattern of crack evolution were investigated under optical microscopy. The paths of the cracks exhibited noticeable deviation, which were further influenced by the mineral grains. Specifically, cracks tended to circumvent harder minerals while gravitating towards softer ones, highlighting the significant role of mineralogical composition in determining the fracture behavior of granite.


Introduction
Heterogeneity is a fundamental attribute of rocks that considerably influences their mechanical strength and crack propagation behavior.A notable aspect of granular-structured rocks like granite pertains to the composition of mineral grains such as quartz, feldspar, and mica.Understanding how these mineral grains influence mechanical strength and crack propagation in rocks is essential for a deeper comprehension of fracture mechanisms within such granular formations.
The semicircular bending (SCB) test is recognized by the International Society for Rock Mechanics as the optimal method for Mode I fracture toughness testing [1], has garnered widespread acclaim for its utility in investigating rock fracture characteristics.Extensions of numerical work on this test have provided analytical functions as approximate stress intensity factors for Mode I variations [2].
Khan et al. [3] utilized the SCB test to explore the impact of various crack types on the strength of limestone layers, whereas Zhou et al. [4] applied the SCB method to evaluate the stress intensity factor distribution in sandstone and its fracture behavior.In the present study, we employed the ISRMendorsed SCB approach to test the Mode I stress intensity factor [5], specifically when the crack is oriented at 0° with respect to the vertical direction.
Although the SCB test serves as an adept method for studying crack propagation in rocks, only a handful of studies have investigated into crack propagation patterns in granular-structured rocks, especially regarding the role of mineral grains on crack behavior.Drawing on SCB tests, this study examines four types of granular-structured rocks (three variations of granite and one diabase rock).We implemented crack mouth opening displacement (CMOD) servo-controlled loading to derive Load-CMOD curves, with a high-speed camera capturing the detailed crack propagation sequence.Digital image correlation (DIC) facilitated the analysis of quasistatic crack evolution in crystalline rocks.Concurrently, observations from optical microscopy were employed to correlate the distribution of mineral grains with crack evolution patterns.This investigation aims to enrich our understanding of how microscopic structural features of rocks influence their fracture mechanisms.

Design and Material Selection for SCB Samples
The mechanical properties of granular-structured rocks-bonded with mineral grains-are deeply influenced by mineralogical composition and particle size.In this investigation, three varieties of granite and one type of diabase were selected as experimental subjects, each displaying unique granular structural traits, as illustrated in Figure 1.For simplicity, these materials are labeled as Granite X, Granite L, Granite M, and Diabase S, which were correspondingly identified as X, L, M, and S in the sample codes.The thin-section petrographic analysis was performed on these four materials, yielding the following insights.Granite X is composed of approximately 25% quartz, 30% plagioclase, 35% alkali feldspar, 6% biotite, and 4% common hornblende, showcasing hypidiomorphic and striped structures.Granite L comprises approximately 35% quartz, 35% plagioclase, 27% alkali feldspar, and 3% biotite, with both hypidiomorphic and striped structures visible, alongside vermicular structures under microscopic examination.Granite M, similar to Granite L but lacking vermicular structures, contains approximately 25% quartz, 30% plagioclase, 35% alkali feldspar, and 10% biotite.These granites are categorized as plagioclase granites.Diabase S is distinct from the plagioclase granites and is classified as diabase with a composition of ~60% plagioclase, 3% biotite, and 37% pyroxene, featuring relatively smaller mineral grains.
The geometry of the experimental samples is depicted in Figure 2, which were prepared with a semicircular diameter of 100 mm and a thickness of 20 mm.A central crack, 15 mm in length and 1 mm in width, was precisely introduced using a wire-cutting technique; the crack orientation was perpendicular to the vertical axis.The support span was established at 80 mm.The experimental setup was divided into two groups, A and B, with two specimens from each granite type.

Experimental Equipment and Loading Process
To manage quasistatic crack propagation in the SCB samples and document the entire crack initiation and propagation process, the MTS815.04high-rigidity rock mechanics testing system, provided by the Shaoxing University of Arts and Sciences, was employed for servo loading.The CMOD was measured using an extensometer and servo-controlled to increment at a rate of 0.02 mm/min until the Load-CMOD curve plateaued, signaling the cessation of loading.Furthermore, the entire testing procedure was recorded using an i-speed 716 high-speed camera from the Key Laboratory of Geotechnical and Underground Engineering of the Ministry of Education at Tongji University, complemented by two 600 W halogen lamps for additional illumination.

Digital Image Correlation Analysis Method
DIC is a noncontact full-field measurement technology that has been extensively applied in the field of rock mechanics in recent years.Its fundamental principle involves comparing pixel variations between initial reference images and subsequent post-deformation images to derive displacement and deformation data of the object's surface, thereby facilitating measurement or strain analysis.
The DIC analysis software utilized in this investigation was built upon the open-source platform Ncorr [6].The final frame at the end of the experiment was selected as the final image for analysis.Retrospectively, one image every 30 s was selected for DIC analysis.All images were initially processed using a MATLAB script, with the selected images subjected to further analysis as needed.

Load-CMOD Curve Characteristics
By controlling the gradual opening of the crack through servo loading, a quasistatic crack propagation process was obtained.Based on the load-CMOD curves, the post-peak load progressively declined with widening crack openings.
Overall, the Load-CMOD curves demonstrated a uniform pattern, as depicted in Figure 3. Conversely, the load-axial displacement curves showed greater variability across different samples.Considering the sample L-B as an example and drawing insights from DIC observations of the crack propagation sequence, the Load-CMOD curve can be segmented into three distinct stages: pre-crack initiation, initial crack initiation, and stable crack propagation.
During the pre-crack initiation phase, both the Load-CMOD and load-axial displacement curves display a nearly linear progression, primarily indicative of elastic deformation in the sample.This phase concludes as the nonlinear deformation starts to appear near the crack tip, implied by a reduction in the slope of the axial load increase including that in CMOD, as marked at instant "a" in Figure 4.The phase of the initial crack initiation is marked by a rapid decrease in the slope of the axial load as it relates to CMOD, yielding the peak load that indicates the commencement of crack formation from the preexisting crack tip, illustrated as instant "b" in Figure 4.During the stable crack propagation stage, the load-CMOD curve exhibits a unilateral convex fall, with the rate of the axial load reduction gradually decreasing with the crack propagation, as depicted from instants "c" to "e" in Figure 4.This trend was consistent across samples prepared from various granular rock types, as demonstrated in Figure 5. Table 1 presents the peak load values corresponding to CMOD for each type of sample.Notably, the deformation observed in the granite sample M was significantly more pronounced than that in the other materials, with the differences in peak CMOD values among these materials being relatively small.In the Load-CMOD curves, the sample of Granite M manifested distinctly "softer" behavior in comparison to the samples of the other three materials.

Analysis of Static Crack Propagation Evolution in Granular Structured Rocks based on DIC
The crack-propagation evolution process was obtained based on the major strain field.In the SCB test, the crack propagation evolution process for most samples was gradual damage evolution, characterized by continuous forward extension of the localized strain band in the major strain field and a gradual increase in the crack opening width.As illustrated in Figure 6, using sample L-B as a case study, the crack progressively extends towards the loading point post-initiation, with the damage evolution process unfolding as follows: initially, in the first phase of the Load-CMOD curve, no strain localization was observed.Notably, the strain localization bands start to emerge near the tip of the pre-existing crack as the load approaches its peak value, marking the entry into the second stage of the Load-CMOD curve.At the peak load, crack initiation occurs; thereafter, the strain localization band continues to advance, progressively widening the crack.Figure 6(c) depicts a sampling line within the strain localization band, indicating a descending trend in crack opening width from bottom to top.The crack propagation is gradual, yet the orientation of the strain localization band does not weaken from bottom to top, which is potentially influenced by the local distribution of mineral grains.Notably, the strain localization band initiates sharp turns, typically at significant angles, where the strain value increased remarkably.

Patterns of Mechanical Response Influence by Mineral grains
Upon analyzing all eight samples, the mechanical responses of groups A and B were observed to be similar, thereby showcasing comparable Load-CMOD curves and peak loads, as presented in Figure 7. Nonetheless, a notable difference in the peak load was observed among the 0° granite L samples between the two groups, exceeding the average fluctuation range, as indicated in Figure 7.In samples bearing higher loads, large, hard mineral grains were located near the pre-crack tip.Further examination identified a link between the mineral grains and peak load: samples with quartz particles near the precrack tip demonstrated significantly higher peak loads compared to others.

Influence of Mineral grains on Crack Propagation and Evolution
To scrutinize the macroscopic crack propagation path, the major strain field at the loading's conclusion was analyzed.The color range for the major strain field was set between 0 and 0.03, with the localized band extracted through image-processing software, as displayed in Figure 8.This analysis revealed that the macroscopic crack propagation path follows a distinct pattern: (1) The overall path of macroscopic cracks exhibited strong consistency across each sample pair, with variations only in the local distortion.(2) Predominantly, the crack propagation direction aligns toward the loading end.As the pre-crack inclination angle widens, the crack propagation path veers from the vertical towards the loading point.(3) The diffuse localized band possesses a certain breadth that slightly masks the actual minor bending traits of the crack.Nonetheless, the crack extension is not "smooth" but exhibits twists and even notable deviations.(4) Fracture mechanics theory posits that cracks originate from the pre-crack tip, with experimental findings demonstrating that crack initiation typically occurs near the pre-crack tip, as depicted in Figure 9(a).

Conclusions
In this investigation, the Load-CMOD curves for the four types of crystalline rocks under servocontrolled loading showcased a consistent pattern.These Load-CMOD curves obtained across various granular-structured rock materials are categorized into three phases: pre-crack initiation, initial crack initiation, and stable crack propagation.Within the major strain field, the evolution process of crack propagation in the samples represented a continuous damage evolution, with the localized strain band progressively advancing and the crack opening width incrementally enlarging.The mineral grains exert a profound impact on crack propagation within rock materials, with cracks generally following along mineral boundaries, thereby skirting around the mineral grains and inducing localized curvature.This behavior illustrates that mineral grains sway the continuous trajectory of crack propagation, typically avoiding hard minerals such as quartz, and therefore, directing toward "softer" minerals.

Figure 1 .
Figure 1.Four varieties of granite used in this study.

Figure 2 .
Figure 2. Microscopic characteristics of the four experimental materials.

Figure 4 .
Figure 4. Evolution of the major strain field in sample L-B.

Figure 6 .
Figure 6.(a) Major strain evolution process in sample X-A; (b) corresponding instants and Load-CMOD curves; (c) horizontal displacement distribution of sampling lines.

Figure 7 .
Figure 7. Relationship between Load-CMOD curves and mineral particle distribution near the crack tip in granite X, M, S, L.

Figure 8 .
Figure 8. Macroscopic crack propagation paths of various samples.

Figure 9 .
Figure 9. (a) Crack initiation locations in some samples; (b) Crack propagation and local mineral distribution.

Table 1 .
CMOD values at peak load for each sample.