To investigate the fracture characterizations of rocks under high strain rate tensile failure, a series of dynamic Brazilian tests was conducted using Split Hopkinson pressure bar (SHPB), and a high-speed digital camera at a frame rate of 50,000 frames per second (FPS) with a resolution of 272
Fully understanding the dynamic rock mechanics is of great importance in dealing with a wide range of civil engineering applications, e.g., earthquakes, mining, subway tunnel excavation, blasting events, and protective construction project [
Moreover, it has been generally recognized that rock and rock-like materials are much weaker in tension than compression. Therefore, accurate determination of dynamic response and fracture properties of rocks under high strain rate tensile failure is important. In general, dynamic tension testing methods are being continuously improved from the original quasistatic ones to precisely determine the dynamic tensile strength which can be approximately classified into two categories: direct tensile and indirect tensile testing methods [
More specifically, the primary testing methods to determine the dynamic tensile strength of rock are basically extended from corresponding quasistatic ones and mainly include BD or FBD method, bending [
Since dynamic fracture of rock material is a very complex behavior, some traditional contact measurement approaches like resistance strain gauges cannot provide enough information to reveal the dynamic fracture process of rock. Therefore, many noncontact and optical measurement techniques have been adopted and developed as a promising way in the experiment to record the fracture process and further reveal the fracture process and failure mechanisms of rock materials [
Nevertheless, with regard to the crack evolution characteristics and failure process, the investigation is more challenging than that of stress-strain on the rock specimen in SHPB experiments since there are no effective characteristic parameters that can quantitatively describe crack propagation. To the best of our knowledge, research studies into the relationship between crack propagation and mechanical properties are relatively few. Therefore, we proposed a data processing method based on Ratsnake graphic annotation software [
The dynamic Brazilian tensile test is conducted using the SHPB system at China University of Mining and Technology Beijing (CUMTB), and the schematic and physical map of the experimental setup are shown in Figures
Schematic map of the SHPB experimental system.
Physical map of the SHPB experimental system.
The SHPB system mainly consists of power system, bars, strain wave collector, and high frame rate camera. In order to satisfy the one-dimensional stress wave propagation wave, the length of the bars should be 30 times of the bar diameter [
To visualize the fracture process and further reveal fracture mechanism, FASTCAM SA5 (16G) camera was employed to capture the fractured images of rock, which adopts the CMOS sensor with a 20
The rock samples utilized in the experiment are manufactured by sandstone selected from a quarry in the Fangshan area of Beijing, China. According to the ISRM suggestion for BD specimens preparation, the rock specimens were cut from the same rock block without obvious bedding and manufactured to a cylinder with a dimension of 50 mm in diameter and 25 mm in length. Moreover, two ends of the rock specimen were finely ground to be flat within an accuracy of
SHPB is an ideal apparatus for testing the dynamic response of materials, and its principle is based on the one-dimensional (1D) stress wave propagation. To accurately calculate the dynamic properties of rock material under SHPB loading, the following three assumptions also require to be satisfied [
Also, the dynamic forces on the incident and transmitted ends,
Figure
An overview of the proposed approach for the investigation of dynamic fracture process of rock materials under SHPB impact loading. (a) an input video of rock fracture process; (b) an algorithm for multicracks extraction; (c) crack extraction results for a fracture process video; (d) dynamic strain-stress response of rock specimens; (e) the formula of Pearson’s correlation coefficient; (f) matrix of crack evolution features; (g) matrix of dynamic mechanical properties; (h) a correlation matrix heat-map of relationship between crack evolution features and dynamic mechanical properties.
As illustrated in Figure
An illustration of the correlation matrix heat-map with loading condition, crack propagation process, and dynamic mechanical properties.
Given paired data
In the correlation matrix heat-map, larger positive values were represented by dark red colors denoting a strong positive correlation between two variables while larger negative values were represented by dark blue colors which indicate a strong negative correlation between two variables.
Over the past few decades, there have been some investigations for crack propagation velocities of rock materials under dynamic loading which provide a promising way to explore the fracture mechanisms of rock materials [
In this study, the crack propagation velocity
An illustration of crack propagation velocity computation using crack length.
An illustration of crack propagation velocity computation using crack area.
To visualize the relationship between these two crack velocity variables, Figure
Relationship between
Since cracks on rock surface are an important index to measure the state of rock material and fractals exhibit the ability for measuring the complex topological pattern, many significant endeavors have been made to investigate the fractality of cracks to the mechanics of fracture [
In mathematics, a fractal dimension is used to evaluate the fractal patterns by quantifying their complexity as a ratio of the change in detail to the change in scale [
Therefore, the box-counting dimension
Figure
An illustration of different box scales to fully cover cracks.
(a) Number of covered boxes versus box size; (b) fractal characteristics of crack for rock material under different velocities.
In general, the higher fractal dimension indicates a more curved and intricate crack propagation path. Therefore, according to the above method, the fractal dimension of cracks in each frame of the rock fracture process has been increasing. Figure
Figure
Relationship between
In addition to adopting the crack area
An illustration of crack morphological features. (a), (c), and (e) are original images represent crack initiation, propagation, and coalescence, respectively; (b), (d), and (f) are extracted cracks from corresponded images.
As shown in Figure
(a) Relationship between
It has been generally recognized that, for a valid and typical dynamic Brazilian test, crack should be first appeared along the impact direction somewhere near the center of the specimen and then propagates bilaterally to the loading ends. According to the row and column index of the crack center, Figure
Crack distribution for rocks under different impact velocities.
Figure
Incident, reflected, and transmitted signals of rocks under different impact velocities.
It has been generally recognized that the fracture of rock under loading rates is the process of accumulation and dissipation of energy [
Assuming that all the energy loss at the specimen and bar interfaces can be negligible, the energy absorbed by the rock specimen
Figure
Relationship between
Moreover, substantial efforts have been devoted to performing quantitative measurements on fracture surface, and it has been well recognized that surface roughness in rock-like materials exhibits self-similarity properties at least over a given range of length scales. In other words, the fracture surface topography of rock-like materials reveals inherent details associated with energy dissipation mechanisms that govern the fracturing process. Therefore, the relationship between fractal dimension and absorbed energy was first calculated, and the result is shown in Figure
(a) Relationship between
On the other hand, Figure
According to the incident
Figure
Curves of strain parameters with crack propagation velocity
Curves of strain parameters with crack propagation velocity
In this study, the Brazil test of rock specimens was performed under different impact velocities using the SHPB system to explore fracture characterizations of rocks under dynamic loads. Based on image processing technique, crack propagation process was quantitatively described from three perspectives: the crack propagation velocity, crack fractal characteristic, and crack morphological features. According to the recorded strain wave signals, the dynamic mechanical properties of rocks were also calculated, and the relationship between impact velocity and crack propagation process was explored and analyzed. The main conclusions are listed as follows: Crack propagation velocities The proposed two crack features, The energy absorbed by the rocks increases with the increase of impact velocity The mean strain rate and max strain both decrease with increase of crack propagation velocity, which shows that there is a certain relationship between the crack propagation process and dynamic mechanical properties of rocks under dynamic loading
In the future work, we will conduct the static tensile tests using the BD specimen on the same rock material and compare the static and dynamic results in terms of mechanical properties and crack propagation process.
Mean strain rate (
Max stress (MPa)
Max strain (
Cross-sectional area of the bar (
Crack length (mm)
Crack quantification area (pixels)
Cross-sectional area of the specimen (
Crack feature descriptor—anisometry
Longitudinal stress wave speed of the bar (m/s)
Crack feature descriptor—compactness
Fractal dimension
Young’s modulus of the bar (GPa)
Length of rock specimen (mm)
Dynamic forces on incident and transmitted ends (N)
Pearson’s correlation coefficient
Crack propagation velocity (m/s)
Impact velocity (m/s)
Fractal dimension velocity (
Crack propagation velocity (pixels/s)
Anisometry velocity (anis/frame)
Compactness velocity (comp/frame)
Absorbed energy (J).
The data utilized in this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This research was financially supported by the National Natural Science Foundation of China (nos. 51274206 and 51404277). This support is greatly acknowledged and appreciated.