It is of significance to comprehend the effects of rock microstructure on the tensile strength under different loading rates caused by mining disturbance. So, in this paper, three kinds of sandstones drilled from surrounding rocks in Xiao Jihan Coal to simulate the in situ stress state, whose average grain size is 30
In deep mining activities, impact loadings such as blasting and drilling can produce compressive stress wave, which is reflected as tensile wave at a free surface around the openings. The wave leads to the tensile failure of the deep surroundings since it is much weaker in tension than in compression. Therefore tensile failure as a major failure mode of rocks in underground rock engineering projects should be paid attention to as illustrated in Figure
Potential sources of tensile failure around an underground opening [
For years, significant progress has been made in the mechanical behavior of various types of geomaterials under high loading rates [
As we know, the rock microstructure has an obvious effect on the strength and failure model. The effects of presence of bedding or cleavage planes on rock strength were discussed, such as in Yule marble [
Only a limited amount of work has been done on the effect of microstructure properties (e.g., mineral content, grain shape and distribution, grain size, and microcracks distribution) on rocks [
The above researches and analysis can be summarized through the following conclusions: (
In this paper, the experimental rock discs are drilled from the surrounding rocks in the field of Xiao Jihan Coals and processed to Brazilian disc. Furthermore, the grain sizes of sandstones can be determined by the depth of boreholes, which are grouped by three kinds of grain sizes (fine grain, medium grain, and coarse grain). Therefore the grain size as a key factor of microstructure can have mechanical influence and is taken into consideration. Mesostructure parameters analysis of the above samples can be obtained through optical microscopy, SEM, and X-ray diffraction. SHPB experimental system is conducted on three kinds of grain sizes of sandstones under different impact velocities loaded by pendulum hammer with the design of CRISR team in Northeastern University. In summary, the coupled effect of grain size and loading rate on the strength and failure modes of sandstones under dynamic loadings is discussed as follows.
The rock samples are three types of sandstones as illustrated in Figure
Basic parameters of the sandstones with different sizes.
Types of sandstone | Young’s modulus (GPa) | Poisson’s ratio |
|
Compressive strength (MPa) | Tensile strength (MPa) |
|
Density (kg/m3) |
---|---|---|---|---|---|---|---|
Coarse grain | 13.63 | 0.236 | 2501 | 48.6 | 3.99 | 0.52 | 2278 |
Medium grain | 35.8 | 0.261 | 2658 | 62.57 | 5.8 | 0.58 | 2354 |
Fine grain | 53 | 0.285 | 2899 | 123.56 | 12.62 | 0.73 | 2700 |
Three types of sandstones of Brazilian specimen.
Thin sections produced from each type of sandstone are analyzed by a polarized microscope, with determination of the grain size distribution. Figures
Microscopic images of thin sections and corresponding grain size distribution of the three types of sandstones.
Initial grain size distribution of the granular sample.
Mineralogical content is obtained from the studied rocks with an X-ray diffraction test illustrated in Figure
Mineral compositions of the three types of sandstone.
Mineral | Mass percentage | ||
---|---|---|---|
CG | MG | FG | |
kaolinite | 12 | 10 | 8 |
Quartz | 50 | 40 | 55 |
Plagioclase | 20 | 25 | 22 |
K-feldspar | 18 | 25 | 15 |
XRD graphs of sandstones with three kinds of grain sizes.
As shown in Figure
The pendulum hammer-driven SHPB experimental apparatus.
The impact velocities are originated from the different swing angles of pendulum hammer. In this paper, four swing angles of 40°, 50°, 70°, and 90° are set under dynamic experiments corresponding to the four impact velocities of 2.0 m/s, 2.5 m/s, 3.3 m/s, and 4.2 m/s. Moreover, the swing angle of 40° is the critical value to make the Brazilian specimens fail. To be specific, when the impact velocity is lower than 2.0 m/s, the sandstones show a complete status and cannot cause the failure.
International Society for Rock Mechanics issued the suggested methods on dynamic Brazilian test for determining the dynamic tensile strength and fracture toughness of rock materials. The rock specimen is impacted in radial direction and the loading condition is shown in Figure
Wave propagation between bar and specimen interfaces.
There are two fundamental assumptions on the conventional SHPB experimental technique. One is dynamic stress equilibrium. The stress at the contact area between rock disc and incident and transmission bars becomes equalized, after the stress wave propagates and is reflected several times, if the length of rock specimen is much less than wave length of the incident stress wave. The second is the one-dimensional elastic stress wave theory is valid when the stress wave propagates in both the incident and transmission bars without dispersion. During the SHPB experiment, the contact forces between rock specimen and incident and transmission bar (interfaces I–I and interfaces II–II) are denoted with
The stress field reflects back and forth increasing in magnitude, and the specimen remains in equilibrium until the time of failure, once the specimen is in equilibrium. The Brazilian static stress relationship is also applied to calculate the dynamic tensile strength of a specimen loaded in the SHPB test. This principle is also applicable for the pendulum hammer-driven SHPB test as proposed in this study. Consequently, the tensile stress at the center of the Brazilian disc specimen can be calculated as
Dynamic Brazilian tests are carried out by means of the pendulum hammer-driven SHPB apparatus. The sandstone specimens (three kinds of grain sizes) are 50 in diameter and 25 mm in thickness. The cylindrical surfaces have no signs of obvious tool marks. End faces flat to 0.25 mm are parallel to within 0.25°. The incident bar with pendulum hammer is impacted under different velocities, which generates the incident waves presented in Figure
(a) Measured incident stress waves under different impact loadings and (b) complete strain-rate curve under certain velocities (
It can be seen from Figure
Figure
Original signals in a typical dynamic Brazilian test.
Earlier researches on static and dynamic BD tests have all proven that the BD test can obtain accurate strength results once the stress force equilibrium should be satisfied before the specimen fails. Figure
Dynamic force balance of Brazilian samples (
Three kinds of grain sizes were grouped and tested by different impact velocities of
Summary of dynamic tensile test results with different grain sizes.
Types of sandstone | Impact velocity (m/s) | Specimen number | Diameter (mm) | Thickness (mm) | Stress rate (GPa/s) | Dynamic tensile strength (MPa) |
---|---|---|---|---|---|---|
Coarse grain | 2.0 | C-1 | 49.98 | 24.97 | 25.7 | 5.34 |
2.5 | C-2 | 49.88 | 24.99 | 65.5 | 7.57 | |
3.3 | C-3 | 50.12 | 25.03 | 125.4 | 10.23 | |
4.2 | C-4 | 50.23 | 25.12 | 180.7 | 13.75 | |
|
||||||
Medium grain | 2.0 | M-1 | 48.73 | 24.87 | 62.5 | 10.4 |
2.5 | M-2 | 49.23 | 25.23 | 88.2 | 13.6 | |
3.3 | M-3 | 49.87 | 24.96 | 126.5 | 17.8 | |
4.2 | M-4 | 50.24 | 24.98 | 176.7 | 22.5 | |
|
||||||
Fine grain | 2.0 | F-1 | 49.99 | 25.01 | 86.8 | 14.3 |
2.5 | F-2 | 48.94 | 25.14 | 115.7 | 19.5 | |
3.3 | F-3 | 51.22 | 24.99 | 227.5 | 29.8 | |
4.2 | F-4 | 49.87 | 24.98 | 328.6 | 36.5 |
The time history of tensile stress at the center of Brazilian disc sample of three kinds of sandstones.
In this study, the major factors affecting the strength of the sandstones are considered in this paper, which are loading rates and grain sizes. According to (
The stress rate can be calculated by (
Dynamic Brazilian results obtained in this paper and their comparison to the existing results.
It is found that the dynamic tensile strength is larger than the static tensile strength of 3.99, 5.8, and 12.62 MPa (representing CG, MG, and FG). In particular, the dynamic tensile strength increases with the rising impact velocity of the pendulum hammer, thus confirming the loading rate dependency of tensile strength of the samples. Figure
The relationship of loading rate dependence and dynamic tensile strength increase index of three kinds of grain sizes.
FG sandstone is the most responsive to loading rates compared to MG and CG sandstones, which shows a steeper increase of peak strength under different impact velocities. This phenomenon is perhaps mainly resulting from FG sandstone with the relatively smaller grain size, whose microcracks, developing during dynamic loadings, are much smaller and more scattered, as the grains are finer. Thus, the applied stress is inclined to disperse within the specimen. This applied stress in greater diffusion causes that the rock specimen at higher loading rates can stiffen much further and bring about greater strength increase compared with medium and coarser grain sandstones.
Figure
The dynamic strength versus stress rates for sandstones with different grain sizes.
It is interesting that the results show the rate-sensitivity of fine grain can be higher than that of coarse grain sample. At mesoscale, rock specimen is considered as a heterogeneous and composite material consisting of different grain sizes and cement. Many earlier researches have been made to demonstrate that increase of the rock heterogeneity contributes to an increase in the strain-rate dependency [
According to the crack growth criterion, cracks would undergo growth when
According to the general principle of Brazilian test, the cracks initiate at the center of the Brazilian disc specimen caused by tensile stress and growth to the two sides of specimen, thus dividing the specimen into two halves. Figure
Failure modes of sandstone samples during dynamic Brazilian tests under different loading rates.
This paper picks sandstones from Xiao Jihan Coal processed to Brazilian disc and uses the pendulum hammer-driven SHPB system to study the effect of grain size on the mechanical behaviors under different impact velocities.
The result reveals that three kinds of Brazilian disc are enhanced in tensile strength with the increase of the loading rates, which show the rate dependency for many rock materials. To be specific, FG sandstone is most sensitive to loading rates, which has a maximum value of dynamic increase factor, while MG and CG samples show a relatively lower value and dynamic tensile strength. Moreover, a model is introduced to explain the rate dependence of Brazilian disc with different grain sizes. Another important finding is samples with different grain sizes that represented different failure modes. With the rising impact velocities, each sample shows an increasing failure zone caused by tensile and shear stress, while the fine-grained samples represent a more obvious coupled failure model compared to medium and coarse grained samples.
The damage and failure of surrounding rock are closely related to the rock microstructure and stress wave induced by the drilling and blasting in mining. Therefore, the coupled effect of loading rates and grain size on dynamic tensile strength of sandstones is discussed in this paper. Although it is mainly mechanism study, the results can also be used to provide a theoretical foundation for optimizing the parameters of the explosive during blasting process in different mining zones [
The authors declare that they have no conflicts of interest.
This work was funded by the National Science Foundation of China (Grant nos. 51525402 and 51304037) and the Fundamental Research Funds for the Central Universities (Grant nos. N160104008 and N160103005).