In order to identify the microstructure inhomogeneity influence on rock mechanical property, SEM scanning test and fractal dimension estimation were adopted. The investigations showed that the self-similarity of rock microstructure markedly changes with the scanned microscale. Different rocks behave in different fractal dimension variation patterns with the scanned magnification, so it is conditional to adopt fractal dimension to describe rock material. Grey diabase and black diabase have high suitability; red sandstone has low suitability. The suitability of fractal-dimension-describing method for rocks depends on both investigating scale and rock type. The homogeneities of grey diabase, black diabase, grey sandstone, and red sandstone are 7.8, 5.7, 4.4, and 3.4, separately; their average fractal dimensions of microstructure are 2.06, 2.03, 1.72, and 1.40 correspondingly, so the homogeneity is well consistent with fractal dimension. For rock material, the stronger brittleness is, the less profile fractal dimension is. In a sense, brittleness is an image of rock inhomogeneity in macroscale, while profile fractal dimension is an image of rock inhomogeneity in microscale. To combine the test of brittleness with the estimation of fractal dimension with condition will be an effective approach for understanding rock failure mechanism, patterns, and behaviours.

Many investigations showed that rock failure patterns are related the inhomogeneity of rock microstructure [

Bearing this in mind, we firstly used the high-low vacuum scanning electron microscope named after JSM-6510LV which was manufactured by the JEOL, to learn the microstructure of four type rocks: grey diabase, black diabase, grey sand stone, and red sandstone. We then analysed the relations between inhomogeneity of these rocks and the profile fractal dimensions and further investigated the relation between brittleness and rock profile fractal dimension [

The scanning device is a new type of SEM called JSM-6510LV, which was manufactured by the JEOL. It consists of the following basic components: electron optics system, scanning system, signal detection amplification system, image display and record system, battery, and vacuum.

The experimental procedure was as follows: first, a 50.0 mm diameter borehole was drilled, and the boring sample was taken from the hole. Second, some standard specimens with 100 mm high and 50 mm wide were cut processed. Third, compressive test was carried out in RLJW-2000 servo compression test machine. Fourth, the rock fragments were filled with nitrogen gas, with a pressure of 2 bars, blew axially from the nozzle to protect the focusing lens and to assist the scanning process. Finally, the scanning work was carried out using a continuous wave and multimode CO_{2} laser with a maximum output power of 2 kW. Laser parameters used in the experiment were as follows: laser power 1000 W, beam size in diameter 4.0 mm, and scanning velocity 8 mm/s. The focusing lens was protected by a coaxially flowing gas N_{2}. The cross-sections or surfaces were characterized by SEM incorporating energy dispersive X-ray analysis (EDX) using a JSM-6510LV scanning electron microscope.

Fractal geometry popularized by Mandelbrot [

In this paper, the box counting approach suggested by Sarkar and Chaudhuri [

By changing the scale

Flow chart for calculating fractal dimension.

In order to estimate the different rock profile fractal dimension, we firstly obtained the images of four type rocks: black diabase, grey diabase, grey sandstone, and red sandstone; by using JSM-6510LV scanning electron microscope, the scanning amplification factor was 1000. The microstructures of above four type rocks were obtained by SEM, as shown in Figure

SEM images of grey diabase with different magnifications.

Magnification 500

Magnification 1000

Magnification 2500

Magnification 5000

We firstly obtained the SEM scanned images of above four kind stones with magnification 500. We then easily used DIP method and formula (

In order to investigate the self-similarity of rock microstructure in different microscales, we obtained the SEM scanned images with four magnifications: 500, 1000, 2500, and 5000 in centre region of a sample, as shown in Figures

Fitting results of fractal dimension for different magnification.

Rock type | Magnification 500 | Magnification 1000 | Magnification 2500 | Magnification 2500 | Average | |||||
---|---|---|---|---|---|---|---|---|---|---|

RC | RC | RC | RC | |||||||

Grey diabase | 1.92 | 0.87 | 1.87 | 0.82 | 2.17 | 0.91 | 2.28 | 0.95 | 2.06 | 0.89 |

Black diabase | 1.95 | 0.89 | 1.85 | 0.80 | 2.20 | 0.90 | 2.12 | 0.93 | 2.03 | 0.88 |

Grey sandstone | 1.77 | 0.75 | 1.72 | 0.72 | 1.70 | 0.65 | 1.68 | 0.61 | 1.72 | 0.68 |

Red sandstone | 1.35 | 0.62 | 1.59 | 0.74 | 1.38 | 0.61 | 1.29 | 0.59 | 1.40 | 0.64 |

SEM images of black diabase with different magnifications.

Magnification 500

Magnification 1000

Magnification 2500

Magnification 5000

SEM images of grey sandstone with different magnification.

Magnification 500

Magnification 1000

Magnification 2500

Magnification 5000

SEM images of red sandstone with different magnification.

Magnification 500

Magnification 1000

Magnification 2500

Magnification 5000

Fitted

Magnification 500

Magnification 1000

Magnification 2500

Magnification 5000

We found that diabase and black diabase have the same fluctuation pattern of “high-low-high” (Figure

RC variation with magnification.

As we know, rock is a typical inhomogeneous material. In order to investigate the macromechanical property of rock influenced by inhomogeneity, a concept named after brittleness [

The brittleness,

Typical rock brittleness obtained by experiment.

Order | Rock type | |||
---|---|---|---|---|

a | Grey diabase | 127.9 | 53.3 | 2.40 |

b | Black diabase | 102.7 | 33.7 | 3.05 |

c | Grey sandstone | 75.4 | 20.8 | 3.63 |

d | Red sandstone | 68.8 | 17.3 | 3.96 |

Through uniaxial compression tests, we found the four kinds of stone behaved different failure patterns (Figure

Rock failure patterns under uniaxial compression.

Grey diabase

Black diabase

Grey sandstone

Red sandstone

Comparing estimated fractal dimension with brittleness of above four kind rocks, we found that the less the rock brittleness is, the larger the rock profile fractal dimension is, as shown in Figure

Corresponding relationship between fractal dimension and brittleness of rocks.

The aim of the laboratory SEM scanning tests and fractal dimension estimation was to identify the influence of microstructure inhomogeneity on rock mechanical property. By comparing with the past investigation, this research contains at least three original aspects.

The SEM tests on microstructure inhomogeneity and fractal dimension estimation of four type rocks were performed.

The differences of self-similarity of microstructures for different rocks were investigated primarily.

The relation between rock profile fractal dimension and rock brittleness influenced by different inhomogeneities was obtained.

The investigations showed the following.

The self-similarity of rock microstructure markedly changes with the scanned microscale. Different rocks behave different fractal dimension variation patterns with the change of magnification. So it is conditional to adopt fractal dimension to describe rock material. It is suitable for some rocks, but it is not suitable for some other rocks. For instance, grey diabase and black diabase have high suitability, and red sandstone has low suitability. The suitability of fractal dimension describing method for rocks depends on both investigating scale and rock type.

The homogeneities of grey diabase, black diabase, grey sandstone, and red sandstone are 7.8, 5.7, 4.4, and 3.4, separately; their average fractal dimensions of microstructure are 2.06, 2.03, 1.72, and 1.40, correspondingly, so the homogeneity is well consistent with fractal dimension.

The brittleness of black diabase, grey diabase, grey sandstone, and red sandstone are 2.40, 3.05, 3.63, and 3.96, separately. For rock material, the stronger brittleness is, the less profile fractal dimension is. In a sense, brittleness is an image of rock inhomogeneity in macro-scale, while profile fractal dimension is an image of rock inhomogeneity in microscale.

To combine the test of brittleness with the estimation of fractal dimension with condition will be an effective approach for understanding rock failure mechanism, patterns, and behaviours.

This work was supported in part by the National Basic Research Program of China (973 Program) Grant No. 2010CB226805, China Natural Science Fund (no. 51074099, no. 51004068), and SDUST Research Fund (no. 2010KYTD105).