The work presented in this paper was conducted to quantify the relationship between the pore characteristics and mechanical properties of white sandstone. The study include tests carried out under the coupling effects of chemical corrosion, temperature, nuclear magnetic resonance, and mechanical tests. Computer fractal theory was employed to describe and quantify the characteristics of the growth of pores in white sandstone under the same coupling effect. A custom developed program code, in the MATLAB software platform, was used for calculating the growths of the pores in white sandstone when subjected to coupling effects. The correlation between the computer fractal dimension of the growth of the pores in rock and characteristics of mechanical damage was accordingly analyzed. The results showed that when the temperature was set at a level lower than 100°C, it caused damage to the rock and strength reduction, primarily due to the rates of chemical reactions, the generation, and evolution of pores in the rock mass under the coupling effects of chemical corrosion and temperature. Overall, it was observed that the higher the value of the computer fractal dimension, the higher the growth of the pores, and the lower the uniaxial compressive strength of the white sandstone.
New pores usually appear in the rock mass due partly to chemical corrosion. As the corrosion further intensifies, additional pores will develop and grow, along with the previous pores inside the rock. Damage also concurrently occurs in the inside of the rock under the influence of temperature. The coupling effect of these two factors will further accelerate the deterioration of rock. Therefore, determining the growth status of the pore structures inside the rock and analyzing the relationship between the characteristics of the pore structure and the macro-mechanical properties of the rock in such conditions are of great significance as it sheds light on the mechanism of rock damage.
Fractal, a term derived from the Latin word
Many researchers have devoted time to study the mechanical properties of rocks under the effects of a single environmental factor or the combined effects of multiple environmental factors, through the application of computer fractal theory in rock mechanics. Li et al. studied the damage characteristics of sandstone pore structure under freezing and thawing effects and associated the rock NMR results with mechanical failure characteristics [
However, the damage analysis in most of the above studies was based on the macro-mechanical parameters. The rock damage and degradation mechanism under the influence of a single environmental factor or multiple environmental factors were proposed based on conjecture, from the perspective of macroscopic appearance. In essence, this subjective deduction cannot fully nor accurately reflect the real damage of a rock from a mesoscopic perspective. Although some researchers have taken a lead in successfully using methods, such as nuclear magnetic resonance technology and computer fractal theory, to analyze the changing behavior of rock pore structure, under the influence of a single or the combined influence of multiple environmental factors. Besides, many researchers have also managed to successfully correlate the macro-mechanical parameters. However, the inaccurate processing of the pore image along with the existence of defects in the programming of computer fractal dimensions, often led to a certain deviation in the analysis results. Furthermore, there are relatively few studies on the mechanical properties of white sandstone under the coupling effects of chemical corrosion and temperature. Thus, the connection between the macroscopic mechanical properties of white sandstone and mesoscopic damage should be investigated along with the corresponding quantitative analysis.
Based on existing studies, white sandstone samples were first soaked in acidic, neutral, and alkaline solutions at different temperatures. The treated white sandstone samples were then subjected to nuclear magnetic resonance and uniaxial compression tests. The macroscopic mechanical property and mesoscopic damage of the white sandstone samples were then analyzed. Lastly, the fractal characteristics of the sandstone pore development were analyzed after the introduction of value filtering and edge processing to the programming of the computer fractal dimension. In this paper, the computer fractal dimension of pore evolution in the rock was successfully correlated to the macroscopic mechanical behavior. A quantitative analysis was also carried out to shed light on the mechanism of rock damage under the coupling effects of chemical corrosion and temperature.
The rock samples were sourced from Zigong in Sichuan Province, China. The rock was characterized with good macroscopic homogeneousness. Thereafter, the rock was then fabricated into a standard rock sample with dimensions of 50 mm × 100 mm through cutting, coring, and sanding. This standard rock sample did not contain any obvious visual defects such as cracks or joints. The smoothness of its two ends was lower than 0.05 mm. Besides, the deviation of the angle between the two ends and the plane vertical axis was lower than 0.25°. XRD analysis (presented in
The steps of the test were as follows: The rock samples were placed in an RPH-80, constant temperature and humidity chamber, and dried at a constant temperature of 25°C for 96 h. About 20 L H2SO4 solution with a concentration of 0.1 mol/L and 20 L NaOH solution with the same concentration of 0.1 mol/L were prepared. Distilled water (20 L) was set as the control of the neutral pH environment. The white sandstone samples were soaked in the as-prepared H2SO4 solution, NaOH solution, and distilled water, respectively. The solutions and distilled water with samples in them were then placed in the RPH-80 constant temperature and humidity chamber. The temperature inside the chamber was adjusted to 0, 25, 50, 75, and 100°C by adjusting the heating rate to different levels. The samples will react with the chemicals during the soaking process, thus resulting in the shifting of the pH value of the solutions. Therefore, the pH value of the solutions should be monitored on daily basis during the soaking process. Besides, the pH value of the solutions should be adjusted to the original value by adding acidic or alkaline solutions into the original solutions. When the pH value of the 100°C H2SO4 solution no longer varied, the white sandstone samples were retrieved from the chemical solutions at different temperatures.
After the soaking treatment of the rock samples in the chemical solutions at different temperatures, the white sandstone samples were subjected to nuclear magnetic porosity test. This was done using a MesoMR23060HI magnetic resonance imaging analyzer. The samples were then subjected to a uniaxial compression test (with a monotonic loading rate of 50 N/S under the stress control mode) using a TAW-200 electronic multifunctional material mechanics testing machine. Lastly, the computer fractal dimension of the pores in the white sandstone, under the coupling effects, was obtained from computations using custom developed codes in the MATLAB software platform. The degree of pore development was analyzed and quantified using the fractal characteristics of the sandstone.
Rock sample # | Soaking solution | pH value | Temperature °C | Uniaxial compressive strength |
---|---|---|---|---|
A0 | H2SO4 | 1 | 0 | 27.5 |
A25 | H2SO4 | 1 | 25 | 25.5 |
A50 | H2SO4 | 1 | 50 | 25.0 |
A75 | H2SO4 | 1 | 75 | 23.0 |
A100 | H2SO4 | 1 | 100 | 12.8 |
B0 | Distilled water | 7 | 0 | 32.5 |
B25 | Distilled water | 7 | 25 | 31.6 |
B50 | Distilled water | 7 | 50 | 30.2 |
B75 | Distilled water | 7 | 75 | 29.4 |
B100 | Distilled water | 7 | 100 | 27.1 |
C0 | NaOH | 13 | 0 | 27.0 |
C25 | NaOH | 13 | 25 | 25.2 |
C50 | NaOH | 13 | 50 | 25.0 |
C75 | NaOH | 13 | 75 | 22.5 |
C100 | NaOH | 13 | 100 | 15.7 |
It can be seen from
The reason is that when the temperature is lower than 100°C, the damage to the rock caused by temperature is negligible. At these temperature conditions, the rock damage and degradation is mostly due to the chemical (acid or alkali) environment, thus resulting in the decline in its uniaxial compressive strength. Higher temperature causes damage to the rock, thus reducing its strength mainly by affecting the rate of the chemical reactions.
Two-dimensional nuclear magnetic resonance images that represent the position of the central cross-section of each rock sample are presented in
It can be seen from
The reason is that in an acidic or alkaline environment, minerals such as kaolin in the rock sample undergo chemical reactions with H2SO4 or NaOH to form water-soluble substances. Furthermore, an increase in temperature promotes the chemical reaction rate, resulting in the occurrence of new pores or an increase in the size of initial pores. In a neutral environment, minerals in the rock sample hardly dissolve in water or react with water.
Various geometric properties of the rock, such as pore distribution, crack distribution, crack density, fracture toughness, etc., all exhibit fractal characteristics. Without doubt, fractal theory has become an indispensible bridge between macroscope and microscope. The coupling effects of chemical corrosion and temperature results in the appearance of new pores in the rock mass. These pores inherently affect and to some extent govern the mechanical properties of the rock. Therefore, fractal theory can be used to describe the characteristics of the pore distribution, thus quantitatively illustrating the relationship between pores and mechanical properties of the rock.
The NMR images of the rock obtained via MRI technology veritably reflect the characteristics of the pore growth. It raises the possibility for the calculation of the pore fractal dimension. In this paper, the box dimension was used to mathermatically characterize the fractal characteristics of the pores in the rock under the coupling effects of chemical corrosion and temperature. The computational characterization is based on
where
According to the MRI images in the center area of each rock sample presented in
During program execution and running the MATLAB code, the data was subjected to median filtering after image binarization to improve accuracy and precision of the pore image. During computer fractal dimension programming, the edges were first marked out in the grayscale image. The computer fractal dimension of the area within this boundary area was calculated. The interference outside of the pore graphics was ruled out to ensure a more accurate and precise calculation of the computer fractal dimensions. The computer fractal dimension of a Sierpinski triangle is 1.58. The box dimension calculated in this study was 1.58210, indicating that computational results with very high precision can be obtained with custom developd program codes. This ultimately improves the accuracy of the calculation results of the computer fractal dimension analysis.
Each MRI image was subjected to the measurement of computer fractal dimension of the pores in the rock. The computer fractal dimension of each sample was thereafter calculated and the results are listed in
Rock sample# | Soaking solution | pH value | Uniaxial compressive strength |
Fractal dimension, D | Correlation coefficient |
---|---|---|---|---|---|
A0 | H2SO4 | 1 | 26.8 | 1.53503 | 0.9807 |
A25 | H2SO4 | 1 | 25.1 | 1.53558 | 0.9798 |
A50 | H2SO4 | 1 | 24.9 | 1.53550 | 0.9798 |
A75 | H2SO4 | 1 | 23.0 | 1.53760 | 0.9809 |
A100 | H2SO4 | 1 | 12.8 | 1.53797 | 0.9807 |
B0 | Distilled water | 7 | 32.5 | 1.53060 | 0.9801 |
B25 | Distilled water | 7 | 31.6 | 1.53071 | 0.9801 |
B50 | Distilled water | 7 | 30.2 | 1.53157 | 0.9803 |
B75 | Distilled water | 7 | 29.4 | 1.53156 | 0.9816 |
B100 | Distilled water | 7 | 27.1 | 1.53191 | 0.9809 |
C0 | NaOH | 13 | 27.2 | 1.53091 | 0.9811 |
C25 | NaOH | 13 | 25.2 | 1.53280 | 0.9798 |
C50 | NaOH | 13 | 25.0 | 1.53503 | 0.9807 |
C75 | NaOH | 13 | 22.5 | 1.53519 | 0.9908 |
C100 | NaOH | 13 | 15.7 | 1.53550 | 0.9798 |
It can be seen from
It can be seen from
The computer fractal dimension (D) of the pores in the white sandstone under acidic and alkaline conditions exhibits an overall increasing trend with an increase in the temperature. Under neutral conditions, the computer fractal dimension (D) of the pores remains unchanged with an increase in the temperature. Overall, the above results suggest that as the number of pores in the white sandstone increases with an increase in temperature under acidic and alkaline conditions, the pore sizes become larger and the pore distribution becomes more uneven as well. Under neutral conditions, whilst the number of pores exhibited an increasing trend with increasing temperature, the pore distribution remained unchanged.
The probable reason is that the white sandstone underwent corrosion in acidic or alkaline environments. As a result, new pores appeared and the initial pores became larger. Besides, the high temperature accelerated the rate of chemical reactions. However, in the neutral environment (pH = 7), the white sandstone remains unchanged even with an increase in temperature.
In response to the coupling effects of chemical corrosion and temperature, it can generally be observed from
When the temperature was lower than 100°C, the damage to the rock caused by temperature was negligibly small. However, the damage under different chemicals (namely acidic and alkaline) environments resulted in a decline of the uniaxial compressive strength. Whilst the results indicated that that temperature could potentially cause rock damage, the decay in strength was predominantly driven by the rate of the chemical reactions.
The computer fractal dimension of the pores in the white sandstone under acidic and alkaline neutral conditions was larger than that under neutral conditions. In general, the computer fractal dimension (D) of the pores in the white sandstone exhibited an overall increasing trend with an increase in the temperature. With increasing temperature, the pore size increased with pore distribution becoming more uneven under both acidic and alkaline conditions. In the neutral environment (pH = 7), the computer fractal dimension (D) of the pores in the white sandstone increased in size, but the distribution remained unchanged.
The development of pores in the white sandstone exhibited good correlation with the strength decay due to the coupling effect of chemical corrosion and temperature variations. That is the larger the value of the computer fractal dimension, the more is the growth in the pores, and the smaller the uniaxial compressive strength of the white sandstone.