Traditional rock fragmentation analysis
Rock blasting fragmentation pertains to the geometric dimensions of rock fragments resulting from blasting technology, typically quantified by the maximum span between the opposite ends of the fragmented rock. When the dimensions of the blasting block conform to the specifications for the intake size of the shovel transport equipment container or initial crushing machinery, it is deemed as qualified block size. Conversely, when the block size surpasses the qualified dimensions, it is collectively termed as a large block, alternatively known as an unqualified rock block size. The percentage of unqualified rock blocks in the overall quantity of blasted rock constitutes the large block yield rate. This serves as a crucial blasting quality metric in production and forms the fundamental basis for further refining blasting parameters. The classification of a large block here is a relative indicator, primarily contingent upon the mining and transportation equipment in use.
Typically, the degree distribution of blasting blocks is determined through manual screening with sieves with varying aperture sizes. The calculation formula of block size is as follows:
The proportion of block size that did not pass the size X mm sieve:
$${{\text{t}}_1}=\frac{{{P_1}}}{P} \times 100$$
The proportion of block size that did not pass the Y-mm sieve:
$${{\text{t}}_2}=\frac{{{P_2}}}{P} \times 100$$
Correction coefficient for rock block size error:
$$K=\frac{{P – ({P_1}+{P_2}+…)}}{{({P_1}+{P_2}+…)}}$$
According to the correction coefficient K, the corrected weight is:
$$P_{1}^{\prime }={P_1} \cdot (1 \pm K)$$
$$P_{2}^{\prime }={P_2} \cdot (1 \pm K)$$
$$P_{{\text{n}}}^{\prime }={P_n} \cdot (1 \pm K)$$
In the formula, P – total weight of blasted rock, kg;
P1, P2… – weight of rocks that have not passed various sizes and specifications of sieves, kg;
P1 ‘, P2’ Pn ‘- P1, P2… Pn corrected weight, kg.
On this basis, the percentage of rocks of various sizes in the total weight can be calculated, reflecting the Degree distribution of rock blocks.
Intelligent identification program for blasting fragmentation
The main program for intelligent identification of blasting fragmentation is as follows:
Firstly, develop a computer algorithm and program for blasting block size AI recognition. After extensive training through deep learning, the calculation model can meet the requirements of accurately identifying key parameters such as rock block boundaries, maximum length, perimeter, and area.
Then, after the rock is blasted, a self-made frame scale is placed on the blasting pile, and photography methods are used to collect photos of the blasting pile after the rock is blasted.
Finally, import the blasting pile photos into an AI computer program, export the identified blasting block size parameters in the form of images, tables, etc., to guide the analysis of blasting block size composition.
Intelligent identification and analysis of blasting fragmentation
The side length of the square benchmark shown in the photos of blasting block sizes collected at the mine site measures 1 m. The block recognition effect map was acquired through the application of the blasting block AI image analysis method, as depicted in Figs. 6 and 7.
Fragmentation identification effect.
Block volume and perimeter.
As evidenced in Figs. 6 and 7, it can be seen that the image analysis of blasting block size can achieve good recognition results. Quantitative evaluation reveals that the maximum blasting block volume is 0.598 m2, corresponding to a maximum circumference of 3.371 m, and an equivalent circular diameter (De) of 87.27 cm. Among these blocks, a total of 26 have a volume of exceeding 0.1 m3, with an equivalent diameter ranging from 36.41 to 87.27 cm.
Specifically, only four blocks exhibit equivalent diameters greater than 75 cm, measuring 87.27 cm, 76.32 cm, 75.88 cm, and 75.18 cm, respectively. Overall, there is a consistent correlation between the volume of blasting blocks and the circumference: as block volume increases, so does the circumference. Consequently, both the equivalent diameter and circumference can serve as effective indicators for evaluating the block size. However, due to variations in block morphology, some blocks may possess relatively large perimeters despite having smaller volumes.
The accuracy of artificial intelligence-based recognition of blasting block sizes is influenced by multiple factors. Firstly, the clarity of the images of the blasting blocks significantly impacts the precision of boundary delineation and size recognition, with a positive correlation between image clarity and recognition accuracy. Utilizing high-definition digital cameras to capture high-resolution images can effectively enhance the accuracy of block size recognition. Secondly, due to the mutual occlusion and overlap between blasting blocks, certain errors in recognition accuracy are unavoidable. To minimize these errors, an appropriate image acquisition angle should be selected to avoid significant tilt between the acquisition equipment and the blasting pile. Ideally, the acquisition equipment should be positioned parallel to the blasting pile to achieve optimal imaging results.
Distribution characteristics based on block recognition
The factors affecting the fragmentation of mineral rock blasting include rock mass structure, mineral rock properties, free surface characteristics, charge structure, explosive consumption per unit, blasting method, among others. Utilizing the identification results of blasting fragmentation, the distribution characteristics of fragmentation are examined through the lens of mathematical analysis models.
(1) Pearson curve fitting analysis.
Ten analyses were conducted utilizing the developed blasting fragmentation image analysis method. The radar chart (Fig. 8) and bar chart (Fig. 9) illustrate the blasting fragmentation distribution from ten experiments. On average, 50% of the block size is confined within 63.4 mm, and 80% is within 113.8 mm; notably, 90% of the fragmentation is under 200 mm, demonstrating effective control over blasting fragmentation, which facilitates subsequent mining and rock excavation operations.
Radar map of block size distribution.
Bar chart of block size distribution.
Here, we delve deeper into the distribution of blasting fragmentation intervals and present a histogram depicting typical fragmentation distributions, as illustrated in Fig. 10. It is evident that the blasting fragmentation adheres to a distinct normal distribution pattern. The highest proportion of blocks, approximately 21%, falls within the size range of 50–60 mm. Additionally, around 60% of the blocks measure between 30 and 100 mm. The distribution of block sizes aligns with natural laws.
Typical block size distribution and proportion relationship.
While analyzing the trend of block size distribution changes, a cumulative curve graph depicting the distribution was plotted, as exemplified in Fig. 11. Upon inspecting Fig. 11, it becomes apparent that the curve assumes an approximate “S” shaped. Broadly, this can be categorized into three phases: slow growth, rapid growth, and gradual growth, with each phase exhibiting a distinct pace of development. During the slow growth phase, despite x undergoing growth, the progression of y remains relatively sluggish, manifesting as a gently ascending trend in the curve. In the rapid growth phase, as x augments, the rate of increase in y progressively accelerates, leading to a steep upward trajectory in the curve. Finally, in the gradual growth phase, as x continues to rise while y advances slowly, the growth rate diminishes towards zero,, causing the curve to progress nearly horizontally.
The cumulative distribution of fragment size exhibits an “S”-shaped curve, reflecting the dynamic mechanism of energy propagation and crack extension during rock fragmentation. can be specifically divided into the following three stages:
(1) Initial stage (inefficient fragmentation zone): At the initial stage of stress wave propagation, energy is concentrated on the defects of the rock (such as microcracks and joints), forming an initial crack network. At this time, the energy distribution is uneven, and only local areas reach the threshold, resulting in a low generation rate of small-sized fragments and a slow increase in the cumulative percentage.
(2) Intermediate stage (efficient fragmentation zone): As quasi-static pressure of the explosive gas continues to act, cracks rapidly expand and intersect with each other. During this stage, energy is effectively converted into fragmentation work, and a large of medium-sized fragments are generated, leading to a rapid rise in the cumulative percentage and the maximum slope of the curve.
(3) Late stage (energy decay zone): the energy decays to the point where it is no longer sufficient to drive further crack extension, the remaining large blocks of rock are not fully fragmented due to insufficient energy, and the curve tends to saturate. At this time, the curve is flat, corresponding to the low-frequency distribution of large fragment sizes.
Cumulative percentage of rock fragmentation.
According to the “S” shaped distribution pattern of mineral rock block size, the Pearson curve proposed by P. F Verhulst is used for regression analysis, and the expression is as follows:
$$y=\frac{a}{{1+b{e^{ – kx}}}}$$
In the formula, a, b, and k are the parameters of the Pearson model.
Analyze and obtain the fitting function:
$$y=\frac{{95.6935}}{{1+29.8112 \cdot {e^{ – 0.0665x}}}}$$
The relevant graph of fitting analysis is shown in Fig. 12. It can be seen that the fitting result is very good, with a regression coefficient R2 of 0.9878, which meets the requirements of data regression accuracy. By using this fitting function, the distribution characteristics of rock blasting fragmentation can be well predicted.
Relevant figures of fitting analysis.
(2) Revise the R-R model analysis.
There are currently many distribution functions used to describe the size distribution of explosive piles29,30,31,32,33,34,35,36, among which the most representative and widely used is the R-R (Rosin Rammler) distribution function, which is expressed as:
$$y=1 – \exp [ – {(\frac{x}{{{x_0}}})^n}]$$
In the formula: y – cumulative screening rate when the block size is X,%; X0– characteristic rock block size, which is the block size when the accumulated amount under screening is (1–1/e)% (i.e. 63.21%); N – Uniformity index.
Here the R-R model is divided into intervals dominated by different fracture mechanisms at the threshold xc= e·x0 (about 2.718₀). Its theoretical basis is as follows:
① Energy critical condition.
When the crack extension length reaches xc= e·x0, the ratio of fracture energy release rate (G to material fracture toughness (KIC) reaches the critical value. At this time, the energy propagation pattern changes from the dominant stress wave (short crack) to the dominant gas (long crack), resulting in a sudden change in the crushing mechanism.
② Characteristics of the exponential function.
At x = x0, R(x) = 1/e, corresponding to the cumulative distribution of 36.8% passing rate. When x = e·x0, R(x) = exp(− en) its value significantly decreases, reflecting the need to describe the block size distribution parameters in segments.
Here the R-R equation is transformed into a linear formula:
$$\text{ln}\text{ln}[1/(1-\text{y})]=\text{n}(\text{lnx}-{\text{lnx}_0})=\text{nlnx}-{\text{nlnx}_0}$$
$$\text{Y}=\text{BX}+\text{A}$$
In the formula, Y = lnln[1/(1-y)], B = n, X = lnx, A=-nlnx0。.
The scatter plot of the relationship between ln (x/x0) and lnln [1/(1-y)] is calculated here, as shown in Fig. 13.
Relationship between ln (x/x0) and lnln [1/(1-y)].
According to Fig. 13, it can be observed that ln (x/x0) does not have a completely linear relationship with lnln [1/(1-y)], and there is a phenomenon of slope variation; As the value of ln (x/x0) increases, the growth rate of ln [1/(1-y)] shows a decreasing trend, indicating that the value of (x/x0) has a direct impact on the block size distribution. Therefore, the R-R model isn’t accurate for block size distribution, and a modified R-R model using piecewise function is needed to more accurately express the relationship between them two. Meanwhile, considering the size relationship between x and x0, a three-stage linear function is used for fitting, and the modified R-R model is shown in Table 1, where the slope of the line represents the value of n. It can be seen that as the value of (x/x0) increases, the value of n shows a gradually smaller trend of change. The segmented function is used here to represent the modified R-R model, which can better reflect the distribution characteristics of blasting fragmentation and provide guidance for accurate prediction of fragmentation distribution.
