Numerical study on the behavior of blasting in deep rock masses
Introduction
With the continuous development of worldwide economy, the demand for mineral resources is increasing. The mineral resources at shallow depths have gradually been exhausted, and mining activities are increasingly conducted in deep rock masses. Also, tunnels serving for hydraulic engineering and infrastructures need to be excavated in mountainous areas. Therefore, high in-situ stress is inevitably encountered in engineering projects (Jayasinghe et al., 2019, Yang et al., 2017, Cao et al., 2016, Lu et al., 2012). Buried depths of many mines in Canada and the United States exceed 2000 m (Zhou et al., 2018). The Mpaneng Mponig Gold Mine in South Africa has reached a depth of 4530 m (Dou et al., 2020). The Jinping-II diversion tunnels' buried depth in China has reached 2500 m, with the maximum in-situ stress exceeding 60 MPa (Jiang et al., 2010).
At present, in mining engineering and tunnel excavation, the drill and blast technique is still widely used due to its low-costing and high efficiency (Liu et al., 2018, Zhao et al., 2017, Iwano et al., 2020, Li et al., 2018, Wan et al., 2019). The mechanical properties and failure mechanisms of rocks in high in-situ stress conditions are different from those of shallow rock masses. During the rock blasting at great depths, the rock is subjected to both in-situ stress and blasting load. However, so far, the combined effects of the static in-situ stress and the dynamic blasting load on the blasting behavior in deep rock masses have not been thoroughly studied. Lu et al. (2012) studied the contour blasting under lithostatic stress and obtained the conclusion that the traditional pre-splitting blasting scheme was inapplicable when the lithostatic stress surpassed 10–12 MPa. Therefore, it is necessary to have a sounding understanding of the blasting mechanisms in rock masses under high in-situ stresses.
In the last few decades, researchers have used various methods, including theoretical analysis, field blasting tests, and numerical simulations, to study the blasting mechanism in rock masses. The existing blasting theory is mainly based on researches by Kutter and Fairhurst (Kutter and Fairhurst, 1971). They pointed out that three zones, including the crushed zone, the cracked zone, and the elastic vibration zone, would be formed after blasting, and the in-situ stress has an important influence on the propagation of cracks induced by blasting. Miklowitz (1984) presented the governing equation for stress waves spreading in rock masses for the case of cylindrical charges. The equation presented by Kirsch (1898) can be used to obtain the stress distribution around the blasthole when subjected to lithostatic stress. Yi et al. (2018) theoretically analyzed the blasting process under in-situ stresses by using Kirsch equations and the governing equation for stress waves spreading in rock masses. In terms of field blasting tests, the research conducted by Nicholls et al. (1966) showed that the pre-split blasting was the most effective in the maximum in-situ stress direction. Yang et al. (2019) carried out blasting experiments under high confining pressures using polymethyl methacrylate specimens. Using the advanced high-speed DIC test system, He et al. (2018) conducted blasting experiments under diverse pre-compressive stresses and observed that the crushed zone after blasting gradually decreased with rising lateral pressure coefficients. Field blasting tests performed by Zhang et al. (2017) showed that the explosion crater volume decreased first and then increased with increasing equibiaxial confining pressures. However, due to the limitations that field blasting tests are difficult to prepare and expensive and fractures formed after blasting are difficult to observe, these limited experimental studies have not thoroughly explored the influences of in-situ stresses on the blasting behavior in deep rock masses.
In recent years, the finite element method (Liu et al., 2019, Chao et al., 2020), finite difference method (Zhu et al., 2007, Zhu et al., 2008, Wang et al., 2019, Wang et al., 2017, Wang et al., 2021), distinct element method (Hajibagherpour et al., 2020), smoothed particle hydrodynamics method (Gharehdash et al., 2020), and hybrid methods (Yuan et al., 2018) have been extensively used by researchers to study failure responses of rocks. Also, the influence of in-situ stress on the blasting behavior is concerned. For example, Donze et al. (1997) pointed out that cracks induced by shock waves were aligned with the higher stress direction. Ma and An (2008) found that rock failure was greatly affected by the loading rate of the blasting load and cracks tended to expand in the confining pressure direction. Wang and Konietzky (2009) numerically studied the mechanisms of blasting behavior of jointed rock masses under pre-compressive stress and the results indicated that cracks under the blasting load preferentially propagated in the higher stress direction. Lak et al. (2019) applied the hybrid method to predict the crack propagation and the results showed that crack lengths in the higher stress direction were greater than that in the lower stress direction. Han et al. (2020) explored the contour blasting of tunnel excavation under in-situ stresses by using the combined finite discrete element method. The results indicated that smooth blasting was considerably affected by in-situ stress and rock fractures developed more easily in the higher stress direction. These studies indicate that under in-situ stresses, blasting-induced cracks tend to propagate in the direction of the higher stress.
However, the effects of in-situ stresses on the crushed zone caused by blasting are still unclear. Yilmaz and Unlu (2013) used FLAC code to study the mechanism of rock blasting under various pre-compressive stresses and the results showed that the loading rate of the blasting has a great impact on the crushed zone and the cracked zone, respectively. The results also indicated that pre-compressive stresses can significantly affect the cracked zone and cracks tend to develop in the higher stress direction. In contrast, pre-compressive stresses almost have no effect on the crushed zone. Nevertheless, the rock material model used in the aforementioned study only considers the effect of strain rate and the effect of confining pressure is omitted, with pre-compressive stress having a slight influence on the crushed zone. Tao et al. (2020) investigated the influences of in-situ stress on the blasting and the results showed that blasting-induced cracks tend to propagate in the direction of higher stress. The study proposed that in equibiaxial pressure conditions, the area of the crushed zone declines with rising in-situ stress; in anisotropic pressure conditions, the crushed zone is elliptical in shape. However, the level of in-situ stress in the aforementioned studies is relatively small, with the maximum in-situ stress of 12 MPa. It only can simulate the in-situ stress at a shallow depth, whilst the blasting results under higher in-situ stress cannot be simulated. Xie et al. (2016) conducted a numerical simulation study on cut blasting in deep rock masses. The results showed that the in-situ stress inhibits the extension of rock damage. With rising in-situ stresses, the area of the damage zone gradually declined and tended to develop in the higher stress direction, and the extension of the tensile damage zone was influenced by the lateral pressure coefficient. Then Xie et al. (2017) used the verified RHT model to carry out numerical studies and optimized the cut blasting scheme in deep rock masses. Yi et al. (2018) applied LS-DYNA code to numerically study the effects of in-situ stresses on single-blasthole blasting and the results showed that in-situ stresses have an inhibition effect on the generation of rock fractures. Based on the aforementioned analysis, it can be concluded that the in-situ stress has a small impact on the damage zone and a large impact on the crack expansion, with damage development tending to along the higher stress direction. However, there is no detailed discussion of the crushed zone in the above research.
The theoretical analysis of blasting is quite difficult due to its transiency and complication. Furthermore, the fracture zone formed after the field blasting test is pretty hard to observe. Thus, it is necessary to conduct a reliable numerical study to explore the blasting behavior. According to systematic statistics, the selected material model has great influences on the results of numerical simulations (An et al., 2017). Therefore, in this study, the RHT model, which considers the effects of confining pressure, strain rate, strain hardening, and damage softening (Xie et al., 2017), is used to carry out the numerical research, and the accuracy of this model is validated by comparing numerical results with experimental results. Moreover, to understand the behavior of rock blasting in deep underground thoroughly, a series of numerical simulations were conducted. First, the theoretical analysis of the influence of in-situ stress on the blasting behavior for the case of a single-blasthole was carried out, and the effects of in-situ stress on the crushed zone and the cracked zone were analyzed based on numerical simulation results, respectively. Then, based on the actual blasting schemes (especially the pre-split blasting), the simplified models, i.e., numerical models with double-blasthole were built and the effects of lateral pressure coefficients, buried depth and blasthole layouts were studied. It is expected to provide insights for the design of blasting schemes in deep rock masses.
Section snippets
General descriptions
The blasting in deep rock masses can be simplified to the plane strain issue, as shown in Fig. 1(a). There is a blasthole in the infinite and isotropic rock mass. The rock mass is subjected to horizontal stress σh and vertical stress σv. The in-situ stress in the vertical and horizontal directions are calculated according to the empirical formula (Brown and Hoek, 1978) and the formula presented by Stephansson et al. (1986), as follows:
where γ is the
Material models for numerical simulations
The former theoretical analysis simplifies the target issue to a certain extent based on the classical elasticity theory. However, the rock mass is a complex medium. Although the aforementioned theoretical analysis can provide a general understanding about the stress distribution in the rock mass, there is a large difference between the real and the theoretical situations when the theory of elasticity is applied to calculate the nonlinear and large deformation dynamic of deep rock masses caused
Setups for numerical simulations
Pre-split blasting is widely employed in underground rock engineering. For example, as shown in Fig. 3(a), when the drill and blast technique is adopted to excavate the tunnel, the pre-split blasting is used to form a fracture surface which can reduce the damage induced by production blasting. In Fig. 3(b), the pre-split blasting is applied in mining engineering to keep the stability of the remaining rock mass. A connecting crack along adjacent blastholes and the half cast ratio are two key
Discussion
As shown in Fig. 3(a) and (b), pre-split blasting is widely used in practical engineering. Based on the analysis in Section 4.2, it can achieve the best blasting results when blastholes are drilled along the direction of the higher stress. However, the environments of practical blasting projects are often complicated. Rock blasting at different depths may have diverse results. It cannot guarantee that blastholes are drilled exactly parallel to the higher stress direction. Therefore, it is
Conclusions
In-situ stresses significantly affect the behavior of blasting in deep rock masses. Effects of in-situ stress on the blasting are theoretically analyzed. Then the RHT model considering the effect of strain rate and confining pressure is validated. Based on this material model, the LS-DYNA software is used to conduct numerical simulations of the blasting under different in-situ stress. Factors including in-situ stress levels, lateral pressure coefficients, buried depths and blasthole layouts are
CRediT authorship contribution statement
Xiaohan Li: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Data curation, Writing - original draft. Zheming Zhu: Conceptualization, Funding acquisition, Writing - review & editing. Meng Wang: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Software, Writing - review & editing, Visualization, Supervision. Duanying Wan: Methodology, Data curation, Visualization. Lei Zhou: Visualization, Validation. Ruifeng Liu:
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This research was funded by the National Natural Science Foundation of China (grant number U19A2098), the open fund of MOE Key Laboratory of Deep Underground Science and Engineering (DESEYU202101), the Sichuan Science and Technology Program (2021YJ0511).
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