For limiting the damage range caused by explosive shock loads in vertical crater retreat (VCR) mining, the blasting damage characteristics of surrounding rock were studied by two methods: numerical simulation and ultrasonic testing. Combined with the mining blasting in Dongguashan Copper Mine of China, the VCR blasting shock characteristics under different conditions are obtained by using LSDYNA. Based on statistical fracture mechanics and damage mechanics theories, a damage constitutive model for rock mass subjected to blasting shock load was established. Then by using the fast Lagrange analysis codes (FLAC3D), the blasting damage characteristics of surrounding rock were analyzed by applying the blasting shock loads obtained from the VCR mining and the damage zone is obtained. At last, the relationship between the amount of explosives and the radius of damaged surrounding rock mass was discussed, and its formula was also derived. The research provides a theoretical basis for rationally controlling stope boundaries and optimizing mining blasting parameters.
VCR (vertical crater retreat) mining technology is widely used in mine engineering because it possesses many better features, such as higher efficiency and more simple operation. In the mining process, the blasting shock originating simultaneously from the rockfracturing blasting load also can damage surrounding rock. For better control of the stope boundary, it is a key prospect in engineering application to ascertain damage characteristics of surrounding rock under mining blasting shock load and to optimize blasting parameters.
Damage effects of rock mass under blasting load were extensively studied at home and abroad, but these researches were mostly based on insite tests and laboratory experiments [
Based on the theories in statistical fracture mechanics and damage mechanics, a damage model for rock mass subjected to blasting load was established. At the same time, damage characteristics of surrounding rock subjected to mining blasting shock load in VCR mining and conventional blasting shock load were analyzed by numerical simulations.
Dongguashan Copper Mine is located in Tongling, Anhui, China. It has the ability to produce around 4.3 million tons of copper ore annually, and its service life is 28 years. As the largest copper mine of downhole pit mining in Asia, its mining depth is more than 1000 meters, which ranks the first among the nonferrous metal mines in Asia. The deposit is as long as more than 1800 m in trend, more than 500 meters wide, and 20–70 m thick. It is divided into panels every 100 m, and there is an 18 m wide barrier pillar in each pair of adjacent panels. A panel is 100 m wide, whose length and height equal the width and the thickness of the deposit, respectively. Every panel consists of 20 stopes, which are arranged along the trend of the deposit and 18 m wide. The room stope and pillar stope are 82 m long and 78 m long, respectively. In the mining blasting process, it is significant to control the stope boundary for safety of underground mining construction in the mine.
VCR mining method was adopted for underground mining in Dongguashan Copper Mine. According to the reality, largediameter deephole blasting is introduced. The blasthole diameter is 165 mm, the charge length is 1.5 m to 10.5 m, and the stemming length is 1.2 m to 2.0 m. In this study, a threedimensional model is established using the software LSDYNA, as shown in Figure
LSDYNA model.
In LSDYNA simulation, MohrCoulomb (MC) model is selected as rock material’s model [
Parameters of the rock material.
Density 
Elastic modulus (GPa)  Poisson’s ratio  Cohesion (MPa)  Internal friction (°) 

3.22  69.00  0.31  21.43  56.21 
The JWL state equation can simulate the relationship between pressure and specific volume in the explosion process [
Parameters of the explosive.
Density (g·cm^{−3})  Detonation velocity (cm· 







1.09  0.4  214.4  18.2  4.2  0.9  0.15  4.192 
Due to the model which is built symmetrically, a quarter of the model is calculated to reduce the size of the research object. So the model was simplified as a 10 m cube, and the charge length is 3 m, 3.5 m, 4.0 m, 4.5 m, 5.0 m, 5.5 m, and 6.0 m, respectively. The charging length of 6.0 m is shown in Figure
Numerical models with 6 m charging length.
As illustrated in the rock blasting theory, the crushed zone radius is 23 times larger than the blasthole radius [
Monitoring element in the model with 6 m charging length.
Figure
Pressure time history of Element H54050.
According to statistical fractured mechanics [
a rock material does not fail if the applied stress is lower than its static strength;
when a rock material is subjected to a stress higher than its static strength, a certain time duration is needed so that the fracture can take place;
the dynamic fracture stress of a rock material is higher than its static strength and is approximately cube root dependent on the strain rate.
So damage due to blasting loading can be defined as the probability of fracture, written as follows:
Tensile strain is a quite important index to evaluate whether rock mass is damaged or not [
According to the
Like the blast model above, a 3D model was established using FLAC3D. Hexahedral solid element is selected when the model is meshed. Due to the model which is built symmetrically, a quarter of the model is calculated to reduce the size of the research object. For example, when the charge length is 6 m, a 10 m long, 14 m wide, and 14 m high model is established, as shown in Figure
Numerical model with the charging length of 6 m.
The boundary conditions are the same as those in Section
For example, when the charge length is 6 m, the damage growth on the free surface and along the height direction is shown in Figures
Damage growth on the bottom free surface.
Damage growth along the height direction.
Figures
Using the same way, the damage zone with the charge length of 3 m, 3.5 m, 4.0 m, 4.5 m, 5.0 m, 5.5 m, and 6.0 m is shown in Figure
Damage zone after mining blasting.
Figure
Damage zone radiuses with different charge weights.
Charging length (m)  Maximum onestage charge weight (kg)  Damage zone radius (m) 

3  696.75  5.504 
3.5  812.875  5.942 
4  929  6.478 
4.5  1045.125  6.763 
5  1161.25  7.065 
5.5  1277.375  7.684 
6  1393.5  8.141 
Based on the insite parameters, the statistical relationship between charge amount and damage zone radius is established.
As shown in Figure
Fitting curve between damage zone radius and charge weight.
The rooms and barrier pillars are 18 m wide. As illustrated in (
The following conclusions can be drawn.
Based on statistical fracture mechanics, damage due to blasting shock load can be defined in the probability form. The damage model was established. And the damage characteristics were obtained by numerical simulation.
Under blasting shock load, the rock mass is not damaged yet at the initial stage after detonation whether on the free surface or along the height direction. The damage of rock subject to blasting load needs some time to develop. Damage under blasting loads grows faster within the first 1.5 ms after denotation than that in the latter 1.5 ms.
According to the results in different blasting conditions, the statistical relationship between charge amount and damage zone radius is established. Furthermore, the maximum onestage charge was proposed to be less than 1848.26 kg on the purpose of controlling the stope damage boundary.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The study was sponsored by the National Natural Science Foundation of China (Grant nos. 41372312 and 51379194), the Fundamental Research Funds for the Central Universities, China, University of Geosciences (Wuhan) (Grant no. CUGL140817), and the China Postdoctoral Science Foundation (Grant no. 2014M552113). The authors are also grateful to the China Scholarship Council (CSC) for the support.