Aiming at surrounding rock damage induced by dynamic disturbance from blasting excavation of rockanchored beam in rock mass at moderate or far distance in underground cavern, numerical model of different linear charging density and crustal stress in underground cavern is established by adopting dynamic finite element software based on borehole layout, charging, and rock parameter of the actual situation of a certain hydropower station. Through comparison in vibration velocity, contour surface of rock mass excavation, and the crushing extent of excavated rock mass between calculation result and field monitoring, optimum linear charging density of blast hole is determined. Studies are also conducted on rock mass vibration in moderate or far distance to blasting source, the damage of surrounding rock in nearfield to blasting source, and crushing degree of excavated rock mass under various in situ stress conditions. Results indicate that, within certain range of in situ stress, the blasting vibration is independent of in situ stress, while when in situ stress is increasing above certain value, the blasting vibration velocity will be increasing and the damage of surrounding rock and the crushing degree of excavated rock mass will be decreasing.
Jinsha River Basin, which lies on the upstream of Yangtze River in China, has witnessed the development and construction of large numbers of water conservancy and hydropower projects. Due to the fact that most basin area of Jinsha River locates on the towering and steep mountains, the work of layout, construction, and operation of building hub should be conducted by the framework of underground cavern. Meanwhile, a certain amount of underground caverns in a largescale and ultralarge type appear along with the enlargement of hydropower in scale. The rockanchored beam is frequently used as the load bearing of crane in caverns in order to reduce the span of underground powerhouses and accelerate the progress of construction.
The rockanchored beam is widely used in hydropower projects as the essential construction in underground caverns which makes the first success in Norway [
However, with considerable difficulty, the excavation of rockanchored beams is in high quality requirements, which directly affects the operation conditions of bridge cranes after construction. In order to make cracks form successfully in adjacent blast holes and reduce the damage of remaining rock mass to minimum, the construction site usually meets the requirements of excavation by means of controlling the charging of the blast hole and blast holes spacing.
Considering the noncoupling charge structure applied in driving blasting, it is the most reasonable to adopt the fluidstructure interaction algorithm to simulate the blasting process [
But the aforesaid algorithms could only simulate the shock response of the nearfield of blasting source. There is still a way to go for the simulation of the whole process from the blasting of nearfield of blasting source to the blasting vibration spreading of explosion of farfield [
In recent years, Ma et al. [
The paper is based on the basic mechanical properties and blasting parameters of rock mass in the process of excavation program of underground caverns in Baihetan hydropower station in Yunnan, China. First, the research adopts threedimensional models in the calculation of vibration speed of the blasting of rock mass in the moderate and far distance and twodimensional models in the simulation of crushing conditions of rock mass in nearfield of blasting sources and explosion. At the same time, the research also includes the comparison of contour surface and vibration speed in the measuring point between the model and the filed. Then, the paper does the study of rock mass vibration in the moderate or far distance of blasting, the damage of surrounding rock in nearfield of blasting source, and crushing degree of excavated rock mass under different crustal stress.
This article uses dynamic finite elements analysis software ANSYS/LSDYNA, which is a typical dynamic finite element calculation software. It does not open source, so the programming code can not be downloaded. The solving equation used in LSDYNA for dynamic calculation is motion equation:
ANSYS uses Newmark integration method to solve kinetic equation. It’s basic idea is to change the requirement that any time
The solving equation used for static calculation is as follows:
Comparing (
Due to the fact that the blast holes studied in this paper are small in size and large in amount, it is inconvenient to build the blast hole model through the method of explosion load exertion in threedimensional model. According to the equilibrium principle, exerting the peak pressure of shock waves on the blast holes walls is equivalent to the value on lines of centers of blast holes [
The curved diagram of explosion load.
Overseas scholars have come up with CJ theory, which simplifies the detonation wave to strong discontinuity surface contained chemical reactions and gives the conclusion of stable spread of detonation wave under the circumstances of CJ conditions. The simplified load peak value
As shown in Figure
The equivalent load exerting on lines of centers of blast holes.
The principle of rock mass damage depends on the property of rock mass as well as the practical force conditions. The pressure of rock mass, taking the Mises damage rule, forms the crushing area of rock mass blasting, while the cracks area is the result of the damage of tensile force. The damage rule of rock mass is as follows:
In order to reduce the damage of surrounding rock on site, grooving has been done on part of blast holes as shown in Figure
Grooved blast holes.
Grooved blast holes size.
Hole wall of groove hole load distribution.
As shown in Figure
The dynamic compressive stress of rock increases with the improvement of loaded strain rate, generally approximated by the following equation [
The loaded strain rate of rock
For the lack of corresponding analytical data of experiments and theories, the value of dynamic tensile strength approximates
The paper applies the fluidstructure interaction algorithm on the calculation of explosive, rock, and air through twodimensional model, taking the tensile strength of rock as the criteria of rock mass fracture, in order to observe the damage of surrounding rock and the crushing condition of excavated rock mass under the circumstances of noncoupling charge. The damage and crushing rate of rock mass under the effect of blast by explosive have long been researched. Both domestic and overseas scholars have drawn quite a few remarkable conclusions through experimental research and theoretical analysis. However, these conclusions differ from one another due to the differences between experimental conditions. The paper will research on the damage of rock mass and crushing rate under different crustal stress with the reference of actual operation situation on site.
In rock medium, the analysis of static problems is based on isotropic strengthened constitutive model, while the analysis of cyclic loading and dynamic issue is based on two constitutive models, namely, the kinematic strengthened constitutive and the mixed strengthened constitutive models. Particularly, during the blasting process, under the conditions of comparable large strain of rock mass in nearfield, the effect of strain rate is quite apparent. Considering the aforesaid factors, it is more appropriate to build the model of plastic kinematic strengthened constitutive in the analysis of dynamic problems of underground blasting programs, for the model conforms with the conditions in real project. The strain rate is considered in CowperSymonds model; the yield stress is expressed in factors related to the strain rate [
When the material is in hardening stage, the efficient plastic strain rate
Baihetan hydropower station, located in the upstream of Jinsha River in southwest China, has a capacity of 2060 billion cubic meters in reservoir and the underground powerhouses install 16 hydroelectric generating sets with the capacity per set of 1000 MW. The installed capacity drafted in the beginning is 16 million KW, and the average annual electric energy production is 6024 billion KWH. The station will become the second largest hydropower station which is next only to Three Gorges after completion, which makes the high demand of quality of rockanchored beam of rock mass in underground plants. Thus, there is strong need for the fine control of blasting excavation of the rockanchored beam in order to keep the damage of surrounding rock caused by blasting in a small extent.
The charging parameter of blast holes in single blasting excavation on site is shown in Table
Different blast hole layout and charge parameter.
Name  Hole diameter  Hole distance  Hole depth  Hole amount  Cartridge diameter  Charging density 

① Vertical holes  Φ 42 mm  30 cm  248 cm  68  Φ 25 mm  65/70/85 g/m 
② Oblique holes  Φ 42 mm  30 cm  260 cm  68  Φ 25 mm  65/70/85 g/m 
③ Auxiliary holes  Φ 42 mm  90 cm  242 cm  22  Φ 25 mm  186/206/250 g/m 
The plane figure of blast holes detonation network and the profile map of blast holes (unit: cm).
Taking the blasting excavation of the protective layers of rockanchored beams in the underground main power house of the right bank of the dam as an example, the blasting excavation of protective layers of rockanchored beams drills the vertical smooth blasting holes, oblique smooth blasting holes, and auxiliary blast holes manually in the rate of 20.4 m excavation length each time. Meanwhile, the blasting vibration monitoring is conducted on the sidewalls near excavated rockanchored beams. The measuring point vibration monitoring of nearfield rock during the process of blasting excavation is conducted in order to make sure the disturbances of blasting excavation to surrounding rocks in a safety range. Meanwhile, for ascertaining the safety of monitoring equipment, the nearest measuring points are arranged 10 m away from the boundary of the excavation area, and then one measuring point is arranged every 5 m, and a total of five measuring points are arranged. It is as shown in Figure
The schematic diagram of measuring point layout of blast vibration velocity (unit: m).
The elevation of rockanchored beams excavated on site ranges from EL. 602.40 m to EL. 606.90 m. Part of blast holes are grooved to ensure the quality of excavation and observe the protection effect on surrounding rock compared with circular blast holes. Figure
The front view and side view of blasting test of rockanchored beam (unit: m).
The rock parameter [
Rock mass physical and mechanical material.







2.7  50.0  0.22  6.0  78.0  8.0 
Among them,
According to the construction design of the main underground powerhouse, the dynamic finite element program is used to establish the calculation model shown in Figure
The front view and side view of calculation model of blasting excavation of rockanchored beam (unit: m).
Due to the fact that the Vshape grooving has been done on part of smooth blasting holes in the blasting excavation process of rockanchored beam on site, twodimensional crack forming model of blast holes is added in order to compare the effect of crack forming of grooved blast holes with that of circular blast holes. In the model, the spacing and array pitch of blast holes are shown in Figure
The calculation model of twodimensional plane (unit: cm).
Size diagram of explosive and air
Size diagram of explosive and rock
The state equation of detonation products applies the JWL equation of state [
The specific parameters of rock emulsion explosive in model and the JWL state equation are shown in Table
Explosive and JWL state equation parameters [








3200  214  0.18  4.15  0.95  0.15  4.19 × 10^{9} 
Among them,
Conducting three groups of numerical calculations according to the linear charging density on site, calculations of three groups of equivalent load are based on formulas (
Through extracting the vibration velocity on measuring points shown in Figure
The comparison of vibration velocity of measuring points in numerical simulation and field measurement.
MP1 vibration curve in the
MP1 vibration curve in the
MP1 vibration curve in the
Equivalent load 17.9 MPa–14.1 MPa
Equivalent load 19.3 MPa–15.2 MPa
Equivalent load 23.4 MPa–18.5 MPa
Selecting one group unit from the rockanchored beam region of rock mass shown in Figure
Stress values of five measuring points of rockanchored beam.
Direction  Measuring points  Average value  

1^{#}  2^{#}  3^{#}  4^{#}  5^{#}  

0.45  0.33  0.25  0.20  0.17  0.28 

11.55  15.92  13.81  13.28  13.22  13.56 

20.42  20.46  20.08  20.22  20.43  20.32 
A comparison is made among the twodimensional plane figure of cracks and the figures of contour surface and rock mass crushing on site in three values of different linear charging density. As shown in Figure
When the linear charging densities of the smooth lasting holes and auxiliary holes are 65 g/m and 206 g/m, respectively, it is shown in the figure that the cracks between grooved smooth blasting holes are quite flat and the damage to surrounding rock is rather small, while there are no penetrating cracks formed between circular smooth blasting holes, which indicates that such charging is too small to form cracks between circular blast holes. However, the grooved blast holes take effect on energy gathering and guiding so as to utilize the more blasting power on crack forming of rock between blast holes. Furthermore, the crushing degree of excavated rock mass is rather small and the boulder frequency is large, so the demand of crushing degree could not be reached.
When the linear charging densities of smooth blast holes and auxiliary holes are 70 g/m and 206 g/m, respectively, penetrating cracks could be formed between blast holes after the blasting. However, cracks between grooved blast holes are more flat than those of circular blast holes, which indicate that penetrating cracks could be formed among blast holes in different shapes under such charging. Moreover, the crushing degree of excavated rock mass is large so it is convenient for the shipment of crushing rock mass.
When the linear charging densities of smooth blast holes and auxiliary holes are 85 g/m and 250 g/m, respectively, besides the cracks forming among smooth blast holes of different shapes, serious damage of surrounding rocks also takes place and the crushing degree of rock mass is rather large.
The comparison of excavated contour and crushing rate of rock mass in numerical simulation and field measurement under different charge amount.
The linear charging density is 65 g/m
The linear charging density is 70 g/m
The linear charging density is 85 g/m
According to the contour surface of cracks forming on site, the damage reaches the largest extent where vertical smooth blast holes intersect with the oblique ones. The fact consists with the research conclusion of Dong et al. [
Based on the aforesaid analysis, when the linear charging density is 70 g/m, the penetrating cracks could be formed among smooth blasting holes and the damage to surrounding rocks is in low extent. Furthermore, when grooved blast hole is applied, the penetrating cracks could be much easier to form among blast holes and the damage to surrounding rocks is rather small.
According to the analysis of Sections
The comparison of vibration velocity in the same measuring point under different crustal stress.
Perpendicular to tunnel axis direction
Upright direction
Parallels to tunnel axis direction
According to the vibration velocity in three directions shown in figures, the vibration velocity of measuring points in direction
According to the calculation and analysis in Section
Stress values of
Crustal stress/MPa  Measuring points  Average value/MPa  

1^{#}  2^{#}  3^{#}  4^{#}  5^{#}  
0  0  0  0  0  0  0 
5  4.65  4.57  4.60  4.64  4.64  4.62 
10  9.30  9.13  9.18  9.28  9.28  9.23 
20  18.60  18.26  18.38  18.56  18.55  18.47 
40  37.18  36.50  36.73  37.09  37.07  36.91 
80  74.90  73.70  75.20  76.73  77.80  75.67 
Keeping the charging of blast holes in a certain amount and exerting the average value of stress in
The damage depth, area of surrounding rocks, and the crushing rate of excavated rock mass.
Crustal stress/MPa  0  5  10  20  40  80 

Damage depth of surrounding rocks/cm  >50  >50  ≈20  ≈10  <10  ≈10 
Damage area of surrounding rocks/%  >50  >50  ≈40  ≈20  <20  ≈6.7 
Crushing rate of excavated rock mass/%  >75  >70  >70  >50  <30  <10 
The crack forming diagram of rock mass under different crustal stress.
0 MPa
5 MPa
10 MPa
20 MPa
40 MPa
80 MPa
As shown in Figure
According to the reference of Figure
The following conclusions could be drawn according to the analytical comparison of dynamic finite element calculation and onsite test:
The vibration velocity test of three directions of surrounding rocks in moderate and far area blasting excavation of rockanchored beams found out that the vibration velocity of rock mass perpendicular to the blasting excavation surface is the largest which should be used as the reference of vibration velocity control in rock mass excavation.
The numerical simulation and onsite test indicate that when grooved and circular blast holes blast under the same charge amount, the grooved one is proved to carry out fine energy gathering effect as well as reduce the damage to surrounding rocks on a certain extent.
Research on blasting excavation of underground caverns under different crustal stress found that, in identical charge amount, the crushing degree of rock mass and the damage to surrounding rocks decreases with the increase of crustal stress. When crustal stress is 0–40 MPa, the blasting vibration velocities of moderate and far area of rock mass approximate and when it reaches 80 MPa, the blasting vibration velocity on the same measuring point increases, so adjustments of blast holes layout and charge amount need to be done based on different crustal stress.
Due to the absence of practical situation of fine blasting project of rockanchored beam excavation on underground caverns in high crustal stress, the results of numerical simulation could not be proved. Experiments and researches on such problem will be continued.
The authors declare that they have no conflicts of interest.
This work is supported by the National Natural Science Foundation of China (51274157 and 51309183), PLA University of Science and Technology (no. DPMEIKF201410), the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Grant no. Z015005).