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The quality of smooth blasting including the volume of over-/underbreak and blasting-induced damage of surrounding rocks has been extensively considered to be highly correlated to both the cost and advancement rate of rock tunnelling excavated by the drill-blast method. A general control strategy for smooth blasting is too difficult to be available due to the uncertainties and complexity of rock masses, as well as the varying blasting operations. As prerequisite for the evaluation of the blasting quality, effective identification of the influential factors affecting smooth blasting usually plays a significant role in the improvement of smooth blasting design. Compared to the expensive and time-consuming experiments including physical modelling and field tests, numerical modelling, as a cost-efficient approach, offers an attractive alternative to investigate the influential factors in terms of weight, which might be more applicable and reliable for the optimization of smooth blasting parameters. In this case, the dominant factors and secondary factors can be quantitatively identified. Considering the dominant factors often orient the development of things; in this work, a numerical-based approach was proposed to quantitatively identify the dominant factors influencing the quality of smooth blasting. Proposed 3-dimensional blasting modelling was based on LS-DYNA to simulate the occurrence of smooth blasting in rock masses, and the erosion algorithm was also employed to determine the fracturing of jointed rocks. The orthogonal experimental design method was utilized to optimize the experimental arrangement. Seven factors with 4 levels including the perimeter hole spacing, line of least resistance, charge concentration, charging explosive, type of rock mass, detonation velocity, and drilling deviation were taken into account. The geological setting and project background of a real rock tunnel served for the Chengdu-Chongqing high-speed railway were selected as the site conditions to perform the numerical investigation. Calculated area and distance of overbreak as the observed parameters indicating the quality of smooth blasting were utilized to determine sensitivities of factors based on the range analysis of orthogonal experiments. The results suggested that the type of rock mass has the greatest influence on the blasting quality, whereas the charge concentration and detonation velocity can be considered as the secondary factors under the specific site conditions. The proposed numerical approach for assessing influential factors of quality of smooth blasting under specified geological conditions is expected to improve the parameter design and operation of smooth blasting in practical applications.

The drill-blast method has been extensively applicable in rock tunnelling owing to its flexibility and compatibility under complicated geological conditions. In the case of drill-blast excavation, the opening tunnel contour and damage caused by blasting will affect not only the cost and advancement rate of tunnelling but also the stability of surrounding rocks [

However, the task of quality evaluation of smooth blasting is highly challenging due to the complicated site conditions and varying blasting operations. A literature review on blasting quality evaluation reveals that most research studies focused on the overbreak or underbreak evaluation, rock damage, and ground vibration assessment, as well as the blasting control [

In this work, the LS-DYNA code and erosion algorithm were coupled to perform the 3D numerical investigation under the geological setting and project background of a real rock tunnel served for Chengdu-Chongqing high-speed railway. In order to optimize the experimental conditions and reduce the times of investigations, the orthogonal experimental design method was utilized. On the basis of range analysis, calculated area and distance of over-/underbreak were predefined as the observed parameters that indicate the quality of blasting to determine the sensitivity of the factors. Proposed numerical approach is expected to improve both design and operation of smooth blasting parameters in practical applications.

In general, the quality of smooth blasting in rock tunnelling always depends on various factors including the perimeter hole spacing, least resistance line, and charge concentration. For full understanding of all possible effects caused by these factors, full factorial design might be the best candidate for experimental arrangement. However, the full factorial design is always time-consuming, laborious, and inefficient, owing to the large sample size which grows exponentially with the number of factors [

The influential factors involved in this investigation include peripheral hole spacing

Rock damage modelling is virtually associated with the dynamic behavior of rocks under blasting loading. The dynamic mechanical behavior of brittle materials such as concrete and rocks, in most cases, could be described by the Holmquist–Johnson–Cook (HJC) model, Riedel–Hiermaier–Thoma (RHT) model, Taylor–Chen–Kuszmaul (TCK) model, continuous smooth cap (CSC) model, and the Karagozian–Case (K-C) model [_{c} is the uniaxial compressive strength under static loading,

Original Holmquist–Johnson–Cook (HJC) model [

The damage factor

The relationship between the hydrostatic pressure and the volumetric strain of the rock and concrete is expressed by the segmental state equation shown in Figure

Stage

Loading section:

Unloading section:

Stage

Loading section:

Unloading section:

There is no hole in this stage, and the concrete and rock are crushed completely.

The joints in rock masses are modeled using the bilinear kinematic model in LS-DYNA. This model is increasingly employed in joint modelling due to the small number of parameters involved in the model, and thus, it is easy to use [

The air radial noncoupling charging structure is predefined as the structure of the blasting hole. The null air material model and linear polynomial state equation are employed to describe the charging structure. The linear polynomial state equation for the null air material can be expressed as follows [

The rock failure under blasting loading is usually determined by the rock properties and stress state. The failure criterion of rocks depends on characteristics of the failure, crushing, and rupture zones produced after blasting. In the crushing zone, the effect of high-pressure detonation generated by blasting is remarkably more intensive than that produced by dynamic loading. In this case, the failure criterion of Mises is considered to be applicable [

As fracturing of rocks differs from that of the joints, the erosion algorithm, which allows several fracture criteria to be predefined in the modelling, is employed to determine the fracturing processes of different materials [

Reasonable boundary conditions are highly correlated with the reliability of the numerical simulation. The boundary might make the stress wave refract or reflect, resulting in unpredictable changes in the propagation of the wave [

In numerical investigations, the mesh size usually influences the accuracy and reliability of calculations remarkably. In this study, the number of cells is up to 16 within one load wavelength, and thus, the waveforms and peak values of all calculated physical quantities tend to be convergent. The unstructured grids are generated using HyperMesh software. The cell size depends on the element size and related density. Mesh smoothing is performed by an automesh smoothing algorithm.

Developed numerical model should be validated with a real blasting case before conducting the numerical experiments. Any inappropriate and irrational inputs must be corrected and improved firstly. Then, the refined numerical model can be utilized to perform the orthogonal experiments if the calculated results are consistent with those of the site.

On the basis of results of the numerical experiments, sensitivity analysis is performed to determine the level of importance of each influential factor. The dominant factors are defined as the sensitive factors that have more significant influences on the quality of smooth blasting. According to practical experiences and previous investigations, in this work, the calculated area and distance of overbreak or underbreak are defined as the observed characteristic parameters representing the blasting quality [

For an observed parameter, the value of range

If the levels of factors are not identical, the value of

The mountainous rock tunnel involved in this investigation is situated in Chongqing of China which served for the Chengdu-Chongqing high-speed railway. The cross section of the rock tunnel is horseshoe-shaped. Excavation radius and height are 7.45 m and 11.08 m, respectively. The length of the tunnel is around 5050 m. The distance between the studied tunnel and the vicinity one is 5 m. The lithology of surrounding rock masses mainly includes Jurassic sandstone, siltstone, and mudstone with highly developed fractures and joints. In this work, the surrounding rocks involved mainly consist of sandstone and silt stone which are also considered as the major water-bearing formations, and relevant properties of rocks are illustrated in Table ^{3}/d. The smooth blasting and benching tunnelling methods are employed to perform the excavation. The geological setting and site conditions of this tunnel are chosen as the inputs of the numerical investigation.

Properties of the rock mass.

Level | Physical-mechanical parameters of the rock mass | ||||||
---|---|---|---|---|---|---|---|

Type | Density (g/cm^{3}) | Internal friction angle (°) | Cohesion (MPa) | Elastic modulus (GPa) | Poisson’s ratio | Joint (set) | |

1 | III | 2.45 | 33 | 0.6 | 10 | 0.28 | 0 |

2 | IV | 2.15 | 15 | 0.05 | 1.2 | 0.4 | 2 |

In this work, the factors influencing the quality of smooth blasting include perimeter hole spacing

Factors and levels for the orthogonal design.

Level | Factors | ||||||
---|---|---|---|---|---|---|---|

Perimeter hole spacing | Least resistance line | Charge concentration | Charging explosive | Type of rock mass | Detonation velocity | Drilling deviation | |

1 | 50 | 55 | 0.93 | 0.15 | III | 3200 | Qualified (1) |

2 | 60 | 60 | 1 | 0.25 | IV | 5200 | Poor (2) |

3 | 70 | 65 | 1.07 | 0.35 | — | — | — |

4 | 80 | 70 | 1.14 | 0.45 | — | — | — |

As the interactions of factors are not taken into account in this study, the numerical experimental arrangement is based on orthogonal table L16 (44 × 23) with 16 investigations, as shown in Table

Orthogonal test design of tunnel blasting quality.

Test no. | Factors | ||||||
---|---|---|---|---|---|---|---|

Perimeter hole spacing | Least resistance line | Charge concentration | Charging explosive | Type of rock mass | Detonation velocity | Drilling deviation | |

1 | 50 | 55 | 0.93 | 0.15 | 1 | 3200 | 1 |

2 | 50 | 60 | 1 | 0.25 | 1 | 5200 | 2 |

3 | 50 | 65 | 1.07 | 0.35 | 2 | 3200 | 2 |

4 | 50 | 70 | 1.14 | 0.45 | 2 | 5200 | 1 |

5 | 60 | 55 | 1 | 0.35 | 2 | 5200 | 1 |

6 | 60 | 60 | 0.93 | 0.45 | 2 | 3200 | 2 |

7 | 60 | 65 | 1.14 | 0.15 | 1 | 5200 | 2 |

8 | 60 | 70 | 1.07 | 0.25 | 1 | 3200 | 1 |

9 | 70 | 55 | 1.07 | 0.45 | 1 | 5200 | 2 |

10 | 70 | 60 | 1.14 | 0.35 | 1 | 3200 | 1 |

11 | 70 | 65 | 0.93 | 0.25 | 2 | 5200 | 1 |

12 | 70 | 70 | 1 | 0.15 | 2 | 3200 | 2 |

13 | 80 | 55 | 1.14 | 0.25 | 2 | 3200 | 2 |

14 | 80 | 60 | 1.07 | 0.15 | 2 | 5200 | 1 |

15 | 80 | 65 | 1 | 0.45 | 1 | 3200 | 1 |

16 | 80 | 70 | 0.93 | 0.35 | 1 | 5200 | 2 |

The material parameters for the HJC model are determined on the basis of previous research [

Properties of rock masses for the HJC model.

Density (g/cm^{3}) | Cohesion (MPa) | Elasticity modulus (GPa) | Poisson’s ratio | |||
---|---|---|---|---|---|---|

2.45/2.15 | 0.6/0.05 | 10/1.2 | 0.28/0.4 | 0.79 | 1.6 | 0.007 |

D1 | D2 | N | T | K1 | K2 | K3 |

0.04 | 1.00 | 0.61 | 3.15E-05 | 0.174 | 0.388 | 0.298 |

Properties of joints for the bilinear kinematic model.

Density (g/cm^{3}) | Elastic modulus (105 MPa) | Poisson’s ratio | Compressive strength (105 MPa) | Shear strength (105 MPa) | Hardening parameter |
---|---|---|---|---|---|

2.4 | 0.45 | 0.27 | 6.00E-03 | 0.177 | 0 |

The parameters of the rock emulsion explosive determining the model of explosive materials and the parameters for the state equation are shown in Table

Parameters used for the high-performance explosive material model.

Density (g/cm^{3}) | Detonation velocity (cm/ | CJ pressure (105 MPa) | _{1} | _{2} | Omeg | |||
---|---|---|---|---|---|---|---|---|

1.3 | 0.4 | 0.106 | 2.144 | 0.00182 | 4.2 | 0.9 | 0.15 | 0.04192 |

Parameters used for the null air material model.

Density (g/cm^{3}) | ||||||||
---|---|---|---|---|---|---|---|---|

1.54 | 0 | 0 | 0 | 0 | 0.4 | 0.4 | 0 | 2.50 |

The dimensions of the numerical model in

The 3D numerical model for tunnel smooth blasting. (a) The calculation domain. (b) Three types of elements.

For the joints with an inclination of 0°, the fracture surface is symmetrically distributed on both sides [

Schematic of the joints.

The process of formation of smooth blasting is shown in Figure

Process of smooth blasting. (a) 33

In general, the geometry of the tunnel sidewall and roof after blasting is in line with expectations. Although the tunnel contour has a continuous even surface, most overbreaks do exist at the sidewall and roof, whereas the underbreaks commonly occur at the bottom. The developed model has been validated by a real blasting case in this tunnel to improve the accuracy of the investigation. The actual contour of the real blasting case conducted on-site was measured using a tunnel profilometer. By comparing the measured data with the calculated results from numerical modelling, both positions and dimensions of the over-/underbreaks obtained on-site were consistent well with the numerical modelling results, as shown in Figure

Validation of numerical modelling with the site data.

The actual dimensions of the cross section after blasting were calculated to quantitatively determine the quality of smooth blasting in this investigation. The cross section with a distance of 1.8 m from the initial tunnel face before blasting is selected to estimate the blasting quality characterized by area and the maximum value of distance of the over-/underbreak. For quantitative evaluation of the aforementioned parameters associated with the quality of smooth blasting, the area of the designed cross section is predefined at 145.1 m^{2}, considering the acceptable deformation of the surrounding rock mass which is predefined as 20 cm. Then, the coordinates of the actual contour after blasting can be obtained from the numerical model and thus be compared with those of the designed contour, as shown in Figure

The actual tunnel contour after blasting (based on the 15th test in the orthogonal table).

Calculated results.

Test no. | Cross-section area (m^{2}) | Underbreak area (m^{2}) | Overbreak area (m^{2}) | Maximum distance of overbreak (m) | Maximum distance of underbreak (m) |
---|---|---|---|---|---|

1 | 154.29 | 0.78 | 9.97 | 1.1 | 0.53 |

2 | 158.45 | 0.57 | 13.92 | 0.86 | 0.38 |

3 | 148.32 | 3.9 | 7.12 | 1.18 | 0.56 |

4 | 154.55 | 1.63 | 11.08 | 0.85 | 0.34 |

5 | 147.4 | 2.04 | 4.34 | 0.42 | 0.54 |

6 | 145 | 2.71 | 2.61 | 0.43 | 0.52 |

7 | 153.77 | 0.94 | 9.61 | 0.99 | 0.53 |

8 | 165.94 | 0.11 | 20.95 | 1.17 | 0.26 |

9 | 163.79 | 0.02 | 18.71 | 0.84 | 0.13 |

10 | 167.48 | 0.00 | 22.38 | 0.97 | 0.00 |

11 | 152.46 | 0.15 | 7.51 | 0.43 | 0.23 |

12 | 152.18 | 0.27 | 7.35 | 0.48 | 0.25 |

13 | 151.81 | 0.44 | 7.15 | 0.46 | 0.44 |

14 | 151.76 | 0.39 | 7.05 | 0.82 | 0.42 |

15 | 166.69 | 0.00 | 21.59 | 0.91 | 0.00 |

16 | 163.89 | 0.01 | 18.8 | 0.96 | 0.04 |

For the area of the cross section after blasting under influential factors with various levels, it can be seen that the maximum value is up to 167.48 m^{2}, which occurs under the conditions of the 10th test, whereas the minimum value is 145 m^{2} that is observed under the conditions of the 6th test, as shown in Figure ^{2}, which is also observed under the conditions of the 10th test, while the minimum overbreak area is 2.61 m^{2}, which still occurs under the conditions of the 6th test. Meanwhile, for the area of underbreak, the maximum value is 2.74 m^{2} that occurs under the conditions of the 6th test. However, there is no underbreak observed in 10th and 15th tests.

Calculated areas of the cross section and over-/underbreak.

Deviations of the actual contours can also be estimated by comparative calculation. For each test, the maximum value of the deviations of over-/underbreak on different points of the actual contour was defined as the distance of over-underbreaks under corresponding test conditions. For the distance of overbreak, the maximum and minimum values of 1.18 m and 0.42 m are found in the 3rd test and 5th test, respectively, as illustrated in Figure

Calculated distance of over-/underbreak.

The dominant factors usually determine the advancement rate and development of things. Whether a factor becomes a dominant factor depends on its effect level on the thing. The level of importance of each factor affecting the quality of smooth blasting relies on the properties of the factor and its level. Quantitative determination of the effect of every factor is more reliable and applicable than the conventional qualitative estimations. On the basis of results obtained via numerical investigation, the sensitivity of each influential factor can be determined by range analysis derived from the orthogonal experiments. In this work, the area and distance of over-/underbreak are predefined as the observed parameters that represent the quality of smooth blasting. The sensitivities of the factors including peripheral hole spacing

Regarding the area of overbreak, the results of range analysis are given in Table

Range analysis for the overbreak area.

Factor | |||||||
---|---|---|---|---|---|---|---|

10.52 | 10.04 | 9.72 | 8.50 | 16.99 | 12.39 | 13.11 | |

9.38 | 11.49 | 11.80 | 12.38 | 6.78 | 11.38 | 10.66 | |

13.99 | 11.46 | 13.46 | 13.16 | ||||

13.65 | 14.55 | 12.56 | 13.50 | ||||

_{j} | 4.61 | 4.50 | 3.74 | 5.00 | 10.22 | 1.01 | 2.45 |

4.149 | 4.05 | 3.366 | 4.5 | 20.524 | 2.028 | 4.92 |

Overbreak area under various levels.

For the area of underbreak, the results of range analysis are shown in Table

Range analysis for the underbreak area.

Factor | |||||||
---|---|---|---|---|---|---|---|

1.72 | 0.82 | 0.91 | 0.60 | 0.30 | 1.03 | 0.64 | |

1.45 | 0.92 | 0.72 | 0.32 | 1.44 | 0.72 | 1.11 | |

0.11 | 1.25 | 1.11 | 1.49 | ||||

0.21 | 0.51 | 0.75 | 1.09 | ||||

_{j} | 1.61 | 0.74 | 0.39 | 1.17 | 1.14 | 0.31 | 0.47 |

1.449 | 0.666 | 0.351 | 1.053 | 2.289 | 0.623 | 0.944 |

Underbreak area under various levels.

Regarding the distances of over-/underbreak, the range analysis results are given in Tables

Range analysis for the distance of overbreak.

Factor | |||||||
---|---|---|---|---|---|---|---|

0.998 | 0.705 | 0.730 | 0.848 | 0.975 | 0.838 | 0.834 | |

0.753 | 0.770 | 0.668 | 0.730 | 0.634 | 0.771 | 0.775 | |

0.680 | 0.878 | 1.003 | 0.883 | ||||

0.788 | 0.865 | 0.818 | 0.758 | ||||

_{j} | 0.318 | 0.173 | 0.335 | 0.153 | 0.341 | 0.066 | 0.059 |

0.286 | 0.156 | 0.302 | 0.138 | 0.685 | 0.133 | 0.118 |

Range analysis for the distance of underbreak.

Factor | |||||||
---|---|---|---|---|---|---|---|

0.453 | 0.410 | 0.330 | 0.433 | 0.234 | 0.320 | 0.290 | |

0.463 | 0.330 | 0.293 | 0.328 | 0.413 | 0.326 | 0.356 | |

0.153 | 0.330 | 0.343 | 0.285 | ||||

0.225 | 0.223 | 0.328 | 0.248 | ||||

_{j} | 0.238 | 0.188 | 0.050 | 0.185 | 0.179 | 0.006 | 0.066 |

0.214 | 0.169 | 0.045 | 0.167 | 0.359 | 0.012 | 0.133 |

Distance of overbreak under various levels.

Distance of underbreak under various levels.

In general, the numerical investigation indicated that overbreak caused by smooth blasting is much greater than underbreak. In view of this, the overbreak caused by blasting should be paid special attention in practical applications owing to it correlates closely to the cost and safety of tunnelling. Based on the sensitivity results, the type of rock mass has the greatest influence on both overbreak and underbreak. This reminds us that the properties of surrounding rock masses should be focused firstly. Accordingly, the determination of parameters of smooth blasting considerably depends on the rock masses. For estimation of both overbreak and underbreak, the effects caused by the charging concentration and detonation velocity are very limited. If the area/volume of overbreak is defined as the observed parameter representing the blasting quality, the dominant factors can be determined in the descending order as the type of rock mass, drilling deviation, charge explosive, perimeter hole spacing, and least resistance line. In blasting design, values of dominant factors should be close to their optimal levels. The charge concentration and detonation velocity, however, can be considered as the secondary parameters for smooth blasting. The values of secondary factors could be flexibly defined in consideration of both cost and construction rate.

In order to quantitatively understand the effects of influential factors that affect the quality of smooth blasting, specifically the damage of the surrounding rock mass, a numerical investigation is conducted in this work. Instead of costly and time-consuming field/laboratory physical tests, the arrangement of numerical experiments performed by LS-DYNA 3D is optimized by the orthogonal design to improve the efficiency of the numerical investigation. Considering the fracturing of rocks differs from that of the joints, the effect of pre-existing fractures and joints on rock responses under blasting should be paid special attentions. Moreover, the influences of brittle nature of rock materials on the dynamic behavior of rocks should be emphasized in determination of values of parameters of the HJC model. The range analysis is employed to determine the sensitivity of the factors involved. The area and distance of overbreak are defined as the indicators that represent the quality of smooth blasting. Results indicate that the shape of the tunnel contour is of regularity, and under-/overbreak is inevitably caused. Under the same conditions, the magnitude of overbreak is much greater than that of underbreak. This is consistent with the conservative design concept of practical applications. The type of rock mass, as the most important factor, greatly influences both overbreak and underbreak, and thus, it deserves the most attention to be paid in the blasting design. On the other hand, it is found that charge concentration and detonation velocity have little effect on the overbreak, which can be considered as the secondary factors for smooth blasting. For the improvement of parameter design of smooth blasting, therefore, the values of dominant factors including the type of rock mass, drilling deviation, charge explosive, perimeter hole spacing, and least resistance line should be predetermined at their optimal levels, and for the secondary factors including charge concentration and detonation velocity, the values can be determined flexibly based on both the cost and operation conveniences. In practice, the lower the magnitude of over-/underbreak, the better the quality of smooth blasting. With the specific geological conditions of this case, the optimum level of charging explosive is 0.15 kg/m, for perimeter hole spacing is 60 cm, and for least resistance line is 55 cm.

The cost-efficient numerical investigation method offers a promising alternative to well understand the influential factors that affect the quality of smooth blasting. Due to the complexity and uncertainties of geological conditions, the results obtained might vary with the specific site conditions. However, this work presents an efficient approach to quantitatively investigate the influential factors of smooth blasting, and it is believed to be beneficial for the optimization of parameter design of smooth blasting.

The data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The financial support for this research project by the National Natural Science Foundation of China (nos. 41602308 and 41572299), the Zhejiang Provincial Natural Science Foundation of China under (no. LY20E080005), the Zhejiang Science and Technology Project (no. 2016C33033), and the Foundation of China Railway No.2 Engineering Group Co., Ltd. (no. 201218) was gratefully acknowledged.