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Blasting excavation of a bedding rock slope is a common problem in highway construction in mountainous areas. Accurate simulation of damage area caused by blasting excavation is of great significance for the subsequent maintenance of slopes. Based on a highway construction project in Guangdong province of China, a tensile and compressive damage model was used to simulate the whole process of blasting excavation of a typical bedding rock slope. The analysis results show that damage first appears just around the blasting hole and then develops to the both sides and the bottom of the blasting hole, and finally a large range of damage appears in the lower part of the blasting hole, and the damage depth on the right-side slope is around 2 m, which is in consistent with the scene. Besides, damage also occurs in the middle of the bedding rock mass of the slope. At the same time, the history analysis of vibration velocity also indicates that tensile failure appears on the right-side slope under the blasting hole. Therefore, the stability of the slope can be assessed by analyzing the distribution of damage factors and the vibration velocity characteristics synthetically. In addition, parameter analysis was also carried out to optimize the blasting design by controlling the blasting load so as to obtain the ideal blasting excavation effect and ensure the stability of the slope under blasting load.

During the construction of highways, it is inevitable to encounter various complicated geological conditions, such as the excavation of rocky high slopes. Compared with the soil slope, the strength of the rock slope is greater and the excavation is more difficult, so blasting excavation is often required. In the dynamic response analysis of blasting excavation of the slope, there are many influencing factors: the characteristic parameters of rock, blasting, and groundwater, in which blasting is a transient process of high temperature, high pressure, and high speed, which is different from the general load. At present, the research on the stability of the high cut slope mainly focuses on the long-term safety and stability of the rock slope caused by unloading after the excavation of the rock mass [

In this paper, three-dimensional numerical analysis of the blasting excavation process of a bedding rock slope was carried out by using a tensile and compressive damage plastic model. The damage occurrence and development rules of rock mass in the blasting process of the rock slope and the diffusion characteristics of blasting vibration velocity in rock mass were studied. Then, the blasting excavation effect and the stability of the rock slope were judged according to the distribution of blasting damage area and vibration velocity. Furthermore, through the parameter analysis, the design parameters of blasting excavation were optimized to ensure the blasting excavation effect and the overall stability of the rock slope.

The development of a rock mass blasting model can be divided into three stages: elastic stage, fracture stage, and damage stage. The damage model simulates the damage and failure process of rock mass under blasting load through damage variables and gradually becomes an important model to study the damage characteristics of rock during blasting excavation [

Stress and strain curves (a) uniaxial tensile rock mass and (b) uniaxial compression rock mass.

Under uniaxial tension, the stress-strain response follows the linear elastic relationship until the value of the failure stress

It is assumed that the uniaxial stress-strain curve can be transformed into a relationship between stress and plastic strain. Therefore,

When the specimen is unloaded from the softening section of the stress-strain relation curve, the unloading section is weakened (the slope of the curve decreases), as shown in Figure

The damage factor ranges from 0 (for nondestructive materials) to 1 (for completely damaged materials).

If _{0} is the initial (nondestructive) elastic stiffness of the material, the stress-strain relationship under uniaxial tension and compressive loads is

The “effective” tensile and “effective” compressive stress are

The effective stress determines the size of the yield (or failure) surface.

The damaged plasticity model assumes that the reduction of the elastic modulus is given in terms of a scalar degradation variable

The stiffness degradation variable,

In this paper, a bedding rock slope under construction is studied, which is located beside a highway in northern Boluo County, Guangdong Province of China. The studied slope is located in the hilly area, and the terrain is rugged. The slope elevation is about 122∼202 m, and the natural slope angle is about 30°. The slope has been excavated to 5th grade and 6th grade, and the outcrop is medium to microweathered granite. The cross section of the slope is shown in Figure

Distribution of slope strata. (1) Silty clay, (2) fully weathered granite, (3) strongly weathered granite, (4) moderately weathered granite, and (5) microweathered granite.

The slope was excavated by explosive blasting in the construction process. According to the site construction, blasting vibration expanded the crack surface near the location of slope blasting so that the crack surface was penetrated and the rock mass collapsed along the sloping structural surface. The collapse ranged from the 5th grade slope to the platform. The partial failure of the platform was 0.5 m wide, about 60 m in length, and the depth was about 2 m. The partial collapse location of the slope is shown in Figure

Local collapse of the slope caused by blasting excavation. (a) Sliding surface. (b) Collapse on-site.

Blasting excavation will cause inevitable damage to the slope, which may cause certain hidden danger to the slope in the future. How to precisely control the damaged area of the blasting slope is an urgent problem to be solved in the current blasting excavation, which is of great significance for the slope reinforcement and the landslide prediction. With the development of computer, numerical calculation has become an effective tool for blasting excavation research [

In this paper, the blasting excavation process of the bedding rock slope introduced in Section

Finite element model of the bedding rock slope (different rocks in different colors).

The Mohr–Coulomb model is used to simulate the silty clay layer, and the tensile and compressive damage plastic model is used to simulate the strongly weathered granite, moderately weathered granite, and lightly weathered granite.

Laboratory tests of granite with plastic damage were conducted to provide material parameters for the finite element models, as listed in Table

Parameters of the rock-soil model.

Rock and soil type | Unit weight (kN/m^{3}) |
Cohesion (kPa) | Internal friction angle (°) | Compressive strength (MPa) | Tensile strength (MPa) | Poisson’s ratio | Damping ratio |
---|---|---|---|---|---|---|---|

Silty clay | 18.0 | 19 | 18 | — | — | 0.3 | 0.03 |

Strongly weathered granite | 21.0 | 31 | 32 | 10.95 | 0.32 | 0.28 | 0.03 |

Moderately weathered granite | 22.0 | 34 | 34 | 15.19 | 1.07 | 0.25 | 0.03 |

Microweathered granite | 22.5 | 37 | 35 | 16.50 | 3.56 | 0.21 | 0.03 |

Due to the reflection and scattering effects of waves, the mesh boundary may reflect energy to the simulation region, which will affect the calculation results. Therefore, boundary conditions should be taken into account when solving a dynamic problem. In order to reduce the reflection of boundary on the wave, infinite elements are set on the left side, the right side, and the bottom surface to simulate the semiinfinite space of rock and soil mass, as shown in Figure

The mesh size directly affects the accuracy and convergence of the whole model. According to the properties of rock mass, if Poisson’s ratio is neglected, the wave velocity can be estimated as

Numerical simulation shows that the span of the blasting load is relatively appropriate within 10 units of finite element because the duration of load is 0.007 s, so the length of wave propagation after the blasting load is _{d} ×

The blasting site is located on the slope of the fifth grade, passing through three rock layers from top to bottom, namely, highly weathered granite, moderately weathered granite, and microweathered granite. The location of the blasting hole is shown in Figure

Position of the blasting hole.

The blasting load is mainly caused by the gas expansion pressure generated by the explosion. If the coupled charge condition is adopted, the wall pressure of the blasting hole is

If the uncoupled charge condition is adopted, the wall pressure of the blasting hole is^{3});

Since the explosive blasting is a complex instantaneous process, in order to facilitate the analysis, the blasting load is simplified as follows: the time history curve of the blasting load is simplified as a triangle, that is, the load rises linearly to the highest load in the first 1 ms before unloading, and then the linear drop of the pressure lasts 6 ms [

In this paper, the numerical analysis of the corresponding field for coupling charging conditions of the blasting scheme is performed. According to field data, the diameter of the blasting hole is 80 mm, the inclination angle of the drilling hole is 40°, the hole spacing is 2.0 m, the detonation velocity is 3600 m/s, and the explosive density is 1000

Time history diagram of equivalent load (with a peak value of 1620 MPa).

The distribution and development law of damage factors in rock mass under blasting load was analyzed, as well as the diffusion characteristics of rock mass vibration velocity. The blasting mechanism of the rock mass slope and the influence of blasting excavation on the stability of the rock mass slope were analyzed and discussed in combination with the practical project corresponding to the numerical model.

According to the numerical simulation of the blasting process, the change and development process of damage factors of the slope rock mass during the blasting process can be obtained. The distribution of damage factors of the slope rock mass at different times is shown in Figure

Time history contours of the slope damage factors after blasting at (a) 1 ms, (b) 3 ms, (c) 5 ms, and (d) 7 ms.

According to the numerical analysis of the damage evolution of the rock mass in the blasting process, it can be seen that the blasting excavation in the bedding slope will cause damage to the weathered granite, and the damage in the lower part of the blasting hole will be serious, causing the crack between rock layers to expand and cause the collapse. The results of the numerical analysis are in good agreement with the on-site postblasting condition of the actual slope.

The study of Bauer and Calder [_{pp}) and the rock damage effect.

Rock damage effect under different _{PP} [

_{PP} (m/s) |
Rock mass damage effect |
---|---|

(0, 0.25) | Complete rock will not crack |

(0.25, 0.635) | Slight tensile cracking |

(0.635, 2.54) | Severe tensile cracks and some radial cracks |

(2.54, +∞) | The rock mass is completely broken |

In this paper, the time history of vibration velocity of the slope after blasting is numerically analyzed. Figure

Time history contours of slope vibration velocity after blasting at (a) 1 ms, (b) 1.5 ms, (c) 2 ms, (d) 3 ms, and (e) 7 ms.

Based on the damage evolution of rock mass and the characteristics of blasting velocity transmission and distribution under blasting load, it can be seen that under the action of blasting vibration, in addition to the blasting excavation effect, blasting damage and vibration velocity of slope rock mass will also develop towards the deep slope. If the rock mass slope itself has a crack surface, the cracks caused by the blasting damage will disturb and increase the existing crack surface and eventually cause the crack surface to be penetrated and the rock mass to collapse along the downdip structure surface.

From the above analysis, it can be seen that blasting excavation under coupled charging condition disturbs the existing crack surface of slope rock mass due to blasting vibration, which makes the crack surface to pass through the whole rock mass, together with the damage of rock mass itself, and eventually leads to slope collapse. In this section, according to blasting theory and equations (

Under the condition of uncoupled charge, the charge diameter is 70 mm, and the other conditions are the same as the coupled charge conditions. According to equation (

Contours of blasting vibration velocity at 2 ms under different charging conditions. Blasting load: (a) 1620 MPa and (b) 727.1 MPa.

As shown in Figure

It can be seen that changing the charging condition can significantly reduce the blasting load. Although the right-side slope is not affected, the left-side slope cannot achieve an ideal blasting effect (the vibration velocity of the left-side slope reaches 0.635 m/s or more). Therefore, changing the charging conditions is not recommended.

If charging conditions remain the same, changing the density of explosive results in slight reduction in the blasting load, that is, if the density of explosive is changed from 1000

Contours of vibration velocity of 2 ms blasting under different explosive densities. Blasting load: (a) 1620 MPa and (b) 1296 MPa.

In order to investigate the relationship between the magnitudes of blasting load and the maximum vibration velocity, models with different blasting loads are calculated. Figure

Maximum vibration velocity at 1 ms under different blasting loads.

Maximum vibration velocity attenuation under different blasting loads within 1∼3 ms.

In this paper, the whole process of a typical rock slope blasting excavation is simulated by using a plastic model of tensile and compressive damage, and the slope stability is assessed by analyzing the damage factors and vibration velocity characteristics synthetically. The main conclusions of this study are as follows:

According to the numerical simulation results of this typical rock slope, when the blasting load is 1620 MPa, the degree of slope damage increases with time, and a broken zone will form around the blasting hole. The moderately weathered granite in the bedding strata will be damaged, and the damage factor is between 0.8 and 0.9, indicating that the moderately weathered granite is more likely to be damaged.

The influence range of blasting can be obtained by analyzing the diffusion characteristics of vibration velocity. According to the time history analysis of vibration velocity, the rock mass on the right side of the slope will suffer from tensile fracture.

Blasting load can greatly be reduced by changing the charging conditions, but changing the explosive density can only slightly reduce the blasting load. When the charging condition is reduced from 1620 MPa to 727.1 MPa, the blasting effect of the left-side slope is not ideal, although the right-side slope will not collapse. By changing the explosive density and setting the blasting load to 1296 MPa, the right-side slope is relatively safe, and an ideal blasting effect is formed on the left-side slope.

The maximum vibration velocity increases linearly with the increase of blasting load, but the attenuation rate is almost unaffected by the magnitude of blasting load. Therefore, when high-intensity explosives are applied in engineering, the vibration will have a long-term influence on the slope.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

The research was supported by the Natural Science Foundation of Guangdong Province (no. 2018A0303130150) and Science and Technology Project of Zhejinag Provincial Department of Transportation (no. 2014H27).