Stability Analysis of Blasting Excavation for High Rock Slope of Highway Reconstruction and Expansion

To analyze the stability of high rock slopes under millisecond blasting in the paper, time-history curves of millisecond blasting dynamic loads are established based on eld data from the reconstruction and extension project of the Beijing-Shanghai Highway. Numerical simulations and eld monitoring data are used to study the dynamic response characteristics of the slope stress, displacement, velocity, and safety factor at dierent times. e results show that the local shear stress near the blasting area is greater than the shear strength of the rockmass, which has a good eect on precracking. Additionally, the peak vibration law of the particles near the blasting area is found to change synchronously with the application of the dynamic blast load; as the distance increases, the law gradually weakens and peak vibration occurs only near the maximum value. Moreover, the safety factor of the slope exhibits a decreasing periodic variation. When the dynamic blast load F reaches the maximum load Fmax and 0.6 Fmax, the corresponding safety factor reaches the minimum load.


Introduction
With the increasing tra c ow in China, the existing highway lanes di cultly meet the actual societal needs, and the number of highway reconstruction and expansion projects is sharply increasing [1][2][3][4]. Consequently, the stability problems of the secondary excavation of existing slopes during the reconstruction and expansion process have become popular research topics. e reconstruction and extension construction without tra c interruption is a big feature of expressway reconstruction and extension projects. In order to speed up the construction progress, blasting excavation has become an important means of slope excavation. e determination of blasting dynamic load is the key to the research. Henrych and Chen [5,6] believed that the blasting dynamic load was a triangular pulse function and set the blasting time to 7 ms. ey considered a linear change with a shorter rise time and a longer fall time. Sitnikova [7] believed that the blasting dynamic load rst increased linearly within a period of time and then began to decay exponentially. Aksoylar and Balkan [8,9] believed that the blasting dynamic load was a changing nonlinear function relationship.
Jiang [10] simulated the change of blasting dynamic load by changing the stress-strain relationship. Liu and Wang proposed e ective models for calculation of the equivalent uniform blast load for non-uniform blast load using the equivalent singledegree-of-freedom (SDOF) approach [11,12].
After determining the blasting dynamic load, the study of blasting stability has become the focus of research. Dowding and Zhang [13,14] used numerical simulation software to study the energy distribution characteristics and waveform response characteristics of each frequency band of the slope under blast loads. Kesimal [15] studied the e ect of blast acceleration on slope shear failure via on-site blast monitoring, laboratory test evaluations, and the limit equilibrium method and considered that uncontrolled blast acceleration and heavy rainfall have greater impacts on slope shear failure. Hu and Ren [16,17] used ANSYS software to study the dynamic response characteristics of the secondary excavation of slopes under blast loads and predicted the entire process of slope damage.
Some scholars have also studied millisecond blasting. Millisecond blasting is a blasting method in which blasts are made in a certain order at a time interval of milliseconds between blastholes and rows or within blastholes [18,19]. Blair [20][21][22][23] studied the vibration e ect of millisecond blasting, based on which a nonlinear superposition model of single-hole blasting and a linear superposition model of porous microblasting were proposed via the analysis of experimental data. Chen and Liu [24,25] analyzed the e ect of the millisecond blasting of a cylindrical charge structure on the slope vibration e ect via vibration velocity waveform function prediction. Mandal [26] studied the calculation method of the vibration velocities of di erent measurement points under the condition of a single-hole cylindrical charge with a millisecond blasting time interval of 1 ms. Kalinski [27] used numerical simulation to study the e ects of the hole distance, blasting direction, and millisecond blasting time interval on the vibration e ect of porous millisecond blasting. Yang [28] studied the main crack propagation characteristics of millisecond blasting under respective time-delay conditions of 20 μs and 40 μs and compared the di erences in the shape and process of the failures of the specimen under the two conditions.
Based on the blasting project on the left side of section K551 + 714∼K552 + 116 of the reconstruction project of the Beijing-Shanghai Expressway, numerical simulation software was utilized in the present study to establish a dynamic load time-history curve between blastholes under di erential blasting. e mechanism of millisecond blasting is proven via the slope shear stress, displacement, and velocity of di erent measurement points, and the distribution law of the safety factor.

Engineering Background.
e slope was originally constructed by mechanical crushing, and the remaining rstgrade platform and some second-grade platform were not excavated. Millisecond blasting was employed to speed up the progress of the project. e dotted lines in Figure 1 indicate the blasting area; its east-west length is 300 m, the subgrade is 15 m wide from north to south, the top of the blasting step is 14 m, the average height is 9 m, and the slope height is 39.7 m. e main lithologies of the slope are strongly and moderately weathered limestone as shown in Figure 2.

Blasting Parameters.
e parameters of this blasting are selected as shown in Table 1. e layouts of the blasthole charge and the blasthole depth are, respectively, illustrated in

Determination of Equivalent Dynamic Blast Load.
Determining a reasonable dynamic blast load is the key to the accurate calculation of numerical simulation, but there exists no systematic and perfect theoretical method by which the dynamic blast load could be determined at present. In this paper, via the use of the stress time-history analysis, the dynamic blast load is considered to be equivalent to a uniformly distributed concentrated force acting on the normal direction of the blasthole wall. Because the blasthole diameter is greater than the charge diameter, it is an uncoupled charge. According to the Chapman-Jouguet theory of the detonation waves of condensed explosives [29], the calculation formula of the blasthole wall pressure P b is modi ed by where P b is the blasthole wall pressure (Pa), ρ 0 is the explosive density and is equal to 1300 kg/m 3 , Dis the blasting velocity and is equal to 3600 m/s, k is the isentropic index and is equal to 3, d e is the charge diameter and is equal to 70 mm, and d h is the blasthole diameter and is equal to 90 mm. e time-history curve of the equivalent dynamic blast load is determined according to (2) proposed by National Highway Institute in the United States [30], and other parameters are calculated according to the work by Zou [31].
where P(t) is the equivalent dynamic blast load (Pa), B is the blast load constant, T r is the rising time of the dynamic blast load (ms), and L 1 is the charge length and is equal to 7.5 m.
e following values are yielded after calculation: P b 466.2 MPa, B 470, and T r 2.083 × 10 − 3 s.
During numerical simulation modeling, the applied dynamic blast load is converted to the nodal force acting on the element, which is calculated by where r is the distance between two vertical nodes of the blasthole in the model and is equal to 1 m and F is the dynamic blast load applied to the actual model (MPa). Figure 5 presents the equivalent dynamic blast load timehistory curve when the blasting time is set as 50 ms, the in uence of the blasthole distance is a, and the proportionality factor is set to 1/a during modeling.
By derivation of (5), the corresponding time at the peak value is determined to be t 2.086 × 10 − 3 s, which is consistent with the calculation in (4). By substituting it back into (5), the corresponding maximum dynamic load is determined to be F(2.086 × 10 − 3 ) 10.33 Mpa.
According to the situation of the site, the connection mode between blastholes is an Ms-4 connection. According to State Administration of Work Safety [32], the time interval of the

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Ms-4 connection is 75 ms (+15, −10). Because the load is converted into a nodal dynamic force and acts on the wall of the blasthole, it is considered that the interior of the blasthole is simultaneously blasted, and the time interval between blastholes was set to 75 ms in the numerical simulation calculation, that is, 75 ms for the 1st blasted, 150 ms for the 2nd blasted, 225 ms for the 3rd blasted, and 300 ms for the 4th blasted.

Mechanical Parameters and Boundary Conditions.
e surrounding rock was calculated by the Drucker-Prager yield criterion [33]. is strength theory reflects the influences of volumetric stress, shear stress, and intermediate principal stress on the rock strength and can reflect the reality better than other strength theories. e assumptions obtained by this model are sufficiently reliable for general nonlinear geotechnical analysis, so they are widely used to simulate geotechnical materials. According to the geological prospecting data, the rock mass in the blasting area is divided into four parts, and the material mechanical parameters of the calculation model are reported in Table 2.
When performing dynamic blast analysis, the influence of the reflected stress wave on the boundary surface must be considered. In this work, the viscous boundary condition proposed by Lysmer and Wass is used to absorb the incident wave on the boundary and to reduce its influence on the numerical simulation results [34].

Model Building.
e left slope of section K551 + 714-K552 + 116 was considered as a prototype, and a row of blastholes was selected for research. MIDAS-GTS software was used to build the 2D model. e slope rate was 1 : 0.75, the slope height was 39.7 m, the step height was 10 m, the platform width was 2 m, the total model length was 176 m, the height was 82.7 m, the slope to the right boundary was 60.6 m, and the top of the slope to the left boundary was 80.2 m. e model grid was divided into 4197 units, as presented in Figure 6, and the corresponding stratum distribution map is exhibited in Figure 7.

Analysis of Calculation Results
In software, the nonlinear time-history + SRM module is a nonlinear dynamic analysis. e stress state of the rock and soil corresponding to this time point can be obtained by inputting the time in the nonlinear time-history analysis.
is numerical simulation mainly studies the stability of the blasting area and its surrounding environment and investigates the stress field, displacement field, and velocity field at different positions in the blasting area and the safety factor of the slope at different times. e specific analysis is as follows.

Stress Field Analysis at Different Blasting Periods.
It can be seen from Figure 8 that after the first to fourth blastholes were blasted, a large shear stress appeared on the first-grade slope, and the maximum values were 1.54 MPa, 3.11 MPa, 3.25 MPa, and 2.05 MPa, respectively. roughout the blasting process, due to the blast load, a concentrated area of shear stress appeared in the first-grade slope, which is in line with the actual situation. Moreover, a phenomenon of shear stress concentration on the second-and third-grade slopes also occurred. At this time, the shear stresses were 1.24 MPa and 0.58 MPa, respectively; while these did not cause slope instability in the model, attention should be paid to these slopes during actual construction.
Based on the preceding analysis, and according to the stress variation trend, the shear stress nephograms of the slope at each time point within 75 ms after the third blasthole was blasted are presented in Figure 9.
It can be seen from Figure 9 that, during the blasting period of the third blasthole, the stress range of the slope gradually expanded, and the maximum shear stress first increased and then decreased. At 170 ms, near the blasting area, the shear stress reached the peak value of 4.21 MPa, which is slightly larger than the shear strength of the rock mass. is demonstrates that the rock mass in the blasting area experienced local shear failure, and a good precracking effect was obtained during the blasting process of the slope. With the gradual diffusion of the stress field, the shear stress at the toes of the second-grade and third-grade slopes increased slightly, reaching respective maximum values of 2.11 MPa and 1.90 MPa at 200 ms, while the shear stress change of the fourth-grade slope was small with a value of approximately 0.17 MPa.
During the entire blasting process, the four blastholes were blasted in sequence, and the shear stress first increased and then decreased due to the influence of the distance. e former blasthole caused local cracks to form in the rock mass, thereby creating a precracking condition for the later blasthole, and the generation of local cracks slowed the diffusion of stress in the rock mass and promoted the accumulation and superposition of stress. e existence of local cracks will also make the stress waves refract and reflect at the cracks, reduce the disturbance of the load, and play a good role in shock absorption, which is beneficial to the later excavation of the slope.

Analysis of Displacement Field in Different Time Periods.
It can be seen from Figure 10 that after the first blasthole was blasted at 75 ms, the maximum displacement at the top of the first-grade slope was 3.59 mm, and there was no obvious displacement change at other positions.
ereafter, the range of the plastic area of the slope continued to expand. After the third blasthole was blasted at 225 ms, the displacement value at the top of the first-grade slope was 12.55 mm, and the second-, third-, and fourth-grade slopes began to show significant displacement changes with values of 2.92 mm, 2.77 mm, and 2.52 mm, respectively. After the fourth blasthole was blasted, due to its small length, the charge was reduced as compared to the previous three holes, which led to the slower expansion of the plastic zone. At 300 ms, the displacement at the top of the first-grade slope was 16.25 mm, and the displacements at the top of the second-, third-, and fourth-grade slopes were 4.13 mm, 3.89 mm, and 3.85 mm, respectively.

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To study the regional stability of the millisecond blasting of the slope, the displacement nephograms within 75 ms after the fourth blasthole was blasted are shown in Figure 11.
It can be seen from Figure 11 that, during the period when the fourth blasthole was blasted, the overall displacement increment of the slope first increased and then decreased. At 255 ms, the maximum displacement was 19.27 mm at the top of the unexcavated slope, and the displacements at the tops of the second-, third-, and fourthgrade slopes were 5.88 mm, 5.44 mm, and 4.91 mm, respectively. After that, the displacement increment gradually decreased due to the disturbance of the rock mass and the decrease of the blast load. Before and after construction, four measurement points were arranged at the top of the slope, the third platform, and the secondary platform, and the layout of the measurement points is depicted in Figure 12.
e displacement changes of each measurement point before and after blasting are reported in Table 3.
According to the on-site measurement data as shown in Table 3, it can be judged that the measured slope displacement before and after blasting was smaller than that of each point during the blasting process. is is because the  Advances in Civil Engineering dynamic blast load disappeared, the stress in the rock was redistributed, and the slope gradually tended to be stable. e average displacement of each measuring point of the secondary platform, tertiary platform, and slope top is 1.8 mm, 1.525 mm, and 1.025 mm, and the displacement value decreases step by step, which is similar to the result of numerical simulation.
is demonstrates that there is a collision process between two adjacent blastholes in the process of crushing during millisecond blasting, which makes the distance between the crushed rock and soil relatively close and plays a weak precracking role but does not produce a large slip. Figures 13(a)-13(c) present the time-history curves of vibration velocity at different measurement points of the slope. Due to the short distance from the slope, the change of the vibration velocity at each measurement point of the slope foot exhibited obvious synchronization with the load time-   Advances in Civil Engineering history curve. Additionally, in each time period after the dynamic blast load was applied, obvious uctuation peaks appeared. With the increase of the distance, due to the lag e ect of the blast load, the vibration velocity at the four measurement points at the top of the slope started to increase sharply at 130 ms, and peak uctuations occurred only after the fourth blasthole was blasted. e change rule at the toe of the second-, third-, and fourthgrade slopes is between those at the top and bottom of the slope. e peak vibration velocity of each measurement point decreased with the increase of the distance from the center of the explosion. e peak velocity of the slope foot was the largest, that of the slope surface was the second largest, and that of the slope top was the smallest, which is consistent with the actual situation.

Velocity Field Analysis at Different Periods.
In addition, the maximum peak velocity at 80 m at the top of the slope was 1.8 cm/s, which is less than the safe peak value of 2.5 cm/s speci ed in the Blasting Safety Regulations, indicating that the use of millisecond blasting has a lesser impact outside the blasting area and meets the safety requirements. According to Huang [35], the velocity of each measurement point was less than 26 cm/s. Tensile cracks may appear locally on the slope rock mass, but these do not pose a hazard to the safety of the slope. According to the on-site investigation, there were local tension cracks on the rst-grade slope (as depicted in Figure 14), but no obvious displacement changes occurred, which is in line with the actual on-site construction situation.

Analysis of Safety Factors in Di erent Time Periods.
Before blasting, the static SRM method was used to analyze the safety factor. e nonlinear time-history added SRM method was then used to analyze the safety factors at each time point of slope blasting excavation. Figures 15  and 16 present the changes in the safety factor at di erent points in time.
It can be seen from Figures 15 and 16 that the change laws of the safety factor curves for the four blasting operations are consistent. Under the action of the dynamic blast load, the slope safety factor exhibited the following trend: decreasing, increasing, decreasing, increasing, and stabilizing. After half of the mechanical excavation of the slope, the safety factor calculated by static SRM was 2.206. Within 0-2 ms of the dynamic blast load, the original stress balance of the slope was destroyed by the shock wave of the dynamic blast load that was applied instantaneously, causing disturbances in the slope and resulting in the sudden decrease of the slope safety factor. e dynamic blast load at 2 ms reached the maximum, and the safety factor of the slope was reduced to the lowest value, about 1.076. At 2-5 ms, due to the decrease of the dynamic blast load and the short application time, the cumulative e ect of the load was not obvious, and the safety factor slightly increased. At 5 ms, the dynamic blast load decreased to 0.6 F max , and the corresponding safety factor increased to 1.098. At 5-10 ms, the dynamic blast load was still reduced, but due to the long period of load application, a signi cant cumulative e ect occurred, resulting in the decrease of the safety factor of the slope. At 10 ms, the dynamic blast load decreased to 0.1 F max , corresponding to the decrease of the safety factor to 1.082, which was still greater than the safety factor corresponding to F max . At 10-20 ms, due to the obvious decrease of the load, the cumulative e ect became weaker, resulting in the gradual increase of the slope safety factor. At 20 ms, the dynamic blast load tended to 0, corresponding to the increase of the safety factor to 1.100. At 20-75 ms, because the rst blasthole was completed and the second blasthole had not yet been blasted, the cumulative load e ect gradually dissipated, and the safety factor of the slope gradually stabilized. e corresponding safety factor was 1.117 at 75 ms.
During the subsequent blasting of the second to fourth blastholes, the safety factor gradually decreased and the change law was similar to that of the blasting of the rst blasthole. After the fourth blasthole was blasted, the minimum safety factor was 1.063, and the slope was in a stable state. is demonstrates that a good blasting e ect of the slope was achieved via the use of millisecond blasting, and its stability was within a safe range. However, due to the small safety factor, it is recommended to add necessary support measures during blasting construction to improve the stability of the slope.
To better re ect the advantages of millisecond blasting and explore its mechanism, the simultaneous blasting method was employed and the time-history curves of vibration velocity at the same measurement points and the safety factors at di erent points in the slope were determined, as presented in Figures 17 and 18.

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Because the duration of the blasting of one blasthole via millisecond blasting is 75 ms, the vibration velocity timehistory curve of each measurement point of the slope within 100 ms was selected for research. It can be seen from Figures 17(a)-17(c) that the peaks of the vibration velocity of di erent measurement points for simultaneous blasting are larger than those for millisecond blasting. Additionally, the peaks between the measurement points exhibit a declining and lagging phenomenon, which is similar to the change of the vibration velocity of di erent measurement points under dynamic blast loads studied by Jiang [36]. It can be seen from Figure 18 that, with the increase of time, the safety factor of simultaneous initiation of the slope gradually decreases, and at the same time point, the safety factor of simultaneous blasting is smaller than that of millisecond blasting, and the stability of the slope is lower. On the one hand, the use of millisecond blasting can reduce the vibration velocity of the rock mass inside the slope, reduce its disturbance, and play a certain role in reducing vibration. On the other hand, due to the obvious resonance phenomenon between the measurement points, when the rock masses in the blasting area collide with each other after weak loosening due to millisecond blasting, the internal energy of the blasting is reduced, which has a good loosening e ect.

Conclusion
(1) e blasting load constant B was calculated by the equivalent dynamic blast load, which can e ectively simulate the blast load time-history curve. (2) e displacement and maximum shear stress in the blasting zone present the trend from increase to decrease under dynamic blast load. e maximum displacement was 19.27 mm, which indicates that millisecond blasting does few impacts to the stability of the slope. e maximum shear stress was 4.21 MPa, which slightly exceeds the compressive strength of the rock mass. e local rock mass in the blasting area experienced shear failure, which caused weak loosening e ect.
(3) Compared with simultaneous blasting, the peak vibration velocity of millisecond blasting is lower, and its resonance e ect causes adjacent fragmented rock masses to collide with each other on the slope; this makes them rupture uniformly, reduces the displacement and velocity, and improves the blasting e ciency and energy utilization rate, thereby reducing slope disturbance and playing a good role in reducing vibration. (4) e safety factor of high rock slopes periodically changes with the application of the millisecond blasting load, and the variation range is 1.06-1.11. When the dynamic blast load F reaches the maximum value (F max ), the corresponding safety factor is reduced to the minimum. When F 0.6 F max , the slope begins to be a ected by the obvious cumulative load e ect and the safety factor decreases. Until F � 0.1 F max , the cumulative effect of the load is slowed, the effect on the slope is small, and the safety factor begins to increase and gradually stabilizes. During the construction of the blasting project, these three time points should be considered.

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

Conflicts of Interest
e authors declare no conflicts of interest.