Research on the Cumulative Damage Law of Surrounding Rock under Cyclic Blasting Action

In order to study the cumulative damage characteristics and laws of rock masses under cyclic blasting loads, based on the finite element software ANSYS/LS-dyna and the HJC constitutive model, a single blasting damage analysis is conducted first, and the accuracy of the results is verified. On this basis, numerical simulation studies on the cumulative damage of rock masses under cyclic blasting are carried out separately. The results indicate that the cumulative damage evolution cloud map of the rock mass under cyclic blasting is similar to that of a single blasting action, showing an inverse S-shape overall. The damage increment of the rock mass decreases with the increase of blasting times, and in the central area of the damage zone, the rock mass is particularly affected by the superimposed effect of cyclic blasting loads. Cyclic blasting fully reflects the accumulation of damage to the rock mass under multiple cyclic blasting loads, and there is a certain relationship between rock mass damage and the distance between the blasting centers. As the distance between the blasting centers increases, the amount and increment of rock mass damage generated by blasting continue to decrease.


Introduction
The drilling and blasting method have the characteristics of good flexibility, high efficiency, and low cost, and has become an important construction technology in tunnel and underground engineering construction [1].The blasting impact load generated during tunnel drilling and blasting construction not only efficiently breaks the rock mass, but also inevitably causes damage to the rock mass, which can damage the mechanical properties of the rock and seriously affect the safety and stability of the project.Therefore, in the process of tunnel construction and excavation, the development of construction plans and the design of tunnel support structures often focus on considering rock damage [2][3][4].At present, domestic and foreign researchers have done a lot of work on rock mass damage caused by single blasting load, and have achieved many research results [5,6].In the actual tunnel construction process, the blasting damage to the rock mass is actually a cumulative and superimposed process.Therefore, some scholars have conducted in-depth research on the problem of rock mass damage under multiple impact loads, such as XIAO's cyclic loading tests based on granite, which have obtained the law of "anti S" type nonlinear damage of rock mass and revealed the cumulative damage mechanism of rock mass under cyclic loads [7].Based on the on-site testing results of surrounding rock acoustic waves, Yan Changbin deduced that the cumulative damage of the rock mass exhibits a non-linear relationship with the increase of blasting times [8].Huang Youpeng et al. studied the range and distribution of blasting damage to rock mass under a single blasting action using numerical simulation methods [9].
The above research has made preliminary discussions on evaluating the damage of rock masses.However, there is currently a slight lack of research on the cumulative evolution law and spatial

Analysis of Surrounding Rock Damage in Single Blasting
In the calculation process of the blasting model, the damage degree of the rock is characterized by the inherent damage variable D in the rock material: crushing zone (D=1), crack zone (0<D<1), and elastic vibration zone (D=0).At the same time, the damage evolution process of the rock mass after blasting is recorded step by step by setting the historical variable history var #.This section first simulates and analyzes the single blasting of rocks, studies the distribution characteristics of damage in surrounding rock, and verifies the feasibility of the research method and the established numerical simulation calculation.Then, based on this, analyze the cumulative damage evolution law of surrounding rock under multiple cyclic blasting loads.
As shown in figure 2, the damage situation of the rock mass during the first blasting process shows that over time, a blasting cavity area gradually forms inside the rock mass.The red part in the figure shows that the rock mass damage variable near the blast hole is D=1, which is a completely fractured area; Different degrees of damage areas are formed from the center of the blast hole from near to far, with damage variables ranging from 0 to 1 and decreasing with increasing distance.This area is a crack zone; The rock far from the borehole is not affected by blasting, and the damage variable D=0 in this area is the elastic vibration zone.At that time, the blasting cavity area expanded with time, and the damage area of the rock mass gradually developed along the radial and axial directions.As a result, the damage area of the rock mass continued to develop away from the explosive and gradually stabilized.During actual tunnel blasting operations, the range of blasting damage caused by blasting is a key indicator for evaluating the blasting effect.In order to more intuitively and accurately describe the damage changes after rock blasting, combined with the first blasting excavation damage evolution effect diagram in figure 3, the cross-sectional area of the largest damage area along the borehole diameter (coordinate Z=-15.5) is extracted as the research reference plane, and the distribution characteristics of damage in,, and time are analyzed, At the same time, use the Reflect model command in the LS-Propost post-processor to symmetrize the model in the XZ and YZ planes, and restore the 1/4 model to the complete model, as shown in figure 3. From figure 3, it can be seen more directly that the damage evolution law of rock mass during blasting occurs.As the calculation time increases, larger and larger blasting cavities are formed in the rock mass around the borehole, and the damage area continues to expand outward.The damage is a circular distribution feature centered on the borehole axis, and the degree of damage decreases and gradually stabilizes as the distance from the borehole center increases.The radius of the crushing area (D=1) R1=12.5cm(4.2 R) and the radius of the crack area (0.05<D<1) R2=23.8cm(7.9 R).
In practical engineering, due to the influence of various factors such as rock types and geological structures, it is currently difficult to summarize a unified and effective method for determining the damage range of surrounding rock after blasting.Based on extensive research by scholars both domestically and internationally, a series of empirical methods have been proposed to estimate the blasting crack zone in the blasting crushing zone.Among them, Hanukayev [11] believes that the crushing zone generated after explosive initiation is 2-5 times the radius of the explosive, and the blasting crack zone is 10-15 times the radius of the explosive.Based on this, the simulated charging radius in this article is 3cm.Based on previous research results, it can be estimated that the radius of the crushing area generated after blasting is 6-15cm, and the radius of the crack damage area is 30-45cm.It can be found that the difference between the numerical simulation results and the calculation results is not significant, indicating that the results in the numerical simulation have a certain degree of reliability.

Analysis of Cumulative Damage to Surrounding Rock during Cyclic Blasting
Based on the good excavation effect of the first blasting, the model was subjected to fixed-point cyclic blasting using LS-dyna restart technology.This study included a total of 11 numerical simulations of cyclic blasting, with the explosive material parameters, explosive location, and rock parameters being the same for each blasting.Figure 4 shows the cumulative damage cloud map (left) and cumulative damage perspective contour map (right) of the 3D 1/4 model after each charge blasting.From figure 4, it can be seen that after each fixed-point cyclic blasting, the rock mass forms larger crushing and fracture zones along the borehole diameter and axial direction.At the same time, the blasting stress wave propagates to the free boundary (Z=60) to form a reflected tensile wave, which also leads to a larger compression crushing zone in the upper surface area.In order to quantitatively study the cumulative damage characteristics and laws of rock masses under blasting cyclic loads, we hereby obtain the damage distribution feature cloud map of the cross-section (Z=45.5)located at the center of the explosive in the rock mass after each blasting calculation, and extract the rock mass damage values under different blasting center distances.Figure 5 shows the variation of the damage value of rock mass with the distance between blasting centers under different blasting times.As the distance between the blasting centers increases, the damage curves after each blasting have a similar distribution pattern, showing an inverse "S" shape distribution.As the number of blasting times increases, the range of the crushing zone also increases (D=1), and the range of the crack zone (0.05<D<1) also expands significantly.After the 11th blasting, the radius of the rock fragmentation zone reaches 16cm, and the radius of the crack zone reaches 25.7cm.The distance between adjacent curves decreas es with the increase of cyclic blasting times, and the damage increment of rock mass decreases with the increase of blasting times.It can be seen that the cumulative damage of rock mass is not a simple superposition of single charge blasting damage, but has a non-linear correlation with the number of cyclic blasting times.Figure 6 shows the distribution of cumulative damage increment (Δ D) with respect to the distance between the blasting centers under the action of fixed point cyclic blasting at section Z=45.5.Due to the fact that the cumulative damage increment is the difference between the damage values of two adjacent cycles of blasting, the curves Li (i=1-10) in the figure represent the relationship between the cumulative damage increment Δ D of the i+1 fixed point cycle blasting and the i-th fixed point cycle blasting with the variation of the blasting center distance.The variation pattern is generally that it first rapidly increases, then slowly decreases and tends to stabilize.The cumulative damage peak is mainly concentrated in the central left of the total damage area, with a blast center distance of R=15~19cm.The cumulative damage peak also increases with the increase of blasting times, further reflected in the continuous expansion of the rock damage area under the action of fixed point cyclic blasting.Moreover, in the central area of the damage area, the rock mass is particularly affected by the superposition of fixed point cyclic blasting loads, This is consistent with the results of numerical simulation research on cumulative damage of rock mass under cyclic blasting loads by Li Yunzhong et al. [12].

Conclusion
This article conducts numerical simulation on the cumulative damage problem of rock mass under cyclic blasting, analyzes the evolution process and laws of rock mass damage under cyclic blasting, and the main conclusions obtained are as follows: (1) By introducing the damage variable D in the HJC constitutive model, the distribution and evolution of rock damage under single and cyclic blasting loads were studied, demonstrating the feasibility of restart technology in studying cyclic blasting.
(2) Under the action of circular blasting, as the number of blasting increases, the range of rock damage zone continues to expand and the cumulative damage increment Δ D gradually decreases.In the central area of the damage zone, the rock mass is particularly affected by the superposition of fixed point cyclic blasting loads.
(3) Through numerical simulation research on cyclic blasting, it has been demonstrated that multiple cyclic blasting loads can accumulate damage to the rock mass, and there is a certain relationship between rock mass damage and the distance between the blasting centers.As the distance between the blasting centers increases, the amount and increment of rock mass damage caused by blasting continue to decrease.

Figure 2 .
Figure 2. Schematic diagram of the evolution effect of the first blasting damage.

Figure 3 .
Figure 3. Damage Time History Evolution of Z=45.5 Section.

Figure 4 .
Figure 4. Damage evolution law of rock mass under different fixed point blasting times.

Figure 5 .
Figure 5. Accumulated damage distribution of rock mass under different blasting times.