Research on Cumulative Damage Induced by Cyclic Blasting of Tuff

This article establishes a numerical model for cumulative damage of surrounding rock that can simulate the characteristics of progressive cyclic blasting in tunnels based on explicit dynamics and “restart” technology, and conducts research on the cumulative damage law of surrounding rock induced by tunnel blasting. The results show that: (1) considering the characteristics of progressive cyclic blasting in tunnels, the degree and range of surrounding rock damage are significantly increased compared to single blasting, with an increase of about 50%; (2) the amount of damage caused by blasting in the surrounding rock follows a Boltamann function (S-shaped curve) evolution feature as the distance between the blasting centers increases. In practical applications, when evaluating the degree and range of damage to the surrounding rock at the current location, additional cumulative damage caused by adjacent footage cycles should be considered, and the damage value can be 1.5 times the damage value of the current single blasting condition


Introduction
Drilling and blasting method have the advantages of good flexibility, high efficiency, and low cost, and is the most widely used excavation technology in tunnel and underground engineering construction.In the process of drilling and blasting excavation, blasting impact load will inevitably cause damage to rock mass and lead to deterioration of rock mechanical properties, thus affecting the safety and stability of engineering construction [1][2][3].Therefore, the damage range and degree of surrounding rock induced by blasting excavation should be fully considered in the formulation of tunnel construction scheme and the design of supporting structure [4][5][6][7][8].
In recent years, domestic and foreign scholars have carried out a lot of research on the damage effect of rock mass induced by a single blasting load [9,10].For example, Huang Yopeng et al. studied the range and distribution law of rock mass blasting damage under a single blasting load through numerical simulation [11].However, due to the limitation of tunnel construction method, rock mass is often affected by multiple blasting in practical engineering, and the damage of rock mass is also reflected as a cumulative process.Therefore, it is not enough to restore the actual situation only to study the development law or mechanism of rock mass damage under single blasting load.Therefore, some scholars have carried out in-depth research on the problem of rock mass damage under multiple impact loads.For example, XIAO et al. studied the "inverse S" type nonlinear damage law of rock mass based on cyclic loading test of granite, and revealed the cumulative damage mechanism of rock mass under cyclic loading [12].Based on the acoustic field test results of surrounding rock, Yan Changbin deduced that the cumulative damage of rock mass presents a nonlinear functional relationship with the increase of blasting times [13].Yang Jianhua et al. simulated the cumulative damage effect of rock mass under repeated explosion loads during millisecond blasting of the whole section of a circular tunnel, revealing the law that the damage range and degree of surrounding rock increase with the number of repeated explosion loads [14].Zhang Guohua et al. studied the cumulative damage range of surrounding rock of large section tunnels constructed by double-wall diversion method in the operation of prop-type repeated blasting combined with the field acoustic monitoring of large section tunnels in Dabao Mountain [15].Cao Feng et al., taking Juntian bifurcated tunnel as the engineering background, studied the influence of cyclic blasting load on rock inclusion in a tunnel with a small clear distance [16].
The above research results have reference value for evaluating the damage of rock mass caused by tunnel drilling and blasting.However, in the actual construction process of tunnel drilling and blasting method, the excavation cycle is a "successive detonation" process, and its load size (charge amount), action time (staged detonation) and action object (layered blasting) are significantly different from the conventional cyclic dynamic load action, which makes the calculation of cumulative damage caused by tunnel blasting to rock mass extremely complicated.It also makes the existing calculation theory and method based on regular cyclic dynamic load action difficult to apply.In this paper, based on the actual situation of tuff tunnel blasting construction, explicit dynamic finite element method is used to establish a fine model of hole blasting that can simulate tunnel propulsive blasting, and the cumulative damage law of blasting load on the surrounding rock mass under multiple blasting conditions in a single hole is discussed.The research results can provide reference for smooth blasting design and overcutting control of tuff tunnel.

Basic Ideas
At present, the study of tunnel blasting simulation usually simplifies the blasting load caused by the simultaneous initiation of single or porous holes into a one-time impact load, and then analyses the stress of rock mass.In fact, the surrounding rock damage caused by tunnel blasting is the superposition result of multiple blasting actions.Therefore, based on ANSYS/LS-DYNA program, the tunnel perforation is regarded as a cylinder structure, an explicit dynamic finite element model is established, and the "restart" [17] method which can consider the cumulative effect is adopted to simulate the initiation and successive action process of multiple explosives.
(1) Stress initialization of rock mass is carried out through the *STRESS_INITIALIZATION function, so that the stress, displacement, and damage state generated after the completion of the current calculation of rock mass element can be retained, and it will be used as the initial condition for the next blasting calculation.
(2) Use *DELETE_PART to update the rock unit at the location of the last explosive and the next addition of explosive, and define the initial volume fraction of explosive and mud with *INITIAL_VOLUM EFRACTION_GEOMETRY.
(3) Modify the solution time in the restart K file and add explosives and mud.

Calculation Model
The tunnel cyclic blasting process is simplified into the following model: Considering symmetry, a three-dimensional one-quarter model of a single charge hole is established, with the model size of 60×60×60 cm, as shown in figure 1.The hole radius is 3 cm; From the hole opening to the inside, the hole is successively arranged as a 5 cm long empty section, a 3 cm long mud plugging section and a 5 cm long explosive coupling filling section.In the model, ALE mesh is used to model explosives, air and mud, and the model unit adopts multisubstance algorithm, that is, multiple substances are allowed to be contained in the same grid, and the interaction between substances is realized based on coupling algorithm.The rocks are Lagrange grid.
The model boundary is set as follows: the X=Y=0 surface is the symmetric plane, the top surface (Z=0) is the free boundary, the bottom surface (Z=60) and the side (X=Y=60) are set as the nonreflective boundary.Blasting adopts coupling cylindrical charge center initiation mode.
In the model, ALE mesh is used to model explosives, air and mud, and the model unit adopts multisubstance algorithm, that is, multiple substances are allowed to be contained in the same grid, and the interaction between substances is realized based on coupling algorithm.The rocks are Lagrange grid.
The model boundary is set as follows: the X=Y=0 surface is the symmetric plane, the top surface (Z=0) is the free boundary, the bottom surface (Z=60) and the side (X=Y=60) are set as the nonreflective boundary.Blasting adopts coupling cylindrical charge center initiation mode.

Material Ontology and Parameters
When an explosion occurs, the rock is in a state of high strain rate and large strain.The constitutive model used in this paper is the HJC (Holmquist Johnson Cook) dynamic damage constitutive model, with specific parameters listed in reference [18].The specific parameters of the explosives used in this article can be found in reference [19], and the specific parameters of the air used in this article can be found in reference [20].

Calculation of Working Conditions
In order to more realistically reflect the tunnel cycle of excavation, successive detonation of the construction process, the numerical simulation is set up as shown in figure 2 calculation conditions, that is, according to the figure shown in the order of (1) → ( 5) sequential progressive detonation, each detonation of the amount of explosive, the length of the gun hole, etc., are the same, the length of each explosive section of 5 cm, the length of the gun mud is 3 cm, each time the calculation is completed the final value of the damage to the rock as the next rock body detonation of the damage to the initial value of the damage to the sequential calculations and monitoring of the explosives in the centre of the position (Y = 18 cm) at a total of five analysis points of the damage situation.

Model Reliability Analysis
In order to clarify the reliability of the above calculation model, this paper carries out the calculation of a single blasting condition, i.e., blasting only once at ① shown in figure 2, and compares the size of the calculated rock damage area with the existing results.The contour plots of the damage development of the rock and its Z=10.5 cm section under this condition are given in figure 3 and figure 4, respectively.In the figure, the area within the red contour represents the completely damaged zone (crushed zone), with the value of the damage variable D=1; the area outside the blue contour represents the undamaged zone (elastic zone), with the value of the damage variable D<0.05; the area between the red and blue contours is the damaged zone (fissure zone), with the value of the damage variable in the range of 0.05<D<1 [11].It can be seen from the analysis of figure 3: (1) After detonation, the damage area expanded outward in concentric circles over time, and the media around the shell hole formed an obvious crushed zone.Statistical measurements obtained completely crushed zone (D = 1) radius of 11.5 cm (4.2 R); fissure zone (0.05 < D < 1) radius of 24.1 cm (8.0 R).
(2) Due to the influence of many factors such as rock type and geological structure, it is still difficult to obtain an accurate and uniform method for determining the damage range.Domestic and foreign researchers and scholars through a large number of studies, put forward the estimation method of rock blasting crushing zone.Dai Jun [20] proposed that the radius of the crushing zone under the condition of columnar coupling charge Ra is: The radius Rb of the rift zone is: where, ; ρe, ρ0 for the density of explosives and rock; D0, Cp for the explosive velocity, the speed of sound in the rock; rb for the radius of the borehole; σR for the radial stress on the interface between the crushed zone and the fissure zone of the rock.α, β are the attenuation coefficients of the propagation of the load in and out of the crushed zone; μd is the dynamic Poisson's ratio of the rock, taking μd = 0.8 μ; σCD is the compressive strength of the rock in single dynamics, and μd is the dynamic compressive strength of the rock.cd c 3   = , σc is the uniaxial static compressive strength, ε is the loading strain rate, take ε=100s-1; σtd is the unidynamic tensile strength of the rock, σt is the static tensile strength.Substitution yields the radius of the crushed zone Ra = 10.3 cm and Rb = 26.84cm.

Calculation of Working Conditions
The state of damage development in the rock after five progressive blasts is given in figure 5.It can be analysed from this: (1) after each progressive blasting, the existing rock body in the original damage on the basis of further induced new damage, the scope and extent of damage are increased, especially in the direction of the axis of the borehole, the expansion range increases significantly.It can be seen that, for the analysis of the surrounding rock damage caused by tunnel construction blasting, the traditional single blasting calculation is difficult to reveal the actual situation of rock damage, which is biased towards insecurity.
(2) The cumulative damage value of each monitoring point increases with the increase in the number of blasts, as shown in figure 6 and figure 7, each progressive blasting will cause a larger amount of damage and damage increment to the rock closer to the point of initiation, while the damage increment of the rock body in other locations is relatively small.It can be seen that the damage to the rock body under the action of blasting is superimposed many times and irreversible, and with the increase in the distance from the centre of gravity, the amount of rock damage and damage increment continue to decrease.(4) In order to further analyse the relationship between the cumulative damage variables of the rock body with the number of progressive segments and the bursting core distance, in each progressive segment blasting, extract the damage values of the rock body directly above the explosive in the progressive segment with the bursting core distance R of 16 cm, 18 cm (the monitoring point has been studied), 20 cm, 22 cm, respectively, to characterize the cumulative superposition effect of the damage generated by the blasting progressive segments, as shown in figure 8. from this analysis, it can be seen that the damage values of the rock body units with the same bursting core distance R from the current blast segment show a trend of increasing and then slowly stabilizing in different bursting core distance R. Each progressive blasting, the damage value of the rock unit with the same blast centre distance R from the current blast section shows a tendency of increasing and then stabilizing slowly, and there is a similar pattern at different blast centre distances R.

Quantitative Analysis of Damage Characteristics
Based on the above analysis, in order to quantitatively reveal the cumulative damage law of the rock body induced by blasting, the cumulative damage stabilisation values of the rock body under different bursting centre distances R after five progressive blasts and the damage values of the rock body under each bursting centre distance of the rock body cross-section of Z=10.5 cm for a single blast in figure 4 were extracted, as shown in figure 9. further, according to the damage attenuation tendency, a Boltamann function can be fitted [21], and then the further, according to the damage attenuation trend, the Boltamann function can be fitted [21], and then the rock damage distribution function induced by single and progressive blasting at different blast centre distances can be obtained: where D1 is the value of perimeter rock damage induced by a single blast; D2 is the value of perimeter rock damage induced by progressive multiple blasts; and R is the blast centre distance.
Analysis can be seen: (1) There is a significant non-linear relationship between the perimeter rock damage and the number of blasts, i.e., the value of the perimeter rock damage decreases with the increase of the blast centre distance, which is an "S" shaped evolution, which is consistent with the law based on the acoustic test of the perimeter rock damage obtained by Yan Changbin et al. [13].
(2) single and progressive blasting damage zone radius of 24.8 cm and 38.0 cm, respectively, in contrast, progressive blasting damage is about 1.5 times the degree of single blasting damage.Analogous to the actual tunnel blasting and excavation process, the damage produced by "sequential" blasting of explosives is not only caused by the current blasting of the excavated section, but also by the influence of blasting in its neighbouring scales.
Therefore, when analysing the degree and extent of damage to the surrounding rock at the current location, calculating only the blasting conditions of the current excavation cycle will underestimate the actual damage characteristics of the tunnel surrounding rock, which may result in a wider range of overexcavation conditions and rock loosening.In practice, the additional cumulative damage brought about by the neighbouring feed cycles should be taken into account, and its damage value can be taken as 1.5 times of the damage value of the current blasting conditions.

Conclusion
In this paper, based on explicit dynamics and "restart" technology, a numerical model of cumulative damage to the surrounding rock that can simulate the characteristics of progressive cyclic blasting in tunnels is established, and the above research conclusions are obtained: (1) For the rock studied in this paper, considering the characteristics of progressive cyclic blasting in tunnel, the degree and scope of damage to the surrounding rock increases significantly compared with that of single blasting, with an increase of about 50%; (2) For the rocks studied in this paper, with the increase of the distance from the center of blasting, the amount of damage caused by blasting to the surrounding rock follows the evolutionary characteristics of the Boltmann function (S-shaped curve).In practice, when evaluating the degree and scope of damage to the surrounding rock at the current location, the additional cumulative damage caused by adjacent scaling cycles should be taken into account, and its damage value can be 1.5 times the current damage value of the single blasting conditions.

Figure 2 .
Figure 2. Calculation conditions and analysis points.

Figure 3 .Figure 4 .
Figure 3. Schematic diagram of damage evolution effect of the first blasting.

Figure 5 .Figure 6 .
Figure 5. Damage nephogram of rock mass under progressive blasting condition.(3)Comparison of test point 1 and test point 5, test point 1 in the process of five propelled blasting have damage accumulation, test point 5 in the first two propelled blasting almost no damage accumulation, can be seen only to reach the damage threshold, the surrounding rock will produce damage.

Figure 7 .
Figure 7. Relationship between cumulative damage increment △D and initiation step.

Figure 8 .
Figure 8. Cumulative damage change laws of monitoring points.

Figure 9 .
Figure 9.The cumulative damage pattern of single and progressive blasting under different blast center distances.