Full Field Strain Analysis of Blasting Under High Stress Condition Based on Digital Image Correlation Method

,e depth of mineral resources like coal continuously increases due to the exhaustion of shallow resources, and the characteristic of high ground stress in deep ground inevitably affects fracture of rock blasting. Combining with high-speed photography technology, the digital image correlation method (DIC) is introduced into experimental study on explosive mechanics. And strain evolution process of blasting under high stress condition is obtained by using the model experiment method. ,e preliminary results show that high stress condition has no obvious effects on the propagation law of blasting stress wave or its stress peak in the medium. In addition, it is found that medium in the “elastic vibration area” by conventional blast zoning is not always “elastic,” and on this basis, the concepts of “plastic area” and “quasielastic area” are put forward. ,e high stress condition does not influence partition range of above “plastic area” or “quasielastic area,” but in the “plastic area,” the high stress condition decreases both plastic strain value and its decay rate of relevant gauging points.


Introduction
In recent years, the state of mineral resource exploitation like coal is shifted from the open air to the underground and from the shallow to the deep; resource exploitation environment is more complex, and the exploitation difficulty increases dramatically.He [1] pointed out that the high ground stress is a significant difference between deep mining and shallow mining, which is also a problem that must be faced and solved by deep mining.With deepening of resource exploitation, corresponding construction methods also need to consider the characteristics of deep mining and make technological innovation to better serve high efficient utilization of resource.Drilling and blasting, as a traditional and effective construction method, is widely used in rock crushing and rock roadway excavation.In the process of blasting excavation of an underground hydropower station, Lu [2] found that the high ground stress is one of the main reasons for crack expansion in contour blasting and considered it is unreasonable for deep rock blasting design according to shallow rock blasting parameters when the ground stress exceeds 10-12 MPa.Nevertheless, in current deep rock blasting construction, the design of blasting parameters does not take the impact of high ground stress into account, resulting in unreasonable use of explosive energy and poor blasting effect.
Many scholars and researchers have noticed that the high ground stress cannot be ignored for rock blasting [3][4][5][6][7][8][9][10]. Kutter [3] published a classical literature about the blasting failure mechanism, in which he found the crack propagation gave priority in the direction of maximum principal stress in static stress field by using polymethyl methacrylate (PMMA) and rock materials.Bai [4] also found the ground stress field has a guiding effect on the expansion of blasting induced crack, and main direction of the crack propagation tends to the direction of the maximum principal stress.It is thought that the increase of hole spacing or reduction of the charge amount in the direction of the maximum principal stress can improve blasting quality and reduce explosive consumption [5].Yan [6] believed that the coupling effect of blasting loading and high ground stress on damage of the surrounding rock is greater than the effect of their linear superposition.Wei [7] carried out the numerical simulation of slit-charge blasting under different high stress conditions, it is found that the crack propagation direction is controlled by the incision angle and the direction of maximum ground stress, and the crack propagation scale is mainly controlled by the value of ground stress.
From the existing research, the study of deep rock blasting response is focused on expansion of blasting induced cracks.Due to the limitations of relevant test methods and experimental equipment, influence of high stress condition on blasting stress wave propagation is rarely studied.In this paper, the full field strain evolution of blasting under high stress condition is analyzed by model experiment with experimental system of high-speed digital image correlation.

Experimental System.
In recent years, the digital image correlation method (DIC) [11][12][13][14] has been successfully applied to experimental research in many fields as an effective optical testing technology and has become an important test method for modern photometric mechanics.
e basic measurement principle of DIC is that speckle field is made on the surface of the specimen before experiment, and then an image acquisition system is used to collect the speckle patterns before and after deformation of the object.After the image processing, the speckle patterns are transformed into two digital gray fields.
rough correlation processing of the gray fields, the displacement field of object surface is obtained.
en, according to the relationship between displacement and strain, the strain field of object surface is obtained.
From existing literature records, DIC method has been gradually applied to the study of blasting problem.Based on the high-speed DIC, He [15] performed a laboratory experiment to investigate the dynamic response of rock subjected to couple static and dynamic stresses from active confining pressure and blasting.In addition, by using highspeed 3D DIC, the crack propagation process and the 3D deformation characteristics of cylindrical concrete specimens under blast loading were analyzed [16].
As shown in Figure 1, the experimental system of highspeed digital image correlation used in this experiment is mainly composed of high-speed camera, VIC-2D analysis software, lighting system, and synchronous control system.
e camera uses μCMOS sensor, and it is possible to realize highspeed acquisition without lowering the image resolution.Its image resolution is fixed to 924 pixels × 768 pixels, the number of acquisition is 180, and the fastest shooting speed is 5 × 10 6 fps.e shutter time of the high-speed camera in this experiment is 1 μs.
(2) VIC-2D software.e software has the function of automatically calibrating the scale factor of the graph and uses the normalized squared correlation function to carry on the correlation calculation, which is not sensitive to bright light change.e optimal calculation is carried out under the premise of satisfying the accuracy and the calculation speed. is software is widely used in digital image correlation analysis at home and abroad.(3) SI-AD500 lighting system.
e system consists of a controller and a flash.
e controller is a fourchannel CU-500 controller that can control multichannel simultaneous or sequential operation.e flash is FH-500 xenon lamp, which can achieve 2 ms constant light intensity of lighting time to ensure the ultra-high-speed camera on the exposure requirements.(4) Synchronous control system.e operation of highspeed camera poses a high demand for synchronous control.e HD 12-2 synchronous control system is designed and developed by our team, and it can set startup sequence and delay time of the explosive initiation, the camera, and the lighting system.
For blast research, a start trigger mode was used in the experimental system.When the trigger signal is manually given, the lighting system is initiated.After 50-100 μs, the intensity of the light field reaches a steady value, and the high-speed camera begins to acquire images, whereupon the explosive in the specimen blasthole is detonated.
Figure 2 presents the front view of the self-designed dynamic-static loading device, which can apply dynamic blasting stress and static compressive stress on the specimen.
e dynamic blasting stress is generated by the detonation of explosive in the middle of the specimen, and the static compressive stress is provided by jack.A stress sensor with a range of 5t, and an accuracy of 0.1 kg is used for real-time measurement of the compressive stress.In addition, the jack can also record the reading of the pressure sensor and do some relevant conversions.rough calculation, the σ applied by jack which is regarded as an equivalent principal stress difference can be obtained.e lead azide (Pb(N 3 ) 2 ) is placed in the borehole of specimen and blocked with the jig, and then the detonation is achieved by high voltage discharge.
e related parameters of Pb(N 3 ) 2 are listed in Table 1.

Specimen Parameters.
e model material used in this experiment is polycarbonate (PC), and related material parameters of PC are shown in Table 2. e specimen size is 2 Shock and Vibration 315 mm×285 mm×8 mm, and a borehole with d 5 mm in diameter is prefabricated in the center.e speckle is printed on the surface of specimen using the UV plate printing technique; the speckle diameter is 1.2 mm, the speckle density is 75%, and the speckle irregularity is 75%.e size of the subset used in the experiment is 29 × 29 pixels, and the calculation step is 7 pixels.Two groups of specimens are designed in the experiment, specimen T1 (σ 0 MPa, under normal stress condition) and specimen T2 (σ 6 MPa, under high stress condition).Eight gauging points are selected in each specimen for strain monitoring as shown in Figure 3. e polar coordinate system is established with the center of borehole as the coordinate origin.e distance s between gauging points G1, G2, G3,•••, G8 and the borehole is respectively 35 mm (7d), 40 mm (8d), 45 mm (9d), and 70 mm (14d).

Strain Evolution.
e explosive initiation time is t 0 μs, and Figure 4 shows the maximum principal strain under the action of blasting stress wave at di erent time.e measurement accuracy of full eld strain by DIC method depends on the image resolution and speckle quality.e image resolution of the experiment system is 924 pixels × 768 pixels, and the pixel size is 30 μm × 30 μm.Before the blasting experiment, speckle quality needs to be calibrated.Figure 5 is the calibrated strain curve, which shows that the measurement error of the radial strain does not exceed ±20 με and the measurement error of the circumferential strain does not exceed ±10 με.It proves that the   Shock and Vibration experiment system can provide su cient accuracy for full eld strain measurement under blasting loading.e radial strain ε ρ and the circumferential strain ε θ within 100 μs after detonation are extracted.During this period, the blasting stress wave propagates in the specimen plane without reaching the boundary of the specimen, so no re ection of the stress wave occurred.e radial strain and circumferential strain of the eight gauging points on each specimen are extracted and subjected to denoising to obtain the strain curves as shown in Figures 6 and 7.In the gures, tensile strain is positive, and compressive strain is negative.Under the action of blasting stress wave, the radial direction of the gauging point is subjected to compressive stress, and the circumferential direction is subjected to tensile stress due to the Poisson e ect of material.After blasting stress wave acts on a certain gauging point, the elastic strain accumulated in the medium is released, the radial compressive strain gradually decreases, and the stress state is even changed from compressive to tensile.For specimen T1 and T2, from the gauging points G1 to G8, peaks of the radial strain and circumferential strain gradually decay as the distance from borehole gradually increases.
Under blasting loading, the relationship between stress attenuation and distance satis es the following equation: where σ s is the stress peak of a certain gauging point; r is the ratio of s (the distance to borehole center) and r (the charge radius); σ 0 is the initial stress at the borehole; and n is the stress attenuation coe cient.
According to the correspondence between stress and strain on the medium, the circumferential stress peak σ θ and the radial stress peak σ ρ of the specimens shown in Table 3 are obtained.According to the data in Table 2, the scatter plot of corresponding stress peak in Figure 8 is obtained.It can be found that the stress peak of specimen T1 and T2 is basically equal.It proves that the high stress condition has no obvious e ect on the stress peak or the stress change under blasting loading.e circumferential stress peak σ θ and the radial stress peak σ ρ are tted, the attenuation law of σ θ satis es that σ θ 884/r 1.80 , and the attenuation law of σ ρ satis es that σ ρ −225/r 1.04 .e attenuation coe cient of the circumferential stress is 1.80, and the attenuation coe cient of the radial stress is 1.04.It can be deduced that circumferential stress peak and the radial stress peak at borehole are, respectively, 884 MPa and −225 MPa.

Strain Partition.
e specimen strain is generated under the action of blasting stress wave.After the action of blasting stress wave, strain at the gauging point is not completely restored, and the unrestored strain is plastic strain.In later stage of the strain curves, the strain hardly changes with time as shown in Figures 6 and 7. Table 4 shows the plastic strain values of gauging points in specimen T1 and T2 under the action of blasting loading, and Figure 9 shows the image relationships corresponding to the relevant data in Table 4.In Table 4 and Figure 9, ε p ρ and ε p θ , respectively, represent the radial and circumferential plastic strain of gauging points.With increase of the distance s from the borehole, the plastic strain gradually decreases.At G6 (s 12 d) and the following gauging points, the plastic strain is basically stable at a small value where the radial plastic strain is less than 100 με and the circumferential plastic strain is less than 200 με.It can be seen that G6 is a turning point of plastic deformation of the specimen under the action of blasting stress wave.When s＜12 d, the plastic strain is larger, and it decreases signi cantly with the increase of the distance s; when s＞12 d, the plastic strain is smaller and does not change obviously with the increase of the distance s.Shock and Vibration According to conventional blasting theory, under the action of blasting loading, areas around the borehole [17] are crushing area, fractured area, and elastic vibration area from the near to the distant.at is, the surrounding medium of borehole is crushed dramatically under strong blasting loading to form the crushing area; subsequently, driven by the quasistatic action of the blasting gas, some of the microcracks in the crushing area are extended to longer radial and circumferential cracks to form the fractured area.In the periphery of the fractured area, it is considered that the e ect of blasting stress wave and blasting gas is not su cient to cause further damage to the medium, which is called elastic vibration area.In this experiment, due to the small charge amount, there is no obvious crushing area or  erefore, the propagation characteristic of blasting stress wave in the abovementioned elastic vibration area is mainly studied.
rough above analysis of measured strain, it is found that strain of gauging point in the elastic vibration area is not all "elastic."In the area of s＜12 d, the plastic strain is relatively large, and the decay trend is signi cant with s, and such area can be called "plastic area."In the area of s＞12 d, the plastic strain stabilizes in a small range, and such area can be called "quasielastic area.".In view of this, the de nition of "elastic vibration area" is not rigorous.Based on the experimental results, it is suggested that the "elastic vibration area" in traditional blasting partition should be further modi ed as "plastic area" and "quasielastic area." For both specimen T1 and T2, the boundary of "plastic area" and "quasielastic area" is the position of gauging point G6 (s 12 d), so the high stress condition of specimen T2 has no obvious e ect on the division of "plastic area" and "quasielastic area."By comparing the plastic strain and its variation trend in the plastic area shown in Figure 9, it is found that both radial plastic strain and circumferential strain of the gauging points in the plastic area of specimen T2 are smaller than those correspondingly of specimen T1.In addition, in the plastic area, the plastic strain attenuation of gauging points in specimen T2 is relatively slow with the distance s. at is, the plastic strain decay rate of gauging points in specimen T2 is always smaller than that in specimen T1.

Conclusion
By combined loading of high static stress and dynamic blasting stress, full eld strain evolution of blasting under high stress condition is studied.Experimental results show that the high stress condition has no obvious e ect on the propagation and attenuation of blasting stress wave.e circumferential stress peak σ θ and the radial stress peak σ ρ     Shock and Vibration are fitted, the attenuation law of σ θ satisfies that σ θ � 884/r 1.80 , and the attenuation law of σ ρ satisfies that σ ρ � −225/r 1.04 .e attenuation coefficient of the circumferential stress is 1.80, and the attenuation coefficient of the radial stress is 1.04.Based on the experimental results, the definition of "elastic vibration area" is not rigorous.It is suggested that the "elastic vibration area" in traditional blasting partition should be further modified as "plastic area" (s＜12 d) and "quasielastic area" (s＞12 d). e high stress condition has no obvious effect on the division of "plastic area" and "quasielastic area."While in the plastic area, both plastic strain and its decay rate of gauging points in high stress condition (σ � 6 MPa) are smaller than those in normal stress condition (σ � 0 MPa).

Figure 1 :
Figure 1: Experimental system of high-speed digital image correlation.

Figure 6 :Figure 7 :
Figure 6: Curves of strain with time in specimen T1.(a) Radial strain and (b) circumferential strain.

Figure 8 :
Figure 8: Stress peaks and tting curves of gauging points.

Table 2 :
Related material parameters of PC.

Table 3 :
Stress peaks of gauging points in specimen T1 and T2.

Table 4 :
Plastic strains of gauging points in specimen T1 and T2.