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Blast induced rock mass damage and crack propagation play important roles in structure safety and stability in mining, quarrying, and civil constructions. This paper focuses on the effect of small blasthole diameter blast on crack propagation and damage accumulation in water-bearing rock mass containing initial damage composed of inherent geological discontinuities and previous multiblast induced damage. To elucidate this effect, theoretical analysis of calculation method for several important blast influencing factors is firstly presented. Secondly, definition of a practical damage variable using ratio of longitudinal wave velocity in rock mass before blast occurrence to that after blast occurrence and derivation of a damage accumulation calculation equation accounting for initial damage and blasting effect are described. Lastly, a detailed description of the conducted in situ blast tests and plan layout of the sonic wave monitoring holes is reported. The results indicate that blast activates and then extends the initial cracks in rock mass, leading to accumulation of rock mass damage. The rock mass damage accumulation can be conveniently quantified using the proposed damage variable. When the damage variable reaches its threshold of 0.19, occurrence of damage in the surrounding rock mass is indicated. It is also found that the blast induced rock mass damage extent and the blast induced vibration velocities decrease nonlinearly with increasing the distance between blast source and monitoring position.

The application of the drill and blast method (DBM) remains a preferred rock mass excavation method worldwide in engineering practice such as underground caverning, mining, quarrying, tunneling, and dam construction. Despite the advantages of DBM including low construction cost, short construction period, wide acceptability, and broad applicability [

Blast induced rock mass damage, defined as the propagation of inherent geological discontinuities and/or the formation of new cracks along weak planes in rock mass [

To calculate and predict PVV or BVV, a variety of models have been proposed in the literature based on empirical and/or semiempirical formulae using field monitoring data [

Apart from PPV or BVV as an indicator of the extent of blast induced rock mass damage, rock mass crack initiation and propagation induced by blast also indicate the adverse effect of blasting on the surrounding rock mass. During blasting, the explosive chemical reaction in blasthole changes the explosive from a condemned material to a gaseous product of high pressure and high temperature. In the meantime, stress wave (or shock wave) and explosion gas pressure are produced and loaded on the surrounding rock mass. The stress wave propagates at a higher velocity for a shorter duration in comparison to the explosion gas pressure [

Despite the wealth of the studies on blast induced rock mass damage and blast induced rock mass crack initiation and propagation, it is far from complete for study of blast induced crack propagation and damage accumulation in rock mass containing initial damage composed of inherent geological discontinuities and previous multiblast induced damage [

Although the existence of water medium in water-bearing rock mass can exert an influence over the blasting effect, the stress wave aroused in water in blasthole satisfies the fundamental equations for wave. These equations are expressed as

On the interface between explosive and water, the following equation is satisfied:

At the moment blasting begins, assuming water pressure

An isentropic process can be approximately assumed during shock wave propagation, indicating that water medium’s state equation can be expressed as

The density of water medium subject to compression of shock wave during water-coupling blasting becomes

Energy attenuation and reduction in peak pressure can occur for shock wave when propagating along blasthole radial direction and compressing water medium. For column charge blasting, the reduction in shock wave’s peak pressure can be expressed as a function of distance:

Propagating of shock wave to blasthole wall produces a blasthole wall pressure of

Therefore, some parameters corresponding to blasthole wall, according to Kachanov [

Reflected wave and transmitted wave are produced from blasthole wall when radially propagated shock wave reaches blasthole wall. To theoretically solve this problem, elastic theory and wave theory can be referred to. The shock wave pressure on blasthole wall under the normal incidence circumstance is calculated as

However, coupling charge blasting is hardly encountered in underground rock mass excavation. Generally, there is no choice but treating air or water as the axial cushion and water contained in rock mass as axially decoupled charge structure when implementing analysis. In the experimental study by the authors, in situ blasting tests are performed treating water as the cushion, taking into consideration that rainwater has flowed into blasthole exposed to nature. Initial damage, such as crack, is believed to have been existing in the in situ surrounding rock mass relative to the blasthole due to influence of previous multiblasting tests in the blasthole. In that crack, water is filled; therefore, in study the fact that blasting exerts influence over the crack water in the in situ surrounding rock mass to the blasthole can be considered as axially water-decoupled.

For convenience in terms of comparison and analysis, the blasthole located out of the rock mass crack water is selected as the study object for decoupled blasting with air as its cushion. For decoupled charge blasting, the produced stress wave and detonation gas will compress the decoupled medium. This compression leads to an increase in the decoupled medium’s pressure. Upon reaching peak pressure, the detonation energy will be transmitted to rock mass through the decoupled medium. A ‘squeezing’ effect on the surrounding rock mass relative to the blasthole can be produced by the energy that is transmitted from blasting stress wave or by detonation products through rock mass crack water [

When air is the cushion at the bottom of blasthole, the density of detonation gas that fills the whole blasthole due to expansion can be expressed as follows [

Meanwhile, detonation gas’s pressure is

And the sound velocity of detonation gas is

When water in blasthole is the cushion at the bottom of blasthole, the density of water subject to squeeze given by blasting stress wave and detonation gas can be expressed as

In the meantime, the pressure in blasthole is

The dynamic failure process of water-bearing rock mass subject to blasting shock wave is a process during which damage accumulates till rapture failure of rock mass occurs. A good deal of defects, such as microfissure and microcracks, exist in rock mass as a brittle material. The existence of water in rock mass expedites stress wave propagation. Rock mass’s macro-mechanical properties can be weakened due to microcrack initiation, propagation, and even penetration in rock mass, under the effect of water-decoupled blasting. Definition and selection of damage variable are implemented by the authors with the help of the understandings discussed above. In an in situ blasting test coupling charge with air being the cushion and coupling charge with water being the cushion are performed simultaneously. In this context, for simplicity, analysis of decoupling charge with air or water being the cushion is merely conducted in this experimental study. With water being the cushion and rock mass crack as well as blasthole being filled with water, the equations presented above can be used to calculate the parameters corresponding to water-coupling and water-decoupling charges. The calculated parameters enable analysis of the experimental results.

A damage variable is a representation of deterioration degree for material or structure. To define a damage variable, both micro- and macroparameters can be used. The microparameters include crack number, crack length, crack area, and crack volume, etc. And elasticity modulus, yield stress, tensile strength, and density are some of the macroparameters [

Assume that rock mass damage is isotropic, rock mass damage can also be quantified using the change in ultrasonic velocity in rock mass. Calculation of longitudinal wave velocity is performed using_{0} and_{1} are, respectively, longitudinal wave velocities before and after damage occurrence,_{0} and_{1} are, respectively, rock mass densities before and after damage occurrence, and

In general, detection and representation of rock mass damage are implemented using the difference between longitudinal wave velocity in rock mass before damage occurrence and longitudinal wave velocity in rock mass after damage occurrence. Therefore, the damage variable in (

Note that the difference between_{0} and_{1} is negligibly small, the damage variable,

According to the Chinese construction specification [

Regarding

Original defects of various types exist in rock mass subject to blasting effect. These defects can be regarded as rock mass’s initial damage,

The initial damage,_{0}, can be calculated using the effective area,_{0}. Assume that in a rock mass of dimension 2_{0}, is calculated by

As is shown in Figure

Schematic illustration of rock mass damage evolution induced by multiblasting.

Consequently, for rock mass containing initial damage, the rock mass damage variable in the far-field of blasting source after multiblasting of

And the general form of

The existence of initial damage in rock mass, such as joint fissure, causes the blasting stress wave to decay in rock mass. The decay degree is varying depending on the joint fissure distribution and form. Figure

Schematic illustration of rock mass damage induced by single-hole blasting.

The decay of the original axial stress peak for air-coupling charge blasting satisfies the following equation:

Water-coupling blasting is formed when a great deal of water fills rock mass crack and blasthole. For this case, the shock pressure on blasthole wall can be calculated using (

The particle vibration velocity,

The dynamic stress peak at this point produced by blasting is

The total crack length in a rock mass of reference dimension 2

Combination of (

Characteristics of blasthole wall crack propagation before and after blasting occurrence are shown in Figure

Photograph showing crack propagation in blasthole before and after multiblast.

Before blast

After blast

Schematic illustration of I-type crack in blasthole induced by blasting.

For I-type crack, unstable propagation occurs when the strain energy release rate reaches its threshold, which is

Because I-type crack dominates the blasthole wall original crack, the stress intensity factor for the blasthole wall original crack can be approximately calculated by

As the criterion for dynamic crack propagation is complex, approximate treatment is implemented, which gives that the original crack propagation is induced by the blasting stress wave. Therefore, a quasi-static criterion for blast induced crack propagation is derived and is expressed as

The minimum detonation pressure corresponding to initial propagation of the original crack, according to manipulation of (

By using the equations presented above, the minimum explosive equivalent required for propagation of original crack in in situ blasting tests can be derived, which lays the foundations for further calculation of the blasting energy and the damage diameter, etc.

The in situ blasting tests in this study are conducted in an outdoor blasting test site. The blasthole and the sonic wave monitoring holes (SWMHs) are drilled into marble rock mass. The blasting pattern used is characterized by single-blasthole, small explosive equivalent, and multiblasting. The use of the blasting pattern is to study the blast induced rock mass damage accumulation characteristics of different distances to a particular geological section. To monitor the blasting sonic wave velocity, the intelligent sonic tester Geode is used. And an ultraportable microseismograph is utilized to monitor the blasting vibration. A high-precision, high-resolution digital camera is used to photograph the blasthole crack propagation before and after blasting occurrence.

The plan layout of blasthole and SWMHs is shown in Figure

Layout of blasthole and sonic wave monitoring holes.

Three-dimensional illustration of locations of blasting source, blasthole, and sonic wave monitoring holes.

Discussions of single-blasthole blast induced sonic wave velocity, particle vibration velocity, and rock mass damage accumulation for different distances to the blasting source are made in this study. The basic parameters in this experimental study are rock mass density ^{3}, original rock mass damage variable _{1} = 55 mm and_{2} = 35 mm, explosive density ^{3}, detonation velocity = 4000 m/s, and rock mass Poisson’s ratio

In situ blasting tests of different explosive equivalents and of different blasthole depths are conducted in this study. SWMH No. 9 as shown in Figure

Particle vibration velocity-time curve for sonic wave monitoring hole No. 9.

Particle vibration velocities for various distances between blasting source and sonic wave monitoring hole.

Experimental and theoretical sonic wave velocities versus distance between blasting source and sonic wave monitoring hole.

Experimental and theoretical curves showing accumulated rock mass damage.

The deep blasthole camera detection before and after blasting occurrence indicates that the blast induced rock mass crack propagation pattern is rather complex. Nevertheless, the rock mass crack length increment induced by the first blasting, Δ

It is indicated from Figures

Figure

The conclusions drawn from this study are summarized as follows.

For small blasthole blasting in rock mass containing initial damage, the method of calculating relevant parameters is analyzed. The analysis is conducted under four different circumstances which are water being the cushion at the bottom of blasthole, air being the cushion at the bottom of blasthole, coupled charge, and decoupled charge. To conveniently characterize rock mass damage, a damage variable is defined using the rate of change in the longitudinal wave velocities in rock mass before and after blasting. And the equation for calculating blast induced rock mass damage accumulation is derived.

In situ small blasthole blasting tests are conducted. The blasthole wall crack propagation subject to blasting is experimentally observed and theoretically calculated. Analysis of the derived results indicates that blasting activates the original crack in rock mass, and the effect of the first blasting dominates. Besides, occurrence of rock mass damage adjacent to the blasthole can be identified when rock mass damage variable satisfies_{n} >_{cr} = 0.19.

Experimental results indicate that the distance to blasting source controls the extent of blast induced rock mass damage. With an increase in the distance to blasting source, a nonlinear decrease in rock mass damage increment or accumulated rock mass damage is observed, and the rate of the decrease drops gradually. This phenomenon is also applicable for the particle vibration velocity.

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

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research work was funded by the CRSRI Open Research Program (CKWV2017509/KY), the National Natural Science Foundation of China (51774107; 51774131), the Opening Project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (KFJJ17-12M), the Opening Project of Work Safety Key Lab on Prevention and Control of Gas and Roof Disasters for Southern Coal Mines, Hunan Provincial Key Laboratory of Safe Mining Techniques of Coal Mines (Hunan University of Science and Technology) (2017), the Fundamental Research Funds for the Hefei Key Project Construction Administration (2013CGAZ0771), and the Fundamental Research Funds of the Housing and Construction Department of Anhui Province (2013YF-27). All the financial support is gratefully acknowledged.