Practical Assesment Of Rock Damage Due To Blasting.pdf

International Journal of Mining Science and Technology xxx (xxxx) xxx

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Practical assessment of rock damage due to blasting Jhon Silva a,⇑, Tristan Worsey a, Braden Lusk b a b

Department of Mining Engineering, University of Kentucky, Lexington, KY 40508, USA Department of Mining and Nuclear Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA

a r t i c l e

i n f o

Article history: Received 8 August 2017 Received in revised form 20 February 2018 Accepted 14 November 2018 Available online xxxx Keywords: Blasting Fracture Fracture extension Peak particle velocity

a b s t r a c t Blasting is the most cost effective methodology to break rock for mining or civil engineering applications. A good production blast will break only the rock that is needed to be removed, leaving the host rock with minimal damage. The control of rock damage due to blasting is very important when it comes to mine or construction design, safety, and cost. Damage to the host rock due to a production blast could result in failures, overbreak and unstable ground. Knowing how far the fractures generated by a production blast will go into the host rock is a valuable tool for engineers to design a safe highwall while keeping the actual excavation close to the design. Currently, there are several methods available to predict damage due to blasting. The accuracy of many of these methods is questionable, and in most cases, the methodologies over predict the results. This often leads to inefficient mines and poor construction works. When the current methodologies are reviewed, each one presents sound approaches, but in many cases they also lack consideration of other variables that, according to the authors, need to be included when predicting blast damage. This paper presents a practical methodology to assess the rock damage from blasting by combining other methodologies. The proposed method allows consideration of more variables when compared to available methods, resulting in a more accurate rock damage assessment. The method uses the estimation of the generated levels of peak particle velocity with the distance from a production blast presented by Persson and Holmberg, the peak particle velocity damage ranges proposed by Forsyth and the relationship between the static compressive strength and dynamic compressive strength of rocks from Liu. The new methodology was validated using the data published in a large-scale study performed in granite by Siskind. Ó 2018 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction Rock damage due to blasting is a very important topic when it comes to ground control in surface mines, construction works, underground mines, and tunnels. Blast induced rock damage can induce ground failures that cause serious safety hazards, production losses and lawsuits. Knowing the limit of rock damage due to blasting will make safer and more productive mines and construction operations. Currently, there are several methods available to predict damage due to blasting including Holmberg-Persson, Ash, Johnson, CSM, NIOSH modified, and Powder Factor approach, among others [1–4]. In most of the cases, such methodologies over predict the assessments, providing poor results despite its sounding approaches. This paper presents a practical methodology to assess the rock damage from blasting by combining other methodologies. ⇑ Corresponding author. E-mail addresses: [email protected] (J. Silva), [email protected] (T. Worsey), [email protected] (B. Lusk).

The proposed method includes equations from Holmberg and Persson, Liu, and Forsyth [1,5,6]. The new methodology was validated using the data published in a large-scale study performed in granite by Siskind, resulting in accurate predictions when compared to current methods to assess rock damage from blasting [7]. According to Sun, there are no less than 18 methods that have been proposed to predict damage due to rock blasting [8]. Many of the methodologies to assess rock blast damage are based on numerical modeling, such as Blair, Ansys, Jaroslav, and few proposals are based on observations (empirical approach) from testing, including Esen et al., Olsson and Bergqvist, Olsson et al. [9–14]. With the advanced in computational tools, (hardware and software) soft computing techniques have been also applied to the rock extension damage problem. The expression ‘‘soft computing” was introduced by Lotfi Zadeh to solve problems that doesn’t have an exact solution and are tolerant to imprecisions and approximations [15,16]. A comprehensive review of soft computing technology applications in several mining problems can be found in Jang and Topal [17]. Most of the proposals of soft computing techniques applied to the rock damage extend assessment can be found in

https://doi.org/10.1016/j.ijmst.2018.11.003 2095-2686/Ó 2018 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article as: J. Silva, T. Worsey and B. Lusk, Practical assessment of rock damage due to blasting, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2018.11.003

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Mottahedi, Sereshki and Ataei [18]. Table 1 summarizes some of the available rock damage extent models, primary assumptions, advantages and disadvantages. As seen in Table 1, most of the methodologies calculate a particle velocity value (PPV) produced by the detonating charge in the borehole and then such value is compared against a PPV value that is known or adopted (most of the time based on site specific field tests) that will produce some damage in the rock or rock mass. Table 2 includes one of the peak particle velocity damage criterion modified from Bauer and Calder [19]. The calculation of the PPV can be done using modifications to the scaled distance equation or using soft computing methodologies such as in Khandelwal and Singh or Verma and Singh [1,20– 22]. The selection of particle velocity as a parameter is driven by the simplicity in measuring using conventional geophones. When PPV is used as a parameter, the damage zone is calculated as the distance between the borehole and the location in the rock mass where the PPV value doesn’t cause any fracturing or damage in the intact rock/rock mass. Table 1 also shows that the pressure generated by the explosives in the borehole is chosen as the main blast damage parameter for another researcher. When the pressure is used as a parameter, the damage zone is determined by comparing the strength of the rock/rock mass against the compressive and tangential stresses generated by the explosive charge. It is assumed that there is not damage in the rock/rock mass if the produced stresses are lower than the strength of the material. A disadvantage of this approach is the uncertainty in the value used as the pressure generated in

Table 2 PPV criterion for blast-induced damaged, modified from Zadeh [15]. PPV (mm/s)

Effect

<250 250–635 635–2540 >2540

No fracturing of intact rock Minor tensile slabbing will occur Strong tensile and some radial cracking Complete break-up of rock mass

the wall of the borehole (borehole pressure). Some studies compute the borehole pressure by dividing the detonation pressure (the energy storage in the explosive) by two (2.0) Cook or assuming that the detonation pressure is equal to the borehole pressure Hino [23,24]. More recent and sophisticated proposals involve the stiffness of the borehole wall (stiffness of the surrounding rock) in the calculation of the borehole pressure to estimate the damage zone. The uncertainty of the borehole pressure value used in the assessment of the damage zone is increased by the difficulty to measure this parameter especially for regions close to the borehole. 1.1. Traditional blast damage zone prediction models There are various definitions of the blast damage zone (BDZ). According to Singh, the BDZ is the extent of the zone where the blast hole changes the rock mass properties, downgrading its performance and behavior [25]. Scoble et al. defines the BDZ as the reduction in integrity and quality of the damaged rock mass [26]. The National Institute of Occupational Safety and Health (NIOSH) defines the BDZ as the unintended collateral damage and

Table 1 Rock damage extend models. Model

Year

Procedure

Advantage

Disadvantage

Holmberg-Persson

1978

Calculate PPV to compare against PPV damage ranges

-Developed for cylindrical charges -Easy to use when all parameters are known

Swedish Rock Engineering Research Organization (SevBeFo)

1996

Fractures mechanics theories. Calculates extent of damage zone around a borehole

-Uses gas pressures generated in the borehole -Explosive properties included Velocity of Detonation (VOD) and isentropic properties of the explosive

Colorado School of Mines (CSM)

1969

Calculate PPV to compare against PPV damage ranges

Hustrulid-Lu

2002

Calculate PPV to compare against PPV damage ranges. Improved from CSM approach

Modified ash

2010

Calculates extent of damage zone around a borehole using the explosive energy

Rock constant approach

2010

Based on Holmber’s approach for tunnels. Calculate extent of damage zone around a borehole Based on hydrodynamic studies by Hustrulid. Calculate PPV to compare against PPV damage ranges

2013

Based on Artificial neural network (ANN) and multiple regression

-Uses gas pressures generated in the borehole -Uses Poisson ratio, density of the rock and longitudinal wave speed of the rock -Uses gas pressures generated in the borehole -Introduces attenuation formulations for the PPV -Uses basic properties of explosives -Uses ANFO as reference -Easy to use -Uses basic properties of explosives -Uses ANFO as reference -Easy to use -Uses basic properties of explosives -Includes compressive strength of the rock as a variable -Easy to use -Considers rock and rock mass parameters (UCS, RQD, RMR)

-Properties of explosive are not considered -Not strong theoretical support for its derivation -Parameters of the equation are established after several tests -Difficult to follow because the complexity of the formulation and the number of variables Fracture toughness parameter from the rock needs lab testing -Too many ‘‘correction” factors in the final formulation -Cylindrical charges divided into a chain of spherical charges -Number of field tests needed to be conducted to find inelastic coefficient -Number of field tests needed to be conducted to find constant parameters (attenuation) in the equation

2015

Based on Fuzzy Logic techniques and linear multiple regressions

Neiman hydrodynamic Approach

Jang and Topal–artificial Neural Network Approach Mohammadi et al.– fuzzy Logic Approach

-Considers rock mass parameters (RMR), -Considers blasting parameters (powder factor, ratio of contour holes to total holes)

-Only density of the rock is accounted as a rock variable -No rock properties are included -Degree of hole confinement difficult to assess -Explosive energy parameter difficult to assess

-Blasting parameters are not involved in the problem. -A large data set of blasting parameters (202 data sets) are required to obtain a reliable model. -Applied in a site specific project (Alborz tunnel)

Please cite this article as: J. Silva, T. Worsey and B. Lusk, Practical assessment of rock damage due to blasting, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2018.11.003

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weakening of the rock mass around the periphery of an underground excavation due to explosive use. The idealization of the explosion in a borehole in a rock mass indicates that there are four zones surrounding the borehole studied by Whittaker et al.: (a) the crushing zone, (b) the crack/fracture zone, (c) the fragment formation zone; and (d) the elastic zone [27]. Fig. 1 shows the different zones and a typical radial crack pattern observed around a blast hole. The crushing zone is the zone of material adjacent to the blasthole. Usually this zone is in direct contact with the explosive. The diameter of this zone is a function of many variables such as coupling ratio, explosive type, rock and rock mass properties among others. Its determination is not easy and in most of the cases the boundary between the crushing zone and the fracture zone is not evident. In the fracture zone, the presence of fractures is considerable (high fracture density zone) and as mentioned before, in most of the cases its boundary is combined with the crushing zone boundary. Beyond the fracture zone, there is the fragment formation zone. In this zone there are fractures but the density is lower compared to the fracture zone. Usually, the fragment formation zone cracks are evident in the remained rock mass of walls of a tunnel or in the face of a slope. The depth of this zone will influence the ground control required to guarantee the stability of excavations, highwalls and slopes. Fig. 1 also shows a simplification of the different cracks created by a blast hole. According to Saiang, the generated cracks can be classified as: (a) macroscopic and microscopic, of different shapes and sizes; (b) in a horizontal section, they will follow a radial distribution and are highly anisotropic and non-persistent and, (c) the fracture distribution and its nature (including the extent and the intersection of the cracks) have spatial characteristics which depend on factors such as explosive properties, blast hole geometry, and rock/rock mass properties [28]. A damage zone prediction model will assess the extent of the crack/fracture and the fragment formation zone accurately.

Fig. 1. Typical radial crack pattern observed around a blast hole [27].

2. Methodology in this paper The studies from Holmberg and Persson, Liu et al., Fleetwood, and Forsyth were used to propose the practical methodology to assess rock blast damage included in this paper [1,6,5,29]. Next a more in depth overview of those studies is included. 2.1. Holmberg and Persson 1970 In the late 1970s, Holmberg and Persson (H-P) introduced the Swedish approach to contour blasting [1]. The approach is based upon rock damage being related to peak particle velocity using the basic equation given by:

PPV ¼

KQ a

ð1Þ

Rb

where PPV is the peak particle velocity; K, a and b are constants; Q the explosive charge; and R the distance. The constants are site specific and could be estimated from a set of seismograph records. The H-P model breaks down the explosive column into segments and sums the contribution of each segment at a point according to Eq. (1). By doing this, the discrete formulation of Eq. (1) corrected by Hustrulid and Lu, is given in Eq. (2) [30].

0

1

H B X C DL B C PPV ¼ Kqa 2ba A @ DL¼T ð r o Þ 2 þ ð z  zo Þ 2

ð2Þ

where q is the loading density of the explosive per unit length; H the depth to the bottom of the explosive column; T the depth to the top of the explosive column; DL the incremental charge length; and r o and zo the coordinates of the point in space under consideration. As mentioned before, the detailed derivation of Eq. (2) can be found in Hustrulid and Lu [30]. By using Eq. (2) for a specific site, it is possible to develop vibration contours around a blasthole as shown in Fig. 2a, adapted from Erickson [31]. Fig. 2b shows the prediction of the PPV for different loading densities and distances from the blasthole for points in the mid part of the explosive column, adapted from Iverson et al. [32]. To be able to use these curves for design, one must determine the PPV value associated with unacceptable damage. For example if 1500 mm/s is adopted as a PPV limit value, the extension of the damage zone will go up to 0.65 m (Fig. 2b) for a loading density explosive charge of 1.0 kg/m and up to 1.37 m if the loading density is 2.5 kg/m.

Fig. 2. H-P model PPV estimation results around a blast hole.

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The validity of the two fundamental assumptions of the H-P method are as follows: the entire charge detonates instantaneously; and the amplitudes are simply summed without considering arrival direction. The shape of the explosive charge between spherical and cylindrical has been discussed by others, including Blair and Minchinton, and Iverson et al. [9,32]. One disadvantage of Eq. (2) is the assumption that in the formulation, every elemental charge contributes to the generation of the with the same weight or proportion. This disadvantage is more evident for high column lengths of explosive. Iverson et al. corrected the original error of the H-P model by re-writing Eq. (1) as follows [32]:

PPV ¼

KQ a

ð3Þ

b

R 

where R is the average distance to the observation point for all of the elemental charges and can be evaluated as: 

R¼

1 L

Z

L

h

ðz  zo Þ2 þ ðr  r o Þ2

i0:5

ð4Þ

dz

0 

The solution proposed by Iverson et al. involves determining R 

and obtains PPV using Eq. (3) [25]. Fig. 3 shows the value of R for different heights of explosive columns at different point locations ro for points in the mid part of the explosive column. In Fig. 3, for example, if the explosive column is 3 m (L ¼ 3 m), and the point 

is located at ro ¼0.6 m, and the average distance is 1 m (R ¼1 m). On the other hand, for the same distance, (ro ¼0.6 m) if the explosive column is L ¼ 16 m high, the average distance will be 

R ¼4.1 m. If it is considered that the PPV is a function of the distance, in the case of L ¼ 16 m high column, the underprediction of the PPV will be important. As the H-P method continues to be reviewed, there are different modifications available that attempt to improve the accuracy of predictions, such as Arora and Dey; Inverson et al., and Smith [32–34]. Despite the limitations mentioned before in the original

formulation and its questionable accuracy, the H-P method, is popular and its popularity lies in the use of the scaled distance concept that is of relatively easy understanding and implementation and it will be used in this paper in its basic formulation (Eq. (1)). 2.2. Relevant results of studies by Liu, Forsyth, and Fleetwood Some materials possess properties which are strain rate sensitive. Strain rate sensitivity is observed when the stress-strain properties of a material change according to the strain-rate regime affecting the way the material responds under loading conditions. Despite the lack of a formal consensus on the manner in which material parameters are affected by strain-rate loading conditions, those changes can be characterized according to the behavior of the initial Young’s modulus and the ratio of the dynamic strain ðed Þ to the static strain ðes Þ at the maximum stress ðrd =rs Þ. A study presented by Liu et al., using a split Hopkinson pressure bar (SHPB) determined the dynamic strength properties of three different types of rocks [5]. The rocks under study were samples of amphibolite, sandstone and sericite-quartz schist. Fig. 4 shows the dynamic properties of the tested rocks under different strain rate conditions reported by Liu et al. [5]. According to the study, if a strength increase factor ðgÞ is defined to measure the changes in the strength of the material for different dynamic conditions, it will be possible to asses the dynamic strength from a static test, knowing the strain-rate. The expression of the strength increase factor for the different types of rock and the strain rate reported by Liu are included in the set of Eq. (5) as:

gamp ¼ 0:44598  e_ ð1=3Þ  0:37798 gsas ¼ 1:41039  e_ ð1=3Þ  3:58302 gsqs ¼ 2:09497  e_ ð1=3Þ  7:96242

For example if a strain rate is 100 s1, the increase factor will be 1.69 and 2.96 for the amphibolite and the sansdtone respectively. Forsyth, assuming a plane wave condition, discusses a relationship between the PPV and the material properties to calculate the PPV damage threshold given by Forsyth [6]:

PPV max ¼ 0:1  UCS



Fig. 3. Average distance R for various location points r o .

ð5Þ

Vp E

ð6Þ

where PPV max is the critical peak particle velocity above which the rock will fail under tension, mm/s, 0:1UCS the uniaxial tensile stress estimated as the tenth percent (0.1) of the uniaxial compressive strength ðUCSÞ, in MPa; V p the P-wave velocity; m/s; and E the static Young’s Modulus, GPa. Fleetwood et al. discusses the improvements in the accuracy of the estimation of the PPV threshold value when Eq. (4) is used with the dynamic properties parameters of the rock instead of the static values as proposed originally by Forsyth [6,29]. The strain rate estimated by Fleetwood et al., in the case study presented was

Fig. 4. Stress-strain curves for amphibolites, sandstone and sericite-quartz schist [5].

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between 10 and 100 s1, in agreement with information provided by Chitombo et al. for blasting events [29,35]. For the case study presented by Fleetwood et al., the PPV threshold damage estimated using dynamic parameters in Eq. (4) was five times higher than the application of the original formulation with static values [29]. The results were validated according to the level of damage observed in the walls of the tunnel and the recorded PPV values. 3. Proposed steps for the assessment of the rock damage due to blasting While there are several methods to predict damage due to rock blasting, none of the methods encompass all the parameters that should be included in the analysis [29]. The steps discussed in this paper, takes the most significant parts from different rock blast damage studies, to create a simple but logical sequence to include the variables that should be considered in a rock damage analysis. The proposed sequence is a first attempt to create a practical and comprehensive rock blast damage model utilizing important aspects of the other methods available. Further study will be required to refine the methodology. The five steps proposed to assess blast rock damage are as follows:

Table 3 Physical properties of Lithonia granite from study by Siskind [7]. Parameter

Value

Specific gravity Weight density (kg/m3) Longitudinal propagation velocity, in situ (m/s) Longitudinal bar velocity (m/s) Tensile strength (N/m2) Compressive strength (N/m2) Modulus of rigidity (N/m2) Young’s modulus (N/m2) Poisson’s ratio in situ

2.63 2630 5550 2740 3.10  106 207  106 10.3  109 20.7  109 0.26

The steps of the proposed methodology in this paper are explained in detail using the data from Siskind and included in Table 3. 3.2. Detailed steps for the assessment of the rock damage due to blasting Step 1: static material properties According to Table 3, the UCS of the rock is 207  106 N/m2 and the Young Modulus is 20.7  109 N/m2. Step 2: dynamic material properties

(1) Determine the static material properties for the rock under study including UCS, Young’s Modulus and P-Wave velocity (2) Determine the dynamic material properties based on the strain rate levels expected from blasting (3) Determine a PPV damage limit using Forsyth, Eq. (4) and the dynamic material properties [6]. (4) Using the H-P blast damage model, determine the isovibration contours around a single hole. To use the H-P model, it is required to know the parameters in Eq. (2) ðK; a; bÞ. Those parameters can be assessed using a traditional blast vibration analysis relating scaled distance to PPV from a database of seismograph information collected at the site. (5) Compare the PPV damage limit value calculated in step 3 against the iso-vibration contours calculated in step 4 to assess the area where damage limit PPV values will be reached. The calculated area will be a prediction of the envelope subject to blast induced vibration damage. To validate the accuracy of the results using the previous steps the study presented by Siskind was used [7]. 3.1. Retrospective case study utilizing USBM RI 7901 Siskind conducted a study on a full scale blast in Lithonia Granite, Lithonia, GA [7]. This rock has been used for testing in the US because its orthotropic characteristics. The blast used large diameter holes of 165 mm and ANFO. The measurements taken before and after the blast to indicate the extent of damage in cores recovered using horizontal core drilling were acoustic pulse velocity, porosity, permeability, compressive strength, and, Young’s modulus. According to the measurements, the acoustic pulse velocity is the most sensitive parameter to measure the extent of the damaged rock due to blasting. For the test setup by Siskind, it was found that there was heavy damage (severely fractured zone) between the center of the blast hole and a distance of 64 cm (8 blast hole radii), and slight damage between 64 and 114 cm (8– 14 blasthole radii) [7]. Beyond 114 cm no damage was reported according to the measured parameters. Table 3 includes the physical properties of the Lithonia granite.

The dynamic properties can be estimated based on the static values through the strength increase factor ðgÞ. Using the results from Liu and assuming a value for g ¼ 3 the dynamic compressive strength is given by:

UCSdyna ¼ 3:0  UCSstatic UCSdyna ¼ 3:0  207  106 N=m2 ¼ 621  106 N=m2 Step 3: PPV damage limit using dynamic material properties Using this dynamic UCS in the Forsyth equation (Eq. (4)), the PPV damage limit is given by:

PPV max ¼ 0:1  UCS

Vp E

m=sec PPV max ¼ 0:1  621 MPa 5550 20:7 GPa mm m PPV max ¼ 16; 650 sec ¼ 16:65 sec

Step 4: PPV values generated around a single hole using H-P model The basic equation (Eq. (1)) was used to calculate the generated PPV according to the H-P model. The parameters used were originally suggested by Holmberg-Persson and given by: K ¼ 700; a ¼ 0:7; b ¼ 1:5. The amount of explosive per hole was calculated from the original RI 7901 report and corresponds with 277 kg of explosive [7]. Fig. 5 shows the expected PPV values for the 165 mm blast-hole diameter in the midpoint of the

Fig. 5. PPV produced by a single hole according RI 7901 [7].

Please cite this article as: J. Silva, T. Worsey and B. Lusk, Practical assessment of rock damage due to blasting, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2018.11.003

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Fig. 6. PPV expected values and PPV maximum limits.

blast-hole, using the parameters originally recommended for the H-P model.

into these naturally occurring cracks and will tend to extend and/ or expand these preexisting cracks preferentially to causing damage to the intact rock material at distance. For this reason, estimation and prediction of rock mass damage is related more to the existing geologic conditions than it is to the intact strength of the rock material. Conversely, in massive rock material, predictive models considering the rock strength are more reasonably applied to predict the extent of damage. For this reason, the comparison data utilized for the damage prediction methodology presented in this paper was taken from a rock deposit that is more massive in nature. For a definitive model that considers both damage to intact rock and damage to the rock mass, other parameters will need to be considered. The methodology in this paper advances understanding and provides a tool for assessing the damage to intact rock surrounding a borehole in typical blasting scenarios.

Step 5: PPV values generated vs maximum limits Fig. 6 shows the comparison between the produced PPV and the PPV limits below which no fracture damage is expected. 4. Results The extent of rock damage predicted using the static value of the UCS is 3.47 m. The extent of rock damage predicted using dynamic compressive strength (3.0) is 1.67 m. And the extent of rock damage predicted using 1000 mm/s as the limit of damage as suggested by Holmberg-Persson is 2.34 m. If the measured value reported in the RI 7901 (1.14 m) is assumed as the accurate value, the error in the estimation of the damage fracture distance is included in Table 4 [7]. One potential source of error in the calculation of damage extent is the lack of empirical data for the site constants to be utilized in the H-P model. By utilizing actual site constants and data from the Lithonia site, it may be possible to assess the validity of this method further. That data was unavailable for this research. 4.1. Discussion The extent of rock damage due to blasting is an important parameter to understand the development of mines, civil infrastructure, and development projects. A number of theories have been presented to estimate the range of damage for typical blasting scenarios. These theories have historically overestimated the extent of damage to the rock material, and have not been very effective at assessing the damage to the rock mass which is more complex with limited understanding of structural and regional geology. During the blasting process, multiple phases of loading occur that can cause damage to the rock mass. Most practitioners agree that the initial shock and pressure loading serves to extend preexisting micro cracks in the rock material surrounding the borehole. These cracks are further extended by gas pressure that results from the completed detonation process within the hole. In massive rock, the extent of these cracks is the sum of the rock damage observed. In cases where geologic cracking, discontinuities, and joint/bedding planes are present, the gas pressure is often directed

4.2. Further research areas There are only a handful of large scale tests out there that do a good job at proving when blast damage ceases to exist. Doing large scale testing in different geology types would help validate the model. The topic of damage due to blasting is important. For such an important topic, the gap in the literature is inexplicable. The evaluation is time consuming and expensive, probably driving the lack of reported data. The method used above uses constants from Persson and Holmbergs book. Further research into how these constants change is necessary to make a more accurate model. These constants could be used to calibrate models with different parameters or geology types. Also, the equation in step 4 from the Persson and Holmberg book is scrutinized for using an equation of a spherical charge circle instead of a cylindrical weighting each explosive increment charge same. Future research comparing an equation using a cylindrical charge and weighting the contribution to the PPV for each charge according to the distance will give a better prediction and is needed. The new method used an adjustment factor to predict the value of dynamic strength. Future research is needed with tested values for dynamic compressive strength. Also, using tests that take into account confinement and dynamic situations to predict damage range could be useful. Triaxial testing which takes confinement into account will give compressive results that are higher than UCS tests. Increased strength with increased load rate is also seen giving evidence that dynamic strength is a more realistic property to use for damage prediction. One dynamic testing method that could use future research for damage prediction would be the Split Hopkinson pressure bar. There are many parameters that are not present in this model. At the moment, this prediction method incorporates the most practical variables for predicting rock damage due to blasting. There is still much to do to incorporate the different variables that go into rock damage. Other variables that could possibly contribute to rock damage due to blasting are timing of shot, hole diameter, blast design parameters, confinement, energy of explosives, geological conditions, and preexisting fractures or discontinuities.

Table 4 Comparative results different methodologies. Parameter

Actual value (measured)

Damage extent (m) Error (%)

1.14 0.0

Methodology in use Proposed methodology

Using 1000 mm/s criterion

Using static parameter

1.67 46.5

2.34 105.3

3.47 204.4

Please cite this article as: J. Silva, T. Worsey and B. Lusk, Practical assessment of rock damage due to blasting, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2018.11.003

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5. Conclusion Currently there are methods in the literature that predict damage due to blasting. Most of them are very conservative methods that only use a couple of parameters for the prediction. Each one of these methods has a very sound approach that just lacks further research to introduce more variables into the model. This new method takes the sound parts of other methods and combines them to create a prediction method that uses more variables that influence rock damage due to blasting. Combining these methods into one method better predicts rock damage due to blasting when compared to the large-scale damage study performed by Siskind. Being able to more accurately predict rock damage due to blasting will help design more efficient mines and help avoid legal cases involving blast damage.

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Please cite this article as: J. Silva, T. Worsey and B. Lusk, Practical assessment of rock damage due to blasting, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2018.11.003