Influence of Preconditioning and Tunnel Support on Strain Burst Potential

Abstract

Strain burst hazard is one of the main challenges that faces deep underground environments. To manage it, it is needed to assess its probability occurrence (or potential). Various methods have been proposed over the years to assess the phenomenon early on. However, due to uncertainties in rock mass properties and the physical processes of the phenomenon, mitigation measures are an additional important line of defense to ensure workplace safety. While work has been carried out to assess the rockburst hazard better and improve support systems, the effect of mitigation measures on strain burst hazard potential is unclear. This paper studies the influence of the implementation of shotcrete and rockbolts support and destress blasting in tunnels on strain burst potential, based on two-dimensional numerical models of circular tunnels. The results highlight that, as expected, the use of mitigation measures allows the strain burst occurrence to decrease. However, the strain burst hazard level does not decrease easily, even when using mitigation measures. In the case of serious overbreak hazards, only a combination of system support and destress blasting seems to have an impact on these events, and not for all the simulated cases.

1. Introduction

Deep underground mining and civil tunnels are associated with high stress magnitudes that can lead to serious ground control problems [1,2]. One of these main problems are the rockbursts, which are explosive failures of rock that occur when high stress concentrations are induced around underground openings in brittle rock masses [3]. Usually, rockbursts are divided into three categories based on their mechanism of occurrence [4,5,6]: (1) pillar bursts caused by the complete collapse of support pillars; (2) fault slip bursts caused by the slippage of some pre-existing faults due to stress changes generated by underground excavation; and (3) strain bursts caused by high stress concentrations at the edge of mine openings that exceed the strength of the rock [7,8]. The most frequent rockburst mechanism in tunneling corresponds to strain bursting [4]. This phenomenon can be preceded by the visible extension of fractures under compressive loading, known as spalling damage [8].

As spalling damage and associated strain bursting present significant issues in underground environments, it is necessary to assess this hazard early by defining the extent and intensity of the event. However, due to the complex nature of the rockburst phenomenon, rockburst prediction is quite difficult. Over the years, various methods have been developed based on empirical knowledge [9,10,11], numerical modeling [3,12,13,14] or statistical analysis [15,16,17]. A comprehensive review of some of these methods and others can be found in the work of Zhou et al. [18]. Rockburst charts, which are simple and straightforward to use, can also be adopted as valuable design tools for the preliminary rockburst potential estimation by practical engineers. Additionally, these charts can be used to help predict the demand of rock support [19]. One of these well-known charts is the one proposed by Kaiser et al. [20] and completed by Martin et al. [21], and is based on historical cases. A more rigorous chart has been proposed by Diederichs [3] using numerical models integrating the damage initiation and spalling limit (DISL) approach [8]. Both of these charts have been shown to successfully estimate the burst potential by predicting the depth of brittle failure around tunnels [22,23,24]. Using these charts to assess the rockburst hazard early, it is often possible to reduce the risk by selecting appropriate mining or excavation methods and sequences [4]. Moreover, due to uncertainties in rock mass properties and boundary conditions, mitigation measures are an additional important line of defense to ensure workplace safety.

Rock support systems that can resist under rockburst conditions are widely used to mitigate strain burst. They have to meet the following three primary support functions [20,25]: (1) reinforce the rock mass to strengthen it and control bulking through, for example, rebar or stiff friction bolts; (2) retain broken rock to prevent fractured block failure and unraveling through, for example, mesh, shotcrete or spay-on-liner; and (3) hold fractured blocks and securely tie back the retaining elements to stable ground through, for example, deformable cables and yielding bolts. Classically, shotcrete and rockbolts are the main support systems used in tunneling [26]. In that case, the shotcrete is used to enhance the surface-retaining capacity of the support system while the rockbolts must be able to dissipate the excessive release energy. Preconditioning can also be used to defuse burst activities caused by stress changes during rock excavation. In particular, destress blasting, which is a method of preconditioning consisting in the blasting of highly stressed rock to reduce the local stress and stiffness of the rock [27], is now implemented as a standard rockburst measure across the many mining regions around the world [28,29,30,31].

While work has been done to assess the rockburst hazard better [3,18,32], and improve the rock support system and preconditioning measures currently implemented [7,25,28,33,34], the effect of mitigation measures on strain burst hazard potential is unclear. This paper studies the influence of the implementation of shotcrete and rockbolts support and destress blasting in tunnels on strain burst potential. More specifically, two-dimensional numerical models of circular tunnels are realized considering the DISL approach to represent brittle spalling behavior. These models are compared to the well-known depth of failure charts. Strain burst hazard levels are defined and compared in four cases: (1) no mitigation measures are considered, (2) shotcrete and rockbolts are applied around the tunnel, (3) destressing blasting is used to manage the strain burst, and (4) both shotcrete and rockbolts, as well as destressing, are considered. This works focuses on the strain burst hazard assessment and is looking to compare hazard levels with or without any mitigation measures, which is an aspect unknown to date.

2. Assessment of Strain Burst Hazard

2.1. Strain Burst Charts

The strain burst failure process is driven by stress increases around the excavation in such a manner that the stress reaches the rock mass strength [35]. Therefore, it is possible to estimate the strain burst hazard by assessing the stresses around the excavation and comparing them with the brittle rock mass strength. Based on this premise, and considering field observation of brittle rock failure, Kaiser et al. [20] proposed an empirical relation to estimate the depth of spalling failure. In this relation, the depth of failure, Rf, is normalized to the tunnel diameter, a, and is plotted as a function of the ratio between the maximum wall stress, ${\sigma }_{max}$(${\sigma }_{max}=3{\sigma }_1-{\sigma }_3$, where σ1 and σ3 are the total major and minor principal stresses, respectively), and the uniaxial compressive strength (UCS) of intact rock. Martin et al. [21] completed the relation through a review of available literature [36,37,38,39,40,41,42], where twenty-three cases of spalling failure have been studied (reported in [21]). Figure 1 presents the measured depths of failure given by the literature.

A more rigorous chart has been proposed by Diederichs [3] based on numerical analysis using the damage initiation and spalling limit (DISL) approach [8], detailed below. The failure depth is predicted as a function of maximum wall stress, the crack initiation stress (CI) and the in situ stress ratio, K (Figure 2). CI is equal to 0.5 UCS if no data exist.

2.2. Damage Initiation Spalling Limit (DISL) Approach

The damage initiation spalling limit (DISL) approach is a method developed by Diederichs [8] so engineers could simulate the brittle fracture response in conventional and readily available engineering design software. The method utilizes the generalized nonlinear Hoek & Brown failure criterion [43] to define the limiting stress envelopes, as presented in Figure 3. The lower bound strength corresponds to the damage initiation, while the upper bound strength corresponds to the crack interaction. A transitional curve for in situ rock strength extends between both bounds and is referred to as the spalling limit. In the figure, any stress path that remains below the damage initiation threshold will be elastic and incur no damage. This threshold involves a minimal confinement dependency (elevated cohesion and low friction), while the spalling limit is defined by elevated friction and a cohesion loss [44]. For numerical purposes, the damage initiation limit can be assigned a “peak” parameter and the spalling limit corresponds to “residual” strength parameters. The damage initiation limit and spalling limit can be related to the damage zones, as shown in Figure 3. The damage initiation limit corresponds to the transition between the excavation influence zone (EIZ) and the outer excavation damage zone (EDZo), while the spalling limit corresponds to the transition between the inner excavation damage zone (EDZi) and highly damaged zone (HDZ).

Various methods and discriminants exist to estimate the potential of rockburst occurrence. A simplified approach consists in evaluating a single-index empirical criterion to assess the rockburst hazard. These criteria are often based on the theories of strength, energy and stiffness. A review of some of these criteria and discriminants can be found in the work of Qiu & Feng [46]. One of these discriminants is the ${\sigma }_{max}$/UCS ratio.

Table 1. Values of the ${\sigma }_{max}$/UCS ratio and associated rockburst potential.

Wang et al., 1998 [47]		Hoek and Marinos, 2000 [48]		Diederichs and Martin, 2010 [49]
${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{x}}/\mathit{UCS}$	Rockburst Potential	${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{x}}/\mathit{UCS}$	Rockburst Potential	${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{x}}/\mathit{UCS}$	Rockburst Potential
<0.34	Few spalling	<0.3	No rockburst	<0.4	Stable (no stress damage)
0.34–0.42	Severe spalling	0.3–0.5	Weak rockburst	0.4–0.6	Minor spalling
0.42–0.56	Moderate damages	0.5–0.7	Strong rockburst	0.6–0.8	Moderate overbreak
0.56–0.7	Intense rockburst	>0.7	Violent rockburst	>0.8	Serious overbreak

summarizes the values of the ratio with the associated rockburst potential. Over the years, thanks to the increase of historical cases and advances in numerical modeling, the values of the ratio and the associated rockburst potential have evolved. However, the range of values has stayed similar.

3. Methodology

To evaluate the influence of the implementation of shotcrete and rockbolts support and destressing on strain burst potential, the following steps have been defined:

• Numerical modeling of the strain burst considering the DISL approach;
• Comparison of the results with the rockburst graphs of Mathews et al. [21] and Diederichs [3] to validate the models. Excavation damage zone depth of failure is also considered;
• Definition of the strain burst potential for each model;
• Integration in the numerical models of mitigation measures: (1) shotcrete and rockbolts support, (2) destressing, and (3) a combination of shotcrete support and destress blasting;
• Evaluation of the influence of the mitigation measures on the strain burst potential assessed previously.

Fifty preliminary models were run, considering five different GSI values, five different UCS values and two different tunnel depths. These preliminary models evaluate the influence of the fracturing of the rock mass, of the strength of the rock mass and of the stress’s environment. They do not consider any mitigation measures. When integrating these mitigation measures, only the deeper tunnels are considered as they are the ones presenting a higher strain burst occurrence probability.

3.1. Numerical Modeling of the Strain Burst and Mitigation Measures

Two-dimensional finite element software RS2 Version 11.013 [50] is used to simulate the strain burst potential considering the DISL approach. The models, boundary conditions and geomechanical characteristics are presented below, followed by the procedure used to integrate mitigation measures.

3.1.1. Characteristics of the Models

The models represent a circular tunnel of radio five meters, included in a box of dimension 30 × 30 m to ensure that there is no influence of the boundaries (Figure 4). The models are meshed using triangular nodes. The size of the elements is defined with a gradation from the cavity toward the limits. They are smaller close to the tunnel and grow larger close to the boundaries. To define the stress environment, two tunnel depths were considered: 1000 and 2000 m. As strain bursts occur in brittle rock, it can be assumed that the intact rock density is 2700 kg/m³ [51]. Considering a stress ratio, K, of 1.5, the stress environment corresponding to a tunnel of 1000 m depth presents an in situ major stress, σ1, equal to 40 MPa and an in situ minor stress, σ3, equal to 27 MPa. In the case of the 2000 m deep tunnel, the in situ major stress, σ1, is equal to 80 MPa and the in situ minor stress, σ3, is equal to 53 MPa.

3.1.2. Mechanical Parameters

An elastoplastic model is assumed for the rock mass surrounding the tunnel. The brittle rock failure behavior is define considering the DISL approach. The crack initiation stress (CI) is considered equal to 0.5 UCS, as proposed by Diederichs [3]. The mechanical and strength properties of the intact rock are presented

Table 2. Mechanical and strength properties of the intact rock.

Young’s Modulus (E)	Poisson’s Ratio (υ)	Uniaxial Compressive Strength (UCS)	Tensile Strength (σt)	Hoek & Brown Material Constant a	Hoek & Brown Material Constant s	Hoek & Brown Material Constant mi
50 GPa	0.25	120–320 MPa	7 MPa	0.5	1	25

. They have been defined to be consistent with a high strength rock as an Andesite rock [52]. As the stain burst is assumed to occur when a competent rock suffers high stress [3], in this study the uniaxial compressive strength (UCS) is considered to vary from very strong to extremely strong [53,54,55], with steps of 70 MPa. The material constant, m_i, is equal to 25, as for volcanic rock.

The mechanical and strength properties of the rock mass are presented in

Table 3. Mechanical and strength properties of the rock mass.

Geological Strength Index (GSI)	Rock Mass Young’s Modulus (Erm)	Rock Mass Poisson’s Ratio (υrm)	Rock Mass Uniaxial Compressive Strength (UCSrm)	Rock Mass Tensile Strength (σtrm)
55–95	20.4–49 GPa	0.18–0.24	10–242 MPa	0.2–8.8 MPa

. Diederichs [8] showed that brittle spalling damage initiates for massive or moderately jointed rock (GSI higher than 55). Therefore, five rock mass qualities are considered and vary with a step of 10. The rock mass uniaxial compressive strength and tensile strength are calculated considering the Hoek & Brown failure criterion [43,56], and the rock mass Young’s modulus and Poisson’s ratio are calculated considering the Hoek & Diederichs model [57]. For each of these parameters, the GSI is needed to assess their value, and they therefore depend on it.

3.1.3. Integration of Mitigation Measures

To model the shotcrete and rockbolts support system, an internal pressure is applied at the edge of the tunnel. The applied pressure is determined from the convergence-confinement method [58,59]. The support characteristics have been defined using the RocSupport software Version 5.005 [60]. The rockbolts are considered to present a diameter of 34 mm, with a capacity of 0.354 MN. The spacing between the bolts is 0.2 m. The shotcrete presents a thickness of 0.30 m, a Young’s modulus of 30 GPa and a Poisson’s ratio of 0.2. The applied pressure is equal to 0.2 MPa (Figure 4), which means that the internal pressure of the shotcrete and rockbolts is equivalent to 20% of the in situ stress, σ1. To be noted, this is an implicit way of modeling a rockbolts support system. To go further, one could explicitly define each rockbolt around the excavation. This has not been done in this work.

To model the preconditioning by destress blasting, the method proposed by Tang & Mitri [61] is followed. This method proposes modeling the preconditioning by modifying the elastic constants that simulate the effect caused by induced fractures in the rock mass. To achieve this, the proposed model considers the parameters α and β that represent the rock fragmentation and stress dissipation, respectively. For the proposed work, the parameter α is taken as equal to 0.5 and the parameter β is taken as equal to 0.2. Considering these parameters, the elastic rock mass parameters are modified in the destressed zone around the tunnel. In this zone, the rock mass Young’s modulus varies from 10.2 GPa to 24.5 GPa, and the rock mass Poisson’s ratio varies from 0.27 to 0.36, in function of the GSI values. In the models, a section of 2.5 m is considered to be destressed (Figure 4).

3.2. Validation of the Models and Assessment of Strain Burst Potential

To validate the preliminary models, the depth of failure is measured around the excavation. Two depths are considered (Figure 5):

• The depth of failure of the spalling limit. This is measured when 100% plasticity is observed;
• The depth of failure of the damage initiation limit. This is measured at the transition between no plasticity and plasticity.

Figure 6 presents both limits considering the three mitigation measures used in the work.

Then, these measured depths of failure are compared to the graphs proposed by Martin et al. [21] (Figure 1) and Diederichs [3] (Figure 2). Moreover, in situ measurements of the excavation damage zone depth (compiled from the literature in [44]) are compared with the measured depth of failure.

The strain burst potential is assessed considering the empirical criterion proposed by Diederichs & Martin [49], based on the ${\sigma }_{max}$/UCS ratio (see Table 1). This potential is evaluated for the preliminary models and when considering mitigation measures. Then, the proportions of no stress damage, minor spalling, moderate overbreak and serious overbreak are compared in each case to highlight the influence of the support system, destressing, and a combination of a support system and destressing on strain burst potential.

4. Results

4.1. Models’ Validation

Figure 7 presents the comparison between the depths of failure for the spalling and damage initiation limits of the 50 preliminary models compared with the published graphs of Martin et al. [21] (Figure 7a) and Diederichs [3] (for a K = 1.5) (Figure 7b). Moreover, the published [44] depths of failure of the outer excavation damage zone (EDZ_o) and highly damaged zone (HDZ) of mudstone for a stress ratio, K, of 1.5 are presented. Figure 6a shows a good correlation between the depths of failure of the empirical data and the depth of failure of the spalling limit. It can be noted that, when presenting a ratio between the maximum wall stress, ${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{x}},$ and the uniaxial compressive strength (UCS) of intact rock higher than 1, there are no empirical data, and in this case the depths of failure of the numerical models are lower than the ones expected with the empirical relation. From Figure 7b, a consistency can be observed between the damage initiation and spalling limit of the preliminary models and the mudstone. Moreover, the preliminary models’ depths of failure better fit the model proposed by Diederichs [3] for a ${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{x}}$/UCS ratio higher than 1.

To go further, a nonlinear regression analysis was conducted to determine the best fit equation to the damage zone of the preliminary models and compare them with the ones assessed for three rock types studied by Perras & Diederichs [44]: mudstone, granite and limestone. The mean uniaxial compressive strength (UCS) of each type of rock is also presented. The results are shown

Table 4. Multiplier (B) and exponent (D) for the best fit damage zones, damage initiation and spalling limit for the various cases modeled, compared with published work.

Rock Type	Stress Ratio K	Mean UCS (MPa)	Zone	B	D	R2
Andesite (from this work)	1.5	220	Damage initiation limit	1.07	0.43	0.83
			Spalling limit	0.55	0.42	0.79
Mudstone [62]	1.5	48	EDZ0	0.71	0.59	0.93
			HDZ	0.2	0.52	0.67
Granite [62]	1.5	246	EDZ0	0.62	0.58	0.81
			HDZ	0.09	0.62	0.48
Limestone [62]	1.5	113	EDZ0	0.66	0.63	0.95
			HDZ	0.18	0.34	0.42

. The form of the equation was first proposed by Perras et al. [62], where the multiplier and the exponent in the general form of the Equation (1) are B and D, respectively:

$$\mathrm{Rf}/\mathrm{a}=1+\mathrm{B}({\sigma }_{max}/\mathrm{CI}-1{)}^{\mathrm{D}}$$

(1)

The table shows higher R² values for the EDZ₀ and damage initiation limit than for the HDZ and spalling limit. While the mudstone presents the higher difference in terms of UCS with the andesite studied in this paper, it presents the best correlation in terms of multiplier and exponent.

4.2. Influence of Mitigation Measures on the Depth of Failure and Strain Burst Potential

Figure 8 presents the depths of failure for the spalling and damage initiation limits considering the rock mass without any mitigation measures, with a support system, considering destress blasting, and considering a combination of destress blasting and a support system. It highlights that, when only considering destress blasting, the depth of failure does not decrease as could be expected. This can be explained by the defined destressed zone itself, as it corresponds to a ratio Rf/a of 2. In other words, the destress blasting could debilitate the rock mass and therefore generate major brittle failure. When considering a support system or a combination of both studied mitigations measures, the depth of failure decreases drastically.

Table 5. Multiplier (B) and exponent (D) for the best fit damage initiation and spalling limit considering no mitigation measures, a support system, destress blasting, and a combination of a support system and destress blasting.

Mitigation Measures	Zone	B	D	R2
Without any mitigation measures	Damage initiation limit	1.06	0.42	0.80
	Spalling limit	0.55	0.43	0.78
Support system	Damage initiation limit	0.15	1.4	0.89
	Spalling limit	0.06	1.60	0.88
Destress blasting	Damage initiation limit	0.79	0.54	0.88
	Spalling limit	0.48	1.05	0.89
Destress blasting combined with support system	Damage initiation limit	0.11	1.33	0.97
	Spalling limit	0.04	2.00	0.90

presents the best fit for each studied case, based on Equation (1). In all cases, the spalling and damage initiation limits present a low scatter with a high R².

Based on Table 1 presented in this paper, and the work of Diederichs and Martin [49], the level of rockburst potential can be defined. Three levels are defined: a low hazard corresponds to a minor spalling (${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{x}}$/UCS between 0.4 and 0.6), a medium hazard corresponds to a moderate overbreak (${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{x}}$/UCS between 0.6 and 0.8) and a high hazard corresponds to a serious overbreak (${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{x}}$/UCS higher than 0.8). Figure 9 presents the influence of the mitigation measures on these levels. It highlights, similarly to previously, that, when considering a support system combined with destress blasting, the occurrence of strain burst, regardless of the level of the hazard, decreases by more than half. When considering only a support system, minor spalling and moderate overbreak can be controlled. Indeed, the five low and five medium hazard cases do not occur when the use of a support system is proposed. However, the high hazard cannot be mitigated. The use of only destress blasting does not have an impact on a medium hazard (the five cases occur at the same hazard level as when no mitigation measure is proposed), nor on the high hazard level. However, destress blasting allow the occurrence of a low hazard to be mitigated. Finally, when a combination of a support system and destress blasting is used, minor spalling and moderate overbreak can be controlled (the 10 low and medium cases are mitigated). Moreover, on some occasions, the combination of mitigation measures has an impact when facing a serious overbreak hazard. Indeed, from the initial high-level cases that occur when considering no mitigation measures, only a support system and only destress blasting, a third of them can be mitigated using a combination of mitigation measures. However, there are still two-thirds of the serious overbreak that occur even when using all mitigation measures. This shows the challenge that presents in strain burst hazard management, as it does not seem possible to decrease in all cases the hazard level for the strongest events.

5. Influence of Intact Rock Strength and Rock Mass Quality on Level of Strain Burst

The models realized have highlighted the influence of mitigation measures on low and medium strain burst hazards. However, as shown in Figure 8, when facing severe strain burst, only a 30% of the cases are mitigated. For the other 70% of the cases (10 events on 15 initial events without any mitigation measures), no mitigation measures have proven to be efficient. To understand these cases better, an analysis of the intact rock strength (UCS) and the rock mass quality (GSI) is realized. These two parameters are considered as it is recognized that they both have an impact on strain burst potential (lower GSI reduces the potential for bursting and higher UCS increases the potential of bursting) [3].

Figure 10 presents the influence of the UCS (Figure 10a) and the GSI (Figure 10b) values on the number of events and the occurrence of the strain burst, considering the various mitigation measures studied. It shows that, regardless of the GSI values, the number and occurrence of the events do not vary with the mitigation measures proposed. Conversely, when increasing the UCS value, it can be observed that the mitigation measures allow the number and occurrence of events to be decreased. More specifically, for a UCS of 220 MPa, only the combination of a support system and destress blasting have an impact on the events. For a UCS of 270 MPa, the combination of a support system and destress blasting, and the support system alone, have an impact on the events. Finally, for a UCS of 320 MPa, each time that a mitigation measure is implemented, the occurrence of an event can be reduced to none.

The lack of influence of the GSI on the number and occurrence of events can be questionable as it is assumed that it should have an impact on the hazard level (burst potential) and therefore the occurrence of the events. However, due to the formulation of the DISL approach considered in the numerical models, the GSI is not comprehensively integrated in the models, and this could explain these results. This theory should be explored in a further study, for example, by integrating directly in the model family of discontinuity.

6. Discussion and Concluding Remarks

The work presented in this paper has allowed the following elements to be highlighted:

• It is possible to identify damage zone depths in brittle rocks numerically by considering the plasticity degree of the models. The highly damaged zone (HDZ) is related to 100% plasticity and corresponds to the proposed spalling limit. The outer excavation damage zone (EDZ_o) is related to the transition between no plasticity and plasticity and corresponds to the proposed damage initiation limit. Both limits present coherent results with in situ measurements [44] in similar conditions (stress ratio, K, and intact rock strength);
• As expected, the use of mitigation measures allows the strain burst occurrence to decrease. This is in agreement with published work to date [7,63,64,65]. However, the strain burst hazard level does not easily decrease even when using mitigation measure. In the case of a serious overbreak hazard, only a combination of system support and destress blasting seems to have an impact on these events, for rock mass presenting high strength (very and extremely strong intact rock presenting a uniaxial compressive strength higher than 220 MPa). For a rock mass presenting a uniaxial compressive strength lower than 220 MPa (with the in situ major stress, σ1, equal to 80 MPa and the in situ minor stress, σ3, equal to 53 MPa), in all cases, none of the mitigation measures could remove the occurrence of the serious event;
• While the DISL method is easy to use and allows the brittle failure to be modeled, it does not consider comprehensively the rock mass discontinuities, and that could be a limitation when assessing the strain burst hazard. Indeed, it is assumed that a GSI higher than 55 is needed for a spall to occur. However, it is understood that the quality of the rock mass could influence the level of the hazard (considering the depth of failure), and it cannot be studied in this study.

In this study, the choice was made to only consider shotcrete and rockbolts system support and destress blasting as potential mitigation measures. In reality, it is well known that the management of rockburst is through a multipurpose support system consisting of stiff reinforcement functionality to maintain rock mass integrity and internal strength, dynamic displacement and energy capacity in the event of violent rupture, and integrated surface retention to resist uncontrolled bulking and to ensure energy transfer [20,26]. Therefore, there are intrinsic limitations of the presented work as only two of these elements are considered. However, it is also assumed that, in many conditions, some level of dynamic rupture is inevitable and cannot be engineered away [3,66]. The presented work gives an additional insight toward understanding why, considering the intact rock strength particularly. It aims to give indications when dealing with strain burst hazard management. Support systems and/or preconditioning are strong tools to mitigate low-to-medium strain burst hazards. However, when dealing with high level hazards, a systematic use of these tools is not enough to ensure the non-occurrence of an event. In that case, a specific analysis needs to be realized to define the proper mitigation measures that need to be applied. This highlights the need to assess the level of hazard in a preliminary analysis properly, to be able to not overestimate the support system proposed and optimize the resources in a project. Further work needs to be done to validate these results, considering, for example, other types of support systems. Moreover, the explicit modelling of rockbolt could be realized to validate these preliminary results. This was not carried out in this work; however, the internal pressure applied in the models represents properly the support effect of rockbolts and shotcrete, which was the objective of this work.

Finally, the definition of the two damage zone depths can be used in a complementary way to define mitigation measures, ensuring, for example, that the rockbolts are anchored out of a damage zone, or using the damage zone in a preconditioning design.