Assessment of Rockburst Risk

C H A P T E R

11 Assessment of Rockburst Risk S U B C H A P T E R

11.1 Single and Comprehensive Index Methods of Rockburst Risk Assessment Shili Qiu, Xia-Ting Feng Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China

The purpose of a rockburst risk assessment is to determine the potential of a rockburst occurrence, to identify possible rockburst types, and to assess the rockburst damage degree or intensity (i.e., five intensities represented by extremely intense, intense, moderate, slight and no rockburst), or rockburst damage depth. Specifically, it needs to be pointed out that so far, the prediction of rockburst occurrence time is difficult; there are no relatively good theoretical methods or technical approaches. From various perspectives (e.g., strength, stiffness, fracture damage, mutation, fractal, and energy of rock mass), scholars have put forward a large number of indices to assess the rockburst risk, proneness, and vulnerability of rock mass during tunneling. Single and comprehensive index assessment methods for rockburst risk include an assessment through a variable formula, evaluation using empirical criteria, predictions based on the artificial neural network, a support vector machine, a comprehensive evaluation by fuzzy mathematics, the analysis of distance discriminant, etc. These methods basically use the same evaluation parameters, such as maximum tangential stresses, uniaxial tensile and compressive strength, and elastic energy of rockbursts. Moreover, some scholars have integrated the empirical criteria of single indices to form evaluation or classification models of multiple indices. Therefore the empirical method of rockburst risk assessment can be generally divided into two categories, including empirical criterion of a single index and empirical assessment indices or systems of multiple factors. In this section the empirical indices and their methods are reviewed. Some advantages and disadvantages of these indices also are discussed and analyzed. A novel rockburst vulnerability index considering multiple rockburst control factors is proposed, and its application in the Jinping headrace tunnels also is demonstrated. The dynamical assessment of rockburst based on novel index is discussed.

11.1.1 EMPIRICAL CRITERIA OF ROCKBURST EVALUATION BASED ON A SINGLE INDEX The single-index empirical criterions of rockburst assessment are often based on the theories of strength, energy, and stiffness. Table 11.1.1 summarizes the empirical criteria of rockburst proneness commonly used across the world.

Rockburst https://doi.org/10.1016/B978-0-12-805054-5.00053-6

341

© 2018 Elsevier Inc. All rights reserved.

342 TABLE 11.1.1

11. ASSESSMENT OF ROCKBURST RISK

Some Criteria and Classification of Rockburst Risk Assessment

Classifications

Criteria

Discriminants

Criterion thresholds

Rockburst levels

Remarks

The influences of tunnel excavation and characteristics of deviator stress in the initial stress field can be reflected

Hoek criterion (Hoek & Brown, 1990; Hoek & Marinosm, 2000)

σ max/σ c

<0.7

Intense rockbursts

¼0.42– 0.56

Moderate damages

¼0.34– 0.42

Severe spallings

<0.34

A few spallings

>0.5

Potential rockburst damages

σ max represents the maximum tangential stresses of surrounding rocks σ v indicates stress levels acted in the vertical direction of tunnels σ c denotes uniaxial compressive strengths of rocks

¼0.2–0.5

Damages of stripping and spalling

<0.2

No rockburst or being stable after supports

<0.083

Intense rockbursts

¼0.083– 0.15

Moderate rockbursts

¼0.15– 0.20

Weak rockbursts

>0.20

No rockburst activity

<0.3

No rockburst activity

¼0.3–0.5

Having certain possibility of rockbursts

¼0.5–0.8

Rockbursts are bound to happen

>0.8

Intense rockbursts

<0.3

No rockburst

¼0.5–0.7

Rockbursts are bound to happen

>0.7

Intense rockbursts

¼5–2.5

Moderate rockburst activities

<2.5

Intense rockbursts

>14.5

No rockburst

¼14.5–5.5

Small amounts of rockburst activities with slight emission phenomena

¼5.5–2.5

Moderate rockburst activities with strong emission phenomena

<2.5

Intense rockbursts with loud burst sounds

<4.0

Rockburst occurrence with ejection of rock masses

¼4.0–7.0

Rockburst possibly occurs and phenomena of stripping and chipping are found on rock masses

σ v/σ c

Russenes criterion (Jager & Cook, 1996)

Turchaninov criterion (Jager & Cook, 1996)

Criterion of Erlangshan tunnel (Xu & Wang, 1999) Not revealing the influences of tunnel excavation and characteristics of the deviator stress in the initial stress field

Is(50)/σ c

ðσ θ + σ L Þ=σ c

σ θ/σ c

Barton criterion (Barton et al., 1974)

σ c/σ 1

Tao criterion (Tao & Pan, 1992)

σ c/σ 1

National standard GB50218-94

σ c/σ 1

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

Is(50) demonstrates the point loading strength fixed by rocks σ θ is maximum tangential stresses of surrounding rocks in tunnels

σ θ shows tangential stresses of caverns σ L represents axial stresses of caverns σ c denotes uniaxial compressive strengths of rocks σ θ indicates tangential stresses of caverns σ c represents uniaxial compressive strengths of rocks σ 1 denotes maximum principal stresses of surrounding rocks σ c is uniaxial compressive strengths of rocks σ 1 represents maximum principal stresses of surrounding rocks σ c is uniaxial compressive strengths of rocks

σ 1 is maximum principal stresses of surrounding rocks σ c indicates uniaxial compressive strengths of rocks

343

11.1.1 EMPIRICAL CRITERIA OF ROCKBURST EVALUATION BASED ON A SINGLE INDEX

TABLE 11.1.1 Classifications

Some Criteria and Classification of Rockburst Risk Assessment—cont’d Criteria

Discriminants

Criterion thresholds

Rockburst levels

Remarks

Brittleness criterion (Xu & Wang, 1999)

σ c/σ t

<10

No rockburst

¼10–14

Weak rockbursts

¼14–18

Moderate rockbursts

>18

Intense rockbursts

σ c denotes uniaxial compressive strengths of rocks σ t is uniaxial tensile strengths of rocks

<2.0

No rockburst

¼2.0–6.0

Weak rockbursts

¼6.0–9.0

Moderate rockbursts

>9.0

Intense rockbursts

<2.0

No rockburst

¼2.0–3.5

Weak rockbursts

¼3.5–5.0

Moderate rockbursts

>5.0

Intense rockbursts

<1.0

Rockbursts probably occur

U/U1

Brittleness index

Elastic deformation energy index Wet (Gu, Hou, & Chen, 2002)

Wsp/Wst

Impact index (Gu et al., 2002)

Km/jKsj

U represents total deformations of rocks before reaching peak strengths U indicates permanent deformations of rocks before reaching peak strengths Wsp Indicates the elastic strain energies released by rocks, when 0.05c is unloaded after loading (0.7–0.8)c to the rock specimens 5. Wst is the energy consumed by the plastic deformation and generation of micro cracks in the rocks Km indicates the stiffness in the loading process of the stress-strain curve jKsj shows the stiffness after reaching the peak of the stress-strain curve

Whether a single factor for estimating the rockburst risk and proneness can reflect the influences of the tunnel excavation and the characteristics of deviator stress in the initial stress field (the size of the excavation and the tunnel types) is studied. On this basis the factors can be classified into two categories: those that can and those that cannot reflect the above influences and characteristics. In fact, certain factors in the indices in Table 11.1.1 reveal the influences in excavation and consider the effects of the tunnel size in the calculating process. For example, for the criteria proposed by Hoek, Russenes, and Turchaninov that were used in the Erlangshan tunnel to adopt the maximum tangential stresses around tunnels as the main factors, we need to evaluate the stress values when determining the values of criteria. In general, numerical simulation that is mainly realized using elastic models must be performed in the calculating process, so the influences of the size of excavated tunnels are considered. For instance, different concentration degrees of stresses are found around the tunnel with gate- and surround-shaped excavation sections. In addition, when using a numerical calculation to determine the maximum tangential stresses around the tunnels, the concentration degrees of stresses can be directly affected by the characteristics of the deviator stress in the initial stress field. It is obvious that single indices (such as the criteria of Hoek, Russenes, Turchaninov, and Erlangshan tunnel) in Table 11.1.1 can reflect the influences of tunnel excavation and the characteristics of the deviator stress in the initial stress field. However, some criteria, including the Barton criterion, Tao criterion, and that used in the national standard of China, GB50218-94, merely employ the maximum principal stresses in the in situ rock stress field as characteristic parameters. Thus, these criteria fail to show the influences of excavation shape or size and characteristics of deviator stress in the initial stress field. Furthermore, the criteria based on elastic strain energy index Wet, impact index, and brittleness utilize the mechanical properties of rocks. These criteria neither reflect the influences of tunnel excavation and characteristics of deviator stress in the initial stress field nor consider the characteristics of in situ stresses.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

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11. ASSESSMENT OF ROCKBURST RISK

11.1.1.1 Strength-Stress Ratio or Stress-Strength Ratio Hoek and Brown (1990) summarized the cases of brittle failure (such as rockbursts, spalling) of side walls occurring in the tunnels excavated in quartzite with rectangular shapes in South Africa in their book, Underground Excavation in Rock. By using the ratio of the maximum principal stress in far fields to the short-term uniaxial compressive strength of rocks as the assessment index for brittle failures, brittle rock failures are classified into different models. The significance of stress classification methods of Hoek and Brown is that it establishes the relationship between the brittle failure characteristics of hard rocks and the relative values (σ v/σ c) of the maximum stress in the far fields. On this basis the controlling effects of σ v/σ c on the brittle failures of hard rocks are confirmed. Based on the theories of stress strengths or the ratio of strength to stress, the Q system classification established by Barton, Lien, and Lunde (1974) through engineering practices in Norway includes the stress reduction coefficient. Russenes believed that the rockburst activities are a function of the maximum tangential stresses and the point loading strengths (Is) of rock in tunnels ( Jager & Cook, 1996). Based on this, the rockbursts can be divided into three types. In fact, Russenes and Barton criteria show a certain inheritance relationship, because the point-loading strengths are directly related to the compressive strength of rocks; that is, σ c ¼ 22 Is(50), where Is(50) is the index of point-loading strengths when the equivalent core diameter is 50 mm, and the maximum tangential stress σ θ is pertinent to the shape of tunnels and the level of in situ rock stress. The engineering practices across the world show that the stress concentration coefficient generally ranges from 2 to 3, namely σ θ ¼ ð2  3Þσ 1 . Moreover, according to the experience of mining construction in Hibbing plots of Kola Peninsula, rockburst activities are determined by the ratio of the sum of tangential stress and the axial stress of the tunnel to the uniaxial compressive strength ( Jager & Cook, 1996). In fact, this criterion has the same theoretical basis with the criteria of Barton and Russenes. Considering rockbursts are still likely to occur in engineering practices when σ c/σ 1 is large, Tao and Pan (1992) revised the Barton criterion appropriately.

11.1.1.2 Energy and Brittleness Indices Based on the stress-strain curve of rocks, a scholar of the Academy of Mining Sciences in Poland determined the rockburst proneness by using the ratio of elastic strain energies stored in rocks to the loss of strain energies caused by permanent deformations and fragmentations. The most important contribution of the index is that it considers the energy process in the deformation and failure of rocks. In addition, by means of the stiffness theories, the impact index measures the rockburst proneness using the difference between the values of the stiffness before and after rock failures. In the same way the brittleness index adopts the difference in the ratio of tensile to compressive strengths of rocks. These three single indices only reflect the rockburst proneness of rocks, but they do not consider the stress conditions of rocks, so they cannot distinguish rockburst risks under different conditions of in situ rock stresses.

11.1.2 EMPIRICAL INDICES OR EVALUATION SYSTEMS OF MULTIPLE FACTORS OF ROCKBURSTS Empirical indices or systems of multiple factors for evaluating rockburst risks are based on the various rockburst cases and adopt important controlling factors of rockbursts to evaluate risk. On this basis, appropriate empirical mathematical models or evaluation systems are established. At present, a variety of empirical methods and evaluation systems have been proposed. The controlling factors of rockbursts are selected according to the needs of specific projects and the types of existing data and information. By carrying out empirical analysis of rockburst predictions based on cases in Canada, Kaiser, Tannant, McCreath, and Jesenak (1992) pointed out that four factors need to be considered in the estimation of rockburst damages. These factors include the rock mass quality, the possibilities of failures or the stress conditions, the local stiffness of rock masses, and the support. Gill, Aubertin, and Simon (1993) proposed a method, composed of zoning, the identification of certain rock structures, stability analysis, and stiffness comparison, for evaluating rockburst possibilities in underground excavations. This evaluation method not only considers the conditions and functions of vulnerable rock structures in forming these two kinds of rockbursts, but it also selectively analyzes the stiffness affecting rockburst intensities. In fact, this method provides a systematic process for evaluating rockburst proneness. Durrheim et al. (1998) established an empirical analyzing procedure for predicting rockbursts that were suitable for the mining layout conditions in South Africa. In addition, Essrich (1997) proposed seismic hazard assessment for evaluating seismic risks of gold mines. In this method, six parameters are introduced, including average seismic index,

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

11.1.3 ROCKBURST VULNERABILITY INDEX

345

cumulative apparent volume of vibration, energy release rate (ERR), face configuration rating, geological factors, and ore output. Each of these parameters is set to several grades. The level of vibration risks is assessed based on the sum of the grades of the six parameters. According to statistical analysis of 250 rockburst events in 80 rockburst cases in Australia and Canada, Heal, Potvin, and Hudyma (2006) put forward the excavation proneness (EVP) index. Meanwhile, four parameters (stress condition (E1), capacity of support system (E2), excavation span (E3), and geological structure (E4)) are introduced. These four parameters can be divided into factors (E1 and E2) for causing damages and factors (E3/E4) relating damages depth. By using the index, an exponential relationship between EVP and rockburst levels is obtained by statistical analysis. Feng, Xie, Wang, and Pan (2000) presented that brittleness coefficient B of rocks is calculated by using uniaxial tensile strength and compressive strength of rocks, prepeak strain value, and postpeak strain value. In this way, a new discriminative condition for rockburst proneness is established; when B  3, 3 < B < 5, and B 5, there is no, low, or high rockburst proneness, respectively. Based on the analysis of rock brittleness, Bukowska (2006) established a system for evaluating the possibility of rockburst occurrence with regard to the rockburst problems in the coal mining areas of Upper Silesian. Moreover, Bukowska considered many factors controlling rockburst occurrences in coal seams, including the depth and thickness of coal seams, the structure of rock masses, the mechanical properties of rocks, the energy characteristics of rocks, the distance between the rock strata of potential seismic sources and coal seams, and the maximum vibration energies of coal seams. Similar studies can be seen from Jiang’s team (Wang, Jiang, et al., 2016; Zhu, Dou, et al., 2016; Zhu, Feng, & Jiang, 2016) and Du’s team (Cao et al., 2016; Li et al., 2016; Wang, Gong, Li, Dou, & Cai, 2016; Zhu, Dou, et al., 2016). New theoretical methods are emerging for establishing evaluation systems of multiple indices. For example, by using comprehensive evaluation methods, in fuzzy mathematics, extenics, gray correlation analysis, and fuzzy pattern recognition to select the main factors affecting rockbursts, the occurrence and intensity of rockbursts are predicted (Wang, Li, Lee, Tsui, & Tham, 1998; Wong, 1992). Moreover, being the first one to apply an artificial intelligence method for rockburst assessment, Feng and Wang (1994) established the adaptive pattern recognition to evaluate rockburst risks in underground tunnels. Based on this method, rockburst risks are evaluated with a strength-stress ratio (σ θ/σ c), a ratio of tensile to compressive strength (σ c/σ t), and impact energy index (Wet) as the controlling factors. The expert system for evaluating rockburst risks in deep gold mines in South Africa was proposed by Feng, Webber, and Ozbay (1996) to estimate the levels of rockburst risks based on various factors. The factors include the mining advancing method, the exploitation degree, the function of geological structure, the distance to the main geological structures, the local support effect, the regional support effect, trench support effect, mining layout, ERR, and residual shear stress. By introducing the rough set and genetic algorithm, Yu, Liu, Lu, and Liu (2009) built a decision method of rockburst possibility by taking nine decision factors into account. These factors include the mining depth, angle of deposits, types of structural planes (such as faults and dykes), mining methods, permanent support type, temporary support types, regional support technology, and width and span of mining fields. The shortcoming of this method is that it cannot predict the intensity of rockbursts. It is obvious that more and more attention has been paid to the studies of risk assessment and the prediction method of rockbursts based on multiple indices (Durrheim et al., 1998). However, according to the existing research, these methods have the following characteristics: First, based on the different types of projects, such as the different mining fields, roadways, and tunnels, various factors are considered to evaluate the levels of rockburst risks. Second, these methods mainly estimate the levels of rockburst risks without considering the depth of the damage pits and the occurrence time of the rockbursts. Therefore the method of how to reasonably determine the main independent factors and indices in order to calculate the depth of rockburst pits and the occurrence time of rockbursts according to the specific engineering types needs to be further explored.

11.1.3 ROCKBURST VULNERABILITY INDEX On the basis of summarizing the main results, theories, and methods of rockburst vulnerability evaluation, the development process and basic framework of a new rockburst vulnerability evaluation method for deep-buried tunnels are put forward by Qiu, Feng, Zhang, and Wu (2011). They analyzed 62 rockburst cases that occurred in the Jinping II tunnels, and the characteristics and main controlling factors of rockburst are revealed. A new empirical index assessing the rockburst vulnerability indices (RVI) and their established methods and the principle of selecting controlling factors are proposed, as shown in Eq. (11.1.1). RVI is constituted by four controlling factors, namely stress control factor Fs, petrophysical factor Fr, rock system stiffness factor Fm, and geological structure factor Fg, which respectively reflect the contribution of rockburst controlling factors of rockburst vulnerability. It was found that there is a significant correlation between the failure depth of rockburst and RVI. An empirical equation is established, and its

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

346

11. ASSESSMENT OF ROCKBURST RISK

determination coefficient is more than 80%. The empirical equation can be used for evaluating rockburst vulnerability and its damage level. The applicability of RVI method is verified through the analysis of representative rockburst cases occurred in the Jinping II tunnel project. RVI ¼ Fs Fr Fm Fg

(11.1.1)

11.1.3.1 Constitution and Configuration and Established Methods for the RVI System RVI system is a semiquantitative empirical index for evaluating the occurring possibility of rockbursts in deep-buried tunnels. Fig. 11.1.1 shows the development process of the RVI system and its constitution and configuration. The RVI system was developed to study the occurrence laws and major characteristics of rockbursts in deep-buried tunnels and to determine the key factors for controlling rockburst occurrence, so as to confirm the mathematical forms of the RVI and its constitution and configuration. Moreover, the RVI provided a basis for evaluating and verifying the application effects of RVI in engineering. The empirical indices can be expressed in many mathematical forms, such as the product and quotient of Q system of rock masses, the sum form RMR system for the surrounding rock classification, and the product, quotient, or sum of weighted coefficients. No matter what kind of forms is utilized, the development process of the RVI system needs to follow a principle, namely, the monotonic increase of RVI values. This increase indicates that the considered controlling factors positively affect the increase process of rockburst tendency. Moreover, those controlling factors are not coupled. The scoring of controlling factors determines the mathematical forms in which RVI values increase gradually

Database of rockburst cases

Determining rockburst controlling factors

Establishing mathematical expression of RVI

Large errors

Summarization of research literature of rockburst controlling factors Analysis of controlling factors of rockburst cases Selection and relevant analysis of controlling factors

Referring to the established methods of Q and RMR systems Monotonic increasing principles of RVI values

Determining scores of controlling factors

Relevant analysis of RVI values and rockburst depth Requirements for prediction accuracy

Establishing empirical equations for evaluating failure degree

Nonlinear fitting between RVI values and failure depth

Verifying from rockburst cases Small errors

Engineering application

FIG. 11.1.1 Development process of RVI system and its constitution and configuration.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

11.1.3 ROCKBURST VULNERABILITY INDEX

347

with the increase of rockburst tendency. Furthermore, the scores represent the contribution rate of each controlling factor to a rockburst occurrence. The determined scores of each controlling factor, in Eq. (11.1.1), shows that there is a linear relationship between the RVI and failure depth of rockbursts. The last constitution part of the RVI system is the dynamic feedback mechanism. The proposed index system needs to be verified by using existing typical rockburst cases. With the constant supplements of data regarding the rockburst cases, controlling factors and scores have to be adjusted and corrected continuously. The introduction of the dynamic feedback mechanism ensures the high accuracy and applicability of the RVI system.

11.1.3.2 The Selection of Rockburst Controlling Factors and Their Controlling Effects 11.1.3.2.1 Stress Control Factor, Fs The in situ stress conditions of rocks is an important controlling factor of rockbursts, so the controlling effects of the stress condition have to be considered in the evaluation process of rockburst potential. However, it is limited to reflect stress levels by merely using the maximum principal stress σ 1 or vertical stress σ v. This is because the effects of the size and shape of the excavated tunnels in the secondary stress fields are ignored, which may cause an underestimation of the failure possibility. In contrast the tangential stress σ θ is more reasonable, but when the shapes of excavated tunnel are complex, σ θ has to be obtained by using numerical methods, which hinders the direct application of tangential stress in the empirical indices. Therefore, considering the characteristics of deep-buried tunnels, this research puts forward a new method for evaluating the stress influences of rockbursts, as demonstrated in the following formula. It is assumed that the stability of deep-buried tunnels is determined by the stress condition in the plane vertical to the axis of excavated tunnels; in other words, supposing that plane stress condition is applicable: Fs ¼

100 σ v ðAk + BÞ σc

(11.1.2)

where the parameter k represents the ratio of horizontal stresses to vertical stresses in the in situ stress fields and is determined by the back analysis results of in situ stress fields in engineering areas or in situ stress test results. σ v and σ c can be evaluated according to deep-buried conditions and determined through tests. Furthermore, parameters A and B stand for coefficients relating to the shape and size of excavated tunnels and the deflection angle β of the vertical stresses, expressed as: ) A ¼ f1 ðβ Þ (11.1.3) B ¼ f 2 ðβ Þ where f1 and f2 indicate the functions relating to the shape and size of excavated tunnels. The meanings of k and β are shown in Fig. 11.1.3. From the perspective of mechanics, the numerator in Eq. (11.1.3) is the estimated concentration degree of the maximum stresses in the secondary stress fields after the excavation sections are tunneled, and Ak + B indicates the estimated stress concentration coefficients. 11.1.3.2.2 Petrophysical Factor, Fr The mechanical properties of rocks intensely control rockburst vulnerability. Brittleness indices (e.g., as the uniaxial tension-compression ratio and impact energy index, Wet) are generally used to evaluate rockburst vulnerability. Through further analysis, it is found that brittleness is not enough to evaluate rockburst vulnerability, and the evaluation needs to be further conducted from the perspectives of the petroproperty and the level of resistance to the high-stress damages of rocks. Based on the heterogeneities of the mineral compositions of rocks and the differences of particle size, the influences of rock mechanical properties on rockburst vulnerability were described. In addition, this research put forward the petrophysical factor Fr as one of the rockburst controlling factors for the RVI evaluation system and determined the value of Fr through empirical grading. The mathematic form of petrophysical factor Fr is Fr ¼ Mh Gs

(11.1.4)

where Mh and Gs represent the scores of mineral heterogeneity factor and the grain size factor, respectively. The Mh scoring system was determined in accordance with the stiffness or strength heterogeneity factor (SHF), while the Gs scoring system was decided by the grain or particle size of rocks.

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348

11. ASSESSMENT OF ROCKBURST RISK

TABLE 11.1.2

Scoring Systems of Mineral Heterogeneity Factor Mh and Grain Size Factor Gs Mh scoring system

Gs scoring system

Jinping marbles

SHF factor

Mh score

Grain size (mm)

Gs score

Description

T52y grayish-white fine grained marble

1.39

1.0

<0.1

1.0

Micrograin

T52y grayish-white marble with medium-coarse grains

1.35

1.2

0.1–1.0

1.2

Fine grain

T2b grayish-black-and-white fine-grained marble

1.30

2.0

1.0–3.0

1.4

Medium grain

T2b grayish-black-and-white marble with medium-coarse grains

1.34

1.6

>3.0

1.4–2.0

Coarse grain

Our research suggests establishing the Mh and Gs scoring systems by using mineral heterogeneity degree and grain size as the standards, as demonstrated in Table 11.1.2. The Gs scoring system was established according to the general grain classification criteria in rock mineralogy. 11.1.3.2.3 Rock System Stiffness Factor, Fm Although system stiffness is very important and essential to assessing rockburst vulnerability, it is difficult to measure, evaluate, and quantify. In mining engineering, the system stiffness of mines and surrounding rocks can be determined by testing the in situ deformation and load, while that of single and intact rock masses before and after high-stress damages is hard to measure and evaluate. In the evaluation of the damage degree of rockbursts, Kaiser et al. (1992) proposed the concept of local mining stiffness (LMS) to measure the loading system stiffness in the interaction between areas to be excavated and the adjacent excavated areas. Based on the concept of LMS, this study put forward a rock system stiffness factor Fm to quantify and evaluate the interaction between the areas to be excavated and the adjacent excavated areas. It is expected to reflect the ability of releasing stresses or responding to deformations of the areas to be excavated, engineering excavation layouts, effects of shapes of area to be excavated, and the ability of stress redistribution. The scoring principles of rock system stiffness factor Fm and the excavation environment are demonstrated in Table 11.1.3. As for deep-buried tunnels in the Jinping II hydropower station, the stiffness environment concerning the rock system stiffness factor Fm is displayed in several typical forms, as illustrated in Fig. 11.1.2. Fig. 11.1.2A shows that when a single tunnel is excavated in the intact and undisturbed rock masses, the stresses of the surrounding rocks are rapidly adjusted or transferred into support systems, so the system shows high stiffness. Fig. 11.1.2B and C indicate that the second excavation in the areas influenced by single excavated structures results in the rapid energy releases in the existing secondary stress field, indicating medium stiffness. In addition, Fig. 11.1.2D and E demonstrate that when the excavation is conducted in the complex stress fields formed by multiple excavated structures, the system stiffness of surrounding rocks is low, so rockburst risk is high. 11.1.3.2.4 Geological Structure Factor, Fg The geological structures, mainly regional structures (folds and regional faults) and local structures (fractures or fissures, joints, and beddings), strongly control the occurrence of rockbursts. The effects of these structures on rockbursts are reflected from two aspects: TABLE 11.1.3

Scoring System of Rock Mass System Stiffness Factor Fm

Fm score

Description of excavation environment

1.0

Excavation environment with high stiffness: Single planes of undisturbed original rocks are excavated or the areas to be excavated are two times of the tunnel diameter to excavated structures. In such condition, the excavation is slightly affected by excavated structures

1.5

Excavation environment with medium stiffness: areas to be excavated are located in the adjacent to excavated structures and stresses in the areas are relieved in at least one direction

2.0

Excavation environment with low stiffness: The areas influenced by two or more excavated structures (stress concentration areas for example) are excavated, and the areas release stresses and are deformed in multiple directions

Note: The influencing ranges of stiffness are 2 times that of excavated tunnel diameter.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

349

11.1.3 ROCKBURST VULNERABILITY INDEX

FIG. 11.1.2

Different system stiffness conditions in the headrace tunnel project of Jinping II hydropower station. (A) A single tunnel is excavated. (B) A branch tunnel is excavated. (C) A single tunnel is excavated near to the excavated tunnel. (D) and (E) multiple tunnels are excavated.

(A)

(B)

(C)

(D) Unexcavated rock masses and surrounding rocks

Excavated tunnels

(E) Excavation direction

(1) Geological structures change the local stress conditions or produce in situ stress fields and singularity of energy fields. Research achievements relating to in situ stress measurements and analysis from all over the world show that in situ stresses in the core of synclinal folds and the two limbs of anticlines are generally higher than those at other fold positions. Moreover, the existence of such fold structures is expected to change the ratio of the maximum to minimum principal stress and the direction of stress fields. The stress fields near the fault zones are extremely complex, and areas with ascending local tectonic stress are likely to be formed in the areas with certain distances from the fault zones and at the ends of faults. In addition, mechanical discontinuity planes, such as fractures, joints, fissures, beddings, and lithologic interfaces, can lead to the discontinuous distribution of stress, strain, and strain energy in the both sides. Therefore high strain energies are accumulated between the working faces to be excavated and the discontinuous surfaces. Discontinuous surfaces block energy transfers, and local stress can also be concentrated on the tips of discontinuous surfaces with common extension. (2) Geological structures are likely to cause slippages and energy releases of stiff structural surfaces. Due to the excavation, faults or compressive (twisted) structural surfaces are activated, resulting in shear slip. Furthermore, energies are released in fluctuation forms, which lead to damages and even ejections of surrounding rocks on the adjacent excavated surfaces. Faults or compression (twist) structural surfaces are activated in two ways: by decreasing the normal pressure of structural surfaces, then by increasing the tangential driving force of structural surfaces. The rockburst cases took place during the excavation of the headrace tunnels in the Jinping II hydropower station reflect that geological structures greatly control rockbursts. Fig. 11.1.3A shows the relationship between the distribution laws of tunnel axes and fold structures for the rockburst cases database of the headrace tunnels in the Jinping II hydropower station. This relationship indicates that rockbursts with a moderate or higher intensity in the headrace tunnels are controlled by geological structures, and the occurring frequency and intensity of rockbursts increased in the adjacent areas of fold cores and tunnels with significant fold structures. Local geological structures (faults and joints) also strongly controlled rockbursts. Through analyzing the structural surfaces exposed by rockbursts and the development of fracture structures influencing rockbursts, it is found that three groups of structural surfaces strongly controlled rockbursts. (1) Structural surfaces in Group #1 were generally NW- or NWW-trended ones, which

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

350

11. ASSESSMENT OF ROCKBURST RISK

FIG. 11.1.3 Relationship between

Headrace tunnel #2

rockbursts and geological structures of the headrace tunnel in Jinping II hydropower station: (A) relationship between rockbursts and fold structures (the geometric centers of labeled points are the actual positions, and the legend denotes the failure depth of rockbursts) and (B) relationships of rockburst failure depth with faults and structural surfaces.

K8

K9

K10

K11

Auxiliary tunnel #A

K12 K13 Auxiliary tunnel #B

K6

K7

K8

K9

K10

K11

K12

Rockburst damage depth 0.5–1.0 m 1.0–2.0 m 2.0–3.0 m > 3.0 m K6

K7

K8

K9

K10

K11

(A)

Rockburst failure depth, d(m)

6 5

Intact rock masses without structural surfaces Few structural surfaces in local region Near to faults or influencing zones

4 3 2 1 0 0.3

(B)

0.8

1.3

1.8

2.3

Stress controlling factor, Fs / 100

showed a small angle with tunnel axes. A majority of these tensile structural surfaces were faults, while most compressive or twist-compressional surfaces were rigid fractures. (2) Structural surfaces in Group #2 were compressive and twist-compressional ones, including beddings and fracture surfaces developed in the NE or NNE direction, and had a large angle with tunnel axes. (3) Group #3 contained compressive structural surfaces trended in EW or NEE direction. The three groups of structural surfaces commonly demonstrated a large inclination (generally more than 60 degrees) and were developed separately and sporadically with a long group development time. As a matter of fact, structural surfaces with different properties and occurrences were exposed in the excavation of the headrace tunnels. However, a few rockburst cases only occurred in some regions where three or more groups of structure plane were observed, indicating that the structural surfaces with specific conditions (occurrence, property, and tunnel space relationship) is favorable for the occurrence of rockbursts. Fig. 11.1.3B displays the relationship between the damage depth of the rockbursts the and controlling effects of the geological structures. As can be seen from the figure, the damage depth of rockbursts affected by structural surfaces and faults was deeper than that of intact rock masses. In addition the vulnerability of the extremely Intense rockbursts increased in regions containing structural surfaces and influenced by faults. After deeply analyzing the controlling mechanisms of the three groups of structural surfaces on rockbursts, the authors considered that the tensile structural surfaces in Group #1 generally formed local stress concentration areas in the influencing areas or tip regions and rockbursts happened when excavation surfaces were closed to or exposed in these areas. When the three groups of structural surfaces were compressive or twist-compressional ones, the accumulation effects of deformation and energy were formed between excavation and structural surfaces, thus producing concentration areas with high energies. After losing surrounding rock pressures and decreasing rock mass strength because of the excavation, rockburst damages took place due to energy release. When the tip regions of the structural surfaces were approached or exposed, the high-stress concentrations also caused rockbursts. Although serious

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

11.1.3 ROCKBURST VULNERABILITY INDEX

351

TABLE 11.1.4 Scoring System of Geological Structure Factor Fg Fg score

Description of geological structure characteristics

1.0

Rock masses in the areas to be excavated are intact. and lithology dose not change in an obvious manner. The areas are not in lithology interfaces, synclinal cores, or anticlinal limbs

2.0

Rock masses in the areas to be excavated are intact, and working faces approached influencing areas of regional faults, local fracture structures, or structures such as folds. Structural surfaces are not developed in an obvious manner

3.0

The areas to be excavated have intact rock masses. They are far away from influencing areas of faults and are not in synclinal cores or anticlinal limbs. However, there are small amounts of stiff structural surfaces with poor extension, including joints and fracture surfaces, or excavation surfaces are near the tips of weak structural surfaces (e.g., twist-compressional joints and fracture surfaces)

4.0/5.0a

Rock masses in the areas to be excavated are intact, and working faces are near to faults (possibly inducing fault dislocation) and influencing the areas of structures, such as faults. Moreover, there are small quantities of stiff structural surfaces with poor extension, including joints and fracture surfaces, or excavation surfaces are close to the tips of weak structural surfaces (twist-compressional joints and fracture surfaces)

Note: When working faces are close to the fault areas, Fg was scored as 4.0; when the working faces approach the structural areas of folds, Fg was valued as 5.0. The term ‘approach’ refers to the distance within two times of the excavated tunnel diameter.

a

rockbursts caused by regional fractures and slippages were not found in the excavation of the headrace tunnels, local slippages of three groups of structural surfaces did happen. Based on the above analysis, the controlling effects of geological structures on rockbursts were semiquantitatively introduced into the RVI evaluation system using the geological structure factor Fg. The factor is expected to quantify the controlling effects of geological structures in increasing the rockburst vulnerability, damage possibility, and damage depth. The characteristics of geological structures and the scoring of Fg are shown in Table 11.1.4.

11.1.3.3 Empirical Relationship Between RVI and Rockburst Failure Depth The prior sections present the selection and determination method of the rockburst controlling factors and scores of corresponding factors. On this basis, the value of the RVI system is obtained according to Eq. (11.1.1). In order to use the RVI system to evaluate rockburst vulerability and damage degree, the relationship between RVI value and rockbursts needed to be studied, and the most direct and effective method is to analyze the relationship between the RVI value and rockburst failure depth. Fig. 11.1.3 illustrates the mathematical relationship between the damage depth and RVI value of cases in the engineering rockburst database for the headrace tunnel in Jinping II hydropower station. Therefore the RVI established in this study can be fitted with rockburst failure depth using a linear relationship, namely, df ¼ 0:0008RVI + 0:2327

(11.1.5)

where df represents normalized rockburst failure depth, and it is the ratio of the actual rockburst failure depth to the equivalent radius of the excavation section sizes of tunnels. Owing to the fact that the fit accuracy of the Eq. (11.1.5) is more than 80%, it can be used as an empirical equation for evaluating rockburst vulnerability. In Eq. (11.1.5), the rockburst failure depth considering excavation section size effect is normalized by using hydraulic radius Rf (i.e., the ratio of the area to the perimeter of excavation sections). Therefore the expression for predicting rockburst damage depth obtained by using Eq. (11.1.5) is Df ¼ Rf ð0:0008RVI + 0:2327Þ

(11.1.6)

where Df stands for the predicted rockburst failure depth. It can be seen in Fig. 11.1.4 that the failure depth is discrete and can be reasonably expressed as a range. This range can be represented by using the upper limit dub f and the lower of the failure depth, as shown in the two dotted lines in Fig. 11.1.3. limit dlb f

11.1.3.4 Rockburst Case Verification Based on RVI This section empirically verified and analyzed two kinds of the typical rockbursts, including structural-slip and strainburst, and validated the applicability of the RVI by comparing the predicted results with the actual field damage of the two rockbursts. The verification and analysis of structural rockburst was the back analysis of the case that

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

352

11. ASSESSMENT OF ROCKBURST RISK

FIG. 11.1.4 Relationship between the failure depth of rockbursts and the RVI in the headrace tunnel. Normalized rockburst failure depth, df(m)

3

df = 0.0008 RVI + 0.2327 R2 = 0.8102

Rockburst cases

dfub = 0.001 RVI + 0.5327

2

1

dflb = 0.0007 RVI + 0.0327 0

0

500

1000 RVI

1500

2000

occurred, in which the excavated and geological conditions were relatively clear and most of field data were investigated and collected. The strainburst case occurred after the RVI analysis was conducted, so that the application of this case suggested a successful assessment of the rockburst damage of the RVI method in the Jinping headrace tunnel project. 11.1.3.4.1 Case Example 1 (1) Engineering conditions and occurrence process of rockbursts On July 14, 2010, when the No. 4 headrace tunnel in the Jinping II hydropower station was tunneled westward to chainage K9 + 728, an extremely intense rockburst occurred, in which the damage zone located from the south sidewall to the arch foot in chainage of K9 + 734–K9 + 728 of the tunnel behind the tunnel face. The damage location and the construction layout are illustrated in Fig. 11.1.5. The failure depth in south sidewall, near to K9 + 742–K9 + 728 section, was up to 3–5 m, and the damage depth was about 2.0 m in the intersection close FIG. 11.1.5 Locations and photographs of rockburst at chainage K9 + 734–K9 + 728 in the No. 4 headrace tunnel.

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353

11.1.3 ROCKBURST VULNERABILITY INDEX

to the K9 + 776 section between the TBM maintenance tunnel and the No. 4 headrace tunnel. Moreover, during July 7–9, 2010, an intense rockburst happened at chainage K9 + 734–K9 + 732 in the headrace tunnel with a failure depth of 2.5 m. (2) Geological structure and stress condition The overburden of the tunnel excavated in this case is about 2400 m. The rock masses in this tunnel section are composed of T2b grayish-white and gray medium-coarse marble and were relatively intact. Two joint sets were found at chainage K9 + 721. The first joint set was a compressive structure, and its strike direction and dip angle were N 20°W and NE 55°–60°, respectively. The second joint set was also compressive, which has N 80°E in the strike direction and SE 70° in the dip angle. In addition, two NWW-strike dissolution fractures 20 cm in width were revealed as well in the front of and behind chainage K9 + 696 of the headrace tunnel. The failure information of the surrounding rock masses along the No. 4 headrace tunnel revealed that in the tunnel section with chainage K9 + 750–K9 + 810, stress failure mainly occurred in the cross sections from the north sidewall to the spandrel. However, the variant stress failure locations at chainage K9 + 750–K9 + 728, to some extent, indicated the deflection of local in situ stress field, which is possibly associated with the fact that the tunnel section was close to the axis of the synclinal structure. (3) RVI calculation and comparative verification The RVI was calculated based on the aforementioned field information. The application effect of the RVI method was verified by analyzing the difference between the actual rockburst failure depth and the one calculated by the RVI index. The calculated parameters of the RVI are demonstrated in Table 11.1.6. σ v was estimated according to the overburden of the overlying rock masses. As the overburden was about 2400 m, σ v was valued as 60 MPa. The uniaxial compressive strength of the marbles was about 120 MPa. Because k is difficult to be accurately determined, it was selected in the range from 0.6 to 0.8 through the inversion of the stress failure of the surrounding rocks. The deflection angle β was valued as 10°–20°. It was finally determined by Eqs. (11.1.2) and (11.1.3) that Fs ¼ 174–175. The rock in the rockburst tunnel section was T2b grayish-white and gray medium-coarse marble with strips and spots so that the factor Mh was valued as 2.0. The grain size of marble was 1–3 mm, indicating that marbles had medium-coarse grains, thus the factor Gs was 1.4. The final rock petrophysical factor Fr was 2.8. As the rockburst occurred during the excavation of the auxiliary and support branch tunnel, the rock stiffness factor Fm was 1.5. Moreover, the location of this rockburst approached the synclinal core with two unfavorable structural surface groups, so the geological structure factor Fg was valued as 5.0. Finally, the RVI was calculated by Eq. (11.1.1) and was in the region from 3645 to 3679. In order to estimate the failure damage depth of the rockburst, the equivalent radius was firstly determined as 1.8 for the upper bench excavation of the No. 4 headrace tunnel. In accordance with Eq. (11.1.5), the failure depth was predicted as 5.67–5.71 m. The calculated RVI parameters and the calculation results of the structural rockburst cases are shown in Table 11.1.5. By comparing the actual and predicted failure depths, the relative error was about 14%, and the prediction results were slightly larger than the actual damage degree. It is also noted that the larger RVI results were probably due to the fact that the implemented support system could reduce the degree of damage. However, this result provided the damage degree and rockburst intensities while the occurrence conditions of rockbursts were met, and it also demonstrated that the RVI is applicable in evaluating damage degree of rockbursts.

TABLE 11.1.5 Calculated Parameters and Results of a Rockburst Affected by Structural Planes Fs σ v (MPa)

σ c (MPa)

k

β (degrees)

a

b

c

Result

60

120

0.6–0.8

10–20

0.0006

0.0399

0.1706

174–175

Fm

Fr Mh

Gs

Result

2

1.4

2.8

Single and support tunnel

Fg Result

Unfavorable structural surface and synclinal core

1.5

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

RVI Result

Result

5.0

3645–3679

354

11. ASSESSMENT OF ROCKBURST RISK

11.1.3.4.2 Case Example 2 The microseismic monitoring on December 17, 2010 showed that microsemic events frequently occurred at chainage of SK8 + 860–SK8 + 870 of the drainage tunnel and increased suddenly. In order to evaluate the risk and damage degree of rockbursts, the RVI method was used to evaluate rockburst risk before the excavation. (1) Geological structures, in situ stress and engineering conditions at chainage of SK8 + 860–SK8 + 870 in the drainage tunnel Due to the fact that the analyzed tunnel section was not excavated, most of the information used in the RVI method has been assessed from those collected in the excavated tunnel section and in other neighboring tunnels in the same or similar geological unit, which is behind the excavation face. Therefore this is a dynamical analysis method, which will be discussed in detail in Section 11.1.4. This tunnel section was excavated by using the D&B method, and there was no branch tunnel. Moreover, the tunnel was supported immediately after being excavated. The tunnel overburden was about 2400 m. The geological investigation revealed that the rock masses in the excavated section behind SK8 + 870 were intact with few developed structural surfaces and were mainly composed of grayish-white, thick-bedded and coarse marbles. The tunnel section SK8 + 860–SK8 + 870 corresponded to BK9 +338–BK9 + 348 and AK9 + 342–AK9 + 352 of auxiliary tunnels A and B, where the intact surrounding rocks (Class II) were exposed with few closed structural surfaces in local areas. As for the regional geological structure, the predicted section was located in the right of the synclinal core. The inversion results of in situ stress field in the section demonstrated that the ratio of horizontal to vertical stress in the excavation fractures of this tunnel section was close to 0.75, and the deflection angle of vertical stresses was about 10 degrees. (2) Calculation and analysis of the RVI at chainage of SK8 + 860–SK8 + 870 in the drainage tunnel The same RVI calculation steps utilized for structural rockburst case are used, and the calculated parameter list is demonstrated in Table 11.1.6. RVI value of the predicted tunnel section was computed as 753–775, and the equivalent radius was 1.77. According to Eq. (11.1.5), the calculated failure depth was 1.47–1.51. (3) The actual rockburst damage at chainage SK8 + 860–SK8 + 870 in the drainage tunnel On December 18–19, 2010, a rockburst with the largest failure depth upon to 1.5 m took place at chainage of SK8 +866-SK8 + 872, and its damage field photos are shown in Fig. 11.1.6. Moreover, the rockburst failure depth TABLE 11.1.6

Calculated Parameters and Results of the Strainburst Case Fs

σ v (MPa)

σ c (MPa)

k

β (degrees)

a

b

c

Result

60

120

0.75

10–20

0.0013

0.0870

0.6545

168–173

Fm

Fr Mh

Gs

Result

1.6

1.4

2.24

Single tunnel

Fg Result

No structural surface and synclinal core

1

FIG. 11.1.6

Rockburst damage occurred in the drainage tunnel at chainage SK8 + 865–SK8 + 872.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

RVI Result

Result

2

753–775

11.1.4 DYNAMICAL ASSESSMENT OF ROCKBURST RISK BASED ON AN EMPIRICAL INDEX

355

was close to the assessment results. The above results indicated that the RVI is able to accurately assess rockburst vulnerability and damage degree. In two strainburst and structural rockburst cases, the RVI analysis results showed that the rockburst occurrence was closely related to controlling factors. For example, when the stress conditions were identified accurately, the rockburst failure was determined. However, some differences were found in the structural rockburst case, the damage degree of which was controlled by the properties of geological condition. Compared with stress conditions, the evaluation of the influencing degree of the geological factor is more complex and difficult; a rational evaluation of the geological condition needs more than our engineering experiences.

11.1.4 DYNAMICAL ASSESSMENT OF ROCKBURST RISK BASED ON AN EMPIRICAL INDEX Underground engineering design and construction is often divided into multiple stages. For a rockburst risk assessment, multiple engineering stages lead to a dynamic process, which depends on the amount of data the researcher possesses. The RVI method demonstrated in Section 11.1.3 is used to illustrate a rockburst risk assessment process. Here, we focus on two important stages of the project, the feasibility study phase and the design and construction phase.

11.1.4.1 Feasibility Study Phase In the feasibility study phase, the rockburst risk assessment generally serves as a parameter to decide the selection of the engineer site and the tunnel line, as well as to design the tunnel size, its shape, and so on. However the data information used for rockburst risk assessment is limited, which is mostly based on preliminary observations, similar engineering analogies, and empirical deductions. The rockburst control factors used in the RVI method can’t be determined by an accurate factor value; the petrophysical factor and the geological structure factor have greater uncertainty than the stress control factor and rock system stiffness factor. At this point the most unfavorable conditions are often considered, leading to a preliminary perception of the maximum likelihood of a rockburst. Therefore the application of the RVI method in this stage is more biased towards the recognition and understanding of the overall rockburst risk of the project. Based on rockburst risk assessment of RVI method, we can divide rockburst risk distribution and zone and then initially determine rockburst intensity and its respective support method.

11.1.4.2 Design and Construction Phase In the design and construction phase, the more detailed rockburst control factor data, including excavation information, lithologic information, geological structure information, and even geostress information, can be more accurately obtained. Therefore the aim of the rockburst risk assessment in this stage is more used to guide the design of support parameters, to establish a rockburst avoidance strategy, and to identify a high rockburst risk source. Fig. 11.1.7A shows the flowchart dynamical rockburst risk assessment method in the design and construction phase. The dynamical modification of field feedback verification process is concentrated on three unreasonable levels: (1) Primary unreasonable. In this level, the accuracy of rockburst assessment depends on the reasonable selection of priori information, such as stress and geology in excavated tunnel section, which can be used to characterize the respective condition in an unexcavated tunnel section, as shown in Fig. 11.1.7B. (2) Intermediate unreasonable. The empirical function between the rockburst intensity or failure depth and RVI index has some errors. A novel assessment model needs to be established. (3) Serious unreasonable. Some rockburst control factors are unreasonable. We must reselect control factors to establish or modify the RVI index. Most importantly, with a tunnel excavation, more new cases of rockburst will be added to the rockburst case database. As more in-depth rockburst mechanisms and control mechanisms are understood and revealed, then more accurate RVI index and assessment models are established.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

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FIG. 11.1.7

Dynamical rockburst risk assessment method in design and construction phase: (A) dynamical assessment flowchart and (B) dynamical assessment information.

References Barton, N., Lien, R., & Lunde, J. (1974). Engineering classification of rock masses for the design of tunnel support. Rock Mechanics, 6, 189–236. Bukowska, M. (2006). The probability of rockburst occurrence in the Upper Silesian Coal Basin Area dependent on natural mining conditions. Journal of Mining Science, 42(6), 570–577. Cao, A. Y., Dou, L. M., Wang, C. B., Yao, X. X., Dong, J. Y., & Gu, Y. (2016). Microseismic precursory characteristics of rock burst hazard in mining areas near a large residual coal pillar: A case study from Xuzhuang coal mine, Xuzhou, china. Rock Mechanics and Rock Engineering, 49(11), 4407–4422. Durrheim, R. J., Roberts, M. K. C., Haile, A. T., Hagan, T. O., Jager, A. J., Handley, M. F., et al. (1998). Factors influencing the severity of rockburst damage in South African goldmines. Journal of the South African Institute of Mining and Metallurgy, 98(2), 53–57. Essrich, F. (1997). Quantitative rockburst hazard assessment at Elandsrand Gold Mine. The Journal of the South African Institute of Mining and Metallurgy, 97(7), 319–342. Feng, X. T., & Wang, L. N. (1994). Rockburst prediction based on neural network. Transactions of Nonferrous Metals Society of China, 4(1), 9–14. Feng, X. T., Webber, S., & Ozbay, M. U. (1996). An expert system on assessing rockburst risks for South African deep gold mines. Journal of Coal Science and Engineering, 2, 23–32. Feng, T., Xie, X. B., Wang, W. X., & Pan, C. L. (2000). Brittleness of rocks and brittleness indices for describing rockburst proneness. Mining and Metallurgical Engineering, 20(12), 18–19 [in Chinese]. Gill, D. E., Aubertin, M., & Simon, R. (1993). A practical engineering approach to the evaluation of rockburst potential. Rockbursts and seismicity in mines. Rotterdam: Balkerma (pp. 63–68). Gu, M. C., Hou, F. L., & Chen, C. Z. (2002). Study on rockburst in Qinling tunnel. Chinese Journal of Rock Mechanics and Engineering, 9, 1324–1329 [in Chinese]. Heal, D., Potvin, Y., & Hudyma, M. (2006). Evaluating rockburst damage potential in underground mining. In The 41st U.S. symposium on rock mechanics.

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Hoek, E., & Brown, E. T. (1990). Underground excavation in rock. Oxon: Spon Press (pp. 218–222). Hoek, E., & Marinosm, P. (2000). Predicting tunnel squeezing problems in weak heterogeneous rock masses. Tunnels and Tunnelling International, 32(11), 45–51. Jager, J. C., & Cook, N. G. W. (1996). Fundamentals of rock mechanics (2nd ed.). London: Chapman & Hall (pp. 470–471). Kaiser, P. K., Tannant, D. D., McCreath, D. R., & Jesenak, P. (1992). Rockburst damage assessment procedure. In P. K. Kaiser, & D. R. McCreath (Eds.), Rock support in mining and underground construction (pp. 639–647). Rotterdam: Balkema. Li, Z. L., Dou, L. M., Cai, W., Wang, G. F., Ding, Y. L., & Kong, Y. (2016). Roadway stagger layout for effective control of gob-side rock bursts in the longwall mining of a thick coal seam. Rock Mechanics and Rock Engineering, 49(2), 621–629. Qiu, S. L., Feng, X. T., Zhang, C. Q., & Wu, W. P. (2011). Development and validation of rockburst vulnerability index (RVI) in deep-buried and hard rock tunnels. Chinese Journal of Rock Mechanics and Engineering, 6, 1126–1141 [in Chinese]. Tao, Z. Y., & Pan, B. T. (1992). Principle and methods of rock mechanics. Wuhan: China University of Geosciences Press (pp. 49–54) [in Chinese]. Wang, G. F., Gong, S. Y., Li, Z. L., Dou, L. M., & Cai, W. (2016a). Evolution of stress concentration and energy release before rock bursts: Two case studies from Xingan coal mine, Hegang, China. Rock Mechanics and Rock Engineering, 49(8), 3393–3401. Wang, J. C., Jiang, F. X., Meng, X. J., Wang, X. Y., Zhu, S. T., & Feng, Y. (2016b). Mechanism of rock burst occurrence in specially thick coalseam with rock parting. Rock Mechanics and Rock Engineering, 49(5), 1953–1965. Wang, Y. H., Li, W. D., Lee, P. K. K., Tsui, Y., & Tham, L. G. (1998). Method of fuzzy comprehensive evaluations for rockburst prediction. Chinese Journal of Rock Mechanics and Engineering, 17(5), 493–501 [in Chinese]. Wong, I. G. (1992). Recent development in rockburst and mine seismicity research. In Proceedings of the 33th U.S. symposium on rock mechanics, Santa Fe, NM, pp. 1103–1112. Xu, L. S., & Wang, L. S. (1999). Study on the laws of rockburst and its forecasting in the tunnel of Erlang Mountain road. Chinese Journal of Geotechnical Engineering, 21(5), 569–572 [in Chinese]. Yu, H. C., Liu, H. N., Lu, X. S., & Liu, H. D. (2009). Prediction method of rockburst proneness based on rough set and genetic algorithm. Journal of Coal Science and Engineering, 15(4), 367–373 [in Chinese]. Zhu, G. A., Dou, L. M., Cai, W., Li, Z. L., Zhang, M., Kong, Y., et al. (2016a). Case study of passive seismic velocity tomography in rock burst hazard assessment during underground coal entry excavation. Rock Mechanics and Rock Engineering, 49(12), 4945–4955. Zhu, S. T., Feng, Y., & Jiang, F. X. (2016b). Determination of abutment pressure in coal mines with extremely thick alluvium stratum: A typical kind of rockburst mines in China. Rock Mechanics and Rock Engineering, 49(5), 1943–1952.

S U B C H A P T E R

11.2 Neural Networks for Rockburst Risk Assessment for Deep Tunnels Xia-Ting Feng*, Dongfang Chen† †

*Northeastern University, Shenyang, China Wuhan University of Technology, Wuhan, China

Under influence of complicated engineering and geological conditions, rocks response highly nonlinear mechanics characteristics after excavation. As an intelligence algorithm, the neural network method can provide advantages in this aspect. Compared with traditional methods, neural networks bestow the following advantages: (a) they reduce the interference of artificial factors; this method has a strong antijamming capability and is more objective in its use of previous engineering data to research present problems instead of building analytical criteria; (b) they view rockburst avoidance or occurrence as based on some necessary conditions as criteria rather than pursuing a complex physical mechanism; (c) they can also consider a variety of factors for some types of failure mode, including quantitative and qualitative factors. This makes the estimation more reliable and persuasive; and (d) more importantly, they start from the premise of sufficient and accurate samples and test errors being within an acceptable range of data output from a trained network model of any type of rockburst. The comprehensive integration of these methods can improve the reliability in estimating rockbursts and provide an early warning of their risk. The application of the neural network in rock mechanics is an important part of intelligent rock mechanics theory (Feng, Webber, & Ozbay, 1997; Feng, 2000). An artificial neural network has been successfully applied in the stability prediction for numerous engineering projects around the world to predict roof pressure in coal mines (Feng, Wang, & Yao, 1996), the deformation modulus of rock

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

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masses (Abbas & Morteza, 2010), soil collapse (Adnan & Nabil, 2004) and maximum surface settlement caused by earth pressure balance (EPB) shield tunneling (Suchatvee & Herbert, 2006). By this method, there are also some researches which focus on rockburst prediction. Early on, the neural network has been used to predicted rockburst in underground openings (Feng, 1994a, 1994b) and at great depth induced by mining (Feng, Wang, Ozbay, & Webber, 1998; Feng, Webber, & Ozbay, 1998). Particularly, this technique has been applied to rockburst assessment in deep gold mines in South Africa, which got a preferable predication performance (Feng, Katsuyama, Wang, et al., 1997; Feng, Wang, et al., 1998; Feng, Webber, & Ozbay, 1997; Feng, Webber, et al., 1998). On the basis of advantages and application of neural network, this method is chosen to assess the rockburst risk for the Jinping deep tunnels during excavation.

11.2.1 BASIC THEORY OF NEURAL NETWORK As an emerging branch of intelligence science and an information processing system imitating the functions and structure of human brain, the artificial neural network has grown at a high speed since the 1980s. Composed of a large amount of simple processing elements which are connected together (see Fig. 11.2.1) following certain rules, the network can respond to an external stimulus and handle information in a dynamic manner. Likewise the human brain, the processing sequence, and the structure of the network are parallel. Endowed with a strong learning ability, the artificial neural network is able to adapt to the external environment through learning. In the network, knowledge is distributed in the whole system instead of being stored in some specific memories. To store knowledge, it calls for sufficient connections. In addition, even inaccurate and incomplete data existed, the network can eliminate the distraction by its highly fault toleration. With these advantages the artificial neural network can be used to obtain an approximately optimal solution from distorted and limited information if trained properly (Hertz, Krogh, & Palmer, 1991). To reduce the difference between the calculated and expected outputs, an artificial neural network (ANN) updates its weight values using a back-propagation algorithm. As shown in Fig. 11.2.2, the back-propagation neural network (BPNN) is a common multilayer feed-forward algorithm that is trained by backward error propagation. The error signal, which originates at the output layer neurons, was back propagated through the network in the direction towards the input layer; the weights were updated and the error reduced. There are many ways to connect neurons into a network. One standard way is a multilayer feed-forward neural network. As 1-hidden-layer net with enough hidden units can represent any continuous function of the inputs with arbitrary accuracy and 2-hidden-layer net can even represent discontinuous functions, so two hidden layers comprising 5–50 nodes were selected in the search space in the evolution of the structural parameters of the neural network. To produce reasonable results, the hidden layers and connection weights have to be carefully determined by training. But due to the complexity of rock mechanical problems, the error surface is often rugged, and the gradient descent procedure is limited. In this case, a conventional back-propagation algorithm is often not free from escaping to local minima that will result in inconsistent and unpredictable performance. Hence, the parameter settings, especially the hidden layers (i.e., the number of neurons in each hidden layer) need to be optimized

FIG. 11.2.1 Structure of neural network.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

11.2.1 BASIC THEORY OF NEURAL NETWORK

359

FIG. 11.2.2 Basic principle of neural network training. Inputs

Forward analysis

Error back propagation

ANN model

Correction

Calculated output

Comparison

Expected output

during training process. A genetic algorithm (GA) (Goldberg, 1989) has been proposed for such optimization. By employing genetic algorithm, the structure parameters of hidden layers and initial weights are evolved in a nested manner. The structure parameters are evolved in the outer GA procedure, and the initial weights of the evolved model structure are then evolved in the inner GA procedure, in which a back-propagation algorithm is used to evaluate the fitness of the initial weights. As shown in Fig. 11.2.3, a Visual C++ program has been developed for this improved training process. During the training process, fitness is the fundamental information to control the evolution process in a genetic algorithm through so-called natural selection. In the inner evolution process, the fitness of each generated initial weight set is calculated based on the difference between the output results of the neural network model trained with

FIG. 11.2.3

Computation process of the evolutionary neural network.

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11. ASSESSMENT OF ROCKBURST RISK

the gradient search procedure starting from the generated initial weight set and the expected results. Namely (if mean square error used), n  2 1X ui  u*i (11.2.1) Fitness ¼ n i¼1 where n is the number of learning cases, ui represents the calculated results, while ui* denotes the expected results. In the outer evolution process, the fitness of each generated model structure is calculated after the initial weight has been optimized using the same expression (Eq. 11.1.1)

11.2.2 DATABASE FOR ROCKBURSTS AT JINPING TUNNELS There are a lot of rockburst cases accumulated in the Jinping tunnels excavation. A neural network model can be implemented through systematic analysis using these cases to assess the possibility, intensity, and depth of rockbursts. Rockburst is caused by several factors. Combining the internal and external causes and considering the influence of lithology, stress, regional structure, and construction factors, we have selected seven factors as input parameters of the neural network model to predict the depth and intensity of rockbursts. These are: the brittleness index, stress-strength ratio, σ 1/σ 3, cover depth, regional structure, rock mass integrity, and support strength. Among them, the brittleness index (nb) can be represented by uniaxial compression strength (UCS) to utimate tensile strength (UTS). The stressstrength ratio is defined by the rock compressive strength to the maximal principal stress of the original rocks. The geological conditions of the Jinping tunnels shows regional structures including synclines, anticlines, and fault zones, that are subdivided into the left, center, and right syncline; a transfer zone from syncline to anticline; the left, center, and right anticline; and the footwall and hanging walls of a fault zone. These structures were respectively encoded from 1 to 9. Based on engineering practices, the rock mass integrity can be assessed by the geometric integrity under macromorphology. In accordance with the Chinese Standard for Engineering Classification of Rock Masses (GB50218-94), the rock mass integrity is classified into three intensities: low, moderate, and high encoded as 1, 2, and 3, respectively. The support strength is divided into four intensities: low (shotcrete), moderate (shotcrete + water swelling anchor), high (shotcrete + absorbing energy anchor), and very high (shotcrete + intensive absorbing energy anchor), and which are encoded as 0, 1, 2, and 3, respectively. The rockburst intensity (classified as 0, 1, 2, and 3 representing no rockbursts and slight, moderate, and intense rockbursts, respectively) and the rockburst depth are considered the output parameters of the neural network model. By systematic geology investigation, rock mechanics experiments, and a daily geology survey, 50 cases of rockbursts, including 13 intense, 22 moderate, 13 slight, and 2 without rockbursts were gathered from the different diversion tunnels of the Jinping II hydropower station (Fig. 11.2.4). The testing and learning samples of the neural network was performed under these preconditions. Among them, six cases are used as the testing samples, which are randomly selected from the total 50 cases.

11.2.3 BUILDING THE NEURAL NETWORK MODEL FOR ASSESSING ROCKBURST RISK Additionally, as important parameter settings, the mutation and crossover operators were 0.3 and 0.6, respectively; while the population size, which was the main control parameter, was valued as 30. It was found that the number of initial weights changed with the structural parameters in the inner GA procedure. Meanwhile, the initial weights, the population size, the crossover operator, and the mutation operator were set as 0.1 to 0.1, 200, 0.6, and 0.3, respectively. With respect to the GA procedures, the employed property parameters were similar: a binary coding, a fitnessproportionate selection, and a standard cost function were adopted as the data type, the selection strategy, the fitness function form, and the genetic operators, respectively. Moreover, the GA procedures also applied an inversion mutation operator as a parameter, which was set as 0.3. As for the rate coefficient of the learning parameters, it was used to control the equilibrium between the stability of the algorithm and the learning rate. So, taking the capability of modern computers into account, a small learning rate (0.1) was selected to guarantee the stability of the training process. The momentum coefficient was also a significant learning parameter and was set at a large value (0.5) to prevent local minima from happening. Additionally, the errors concerning the testing and learning termination were set at 1  108 and 1  105, respectively. For the difference between the data levels and dimensions in the neural network samples, the authors utilized a normalized range of 0.2–0.8 to for elimination.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

11.2.3 BUILDING THE NEURAL NETWORK MODEL FOR ASSESSING ROCKBURST RISK

Systematic geology investigation

361

Rock mechanics experiments Daily geology survey

Data

Sites: Four long deep tunnels; time span: October, 2010–November, 2011

2011-6-12 (1#) K7+213~218

2011-5-16 (1# ) K7+880~887

1# tunnel 2011-7-24 (1#) K6+610~200

2011-02-05 (1#) 8+940~948 2# tunnel 3# tunnel 4# tunnel

FIG. 11.2.4 Rockburst cases collected from the diversion tunnels of Jinping II hydropower station. Nos. 1#–4# are the numbers of the headrace tunnels.

FIG. 11.2.5

Evolution of the best fitness value.

According to the aforementioned learning and testing samples, computation process, and parameter settings, an optimization procedure accomplished with a stable convergence during the second generation was demonstrated in Fig. 11.2.5. Meanwhile, 14 and 17 were shown to be the optimal numbers of nodes in the two hidden layers; it is worth noting that 403 initial weights were used. By using the above optimized parameters, a final training was conducted to construct the model for predicting the intensity and depth of rockbursts. The accomplished training process was displayed in Fig. 11.2.6, for which the mean square errors in the testing and learning are diminished. Figs. 11.2.7 and 11.2.8 are in agreement with each other regarding the depths and the intensities of rockbursts of the testing and learning cases obtained through calculation and in practice. This implies that the neural network model is not only applicable to the known samples, but also to the unknown samples, which are not included in the learning process. Therefore, it is evident that the model is feasible and effective in predicting the intensity and depth of rockbursts.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

362

11. ASSESSMENT OF ROCKBURST RISK

FIG. 11.2.6 Error variation of the neural network classifier based on the optimized neural network structure and initial weights during the model training process.

FIG. 11.2.7 Comparison of the calculated and practical results of the learning and testing cases. (A) Damaged depths and (B) rockburst intensities.

FIG. 11.2.8 Linear regression between the calculated and measured results of the learning and testing cases. (A) Damaged depths and (B) rockburst intensities.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

363

11.2.4 ENGINEERING APPLICATION

11.2.4 ENGINEERING APPLICATION When we put the neural network input parameters of eight sections of different tunnels at Jinping (Fig. 11.2.9) into the neural network model (Table 11.2.1), compared with the actual rockbursts (Fig. 11.2.10), the results of rockburst damage depth and intensities show a good correlation between the calculated and practical results (Table 11.2.2). Although there are some differences between the calculated and practical results for the rockburst damage depth, the average absolute error is only 0.13 m. Therefore considering the rockburst cases in the same engineering as the learning and testing cases and by also taking into account the various influencing factors, the neural network method provides acceptable results for the risk assessment of rockbursts.

Elevation 4000

4000

3500

3500

3000

3000

2500

2500

2000

2000

1500

1500

Q

No.1 tunnel 1 No.2 tunnel 3

2

No.3 tunnel 4

5 No.4 tunnel 6

7

8 0

FIG. 11.2.9

1000

2000

3000

4000

5000

6000

7000

8000

9000

10,000 11,000 12,000 13,000 14,000 15,000

Drainage tunnel Station

Location of rockburst cases.

TABLE 11.2.1 Input Parameters for Assessing the Damage Depth and Intensity of Rockbursts No.

Location

σ 1/σ 3

Brittleness index

Stressstrength ratio

Rock mass integrity

Regional structure

Cover depth (m)

Support strength

1

No.1 headrace tunnel, K8 + 940  8 + 948

1.539

27.439

1.661

1

1

2448

1

2

No.2 headrace tunnel, K8 + 310

1.55

33.088

1.746

1

5

2340

1

3

No.2 headrace tunnel, K9 + 184  K9 + 188

1.407

33.088

1.789

2

1

2318

2

4

No.3 headrace tunnel, K5 + 809

1.342

24.290

1.827

1

4

2078

0

5

No.3 headrace tunnel, K6 + 607  K6 + 614

1.325

33.088

2.16

2

4

2008

1

6

No.4 headrace tunnel, K6 + 075  6 + 105

1.32

33.088

2.086

1

4

1958

2

7

No.4 headrace tunnel K8 + 827  K8 + 818

1.574

27.439

1.631

2

1

2482

1

8

Drainage tunnel, SK5 + 051

1.317

33.366

2.147

2

4

1910

1

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

364

11. ASSESSMENT OF ROCKBURST RISK

FIG. 11.2.10 Actual rockbursts of the estimation examples. (A) A moderate rockburst at K8 + 940  K8 + 948 of No. 1 tunnel, (B) a slight rockburst at K8 + 310 of No. 2 tunnel, (C) a moderate rockburst at K9 + 184  188 of No. 2 tunnel, (D) an intense rockburst at K5 + 809 of No. 3 tunnel, (E) a slight rockburst at K6 + 607  K6 + 614 of No. 3 tunnel, (F) a moderate rockburst at K6 + 075  K6 + 105 of No. 4 tunnel, (G) A moderate rockburst at K8 + 827  K8 + 818 of No. 4 tunnel and (H) a moderate rockburst at SK5 + 051 of drainage tunnel.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

365

REFERENCES

TABLE 11.2.2 Comparison of the Calculated and Practical Results for Rockbursts No.

Rockburst

Calculated results

Practical results

Absolute error

Relative error (%)

1

Damage depth (m)

0.92

1

0.08

8

Intensity

2.18

2

0.18

9

Damage depth (m)

0.25

0.3

0.05

16.2

Intensity

0.74

1

0.26

26

Damage depth (m)

0.83

1

0.17

17

Intensity

2.1

2

0.1

5

Damage depth (m)

2.26

2

0.26

13

Intensity

3.28

3

0.28

9.3

Damage depth (m)

0.34

0.4

0.06

15

Intensity

0.96

1

0.04

4

Damage depth (m)

0.77

1.1

0.33

30

Intensity

1.89

2

0.11

5.5

Damage depth (m)

0.72

0.8

0.08

10

Intensity

1.83

2

0.17

8.5

Damage depth (m)

0.88

0.9

0.02

2.2

Intensity

2.08

2

0.08

4

2

3

4

5

6

7

8

References Abbas, M., & Morteza, B. (2010). Evolving neural network using a genetic algorithm for predicting the deformation modulus of rock masses. International Journal of Rock Mechanics and Mining Sciences, 47, 246–253. Adnan, A. B., & Nabil, K. (2004). Modeling soil collapse by artificial neural networks. Geotechnical and Geological Engineering, 24, 427–438. Feng, X.-T. (1994a). Adaptive pattern recognition to predict rockbursts in underground openings. Journal of Northeastern University, 15(5), 471–475 [in Chinese]. Feng, X.-T. (1994b). Rockburst prediction based on neural network. Transactions of Nonferrous Metals Society of China, 4(1), 9–14. Feng, X.-T. (2000). Introduction of intelligent rock mechanics. Beijing: Science Press [in Chinese]. Feng, X.-T., Katsuyama, K., Wang, Y. J., et al. (1997). A new direction—Intelligent rock mechanics and rock engineering. International Journal of Rock Mechanics and Mining Sciences, 34(1), 135–141. Feng, X.-T., Wang, Y. J., Ozbay, M. U., & Webber, S. (1998). Rockburst induced by mining at great depth and its control strategies—An integrated intelligent system. China Mining Magazine, 7(6), 44–47 [in Chinese]. Feng, X.-T., Webber, S. J., & Ozbay, M. U. (1997). Applicability of artificial intelligence techniques for assessing rockburst risks in deep gold mines. In Proc. of 1st Southern African symposium on rock engineering (ISRM regional conference), South Africa. Feng, X.-T., Webber, S., & Ozbay, M. U. (1998). Neural network assessment of rockburst risks for deep gold mines in South Africa. Transactions of Nonferrous Metals Society of China, 8(2), 335–341. Feng, X.-T., Wang, Y. J., & Yao, J. G. (1996). A neural network model on real-time prediction of roof pressure in coal mines. International Journal of Rock Mechanics and Mining Sciences, 33(6), 647–653. Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Reading, MA: Addison-Wesley publishing company. Hertz, J., Krogh, A., & Palmer, R. G. (1991). Introduction to the theory of neural computation. New York, NY: Westview Press. Suchatvee, S., & Herbert, H. E. (2006). Artificial neural networks for predicting the maximum surface settlement caused by EPB shield tunnelling. Tunnelling and Underground Space Technology, 21, 133–150.

Further Reading Feng, X.-T., & Wang, Y. J. (1998). New development in researching rockburst induced by mining at great depth and its control strategies. China Mining Magazine, 7(5), 42–45 [in Chinese].

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S U B C H A P T E R

11.3 Probabilistic Assessment of Mining-Induced Time-Dependent Seismic Hazards Stanisław Lasocki Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland

11.3.1 FORMULATION OF THE PROBLEM The probabilistic seismic hazard is a potential possibility of the occurrence of ground motion caused by seismicity, expressed in the form of likelihoods. This possibility results from probabilistic properties of the seismic source (source), propagation of seismic waves from the source to a receiver (path), and receiving site (site). The hazard can be quantified in terms of any ground motion parameter of interest or any set of such parameters. However, the seismic risk, which is the probability of loss due to a seismic event, is primarily related to amplitude parameters of ground motion. Therefore the seismic hazard is usually quantified in terms of the amplitude parameters: peak accelerations (horizontal PHA, vertical PVA), peak velocities (horizontal PHV, vertical PVV) and the like, which are sometimes related to specific frequencies (i.e., in terms of the spectral amplitude that is the response spectrum amplitude for a given frequency). Mining-induced seismic sources are in general weak as compared to tectonic earthquakes, and the associating ground motion contains a considerable portion of higher-frequency components that weakly affect surface objects. For this reason the hazard linked to mining seismicity is often expressed by the peak ground motion amplitudes from a specified, low frequency band (e.g., from up to 10 Hz). Farther on, the probabilistic seismic hazard assessment (PSHA) problem will be linked to the ground motion amplitude parameter, but its extension to other motion parameters is also possible. The classic PSHA problem has been formulated for multifault tectonic seismicity (e.g., Cornell, 1968; Cornell & Toro, 1992; Reiter, 1991), which is stationary; that is, its probabilistic properties do not change over time. If amp(x0, y0) is the value of the ground motion amplitude parameter at point (x0, y0) at the surface, the PSHA problem can be formulated by Rðaðx0 , y0 Þ, DÞ ¼ Pr½ampðx0 , y0 Þ  aðx0 , y0 Þ in D time unitsÞ ¼ p

(11.3.1)

where R(a(x0, y0), D) is the exceedance probability function of a; that is, the probability that amp at (x0, y0) will exceed a in the time period D. The objective is to find a for the prescribed values of p, (x0, y0) and D. For stationary seismicity and given p, a(x0, y0) depends only on the time period length, D, during which the point (x0, y0) is exposed to seismic influences, and not on the location of this time period on the absolute time axis. Mining seismicity differs from natural stationary seismic processes in many aspects of which two, the most important for the PSHA problem formulation, are transience and time variability in the time perspective of humans. The transience means that the seismically active sections of the mining rockmass are not permanently active. Seismicity of these sections is correlated in time and space with the activity of mining works carried out in these volumes (e.g., Lasocki, 2008; Orlecka-Sikora & Lasocki, 2002). The seismicity does not occur before the works begin, and it does not continue indefinitely long after the works terminate. The time-variability of seismicity, linked to a specific mine section, results from the variability in time of the mining factors that induce seismicity, like the location of works in combination with the heterogeneity of the rockmass, mining rate, etc. (e.g., Lasocki, 1993a, 2008). These time effects are discussed in Section 11.3.4 and illustrated in Figs. 11.3.3 and 11.3.4. Due to the transience of mining seismicity, the exceedance probability function, R, must be attached to a specified period of time [D1, D1 + D], where D1 is the beginning and D1 + D is the end of the time period for which the hazard is assessed. The PSHA solution, a, refers also exclusively to [D1, D1 + D]. The PSHA problem reformulated for the seismicity induced by mining reads: Rðaðx0 , y0 Þ,D1 , DÞ ¼ Pr½ampðx0 , y0 Þ  aðx0 ,y0 Þ in ½D1 , D1 + D time periodÞ ¼ p

(11.3.2)

The time-variability of seismicity implies dependence on time of the probabilistic functions describing the seismic process, which are components of Pr[•] in Eq. (11.3.2). IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

11.3.2 MODELING THE SEISMIC ACTIVITY OF A FUTURE ZONE

367

In the engineering seismology of natural earthquakes, the seismic hazard is often quantified by a maximum credible amplitude of ground motion for a specified time period T rather than by the amplitude value, whose exceedance probability is determined by Eq. (11.3.1). The maximum credible amplitude is the amplitude value, whose mean return period is T. The maximum credible amplitude and the amplitude from Eq. (11.3.1), a(x0, y0), are strictly related formally and can be calculated one from another. However, in mining engineering seismology the interpretation of a is always straightforward because it is linked to the period of interest [D1, D1 + D], whereas the maximum credible amplitude is meaningful only when T is less than or equal to D. For this reason, we use a here. Eq. (11.3.2) refers to one seismically active area or seismic zone, whose activity is described by the source probabilistic functions, which are presented below. To assess the impact of more than one seismic zone, we aggregate the probabilities (Eq. 11.3.2) of individual zones. Let Rk(a(x0, y0), D1, D) be the exceedance probability of a(x0, y0) in the time period [D1, D1 + D], resulting from the activity of the seismic zone k. Let be L active zones, k ¼ 1,…,L in that time period. The PSHA problem, accounting for these L zones, reads: Rðaðx0 , y0 Þ, D1 , DÞ ¼ 1 

L Y

½1  Rk ðaðx0 , y0 Þ,D1 , DÞ ¼ p

(11.3.3)

k¼1

and its solution is again a(x0, y0), given p, D1, D. Note that none from L zones must be active throughout the whole period [D1, D1 + D]. In the extreme case, we could take into account also a zone, which is not active in this period at all; however, R for such a zone is zero and hence does not add anything in Eq. (11.3.3).

11.3.2 MODELING THE SEISMIC ACTIVITY OF A FUTURE ZONE Natural tectonic seismic zones have been active and persistent since before the existence of mankind and will continue long into the future. Therefore when approaching the PSHA problem for natural seismicity, one can make use of past information on the seismic process in the region of interest and therefore estimate the target probabilities from this information. Because such a seismic process is broadly stationary, these estimations are also valid for anytime in the future. The transience and the time-variability of mining seismicity result in the past and future seismic hazard in the same region being generally different. For obvious reasons, we are interested in the hazard that is relevant for future time periods. This hazard will result from the seismic zones, which will be active in the future in the period [D1, D1 + D], but which have not been necessarily active yet. Often, these will be the zones associated with mining in panels that are only planned to be excavated in the future. In the best case, we can have a zone associated with the panel whose exploitation has already begun before the time D1 and will continue also after D1. For such a zone, we possess some information about its seismicity pattern from the observations from the past before D1, but we have yet to infer anything about the future, [D1, D1 + D]. In any case, whereas the PSHA problem in natural seismicity is, in fact, the transformation of the gathered seismicity data in the hazard information, the PSHA problem in mining seismicity is the prediction of a future hazard based on past seismicity data and plans of future mining works. The locations of the future mining works determine the locations of future zones of induced seismicity (e.g., Kozłowska, 2013). The times of activity of the future zones are deduced from the mining works program; the activity will start with the beginning of the works and will last until some half a year after the work termination (e.g., Cichy & Lasocki, 1982). There can be different ways to model the activity of a future zone by means of possessed information on the zones active in the past. In practical application of PSHA on mining areas, we used the following strategy to model the future seismicity (Lasocki, 2005, 2009; Lasocki, Orlecka-Sikora, Urban, & Kozłowska, 2011; Lasocki et al., 2012). First, whenever it was possible, we were collecting opinions of experts. The specialists of rock mechanics and mining, who knew in details the geological and mining conditions of the mine and panels of interest, were to indicate a group of panels, which were mined out in the past, and which were the most similar to the panel, which was expected to induce the seismicity of the future seismic zone. This judgment comprised also the probabilities that the seismicity of the future zone would repeat the past seismicity patterns. If the expert judgment was not available or was incomplete, we were accepting as alternative models for the future seismic zone activity the activities of the past zones, which were located the closest to the expected location of the future zone. In this approach, it is assumed that the a priori probability of the activity pattern of the past zone to be repeated in the future zone is inversely proportional to the average distance between the past zones and the future zones. In order to evaluate this average distance, the area of the future zone is covered by a fine grid. Let the grid

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

368

11. ASSESSMENT OF ROCKBURST RISK

consist of N nodes, which have coordinates (xi,yi), i ¼ 1,…,N. Next, for every past zone used as a model, we calculate all the distances between N nodes and all epicenter locations of the earthquakes, which occurred in the model zone. Let ν ðkÞ be the number of the model zones for the future zone, and rs ,s ¼ 1, ..,tðkÞ be the distances between the future zone nodes, and the epicenters in the model zone k, k ¼ 1,…, ν. In the presented approach the a priori probability that the future zone activity will follow the activity pattern of the zone k reads: tðkÞ X

w ðk Þ ¼

1=rðskÞ

s¼1

( ðk Þ ν t X X k¼1

)

(11.3.4)

1=rðskÞ

s¼1

This “geographical” approach to modeling future activity can be modified in a specific situation. For instance, it can be constrained by assuming that the model cannot be farther from the future zone than the prescribed average distance, or that when there are two potential models in the same direction from the future zone, only the one closer is taken into account. If L is the number of seismic zones, which are expected to be active during the period [D1, D1 + D], ν(k) is the number of alternative models of the future zone k, k ¼ 1,…,L, and Pr(k,i) is the a priori probability of the realization of the model i of zone k, i ¼ 1,…,ν(k), then the PSHA problem from Eq. (11.3.3) becomes: " # νðk Þ L Y X 1 Prðk, iÞRk, i ðaðx0 , y0 Þ,D1 , DÞ ¼ p (11.3.5) Rðaðx0 , y0 Þ,D1 , DÞ ¼ 1  k¼1

i¼1

where Rk,i(a(x0, y0), D1, D) is the exceedance probability of the value a during the period [D1, D1 + D] due to the seismicity of zone k, when it follows the model i. The last modification concerns the time changeability of the seismicity in the future zone. When the hazard is due to expected seismic activity of many future zones and it is evaluated on a larger area, it can be safely assumed that the seismicity within the future zones does not change in time, though it can follow any of the alternative models (e.g., Lasocki, 2005). However, there can appear specific situations, for which the more detailed insight into the PSHA problem, accounting for the seismicity time changes during the future zone lifetime, has to be undertaken. As it is shown later in this chapter, the source component of PSHA is expressed by the event rate, the source size distribution, and the epicenter distribution of sources. The cloud of mining seismic events locates itself in the direct vicinity of mining works and moves its location along with the advancing works (e.g., Cichy & Lasocki, 1982; Kozłowska, 2013), hence the epicenter distribution changes. Mining seismic sources are in general weak and shallow, and their impact decreases fast with distance. When the hazard is estimated for a specific area located close to a future seismically active zone, then the changes of location of the event cloud can have a significant influence on the total hazard due to that zone. As it is discussed in Section 11.3.4 and exemplified in Fig. 11.3.3, not only does the distribution of the epicenters of the induced seismic sources vary in time, but also the event rate and the source size distribution change in time in a continuous way. There are no ways yet to include in the PSHA problem the continuous time changes of the seismic activities of the model zones. Besides, one cannot expect that a future seismic zone will copy exactly time-variations of its model. However, some general features, like an increased chance for stronger events: when opening up cross cuts, when approaching weak zones, when increasing the gob area etc., can be caught through copying the general features of the seismicity pattern of the model onto an excavation plan of the future zone. In this connection the following strategy, for the first time applied in Lasocki (2009) and Lasocki et al. (2012), is suggested. The time changes of source size distribution of a model zone are analyzed, and on this basis the whole activity period of the model zone is divided into consecutive subperiods of broadly stationary seismicity. The subperiods are proportionally projected on the expected activity period of the future zone. The resultant segments of the future zone area are called subzones, which enter independently in PSHA. The source size distribution of the subzones is assumed to be the same, as the source size distribution of the model zone in the respective subperiod of activity. The division of the future zones into the subzones modifies Eq. (11.3.5) as follows: 8 2 39 νðkÞ nY ðk, iÞ L < Y X     = 1 Prðk, iÞ41  1  Rk, i, j aðx0 , y0 Þ, Dk, i, j1 , Dk, i, j 5 ¼ p (11.3.6) Rðaðx0 , y0 Þ, D1 ,DÞ ¼ 1  : ; i¼1 j¼1 k¼1

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

11.3.3 EXCEEDANCE PROBABILITY OF GROUND MOTION AMPLITUDE

369

where, [Dk,i,j1,Dk,i,j][D1, D1 + D] is the period of activity of the subzone j of zone k. The division into subzones has been done on the basis of model i. n(k,i)   is the number  of subzones of zone k. The division into subzones has been done on the basis of model i. Rk, i, j aðx0 , y0 Þ, Dk, i, j1 , Dk, i, j is the exceedance probability of the value a in the period [Dk,i,j1, Dk,i,j], resulting from the seismicity of the subzone j of zone k, when the seismic activity in this zone is like the one in model i.

11.3.3 EXCEEDANCE PROBABILITY OF GROUND MOTION AMPLITUDE Let us consider again an individual future seismic zone. It is usually assumed that the source effect on ground motion is related only to the event magnitude, and the path effect is related only to the epicentral distance between the seismic source and the receiving point (x0, y0). Though other factors (e.g., the source mechanism, the source directivity, the path anisotropy, etc.) doubtlessly play an important role for the resultant ground motion amplitudes (e.g., Ambraseys, Douglas, Sarma, & Smit, 2005; Orlecka-Sikora et al., 2014; Lasocki & Olszewska, 2017 for mining-induced seismicity), presently there are no reliable ground motion prediction models incorporating such factors. Under the above assumption on the factors representing the source and path effects, the zone seismicity is represented only by the event rate, which determines the probability of event occurrence; the magnitude distribution, which determines the probability of specific event size; and the epicenter distribution, which determines the probability of specific event location. Let the intersection of [D1, D1 + D] with the time period of activity of the considered future zone be [Ds, De]. Following the previous considerations on the time-variability of seismicity in future zones, it is accepted that the source, path, and site effects will remain constant during [Ds, De].1 The exceedance probability of the ground motion amplitude a at (x0,y0); that is, the total probability of occurrence of the ground motion amplitude a at the point (x0,y0) during the period [Ds, De], reads then ∞ ðð

Rðaðx0 , y0 Þ,Ds , De  Ds Þ ¼

Prðampðx0 , y0 Þ  aðx0 , y0 Þjr, mÞf ðrÞf ðmjN ðDs , De Þ 6¼ 0Þdmdr

(11.3.7)

0 M

where, N(Ds, De) is the number of seismic events that will occur in the period [Ds, De]; m is the event magnitude; f ðmjN ðDs , De Þ 6¼ 0Þ is the probability density function (PDF) of m, conditional upon the occurrence of seismic events during the period [Ds, De]; M is the set of all possible magnitudes; r is the epicentral distance between the seismic source and the point (x0, y0); and f(r) is the PDF of epicentral distance, resulting from the 2D PDF of epicenter location; Prðampðx0 , y0 Þ  aðx0 , y0 Þjr,mÞ is the probability of occurrence of the ground motion amplitude a at (x0, y0), when the event of magnitude m is located at the epicentral distance r from (x0, y0). To illustrate the approach presented so far, let us consider a fictitious situation as shown schematically in Fig. 11.3.1. We want to estimate at point x0, y0 on the surface the ground motion amplitude a(x0, y0), whose exceedance probability in the next D months from now is p. Hence D1 in Eq. (11.3.6) is the present moment. We analyze exploitation plans of the mine that generates hazardous seismicity, and we find out that the point x0, y0 in the period [D1, D1 + D] will be impacted by the seismicity accompanying the exploitation of two mining panels. Thus this impacting seismicity will be organized in two seismic zones, Z1 and Z2 respectively, around the mentioned two panels. This means that we must assess and aggregate the exceedance probabilities due to these two zones, and L ¼ 2 in Eq. (11.3.6). Next, we analyze past seismicity, looking for the zones active in the past, which can be used as alternative models of the seismicity in the future zones Z1 and Z2. Suppose that experts have chosen two zones active in the past to be used as models for zone Z1, namely M11 and M12. Suppose that the experts have also determined the probability that the model M11 will be realized in zone Z1 equals 0.6, whereas the probability that the model M12 will be realized in zone Z1 equals 0.4. In this way, we have in Eq. (11.3.6) ν(1) ¼ 2 (two models of zone Z1) and Pr(1,1) ¼ 0.6 and Pr(1,2) ¼ 0.4 (a priori probabilities of the realization of the models). Let for the second zone Z2, the experts have indicated only one model, namely the zone active in the past M21. We have then ν(2) ¼ 1 and Pr(2,1) ¼ 1.0 in Eq. (11.3.6). Finally, let us assume that having analyzed the seismicity of the model zones M11, M12, M21 we have discovered that in order to fulfill the requirement of broad stationarity of the seismic process in zone: (1) M11 should be split into three consecutive parts, M11,1, M11,2, M11,3; (2) Whole M12 can be considered stationary; (3) M21 should be split into two 1

When significant time changes of zone properties in [D1, D1 + D] are expected, the zone is split into subzones of constant properties, and the same approach is applied but for every subzone.

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M21

Pr(1,2) = 0.4

Pr(1,1) = 0.6

50% M 11,1

Z1

f(m | N(D1,D1 + 0.5D)) from M 11,1

M11

f(m | N(D1 + 0.5D,D1 + 0.8D)) from M 11,2

f(m | N(D1 + 0.8D,D1 + D)) from M 11,3

30% 20% M 11,2

D1

M 11,3

D1 + 0.5D

D1 + 0.8D

D1 + D

Z1 f(m | N(D1,D1 + D)) from M 12

X0, Y0

Z2 Z2

Pr(2,1) = 1.0

M 21 30% M 21,1

FIG. 11.3.1

D1 + D

D1

f(m | N(D1,D1 + 0.3D)) from M 21,1

D1

f(m | N(D1 + 0.3D,D1 + D)) from M 21,2

D1 + 0.3D

D1 + D

70% M 21,2

Time D1

D1 + D

Example illustrating the procedure for assessing mining-induced seismic hazard. See text for further explanations.

consecutive parts, M21,1, M21,2. The way in which we do such partitioning of model zones is presented in Section 11.3.4.3. For the time being, suppose that in result of this partitioning, M11,1 covers 50% of the total lifetime of the model zone M11, and M11,2, M11,3 cover 30% and 20% of this lifetime, respectively. Let it be also that the part M21,1 lasted 30%, and the part M21,2 lasted the next 70% of the lifetime of model zone M21. The final assumption concerns lifetimes of the future zones Z1 and Z2, in comparison with the time period [D1, D1 + D], for which it is to be performed the hazard analysis. For simplicity, let us assume that these lifetimes are exactly [D1, D1 + D], though any generalization of this assumption is also feasible and not difficult. Now we integrate the above presented assumptions. In the present approach to the hazard analysis in mines, we assume that under the relevant a priori probabilities, the zones, which will be active in the future, will reproduce fully the seismicity characteristics of their models. This means that under the probability Pr(1,1) ¼ 0.6, the zone Z1 will reproduce all properties of its model M11. Z1 will have three periods of stationarity like the model has. These periods of stationarity will occupy successive 50%, 30%, and 20% of Z1 lifetime, like it is in the model. In result, when the zone Z1 is modeled by M11, it is split into three subzones, hence n(1,1) ¼ 3 in Eq. (11.3.6). The characteristics of seismicity in these subzones will be the same as the characteristics of seismicity of the parts M11,1, M11,2, M11,3 of the model M11. The same way of thinking concerns the second model (M12) of the zone Z1, linked to the probability Pr(1,2) ¼ 0.4. M12 is not partitioned, thus when the zone Z1 is modeled by M12, it is also not split into subzones, hence n(1,2) ¼ 1 in Eq. (11.3.6). The characteristic of seismicity in zone Z1 will be the same as the characteristic of seismicity of the model M12. There is only one model of zone Z2, M21, which is divided into two stationary parts, M21,1 and M21,2. Accordingly, Z2 is split into two subzones, and n(2,1) ¼ 2 in Eq. (11.3.6). It is assumed that these subzones will last 30% and 70%, respectively, of the total lifetime of Z2. It is further accepted that the seismicity of these subzones will follow respectively the probabilistic characteristics of seismicity of M11,2 and M11,3. To summarize our example: In Eq. (11.3.6), k ¼ 1,…,L indexes the zones, which will be active in the future and will impact point (x0, y0); i ¼ 1,…,ν(k) indexes the models of zone k; and j ¼ 1,…,n(k,i) indexes the subzones of zone k when this zone is modeled by model i. Thus in the example k ¼ 1,2. When k ¼ 1 then i ¼ 1,2. When k ¼ 1 and i ¼ 1 then j ¼ 1,2,3. When k ¼ 1 and i ¼ 2 then j ¼ 1. When k ¼ 2 then i ¼ 1, and j ¼ 1,2. We will have to estimate six exceedance probabilities R1,1,1, R1,1,2, R1,1,3, R1,2,1, R2,1,1, R2,1,2, according to Eq. (11.3.7). For this purpose we will estimate f(mjN(•)), respectively, from M11,1, M11,2, M11,3, M12, M21,1, M21,2. We will divide the area of planned mining works in the panel connected with zone Z1 into the first 50%, the next 30%, and the last 20%. This division will be a basis for the division of zone Z1 into three subzones. Areas of these subzones will be used to determine the distributions of epicenters, f(r) relevant to the three subzones of zone Z1. How to determine distribution of epicenters is presented in Section 11.3.4.4. We will connect these distributions of epicenters, respectively, with f(mjN(•))-s from M11,1, M11,2, M11,3 to get R1,1,1, R1,1,2, R1,1,3. The next distribution of epicenters will be determined for zone Z1 taken as a whole and will be connected with f(mjN(•)) from

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M12 to get R1,2,1. Finally, in the same way as described above, we will determine the distributions of epicenters for the subzones of zone Z2, and we will connect them respectively with f(mjN(•))-s from M21,1, M21,2 to get R2,1,1, R2,1,2.

11.3.4 MODELING PROBABILISTIC DISTRIBUTIONS OF ZONE SEISMICITY 11.3.4.1 Event Rate and Representations of Source Component in PSHA In addition to the postulate from Section 11.3.2 that the probabilistic characteristics of seismic process in future zones can be treated as independent of time, or if not then we are able to divide the future zones in subzones having this property, we assume also that the event occurrence process is Poissonian. In this way, we neglect internal correlations in seismic series. Recent studies indicated that such correlations exist and are significant (e.g., Kozłowska, Orlecka-Sikora, Kwiatek, Boettcher, & Dresen, 2015; Lasocki, 2008; Orlecka-Sikora, Lasocki, Lizurek, & Rudzinski, 2012; We˛glarczyk & Lasocki, 2009), but PSHA in mining seismology still awaits developments regarding the event rate modeling that would take into account the interrelations among events. The occurrence process is assumed Poissonian; that is, the event rate is modeled by the Poisson distribution, where the probability of n events to occur in a time period of length Δt reads: Pr½N ¼ n; Δt ¼

ðλΔtÞn λΔt e n!

(11.3.8)

where λ is the mean event rate. Let n earthquakes be observed in the time period T. The maximum likelihood estimator (MLE) of mean activity rate is ^λ ¼ n=T

(11.3.9)

In order to get f ðmjN ðDs , De Þ 6¼ 0Þ in Eq. (11.3.7), we calculate first the total probability of occurrence of an event m during D ¼ De  Ds: Rðm, DÞ ¼

∞ X

  Pr½N ¼ n Pr magnitude  mjN ¼ ninD

n¼1

¼

∞ X ðλDÞn n¼1

n!

(11.3.10) e

λD

n

f1  ½FðmÞ g ¼ 1  exp fλD½1  FðmÞg

where F(m) is the cumulative distribution function (CDF) of magnitude. R(m, D), referred to as the exceedance probability, is an important representation of the source component of seismic hazard. The other most often used representations of the source component are the mean return period of events of magnitude m, TðmÞ ¼ fλ½1  FðmÞg1

(11.3.11)

and the maximum credible magnitude for D, which is the magnitude of event whose mean return period is D mcred ðDÞ : T ðmcred Þ ¼ D

(11.3.12)

All these representations are relevant if referring to a period [Ds, Ds + D], in which the seismic process can be regarded  as Poissonian.   d d Rðm, DÞ Pr magnitude  mjN 6¼ 0inD ¼  , The conditional magnitude PDF is f ðmjN 6¼ 0 in DÞ ¼  dm dm Pr½N 6¼ 0inD and from Eq. (11.3.8), Pr½N 6¼ 0 in D ¼ 1  eλD , thus f ðmjN ðDs , De Þ 6¼ 0Þ ¼

λDf ðmÞ exp fλD½1  FðmÞg 1  exp ðλDÞ

(11.3.13)

where f(m) is the magnitude PDF.

11.3.4.2 Magnitude The magnitude distribution models, which are most commonly used in seismology, result from a statistical relationship known as the Gutenberg-Richter relation. This relation links linearly the common logarithm of the number of events, n, observed in the consecutive, same-size magnitude bins, to the magnitude values of the

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bin centers mm, log n ¼ a  b log mm, or the common logarithm of the observed number, N, of events whose magnitudes are greater than or equal to any m to m, log N ¼ a  b log m. The relation is obeyed from a certain completeness magnitude, mc. This is the lower limit of magnitude of events, which statistically all are recorded in given monitoring conditions. The Gutenberg-Richter’s relation leads to the left hand side truncated exponential distribution for magnitude, f ðmÞ ¼ βeβðmmc Þ ; FðmÞ ¼ 1  eβðmmc Þ m  mc

(11.3.14)

where β ¼ b ln10 and b is the Gutenberg-Richter b-value. Let {mi, i ¼ 1,…,n} be observed magnitudes, mi mc. The MLE estimator of β is: " #1 n X 1 0 mi  mc (11.3.15) β^ ¼ n i¼1 and mc0 ¼ mc  0.5ε, and ε is the accuracy of magnitude evaluation (usually equals 0.1). In PSHA, however, the double truncated exponential model for magnitude is more popular (e.g., Page, 1968; Cosentino, Ficarra, & Luzio, 1977): f ðm Þ ¼

βeβðmmc Þ 1  eβðmmc Þ ; F ð m Þ ¼ mmax  m  mc 1  eβðmmax mc Þ 1  eβðmmax mc Þ

(11.3.16)

which results from the Gutenberg-Richter relation, and the assumption that there is an upper physical limit of event magnitude, mmax. The popularity of the double truncated exponential model stems from four reasons: First, the deficit of stronger events with respect to the expectations from the unlimited Gutenberg-Richter relation has been observed. Second, the upper-unlimited exponential distribution, Eq. (11.3.14), leads to the divergence of expected value of seismic energy on some values of b, whereas the model with mmax, Eq. (11.3.16), does not. Third, the upper limit of magnitude, specific for particular conditions of seismic zone, is justifiable physically. Fourth, if known, mmax is a very convenient parameter for practical applications; earthquakes stronger than mmax will never occur. The maximum likelihood estimation with respect to β is " # n ^ max  mc 0 Þ 1 1X ðm mi  mc 0  ¼0 (11.3.17)    n i¼1 ^ max  mc 0 Þ  1 exp β^ðm β^ mmax is the limit of distribution, hence it cannot be evaluated from the MLE method. To estimate it, Kijko and Sellevoll (1989) proposed Cooke’s (1979) generic formula: mobs max

ð

^ max ¼ mobs m max +

½FðmÞn dm

(11.3.18)

mc

where mobs max is the maximum observed magnitude. This estimator is biased; its bias and variance were studied by Lasocki and Urban (2011), who provided nomograms, which can be used for bias reduction in the typical situation of mmax estimation. Eqs. (11.3.17), (11.3.18) form a nonlinear system, whose roots are the searched estimates of β and mmax. The variety of combinations of technological and geological factors inducing earthquakes in mines may result in significant deviations of the observed magnitude distribution from the models derived from the Gutenberg-Richter relation. Such deviations have been long noticed (e.g., Kijko, Drzezla, & Stankiewicz, 1987; Maghsoudi et al., 2013), statistically ascertained (Lasocki, 2001; Urban et al., 2016) and explained in connection with a bicomponent seismicity-generating process in a mining environment (e.g., Gibowicz, 1990; Johnston & Einstein, 1990; Kijko et al., 1987; Maghsoudi, Hainzl, Cesca, Dahm, & Kaiser, 2014; McGarr, 2000). Recent studies (Eaton, Davidsen, Pedersen, & Boroumand, 2014; Urban et al., 2016) suggested that incoherence of the magnitude distribution with the Gutenberg-Richter relation may be a general feature of the anthropogenic seismicity, regardless of the technology that induce earthquakes. Because the magnitude CDF appears in the exponent in Eq. (11.3.10), even a tiny misfit of the parametric model of magnitude leads to large, systematic errors of hazard estimates. Therefore Lasocki, Kijko, and Graham (2000) and Kijko, Lasocki, and Graham (2001) first proposed to use the nonparametric kernel estimation method (e.g., Silverman, 1986) to deal with complex distributions of magnitude. The latest forms of kernel estimators of magnitude distribution functions, which include the upper limit for magnitude, read (Lasocki & Orlecka-Sikora, 2008): IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

11.3.4 MODELING PROBABILISTIC DISTRIBUTIONS OF ZONE SEISMICITY

"

373

2 #

  0 n n   X pffiffiffiffiffi1 X 1 m  mi m  mi mc  mi exp 0:5 2π  Φ Φ ωi h ωh ωi h ωi h i¼1 i i¼1 a ^f a ðmÞ ¼ ^ ; F ð m Þ ¼       n n X X mmax  mi m0c  mi mmax  mi m0c  mi Φ Φ Φ Φ ωi h ωi h ωi h ωi h i¼1 i¼1

(11.3.19)

where {mi, i ¼ 1,…,n} are observed magnitudes, Φ(•) denotes the standard Gaussian CDF, h is the smoothing factor, and h is a root of the equation (Kijko et al., 2001): " # " # ( "  "  2 2 # 2 2 #9 = X m  m m  m m  m m  m i j i j i j i j  2n ¼ 0 (11.3.20) 20:5  1 exp   1 exp   2 ; 2h2 4h2 h2 2h2 i, j {ωi, i ¼ 1,…,n} are local bandwidth factors, which cause the smoothing factor to adapt to uneven data density along the magnitude range, " # ef ðmi Þ 0:5 (11.3.21) ωi ¼ g " #1  n n n m  m 2 Y X 1 1 i ef ðMi Þ . exp 0:5 where ef ðmÞ ¼ pffiffiffiffiffi , and g ¼ h 2π nh i¼1 i¼1 If one prefers unlimited magnitude distributions, Eq. (11.3.19) can be easily converted to the unlimited form by setting mmax ! ∞. Studies of the efficiency of this nonparametric approach to seismic hazard estimation, performed on simulated data, showed that it provides results with tolerable, limited errors regardless of whether the actual magnitude distribution follows the Gutenberg-Richter relation or is complex (Kijko et al., 2001; Urban et al., 2016). The only drawback is that this approach is a bit demanding regarding the sample size; it performs well for magnitude data samples of more than 100 elements.

11.3.4.3 Time Variations of Source Components of Seismic Hazard We consider the probabilistic functions representing the occurrence time, magnitude, and location of event, and consequently, the exceedance probability and other representations of the source component in PSHA, as independent of time in seismic zone or in subzone. This is an approximation done merely for practical purposes, because we know that all aspects of the seismic process in mines vary due to time changes of the technological circumstances inducing seismicity. In some cases a deeper insight into time variations of the seismic process can be valuable. Such a case is the problem of seismic hazard changes in a direct region of mining works. The seismicity cloud directly linked to mining works that surrounds the mining front and moves along with the front advancement can change its characteristics. Information on the changes towards an increased probability of occurrence of stronger events is of utmost importance for safety of the mining works. Using statistical testing procedures, Lasocki (1992) and Olszewska and Lasocki (2009) evidenced that the seismic process in the mine is nonstationary but that it can be considered, with a good approximation, as interval stationary. They also concluded that the time intervals, in which the process tends to stationarity, are long enough to provide data samples allowing for the statistical estimation of process parameters. On that basis Lasocki (1993a,1993b) formulated a method to monitor hazard changes in time in mining front region. It boils down to estimate the hazard from the parameters of seismic events that occurred in a prescribed volume around the mining front in a prescribed time window, which directly precedes the time, for which the estimates are issued. Considering the next time point, for which the hazard estimates are to be issued, one takes into account the fact that the mining front moved. The volume surrounding the mining front is also moved accordingly, so that it remains immovable with respect to the front, and the time window is moved to be attached to this next time point. The hazard is quantified by the hazard functions: exceedance probability (Eq. 11.3.10), return period (Eq. 11.3.11), and maximum credible magnitude (Eq. 11.3.12), but the variations in time of other parameters (e.g., event rate λ, Gutenberg-Richter b-value, etc.) can be also traced. The time window length is selected so that the seismic process can be regarded as stationary in this window. This allows for linking the hazard estimates, obtained from the observations in the time window, to the presently analyzed time moment; that is, to the right end of the window. The procedure of data collection for such a time-dependent hazard estimation is shown schematically in Fig. 11.3.2. IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

374

11. ASSESSMENT OF ROCKBURST RISK

FIG. 11.3.2 Scheme of the time-dependent hazard estimation. Assuming that the estimation is performed with a time window length of 10 days, the scheme shows how to collect sample data for hazard functions’ estimation for day 11. Top: The rectangle presents a mining panel. Solid, dashed and dotted vertical segments indicate position of longwall (exploitation front) in day 1, 2, 10 and 11, respectively. Middle: Only the events from the rectangular areas around the longwall positions in day 1, 2, …, 10, respectively, are taken into account. The events that occurred on the hatched area in day 1 are sample data of day 1. Similarly with sample data of day 2, …, day 10. Down: Magnitudes and occurrence times of events, which are included to sample data. The magnitudes from all days from day 1 to day 10 are used to estimate the hazard parameters, which then are attributed to day 11. To obtain the estimates for the next day (day 12) the procedure is repeated starting from day 2.

An example of such a time-dependent hazard estimation is shown in Fig. 11.3.3. The case concerns the local seismicity linked to the longwall 3/503 of the Bobrek colliery in Poland. The panel was excavated throughout some 16 months in 2009 and 2010. The top graph presents daily values of the exceedance probability of M3.0 in 1 day. Two events M3+ actually occurred, and their occurrence times are marked by arrows. Daily event rate values are in the bottom graph. The calculations were done for a rectangular spatial area of [300 m  (the longwall length plus 100 m)], positioned symmetrically with respect to the longwall. The time window of 30 days was applied. The magnitude distribution was modeled by the exponential distribution, Eq. (11.3.14). The data was taken from IS-EPOS Platform for Anthropogenic Seismicity Research (tcs.ah-epos.eu) and processed using Platform’s services. We presented in Section 11.3.2 that in order to incorporate time changes of seismicity characteristics of a model of the zone, which is expected to be active in the future, we break the model into subsequent parts of broad stationarity of the seismic process. Then we divide the target zone into subsequent subzones, whose durations are in the same proportions as those between the parts of stationarity of the model. Finally, we attribute to these subzones the seismicity characteristics, respectively, which have been estimated from the stationary parts of the model. The division of the model on the stationary parts is made on the basis of the above described time-dependent hazard estimation for this model. Such a division is illustrated in Fig. 11.3.4. The curve represents the dependence on time of the exceedance probability of the occurrence of events with prescribed magnitude. The magnitude value is not much important here because the division is done based on time-variations rather than on the exceedance probability values, and the timevariations are the same for every magnitude. Based on the shape of this curve, the seismicity in the analyzed active zone has been divided into three parts: (1) Low hazard part from February to August 2010, (2) High hazard part from September 2010 to May 2011, (3) Low hazard part from June 2011 to June 2012. The first part lasted some 25% of the whole period of activity of the zone; the second part was 32%, and the third part was 43%. The division is very crude, subjective and not equivocal. The exceedance probability is far from being constant in the selected parts, but the fact that the hazard first grew to reach a maximum around December 2010, then dropped down and stabilized is distinctly visible. If this zone were to serve as a model for a zone, which will be active in the future, this future zone will be

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11.3.4 MODELING PROBABILISTIC DISTRIBUTIONS OF ZONE SEISMICITY

FIG. 11.3.3

Time variations of seismic hazard around the longwall 3/503 of Bobrek colliery in Poland. Top—the exceedance probability of M3.0 event in 1 day. Arrows mark times of actual occurrence of M 3.0 events. Bottom—the event rate. See text for further information.

0.2 M3.7

0.18 0.16 R(M3.0, 1day)

0.14

M3.0

0.12 0.1 0.08 0.06 0.04 0.02 0 15-Aug-2009 04-Oct-2009 23-Nov-2009 12-Jan-2010 03-Mar-2010 22-Apr-2010 11-Jun-2010

Time 14

Event rate (1/day)

12 10 8 6 4 2 0

15-Aug-2009 04-Oct-2009 23-Nov-2009 12-Jan-2010 03-Mar-2010 22-Apr-2010 11-Jun-2010

Time

0.08 0.06

R(8,6) = 0.02

R(8,6) = 0.07

R(8,6) = 0.02

0.04

10-Jun-2012

11-Apr-2012

11-May-2012

11-Feb-2012

12-Mar-2012

12-Jan-2012

13-Dec-2011

14-Oct-2011

13-Nov-2011

15-Aug-2011

14-Sep-2011

16-Jul-2011

16-Jun-2011

17-Apr-2011

17-May-2011

16-Feb-2011

18-Mar-2011

17-Jan-2011

18-Dec-2010

19-Oct-2010

18-Nov-2010

20-Aug-2010

19-Sep-2010

21-Jul-2010

21-Jun-2010

22-Apr-2010

22-May-2010

0.00

21-Feb-2010

0.02

23-Mar-2010

Exceedance probability values, R

0.10

Date

FIG. 11.3.4 Example of the division on periods of different hazard characteristics of the zone, which was active seismically in the past. If this zone were to be used as a model for the zone, which is expected to be active in the future, this division would be reflected in the splitting of the future zone into subzones. See text for further explanations.

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11. ASSESSMENT OF ROCKBURST RISK

split into subzones, which will have the percentages of duration the same as above. The seismicity characteristics for these subzones will be taken from the seismicity characteristics of the distinguished parts of this model.

11.3.4.4 Epicenter Location A planned location of mining works delineates the area where events are expected to occur. This is the area of panel to be excavated, plus about a 100-m margin at the farthest location of the mining front and about 50–80 m margins at other boundaries of the panel (e.g., Cichy & Lasocki, 1982; Kozłowska, 2013; Prugger & Gendzwill, 1990; Senfaute, Chambon, Bigarre, Guise, & Josien, 1997; Syrek & Kijko, 1988). It is assumed that the epicenter locations inside this area follow the 2D uniform distribution with PDF: ( 1=jSj for ðx, yÞ 2 S f ðx, yÞ ¼ (11.3.22) 0 for ðx, yÞ 62 S where S denotes the active area, and jSj is its size. For numeric calculations the continuous distribution is replaced by the uniform discrete distribution. To this end the future zone area is covered by a grid of Q nods, with coordinates (xi,yi), I ¼ 1,…,Q, which define possible epicenter locations of future earthquakes. The discrete probability distribution of epicenter location is: Prfðx, yÞ ¼ ðxi , yi Þg ¼ 1=Q i ¼ 1,…, Q

(11.3.23)

The distribution of epicentral distance to the receiving point (x0,y0) is f(r) and now takes the discrete form:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (11.3.24) Prðri Þ ¼ Pr r ¼ ðx0  xi Þ2 + ðy0  yi Þ2 ¼ 1=Q i ¼ 1, …, Q The discretization of the epicentral distance distribution modifies probability, Eq. (11.3.7), into: Q ð X Prðampðx0 , y0 Þ  aðx0 , y0 Þjri ,mÞf ðmjN ðDs , De Þ 6¼ 0Þdm Rðaðx0 , y0 Þ, Ds , De  Ds Þ ¼ 1=Q i¼1

M qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ri ¼ ðx0  xi Þ + ðy0  yi Þ i ¼ 1,…, Q

(11.3.25)

When the number of nodes Q is large, the discretization, which simplifies calculations, does not decrease the accuracy of results.

11.3.5 MODELING CONDITIONAL PROBABILITY OF GROUND MOTION AMPLITUDE The only term in Eqs. (11.3.7), (11.3.25) that has not been discussed so far is Prðampðx0 , y0 Þ  aðx0 , y0 Þjr,mÞ, which represents path and site components of PSHA. This conditional probability results from a statistical model linking the ground motion amplitude to the seismic source size, the distance from the source, and the soil properties at the receiving point. The model is called ground motion prediction equation (GMPE). GMPE most often takes a form of regression (see: Douglas, 2008; Douglas & Aochi, 2008 for comprehensive reviews of GMPE models and identification methods). After testing a number of functional forms for GMPE relevant for mining-induced seismicity, Lasocki (2005, 2013) has suggested the form of pffiffiffiffiffiffiffiffiffiffiffiffiffi (11.3.26) log aðx0 , y0 Þ ¼ α + βm  γ log r2 + d2 + δðx0 , y0 Þ where a(x0,y0) is either any component or the total peak ground acceleration, 10δðx0 , y0 Þ is the local amplification factor at the receiving point (x0,y0), α, β, γ are the regression coefficients, and d is the common depth factor that ensures nonsingularity of Eq. (11.3.26) at the epicenter. In order to assess α, β, γ, h one must have in hand the source and related ground motion parameters; α, β, γ is estimated by means of the linear regression analysis with d selected so that the standard error of estimate is the least. The conditions of ground vibration propagation and the amplifying effects at the site are related to the geological conditions of study area. It has been shown (Lasocki, 2013; Lasocki & Olszewska, 2017) that in the case of mining-induced seismicity, these local conditions and their variability even over a relatively small area have significant influence on

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

11.3.6 EXAMPLE

377

surface effects. Therefore, to obtain an accurate GMPE, the data for the estimation of coefficients should be acquired from a dedicated dense ground motion monitoring network and distributed over the area, for which the PSHA is performed. If the site amplification is not known from independent data on subsurface, and the ground motion database is big enough, relative local amplification factors can be estimated simultaneously with α, β, γ. Given m, r, the probability to exceed the amplitude a(x0, y0) at point (x0, y0) reads Prðampðx0 , y0 Þ  aðx0 , y0 Þjr, mÞ ¼ 1  Ft ðtðaðx0 , y0 Þ, r,mÞ, η  3Þ

(11.3.27)

where Ft ðtðaðx0 , y0 Þ, r,mÞ,η  3Þ is the student’s distribution CDF, η is the number of ground motion records that are used in the estimation of GMPE, pffiffiffiffiffiffiffiffiffiffiffiffiffi log aðx0 , y0 Þ  α  βm + γ log r2 + h2  δðx0 , y0 Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tðaðx0 , y0 Þ, r,mÞ ¼ (11.3.28) XT0 Cb X0 + SEE2 2

3 1 5 T X0 ¼ 4 pmffiffiffiffiffiffiffiffiffiffiffiffiffi , X0 its transposition Cb is the covariance matrix of regression coefficient estimators, SEE is the 2 2 log r + h standard error of estimate.

11.3.6 EXAMPLE To exemplify the use of the described PSHA in mining-induced seismology, we present shortly its application to estimate a long-term seismic hazard for the Zelazny Most tailings pond in Legnica-Glogow Copper District (LGCD) in Poland (Lasocki et al., 2011, 2012). Underground copper-ore mining in LGCD, carried on in three mines at the depth 900–1200 m, is accompanied by intense induced seismicity. Yearly, about 2500 events of local magnitude above 1.0 are recorded by in-mine seismic systems. Occasionally, events of magnitude M4 and stronger occur. The seismic activity results in considerable ground motion, which affects surface structures over the area. One of such structures is the Zelazny Most tailings pond. Its area of about 14 km2 is enclosed within 14.4 km long and locally more than 50 m high embankment dams. The present volume of wastes is 600 m3 and the final volume will be about 1.1 billion m3. The pond is one of the largest waste dumps in the world. To monitor the level of seismic hazard for Zelazny Most, a dense network of accelerometric stations, presently comprising 22 stations, has recorded ground motion for 15 years. The data on seismicity and related ground motion is used to perform PSHA, which is updated every 5–6 years. The last hazard analysis was carried out in 2011 and 2012. Its objectives were: 1. Determine at given points of the dams the values of peak horizontal acceleration (PHA) and peak vertical acceleration (PVA), whose exceedance probability p ¼ 0.05 (5%) in 2011–50. 2. If hazard would be unacceptably high, identify the future seismic zones, which will generate the strongest ground motion. The acceptation level of hazard was PHA ¼ 1.0 m/s2. 3. Provide recommendations for mining operations connected with these zones to reduce the level of hazard. The analysis took into account impact of the seismicity, which could be induced by mining works carried on within a 5.5 km wide zone around the pond. In the considered, 40 years’ time-period, 84 mining panels had been planned on this area, hence 84 future seismic zones were expected. All possessed data on past seismicity in LGCD was used to identify the zones of past activity, which were to serve as models of future seismicity. This data covered the time period since 1972. Altogether, 140 past zones were identified, and their probabilistic properties were assessed. Magnitude distributions were estimated with the upper bounded nonparametric kernel estimators, Eqs. (11.3.16), (11.3.18). Fig. 11.3.5 shows the location of pond and the locations of seismic zones active in the past superimposed on the locations of mining panels planned to be excavated; that is, on the locations of future seismic zones. The GMPE-s (Eq. 11.3.26) for PHA and PVA were pinpointed based on the local ground motion database, which had been gathered during the 11 years’ monitoring period that preceded the time of analysis. The database consisted of more than 3100 three-component accelerograms. The GMPE-s included relative local amplification factors, see Lasocki (2013) for details. The factors, which had been evaluated only at locations of monitoring stations, were attributed to particular points along the dam based on similarity of soil conditions.

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11. ASSESSMENT OF ROCKBURST RISK

FIG. 11.3.5 Distribution of objects of the first stage of PSHA for the Zelazny Most tailings pond in LGCD. Gray area—the tailings pond. Smaller rectangular shapes—panels planned to be excavated. Points—epicenters of seismic events recorded since 1972. Shades of gray mark the membership to seismic zones active in the past. The zones, which overlap spatially, are well separated in time. Ellipse in a thick line marks the panels, which were analyzed in details in the second stage of the analysis.

In the first stage of the analysis all L ¼ 84 zones were included in Eq. (11.3.3). It was assumed that the seismic process within every zone was stationary, hence no further division into subzones was done. As the models for the activity of a future zone only those past zones were accepted, which located no farther than 2 km from the expected location of the future zone. The “geographical” criterion of similarity, Eq. (11.3.4), was used to evaluate the a priori probabilities of realization of the seismicity models in the future zone (Pr(k,i)-s in Eq. (11.3.5). When no past zones fulfilled the 2 km criterion, 10 past zones chosen at random from all 140 were used as equally probable models. The estimated values of PHA with the given exceedance probability, at the prescribed points along the dams, are presented by solid bars in Fig. 11.3.6. At four points the estimates exceeded 1.0 m/s2.

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379

REFERENCES

FIG. 11.3.6 Results of PSHA for the

1.8

Zelazny Most tailings pond. PHA values, whose exceedance probability in the years 2011–50 is 0.05. Bigger bars, or the values obtained in the first stage of the analysis when the seismic process in seismic zones was assumed to be independent of time. Smaller bars—the values obtained in the second stage of the analysis when it was assumed that the excavation would recede from the pond, and the variation of the seismic process in the zones in time was taken into account.

1.6 1.4

PHA (m/s2)

1.2 1.0 0.8 0.6 0.4

0.0

XVW XIIW VIIIW VIaW IIW IaW IW XIXN XVIaN XVIN VIIN VaN IVN IIIcN XXIVE XXIIIE XXIaE XXaE XXE XIXE XVIIIaE XVIIIE XVIIaE XVIIE XVIE XIVaE XIVE XIIIbE XIIIE VaE XIXbS XVIIIS XIS VIS

0.2

Point ID

It is not surprising that the seismic zones, which were mostly responsible for those high PHA values, were those the closest to the pond, marked by red ellipse in Fig. 11.3.5. When these zones were neglected, the PHA values dropped down below 1.0 m/s2. Therefore the second stage of the analysis involved the detailed investigation of the expected impact of these proximate zones. It was recommended that the mining works in these panels began the closest to the pond and then receded. As mining seismicity occurs close to a mining front, in this way the increase of goaf area, which results in an increased potential to generate stronger events, was correlated with farther location from the pond of these potential events. The detailed analysis of planned works in these panels singled out six future zones of seismic activity. The seismic zones active in the past, to be used as models of the seismicity of these future zones, were selected by an expert, based on the similarity of mining and geological conditions. The expert chose three models for each zone and has assigned a priori probabilities of realization of the models in each zone. After the analysis of time changes of the exceedance probability, Eq. (11.3.10), in the models, the total active period of the model was divided into not overlapping, consecutive approximate stationarity periods. The projection of these stationarity periods onto the expected period of activity of the future zone led to distinguishing the subzones. The number of subzones varied in dependence on the considered future zone and the applied model. Altogether, the analysis defined by Eq. (11.3.6) took into account 117 subzones for the considered six zones, each modeled by three models. Results of this part of the analysis are presented as hatched bars in Fig. 11.3.6. The recommended change of the direction of excavation in the most influential zones and the detailed analysis of consequences of this change resulted in the decrease of the expected impact of these zones on the dams to the acceptable level.

References Ambraseys, N. N., Douglas, J., Sarma, S. K., & Smit, P. M. (2005). Equations for estimation of strong ground motions from shallow crustal earthquakes using data from Europe and Middle East: Horizontal peak ground acceleration and spectral acceleration. Bulletin of Earthquake Engineering, 3, 1–53. Cichy, A., & Lasocki, S. (1982). Some possibilities of statistical interpreting mining microseismological data from the point of view of estimating rockburst danger. Publications of the Institute of Geophysics, Polish Academy of Sciences M-5, 155, 85–99 [in Polish, English abstract and figure captions]. Cooke, P. (1979). Statistical inference for bounds for random variables. Biometrika, 66, 367–374. https://doi.org/10.1093/biomet/66.2.367. Cornell, C. A. (1968). Engineering seismic risk analysis. Bulletin of the Seismological Society of America, 58, 1583–1606. Cornell, C. A., & Toro, G. (1992). Seismic hazard assessment. In R. L. Hunter, & C. J. Mann (Eds.), Techniques for determining probabilities of geologic events and processes (pp. 147–166), New York: Oxford University Press. Cosentino, P., Ficarra, V., & Luzio, D. (1977). Truncated exponential frequency magnitude relationship in earthquake statistics. Bulletin of the Seismological Society of America, 67, 1615–1623.

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Douglas, J. (2008). Further errata of and additions to “ground motion estimation equations 1964-2003”. Final Report BRGM/RP-56187-FR, Orleans, France. Douglas, J., & Aochi, H. (2008). A survey of techniques for predicting earthquake ground motions for engineering purposes. Surveys in Geophysics, 29, 187–220. https://doi.org/10.1007/s10712-008-9046-y. Eaton, D. W., Davidsen, J., Pedersen, P. K., & Boroumand, N. (2014). Breakdown of the Gutenberg-Richter relation for microearthquakes induced by hydraulic fracturing: Influence of stratabound fractures. Geophysical Prospecting, 62, 806–818. https://doi.org/10.1111/1365-2478.12128. Gibowicz, S. J. (1990). The mechanism of seismic events induced by mining. In C. Fairhurst (Ed.), Rockbursts and seismicity in mines (pp. 3–27). Rotterdam: Balkema. Johnston, J. C., & Einstein, H. H. (1990). A survey of mining associated rockbursts. In C. Fairhurst (Ed.), Rockbursts and Seismicity in Mines (pp. 121– 128). Rotterdam: Balkema. 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Journal of Geophysical Research, Solid Earth, 120. https://doi. org/10.1002/2014JB011410. Lasocki, S. (1992). Non-Poissonian structure of mining induced seismicity. Acta Montana, 84, 51–58. Lasocki, S. (1993a). Statistical prediction of strong mining tremors. Acta Geophysica Polonica, 41, 197–234. Lasocki, S. (1993b). Statistical short-term prediction in mining induced seismicity. In R. P. Young (Ed.), Rockbursts and Seismicity in Mines 93 (pp. 211– 216). Rotterdam: Balkema. Lasocki, S. (2001). Quantitative evidences of complexity of magnitude distribution in mining-induced seismicity: Implications for hazard evaluation. In G. van Aswegen, R. J. Durrheim, & W. D. Ortlepp (Eds.), Rockbursts and seismicity in mine: Dynamic rock mass response to mining (pp. 543–550). Lasocki, S. (2005). Probabilistic analysis of seismic hazard posed by mining induced events. In Y. Potvin, & M. Hudyma (Eds.), Controlling seismic risk. Proc. sixth int. symp. on rockburst and seismicity in mines 9–11 March 2005, Australia, Nedlands (pp. 151–156). Perth: Australian Centre for Geomechanics. Lasocki, S. (2008). Some unique statistical properties of the seismic process in mines. In Y. Potvin, J. Carter, A. Dyskin, & R. Jeffrey (Eds.), Proc. 1st southern hemisphere international rock mechanics symposium SHIRMS 2008, Perth, 16-19 September 2008 (pp. 667–678). Perth: Australian Centre for Geomechanics. Lasocki, S. (2009). Key-note lecture: Probabilistic seismic hazard analysis for mining-induced seismicity. In C. Tang (Ed.), Controlling seismic hazard and sustainable development of deep mines. Proc. seventh int. symp. on rockburst and seismicity in mines, 21-23 August 2009, Dalian, China (pp. 59–72). New York: Rinton Press. Lasocki, S. (2013). Site specific prediction equations for peak acceleration of ground motion due to earthquakes induced by underground mining in Legnica-Głogów Copper District in Poland. Acta Geophysica, 61, 1130–1155. https://doi.org/10.2478/s11600-013-0139-8. Lasocki, S., & Olszewska, D. (2017). Ground motion prediction equations for mining induced seismicity in Legnica Glogow Copper District in Poland. In: Proceedings 16th world conference on earthquake engineering, 16WCEE 2017. Paper No 4114 (in print). Lasocki, S., & Orlecka-Sikora, B. (2008). Seismic hazard assessment under complex source size distribution of mining-induced seismicity. Tectonophysics, 456, 28–37. https://doi.org/10.1016/j.tecto.2006.08.013. Lasocki, S., & Urban, P. (2011). Bias, variance and computational properties of Kijko’s estimators of the upper limit of magnitude distribution, Mmax. Acta Geophys, 59, 659–673. https://doi.org/10.2478/s11600-010-0049-y. Lasocki, S., Kijko, A., & Graham, G. (2000). Model-free seismic hazard estimation. In H. Gokcekus (Ed.), Proc. int. conf. earthquake hazard and risk in the mediterranean Region, EHRMR’99 (pp. 503–508). Lefkosa: Educational Foundation of Near East University. T. R. N. Cyprus. Lasocki, S., Orlecka-Sikora, B., Urban, P., & Kozłowska, M. (2011). Updated prediction of the influence of seismicity in mines of KGHM “Polska Miedz´” S.A. on the Z˙ elazny Most repository for the period of mining activities. Report. Project KGHM-ZH-U-0076-2011 contracted by KGHM Polska Miedz´ S.A. Hydro-technical Division in Rudna. Lasocki, S., Popiołek, E., Zorychta, A., Orlecka-Sikora, B., Sopata, P., Stoch, T., et al. (2012). Detailed prediction of impacts of tremors and surface deformations induced by mining, on OUOW “Z˙ elazny Most” with an account for OUOW extension and program of copper ore excavation till 2042. In Report. Project KGHM-ZH-U-0076-2011 contracted by KGHM Polska Miedz´ S.A. Hydro-technical Division in Rudna. Maghsoudi, S., Cesca, S., Hainzl, S., Kaiser, D., Becker, D., & Dahm, T. (2013). Improving the estimation of detection probability and magnitude of completeness in strongly heterogeneous media, an application to acoustic emission (AE). Geophysical Journal International, 193, 1556–1569. https://doi.org/10.1093/gji/ggt049. Maghsoudi, S., Hainzl, S., Cesca, S., Dahm, T., & Kaiser, D. (2014). Identification and characterization of growing large-scale en-echelon fractures in a salt mine. Geophysical Journal International, 196, 1092–1105. https://doi.org/10.1093/gji/ggt443. McGarr, A. (2000). Energy budgets of mining-induced earthquakes and their interactions with nearby stopes. International Journal of Rock Mechanics and Mining Sciences, 37, 437–443. https://doi.org/10.1016/S1365-1609(99)00118-5. Olszewska, D., & Lasocki, S. (2009). Non-stationarity and internal correlations of the occurrence process of mining-induced seismic events. In General assembly of international association of seismology and physics of the earth interior, Cape Town, South Africa, 10–16 January. Orlecka-Sikora, B., & Lasocki, S. (2002). Clustered structure of seismicity from the Legnica-Glogow copper distric. Publications of the Institute of Geophysics, Polish Academy of Sciences M-24, (340), 105–119 [in Polish, English abstract and figure captions]. Orlecka-Sikora, B., Lasocki, S., Lizurek, G., & Rudzi nski, Ł. (2012). Response of seismic activity in mines to the stress changes due to mining induced strong seismic events. International Journal of Rock Mechanics and Mining Sciences, 53, 151–158. https://doi.org/10.1016/j.ijrmms.2012.05.010. Orlecka-Sikora, B., Cesca, S., Lasocki, S., Lizurek, G., Wiejacz, P., & Rudzi nski, Ł. (2014). Seismogenesis of exceptional ground motion due to a sequence of mining induced tremors from Legnica-Głogów Copper District in Poland. Geophysical Journal International, 198, 40–54. https:// doi.org/10.1093/gji/ggu109.

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Page, R. (1968). Aftershocks and microaftershocks of the great Alaska earthquake of 1964. Bulletin of the Seismological Society of America, 58, 1131–1168. Prugger, A. F., & Gendzwill, D. J. (1990). Results of microseismic monitoring at the Cory Mine, 1981-1984. In C. Fairhurst (Ed.), Rockbursts and seismicity in mines (pp. 215–219). Rotterdam: Balkema. Reiter, L. (1991). Earthquake hazard analysis. New York: Columbia University Press. Senfaute, G., Chambon, C., Bigarre, P., Guise, Y., & Josien, J. P. (1997). Spatial distribution of mining tremors and the relationship to rockburst hazard. Pure and Applied Geophysics, 150, 451–459. https://doi.org/10.1007/s000240050087. Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman and Hall. Syrek, B., & Kijko, A. (1988). Energy and frequency distributions of mining tremors and their relation to rockburst hazard in the Wujek coal mine, Poland. Acta Geophysica Polonica, 36(3), 189–201. Urban, P., Lasocki, S., Blascheck, P., do Nascimento, A. F., Nguyen Van Giang, & Kwiatek, G. (2016). Violations of Gutenberg-Richter relation in anthropogenic seismicity,. Pure and Applied Geophysics, 173, 1517–1537. https://doi.org/10.1007/s00024-015-1188-5. We˛glarczyk, S., & Lasocki, S. (2009). Studies of short and long memory in mining-induced seismic processes. Acta Geophysica, 57, 696–715. https:// doi.org/10.2478/s1160.

S U B C H A P T E R

11.4 Rockburst Prediction Methods and Their Applicability Krishna Kanta Panthi Norwegian University of Science and Technology (NTNU), Trondheim, Norway

11.4.1 INTRODUCTION Three key engineering geological factors directly influencing the stability of tunnels or underground caverns are rock mechanical properties, in situ stress conditions, and groundwater inflow through fractures and weakness/fault zones (Panthi, 2012). Tunnels and underground caverns passing or located beneath deep rock cover (overburden) are subject to instabilities caused by induced rock stresses. In relatively unjointed and massive strata, if the rock mass strength is less than the induced stresses, the instability may be mainly associated with rock spalling or rock bursting. On the other hand, if the rock mass is weak, schistose, sheared, deformed, or thinly foliated/bedded, squeezing is the most likely scenario (Panthi, 2006). Self-initiated rockburst is the most common type of brittle failure encountered in the tunnels and underground cavern excavated for civil engineering and mining purposes. Diederichs (2014) categorizes brittle failure in tunnels into five groups: moderate spalling/slabbing, severe rockburst, face burst, structural slip burst, and structurally controlled strainburst. The determination of the magnitude and direction of the in situ rock stress is therefore essential for a meaningful assessment of the instability likely to be caused by induced stresses in tunnels and underground openings (Hudson & Harrison, 1997). The rockburst (brittle failure) in tunnels excavated under a high-stress environment has helped to increase the knowledge and understanding of this type of instability. Data and information collected from numerous tunnels and mines were used to develop empirical as well as analytical methods to predict rockburst activities. Most of the proposed methods are mainly based on past experience, often combined with analytical calculations of rock mechanical and stress-related parameters. This section describes four rockburst prediction methods representing both empirical as well as semianalytical methods: the Norwegian rule of thumb (Olsen, 1965); the stress problem classification, part of the Q-system (Barton, Line, & Lunde, 1974); the uniaxial compressive strength (UCS) and tensile strength approach (Diederichs, 2007); and the maximum tangential stress and crack initiation (CI) strength approach (Martin & Christiansson, 2009). While explaining these methods, discussions have also been made on the limitations and extent of their applicability in the engineering decision-making process. It is emphasized here that the name explained above are not directly proposed by the authors who proposed these prediction methods; the name is proposed by this author based on the essence and mechanical properties used in predicting the rockburst phenomenon.

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11.4.2 NORWEGIAN RULE OF THUMB Norway is famous for using tunnels and caverns for harnessing hydropower energy: road and railway tunnels constructed within city areas and the countryside; tunnels and caverns used for food, oil, and gas storages; tunnels and underground caverns for sport activities and water supply; and tunnels for sewer transport. Most of the tunnels built for hydropower, road, and railways are located in the countryside and pass through steep valleyside slopes. One of the major challenges in tunneling through Norwegian rock mass is that it is prone to brittle failure like spalling and rock burst phenomenon. Hence, knowledge associated with brittle failure in tunnels is not new in this country. Already in 1965, Prof. Rolf Selmer Olsen of the Norwegian Institute of Technology (NTH) studied over 60 tunnels passing parallel with valleyside slope where rockbursts and rock spalling were experienced during tunnel excavation (Olsen, 1965). Most of the studied tunnels were passing through the topography where vertical rock cover over the tunnel was relatively small in comparison to the vertical height between the tunnel and the top of the valleyside slope (plateau). It is noted here that most of these tunnels had relatively short distance (mostly not exceeding 300 m) from the surface terrain (Fig. 11.4.1-right). Fig. 11.4.1-left shows tunnels with no rockburst activity, medium rockburst (spalling) condition and high rockburst condition in relation to the vertical height between the tunnel and the top of the valleyside slope (plateau) and the horizontal distance between the tunnel and the top of valleyside slope. As one can see in Fig. 11.4.1, most of the tunnels that had vertical height (h) between tunnel and plateau <500 m and an angle between the tunnel location and plateau <25 degrees mostly did not experienced any rockburst activity. However, those tunnels that had exceeded this threshold mostly had stability problems associated with rockburst or rock spalling. This rule of thumb is a useful tool that can be used to start with the first check on whether there is a potential rock spalling/rockburst activity in tunnels under consideration. Nevertheless, one should note here that this method gives indicative results or potential rock spalling/rockburst activity to those tunnels aligned parallel with the valleyside slope and are located within 500 m from the valleyside slope.

11.4.3 STRESS PROBLEM CLASSIFICATION Barton et al. (1974) of the Norwegian Geotechnical Institute (NGI) proposed the Q-system of rock mass classification, which got a major revision in 1993 with the inclusion of the database from more than 1000 tunnel cases (Grimstad & Barton, 1993). This system is based on a numerical assessment of six different input parameters defined by Eq. (11.4.1): Q¼

RQD Jr Jw   Ja SRF Jn

(11.4.1)

where RQD is the rock quality designation, Jn is the joint set number, Jr is the joint roughness number, Ja is the joint alteration number, Jw is the joint water reduction factor, and SRF is the stress reduction factor.

FIG. 11.4.1 Distribution of tunnels having no rockburst, rock spalling, or severe rockburst plotted against height from tunnel to the top of valleyside slope (plateau) and the horizontal distance between the tunnel and the valleyside top (right) and typical explanation of the condition (right). The figure is developed based on Olsen (1965).

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11.4.5 MAXIMUM TANGENTIAL STRESS AND ROCK SPALLING STRENGTH APPROACH

383

TABLE 11.4.1 Stress Problems Classification in Hard and Competent Rock Mass Based on Q-System Stress class

Description of potential stress induced instability

Ratio between intact rock strength and major principle stress (σ ci/σ 1)

Ratio between maximum tangential stress and intact rock strength (σ θ2max/σ ci)

SC 1

Low stress, near surface, open joints

>200

<0.01

SC 2

Medium stress, favorable stress conditions

200–10

0.01–0.3

SC 3

High stress, very tight structure, usually favorable to blasting except for wall

10–5

0.3–0.4

SC 4

Moderate spalling after > 1 h

5–3

0.5–0.65

SC 5

Spalling and rockburst after few minutes

3–2

0.65–1

SC 6

Heavy rockburst and immediate strain failure

<2

>1

The numerical estimation of each of these six input parameters of the Q-system is explained in a separate table given in Grimstad and Barton (1993), Barton (2002) and others. One of the parameters in Q-system called SRF is associated with stress-induced instability. Part of the SRF table gives classification on rock spalling/rockburst potential in a tunnel built in hard-rock conditions. Table 11.4.1 is the reworked version of the table that classifies rock burst intensity. As can be seen in Table 11.4.1, the stress problems classification method mainly considers three input variables consisting of intact rock strength (σ ci), maximum principle stress (σ 1), and maximum tangential stress (σ θmax). This means that to make an assessment, one should have laboratory-tested intact rock strength and knowledge about the in situ stress conditions of the area in question.

11.4.4 UNIAXIAL COMPRESSIVE AND TENSILE STRENGTH APPROACH Diederichs (2007) proposed qualitative approach for assessing spalling/rock burst failure, which is linked to the UCS and tensile strength (T) of the intact rock. This method recognizes that the crack initiation (CI) in the rock mass occurs as a result of internal heterogeneities and strain anisotropy in the hard, strong, and brittle rock mass under compression and CI is strongly influenced by the internal tensile strength as indicated in Fig. 11.4.2. This method considers that in a spalling condition, there develops extension fractures under the compressive loading in the rock mass, and the rockburst represents a violent rupture in the periphery of the tunnel contour under highstress conditions. It is therefore important to note that in a spalling rock mass, the extension fracture may develop before the actual rockburst by forming parallel and thin slabs in the tunnel periphery. This means that the higher the uniaxial strength (UCS) of rock and the higher the ratio between the UCS and tensile strength (T), the more violent and extensive the damage potential (Fig. 11.4.2) in the tunnel wall.

11.4.5 MAXIMUM TANGENTIAL STRESS AND ROCK SPALLING STRENGTH APPROACH The three approaches discussed above provide a qualitative assessment of the rockburst; however, they provide no clear picture on the severity of the rockburst (depth impact) into the rock mass behind the tunnel wall. On the other hand, knowledge of depth impact (Fig. 11.4.3) is crucial in order to build a strategy on the application of rock support, in particular the length and type of rock anchors and other support means required to achieve sufficient safety while tunneling (Panthi, 2012). The methodology proposed by Martin and Christiansson (2009), as illustrated by Eq. (11.4.2), offers a possibility to assess the extent of rock spalling/rockburst depth impact in the tunnel wall, expressed by Sd.  σ θ max  0:52 Sd r  0:5  σ sm

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

(11.4.2)

384

11. ASSESSMENT OF ROCKBURST RISK

sq−max

sq−max

r

FIG. 11.4.2 Qualitative classification of rock spalling/rockburst potential based on compressive and tensile strength of the rocks. Reproduced from Diederichs, M. S. (2007). Damage and spalling prediction criteria for deep tunneling. Canadian Geotechnical Journal, 44(9), 1082–1116. © 2008 Canadian Science Publishing or its licensors. Reproduced with permission.

Sd

FIG. 11.4.3 A circular tunnel (TBM tunnel) showing potential damage in the tunnel wall due to accumulated major vertical tangential compressional stress due to stress anisotropy.

where Sd is the distance from the tunnel center to the point up to where rock spalling/rockburst failure may extend into the tunnel wall, r is the tunnel radius, σθmax is the maximum tangential compressional stress, and σsm is rock mass spalling strength. Martin and Christiansson (2009) suggest that the magnitude of the in situ spalling strength for glacially eroded massive Scandinavian crystalline rocks lies between 55% and 65% of the intact rock strength, while the laboratory-tested CI strength may be between 40% and 50% of the intact rock strength (σ ci). A comparison of the CI values measured in laboratory uniaxial tests and the rock mass spalling strength suggests that the CI provides the lower bound limit for the rock mass spalling strength. Therefore in crystalline rocks the rock mass spalling strength may lie between 0.4 and 0.6 of the mean UCS.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

REFERENCES

385

11.4.6 APPLICABILITY AND INPUT REQUIREMENTS All four approaches presented above are unique and different in the way the rock spalling/rockburst are assessed in a tunnel passing through strong and brittle rock mass. The Norwegian rule of thumb gives the qualitative assessment on where it is safe to place a tunnel that has to be aligned along the steep slope topography extending from the valley bottom to the top of the hillside. The stress problem classification approach provides a qualitative assessment based on either the ratio between the intact rock strength and major principle stress or the ratio between the maximum tangential compressional stress and intact rock strength of the rock. Similarly, the uniaxial compressive and tensile strength Approach gives a qualitative assessment based on intact rock strength and the ratio between intact rock strength and tensile strength of the rock material. The similarity between the latter two approaches is that both assess the extent of the severity giving “severity class.” The fourth one, the maximum tangential stress and rock spalling strength approach, provides an opportunity to assess the extent of rock spalling/rockburst depth impact, which is valuable information for the needed support design, particularly the estimation of the length of the rock anchors. It is also important to be highlighted that the rock spalling/rockburst assessment using the Stress Problem Classification and Maximum Tangential Stress and the Rock Spalling Strength Approaches require knowledge of the in situ stress condition, both its magnitude and direction, in the vicinity where tunnel will be located. In addition, one should have information on the intact rock strength and method to calculate maximum tangential compressional stress. The maximum tangential compressional stress (σ θmax) can be estimated using Kirsch’s equation defined by maximum and minimum principle stress expressed by Eq. (11.4.3): σ θ max ¼ 3σ 1  σ 3

(11.4.3)

Panthi (2012) recommends that the rock mass spalling strength (σ sm) be replaced with rock mass strength (σ cm) to calculate the rock spalling/rockburst depth impact. For the rock mass influenced by schistosity, rock mass strength (σ cm) can be estimated using equation suggested by Panthi (2006), which is expressed by Eq. (11.4.4). For homogeneous, massive, and crystalline rocks, the rock mass strength (σ cm) can be estimated by Eq. (11.4.5): σ cm ¼

σ 1:5 ci 60

(11.4.4)

σ cm ¼

σ 1:6 ci 60

(11.4.5)

where σ sm ¼ σ cm is the rock mass spalling strength or rock mass strength, and σ ci is the laboratory-tested intact rock strength.

11.4.7 CONCLUSION Assessing rock spalling/rockburst in tunnels passing through massive and brittle rocks is a challenging issue in rock engineering. Different assessment approaches have been applied worldwide, and four of the most common approaches have been discussed in this chapter. All four approaches discussed have strength and weaknesses and should be used carefully. The first three approaches give more of a qualitative assessment, and the fourth one gives more of a quantitative assessment. However, before doing any assessment, the user must have knowledge of the topographic, geological, in situ stress, intact rock strength, and tensile strength of the rock where rock spalling/rockburst potential is assessed.

References Barton, N. (2002). Some new Q-value correlation to assist in site characterization and tunnel design. International Journal of Rock Mechanics and Mining Sciences, 39, 185–216. Barton, N., Line, R., & Lunde, J. (1974). Engineering classification of rock masses for the design of tunnel support. Rock Mechanics, 6, 189–236. Diederichs, M. S. (2007). Damage and spalling prediction criteria for deep tunneling. Canadian Geotechnical Journal, 44(9), 1082–1116. Grimstad, E., & Barton, N. (1993). Updating the Q-system for NMT. In Proceeding of the international symposium on sprayed concrete—Modern use of wet mix sprayed concrete for underground support, Fagernes. Norwegian Concrete Association, Oslo, Norway. Hudson, J. A., & Harrison, J. P. (1997). Engineering rock mechanics an introduction to the principle. Pergamon—An imprint of Elsevier Science. Martin, C. D., & Christiansson, R. (2009). Estimating the potential for spalling around a deep nuclear waste repository in crystalline rock. International Journal of Rock Mechanics and Mining Sciences, 46, 219–228.

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Olsen, S. R. (1965). Stabiliteten i tunneler i dalsider [The stability in tunnels in valley-side slopes]. IVA report 142 (pp. 77–83). [in Norwegian]. Panthi, K. K. (2006). Analysis of engineering geological uncertainties related to tunneling in Himalayan rock mass conditions [Doctoral theses] (p. 41). 1503-8181. Trondheim: Norwegian University of Science and Technology. Panthi, K. K. (2012). Evaluation on rock bursting phenomena in a tunnel of the Himalaya. Bulletin of Engineering Geology and Environments, 71(4), 761–769.

S U B C H A P T E R

11.5 Recognition of Rockburst Intensity Using In Situ-Monitored Microseismicity Bing-Rui Chen, Xia-Ting Feng Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China

11.5.1 INTRODUCTION It is important to recognize the reasonable intensity of rockburst after its occurrence. The engineering measures and economic judgment that will be determined corresponding to the intensity of the rockburst occurred. There have been several methods on the recognition of rockburst intensity after the occurrence of rockbursts. For example, Russnes (1974) classifies rockburst intensity into four levels: none, weak, moderate, and severe rockbursts, according to the sound, shape, and features of the failure after the rockburst. Brauner (1985) classifies rockbursts into three grades based on the intensity of destruction to the surrounding rockmass. Tang (1992) classifies rockbursts into four intensities by considering the mechanical characteristics, the type and the shape of the failure, the intensity of destruction, and the sound of the rockburst. The Canadian Rockburst Research Program’s (CRRP) (1996) classifies the severity of rockburst damage into minor, moderate, and major damage and estimates the severity of rockburst damage based on observations and empirical evidence or stress-to-strength ratios and geometric considerations. The Code for Geological Investigations of Hydropower Engineering’s (CGIHE) method proposed by the National Standards Compilation Group of People’s Republic of China (2008) determines the intensity of rockburst according sound and depth of failure caused by rockburst. These methods have been widely used in rock engineering and have aided in the prevention and the control of rockbursts due to their simplicity and flexibility. However, because rockbursts intensity levels using the methods above are classified according to the apparent characteristics of the rockburst occurrence, such as the type and shape of failure, the intensity of destruction, and the sound of the rockburst, these methods can only be used to evaluate the rockburst intensity after the occurrence and sometimes with the staff’s experience. Moreover, conflicts can occur among the different evaluation indexes, even when they use the same method. For example, a rockburst may be classified as an intense rockburst in terms of the depth and the shape of the rockburst failure zone by an engineer; however, it may also be ranked as a moderate rockburst on the basis of the rockburst sound heard by another engineer when the collapse is dominant. The different intensities that can be obtained for the same rockburst by different engineers are an obvious disadvantage for the prevention and the control of rockbursts, thus a new rockburst intensity recognition method is proposed by Chen, Feng, Li, Luo, and Li (2015). It is meant to quantitatively evaluate the rockburst intensity by using the radiated microseismic energy monitored during occurrence of the rockburst and surrounding rock damage severity. Here, criterion of rockburst intensity and two typical examples were only introduced. The detailed description of the method can be found in the reference (Chen et al., 2015).

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS

11.5.3 TWO TYPICAL EXAMPLES USING THE NEW ROCKBURST INTENSITY QUANTITATIVE RECOGNITION CRITERION

TABLE 11.5.1

387

A Rockburst Intensity Quantitative Recognition Criterion Based on the Rockburst Radiated Energy With Rockmass Failure Intensity

Rockburst intensities

lg(E)

Main phenomena

None

(∞,0]

The crack occurred inside the rockmass, an obvious failure, cannot be found on the surface of rockmass, and the cracking sound could barely be heard. No support system and construction are affected

Slight

(0,2]

Main failure type was slight spalling and slabbing in the surface of the surrounding rockmass. The rockmass was slightly ejected, and the size of ejected fragment was 10–30 cm. The cracking sound could be heard slightly, and the depth of failure was <0.5 m. If rockbolt and shotcrete lining are constructed in time, no support system and construction are damaged

Moderate

(2,4]

The main failure type was severe spalling and slabbing of the surrounding rockmass. The rockmass was obviously ejected, and the size of ejected fragment was 30–80 cm; the cracking sound was like the detonator blasting and lasted for some time inside the rockmass. The failure range was obvious, and the depth of failure was more than 0.5 m and <1.0 m. The shotcrete lining could be damaged among the rockbolts, so construction is slightly affected

Intense

(4,7]

A great deal of rockmass was suddenly ejected, and the failure range was extensive. The size of the ejected fragment was 80–150 cm, and the edge of the failure zone typically has a fresh fracture plane. a last sound could be heard before the rockburst, the rockburst, which sounded like an explosive but was louder and had an impact wave; the depth of failure was more than 1.0 m and <2.0 m. The support system was destroyed and construction were affected

Extremely intense

(7,+∞)

A large block of rockmass was suddenly ejected with an intensive seismicity, and the stability of the whole cave was seriously affected; the failure sound was like thunder or a cannonball and lasted a longer time. The depth of failure was more than 3.0 m; while the failure ranges was more extensive, the size of the ejected rock mass was greater. The support system is seriously destroyed, and construction is seriously affected

Note: lg(E) is the common logarithm of the in situ-monitored microseismic radiated energy. The unit of E is Joule.

11.5.2 A QUANTITATIVE RECOGNITION CRITERION FOR ROCKBURST INTENSITY Recognition of rockburst intensities using in situ-monitored microseismic radiated energy and their phenomena are described in Table 11.5.1. The main phenomena were described from observation at the Jinping II hydropower station. In Table 11.5.1, rockburst-radiated energy was obtained mainly by microseismic monitor system. If several microseismic events were monitored when the rockburst occurred, the microseismic event with the biggest radiated energy was chosen to recognize rockburst intensity.

11.5.3 TWO TYPICAL EXAMPLES USING THE NEW ROCKBURST INTENSITY QUANTITATIVE RECOGNITION CRITERION 11.5.3.1 Rockburst Example I: An Intense Rockburst A rockburst, with a loud sound like blasting, occurred at approximately 11 a.m. on August 12, 2011, from the north sidewall to the north spandrel in the range of chainage K8 + 827–K8 + 852, No. 4 headrace tunnel, Jinping II hydropower station. A V-shaped rockburst failure zone, with a depth of approximately 1.8 m, was formed and the failure plane was fresh. Fig. 11.5.1 shows that the rockbolts and shotcrete were destroyed. The in situ-monitored microseismic radiated energy when this rockburst occurred at 1.66E + 06 J. Then, it was recognized as an intense rockburst, according to Table 11.5.1.

11.5.3.2 Rockburst Example II: A Moderate Rockburst A rockburst occurred at approximately 9 a.m. on June 20, 2011 at the south sidewall of chainage K5 + 623–K5 + 628 in the drainage tunnel at the Jinping II hydropower station. The main failure type was severe spalling and slabbing of the surrounding rockmass. A few rockmass fragments were ejected with a short distance, as shown in Fig. 11.5.2. The in situ-monitored microseismic radiated energy when this rockburst occurred was 3.63E + 03 J. It was recognized as a moderate rockburst according to Table 11.5.1.

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FIG. 11.5.1 An intense rockburst occurred at chainage K8 + 827–K8 + 852 in the No. 4 headrace tunnel on August 12, 2011.

FIG. 11.5.2 A moderate rockburst occurred at chainage K5 + 623– K5 + 628 in the drainage tunnel on June 20, 2011.

11.5.4 CONCLUSIONS A new quantitative recognition criterion for the rockburst intensity was created based on the radiated energy of many rockbursts monitored by the microseismic technique in the Jinping II hydropower station, China. The new criterion classified the rockburst intensity in five levels. The application of this method for the four headrace tunnels and a drainage tunnel at the Jinping II hydropower station showed that the proposed criterion had a good stability and feasibility and could classify rockbursts well if microseismic monitoring was conducted with the rock engineering.

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References Brauner, G. (1985). Ground pressure and coal bumps. Translated by Y. Li (pp. 17–53). Beijing: China Coal Industry Publishing House [in Chinese]. Canadian Rockburst Research Program (1996). Rockburst research handbook: A comprehensive summary of five years of collaborative research on rockbursting in hard rock mines. CAMIRO Mining Division, CRRP. Chen, B.-R., Feng, X.-T., Li, Q.-P., Luo, R.-Z., & Li, S. (2015). Rockburst intensity classification based on the radiated energy with damage intensity at Jinping II hydropower station, China. Rock Mechanics and Rock Engineering, 48(1), 289–303. National Standards Compilation Group of People’s Republic of China (2008). Code for geological investigation on hydropower engineering. Beijing: China Planning Press [in Chinese]. Russnes, B. F. (1974). Analyses of rockburst in tunnels in valley sides. [M.Sc. thesis] (p. 247). Trondheim: Norwegian Inst. of Technology. Tang, Y. (1992). A new classification of rockburst intensity. Geological Review, 38(5), 439–443.

IV. RISK ASSESSMENT AND WARNING OF ROCKBURSTS