2004:22 TECHNICAL REPORT
Seismicity in Mines A Review
Kristina Larsson
Luleå University of Technology Technical Report Department of Civil and Environmental Engineering Division of Rock Mechanics
2004:22 - ISSN: 1402-1536 - ISRN: LTU-TR--04/22--SE PREFACE
This literature review is part of a joint research project between SveBeFo, Boliden Mineral AB, LKAB, and Luleå University of Technology. The project is aimed at increasing the knowledge of seismicity induced by mining in Sweden. The financial support for the project is provided by SveBeFo, Boliden Mineral AB and LKAB.
The work presented in this report is the result of a literature study and several discussion meetings with the project reference group. The reference group consists of M.Sc. Christer Andersson, SKB (Swedish Nuclear Waste Management), Mr. Tomas Franzén, Research Director at SveBeFo, Tech. Lic. Lars Malmgren, LKAB, M.Sc. Per-Ivar Marklund, Boliden Mineral AB, Professor Arne Myrvang, NTNU, Dr. Jonny Sjöberg, SwedPower AB, and my supervisor Professor Erling Nordlund, Division of Rock Mechanics at Ltu.
Thanks also to Mr. Meirion Hughes for checking the language.
Luleå, November 2004
Kristina Larsson
i
ii SUMMARY
The virgin stress state in the rock mass depends on several factors, for instance gravity and tectonics. Around a mine the stress state is disturbed, which leads to locally increased or decreased stresses. The rock mass in Sweden is generally composed of high strength brittle rock types, so the risk of violent failures increases with increasing depth of mining due to increasing stress levels. The problem with violent failures is that they are a safety risk for mine personnel. During the past few years an increased number of violent failures causing fallouts have been observed in both LKAB and Boliden mines. These types of failures are generally called rockbursts, but different mines give different meaning to the phenomena. Therefore the terms seismicity and seismic event will be introduced here. Seismicity is the rock mass response to deformation and failure. A seismic event is the sudden release of potential or stored energy in the rock. The released energy is then radiated as seismic waves. A rockburst is defined as a mining-induced seismic event that causes damage to openings in the rock.
In this literature report, mining induced seismicity is reviewed and the influencing factors described. The state of stress is one important factor that influences the occurrence of rockbursts; hence the state of stress in Scandinavia is described briefly, and examples of how the most common Swedish mining methods influence the stress field are given. The behavior of the rock mass in different situations is described, dealing with the relationship between stress state and seismicity and rock response to energy changes during excavation. Different rockburst mechanisms are described including failure mechanisms and type of damage caused. Rockburst classifications and the varying definitions of rockbursts are briefly summarized. Seismic monitoring is an important tool for many mines today, and is therefore reviewed including a description of the most common seismological terms that are used to describe seismicity. Some different methods of predicting and explaining rockbursts are described. Methods of preventing seismicity, for example different ways of destressing the rock mass and reinforcement have also been reviewed.
iii iv SAMMANFATTNING
Det primära spänningstillståndet i bergmassan beror av flera faktorer, bland annat gravitation och tektonik. Spänningstillståndet runt en gruva är stört, vilket leder till lokalt ökade eller minskade spänningar. Bergmassan i Sverige består generellt av höghållfasta spröda bergarter, varför risken för våldsamma brottförlopp ökar med ökande brytningsdjup på grund av de högre spänningarna. Problemet med de våldsamma brotten är att de utgör en säkerhetsrisk för personalen. Under de senaste åren har antalet våldsamma brott som orsakat utfall ökat i både Bolidens och LKABs gruvor. Dessa typer av brott kallas generellt för smällberg (eng. rockburst), men olika gruvor har olika uppfattning om vad smällberg är. Därför introduceras i denna rapport begreppet seismicitet och seismisk händelse. Seismicitet är bergmassans respons på deformation och brott. En seismisk händelse är en plötslig frigörelse av potentiell eller lagrad energi i berget, vilken avges i form av seismiska vågor. Smällberg definieras som en seismisk händelse som orsakar en skada (utfall) på öppningar i bergmassan.
I denna litteraturrapport beskrivs brytningsinducerad seismicitet och dess påverkande faktorer. Spänningstillståndet är en viktig faktor som påverkar förekomsten av smällberg, varför spänningstillståndet i Skandinavien beskrivs kort tillsammans med en förklaring om hur de vanligaste svenska brytningsmetoderna påverkar spänningsfältet runt gruvan. Bergmassans beteende i olika situationer beskrivs, främst förhållandet mellan spänningstillstånd och seismicitet samt hur bergmassan beter sig vid energiförändringar. Olika mekanismer för smällberg ges en kort beskrivning där också brottmekanismen och typiska skador tas upp. Klassificering av smällberg samt några olika sätt att definiera smällberg beskrivs. Seismisk övervakning är ett viktigt verktyg för många gruvor idag, så en generell översikt ges tillsammans med en summering av seismologiska termer som används för att beskriva seismicitet. Några olika metoder som utvecklats för att beskriva och förutsäga smällberg tas upp. Metoder att förhindra seismicitet, till exempel olika former av avlastning och förstärkning beskrivs också.
v vi LIST OF SYMBOLS AND ABBREVIATIONS
σv ,σz = vertical stress, compressive stresses are taken as positive
σH = major horizontal stress
σh = minor horizontal stress
σ1 = major principal stress
σ2 = intermediate principal stress
σ3 = minor principal stress
σx = horizontal stress in x-direction
σy = horizontal stress in y-direction
σn = stress normal to e.g., fault plane
σs = seismic stress, proportional to seismic energy and seismic moment ε = strain
εs = seismic strain, proportional to seismic moment
εst = static shear strain τ = shear stress
τs = static shear stress
τd = dynamic shear stress
τe = excess shear stress ρ = rock density, kg/m3 or t/m3 g = gravity acceleration, m/s2 γ = unit weight, N/m3 z = depth below ground surface, m k = σH /σv ν = Poisson’s ratio E = Young´s modulus G = shear modulus or modulus of rigidity S = boundary surface
Si = surface of initial excavation
Sm = surface of enlargement V = volume
Vm = volume of enlargement
vii Wk = kinetic or seismic energy
Wr = released energy
Ws = energy absorbed in support deformation
Wt = change in potential energy
Uc = stored strain energy
Um = stored energy in removed rock
Us = energy stored in spring
Uu = increase in stored energy
U1 = initial strain energy of test cell in MGW
U2 = strain energy after event in MGW K = stiffness of spring or surrounding rock F = force, N N = normal force acting perpendicular to surface of interest
µs = static coefficient of friction
µd = dynamic coefficient of friction A = area s = speed φ = friction angle cs = cohesion α = strike angle, or azimuth β = dip angle λ = rake D = average shear displacement d = distance
Λ0 = amplitude Λ = maximum amplitude ∆ = focal depth T = period of the measured wave h = range ϕ = epicentral distance, ° Ξ = epicentral distance in kilometers Γ = instrument magnification factor ∆σ = stress drop
viii r0 = radius of fault f0 = corner frequency
ML = local or Richter magnitude
M0 = seismic moment
MS = surface wave magnitude mb = body wave magnitude
Mw = moment magnitude
Mn = Nuttli magnitude
ES, EP = seismic energy in S-, and P-wave respectively
Et = total seismic energy N = number of events a = constant b = relation between small and large events in a certain time interval ERR = Energy Release Rate ESS = Excess Shear Stress VESS = Volume Excess Shear Stress MGW = Modeled Ground Work LERD = Local Energy Release Density
ID = departure index
Pi , Pj = parameters
RHI = rockburst hazard indication Ψ = function with value 1 or 0 depending on the departure index
Q1 = stress parameter in cell evaluation method
Q2 = strain energy parameter in cell evaluation method
ST = factor of safety tn, tn’ = traction, before and after event un, un’ = displacement, before and after event
ix
x TABLE OF CONTENTS
Preface...... i Summary ...... iii Sammanfattning ...... v List of symbols and abbreviations...... vii Table of contents ...... xi 1 Introduction ...... 1 1.1 Background ...... 1 1.2 Objective and outline of report...... 2 2 Rock stress...... 3 2.1 State of stress in the rock mass...... 3 2.2 Classification of rock stresses ...... 3 2.3 Virgin stresses or in-situ stresses ...... 4 2.3.1 Gravitational stresses...... 4 2.3.2 Tectonic stresses...... 8 2.3.3 Residual stresses...... 9 2.4 Stresses in Scandinavia ...... 10 2.5 Secondary stresses or induced stresses...... 13 2.5.1 General ...... 13 2.5.2 Mining induced stresses ...... 14 3 Rock mass behavior...... 19 3.1 Response of rock to energy changes ...... 19 3.2 Compressive stress and seismicity ...... 23 3.3 Shear stress and seismicity...... 25 4 Rockburst source mechanisms ...... 29 4.1 Seismic events associated with stopes ...... 29 4.1.1 Strain burst...... 29 4.1.2 Pillar burst ...... 29 4.2 Seismic events associated with geologic discontinuities ...... 30 4.2.1 Fault slip...... 30 4.2.2 Shear rupture...... 31 4.3 Rockburst definitions ...... 31 4.3.1 Definition ...... 31
xi 4.3.2 Classification / categorization of rockbursts ...... 34 5 Seismic monitoring and earthquake seismology...... 39 5.1 Introduction ...... 39 5.2 Seismic monitoring ...... 39 5.3 Earthquake seismology ...... 41 5.3.1 Faults and seismic waves ...... 42 5.3.2 Seismic moment and the moment tensor...... 45 5.3.3 Earthquake focal mechanisms and radiation patterns ...... 49 5.3.4 Earthquake location...... 50 5.3.5 Stress drop...... 52 5.3.6 Earthquake magnitude...... 53 5.3.7 Seismic energy...... 57 5.3.8 Corner frequency...... 58 5.3.9 Intensity scale...... 59 6 Description of seismicity...... 63 6.1 Introduction ...... 63 6.2 Describing seismicity without seismic records ...... 63 6.2.1 Energy Release Rate (ERR) ...... 63 6.2.2 Excess Shear Stress (ESS)...... 65 6.2.3 Volume Excess Shear Stress (VESS)...... 67 6.3 Describing seismicity using seismic records...... 68 6.3.1 Departure indexing method...... 68 6.3.2 Cell evaluation method - Modeled Ground Work (MGW)...... 70 6.3.3 Local Energy Release Density (LERD) ...... 73 6.3.4 Seismic Hazard Scale (SHS)...... 74 7 Prevention and control of seismicity...... 77 7.1 Preconditioning and destressing...... 77 7.1.1 South Africa...... 78 7.1.2 Sweden ...... 81 7.2 Fluid injection...... 88 7.3 Reinforcement ...... 89 7.3.1 Introduction ...... 89 7.3.2 Support functions...... 89 7.3.3 Support capacity...... 90
xii 7.3.4 Support systems...... 92 8 Concluding remarks ...... 95 9 References ...... 97
xiii xiv 1 INTRODUCTION
1.1 Background
The virgin state of stress in the Earth’s crust depends on, among other factors, gravity and tectonics. In, or near, a mine the stress state is disturbed by the mining activities leading to locally increased or decreased stresses. The extent and the consequences of a failure are controlled by three fundamental elements: geomechanical conditions, stress state and mining activities. The term geomechanical conditions include intact rock with geological structures (joints, faults, folds etc.) and it is characterized by the strength and stiffness of the intact rock and the joints, water pressure etc. For failure to occur the interaction of all these three factors is required. Depending on the characteristics of the factors, different failure modes can occur. When the rock mass consists of low strength rock types and also has a low quality, high stress levels may lead to massive failures in the rock mass and large plastic deformations. If the rock mass is of high quality and consists of brittle high strength rock types, the risk for violent failures increases. The failures can, in such cases, be relatively restricted to the area closest to the opening or result in rapid movements along geological structures leading to earthquake- like phenomena.
The increasing mining depth in the Swedish underground mines leads to increasing stress levels and thus to increased risk of instability in drifts, ramps, shafts and other underground structures. The high quality of the rock mass in the areas mined today, in combination with increasing stresses will most likely lead to violent failures with an increasing extent and an increase in the volume of fallouts in the future. At larger depths the risk of other phenomena like activation of faults also increases. Slip on a fault releases large amounts of energy that can damage underground constructions. The problem with violent failures is that they are a safety risk for mine personnel. People working close to the face are very vulnerable if the face or roof starts to eject material. Popping noises sometimes precede these kinds of failure, but not always. Popping may also occur without ejection of material, so it may be difficult to determine the risk.
During the past few years an increased number of violent failures causing fallouts have been observed in both LKAB and Boliden mines in Sweden. Despite apparently similar conditions the problems with brittle and violent failures have been observed to vary in intensity. This
1 project was started to appraise the extent of the problem and to find the mechanisms behind the violent failures.
These types of failures are generally called rockbursts. The term is used without discrimination, so a failure that is called a rockburst in one mine may not be considered so in another. Therefore the terms seismicity and seismic event will be introduced here. Seismicity is the rock mass response to deformation and failure. A seismic event is the sudden release of potential or stored energy in the rock. The released energy is then radiated as seismic waves. A rockburst is defined as a mining-induced seismic event that causes damage to openings in the rock. These definitions have been used by for instance Cook (1976), Salamon (1983) and Ortlepp and Stacey (1994). The vagueness of the term rockburst is evident here, since this definition says nothing of how large the damage should be. An event displacing 1 kg of rock and one that closes an entire drift are both rockbursts.
1.2 Objective and outline of report
The objective of the literature report is to review mining induced seismicity and describe the influencing factors. These factors will be studied for some cases in a Licentiate Thesis. The case studies include Canadian and European mines with known seismicity, and some Swedish mines that start to experience seismicity.
Chapter 2 of this report describes the stress state in the rock mass, both virgin and induced stresses. The state of stress is one important factor that influences the occurrence of rockbursts. The project is about problems caused by high stress levels, so the state of stress in Scandinavia is described briefly. Examples of how mining influences the stress field are given. Chapter 3 describes rock mass behavior in different situations, dealing with the relationship between stress state and seismicity and rock response to energy changes during excavation. In Chapter 4, the different rockburst mechanisms are described including failure mechanisms and type of damage caused. Rockburst classifications and the varying definitions of rockbursts are briefly summarized. Chapter 5 is a description of seismic monitoring in general, and a summary of the most common seismological terms that are used to describe seismicity. Chapter 6 describes some different methods of explaining and predicting rockbursts. Chapter 7 deals with methods of preventing seismicity, for example different ways of destressing the rock mass and reinforcement. Chapter 8 gives conclusions drawn from the literature review regarding influencing factors.
2 2 ROCK STRESS
2.1 State of stress in the rock mass
Knowledge of the state of stress in a rock mass is important in many civil, mining, and petroleum engineering problems as well as in geology and geophysics. In general, stress- related problems increase with depth, but excavating at shallow depths may also be challenging, either because of high horizontal stresses or due to the lack of horizontal stresses. (Amadei and Stephansson, 1997)
2.2 Classification of rock stresses
Rock stress can be divided into virgin stress and induced stress. Virgin (or in-situ) stresses are the stresses that exist before any disturbance has occurred, while induced stresses are created by disturbances. A disturbance is a man-made excavation of some kind, for instance an open pit, a tunnel or an underground mine. Amadei and Stephansson (1997) have proposed a stress terminology based on propositions from several authors, see Figure 2.1. In the following chapters the different factors contributing to the virgin rock stress are commented on in more detail.
Rock stresses
Virgin stresses Induced stresses
Gravitational Residual stresses Tectonic stresses Terrestrial stresses stresses
Active tectonic Remnant tectonic stresses stresses
Broad scale Local scale
Figure 2.1. Stress terminology (after Amadei and Stephansson, 1997).
3 2.3 Virgin stresses or in-situ stresses
Virgin stresses are the stresses that exist in the rock mass before any disturbance (e.g., excavation) has occurred. The virgin stresses comprise gravitational, tectonic, residual, and terrestrial stresses. Terrestrial stresses are the stresses induced by diurnal and seasonal variations of temperature, Moon pull and the Coriolis force (Amadei and Stephansson, 1997). These are often neglected but can affect stress measurements at shallow to very shallow depths. They have very little influence on the stress state at depth in Scandinavia and will be left out of the following description.
2.3.1 Gravitational stresses
Gravitational stresses result from the weight of the overburden per unit area at a specific point in the rock mass. The vertical stress component, σv, is normally assumed to be a function of depth and can be defined as
σ v = ρgz Eq. 2-1 where ρ is the density of the rock mass (kg/m3), g is the gravity acceleration (9.81 m/s2), and z is the depth below ground surface.
The horizontal component due to gravitational loads depends on the rock mass properties. If the material can be considered linear elastic and isotropic and a one-dimensional state of strain is assumed, the average horizontal stress is defined, by for instance Herget (1988), as
ν σ = σ Eq. 2-2 H 1−ν v where ν is Poisson’s ratio, which may vary between 0.15 and 0.35 for most rock types.
If the rock material cannot be considered elastic, and the rock cannot resist shear stresses in the long term (i.e., creep due to viscosity will occur) then after some time the magnitude of the horizontal component will equal the vertical component. This is called a hydrostatic or lithostatic stress field (Herget, 1988). In a lithostatic stress field the weight of the overburden acts in all directions. In short, the horizontal component due to gravitational factors can be expressed as
σ H = kσ v Eq. 2-3
4 where k is a factor that varies from 0 to 1 depending on the restraints on displacement.
So far we have assumed that the rock mass is isotropic, but this is seldom true on a larger scale. Anisotropy is common in rock and can be caused by for example bedding, stratification, schistosity planes or jointing. Foliated metamorphic rock types (schists, gneisses), stratified sedimentary rocks (sandstone, limestone) and rocks with regular, closely spaced joint sets have anisotropy as a general characteristic. Amadei et al. (1987) studied the stress field induced in an anisotropic rock mass under gravitational loading assuming a one- dimensional state of strain. They assumed that the rock mass was homogeneous, linearly elastic and that the material was either orthotropic or transversely isotropic. Transversely isotropic means that the rock mass has different properties in two directions, i.e., there are isotropic planes, see Figure 2.2a. Orthotropy means that the rock mass has different properties in all three directions, i.e.,, there are three orthogonal planes of elastic symmetry, see Figure 2.2b.
σz a) σz b)
σx = σy σx
σy = σx σy
Figure 2.2a) Model of transverse isotropy and b) orthotropy.
For an orthotropic rock mass with only gravitational loading, no lateral displacements and a horizontal ground surface, Amadei et al. (1987) derived expressions for the two horizontal stresses. They found that gravitational loading of an orthotropic rock mass induces unequal principal stresses in the horizontal plane. They also suggest that σx and σy are strongly dependent on the degree of anisotropy. For some ranges of the anisotropic rock properties, the horizontal stresses can exceed the vertical stresses, which is not possible in the isotropic solution. In this study by Amadei et al. (1987) it was assumed that the strata were either parallel or perpendicular to the horizontal ground surface. In a study by Amadei and Pan
5 (1992) they examined the gravity-induced stresses in orthotropic and transversely isotropic rock with strata inclined with respect to a horizontal ground surface, see Figure 2.3.
y β x z P
Figure 2.3. Model of transversely isotropic rock mass with strata inclined at a dip, β.
From this model they concluded that if one of the planes of symmetry is parallel to the y-axis the stress components σx, σy and σz are principal stresses. σx and σy are horizontal stresses, and σz is the vertical stress. The conclusion that can be drawn from both these studies is that for orthotropic and transversely isotropic rock masses, the horizontal stresses parallel to the strike and dip direction of the strata are always principal stresses and are not equal. The stress field induced by gravity is three-dimensional for anisotropic rock masses and the horizontal stresses can be smaller than, equal to, or larger than, the vertical stress.
Stratification is common in both volcanic and sedimentary rocks. Lithology and relative stiffness between different layers can cause the in-situ stresses to vary considerably between different layers. Warpinski and Teufel (1991) made stress measurements (using hydraulic fracturing) at Rainier Mesa, Nevada. They found that the minor principal stress could vary between layers and that the stress change could occur on a scale of about 1 m, if the difference in material properties was large enough. From these studies they concluded that the horizontal stresses at Rainier Mesa depended on material properties of the various layers, topography and bedding. They observed several induced hydraulic fractures that changed direction or stopped at a fault, and also measured stress magnitudes that could vary by as much as 2 MPa and have a change of orientation of 20°- 40°. The stress measured was the minimum in-situ stress, and the average was for one hole 3.92 MPa, and for the other 4.21 MPa, which means a 50 % variation in stress across the fault.
6 The distribution and magnitude of horizontal stresses may also be affected by variations in rock mass geology and the existence of geological structures and other heterogeneities, for example orebodies. Local changes in the in-situ stress field can be expected when crossing a persistent discontinuity. Hudson and Cooling (1988) identified three different cases due to the relative stiffnesses of the material in the discontinuity versus the surrounding rock material. If the discontinuity is open, the major principal stress will change orientation to become parallel to the discontinuity, while the minor principal stress will become perpendicular to the joint and be reduced to zero. If the joint filling has roughly the same stiffness as the surrounding rock, the stresses may be virtually unaffected. If the discontinuity filling is stiffer than the surrounding rock, the major principal stress changes orientation to become perpendicular to the discontinuity while the minor principal stress becomes parallel.
According to Amadei and Stephansson (1997) research has shown that the minor and major horizontal stresses (in Australia) often align with orebodies. An orebody can be seen as a heterogeneity, and the disturbance it causes in the in-situ stress field can be understood using the analogy of a solid inclusion embedded into an infinite medium. Using the theory of elasticity it can be shown that the stresses in a solid inclusion embedded in a continuous medium differ from the stresses in the surrounding material. If the surrounding material is of infinite dimensions (isotropic or anisotropic) the stresses in the inclusion are uniform, but if the surrounding material is finite the stresses in the inclusion vary from point to point. The inclusion also affects the surrounding material. How large the zone of influence is depends on the difference in stiffness. In practice this means that heterogeneities can cause disturbances (stress concentrations) in the stress field large enough to cause rockbursts or other stability problems during excavation.
A very common assumption in rock mechanics is that the principal stresses are vertical and horizontal. This is not always true, especially at shallow depths when the ground surface is not horizontal. If we look at a very rocky area consisting of high peaks and deep valleys and only consider gravity-induced stresses and allow no horizontal displacements, we will find that the principal stresses are parallel and normal to the ground surface, see Figure 2.4. As the depth increases, the effect of the rugged topology is reduced and the principal stresses resume the same orientations that they would have had if the ground surface was horizontal.
7
Figure 2.4. Effect of topography.
2.3.2 Tectonic stresses
Tectonic stresses can be divided into two groups, active tectonic stresses and remnant tectonic stresses (Amadei and Stephansson, 1997). To differentiate between them can be difficult and may not always be of interest from an engineering standpoint. However, it must be remembered that the current state of stress in an area may not be related to the geological structures that can be seen. The stresses have most likely been changed by past tectonic events such as faulting or folding. In Figure 2.5 below, the forces responsible for tectonic stresses are indicated. The tectonic stresses on a large scale are caused by (1) shear traction along the base of the lithosphere, (2) slab pull at subduction zones, (3) ridge push from oceanic ridges and (4) trench suction on the overriding plate (Amadei and Stephansson, 1997). On a local scale, tectonic stresses are caused by (5) bending due to surface loads, (6) isostatic compensation and (7) downbending of the oceanic lithosphere.
Oceanic ridge
5 3 4 7 1 6
2
Figure 2.5. Forces causing tectonic stresses (after Amadei and Stephansson, 1997).
One effect of tectonics (ridge push) is that the stresses can be very much higher than the depth would indicate, which can lead to problems related to high stresses even at shallow depths. For instance in Norway during construction of the Kobbskaret road tunnel (Myrvang et al.,
8 1997) heavy spalling occurred with overburdens of only a few tens of meters. The tunnel crosses a mountain range and the measured major principal stress (σ1 = 27 MPa) was oriented parallel with the strike of the mountain range and thus normal to the tunnel axis. The overburden varied from 25 to 600 m and spalling occurred along almost the whole tunnel length. Pushing from the Midatlantic ridge is the primary reason that the horizontal stresses in Scandinavia are significantly higher than the vertical stresses.
2.3.3 Residual stresses
Residual stress is defined as “the stress state remaining in the rock mass even after the originating mechanism has ceased to exist” (Hyett et al., 1986). If a rock mass has been subject to high loads or different conditions in the past, stresses can become locked-in as the conditions change or the load decreases. The reduced loading can be for instance erosion, melt-off of inland-ice, or temperature changes due to cooling of magma. The rock then balances the internal forces (compressive and tensile) and reaches a new equilibrium. The locked-in or internal stresses are called residual stresses or residual strains. Hyett et al. (1986) suggested three fundamental requirements for residual stresses to form:
- a change in the energy level (temperature or stress change), - heterogeneities caused by different constituent parts of the material, and - at least partial compatibility of the constituent parts.
These requirements can be explained by studying a granite block that was formed under high temperature and high pressure. At the time of crystallization all constituent grains interlock perfectly. As the block cools the grains will change shape, the amount of change depending on their respective elastic moduli, coefficient of thermal expansion, and non-preferred orientation of anisotropic grains. If all the grains could strain freely and contained no heterogeneities, each would assume a stress free state. This is not possible since the compatibility of the grain contacts and integrity of the block would not be maintained. Due to the confining effect of neighboring grains, stresses are induced, which are called the residual stresses.
The importance of residual stresses is difficult to estimate, but they are believed to be at least partially responsible for phenomena such as rockbursts, surface spalling and sheet jointing. The residual stresses also contribute to both instantaneous and time-dependent movement
9 when rock is removed – both on a small scale (drilling and coring) and on a large scale (whole excavations) (Amadei and Stephansson, 1997).
2.4 Stresses in Scandinavia
The stress state in Europe has been compiled and analyzed by for instance Müller et al. (1992) as a part of the work with the World Stress Map. Fennoscandia (Scandinavia) is characterized by a thick lithosphere (110 – 170 km) and by a low heat flow (< 50 mW/m2). The area is undergoing crustal uplift as a result of postglacial rebound, and the area of maximum uplift is in the northern Baltic Sea (9 mm/year). Müller et al. (1992) used data from several different types of stress measurements taken at different depths and compiled a stress map for Europe. They found that the orientation of the maximum horizontal stress in Scandinavia showed a larger scatter than in other regions of Europe. The mean orientation of the major horizontal principal stress is N120°E ± 45°. The scatter may be caused by some different sources:
- lateral variation of plate boundary forces, caused by the Jan Mayen Fracture Zone, - a locally radial ridge push, caused by the Iceland hot spot, that is superimposed on the lateral plate boundary forces, and - the physical properties of the Fennoscandian lithosphere, which reduce the mean stress level of the lithosphere and allow local inhomogeneities (density, strength) to have an important influence on the stress field.
The conclusion is that the stress field in Scandinavia is a combination of plate boundary forces in combination with local sources, for example flexural stresses. The large scatter may also suggest that the horizontal principal stresses are very close in magnitude, an observation that is supported by the occurrence of focal mechanisms of different styles close to each other.
Stephansson (1993) compiled data from stress measurements (by hydraulic fracturing) in Scandinavia and found that the major and minor principal horizontal stresses varied with depth, z, as:
σ H = 2.8 + 0.04z [MPa] Eq. 2-4a
σ h = 2.2 + 0.024z [MPa] Eq. 2–4b
10 Stephansson (1993) also summarized the results from all overcoring stress measurements made in Sweden, and found that the major, intermediate and minor principal stresses varied with depth, z, as (z < 1000 m):
σ 1 = 10.8 + 0.037z [MPa] Eq. 2-5a
σ 2 = 5.1+ 0.029z [MPa] Eq. 2–5b
σ 3 = 0.8 + 0.020z [MPa] Eq. 2–5c
These data are taken from the Fennoscandian Rock Stress Data Base (FRDSB), which forms a subset of the World Stress Map Project. This is a database of tectonic stresses in the Earth’s crust, where the tectonic stress directions are determined by using four categories of stress indicators (Reinecker et al., 2004):
- earthquake focal mechanisms, - well bore breakouts and drilling induced fractures, - in-situ stress measurements (overcoring, hydraulic fracturing, borehole slotter), and - young geologic data (from fault slip analysis and volcanic vent alignments.
The database contains more than 13000 data points that are ranked according to their reliability as a tectonic stress indicator. There are five categories, A-E, where A is the most reliable. Normally only data from categories A-C are displayed on the maps. For Scandinavia, the most recent map is shown in Figure 2.6. From the map it can be seen that the directions of the major horizontal stress vary to a large extent.
11 0û 10û 20û 30û
Method: focal mechanism breakouts drill. induced frac. borehole slotter overcoring hydro. fractures geol. indicators Regime: 70û NF SS TF U 70û Quality: A B C
(2004) World Stress Map
60û 60û
0û 10û 20û 30û World Stress Map Rel. 2004 Projection: Mercator Heidelberg Academy of Sciences and Humanities Geophysical Institute, University of Karlsruhe
Figure 2.6. Scandinavian stress map, after Reinecker et al. (2004).
12 2.5 Secondary stresses or induced stresses
2.5.1 General
Secondary stresses (or induced stresses) are the result of redistribution of the primary stresses because of a disturbance. The disturbance can be either natural, like a change in conditions (drying, swelling, or consolidation), or be caused by human actions (excavation, pumping, or energy extraction) (Herget, 1988). If the rock is assumed to be elastic and under uniaxial loading, the redistributed stresses form “streamlines” around the opening, which in fact are major principal stress trajectories. An example for a circular excavation is shown in Figure 2.7.
Figure 2.7. Major principal stress trajectories around a circular cross section.
Shorter distance between the flow lines indicates an increase in stress, and a wider spacing indicates a decrease in stress compared to the virgin state of stress. At a distance of about three diameters away from the boundary of the opening the stresses are virtually undisturbed; hence a single excavation only disturbs the stress field very locally
When the cross section is changed from circular to some other shape, the difficulty in finding closed form analytical solutions for the state of stress around the excavation increases dramatically. A rounded shape gives a smoother flow around the excavation, compared to e.g., a square or rectangular shape. The corners become points of stress concentration. If the cross-section of the opening is much longer in one direction, and has sharp corners, zones with decreased stresses may form in the middle of the roof, see Figure 2.8, while there are zones of increased stresses in the walls.
13
Figure 2.8. Flow lines around parallel tunnels with rectangular cross section (Hoek and Brown, 1982).
If more excavations are added close to the existing one in Figure 2.7, the stress field will be disturbed over a larger area. The stress distribution around an opening will influence the state of stress around the others, making it difficult to calculate the secondary stresses. The simplest case is that of two parallel circular tunnels. The stress field around the tunnels is still not too complicated and can be treated analytically. When the cross-sections become more complicated (i.e., not circular), or the number of excavations exceeds two, numerical methods have to be used to study how the openings will influence each other, and what the resulting secondary stresses are.
2.5.2 Mining induced stresses
A mine can consist of many different kinds of excavations spread over a large area; hence the disturbance of the local stress field can be extensive. The complex layout and the time dependent mining sequence may make it difficult to determine the secondary stresses around the openings and in the rock mass surrounding the mine. As a mine grows, the zone around it in which the stress field is disturbed also grows. The stresses induced by mining are results of increasing the drift system and its interaction with hangingwall caving, stiffness changes, yielding of pillars, reactions to backfilling, effects of ore flow, etc. (Jeremic, 1987). Different mining methods disturb the stress field in different ways. The stress mechanisms of the two most common Swedish mining methods, sublevel caving and cut-and-fill mining, will be described below.
Sublevel caving mining method Sublevel caving is a large-scale mining method and is mainly used in large, relatively steeply dipping (≥ 60°) orebodies. The ore is extracted at sublevels developed at regular intervals in
14 the orebody. The hangingwall fractures and collapses – thus, the ground surface must be allowed to subside. Only a negligible part of the stresses pass through the caved rock because of its low stiffness compared to the rest of the rock mass. The major part of the stress perpendicular to the orebody is redistributed under the caved zone, see Figure 2.9.
Broken waste Principal stress rock trajectories
Broken ore
Footwall drifts
Figure 2.9. Schematic figure of stress redistribution under the caved zone.
The deeper the mine the higher the stress concentrations in the bottom become. The stress perpendicular to the orebody is highest about 50-100 m below the bottom of the cave (Sjöberg et al., 2001) and drifts oriented parallel to the orebody (e.g., footwall drifts) become highly stressed. The stress parallel to the orebody is also partly redistributed under the cave, but in this case the major part is redistributed “horizontally” to the foot- and hangingwall, see Figure 2.10. This stress redistribution affects crosscuts and access drifts perpendicular to the orebody. Hangingwall Principal stress trajectories Orebody
Footwall Figure 2.10. Schematic figure of stress redistribution around the orebody.
15 As an example of the stress redistribution around the cave we study a footwall drift on the development level. When it is excavated it is subjected to a stress field that is close to the virgin stress field in the area, both regarding orientation and magnitude of the major principal stress, see Figure 2.11a. As mining and the caving progresses downward to the level of the drift, the secondary stresses around the footwall drift increase as the horizontal stresses are forced under the cave. The direction of the major principal stress (i.e., the stress that is not disturbed by the opening itself, but from the caved area) rotates so that it is not horizontal anymore, see Figure 2.11b. The stress level around the drift can be high enough to cause compressive failure at the boundary. When the extraction level has passed the level of the footwall drift by 100 m or more, the stresses decrease to a level that can be lower than the virgin stress state, and the major principal stress has rotated to become more or less parallel to the orebody, see Figure 2.11c. At this time fallouts of broken rock are likely to occur, since the stresses are too low to retain the blocks.
σ1 a) b) c)
σ1
σ1 σ1
σ1
σ1
Figure 2.11. Rotation of stress field during the life of a footwall drift.
Permanent installations like ore passes and ventilation shafts are also affected by the stress redistribution. All these excavations are located some distance away from the orebody and are constructed years before the ore extraction reaches that level. A shaft for instance is subjected to varying stress conditions along its length. The bottom part may be subjected to an undisturbed stress field, the middle part of the shaft may be very highly stressed, while the top part has a significantly lower stress state (almost destressed). This is caused by the varying stress field with respect to magnitude and orientation.
Cut-and-fill mining method Cut-and-fill mining is a common mining method both in Sweden and abroad, since it can be used in orebodies with varying dimensions. In short, in the overhand cut-and-fill method the ore is removed in horizontal lifts, starting from a bottom cut and proceeding upwards. Each
16 lift consists of eight to ten slices, giving a lift height of 40 to 60 m, and then a sill pillar is left. As each slice is mined out, it is backfilled and serves as a working platform for the next lift. The stress situation of the overhand cut-and-fill method can be described as in Figure 2.12. As mining progresses upward, the loading of the orebody above and below the stope increases. When the stope approaches the mined out (and backfilled) excavation above, the remaining ore forms a horizontal sill pillar subjected to very high stresses. If the stresses in the pillar approach the strength, failure will occur either in the pillar itself or in the sidewall rock.
Figure 2.12. Stress increase in stope roof as mining progresses upward, after Krauland and Söder (1989).
When the sill pillar has failed, the decrease in stiffness leads to redistribution of stresses over and under the stope. Sometimes uppers are used to remove all, or almost all, of the sill pillar. Often the mine started out as an open pit and then went underground leaving a crown pillar, which will be increasingly fractured as mining takes place underneath, similar to the sill pillar described above. When it has failed completely, the stress redistribution around the mine is similar to that which occurs in sublevel caving.
17 18 3 ROCK MASS BEHAVIOR
3.1 Response of rock to energy changes
When rock is removed to create an excavation the remaining rock mass and the installed reinforcement is deformed. Fractures are often created in this process and sometimes seismic waves are generated. Deformation of the reinforcement, fracturing of the rock mass and the creation of seismic waves require energy. Analyzing the energy changes when making an opening underground is therefore important. Also some criteria for analyzing rockburst potential are based on the law of conservation of energy. The analysis is based on changes in geometry between Figure 3.1a and Figure 3.1b, i.e., from state I to state II and the assumption of a linear elastic rock mass. As the excavation is enlarged the surrounding rock mass moves toward the created opening, resulting in a change of potential energy (Wt). The removed rock also contains stored energy (Um). The sum of these terms represents the energy formed as a result of the enlargement and this energy must be dissipated (Hedley, 1992).
a) Case I b) Case II tn-1 tn-1
tn tn
t1 t1 V V tm+1 tm+1 t2 t2 t tm Vm m Sm
t3 t3 tm-1 tm-1
Si Si t4 t4
S S
Figure 3.1. Model of energy change during underground excavation of rock.
The following analysis assumes that the rock mass is linearly elastic and that no energy is consumed in fracturing or non-elastic deformation. The stresses that acted on the removed rock are transferred to the surrounding rock mass, which increases its stored strain energy
(Uc). If the excavations are supported then some energy is absorbed in deforming the support
19 (Ws). The energy remaining is referred to as released energy (Wr). The law of conservation of energy gives
Wt +U m = U c +Ws +Wr Eq. 3-1
If the rock was removed instantaneously this would cause vibrations in the rock mass, and equilibrium would be restored by damping and in the process seismic energy or kinetic energy
(Wk) would be dissipated (Hedley, 1992). The energy that has to be released is the sum of the energy stored in the removed rock (Um) and the kinetic energy (Wk). For elastic conditions there are no more alternatives, which means that
Wr = U m +Wk Eq. 3-2
The seismic energy component contributes to the damage caused by a rockburst, and it is seismic energy that is recorded by seismic systems. Combining Equations 3-1 and 3-2 gives
Wk = Wt − (U c +Ws ) . Eq. 3-3
If the excavation is unsupported the relationship between the energy components can be illustrated by an example with two identical specimens under constant load in a press
(Hedley, 1992), see Figure 3.2a. The stored strain energy (Um) in both samples would be equal, see Figure 3.2b. If the load remained constant and then one of the samples was removed instantaneously, the stress on the remaining specimen as well as the displacement between the load platens would double. The stored strain energy in the removed sample (Um) would be released, and the remaining specimen would have to carry the increase in stored strain energy (Uc). The load platens would follow the displacement of the remaining specimen, resulting in a change in potential energy (Wt). The various energy components are shown in Figure 3.2b, with the following relationships:
U c = 2U m +U u Eq. 3-4
Wt = 2(U m +U u ) Eq. 3-5
Wr = U m +U u = Wt / 2 Eq. 3-6
Wk = U u Eq. 3-7
20 where Uu is the increase in stored strain energy if the stress increase had occurred on an unstressed sample (Hedley, 1992).
a) b) Constant load 2σ1
Uu
Uu One sample removed σ1
Um 2Um Stress in remaining sample Stress in remaining u 2u Displacement
Figure 3.2. Energy components when one specimen is removed from a press with constant load, after Hedley (1992).
When mining takes place in very small steps (incremental, infinitesimal), the limiting conditions are:
∆Wt = ∆U c , ∆Wr = ∆U m and ∆Wk = 0 Eq. 3-8
Some interesting points that can be seen from these energy relationships are:
- If there is no support, all energy components can be expressed in terms of Um and Uu. - If mining is done in small steps (infinitesimal), the process is stable and no seismic energy is released. Some mines that implement incremental mining may still be experiencing rockburst. This means that there are some other sources of energy being released, perhaps due to inelastic conditions for instance fracturing of pillars or slip along a discontinuity. - The change in potential energy is the driving force; if this can be reduced the other energy components are reduced correspondingly. - Support (backfill) is favorable in two ways; it reduces the change in potential energy by reducing volumetric convergence of the stope, and it absorbs energy, which means that less energy is available for release as seismic energy.
21 Seismic efficiency is a ratio used to describe rockburst potential. It is defined as the proportion of energy released as seismic energy (Wk/Wr). The higher the ratio the higher the rockburst potential.
To numerically study the energy components during incremental mining, Hedley (1992) studied an unsupported stope in a vertical orebody. The orebody was 3 m wide and 30 m high, mined in ten cuts. A pre-mining horizontal stress of 50 MPa was used. The change in the seismic potential energy (Wt) for each cut is obtained by subtracting the total change in potential energy of the previous cut from the present cut. Figure 3.3 shows how the energy components change for each cut. The increase is linear as the mining progresses upwards. The ratio Wk/Wr shows that 72 % of the total released energy is seismic energy.
Figure 3.3. Energy components per cut during mining of a vertical stope, from Hedley (1992).
As an experiment, the topmost slice was divided into three 1 m slices to compare the seismic efficiency between a 3 m slice and a 1 m slice. A 1 m slice should be a good approximation of incremental mining. The reduction in slice height led to a decrease in seismic efficiency from 72 % to 59 % (Hedley, 1992), but is still far away from a zero seismic efficiency, i.e., that no seismic energy is released. The equations used for calculation of the energy components can be found in Hedley (1992).
22 3.2 Compressive stress and seismicity
Earlier it was assumed that stiff rock with higher uniaxial compressive strength and higher Young’s modulus could store more strain energy than softer and more deformable rock. This is not always true, which is illustrated in Figure 3.4. Brittle rocks usually have a steeper unloading curve than soft rocks. In Figure 3.4 the area under the graph of the load- displacement curves of both the brittle and the soft rock is approximately the same, which means that both types of rock consume the same amount of stored strain energy during the failure process.
Stiff ore Soft ore
Stiff side- Soft side- wall rock wall rock
σ1 σ1
σ1 σ1
σ1 σ1 Stiffness of Stiffness of surrounding rock, K Stiff ore surrounding rock, K
Soft ore
Wk
Displacement Displacement
Figure 3.4. Stress-displacement relations for the combinations stiff rock – soft sidewall rock and soft ore – stiff sidewall rock respectively.
23 When excavating in a stiff and brittle part of the rock mass where the surrounding rock has a lower stiffness (stiffness of surrounding rock = K) than the unloading stiffness of the brittle rock (the slope of the unloading curve), the failure process often becomes violent, see Figure 3.5. If the unloading stiffness is lower than the stiffness of the surrounding rock the failure process will be non-violent, see Figure 3.5. This means that a strain burst can occur even if the rock mass consists of only one rock type, since the unloading stiffness still can be higher than the stiffness of the surrounding rock mass. In Figure 3.5 the response of the rock mass is modeled by a rock specimen tested in a testing machine that is either stiff or soft. In the load displacement curves, Um is the energy in the specimen, Us is the energy stored in the spring, and Wk is the kinetic energy.
Figure 3.5. Model of the interaction between e.g., surrounding rock and ore (from Hedley, 1992).
Seismic events are either compressive failures of the rock mass or slip on a discontinuity. One pre-requisite for seismicity is a state of stress satisfying a yield criterion. Wawersik and Fairhurst (1969) showed that stress alone is not sufficient to describe mechanical consequences of a rock mass failure. Yield (failure) can be aseismic or seismic depending on local strain energy density and the energy required to induce yield under the state of rock mass confinement at the locus of rock failure. Wawersik and Fairhurst (1969) found after
24 testing samples in uniaxial and triaxial compression that the modes of response could be divided into two classes. In the first class the rupture was stable, meaning that it took an increase in load to decrease the load carrying capacity. In the second class the rupture was unstable or self-sustaining, which means that the energy stored in the sample exceeded the energy needed to cause fracture propagation. Another observation was that for a particular rock material the classes of rupture could be separated as a function of the degree of confinement during testing. At high confining stresses the unstable rupture could be suppressed even for high axial loads, and a greater portion of the energy was dissipated as post-peak yield.
3.3 Shear stress and seismicity
Mining induced seismicity (fault-slip) and earthquakes have the same basic mechanisms but occur on different scales. The same problems of prediction apply to both. A large amount of work has been spent on solving the problem of predicting earthquakes. One problem is the difficulty of understanding exactly why they occur. H. F. Reid was one of the first to develop a theory of the physics of earthquakes. After studying the 1906 San Francisco earthquake he presented the elastic rebound theory (from Shearer, 1999). The theory involves gradual stress and strain accumulation, which is (suddenly) released by movement along the fault. This is now recognized to be the primary cause of tectonic earthquakes in the crust. A simple model demonstrating the mechanism of slip on a fault is shown in Figure 3.6.
N K F mg τ
σn
Figure 3.6. Model of slip along a discontinuity.
A block of weight mg loaded with a normal force N is resting on a smooth horizontal surface. The block is then loaded with a force F acting parallel to surface on which the block rests. The force F is transferred to the block via an elastic spring with stiffness K. On the contact surface between the block and the surface the normal stress σn and shear stress τ are acting.
As long as the block is immobile the shear strength will be µsσn, where µs is the static coefficient of friction. The system is thus in equilibrium as long as
25 µ sσ n −τ > 0 . Eq. 3-9
If the force F is increased so that
τ = µ sσ n Eq. 3-10 we have an unstable equilibrium. The block will start moving for a small increase of the force F, which corresponds to a small increase of the shear stress. A decrease of the normal stress or the coefficient of friction will also cause the block to move. When the movement has started the coefficient of friction decreases to µd and the block is accelerated by a force that initially is equal to A(µs - µd)σn, where A is the contact surface between the block and the horizontal surface. A stable equilibrium is reached when the shear stress equals µdσn.
The movement of the block (in Figure 3.6) as a function of time is shown in Figure 3.7b. Here it is assumed that the free end of the spring has a constant velocity, s, in the direction away from the block. If the end of the spring continues to move away from the block with a constant velocity a new period of relative displacement between the block and the underlying surface will occur at time t2.
K
Figure 3.7a) Stress-displacement curve for a block and b) movement of the block as a function of time.
Figure 3.7a shows the stress-displacement curve for a block. Here the described course of events is illustrated, where the relative movement starts when the shear stress equals µsσn and stops when it has been reduced to µdσn. The curve that describes the movement of the block can be non-linear even if the spring has a linear unloading curve K as illustrated in Figure 3.7a. The area between these two curves represents the energy that is transformed from strain energy (potential energy) in the spring to kinetic energy for the block.
26
In the model described above, the shear stresses on the fault build up until they reach the maximum shear strength of the fault, and then the earthquake occurs. This is termed stick-slip behavior. If s, µs and µd are all constant the “earthquake” will occur at regular time intervals. If the dynamic coefficient varies between the events, the time until the next event is predictable but the size of the coming event is not. The time until the next event is proportional to the amount of slip in the previous, which terms this model time-predictable (Shearer, 1999). If the static coefficient varies instead, the time between the events cannot be predicted. The amount of slip in the next event however, is proportional to the time since the last event, and the model is hence called slip-predictable (Shearer, 1999). The problem is that when both µs and µd vary neither the time nor the amount of slip can be predicted. An assumption made in all these models is that the faults can be divided into segments that are not interacting with each other. The Earth is however more complex than this since several segments on a fault can interact and produce an earthquake, or that even two or more faults can interact. The effects of these interactions have been modeled using the block-slider model, Figure 3.8, where several blocks are connected by springs to each other and to a bar being pulled at a constant speed, s. The slip of one block can set off adjacent blocks and lead to large events. This type of model can produce a wide range of event sizes and a b-value (for definition, see equation 5-12) close to that observed for real seismicity. The model can also produce a chaotic order of events with no defined characteristic event or recurrence time.
s
Figure 3.8. The block-slider model, after Shearer (1999).
The recurrence time of an earthquake can be modeled reasonably well as a Poisson process, i.e., the probability of an earthquake at any given time is constant and independent of the time of the last event (Shearer, 1999). Smaller earthquakes can be statistically modeled since they occur frequently and have been cataloged for some time. Large earthquakes occur less frequently so no statistical models can be tested due to lack of data. Even if long-term prediction of earthquakes seems impossible, that does not mean that it is not possible to
27 predict events on a timescale from years to tens of years given sufficient knowledge of stresses, strains and the local strength of faults. Prediction on the timescale minutes to months is problematic. The focus so far has been on identifying definite precursors, i.e., anomalous behavior observed prior to an earthquake. Possible precursors presented over the years are changes in seismicity patterns, variation of the rate of emission of radon gas and electromagnetic anomalies. However, the only definite precursor found so far is foreshocks, which are events close in time and space to a subsequent main shock. The only problem is that they do not always occur. One possible explanation to why earthquakes seem impossible to predict was presented by Brune (1979). He proposed that large earthquakes start as smaller earthquakes that start as even smaller earthquakes and so on. This makes it nearly impossible to predict large earthquakes since even if every small tremor could be predicted how would you decide which one would start a sequence of ever increasing events leading to a large event? In his model he assumed that large parts of the fault existed at a state of stress below that required to initiate slip, but that it can be triggered by nearby earthquakes or propagating ruptures. He also suggested that precursory phenomena occur when the fault is close to the yield stress. Support for his theory is that studies of the beginnings of earthquakes of different sizes have shown no differences between large and small events. This means that from the initial part of a seismogram, i.e., a graphical recording of an earthquake made by a seismograph (Udías, 1999), it is impossible to say how large the event will become. This seems to indicate that even prediction of small earthquakes is practically impossible.
28 4 ROCKBURST SOURCE MECHANISMS
In this chapter the different mechanisms causing rockbursts will be discussed. A summary of the different terms used by other authors is also given. Many authors (eg., Cook, 1976; Salamon, 1983; Ortlepp and Stacey, 1994) seem to agree on the basic definitions of the terms seismic event and rockburst. A seismic event is the sudden release of potential or stored energy in the rock. The released energy is then radiated as seismic waves. A rockburst is defined as a mining-induced seismic event that causes damage to openings in the rock. There are two general types of seismic events; those directly associated with stopes and those associated with movement on major geologic discontinuities (Gibowicz and Kijko, 1994).
4.1 Seismic events associated with stopes
These types of events occur in close proximity to excavations, and are a direct result of the stress redistribution around the excavation. They are most likely to occur where the stress is highest. The characteristic of this type of event is that the damage and the failure coincide. That is, the location of the damage and the location of the energy release are one and the same. Several types of failures belong to this category, the three most common will be described here; strain burst, pillar burst and face burst. These types of events cannot occur if there is no opening (Ortlepp, 1997).
4.1.1 Strain burst
A strain burst is probably the most common form of rockburst both in mines and in civil engineering structures. The term is used to describe an event of violent failure where relatively small pieces of rock are ejected from the boundary of an excavation. This failure causes spalling or slabbing of surface rock; hence pre-existing geologic discontinuities are not required for fallouts to occur. Strain bursts may be a form of local rock mass failure. The rock pieces that are ejected are usually thin with sharp edges. If the rock near the excavation is jointed the failure does not go through intact rock, but instead causes buckling of thin laminates of near-surface rock. A strain burst usually causes relatively limited damage, since the amount of energy that is released is fairly small.
4.1.2 Pillar burst
Pillar burst is a term used for violent pillar failures, and is also a result of local stress redistribution. The damage resulting from a pillar burst can be severe depending on the
29 location of the failed pillar and the state of surrounding pillars and rock. The amount of energy released by a pillar burst is much larger than that from a strainburst, so the radiated seismic wave may cause damage in other areas such as shake-down of loose rock. The sudden loss of support from one pillar causes stresses to be redistributed to nearby pillars, which in turn may fail violently depending on how close they are to failure. A domino effect of pillar failures may result, which may lead to collapse of that mining area.
Face burst is a form of strain burst and is caused by the accumulation of strain energy in the fractured rock mass ahead of the face. Face bursts are accompanied by violent ejection of material from the face into the excavated area.
4.2 Seismic events associated with geologic discontinuities
These seismic events are also a result of stress redistribution from mining, but on a larger scale. As a mine grows, a larger area around it is affected by the stress redistribution. This can lead to reactivation of faults in the area or violent formation of new fractures through intact rock. The most common type of large-scale seismic event is fault slip. Another phenomenon is shear rupture, whose occurrence has so far only been positively proven in South Africa (Ortlepp, 1997). The damage caused by these events can be very severe, and they can affect a large area and even be felt on the surface. These events can be described as mining induced earthquakes, and may also cause damage on the surface.
4.2.1 Fault slip
Fault slip is the term used to describe slip on a geologic structure. Mining activities can influence faults in two ways. The first is that mining in the area reduces the clamping force across the fault, which leads to reduced shear resistance along the fault. The other is that mining increases the shear force along the fault, so that slip occurs. The damage to excavations is caused by the energy that is released when the slip occurs. The released energy is radiated as a seismic wave, and when the wave hits an opening in the rock it causes
- ejection of blocks defined by existing joints, - a tensile stress close to the boundary of the opening, which results in a tensile failure and ejection of the failed rock, and - a large compressional stress, which results in a failure that can be followed by ejection of rock.
30 4.2.2 Shear rupture
Shear rupture is a shear failure through intact rock, which occurs suddenly and causes radiation of seismic waves and damage to nearby excavations. It requires a triaxial state of stress and occurs when the compressive stresses ahead of a mining face exceeds the shear strength of the rock. Another requirement is that the rock mass has to be free of joints. The type of damage caused by shear rupture is the same as for a fault slip event.
4.3 Rockburst definitions
4.3.1 Definition
The definition of a rockburst mechanism seems to differ among different authors. Some make a distinction between the seismic source mechanism and the rockburst damage mechanism (Ortlepp, 1997) while others use the term modes of failure (Kaiser et al., 1995), to describe the same occurrences.
Ortlepp and Stacey (1994) suggested a classification scheme for seismic event sources in tunnels, see Table 4-1. Their classification was based on first motions from seismic records, the Richter magnitude of the events, and the postulated source mechanism.
Table 4-1 A suggestion for a classification scheme of seismic event sources in tunnels (after Ortlepp and Stacey, 1994).
Postulated source First motion from Richter magnitude Seismic event mechanism seismic record ML Superficial spalling with Usually undetected, Strain-bursting violent ejection of -0.2 to 0 could be implosive fragments Outward expulsion of pre- Buckling existing larger slabs Implosive 0 to 1.5 parallel to opening Violent expulsion of rock Face crush Implosive 1.0 to 2.5 from tunnel face Violent propagation of Shear rupture shear fracture through Double-couple shear 2.0 to 3.5 intact rock mass Violent renewed movement Fault slip Double-couple shear 2.5 to 5.0 on existing fault
Ortlepp (1997) proposed a rockburst flow chart (Figure 4.1) to visualize the connection between his definitions of source mechanism and damage mechanism, and to show a few of
31 the large number of factors contributing to the problem. First he describes event types (in the horizontal direction) – strain burst, buckling, face crush/pillar burst, shear rupture and fault slip. He then continues to define some important parameters describing the source mechanism, such as magnitude, instability process, seismic signature and requisite conditions. The instability processes are: spalling/buckling, euler-type instability, compression slabbing/column crushing/dilation, and the stick slip behavior on faults. Seismic signature describes the reaction to the event, e.g., if the event is implosive, if it is a shear event etc. The last parameter is the requisite condition, which for a strain burst is that the failure surface must be close to a free surface. If all conditions for the source mechanism are met a seismic event takes place.
Ortlepp defined rockburst as a seismic event coupled with a damage mechanism and a damage type. The damage mechanism depends on factors that determine the intensity of the seismic impulse and factors that influence the site response. A few of the factors he mentions as important for the intensity of the seismic impulse are amount of energy available, source distance and dimension, and geological structures. Factors that influence the site response are for example excavation geometry, characteristics of the surrounding rock (strength, brittleness etc.), and characteristics of the existing support (strength, density, quality etc.). Finally he specifies some damage types, for instance ejection, bulking, falls of ground, and shake-out.
32 EVENT strain burst buckling face crush, pillar shear rupture fault slip TYPE burst
Magnitude -0.2 to 0 0 to 1.5 1.0 to 2.5 2.0 to 3.5 2.5 to 5.0 (ML Richter)
Instability spalling / euler-type compression stick-slip release of strain process buckling instability slabbing, column energy from stressed volume crushing, dilation surrounding slip surface
Seismic implosive implosive implosive plus double-couple fault-slip first signature shear motion
Requisite failure surface free surface stress > strength shear stress exceeds SOURCE MECHANISM close to a free >> lamina in destroyed conditions shear strength shear strength surface thickness volume of rock at asperity
SEISMIC EVENT
Factors amount of source particle motion; shear geological structure or determining energy available distance or compression major excavations intervening to cause intensity of reflection, shielding, seismic rate of liberation source ray path properties channeling or focusing of impulse of energy dimension stress transient
Factors excavation characteristics of surrounding rock: strength, brittleness, fabric, influencing geometry: size structure, intensity of induced fracturing shape site response site amplification characteristics of existing support: length, strength, density, features: stress yieldability, quality of containment cladding
DAMAGE MECHANISM intensity, distribution
DAMAGE ejection disruption and convergence or shake-out TYPE displacement heave buckling gravity fall of ground associated with large, distant enhancement seismic event
ROCKBURST
Figure 4.1. Rockburst flow chart, after Ortlepp, 1997.
33 4.3.2 Classification / categorization of rockbursts
This section will treat the different ways of classifying, categorizing and naming rockbursts that can be found in the literature. In Table 4-2 some of the different methods are summarized and in the following text each method is described in more detail.
Table 4-2 Compilation of authors and their different methods of classification.
Method of classification Amount of rock Underlying Distance Relation to displaced, maximum mechanism Author from /effect mining magnitude, causing inside mine situation and amplitude on seismic workings stress level seismograph events Scott, 1990 X Scott et al., 1997 X Johnston and Einstein, 1990 X Knoll and Kuhnt, 1990 X X Gaviglio et al. 1990 X Krishnamurthy and Shringarputale, 1990 X Bigarrre et al. 1993 X Vervoort and Moyson, 1997 X Wong 1992 X Morrison and MacDonald, 1990 X Hedley, 1992 X Brummer and Rorke, 1990 X Gill et al. 1993 X Kleczek and Zorychta, 1993 X Yi and Kaiser, 1993 X Kaiser and Maloney, 1997 X Arabasz et al. 1997 X
Amount of rock displaced and maximum magnitude Classification of rockbursts according to the amount of rock they displaces and their maximum magnitude or amplitude on a seismograph recording is used by Scott (1990) and Scott et al. (1997). These authors define a seismic event as an arrival marked by a phase change or amplitude build-up on a seismic record. Their definition of seismic events includes microseismic events, rockbursts and earthquakes, and all of them can cause damage to openings in rock. The scaling of events according to intensity from small to large can be seen in Table 4-3.
34 Table 4-3 Classification according to damage caused by seismic event.
Author Amount of damage Small seismic events Large seismic events Scott, 1990 bumps knocks strain burst crush burst Microseismic events Rockbursts Scott et al., 1997 strain burst crush burst slip burst
According to these authors strain bursts are the cause of limited and localized damage, while crush and slip bursts can cause extensive damage to drifts and stopes. Events exceeding 0.5 Richter magnitude, that displace more than 10 tons of rock into an opening, or have a peak amplitude greater than 30 mm on a seismograph, are classified as large seismic events or rockbursts. Microseismic or small seismic events are defined as events that displace less than 1 - 2 m3 of material into a mine opening, have a Richter magnitude less than 0.5, or result in less than 30 mm displacement on a seismograph. These microseismic events generally occur near drifts, haulage way or stopes, and cause popping, spitting (ejection of small rock fragments) and spalling of the surrounding rock mass.
Distance from, or the location of the effect inside, the mine workings Johnston and Einstein (1990), Knoll and Kuhnt (1990), Gaviglio et al. (1990), Krishnamurthy and Shringarputale (1990), Bigarre et al. (1993), Vervoort and Moyson (1997) and Wong (1992) all use the distance from the mining face or the location of the effect as a basis for their classification of seismic events or rockbursts. The differences can be found in Table 4-4. There is commonly one category “type 1” which is closely associated with active mining faces. These events are a function of mining rate and are of low to medium magnitude. They occur at or close to the mining face. The actual distance varies depending on author. The other category “type 2” is only indirectly associated with mining activities, since it results from regional stress redistribution caused by large working areas or whole mines. These are usually located on a pre-existing zone of weakness or a geological discontinuity that can be located as far away as 3 km. The coal industry has a slightly different approach – they treat pillar failure as a separate group, called “Type 3” in Table 4-4. The pillars mentioned are stiff and become overstressed because of the mining geometry.
35 Table 4-4 Classification of events according to distance from mining face.
Author Distance from mining face Johnston and Einstein, Type 1, ≥ 100 m Type 2, ≥ 3 km 1990 Type 1, close to mining Type 2: indirectly Knoll and Kuhnt, 1990 face, no distance specified connected to mining activities Type 3: unmined pillars Gaviglio et al., 1990 Type 1: ≥ 30 m Type 2: ≥ 100 m overstressed because of (coal) mining geometry Krishnamurthy and Type 1: at reef workings Type 2: in footwall Type 3: in old workings Shringarputale, 1990 openings, not close to the far from the face (coal) face Type 1: ends of faces Type 2: 50-150 m ahead Type 3: unmined pillars Bigarre et al. 1993 (coal) of or behind face overstressed Category 1: at excavations Category 2: further away Vervoort and Moyson, (strain bursts) from excavations, no 1997 distance specified Type 1: few tens of meters Type 2: near-vicinity to Wong, 1992 from active workings several hundred meters
Relation to mining situation and stress level Morrison and MacDonald (1990) and Hedley (1992) classify rockbursts based on their relation to the mining situation and the stress level. They recognize that the fundamental cause of all mining related seismic events is the same, i.e., the stress redistribution and relaxation of rock around the excavations. They categorize their events as occurring in two or three phases, see summary in Table 4-5.
Table 4-5 Classification according to mining stage.
Mining stage Author Development Extraction, active mining Mined out, whole mine Morrison and Phase 1 events: in Phase 2 events: in or close Phase 3 events: some MacDonald, 1990 development drifts to active orebody distance away Inherent bursts: in Hedley, 1992 Induced bursts: in remaining structures (pillars) development openings
Morrison and MacDonald’s phase 1 events occur in development drifts when the pre-mining stresses are high enough to cause failure by relaxation of stored strain energy. Phase 2 events occur in or close to the orebody in the abutments (or pillars) due to redistribution and concentration of stresses caused by the mining operation. Phase 3 events occur some distance out in the walls of an extensively mined orebody, and are the result of regional stress redistributions caused by the whole mine. The mechanism is always fault-slip, and it is not the event itself that damages mine openings, but rather the vibrations caused by the event.
36 Hedley’s term for phase 2 and 3 events are induced bursts. Hedley also has a third type of burst, fault slip, which can be either an inherent or induced burst, depending on the mining stage at which it occurs.
Underlying mechanism causing seismic event Brummer and Rorke (1990), Gill et al. (1993), Kleczek and Zorychta (1993), Yi and Kaiser (1993), Kaiser and Maloney (1997) and Arabasz et al. (1997) all classify rockbursts based on the underlying mechanism that caused the seismic event. There are two mechanisms causing seismic events: instantaneous slip on an existing geological discontinuity (fault slip) or instantaneous fracturing of highly stressed rock.
Table 4-6 Classification according to underlying mechanism.
Author Underlying mechanism Brummer and Rorke, 1990 Sudden crushing or Sudden failure of rock in Shear-slip on geologic fracturing of rock near pillar foundations discontinuity mining face Gill et al., 1993 Type 2: failure of rock Type1: fault slip mass itself, strain and pillar bursts Kleczek and Zorychta, Concentration of static Action of dynamic load 1993 stresses created by mining tremors Yi and Kaiser, 1993 Strain burst (mech II) Pillar burst (mech I+II) Fault slip (mech I) Kaiser and Maloney, 1997 Self-initiated (strain burst) Remotely triggered (fault slip) Arabasz et al., 1997 Static stresses near mine Dynamic effects from openings seismic slip
These two mechanisms have commonly lead authors to define two classes of rockbursts. In Table 4-6 rockbursts are grouped by using the type 1 and type 2 rockburst defined by Gill et al. (1993). The type 1 bursts are those resulting from the dynamic loads imposed by fault-slip events and the type 2 bursts result from failure of the rock mass itself. Sometimes there is a third type defined, which is a combination of the two mechanisms, and is referred to as pillar burst.
There are other authors using classifications of rockburst which do not fit into any of the categories above. Petukhov (1990), for example, is the one who has found most classes of rockbursts. He proposes five subgroups of rockbursts, that are differentiated by sound, amount of dust dispersed, amount of shaking, location of damage in correlation to mining stage and whether or not the mining operations are interrupted
37 38 5 SEISMIC MONITORING AND EARTHQUAKE SEISMOLOGY
5.1 Introduction
Seismic monitoring in mines is used to quantify the exposure to seismicity and is also a tool to guide efforts to prevent or control seismicity. Mendecki et al. (1999) defined the following objectives for monitoring of the rock mass seismic response to mining:
- Location of potential rockbursts: to indicate the location of potential rockbursts associated with intermediate or large seismic events and to assist in possible rescue operations. - Prevention: to confirm assumptions and parameters used for mine design and numerical modeling, in order to improve design layouts, mining sequencing, support strategies etc. - Control: to detect changes in seismic parameters over time and space, in order to guide control measures such as timing and location of destress blasts, suspension /resumption of mining in a given area, manage exposure to seismicity etc. - Warnings: to detect unexpected or strong changes in seismic parameter behavior or to recognize patterns that could lead to dynamic instabilities at working places. This would help manage exposure to potential rockbursts. - Back-analysis: to improve the efficiency of the mine design and monitoring processes. Numerical and seismic back-analysis of large instabilities are important even if there was not much damage. The seismic rock mass behavior associated with pillars, backfill, different mining layouts, methods and rates of excavation are also important to analyze to make mining safer and more productive.
The information recorded by the monitoring system is hidden in seismic waves – to extract the information for use in mine sequencing etc., methods used in earthquake seismology have been adopted. Since seismic monitoring and the study of rockbursts and seismicity in mines are applied forms of seismology, and many of the terms used in literature dealing with rockbursts are borrowed from this field, this chapter will first describe seismic monitoring in general and then some parameters from seismology used to describe seismicity are explained.
5.2 Seismic monitoring
A seismic event is a sudden inelastic deformation in a given volume of rock (seismic source) that radiates detectable seismic waves. The amplitude and frequency of these waves depend on the strength and state of stress of the rock, the size of the seismic source and the magnitude
39 and the rate at which the rock is deformed during fracturing (Mendecki et al., 1999). To describe a seismic event quantitatively, the time of occurrence and the location along with either of the combinations seismic moment – radiated seismic energy, or seismic moment – stress drop are needed. A seismic system can only measure the portions of strain and stress that are associated with recorded seismic waves. When a number of seismic events within a given volume and over a certain time have been recorded and processed, the changes in the strain and stress regime in that volume can be quantified. This gives the opportunity to validate results obtained from numerical modeling, where elastic parameters (E,ν) are assumed to be constant within a given volume, making stress a function of strain (σ = Eε). The strain and stress changes caused by seismicity, however, are independent (Mendecki et al., 1999). Seismic strain in a given volume is proportional to the seismic moments (εs∝ΣM0), and the stress is proportional to the ratio of seismic energies to seismic moments
(σs∝ΣEs/ΣM0).
The largest events that a mine seismic system has to record range between moment magnitude
Mw = 3 and Mw = 5, and the smallest are between Mw = -4 and Mw = -3 (Mountfort and Mendecki, 1997). The range of frequencies that need to be recorded to make processing meaningful is determined from the expected corner frequencies (see section 5.3.8) of the events in the volume to be monitored. The part of the frequency spectrum where most of the energy is released depends on the size of the event. For a large event low frequencies dominate, i.e., frequency decreases with increasing size, and high frequencies are attenuated faster with increasing distance away from the event (Jaeger and Cook, 1979). For the seismic moment to be correctly determined, the requirement is frequencies five times lower than the corner frequency of the largest event to be analyzed, and to correctly estimate seismic energy the requirement is frequencies at least five times higher than the corner frequency of the smallest event to be analyzed. Seismic events induced by mining have been shown to radiate seismic energy from 10-5 J for microseismic events to 109 J for large rockbursts. The local magnitudes corresponding to this energy release are ML = -6 and ML = 5, respectively (Jaeger and Cook, 1979). The frequencies corresponding to the energy release ranges from less than 1 Hz to over 10 kHz. The choice of sensors to use in a seismic network depends on the desired area of coverage and the sensitivity of the system. Two types of sensors cover the frequency interval 1 Hz to 10 kHz, miniature geophones and piezoelectric accelerometers (Mendecki et al., 1999). Geophones are suitable in sparse networks, where the distance between the sensors
40 is 1 km on average, for instance in monitoring several mining operations on a regional basis. They are sensitive enough to record relatively distant events, i.e., they can record low frequencies at large distances, and the risk of a large event occurring close enough to cause clipping of the signal (i.e., exceeding of the maximum recordable ground motion) of more than one sensor at a time is remote. Piezoelectric accelerometers are suitable in dense networks, where the distance between the sensors is about 100 m on average. Many sensors must be close together within the volume of interest, since the high frequencies they are sensitive to quickly attenuate with distance. These accelerometers are good for mine-wide monitoring.
Installation of both types of sensors should be in boreholes extending outside the fractured rock surrounding an excavation. The sensor should be grouted in the hole to give good coupling to the rock The grout should have similar acoustic impedance (product of density and velocity of propagation) as the surrounding rock (Mendecki et al., 1999). The hole should be completely filled around the sensor to avoid trapping acoustic energy. The sensors should also be installed with a known orientation. For geophones it is important that the orientation is within 5° of the vertical or horizontal otherwise they may not operate properly. Knowledge of the orientation of the sensor also provides information useful for the localization of events, and for the correct determination of the moment tensor.
5.3 Earthquake seismology
Encyclopædia Britannica defines seismology as the ”scientific discipline that is concerned with the study of earthquakes and of the propagation of seismic (elastic) waves within the Earth”. It is also ”a branch of geophysics that has provided much information about the composition and state of the planet's interior” (Encyclopædia Britannica, Accessed October 1, 2002). Since the initiation of seismic waves is also an important part of the rockburst problem it is reasonable to assume that physical and mathematical relationships that have been developed for description and analysis of earthquakes also should hold true for mining induced seismicity, even if the scale may have to be adjusted. Van Aswegen et al. (1997) state that the physical laws that govern the deformation processes on the centimeter to kilometer scale are practically the same, which means that seismology has some scale independence. This leads to the interesting conclusion that crustal seismological theory can be applied to phenomena ranging from micro-tremors and laboratory results to earthquakes. Mine tremors
41 can be seen as a step in between these extremes, where some events are on the same scale as earthquakes and some are on the laboratory scale.
5.3.1 Faults and seismic waves
Faults are central to earthquake studies and some of the definitions used in seismology might diverge from the way faults and joints are described within the field of rock mechanics; hence the seismological definitions are stated below.
Strike or azimuth, α, is defined as the angle from north, while dip, β is defined as the angle from the horizontal, see Figure 5.1. The slip vector is defined by the movement of the hangingwall relative to the footwall and the rake, λ, is the angle between the slip vector and the strike. The rake for vertical faults is defined with the hangingwall to the right of an observer looking along the strike.
HW
Strike N α
Slip Dip FW λ β rake
Figure 5.1. Definitions after Shearer (1999).
To describe the relative movement of the hangingwall with respect to the footwall, the terms strike-slip and dip-slip have been introduced. Strike-slip means horizontal movement between the fault surfaces while dip-slip means movement along the dip. If you are standing on the footwall and the hangingwall is moving to the right or to the left, you have a right-lateral or left-lateral strike-slip motion, respectively.
If the hangingwall is moving downwards in regard to the footwall, the fault is called a normal fault. If the hangingwall is moving upwards, we have reverse faulting. Depending on the dip angle the reverse fault can have different names. If the dip is less than 45°, the term is thrust
42 faulting, and if the fault is almost horizontal (dipping about 0 - 15) it is called overthrust faulting, see Figure 5.2.
HW
HW HW
FW FW FW
Figure 5.2 From left to right: normal faulting, reverse faulting and overthrust faulting.
Academic Press (www.academicpress.com) defines an earthquake as: “a movement or trembling of the earth caused by a sudden release of stresses within, usually less than 25 miles below the surface; major earthquakes cause significant damage”. The release of stresses is simultaneous with radiation of seismic waves from the source area. There are two types of seismic body waves, P-waves (or compressional waves) and S-waves (or shear waves) (Shearer, 1999). P-waves are also referred to as longitudinal or dilatational waves. S-waves cause no volume change in the material. In a P-wave, the particles move in the direction of propagation, while in an S-wave the particles move perpendicular to the direction of propagation, see Figure 5.3.
Figure 5.3. Particle movement in P-wave (top) and S-wave (bottom), from Shearer (1999).
The two types of waves propagate through the earth at speeds that increase with depth, see Figure 5.4. The P-wave is always faster than the S-wave, and can propagate through all layers
43 of the Earth, but since the S-wave is a shear wave it cannot propagate through the fluid outer core. Typical propagation velocities of P-and S-waves in granite near the surface of the Earth are 5.5 km/s and 3 km/s respectively.
Figure 5.4. Variation of P- and S-wave velocities with depth beneath Earth’s surface, from Kulhánek (1990).
Because of the velocity variations, the path of the seismic wave is a curve with the concave side upwards (Arvidsson et al., 2000). This curved path is the shortest time-path through Earth, see Figure 5.5. As a consequence of this, waves traveling to more distant measuring stations penetrate to greater depths than waves going to nearer stations. The curved path is also one reason that the P-waves of a near surface event (< 10 km depth) at teleseismic distances usually have a downward first motion. The distance between the focus of the event and the recording station is expressed as the angle between the source and the receiver, with the point in the centre of the Earth. This means that 1° equals 111 km. Teleseismic distance is a distance of more than 10° from the source.
44
Figure 5.5. Examples of propagation paths from a surface earthquake, from Kulhánek (1990).
5.3.2 Seismic moment and the moment tensor
The seismic moment, M0, or the scalar moment is a measure of earthquake strength and is the most reliable measure of the strength of a seismic event (Gibowijcz and Kijko, 1994). It is defined in terms of parameters of the double-couple shear dislocation source model, and is expressed as follows
M 0 = GDA , Eq. 5-1 where G is the shear modulus at the source, D is the average shear displacement and A is the area over which slip occurred. Sometimes the seismic moment can be calculated from Equation 5-1 using field data, but most often it is estimated from seismic records. This, however, requires more complicated calculations.
An earthquake is assumed to be slip on an internal discontinuity (fault) in a rock mass. To understand how seismic waves are generated and how the radiated energy relates to the source we have to study the physical properties of the source, and find a mechanical model representing the physical fracturing. The first mathematical formulation of the earthquake mechanism used the point-source approximation, which is valid if the observation points are at a sufficiently large distance with respect to the source dimension and wave lengths are large
45 (Udías, 1995). This method represents the source by a system of body forces acting at a point, and since the forces must represent the fracturing they are called equivalent forces. A single force acting at a point can only result from external forces, otherwise momentum would not be conserved. Internal forces representing the point source must act in different directions. The simplest force system conserving momentum is the simple force couple or dipole, Figure 5.6, meaning that there is no net moment.
d
Figure 5.6. A simple force couple, or dipole.
If the forces are separated by a distance, d, in the direction perpendicular to the force orientation, the momentum is no longer conserved unless there is another force couple balancing the momentum. So a double-couple is a pair of force couples that ensures conservation of momentum, that is, the net torque is zero, see Figure 5.7.
d
Figure 5.7. Unbalanced force couple (left) and balanced double-couple (right).
Force couples can be used to represent shear fractures, which is used in the formulation of the moment tensor. To explain this we start with a simple point source. A point source can be illustrated by an explosion on the surface of the sun. Since the sun’s surface is a liquid, the explosion causes waves to propagate outwards in concentric circles (similar to those caused by a stone hitting a water surface). The force diagram from the explosion can be seen in Figure 5.8, along with an illustration of the first motion of the wave.
46 +
-
Figure 5.8. Force diagram from explosion and first motion of resulting wave (Andersen, 2001).
The motion of the wave can be described using force-couples. The three force couples needed for the description of an explosive source are shown in Figure 5.9 along with the other six force-couples forming the moment tensor.
3 3 3 M11 M12 M13
2 2 2
1 1 1
M11 0 0 3 3 3 M21 M22 M23 0 M 0 22 0 0 M 33 2 2 2
1 1 1
3 3 3 M31 M32 M33
2 2 2
1 1 1
Figure 5.9. The moment tensor with the three force couples describing an explosive source circled (Andersen, 2001).
Any shear type movement can be described using combinations of the force couples in the tensor. If we assume a vertical fault along which slip is initiated, P-waves will radiate outwards from the point of initiation. The P-wave will form compressional (motion away from the source) and dilatational (motion towards the source) quadrants around the source. The compressional quadrants are denoted P+ in Figure 5.10 and the dilatational are denoted P-.
47 + P+ - P- Negative (down( ) P- P+
+ -
Positive (up)
Figure 5.10. Polarization of P-wave around the source of slip (Andersen, 2001).
The strongest movements are found in the middle of each quadrant, at a 45° angle to the fault planes. If the two fault planes from Figure 5.10 are denoted X1 and X2 and the double-couple force system causing slip on the faults are drawn in an X1 – X2 – coordinate system as in Figure 5.11, then the double-couple can be equivalently represented by a pair of orthogonal dipoles without shear. These dipoles are also called principal axes, and are denoted P- and T- axes, where P is the compressional axis and T is the dilatational axis.
x2 x2 P-axis
x1 = x1
T-axis
Figure 5.11. Representation of double-couples as principal axis (Andersen, 2001).
In the double couple model there are two different fault planes corresponding to the same seismic observations. The real fault plane is termed the primary fault plane and the other the
48 auxiliary fault plane. To determine which plane is the primary or auxiliary additional information like aftershock locations or surveyed surface ruptures is necessary.
The moment tensor is a general representation of the forces that can act at a point in an elastic medium. Although it is an idealization, it has proved to be a good approximation for modeling distant seismic responses for sources that are small compared to the seismic wavelength (Shearer, 1999). Since the moment tensor is symmetric it can be diagonalized, i.e., its eigenvalues and eigenvectors can be calculated, and it can be further divided into an isotropic part and a deviatoric part. The sum of the eigenvalues, m1 + m2 + m3, describes a volume change at the source (Andersen, 2001), for instance
- if (m1 + m2 + m3) > 0, the isotropic component is due to an explosion
- if (m1 + m2 + m3) < 0, the isotropic component is due to an implosion
- if (m1 + m2 + m3) = 0, the isotropic component vanishes and the moment tensor has only deviatoric components
- if (m1 + m2 + m3) = 0, and either m1, m2 or m3 = 0, the deviatoric component represents a pure double-couple source.
5.3.3 Earthquake focal mechanisms and radiation patterns
The first motion of the P-wave has been the most common method for determining the focal mechanism of an earthquake. It has the advantage that only the vertical component needs to be recorded, and it is often easy to find from the seismogram at the same time as the arrival time is picked. The first motion of the P-wave at a surface receiver determines whether the wave (ray) left the source in a compressional (upward motion) or dilatational (downward motion) quadrant (Shearer, 1999). The rays are then projected back, using ray theory, so that the angle at which they left the source can be determined. The result is plotted on a focal sphere, i.e., an imaginary sphere surrounding the source. Often, only the lower hemisphere is plotted, since most rays depart downward from the source, at least at teleseismic distances. If there are enough measurements plotted, the focal sphere can be divided into compressional and dilatational quadrants. The great circles separating the quadrants represent two orthogonal planes that determine the focal mechanism. As mentioned before, without additional information it is not possible to distinguish between the true fault plane and the auxiliary plane. In Figure 5.12 different focal mechanisms are shown, together with their corresponding fault planes. The focal sphere is a good way of showing different focal mechanisms. The
49 compressional quadrant is shaded, making the focal sphere look like a beach ball. Normal and reverse faulting can be separated in these kinds of plots by noting if the center is black or white. Normal faulting has a white center, and reverse faulting has a black center.
Figure 5.12. Focal spheres and their corresponding fault geometries, from Shearer (1999).
5.3.4 Earthquake location
The first source parameters to be determined are usually the origin time and hypocenter (x, y, z). Epicenter is the point (x, y) on the Earth’s surface directly above the hypocenter. For large earthquakes the hypocenter is not necessarily the “center” of the earthquake, but the point from which seismic energy begins to radiate. The hypocenter can be determined from the arrival times regardless of the size and duration of the event (Shearer, 1999). Different methods can then be used to invert the travel times to obtain the location. A better location (less error) can be obtained if several types of waves are measured. If only P-wave arrival
50 time data is available the event can easily be mislocated. For example, if a fault separates two blocks of crust with different velocities, the fault location tends to be mislocated off the fault, into the block with faster velocity, see Figure 5.13. Also a poor distribution of stations around the source can generate a large location error. If the earthquake occurs outside the seismic network, the distance to the event is not well constrained, see Figure 5.14a, and the errors in location form an ellipse with the long axis away from the seismic network. The location of the event could be improved by having another station on the opposite side of the event.
Slow Fast
Fault Location error
Figure 5.13. Location error caused by model errors, after Shearer (1999).
a) b)
Distant stations
Error ellipse Depth error
Earthquake
Seismic network
Figure 5.14. Location errors caused by distribution of seismic array, after Shearer (1999).
If only distant stations recording P-wave arrivals are available, the depth of the hypocenter is difficult to specify since the takeoff angles of the rays are very similar, see Figure 5.14b. A few stations at closer ranges help to pinpoint the depth of the earthquake, alternatively the
51 stations should record also the arrival of the pP-wave, i.e., the wave that from a deep focus earthquake, propagated upwards and was reflected at the Earth’s surface, see Figure 5.15.
Figure 5.15. Examples of propagation paths from a deep focus earthquake, from Kulhánek (1990).
Another way to enhance the location accuracy is to measure both P- and S-wave arrival times. The S-wave travels at a lower speed, so the time difference between the arrivals can be used to estimate the source-receiver range at each station. A rule of thumb is that the distance to an event in kilometers is about 8 times the difference in S – P arrival times in seconds (Shearer, 1999).
5.3.5 Stress drop
Shearer (1999) defines stress drop, ∆σ, as the average difference between the stress across the fault before and after an earthquake. Stress drop is the stress estimate that best represents stress change (Gibowicz and Kijko, 1994). The dynamic stress drop (or effective stress), which is the difference between initial shear stress and the kinetic friction on the fault, can be determined from seismic data. There are several different methods of determining the stress drop, of which some use records of ground velocity and ground acceleration. The static stress drop can be calculated using the relationship
7M 0 ∆σ = 3 , Eq. 5-2 16r0
52 which assumes total stress release. Equation 5-2 represents the uniform reduction in shear stress producing seismic slip over an assumed circular fault, where M0 is the scalar seismic moment and r0 is the radius of the circular fault.
Stress drops can vary considerably from event to event. For mine tremors the range is from 0.01 to 10 MPa (Gibowicz and Kijko, 1994). For earthquakes near plate boundaries (interplate earthquakes) the stress drop is on average 3 MPa, while intraplate earthquakes (in the interior of a plate) have an average stress drop of about 10 MPa (Shearer, 1999).
5.3.6 Earthquake magnitude
Today there exist several different types of magnitude scales, and the most popular ones relate to the largest amplitude recorded for the event. The most common magnitude scales are the local or Richter magnitude, ML, the body wave magnitude, mb, and the surface wave magnitude, Ms. The magnitude is related to the energy release and is independent of the generating mechanism (Udías, 1999). The energy is proportional to the square of the amplitude, which means that the magnitude is then proportional to the logarithm of the energy. Since amplitude is easy to measure this is a major reason for the popularity of magnitude scales (Shearer, 1999). One of the limitations of the magnitude scales is that the amplitude is measured for one single frequency (period), which then defines the magnitude as seismic energy radiated over a fixed, narrow frequency band. Since the frequency distribution changes with earthquake size, different magnitude scales differ from each other when applied to the same seismic event, depending on the frequency band for which they were defined. Another serious drawback of the magnitude scales is that they tend to saturate, i.e., the predicted amplitude at a given frequency never exceeds a maximum value (Shearer, 1999). The seismic moment is a better measure of earthquake size, but the magnitude scales remain popular.
Richter introduced the local magnitude scale, ML, in the 1930’s. He noticed from plots of log Λ (logarithm of amplitude) versus range that different earthquakes seemed to have a similar decay rate. Richter defined the magnitude as the logarithm of the maximum amplitude Λ0 (in micrometers) measured by a standard Wood-Anderson seismograph at a distance of 100 km from the epicenter. The assumption behind the definition is that the ratio of maximum amplitudes at two given distances is independent of the azimuth and is the same for all earthquakes considered (Gibowicz and Kijko, 1994). This gives the relation
53 M L = log10 Λ(d) − log10 Λ 0 (d) Eq. 5-3
where Λ is the maximum amplitude of the current event at distance d, and Λ0 is the amplitude of an M = 0 earthquake recorded at distance d (Udiás, 1999). Values of Λ0 for distances between 10 and 600 km can be found in tables, e.g., in Udiás (1999). The advantage of the Richter scale is that other subsequently derived magnitude scales have been related to it, which makes comparison between events from all over the world easier. Disadvantages are that it was defined for a southern California range - amplitude relationship and makes use of an instrument rarely used today.
The so-called body wave magnitude, mb, is a more general magnitude scale for global seismology, and is defined as
mb = log10 (Λ /T ) + Q(h,∆) Eq. 5-4 where Λ is the maximum amplitude, T is the corresponding period of the measured body waves, and Q is an empirical function of range, h, and focal depth, ∆. The amplitude measurements are usually performed on the first few cycles of the P-wave arrival. The body wave magnitude scale has been calibrated to the local magnitude scale for small seismic events in California (Shearer, 1999). Saturation starts at about mb = 5.5 and is total at about mb = 6.5, which means that the magnitude rarely exceeds 6.5 even for very large events.
Another global magnitude scale is the surface wave magnitude, Ms, which can be defined as
M s = log(Λ /T) +1.66logϕ + 3.3 Eq. 5-5 where Λ is the maximum amplitude and T is the corresponding period of the Rayleigh wave, ϕ is the epicentral distance in degrees, and 3.3 is a calibration constant. The period is usually 20 s. The surface wave magnitude can only be applied to near surface events, since the amplitudes of surface waves are greatly reduced with depth. The saturation of the surface wave magnitude begins at about Ms = 7.0. The body wave and surface wave magnitudes only coincide at about Ms = 6.6, for smaller magnitudes mb is larger and for greater magnitudes Ms is larger, see Figure 5.16. The relationship between the two magnitudes is
mb = 0.63M s + 2.5. Eq. 5-6
54 This relationship indicates that smaller earthquakes (Ms<6.5) are better measured by mb, since the scale for Ms underestimates the size of small earthquakes (Udiás, 1999) and greater earthquakes are better measured by Ms since that scale behaves well in the range 6.5 – 8.0, but saturates strongly above Ms = 8.
9
8
7
6
b 5 , m s
M 4
3 Ms 2 mb
1
0 0123456789 M s
Figure 5.16. Relationship between surface wave magnitude, Ms, and body wave
magnitude, mb.
The difference between the scales and the saturation effect were the motivation for the introduction of the moment magnitude, Mw, for great earthquakes by Kanamori. Later the moment magnitude was used as a measure of earthquake strength. The formal definition of
Mw is made by Hanks and Kanamori (1979)
2 M = log M −10.7 Eq. 5-7 w 3 0
7 where M0 is the seismic moment measured in dyn cm (10 dyn cm = 1 Nm). The advantage of this scale is that it is related to a physical property of the source through the seismic moment, and that it does not saturate, even for very large events.
For mining-induced seismic events in Canada, the Nuttli magnitude scale is used. It is defined as (Hedley, 1992):
Λ M n = −0.1+1.66logΞ + log Eq. 5-8 ΓT
55 where Ξ is the epicentral distance in kilometers, Λ is half the maximum peak-to-peak trace amplitude in the S-phase, Γ is the instrument magnification factor, and T is the period in seconds. The relationship between the Nuttli and the Richter magnitudes varies, but in the range of interest for rockbursts (between 1.5 < ML < 4.0) the Nuttli scale gives values that are 0.3 to 0.6 units higher than the Richter scale for the same event. Several authors have formulated relationships for the two scales, and three of them are shown in Figure 5.17.
7
6 Boore and Atkinson Hasegawa Geopysics Division
5 L
4 magnitude, M r ichte
R 3
2
1
1234567 Nuttli magnitude, Mn Figure 5.17. Relationship between Nuttli and Richter magnitude scales, after Hedley (1992).
The relationships plotted in Figure 5.17 are defined as follows:
M L = 1.25M n − 0.88 Eq. 5-9
which was defined by the Geophysics Division of Canada and is valid for 1.9 ≤ Mn ≤ 2.7,
M L = M n − 0.3 Eq. 5-10
defined by Hasegawa in 1983 and valid for 2.8 ≤ Mn ≤ 3.8, and
2 M L = 2.715 − 0.277M n + 0.127M n Eq. 5-11
56 defined by Boore and Atkinson in 1987 and valid for 4.5 ≤ Mn ≤ 7.0. All these relationships are taken from Hedley (1992).
Large earthquakes occur more seldom than small earthquakes, and the same is true for seismic events in mines. This magnitude-frequency relationship was described by Gutenberg and Richter and can be written as
log N = a − bM Eq. 5-12 where N is the number of events with magnitude in the range M ± ∆M. Equation 5-12 can be interpreted either as a cumulative relationship, if N is the number of events of magnitude equal to or larger than M in a given time interval, or as a density law, if N is the number of events in a small magnitude interval around M (Gibowicz and Kijko, 1994). The parameter a is a measure of the level of seismicity. The parameter b describes the relative number of small and large events in a certain time interval. The b-value typically varies between 0.8 and 1.2, and b = 1 means that the number of earthquakes increases by a factor of 10 for every unit drop in magnitude (Shearer, 1999).
5.3.7 Seismic energy
The total elastic energy radiated by an earthquake can be represented by the radiated seismic energy (Gibowicz and Kijko, 1994). The seismic energy describes the potential for earthquake damage to artificial structures, such as buildings, better than the seismic moment. Seismic energy is commonly used as a measure of the size of seismic events in mines (Gibowicz and Kijko, 1994). The ratio of P-wave energy to S-wave energy is an indicator of the type of focal mechanism causing the event. For natural earthquakes the ratio ES/EP ranges between 10 and 30. If a large percentage of the total energy is contained in the S-wave the source mechanism is most likely a shear failure (Hedley, 1992). For small seismic events in mines the ratio however may range between 1.5 and 30. The low amount of energy in the S-waves may be explained by these tremors being caused by another mechanism than a double-couple. The total seismic energy, Et, radiated by a fault can be estimated from earthquake magnitude. Gutenberg and Richter derived an empirical relationship relating seismic energy and body wave magnitude
log Et ≈ 5.8 + 2.4mb Eq. 5-13
57 -7 where Et is the total seismic energy in ergs (1 erg = 10 J) and mb is the body wave magnitude (Shearer, 1999). Gutenberg and Richter also developed the following relationship between the local magnitude and seismic energy
logWk = 1.5M L −1.2 Eq. 5-14
where Wk is the energy in MJ (Hedley, 1992). A similar relationship has been developed for the Ontario mines (Hedley, 1992) relating Nuttli magnitude and seismic energy
logWk = 1.3M n −1.75. Eq. 5-15
5.3.8 Corner frequency
The corner frequency, f0, of a seismic event is the predominant frequency radiated from the source and it is related to the seismic moment and the stress drop (Mendecki et al., 1999). The relationship for the S-wave in hard rock is
3 f 0 = 1815 ∆σ / M 0 Eq. 5-16
where ∆σ is the stress drop and M0 is the seismic moment. A velocity seismogram and the corresponding frequency spectrum for the S-wave is shown in Figure 5.18. The lower frequencies contain information on the coseismic strain changes, i.e., changes in strain caused by seismicity, while the higher frequencies contain information on the coseismic stress changes.
58 a)
b)
Figure 5.18. a) Velocity seismogram for a seismic event, and b) the corresponding frequency spectrum of the S-wave (from McGarr, 1984).
5.3.9 Intensity scale
The seismic intensity is another measure of the size of an earthquake and describes the intensity of ground shaking determined by damage to structures and perceptions of people who experienced the earthquake. The most used scale today is the Mercalli scale, which ranges from I to XII, see Table 5-1. An intensity scale is also a way of estimating the size of historical earthquakes from newspaper articles, photographs and witness interviews.
Table 5-1. The abridged modified Mercalli intensity scale, after Bolt 1993.
Average Average peak peak velocity Intensity acceleration (g = (cm/s) value Intensity description gravity = 980 cm/s2) I Not felt except by a very few under especially favorable circumstances II Felt only by a few persons at rest, especially on upper floors of buildings. Delicately suspended objects may swing.
59 Table 5-1. (continued).
Average Average peak peak velocity Intensity acceleration (g = (cm/s) value Intensity description gravity = 980 cm/s2) III Felt quite noticeably indoors, especially on upper floors of buildings, but many people do not recognize it as an earthquake. Standing automobiles may rock slightly. Vibration like passing truck. Duration estimated. 1 – 2 IV During the day felt indoors by many, 0.015g – 0.02g outdoors by few- At night some awakened. Dishes, windows, doors disturbed; walls make creaking sound. Sensation like heavy truck striking building. Standing automobiles rocked noticeably. 2 – 5 V Felt by nearly everyone, many awakened. 0.03g – 0.04g Some dishes, windows, and so on broken.; cracked plaster in a few places; unstable objects overturned. Disturbances of trees, poles and other tall objects sometimes noticed. Pendulum clocks may stop. 5 – 8 VI Felt by all, many frightened and run 0.06g – 0.07g outdoors. Some heavy furniture moved; a few instances of fallen plaster and damaged chimneys. Damage slight. 8 – 12 VII Everybody runs outdoors. Damage 0.10g – 0.15g negligible in buildings of good design and construction; slight to moderate in well- built ordinary structures; considerable in poorly built or badly designed structures; some chimneys broken. Noticed by persons driving cars. 20 – 30 VIII Damage slight in specially designed 0.25g – 0.30g structures; considerable in ordinary substantial buildings, with partial collapse; great in poorly built structures. Panel walls thrown out of frame structures. Fall of chimneys, factory stacks, columns, monuments, walls. Heavy furniture overturned. Sand and mud ejected in small amounts. Changes in well water. Persons driving cars disturbed. 45 – 55 IX Damage considerable in specially 0.50g – 0.55g designed structures; well-designed frame structures thrown out of plumb; great in substantial buildings, with partial collapse. Buildings shifted of foundations. Ground cracked conspicuously. Underground pipes broken.
60 Table 5-1. (concluded).
Average Average peak peak velocity Intensity acceleration (g = (cm/s) value Intensity description gravity = 980 cm/s2) More than 60 X Some well-built wooden structures More than 0.60g destroyed; most masonry and frame structures destroyed with foundations; ground badly cracked. Rails bent. Landslides considerable from riverbanks and steep slopes. Shifted sand and mud. Water splashed, slopped over banks. XI Few if any (masonry) structures remain standing. Bridges destroyed. Broad fissures in ground. Underground pipelines completely out of service. Earth slumps and land slips in soft ground. Rails bent greatly. XII Damage total. Waves seen on ground surface. Lines of sight and level distorted. Objects thrown into the air.
61 62 6 DESCRIPTION OF SEISMICITY
6.1 Introduction
This chapter summarizes some methods developed for the description, management and control of rockbursts. A correct prediction would increase safety and decrease production losses due to production stops and loss of drifts and stopes. The first three methods can be used without having seismic records as a reference, and are commonly used to evaluate the effects of a planned mining sequence. They can also be used for back-calculation of known rockbursts if seismic records are kept. The other methods use numerical modeling in combination with the seismic history of a mining step to try and predict areas where rockburst may occur in the future. These methods are also used to identify hazardous areas in the mine. All these methods strive at predicting rockbursts, – a fairly good prediction of the location can usually be made based on seismic history in combination with stress analysis, but the time of occurrence is not possible to predict.
6.2 Describing seismicity without seismic records
6.2.1 Energy Release Rate (ERR)
The energy that is stored in the part of the rock mass to be excavated, ∆Um/∆A (see Figure 6.1), is a measure of the stress concentration at the front if failure does not occur. The quantity
∆Um/∆A is called Energy Release Rate or ERR, where ∆A is the change in area defined as the length of the round multiplied by the height of the mining stope. The relationship between measured seismic magnitude and the strain energy released in one mining step with the method longwall mining has been studied extensively in South Africa.
∆A
Figure 6.1. Mining area according to the South African definition
63 A relationship between ERR, number of damaging bursts, and rock conditions for longwall mines has been established by Jaeger and Cook (1979). A damage criterion has then been formulated from this relationship (Jaeger and Cook, 1979; Hedley, 1992), relating the ERR and the number of seismic events (Figure 6.2). The diagram shows that damage is negligible 2 when ∆Um/∆A is less than 15 MJ/m while extreme damage occurs if the release of energy 2 ∆Um/∆A is larger than 100 MJ/m .
Figure 6.2. Relationship between ERR and number of seismic events (modified after Jaeger and Cook, 1979)
The ERR gives a hint of the rockburst potential within the mine workings. The ERR is closely related to the volumetric closure, which both can be easily calculated for elastic conditions but they give little information of the behavior of fractured rock masses (Spottiswoode, 1990). ERR was (1990) used widely for designing mining layouts in deep mines with the purposes of reducing seismicity, and is still used today in some mines.
64 6.2.2 Excess Shear Stress (ESS)
The quantity Energy Release Rate is only a measure of the rockburst potential of a mining stope and does not give any information about the risk of seismic activity along large geological structures. Slip on such structures has from South African experience been observed to cause substantial damage in large parts of a mine. In the Sudbury mining area in Canada it is assumed that all seismic events causing Richter magnitudes greater than 3.0 are so called mining induced earthquakes.
Ryder (1988) developed a criterion based on the excess of shear stresses along a discontinuity (“Excess shear stress”). The model used is the stick-slip model described in Chapter 3.3. At the point where slip occurs, the balance between shear forces and counter forces can be expressed as
τ sssn=+c µ σ Eq. 6-1
where τs is the static shear strength, cs is cohesion, µs is the static coefficient of friction and σn is the normal stress.
When slip has been initiated, the dynamic coefficient of friction and the normal stress determine the shear resistance. The cohesion is assumed to become zero when slip has been initiated. The difference between the static and dynamic shear stress equals the excess in shear stress (ESS), τe
τesdssndn=−=τ τ c + µ σ − µ σ . Eq. 6-2
Ryder (1988) suggested a preliminary value of the critical excess shear stress in the order of 5 to 10 MPa for existing weakness planes while the corresponding value for failure through intact rock would be 20 MPa. A typical value of the static coefficient of friction is 0.6, which corresponds to a friction angle of 30o. The values stated here are valid for South African rock conditions.
Ryder’s concept for slip on a fault is illustrated in Figure 6.3. The fault plane is assumed to have an uneven static shear strength distribution caused by irregular contact surfaces and varying frictional properties, which is represented by the uppermost curve in Figure 6.3. When slip is initiated the shear strength instantaneously drops to a smoother shear strength
65 distribution with lower magnitudes. If the static shear stress distribution at any point becomes high enough to equal the static shear strength, slip is initiated at this point causing an immediate decrease of the shear strength to the level of the dynamic shear strength (stress drop). High stress concentrations on the boundary of the slip surface cause the slip to expand into the area around the point at which slip was initiated. The area of slip propagates along the fault to areas of lower excess shear stresses. Since the process is dynamic, slip can also occur in neighboring areas where the static shear strength is lower than the dynamic.
Figure 6.3. The ESS-concept according to Ryder, 1988.
In South Africa ESS is used to predict the risk of slip on faults as follows: Using numerical modeling of different mining sequences, normal and shear stresses along a given fault are calculated. If the static shear stress exceeds the static and dynamic shear strength, the area where slip may occur is calculated, see Figure 6.4. As a rule of thumb it is assumed that if the maximum excess shear stress is of the order of 5 to 10 MPa slip occurs and the displacement along the fault is calculated. To obtain better values for calculating the critical excess shear stress it is assumed that a fault without filling has a friction angle in the interval 28 - 30o (which is close to the base friction angle) while the friction angle of a clay-filled fault is in the interval 10 - 15o. In areas with high seismic activity some kind of seismic monitoring is performed. With these instruments the stress drop due to slip on a fault can be determined. Based on these measurements the dynamic coefficient of friction for a specific fault can be
66 determined, thus gaining better data for predicting the risk of a seismic event in the form of fault slip.
Figure 6.4. ESS contours and faults where there is a risk of slip.
Figure 6.4 shows an example of how the technique described above has been used to predict the risk of slip on faults dipping 70o. The tangents indicate the most probable point of slip initiation for three possible maximum stress drops, τe = 10, 5 and 2 MPa. The length of the line indicates the associated length of rupture, and next to each line are the estimated magnitudes. Ryder showed that for the combination of primary stresses and mining method (longwall mining) representative of South Africa, faults dipping 70o or 130o are easiest to activate. To estimate the magnitude of the potential seismic event, in this case slip along a part of a fault, Equation 5-1 is used.
6.2.3 Volume Excess Shear Stress (VESS)
Spottiswoode (1990) suggested an alternative model called the Volume Excess Shear Stress (VESS) which relates slip on discontinuities with the seismic moment. The seismic moment can be calculated using Equation 5-1, which when extended to three dimensions becomes
67 M = G ∆ε dV Eq. 6-3 0 ∫ st
where G is the modulus of rigidity or shear, and ∆εst is the static shear strain change associated with the seismic event. Using τ∆εst = G∆τ Equation 6-3 can be rewritten as
M = ∆τdV Eq. 6-4 0 ∫ where the right hand side of the equation is termed Volume Excess Shear Stress (VESS). Some assumptions are connected to this definition. First, it is assumed that all positive ESS values are reduced to zero through shear slip during seismic events. This means that after the slip has taken place there are no excess shear stresses left on the fault. Contributions caused by integration outside the volume of positive ESS are assumed to be unimportant and are neglected. VESS is calculated by integration of ESS over the positive region. VESS was tested by Spottiswoode (1990) in two ways. First, the maximum seismic moment release for a given region at any time M0,max was calculated with Equation 6-4, resulting in an estimation of the magnitude of the largest event possible in that region, assuming that the largest event causes half of the volumetric change. Secondly, the cumulative seismic moment during a given time period was determined from changes in VESS. It was found that the cumulative seismic moment calculated using VESS did not correlate well with the observed value, as it was about five times smaller than the observed value. The VESS method, however, quite accurately estimated the magnitude of the largest event.
6.3 Describing seismicity using seismic records
6.3.1 Departure indexing method
Poplawski (1997a, b) developed a method called the “departure indexing method”. It was developed after studying the seismicity in Mt Charlotte Mine (Australia), where seismic events or rockbursts are often indicated by turbulence in seismic and static parameters prior to the event. The departure indexing method is based on assessing this turbulence. The departure index (ID) is the ratio of the actual value (of a parameter or ratio of parameters) for a single given seismic event to the average value over a specific period of time. It is expressed as
(Pi / Pj ) msd I D (Pi / Pj ) = Eq. 6-5 (Pi / Pj ) aver(T =t)
68 where ID(Pi/Pj) is the departure index of a given ratio of the parameters Pi and Pj, which are the seismic parameters used for the analysis. (Pi/Pj)msd is the ratio of seismic parameters for a given seismic event, and (Pi/Pj)aver(T=t) is the ratio of seismic parameters averaged over a number of events during a selected time period. Examples of parameters that can be used in the analysis are seismic energy of P-and S-wave, apparent volume, seismic moment, seismic radius, b-value, corner frequency of P- and S-wave, and static stress drop. The seismic monitoring system records values of these parameters, and an algorithm calculates the departure index. The advantages of the method are that
- several seismic parameters and ratios can be analyzed simultaneously, - it is also a robust method, since unitless ratios are used instead of true values, which takes care of systematic errors in measurements etc., - as many seismic parameters as deemed necessary can be included, - different parameters can have different criteria, and - it is flexible, as indices can be excluded or added as knowledge and available data increases.
The departure index can also be used to evaluate the rockburst hazard. The rockburst hazard indication (RHI) is expressed as
RHI = ∑{ΨD1 (Pi / Pj )1 + ... + ΨDn (Pi / Pj ) n } Eq. 6-6 where
1 if I D ≥ I D,crit ΨD (Pi / Pj ) = . Eq. 6-7 0 if I D < I D,crit
This means that when ΨD = 1, there is seismic risk and that departure index contributes to the rockburst hazard indication, and when ΨD = 0 there is no seismic risk, and consequently this departure index does not contribute. The value of the rockburst hazard indication is after calculation compared to a critical value, which is based on experience from the mine in question. When the rockburst hazard indication exceeds the critical value, it means that a rockburst is imminent (Poplawski, 1997).
69 6.3.2 Cell evaluation method - Modeled Ground Work (MGW)
An increase in the number of incidents (damage to mine openings and human injuries) related to seismicity in Australian mines has lead to a need of a method for managing seismic hazard. Such a method was proposed by Beck (2000) and it compared different excavation options in terms of a quantitative assessment of seismic hazard. This assessment was made using a three-dimensional elastic boundary element model of the host rock mass. Parameters from the analysis could then be compared to records of observed seismicity to provide probabilistic relations between seismic event occurrence and event strength. Beck suggested that the parameters that should be used for event occurrence relations and event strength estimates were Factor of Safety against seismic failure for seismic event types determined by back calculation and Modeled Ground Work (MGW) or Local Energy Release Density (LERD). Both MGW and LERD are numerical models for comparing the load-deformation state of a volume of rock before and after an event. This is done by simulating the event as a change of material properties within the volume. These methods are described below.
Beck and Brady (2002) stated that a seismic event can occur if the conditions of a stress state sufficient for failure and an energy condition such that failure is violent, are met. They presented the hypothesis that the potential for rock mass failure and strain energy density distribution are the most relevant physical parameters affecting the occurrence of induced seismicity. The cell evaluation method was developed for evaluating the magnitudes of the controlling parameters throughout the mine domain. The method requires that the whole volume of influence of an historical mining step can be discretized into regular test volumes (finite cells). Another assumption is that the evolution of the mining geometry and field observations of seismic events (location and magnitude) are available in the volume of interest. The controlling parameters (yield potential and strain energy state) are calculated in each cell. By comparing and correlating the parameter values in the cells with the rate of occurrence of seismic events (in reality) a multi-variate probabilistic relation between the parameters and the seismic outcomes of a step in an excavation sequence may be defined.
The controlling parameters are defined as an independent measurable, or calculable state,
Qi, i > 1, that defines the condition at a point in the rock mass; hence it can be used for correlation with historical seismic records and thereby to determine likelihood and magnitude
70 of seismic events resulting from future mining activity. The probability of an event X of magnitude x is:
p(X x ) = f (Q1,Q2 ) Eq. 6-8
When designing an underground structure it is necessary to analyze the energy changes caused by making the excavation. Where dynamic behavior is important, both stresses and energy state must be considered. Beck and Brady (2002) assume that the occurrence of seismicity depends on i) a stress state sufficient to initiate compressive failure in the rock mass or slip on a discontinuity (generical term is yield, Q1) and ii) a strain energy state in the source volume for rock yield and in the surrounding rock (Q2).
Beck and Brady propose in their model the use of a “factor of safety” to evaluate the stress parameter (Q1) for different types of events and to provide a quantitative measure for planned mining. The factor of safety is defined as the ratio of rock strength to rock stress. For slip on a discontinuity with zero cohesion and using Coulomb’s failure criterion, the factor of safety is defined as
σ tanφ S = n Eq. 6-9 T τ
where σn is the normal stress acting on the discontinuity, φ is the friction angle and τ is the maximum shear stress.
Beck and Brady (2002) developed the definition/specification of the strain energy parameter
(Q2) after studying the results by Wawersik and Fairhurst (1969) regarding the energy of specimen rupture. Beck and Brady specified that Q2 ideally should uniquely describe the state of the factors that control rupture violence. Possible parameters are ERR, ESS, LERD and MGW. To describe their model Beck and Brady used MGW, formulating the probability of an event X of magnitude x as
p(X x ) = f (ST , MGW ) Eq. 6-10
The functional relation f is found by establishing how often different combinations of ST and MGW result in seismic yield, and thus the probability that these combinations result in future seismicity can be calculated.
71 Beck and Brady applied the method to mining steps in two different mines and found that it was possible to establish relations between seismic event strength, event probability, MGW and ST. They went on to show how these relations could be used to quantify the seismic risk of a planned excavation step. This is done in four steps:
1. A regular volumetric grid is established around the likely volume of influence of the proposed mining geometry.
2. At the test cell centers Q1 = ST is calculated, the potential event types in each test cell
is recorded, and Q2 = MGW related to the specific type of seismic event associated to
the value of ST is determined. 3. The expected probability of event occurrence within the cells is determined using plots derived empirically for the particular mine site or stope block. 4. When seismically susceptible cells are identified, MGW is compared to the derived seismological relations to estimate the event strength.
The procedure was evaluated for cases from the same mines as used previously and the method gave good agreement between assessment of event probability and later observations of event occurrence. Event strength is another important issue for a mine and here also there was good agreement between predicted results and field observations. The conclusion from the case studies is that the method produces usable relations for management of seismic risk, and suggests that the cell evaluation method has a potential use as a framework for evaluating seismic hazard generally.
MGW – Modeled Ground Work
MGW is used as the strain energy parameter Q2 in the cell evaluation method. The MGW is determined by studying a volume of rock consisting of a number of arbitrarily shaped test cells. Due to the presence of excavations the test volume has a disturbed stress field. This stress field is assumed to cause an episode of degradation (an event) of the rock mass properties, either due to fault slip or rock mass compressive failure. The initial strain energy of the test cell associated with pre-event traction (txi, tyi, tzi) and displacement (uxi, uyi, uzi) is
n n n 1 U1 = ∑txiuxi + ∑t yiu yi + ∑tziuzi , Eq. 6-11 2 i=1 i=1 i=1
72 where n is the number of elements on the surface of the test volume. The strain energy after the episode of rock mass degradation (post-event) is:
1 n n n U t ' u ' t ' u ' t ' u ' Eq. 6-12 2 = ∑ xi xi + ∑ yi yi + ∑ zi zi 2 i=1 i=1 i=1
MGW is defined as the area below the model characteristic curve, see Figure 6.5, and is expressed as:
3 n 1 ' ' MGW = ∑∑ 2 (tij + tij )(uij − uij ) . Eq. 6-13 i==11 j
Model response Before mining step
Model characteristic
After mining step / before seismic event
Test cell After seismic event / test reaction cell failure
Test cell Area = MGW reaction / surface traction Deformation
Figure 6.5. Calculation of MGW, after Beck and Brady (2002).
6.3.3 Local Energy Release Density (LERD)
Local Energy Release Density (LERD) was developed by Wiles (1998) and corresponds to the loading system stiffness, and is defined as the area under the load-deformation curve divided by the sample volume (or sample area if a fault is studied). The LERD is determined by specifying a test block, and then calculating the stresses and displacements on the surface of this block at a given mining step (stage I), and then calculate them again after some alternate material has been substituted into the test block (stage II), see Figure 6.6. The properties of the alternate material should represent the failed state. For pillars, the worst case is a complete loss of the pillar, which would correspond to excavation of the test block, while for a fault a
73 material with reduced cohesion and friction is a more realistic substitute. When the calculations of stresses and displacements are completed, the original material is replaced, and then the process is repeated for all other test blocks at each mining step. The total energy released by the system is found by first integrating the stresses over the area (to obtain the load) and then to integrate the load over the displacements resulting from the substitution of the alternate material. Finally the total energy released is divided by the test block volume, so the LERD will be expressed in MJ/m3. This way of determining LERD means that it is a local rock mass characteristic that will vary in magnitude from one place to another, and also that the value at any location will change as mining progresses. This means that for instance a pillar can pass in and out of the burst prone state as mining proceeds.
P
Stage I Stage II δ
Figure 6.6. Loading system response, after Wiles (1998).
The LERD-method was tested on some cases taken from INCO’s Creighton Mine (Sudbury, Canada), where stress state and LERD were calculated as mining progressed. The back- calculation was used to verify the method. The results indicated that locations that had a critical level of LERD and stress, were locations that were reported to have burst. By studying the distribution of LERD, the most likely location of a rockburst could be identified, and also the type of the anticipated failure was indicated as progressive or violent (Wiles, 1998).
6.3.4 Seismic Hazard Scale (SHS)
The seismic hazard scale was developed by Hudyma (2004) and is based on a world wide survey of mine seismicity in underground, mechanized, hardrock mines. A total of 73 mines from 11 countries responded to the survey. The goal of the survey was to identify factors that make an orebody and a mine seismically active (Hudyma, 2004). The mining methods of the
74 mines that responded were open stoping (52 mines), entry methods, i.e., cut-and-fill and room-and-pillar, (12 mines), sub-level caving (7 mines) and block caving (2 mines). The survey had 148 questions, which included questions regarding rock properties, geology, stress, orebody, mining method, mining geometry, seismicity, methods of managing seismicity, and related rock mass damage. The data collected was used to train an artificial neural network to replicate the results of the survey. Seismic hazard is defined as the likelihood of occurrence of events of a certain magnitude (Hudyma, 2004). The seismic hazard scale (SHS) uses three common mine seismicity parameters to rate the relative occurrence of seismic events of various sizes in a mine. The parameters are
- the rate of occurrence of events of a certain magnitude, - the power law relation for mine seismicity, i.e., Equation 5-12, and - the maximum observed event magnitude.
The SHS assumes a b-value = 1, which means a 10 fold increase in number of events for each unit decrease in magnitude. The SHS has been used to investigate seismic hazard for events up to ML = 2 - 3. Events of larger magnitudes (large fault-slip events) may not follow the scale, since their b-value may be less than one. Also the failure mechanism of large events may be different than for smaller events, so using the SHS methodology could lead to misleading estimates of seismic hazard (Hudyma, 2004). Depending on the mining method the applicability of the SHS varies, due to the distribution of mining methods in the participating mines. This concerns mainly sub-level caving mines, where it should be remembered that only seven mines responded to the survey. The SHS is not valid for block caving mines since only two mines completed the survey. Another aspect is that the SHS is a measure of past seismicity in the mine, and if the rock mass conditions change or if the mechanisms or driving forces of future seismicity change, forecasting using the SHS may be misleading.
Hudyma (2004) developed a method to calculate the seismic hazard for different mines and orebodies (some mines provided information on more than one orebody), and then the SHS was plotted against several geotechnical, mining and geological parameters. The resulting correlations between SHS and the different parameters are summarized in Table 6-1.
75 Table 6-1. Summary of correlation between SHS and geotechnical, mining and geological parameters (Hudyma, 2004).
Strong correlation Weak correlation No correlation
pre-mining stress depth of mining horizontal to vertical stress ratio uniaxial compressive strength of orebody size Young’s modulus the rock mining induced stress* stoping width rock mass quality stage of mine extraction* mine fault displacement history use of regional mine pillars use of local rib and sill pillars percentage of orebody extraction* fault thickness between stopes fault thickness in low pre-mining use of pillarless mining sequences stress conditions stope size size of production blasts induced stress on mine faults fault continuity fault infilling fault planarity * indicates that the correlation is strong or moderate.
The advantage of the SHS is that a mine can evaluate the seismic hazard without having data from a seismic monitoring system. The SHS also gives a reasonable estimate of the maximum size of events that can occur in the mine (Hudyma, 2004).
76 7 PREVENTION AND CONTROL OF SEISMICITY
The cause of rockbursts is (in many cases) a combination of stiff rock and stresses high enough to exceed the strength of the rock. It should be noted that strain energy is accumulated in a volume of rock, but that the energy is dissipated along surfaces within the volume (Blake et al., 1998). The potential of violent failure is also higher in homogenous rock, i.e., rock with less natural discontinuities or with little variation in mineralogy. An inhomogeneous rock mass is more likely to develop micro-fractures, or shear along pre-existing joints, leading to lower stiffness and greater energy dissipation (Blake et al., 1998). To alleviate violent failure one can either make the rock less stiff by creating shear along existing weakness planes or decrease the stresses acting on the piece of ground subject to bursting.
To soften the rock or transfer the stresses several approaches can be used. Changing the mining layout can ensure that pillars are not overstressed. Changing the shape of an opening can also decrease stress concentrations in unfavorable locations on the boundary. If it is not possible to change the shape of the openings or the mining layout there are other methods of accomplishing a reduction in the potential for violent failures, which may be less efficient but yet sufficient.
7.1 Preconditioning and destressing
Preconditioning is the “method, which makes use of explosives ahead of mining faces to control and limit the amount of damage resulting from face bursts” as defined by Toper et al., 1998. Preconditioning is used to destress the immediate rock mass by setting of a blast resulting in stresses or overburden loads being transferred to the adjacent rock not affected by the preconditioning blast (Toper et al., 1997).
It was noted above that to reduce the potential for violent failure, either the stiffness of the rock should be decreased or shearing on existing fracture surfaces should be promoted. There are two ways of accomplishing this by destress blasting. The first alternative is to blast as heavily as possible without damaging the excavation too much. The idea is to soften a certain region by creating as dense a zone of microcracks as possible. The softening will lead to an alteration of mechanical response of the rock mass from elastic-brittle to plastic deformation (Blake et al., 1998).
77
Toper et al. (1997) uses the second approach and states that preconditioning does not cause formation of any new fractures ahead of the face but instead leads to slip on pre-existing fractures due to the high gas pressure from the explosion. The fractured rock mass that results from the preconditioning blast forms a “protective cushion” ahead of the face. If a seismic event would occur at some distance from the preconditioned face the dynamic tensile wave from that event would not cause as much damage as for a normal face. The effect of a preconditioning blast is localized in space, so to avoid face bursting on a specific panel, that particular face must be preconditioned. The effect is also limited in time. Since the mechanism of preconditioning is one of stress transfer as a result of induced deformations in the fractured rock ahead of the face, the fractured zone is still capable of carrying high loads. It is therefore possible that future mining can transfer stresses back toward the previously preconditioned face and that a face burst may occur. An example of this from Western Deep Levels South Mine (South Africa) is described by Toper et al. (1997). Mining on a panel (E) that had been pre-conditioned was stopped, while mining continued on neighboring panels (C and F). Two weeks later a magnitude 1.1 event occurred in the vicinity of panel E, triggering a face burst on that panel, which destroyed a supporting pack.
As a general rule destressing of development drifts is often successful, and many mining companies have developed their own standards, which cover drill patterns, explosives, charging and blasting (Blake et al., 1998). Destressing of pillars is more difficult, since the effect of the blast is not well understood. Destressing of one pillar also transfers stresses to neighboring pillars, which in turn may become to highly stressed.
7.1.1 South Africa
Preconditioning (or destressing) was introduced as a way of improving rockburst conditions in deep mines. The first mine to apply it was East Rand Proprietary Mines (ERPM) in the 1950´s (Toper et al., 1998). Several different techniques have been developed around the world due to the different rock conditions that exist. In South Africa where longwall mining is common face bursts often occur, and two techniques for preconditioning the faces have been developed: the face parallel and the face perpendicular methods.
78 Face-parallel method A good mining layout is shown in Figure 7.1, where drilling and blasting of the preconditioning holes has been integrated into the production cycle. Each panel has a maximum length of 20 m, and the panel lead has been minimized. Panel 2 has been mined to the limit (i.e., the previous preconditioning hole) and the next hole is drilled at about 5.5 m from the current face.
Unmined Length = 20 m
Panel 1 5.5 m lead
Previous pre- conditioning hole Panel 2
New pre- conditioning hole Panel 3
Figure 7.1. Preconditioning layout in an overhand mining sequence (after Toper et al., 1998).
The preconditioning hole should be drilled parallel to the reef plane along the reef/footwall contact. The hole is drilled in the fractured zone ahead of the face and should extend into the next panel. To ensure proper destressing of the entire face it is important that the holes are parallel to the face. It is also important that the hole is drilled in the correct position ahead of the face. If it is drilled too far away drilling will be difficult because of high stresses and blasting could lead to stresses being transferred back towards the face. The actual position of the hole is site-specific and depends on both stress state and the size of the charge to be used.
Face perpendicular method In this method the holes are drilled perpendicular to the face and parallel to the ore body (which in South Africa is almost always tabular), see Figure 7.2. The holes in a new round are
79 offset horizontally by 0.5 m from the previous ones to avoid drilling into old sockets. Each production blast moves the face forward about one meter so every three production blasts the preconditioning holes are drilled in the same position. Research referenced by Toper (1997) has shown that the spacing between the holes should not exceed 3 m. This has been concluded since the radius around the holes affected by a trial blast was about 1.5 m. Trial and error has also lead to the conclusion that a length of 3 m and a diameter between 36 mm and 40 mm is the optimum.
0.5 m
Day 3 3 m Day 2 Day 1 3 m
Direction of face advance
Figure 7.2. Face perpendicular preconditioning holes, after Toper et al., 1997.
The preconditioning holes in Figure 7.2 are drilled at mid-height of the stope to reduce the risk that any of the production holes intersect the preconditioning holes, see Figure 7.3. The preconditioning holes are charged for the bottom 2 m and top-primed and then the remaining 1 m is stemmed using for example bentonite or angular sand.
Hangingwall
Preconditioning hole Production holes
Footwall 1 m 2 m Figure 7.3. Cross sectional view of face perpendicular layout after Toper et al., 1997.
80 Both the face parallel and the face perpendicular methods have lead to a decrease in the number of face bursts and have improved working conditions. Both methods also improve the drilling rates for the production holes, since it is faster to drill through fractured rock than intact rock.
7.1.2 Sweden
Destressing has been used in several Swedish mines, among others Näsliden, Laisvall, Malmberget and Kristineberg mine. The two first mines have now been closed, but it is still interesting to see how it was done there. Destressing performed by Boliden up until 1988 was summarized by Krauland and Söder (1988).
Näsliden mine The first attempt was made in Näsliden mine in 1978. The mining method used was cut-and- fill and the stress situation was characterized by high horizontal stresses causing extensive spalling of the roof of the stopes, often in combination with minor rockbursts. The orebody was tabular and steeply dipping. The destressing attempt had two objectives, namely
- to show and quantify the destressing of a cut-and-fill stope by a correctly placed destressing slot, and - to find a good explosive and to examine the crushing of the rock around the blasthole.
To determine the correct placement of the destressing slot, numerical models were analyzed using a finite element-program. The purpose of the destress blast was to decrease the stiffness of a part of the rock mass close to the excavation, so that the stresses were redistributed away from the boundary of the excavation. The model showed that if the ratio of the stiffness of the destress slot to the stiffness of the in-situ rock was 2.5% - 10% the horizontal stresses in the roof decreased by 37 - 60%, see Figure 7.4.
81 Before Destress slot destressing Reduction of Young’s modulus of rock in slot
Eslot
Eoriginal
without destressing
with destressing
destress slot
Figure 7.4. Modeling of the effect of destressing of the roof in a cut-and-fill stope, by a destressing slot in the footwall, after Krauland and Söder (1988).
Field trials were then performed in the #3 stope, to validate the model results. The slot was blasted in the footwall rock to destress the roof. The destressing of #3 stope failed because the rock was not sufficiently crushed around the blastholes. The reason for this was that the explosive had too low detonation velocity, and that the slot had been placed in a ductile chlorite. After some investigation it was determined that an explosive with a high detonation pressure should be used. Some conclusions could be drawn from the failed attempt for destressing to be successful:
- the rock should be highly stressed and preferably brittle, - the loading situation should be simple so that the destress slot can be placed correctly,
82 - the stability problems should be bad enough for shotcrete and rock bolting not to be sufficient, - the destress slot should be placed far enough into the rock mass so that the blasting does not damage the roof or walls of the excavation, and - several destressing holes should be placed close to each other so that a slot of cracked rock is formed.
In 1988, destress blasting was attempted in #5 stope because of high horizontal stresses leading to rockburst problems and intensive spalling of the roof. The high stresses were caused by a diminishing sill pillar. To get a more stable roof destress blasting was tried during mining of the last but one slice. The height of the sill pillar at that time was 10 m. The destress holes were blasted together with the production rounds. During the first four rounds there were no noticeable effects, but after the fourth round the rockbursts stopped and the extent of spalling of the roof decreased.
Laisvall mine Laisvall mine was a room-and-pillar mine characterized by high horizontal stresses despite a relatively low depth, about 220 m (Engberg, 1989). The vertical stress is gravitational and approximately 6 MPa at this depth, but horizontal stresses of between 20 and 25 MPa have been measured, which leads to a horizontal to vertical stress ratio of 3.3 – 4.2. The orebody is tabular and subhorizontal. The mining layout of the trial area, Nadok 1400, is shown in Figure 7.5.
1400-drift
1500-drift
Figure 7.5. Wedge-shaped mining area in Nadok 1400, after Engberg (1989).
83 The 1400-drift was excavated first, followed by the 1500-drift which was about 15 m behind. Mining perpendicular to the two main drifts was carried out so that the mining front became wedge-shaped. Spalling failures in the roof took the form of an inverted keel, see Figure 7.6, and occurred mostly during excavation of the first drift. The depth of the failures was 0.8 – 1.5 m. Thus, it seemed that the second drift was excavated in a destressed area. Bolting was not sufficient to stop the spalling and secure the stability of the drift; hence it was decided to try destress blasting.
Figure 7.6. Inverted keel spalling failures, after Engberg (1989).
The destress blasting was conducted using three parallel holes that were drilled together with the production round. The holes were located in the right abutment with a c/c of 1.4 m. The average direction is 42° away from the drift and about 25° upwards, see Figure 7.7.
Destress hole 42°
25° Destress holes
1.4 m 3 m
Figure 7.7. Layout of destress holes (after Engberg, 1989).
The bottom part of the holes (0.6 - 0.7 m) were charged with 1 kg of explosives, and the holes were blasted with the production round. Drilling into the area that was blasted gave an approximate size of the cracked zone of 2-2.5 m width and 1.5 m height. The cracked zone was most likely affected by the anisotropy of the clay schist in the roof so that the zone of damage was not perpendicular to the axis of the hole. Rather it had propagated along the weakness planes of the clay schist, see Figure 7.8.
84
Figure 7.8. Rotation of cracked zone, after Engberg, 1989.
Damage mapping of the roof was performed in two areas. Destress blasting had been conducted in one area, and the damage here was less extensive regarding both area and depth of failure. In a few places the destress blasting had not been performed as planned and in these areas the roof damage had increased (Engberg, 1989). This indicated that the destress blasting was effective in reducing the stresses in the roof.
Malmberget mine During excavation of the main level at 815 m (1985) the drifting was slow due to severe seismicity problems. The layout of the main level is shown in Figure 7.9. The main rocktypes in the area are red- / redgrey leptites, which are sometimes gneissic in structure and can also sometimes be weathered. Biotite and granite occur as veins. The transportation drift had an area of 60 m2, and the seismicity led to spalling of the roof up to a height of about 4 m above planned roof level. The spalling resulted in either a sloping roof or a “church” forming, see principal sketch in Figure 7.10. To increase the safety and also increase the drifting rate, trials with destress blasting were conducted.
85
Figure 7.9. Layout of main transportation level 815 m (Borg, 1988).
The first step was to observe the seismic events and try to correlate them with geology. It was found that the worst problems occurred in aplite and red leptite, which are the two rock types that have the highest uniaxial compressive strengths, 194 MPa and 178 MPa, respectively. These rocktypes resulted in the largest overbreak (Borg, 1988). Water bearing zones also caused a lot of seismicity, but no problems with overbreak. In step 2, a numerical analysis of the stress situation around the drift, both with and without a destressing slot, was performed.
a) b)
9.8 m
Figure 7.10. Principal sketch of a) sloping roof profile and b) churching (Borg (1999).
86 The slot had a height of 1 m or 2.7 m and a length of 4 m, see Figure 7.11, and was modeled as a zone with lower Young’s modulus (from 12 to 28 GPa) than the surrounding rock (40 GPa). The numerical model assumed that the rock was isotropic and elastic and that there were no dynamic sequences.
9.8 m Figure 7.11. Principal sketch of drift with a 2.7 m high slot used in numerical modeling.
The numerical modeling showed that the slot decreased the stresses in the center of the roof, and a high, long and soft slot was most advantageous. Taking both these results and previous destressing experiences (from e.g., Boliden mines) into account it was decided to try destress blasting in one of the sidewalls with the layout in Figure 7.12 (Borg, 1988). The idea was to redistribute the stresses near the boundary of the excavation farther into the rock, and to avoid damaging the rock close to the boundary. Slot
Drill holes
9.8 m
Figure 7.12. Suggested layout of destress blasting after Borg (1988).
After a few rounds with this layout it was decided to drill only three holes to avoid damaging the boundary rock too much. Hence destressing of both sides of the drift was done using the same layout on both sides. The original drill plan is shown in Figure 7.13, and Hole 0 is the one that was subsequently removed. The distance between the holes was 1 m, measured
87 perpendicularly to the hole axis. The holes were charged with one kilo of explosives, packed into the hole bottom.
Hole 3 Hole 2 Hole 1 Hole 0
Figure 7.13. Plan section of drift showing hole layout.
The result of the trial with destress blasting was that the seismicity and overbreak decreased noticeably in the sections that were destress blasted.
7.2 Fluid injection
The major source of large seismic events is slip on faults. Injection of fluids into for instance oil reservoirs has been noted to cause seismicity along faults (Board et al., 1992). The explanation for this is that the injected fluid decreases the normal stress across the fault, which leads to slip. Board et al. (1992) made an experiment with injection of water into a fault below a pillar in a deep gold mine. The fault was fairly planar, and had a width of 1 m, and was chosen for the experiment since it had been seismically active. The injection point and the injection pressure necessary to induce slip were determined using a combination of the properties of the fault (geology, roughness, infilling), seismic monitoring, and numerical modeling to determine the stress conditions on the fault. The result of this modeling was that fault slip could be initiated with a water pressure of about 20 MPa, and that significant stress transfer could occur as a result of the slip. One borehole penetrated the fault just beneath the pillar where the normal stress was expected to be highest. The hole was cased along its entire length except across the fault and a pumping system capable of producing 30 MPa at 80 l/min was installed. After about 10 min of pumping a quasi-static condition of about 20 MPa was reached. Pressure drops, ranging from less than 1 MPa to about 4 MPa, started to occur when the pressure was between 15 and 20 MPa. The larger of these pressure drops corresponded to seismic events of magnitudes ML = -1 to -0.75, of which seven were located in the vicinity of the injection hole. The radius of influence from the injection hole was about 2 m (assuming
88 radial flow), hence the area that had enough pressure to initiate slip was rather small. A slip radius of about 2 m is consistent with the small event magnitudes (Board et al., 1992).
7.3 Reinforcement
7.3.1 Introduction
Reinforcement is used in almost all underground mines to stabilize mine openings and secure the safety of the personnel. The reinforcement standards differ between countries, companies and mines, depending on different cultures and requirements. Most mines probably start out reinforcing to keep wedges in place, but as the mine grows in size, age, and depth, other problems often come up. One of the problems that seems to occur with increasing depth is seismicity and rockburst. Since seismicity is a dynamic problem the reinforcement used for static stabilization may not be sufficient. If the problem is localized to only a portion of the mine, destressing may be attempted to relieve the stresses. However, if destressing is not sufficient to entirely prevent rockbursts from occurring, reinforcement has to be used to stabilize the rock around the excavation.
7.3.2 Support functions
The reinforcement must be able to withstand both high static and high dynamic loads in order to be efficient. The principal functions of the support is to reinforce the rock mass to prevent failure, and if this is unsuccessful, to retain and hold loose material (Kaiser et al., 1995). The purpose of reinforcing the rock mass is to strengthen it and help it support itself. Even if fracture initiation cannot be prevented, the reinforcement helps to control bulking of the rock mass and thus ensures interblock friction and rock mass cohesion. The retaining function of the reinforcement is necessary for safety reasons, but is also important under high stress conditions to prevent progressive failure leading to unraveling of the rock mass. The retaining elements may be either stiff and strong (cast concrete lining) or soft and yielding (mesh). There are also support elements that under large displacements change from stiff to ductile behavior, such as mesh reinforced shotcrete. The shotcrete has two functions; it retains loose material, and it strengthens the rock mass by preventing loosening at the surface. The purpose of the holding elements is to secure the retaining elements of the support system to stable ground (firm rock) and to prevent gravity falls during and after a rockburst. The holding elements can be high-strength bolts anchored in stable rock (grouted cable bolts), but when large displacements are likely to occur between the head and the anchor, yielding elements
89 may be preferable. The holding elements may in some cases be required to absorb energy to decelerate ejected blocks, but in other cases they may only be required to move without absorbing energy (Kaiser et al., 1995). A support system is made up of separate elements that work together to perform the reinforcing, retaining and holding functions described above, see Figure 7.14. This requires a good design of the connections between the elements, for example shotcrete and bolts.
Figure 7.14. The primary functions of support elements, from Kaiser et al. (1995).
7.3.3 Support capacity
The characteristics of a support element or system can be described as stiff or soft, strong or weak, brittle or ductile. The properties desired of support to be used in rockburst areas depend on the intended role of the support and of the severity of damage expected from a “design” rockburst. At first, when the rockburst problem is small, stiff and strong support is preferred to reinforce the rock to prevent loosening and weakening close to the opening. If severe rockburst damage can be expected in an area the support should not only reinforce the rock to keep it from bulking but also be ductile and able to yield. Kaiser et al. (1995) summarized different support element characteristics and their functions, see Table 7-1. In general, holding elements (bolts) need to be stronger and stiffer than retaining elements (mesh and shotcrete) (Kaiser et al., 1995). There are yielding bolts designed to handle large deformations and still keep their load carrying capacity, one such example is the cone bolt.
90 Table 7-1. Characteristics of different supports and what functions they fit best for, after Kaiser et al. (1995).
Support Support functions characteristics Reinforcing Retaining Holding Stiff Grouted rebar Shotcrete Grouted rebar Soft - Mesh Long mechanical bolts Strong Cable bolt Reinforced shotcrete Cable bolt Weak Thin rebar #9 gauge mesh Split Set bolt Brittle Grouted rebar Plain shotcrete Grouted rebar Yielding Cone bolt Chain-link mesh Yielding Swellex
Kaiser et al. (1995) estimated that a holding element that could accommodate deformations of up to 300 mm at loads greater than 100 kN would be best for burst-prone ground. They tested several holding elements and found that none quite matched these requirements. The bolts that best matched the requirement included cone bolts, yielding Super-Swellex bolts and cable bolts that allow slip. Retaining elements are in general weak and soft, with the exception of shotcrete. At small wall deformations (> 50 mm) corresponding to the peak load capacity of standard non-yielding bolts, mesh provides little support. When the rock supports itself or when competent rock arches form between the rock bolts the weight of rock that the mesh has to support can be quite small. However, if key blocks in a stable arch start to unravel, the arch looses its stability and the support has to carry the weight of the rock. To help the rock support itself it is important to restrict the movement of key blocks. In this regard a mesh with stiff load-displacement is a better support since it will minimize the deterioration of the rock above. For this reason it is better to use a diamond bolt pattern than a square because the distance between the bolts will be smaller and that also helps to minimize loosening of the rock mass. If mesh is combined with shotcrete the initial stiffness increases, and even at large displacements when the shotcrete has fractured it still has significant retaining capabilities. The shotcrete also prevents corrosion of the mesh and it strengthens the rock mass by suppressing dilation.
The energy absorption capacity is another important property and differs between support elements. Regular bolts can dissipate 1 – 5 kJ, while yielding bolts can dissipate about 30 kJ (Kaiser et al., 1995). The energy absorption of mesh or shotcrete depends on the deformed area. If the deformation is smaller than 200 mm the energy dissipation of mesh alone is quite low, so the holding elements would have to take care of most of the energy. In combination
91 with shotcrete, however, the capacity is 3-5 times higher than for mesh alone, for displacements of 50-100mm.
Kaiser et al. (1995) summarized a number of tests performed and formed design values for load, displacement and energy absorption capacities for some common support elements used in Canada, see Table 7-2.
Table 7-2. Design values for load-displacement parameters of support elements, after Kaiser et al. (1995).
Description Peak load Displacement limit Energy absorption [kN] [mm] [kJ] resin-grouted rebar (19mm) 120-170 10-30 1-4 cable bolt (16mm) 160-240 20-40 2-6 2 m mechanical bolt (16 mm) 70-120 20-50 2-4 4 m cable bolt (16mm) 160-240 30-50 4-8 grouted smooth bar (16mm) 70-120 50-100 4-10 Split Set bolt 50-100 80-200 5-15 yielding Swellex bolt 80-90 100-150 8-12 yielding Super Swellex bolt 180-190 100-150 18-25 Cone bolt (16 mm) 90-140 100-200 10-25 #6 gauge welded-wire mesh 24-28 125-200 2-4/m2 #4 gauge welded-wire mesh 34-42 150-225 3-6/m2 #9 gauge chain-link mesh 32-38 350-450 3-10/m2 shotcrete and welded-wire mesh 2 x mesh < mesh 3-5 x mesh*
The energy absorption of the shotcrete and welded-wire mesh combination (marked with * in Table 7-2) is valid at displacements below 100 to 150 mm. The displacement limit and energy absorption in Table 7-2 were taken at the point of failure for rock bolts and at the peak load for mesh and shotcrete (Kaiser et al., 1995). The gauge numbers of the mesh corresponds to the diameter of the wire (www.screentg.com). A 4 gauge wire has a diameter of 5.723 mm, a 6 gauge wire has a diameter of 4.877 mm, and a 9 gauge has a diameter of 3.767 mm (www.twpinc.com).
7.3.4 Support systems
A support system is a combination of support elements that provides one or more of the reinforcing, holding or retaining functions. One important aspect is that the support elements
92 have to be well connected to each other to make the system effective. Kaiser et al. (1995) noted three common weaknesses of support systems.
- the use of small rockbolt plates to connect to mesh and retaining elements. A strong connection can be formed using larger rockbolt plates or load spreaders. - too small overlap for mesh sheets can form a line of weakness. This can be avoided using an overlap of at least one mesh square, use of mesh clips or addition of shotcrete. - lacing can transfer significant loads to the holding elements, so the connections are critical. It is important that no bending moments or stress concentrations occur at these connections.
In order to have an efficient support system it is essential that the required properties are matched to the anticipated rockburst damage. Sometimes the rockbursts can be so severe that they cause violent ejection of rock despite a reasonable support system. This upper limit of energy absorption is called Maximum Practical Support Limit (MPSL) and lies around a capacity of 50 kJ/m2 (Kaiser et al., 1995). When this limit is reached other measures have to be considered, like changing excavation geometry, mine sequencing or destressing. Several factors contribute to the MPSL, but it generally occurs when the thickness of the fracture zone around the excavation exceeds 1.5 – 2 m, or when wall displacement exceeds 300 mm (Kaiser et al., 1995).
93 94 8 CONCLUDING REMARKS
This literature review is not intended to cover every aspect of seismicity, but instead to cover basic concepts and terminology. The literature review will also provide the background information for selection of important parameters, to be studied in the cases included in the Licentiate Thesis.
The importance of the in-situ stress state in the rock mass around the mine cannot be underestimated. Knowledge of how mining influences this stress state is important; – back- analysis of failures can provide valuable information. Mining should be planned keeping seismicity in mind, since a small change in layout or sequence can improve stress conditions around the stopes. The size of stopes, and the amount of rock blasted in each round affect the amount of available seismic energy. Incremental mining reduces the amount of energy available as seismic waves, but it can be favorable to blast a large round, because much of the seismicity occurs directly after blasting. The reason for this is that the blast gives the rock mass a “shake”, so that structures and rock close to failure actually fail. For a large blast no personnel are allowed underground, so by the time all the gases have been ventilated most of the stress redistribution has already taken place. Thus, the risk of a seismic event that can endanger personnel in the vicinity of the stope has been greatly reduced. A system for mapping of seismic failures has to be developed, to ensure that seismically active areas are known, so that e.g., the correct reinforcement is used. In mines where seismicity is a problem, and the mining method allows, backfill should be considered. Backfill has many advantages; it provides support for stope walls – preventing progressive spalling, it prevents closure of stopes, and it absorbs energy released by seismic events.
Another important factor to be considered is the location of geologic structures both in the mine and in the surrounding rock mass. As mining progresses the faults may become seismically active, and the consequences of slip can be disastrous. When planning the production, mining should start at the fault and proceed away from it, where possible. If this mining sequence is impossible, the support has to be designed with dynamic behavior in mind.
Seismic monitoring should be considered in mines that experience seismicity, since it not only can be used to locate and determine the size of seismic events, but also can provide valuable
95 information about the state of the rock mass surrounding the mine. Using data from the seismic system for calibration of numerical models is quite common in mechanized hard rock mines (Potvin and Hudyma, 2001). Analyzing the seismic source parameters can be very valuable, but requires a substantial effort and time. Large volumes of data are needed, and the variations in the seismic source parameters must be studied in localized areas, by isolating individual sources and source mechanisms. An example is the study by Alcott et al. (1998), where temporal increases in seismic moment, seismic energy, and apparent stress were correlated with major failures occurring in the mine. The data used for analysis was hand- picked, which ensures high quality data, but requires expertise and time. Usually there is only one person in charge of the seismic system, which is usually an engineer with limited time to spend on analysis. To perform this kind of seismological analysis routinely, better automatic picking of first arrivals by the system is necessary, along with development of automatic tools to give a first estimate.
The conclusion from this literature review is that the parameters that should be studied in the mines are:
- virgin stress state, - geology and rock properties, and - mining method.
Destressing, reinforcement practices, and the use of data from seismic monitoring systems should also be studied. This information can provide ideas for the Swedish mines starting to experience seismicity or that have decided to invest in seismic monitoring systems.
96 9 REFERENCES
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