An Investigation of Stress Wave Propagation Through Rock Joints … · Ground vibration is an unavoidable side-effect and one of rock blasting’s main environmental impacts. Stress

An Investigation of Stress Wave Propagation

Through Rock Joints and Rock Masses

Summary of the thesis submitted by Dr. Ricardo Resende

at the Faculty of Engineering of the Porto University, Portugal,

in September 2010

Ricardo Resende Rocha Medal Thesis Summary

1

Contents

Abstract 2

1. Introduction 3

2. Basics 6

Rock joints 6

Discussion 9

3. Micromechanical Modelling of Stress Waves Across Rock Joints 10

Joint behaviour simulation 11

Dynamic properties of Bonded Particle Models 13

Propagation of compressive stress waves across fractures in BPM 14

Results and Discussion 15

4. Underground Stress Wave Propagation Testing and Simulation 20

Results of the vibration propagation test 23

Numerical modelling of stress wave propagation 24

Discussion 33

5. Large Scale Underwater Blasting 34

Vibration control during the Leixões harbour deepening works 34

Attenuation Law 35

Numerical modelling 36

Discussion 40

6. Conclusions 42

Bonded particle modelling of dynamic rock joint behaviour 42

Underground vibration propagation and modelling 42

Large scale underwater blasting 43

Selected bibliography 44


2

Abstract

Ground vibration is an unavoidable side-effect and one of rock blasting’s main environmental

impacts. Stress waves disturb populations, may damage sensitive equipment, compromise

serviceability of constructions and, in extreme cases, cause structural damage.

A more profound knowledge of how stress waves propagate in fractured rock masses is needed to

control and manage vibration impacts: traditional methods of prediction such as empirical equations

must be complemented with numerical models that can cope with blast and ground variability.

This thesis contributes to these goals through several means. The first is the development of a

micromechanical numerical model that simulates propagation of stress waves in rock and through

rock joints, which are the most important structural features of rock masses. This innovative model is

based on the particle discrete element method. The dynamic properties of a non-structured

assembly of circular particles are studied, and a new joint contact model is developed allowing the

simulation of rock joints with realistic roughness, contact creation and erosion. This model performs

well in static and dynamic tests, agreeing with the Displacement Discontinuity Theory for rock joints

seismic behaviour.

In a second study, a blast test was performed in a network of adits excavated in rock at a depth of a

few hundred metres and helps clarifying how vibrations travel and are affected by natural and man

made structures. A discussion of two and three-dimensional simulation of blasting stress wave

propagation is followed by the modelling of the test using two and three dimensional numerical

models. The general performance of the models is assessed, while different simulation options are

evaluated. This study delivers important conclusions on how to simulate stress wave generation,

propagation and measurement.

In the third study the object of attention is a larger, underwater, blasting operation. Statistical,

artificial intelligence and numerical modelling techniques suited for the low level of information on

the blasting and the ground are used and developed to study peak particle velocity dispersion.

Simple three-dimensional numerical models were built to test the influence of hypothetical ground

singularities on the peak particle velocity attenuation. These models are a great improvement over

the means usually employed to study wave propagation, showing how dykes, softer ground zones

and blast characteristics may influence vibration levels.


3

1. Introduction

Public awareness and intolerance to annoyances related to construction has grown steadily in the

last decades. The impacts of the underground construction in cities are evident, especially when rock

is blasted. Rock blasting direct environmental consequences are stress wave generation, noise, which

in extreme cases may result in shock waves, and dust and rock projection. Ground vibration, which is

one of the most hazardous and also most difficult to mitigate, induces discomfort in people, be it

directly through the ground or via buildings or other structures. Vibration may also damage or

disrupt equipments and cause aesthetic and, in extreme cases, structural damage.

The most significant structural feature of rock masses is fracturing. Rock masses are stricken by

fractures and faults of different origins and jointing plays an important role in the way most rock

masses bear loads, deform and fail. Interaction with discontinuities through reflection, refraction and

absorption mechanisms is the major cause of stress wave attenuation. Though it is notoriously hard

to investigate joint structure under dynamic loading, the wave–discontinuity interaction has been

subject to experimental and analytical investigations. The resulting Displacement Discontinuity

Theory adequately explains rock joints’ basic dynamic behaviour, but many questions remain

unanswered.

There is need for tools that evaluate the way in which vibrations are generated, propagate across the

ground and damage structures or equipment and disturb people. The problem has traditionally been

addressed by means of semi-empirical attenuation laws parameterized from in-situ measurement.

This method yields results that can be directly compared with regulatory limits and is expedite and

economical, but include only blast energy and the distance to the blast. Other important factors that

are not so easily characterized by scalar variables aren’t considered. These include preferential

directions of vibration emission at the source, ground heterogeneities that may attenuate or channel

vibrations or even ground excavations that block the vibrations.

Three important needs were identified in the domain of stress wave propagation in rock masses, and

three corresponding lines of action are developed.

The first is the simulation and understanding of stress wave interaction with rock joints.

Stress wave – rock fracture interaction is a fundamental investigation area that is mainly done by

laboratory testing of small size samples and must evolve to larger in-situ studies. Particle

micromechanical models replicate the microstructure of rock and its internal mechanisms of

deformation and failure, but their application to the simulation of stress wave propagation in rock is,

at best, incipient. They are used, here, as a complement to laboratory and theoretical study of stress


4

wave–rock fracture interaction. The purpose of this line of investigation is to establish the soundness

of micromechanical models in the simulation of stress wave propagation in rock masses. The studies

done in this field are presented in chapter 3.

The second line of action, closer to the underground engineering practice, aims to answer to the

need for greater insight on how stress waves propagate in rock masses with presence of excavations

and other singularities. A more profound perception and knowledge will lead to better blasting plans,

especially near vulnerable targets, and also to more efficient vibration monitoring. To contribute to

this goal, two case studies are analysed. The first case comprises in situ blast test in the Bemposta

hydroelectric underground complex. The test preceded the excavation of a new hydraulic circuit and

powerhouse and involved blasting and vibration measurements along a network of adits excavated in

rock at a depth of a few hundred metres. In the second case, the vibration monitoring data from a

large underwater blasting operation in an international ocean harbour are compiled and analysed

with the help of statistical tools and numerical models. Important insights in the evolution of stress

waves in rock masses are drawn from the results. The interpretation of these these and the

knowledge gained with them are presented at the beginning of chapters 4 and 5.

The third line of action is the development and improvement of numerical models to simulate

vibration propagation in rock masses at several scales and levels of information of the rock mass

properties. There is a clear need for increased modelling of the propagation of stress waves in rock

masses through more advanced numerical models that permit not only reproduction and

understanding of observed stress waves in complex realistic sites, but also qualitatively forecast

vibration propagation in hypothetical scenarios. Dynamic simulation of blasting still lacks concrete

methodologies or guidelines. For this purpose, two and three-dimensional numerical models were

used to simulate the blast test on the underground hydroelectric complex and the harbour

underwater blasting works and to test a number of hypothetical conditions of the blasts and the

ground. This provides guidance on best practices for the efficient simulation of blast loading, quality

of wave propagation, vibration extraction and treatment, contributing to establishing guidelines for

the dynamical simulation of blast vibration propagation and impact in rock masses. The

developments in the numerical models and the numerical simulations are included in the

applications presented in chapters 4 and 5.

Along the three applications there is an evolution of scale (Figure 1). Fractures studied in the first

application are some centimetres long and are modelled by particles of about 1 millimetre. As such,

the level of characterization (geometric and mechanical) of the problem must be almost grain-size.

On the underground blast test there is a huge jump in geometric scale, which goes up to dimensions

in the order of one hundred metres. The level of information of the rock mass decreases accordingly.


5

Finally, in the underwater blast monitoring the working area is more than two kilometres long and

there is almost no information on the ground characteristics. The methods used and developed

across these situations range from pure phenomenological exploratory micromechanical models to

widely used and established attenuation laws.

Engineering

practice

Research

Scope of

application

ScarceVery detailed

Level of Information

Physicalscale

Millimetres

Hundredmeters

Kilometre

Figure 1: Evolution of physical

scale, scope and level of

detail along the thesis

studies. The smallest circle

represents the

micromechanical simulation,

the middle circle the

underground blast test and

the largest circle the

underwater blasting

monitoring.

The following paper, originated from the micromechanical modelling of fracture – stress wave

interaction, was published in the 2010 Rock Mechanics and Rock Engineering’s special issue dedicated

to rock dynamics and earthquake engineering.

Resende, Lamas, L.N.,Lemos, J.V., Calçada, R. Micromechanical Modelling of Stress Waves in Rock and

Rock Fractures. Rock Mechanics and Rock Engineering Special Issue: Rock Dynamics and Earthquake

Engineering; Guest Editors: Prof. Giovanni Barla and Prof. Jian Zhao, 43(6):741-761.


6

2. Basics

Rock masses have flaws differing in size, shape, filling and origin, from microscopic voids and cracks

to faults that are several meters wide, all changing the way in which vibrations propagate. When a

wave interacts with a heterogeneity it can be transmitted, reflected, converted into other kinds of

waves and into sound or heat with loss of mechanical energy.

Three general classes of models have been proposed to describe the propagation of stress waves in

rock masses. An excellent in-depth review of these classes can be found in Cai (2001). In the first

class we have equivalent-continuum models. The rock material and the heterogeneities are modelled

together in a homogeneous continuous material, with properties that balance the intact solid matrix

characteristics and the imperfections’. Wave propagation velocity results from equivalent elastic

parameters. Amplitude loss can be introduced through hysteretic damping included in the

constitutive model or by damping in the equation of motion.

Wave scattering models (e.g. Hudson 1981) are an intermediate class. Waves progressing through

the solid are considered to be scattered by cracks much shorter than the wavelength and far apart

from each other so that no interaction between individual cracks is possible. Cracks are represented

as collections of disc-shaped voids, filled with a fluid (whose bulk and viscosity moduli can be set up

to represent air). Laboratory tests on intact and heat or load damaged samples showed the good

performance of these models, including frequency-dependent attenuation. The frailty of wave

scattering models becomes evident when cracks have large dimensions.

Finaly, the Displacement Discontinuity Theory, or DDT (Schoenberg, 1980), provides a structure to

support wave interaction with macroscopic fractures. DDT does not refer explicitly to the

microstructure of rock masses since fractures are treated individually as non-welded discontinuities

with stress continuity and displacement discontinuity, thus providing a simple theoretical

formulation for the individual wave-joint interaction.

Rock joints

Being the main obstacle to stress waves, rock joints reduce the dynamic quality of the rock mass, in

the same way as they affect static stiffness. In general, jointing causes stress wave peak particle

velocity to decrease, delays wave propagation velocity and filters some frequencies. Nevertheless,

until recently, the influence of joints in the dynamic response had received far less attention than the

voids and micro cracks in the rock matrix, up to a point where joints have been treated as collections

of co-planar cracks (Myer, 2000). In the author’s opinion, this can be attributed to two reasons. The


7

first is that most rock dynamics’ research has been carried out by geophysics and petroleum

researchers. Since they tend to look to rock masses at a bigger scale than rock mechanics, the

dimension of the conceptual models is usually much larger than the joint spacing, leading to rock

mass’ idealizations in terms of distributed features and properties. The second reason is that up to

some years ago investigation methods and hardware capacity did not allow realistic discrete

representation of joints and joint sets.

King et al. (1986) performed a field test that revealed the role of rock joints in wave propagation,

separating it clearly from the effect of rock material. They blasted a charge in a vertical basalt

columnar formation while measuring the waveforms of the seismic waves in the same column and in

neighbour ones, so that it was possible to measure waves that travelled similar distances in

directions parallel and perpendicular to the predominant jointing. Three different facts were

observed when comparing the time-histories (Figure 2) corresponding to direct waves and to waves

that crossed the joints: taking in consideration their distance to the blast, the latter were delayed,

their amplitude was much lower and their principal frequencies were shifted down.

In the authors’ opinion, the main questions demanding to be answered are, then: how can we

quantify the influence of jointing in the amplitude, velocity of propagation and frequency of

transmitted waves? Can a model correctly cover all aspects? What are the major joint features,

concerning dynamic behaviour: roughness, mating, normal stress, shear stress, aperture, filling?

Kendall and Tabor (1971) recognized that the amplitude and phase delay of the transmitted and

reflected waves originated by a compression wave depend on the relation between joint normal

stiffness, impedance of the rock material and wave frequency.

Figure 2: Comparison between

compressive waves propagated

parallel and across well-defined

jointing. Taken from King et al.

(1986)


8

Later, Schoenberg (1980) expressed the joint dynamic response through its compliance, the inverse

of stiffness, managing to integrate the wave equation of P and S waves of arbitrary angles of

incidence.

Pyrak-Nolte and co-workers. (1987) expanded Schoenberg’s solution to the case of discontinuities

filled with Kelvin and Maxwell fluids: joint dynamic response is expressed by means of joint normal

and shear stiffness in parallel with fluid’s viscosity and compressibility.

The Displacement Discontinuity Theory (DDT) has been thoroughly verified by means of

measurement of transmitted ultrasonic waves across natural rock, cement and steel joints. Figure 3

shows the amplitude spectra of compressive waves after they cross intact rock and fractured rock

samples under varying compression. Wave amplitude in intact rock is similar in both samples. The

first effect that can be observed is that when compression stress is enough to close the fracture

(70 MPa) increasing it does not affect wave transmission. In a well mated fracture (mating is higher in

sample E32 and lower in E30) the transmitted wave is higher for the same compression level. It can

also be observed that under low stress (2.9 MPa) sample E32 transmits nearly nothing, while E30, the

well mated fracture, still transmits about 10 % of peak amplitude. DDT predictions of the transmitted

waves are shown in the same figure. The predicted waves are obtained by finding a joint stiffness

that generates a wave transmission function that, multiplied by the incident wave, results in a

transmitted wave that fits the wave recorded in the test. Each joint will, then, display several values

of dynamic joint stiffness. This stiffness grows with the normal stress applied to the joint, similarly to

static joint stiffness. It can be observed that theoretical and laboratory curves match is not always

perfect, especially at high frequencies, which may be caused by dynamic stiffness not being

completely frequency-independent.

Figure 3: Wave spectra from measurements and DDT predictions from fractures with good (right) and bad

mating (left) (Pyrak-Nolte et al. 1990)


9

Discussion

Although some questions remain unanswered, the existing theoretical background provides a

satisfactory theoretical framework through which fracture interference in wave propagation in rock

masses can be understood. However, there is still a gap between the laboratory experiments that

verify Displacement Discontinuity Theory and the in situ practical cases. In the field, rock mechanics

practitioners don’t work on small samples but on rock masses with extensive sets of rock joints with

little known characteristics. Some of the questions, whose answers will contribute to fill this gap, are:

Is there a direct relation between static and dynamic joint shear and normal stiffness?

What are the properties that drive dynamic response of joints? Does dynamic stiffness

depend on the same joint features as static stiffness, namely aperture or asperity

distribution, rock wall hardness, filling? What is the relative importance of each feature?

Is it possible to predict joint dynamic response by observation of joint properties?

Can a detailed rock joint numerical model (including asperity geometry and rock properties)

simulate and predict static and dynamic response?

How can the dynamic effects of fractures be represented in a numerical model that, due to

its dimension, cannot yet represent every fracture? Can dynamic properties be scaled to a

smaller number of fractures or included into a material model?


10

3. Micromechanical Modelling of Stress Waves Across Rock

Joints

To model wave propagation and capture the complete waveforms, a long, 90x600 mm, rock

specimen is produced (Figure 4). The procedure employed to generate the particle assembly is

adapted from Potyondy (2004). It is composed by 34,773 particles with radii varying uniformly

between 0.50 and 0.83 mm. Disk density is set to 3150 kg/m3 resulting in a continuum-equivalent

porosity of 2700 kg/m3. Contacts normal stiffness is set to 6.2 x 1010 N/m, 2.5 times the shear

stiffness. To define the model borders, where loads and other boundary conditions are applied, a

strip of balls is identified at the top, sides and bottom of the sample. An unconfined compression test

of the assembly shows Young's modulus is constant in the range of compressive stresses of interest

with an average value of 43.5 GPa, while Poisson's ratio is 0.2.

Figure 4: Complete model used for dynamic study of

bonded particle dynamic properties. Waves are

injected at the bottom and measured in sections 1 to

5


11

Joint behaviour simulation

Rock joints behaviour under compression has been object of less attention than shear behaviour, but

the demand for the models that realistically incorporate joint closure is driven by the simulation of

hydrocarbon reserves, thermal energy production and storage of CO2 and radioactive waste.

Particle models have been used to model static tests of rough undulating rock joints in shear

(Cundall, 2000; Kusumi et al., 2005). Gutierrez and Barton (1994) employed UDEC to represent a

shear test of a rock joint. Karami and Stead (2008) used the hybrid FEM/DEM code ELFEN to model

the shear behaviour of several JRC profiles under varying normal stresses. Several authors have

employed block discrete element and particle models in a larger scale to represent large volumes of

rock masses including several joint sets, but topography of walls discontinuities is not represented.

Inter-particle contact drives the macroscopic behaviour of synthetic rock samples, but

microproperties are not related to measurable properties like Young’s modulus or Young’s ratio

through analytical laws. Normal displacement in rock joints is mostly caused by elastic asperity

deformation followed by partial or total crushing. It is then postulated that after suffering a certain

amount of deformation and crushing the contact area of each asperity increases and consequently

the same happens to the contact stiffness. To simulate this behaviour, a new contact constitutive

model is developed and compiled, resulting in a C++ dynamic linked library that is invoked by PFC. The

constitutive model is bi-linear in shear and compression, shear strength is governed by a Mohr-

Coulomb and tensile strength is null. The force vs ball overlap curve is shown in Figure 5.

Initial and final stiffness are set as a percentage of the stiffness of the contacts in the rock material

(kn) via the multipliers dki and dkf. The point where stiffness value increases is defined as a fraction of

the radius of the smallest ball in the pair. To conserve model’s simplicity, shear and compressive

stiffness evolve in parallel, and final stiffness is equal to the rock matrix stiffness (implies that dkf=1).

The behaviour is then defined by two parameters only: initial percentage of the rock stiffness, dki,

and percentage of the radius of the smaller ball in contact that triggers hardening: dradius.

Figure 5: Joint constitutive model

diagram


12

Other strategies to represent asperity degradation were studied, such as diminution of ball radius,

ball deletion or ball breakage in a number of smaller particles. Although not completely discarded for

future developments, the alternatives have shown to be too demanding in CPU time or to complex

more difficult to implement adequately.

The normal stress vs normal displacement curve for the parameters dki=1%, dradius=10% and dkf=100%

is depicted in Figure 6. The curve shows the main characteristics of rock joint normal tests. Initial

stiffness is low due to the small number of contacts, but it increases gradually leading to an

asymptotical curve. Figure 7 shows how compressive stress going through active contacts, a great

tool to understand the mechanics of joint.

This method of joint closure modelling still needs improvement, but already provides a simple

method to model joint closure and its main features. Mechanics of joint normal behaviour is

correctly represented and, though very simple, the method of joint generation resulted in a

competent two dimensional representation of planar, low roughness, joints.

0 2 4 6

x 10-4

0

20

40

60

80

100

120

joint displacement [m]

norm

al str

ess [

MP

a]

0 1 2 3 4 5

x 1011

0

20

40

60

80

100

120

normal stiffness kn [Pa/m]

norm

al str

ess [

MP

a]

(a) (b)

Figure 6: Normal stress vs

joint closure (a) and

tangent joint stiffness (b)


13

Figure 7: Evolution of contact forces through the test, with black lines denoting compression and red lines,

tension; green balls are in contact, red balls are in contact and in the second branch of the constitutive model

Dynamic properties of Bonded Particle Models

Prior to the study of dynamic properties of the rock bonded particle models, several adaptations of

the method had to be performed. To avoid wave reflections in the boundaries, a mixed boundary

condition, in which static and dynamic loadings coexist with an absorbing boundary, is implemented

in PFC2D via a FISH function. To the authors’ knowing, this is the first time that dynamic boundary

conditions are implemented in a discrete element particle model. The hybrid boundary was

successfully tested with pure shear and compressive waves hitting the boundaries at normal angles.

Verification of the equivalence between force and displacement\velocity\acceleration loading also

had to be performed, and a method for the transition between static and dynamic analysis was

developed. Details of these developments can be found in the thesis full text.

To simulate the stress-wave interaction with the fracture it is necessary to understand how waves

are changed while they cross the dense, non-organized, bonded particle assemblies that simulate the

rock material. Waves propagating in a numerical model inevitably have their characteristics

degraded, and the principle behind wave transmission quality is that the shortest wavelength of

interest must be correctly represented. Quality requirements differ with the modelling situation: if


14

only the wave arrivals are needed, more degradation can be allowed but if peak amplitude or the

entire waveform are to be used, as is the case here, quality requirements increase.

To determine the adequate number of particles per wavelength, compressive waves with central

frequencies from 5 to 200 kHz were injected at the base of the model and measured along the

model, in the five sections shown in Figure 4. The decay of peak amplitude along the model was the

chosen quantitative indicator of wave quality. Dynamic properties of organized hexagonal and

rectangular packings were studied in parallel with the bonded particle models, the conclusions on

their properties and comparison with the rock model are reported in the thesis.

First, it was found that, as is characteristic of dispersive mediums, wave velocity grows slightly with

frequency, as shown in Figure 8. For the static properties previously presented (static Young’s

modulus of 43.5 GPa and a 0.2 Poisson's ratio) the Bonded Particle Model has a compressive wave

velocity of approximately 4200 m/s.

Regarding wave quality degradation, it was found that if a maximum amplitude loss of 5% from

beginning to end of the model is set, the wave frequency and associated wavelength/particle

diameter relation that complies is 82 particles per wavelength. It was also found that the BPM model

is much more demanding in terms of number of particles per wavelength than all organized packings.

5 10 20 30 40 80 120 150 2000.98

0.99

1

1.01

1.02

1.03

1.04

wave frequency [kHz]

variation o

f w

ave v

elo

city [

%]

BPM

Rectangular

HexaKn=Ks

HexaKn=2.5Ks

Figure 8: Relative

variation of compressive

wave velocity with peak

frequency

Propagation of compressive stress waves across fractures in BPM

Wave-fracture interaction numerical tests come in the sequence of the static joint closure tests and

on the knowledge on wave propagation gained in the previous section. At the end of each load

increment of the joint compression calculation a Ricker wave with a peak frequency of 15 kHz was

injected at the bottom boundary. The input wave, the wave that crosses the fracture (Transmitted)


15

and the wave that is bounced back (Reflected) are processed and the fracture dynamic behaviour is

calculated according to the Displacement Discontinuity Theory (Pyrak-Nolte et al., 1990).

In the joint closure tests, a vertical downwards force corresponding to the normal stress was installed

in the balls at the top boundary. In the dynamic calculation this force was maintained and an

absorbing boundary was added. The balls movement at the bottom boundary was constrained and a

Ricker waveform velocity time-history was injected there. Horizontal movement at the lateral

boundaries was constrained to prevent formation of surface waves and zero damping was used.

Figure 9 shows the wave passage across a compressed joint. One of the rewards of micromechanical

models is the visualization of this kind of fast and microscopic phenomenon. The following link opens

a movie that shows wave passage across the joint under growing normal loading, showing the

passage and reflection of the waves: http://www.youtube.com/watch?v=kqRIuH7Ougs.

22

6

(a) (b)

Figure 9: Ball velocity vectors of wave passing across fracture. Vectors and balls (left); velocity vectors only

(right)

Results and Discussion

According to the Displacement Discontinuity Theory, the analysis of the waves that originate from a

rock fracture when it is excited by an impinging wave allows the identification of the dynamic, or

seismic, stiffness of the fracture. It is expected that the more the fracture is compressed the better it

will transmit the wave.

Since the input wave frequency content ( )I and the rock impedance are known, it is possible to

find a dynamic stiffness dynk that generates transmitted and reflected wave curves ( )T and ( )R

that adjust to the ones recorded in the model. In laboratory tests of rock fractures (Cai, 2001; Pyrak-

Nolte et al., 1990, among others), a good adjustment between measured and theoretical wave

amplitudes has been observed across the frequency spectrum. Can the numerical models that mimic

the fracture microscopic deformation mechanics do the same?

http://www.youtube.com/watch?v=kqRIuH7Ougs


16

Figure 10 shows how waveforms of reflected and transmitted waves evolve as compression

increases. When the joint is lightly closed, the transmitted wave is nearly imperceptible and the

reflected wave almost equals the input wave. With increasing compression, the transmitted wave

grows and the reflected wave shrinks.

0 50 100 150 200-0.01

0

0.01 = 1 MPa

0 50 100 150 200-0.01

0

0.01 = 5 MPa

0 50 100 150 200-0.01

0

0.01 = 25 MPa

velo

city [

m/s

]

0 50 100 150 200-0.01

0

0.01 = 80 MPa

0 50 100 150 200-0.01

0

0.01 = 120 MPa

time [s]

0 50 100 150 200-0.01

0

0.01 = 17.5 MPa

Figure 10: Input (blue), Reflected (red) and Transmitted (green) waves from fracture submitted to increasing

normal stress

Since each wave passage through the joint produces a reflected and a transmitted wave, two seismic

stiffness values ( Rk and Tk ) can also be determined. This is an advantage in relation to the

laboratory tests found in the literature where only the transmitted waves are usually measured.

Figure 11 displays the fit between the reflected and transmitted frequency amplitudes and DDT’s

prediction of transmitted and reflected waves. To find these, optimal dynamic stiffness values Rk

and Tk are calculated through an optimization algorithm. This fit is better in transmitted waves,

which can eventually be explained by the fact that these are not contaminated by the incident wave.

Both model and predicted reflected waves’ central frequency increase with compression stress, but

this effect is more pronounced in the fracture model. As a whole, model and predicted transmitted

waves match up quite well, the correspondence being almost perfect in lower frequencies. It is

thought that this divergence can be due to dynamic stiffness not being constant but a function of

frequency. Pyrak-Nolte and Nolte (1992) investigated this hypothesis and found that the relation of

the wavelength to the irregular spacing between contact zones in the fracture may be the key to this

behaviour. It should be noted that the developed joint model can be used to study this hypothesis.


17

0 50 100 150 200 2500

5 = 1 MPa

0 50 100 150 200 2500

5 = 5 MPa

0 50 100 150 200 2500

5 = 17.5 MPa

0 50 100 150 200 2500

5 = 25 MPa

0 50 100 150 200 2500

5 = 80 MPa

0 50 100 150 200 2500

5 = 120 MPa

angular frequency [ 103 2/s]

0 50 100 150 200 2500

5 = 1 MPa

0 50 100 150 200 2500

5 = 5 MPa

0 50 100 150 200 2500

5 = 17.5 MPa

0 50 100 150 200 2500

5 = 25 MPa

0 50 100 150 200 2500

5 = 80 MPa

0 50 100 150 200 2500

5 = 120 MPa

angular frequency [ 103 2/s]

Figure 11: Reflected frequency amplitudes (in red, top plot) and transmitted (in green, bottom plot) frequency

amplitudes for the different normal stress tests. Predicted theoretical values are in black and the input wave, in

dashed blue, is shown for reference

As predicted by the Displacement Discontinuity Theory and observed in laboratory tests, the fracture

acts as a low-pass filter transmitting lower frequencies preferentially, this effect being stronger under

lower normal stresses. But, the wave is not completely transmitted and the reflected wave is still


18

visible under the maximum stress, meaning that the fracture is not totally closed. This is consistent

with the fracture static behaviour, since the stress-displacement curve of the static joint compression

test is also not completely vertical at the maximum stress level, possibly because the rock behaviour

is purely elastic.

The evolution of the transmitted and reflected dynamic stiffness with static normal stress is pictured

in Figure 12. The small gap between Rk and Tk is thought to be due to the better quality of the

transmitted wave. Energy conservation and the match between both stiffness values demonstrates

that the particle model correctly simulates the dynamic behaviour of rock joints. The trend followed

by the static and seismic stiffness, both being tangent values, is similar, with dynamic value being

higher. In tests of static and dynamic properties of rock and rock joints, dynamic values are generally

higher. Cai (2001) tested artificial cement mortar joints with compression stress from 2 to 20 MPa

and a central wave frequency of 20 kHz under three growing deformation velocities: quasi-static,

dynamic deformation on a dynamic press and ultrasonic waves. He found that dynamic stiffness on

wave passage tests is typically 2 to 3 times the value of dynamic deformation tests, which is itself 1.2

to 2 times the static stiffness. Seismic stiffness values are in the 20 to 1200 GPa/m range, depending

on the compression and the density of contacts in the joint. The values found in the current study are

in the same order of magnitude, increasing from 100 to 1,200 GPa/m for compression stresses of 1 to

120 MPa. On the other hand, values determined by Pyrak-Nolte et al. (1990) for transmission of

waves across natural fractures on quartz compressed up to 85 MPa yielded much larger seismic

stiffness values, from 2000 to 150,000 GPa/m. However, the wave central frequency is higher, from

500 to 1000 kHz. The static stiffness for the same samples is in the same order of magnitude but

always lower ranging from 2000 to 30,000 GPa/m.

0 20 40 60 80 100 1200

2

4

6

8

10

12x 10

11

normal stress [MPa]

join

t norm

al stiff

ness [

Pa/m

]

kStatic

kR

kT

Figure 12: Evolution of the dynamic and

static tangent stiffness with normal stress


19

Even though no viscous parcel is present in the discrete element model as it was employed and no

strain-rate effects are included in the contact models of the joint and rock material, dynamic elastic

parameters are higher than static parameters. The reasons for this difference, also found in

laboratory and field tests, are identical for fractures and for intact rock. First, due to inertia effects

when rates of deformation are high, the fractures and asperities do not have enough time to deform.

Second, the stress level induced by the dynamic wave is much smaller than the static stress. Third,

stress wave amplitude is several orders of magnitude smaller than the static stress in the joint. The

wave excites the fracture around the current location in the stress-displacement curve without

changing its configuration.


20

4. Underground Stress Wave Propagation Testing and

Simulation

This chapter describes a vibration propagation test on an underground complex set in a good quality

rock mass, followed by 2D and 3D dynamic numerical modelling. The motivation for the test was the

control of blast vibrations during excavation of a new hydraulic circuit near a hydroelectric complex.

Low intensity blasts were performed to define an attenuation law, the traditional approach. However,

this method has several, already discussed, shortcomings. This chapter develops a 3D

dynamic model that includes the effect of geological accidents in the wave path, the

“shadow” effect of excavations, the transition of vibrations from the rock to the structures.

Bemposta dam (Figure 13) is a concrete dam, with an underground circuit and a powerhouse cavern

on the right bank. Several auxiliary adits were excavated in the rock to gain access to the complex

during construction and have not been used since. The planned upgrade of the dam consisted on the

construction of a new hydraulic circuit in the right bank and the installation of a new turbine on a

circular shaft (Figure 14). The construction of involved blasting of large quantities of rock nearby the

old cavern and the dam owner was not interested in losing electricity production during the

construction.

Figure 13: The dam and the right bank of the Douro River one year after the test when the new circuit

construction was starting. The old outake is visible, as well as the end of one of the auxiliary galleries above it


21

Figure 14: Map of the dam site showing major geological features, the existing (dashed line) and planned (light

red) underground excavations at the time of the test, in 2006 (EDP 2007)


22

The powerhouse is a 19 x 25 x 76 m brick-shaped, lined cavern. The unlined auxiliary tunnels,

excavated by drill-and-blast, have 6 m wide, 4 m tall horseshoe shape (Figure 15). The interested rock

mass consists of gneissic granites and migmatites with pegmatitic intrusions. Two major discontinuity

sets were found.

Figure 15: 3D representation of the underground complex (hydraulic intake and outlet tunnels are not shown)

Low-intensity blasts were performed in the Outlet (12 blasts) and Intake (9 blasts) adits. Small

(< 0.5 kg) Gelamonite charges were installed in 25 mm boreholes drilled 1.5 m from the floor

perpendicularly to the adit’s wall. Rock mass vibration was measured by an array of six triaxial

accelerometers bases installed on adits’ walls and floor (Figure 16), on the powerhouse cavern and

elevator shaft. This thesis summary focus is on the area highlighted in Figure 17.


23

Figure 16: Data acquisition system (left), triaxial base installed in the wall of an adit (right)

Figure 17: Blasts (red) and monitoring

devices location. Cyan represents the

triaxial accelerometer, green and

yellow other measurement systems

not used in this analysis.P2 and P4 are

in opposite walls of the adit, while P3

is on the floor, and P1 is inside a

concrete plug

Results of the vibration propagation test

A peak particle velocity (PPV) vs scaled distance (R/W1/3) plot of the blasts, grouped in similar source-

target paths, is presented in Figure 18. The point cloud has the usual shape for such plots: dispersion

is high and proportional to the velocity values. The same data classified according to the blast-to-

sensors path, shows that where there is a direct path between the blast and the sensor, vibration is

stronger and dispersion diminishes.


24

Figure 18: PPV vs R/W1/3

plots: blasts divided in sets (left); blasts divided in direct and indirect paths (right)

Figure 19 shows the outcome of blast B15 and enlightens on part of cause for such a high dispersion.

P2, P3 and P4 are nearly at the same distance from the shots, but amplitude in P4 is much lower. P6,

receiving vibrations indirectly also has lower than expected vibration.

Figure 19: PPV vs R/W1/3

from blast B15

Numerical modelling of stress wave propagation

Numerical modelling of blast generated stress waves f o r vibration prediction remains relatively

unusual: practicing engineers depend almost exclusively on semi-empirical methods. The greatest

benefit of numerical models comes when they are used as a complement to observation and semi-

empirical laws, justifying and narrowing predictions, while investigating hypotheses and new

scenarios.


25

The dimension and complexity of the Bemposta site make it too large to be represented in one single

model, so partial two and three dimensional models were developed. Descriptions of the modelling

process steps are scarce, rendering the whole process still obscure. The intention of this section is to

shed some light on this process, showing how results are influenced.

The adits’ geomechanical classification, (Figure 20) shows no dramatic changes from place to place

but provides no information on the rock between the adits, since exploration boreholes were drilled to

the area outside the test volume. Migmatitc rock does show relevant schistosity, but its attitude

changes dramatically from place to place, making it hard to model. An elastic linear model with

uniform properties was used across the model. Model parameters were derived from wave velocity

measured in the test and ultra-sound core testing. Compressive and shear wave velocity were set to 4000 and

2450 m/s.

Figure 20: Geotechnical and geomechanical survey of the test adits (EDP 2007)

2D model

Nevertheless blast wave propagation being inherently three-dimensional, 2D models explore some

aspects of the modelling process. A plane model (Figure 21) is used to simulate a cross section that

intercepts the two adits involved in sets 1 and 2. The two tunnels were represented as being parallel.

The model is 61 x 48 m with 0.25 m square zones, guaranteeing good transmission of frequencies up

to 1500 Hz.


26

Figure 21: Underground complex showing the cross section of the 2D model (left); finite-difference 2D model of

blast

The blast was simulated via normal stress and velocity time-histories, applied at the face of a zone

1.5 m from the floor on the wall of the Outlet tunnel. Figure 22 shows that a stress loading replicates

reality better than velocity, so the former were applied in following simulations. Figure 23 displays

PPV from the test and the numerical simulation, measured on the walls and floor of the target adit.

The model reproduces the much lower vibration in P4, which is indirectly hit by the vibration.

Figure 22: Velocity time-histories recorded at the Target tunnel due to stress (left) and velocity (right) loading

in the source tunnel

P2

P3

P4

B15


27

Figure 23: PPV in bases

P2, P3 and P4,

normalized in P2, from

blast tests B11, B12; B13

and B15 and from the

2D model

3D model

A FLAC3D model of the final parts of the two adits including accelerometer bases P1 to P5. Figure 24

shows the model limits and a plan view of the model, with equivalent location of blast loads and

accelerometers base. Figure 25 displays perspectives of the grid, which is is 110 m long, 60 m high

and its width varies from 40 m to 110 m.

Figure 24: Representation of the underground complex showing the 3D model bounding box (left); op view of

the adits "negative" with location of blasts (blue and yellow stars) and accelerometer bases (green circles)

(right)


28

Figure 26 shows the tunnels “negatives”. The target adit, where the velocity measurements are

made, is modelled in detail, while the emissor tunnel, where blasts are simulated, is simulated in a

much cruder way, to prevent an excessive size of the model, whose grid has 640,000, 1 m long,

zones, taking about 2 Gbytes of RAM.

Figure 25: 3D model of the Surface and Outlet adits with the adits' "negative" over the grid

Figure 26: Comparison of the real geometry and the 3D grid of the source (left, top and bottom) and target

(right, top and bottom) adits


29

Comparison with test blast – reference model

The result of the numerical simulation of blast B15 (0.2 kg of explosive) is shown in Figure 27. The

match is reasonably good in P3, P4 and P5, similarly to the 2D simulation. In P1, inside the concrete

plug, the model visibly overshoots the test result.

Figure 27: Comparison

of the PPV from the test

blast and the 3D

numerical model. PPV in

bases P1 to P5 is

normalized in P2 (from

left to right: P2–P3–P4–

P1–P5)

Vibration measurement localization

This section evaluates sensitivity to small changes in the measurement locations. First, the velocities

were measured in gridpoints deviated 1.5 m from the correct locations of the accelerometers, as

represented in Figure 28. The plot in Figure 29 shows that moving the probe in the direction of the

adit’s length (“Before” and “After”) has no expressive influence, except in P1, where moving closer to

the plug hinders amplification due to the free surface of the floor. When the probe is moved up

(“Above” and “Below”) in the walls that face the blast (P2, P5), the effect is also considerable. In P4,

in the wall opposite to the blast, the lower probe receives more energy than the middle and top

ones, which is explained by the inferior blast location. There is significant amplification/attenuation

due to small changes in the way vibrations are measured, which is an important aspect of vibration

monitoring.


30

Figure 28: Views of the target adit interior showing the exact (green circles) and alternative (colored

triangles) measurement points

Figure 29: PPV evolution

when place of velocity

probing is changed in the

Surface adit’s wall and

floor (from left to right:

P2–P3–P4–P1–P5)

In a second calculation vibrations were measured along a line starting on the tunnel surface into the

rock, to find how amplitude changes when approaching a cavity. Amplitude reduction (Figure 30) is


31

explained by the free-surface amplification effect that occurs in the first three metres around the

adit. The more oblique the path between the blast and the base, the smaller the amplification. In

base P4, where waves do not arrive directly to the wall, but from above and below, there is almost

no amplification.

Figure 30: PPV evolution when

velocity is recorded in the rock

mass (from left to right: P2-P3-

P4-P1-P5)

Excavation Damaged Zone (EDZ)

It is well known that the material around a blasted excavation presents weaker mechanical

properties and higher permeability. EDZ was simulated by decreasing the elastic properties in the

first two meters around the target adit (Figure 31).

Figure 31: Seismic velocity variation as a function of radius in a blast-excavated pressure tunnel. Taken from

Kujundzic et al (1970) (left); EDZ simulation on target adit: red zones have a 70% reduction in elastic properties

(right)


32

When a stress wave crosses the interface between two materials of different elastic properties,

amplitude changes proportionally to the ratio of impedances. As EDZ stiffness is 70% smaller, the

ratio is (1/0.3)0.5 = 1.8. Figure 32 shows PPV increases by a factor of 1.7 to 2.2. Effects such as

formation of other types of waves or wave trapping in the EDZ, can also be investigated with this

model.

Figure 32: PPV evolution

EDZ (from left to right:

P2–P3–P4–P1–P5)

Geometry modelling detail – concrete plug discretization

The Surface adit ends in a concrete plug with a 5 m initial hollow part (Figure 33) where P1 was

installed. In the previous models the plug was represented from the section where it fills the whole

adit and vibration corresponding to base P1 was picked on the adit floor.

The calculation shows that a more realistic representation of the plug results in 50% lower PPV

with no effect in the other places. This puts the model’s response in this point very near to the

tests’ (Figure 27) and demonstrates, again, that PPV is very sensitive to changes in the way vibrations

are measured.


33

Figure 33: Realistic geometrical representation of the Surface adit’s concrete plug and base P1

Discussion

The contributions are grouped in three parts. First part shows that a considerable part of the

vibration dispersion is due to the path that stress waves follow from origin to destination. This is the

most important factor in this, and possibly most sites with good rock quality.

A second set of contributions derives from work not entirely presented in this summary and is linked

to the simulation of wave propagation in rock masses with excavations. The possibilities and limits of

the conditions in which wave propagation can be simulated in one, two and three dimensional finite

difference models were studied. The two-dimensional run and the parametric study of the test blast

in three dimensions helps in establishing the conditions for good numerical simulation practice in

stress wave propagation and monitoring, while also hinting on how deep a numerical analysis can go

in the exploration of this class of problems.

The most important characteristics of load representation and stress wave capture were found.

When motion is extracted in underground openings’ surfaces it is amplified, so the underground

opening geometry should be faithfully represented and motion recorded in a grid-point or node in

the exact place. Adits and caverns’ dimensions and details, lining properties or the excavation

damage zone should also be simulated accurately. Also, placement of model limits must be carefully

considered: is the representation of free-surfaces necessary or is the representation of an interior

volume surrounded by absorbing boundaries that simulate an infinite medium enough? Finally,

geometry of the place where the blast is simulated does not seem to be so important: it should

emulate the basic shape of its real correspondent in order to retain its dynamic characteristics. Blast

loads should be generated as stress/force instead of displacement/velocity/acceleration loadings.


34

5. Large Scale Underwater Blasting

Vibration nuisance level depends mainly on vibration intensity and frequency content and these

depend mainly on the charge in each blast time delay, distance from the blast location and geology

of the ground crossed by the waves. Other less relevant factors are the type of rock where the blast

occurs and the geometric configuration of the blast (existence of free surfaces, borehole length,

steeming, etc.).

In most practical situations it is not possible to monitor all structures that may be hit by vibrations so

spots where vibration is measured must be picked having in mind two goals: the immediate

protection of existing structures and future analysis that extrapolates the results to places where

measurements could not be made. Unfortunately, it is often difficult to find places that satisfy both

requirements.

The works for increasing the depth of the Leixões Harbour in a densely populated urban area

involved blasting a large volume of submerged rock. The monitoring of vibrations was achieved

through the use of several seismometers positioned according to a continuously updated plan. Upon

completion of the blasting it was necessary to provide the Harbour Administration with elements to

assess which complaints from the population (mainly related to cosmetic cracking inside buildings)

were fair. Vibrations measured at the monitoring points were extrapolated and peak velocity values

in non-monitored buildings were estimated and compared with the limits of the Portuguese vibration

code. Two different estimation methods were used. The first consisted on the classical approach of

adjusting an attenuation equation. The second method made the use of Multilayer Perceptron

Neural Networks and is presented in the complete thesis text. A velocity distribution was estimated

for the region around the harbour, allowing the drawing of iso-velocity maps.

Finally, numerical modelling was employed to study if these tools are adequate to study alternative

scenarios.

Vibration control during the Leixões harbour deepening works

The Leixões Harbour is located in the metropolitan area of Oporto, the second Portuguese city. Set

on the mouth of river Leça, the harbour is crossed on the Eastside by a 6-lane motorway (Figure 34).

The underlying inland rock mass consists of fractured alkaline granite, outcropping schist formations

are visible at the transition from land to sea, but geotechnical characteristics of the superficial

ground are not thoroughly known by the authors, as the land is heavily built. The soil overlying the

rock substratum inside the harbour area was deposited during the harbour construction. From


35

contact with the population it was learned that a number of older buildings have shallow foundations

on sand.

Figure 34: Aerial view of

the Leixões harbour

(from www.apdl.pt)

The blasting area was extensive and included the whole harbour. Monitoring points were chosen

between the blasts and the built areas, and also in some of the most representative structural

typologies. Blasting was done during 2006 by three companies. Each blast consisted of successive

detonations in boreholes arranged in a regular 2.0 x 2.5 m mesh. Electronic-delay caps were used to

reduce the instantaneous charge but in some occasions two or more explosive columns were

detonated simultaneously originating larger vibration values.

Attenuation Law

It is possible (Dowding, 1996) to establish a law that characterizes the attenuation of Peak Particle

Velocity (PPV):

PPV(W,R) = k Rm

Wn

where R is distance to the blast, W is the instant charge weight and parameters k, m and n depend

on the characteristics of the blast and propagation path. The resulting law (PPV = 1904 R-1.46 W0.31)

only gives average PPV values, meaning that there is a 50% probability that this value is exceeded in

any given blast. Therefore, an upper-limit equation, corresponding to a 5% probability was also

determined. This equation was compared with peak vibration values measured by a second entity

and was used to address populations complains with good results (Figure 35).

http://www.apdl.pt/


36

Figure 35: Attenuation

laws (50 and 95%

percentile) obtained by

non-linear regression

Figure 36 shows the distribution of peak velocities in the surrounding area of the harbour obtained

by the attenuation law and also a neural network model (not presented in this summary).Both

methods provided similar results and overall matched peak particle velocity values.

Figure 36: Iso-velocity lines calculated using the 50% regression equation (black) and neural network (red).

Velocities increase from the inside to the outside. Numbers in blue indicate monitoring stations

Numerical modelling

A FLAC3D model with 500,000 cubic-shaped zones with 3 m long sides representing a section of the

canal was built (Figure 37). Model length, width and height are is 850 m, 90 and 165 m, respectively.

Compressive and shear wave velocity are 3000 and 1500 m/s, so compressive waves with

frequencies up to 125 Hz (Itasca, 2008) are propagated without loss of quality. Absorbing boundaries

were installed in four lateral borders and at the base.


37

Loading was simulated by a negative exponential wave (Figure 38) applied within an element dug in

the centre of the channel. The actual loads consist of multiple sequential blasts, but it is considered

that the time delay is enough for each burst to generate a distinct wave. Thus, in the model, the load

simulates the explosion that causes the larger wave amplitude.

Figure 37: Finite-difference model

Figure 38: Velocity waveform of the blast function (top left) and its frequency content (bottom left), loading

location, in the bottom of channel (right)


38

Reference model

Figure 39 shows the horizontal and vertical displacement (in the x-direction) along a 500 m line

starting at the quay, going from north to south. The elliptical shape of the curve is typical of Rayleigh

surface waves.

Figure 40 shows evolution of PPV in the same alignment and, for comparison, the average

attenuation law. Unlike the law of mitigation, the curve of the numerical model is not linear (in

logarithmic space). Not being wedged to a pre-determined shape, the numerical model delivers a

more faithful reproduction of reality, especially near the source.

Figure 39: Horizontal vs vertical displacement along the surface of the model (the progression of the wave is in

the positive direction)


39

Figure 40: PPV vs distance to the

canal axis

Fault with soft soil filling

This calculation tested the influence of a vertical fault located 60 m from the quay wall (Figure 41).

For a filling stiffness that is 1/500 of the remaining rock’s, the influence of the fault width (set to 3

and 9 m) was tested. Then, for a 3 m fault width, the effect of filling stiffness (1/100, 1/500 and

1/1000 that of the rock) was studied. The PPV plot (Figure 42) shows that waves reflect at the fault,

causing amplitude to decrease after the fault and to increase between the fault and the quay wall, in

the area where the incident and reflected waves overlap. As expected, the reflection increases with

fault width and with contrast of the ground properties.

Figure 41: Detail of the 3 m (left) and 9 m wide fault, located 60 m away from the quay wall.


40

Figure 42: Effect of fault thickness (left) and fault filling stiffness (right)

Geometry and material modelling detail

This calculation tested how a greater detail in the representation of the quay wall and filling

influences vibration levels. The quay was built by filling the banks of a stream that used to run where

the channel is today with loose material. The filling material of the quay wall was modeled by

assigning it a stiffness 1/100 and 1/500 of the bank’s rock (Figure 43). The PPV plot shows that there is

a local increase of vibration intensity in the region with softer material but it vanishes with distance.

Figure 43: Simulation of quay filling material properties (left); PPV evolution with quay filling stiffness (right)

Discussion

Several finite-difference numerical models demonstrated how singularities of the ground such as

faults, or the detail in representing ground and structural characteristics, may cause considerable

variations in the amplitude of the vibration. Other scenarios addressing loading and other types of

ground singularities were studied and are not presented in this summary for lack of space. The

numerical models accuracy is proportional to knowledge on the blasting actions and the ground.


41

Results must be received and used accordingly. Due to inherent phenomenon three-dimensionality

and the demands of a dynamic calculation, even simple models are expensive from the

computational point of view, but deliver results that are an useful upgrade to traditional attenuation

laws.


42

6. Conclusions

Bonded particle modelling of dynamic rock joint behaviour

A simple method to generate a fracture in the BPM model is proposed and a contact constitutive

with stiffness hardening is employed in wall-to-wall interaction. The goal of the first part of the study

is to reproduce the response of a rock joint under normal loads. The limitations of this part of the

study are also the ground for future developments. First, rock non-linear behaviour and failure

should be integrated in the model. Second, real joint profiles are extremely varied with peaks and

valleys of different wavelengths and heights, so richer and more varied joint topographies should be

tested. Third, though having a physical meaning, the contact model parameters do not correspond to

rock joint walls measurable characteristics like hardness or wall material strength, so a

correspondence should be investigated. Fourth, 3D modelling will allow for a better representation

of the joints rich spatial variation.

On the second part of the work, the conditions for propagation of stress waves on bonded particle

models of rock were tested and a number of modelling details such as the transition from static to

dynamic calculation modes, static and dynamic load conditions and absorbing boundary were

implemented.

Then, stress wave interaction with rock fractures was simulated. Compressive waves are sent into

compressed fractures and the resulting waves are captured and compared with the theoretical

solutions. Transmitted and reflected waves are captured with good quality, energy conservation is

verified, and dynamic fracture stiffness values for both waves are in agreement. Moreover, when

dynamic and static joint stiffness are compared, the former shows to be higher, as in experimental

studies.

Underground vibration propagation and modelling

A global analysis of the test results showed that wave travel path is the main cause of high PPV

dispersion (even in such a controlled environment). A more detailed analysis of the test, by dividing it

in sets according to blasts and sensors location, and analysis of individual blasts, shows other sources

of dispersion, part of which were then studied using numerical modelling. The test was simulated in

2D and 3D models. The first showed the possibilities and shortcomings of in-plane stress wave

simulation. It was possible to run a series of different simulations that studied the impact of the way

vibration is picked up from the model, the detail of geometrical representation, rock properties

around the excavation and the input of the blast.


43

Regulations focus on above-ground structures. When protecting targets housed in caverns or

tunnels, guidance on how to perform vibration measurement is, to say the least, scarce. Vibrations

are significantly altered by excavations, so they should, if possible, be measured both in the surface

of the excavations and inside the rock mass, outside their zone of influence. Since the shape of the

excavations influences appreciably the way in which they are amplified, the placement of the sensors

should take this into account.

Large scale underwater blasting

There is a hundred to thousand-fold jump in scale between chapters and the level information on the

rock mass and detail in the model declines accordingly. In the last chapter, very little is known about

the geology, in clear contrast with previous ones, so the models employed reflect this.

High dispersion of vibration peaks is usual in most blasting situations, and this is increased here due

to the large scale of the problem. A classical attenuation model consisting on empirical laws

corresponding to different levels of confidence was developed and proved very useful to the Port

Authority during claim management. This model was complemented with a numerical model that

confirms and expands its predictions opening the way to a more sophisticated and useful method of

vibration impact mitigation.


44

Selected bibliography

Cai, J. G. Effects of Parallel Fractures onWave Attenuation in Rock. PhD thesis, Nanyang Technological University (2001).

Cundall, P. “Numerical experiments on rough joints in shear using a bonded particle model.” In F. K. Lehner and J. L. Urai (editors), “Aspects of Tectonic Faulting (Festschrift in Honnour of Georg Mandl),” 1–9. Springer-Verlag, Berlin (2000).

Dowding, C. H. Construction Vibrations. Prentice Hall International Series in Civil Engineering and Engineering Mechanics. Prentice Hall, 1st edition (1996).

Gutierrez, M. and Barton, N. “Numerical modelling of the hydro-mechanical behavior of single fractures.” In “1st North-American Rock Mechanics Symposium,” Balkema, Texas, Austin (1994).

Hudson, J. “Wave speeds and attenuation of elastic waves in material containing cracks.” Geophysical Journal of the Royal Astrophysical Society, 64: 133–150 (1981).

Karami, A. and Stead, D. “Asperity degradation and damage in the direct shear test: A hybrid FEM/DEM approach.” Rock Mechanics and Rock Engineering, 41(2): 229–266 (2008).

Kendall, K. and Tabor, D. “An ultrasonic study of the area of contact between stationary and sliding surfaces.” Procedings of the Royal Society of London, A 332: 321–340 (1971).

King, M. S., Myer, L. R. and Rezowalli, J. “Experimental studies of elastic-wave propagation in a columnar-jointed rock mass.” Geophysical Prospecting, 34: 1185–1199 (1986).

Kusumi, H., Matsuoka, T., Ashida, Y. and Tatsumi, S. “Simulation analysis of shear behavior of rock joint by distinct element method.” In Konecny (editor), “EUROCK 2005 - Impact of Human Activity on Geological Environment,” Taylor and Francis, Brno (2005).

Myer, L. R. “Fractures as collections of cracks.” International Journal of Rock Mechanics and Mining Sciences, 37(1-2): 231–243 (2000).

Potyondy, D. O., Cundall, P. A. and Lee, C. A. “Modelling rock using bonded assemblies of circular particles.” In “Rock Mechanics US’ 96,” (1996).

Pyrak-Nolte, L. J., Cook, J. M. and Myer, L. R. “Seismic visibility of fractures.” In I. W. Farmer (editor), “28th US Symposium on Rock Mechanics,” Balkema, Tucson (1987).

Pyrak-Nolte, L. J., Myer, L. R. and Cook, N. G. “Transmission of seismic waves across single natural fractures.” Journal of Geophysical Research, 95(B6): 22 (1990).

Schoenberg, M. “Elastic wave behavior across linear slip interfaces.” Journal Acoustic Society of America, 68(5): 1516–1521 (1980).

Documents

An Investigation of Stress Wave Propagation Through Rock Joints … · Ground vibration is an unavoidable side-effect and one of rock blasting’s main environmental impacts. Stress