Measurement of discontinuities for rock mass ... - Aalto

Measurement of discontinuities for rock mass characterizationEngineering geological field methods

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What can be found on this outcrop of Tampere

Schist Belt?

What are the qualitative conditions of their

formation in terms pressure and temperature?

What is the relative sequence of events?

What is “unnecessary information” if your

objective is to conclude about

The paleosedimentary environments or

temperature and pressure history of the

rocks

Find ore deposits (e.g. gold) from the

area

Find a suitable rocks for aggregate

production

Find a hard-rock aquifer

Geological field observations

Primary structures• Bedding and lamination• Graded bedding (normal grading)• Load structures

Deformation structures• Foliations (at least 2 generations of schistosity can be

found)• Folding (bending of primary bedding to subvertical)• Faulting (sinistral or left handed faults)• Joints and veins

Recording the attitude and orientation of the structures• Coordinates of observation point• Strike, dip direction and dip• Plunge and bearing (also known as trend)

Example: Urban rock engineering geology

One of the key criteria for rock

engineering is the thickness of sound

roof above the excavation

support may become too expensive

Planning project starts commonly by a

visit to a local (municipal) civil

constructions department /geotechnical

office

Digital data

Maps

Tunnel images

Reports

Mapping of

Design of investigation program

• Drilling and core sampling- Public areas are limited!

- Basements of existing buildings, existing tunnels and underground spaces

- Increasingly using electric rigs

- Almost entirely oriented drilling

• Geophysics- Borehole to borehole, or borehole to surface methods

- Possibility use e.g. explosive in seismic sounding is increasingly limited!

• Rock mechanical measurements- In-situ stress measurements by overcoring/hydraulic fracturing

- Modelling

• Geostatistics and geometric modelling

o Leapfrog, Move, Gocad..etc

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Field observations and core logging

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Scanlines

Image interpretation

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Aalto Start-UP

LaDiMo Oy

Jorma PalménCto, founder+358 50 5259028 jorma.palmen@aalto.fi duo

Metsänneidonkuja 10, 02130 Espoo, Finland

Otaniemen opetustunneli, 3,5

miljoonaa pikseliä

Stochastic models and 3d-visualizations

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Engineering geological challenges in Mines

Characterization of rock joints

and fracture zones

Stability of excavations

• Cold conditions in open

pits

• Strong horizontal stresses

in underground mines

• Alteration and weathering

along fractures, joints and

micro cracks

• Minerals with adverse effects to mineral processing

• Clays, sulfates, talc,

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Data collection

Core logging and mapping of

both mining geological and

engineering geological data - RQD, disking

- oriented drill cores

In most underground tunnels

and mines tunnels are

systematically shotcreted- no working allowed in unsupported

areas

Geological mapping

”competes” against time with

bolting and shotcreting

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Stereophotogrammetric

imaging in Kittilä mine

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Measuring methods

Stereophotogrammetry and image interpretation

New point-cloud methods

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Data sources

Open point cloud+ q-compass software

Point-clouds to grid+ interpretation of attitude (strike, dip direction and dip)

DSE Discontinum set extraction

An open source software where you can combine point-cloud grid and image and

subsequently, analyze fracture parameters

https://www.holcombe.net.au/software/

Stereonet

DIPs software

Tutorial for Terzhagi-correction

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• Fracturing effects– Stability and risks of rock fall

– Drillability (stucking)• Depends also on the rock type

(hardness, mineralogy)

• Density of fractures

– Blasting

– Excavation• Optimal fracture density for

dimension stones and aggregates

Selected technique

Even when rocks can be excavated by ripping (left), the direction of ripping should be in the direction of the dip!!

Directional distribution of discontinuities

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Stereoplots

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1:rako 11:rako 1

2:rako 2

2:rako 2

3:luiska

3:luiska

N

S

EW

OrientationsID Dip / Direction

1 70 / 2652 50 / 1403 65 / 175

Equal AngleLower Hemisphere

0 Poles0 Entries

Stereoplots for

Visualization of dataMeasurement of angles and directionsDistinction of patterns and joint setProbabilistic distribution analysis

Projection hemisphere

Lower or upper hemisphere projection

• lower hemisphere more common

• Graphs are otherwise identical but

• A 180-degree error possible if not mentioned which projection used

Wulff’s stereographic projection

• Equal angle projection

• preserves angles

Schmidt’s projection

• Equal area projection

• Preserves visual density of poles

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Planar structures

The attitude of planar geological structures

• Kulku (strike), kaadesuunta (azimuth, dip direction), kaade (dip) o Define 2 vector directions that are needed to define the plane orientation

Pole vector (normaali vektori) is an alternative way to determine the orientation (attitude ) of a plane

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Linear structures

- Kaadesuunta (engl. Trend tai bearing, tai plunge direction), kaade (plunge)

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Other orientation data

Structures related to underground construction

• Plunge and bearing of the drill hole direction

• the direction where drilling has proceeded

- E.g. in an underground tunnel, a drill hole plunging 45 degrees can be inclined upwards or downwards

- Most commonly negative plunge indicated upward direction, positive downwards!

• Kallioleikkaustasot

Kalliossa vaikuttavat voimat

• Vektoreita, joiden suunta voidaa esittää stereografisella projektiolla (magnitudia ei)

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b- and p-plots

Planes can be represented as projected cross-lines (b-plot)

or as projected crossing points of the normal vector of the planes (p-plot)

b-plot clear only when there are about less that 10 planes

p-plots used for larger data sets

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How to measure the orientation of the intersections of

two planes

Solution 1. Draw two great circles. (Read the

intersection as a linearstructure, example A)

Solution 2: determine the intersection of two planes

by using their normals

• Normal vectors (poles) of the two planes define (a fictious) plane. The normal this third plane is the intersection line

of the two original ones

Equal angle -projektion

Wulff’s projektion

Note that the projection takes

place through the point T

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Unit area spheres

(1 % the total area)

Pitch and rake

Alternative ways to express orientation:

”Pitch” and”rake”

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111/45

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Equal area -projection

Schmidt-net

Does not disturb density distribution

of linear structures

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Unit area spheres

(1 % the total area)

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• Distribution of

poles

• examples

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Deformation analysis

Note also how rake/pitch can be read along the small circle

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Applications in engineering and mining geology (and rock mechanics)

• Quantitative estimates

• Confidence limits and statistical parameters of theestimates

• Examples of possible distributions

• Uniform, point distribution, plane, girdle

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How statistical distribution of orientation data is

described?

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– Uniform

– Point distribution

– Girdle

– We need quantitative estimates!

Why I do not use

term random?

Directional cosines

For calculations of vectors (lineation,

normal of plane or borehole trend

and plunge) are expressed as

directional cosines

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Fisher-distribution on stereografic projection

• Fisher-distribution on sphere (theoretical background)- http://digital.library.adelaide.edu.au/dspace/bitstream/2440/15264/1/249.pdf

- http://www.jstor.org/pss/2346346

• Shape of point distribution can be described by a K-term (k like concentration) and a unit vector l,

• In addition to dip direction (a) and dip (b) and trend (a)and plunge (b), l can be expressed with its directional cosines in NED-coordinates:- ln, le, ja ld (northing, easting, down)

- Linear structures. Poles of planes

- ln= cos(b)×cos(a) ln= -sin(b)×cos(a)

- le= cos(b)×sin(a) le= -sin(b)×sin(a)

- ld= sin(b) ld= cos(b)

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Properties of Fisher-distribution?

Basic underlying assumption of Fisher distribution: directional vector population is randomly

distributed around some mean vector

Statistical sample driven out of this distribution (randomly selected vectors i.e. geological

observations) is distributed and scattered around ”the mean vector orientation”

The observation vector deviates from the mean vector by an angle q..(q+dq) with probability of P(q)

Where n is defined based on the following:

• A collar with which has a width of dq and deviates from the ”real” direction by angle q, has a surface area proportional to sin q

• Cumulative probability= 1

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( ) qnq q dP K coseKK e

K--

e

sinqn

Calculation of mean vector

Assuming N observations randomly distributed around a mean:

1) calculate the arithmetic means of directional cosines

2) Length of the resultant vector

(2)

3) Estimate directional cosines of the mean vector (estimate based on N samples)

(3)

4) Calculate dip direction and dip/trend and plunge

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( ) ,/ Nlc nn ( ) ,/ Nlc ee ( ) Nlc dd /

222

den cccR ++

,/ Rcl nn ,/ Rcl ee ,/ Rcl dd

Directional dispersion/concentration

Assuming N directional observation (lineations or poles to plane) randomly

distributed around some mean vector,

Their distribution can be estimated based on Fisher’s K-parameter.

• K can get values from zero (uniform distribution) to infinity (all parallel, ”single point”).

• K-parameter can be roughly estimated (when R>0.65) (4) or when N>30 (5)

K= 1/(1-R) (4)

• (5)

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https://www.rocscience.com/help/phase2/webhelp/phase2

_model/Fisher_Distribution.htm

Confidence limit of the mean vector estimate

Confidence limits can be represented as cone of confidence on the stereonet,

Forms a circle around the mean vector

If N ×R×K > 3 the semi-apical angle

Where a it the probability (0,01 when the confidence limit is 0.99 or 99 %)

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)/(ln1arccos KRNad +

Bingham-distribution

• Can be applied to all three types of directional distribution

• Assumes orthogonally symmetric distribution

• Can be used to assess 3D-distributions

• And to produce confidence limit estimates

• Starts from calculation of eigenvalues and -vectors for observation data

• Confidence limits are elliptic cones, with semi-epical angles d :

t1

t3 (largest Eigen value)

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( )( )( )1

2

3

2

2

2/2

12

sincos

1sin

ttt

t

-+

-

--

mm

ad

N

( )( )( )3

2

2

2

1

2/2

32

sincos

1sin

tttt

-+

--

--

mm

ad

N

Eigen vectors of directional data

Magnitudes of Eigen vectors (Eigen values) can be used to describe the orientations

l1 l2 l3 uniform distribution

l1 > l2 l3 girdle

l1 >> l2 > l3 point distribution around a mean vector

Rakoparvien ominaisvektoreita voidaan käyttää myös paleojännitystilan määrityksiin

(mm. konjugaattirakoparvien ja haarniskapintojen suunta-analyysi)

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How to calculate Eigenvectors for directional data

Transfer dip and dip direction to directional

cosines

Calculate summs of directional cosines and

represent them in a matrix form

Calculate A with the matrix and its transpose

Eigenvalue equation has the following form where

x is not a zero vector

• X is Eigen vector and lamda is the Eigen value

• Lamda’s can be calculated from the determinant in thebracket

(e.g. Matlab, excel)

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( ) ( ) ( ) zen lclbla ,,

c

b

a

( ) Acba

c

b

a

xxA l

( ) 0- xIA l

Bootstrap-jakauma

• To generate a bootstrap uncertainty estimate for a given statistic from a set of data, a subsample of a size less than or equal to the size of the data set is generated from the data, and the statistic is calculated. This subsample is generated with replacement so that any data point can be sampled multiple times or not sampled at all. This process is repeated for many subsamples, typically between 500 and 1000. The computed values for the statistic form an estimate of the sampling distribution of the statistic.Forexample, to estimate the uncertainty of the median from a dataset with 50 elements, we generate a subsample of 50 elements and calculate the median.

http://www.itl.nist.gov/div898/handbook/eda/section3/b

ootplot.htm

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Paper 103, CCG Annual Report 12, 2010 (©2010)

Relating Different Measures of Fracture Intensityhttp://www.ccgalberta.com/ccgresources/report12/2010-103_different_measures_of_fracture_intensity.pdf

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Modern fracture modelers generally characterize fracture intensity in one of the following ways:

Lineal fracture intensity, expressed as the number of fractures per unit length (L‐1 ).

Areal fracture intensity, expressed as the number of fractures per unit area (L‐2 ).

Volumetric fracture intensity, expressed as the number of fractures per unit volume (L‐3 ).

Areal fracture density, expressed as length of fracture traces per unit area (L‐1 ).

Volumetric fracture density, expressed as the area of fractures per unit volume (L‐1 ).

Fracture porosity, expressed as the volume of fractures per unit volume of rock

(dimensionless).

Fracture Counts: The total number of fractures. Can be measured along a line, in an area, or in

a volume.

Fracture spacing and intensity of a fracture set

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Direction of measurements(borehole, traverse)

Direction that we want actually to measure = normal to the fracture set

δ

mittaussuunta(kairareikä, traversi)

suunta, jonka rakotiheyden haluamme mitata = rakoparven normaalin suunta

δ

Directional bias

A principal problem for fracture analysis is that results measurements depend

direction of measurement

What is needed to estimate is the fracture intensity in “ the mean normal direction”

N fractures l length

l fracture intensity

ls observed fracture density at the scanline

Observed fracture density is ”biased” by factor cos d

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scanline

suunta, jonka rakotiheyden haluamme mitata = rakoparven normaalin suunta

δFracture intensity of a rock- The result can be extended to the case where the contains more than one fracture

sets (m sets)

- Observed frequency along scan line intensities i:th set

- The contributions of each set to the observed intensity could be summed as

- According to Terzaghi (1965)the are still bias-effects on the measurements?

• E.g. if there are fractures that are striking closely the observation line e.g. d = 87 degrees?

o The accuracy of dip/dip direction measurement by compas is about +-2 degrees

o Fractures can be undulous which makes assessing di and dip direction even more difficults

Impact of Cos d values can become too high and have a strong effect

Whan can be done to recude the bias?

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lsi intensity of a single set along a

scanline

li intensity of a single set

ls fracture intensity along scanline

ls length of scanline

Ni (weighted) number of samples

Reduction of sampling bias

To measure fracture intensity we should actually have 3 orthogonal directions

(luxury) and average the measurements (no bias correction needed, theoretically!)

We can carry out the weighting procedure:

For fractures wich have their normal ”semiparallel” to the observation line, the

weight is fixed to a value that correspond to the accuracy limit value of the

measurement (typically 5 to 15 degrees)

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Weighted number of fracture

• In borehole measurements/scan-linemeasurements

• Cosine of angle between the normal of thediscontinuity and the measurement direction is a weighting factor (or a coefficient of vectormagnitude)

• Weighting can be done by (treating each fracture as a fracture set) calculating a weighting factor (cos d)

• Can be calculated if dip and dd of a discontinuityand trend and plunge of the scan-line or borehole is known

• for d> e.g. 85o d=cos 85o

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scanlineunta(suunta, jonka

rakotiheyden haluamme mitata = rakoparven normaalin suunta

δ

Example

Example

Mira Markovaara-Koivisto

(2017, PhD-manuscript)

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Terzaghi-correction and sampling bias

Assessment of 3d-distribution of fractures based

on 1D-measurements such as boreholes always

involves a bias

• Unweighted borehole measurement underestimate density of fractures parallel to the borehole!

• Furthermore: boreholes can be curved!

• Weighting factor taking this into account is known as Terzaghi-correction

• Logging procedures will be a topic of one of the lecture and excercise

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More about statistical treatment of fracture data

Priest, S., D., 1985. Hemispherical Projection Methods in Rock Mechanics. George

Allen & Unvin

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What are these rocks?

Foliation?

Bedding / layering

A fracture surface from each

What are these rocks? Origin!

Foliation

Bedding / layering

A fracture surface from each?

Fracture minerals?

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What are these rocks? Origin!

Foliation?

Bedding / layering?

Fold axis

What are these rocks? Origin!

Foliation?

Bedding / layering?

Foliation?

Natural fractures? Roughnes?

Or just man made surfaces

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What are these rocks? Origin!

Foliation?

Bedding / layering?

Foliation?

Natural fractures? Roughnes?

Or just man made surfaces

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What are these rocks? Origin!

Foliation?

Bedding / layering?

Foliation?

Natural fractures? Roughnes?

Or just man made surfaces