MASTER'S THESIS
DETERMINATION OF JOINT SHEARSTRENGTH USING
PHOTOGRAMMETRY
Mikael NilssonFilip Wulkan
Master of Science in Engineering TechnologyCivil Engineering
Luleå University of TechnologyDepartment of Civil, Environmental and Natural Resources Engineering
Avdelningen för Geoteknologi
Institutionen för Samhällsbyggnad och Naturresurser
Luleå tekniska universitet
971 87 LULEÅ
DETERMINATION OF JOINT SHEAR
STRENGTH USING PHOTOGRAMMETRY
Authors: Mikael Nilsson and Filip Wulkan
Luleå 2011
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Foreword
This report is the result of a joint venture by Luleå University of Technology,
Luleå Sweden and The University of New South Wales, Sydney Australia. The
bulk of the work has been carried out at UNSW under the supervision of Glenn
Sharrock PhD UNSW.
The report is a mandatory part of the Master Thesis examination at LTU, and
will serve as a foundation of continued research within the associated subject.
We would like to extend our gratitude to Bergsprängningskommittén
Stockholm, and the Erik Tanner Foundation for their financial support as well
as Glenn Sharrock – UNSW for his academic support.
We would also like to acknowledge Jenny Greberg – LTU whom initiated this
project and lastly our examiner Catrin Edelbro – LTU for her input on the final
version of this thesis.
Mikael Nilsson, Filip Wulkan
1/9/2011 LULEÅ
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Abstract
This master thesis presents the development and finalization of a procedure
document useable for determination of joint shear strength. The procedure is
presented as a step by step instruction ranging from the imaging of a rock sample
to evaluation of the acquired data and the generation of a numerical model.
Imaging is performed using a Camera with a fixed lens in combination with the
photogrammetry software 3DM CalibCam and 3DM Analyst. The resulting
photogrammetry data is exported in the form of a data terrain model (DTM). The
DTM is used to generate the input to a numerical shear-box model using a
combination of Microsoft Excel and numerical analysis (UDEC). The shear box
model emulates a push-pull test where the upper block is forced to move across
the surface of the lower block while subjected to a constant normal load.
Evaluation of the DTM accuracy is carried out by means of a laser scan. The
DTM and the laser scanned surface are compared using computer assisted design
(CAD) software. The comparison proves that the DTM is accurate on a scale
smaller than one millimeter.
As part of future research, calibration of the model will be performed using shear
strength data from actual push pull test on the same block sample. The constant
normal stiffness will be taken into account by an alteration of the boundary
conditions.
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TABLE OF CONTENT
FOREWORD ...................................................................................................... 3
ABSTRACT ........................................................................................................ 5
TABLE OF FIGURES ........................................................................................ 8
1 INTRODUCTION ..................................................................................... 9 1.1 Background ...................................................................................... 9 1.2 Aims and objectives ....................................................................... 10 1.3 Scope .............................................................................................. 10
2 LITERATURE REVIEW ........................................................................ 11 2.1 Photogrammetry ............................................................................. 11 2.2 Roughness ...................................................................................... 14
2.3 Bartons joint model ........................................................................ 16
2.4 Numerical modeling ....................................................................... 19 2.5 UDEC theory ................................................................................. 20
3 METHODOLOGY .................................................................................. 22
3.1 Equipment ...................................................................................... 22 3.2 Photogrammetry ............................................................................. 23
3.3 Surface data evaluation .................................................................. 27 3.4 Numerical modeling ....................................................................... 30
4 RESULTS ................................................................................................ 33 4.1 Photogrammetry ............................................................................. 33 4.2 Surface data evaluation .................................................................. 34 4.3 Numerical modeling ....................................................................... 35
5 ANALYSIS ............................................................................................. 36 5.1 Photogrammetry ............................................................................. 36 5.2 Surface data evaluation .................................................................. 36
5.3 Numerical modeling ....................................................................... 36
6 DISCUSSION ......................................................................................... 37
7 CONCLUSIONS ..................................................................................... 39 7.1 Future research ............................................................................... 39
8 REFERENCES ........................................................................................ 41
9 APPENDIX ............................................................................................. 44
9.1 APPENDIX 1 ................................................................................. 44
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Table of figures
FIGURE 1 SHOWS JRC PROFILES .................................................................................. 9 FIGURE 2 SHOWS A VISUAL ILLUSTRATION OF THE RELATIONSHIP BETWEEN L0* AND * ....... 18 FIGURE 4 SHOWS THE BLOCK ROUNDING AT CORNER ..................................................... 21 FIGURE 5 SHOWS THE PLACEMENT OF THE PINS ............................................................ 23 FIGURE 6 SHOWS POINT GENERATION......................................................................... 24 FIGURE 7 SHOWS 3DM ANALYST PREPARING A DTM ................................................... 24 FIGURE 8 SHOWS AN UNDRAPED DTM MODEL, THE GRAY SQUARES SHOW CAMERA POSITION
WHEN THE PICTURES WERE CAPTURED ................................................................ 25 FIGURE 9 SHOWS A DRAPED DTM MODEL. ................................................................. 25 FIGURE 10 SHOWS THE LASER SCAN IN PROGRESS ......................................................... 26 FIGURE 11 SHOWS RESULTS FROM THE LASER SCAN ....................................................... 26 FIGURE 12 SHOWS THE TWO DTMS .......................................................................... 27 FIGURE 13 SHOWS THE REMAINING DATA ................................................................... 28 FIGURE 14 SHOWS THE ZONED MODEL AFTER DISCRETIZATION ........................................ 32 FIGURE 15 SHOWS THE FINAL DTM SURFACE IS IN FORM OF A DRAPED SURFACE ................ 33 FIGURE 16 SHOWS A HISTOGRAM SHOWING TRUE DEVIATION BETWEEN POINTS FROM THE
LASER SCAN AND THE POINTS ACQUIRED THROUGH PHOTOGRAMMETRY .................... 34 FIGURE 17 SHOWS THE FINAL SHEAR-BOX MODEL ......................................................... 35
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1 INTRODUCTION
1.1 Background
In 1977 N.Barton and V.Choubey published “The shear strength of Rock Joints
in theory and Practice” in which the Mohr-Coulomb shear strength equation
(Itasca Consultig Group Inc, 2006)
(1) for a joints shear strength was criticized and subsequently substituted with the
new standard equation (1.1)*.
(1.1)
New variables introduced were “joint compressive strength” (JCS)=the
compressive strength of the joint wall, r=residual friction angle (derived using
the basic friction angle and Schmidt rebound on both dry unweathered sawn
surfaces as on wet joint surfaces) and the “Joint Roughness coefficient” or
JRC. JRC is a measurement of the surface roughness of a joint subjectively
given a number between 0 and 20 depending on
the resemblance to any of the Barton standard
profiles [1]. Figure 1 shows JRC profiles.
Due to the subjectivity of the roughness
evaluation and its influence on the equation a
more exact, while still easily implemented,
evaluation method would be desirable.
Today advances in digital imagining and
photogrammetry software may hold part of the
solution as the subjective “translation” of the
physical joint surface to actual input data can be
handled by computer software. Software in turn,
is easily standardized and will produce consistent
roughness values independent of the user, making
a standardized numerical shear strength model plausible.
*The equation (1.1) was first published by N.Barton in 197, current standard
according to Bryan et al (Tatone & Grasseli, 2010)
Figure 1 shows JRC profiles
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1.2 Aims and objectives
The aim and objective of this thesis is to develop a new procedure for factoring
in the joint roughness in shear strength evaluation. This procedure will replace
the subjective JRC estimation performed by personnel in the field with
software based evaluation of the surface roughness. By shifting from manual to
automatic raw-data interpretation more consistent roughness values will be
produced regardless of collection point. The new model will also make it
possible to shear one sampled surface repeatedly under increasing normal
stress. This option is not available for physical lab test as shearing will
irretrievable alter the characteristics of the sample, the model on the other hand
can easily be reset to its original state.
1.3 Scope
Due to the fact that according to Barton (Barton & Choubey, 1977) joint
surface roughness is a major factor of influence for unfilled joints only, this
thesis will concentrate on unfilled joints only.
As a proof of concept photogrammetry evaluation will be performed on a lab-
sized sample only (Hawkesbury sand-stone), large/field scale imaging is
outside the scope of this thesis.
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2 LITERATURE REVIEW
2.1 Photogrammetry
According to (Tonon & Kottenstette, 2006) the use of photogrammetry greatly
simplifies analysis of large portions of rock mass including inaccessible and
hard to get to areas compared to traditional mapping. The ability to collect
large sets of data gives a more realistic picture of joint orientation and provides
details that easily could be overlooked by manual mapping. A 3D model can be
saved for the future to be used as reference at a tunnel construction that later
will be shotcreted. Photogrammetry saves both time and money and will not
affect the production in mining as much as traditional mapping. The limitation
for photogrammetry is however all about distance/accuracy dependence. For
determination of JRC high-resolution close up images are required. The
lighting also plays a crucial part for the accuracy of the model. Capturing
images in a tunnel requires a lot of light to prevent shadow formation, shadows
significantly reduces the accuracy on the model (Tonon & Kottenstette, 2006).
In Sweden photogrammetry has been used to map tunnels in great detail. Using
photogrammetry cracks, water, rocks and minerals can quickly be mapped.
During the construction of the nuclear fuel repository in Forsmark
photogrammetry has been used by the geologists to get a more precise and
detailed general view over the tunnel. Photogrammetry makes the work easier,
more efficient and more accurate than traditional mapping. During traditional
mapping, all the geological data must first be written down by hand and
structures located on the tunnel wall must be sketched. Finally the data must
still be input into a computer system for storage and advanced analysis.
(Svensk Kärnbränslehantering AB, 2011).
A number of commercial photogrammetry software are available, the function
of this software ranges from simple DTM creation to advanced discontinuity
evaluation with respect to location, dip and dip direction. Examples of software
are Maptek VULCAN used in combination with Adam Technologies 3DM
analyst (Birch, 2006), (Sturzenegger, M & Stead, D, 2009), SiroVision
SiroJoint (William & Haneberg, 2011) and Photomodeler Scanner (Kolecka,
2011).
To become familiar with the 3DM Analyst Mine Mapping Suite chosen for
work in this thesis the user guide written by Adam Technology (Ford, 2007)
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was studied and referenced in part below. 3DM Analyst and 3DM CalibCam
are both Photogrammetry software using the principle of converting 2D images
to 3D models. This is done by using multiple images of the same surface/object
captured in slightly different angles. Referring to locations (points) that can be
easily identified on all images, the model is created by projecting one image
over the other. In order to achieve an acceptable degree of accuracy the camera
used must first be calibrated. 3DM CalibCam is a camera calibration and block
adjustment program, designed to be used with 3DM Analyst.
CalibCam is suitable for use regardless of the distance to, and scale of, the
target object, both lab size samples and terrestrial areas can be successfully
modeled. Important is that the camera used has a mounted fixed lens, lenses
allowing zooming must not be used.
The most popular targets are open pit or rock faces/cuts, tunnels and aerial
topography. For tunnel work special research is carried out to optimize
lightning, camera mount and image capturing techniques. In tunnel application
the distance to target is quite fixed and the accuracy of the result surface is
about 5 mm, which also makes it possible to do shotcrete thickness calculations
(Ford, 2007).
In a case study by (Kwang-Yeom, Chang-Young, & Lee, 2008) at the Magu
tunnel at Cheongwon-Sangju Express Highway it was shown that
photogrammetry can be used to measure displacement in a tunnel. 12 points on
the right and left wall was pre-surveyed using a total station, the points were
also imaged by digital photogrammetry with a camera distance of 5 to 20m.
The distance between the points was compared for the DTM and the total
station measurements, a average deviation of 2-3mm could be observed
between the methods. Systematic measurement was shown to be the most
important factor for making reasonable support decisions.
Both photogrammetry as well as laser scans might be used for discontinuity
detection and evaluation. In 2009 (Sturzenegger, M & Stead, D, 2009)
published a paper on this subject in which three locations were surveyed using
both laser scanning and digital photogrammetry. The software used for the
photogrammetry image processing was DM CalibCam and 3DM Analyst
developed by Adam Technologies. Each location was imaged using 5 different
set-ups and the accuracy and precision of the distance to pre-determined points
as well as the dip and strike of pre-determined discontinues evident in the
resulting DTM was evaluated for each set-up. The set-ups are described in
short below;
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A - The line-of-sight of the camera/laser scanner is measured with a compass.
The scale is provided through measurement of the distance between the two
camera positions. The tilt must be zeroed, the use of a tripod is necessary.
B - Three sets of photographs are taken from three surveyed camera positions,
with this approach no control point is located near the rock cut. The use of a
tripod is necessary to keep the camera at constant location
C - Six or more targets are located on a rock cut and surveyed with the total
station, No camera/scanner position needs to be surveyed
D - One surveyed control point is located in the field of view in addition to two
surveyed camera stations, The use of a tripod is necessary
E - Three targets are located at right angles indicating the z and x (or y) axes of
a local reference system, the distance between two targets is measured to
provide the scale.
- The set-up descriptions are quoted from the article, some information have been
omitted –Authors comment
Accuracy is determined by measuring the distances to a few pre-determined
points surveyed by total station, the accuracy is defined as the sum of the
deviation from these surveyed distances and the modeled distances divided by
the number of control points. The precision is defined as the standard deviation
of the accuracy. The dip and strike of the control discontinuities was mapped
using a compass clinometer.
The point accuracy was found to be highest (having the lowest deviations) for
set-up C followed by D and last B, A and E could not be evaluated for
accuracy since the lack of surveyed points means only relative-only points are
generated and the DTM is created in a local coordinate system not connected
to the real world (there is no camera – point distance to evaluate). In spite of
this A and E may be evaluated for precision since the relative distances to the
control point within the DTM as well as the true distances are known. For B,
C and D precision is highest for C and lowest for B the same order as for the
accuracy. A and E have significantly lower precision than B,C and D. The
numerical values of accuracy and precision vary from a few millimeters for C
to around 1m for the worst case in each location.
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The discontinuity evaluation is not significantly influenced by the set-up used
but also here set-up C yields the best results when compared to the field
measurements. Taking into account known sources of error a deviation of 4°
and 6° from the field measurements are denoted to represent dip and dip-
direction respectively (Sturzenegger, M & Stead, D, 2009).
In 2011 (Kolecka, 2011) published a paper in which the results from large scale
photogrammetry and terrestrial laser scanning (TLS) was compared. TLS
works by analyzing a reflected laser pulse, both regarding arrival time and
intensity. In some devises the intensity of the reflected laser pulse is used as
indicators of materials of different characteristics, the intensity values are
evaluated with respect to the optical wavelength. TLS field equipment is in
general heavy and cumbersome compared to photogrammetry devices which
are basically nothing more than “of the shelf” digital cameras. The simplicity
of photogrammetry equipment also means less training for the operators and
faster execution, low texture features may however prove difficult to image
properly. Systems incorporating both sensor techniques are available.
In order to compare the two techniques a 300m high rock slope was imaged
using both TLS and photogrammetry. The distance between target and sensor
was 200-1150m for the photogrammetry camera and 1650-2250m for the TLS.
The end result showed a deviation between the data sets of 0.25 ± 0.12 m
(Kolecka, 2011).
(Sturzenegger, Stead, & Elmo, 2011) Made an attempt to estimate the trace
length and trance intensity in a rock mass using photography in combination
with laser scanning. The endeavor was not completely successful as the trace
length were systematically underestimated compared to values obtained from
field mapping (scan-line) at the same time as the trace intensity was
overestimated for the same sampling window. The same year Gigli et al (Gigli
& Casagli, 2011) attempted a similar experiment using laser scan only while
using a Matlab algorithm to evaluate the modeled surface instead of
commercial software. Gigli presents data with good correlation to field mapped
data but still emphasizes the need for “...field analysis based on geologic
experience …in order to validate the semi-automatically extracted data..”.
2.2 Roughness
According to (Tatone B, 2009) the surface roughness of unfilled rock joints has
a large influence on the behavior of rock masses. Most of the researches have
been restricted to small joints surfaces. That means that the large-scale
components of roughness are often neglected. That can lead to an
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underestimation of roughness which can lead to miscalculations and false
assumptions about the behavior of rock masses.
Under low stress conditions rock mass behavior is mostly controlled by sliding
along existing discontinuities rather than failure of the intact rock material
(Tatone B, 2009). That means that roughness is an exceedingly important
factor at engineering at shallow depth e.g. a tunnel or a road cut.
Close-range photogrammetry for rock mass characterization including the
measurement of discontinuity surface topography was first proposed in the
early 1970`s by Barton et. al (Tatone B, 2009) This work led to the inclusion of
photogrammetry as a suggested method for measurement discontinuities but
the method was limited due to the difficulties of automating the computations
required to extract 3D data.
Tatone also shows that the discontinuity roughness increases as a function of
the sampling window size contrary to what was commonly assumed. More
importantly, it is shown that the estimated roughness significantly decreases as
the resolution of surface measurements decrease, which could lead to the
under-estimations of roughness and, consequently, discontinuity shear strength.
This master thesis can be a base to produce a better way to determine the
roughness for a joint surface even if the now work is in laboratory scale, a large
scale test can be done in similar way.
Today advances in digital imagining and photogrammetry software may hold
part of the solution as the subjective “translation” of the physical joint surface
to actual input data can be handled by computer software. Software in turn, is
easily standardized and will produce consistent roughness values independent
of the user, making a standardized numerical shear strength model plausible.
The research indicated that photogrammetry can be a fine alternative to get an
approximate image of a joints surface roughness, which can give a better value
and decrease miscalculations in engineering in for example a tunnel project or
a road-cut. (Tatone B, 2009)
(Asadollahi & Tonon, 2010) Did in 2010 a critical review of the Barton shear
strength equations, the emphasis was on how the Barton - Brandis equations
predicts post-peak shear strength, dilation and surface degradation. The main
problems stated is that according to Barton et al the peak shear displacement is
independent of normal stress as well as zero dilatation is developed up to one-
third of the peak shear displacement, experimental results show that this is not
always the case. In addition Asadollahi et al presents an equation in which the
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peak shear displacement decreases with increasing JRC (2.1), that is rougher
joints need smaller displacements to reach peak shear stress than smooth joints.
This conclusion is the opposite of what was shown by Barton in the 1980´s (2).
(2)
(2.1)
The Barton Brandis shear strength equation (1) is found to be accurate in
replicating the experimental shear strength results related to the data used by
Asadollahi et al to develop their modified equations.
2.3 Bartons joint model
The information in the following subchapter is based on the work of (Barton &
Choubey, 1977)
The first and foremost divider when characterizing rock joints is to determine if
the rock joint is in-filled or unfilled. For an unfilled rock joint the joint
characteristics such as roughness and compressive strength are all important
whilst for an in-filled joint the fill materials properties dominate the behavior.
Due to the nature of this report only material regarding unfilled joints will
be quoted – Authors comment.
There are several external factors that determine the shear strength of rock
joints such as moisture and normal stress. The unconfined compression
strength of a rock may decrease with up to 30 % when comparing “air dry”
samples to samples “saturated in situ”, this means that for a minimum field JCS
wet joint surfaces should be tested in favor of dry samples. Shear strength of
joints tend to increase under increasing normal loads especially for joints with
high values of JCS and JRC. This is due to a change in behavior from sliding
on to increased crushing of asperities. The proper determination of JRC is thus
more important in low stress environments where JRC more strictly govern the
behavior. As for the problems related to scale effects they can be addressed by
a two step test. First a reduced JCS may be roughly estimated by reducing the
original value by a factor of i.e. 2.5 for dense rocks. Push pull or tilt tests may
then be carried out and a scaled JRC can be derived through back-calculation.
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JRC can be calculated from tilt test by usage of the equation
(2.2)
Where =arctan(0/n0)
Barton stresses that “- an underestimation of r results in an overestimated JRC
value, and vice versa. This automatic compensation of errors is one reason for
the method providing such accurate estimates of peak arctan [/n.])” (Barton
& Choubey, 1977)
Note that the equation (2.2) is only Barton’s shear equation (1.1) solved for
JRC;
Using numerical shear-tests may produce similar results as from in-situ push-
pull tests, thus might Barton’s shear equation be used for back calculation of
JRC using the model described in section 3.4 – Author’s comment
In 2010 (Tatone & Grasseli, 2010) published a paper presenting a new 2D
discontinuity parameter to replace the manually determined JRC. The
parameter is based primarily on two assumptions; the shearing of a
discontinuity is related to a breakage of part of the sheared surface only and
this breakage is found at asperities which have a dip direction opposing to the
shear direction. To determine if an asperity is opposing the shearing or not the
variable * is introduced and denoted a value e.g. 5°. That is all sections of a
joint representation dipping between 5 and 90° towards the shear direction will
be considered as opposing surfaces. * is additionally connected to the term
L* which is the normalized section length defined as
(3)
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Where L0 is the normalized
length of the profile
corresponding to an angular
threshold of 0°,*max is the
maximum (encountered)
inclination of the profile and C is
a dimensionless fitting
parameter. Figure 2 Shows a
visual illustration of the
relationship between L0* and *.
A four step procedure has been
developed for the determination
of the joint roughness using these
new parameters. The first step is
acquisition of the sections that
will be analyzed, this might be
done by either manual methods
such as use of profilometer or
automated methods like laser
scanning or photogrammetry.
The second step is alignment,
sections are aligned through a
“best fit” plane and in the
direction of intended shear.
Thirdly the aligned profiles are
evaluated using equation 3 for
the value of *max/(C+1). The last step is to analyze the results from the
evaluation step, in the paper by Bryan et al this comparison is made with
values derived from a 3D roughness evaluation not described in the paper.
The new parameter *max/(C+1) is evaluated in relation to JRC by digitalized
versions of the Barton – Brandis standard profiles. This results in two
equations depending on the sampling interval:
(for 0.5mm sampling interval) (3.1)
Figure 2 Shows a visual illustration of the
relationship between L0* and *
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(for 1.0mm sampling interval) (3.2)
2.4 Numerical modeling
(Bondakdar & Martazi, 2009) imported digitalized versions of Barton’s
profiles from Jprofiler and JRefiner into UDEC to examine the influence of
roughness. The sampling scale used was 1 (one) centimeter thus disregarding
roughness related to asperities of lesser amplitude. The influence of roughness
was examined using two basic models, a block sliding down an inclined
surface and a shear box working under constant normal load, asperity damage
was evaluated from plastic zones.
Even though the results from this study were in good agreement with the
Barton 1977 equation the sampling scale and lack of actual surface samples, as
well as the proposed damage evaluation technique, leaves the question on
digitalized interpretation of joint roughness open.
Also (Karami & Stead, 2008) evaluated joint roughness using a FEM/DEM
model and digitalized versions of Barton’s standard profiles. A virtual shear
box was constructed and Barton profiles of JCR 8-10 and 18-20 were sheared.
The main quantity being investigated was shear displacement and dilatation,
damage to asperities was evaluated using Rankine failure incorporated into a
Mohr-Coulomb model. The models were in good agreement with Barton’s
laboratory tests but just as for the previously described paper no actual joint
surfaces were investigated.
According to (Tatone B, 2009) several optical instruments have emerged
during the last decades as a good and attractive alternative for measuring
discontinuity surfaces both in the laboratory and on site. These systems
include, among others, terrestrial photogrammetric systems and laser ranging
devices.
Today powerful photogrammetric-software and high quality digital cameras are
available and a photogrammetric system is a fast, inexpensive and accurate
method to measure the surface of a small or large joint surface.
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Using line segments obtained from actual high resolution site photos instead
for those derived from the standard profiles should increase the validity of a
UDEC model based on roughness profiles.
2.5 UDEC theory
The information in the following subchapter is based the manual from (Itasca
Consultig Group Inc, 2006)
UDEC is a distinct element program using discontinuum analysis, that is the
program is able to incorporate joints and contacts into the calculations as well
as calculations regarding the homogeneous rock mass. This means that two
types of mechanical behavior must be accounted for: the behavior of the
discontinuities and the behavior of the solid material. The behavior of the
discontinuities are modeled as changing boundary conditions, the behavior of
the entire model is determined by a time step algorithm.
The time step algorithm creates a dynamic environment where forces and
displacements are calculated for each time step depending on the movement of
the blocks (each modeled block is divided into an assembly of discrete blocks
by discretization), the time step is sufficiently small that the disturbances
caused by the movement cannot propagate between two blocks during the time
step itself. Thus with each new time step new contact forces between
neighboring blocks are generated and new movement is initialized. This
continues until the resultant forces nears zero and no more movements are
initialized and thus the model approaches equilibrium, the time step will also
cease if continuing failure occurs.
As previously stated discontinuities in the rock mass are considered as
boundary conditions or as contact surfaces, data elements are created at all
gridpoints along the boundary (for deformable blocks) to represent point
contacts, calculations are not carried out for the entire length of the
discontinuity but only at the specified point contacts. To prevent “hang ups” of
rotating blocks due to sharp corner-to-corner contacts a rounding is applied to
the block shape to allow smooth sliding, this corresponds to the real behavior
of sharp corners being crushed due to extreme stress concentration. Figure 3
shows the block rounding at corner.
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Figure 3 shows the block rounding at corner
One should also note that the point contacts are created separately for each
block, that is that where two blocks are in contact two unique point contacts
may be created at the exact same coordinates but “belonging” to different
blocks. In other words, the data elements belong to the individual blocks and
not the discontinuity which is not a true object but a boundary condition.
Due to the characteristics described above UDEC is chosen as the
programming base for the numerical model in section 3.4 - Author’s comment
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3 METHODOLOGY
This section contains a chronological description of the steps needed to create
and evaluate a Digital Terrain Model (DTM) using photogrammetry and
numerical modeling.
3.1 Equipment
3DM Analyst is used to create the initial DTM. 3DM Analyst is a product of
Adam Technology, Perth, Western Australia. The target of the software is to
create a 3D model from two or more digital 2D images. This is done by finding
same points on each image and projecting rays into the scene through the
perspective centre and thus finding the location where the rays will intersect.
3DM Analyst uses an algorithm named “least square bundle block adjustment”.
To navigate the model a relative only coordinate system is used (relative only
implies that only the relative distance between the points is know, not the
placement of the points in “the real world”. With eight known points, and thus
the distance between, them 3DM Analyst can generate a 3D model with very
high accuracy. (Somervuori & Lamberg, 2010)
For the purpose of data collection, a camera –Canon EOS 5D mark II, with
remote release and tripod is used to take a series of images. The images are
then to be digitalized in CalibCam 2.1. The 3D model (DTM) is constructed in
3DM Analyst. Rhinoceros 4.0 slices the model into linear segments
(coordinate-lines). To determine the accuracy of the model a Faro Platinum
laser scan is used to. The laser scan has a precision of 0,3mm (this number is
derived from the experiments described in section 3.3.
The sample used is a piece of sandstone of size of 195*145 mm, the sample is
cut from a larger block, the modeled surface is a natural joint. To simplify the
creation of the relative only coordinate system pins are glued on the examined
surface for easy determination of natural points, the 2D distance (denoted here
as X and Y direction) between the pin “tips” is recorded for later (see section
3.2).
The images of the stone is captured from two slightly different directions, the
capture distance is small in order to achieve a higher resolution of the joint
surface. The actual distance is around 0.5 meter from the stone and
approximately 0.3 meter between the two camera stations. To get correct
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camera calibration with the correct adjustment a camera calibration file is used
in CalibCam (the calibration file was supplied by Adam Technology).
Using relative orientation 3D images are created within a locally generated
coordinate system. These images can be measured by the known eight points
on the stone with known distance in x and y.
In order to produce a good DTM (digital terrain model) over 200 images and
30 models were created. The images were taken both in laboratory and
outside. The best images were captured in the laboratory with a natural
background and the distance between the target and the camera around 0.5
meters with 0.3 meters between the camera locations.
3.2 Photogrammetry
Figure 4 shows the placement of the pins
To achieve the correct scale on the digitized image both natural points and
relative only points are used. Relative only points are automatically generated
between a pair of images. These points provide common points between two
photos and are used to construct the 3D images. Natural points (manually
denoted from pin locations, see section 3.1) are used to be scale the model
using the scale bars tool. With known distance between the pins CalibCam can
scale the model; Figure 4 shows the placement of the pins, Figure 5 shows
point generation
_____________________________________________________________________
24
Figure 5 shows point generation
The simplest way to digitize the relative-only points is by a relative-only
orientation execution (coordinate-system generation) followed by a resection
and a bundle adjustment. The project is then saved and exported to 3DM
Analyst in order to create a 3D model over the surface, Figure 6 shows 3DM
Analyst preparing a DTM. 3DM Analyst finally creates the DTM.
Figure 6 shows 3DM Analyst preparing a DTM
Figure 7 shows an undraped DTM model, the gray squares show camera
position when the pictures were captured, Figure 8 shows a draped DTM
model..
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25
Figure 7 shows an undraped DTM model, the gray squares show camera
position when the pictures were captured
Figure 8 shows a draped DTM model.
To determine the accuracy of the model a laser scan over the photographed
surface is carried out. Figure 9 shows the laser scan in progress, in order to
simplify comparison with the photogrammetry data the pins (se section 3.1) are
allowed to remain on the surface even after the creation of the photogrammetry
DTM.
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26
Figure 9 shows the laser scan in progress
Figure 10 shows results from the laser scan
The result from the laser scan is a DTM in *.DXF format, Figure 10 shows
results from the laser scan.
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27
3.3 Surface data evaluation
Before the data from the photogrammetry software may be used for the
generation of a numerical model the accuracy of the data must first be
evaluated, this subchapter aims to outline the procedure used for this
evaluation
A contour / landscape 3D surface (DTM) is exported from 3D Analyst (blue)
into the CAD program Rhinoceros 4.0 together with a laser scan (green) of the
same surface, Figure 11 shows the two DTMs. Using unique and easily
determined control points (pins) on the object the two surfaces are rotated into
the same position in 3D-space.
Figure 11 shows the two DTMs
In order to simplify the data evaluation the two surfaces are cropped to include
only areas found in both data sets. Due to problems during the laser scan data
corresponding to a small square in the mid section of the surface is missing, the
relative size of the affected area led to the conclusion that cropping of this area
in both data sets should not compromise the validity of the evaluation.
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28
Figure 12 shows the remaining data
Both surfaces are sliced into line segments and overlapping data is compared,
Figure 12 shows the remaining data, by exporting point coordinates to a excel
spreadsheet. Creating line segments with fixed initial coordinates means that
the lines will exactly follow one coordinate axis which in turn can be used for
line or row identification. Due to the arbitrary rotation of the surfaces in the
global Rhinoceros coordinate system the line segments are in this example
created along the z-axis, resulting in a number of two dimensional line
segments with two corresponding row numbers (one for the laser scan and one
for the photographed surface), see Table 1- Line-strings exported from
Rhinoceros” row-by-row”.
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29
Photo Laser
X Y Row number X Y Row number ABS diff Diff
400,034 -58,867 537,277 400,034 -58,487 537,277 0,380 0,380
399,534 -58,858 537,277 399,534 -58,315 537,277 0,543 0,543
399,034 -58,899 537,277 399,034 -58,283 537,277 0,616 0,616
398,534 -58,701 537,277 398,534 -58,286 537,277 0,415 0,415
398,034 -58,529 537,277 398,034 -58,253 537,277 0,276 0,276
397,534 -58,432 537,277 397,534 -58,244 537,277 0,188 0,188
397,034 -58,373 537,277 397,034 -58,237 537,277 0,136 0,136
396,534 -58,394 537,277 396,534 -58,226 537,277 0,169 0,169
396,034 -58,346 537,277 396,034 -58,230 537,277 0,116 0,116
395,534 -58,303 537,277 395,534 -58,233 537,277 0,070 0,070
395,034 -58,306 537,277 395,034 -58,169 537,277 0,137 0,137
394,534 -58,276 537,277 394,534 -57,923 537,277 0,353 0,353
394,034 -58,293 537,277 394,034 -57,805 537,277 0,489 0,489
393,534 -58,216 537,277 393,534 -57,852 537,277 0,364 0,364
393,034 -58,172 537,277 393,034 -57,829 537,277 0,343 0,343
392,534 -58,181 537,277 392,534 -57,719 537,277 0,462 0,462
392,034 -58,151 537,277 392,034 -57,797 537,277 0,353 0,353
391,534 -58,092 537,277 391,534 -57,835 537,277 0,257 0,257
391,034 -58,030 537,277 391,034 -57,849 537,277 0,181 0,181
390,534 -57,991 537,277 390,534 -57,895 537,277 0,096 0,096
390,034 -57,963 537,277 390,034 -57,960 537,277 0,003 0,003
389,534 -57,973 537,277 389,534 -58,024 537,277 0,051 -0,051
389,034 -58,159 537,277 389,034 -58,093 537,277 0,066 0,066
388,534 -58,266 537,277 388,534 -58,200 537,277 0,066 0,066
388,034 -58,313 537,277 388,034 -58,361 537,277 0,048 -0,048
387,534 -58,384 537,277 387,534 -58,522 537,277 0,137 -0,137
387,034 -58,513 537,277 387,034 -58,680 537,277 0,167 -0,167
386,534 -58,726 537,277 386,534 -58,863 537,277 0,137 -0,137
386,034 -58,933 537,277 386,034 -59,045 537,277 0,111 -0,111
385,534 -58,998 537,277 385,534 -59,170 537,277 0,172 -0,172
Table 1- Line-strings exported from Rhinoceros” row-by-row”
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30
For two lines with the same row number a point has been generated on each
line at coordinate x, the location on the line, and coordinate y, the relative
height of the asperity. Comparing the relative height of points with the same
location of two corresponding lines gives the deviation between the data from
the laser scan and the data from photogrammetry. Numerical results are
presented under section 4.1.
All photogrammetry data is exported as .txt files and imported into Microsoft
Office Excel 2007.
3.4 Numerical modeling
The numerical model is written in Itasca UDEC code format using Microsoft
Excel to auto-generate input-lines in response to imported coordinates. The
Excel workbook consist in this case of three work sheets; input, code
generation and output. Explanatory screenshots of the two first worksheets can
be found in appendix 1, “output” is copied VALUES of “code generation”,
“output” is after completion of code generation copied to a .txt file. The .txt file
is then CALLed by UDEC.
Input:
Raw coordinates are imported from .txt files, import options are chosen so that
x, y and z coordinates are stored in separate columns.
Code generation:
Model scale is in meters, a maximum of 3 decimals are used.
Rounding of the model is set one order of magnitude smaller than the rounding
of the joint data (if joint data is rounded to the closest millimeter the model
rounding is 1/10 millimeters)
The block (model outline) is a rectangle whose dimensions are determined by
the joint data as seen in Table 2 block generation tablet.
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31
Table 2 block generation tablet
The rough joint is modeled by reading the coordinates from the input sheet in a
repeating pattern following the CRACK command; see Table 3 Principle of
CRACK command generation.
Table 3 Principle of CRACK command generation
CRACK Xn Yn Xn+1 Yn+1
CRACK Xn+1 Yn+1 Xn+2 Yn+2
CRACK Xn+2 Yn+2 Xn+3 Xn+3
Apart from the modeled joint two secondary rough joints are generated two
millimeters above and below the original joint in order to enable discretization
of different density in different parts of the model (zoning is denser close to the
modeled joint). For the secondary joints the same basic data as for the
modeled joint, displaced ±2mm, is used but subjected to a higher degree of
rounding (2 to 1), this produces joints of roughly the same appearance but with
significantly fewer data-points.
In order to be able to zone the model a vertical joint must also be generated
thru the model, the joint is in this case modeled thru origin, the reason for this
is the internal memory allocation subroutine built into the code. Figure 13
shows the zoned model after discretization, the window has been zoomed to
show only the mid section of the model.
Block X1 Y1 X2 Y2 X3 Y3 X4 Y4
From joint
sample
xmin ymin-
0,3m
xmin ymax+0,3m xmax ymax+0,3m xmax ymin-
0,3m
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32
Figure 13 shows the zoned model after discretization
Rock properties are assigned using a general PROPERTY MAT command.
Two sets of joint properties are assigned, one for the modeled joint and one for
the secondary and vertical joints. The properties of the secondary and vertical
joints should be chosen so that the behavior mimics the intact rock, the
properties of the modeled joint are true joint properties.
The joint properties are assigned using the JOINT MODEL AREA command
in combination with a RANGE based on the same syntax as displayed in table
3.
The model is then discretized and histories are placed where needed for any
specific run, model is solved to an equilibrium state and new boundary
conditions are given to initiate shearing of the joint, preferably by use of the
XVELOCITY command.
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33
4 RESULTS
4.1 Photogrammetry
The methodology of creating a DTM is outlined in section 3.2. The final DTM
will be sectioned for evaluation and modeling purposes. Figure 14 shows the
Final DTM surface is in form of a draped surface.
Figure 14 shows the Final DTM surface is in form of a draped surface
The DTM is exported as a draped triangular surface rather than a point cloud to
simplify sectioning in later steps. The averaging error due to the triangular
surface approximation is assumed to be insignificant.
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34
4.2 Surface data evaluation
Before the data acquired from photogrammetry is used for model generation
the accuracy of the imaging is tested, the methodology for this test is outlined
in section 3.3
Mean and median deviation are calculated for absolute values of deviation
since for the intended application the relative deviation is important in contrary
to the true mean where deviations of opposite signs cancel each other out.
Mean deviation for this set up was 0,285mm, median 0,199mm and the largest
single deviation recorded was 3,35mm, Figure 15 shows a histogram showing
true deviation between points from the laser scan and the points acquired
through photogrammetry
Figure 15 shows a histogram showing true deviation between points from the
laser scan and the points acquired through photogrammetry
0
500
1000
1500
2000
2500
-2 -1,5 -1 -0,5 0 0,5 1 1,5 2
Freq
uen
cy [n
um
ber
of p
oin
ts]
Range [mm]
Distrubution of devaiation between surfaces
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35
4.3 Numerical modeling
The data from the photogrammetry imaging is used for model generation
according to the methodology outlined in section 3.4. Figure 16 shows the
Final shear-box model is the end result. The final model emulates a push-pull
test where the upper block is forced to move across the surface of the lower
block while subjected to a constant normal load.
Figure 16 shows the Final shear-box model
Failure is modeled by separation of the blocks in combination with
elastic/plastic failure of the asperities. The model has not been calibrated to
accurately the sample due to lack of lab test data. Because of this there are no
numerical results to present.
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36
5 ANALYSIS
5.1 Photogrammetry
The DTM is a full 3D surface is the sense that it can be rotated in any direction
in 3D space yet it is still only a 2D surface in the sense that it has no “depth”
meaning that the thickness of the surface infinitely small.
5.2 Surface data evaluation
The frequency of points deviating more than 0,5mm in either direction is
considered so small that the data set obtained from photogrammetry is
considered accurate enough to be used as input data into a numerical model
with an accuracy of 1mm.
5.3 Numerical modeling
The lack of strength parameters from lab tests prevents the calibration of the
shear box model. The function of the model has been tested using “mock” data
to show block separation, extremely high joint normal stiffness was used to
prevent the UDEC “contact overlap” error.
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37
6 DISCUSSION
Photogrammetry is in this thesis evaluated for a lab-size sample, it is however
still possible to draw conclusions related to photogrammetry and numerical
modeling as a whole from the experiments performed within the scope of the
work.
A problem with large scale photogrammetry might be to generate a proper 3D
Model over the target only. In the laboratory scale trials a common problem
was when the DTM generation was attempted not only the sought area but
often the bi-areas (background) were modeled as well. For subterranean
imagining lighting is of great importance as it was observed that shadows on
the images will dramatically reduce the accuracy of the DTM. In good lighting
conditions off the shelf equipment will as is shown in this thesis produce
acceptable results when an accuracy of 0.1-1 mm is required.
The advantages of photogrammetry over laser scanning are mainly economical.
Even though the analysis of photogrammetry data may sometimes be more
labor intensive the bulk of the work hours will be put in at the office rather than
on site. Laser scanning equipment and set-up will in many cases cause longer
disturbances at the production site (subterranean construction excluded) than
what is required for simply capturing a couple of image pairs. In addition
photogrammetry will produce more bi-data such as color of the rock mass
which in turn can later be used for determination of rock type and indicate
streaks of intrusive rock.
The choice to use UDEC for the numerical modeling is of course connected
with both advantages and problems. Initially the continuum modeling code
_____________________________________________________________________
38
FLAC was considered as an alternative to the discontinuity code UDEC. The
choice whether to model a rough joint in a continuum or discontinuum
environment is not as straight forward as it might seem at first glance. UDEC
was never developed to model rough joints per say, only to imitate them using
joint shear stiffness and predetermined dilatants behavior. Modeling of the
shear behavior in FLAC could have been achieved by allowing plastic failure
around a zone defined by the rough joint which is a well defined within the
code. The determining factor in the choice of code-environment was the option
to incorporate Voronoi tessellation to model the failure rather than to rely on
plastic failure. The preparation of Voronoi tessellation was a request from the
University of New South Wales and was attempted but had to be abandoned
due to lack of time and calibration data. Instead the choice was made to model
shear failure by separation of blocks and elastic/plastic deformation of
asperities, block separation is well defined in the UDEC environment and the
inherent problem of modeling rough joints was overcome by substituting the
rough joint by a large number of intersection smooth joints initially without
denoted shear stiffness.
The numerical model scale was set to 1mm as a compromise between
computation time and model accuracy. In addition the aim was to create a
general model for determination of shear strength in relation to a rock mass. If
asperities of to low magnitude are modeled the individual grains in a rock will
start to influence the strength in the way that failure will be influenced by the
bounding-strength between individual grains. Even though this is an important
part of the rock strength the modeling will be infinitely more complex as the
different mineral grains constituting a rock type may be associated with greatly
differing bound-strength. Modeling on a scale of 1mm will in the majority of
rock types utilize asperities of such magnitude that the strength parameters are
the same for all asperities (in a way the mean of the mineral bound-strength)
whilst still achieving an acceptable accuracy of the failure stress.
_____________________________________________________________________
39
7 CONCLUSIONS
The main conclusions of this thesis are
By usage of photogrammetry, it’s possible to create a digitalized joint surface
of such accuracy that it can be used as input to a numerical model.
A numerical model can be designed and prepared so that joint data, in the form
of line segments, by a simple set of commands, can be imported to produce a
virtual shear box set-up.
The off the shelf equipment used for this thesis is advanced enough to achieve
the objective of the thesis.
7.1 Future research
To continue this work the numerical shear-box model should be calibrated
using laboratory tests on the photographed rock sample or equivalent data to
produce true shear strength.
Once the model has been calibrated for plastic failure Voronoi tessellation
should be utilized to study the failure-behavior on the asperity scale.
Additionally Field test of large scale discontinuity mapping should be
attempted for shear strength determination of natural failure surfaces
.
References
41
8 REFERENCES
Asadollahi, P., & Tonon, F. (2010). Constitutive model for rock fractures:
revisiting Bartons emperical model. Engineering Geology 113 , 11-32.
Barton, N., & Choubey, V. (1977). The Shear Strenght of Rock Joints in
Theory and Practise. Rock Mechanics 10 , 1-54.
Birch, S. J. (2006). Using 3DM Analyst Mine Mapping Suite for Rock Face
Characterization. ADAM Technology , Western Australia.
Bondakdar, A., & Martazi, A. (2009). Implementation of Joint roughness into
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Ford, A. (2007). 3DM Analyst - 3D Measurement Software.
Gigli, G., & Casagli, N. (2011). Semi-automatic extraction of rock mass
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of Rock Mechanics & Mining Sciences 48 , 187-198.
Itasca Consultig Group Inc. (2006). UDEC Universal Distinct Element Code -
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Karami, A., & Stead, D. (2008). Asperity degradation and damage in direct
shear test: A hybrid FEM/DEM approach. Rock mechanics and rock
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Methods for Digital Terrain Modelling of Steep Mountain Slopes. Department
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Photogrammetry and Terrestial Laser Scanning for Discintinuity
Characterization on Rock Cuts. Engineering Geology 106 , 163-182.
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Engineering Geology 119 , 96-111.
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31, 2011, from Nyhetsarkiv:
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Tatone B. (2009). Quantative Characterization of Natural Rrock Discontinuity
Roughness In-situ and in the laboratory. University of Toronto .
Tatone, B. S., & Grasseli, G. (2010). A new 2D Discontinuity roughness
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Tonon, F., & Kottenstette, J. T. (2006). Laser and Photogrammetry methods for
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References
43
Appendix
44
9 APPENDIX
9.1 APPENDIX 1
Layout of “input” spreadsheet
x y z -0,0031904505 63,5102360000 1,3114029410 -0,0031904505 62,5243861600 1,5526259610 Joint data -0,0031904505 61,5242520300 1,5757908960 Jkn 1,00E+16 1,00E+15 -0,0031904505 60,5237929200 1,6613827720 Jks 1,00E+16 1,00E+15 -0,0031904505 59,5229720400 1,8164746070 Jfrict 27 30 -0,0031904505 58,5229915400 1,8101257810 Jcohes 0 1,00E+07 -0,0031904505 57,5228711900 1,8306421640 jtens 0 2,00E+07 -0,0031904505 56,5209563200 2,1958909980 -0,0031904505 55,5186237900 2,6413733720 -0,0031904505 54,5161319500 3,1174592640 -0,0031904505 53,5144958900 3,4291482920 -0,0031904505 52,5136822600 3,5828465230 -0,0031904505 51,5116148700 3,9773951660 -0,0031904505 50,5096036800 4,3611457680 -0,0031904505 49,5095630000 4,3663585680 -0,0031904505 48,5096899600 4,3393657640 -0,0031904505 47,5111478700 4,0566958580 -0,0031904505 46,5103338500 4,2104688860 -0,0031904505 45,5096541200 4,3384431980 -0,0031904505 44,5100184700 4,2658477470 -0,0031904505 43,5090431200 4,4506117810 -0,0031904505 42,5083148700 4,5879076230 -0,0031904505 41,5063841300 4,9562049730 -0,0031904505 40,5066550000 4,9015688430 -0,0031904505 39,5062395500 4,9787750920 -0,0031904505 38,5060507800 5,0124350420 -0,0031904505 37,5071150300 4,8053869300 -0,0031904505 36,5068688600 4,8500741800 -0,0031904505 35,5071309400 4,7971250850
Coordinate strings from Rhinoceros
Appendix
45
jcohes ='Joint data'!$I$7
=L1002
='Joint data'!$G$7 range =B7 =D7 =C7 =E7
='Joint data'!$G$7 range =B8 =D8 =C8 =E8
='Joint data'!$I$7 range =B149 =D149 =C149 =E149
='Joint data'!$I$7 range =B150 =D150 =C150 =E150
Layout of “code generation “spreadsheet
; number of decimals + on order of magn round 0.0002 ; xmin ymin xmin block =AVRUNDA(MIN('Joint data'!B:B)/100;3) =AVRUNDA(MIN('Joint data'!C:C)/100-0,3;3) =B4
; x1 y1 x2 crack =OM(G7=FALSKT;AVRUNDA('Joint data'!B2/100;3);0) =OM(G7=FALSKT;AVRUNDA(('Joint data'!C2)/100;3);0) =AVRUNDA('Joint data'!B3/100;3) crack =OM(G8=FALSKT;AVRUNDA('Joint data'!B3/100;3);0) =OM(G8=FALSKT;AVRUNDA(('Joint data'!C3)/100;3);0) =AVRUNDA('Joint data'!B4/100;3) crack =OM(G9=FALSKT;AVRUNDA('Joint data'!B4/100;3);0) =OM(G9=FALSKT;AVRUNDA(('Joint data'!C4)/100;3);0) =AVRUNDA('Joint data'!B5/100;3) crack =OM(G10=FALSKT;AVRUNDA('Joint data'!B5/100;3);0) =OM(G10=FALSKT;AVRUNDA(('Joint data'!C5)/100;3);0) =AVRUNDA('Joint data'!B6/100;3) crack =OM(G11=FALSKT;AVRUNDA('Joint data'!B6/100;3);0) =OM(G11=FALSKT;AVRUNDA(('Joint data'!C6)/100;3);0) =AVRUNDA('Joint data'!B7/100;3)
crack 0 -2 0 prop jmat=1 jks ='Joint data'!$I$5
prop mat=1 dens=2700 g =D1002
joint model area jks ='Joint data'!$G$5 jkn joint model area jks ='Joint data'!$G$5 jkn joint model area jks ='Joint data'!$I$5 jkn joint model area jks ='Joint data'!$I$5 jkn
ymax xmax ymax xmax ymin =AVRUNDA(MAX('Joint data'!C:C)/100+0,3;3) =H4 =E4 =AVRUNDA(MAX('Joint data'!B:B)/100;3) =C4
y2 Control =AVRUNDA(('Joint data'!C3)/100;3) ; =OCH(D7=0;E7=0) =AVRUNDA(('Joint data'!C4)/100;3) ; =OCH(D8=0;E8=0) =AVRUNDA(('Joint data'!C5)/100;3) ; =OCH(D9=0;E9=0) =AVRUNDA(('Joint data'!C6)/100;3) ; =OCH(D10=0;E10=0) =AVRUNDA(('Joint data'!C7)/100;3) ; =OCH(D11=0;E11=0)
2 ; for zoning jkn ='Joint data'!$I$4 jfrict ='Joint data'!$I$6 jtens ='Joint data'!$I$8
k =F1002 ten =J1002 cohes
='Joint data'!$G$4 jfrict ='Joint data'!$G$6 jtens ='Joint data'!$G$8 jcohes ='Joint data'!$G$4 jfrict ='Joint data'!$G$6 jtens ='Joint data'!$G$8 jcohes ='Joint data'!$I$4 jfrict ='Joint data'!$I$6 jtens ='Joint data'!$I$8 jcohes ='Joint data'!$I$4 jfrict ='Joint data'!$I$6 jtens ='Joint data'!$I$8 jcohes