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

_____________________________________________________________________

3

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

_____________________________________________________________________

4

_____________________________________________________________________

5

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.

_____________________________________________________________________

6

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

_____________________________________________________________________

7

_____________________________________________________________________

8

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

file:///C:/Mina%20dokumet/Dokument/Skola/LTU/X-jobb/Rapport/X-jobbsrapport%20korrigerad.docx%23_Toc302676958file:///C:/Mina%20dokumet/Dokument/Skola/LTU/X-jobb/Rapport/X-jobbsrapport%20korrigerad.docx%23_Toc302676959

_____________________________________________________________________

9

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

_____________________________________________________________________

10

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.

_____________________________________________________________________

11

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)

_____________________________________________________________________

12

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;

_____________________________________________________________________

13

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.

_____________________________________________________________________

14

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

_____________________________________________________________________

15

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

_____________________________________________________________________

16

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.

_____________________________________________________________________

17

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)

_____________________________________________________________________

18

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 *

_____________________________________________________________________

19

(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.

_____________________________________________________________________

20

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.

_____________________________________________________________________

21

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

_____________________________________________________________________

22

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

_____________________________________________________________________

23

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..

_____________________________________________________________________

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.

_____________________________________________________________________

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.

_____________________________________________________________________

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.

_____________________________________________________________________

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”.

_____________________________________________________________________

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”

_____________________________________________________________________

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.

_____________________________________________________________________

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

_____________________________________________________________________

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.

_____________________________________________________________________

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.

_____________________________________________________________________

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

_____________________________________________________________________

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.

_____________________________________________________________________

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.

_____________________________________________________________________

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

discontinuum modeling of jointed rock masses. Amirkabir University of

Technology .

Ford, A. (2007). 3DM Analyst - 3D Measurement Software.

Gigli, G., & Casagli, N. (2011). Semi-automatic extraction of rock mass

structural data from high resolution LIDAR point clouds. International Journal

of Rock Mechanics & Mining Sciences 48 , 187-198.

Itasca Consultig Group Inc. (2006). UDEC Universal Distinct Element Code -

User's guide. Itasca.

Karami, A., & Stead, D. (2008). Asperity degradation and damage in direct

shear test: A hybrid FEM/DEM approach. Rock mechanics and rock

engineering , DOI 10.1007/s00603-007-0139-6.

Kolecka, N. (2011). Photo-based 3D Scanning - Competitive Data Aquisition

Methods for Digital Terrain Modelling of Steep Mountain Slopes. Department

References

42

of GIS, Cartography and Remote Sensing, Jagiellonian University , Krakow,

Poland.

Kwang-Yeom, K., Chang-Young, K., & Lee, S.-D. (2008). Measurement of

tunnel 3-D displacement using digital photogrammetry. World tunnel congress

2008- Underground facilities for better environment and safety - India .

Somervuori, P., & Lamberg, M. (2010). Modern 3D Photogrammetry method

for rock mechanics, geological mapping, 3D model and documentation of open

pit faces and tunnels. WSP Finland .

Sturzenegger, M & Stead, D. (2009). Close-range Terrestial Digital

Photogrammetry and Terrestial Laser Scanning for Discintinuity

Characterization on Rock Cuts. Engineering Geology 106 , 163-182.

Sturzenegger, M., Stead, D., & Elmo, D. (2011). Terrestrial remote sensing-

based estimation of mean trace length, trace intensity and block size/shape.

Engineering Geology 119 , 96-111.

Svensk Kärnbränslehantering AB. (2011, April 14). SKB.se. Retrieved Augusti

31, 2011, from Nyhetsarkiv:

http://www.skb.se/Templates/Standard____31608.aspx

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

parameter and its correlation with JRC. International Journal of Rock

Mechanics & Mining Sciences .

Tonon, F., & Kottenstette, J. T. (2006). Laser and Photogrammetry methods for

rock face characterization. Report on a workshop held june 17-18, 2006 in

Golden Colorado .

William, K. P., & Haneberg, C. (2011). Photogrammetric and LIDAR 3-D

Rock Slope Discontinuity Mapping and Interpretation Surveys To Improve

Baseline Information for Supporting Design and Construction of Capital

Improvement Projects at Hydroelectric Facilities. American Rock Mechanics

Association .

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