lecture 7 rock fracture mapping

8/13/2019 Lecture 7 Rock Fracture Mapping

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MAPPING OF ROCK FRACTURES USING 3-D LASER SCANNING TECHNIQUE IN ANAUTODESK 3-D STUDIO MAX ENVIRONMENT

A. K. L. Kwong and C. F. LeeDepartment of Civil Engineering, The University of Hong Kong

Hong Kong, China ( [email protected] and [email protected])

ABSTRACT

During the process of investigation, design and upgrading of rock slopes, the orientation and spacing of structuraldiscontinuities or joints in a rock mass should be thoroughly mapped in the field so that any unstable blocks can beidentified and stabilization measures designed. The orientation of structural discontinuities is traditionally measuredmanually using geological compass placed directly at the exposed surfaces. Scaffolding is usually erected to enable thegeologist to physically access the exposed rock surface. A large number of measurements are usually required in orderto obtain a statistical mean of the fracture orientation. With the ongoing advances of digital technology, 3-D laserscanning technique can be used to replace direct physical access and large number of manual measurements can becompletely eliminated. A prototype system is described in this paper that combines the non-contact measurementtechnologies of photogrammetric imaging and 3-D laser scanning to create dimensionally accurate and pictoriallycorrect 3 dimensional models and orthoimages of rock fractures. By taking photographs from at least two differentlocations, lines of sight are mathematically intersected to produce the 3-D coordinates of the key reference points in arock face. Automatic 3-D laser scanning unit is then used to produce the 3-D coordinates of the entire rock surface. Byoverlapping the images rectified from photogrammetry technique with the coordinates from 3-D laser scanning in anAutodesk 3-D Studio Max environment, the coordinates of any objects in the photographs can be selected and theirorientation such as dip angle and dip direction calculated automatically. A case study is presented to compare the

orientations of fracture planes measured using geological compass and that from the prototype system developed.KEYWORDS

Rock slopes, fracture spacing, dip angle, dip direction, photogrammetry, 3-D laser scanning, Autodesk 3d studio max.

INTRODUCTION

Hundreds of slopes in Hong Kong are being investigated, designed and upgraded every year to reduce the likelihood oflandslides and the potential loss of life and economic losses. During the process of investigation, design and upgradingof rock slopes, the orientation and spacing of structural discontinuities or joints in a rock mass must be thoroughlymapped in the field so that any unstable blocks can be identified and stabilization measures designed.

Conventional mapping of rock joint orientation and spacing requires scaffolding to access to the rock face so that ahand-held geological compass can be placed directly at the rock joint surface to obtain the dip angle (maximum angle ofa plane relative to horizontal) and the dip direction (angle measured clockwise from the north to the line of the dip).Because of scale effect, large amount of geological data has to be collected and plotted to come up with aninterpretation of statistically significant trends. The process is rather time-consuming, potentially hazard to thegeologists and workers, and limited to accessible areas only.

The purpose of this paper is to introduce the non-contact measurement techniques of Photogrammetry and 3-D LaserScanning and apply them to map the structural discontinuities so that the need to directly access the rock surface viascaffolding is removed. By eliminating the need for scaffolding, the cost of site investigation and the potential ofworkers falling off the slopes can be substantially reduced.

BACKGROUND OF PHOTOGRAMMETRY AND 3-D LASER SCANNING

Photogrammetry is a 3-Dimensional mapping technique that uses photographs as the fundamental medium formeasurement. By taking photographs from at least two different locations, lines of sight are mathematically intersected
mailto:[email protected]:[email protected]


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to produce the 3-D coordinates of any points of interest. Control points and tie points are identified in the overlapping photographs during the photogrammetry process in order that the orientation and location of the camera and the photosare fixed relative to each other. Once the orientation and location of the photos are fixed relative to the camera and 3-Dcoordinates of the tie points are determined, the 3-D coordinates of any points of interest between the tie points can beinterpolated. If the points of interest between the tie points have regular shape, for example a planar surface, then the

use of the photogrammetric process alone is adequate in forming a model that truly represents the coordinates and photographic textures of an object in space.

The generic application of photogrammetry is in the creation of topographic maps at various scales from aerial photography. The procedures for this operation are well established with commercial systems of various levels ofsophistication and automation readily available. Traditionally, topographic maps were produced in vector form thefeatures seen in the photographs represented by lines and symbols. The advent of digital techniques has allowed the pictorial information to be included in the map. Such products are called orthimagemaps and are becoming astandard topographical mapping product.

For object that has a regular shape, photogrammetry is a useful and accurate technique in converting objects within pairs of 2-D photographs back to 3-D geometrical shape where measurements or coordinates can be taken directly fromthe model. However, using photogrammetry technique to create dimensionally accurate model for fractures in a rockslope surface is much less accurate because its surface profile is highly irregular between the tie points and identifyingcommon tie points in overlapping photos is not easy in rock fractures due to its plain texture appearance. A largenumber of overlapping photographs are also needed to create a model for the entire slope surface.

The application of photogrammetry to geological mapping has mainly been confined to the use of aerial photographyand conventional photogrammetric mapping techniques to produce small-scale geological maps. A recently reportedapplication of ground-based photography (terrestrial photogrammetry) similar to that applied here is the work ofRobertson (1998) where he carried out the geological mapping of a dam abutment by applying photogrammetrytechnique to historic photographs. It provided the identification of the geological features on copies of the photographsand did not provide useful maps of the features. It is not reported what the accuracy achieved when comparing the jointorientation obtained from photographs with that obtained from field mapping. In earlier research, Murlaz (1992)reported the use of photogrammetric techniques in the geological mapping of the high walls of open-cast mines.Orthophotographs were produced by registering photographs with information with map contents. No assessment ofthe accuracy of the interpretation of the strata or geometric of the orthophotos was made.

Because photographs are a perspective projection, they cannot be used directly as an accurate map. The creation oforthoimagemaps requires the effects of terrain relief to be removed by the application of a surface model through a process called differential rectification. Surface models can be extracted from the overlapping photographs, but there isthe general requirement that the photographs are parallel with the coordinate system defining the plane of the surface to be mapped. Most commercial photogrammetric systems have this requirement. In the mapping of slopes, thecoordinate system is defined in terms of local topographic coordinates XY forming the horizontal plane and Z beingthe vertical direction therefore the slope surface is oblique to the coordinate system.

Terrestrial 3-D laser scanning is a relatively new technology that has found many applications in the engineering field.A typical portable 3-D laser scanner is capable of recording positions of hundreds of thousands of points in 5 to 15minutes with 2 mm accuracy in a 50m-target range. The minimum vertical and horizontal point-to-point measurementspacing can be less than 4 mm at 50m-target range. With a field of view of 40 horizontally and vertically and amaximum of 1000 rows and columns of points, this equates to an average point spacing of about 35 mm at a distance of50 metres. Inside the scanner, two mirrors rapidly and systematically sweep narrow, pulsing laser beam over the chosentarget (or scene). A time-of-flight method is used to measure how long it takes for each laser pulse to hit a surface andreturn to the scanner without the need of a reflector. Range measurements are generated for every laser pulse whileintegrated optical encoders record mirror angles. The resulting positions commonly known as point cloud aredisplayed graphically, as they accumulate in real-time, on the systems laptop.

The point cloud is a true 3-D representation of the surfaces seen by the scanner and can be coloured according to eitherthe intensity of the return laser pulse (which is influenced by the physical characteristics of the surface each pulsestrikes) or by the distance from the scanner to the surface. It can be viewed from any direction and accuratemeasurements of distance, area and volume can be made between user-selected sets of points. Further processing of the point cloud allows contours, profiles, 2 dimensional drawings and 3 dimensional CAD objects and models to be created.


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Ono et al. (2000) tested a laser scanner for the mapping of mud slides in Japan and found that it was an efficient andaccurate method. Other work such as that of Lichti et al. (2002) have focused on the verification of the accuracy andapplication of laser scanning; and Adams et al. (2001) through comparisons with photogrammetrically derived surfacemodels. In general they have found that laser scanners can produce the surface models to a higher level of accuracy anddensity and in a shorter time than through photogrammetry.

Feng (2001) used a 3-D laser scanner (LARA) to quantify fracture geometry from exposed rock faces and comparedwith that obtained from conventional reflectorless total station surveying equipment. It was found that good matcheswere achieved between the two methods.

One shortcoming of the 3-D laser scanner is that although the points on the surface have 3 dimensional coordinates, theintegrated internal camera has very low resolution and is suitable only for defining the scan area. Its application torendering the model for accurate visual interpretation, such as that of geological strata, is limited. This can beovercome by using high-resolution images from an independent camera, which could then be merged with the pointcloud.

The primary objective of this paper is to introduce a technique that will allow this to be done - integrate photographicimages from an independent camera using photogrammetric techniques with the true 3-D point coordinates obtainedfrom the laser scanning technique. This integration can be carried out through a 3-D AutoCAD environment. After the photographic images and 3-D points are merged into an Autodesk 3-D Studio Max environment, the orientation of theslope surface, dip angle and dip direction of specific fracture planes, spacing of joint planes can be clearly identified andmapped.

PHOTOGRAMMETRIC PROCESS

Due to the geometric distortion associated with raw photographs, photographs have to be rectified before reliablemeasurements can be obtained from it. The geometric distortion is caused by various systematic and nonsystematicerrors such as camera and sensor orientation, terrain relief, earth curvature, film and scanning distortion, andmeasurement errors (Wolf, 2000).

To rectify image data, various geometric modeling methods such as finite element analysis (rubber sheeting) andcollinearity equations can be applied (Yang, 1997). The collinearity equations use the principle of triangulation todetermine 3-D positions, similar to the concept used by land surveying. It assumes collinearity relation exists among a point in object space, its corresponding point on the projected plane, and the perspective center of the camera. A veryreliable modeling technique called bundle block adjustment (Leica Geosystems, 2003a) in the triangulation process,uses measured image coordinates, control point information, line segments in object space and other observations todetermine both the camera orientation (i.e., camera position and aiming angle) and the 3-D object coordinates at thesame time. A block of images contained in a project is simultaneously processed in one solution. A statisticaltechnique known as least squares adjustment is used to minimize and distribute error for the entire block. The resulting parameters are referred to as exterior orientation parameters. In order to estimate the exterior orientation parameters, aminimum of three Ground Control Points (GCPs) is required for the entire block, regardless of how many images arecontained within the project (Leica Geosystems, 2003a).

Typical procedures involved in creating orthophotos are as follows:

1. Provide the geometric properties of the camera to the model (normally known as the Interior Orientation anddetermined by calibration) such as defining the x and y pixel size of the digital camera Charge Coupled Device(CCD), principal point x 0 , principal point y 0, focal length of the camera, and lens distortion parameters. The purpose of interior orientation is to define an image or photo-coordinate system within each image of the block,in order to determine the origin and orientation of the image/photo-coordinate system for each image in the block.

2. Add images to the block.3. Identify Ground Control Points (GCPs) in the images.4. Perform Automatic Tie Point Generation. A tie point is the image/photo-coordinate position of an object

appearing on two or more images with overlapping areas. Automatic tie point generation makes use of digitalimage matching techniques to automatically identify and measure the image positions of common pointsappearing on two or more overlapping images.

5. Perform Block Aerial Triangulation. This is the process that uses the collinearity equations to mathematicallydefine the spatial relationships between the images contained within a block, the camera that obtained the images,and the ground.


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The systematic error associated with the block of images, camera positions, lens distortion and ground control pointcoordinates etc. can be minimized using the method of least squares. This method is usually referred to as the standarderror, which is computed based on the summation of image coordinate residuals and ground coordinate residuals forthat particular iteration of processing. At each iteration of processing, the exterior orientation parameters of each

camera station and X, Y and Z coordinates of tie point are estimated. The newly estimated exterior orientation parameters are then used along with the GCP and tie point coordinates to compute the new x and y image coordinatevalues. The newly computed image coordinate values are then subtracted from the original image coordinate values.The differences are referred to as the x and y image coordinate residuals. This process is iterated until the solutionconverges below a pre-set threshold of say 0.001.

Once the process is finished, the position (x 0, y0, z0) and orientation (Omega ( ), Phi ( ), Kappa ( )) of each image in a block, at the time of image capture, will be known. The six transformation coefficients relating the scale and rotationdifferences between the file or pixel coordinate system of the image and the film or image space coordinate system arealso determined.

The X, Y and Z coordinates of tie points can be computed and converted to control points if necessary.

6. Create Orthoimages. If the effects of topographic relief displacement are large, an orthorectification process can be used to rectify an image so that every point on an image would look as if an observer were looking straightdown, along a line of sight that is orthogonal to the earth. The orthorectification process takes the raw digitalimagery and takes each pixel of a Digital Terrain Model (DEM) and finds its equivalent position in the aerialimage. A brightness value is determined for this location based on resampling of the surrounding pixels. The brightness value, elevation, and exterior orientation information are used to calculate the equivalent location inthe orthoimage file.

3-D LASER SCANNING PROCESS

The principles of using laser scanner to obtain the X, Y and Z coordinate of a point have been described. The typical processes in 3-D laser scanning are as follows:

1. Set up control targets within the interest area required scanning.2. Determine the range, sample spacing and number of points to be scanned.3. Scan the area of interest and the control targets.4. Carry out registration of the scan. Registration is the process of integrating more than one scanned areas into a

single coordinate system. The integration is based on a system of constraints, which are pairs of equivalentobjects that exist in two scanned areas. Results of the registration process will create an optimal overallalignment transformation for each scanned object such that the constrained objects are aligned as closely as possible in the resulting scanned area that has been merged together.

5. Create a mesh for the scanned object. A mesh is a series of triangles created using the points in a point cloud,vertices, poly lines, or any combinations of the three as vertices.

6. Export the coordinates of the point or the mesh for further modeling and rendering.

INTEGRATING POINT CLOUD WITH ORTHOPHOTOGRAPHS IN AN AUTODESK 3-D STUDIO MAXENVIRONMENT

As stated earlier, laser scanning can produce a huge database of points with true 3-D local coordinates that can beviewed but the surface textures of the object are poorly captured. By contrast, photogrammetry offers the real texture ofan object that can be visualized but the coordinates of the point are interpolated between the control points.

By combining the photo images from photogrammetry and accurate coordinates from 3-D laser scanning, the photographs can be turned into dimensionally accurate and visually complete 3-D maps of the slope and hence thestructural discontinuities orientation and spacing can be manually mapped on the photographs, reducing the need andextent of scaffolding.

For this mergence to become a reality, a platform of storage, manipulation and visualization of data acquired from both photogrammetry and laser scanning is needed. Automated periphery functions such as the algorithms for computingorientation (dip angle and dip direction) can be added into the system to enhance the value of the system.


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The processes to be accomplished for achieving this scheme of mergence are summarized below with a flow chartshown on Figure 1.

1. Carry out calibration for the camera.2. Acquire suitable control points.

3. Capture images using the calibrated camera.4. Determine interior orientation of the images.5. Calculate exterior orientation of the images.6. Capture point cloud using the laser scanner.7. Carry out registration of different point clouds and import local coordinate systems.8. Rotate the point clouds so that their coordinate system will align with that of the camera system.9. Create a Triangulation Irregular Network (TIN, ESRI (2002)) from the rotated point cloud and export into 3-D

Studio Max as one layer. TIN is a data structure that consists of nodes that stores z-values connected by edges toform contiguous, non-overlapping triangular facets.

10. Rectify the photos using the TIN created from point clouds.11. Using the camera exterior orientation information, export the rectified image as another layer into the 3-D Studio

Max.12. When the two layers are overlapped, point clouds and surface textures can be visualized and rotated together.13. An automated algorithm can be written within the 3-D Studio Max program to select the fracture planes that are

of interest and perform automatic computation of orientation (dip angle and dip direction).14. Repeat the automated algorithm to perform the dip angle and dip direction calculation of other fracture planes

that are of interest.

AUTOMATIC CALCULATION OF DIP ANGLE AND DIP DIRECTION OF FRACTURE PLANES

After the images and meshes are overlaid and attached together, an automated algorithm was written to select thefracture planes that are of interest and perform automatic computation of orientation (dip angle and dip direction).

COMPUTATION OF DIP ANGLE AND DIP DIRECTION

In geological terms, Dip Angle (DA) is the maximum downward inclination of a structural discontinuity plane to thehorizontal, defined by (0 90 ) as illustrated in Figure 2.

Dip Direction (DD) is the direction of the horizontal trace of a line to dip angle, measured clockwise from the North,defined by (0 360 ) as illustrated in Figure 2.

If a right-handed Cartesian system is adopted, then the positive Y-axis is directed to the North, the positive X-axis isdirected to the East and the positive Z-axis is directed upward for a X-Y plane that is horizontal.

The formula from analytical geometry can be used to compute the dip angle and dip direction of a fracture plane, whichis modeled as a best-fit plane intersecting the point clouds that are of interest.

Since the fracture plane is usually wavy, the orientation of the best-fit plane will be affected by the density anddistribution of the point cloud. Therefore, a least squares approach that uses multivariate linear regression method can be used to define the best-fit plane representing the fracture plane.

The equation of the best-fit plane representing the fracture plane can simply be expressed as:

yb xbb z 210 ++= (1)

Using the method of least squares, it can be assumed that the best-fit plane is produced when the minimal sum of thedeviations squared (least squares error) from a given set of data is found. In equation form, this is:

( )[ ++= 22102min iii yb xbb z ] (2)

For n number of points captured, the following matrix can be formed and the coefficients of the equation b can be obtained by solving the matrix using either Gaussian Elimination or Crammers Theorem. In matrix algebra,

,,, 210 bb


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solution of the best-fit plane in space depends on the existence and uniqueness of the matrix and two cases must beconsidered.

Photogrammetry Process Laser Scanning Process

CameraCalibration

Determine Orientationof Camera when

Object was captured

Rectification - PerformRe-sampling of Pixels

Create Mesh or TINfrom Point Cloud

Based on Camera Orientation,rotate point clouds so that thetwo coordinate systems align

Capture Terrestrial

Images

Provide InteriorOrientation of

Camera

Identify ControlPoints and Tie

Points

Laser Scanningof object

Laser ScannerRegistration

Determine Exterior

Orientation of objects

3-D Visualization ofpoint cloud and texture

in 3-D Studio Max

Algorithm to selectfracture planes

Perform least squarecalculations of best-fit

plane to obtain dip anglean dip direction

Figure 1. Flowchart illustrating the procedures of merging photogrammetry with laser scanning


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Figure 2. Determination of dip angle and dip direction of a fracture plane from point cloud

=

=

=

=

===

===

==

n

iii

n

iii

n

ii

n

ii

n

iii

n

ii

n

iii

n

ii

n

ii

n

ii

n

ii

z y

z x

z

b

bb

y y x y

y x x x

y xn

1

1

1

2

1

0

1

2

11

11

2

1

11

(3)

where are coordinates of the captured points.iii z y x ,, If the determinant (D) of the matrix is equal to zero, then either the points captured are collinear (i.e., points rest on aline and do not form a plane) or the fracture plane happens to be vertical to the X-Y plane and parallel to the Z-axis.

The former case can be avoided by making sure that the selected points are non collinear. For the latter case, the DipAngle is obviously equal to 90 and since the fracture plane is vertical, the equation of a plane can be degenerated intoan equation of a line, expressed simply as follows, again using the least squares method:

=

=

=

==

=n

iii

n

ii

n

iii

n

ii

n

ii

y x

y

b

a

y x x

xn

1

1

11

1 (4)

This time, the solution of the best-fit line in the X-Y plane again depends on the existence and uniqueness of the matrixand two cases need to be considered.

If the determinant (D) of the matrix is equal to zero, then there is no solution to Equation [4] and it implies that the lineis parallel to the Y-axis (North) and the Dip Direction is either 90 or 270 .


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If the determinant (D) of the matrix is not equal to zero and b is greater than or equal to zero (means that slope is positive in the X-Y plane), then the Dip Direction can be determined by:

=

0

10

0

10 180tan360180tan180 bor b DD (5)

If the determinant (D) of the matrix is not equal to zero and b is less than or equal to zero (means that slope is negativein the X-Y plane), then the Dip Direction can be determined by:

=

010

01 180tan180

180tan bor b DD (6)

If the determinant (D) of the matrix describing the best-fit plane in Equation [3] is not equal to zero, then the fracture plane is either inclined or parallel to the horizontal X-Y plane. The determination of Dip Angle and Dip Direction can

be obtained by comparing Equations [1] and [3].

If and are both equal to zero, then the fracture plane is horizontal and the Dip Angle is 901b 2b and Dip Direction does

not exist. Otherwise, the fracture plane is inclined to the X-Y plane and determination of Dip Angle and Dip Directioncan be based on unit vector computation.

From analytical geometry point of view, Dip Angle is actually the angle between the fracture plane and the horizontal plane and it can be determined by the inner product of the unit vector, ( )1,0,0k , of the positive Z-axis and the normalvector, , of the fracture plane (see Figure 3), as follows:( 1,, 21 bbn )

b1, b2, -1

Figure 3. Determination of Dip Angle based on Unit Vector

cosnk nk = (7)

or,

1

1cos

2

2

2

1

1

++=

bb (8)


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From analytical geometry point of view, Dip Direction is actually the angle counted clockwise from the positive Y-axisto the horizontal component vector of the maximum inclination line or the horizontal component vector of the normalvector of the fracture plane (see Figure 4).

(b1, b2, -1)

Figure 4. Determination of Dip Direction based on Unit Vector

Let be the unit vector of the positive Y-axis and( 0,1,0 j ) ( )0,, 21 bbhn be the projection of the normal vector n ontothe horizontal plane. Similar to Equation [7], the Dip Direction can be calculated as follows:

coshh n jn j = (9)

2

2

2

1

21cos

bb

b

+

= (10)

The normal vector of a plane may point upward relative to a horizontal plane or it may point downward relative to ahorizontal plane. Depending upon the pointing directions of the normal vector relative to the horizontal plane, the DipDirection calculated from Equation [10] may differ by 180 .

To follow the same geological definition, Dip Direction is determined by the upward normal vector of a fracture plane.Therefore, the directional cosine value of the normal vector is checked to determine which quadrants the normal vectoris located in a Cartesian coordinate system and to identify whether the normal vector is upward or downward relative tothe horizontal plane. The directional cosine value of the normal vector is simply as follows:

222

21

222

21

2

22

2

2

1

1

1

1cos

1cos

1

cos

++=

++=

++

=

bb

bb

bbb

b

(11)

where the three angles, ( ) , ( ) and ( ) are the angles relative to the positive X-axis, Y-axis and Z-axis respectively.For plane that does not pass through the origin, b is the distance from the origin to the plane. When b ,0 00

222

21 1++ bb should have negative - sign to satisfy all the points in Equation [1]. When b ,00

lecture 7 rock fracture mapping

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