1. C.J. Pretorius¹, W.F. Schmidt¹ C.S. van Staden¹
K. Egger²
¹ Department of Water Affairs and Forestry, Republic of South Africa
² Schneider Ingenieur AG, Chur, Switzerland
10th INTERNATIONAL SYMPOSIUM ON DEFORMATION MEASUREMENTS
Orange, California, USA
THE EXTENSIVE GEODETIC SYSTEM USED FOR THE
MONITORING OF A 185 METRE HIGH ARCH DAM
IN
SOUTHERN AFRICA

2. •Provide Lesotho with hydro-
electricity
Features:
•double curvature arch dam
•185 m high above foundation
•crest length of 710 meter
•crest thickness 9 meter
•base width 60 meters
•To supplement water to the
Gauteng industrial area of the
Republic of South Africa;
Main objectives:
Katse Dam

3. Lesotho Highlands Water Project

4. Reference : Meas 9101
Point P01
Meas du dv dz
9211 .0 .4 .4
9612 .1 .1 -11.6
9709 -.2 .1 -13.3
9803 -.2 .2 -14.6
9807 .1 .0 -15.3
Point P02
Meas du dv dz
9211 .0 .3 -.5
9612 -9.9 2.4 -8.7
9709 -11.8 5.0 -17.3
9803 -12.4 5.1 -18.1
9807 -11.9 5.4 -19.1
Point P08
Meas du dv dz
9211 3.2 -.6 -1.7
9612 4.0 -.7 -11.1
9709 3.9 1.0 -13.6
9803 3.6 1.4 -14.2
9807 3.8 .1 -15.4
Deformations after impounding started 1996

5. • Correlation between pendulums and the Geodetic triangulation may take place
on the crest of the dam, galleries inside the dam wall and exits on the downstream
face of the dam
Concept of the Geodetic Deformation Measurements
• Close correlation between Instrumentation and Geodetic measurements
Correlation between Instrumentation and the Geodetic System
• Results of instruments which record relative displacements, when evaluated
together with Geodetic results, their relative displacements become absolute
• Multistage Geodetic system - full, reduced and mini measurements
have to be employed
• Establishment of an extensive triangulation network
Measurement intervals
• Concrete dams are subject to expansion and contraction because of changes in
temperature and pressure of the water load between summer and winter
• Monitoring therefore takes place during late summer (February) and winter (August) when
the expansion and contraction is at its maximum and minimum

6. INTRODUCTION
Basic Layout:
• Instrumentation
• Pendulums
• Triangulation Network
• Traverses & Pendulums

7. 43 Vibrating Wire Extensometers
442 Vibrating wire Jointmeters
28 Vibrating wire Strain gauges
64 Thermometers
100 Vibrating wire Piezometers
22 Vibrating wire pressure transducers
24 Clinometer
8 Trivec stations
.... Leakage Weirs
.... Water Level measuring Devices ext
INSTRUMENTATION
Consists of:

8. Equipment Used
Leica TC2002 Leica TCA2003 Kern H.D. Tripod Kern Plummit
Kern E2 Iseth Distometer Leica NA3003 60 cm Digit Scale
Illuminated Target Altrimetric 60cm
Digit Scale
Crest Targets
Instrument Adaptors
Vertical Target
Illuminated Targets

9. TRIANGULATION NETWORK
5 Primary Pillars
7 Secondary Pillars
4 Crest Pillars
6 Gal Exit Pillars
4 Exit Brackets
6 Primary Benchmarks
22 Secondary Benchmarks

10. TRAVERSES & PENDULUMS
17 Hanging Pendulums9 Inverted Pendulums
6 Optical Align Brackets
6 Pendulums Anchors
2060
2005
1945
1900
Traverse Brackets

11. Crest Pillar
2 Altrimetric wire anchors
The Arch Dam
19 Parapet targets
Gal Exit Pillars
6 Opt. A. Points

12. Connections Traverse - Net
Pendulum
Chamber
Gal Exit Pillar with
pendulum chambers
Opt Alignment Point
Inverted Pendulum

13. El : 2005
D- GALLERY
7 Hanging Pendulums
7 Pendulum Anchors
5 Gal Exit Points
38 Traverse Brackets
6 Pillars

14. D - ACCESS
El:2008 - 2000
Pillars
Station Points
Brackets
Exit
Exit

15. Dam Wall
E Gallery
Left Flank
Rock Abutment
Gallery Exit
Pillar
Gallery Exit
Point
Traverse Pillars/Brackets
E - ACCESS
El: 1994 - 2036
Gallery Exit
Bracket

16. Crest Benchmarks Traverse Brackets Altrimetric Wires
PRECISE LEVELLING
ON DAM WALL

17. Adjustment Method used
• Helmert/91 program system
• Three-dimensional adjustment
• Based on theory of least squares
Definition of Adjustment
• Constants and Unknown parameters (co-ordinates etc.)
• Definition of the generalised Helmert - transformation
• Definition of an adequate stochastic model

18. Network
Mean Error Ellipses (U,V) Code A B Theta Mhe
mm mm o mm
Primary Pillar : P01 .39 .28 58.58 1.49
El 2060 Pillar : P115 .23 .19 85.13 .46
Alignment Point : R111 .40 .39 122.11 .50
Parapet Target : 111 .54 .52 37.04 .50
Bench mark : C11 ..... ..... ........ .47
El 2005 Pillar : P200 .27 .22 90.44 .43
El 1945 Pillar : P300 .28 .23 88.46 .42
The mean error ellipses depend on:
• Accuracy of observations
• Geometry of the geodetic network, and
• Selection of fixed points/Helmert control points

19. Traverses
Mean Error Ellipses (U,V) Code A B Theta Mhe
mm mm o mm
El 2005 Right Flank : 253 .34 .29 160.15 .30
Centre Bracket : 200 .14 .09 179.06 .17
Left Flank : 236 .22 .16 38.04 .24
El 1945 Right Flank : 337 .67 .22 150.49 .37
Centre Bracket : 300 .13 .10 179.42 .24
Left Flank : 336 .62 .21 28.16 .42
El 1900 Right Flank : 427 1.93 .57 153.31 .67
Centre Bracket : 400 .70 .44 179.20 .59
Left Flank : 426 1.67 .52 27.55 .69
Optical Align Point El 2052 : TA11 .47 .42 73.47 ....
Hanging Pendulum : DH0 .49 .39 101.09 ....
Inverse Pendulum :VKM0 1.37 .59 177.18 ....
Altrimetric Wire : AW11 .... .... .... .35
Mean error ellipses refer to Optical Alignment and Gallery
exit points as fixed points in the adjustments

20. Horizontal Displacements
El. 2060
Winter
Summer
-16 mm

21. Summer
Winter
- 5 mm
Horizontal Displacements
El. 2005

22. Summer
Winter
- 4.3 mm
Vertical Displacements
El. 2060

23. 0.2 mm
Vertical Displacements
El. 2005

24. Left- Right Flank Contour Displacement
El. 2060, 2005, 1945 and 1900
Right Flank Left Flank
-7.5 - -8.5 mm+7.5 - +8.5 mm

25. Up/Downstream Contour Displacement
El. 2060, 2005, 1945 and 1900
-20.0 - -17.5 mm -10.0 - -7.5 mm-10.0 - -7.5 mm

26. Vertical Contour Displacement
El. 2060, 2005, 1945 and 1900
-7.5 - -6.25 mm

27. Mapeleng Crack
Upstream 10 Km on right flank
1.5 Km long , up to 70mm wide

28. • The Geodetic Scheme is of a high standard
• The scheme gives a high degree of information on the behaviour of the
dam
• Scheme is not only based on the network and traverse disposition but
also on the inclusion of the total pendulum system
• Scheme offers a variety of reduced measurements
• Easily accessible and ensure a high efficiency
• Provides adequate geodetic information of the structure and the
surrounding areas over a long period of time.
Conclusions