C.J. Pretorius¹, W.F. Schmidt¹ C.S. van Staden¹ K. Egger²

¹ Department of Water Affairs and Forestry, Republic of South Africa² Schneider Ingenieur AG, Chur, Switzerland

10th INTERNATIONAL SYMPOSIUM ON DEFORMATION MEASUREMENTSOrange, California, USA

THE EXTENSIVE GEODETIC SYSTEM USED FOR THE MONITORING OF A 185 METRE HIGH ARCH DAM

IN SOUTHERN AFRICA

• 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

Lesotho Highlands Water Project

Reference : Meas 9101

Point P01Meas du dv dz

9211 .0 .4 .49612 .1 .1 -11.69709 -.2 .1 -13.39803 -.2 .2 -14.69807 .1 .0 -15.3

Point P02Meas du dv dz

9211 .0 .3 -.59612 -9.9 2.4 -8.79709 -11.8 5.0 -17.39803 -12.4 5.1 -18.19807 -11.9 5.4 -19.1

Point P08Meas du dv dz

9211 3.2 -.6 -1.79612 4.0 -.7 -11.19709 3.9 1.0 -13.69803 3.6 1.4 -14.29807 3.8 .1 -15.4

Deformations after impounding started 1996

• 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

INTRODUCTION

Basic Layout:

• Instrumentation• Pendulums• Triangulation Network• Traverses & Pendulums

43 Vibrating Wire Extensometers442 Vibrating wire Jointmeters 28 Vibrating wire Strain gauges 64 Thermometers100 Vibrating wire Piezometers 22 Vibrating wire pressure transducers 24 Clinometer 8 Trivec stations .... Leakage Weirs .... Water Level measuring Devices ext

INSTRUMENTATION

Consists of:

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 TargetsInstrument Adaptors

Vertical TargetIlluminated Targets

TRIANGULATION NETWORK

5 Primary Pillars

7 Secondary Pillars

4 Crest Pillars6 Gal Exit Pillars4 Exit Brackets

6 Primary Benchmarks

22 Secondary Benchmarks

TRAVERSES & PENDULUMS

17 Hanging Pendulums9 Inverted Pendulums

6 Optical Align Brackets6 Pendulums Anchors

2060

2005

1945

1900

Traverse Brackets

Crest Pillar

2 Altrimetric wire anchors

The Arch Dam

19 Parapet targets

Gal Exit Pillars

6 Opt. A. Points

Connections Traverse - Net

Pendulum Chamber

Gal Exit Pillar with pendulum chambers

Opt Alignment Point

Inverted Pendulum

El : 2005D- GALLERY

7 Hanging Pendulums7 Pendulum Anchors

5 Gal Exit Points

38 Traverse Brackets

6 Pillars

D - ACCESSEl:2008 - 2000

PillarsStation Points

Brackets

Exit

Exit

Dam WallE Gallery

Left FlankRock Abutment

Gallery ExitPillar

Gallery ExitPoint

Traverse Pillars/Brackets

E - ACCESSEl: 1994 - 2036

Gallery ExitBracket

Crest Benchmarks Traverse Brackets Altrimetric Wires

PRECISE LEVELLINGON DAM WALL

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

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

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 .24El 1945 Right Flank : 337 .67 .22 150.49 .37 Centre Bracket : 300 .13 .10 179.42 .24 Left Flank : 336 .62 .21 28.16 .42El 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 Galleryexit points as fixed points in the adjustments

Horizontal Displacements El. 2060

Winter

Summer

-16 mm

Summer

Winter

- 5 mm

Horizontal Displacements El. 2005

Summer

Winter- 4.3 mm

Vertical Displacements El. 2060

0.2 mm

Vertical Displacements El. 2005

Left- Right Flank Contour DisplacementEl. 2060, 2005, 1945 and 1900

Right Flank Left Flank-7.5 - -8.5 mm+7.5 - +8.5 mm

Up/Downstream Contour DisplacementEl. 2060, 2005, 1945 and 1900

-20.0 - -17.5 mm -10.0 - -7.5 mm-10.0 - -7.5 mm

Vertical Contour DisplacementEl. 2060, 2005, 1945 and 1900

-7.5 - -6.25 mm

Mapeleng CrackUpstream 10 Km on right flank1.5 Km long , up to 70mm wide

• 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