monitoring vertical displacements by means of … vertical displacements by means of geometric...

Historical Constructions, P.B. Lourenço, P. Roca (Eds.), Guimarães, 2001 403

1 INTRODUCTION

Safeguarding human life and economic losses are reasons naturally invoked to justify investments in systems to control the security of civil engineering works. Combined with these motives are cultural ones when the engineering work is a historical construction. In fact a good knowledge of the structure, the understanding of its behavior, together with opportune diagnosis of its structural health are important tools to support correct decisions in order to preserving mankind architectural heritage.

The Applied Geodesy Division (NGA) of the Dams Department of the National Laboratory for Civil Engineering (LNEC) was created in 1951 with the main purpose of developing surveying techniques to measure displacements of dams. Since then, this division has also been called to measure displacements of other kind of structures like bridges, earth and rock fills, monuments, etc..

This paper presents the experience of NGA in the restrict area of monitoring vertical displacements of historical constructions by means of geometric levelling.

2 GEOMETRIC LEVELLING

In surveying, levelling is the process of measuring, by direct or indirect methods, vertical distances in order to determine elevations. Two methods are applied: geometric (or direct) levelling and trigonometric (or indirect) levelling. The first one is usually more precise, the monumentation is lighter, equipment and fieldwork are less expensive and operation procedures are easier.

In geometric levelling the difference of height between two points is determined by differences of readings to the staffs placed on those points. The readings are made with a levelling instrument (optical level).

ABSTRACT: Geometric levelling is an old method of geodetic surveying, used to measure differences of elevation between two points at the Earth's surface. The Applied Geodesy Division of the Dams Department of The National Laboratory for Civil Engineering (LNEC) has been measuring vertical displacements with precision geometric levelling at engineering works (dams, bridges, earth and rock fills, etc.) to structural analysis and safety control, for more than half a century. Experience has shown geometric levelling to be a reliable and very precise vertical displacement measurement method. Modern electronic levels, with automatic reading and recording, have significantly improved geometric levelling operational performances. This paper presents geometric levelling and its application to vertical displacements control at five important historical constructions: the aqueduct of "Águas Livres", the western wing of "Praça do Comércio", both at Lisbon, the D.Fernando's city wall and the "Grilos" Church at Oporto and a cloister of the Convent of Christ in Tomar.

Monitoring vertical displacements by means of geometric levelling

Maria João Henriques National Laboratory for Civil Engineering, Dams Department, Lisbon, Portugal

João Casaca National Laboratory for Civil Engineering, Dams Department, Lisbon, Portugal

Comentário: In monitoring surveys, measurements are undertaken to estimate horizontal and/or vertical displacements since, typically, data is analyzed separately on 2-D (horizontal) and 1-D (vertical) dimensions. Quite often, it's sufficient to base monitoring in the analysis of vertical displacements and therefore measurements are made to track changes only in height. In comparison with horizontal displacements (quite often these ones determined by independent methodologies) vertical displacements can be determined with higher accuracy, the monumentation is lighter, equipment and field work are less expensive, operation procedures are easier.

Comentário: In trigonometric levelling the same difference of height is computed from measurements of vertical angles and spatial distances made by theodolites with electronic distance measurement devices (or a total stations). High precision angle and distance measurement equipment is much more expensive than equipment used for geometric levelling and usually less accurate results are obtained.

404 Historical Constructions

An optical level consists of a telescope fitted with cross hairs, rotating around a vertical axis, with a very sensitive spirit level, or other device, fixed to it that enables the line of sight to beca-me horizontal. The reading on a graduated vertical staff is measured through the telescope. If staffs are placed on successive ground points, and the telescope is truly leveled, the difference between the readings at the cross hairs will equal that between the heights of the points. By moving the level and the staffs along a path and repeating the measurement procedures, differences in height can be measured.

The points in a levelling line are classified in three categories: i) object points - points that are to be monitored; ii) reference points; iii) ancillary points. When the reference points are located in the area to be controlled (and therefore might undergo displacements) only relative dis-placements can be determined. If reference points are located outside that area, tied to bedrock or other non-moving structure, absolute displacements can be determined. Although only one reference point is needed in levelling lines, the experience advises to place at least three, only way to identify unstable reference points. A geotechnical expert must choose the position of the reference points. Ancillary points are placed, for instance, to avoid too long distances between level and staffs or to link sectors of a levelling line that, otherwise, would be independent.

2.1 Monumentation

Regarding monumentation, the points are usually materialized by pegs (Fig. 1) sealed on the floor or, less usually, by metal pieces, sealed on a wall. The first are used to place staffs with inferior support, the second one to place hung measuring rules. All points must be well tied to the structure, otherwise displacements might represent monumentation displacements instead of structure displacements. Sometimes is necessary to place the points in protected places (Fig. 1) to prevent damage.

1cm

peg 1 cm

Figure 1 : A peg and its placement (unprotected and protected)

2.2 Measuring Equipment

Automatic levels i. e. optical levels with a built-in compensator, that employs an extremely sensitive pendulum device, which automatically makes the line of sight horizontal, should be used. To improve accuracy a parallel plate micrometer must be fitted over the telescope objective. The parallel plate micrometer permits direct readings on a centimetre graduated staff, to 0.1mm, and estimated readings, to 0.01mm. Digital levels (see Table 1) are automatic levels with a built-in digital image processing system that permits automatic reading of special staffs (coded bar) and electronic recording. Errors caused by man reading and manual recording are eliminated and the speed of levelling can be increased (by about 30%).

M. J. Henriques and J. Casaca 405

Table 1 : Accuracy, levels and staffs. Accuracy

Per 1km double run Level Staff

Automatic level with parallel-plate micrometer

0.3 mm

Digital level (coded bar staff)

0.4 mm

Rigid invar staffs must be used. These have the scales engraved directly into the paint coat on

an invar strip, being this recess in an aluminum or wood staff's profile. Invar is a nickel-steel alloy that has a linear thermal expansion coefficient of 0.7×10-6 ºC (about 15 times smaller than steel), a quite important characteristic since measurements can be made in extreme temperature conditions. If staffs with steel strips are used, differences of heights, computed from measurements made in winter and in summer, can be a consequence of the variation of staff's length. As accessories, the staffs must be equipped with circular levels permanently attached and braces to help hold the staff vertical and steady.

2.3 Displacements Determination

The difference of height

ijjiijij RRRHHH =−=−= (1)

is determined by differences of readings (R) to two staffs placed on two points (points i and j, on Fig. 2). First, the level is set-up on a tripod and levelled with the help of a built in small spherical bubble. The automatic compensator ensures that the line of sight is horizontal so that each staff reading is reliable (staff must be kept vertical during the readings).

i

j

Backsight Foresight

Level of i (Li)

(horizontal line)(horizontal line)

Level of j (Lj)

Hij

Ri Rj

Figure 2 : Difference of height determination The staffs are placed on successive ground points and the difference between the readings at

the level's cross hairs will equal that between the heights of the points. By moving the level and the staffs along a path and repeating this procedure, differences in height can be computed. The knowledge of the height of the first point of a levelling line allows the computing of the heights of any of the remaining points of the line by applying the next expression (where j=i+1):

Comentário: of 0.7*10-6 ºC (steel 11*10-6 ºC),


nkRHHHHk

iij

k

ijik ,,2,

1

11

1

11 K=+=+= ∑∑

−

=

−

= (2)

The vertical displacement, dH, between two epochs of any point of the levelling line, can be determined by (where j=i+1):

nkdRdHdHdHdHk

iij

k

ijik ,,2,

1

11

1

11 K=+=+= ∑∑

−

=

−

= (3)

2.4 Errors

The most important errors that affect geometric leveling are due to: i) non horizontal line of sights (vertical collimation error); ii) reading errors of staff and level micrometer; iii) errors made during manual recordings; iv) tripods placed on non stable surfaces like sandy ground or asphalt; v) thermal effects of the sunrays incidence on the level; vi) influence of magnetic field on automatic levels; vii) staffs graduation; viii) non verticality of the staffs; ix) temperature of the staffs; x) refraction; xi) gravity; xii) relative position earth-moon-sun (earth tide); xiii) crustal movements. The last three causes of errors can be neglected on short levelling lines.

Due to errors made during measurements, each reading has an error ε, unknown, associated, so that

eRµ += (4)

being R the reading and µ the true value (unknown). The error ε can be split into three errors: i) θi (instrumental error due to error of the measuring equipment); ii) θe (environmental error due to measuring conditions); iii) δ (accidental error):

δθθε ++= ei (5)

Errors θi and θe are systematic errors since they will have the same values when the obser-vation conditions are repeated. The accidental error has a random distribution. When high precision is required, special care is taken during measurements in order to reduce these errors. One is to place the level at "equal" distances of the staffs (sighting distances must be equalized to within ±1 m). This care reduces the effect of collimation error (the line of sight is not hori-zontal, as seen in Fig. 3, making an angle α with the horizontal line in all directions) since it equally affects both readings. The height difference, as being a difference of readings, is not affect by this error.

(horizontal line)(horizontal line)

Ri Rjline of sightline of sight

α α

Figure 3 : Collimation error

Equal distances also eliminate the combined effect of curvature and normal refraction, providing that the coefficient of refraction is the same over the both lines of sight. On slopes, backsights have different distances from the ground than foresights and, therefore, light rays undergo different paths (more or less curved, concave or convex, depending on vertical temperature gradients) being back and fore readings differentially affected. This situation should be avoided or by placing additional points or by standing the level higher in order that the line of sight will not be less than 50 cm above the ground. The maximum length of one line of sight should not be more than 30 m to ensure equal atmospheric conditions on both sightseeing.


Other important care is to protect level from effects of temperature, avoiding the incidence of sunrays directly on the level (by keeping the level protected by a sunshade).

Some errors are related to the staffs. The graduation error can be reduced if calibrated staffs are used. The zero error (the zero graduation does not coincide with the base of the staff) is usually a consequence of accidents during handling (the fall of the staff is the most usual) or transportation. Adequate methodologies can eliminate this error being the use of only one staff the easiest one. It's also very extremely important to keep the staff vertical during observations so is fundamental to use staffs with circular adjusted bubbles and braces and, when there is strong wind, keep them vertical with the help of struts.

2.5 Uncertainty of the Displacements

The differences of height, measured by geometric levelling, are supposed to be samples of, stochastically independent, normally distributed random variates, with equal variances. Consequently, displacements between two epochs are also supposed to be samples of normally distributed random variates, though stochastically dependent and with different variances. If the operative methods used to measure the height differences are adequate to eliminate the systematic errors, the random variates:

nkHdHdHdk

iijk ,,2,

~~~ 1

11 K=+= ∑

−

= (6)

are unbiased minimum variance estimators of the displacements of the points. The mean values (M) and variances (V) of the estimators are, respectively:

∑∑−

=

−

=+=+=

1

11

1

11 )

~()

~()

~(),

~()

~()

~(

k

iijk

k

iijk HdVHdVHdVHdEHdEHdE (7)

As the variances of the height differences are supposed to be equal, the variances of the displacements ( 2

kσ ) are related to the variance of the reference point ( 21σ ) and to the common

variance of the height differences ( 20σ ) by:

20

21

2 )1(2 σσσ −+= kk (8)

The standard uncertainty of the displacements is quantified by the standard deviation:

20

21 )1(2 σσσ −+= kk (9)

2.6 Quality Control

In any levelling line, measurements must begin and end on reference points, only way to control the quality of measurements. The difference between the known height and the computed height is the misclosure (∆), and is computed by (where j=i+1):

+−=∆ ∑

−

=

1

11

k

ijin HHH (10)

To control errors, all measurements must be repeated, performing a double run levelling, i. e., the levelling ends at the beginning point. In this case Hn= H1 and the sum of all level differences should be zero.

The misclosure should be computed right after the end of the levelling works. Performing this data pre-processing in the field allows the observation team to repeat the measurements with lower costs and, also important, with no changes of the structure conditions.

The tolerance to misclosure used by LNEC to levelling lines depends on the assumption that the misclosure is entirely caused by accidental levelling errors and the errors of each height


difference have a normal distribution with a standard error of σe Misclosure tolerance (t∆), is a function of the number (n) of height differences measured

n96.1 est =∆ (11)

where 1.96 is the 0.95 quantile of the standard normal distribution. When misclosure exceeds the allowable tolerances all measurements should be repeated.

3 LEVELLING LINES IN PORTUGUESE HISTORICAL CONSTRUCTIONS

In Portugal some important historical constructions have levelling lines in order to control vertical displacements in critical areas. Five constructions have been selected to this paper: the D.Fernando's city wall and the "Grilos" Church at Oporto, a cloister of the Convent of Christ in Tomar, the aqueduct of "Águas Livres" and the western wing of "Praça do Comércio", both in Lisbon.

3.1 D.Fernando's city wall (Oporto)

The D. Fernando's wall replaced the old medieval wall that became obsolete in the 14th century due to the development of the city. In 1336 King D. Afonso IV determined the construction of a new wall. However, this would only be concluded around 1376, in the reign of D. Fernando, whose name it kept. The wall had four doors, protected with towers, and fourteen wickets. A small sector was restored around 1920.

Figure 4 : D. Fernando's city wall The first levelling line was established in 1959 to control the area of implantation of the wall,

nearby a slope area (“Guindais” slope that had suffered a landslide). The line has undergone two important changes to the original design, the last one done in 1976. A total of 34 observation campaigns were made until now. The line has six object points, one reference point and several ancillary points. The prior uncertainty of vertical displacements varies from 0.15mm (point a, the nearest from the reference point) to 0.50 mm (point f, the most distant).

Figure 5 : D. Fernando's city wall: object points positions

OPO

RTO

GA

IA

a

bc

fe

d

MURAL

HA FE

RNAN

DINA

D. LU

IS Bridge


3.2 "Grilos" Church (Oporto)

The church was built in the 16th century in mannerist style. The façade is, perhaps, the most remarkable feature of the monument. Adjacent to the church is the convent surrounded by yards. In the 1990’s several fissures and differential layings were detected.

Figure 6 : "Grilos" church

The levelling line was established in 1994. It has 21 object points and three reference points. The points are located on exterior walls of the church, convent and on yards walls. The levelling line has a complex design. All displacements are determined with a prior uncertainty lesser than 0.5 mm.

Figure 7 : "Grilos" church, convent and yards: object points positions

3.3 A cloister of Convent of Christ (Tomar)

The cloister was built in the 16th century and is the purest example of Renaissance style in Portugal. Convent of Christ, a UNESCO World Heritage Site, was built over a period of six hundred years from the 12th to the 17th centuries. The castle-monastery complex comprises seven cloisters, a temple, a church and a huge bell tower, being its most well known feature the Manueline window on the Chapter house.

Figure 8 : Convent of Christ: convent, church, a cloister and Manueline window

The levelling line was established in 1983. It has three object points and one reference point.

All displacements are determined with a prior uncertainty lesser than 0.25 mm.


3

21

A

Figure 9 : Cloister: object and reference points positions

3.4 The aqueduct of "Águas Livres" (Lisbon)

The construction started in 1732 and the Aqueduct was ready to supply water to the city of Lisbon in 1748. The total length of the Aqueduct and its ramifications is 58 135 metres. The 35-arched structure supporting the Aqueduct, as it crosses the Alcantara Valley, is 941 metres long. Fourteen of the arches are ogival in shape and the other twenty-ones are round, with the tallest being 66m high. The Aqueduct, that survived the 1755 Lisbon earthquake, is out of use since 1967.

Figure 10 : Aqueduct of "Águas Livres" The levelling line as 37 object points, placed on the walkway on the top of the aqueduct, and

four reference points, two on each end. The first observation campaign was made in 1995. The second in 2000.

Figure 11 : Aqueduct's object points positions

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

19 2120 22 23 24 25 27 28 29 30 31 32 33 34 35 36 372618


-2.5

-2.0

-1.5

-1.0

-0.5

0.0

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 Figure 12 : Aqueduct's vertical displacements (point) and displacements prior uncertainty (column)

Figure 13 : Aqueduct's measuring campaign

3.5 Western wing of "Praça do Comércio" (Lisbon)

The buildings of this 250 m side square were built after the 1755 Lisbon earthquake destroyed the Royal palace built in that area. Arcade buildings, specially built to house Government offices, bound the square on three sides. On the fourth side is river Tagus, which influences the stability of all buildings in the area.

Figure 14 : "Praça do Comércio"

The line as seven object points and one reference point, all beside the western wing. Points 1 to 6 are close to the arcades. Point 1 was chosen to be the reference point since it is the farther from river Tagus. All displacements are determined with a prior uncertainty lesser than 0.4 mm.


Tagu

s R

iver

87

654321

Figure 15 : Object and reference points positions

-120

-100

-80

-60

-40

-20

0

20

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

(mm

)

2 3 4 5 6 7 8

Figure 16 : Vertical displacements

4 CONCLUSIONS

Geometric levelling is a non-intrusive, inexpensive, accurate and precise method. These are good reasons for geometric levelling to be the surveying method most applied in the monitoring of portuguese monuments.

REFERENCES

Casaca,J. and Henriques,M.J. 1994. Numerical Modelling of Atmospheric Refraction. In Proceedings of 1. Turkish International Symposium on Deformations, p. 116-125. Istanbul: TMMOB-HKMO.

Casaca,J., Matos,J. and Baio,M. 1999. Topografia Geral, 2nd ed.. Lisbon: Lidel. Cooper,M. 1987. Control Surveys in Civil Engineering. New York: Nichols Publishing Company. Henriques,M.J. 1996. O Efeito da Refracção em Geodesia e Topografia. Dissertation. Lisbon: LNEC. International Organization for Standartization 1995. Guide to the Expression of Uncertainty in

Measurements. Geneve. Unguendoli,M. 1984. Errors in Precise Levelling. In M. Unguendoli (ed.) High Precision Geodetic

Measurements, p. 5-25. Bologna: CUSL. U.S. Corps of Engineers 1994. Deformation Monitoring and Control Survey. Engineer Manual 1110-1-1004.

monitoring vertical displacements by means of … vertical displacements by means of geometric...

Documents