Angular Distortion in Structures: Point vs. Linear Monitoring … · 2018-01-29 · Mair, R. J., Taylor, R.N. and Burland, J. B. (1996). Prediction of ground movements and assessment

KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0

To understand tilt & angular distortion appears to be quite simple. However, since late 1950s’

many reference professionals and academics have been trying to derive relationships between tilt & angular distortion and the risk of damage to buildings.

Regarding instrumentation, more often than not it looks like there are several options to

monitor tilt & angular distortion. A good understanding of the behaviour of the structure is needed, together with careful planning and design for instrumentation and monitoring.

This article presents the basic concepts to help decide how to monitor tilt taking into

consideration the most common issues encountered and the type of data sought.

Angular Distortion in Structures:

Point vs. Linear Monitoring - considerations

In regard to tilt & angular distortion, this articles covers the following points: • Definitions and (typical) values for tilt and angular distortion • Accuracy: MEMS & Electrolytic, ATS • Point tilt meter vs. linear tilt beam • Calculation • Pictures • Summary • References

NOTE: There is still ongoing discussion about tilt & angular distortion in relation to

building and structural damage.


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Item Definition

Tilt

ω

Tilting, ω, normally describes the rigid body rotation of the

whole superstructure or of a well defined part of it. Normally

it is not possible to ascertain the tilt unless details of the

superstructure and its behaviour are known. Even then it can

be difficult when the structure itself flexes. Burland & Wroth

(1975), Settlement of Buildings and Associated Damage.

Angular Distortion or Relative Rotation

β = δ / l

Angular distortion, β, is the ratio of the differential settlement

δ and the distance l between two points. Skempton &

MacDonald (1956), The Allowable Settlements of Buildings.

Relative rotation, β, is the rotation of the straight line joining

two reference points relative to the tilt. Burland & Wroth

(1975), Settlement of Buildings and Associated Damage.

DEFINITIONS AND (TYPICAL) VALUES FOR TILT AND ANGULAR DISTORTION

NOTE: It is crucial to understand beforehand the range of tilt & angular distortion that will

possibly cause unacceptable damage to the structure.

β = δ / l

Dimensionless

β = δ / l

mm/m

β = δ / l

Percentage %

β = δ / l

arc sine 360°

β = δ / l

arcsecond

β = δ / l

arcminute

1/100 10.0mm / 1m 1.00% 0.573° 2062.8arcsecond 34.4arcminute






Typical Values for Angular Distortion β = δ / l


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NOTE: It is not always easy to understand the difference between tilt and angular

distortion at first glance onsite.

ω

Building showing tilt ω, Ciudad de México, June 2017. Tilting around 1/250 or bigger is

noticeable to the naked eye.



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NOTE: Structural angular distortion may come with rigid body tilt or with differential

settlement.

Maximum angular distortion β over a certain distance l, Ciudad de México, June 2017.

β = δ / l

δ

l



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ACCURACY: MEMS & ELECTROLYTIC, ATS

NOTE: Accuracy needed, type of readings output and long-term stability are factors to

consider when choosing tilt measuring equipment.

Item Considerations Remarks

MEMS Tilt Meter

MEMS: Micro-Electro-

Mechanical Systems, polysilicon

springs suspend the MEMS

structure above the substrate

such that the body of the

sensor -”proof mass”- can move

in xy.

Designed to be installed in

either vertical or horizontal

position to measure tilt.

Uniaxial or biaxial options:

range ±5°, ±10°, ±15°.

Accuracy: ±0.02mm/m (range ±5°),

±0.035mm/m (range ±10°), ±0.065mm/

m (range ±15°), or ±0.0125%FS

Excellent thermal stability; unit fitted with

a thermistor.

Output: +/- Volt; 4-20mA; RS-485/BUS

The digital RS-485 output signal

provides high accuracy with the

advantage of being able to create a

digital BUS system where all sensors

can be linked together, reducing cable

quantities.

Electrolytic Tilt Meter

Electrolytic: Sensor’s liquid

includes an electrolyte that

conducts electrons between a

common connection and left

and right electrodes.

Designed to be installed in

either vertical or horizontal

position to measure tilt.

Uniaxial or biaxial options:

range ±5°, ±10°, ±15°.

Accuracy: ±0.035mm/m (range ±5°),

±0.09mm/m (range ±10°), ±0.09mm/m

(range ±15°), or ±0.025%FS

Vibration resistant.

Unit fitted with a thermistor.

Output: RS-485/BUS

The major advantage of the new

electrolytic tilt meter systems is their

long term stability.

Automatic Total Stations

Survey equipment like

monitoring total stations is

often used to monitor

movements from mini prisms

on structures.

3D measurements.

Accuracy: ±1mm, or lower than.

Reading frequency: around 20 minutes

per full set of prisms –control and

reference-.

To achieve higher monitoring

frequencies and accuracies, it is highly

recommendable for ATS systems to be

complemented with MEMS or

electrolytic tilt meters.

ATS systems imply higher purchasing,

installation and maintenance costs.


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ACCURACY: MEMS & ELECTROLYTIC, ATS

NOTE: Structural tilt monitoring equipment and its distribution onsite must be chosen

bearing in mind jobsite conditions and the decision-making data needed.

Type of sensor /

equipment

Affected by temperature

and weather-related

changes

Affected by vibration

MEMS tilt meter

LOW HIGH

Electrolytic tilt meter HIGH

LOW

Automatic Total

Stations HIGH HIGH


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POINT TILT METER vs. LINEAR TILT BEAM

NOTE: Anchoring point tilt meters and linear tilt beams in joints and/or mortar should be

avoided by all means.

Using a point tilt meter or a linear tilt beam (uniaxial/biaxial) is a function of:

f: fabric of the structure f: structural continuity

f: stiffness of the structure f: expected deformation wavelength

General criteria is detailed in the table below, as specified in the references cited at the end of this

f: fabric of the

structure

f: structural

continuity

f: stiffness of

the structure

f: expected

deformation

wavelength

Point tilt meter Linear tilt beam

(length on

request)

Masonry - - short - X

Brick - X

Cast-iron bolted

lining tunnels

- X

Mass concrete X -

Reinforced

concrete

X -

Structural steel or

similar + + long X -

With the means available at the jobsite and right after installation is finished, it is highly recommendable to accurately survey xyz point tilt meters as well as the starting and end points of a tilt beams’ chain. This will be really useful to calculate and understand deformations.

Point tilt meters are used to monitor tilt on structures at individual locations. Linear tilt beams have a defined gauge (beam) length so that changes in tilt can be simply converted to millimetres of movement.


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CALCULATION

NOTE: Sine of the angle is common practice in the structural and geotechnical industry to

calculate movement; tangent of the angle may be used too for angles ranging 0° ↔ ±15°.

Item Considerations Remarks

Measurand

The physical quantity unit

measured in tilt is degrees

(360°).

In the structural and geotechnical

industry, usual tilt ranges are ±5°, ±10°,

±15° Full Scale FS; other ranges are

available upon request.

Measurements in degrees are used in

different calculations knowing the

length of the linear tilt beams or

assuming a certain wavelength for the

deformation when using tilt meters,

degrees 360° can be easily converted

into mm/m.

Sign convention

Sign convention must be

agreed before installation of

any type of tilt meters.

It is common practice to install tilt

sensors so A+ points towards the

expected direction of maximum

movement, both for the uniaxial and the

biaxial options.

Not understanding the directions of

movement may lead to tremendous

errors in the interpretation of

deformation as well as in the

implementation of any remedial

measures.


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NOTE: It is crucial to foresee convenient onsite conditions before installing tilt meters.

PICTURES

Point tilt meters monitoring a reinforced concrete structure –dam-.

Point tilt meters and prisms -ATS– monitoring a building neighboring excavation works.

Point tilt meter

Prism

Prism

ATS


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PICTURES

Linear tilt beams monitoring vertical –higher- and horizontal –lower- movement in a brick wall.

NOTE: Clean and tidy installations favour reliable readings.

Linear tilt beams


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PICTURES

Chained linear tilt beams monitoring horizontal movement in a cast-iron bolted lining tunnel.

NOTE: Using tilt beam chains requires accurate surveying of both end points.

Chained linear tilt beams


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TYPE OF STRUCTURE Rigid body / structure A good understanding of the behaviour of the structure is

needed.

Options to monitor tilt & angular

distortion

Careful planning and design for instrumentation design

and monitoring.

CONCEPT Tilting ω ↔ Angular distortion β Rotation ω ↔ ratio of differential settlement δ and dis-

tance l between two points

MESURAND Basic engineering unit Degrees (360°)

VALUES (TYPICAL) Expected values Anticipated range of tilt & angular distortion affecting the

structure.

TYPE OF TILT SENSOR Readings possibly affected by onsite

conditions

MEMS tilt meter ↔ Electrolytic tilt meter.

Weather related changes and vibration.

TYPE OF INSTALLATION Fabric and structure Point tilt meter @ individual location.

Linear tilt meter @ beam length.

CALCULATION A+ ↔ A-

Range 0° ↔ ±15°

Main foreseen direction of movement.

sin α –common practice in the industry-.

NOTE: Positive installations need planning and good care onsite.

SUMMARY


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NOTE: Since late 1950s’ many professionals and academics have been trying to derive

direct relationships between tilt & angular distortion and the risk of damage to buildings.

REFERENCES

Boone, S. J. (2001). Assessing construction and settlement-induced building damage: a return to fundamental principles. Proceedings, Underground Construction, Institution of Mining and Metallurgy, London, pages 559—570. Burland, J. B., Broms, B. B. and De Mello, V. F. B. (1978). Behaviour of foundations and structures. Building Research Establishment, London. Burland, J. B. and Wroth, C. P. (1974). Settlement of Buildings and Associated Damage. British Geotechnical Society’s Conference on the Settlement of Structures, Cambridge, April 1974. Frank, R. (2011). Geotechnical aspects of building design (EN 1997). Eurocode 2, Background and Applications, Brussels. Mair, R. J., Taylor, R.N. and Burland, J. B. (1996). Prediction of ground movements and assessment of risk of building damage due to bored tunnelling. Geotechnical Aspects of Underground Construction in Soft Ground, Mair & Taylor (eds.), Rotterdam. Skempton A W and MacDonald D H (1956). The allowable Settlements of Buildings. Structural and Building Division Meeting, Structural Paper No. 50, London.

Documents

Angular Distortion in Structures: Point vs. Linear Monitoring … · 2018-01-29 · Mair, R. J., Taylor, R.N. and Burland, J. B. (1996). Prediction of ground movements and assessment