Inclinometer Measurement Quality Control

Monir Precision Monitoring

By ANJIE LIU

4A Civil Engineering

May 2016

20 Keewaydin St.

Waterdown ON L0R 2H6

May 10, 2016

Dr. Jeffrey West

Associate Chair, Undergraduate Studies

Department of Civil and Environmental Engineering

University of Waterloo

Waterloo ON N2L 3G1

Dear Dr. West:

This report, entitled "Inclinometer Measurement Quality Control," was prepared as my 4A

Work Report. This report investigates alternatives for the design, construction and utilization

of an installation for testing the consistency of inclinometer measurements over time. Of the

three reports required by the Department of Civil and Environmental Engineering at the

University of Waterloo, this report is my second.

Monir Precision Monitoring is a company specialized in the utilization of precision

instruments for monitoring structural deflections. My work placement took place at their

office in Mississauga. The services provided include the monitoring of subsurface deflections

using inclinometers, slope deflections using electrolevels, cracking using crack gauges,

vibrations using seismographs and general movements using Robotic Total Stations. My work

placement in the inclinometer department involved frequent site visits to take inclinometer

measurements for shoring structures on construction sites in the Greater Toronto Area,

supervised by manager Brian Tigani.

This report was written solely by me and has not received academic credit at any academic

institution. I would like to thank my co-workers for their guidance and training in the work

contained in this report. I received no further help.

Sincerely,

Anjie Liu

ID# 20 377 899

1

Inclinometer Measurement Quality Control

Monir Precision Monitoring

By

Anjie Liu

4A Civil Engineering

May 2016

2

Summary

Monir Precision Monitoring provides construction monitoring services using precise

measuring instruments. One such service is the monitoring of shorting structure deflections

using inclinometers.

The inclinometer instruments are sent for calibration every two years, as is the practice

recommended by the manufacturer to ensure quality measurements from the instrument.

However, between calibration periods, the inclinometer probes may be subject to impacts that

can reduce their accuracy, due to their frequent transportation and use on construction sites.

The occurrence of any such incidence can be detected in an inconsistency in the inclinometer

probe reading.

This study designs and evaluates alternatives for creating a testing method for inclinometer

probes. Each alternative is designed as a controlled environmental in which the probe can be

used to take a test reading, which is compared with previous readings for consistency. The

objective of the test readings is not to evaluate the absolute quantity of the probe

measurements, but rather the consistency of readings over the period between one calibration

and the next. This would aid to determine whether annual calibrations are sufficient to

maintain the desired level of quality in measurements. It would also serve as in indicator of

incidents that may have damaged the probes.

Four alternatives were evaluated based on their abilities to perform the test, their operability

and their cost. Of the two alternative that were able to perform the test satisfactorily, one was

chosen based on its operability. Recommendations are made regarding the testing procedures.

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TABLE OF CONTENTS

Summary ...................................................................................................................................... 2

LIST OF FIGURES ..................................................................................................................... 4

LIST OF APPENDICES ............................................................................................................. 4

1.0 Introduction ...................................................................................................................... 5

1.1 Application Method of Inclinometer Monitoring ......................................................... 5

1.2 Inclinometer Monitoring Instrument ............................................................................ 7

2.0 Problem Statement ............................................................................................................ 8

2.1 Error Boundaries ........................................................................................................... 9

2.2 General Objectives ...................................................................................................... 12

2.3 Operational Objectives ............................................................................................... 12

2.4 Economic Objectives .................................................................................................. 13

3.0 Solution Alternatives ...................................................................................................... 13

3.1 Fixed Installations ....................................................................................................... 15

3.1.1 Fixed Concrete Encased Installation ................................................................... 15

3.1.2 Fixed Tied Installation ......................................................................................... 17

3.2 Adjustable Installations ............................................................................................... 17

3.2.1 Adjustable Concrete Encased Installation ........................................................... 18

3.2.2 Adjustable Tied Installation................................................................................. 19

4.0 Alternatives Evaluation .................................................................................................. 19

4.1 Concrete Encased Installation Evaluation .................................................................. 20

4.2 Tied Installation Evaluation ........................................................................................ 21

4.3 Adjustable Concrete Installation ................................................................................. 21

4.4 Adjustable Tied Installation ........................................................................................ 22

4.5 Alternatives Comparison ............................................................................................ 23

5.0 Conclusions .................................................................................................................... 24

6.0 Recommendations .......................................................................................................... 25

Bibliography .............................................................................................................................. 26

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LIST OF FIGURES

Figure 1: Inclinometer Casing Installation .................................................................................. 6

Figure 2: Inclinometer Sensor (Digital Inclinometer Spiral Sensor, 2015) ................................. 7

Figure 3: Inclinometer Probe Reading (Digitilt Inclinometer Probe Datasheet, 2009) ............... 8

Figure 4: Inclinometer Probe Measurement Errors over Depth (Mikkelsen, 2003) .................. 10

Figure 5: Extrapolated Errors .................................................................................................... 11

Figure 6: ElectroLevel Sensor (EL Beam Sensors & Tiltmeters, 2013) ................................... 14

Figure 7: Concrete Encased Installation .................................................................................... 16

Figure 8: Fixed Tied Installation ............................................................................................... 17

Figure 9: Adjustment configuration .......................................................................................... 19

LIST OF APPENDICES

APPENDIX A – Sensor Specifications ..................................................................................... 28

APPENDIX B – Hand Calculations .......................................................................................... 29

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1.0 Introduction

One of the services provided by Monir Precision Monitoring is the periodic monitoring of

shoring pile deflections in large excavations. As excavations deepen, the shoring piles along

the perimeter of the excavation experience forces pushing them into the excavated pit and

strain as a result. The purpose of this service is to measure precisely the amount of pile

movement caused by the strain. This can help indicate whether additional supports are

necessary. The same service can be applied to tracking movements for dams and foundations.

1.1 Application Method of Inclinometer Monitoring

To monitor a shoring pile, a plastic tube casing is first installed along the full length of the pile

to be monitored before it is driven into the ground. The plastic casing used by Monir is

composed of ABS plastic and measures 85mm in diameter externally (RST Instruments).

When the pile is installed, the plastic casing remains attached, as shown in Figure 1. The

plastic casing is fully secured to the pile and follows any deflections experienced by the pile.

To take a reading, an inclinometer is inserted into the casing and lowered to the bottom. It is

drawn up by an attached cable and anchored at every 0.5m to measure the slope of the tube at

these intervals from the bottom up. These slopes are then used to map out the overall shape of

the pile.

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Figure 1: Inclinometer Casing Installation

The first reading is taken soon after the pile is driven, before any excavation occurs. This

initial reading is plotted in a straight line as a base reference. Subsequent readings are plotted

in terms of their deviation from the original data to show deflections from the original position

since the first reading. The data from several readings over time are plotted on top of each

other to compare deflections over time.

It is assumed that the very bottom of the pile does not move significantly, since is it driven

several meters below the planned excavation depth. This can usually be confirmed when the

mapped pile shapes show little or no change for the lower portion of the pile. Thus, the plotted

INCLINOMETER CASING

H-PILE

CAISSONS

7

shapes are anchored at the lowest data point, and fan out towards the top depending on the

measured slopes. In addition, total stations are used to monitor targets placed at the top of piles

to cross check measurements.

1.2 Inclinometer Monitoring Instrument

The inclinometers used by Monir Precision Monitor are the Digital Inclinometer Spiral

Sensors provided by RST Instruments, as shown in Figure 2. They are designed to fit inside

the plastic casing such that the wheels on the inclinometer probe run along tracks inside the

casing as illustrated in Figure 3. The arms attached to the wheels are spring hinged to the

probe so that the wheels are pressed against the casing when inserted, holding the probe

centered in place as it runs through the casing. The probe is attached to a cable at one end,

allowing the user to slowly lower it into the casing and pull it back up. The cable is also a data

connection between the probe and a wireless transmitter contained inside the cable reel.

Measurement data from the probe is sent by the transmitter into a hand-held device used for

reading and storing the data. This device can be connected to a computer to upload the data

and generate reports.

Figure 2: Inclinometer Sensor (Digital Inclinometer Spiral Sensor, 2015)

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Figure 3: Inclinometer Probe Reading (Digitilt Inclinometer Probe Datasheet, 2009)

These inclinometers are capable of measuring tilt in two dimensions: in the lateral direction in

line with the wheels, and in the lateral direction perpendicular to the wheels. Typically, for the

purpose of the applications used by Monir, measurements in only one dimension is used, since

clients are usually only interested in the movement of piles in the direction perpendicular to

excavation perimeters. The inclinometer plastic casings have tracks in both directions, but

readings are taken such that the wheels of the inclinometer probe are positioned along the

direction of measurement.

2.0 Problem Statement

The inclinometer probes are extremely sensitive to physical impact. Knocking or dropping a

probe can offset the calibration. Therefore, the instruments are handled with care and

transported in heavy duty protective cases. However, the instruments are taken daily to

construction sites where they may be subject to impacts. Furthermore, piles and casings are

not always kept in good condition or in a clean environment, which adds to the risk of

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undesirable impacts on the inclinometer probes. Risks caused by general wear and tear,

environmental conditions or mishandling are highly probable.

Each probe is sent for calibration every two years, as recommended by the manufacturer.

However, within two years, the calibration of the probe may fall beyond its desired error

margin due to various reasons. Therefore, it is important to develop a method of detection for

the accuracy of the probe readings for quality control purposes. This quality control method

would serve as a check between the calibrations to ensure that the calibrations do not need to

occur more often, or to detect whether a damaging incident has occurred to the probe.

2.1 Error Boundaries

Since the plots of pile measurements are shown as deflections relative to the original position

rather than the absolute deflected shape, the quality control is more concerned with the probe’s

consistency relative to its previous readings rather than accuracy in taking absolute

measurements. The inclinometer probes are accurate to a displacement of ±2mm per 25m

according to the user manual (RST Instruments Ltd., 2014, p. 54). The sensor specifications

are included in Appendix A. This error is accumulated from the readings over 25m. With

readings at every 0.5m interval, there would be 50 readings over this range. However, this is

the absolute error. The relative error of the readings is required to be ±2mm over the entire

length of the pile, as a standard set by Monir.

The errors consist of a random error and a systematic error for each reading. The random error

has been observed to accumulate at a rate equal to the square root of the number of readings

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taken into account when systematic errors sources are removed. The remaining systematic

error then accumulates arithmetically. That is,

𝑇𝑜𝑡𝑎𝑙 𝐸𝑟𝑟𝑜𝑟

= 𝑅𝑎𝑛𝑑𝑜𝑚 𝐸𝑟𝑟𝑜𝑟 + 𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝐸𝑟𝑟𝑜𝑟

= 𝐸𝑅 × √𝑛 + 𝐸𝑆 × 𝑛

where ER is the random error for a single reading, n is the number of readings taken into

account and ES is the systematic error for a single reading. This relationship, shown in Figure

4, was established empirically over readings of 30m (Mikkelsen, 2003).

Figure 4: Inclinometer Probe Measurement Errors over Depth (Mikkelsen, 2003)

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Currently, the deepest shoring piles requiring monitoring is a little over 30m (Monir Precision

Monitoring, n.d.). It would be sufficient for the inclinometers to maintain accuracy over 35m

of readings. To estimate the error composition ratio of such a reading, the error trend in Figure

4 is extrapolated as in Figure 5. The total extrapolated error amounts to +9mm and -10mm,

averaging ±9.5mm.

The random error of a single probe reading was 0.16mm (Mikkelsen, 2003). Over 35m or 70

readings, this would result in a total random error of

𝐸𝑅 = 0.16 × √70 = 1.34𝑚𝑚

Figure 5: Extrapolated Errors

12

The error over 35m would consist of approximately 13% random error and 87% systematic

error. Using this ratio to work backwards from the required ±2mm error margin for 35m, the

error of a single reading is required to be within ±0.056mm.

2.2 General Objectives

In order to detect the accuracy of an inclinometer probe, a controlled environment is required

with known slopes measurable by the probe. The testing apparatus would need to provide an

environment where the slope measured by the inclinometer can be externally measured and

controlled or maintained. In the case that environmental changes alter the installation

sufficiently, it must be made aware. Hence it is recommended to have a secondary measuring

device tracking the installation. The secondary measuring device must have an error margin

smaller than the required error margin of the inclinometer probe tested. The smaller the error

margin of the secondary device, the easier it will be to determine whether the inclinometer has

indeed passed the test.

2.3 Operational Objectives

Since the inclinometer probes are depended upon on an almost daily basis, they must be tested

on a frequent, periodic basis to ensure they do not fail to deliver quality results for every use.

Ideally, the testing method should be performed in-house without requiring third party

services. Therefore, the apparatus required must be located in the office or warehouse and

must be easily operable by any member in the inclinometer department. It is also important for

13

the test to be performed quickly and conveniently due to how frequently they must be

performed. Thus, the testing procedure must be brief and as straightforward as possible.

2.4 Economic Objectives

The overall cost of the quality control method should be kept to a minimum. This includes the

cost of building any required apparatus, maintaining said apparatus, and utilizing it for each

test. The warehouse already contains many spare parts with no immediate usefulness available

for building the installation. The existing inventory will be taken into account for the cost

analysis.

3.0 Solution Alternatives

A practical way to test the reading of the inclinometer is to create a dummy installation that

can be measured by the probe in a way similar to how it is used on-site. This dummy

installation would include a plastic casing the same as that installed on site. The plastic casing

would have a tilt that can be independently controlled or maintained so as to provide a

consistent environment. Several options are considered as ways of building this installation.

For all alternatives, the length of the casing should be sufficient to allow the inclinometer

probe to be fully inserted to take a reading. For a probe length of 710mm, a 750mm casing

would be sufficient. The probe must be positioned as consistently as possible during every

reading to reduce errors created in the testing process. This can be ensured by simply giving

the casing a secure base and keeping it free of debris.

14

The area around the installation must remain clear to prevent the installation from being

altered. The installation should also be protected from mishaps in the warehouse. This can be

achieved by constructing a barrier around the installation. A simple, rectangular wooden box

build around the installation with a removable cover would suffice. The box size should be

minimized to avoid taking up space in the warehouse, but must be large enough or designed in

a way such that all parts of the installation can be accessed.

For the secondary measuring device, ElectroLevel tilt sensors (EL Sensors) pictured in Figure

6 are recommended as they are already available in the warehouse and without foreseeable

future demand. Their error margin is ±3 arc seconds (Durham Geo Slope Indicator, 2013).

This is equivalent to a tilt of ±7.27×10-3mm per 0.5m length and is acceptable as the checking

device since it is an order of magnitude under the required error margin of the inclinometer

probe to be tested.

Figure 6: ElectroLevel Sensor (EL Beam Sensors & Tiltmeters, 2013)

15

Although the EL Sensor cannot measure the tilt of the inclinometer casing exactly the same

way as it is measured by the inclinometer probe, it can be used to monitor deviations of the

casing slope from previous readings. Since the purpose of this test installation is to monitor

consistency rather than absolute accuracy, the EL Sensor is sufficient as a secondary means of

control.

3.1 Fixed Installations

To create a consistent testing environment, the casing may be permanently secured such that

no accidental tampering or environmental changes can alter the slope. The installation would

be fixed to the warehouse floor in a location that conflicts as little as possible with other

warehouse activities.

The warehouse floor is cement and at the same grade as the external ground. There are no

storeys below the warehouse. The structural composition beneath the cement floor is

unknown. However, it is sufficient to carry the floor-to-ceiling warehouse shelves as well as

concrete brick walls. Thus, a small installation such as this would not add a significant load to

the warehouse floor.

3.1.1 Fixed Concrete Encased Installation

To firmly secure the plastic casing and also closely simulate site conditions, the plastic casing

could be encased in concrete, as it would be in a caisson on-site. This way, the casing

deflection and movement is maximally secured. The concrete should be wide enough to

provide stability and durability over time, or to allow the concrete to pour and fill the

16

formwork easily, whichever is greater. However, the dimensions should be kept to a minimum

to reduce shrinkage, creep or changes due temperature. It must also be secured firmly to the

floor of the warehouse.

This installation can be built by bolting a rough wire frame into the cement floor, building

formwork around the frame, and then positioning the plastic casing in the centre while pouring

concrete around it. The finished installation illustrated in Figure 7 would be approximately

285mm in length and width, and 750mm in height. Two EL Sensors would be screwed onto

adjacent faces of the installation to measure tilt in both directions. They should also be secured

with cement adhesives to prevent any detachment.

Figure 7: Concrete Encased Installation

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3.1.2 Fixed Tied Installation

The casing could be tied to a steel post, which is then bolted to the warehouse floor, as

illustrated in Figure 8. To prevent sliding or other minor movements, the casing, ties and post

would be stiffened together at joints with ABS cement or caulking. The EL Sensors would be

tied directly to the plastic casing in the two orientations. They would also be secured with

cement adhesive.

Figure 8: Fixed Tied Installation

3.2 Adjustable Installations

The installation may require adjustments if the deviations of the natural environment exceeds

the permitted error of the inclinometer probes tested. For adjustable installations, the EL

18

Sensors are not merely secondary control devices, but rather essential to the functioning of the

installation. They would be depended up to adjust the installation back to the original tilt as

when the probe test reading was performed.

The adjustments require sufficient finesse to be practical for testing precise instruments. The

desirable resolution of the adjustments is in the same order of magnitude as the EL Sensors’

error margin, which is ±7.27×10-3mm. This resolution should be met as closely as possible,

but further precision beyond this value would be unnecessary.

The range of adjustment, however, does not need to be large, as the installation will not be

altered significantly and only minor, unpreventable deflections in the environment are

expected to alter the tilt of the casing.

3.2.1 Adjustable Concrete Encased Installation

The general structure of this installation alternative is similar to the fixed encased concrete

installation, but with a few additional attachments. To create an adjustable concrete

installation, the concrete should not be in direct contact with the ground to easily allow a range

of movements. The concrete can sit on a base plate attached to the ground by a ball and socket

pin connection to allow tilt adjustments. Two height adjustment screws of fine precisions

would be required to control the tilt adjustment with respect to the two axes. The pin

connection and height adjustment screws can be placed in the configuration in Figure 9.

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Figure 9: Adjustment configuration

3.2.2 Adjustable Tied Installation

The adjustable tied installation shares the same mounting post and EL Sensor attachment as

the fixed tied installation. However, the attachments would require adjustment screws similar

to the height adjustment screws for adjusting the concrete installation, but placed horizontally

in perpendicular orientations.

The casing must be attached by hinge connections that allowed the casing to rotate vertically

in both lateral axes to prevent bending. If bending occurs, the EL Sensors’ measurement of the

casing tilt will be greatly reduced in accuracy.

4.0 Alternatives Evaluation

Each of the four alternatives are evaluated first based on their ability to meet the general

objectives. Only alternatives that meet general objectives are evaluated based on their ability

to meet operational and economic objectives. Alternatives that do not meet the general objects

are discarded from further evaluation.

ADJUSTMENT SCREWS

BALL AND SOCKET PIN

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4.1 Concrete Encased Installation Evaluation

To evaluate the concrete encased installation, concrete volume changes over time are

considered. The phenomena under consideration are shrinkage and thermal expansion. The

shrinkage strain for this dimension of concrete could be as much as 910×10-6, which results in

a shrinkage of 0.091mm (Gilbert, 2001). The thermal expansion of the concrete is determined

by its thermal coefficient and temperature fluctuations. The warehouse is an indoor air

conditioned area, but has a large garage door. To account for periods when the garage door is

open, a larger temperature range is considered. With an average thermal coefficient of 10×10-

6/Cº and a conservatively estimated temperature range from 10 - 30 Cº, the concrete could

experience thermal expansions of up to 0.02mm as an expansion or contraction.

Assuming that there is no differential shrinkage or expansion and that the volume change is

equal on the inside and outside of the concrete, the width of the inside walls surrounding the

plastic casing could expand up to 0.101mm with the thermal and shrinkage volume changes

combined. This change in volume could cause the plastic casing to slope by the same amount

of 0.101mm, which exceeds the error boundary of ±0.056mm required for the inclinometer

probe. Therefore, the permanently secured concreted encased installation is not sufficient for

the testing purposes. This alternative can only be made sufficient by adding adjustment

capabilities.

21

4.2 Tied Installation Evaluation

The first factor taken into consideration is the thermal expansion of the steel post. From the

geometry of the attachment and steel post, if differential expansion is not expected, thermal

expansion should not alter the slope of the plastic casing.

However, it cannot be assumed that the floor under the post will not experience any minute

differential settlement, since is it surrounded by human traffic and other live loads. The exact

settlement of the concrete floor and how much it differentiates cannot be determined due to

lack of loading information and structural property data, such as floor thickness and

composition. It is however reasonable to assume that the tilting caused by the floor

movements would be greater than the tilting caused by the concrete volume change in the

previous installation, since the floor has greater dimensions and experiences greater loads,

resulting in a greater capacity to deflect.

This principle applies to the previously evaluated concrete encased installation as well.

However, in comparison, the tied installation poses a smaller risk of failing the general

objectives, due to the geometry of its composition.

4.3 Adjustable Concrete Installation

The same analysis of volume change in the concrete applied in section 4.1 can also be applied

for the adjustable concrete installation. However, for the adjustable installation, any possible

tilt caused by the concrete’s volume change can be overcome by adjusting the installation.

Thus, this alternative meets the general objectives.

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In terms of performance, the installation may require frequent adjustments prior to performing

test readings as the concrete shrinks and expands over time. Although not difficult, this could

create an inconvenience depending on how easily the casing can be adjusted to its original tilt.

The cost of this alternative includes the cost of the concrete, hinge, base plate, height

adjustment screws and formwork. The short piece of casing and EL Sensor equipment are not

included since they are considered discarded supplies in the warehouse. Furthermore, they are

part of every alternative and do not contribute to cost differences. Table 1 lists the cost

estimates for the parts of this installation.

Table 1: Cost of the Adjustable Concrete Encased Installation

Item Cost Estimate

Concrete $11.74 (Home Depot, 2016)

Hinge $15.95 (Pro-Fit International, 2014)

Base plate $10.00

Adjustment screws 2 × $22.55 (Newport, 2016)

Formwork $5.00

Total $87.79

4.4 Adjustable Tied Installation

The adjustable tied installation is similar to the fixed tied installation except that any changes

in tilt can be resolved through adjustments, allowing this alternative to meet the general

objectives.

23

Since the tied installation is expected to experience less tilt fluctuations than the concrete

encased installation, the adjustable tied installation can be expected to require less frequent or

less extensive adjustments than the adjustable concrete encased installation. This could result

in significant operational time depending on how often the test readings are performed.

The cost of this alternative includes a metal post, bolts, precision adjustment screws, metal

ribbon ties, connection pin hinges, ABS cement and other minor hardware. It should be noted

that some of these parts such as the minor hardware can be found around the warehouse. Table

2 lists the cost estimates of these items.

Table 2: Cost of the Adjustable Tied Installation

Item Cost Estimate Notes

Metal post $15.58 (Home Depot, 2016)

Bolts $10.00

Adjustment screws 2 × $22.55 (Newport, 2016)

Metal ribbon ties 2 × $0.72 (Home Depot, 2016)

Pin hinges 2 × $10.00

ABS cement $2

Total $94.12

4.5 Alternatives Comparison

Of the four alternatives which are shown in Table 3, two meet the general objective

requirements, both of which are adjustable installations. In terms of the economic objective

criterion, the difference in cost between the two objectives are minor in comparison to the

whole cost, especially when taking cost estimate errors into account. Thus, the cost is not a

24

major factor in determining the most preferable alternative. That leaves the operational

criterion as a deciding factor. The adjustable tied installation is the most favourable in terms of

operability, as it will require the least amount of adjustment effort due to a more stable

structure.

Table 3: Alternatives Comparison

Criteria

Installation Alternative Performance Operability Cost

Fixed Concrete Encased Failed n/a n/a

Fixed Tied Failed n/a n/a

Adjustable Concrete Encased Pass Adequate $87.79

Adjustable Tied Pass Optimal $94.12

5.0 Conclusions

Four alternatives were considered in the selection of an installation to performing test readings

of inclinometer probes. They include two fixed installations with one held in concrete and the

other secure to a metal post, and two adjustable installations of similar nature as the two fixed

installations. The analysis considered the ability of each alternative to provide adequate

conditions for the test reading, taking into account acceptable error boundaries. Operability

and cost factors were also considered.

The result of the analysis showed that only two alternatives are capable of performing

adequately. Of these two alternatives, the deciding characteristic is their ease of operation,

since their costs were similar. The most preferable alternative according to these criteria is the

adjustable tied installation.

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6.0 Recommendations

When performing the test readings, it is recommended to take several readings per test, time

permitting. This is to reduce the likelihood of one test passing the error check by sheer luck. A

sufficient amount of tests can be performed to define a normal distribution of test readings.

Using this distribution, it can be determined with a certain confidence level whether the probe

remains within its required accuracy. This is only recommended if the time spent is deemed

worthwhile against the risks mitigated.

26

Bibliography

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Gilbert, R. I. (2001). Shrinkage, Cracking and Deflection-the Serviceability of Concrete

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APPENDIX A – Sensor Specifications

29

APPENDIX B – Hand Calculations