Geokon 4425 User manual

Instruction Manual
Model 4425
VW Convergence Meter
No part of this instruction manual may be reproduced, by any means, without the written consent of Geokon®.
The information contained herein is believed to be accurate and reliable. However, Geokon®assumes no responsibility for errors,
omissions or misinterpretation. The information herein is subject to change without notification.
Copyright © 1985-2019 by Geokon®
(Doc Rev O, 2/21/2019)


Warranty Statement
Geokon warrants its products to be free of defects in materials and workmanship, under normal
use and service for a period of 13 months from date of purchase. If the unit should malfunction,
it must be returned to the factory for evaluation, freight prepaid. Upon examination by Geokon,
if the unit is found to be defective, it will be repaired or replaced at no charge. However, the
WARRANTY is VOID if the unit shows evidence of having been tampered with or shows
evidence of being damaged as a result of excessive corrosion or current, heat, moisture or
vibration, improper specification, misapplication, misuse or other operating conditions outside of
Geokon's control. Components which wear or which are damaged by misuse are not warranted.
This includes fuses and batteries.
Geokon manufactures scientific instruments whose misuse is potentially dangerous. The
instruments are intended to be installed and used only by qualified personnel. There are no
warranties except as stated herein. There are no other warranties, expressed or implied, including
but not limited to the implied warranties of merchantability and of fitness for a particular
purpose. Geokon is not responsible for any damages or losses caused to other equipment,
whether direct, indirect, incidental, special or consequential which the purchaser may experience
as a result of the installation or use of the product. The buyer's sole remedy for any breach of this
agreement by Geokon or any breach of any warranty by Geokon shall not exceed the purchase
price paid by the purchaser to Geokon for the unit or units, or equipment directly affected by
such breach. Under no circumstances will Geokon reimburse the claimant for loss incurred in
removing and/or reinstalling equipment.
Every precaution for accuracy has been taken in the preparation of manuals and/or software,
however, Geokon neither assumes responsibility for any omissions or errors that may appear nor
assumes liability for any damages or losses that result from the use of the products in accordance
with the information contained in the manual or software.


TABLE of CONTENTS
1. INTRODUCTION ...................................................................................................................................................1
2. INSTALLATION ....................................................................................................................................................2
2.1 PRELIMINARY TESTS............................................................................................................................................2
2.2 CONVERGENCE METER INSTALLATION................................................................................................................2
2.3 ELECTRICAL NOISE..............................................................................................................................................4
2.4 REMOVAL ............................................................................................................................................................4
2.5 CABLE INSTALLATION AND SPLICING ..................................................................................................................5
3. TAKING READINGS.............................................................................................................................................6
3.1 GK-404 READOUT BOX.......................................................................................................................................6
3.1.1 Operating the GK-404 ................................................................................................................................6
3.2 GK-405 READOUT BOX.......................................................................................................................................7
3.2.1 Connecting Sensors with 10-pin Bulkhead Connectors Attached ...............................................................7
3.2.2 Connecting Sensors with Bare Leads..........................................................................................................7
3.2.3 Operating the GK-405 ................................................................................................................................7
3.3 GK-403 READOUT BOX (OBSOLETE MODEL)......................................................................................................8
3.3.1 Connecting Sensors with 10-pin Bulkhead Connectors Attached ...............................................................8
3.3.2 Connecting Sensors with Bare Leads..........................................................................................................8
3.3.3 Operating the GK-403 ................................................................................................................................8
3.4 MEASURING TEMPERATURES...............................................................................................................................8
4. DATA REDUCTION ..............................................................................................................................................9
4.1 DIGITS .................................................................................................................................................................9
4.2 TEMPERATURE CORRECTION .............................................................................................................................10
4.3 ROD STRETCH CORRECTION ..............................................................................................................................11
4.4 CORRECTION FOR SAG .......................................................................................................................................12
4.5 ENVIRONMENTAL FACTORS...............................................................................................................................14
5. TROUBLESHOOTING........................................................................................................................................15
APPENDIX A. SPECIFICATIONS.........................................................................................................................17
A.1 MODEL 4425 CONVERGENCE METER ...............................................................................................................17
A.2 THERMISTOR (SEE APPENDIX BALSO) ..............................................................................................................17
APPENDIX B. THERMISTOR TEMPERATURE DERIVATION.....................................................................18
APPENDIX C. SWAGELOK TUBE FITTING INSTRUCTIONS ......................................................................19
C.1 INSTALLATION ..................................................................................................................................................19
C.2 REASSEMBLY INSTRUCTIONS ............................................................................................................................20
APPENDIX D. EXAMPLE CALIBRATION REPORT........................................................................................21

FIGURES
FIGURE 1-MODEL 4425 CONVERGENCE METER........................................................................................................... 1
FIGURE 2-OPERATION CHECK...................................................................................................................................... 2
FIGURE 3-MODEL 4425 CONVERGENCE METER INSTALLATION .................................................................................. 3
FIGURE 4-CONVERGENCE METER INSTALLATION DETAIL -TURNBUCKLE END........................................................... 4
FIGURE 5-LEMO CONNECTOR TO GK-404 ................................................................................................................... 6
FIGURE 6-LIVE READINGS –RAW READINGS............................................................................................................... 7
FIGURE 7-TUBE INSERTION .........................................................................................................................................19
FIGURE 8-MAKE A MARK AT SIX O’CLOCK ................................................................................................................19
FIGURE 9-TIGHTEN ONE AND ONE-QUARTER TURNS .................................................................................................19
FIGURE 10 -MARKS FOR REASSEMBLY ........................................................................................................................20
FIGURE 11 -FERRULES SEATED AGAINST FITTING BODY.............................................................................................20
FIGURE 12 -TIGHTEN NUT SLIGHTLY...........................................................................................................................20
FIGURE 13 -TYPICAL 4425 CALIBRATION REPORT.......................................................................................................21
TABLES
TABLE 1-CONVERGENCE METER LENGTH ................................................................................................................... 3
TABLE 2-ENGINEERING UNITS CONVERSION MULTIPLIERS ......................................................................................... 9
TABLE 3-TRANSDUCER THERMAL COEFFICIENT CALCULATION CONSTANTS .............................................................10
TABLE 4-YOUNG’S MODULUS AND THERMAL COEFFICIENTS.....................................................................................11
TABLE 5-SPRING RATES..............................................................................................................................................12
TABLE 6-DENSITIES ....................................................................................................................................................12
TABLE 7-SAMPLE RESISTANCE ...................................................................................................................................16
TABLE 8-RESISTANCE WORK SHEET...........................................................................................................................16
TABLE 9-THERMISTOR RESISTANCE VERSUS TEMPERATURE .....................................................................................18
EQUATIONS
EQUATION 1-DIGITS CALCULATION............................................................................................................................. 9
EQUATION 2-DEFORMATION CALCULATION ................................................................................................................ 9
EQUATION 3-TEMPERATURE CORRECTION .................................................................................................................10
EQUATION 4-TRANSDUCER THERMAL COEFFICIENT CALCULATION...........................................................................10
EQUATION 5-THERMALLY CORRECTED DEFORMATION CALCULATION ......................................................................11
EQUATION 6-ROD STRETCH ........................................................................................................................................11
EQUATION 7-ROD STRETCH CORRECTION...................................................................................................................11
EQUATION 8-SAG CORRECTION ..................................................................................................................................12
EQUATION 9-CORRECTED DEFORMATION...................................................................................................................13
EQUATION 10 -RESISTANCE TO TEMPERATURE ...........................................................................................................18

1
1. INTRODUCTION
The Model 4425 Vibrating Wire Convergence
Meter is designed to detect the deformation of
rock or soil masses by measuring the contraction
(or elongation) between two fixed anchor points.
Anchor points are established in the mass, and
connecting rods from one anchor lead back to
transducer assembly located at the second anchor
point. Changes in distance between the two
anchors are conveyed by the connecting rods and
measured by the transducer.
The Model 4425 Convergence Meter consists of
three basic components: the two anchor points, 6
mm (1/4") diameter connecting rods, and the
spring-tensioned vibrating wire transducer
assembly. (See Figure 1.) Essential accessories
include: A vibrating wire readout and an
installation tool kit (supplied).
The transducer consists of a vibrating wire sensing
element in series with a heat treated, stress
relieved spring which is connected to the wire at
one end and a connecting rod at the other. The
unit is fully sealed and operates at pressures of up
to 250 psi. As the connecting rod is pulled out
from the gauge body, the spring is elongated
causing an increase in tension, which is sensed by
the vibrating wire element. The tension in the wire
is directly proportional to the extension, so the
convergence can be determined very accurately by
measuring the strain change with the vibrating
wire readout box.
The convergence meter can operate in horizontal,
inclined, or vertical orientations. In areas where
construction traffic is expected or where the
instrument may be left in an exposed location,
some form of protective housing should be
considered.
Turnbuckle
Eye Hook
Swagelok Fitting
Thermistor
Spring
Transducer Shaft
Connecting Rod
Electromagnetic Coil
Instrument Cable
Swagelok Fitting
Eye Hook
Alignment Slot & Pin
Transducer Housing
Swagelok Fitting
Left-Hand Thread
Right-Hand Thread
Figure 1 - Model 4425 Convergence Meter

2
2. INSTALLATION
2.1 Preliminary Tests
Upon receipt of the instrument, the gauge should be checked for proper operation (including the
thermistor). See Section 3 for readout instructions. In position “B” the gauge will read around
2000 when the threaded connector is pulled out approximately 3 mm (0.125").
Figure 2 - Operation Check
CAUTION! Do not extend the connector more than the range of the gauge. Do not turn the
threaded shaft at the end of the gauge more than 180 degrees or gauge failure may occur!
Checks of electrical continuity can also be made using an ohmmeter. Resistance between the
gauge leads (red and black) should be approximately 180 Ω, ±10 Ω. Resistance between the
thermistor leads (white and green) varies with temperature; see Appendix B. Resistance between
any conductor and the shield should exceed two megohms. (For long cables a correction can be
applied, equal to approximately 14.7 Ω per one thousand feet [48.5Ω per km] of 22 AWG
stranded copper leads. Multiply this factor by two to account for both directions.)
2.2 Convergence Meter Installation
1) The first step is to unpack all the various components and lay them on a flat surface in their
relative positions. (Refer to Figure 1 in Section 1.)
2) Next, the two anchor points must be installed. When the locations have been decided, drill
holes to accommodate the anchors. Cement the eyebolt anchors in place using quick-set
(hydraulic) cement or epoxy. Allow the cement or epoxy to set completely before attempting
the installation of the convergence meter.
3) Attach the turnbuckle assembly to the convergence meter by screwing in the left-hand
threaded portion. Use thread locking cement and tighten the lock nut. Set the turnbuckle such
that about 10-12 mm (0.5") of thread is inside from each end
.
4) Measure the total distance from anchor eyebolt to anchor eyebolt, inside to inside at the
points where they will touch the convergence meter eyehooks.
5) Check and confirm the convergence meter length against the length shown in Table 1. The
measurement is made from inside the eyehooks (at the point where they touch the anchor
eyebolts), to the end of the Swagelok fitting. To calculate the rod length that will be needed,
subtract the convergence meter length from the anchor eyebolt to anchor eyebolt distance,

3
add 30 mm (1.2") to account for the distance the rod penetrates the Swagelok fittings. This is
the nominal rod length that will be required.
Range:
12 mm
0.50 inches
25 mm
1 inch
50 mm
2 inches
100 mm
4 inches
150 mm
6 inches
Convergence Meter Length
(Including Swagelok
eyehook assembly):
710 mm
28"
710 mm
28"
865 mm
34"
1195 mm
47"
1615 mm
63.5"
Table 1 - Convergence Meter Length
6) Next, the connecting rods must be assembled. Connect the first length of connecting rod to
the sensor using the Swagelok fitting. Push the rod into the fitting until it hits the stop.
Tighten the Swagelok connector according to the instructions in Appendix C. Connect the
second and successive rods using the Swagelok fittings as described above.
7) Connect the Swagelok eyehook to one end of the rods and the convergence meter to the
other.
8) Hook the eyehook end into the installed eyebolt first.
9) Hook the convergence meter into the other eyebolt. It should go in without having to extend
the convergence meter spring. Remember that if the spring is extended beyond the range
of the transducer the transducer could be damaged.
Tunnel Cross Section
Convergence Meter Connecting Rod
Eyebolt Anchor Eyebolt Anchor
Figure 3 - Model 4425 Convergence Meter Installation

4
10) Connect the readout box. To set the transducer to midrange, rotate the turnbuckle until a
reading of approximately 5500 digits is obtained. To use the total range in convergence, set
the meter at 8000. To use the total range in extension, set the meter at 2500.
11) Tighten the locknuts on the turnbuckle. (See Figure 4 below.)
12) Initial readings must be taken and carefully recorded along with the temperature at the time
of installation.
Figure 4 - Convergence Meter Installation Detail - Turnbuckle End
2.3 Electrical Noise
Care should be exercised when installing instrument cables to keep them as far away as possible
from sources of electrical interference such as power lines, generators, motors, transformers, arc
welders, etc. Cables should never be buried or run with AC power lines! The instrument cables
will pick up the 50 or 60 Hz (or other frequency) noise from the power cable and this will likely
cause a problem obtaining a stable reading. Contact the factory concerning filtering options
available for use with the Geokon dataloggers and readouts should difficulties arise.
2.4 Removal
To remove the system, loosen the turnbuckle all the way and then remove the convergence
meter. Disconnect the Swagelok fittings on the rods and disassemble the rods to a manageable
length. If the rod string needs to be lengthened (or shortened) for the next installation, cut off the
ferrules and reinstall new ferrules for the next installation.

5
2.5 Cable Installation and Splicing
The cable should be routed to minimize the possibility of damage due to moving equipment,
debris or other causes. The cable can be protected by the use of flexible conduit, which can be
supplied by Geokon.
Terminal boxes with sealed cable entries are available from Geokon for all types of applications.
These allow many gauges to be terminated at one location with complete protection of the lead
wires. The interior panel of the terminal box can have built-in jacks or a single connection with a
rotary position selector switch. Contact Geokon for specific application information.
Because the vibrating wire output signal is a frequency rather than a current or voltage,
variations in cable resistance have little effect on gauge readings; therefore, splicing of cables
has no ill effects, and in some cases may in fact be beneficial. The cable used for making splices
should be a high quality twisted pair type, with 100% shielding and an integral shield drain wire.
When splicing, it is very important that the shield drain wires be spliced together. Always
maintain polarity by connecting color to color.
Splice kits recommended by Geokon incorporate casts, which are placed around the splice and
are then filled with epoxy to waterproof the connections. When properly made, this type of splice
is equal or superior to the cable in strength and electrical properties. Contact Geokon for splicing
materials and additional cable splicing instructions.
Cables may be terminated by stripping and tinning the individual conductors and then connecting
them to the patch cord of a readout box. Alternatively, a connector may be used which will plug
directly into the readout box or to a receptacle on a special patch cord.

6
3. TAKING READINGS
3.1 GK-404 Readout Box
The Model GK-404 Vibrating Wire Readout is a portable, low-power, handheld unit that is
capable of running for more than 20 hours continuously on two AA batteries. It is designed for
the readout of all Geokon vibrating wire gauges and transducers, and is capable of displaying the
reading in either digits, frequency (Hz), period (µs), or microstrain (µε). The GK-404 also
displays the temperature of the transducer (embedded thermistor) with a resolution of 0.1 °C.
3.1.1 Operating the GK-404
Before use, attach the flying leads to the GK-404 by aligning the red circle on the silver
“Lemo” connector of the flying leads with the red line on the top of the GK-404 (Figure
5). Insert the Lemo connector into the GK-404 until it locks into place.
Figure 5 - Lemo Connector to GK-404
Connect each of the clips on the leads to the matching colors of the sensor conductors,
with blue representing the shield (bare).
To turn the GK-404 on, press the “ON/OFF” button on the front panel of the unit. The
initial startup screen will display:
Geokon Inc.
GK-404 verX.XX
After approximately one second, the GK-404 will start taking readings and display them
based on the settings of the POS and MODE buttons.
The unit display (from left to right) is as follows:
•The current Position: Set by the POS button, displayed as a letter A through F.
•The current Reading: Set by the MODE button, displayed as a numeric value
followed by the unit of measure.
•Temperature reading of the attached gauge in degrees Celsius.
Use the POS button to select position Band the MODE button to select Dg (digits).
(Other functions can be selected as described in the GK-404 Manual.)
The GK-404 will continue to take measurements and display readings until the unit is
turned off, either manually, or if enabled, by the Auto-Off timer. If no reading displays or
the reading is unstable, consult Section 5 for troubleshooting suggestions.
For further information, please refer to the GK-404 manual.

7
3.2 GK-405 Readout Box
The GK-405 Vibrating Wire Readout is made up of two components: The Readout Unit,
consisting of a Windows Mobile handheld PC running the GK-405 Vibrating Wire Readout
Application; and the GK-405 Remote Module, which is housed in a weatherproof enclosure and
connects via a cable to the vibrating wire gauge to be measured. The two components
communicate wirelessly using Bluetooth®, a reliable digital communications protocol. The
Readout Unit can operate from the cradle of the Remote Module, or, if more convenient, can be
removed and operated up to 20 meters from the Remote Module.
3.2.1 Connecting Sensors with 10-pin Bulkhead Connectors Attached
Align the grooves on the sensor connector (male), with the appropriate connector on the
readout (female connector labeled senor or load cell). Push the connector into place, and
then twist the outer ring of the male connector until it locks into place.
3.2.2 Connecting Sensors with Bare Leads
Attach the GK-403-2 flying leads to the bare leads of a Geokon vibrating wire sensor by
connecting each of the clips on the leads to the matching colors of the sensor conductors,
with blue representing the shield (bare).
3.2.3 Operating the GK-405
Press the button labeled “POWER ON (BLUETOOTH)”. A blue light will begin
blinking, signifying that the Remote Module is waiting to connect to the handheld unit.
Launch the GK-405 VWRA program by tapping on “Start” from the handheld PC’s main
window, then “Programs” then the GK-405 VWRA icon. After a few seconds, the blue
light on the Remote Module should stop flashing and remain lit. The Live Readings
Window will be displayed on the handheld PC. Choose display mode “B”. Figure 6
shows a typical vibrating wire output in digits and thermistor output in degrees Celsius. If
no reading displays or the reading is unstable, see Section 5 for troubleshooting
suggestions. For further information, consult the GK-405 Instruction Manual.
Figure 6 - Live Readings – Raw Readings

8
3.3 GK-403 Readout Box (Obsolete Model)
The GK-403 can store gauge readings and apply calibration factors to convert readings to
engineering units. The following instructions explain taking gauge measurements using Mode
“B”. Consult the GK-403 Instruction Manual for additional information.
3.3.1 Connecting Sensors with 10-pin Bulkhead Connectors Attached
Align the grooves on the sensor connector (male), with the appropriate connector on the
readout (female connector labeled senor or load cell). Push the connector into place, and
then twist the outer ring of the male connector until it locks into place.
3.3.2 Connecting Sensors with Bare Leads
Attach the GK-403-2 flying leads to the bare leads of a Geokon vibrating wire sensor by
connecting each of the clips on the leads to the matching colors of the sensor conductors,
with blue representing the shield (bare).
3.3.3 Operating the GK-403
1) Turn the display selector to position “B”.
2) Turn the unit on.
3) The readout will display the vibrating wire output in digits. The last digit may change
one or two digits while reading.
4) The thermistor reading will be displayed above the gauge reading in degrees
centigrade.
5) Press the “Store” button to record the value displayed.
If the no reading displays or the reading is unstable, see Section 5 for troubleshooting
suggestions.
The unit will automatically turn off after approximately two minutes to conserve power.
3.4 Measuring Temperatures
Each Vibrating Wire Convergence Meter is equipped with a thermistor for reading temperature.
The thermistor gives a varying resistance output as the temperature changes. Usually the white
and green leads are connected to the internal thermistor. The GK-403, GK-404, and GK-405
readout boxes will read the thermistor and display temperature in °C automatically
If an Ohmmeter is used, connect the ohmmeter to the two thermistor leads coming from the
convergence meter. (Since the resistance changes with temperature are so large, the effect of
cable resistance is usually insignificant.) Look up the temperature for the measured resistance
using Table 9 in Appendix B. Alternately, the temperature could be calculated using Equation
10, also found in Appendix B. When long cables are used, the cable resistance may need to be
taken into account. Standard 22 AWG stranded copper lead cable is approximately 14.7Ωper
1000 ft. or 48.5Ωper km. Multiply these factors by two to account for both directions.

9
4. DATA REDUCTION
4.1 Digits
The basic units utilized by Geokon for measurement and reduction of data from vibrating wire
Convergence Meters are “digits”. The units displayed by the GK-403, GK-404, and GK-405 in
position “B” are digits. Calculation of digits is based on the following equation:
Digits = 1
Period2
x 10-3 or Digits=Hz2
1000
Equation 1 - Digits Calculation
To convert digits to deformation the following equation applies:
D = (R1- R0) ×G ×F
Equation 2 - Deformation Calculation
Where;
D is the calculated deformation.
R1is the current reading.
R0is the initial reading usually obtained at installation.
G is the calibration factor, usually in terms of millimeters or inches per digit taken from the
calibration report, an example of which is shown in Appendix D.
F is an engineering units conversion factor (optional), see Table 2.
From→
To↓
Inches
Feet
Millimeters
Centimeters
Meters
Inches
1
12
0.03937
0.3937
39.37
Feet
0.0833
1
0.003281
0.03281
3.281
Millimeters
25.4
304.8
1
10
1000
Centimeters
2.54
30.48
0.10
1
100
Meters
0.0254
0.3048
0.001
0.01
1
Table 2 - Engineering Units Conversion Multipliers
For example, the initial reading, R0, at installation of a convergence meter with a 12 mm
transducer range is 4919 digits. The current reading, R1, is 6820. The Calibration Factor is
0.00258 mm/digit. The deformation change is:
Duncorrected = (6820
−
4919)
×
0.002402 = +4.566 mm
Note that increasing readings (digits) indicate increasing extension.

10
4.2 Temperature Correction
In most cases, temperature correction is not necessary, since the Model 4425 Vibrating Wire
Convergence Meter has a very small coefficient of thermal expansion. However, if maximum
accuracy is desired or the temperature changes are extreme (>10° C) corrections may be applied.
The following equation applies:
Dtemperature = (T1- T0) (K + LKR+ KT)
Equation 3 - Temperature Correction
Where;
Dtemperature is the deformation due to temperature change.
T1is the current temperature in degrees C.
T0is the initial temperature in degrees C.
K is the thermal coefficient of transducer, see Equation 4.
KRis the thermal coefficient of the connecting rod, see Table 4.
L is the length of the connecting rod, in millimeters or inches.
KTis the thermal coefficient of the turnbuckle/spring, 0.0007" or 0.0178 mm/°C.
Tests have determined that the transducer thermal coefficient, K, changes with the position of the
transducer shaft. The first step in the temperature correction process is determination of the
proper transducer thermal coefficient based on the following equation:
K = ((R1×M) +B) ×G
Equation 4 - Transducer Thermal Coefficient Calculation
Where;
K is the transducer thermal coefficient.
R1is the current reading in digits.
M is the multiplier from Table 3.
B is the constant from Table 3.
G is the calibration factor from the supplied calibration report.
Model
Multiplier
Constant
4425-12 mm / 4425-0.5"
0.000375
1.08
4425-25 mm / 4425-1"
0.000369
0.572
4425-50 mm / 4425-2"
0.000376
0.328
4425-100 mm / 4425-4"
0.000398
0.0864
4425-150 mm / 4425-6"
0.000384
-0.3482
4425-200 mm / 4425-8.0"
0.000396
-0.4428
4425-300 mm / 4425-12"
0.000424
-0.6778
Table 3 - Transducer Thermal Coefficient Calculation Constants

11
All of the above thermal corrections describe an expansion of components with an increase in
temperature. Hence, the calculated thermal corrections must be added to the deformation
calculated using Equation 2.
Dtcorrected = Duncorrected + Dtemperature
Equation 5 - Thermally Corrected Deformation Calculation
Experience has shown that the most stable readings are obtained when the system is at a stable
temperature. Taking readings late at night or early in the morning will eliminate the transient
effects of sunlight and rapid warming of sensor components. If a datalogger is used, readings
will show the trends associated with thermal effects during the day and through the seasons, and
allow corrections for these effects to be accurately made.
4.3 Rod Stretch Correction
Rod Stretch= PL
aE
Equation 6 - Rod Stretch
Where;
P is the rod tension (lb. or Newtons).
L is the rod length (inches or mm).
a is the rod area of cross section (sq. inches or square mm).
E is the Young’s modulus (lb./sq. inch or MPa).
P depends on the spring rate, S, of the large exterior tension spring and the amount of
deformation (Dtcorrected), i.e. P = S Dcorrected so that:
Drodstretch=SDL
aE
Equation 7 - Rod Stretch correction
Values for KRand E are as follows:
Rod Material E, Young’s Modulus
K
R
Thermal
Coefficient
Lb./sq. in. MPa Per ºC
Stainless Steel 28.5 x 10
6
0.196 x 10
6
17.3 x 10
-6
Graphite 17 x 10
6
0.117 x 10
6
0.2 x 10
-6
Invar 21 x 10
6
0.145 x 10
6
1.1 x 10
-6
Fiberglass 6 x 10
6
0.041 x 10
6
6.0 x 10
-6
Table 4 - Young’s Modulus and Thermal Coefficients

12
Increasing tensions cause the rod to elongate so that the required correction would be positive,
when Dtcorrected is positive.
Values for S are as follows:
Model Number
Range
Spring Rate
Inches
mm
Lb./in.
Newtons/mm
4425-12
½
12
34
5.95
4425-25
1
25
34
5.95
4425-50
2
50
17
2.98
4425-100
4
100
17
2.98
4425-150
6
150
8.5
1.49
Table 5 - Spring Rates
4.4 Correction for Sag
Correction for sag = - LW2/24P2or -L3ω2/24P2
Equation 8 - Sag Correction
Where;
L = length of rods (The distance over which the measurement is made).
W = weight of rods
P = tension. The springs used have an initial tension of 13 lb. (57.8N), and this must be added to
the force caused by the displacement = SD
ω= weight of rods per unit length (see Table 6)
For convergence the correction is negative, for extensions the correction is positive.
Rod Material Weight per unit length
Lb./inches Kgm/mm
Stainless Steel 0.0139 248 x 10
-6
Graphite 0.00275 49.1 x 10
-6
Invar 0.0139 248 x 10
-6
Fiberglass 0.0035 62.4 x 10
-6
Table 6 - Densities

13
For example:
Consider a horizontal convergence meter consisting of 60 ft. of graphite rods with spring
constant of 17 lb. per inch.
L = length of rods = 60 ft. (The distance over which the measurement is being made.)
W = weight of 60 ft. of graphite rods = 2 lb.
P0= 47 lb. and P1= 30 lb. (These values are obtained from a knowledge of the spring tension at
various extensions, and that an apparent measured convergence of 1.000 inch has taken place.)
The correction to L for sag initially is -60 x 4 / 24 x 47 x 47 = - 0.0045 ft. = - 0.054 inches
The correction for sag at T1is - 60 x 4 / 24 x 30 x 30 = - 0.0111 f.t = - 0.133 inches
So after correction for sag the true convergence is 1 – (0.133 – 0.054) = 0.921 inches
Summing all the various effects:
Dcorrected = Duncorrected + Dtemperature + Drodstretch + Dsag
Equation 9 - Corrected Deformation
Again, consider the following example from a Model 4425-12 Convergence Meter attached to 30
meters of 1/4 inch diameter graphite rod.
R0= 4919 digits
R1= 6820 digits
T0= 15.3° C
T1= 32.8° C
(T1– T0) = + 17.5 °C
G = 0.002402 mm/digit
L = 30 meters = 30,000 mm
S = 5.95 N/mm
a = 31.67 sq. mm
E = 0.117 × 106 MPa
ω = 0.049 Kgm/m = 0.481 N/m (0.033 lb./ft.)
P0= 133 N
P1= 163 N
From Equation 4:
K = ((6820 ×0.000375) + 1.08) ×0.002402 = 0.0087 mm
From Equation 2:
Duncorrected = (6820 - 4919) ×0.002402 = + 4.566 mm
(The plus sign indicates an extension.)

14
From Equation 3:
Dtemperature = + 17.5(0.0087 + 0.2×10-6 ×30,000 + 0.0178) = + 0.568 mm
From Equation 5:
Dcorrected = + 4.566 + 0.568 = + 5.134 mm
From Equation 7:
Drodstretch = 5.95 ×5.045 ×30,000 / 31.67 × 0.117 × 106= +0.243 mm
From Equation 8: (Not required if the convergence meter is vertical)
Dsag =[303x 0.4812/24 x 133 x 133] -[303x 0,4812/24 x 163 x 163] = + 4.918 mm
From Equation 9:
The true extension:
Dcorrected = + 4.566 + 0.568 +0.243 + 4.918 = + 10.29 mm
4.5 Environmental Factors
Since the purpose of the convergence meter installation is to monitor site conditions, factors that
may affect these conditions should always be observed and recorded. Seemingly minor effects
may have a real influence on the behavior of the structure being monitored and may give an early
indication of potential problems. Some of these factors include, but are not limited to, blasting,
rainfall, tidal levels, excavation and fill levels and sequences, traffic, temperature and barometric
changes, changes in personnel, nearby construction activities, seasonal changes, etc.
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