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Instruction Manual
Model 4800 Series
VW Earth Pressure Cells
No part of this instruction manual may be reproduced, by any means, without the written consent of Geokon, Inc.
The information contained herein is believed to be accurate and reliable. However, Geokon, Inc. assumes no responsibility for errors, omissions, or misinterpretation. The information herein is subject to change without notification.
Copyright © 1984-2018 by Geokon, Inc.
(REV S, 04/13/2018)
Warranty Statement
Geokon, Inc. 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, Inc. 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, Inc. or any breach of any warranty by Geokon, Inc. shall not exceed the purchase price paid by the purchaser to Geokon, Inc. 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, Inc. 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
APPENDIX D. TEMPERATURE EFFECT ON EARTH PRESSURE AND CONCRETE STRESS CELLS 30
APPENDIX E. NON LINEARITY AND THE USE OF A SECOND ORDER POLYNOMIAL TO IMPROVE
FIGURES
TABLES
EQUATIONS
E QUATION 7 E XPANSION OF L IQUID FOR A T EMPERATURE R ISE OF 1
C ....................................................................30
1
1. INTRODUCTION
1.1 Theory of Operation
Earth Pressure Cells, sometimes called Total Pressure Cells or Total Stress Cells are designed to measure stresses in soil or the pressure of soil on structures. Cells will respond not only to soil pressures but also to ground water pressures or to pore water pressure, hence the term total pressure or total stress. A simultaneous measurement of pore water pressure (
µ
), using a piezometer, is necessary to separate the effective stress (
σ
') from the total stress (
σ
) as defined by
Terzaghi's principle of effective stress:
σ
'
= σ
-
µ
Equation 1 - Terzaghi’s Principle of Effective Stress
These parameters coupled with the soil strength characteristics will determine soil behavior under loads.
Earth pressure cells of the type described here are the hydraulic type; two flat plates are welded together at their periphery and are separated by a small gap filled with a hydraulic fluid. The earth pressure acts to squeeze the two plates together thus building up a pressure inside the fluid.
If the plates are flexible enough (i.e., if they are thin enough relative to their lateral extent), then at the center of the plate the supporting effect of the welded periphery is negligible and it can be stated that at the center of the cell the external soil pressure is exactly balanced by the internal fluid pressure.
This is true only if the deflection of the plates is kept to a minimum and thus it is important that the cell be stiff. This in a practical sense means that the fluid inside the cell should be as incompressible as possible and that the pressure transducer required to measure the fluid pressure should also be stiff having very little volume change under increasing pressure.
Tests conducted by various researchers (as reported by Dunnicliff, 1988) have shown that the introduction of a flat stress cell into a soil mass will alter the stress field in a way dependent on the relative stiffness of the cell, with respect to the soil, and also with respect to the aspect ratio of the cell, i.e., the ratio of the width of the cell to its thickness. A thick cell will alter the stress more than a thin cell. For these reasons, a thin, stiff cell is best and studies have shown an aspect ratio of at least 20 to 1 to be desirable.
Ideally, the cell ought to be as stiff (compressible) as the soil, but in practice this is difficult to achieve. If the cell is stiffer (less compressible) than the soil then it will over register the soil pressure because of a zone of soil immediately around the cell which is "sheltered" by the cell and therefore does not experience the full soil pressure. This can be represented schematically as
2
Mean
Stress
0
Cell
Figure 1 - Stress Redistribution, Weak Soil with Stiff Cell
As can be seen there is a stress concentration at the rigid rim but in the center of the cell the soil stress is only slightly higher than the mean soil stress, i.e., only slightly higher than the stress which would obtain were the cell not present.
In a stronger soil, the destressed zone around the edge of the cell is more extensive; therefore, the degree of over registration of the mean stress is greater at the center of the cell. This is
represented schematically in Figure 2.
Mean
Stress
0
Cell
Figure 2 - Stress Redistribution, Strong Soil with Stiff Cell
In a stiff soil the cell may be less stiff (more compressible) than the soil, in which case the cell will under register the mean soil stress as the stresses in the soil tend to "bridge" around the cell.
This is represented schematically in Figure 3.
Mean
Stress
0
Cell
Figure 3 - Stress Redistribution, Stiff Soil with Weak Cell
3
Tests conducted at the University of Ohio (Ohio, USA) with several different soil types have shown that for Geokon cells the maximum degree of over or under registration amounts to 15% of the mean soil stress.
Other factors should be kept in mind. The inherent variability of soil properties, which give rise to varying soil stresses at different locations, and a corresponding difficulty in getting a good sample of the mean stress from a limited number of cell locations. In addition, the response of the cell to its immediate surroundings depends mostly on how closely the soil mass immediately around the cell has the same stiffness or compressibility or the same degree of compaction as the undisturbed soil mass. Installation methods will need to pay particular attention to this detail.
1.2 Earth Pressure Cell Design
Earth Pressure Cells are constructed from two stainless steel plates welded together around the periphery to leave a narrow space between them. This space is completely filled with de-aired hydraulic oil, which is connected hydraulically to a pressure transducer. The pressure transducer converts the oil pressure into an electrical signal, which is transmitted through a signal cable to the readout location.
In general, Geokon Earth Pressure Cells use an all welded construction; this means the space confining the oil is entirely metal and does not require any o-rings, which tend to trap air and reduce the cell stiffness. The oil is de-aired using a Nold DeAerator
, which materially improves the fluid stiffness and the performance of the cell. The pressure transducer normally employed is the Geokon Model 4500H, which is available in several different pressure ranges (see Appendix
A.1). The cable is attached to the transducer in a sealed, waterproof manner. For earth pressure cells located inside a soil mass, the cable may be armored and provided with strain relief at the cell to reduce the likelihood of pullout.
Located inside the vibrating wire pressure transducer housing is a thermistor for the measurement of temperature at the cell location. In addition, a tripolar plasma surge arrestor inside the transducer housing protects the vibrating wire pluck and read coils from electrical transients such as may be induced by direct or indirect lightning strikes.
Alternative pressure transducers with voltage (0-100 mV, 0-5 VDC, 0-10 VDC) or current (4-20 mA) output are also available for dynamic readout capability. Consult the factory for additional information.
4
1.3 Earth Pressure Cell Construction
1.3.1 Model 4800 Earth Pressure Cells
Model 4800 Earth Pressure Cells may be rectangular or circular in shape. The standard size for the rectangular Model 4800 is 150 mm
×
250 mm (6"
×
10"), for the circular it is
230 mm (9") in diameter. Standard thickness for both styles is 6 mm (aspect ratio
≈
40).
For laboratory tests, smaller, thinner cells can be manufactured. Contact the factory for additional information.
Pressure Cell Transducer Housing Instrument Cable
(4 conductor, 22 AWG)
6"
150 mm
10"
250 mm
Top View
Side View
Figure 4 - Model 4800 Rectangular Earth Pressure Cell
Pressure Cell Transducer Housing Instrument Cable
(4 conductor, 22 AWG)
9"
230 mm
Top View
Side View
Figure 5 - Model 4800 Circular Earth Pressure Cell
5
1.3.2 Model 4810 Contact ("Fat Back") Pressure Cell
Model 4810 Earth Pressure Cells are designed for measuring soil pressures on structures.
One of the plates is thick and designed to bear against the external surface of the structure in a way that will prevent flexure of the cell. The other plate is thin and reacts to the soil pressure.
Pressure Cell
Transducer Housing Instrument Cable
(4 conductor, 22 AWG)
9"
230 mm
Top View
Mounting Lugs (4 places)
Thin Pressure Sensitive Plate
Side View
Figure 6 - Model 4810 Contact Pressure Cell
1.3.3 Model 4815 Hydraulic Load Cell
Model 4815 Hydraulic Load Cell has been used for the measurement of loads in piles and of concentrated loads on tunnel linings. The pressure transducer housing is connected directly and perpendicular to the thick back plate.
Figure 7 - Model 4815 Hydraulic Load Cell
6
1.3.4 Model 4820 Earth Pressure "Jackout" Cell
Model 4820 Earth Pressure Cells are designed specifically for the measurement of soil pressures on the back side of slurry walls. The pressure transducer housing is connected directly and perpendicular to the thick back plate.
Pressure Cell
Mounting Hole
(6 places, 6.75 mm ID)
Back Plate (with mounting holes)
Transducer Housing
Instrument Cable
(4 conductor, 22 AWG)
6"
150 mm
5"
125 mm
Bottom View Side View
Figure 8 - Model 4820 Jackout Pressure Cell
1.3.5 Model 4830 Push-In Pressure Cell
Model 4830 Push-In Pressure Cells are designed to be pushed in place for the measurement of total pressures in soils and earth fills. The semiconductor pressure transducer enables measurement of dynamic pressures. A thread is provided on the end of the cell to allow for installation using lengths of pipe or drill rods.
Figure 9 - Model 4830 Push-In Pressure Cell
7
2. INSTALLATION
2.1 Preliminary Tests
It is always wise, before installation commences, to check the cells for proper functioning. Each cell is supplied with a calibration sheet, which shows the relationship between readout digits and
pressure, as well as the initial no load zero reading. (Figure 18 in Section 4 shows a typical
calibration sheet.)The cell electrical leads (usually the red and black leads) are connected to a readout box (see Section 3) and the zero reading given on the calibration sheet is compared to the current zero reading. The two readings should not differ by more than
≈
50 digits after due regard to corrections made for different temperatures, barometric pressures and height above sea level and actual cell position (whether standing up or laying down).
By pressing on the cell, it should be possible to change the readout digits, causing them to fall as the pressure is increased.
Checks of electrical continuity can also be made using an ohmmeter. Resistance between the gage leads should be approximately 180 ohms, ± 5%. Check the resistance between the two
thermistor wires (usually white and green). Using Table 6 in Appendix B, convert the resistance
to temperature. Compare the result to the current ambient temperature. (For Model 4800HT see
Table 7 in Appendix C.) Resistance between any conductor and the shield should exceed 20
megohms. Remember to add cable resistance when checking (22 AWG stranded copper leads are approximately 14.7
Ω
per 1,000 feet (48.5
Ω
per km), multiply by two for both directions).
2.2 Pressure Cell Installation
2.2.1 Installation of Model 4800 Earth Pressure Cells Inside Fills and Embankments
Earth pressure cells are normally installed with the flat surfaces horizontal to measure vertical stresses. However, they can be placed at other orientations, inside the fill, to measure stresses in other directions e.g., a cell placed with the flat surfaces vertical will measure horizontal stresses in a direction perpendicular to the plates of the cell. They are sometimes placed at angles of 45 degrees.
Experience has shown that attempts to measure earth pressures in fills frequently meets with failure. The problem is twofold. First, the stress distribution in the fill can be inherently variable due to varying properties of the ground and varying degrees of compaction of the ground. Thus, the soil stress at one location may not be typical of the surrounding locations. Secondly, a cell installed directly in the fill could result in the creation of an anomalous zone immediately around the cell where there may be a different, more fine-grained material, under a lesser degree of compaction. (The material around the cell may be poorly compacted because of the need to avoid damage to the cell.)
8
In an earth fill, this zone of poor compaction would not be expected to be a problem since the earth above might be expected to move downwards to fill the voids and consolidate the ground. However, under the influence of rainwater and vibration, any spaces in the soil immediately around, and especially under, the cell may grow, causing the cell to become completely decoupled from the soil around it. In such situations, the internal soil stresses go around the cell instead of through it. The cell will then register only a very low pressure, which does not change much as the loads increase. This situation occurs frequently.
2.2.1.1 Weak Grout Method
One way to avoid the problem is to cast the cell inside a weak grout. A method used successfully in South Africa, by Oosthuizen et al, essentially uses the techniques similar to the one described in Section 2.2.5. Installation of the cells begins when the fill has reached a height of one meter above the instrument level. The Instrument location and the cable trenches are excavated one meter deep, the instrument pocket, with 45° sloping
Figure 10 - Model 4800 Earth Pressure Cell Installation
9
The cells (Model 4800-1-1P, complete with pinch tubes and lugs) are positioned on a thin layer of non-shrink, sand cement grout, and are nailed in position using the lugs on the cells provided for this purpose. The excavated pocket is then backfilled to a depth of 300 mm with a weak concrete in 100 mm layers, vibrated with a poker vibrator. After 24 hours, the cells are pressurized by pinching the pinch tubes until the pressure in the cell, displayed on a connected Readout Box, starts to change.
The instrument location containing the grouted cells and the cable trench is then backfilled in 250 mm layers, using the same material as the main fill placed by hand and compacted with pneumatic or gasoline backfill tampers, or vibratory trench rollers. After this, standard construction filling and compaction practices can continue.
Earth Pressure Cells clusters, placed according to the methods outlined above, may be installed either in trenches, below the temporary embankment grade, or in ramps above the temporary embankment grade. In dams, for example, it is usually convenient to install in trenches in the impervious rolled fill core, and in ramps in the filter zones and compacted rockfill shell zones. In earth embankments, it is convenient to install in trenches. By doing so, adequate degrees of compaction of the backfill can be more easily obtained without damage to the cell clusters or cable arrays. As the cells are being covered and compacted, repeated readings should be taken to ensure that the cells are continuing to function properly.
See Section 2.3 for cable installation and protection.
Application
Materials
Water
Portland
Cement
Bentonite
Notes
Grout for Medium to Hard
Soils
Weight Ratio by
Weight
30 gallons 2.5
94 lbs.
(One sack)
25 lbs.
(as required)
1
0.3
The 28-day compressive strength of this mix is about 50 psi, similar to very stiff to hard clay. The modulus is about 10,000 psi
Grout for Soft Soils
Weight
75 gallons
Ratio by
Weight
6.6
94 lbs.
(One sack)
39 lbs.
(as required)
1
0.4
The 28-day strength of this mix is about
4 psi, similar to very soft clay.
Table 1 - Ratios for Two Grout Mixes.
2.2.1.2 Alternative Method
In this method, the pressure cell used to monitor vertical earth pressures is placed directly in the fill. The procedures are similar to those in Section 2.2.1.1, except that the pressure cell does not have a pinch tube and the layer of weak grout is dispensed with. Instead, the cell is placed on a pad of quick-setting mortar. This is done to ensure uniform contact with the soil at the bottom of the trench. The cell is then covered by soil placed in
300 mm layers and compacted as before.
10
2.2.2 Installation of Model 4810 Contact ("Fat Back") Pressure Cell
This section details installation instructions for Model 4810 Earth Pressure Cells, which are used for the measurement of earth pressures on structures. In backfills for piers, piles, bridge abutments, retaining walls, culverts and other structures the cells may be installed either inside a concrete structure being poured or directly on the surface of an existing structure. For slurry walls, the Model 4820 Earth Pressure Cell is used as described in
Section 2.2.4.
2.2.2.1 Installation in Poured Concrete
When pouring concrete the cells can be held to the forms using nails through the lugs welded to the edge of the cell. Position the cell so that the thin pressure sensitive plate is directly against the concrete form. Nail the plates to the form lightly in such a manner that they engage the concrete sufficiently and will not pull out of the concrete when the forms are removed. Route the cable inside the concrete to a convenient readout location or to a block out inside where excess cable can be coiled. Protect the cable from damage
during concrete placement and vibration, by tying it to adjacent rebars. See Figure 11.
Concrete Form
Excess Cable
(coiled inside blockout)
Pressure Cell
Double Headed Nails
(through mounting lugs, 4 places)
Side View Front View
Figure 11 - Attachment of Model 4810 to Concrete Form
11
2.2.2.2 Installation on Existing Structures
The lugs welded to the edge of the cell can be used to hold the cell against the structure using nails, lag bolts, tie wire, etc. Even if the surface is smooth, but especially when the surface is rough or irregular, a mortar pad between the cell and the structure is required.
Pipe Straps & Conduit
Concrete Nails
(4 places)
Zone with large aggregate removed
Mortar Pad
Side View Front View
Figure 12 - Model 4810 Contact Pressure Cell Installation
Use the lugs on the cell as a template to locate the position for drilling holes for the installation of expanding anchors or install the anchors nearby and use wire to hold the cells in place. Alternately, the cell may be nailed in place using the lugs as a guide.
Mix up some quick-setting cement mortar or epoxy cement. Trowel this onto the surface then push the cell into the cement so that the excess cement extrudes out of the edges of the cell. Hold the cell in place while the cement sets up then complete the installation by adding the lag bolts (using the expansion anchors) and tightening or nailing the cell in place. Protect the cell, transducer housing, and cable from direct contact with large chunks of rock by covering them with a fine grained fill material from which all pieces larger than about 10 mm (0.5") have been removed. This material is kept near the cell and cable as the fill is placed. Additional cable protection can be achieved by using metal conduit strapped to the surface of the structure.
12
2.2.3 Installation of Model 4815 Hydraulic Load Cell
A particular installation, shown in Figure 13, used the Model 4815 Hydraulic Load Cell
to measure the concentrated load on a tunnel lining from an existing wooden pile
(supporting a building above) that had been cut short by the tunnel excavation in frozen ground. The load cell was designed to measure any increase of load on the tunnel lining that might occur when, at the end of tunnel construction, the ground was allowed to thaw out. The load cell was positioned below the bottom of the pile and temporarily held in place with lugs and a mortar pad until the shotcrete tunnel lining was sprayed.
Figure 13 - Model 4815 Hydraulic Load Cell Measuring Loads on a Tunnel Lining
13
2.2.4 Installation of Model 4820 Jackout Pressure Cell in Slurry Trenches
The Jackout Pressure first needs to be assembled into the Jackout frame. The assembly is
shown in Figure 14. The support plate has a circular hole cut in it and bolt holes to fit the
Jackout Pressure Cell (JOPC), and is connected to one end of a double-acting hydraulic jack by means of steel struts. The support plate and reaction plate are cambered top and bottom to prevent them from snagging on the sides of the slurry trench. The reaction plate is attached to the other side of the double-acting hydraulic jack. The jack is attached firmly to the rebar cable and arranged so that the plates are free to move outwards. The hydraulic line and signal cable are tied off to one of the rebars at intervals of one meter (~ three feet).
When the rebar cage has been lowered to its proper depth, the jack is activated, forcing the two plates out against the trench walls.
Figure 14 - Model 4820 Jackout Pressure Cell Installation
Observation of the pressure indicated by the JOPC (see Section 3 for readout instructions) will indicate when the cell has made contact with the wall. Pump up the jack until the JOPC reading indicates a pressure roughly 70 KPa (10 psi) greater than the slurry pressure at JOPC depth. This ensures that the cell is bearing against the walls of the trench, and that the concrete grout pressure will not close the jack, which could allow the reaction plates to move away from the trench walls. Check the JOPC reading from time to time, because the pressure might bleed away if the walls of the trench are soft and yielding. Repressurize as needed. Leave the jack pressurized until the grout has set up.
14
2.2.5 Installation of Cells to Measure Earth Pressure at the Base of Footings, Floor
Slabs, Pavements, Etc.
Experience has shown that attempts to measure contact earth pressures on the base of footings, floor slabs, pavements, etc., frequently meets with failure. The problem is twofold. First, the contact stress distribution can be inherently variable due to varying properties of the ground and varying degrees of compaction of the ground. Thus the contact stress at one location may not be typical of the surrounding locations. Secondly, a cell installed as described in Section 2.2.1 could result in the creation of an anomalous zone immediately around the cell where there may be a different, finer grained material, under a lesser degree of compaction. (The material around the cell may be poorly compacted because of the need to avoid damage to the cell.)
In an earth fill, this zone of poor compaction would not be a problem, since the earth above would move downwards to fill the voids and consolidate the ground. However, where there is a concrete slab immediately above the cell, this consolidation may not take place. In fact, under the influence of rainwater and vibration, the spaces around the cell may grow, causing the cell to become completely decoupled from the concrete above. In such a situation, the concrete slab bridges over the gap and the loads in the concrete go around the cell instead of through it. The cell registers only a very low pressure, which does not change as the loads increase.
The best way to avoid the problem is to cast the cell inside the concrete if possible. This can often be done when the initial concrete bonding layer is spread over the surface of the ground. At this time a Model 4800-1-1P Earth Pressure Cell with a pinch tube, is pressed into the bonding layer so that it rests against the ground below. A weighted tripod can be used to hold the stress cell in place until the concrete hardens. The pinch tube is arranged to protrude above the bonding layer and, when the concrete has hardened, it is used to pressurize the cell and ensure good contact between the cell and the surrounding
concrete. See Figure 15. The advantage of this method is its simplicity and that it permits
the ground below the concrete to be completely compacted in the normal way.
Model 4800-1-1P
Pinch Tube Concrete Footing or
Concrete Bonding Layer (mud mat)
Compacted Subgrade
Figure 15 - Model 4800-1-1P Earth Pressure Cell Installation
15
2.2.6 Installation of Push-In Pressure Cells to Measure Lateral Earth Pressures
The Model 4830 is designed to be pushed into soft soils using available drill rods, usually
AW. Unless the ground is very soft, it is recommended that a borehole be drilled to within about two feet of the desired location, and then push the cell the rest of the way.
A few things to note and be aware of:
•
Temperature effects
This pressure cell is relatively stiff due to the geometry and the need for a robust construction for pushing into the ground. It is always advisable to obtain the preinstallation zero pressure readings in the borehole at the borehole temperature. It may take a significant amount of time for the sensor to come to thermal equilibrium but this is an important measurement and if it is not possible to take this reading in the borehole, it may be possible to take the reading in a bucket of water that is at the ground temperature.
•
Piezometer Saturation
The piezometer filter and sensor are saturated at the factory and sealed with Mylar tape.
Do not remove the tape until just before the sensor is installed in the ground. The filter is saturated by drawing a vacuum on the sensor and then allowing water to flow into the sensor when the vacuum is released. If the sensor is to be installed and then removed for use at other sites, the saturation process should be performed at each installation. Geokon can supply the necessary portable equipment to accomplish this.
•
Overpressure
When pushing the cell into the ground it is possible that pressures in excess of the sensors full-scale range can be generated causing the sensor to experience a zero shift or even permanent damage. To prevent this, readings should be taken as the sensor is pushed.
When the indicated pressure approaches 150% of full scale the pushing operation should be terminated until the sensor output comes back within its calibrated range.
16
2.3 Cable Installation and Splicing
Cable placement procedures vary with individual installations. In general, however, all installations have in common the following requirements:
1) The cable must be protected from damage by angular particles of the material in which the cable is embedded.
2) The cable must be protected from damage by compaction equipment.
3) In earth and rock embankments and backfills, the cable must be protected from stretching as a result of differential compaction of the embankment.
4) In concrete structures, the cable must be protected from damage during placement and vibration of the concrete.
In embankments, cables may be embedded in a protective covering of sand or selected fine embankment materials. A typical installation might, for example, comprise the positioning of a series of cables on a prepared layer consisting of not less than 200 mm (8") of compacted selected fine material. In order to establish an acceptable grade without undue interference with construction operations, the prepared layer may be located either in a trench or on an exposed ramp. In rockfill dams with earth fill cores, for example, it is frequently convenient to install cable in trenches in the core and fine filter zones, and in ramps in the coarse filter and compacted rockfill shell zones. Individual cables should be spaced not less than 12 mm (0.5") apart, and no cable should be closer than 150 mm (6") to the edge of the prepared layer. In instances in which cables must cross each other, or in which more than one layer of cables must be placed in a given array, the cables should be separated from each other by a vertical interval of not less than 50 mm (2") of hand compacted sand or selected fine embankment material. Since the elongation capability of electrical cable is quite substantial, it is not necessary to install the cable with any
"S" shaped meanders.
During the backfill of trenches in earth dams, a plug, approximately half a meter (two feet) in width, made of a mixture of 5% bentonite (by volume) from an approved source and exhibiting a free swell factor of approximately 600%, and 95% embankment material, can be placed in the trenches at intervals of not greater than 20 meters (50 feet). The purpose of the bentonite plugs is to reduce the possibility of water seepage through the embankment core along the backfilled trenches.
The cable may be marked by using a Mylar cable labels. For an individual cable, the identification number should be taped near the end of the cable. Additional cable labels can be specified to aid in identification if cables need to dug up for splicing, etc.
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.
17
2.4 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.
2.5 Initial Readings
Initial readings must be taken and carefully recorded along with the barometric pressure and temperature at the time of installation. Take the initial readings while the cell is in position, prior to covering it with fill and pouring the concrete. Again, it is imperative that initial readings at zero load are taken!
18
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 gages 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 load cell (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
16). Insert the Lemo connector into the GK-404 until it locks into place.
Figure 16 - 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 be displayed. 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 gage in degrees Celsius.
Use the POS button to select position B and 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 the no reading displays or the reading is unstable, see Section 5 for troubleshooting suggestions.
For further information, please see the GK-404 manual.
19
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 to the vibrating wire gage 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
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 17
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 17 - Live Readings – Raw Readings
20
3.3 GK-403 Readout Box (Obsolete Model)
The GK-403 can store gage readings and apply calibration factors to convert readings to engineering units. The following instructions explain taking gage measurements using Mode "B"
(similar to the GK-401 switch positions "B"). Consult the GK-403 Instruction Manual for additional information.
3.3.1 Connecting Sensors with 10-pin Bulkhead
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 (See Equation 2 in Section
4.1.) The last digit may change one or two digits while reading.
4) The thermistor reading will be displayed above the gage 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.
21
3.4 Measuring Temperatures
Each Vibrating Wire Pressure Cell 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.
1) Connect the ohmmeter to the two thermistor leads coming from the stress cell. (Since the resistance changes with temperature are large, the effect of cable resistance is usually insignificant.)
2) Look up the temperature for the measured resistance in Table 6 in Appendix B. (For 4800HT
models use Table 7 in Appendix C.) Alternately, the temperature could be calculated using
Equation 5 in Appendix B. For example, a resistance of 3400 ohms is equivalent to 22° C.
When long cables are used, the cable resistance may need to be taken into account. Standard
22 AWG stranded copper lead cable is approximately 14.7
Ω
/1000' or 48.5
Ω
/km, multiply by two for both directions.
Note: Geokon readout boxes will read the thermistor and display temperature in
°
C automatically.
22
4. DATA REDUCTION
4.1 Pressure Calculation
The basic units utilized by Geokon for measurement and reduction of data from Vibrating Wire
Earth Pressure Cells are "digits". Geokon Readouts display "digits" in the Earth Pressure Cell reading position. Calculation of digits is based on the following equation:
Digits =
� 1
Period
�
2 x 10
-3
Or
Digits
=
2
Hz
1000
Equation 2 - Digits Calculation
To convert digits to pressure the following equation applies:
Pressure
=
(Current Reading - Initial Reading)
×
Calibration Factor
Or
P = (R
1
- R
0
)
×
G
Equation 3 - Convert Digits to Pressure
The Initial Reading (R
0
) is normally obtained during installation (usually the zero reading). The
Calibration Factor (G, usually in terms of psi or kPa per digit) comes from the supplied
Calibration Sheet (a typical calibration sheet is shown in Figure 18). To convert the output to
other engineering units, multiply the Calibration Factor by the conversion multiplier listed in
From
→
To
↓ psi "H
2
O 'H
2
O mm H
2
0 m H
2
0 "HG mm HG atm mbar bar kPa MPa psi
"H
2
O
'H
2
O mm H
2
0 m H
2
0
"HG mm HG atm mbar bar kPa
MPa
1
27.730
.036127 .43275 .0014223 1.4223 .49116 .019337 14.696 .014503 14.5039 .14503 145.03
1 12 .039372 39.372 13.596 .53525 406.78 .40147 401.47 4.0147 4016.1
2.3108 .08333 1
704.32 25.399 304.788
.003281
1
.70432 .025399 .304788 .001
3.281
1000
1
1.133
345.32
.044604 33.8983 .033456 33.4558
13.595 10332 10.197 10197
.34532 .013595 10.332 .010197 10.197
.3346
101.97
.10197
334.6
101970
101.97
2.036 .073552 .882624 .0028959 2.8959 1
51.706 1.8683 22.4196 .073558 73.558 25.4
.03937 29.920 .029529 29.529 .2953 295.3
1 760 .75008 750.08 7.5008 7500.8
.06805 .0024583 .0294996 .0000968 .0968 .03342 .0013158 1 .0009869 .98692 .009869 9.869
68.947 2.4908 29.8896 .098068 98.068 33.863 1.3332 1013.2 1 1000 10 10000
.068947 .0024908 .0298896 .0000981 .098068 .033863 .001333 1.0132 .001
6.8947 .24908 2.98896 .0098068 9.8068 3.3863 .13332 101.320 .1
.006895 .000249 .002988 .00000981 .009807 .003386 .000133 .101320 .0001
1
100
.1
.01
1
.001
10
1000
1
Table 2 - Engineering Units Multiplication Factors
23
For example, assume an initial reading of R
0
= 9101, a present reading of, R
1
= 7390 and a
Calibration Factor of -0.1192 kPa/digit. The calculated pressure is:
204 kPa = (7390 -9101)
×
-0.1192
(Appendix E shows how a second order polynomial can be used to improve accuracy.)
4.2 Temperature Correction
The vibrating wire earth pressure cell is quite sensitive to temperature fluctuations but often temperature changes in the ground are minor and can be ignored. Corrections for temperature effects on the transducer alone can be made using the Thermal Factor (K) supplied on the
calibration sheet (see Figure 18) along with an equation for its proper use. See Equation 4.
Temperature Correction
=
(Current Temperature - Initial Temperature)
×
Thermal Factor
Or
Pcorrected = (R
0
- R
1
)G + (T
1
-T
0
)K
Equation 4 - Temperature Correction for the Transducer Only.
The Temperature Correction value is then added to the pressure calculated using Equation 3. For
example, assume an initial temperature of 25° C, a temperature at the time of measurement of
12° C and a Thermal Factor of +0.03852 kPa/° C. The thermally corrected pressure is:
203.5 kPa = 204 + (12 - 25) x 0.03852
Note that this correction for temperature applies only to the pressure transducer, not to the entire cell surrounded by soil or soil and concrete each with its own (different) temperature coefficient of expansion.
Commercially it is not practical to measure this effect without incurring huge expenses. The effect is usually small at depths where the temperature is fairly constant, but where temperatures do vary the effect can be quite large. For more information see
Appendix D which gives a theoretical treatment.
In practice, the best way to compensate for temperatures is to derive a factor from simultaneous measurements of pressure and temperature at times when the temperature is changing and when it can be safely assumed that the applied load is not changing.
4.3 Barometric Correction
The pressure transducer used in Geokon Vibrating Wire Earth Pressure Cells is evacuated and hermetically sealed and will respond to barometric pressure fluctuation. If a correction for these fluctuations is required then it is necessary to record the initial barometric pressure (S
0
) and the barometric pressure at the time of each reading (S
1
) and subtract the change (S
1
- S
0
) from the calculated pressure reading.
24
Figure 18 - Sample Model 4800 Calibration Sheet
25
5. TROUBLESHOOTING
Maintenance and troubleshooting of Vibrating Wire Pressure Cells is confined to periodic checks of cable connections. Once installed, the cells are usually inaccessible and remedial action is limited. Consult the following list of problems and possible solutions should difficulties arise.
Consult the factory for additional troubleshooting help.
Symptom: Thermistor resistance is too high
Likely, there is an open circuit. Check all connections, terminals, and plugs. If a cut is located in the cable, splice according to recommended procedures.
Symptom: Thermistor resistance is too low
A short is likely. Check all connections, terminals, and plugs. If a short is located in the cable, splice according to recommended procedures.
Water may have penetrated the interior of the transducer. There is no remedial action.
Symptom: Pressure Cell Readings are Unstable
Is the readout box position set correctly? If using a datalogger to record readings automatically, are the swept frequency excitation settings correct? Try reading the cell on a different readout position. For instance, channel A of the GK-404 and GK-405 might be able
to read the pressure cells. To convert the Channel A period display to digits use Equation 2.
Is there a source of electrical noise nearby? Most probable sources of electrical noise are motors, generators, transformers, arc welders, and antennas.
Make sure the shield drain wire is connected to ground. Connect the shield drain wire to the readout using the blue clip. (Green for the GK-401.)
Does the readout work with another pressure cell? If not, the readout may have a low battery or be malfunctioning. Consult the appropriate readout manual for charging or troubleshooting directions.
Symptom: Pressure Cell Fails to Read
to fill in the actual resistance found. Cable resistance is approximately 14.7
Ω
per 1000' of 22
AWG wire. Multiply this factor by two to account for both directions.
If the resistance reads very high or infinite (megohms), a cut wire must be suspected. If the resistance reads very low (
<
100
Ω
), a short in the cable is likely.
Does the readout or datalogger work with another pressure cell? If not, the readout or datalogger may be malfunctioning. Consult the readout or datalogger manual for further direction.
26
Red
Black
White
Green
Shield
Red
Black
White
Green
Shield
Vibrating Wire Sensor Lead Grid - SAMPLE VALUES
Red
N/A
≅180Ω infinite infinite infinite
Black
≅180Ω
White infinite
Green infinite
Shield infinite
N/A infinite infinite infinite infinite N/A infinite
3000Ω
at
25°
C
3000Ω
at
25°
C infinite
N/A infinite infinite infinite
Table 3 - Sample Resistance infinite N/A
Vibrating Wire Sensor Lead Grid - SENSOR NAME/## :
Red Black White Green
Table 4 - Resistance Work Sheet
Shield
27
APPENDIX A. SPECIFICATIONS
A.1 Earth Pressure Cells
Model:
Ranges:¹
4800
Earth Pressure Cell
(rectangular)
70 kPa (10 psi)
170 kPa (25 psi)
350 kPa (50 psi)
700 kPa (100 psi)
1 MPa (150 psi)
2 MPa (300 psi)
3 MPa (435 psi)
5 MPa (750 psi)
7.5 MPa (1100 psi)
20 MPa (3000 psi)
4800
Earth Pressure
Cell
(circular)
70 kPa (10 psi)
170 kPa (25 psi)
350 kPa (50 psi)
700 kPa (100 psi)
1 MPa (150 psi)
2 MPa (300 psi)
3 MPa (435 psi)
5 MPa (750 psi)
7.5 MPa (1100 psi)
20 MPa (3000 psi))
4810
Contact Pressure
Cell
350 kPa (50 psi)
700 kPa (100 psi)
1 MPa (150 psi)
2 MPa (300 psi)
3 MPa (500 psi)
5 MPa (750 psi)
4820
Jack-Out
Pressure Cell
350 kPa (50 psi)
700 kPa (100 psi)
1 MPa (150 psi)
2 MPa (300 psi)
3 MPa (500 psi)
5 MPa (750 psi)
±0.025% FSR
±0.5% FSR (±0.1% FSR with a polynomial expression)
±0.5% FSR (standard), ±0.1% FSR (optional)
1.5 x Rated Pressure
Resolution:
Accuracy:
4
Linearity:
Overrange:
Operating
Temperature:
Excitation
Frequency
Range
Output
Frequency
Range
Cell
Dimensions:²
(active area)
Coil
Resistance:
150
×
250 mm
6
×
10"
-20 to +80° C
1400-3500Hz
2000-3000Hz
230 mm OD
9" OD
150
Ω
230 mm OD
9" OD
125 mm OD
5" OD
Material:
Weight:
Electrical
Cable:³
2.3 kg. (5 lbs.)
316 Stainless Steel
2.3 kg. (5 lbs.) 4.7 kg. (10.3 lbs.) 2.7 kg. (6 lbs.)
Two twisted pair (four stranded conductor), 22 AWG
Foil shield (with drain wire), PVC jacket, nominal OD=6.3 mm (0.250")
Table 5 - Earth Pressure Cell Specifications
Notes:
¹ Consult the factory for other ranges available
² Consult the factory for other sizes available.
³ Consult the factory for alternate cable types.
4 The stated accuracy is the accuracy of the pressure transducer. The total system accuracy depends on many factors, as discussed in Section 1.1.
A.2 Standard Temperature Thermistor
Range: -80 to +150° C
Accuracy: ±0.5° C
28
44.16K
41.56K
39.13K
36.86K
34.73K
32.74K
30.87K
29.13K
27.49K
25.95K
24.51K
23.16K
21.89K
20.70K
19.58K
18.52K
17.53K
88.46K
82.87K
77.66K
72.81K
68.30K
64.09K
60.17K
56.51K
53.10K
49.91K
46.94K
174.5K
162.7K
151.7K
141.6K
132.2K
123.5K
115.4K
107.9K
101.0K
94.48K
-27
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-38
-37
-36
-35
-34
-33
-32
-31
-30
-29
-28
-48
-47
-46
-45
-44
-43
-42
-41
-40
-39
APPENDIX B. THERMISTOR TEMPERATURE DERIVATION
Thermistor Type: YSI 44005, Dale #1C3001-B3, Alpha #13A3001-B3
Resistance to Temperature Equation:
T=
1
A+B
(
LnR
)
+C(LnR)
3
-273.2
Equation 5 - Resistance to Temperature
Where;
T
=
Temperature in
°
C.
LnR
=
Natural Log of Thermistor Resistance.
A
=
1.4051
×
10-3 (coefficients calculated over the
−
50 to +150
°
C. span)
B
=
2.369
×
10-4
C
=
1.019
×
10-7
Ohms Temp Ohms Temp Ohms Ohms
201.1K
187.3K
-50
-49
16.60K
15.72K
-10
-9
2417
2317
Temp
+
30
31
525.4
507.8
Temp
+
70
71
Ohms
153.2
149.0
53
58
59
60
61
54
55
56
57
62
63
64
65
66
67
68
69
42
43
44
45
46
47
48
49
50
51
52
36
37
38
39
40
41
32
33
34
35
965.0
929.6
895.8
863.3
832.2
802.3
773.7
746.3
719.9
694.7
670.4
647.1
624.7
603.3
582.6
562.8
543.7
1475
1418
1363
1310
1260
1212
1167
1123
1081
1040
1002
2221
2130
2042
1959
1880
1805
1733
1664
1598
1535
5177
4939
4714
4500
4297
4105
3922
3748
3583
3426
3277
3135
3000
2872
2750
2633
2523
8851
8417
8006
7618
7252
6905
6576
6265
5971
5692
5427
14.90K
14.12K
13.39K
12.70K
12.05K
11.44K
10.86K
10.31K
9796
9310
13
18
19
20
21
14
15
16
17
22
23
2
3
4
5
6
7
8
9
10
11
12
-4
-3
-2
-1
0
+
1
-8
-7
-6
-5
24
25
26
27
28
29
Table 6 - Thermistor Resistance versus Temperature
250.9
243.4
236.2
229.3
222.6
216.1
209.8
203.8
197.9
192.2
186.8
181.5
176.4
171.4
166.7
162.0
157.6
353.4
342.2
331.5
321.2
311.3
301.7
292.4
283.5
274.9
266.6
258.6
490.9
474.7
459.0
444.0
429.5
415.6
402.2
389.3
376.9
364.9
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
82
83
84
85
86
87
88
89
90
91
92
76
77
78
79
80
81
72
73
74
75
83.6
81.6
79.6
77.6
75.8
73.9
72.2
70.4
68.8
67.1
65.5
64.0
62.5
61.1
59.6
58.3
56.8
55.6
110.8
107.9
105.2
102.5
99.9
97.3
94.9
92.5
90.2
87.9
85.7
145.0
141.1
137.2
133.6
130.0
126.5
123.2
119.9
116.8
113.8
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
122
123
124
125
126
127
128
129
130
131
132
Temp
+
110
111
112
113
114
115
116
117
118
119
120
121
29
APPENDIX C. HIGH TEMPERATURE THERMISTOR LINEARIZATION
Resistance to Temperature Equation for US Sensor 103JL1A :
1
T=
A+B
(
LnR
)
+C(LnR)
3
+D(LnR)
3
-273.2
Equation 6 - High Temperature Resistance to Temperature
Where;
T
=
Temperature in
°
C.
LnR
=
Natural Log of Thermistor Resistance.
A
=
1.127670
×
10-3
B
=
2.344442
×
10-4
C
=
8.476921
×
10-8
D
=
1.175122
×
10-11
Note: Coefficients optimized for a curve “J” Thermistor over the temperature range of 0°C to
+250°C.
Ohms Temp Ohms Temp Ohms Temp Ohms Temp Ohms Temp Ohms Temp Ohms Temp Ohms Temp
32,650 0
31,029 1
29,498 2
28,052 3
26,685 4
25,392 5
24,170 6
23,013 7
7,402 32 2,157 64 763.5 96 316.6 128 148.4 160 76.5 192 42.8 224
7,098 33 2,083 65 741.2 97 308.7 129 145.1 161 75.0 193 42.1 225
6,808 34 2,011 66 719.6 98 301.0 130 142.0 162 73.6 194 41.4 226
6,531 35 1,942 67 698.7 99 293.5 131 138.9 163 72.2 195 40.7 227
6,267 36 1,876 68 678.6 100 286.3 132 135.9 164 70.8 196 40.0 228
6,015 37 1,813 69 659.1 101 279.2 133 133.0 165 69.5 197 39.3 229
5,775 38 1,752 70 640.3 102 272.4 134 130.1 166 68.2 198 38.7 230
5,545 39 1,693 71 622.2 103 265.8 135 127.3 167 66.9 199 38.0 231
21,918 8
20,882 9
5,326 40 1,637 72 604.6 104 259.3 136 124.6 168 65.7 200 37.4 232
5,117 41 1,582 73 587.6 105 253.1 137 122.0 169 64.4 201 36.8 233
19,901 10 4,917 42 1,530 74 571.2 106 247.0 138 119.4 170 63.3 202 36.2 234
18,971 11 4,725 43 1,480 75 555.3 107 241.1 139 116.9 171 62.1 203 35.6 235
18,090 12 4,543 44 1,432 76 539.9 108 235.3 140 114.5 172 61.0 204 35.1 236
17,255 13 4,368 45 1,385 77 525.0 109 229.7 141 112.1 173 59.9 205 34.5 237
16,463 14 4,201 46 1,340 78 510.6 110 224.3 142 109.8 174 58.8 206 33.9 238
15,712 15 4,041 47 1,297 79 496.7 111 219.0 143 107.5 175 57.7 207 33.4 239
14,999 16 3,888 48 1,255 80 483.2 112 213.9 144 105.3 176 56.7 208 32.9 240
14,323 17 3,742 49 1,215 81 470.1 113 208.9 145 103.2 177 55.7 209 32.3 241
13,681 18 3,602 50 1,177 82 457.5 114 204.1 146 101.1 178 54.7 210 31.8 242
13,072 19 3,468 51 1,140 83 445.3 115 199.4 147 99.0 179 53.7 211 31.3 243
12,493 20 3,340 52 1,104 84 433.4 116 194.8 148 97.0 180 52.7 212 30.8 244
11,942 21 3,217 53 1,070 85 421.9 117 190.3 149 95.1 181 51.8 213 30.4 245
11,419 22 3,099 54 1,037 86 410.8 118 186.1 150 93.2 182 50.9 214 29.9 246
10,922 23 2,986 55 1,005 87 400.0 119 181.9 151 91.3 183 50.0 215 29.4 247
10,450 24 2,878 56 973.8 88 389.6 120 177.7 152 89.5 184 49.1 216 29.0 248
10,000 25 2,774 57 944.1 89 379.4 121 173.7 153 87.7 185 48.3 217 28.5 249
9,572 26 2,675 58 915.5 90 369.6 122 169.8 154 86.0 186 47.4 218 28.1 250
9,165 27 2,579 59 887.8 91 360.1 123 166.0 155 84.3 187 46.6 219
8,777 28 2,488 60 861.2 92 350.9 124 162.3 156 82.7 188 45.8 220
8,408 29 2,400 61 835.4 93 341.9 125 158.6 157 81.1 189 45.0 221
8,057 30 2,316 62 810.6 94 333.2 126 155.1 158 79.5 190 44.3 222
7,722 31 2,235 63 786.6 95 324.8 127 151.7 159 78.0 191 43.5 223
Table 7 - Thermistor Resistance versus Temperature for High Temperature Models
30
APPENDIX D. TEMPERATURE EFFECT ON EARTH PRESSURE AND
CONCRETE STRESS CELLS
The following theoretical treatment is by no means rigorous — there are some questionable assumptions and approximations — but it should give some idea of the magnitude of the thermal effect to be expected on hydraulic earth pressure cells, buried in soil, or installed at the contact between soil and structure, and on concrete stress cells embedded in concrete.
Figure 19 - Radius (R) and Thickness (D)
D.1 Formulas
Consider a circular cell of radius (R) containing a liquid film of a thickness (D), coefficient of thermal expansion Kppm/
°
C, and bulk modulus (G).
For a temperature rise of 1
°
C the expansion (Y
T
) of the liquid film is given by the equation:
Y
T
= KD
Equation 7 - Expansion of Liquid for a Temperature Rise of 1
°
C
Expansion of the liquid is resisted by the confinement of the surrounding medium (soil or concrete) and this causes a pressure rise (P) in the liquid, as well as a compression of the liquid
(Y c
) given by the equation:
Y c
= PD/G
Equation 8 - Compression of Liquid
The net expansion (Y) of the cell is equal to:
Y = D (K- P/G)
Equation 9 - Expansion of Liquid
31
Liquid pressure inside the cell causes deformation of the surrounding medium. The amount of
deformation can be quantified by modification of formula found in Equation 7, where the
deformation (Y), produced by a uniform pressure (P), acting on a circular area, (R) radius, on the surface of a material with modulus of elasticity (E) and Poisson’s ratio (
ν
), is given by:
At the center of the cell:
Y=
2 PR (1-
ν 2 )
E
Equation 10 - Deformation at the Center
At the edge of the cell:
Y=
4 PR (1-
ν 2
)
π
E
Equation 11 - Deformation at the Edge
The difference being:
PR (1-
ν 2
) (2 – 4/
π
)/E
Equation 12 - Difference in Deformation
The above formulas apply to pressures acting on a free surface. However, in the confined case,
Y, at the edge of the cell, can be assumed to be nearly zero. Therefore, Y, at the center, is
assumed to be the same as shown in Equation 12.
If the average Y across the cell is assumed to be half this value, and if the deformation of the medium on either side of the cell is assumed to be the same, then the average total expansion of the cell is given by:
Y = 0.73 PR (1-
ν 2
) x 0.5 x 2/E = 0.73 PR (1-
ν 2
)/E
Equation 13 - Average Total Expansion of the Cell
Equating Equation 9 and Equation 13 gives:
P (D/G + 0.73 R (1-
ν 2
)/E) = KD
Equation 14 - Combined Equations
32
If one side of the cell lies in contact with a rigid structure, e.g., a concrete retaining wall or a concrete bridge footing, then:
Y = 0.73 PR (1-
ν 2
) x 0.5/E = 0.36 PR (1-
ν 2
)/E
And
P (D/G + 0.36 R (1-
ν 2
)/E) = KD
Where (E) pertains to the soil material.
Since these expressions are only approximate, they can be simplified even further:
For all E < 10 x 10
6 psi the term D/G is negligible, so long as the cell is designed and constructed properly, i.e., G is large, (no air trapped inside the cell), and D is small. In addition, the term (1-
ν 2 ) can be replaced by 0.91 since ν usually lies between 0.25 and 0.35.
The total embedment is given by:
P = 1.5 EKD/R psi / o
C
Equation 15 - Total Embedment
And for contact pressure cells:
P = 3 EKD/R psi / o
C
Equation 16 - Total Embedment for Contact Pressure Cells
Some typical values of the various parameters are:
Liquid K x 10
-6
/ ºC
Oil 700
G x 10
6
0.3
psi
Mercury
Water
Glycol
50/50 Glycol/Water
180
170
650
400
3.6
0.3
0.26
0.28
Embedment Material
Plastic Clay
Soil
Sand
Compacted Ottawa
Sand
E x 10
6
psi
0.003
ν
0.001 to 0.02 [Ref 2] 0.25 to 0.45
0.02 to 0.06 [Ref 3] 0.28 to 0.35
0.2
Weathered Rock
Concrete
0.04 to 0.11 [Ref 4]
5.0
Table 8 - Typical Values of Various Cell Parameters
0.25
D.2 Examples
For an oil-filled cell, nine inches diameter, and D = 0.060 inches, totally embedded in:
(For contact pressure cells, multiply the values for P by two.)
Plastic Clay:
E = 3000 psi
ν = 0.3
P = 0.042 psi / o
C
Soil, medium stiffness:
E = 10000 psi
ν = 0.3
P = 0.138 psi / o
C
Coarse Sand:
E = 50000 psi
ν = 0.3
P = 0.69 psi / o
C
For an oil-filled concrete stress cell, nine inches in diameter, and D=0.020 inches totally embedded in:
Concrete:
E = 5 x 10
6
ν = 0.25
psi
P = 22.7 psi / o
C
Completely rigid medium:
P = 210 psi / o
C
For the same cell, filled with mercury instead of oil:
Concrete:
P = 5.8 psi / o
C
Completely rigid medium:
P = 650 psi / o
C
33
34
References:
[1] Roark, R.J. and Young, W.C. “ Formulas for Stress and Strain,” McGraw Hill, fifth edition,
1982, p 519.
[2] Weiler, W.A. and Kulhawy, F.H. “ Factors Affecting Stress Cell Measurement in Soil” J.
Geotech. Eng. Div. ASCE. Vol. 108, No. GT12, Dec., pp1529-1548.
[3] Lazebnik, G.E., “Monitoring of Soil-Structure Interaction.” Chapman & Hall. pp 224.
[4] Fujiyasu, Y. and Orihara, K. “Elastic Modulus of Weathered Rock.” Proc. of the 5 th
Intl.
Symp. on Field Measurements in Geomechanics - Singapore 1999. p 183.
35
APPENDIX E. NON LINEARITY AND THE USE OF A SECOND ORDER
POLYNOMIAL TO IMPROVE THE ACCURACY OF THE CALCULATED
PRESSURE
Most vibrating wire pressure transducers are sufficiently linear (
±
0.2 % FS) that use of the linear calibration factor satisfies normal requirements. However, it should be noted that the accuracy of the calibration data, which is dictated by the accuracy of the calibration apparatus, is always
±
0.1% F.S.
This level of accuracy can be recaptured, even where the transducer is nonlinear, by the use of a second order polynomial expression, which gives a better fit to the data then does a straight line.
The polynomial expression has the form:
Pressure = AR
2 +
BR
+
C
Equation 17 - Pressure Calculation with Second Order Polynomial
Where;
R is the reading (digits channel B)
A, B, and C, are coefficients
Figure 18 shows a typical calibration sheet of a transducer that has a very little nonlinearity. The
figure under the “Linearity (%FS)” column is:
Calculated Pressure -True Pressure
Full
S cale Pressure
x 100%=
G
(
R
1
-R
0
)
P
F.S.
x 100%
Equation 18 - “Linearity (%F.S.)” on Calibration Sheet
Note: The linearity is calculated using the regression zero for R
0 shown on the sheet.
For example, from the typical sheet shown in Figure 18:
P= 210 kPa, G (R
1
– R
0
) = - 0.1192(7223-8983)
Gives a calculated pressure of 209.8 kPa, the error is 0.2 kPa.
Whereas the polynomial expression gives a calculated pressure of:
A (7223)
2 +
B (7223) + 1053 = 209.9 kPa
The actual error is only 0.1 kPa.
This is an insignificant improvement, however, where the nonlinearity is higher, for example
± 0.25% F.S., the improvement could be significant.
36
Note. If the polynomial equation is used it is important that the value of C, in the polynomial equation, be taken in the field, following the procedures described in Section
2.5. The field value of C is calculated by inserting the initial field zero reading into the polynomial equation with the pressure, P, set to zero.
If the field zero reading is not available, calculate C using the zero pressure reading on the calibration sheet.
In the above example, the value of C would be derived from the equation:
0 = A(8981)
2
+ B(8981) from which C = +1053
Equation 19 - Calculating C Using the Zero Pressure Reading from the Calibration Sheet
It should be noted that where changes of earth pressures are being monitored it makes little difference whether the linear coefficient or the polynomial expression is used.
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