Measuring the Early Shrinkage of Mortars

Markus Greim

April 8, 2011

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1 Introduction

All mortars are changing their volume from the moment the binder particles came in contact with water untilseveral months and years. In most practical application this expansion and shrinkage must be minimized.Many theoretical models are describing the cause of this effects, but specially the mechanism in the firsthours are not completely understood yet. One demanding prerequisite for controlling the shrinkage of mortarsare measurement instruments that are able to measure shrinkage and expansion from the early beginning ofhydration and setups that are able to simulate environmental conditions in the field application.

Up to now shrinkage and expansion of building materials is measured by simple mechanical instrumentslike cantilevers. Therefore a certain strength of the material is necessary.

There is a survey given about more modern sensors and instruments measuring also the early shrinkagebefore the setting point. Beneath others a contactless LASER based measurement method with a cone-formedformwork is presented avoiding the problems shown above.

2 Taxonomy of Shrinkage Measurement Systems

As long as a material is in the fluid state shrinkage is not causing a problem. The only thing you have to keepin mind is, that a length change on each site of a 1 cubicmeter cube of 1/1000 is already a volume change ofabout 3 liters.

When the material is setting and/or is in contact with a material that has no shrinkage or expansion, straininside the material or in the contact zone will appear. As soon as this tension will be over the actual tensilestrength of the material, the material structure will be damaged, usually by the occurring of cracks.

Therefore its obvious not only to measure the free shrinkage but also the strain that occur. It’s calledmeasurement of the blocked or restrained shrinkage. The tensile strength and the materials volume is changingmost in the first hours after mixing, so restrained and free shrinkage should be observed as early as possiblein the hydration process.

The process of crystal grow itself is influenced by the environmental conditions like temperature, humidity,freeze thaw cycles, penetration of gas, or salty or acid liquids. This environment must be kept constant todetect the shrinkage of the material itself. But on the opposite the length change may be an indicator for theresistance against an environmental attack on the material. For example for detecting the alkali silica reactionor for indicating the freeze/thaw resistance of concrete.

Figure 1 shows free shrinkage over the time in a general way. We must distinguish 3 ranges of of materialstrength for using different measurement techniques:

• fluid (F)

• starting of setting (S)

• hardened material (H)

These 3 ranges may be subdivided depending on the material geometry and environmental conditions. Forexample:

• rigid volume, no evaporation

• low volume, high surface, high evaporation

1Presentation given at the Third International Drymix Mortar Conference idmmc threepubished in the Drymix Mortar Yearbook 2011 Editor: Ferdinand Leopolder, ISBN 978-3-9814004-1-0

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• high or low temperature

• periodical temperature changes

• humidity gradient

• temperature gradient

The appropriate shrinkage measurement instruments are also shown.

Figure 1: Shrinkage over time

3 Length Change Measurement Sensors

Common for all systems is the requirement to measure very small length or volume changes over the time. Aresolution better then 1µm is usually requested. As comparison: A human head hair has a mean diameter ofabout 120 µm, the wave length of red light is 0.7 µm. The measuring period is quite long, from several hoursand days up to one year and more. So the sensor must also give very stable, non drifting results over a longtime. The scale of the measurement setup is from several centimeter small specimen in a laboratory setup upto deformation measurement of real big structures like dams and bridges. The mostly very slow movement ofthe material is an advantage from the measurement technology point of view.

We can distinguish two kind of measurement transducers for the length change:

1. Systems that are in a direct mechanical contact with the material

2. Systems measuring without touch the distance between the sensors and the surface of the specimen.

If the specimen is submersed in a fluid phase the volume change can be measured indirectly by the buoyantforce, for example with a balance.

The tables in figure 2 and 3 give a survey about the several mechanical touching and touchless sensors.

3.1 Contacting Sensors

3.1.1 Calipers

Calipers are quite robust, but a low accuracy and may not be read out automatically, out fashioned.

3.1.2 LVDTs

The Linear Variable Differential Transformers has a movable ferromagnetic core. Depending on the positionof the core the voltage inducted from the primary to the secondary coil is changed. Mostly pen sized with adiameter of 8mm.

Figure 2: Survey about sensors for contacting distance measurement

3.1.3 Strain Gages

A strain gage is a thin foil, sized several millimeters, with a electrical resistor network printed on. If a thin wireis elongated the diameter of the wire will decrease and the resistance will increase. Most common applicationis measuring the forces on a structure by detecting the deformation with a strain gage. Special strain gages forcementitious system are available. Used for measuring restrained shrinkage.

3.1.4 Fiber Bragg Gratings

On a thin glass fiber on a length of some centimeters the inner glass structure is changed to a kind of opticalgrading [3]. Under a mechanical tension the distance of the slits of the gratings and therefore the spectrum ofthe light, which is crossing the grating, is changed. One single glass fiber of several hundred of meter lengthmay carry several of this length change sensitive areas. Main application is the monitoring of large structuresover months and years.

3.2 Contactless Sensors

Figure 3: Survey about sensors for non contacting distance measurement

3.2.1 Ultrasound

Ultrasound sensors are well known from the car park assistance systems These systems are measuring thetime of flight of sound pulse. The results are quite independent of the surface properties of the reflectingmaterial, but the accuracy and the resolution is quite poor.

3.2.2 Inductive Sensors

A conductive element near by an electro magnetic oscillating circuit is moving the frequency and damping thevoltage depending on the distance from the coil. Very robust, but needs a high conductive target.

3.2.3 Laser TOF

The Time Of Flight of a short light pulse is measured. Due to the high speed of light the time is in the rangeof several pico (10−12) seconds. High measurement range, but the resolution is quite low (0.1 mm). It is wellsuited for big structures.

3.2.4 Laser Triangulation

There is known distance between the light emitter and the detector. Based on the elementary trigonometry lawsthe distance between the emitter and the target can be calculated. Systems have a low absolute measurementrange, but a high resolution, better then the wave length of the used light.

3.2.5 Capacitive Measurement

The capacity of an electrical capacitor is directly proportional to the area of the capacitor plate and inverselyproportional to the distance of the plates. This method is the most accurate method known up to know.The absolute measurement range is less then some millimeters, but the resolution and accuracy are in thenanometer (10−9m) range.

3.3 Future Developments in Sensor Technology

For some applications the accuracy and resolution of the LASER sensors or the LVDTs is not high enough.Capacitive sensors, as written, would be an improvement. But up to now this technology is quite difficult tohandle for practical applications, and the results where strongly influenced, by changes in in the resistance ofthe material surface. Latest developments, integrating different technologies into one singe sensor are verypromising.

Also the Fiber Bragg sensors directly embedded inside the specimen are a very interesting technology. Upto now economical reasons are limiting the application of this sensors to a few big construction projects.

4 Measuring Systems

It is obvious that for the fluid state and the early setting state touching sensors are not appropriate. The sensorcan't be actuated by adherence if the material is still fluid. If the system is hardened a mechanical coupling iseasily possible. This sensors are generally speaking cheaper or have a higher accuracy at the same costs asthe non-contact sensors. So using mechanical sensors is recommended more from the economical point ofview as for technical reasons.

The optimal measurement system is a combination of the appropriate setup and the best fitting sensor.As in all practical applications a lot of details must be regarded and also the economical requirements to

build such a system for a reasonable price. This will be illustrated on some examples for systems designed forthe fluid, setting and hardened state of material for different environmental conditions (see section 2)

4.1 Gauge for hardened specimen

To measure the every day length of a mortar or concrete beam is an apparent easy task. The standardEN 12617-4 [6] is describing such a test procedure. Here an accuracy of ±1.00 µm is required. This cannot be fulfilled by any mechanical indicating caliper, and also the best standard electronic digital caliper withLC display, as used in the machine industry, have (for my knowledge) an absolute accuracy over the wholemeasurement range not better then ± 1.25 µm.

Another very important point is the thermal length change of all materials. Concrete, mortar and steel havea thermal expansion coefficient of about 12 µm/m/K, stainless steel 16 µm/m/K and even quartz glass of 0.5µm/m/K.. As calibration reference bar a so called Invar (Fe: 65%, Ni: 35%) steel bar is required. Also this kindof material is changing with 2 µm/m/K [9].

Modern carbon fibers have an coefficient of 0.2 µm/m/K. As composite materials CFRP rods can even havea negative thermal expansion coefficients. A steel carbon construction can achieve a thermal expansion nearlyzero. Figure 1 (upper right) shows a setup made of steel and carbon.

4.2 Shrinkage Drain

Measuring the shrinkage and expansion during hydration can be done in a kind of mold for the fresh material,which is equipped with a length change sensor. For this purpose at least one side of the mold must be movable.Figure 4 shows an 25 cm long example of such a setup. One meter long drains are common usage. The lengthIt must be kept in mind that shrinkage and expansion is generally in all 3 dimensions. But this volume changeis not absolutely isotropic. For this reason the mold is covered inside with a non sucking but compressiblerubber sheet (about 1..2 mm) to avoid blocking in the drain. The support for the movable anchor has some lossalso in the y and z direction also to avoid blocking in this extra directions. Therefore a gap between the anchorplate and the wall of the drain is necessary, which can be easily sealed with some simple elastic material likeordinary grease (see figure 4. The anchors are a little bit elastic itself to regard that that there is also a lengthchange between the start and endpoint of the anchor.

The sensor has an accuracy of about ±1µm at a stroke of 5mm.

Figure 4: Shrinkage Drain

This kind of setup gives reliable data after certain level of strength of the material. To compare the shrinkagevalues of different materials, you need also results of strength development, for example done with the Vicatapparatus.

4.3 Corrugated Polyethylene Molds

Jensen [10] suggested the use of a corrugated polyethylene mould (see figure 5 insted a steel mold. Firstresults are given about 30 minutes after mixing for cement paste [12]. One disadvantage of this setup formortar is, that aggregates placed in the fins are blocking shrinkage. Especially if the material is segregating.

4.4 Bending drain

The ordinary shrinkage drain, as it is described above, is normally used at constant temperature, constanthumidity and a covered surface of the material to avoid evaporation.

Sometimes the simulation of real world conditions is more interesting. To built in a screed in a house witha floor ground heating is a demanding job [11]. Starting the heating will result in temperature and later on inhumidity gradient in the material. An anisotropy shrinkage, higher on top surface then on the bottom layer willresult in a bending. Is the cementitious material with a size of 100x10x6 cm³fixed at 10 cm before the end,forces on anchor more then 100 N. Would this setup made of 2 mm tin of steel bending would be several 100µm, thats in the range of the common bending at all. The solution is a setup (see figure 6 where the forces aretransferred to a rigid u-shaped steel foundation [7].

Figure 5: Shrinkage measurement with corrugated polyethylene moulds [12]

For the length and height change measurement the same LVDTs as for the bending drain can be used.In the bottom of the drain a computer controlled electrical heating unit can simulate different heating up andcooling down profiles over several days.

4.5 Shrinkage Ring

The Shrinkage Ring is a setup for measuring restrained shrinkage. This means, the material is in a fix me-chanical contact with an infinite stiff mechanical structure so no shrinkage and expansion is possible, insteadof length change the forces are measured.

Such a system could be realized for example by an active controlled mechanical structure, where a hydraulicram compensates each movement and the the forces are measured indirectly over the hydraulic pressure.Such systems have been realized [4] but the technical and the economical expense is quite high.

The standard ASTM C 1581-04. “Standard Test Method for Determining Age at Cracking and InducedTensile Stress Characteristics of Mortar and Concrete under Restrained Shrinkage” [1] is describing a moresimple setup. The material is placed between two concentric steel rings. The outer ring has an inner diameterof 406 mm the inner ring an outside diameter of 330 mm. So the specimen is like a donut with 38 mm thickness.The inner steel ring has a wall thickness of 13 mm with strain gages applied for measuring forces (see figure7). As mentioned before strain gage is basically not measuring forces but even also a length change.

A typical strain of 100 µm/m is an absolute length change at the given geometry of about 116 µm. Soshrinkage is only partly restrained.

4.6 Shrinkage Cone

For measuring shrinkage and expansion for the fluid or just setting material we must use a non contact mea-surement procedure. The standard ASTM C 827-95a “Change in Height at Early Ages of Cylindrical Specimensfrom Cementitious Mixtures” [2] describes a method where a ball with a diameter about 10 mm and a densityof 1.2 kg/dm³ is laid onto the surface of the material which is filled into a cylindrical mold, between 100 and 300mm height. With a light source and a lens the ball is projected onto the wall, where the movement should beindicated with a pencil each hour.

Beside the outfashioned distance measurement technology, the disadvantage of this method is the use ofa rigid cylindrical mold. Under the prerequisite of an isotropic shrinkage and expansion the material is not onlyexpanding in the vertical but also in the horizontal direction. As long as all material is fluid enough, we will getonly a height change, the material which is moving horizontal is also lifted up, like in a thermometer. As soon

Figure 6: Bending Drain

Figure 7: Shrinkage Ring

as the material has a certain stiffness we get an undefined relocation of the material. On the surface we willget a kind of spherical calotte. Higher in the center by an expansion and lower for a shrinking material. Themeasured height change is therefore a mix of the vertical length change and the total volume change.

You can avoid this if you are using a mold formed like a bottom up pyramid or cone. Under the presumptionthat with an isotropic form volume change the angles of a body keep the same smaller cone is only changingits height, there is no relocation of material [8] (see figure 8).

It can be mathematical shown that the volume change is the cube of the height change and vice versa (seeequation 1):

General : V =13πr2h;V ′ =

13πr′2h′

r = h tan(α)⇒ V =13(h tan(α))2πh

α = const ⇒ V = ch3;V ′ = ch′3

V ′

V=h′3

h3⇒ h′

h= 3

√V ′

V

(1)

A practical realization of this setup is shown in figure 9. The double wall cone formed vessel may be tem-perature controlled. A polypropylene foil is avoiding wall friction. A triangulation LASER sensor is measuring

Figure 8: Under the prerequisite of an isotropic shrinkage (expansion) the radius r and the height h of a coneshrink (expand) the same percentage: h′ = k · h and r′ = k · r (k for example 80%)⇒ V ′/V = 0.83 = 0.512

the height change with an accuracy of some µm. To avoid evaporation on the top surface it may be coveredby a transparent silicone oil, or a stainless steel foil. A standard plastic foil is not diffusion resistant. A reflectormay be used if there is a risk of air bubbles growing where the LASER beam is targeting the surface

4.7 Thin Layer Shrinkage Measurement System

to measure the early shrinkage of Self Levelling Underlayments (SLUs) R. Zurbriggen [5] suggested a setupshown in figure 10. Here the material is placed in a flexible thin mold with big surface (ca. 600 cm²) and lowvolume (ca. 0.2 l ). LASER triangulation sensors on each end of the mold are measuring the distance to alightweight Styrofoam reflector. The sum of both distances is the total length change. To get a correlationbetween the shrinkage and the weight loss, the mold is placed onto a balance.

5 Conclusion

Very slow movements over a long time are not accessible for our human visual sense or sense of touch.Making reliable measurement of shrinkage and expansion of building materials is an trivial task only for thefirst glimpse. Not only the selection of the right sensor is important, but the system setup itself should bedesigned very carefully.

Figure 9: The Shrinkage Cone as exploded view. Cone formed vessel, partition foil, specimen and optionalreflector

Figure 10: Basic principle of the thin layer shrinkage measurement system as described at [5]

Contents

1 Introduction 1

2 Taxonomy of Shrinkage Measurement Systems 1

3 Length Change Measurement Sensors 23.1 Contacting Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3.1.1 Calipers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.1.2 LVDTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.1.3 Strain Gages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.1.4 Fiber Bragg Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.2 Contactless Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.2.1 Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.2.2 Inductive Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2.3 Laser TOF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2.4 Laser Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2.5 Capacitive Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.3 Future Developments in Sensor Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4 Measuring Systems 44.1 Gauge for hardened specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44.2 Shrinkage Drain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.3 Corrugated Polyethylene Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.4 Bending drain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.5 Shrinkage Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.6 Shrinkage Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.7 Thin Layer Shrinkage Measurement System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5 Conclusion 8

List of Figures

1 Shrinkage over time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Survey about sensors for contacting distance measurement . . . . . . . . . . . . . . . . . . . . . 33 Survey about sensors for non contacting distance measurement . . . . . . . . . . . . . . . . . . 34 Shrinkage Drain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Shrinkage measurement with corrugated polyethylene moulds [12] . . . . . . . . . . . . . . . . . 66 Bending Drain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Shrinkage Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Under the prerequisite of an isotropic shrinkage (expansion) the radius r and the height h of a

cone shrink (expand) the same percentage: h′ = k · h and r′ = k · r (k for example 80%)⇒V ′/V = 0.83 = 0.512 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

9 The Shrinkage Cone as exploded view. Cone formed vessel, partition foil, specimen and optionalreflector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

10 Basic principle of the thin layer shrinkage measurement system as described at [5] . . . . . . . . 9

References

[1] ASTM C 1581-04. “Standard Test Method for Determining Age at Cracking and Induced Tensile StressCharacteristics of Mortar and Concrete under Restrained Shrinkage” , 2004

[2] ASTM C 827-95a (Reapproved 1997) “Standard Test Method for Change in Height at Early Ages ofCylindrical Specimens from Cementitious Mixtures”, 1997

[3] Bludau W, “Lichtwellenleiter in Sensorik und optischer Nachrichtentechnik”, Springer Berlin 1998

[4] Breitenbücher R, “Zwangsspannungen und Rissbildung infolge Hydratationswärme” Dissertation TUMünchen, München, 1989

[5] Bühler E, Zurbriggen R, “Mechanisms of early shrinkage and expansion of fast setting flooring com-pounds” Tagung Bauchemie, 7./8. Oktober 2004 in Erlangen Neubauer J, Goetz-Neunhoeffer F, hrsg. vonder GDCh-Fachgruppe Bauchemie, 2004

[6] EN 12617-4:2002, “Products and systems for the protection and repair of concrete structures. Test meth-ods, Part 4: Determination of shrinkage and expansion”

[7] Gerstner B, Haltenberger H, Teubert O, Greim M, “Device for measuring deformation of mortar in twodirections under different temperature conditions has sensors for simultaneous measurement of verticaland horizontal mortar movement” German Paten Application DE000010123663A1, 2001

[8] Greim M, Teubert O, “Appliance for detecting initial expansion and shrinkage behavior of building materialsbased on contactless measurement of change in filling level of container of fresh material specimens untilset”, German Patent Application DE000010046284A1, 2000

[9] Ilschner B, Singer RF, "Werkstoffwissenschaften und Fertigungstechnik: Eigenschaften, Vorgänge, Tech-nologien" Springer Berlin 2010

[10] Jensen OM, Hansen PF. “A Dilatometer for Measuring Autogeneous Deformation in Hardening PortlandCement Paste” Materials and Structures : Research and Testing. 28:406-409, 1995

[11] Lorenz OK, Schmidt M, “Aufschüsseln schwimmend verlegter Zementestriche”, ibausil, 13. InternationalaBaustofftagung September 1997, hrsg. Stark J. Band 1, 1997

[12] Lura P, Durand F , Jensen OM, “Autogenous strain of cement pastes with superabsorbent polymers”,International RILEM Conference on Volume Changes of Hardening Concrete: Testing and Mitigation,Jensen OM, Lura P, Kovler K (eds), RILEM Publications SARL 2006