Metrological recording of deformation development in ultra-high performance concrete (UHPC)in a triaxial test cell

1. Introduction and motivationUltra-high performance concrete (UHPC) is a new, very structurally dense concrete with a high strength of up to 250 N/mm2, that issimilar to steel. It is up to ten times stronger than ordinary concrete and demands innovative design concepts, that are more likelightweight construction than traditional concrete construction.

The material advantages and special qualities of UHPC compared to normal concrete, produce structural solutions that arecharacterized by a significantly lower intrinsic weight and by "open structures". This type of structure is vastly more susceptible todynamic excitation and fatigue loading than normal concrete constructions.

As, in UHPC structures, predominantly uniaxial stresses occur in rod-shaped components, and multiaxial stresses in compactcomponents and when introducing concentrated forces, it is the aim of a research project supported by the German ResearchFoundation (DFG) as part of a priority program, to investigate both analytically and by experiment, the fatigue behavior of UHPC underuniaxial and triaxial loading.

The parameters for a three-dimensional, mechanical model for UHPC with anisotropic damage should be defined by analyzingprincipal meridian tests (the rotationally symmetrical stress and deformation states).

2.1. BasicsThe numerical analysis of concrete and reinforced concrete support structures with FEMprograms requires suitable mechanical models, which can realistically describe the non-linear material response, the progressive crack formation and damage, and the potentialfailure states.

A detailed overview of the models developed for the mathematical description of the non-linear material response for standard strength concrete, can be found in[Grünberg/Göhlmann-2005].

The fracture envelope is usually described geometrically as a function of the invariants I1, J2and J3 [Chen-1982]. I1 represents the hydrostatic stress state, whereas J2 and J3 areexpressed by components of the stress deviator.

The formulation in the Haigh-Westergaard coordinates ξ, ρ and θ is useful. Any stress state σis described by the hydrostatic stress component ξ, the deviator stress ρ and the deviatorangle θ (see Figure 1).

2.2. Three-phase model for UHPCTraditional failure models are only of limited use for ultra-high performance concrete. This iswhy the three-phase model has been enlisted and developed for UHPC [Grünberg et al.-2007]. In this model, both the brittle and ductile material responses are described by thecharacteristic curves of the principal meridians, in particular the compressive meridian of thefracture envelopes.

With uniaxial loading, the ultra-high performance concrete is marked by brittle failure both withtension and with compression. This characteristic is not changed by adding fibers. It is to beexpected that this brittleness will substantially modify the tensile and compressive meridiancurves. To develop the three-dimensional mechanical model of UHPC with anisotropicdamage under multiaxial loading, it is necessary to know these compressive and tensilemeridian curves (see Figure 1, right).

2. Three-dimensional, mechanical model for UHPC

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Fig. 1: Fracture envelope, shown in the Haigh-Westergaard coordinates (top) and the three-phase model for UHPC in the principal meridian section

The principal meridian stress states are particularly interesting for the three-phase model thathas been developed. These are the stress states with predominantly compressive loading inthe axial direction and the rotationally symmetrical transverse stress states.

To determine the requisite parameters, static as well as dynamic uniaxial and triaxialexperimental investigations are being carried out at the Institut für Massivbau (Institute forConcrete Construction) at the University of Leibnitz in Hanover.

3.1. Compressive meridian testsThe compressive meridian is particularly important for the application, because this is wherethe stress ratios relevant to building practice are to be found. The stress ratios produced bythe superposition of a low, hydrostatic compressive loading with a high compressive loadingin the axial direction, are investigated in the triaxial test cell. These investigated stress ratiosare found on the compressive meridian and are thus above the uniaxial strength. In concrete,even a low transverse pressure loading can result in a clear increase of the axial bearingstrength.

The investigations were carried out on cylindrical UHPC test specimens = 60 mm). The "M2Qmixture" fromÆ(h = 180 mm, DFG Priority Program 1182 "Sustainable building with UHPC"[Schmidt-2008] was used. A strength of fcm = 198 MPa was achieved in the comparativeuniaxial investigations.

3.2. Triaxial test cell and instrumentationTriaxial test cells have already been used many times to determine the static, multiaxialstrength of concrete [Dahl-1992], [Rogge-2002]. But the more important field of application byfar is geotechnical engineering and rock mechanics. The advantage of this test apparatus isthat the transverse pressure loading is applied to the test specimen hydraulically, withoutpreventing deformation in the axial direction.

Special sealing systems and a specific control for the phase-synchronized loading of thesample were required for the dynamic investigations intended here. The DBTA60-100-RT-DYN triaxial test cell (Figure 2), which is designed for dynamic loadings of up to 5 Hertz, wasdeveloped in cooperation with the manufacturer.

3. Experimental investigations

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Fig. 2: DBTA60-100-RT-DYN dynamic triaxial test cell

The pressure chamber is sealed against the upper load stamp by a step seal let into theupper closure. Axial force is applied by a 1 MN cylinder of an existing universal loading frame.The transverse pressure is generated directly by the servo-hydraulic test device and is driven,phase-synchronized with the 5 Hertz loading frequency, by the PCS 8000 multi-channel controlmade by Walter & Bai. A 3 mm thick, nitrile butadiene rubber sample sleeve protects theUHPC test specimen from the oil.

Because the oil pressure chamber is so large, it is also possible to place additionalmeasurement technology directly on the test specimen, in the surrounding oil (see section3.2.3).

The measurement signals can be taken out of the pressure vessel by a total of 8, 4-wireelectrical leadthroughs. The test cell is designed for oil pressures up to 1000 bar. The volumeof oil in the cell can be reduced from approx. 8 liters to approx. 1.5 liters with the aid of specialaluminum packing, so that a "proper" sinusoidal loading can be implemented in thetransverse direction as well.

3.2.1. Test rig and measurement acquisitionThe triaxial test cell was installed in the existing servo-hydraulic test rig (Figure 3), integratedinto the new control system and connected to the amplifier.

The integration of the manufacturer's individual components (triaxial test cell, hydraulics &control and measurement technology) into a test rig with simple test sequences, is an in-house development of the Institute for Concrete Construction at the University of Leibnitz, inHanover.

Fig. 3: Triaxial test cell in the test rig

Some of the measurement channels are also relevant to control. It is therefore necessary tofirst record these channels (cylinder pressure, LVDTs, circumferential extensometer) with thePCS-8000 control system, and then, in the same control timing (0.125 ms), transfer them tothe amplifier, again via the analog output modules (0-10 V). This diversion is not necessary forthe pressure transmitter (transverse pressure) and the laser distance sensors, as the voltagesignal for both the systems can be measured in parallel.

To enable sufficient measurement channels to be recorded, three carrier frequency amplifiersof the Spider8 type, from HBM, were cascaded, to make a total of 24 measurement channelsavailable. The measured values are recorded and stored on the PCusing catman®Professional (Version 6.0), also from HBM.

A data capture frequency of 100 Hz., was selected for a loading frequency of 5 Hz. Thissampling rate allows the peaks to be recorded with sufficient accuracy, whilst also making itpossible to handle the accumulated volume of data, even in longer tests (up to 1.5 billion loadcycles). The measurement signals of the strain gages and temperature sensors wereexclusively recorded by the amplifier. The modular arrangement of the Spider8 modulesmeans that it is also possible to subsequently add additional measurement channels.

Figure 4 shows a diagram of the test setup with the triaxial test cell, instrumentation, controlsystem. and measurement acquisition.

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Fig. 4: System outline: triaxial test cell, instrumentation, control system and amplifier

More details of the instrumentation used and its special qualities, are given in the sectionsbelow.

3.2.2. Measurement technology outside the triaxial test cellThe PZ-D 1000/600 servo-hydraulic test cylinder made by Walter&Bai, that was used for theaxial loading, has a maximum piston stroke of 250 mm and can apply a load of up to 1 MN.The cylinder displacement is recorded by an LVDT WA200 inductive displacement transducerfrom HBM, with a measuring range of ±200 mm. The load cell between the cylinder and thespherical cap has a measuring range of ±1000 kN.

Fig. 5: Measurement technology outside the triaxial test cell

A P2VA1 pressure transducer (D-1) screwed into the triaxial test cell from outside in the upperarea of the pressure chamber, records the oil pressure (up to 1000 bar) and returns a voltagesignal (0.5-10 V). For some of the tests, an additional P5MA absolute pressure transducer (D-2), with a measuring range up to 500 bar, was used at the lower cell inlet. This measurementsignal was directly acquired by the Spider8 amplifier. On the one hand, this meant that themeasurement signal of the pressure transducer could be monitored (redundancy), and on theother, that this second pressure sensor could be used to check whether a phase shift occursin the pressure chamber during dynamic loading.

The distance between the test bench with the complete triaxial test cell on it, and the sphericalcylinder cap, is registered by three laser distance sensors, L−1 to L−3. The sensors that areused have a measuring range of between 16 and 26 mm, with a resolution of 5 µm, andreturn a voltage signal (0-10 V) for this range. The advantage of laser distance sensors,particularly in dynamic investigations, is that they do not have any mechanical components,and can therefore also endure vast numbers of load cycles without wearing. The deformationsmeasured by the laser distance sensors include not only the pure deformation of the testspecimen, but also deformation content from the upper and lower load stamps, as well as thenon-linear effects of startup.

To exclude this additional and sometimes non-linear deformation content, the instrumentationmust be placed directly on the test specimen, in the oil.

3.2.3. Measurement technology inside the triaxial test cellThe longitudinal and transverse strains are measured directly on the test specimen, using a

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circumferential extensometer in the center of the sample cylinder, and three differentialtransformers, each offset by 120°.

Another way to record the deformation development is to use strain gages (SG), applied to theUHPC test specimen. The special aspect here is that the strain gages are directly exposed toan ambient pressure of up to 1000 bar. Eight pressure-proof electrical leadthroughs (4-pin Lemo S0 4) in the cover of the cell allowyou to be flexible about using different measuring instruments in the cell.

Inductive displacement transducers in a differential transformer circuit (LVDT)

A clamping device for three LVDTs, LVDT–1 to LVDT–3, allows the axial deformation of thesample to be measured very close to the test specimen. According to the manufacturer, theLVDTs can be used at oil pressures up to 1000 bar, and have a measuring range of ± 5 mm.The clamping ring is close to the test specimen, on the upper load stamp, and has amagnetic retainer for the plunger, at 120° increments, to protect the LVDT, should themeasuring range be exceeded (see Figure 6, left).

Fig. 6: Inside setup of triaxial test cell and instrumentation

Circumferential extensometer

The circumferential extensometer is designed for use inside pressure vessels, with mineraloil as the pressure medium (up to 1350 bar), and it allows changes in the circumference ofthe cylindrical concrete sample to be measured. The extensometer is attached directly to thesample by a high-precision chain of special rollers. The complete unit is automatically held bythe integral springs.

The zero point is easily adjusted by a mechanical setting screw. The measuring range of theclip, which has a measurement principle based on a strain gage full bridge, is 12 mm in total(-2 mm to +10 mm). A breakaway device prevents destruction of the extensometer, should thetest specimen suddenly fracture.

To prevent the measurement results being falsified by the elastic MBR sample sleeve, verythin, transparent Fluoropolymer shrink-fit tubing was used for tests with the circumferentialextensometer in the central area of the test specimen (see Figure 6, right).

Strain gages

Whereas the methods of measurement previously described all represent integralmeasurement over the entire circumference and height of the sample, strain gages can beused to observe the local development of deformation. It is worth noting here that when usingstrain gages, preparation of the test specimen, and incorporation into the cell are appreciablymore time-consuming and cost-intensive.

LY41-20/120 strain gages from HBM, with a measuring grid length of 20 mm, are used here.These are applied to the concrete with X60 adhesive, after the surface has been slightlyroughened and cleaned. Solder terminals (LS 5) are also used, as the connection cables willbe loaded more heavily when the test specimen is inserted into the MBR sleeve. As many asthree strain gages can be positioned vertically (SG-l), and horizontally (SG-t), as required. Theconnection cables run inside the sample sleeve and reach the oil chamber at the top end ofthe sleeve (Figure 7).

The active ¼ bridge is extended to a half bridge by a compensating strain gage. Thecompensating strain gage is also located on a UHPC specimen in the oil-filled pressurechamber of the cell. During the tests, both the strain gages are heated equally by the oilcirculating around them. Preliminary tests have shown that the transverse pressure has verylittle influence on the measured values. Strain gage measurement works very reliably in statictests, but with the dynamic transverse pressure loading, there are an increasing number ofstrain gage failures (see section 3.2.5), caused by the tiny air voids close to the surface, belowthe strain gages, that had not previously been visible (see Figure 7, right).

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Fig. 7: Test specimen with strain gages applied

Temperature sensors

An encapsulated Pt-100 sensor (resistance thermometer) was used as a temperature sensorto record the oil temperature in the pressure chamber. Dynamic loading causes the oil in thepressure chamber to heat up to approx. 50°C. A further Pt-100 sensor recorded the ambienttemperature right next to the triaxial test cell in the test rig. The resistor was extended to a halfbridge for connection to the amplifier.

3.2.4. Results of static testsThe static tests always followed the same pattern. In a first step, the hydrostatic stress statewas increased until the desired transverse pressure (here 200 bar = 20 N/mm²) wasachieved, then loading in the axial direction progressed at a constant cylinder advance, untilfracture (here 287.1 N/mm²). The axial stress and the transverse pressure over time areshown in Figure 8.

Fig. 8: Axial and transverse stress curves

After the initial installation of the test rig, extensive test series were carried out with straingages installed in parallel (along and across), LVDTs, circumferential extensometers andlaser distance sensors. Figure 9 (left) shows the axial and transverse strains determined bythe strain gages on the UHPC test specimen. As a comparison, look on the right of Figure 9 atthe axial strains determined from the LVDTs, and the transverse strain defined by thecircumferential extensometers. The measured values of the LVDTs were reduced bycalculating the steel deformation of the load stamp.

Fig. 9: The strain curves of strain gages (left) and LVDTs (right)

Both methods of measurement produced virtually the same axial stress on fracture (εB ≈6.80/00). With the LVDTs, a small, non-linear startup effect is noticeable after starting the initialhydrostatic load. This is as a result of the upper and lower load stamps pressing against thetest specimen. The strain gages purely record the test specimen strain.

The deformation measurements with the laser distance sensors (Figure 10) between the test

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bench and the force plate of the axial cylinder, include far more influences from the test setup.These include elastic content from the steel load stamp and linear deformation content fromthe test setup, as well as content from the non-linear startup effects, that decrease as the axialload increases.

Fig. 10: Deformation measurement by laser distance sensors

3.2.5. Results of dynamic testsBecause of the packing, it is not possible to use all the other instruments on the inside duringdynamic loading. So the only way to record the development of the deformation directly on thetest specimen in these tests is to use strain gages. The problem is that in these tests, thestrain gages fail as the number of load cycles increases.

The dynamic tests carried out for different maximum stresses (75%,..., 50%) are always at aconstant minimum stress (5%). The reference quantity is the particular breaking load understatic, triaxial stress. Figure 11 shows the minimum and maximum strains for each load cycleover the number of cycles, until fracture after 21558 load cycles, for a test with a maximumstress of 55%. Intermediate failures are recognizable by the vertical lines (measured value "-8‰"). SG-1 shows the transverse strain, whereas SG-2 and SG-3 show the axial strain.

If you look at the transverse strains, it is noticeable that here, the strains up to approx. 3500load cycles (point 1) match the expected curve without failures (approx. 20% of the axialstrains). The values then "drift", with the strain differential remaining constant. After barely5000 load cycles, the strain gage finally fails.

Fig. 11: Strain gage measured values during dynamic loading

SG-2 returns realistic measured values up to approx. 13000 load cycles (point 2), even if thereare a few failures. The strain values at minimum stress for SG-3 correspond well to those ofSG-2, up to approx. 5000 load cycles (point 3). SG-3 at minimum stress (minimumcompression of the test specimen) then returns no further measured values, whereas thesame strain gage at maximum compression returns plausible values up until fracture.

Once the strain gages have failed, the last measurand remaining in the dynamic tests issupplied by the laser distance sensors outside the triaxial test cell.

Recognizable in their curve (Figure 12) is the characteristic development of deformation foundin concrete under fatigue loading.

Fig. 12: Deformation measurement of the laser distance sensors during dynamic loading

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4. Summary and perspectiveWith the "triaxial cell" test rig described above, it is possible to determine the triaxial strengths for both static and dynamic loadings.

The use of sensors in the oil-filled pressure chamber of the triaxial test cell is particularly demanding of the measurement technologydeployed. By using special inductive displacement transducers (LVDTs) and a circumferential extensometer, it is possible todetermine the deformations in static loading directly on the UHPC test specimen. These deformations were verified by strain gagesapplied directly to the test specimen. For major test series, this saves cost (the material costs of the strain gages) and time inpreparing the test specimen (attaching the strain gages).

The problem is metrologically recording the development of the deformation in the dynamic investigations. Because packing isrequired, it is only possible to use strain gages here. The repeated dynamic loading vertically onto the surface of the strain gagepushes the strain gage into the tiny air voids in the concrete. This eventually causes the strain gage to fail prematurely. Laserdistance sensors attached outside the test cell record the characteristic curve of deformation development.

Triaxial tests showed that the three-phase model that has been developed, describes the compressive meridian of the fractureenvelope rather well. A transverse pressure loading produces a more ductile material response in the UHPC, compared to the brittlequalities in uniaxial loading.

A detailed report on the ongoing triaxial dynamic investigations and the Wöhler lines that are developed from them, will be given atthe 3rd fib-Congress [Ertel/Grünberg-2010].

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AcknowledgementsThe research project is supported by the German Research Foundation (DFG) in PriorityProgram 1182: "Sustainable building with UHPC".

References[Chen-1982] Chen, W. F.:Plasticity in Reinforced Concrete. McGraw-Hill, New York, 1982.

[Dahl-1992] Dahl, Karre K. B.; The Calibration and Use of Triaxial Cell, Danmarks TekniskeHojskole, 1992

[Düsterloh 2007] Düsterloh, U.: Triaxiale Kompressionsversuche an UHPC-Beton, Bericht(unveröffentlicht), Institut für Aufbereitung und Deponietechnik, Professur für Deponietechnikund Geomechanik, Technische Universität Clausthal, 2007

[Ertel/Grünberg-2010] Ertel, Chr.; Grünberg, J.: “Triaxial Fatigue Behaviour of Ultra HighPerformance Concrete”; 3rd fib International Congress; May 29 – June 2, 2010, Washington,D.C. (accepted)

[Grünberg/Göhlmann-2005] Grünberg, J.; Göhlmann, J.: Versagensmodelle für Beton untermonotoner Beanspruchung und Ermüdung. Bauingenieur, Band 80. März 2005

[Grünberg et al. 2007] Grünberg, J., Lohaus, L., Ertel, C. Wefer, M.: Mehraxiales mechanischesErmüdungsmodell von Ultra-Hochfestem Beton – Experimentelle und analytischeUntersuchungen, Beton- und Stahlbetonbau, Heft 6, 2007

[Grünberg et al. 2008] Grünberg, J., Lohaus, L., Ertel, C. Wefer, M.: Multi-Axial and FatigueBehaviour of ultra–high–performance concrete (UHPC), Proceedings of the 2nd InternationalSymposium on Ultra-High Performance Concrete, 05.-07.03.2008, Kassel

[Kupfer-1973] Kupfer, H.: Das Verhalten des Betons unter mehraxialer Kurzzeitbelastung unterbesonderer Berücksichtigung der zweiaxialen Beanspruchung. DAfStb, Heft 229, Ernst &Sohn, Berlin, 1973.

[Rogge-2002] Rogge, Andreas; Materialverhalten von Beton unter mehraxialerBeanspruchung, Dissertation, Lehrstuhl für Massivbau, TU München, 2002.

[Schmidt-2008] Sachstandsbericht Ultrahochfester Beton, Deutscher Ausschuss fürStahlbeton, Heft 561, Beuth, 2008

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