New Local System of Measurement of Axial Strains for Triaxial Apparatus Using LVDT

Geotechnical Testing Journal, Vol. 28, No. 5Paper ID GTJ11630

Available online at: www.astm.org

E. Ibraim1 and H. Di Benedetto2

New Local System of Measurement of AxialStrains for Triaxial Apparatus Using LVDT

ABSTRACT: This paper presents a new local system of measurement of axial strains for triaxial apparatus using LVDT. The bodies of fournonsubmersible transducers are supported by an independent circular ring, while the rods are simply put on local targets (pins pushed through themembrane into the sample). A flexible metal plate is used to attach the body of the LVDT to the circular ring and a nonrigid connection is consideredbetween the rod and the pin. These original developments allow the system to investigate the soil behavior in large strains, up to 15 × 10−2 m/m,and to accommodate the radial deformation, tilting, and usually inevitable barreling of the sand specimen. The soil stiffness in the small straindomain, less than some 10−5 m/m, can be evaluated with good accuracy, as well as its evolution during triaxial compression or extension tests. Theassessment of errors is discussed and the performance of the device is shown with results of tests on Hostun RF sand.

KEYWORDS: prefailure, small strain, large strain, sand, LVDT, triaxial, local system device, Young’s modulus

Introduction

In many geotechnical problems, the operational strain domainranges from small, less than some 10−5 m/m, to medium, up toaround 10−3 m/m. An accurate laboratory assessment of soil stiff-ness for this strain domain is essential for prediction of defor-mation of ground and settlement of structures under working ordynamic/seismic loading. At the same time, it is a desirable re-quirement of soil laboratory investigation to be able to study theprefailure deformation characteristics and the large strain behavior,up to 15 × 10−2 m/m, using a continuous test on a single specimen.That is, to analyze the soil stiffness with the evolution of the strainand stress levels.

In the laboratory, the measurement of stiffness of soils in the smallstrain domain can be achieved using the following three methods:the resonant column test (Hardin and Richart 1963; Hardin andBlack 1966), the measurements of the body wave velocities withinthe soil element (Shirley and Hampton 1978; Schultheiss 1980;Dyvik and Madshus 1985; Viggiani and Atkinson 1995; Brignoliet al. 1996; Pennington et al. 1997; Cazacliu and Di Benedetto 1998;Modoni et al. 2000), and the direct measurement of small strain andstress amplitude during monotonic or cyclic quasi-static loading.The last method has the advantage of providing direct access tothe stiffness of the soils. An overall review of local measurementsystems with inclinometer levels, Hall Effect transducers, noncon-tact sensors, Linear Variable Differential Transformer (LVDT), andstrain-gaged Local Deformation Transducers (LDT) developed fortriaxial apparatus is presented by Scholey et al. (1995) and Tatsuokaet al. (1997). Besuelle and Desrues (2001) have recently proposeda similar system to LDT for soft rock specimens. Concerning thehollow cylinder torsional apparatus, details of measurement sys-tems are given by Hight et al. (1983), Lo Presti et al. (1993), DiBenedetto et al. (1999), and Connolly and Kuwano (1999).

1 Lecturer in Civil Engineering, University of Bristol, Queen’s Building,University Walk, Bristol, BS8 1TR, UK.

2 Professor, Ecole Nationale des Travaux Publics de l’Etat, DGCB, RueMaurice Audin, Vaulx-en-Velin, France.

It is widely recognized that the stiffness evaluated with traditionalexternal measurement devices is underestimated and is smaller thanthat determined by measurements in the central part of the spec-imen. Jardine et al. (1984) and Baldi et al. (1988) identify thepotential errors induced by compliance of loading system and mis-alignment and specimen bedding/seating effects, but also by insuf-ficient precision and accuracy of the sensors and data acquisitionsystem. Thus, using a local measurement system of strains withvery accurate and reliable transducers is essential in order to havea good evaluation of the quasi-elastic properties of soil materials(Shibuya et al. 1992; Tatsuoka et al. 1994).

In this paper, a new local system of measurement of axial strainsfor triaxial apparatus using Linear Variable Differential Transform-ers is described. This new system developed and tested for sandspecimens allows the exploration of soil behavior both in the smalland large strain domains.

Why Use LVDT Sensors?

The answer to this question is given by their attractive technicalqualities: the stability under changes in temperature and pressure,the good linearity of the output of the signal, the resolution (LoPresti et al. 1994; Da Re et al. 2001). Very important too is theirlow price.

Nevertheless, the use of the LVDT in the triaxial test for localaxial strain measurements is not simple, especially when the anal-ysis of the stiffness of the soil with stress and strain evolution isrequired. Two principal problems must be solved: one is the mount-ing of the transducers—core and body; the other one is the abilityfor the local strain system to accommodate coupled axial and radialdisplacements, taking also into account the tilting and inevitablebarrelling of the cylindrical specimen and the need to minimize thefriction developed between the LVDT core and body.

Basically, two main different mounting solutions are proposed inthe literature.

In the first one, the body and the core are attached directly to thespecimen (Cuccovillo and Coop 1997) or by means of circular splitcollars hinged at one end and connected by a spring at the other

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2 GEOTECHNICAL TESTING JOURNAL

FIG. 1—Schematic representation of different LVDT mounting devices for axial strain measurement.

FIG. 2—Shape of sand samples (initial height 70 mm, aspect ratio 1)with (left) and without (right) frictionless end plates at large axial strains.

(Brown and Snaith 1974; Boyce and Brown 1976; Nataatmadjaand Parkin 1990; Da Re et al. 2001), as schematically presentedin Fig. 1a. As long as the shape of the specimen remains cylin-drical during shear, these axial strain devices should be able toaccommodate radial movements. However, this seems not to bealways possible, especially when granular materials are tested tolarge strains. As can be seen in Fig. 2, the shape of both sandspecimens (dense Hostun RF sand, specimen of 70 mm height andaspect ratio 1) at the end of the triaxial compression tests is far fromcylindrical, even when frictionless end platens are provided. Thiscould alter the LVDT body and core parallelism and, thus, make itmore difficult to maintain these measurement systems in workingconditions up to large strains. Another limitation that can affect theaxial displacement measurement is the self-weight of the transducerand the mounting device. A local yielding of the soil around theattachment points can be generated (Scholey et al. 1995).

In the second mounting solution, Fig. 1b, the weight supportedby the soil is considerably reduced—only the core of the LVDTis fixed to targets placed on the specimen wall, while the bodyis rigidly attached to independent supports (Yuen et al. 1978;Brown et al. 1980; Costa Filho 1985). Again, during the triaxialtest, with horizontal specimen displacements occurring, excessivefriction between the core and the body can cause jamming, mak-ing the measurement system less adapted for large strain investi-gations.

Taking into account these considerations, the following require-ments were proposed for the new LVDT local system of measure-ment of axial strains in the triaxial test:

� To minimize the weight supported by the specimen and to usenonsubmerged sensors;

� To evaluate the prefailure deformation characteristics, but alsoto be able to follow the soil behavior up to large strains (post-failure), without excessive friction between the core and thebody;

� To record the axial displacements without perturbations of thespecimen radial deformation and tilting/barrelling; and

� To be simple and easy to use.

Description of the New Local Axial Strain Device

Figure 3 presents an overall view of the triaxial cell system withthe new local axial device for measurement of axial strains. Thetriaxial cell accommodates specimens of 70 mm height and as-pect ratio 1 with two, top and bottom, enlarged plates. The cellis partially filled with deaired water and the specimen is totallysubmerged; there is no direct contact between the membrane ofthe specimen and the pressurized air (the diffusion of the air intothe specimen is prevented). The axial local strain system includesfour identical LVDTs with a measurement range of ±10 mm. Thisrange makes it possible to reach the behavior of soil in large de-formations (up to 0.15–0.20 m/m). Each transducer is connected toa generator-demodulator signal-conditioning unit, which ensuresthe current supply and the shaping of signal output from the sensor.Even if the resolution of the LVDT sensor is considered infinite, thesensitivity of the signal output is directly affected by the resolutionof the data acquisition system employed. Using a data acquisi-tion unit with a 6 1/2 digit integrating analog-to-digital converter,a minimum range output signal of approximately ±0.01 mV hasbeen recorded for all four transducers. Based on the calibrationfactor obtained using a micrometer with a nonrotating rod (ac-curacy ±0.5 µ m), the corresponding resolution of the LVDT isapproximately ±0.1 µ m (Fig. 4). The LVDT resolution magnitudecombined with other factors mentioned in the next section, con-trol the random errors with which the axial displacement of thespecimen is measured. The assessment of these errors is discussedlater.

The arrangement of the local points of measurement on the speci-men and the corresponding LVDT sensors, noted �1T, �2T, �1B,and �2B, are presented in Fig. 5a. The vertical distance (dTB)


IBRAIM AND DI BENEDETTO ON LVDT 3

FIG. 3—General view of the triaxial test system.

FIG. 4—Resolution of the LVDT.

between the points of measurement is 40 mm, and there is a dis-tance of 15 mm between the top of the specimen and �1T (�2T)and between the base of the specimen and �1B (�2B). The mea-surement points are diametrically opposite for �1T and �2T andfor �1B and �2B (Section A-A, Fig. 5a). The measurement ofdisplacements on the top (T) and on the bottom (B) are carried outin two different vertical planes. With respect to the center of thespecimen, these planes form an angle of approximately 25◦. It isnot possible to mount two LVDTs in the same vertical plane onthe same side of the specimen. The fact that the top and bottomtransducers are in different vertical planes should not be importantwhen computing the average local strain. However, it may raisequestions when comparing Strain 1 with Strain 2. The strain on oneside of the specimen represents, actually, a strain averaged over azone limited by these two vertical planes.

The bodies of the LVDTs are connected independently of thespecimen to a circular ring (Figs. 3 and 6). The parts of the device,which ensure fixing of the body on the circular ring, were designedto facilitate the initial positioning of the LVDT in vertical (Part P1)and radial (Part P2) planes around the specimen (Fig. 6a). A thinflexible metal plate connects these two parts and the body of thetransducer, and this represents the main originality of the device.

In order to prevent the flexing of the plate, due to the weight ofthe transducer, and thus preserve the initial vertical position of thebody, a counterweight is attached to the flexible metal plate as isshown in Figs. 5b and 6a.

The LVDTs are placed above the water level of the triaxial cell,and core extension rods are necessary in order to reach the localmeasurement points. These extensions are made of aluminum andhave an L shape; they simply rest on the target (detail, Fig. 3). Thereis no rigid contact between the core extensions and the targets, andthis represents another original development for the measurementsystem. The targets are pins of 0.5 mm diameter and 25 mm length,pushed through the membrane into the sand specimen. A 2-mm-thick layer of silicone is necessary around the pin to ensure sealingof the membrane (Fig. 3). No leakage problems have been observedduring the tests.

During a triaxial compression test, with the development of thebarrel shape of the specimen, a rotation of the pin with respect tothe measurement point can occur (Fig. 7). The device accommo-dates this rotation of the pin (mainly due to the nonrigid rod-targetcontact), but a displacement error (K) may affect the axial mea-surement. The actual top local displacement (δT ) could be under-estimated (δT − K), whereas the actual bottom local displacement(δB) could be overestimated (δB + K). Overall, these effects maylead to an underestimation of the axial strain. The assessment of theerror represents a difficult task. However, it is minimized becausethe spherical head of the pin is placed as close as possible to thespecimen (3 to 4 mm).

In spite of the initial verticality of the LVDT body, the first exper-imental tests revealed some problems due to the excessive frictionbetween the core and the body, especially at the beginning of thetriaxial loading test. Excessive friction is reflected in discontinuousmeasurement records. For these reasons, an improvement was madeto the L rod extensions by fixing two counterweights, in accordancewith Figs. 5a and 5c. This made it possible to locate the verticalcenter of gravity of the L rod unit plus counterweights on the spher-ical head of the target support. The total weight (nonsubmerged) ofthe LVDT rod, extension, and counterweights is 23 g for �1B and�2B and 19 g for �1T and �2T.

For a large range of sand specimen densities, loose, medium, anddense, no displacements of the targets due to the weight of the rodswere observed. However, the use of this device was not possible for



FIG. 5—Position of local measurement points (a) and solution to provide initial verticality of the body (b) and of the rod (c).

FIG. 6—The LVDT mounts, initial positioning (a), and operating principle of the new local system during axial loading of the sample (b).

very loose sand specimens (relative density, Dr ≈ 0). The rigidityof the internal structure of very loose sand is not sufficient to preventa loss of orientation of the pins due to the weight of the rod (evenwithout the counterweights).

During a triaxial compression or extension test, the initial posi-tion of the local measurement point M changes, axially (δa) andradially (δr), to the current position M′ (Fig. 6). Thanks to the flex-ibility of the plate, which allows the rotation of the LVDT body,and to the nonrigid rod/pin contact, which acts actually as a hingethat allows freedom for the end of the L rod to rotate, the axialdisplacement of the local point can be recorded continuously, i.e.,at the same time as the horizontal displacement develops. Thus, the

designed system is able to investigate the axial behavior at largestrains and to accommodate radial deformation of the specimen.The center of rotation “O” coincides with the center of gravity ofthe LVDTs body. This was made possible by adjusting the lengthof the flexible metal plate.

The local axial measurement system has not been designed to ac-commodate circumferential displacements of the targets imposedby the development of shear band. However, for very limited move-ments, the device remains operational. A relative rotation of the coreextension rod with respect to the LVDT body in the circumferentialdirection occurs, and this is allowed by the existing gap betweenthe LVDT body shaft and core.



FIG. 7—Effects on the axial measurements induced by the rotation of the target due to barrelling of specimen.

The recorded axial displacement showed that friction betweenthe LVDT rod and body remains very small, actually negligible.Visual inspections revealed as well that during the tests the localradial deformation is not inhibited by the local axial strain systemand the pins are not pushed into the specimen. A 20-mm widthof flexible plate and a careful initial positioning of the transducercan be enough to avoid the torsion of the flexible foil during theexperimental test.

It should be noted that the rigid rotation of the LVDT bodyimposed by the radial displacement of the specimen might intro-duce systematic errors on the axial strain measurement. Knowingthe geometry of the specimen, the accurate position of the localmeasurement points, and the dimensions of the LVDT rods, themagnitude of these errors can be assessed without any difficulty.

Assessment of Errors

Systematic Error

The systematic error is considered here in terms of a relative erroron the measured value of the axial strain, Err(εa), and is given bythe following relation:

Err(εa) = εa,r − εa, mes

ε a, mes× 100 (1)

where εa,r is the real axial strain experienced by the specimen andεa, mes is the axial strain provided by the new local axial system. Inorder to assess this relative error, the real axial strain is taken as aknown variable, while the axial strain given by the local system isdeduced. A single value of local axial strain is obtained accordingto the following relation:

εa, mes = δ1T + δ2T − δ1B − δ2B

2dTB(2)

where δ means a displacement, 1 and 2 stand for diametricallyopposite parts of the specimen, T and B indicate the top and thebottom of the local measurement points, and dTB represents theinitial vertical distance between the T and B targets.

The evaluation of the relative error, detailed in Ibraim (1998),reduces, actually, to a geometrical problem; a schematic diagramrepresenting the measurement process for one LVDT is presentedin Fig. 8 (compression test case). The difference between the realand the measured axial displacements is assessed if the segment(L + δa) is compared with the segment OC′. The hypothesis ofhomogenous shape development of the specimen during the triaxial

FIG. 8—Schematic diagram for axial displacement measurement usedfor the assessment of the systematic error due to the rigid rotation of theLVDT (L + δa is compared with OC′).

test (the axial displacement is linear with the height of the specimen)and a fixed value of the Poisson’s ratio of 0.25 are also considered.For both compression and extension tests, the rigid rotation of theLVDT body underestimates the axial displacement.

The assessment of the relative error presents a particular interestfor two distinct test conditions:

� The first is a monotonic triaxial test, in compression or ex-tension, and the question is how much is this relative error,called Err(εa, mon), when the real axial strain ranges between –0.10 m/m and +0.15 m/m.

� The second test condition concerns the soil behavior in thesmall strain domain and the evolution of the elastic proper-ties during triaxial compression or extension tests. A commontest procedure corresponds to the repetition of two stages ap-plied at different levels of the stress path (Fig. 9). First, amonotonic loading (axial compression or extension) bringsthe specimen to a deformed state, 1, 2, . . i, . . n. Second, atthis state, called the investigation point, the behavior of thespecimen in the small strain domain is studied by applicationof a quasi-static axial cyclic loading of small amplitude. Thisstep is repeated up to large strains. It is proposed to eval-uate the relative error, called Err(εa, cycle), when these smallaxial strain cycles of amplitude εa, cycle are applied at differ-ent investigation points of the triaxial compression or exten-sion stress paths. The investigation points considered for thenumerical analysis correspond to ±0.005, ±0.01, ±0.02, and



FIG. 9—General shape of a triaxial test, large strains and small cyclesin different investigation points (i).

±0.05 m/m of the total axial strain, while the chosen cycleamplitude was 5 × 10−5 m/m.

Figure 10a shows only the relative error Err(εa,mon) involved inthe axial strain measurement for monotonic triaxial compressionand extension tests performed up to large strains. The numeri-cal values considered for the geometrical dimensions are givenin Fig. 8. For very small initial axial strains, the relative error isaround 2.8 %. Therefore, the error induced by the rigid rotation ofthe LVDT, for example, for initial axial strains up to 5 × 10−5 m/mis 1.4 × 10−6 m/m. Then, with the evolution of the axial strain, therelative error, Err(εa, mon), decreases in triaxial compression (up to2.3 %) and increases in triaxial extension (up to 3.2 %).

For small axial strain cycles of 5 × 10−5 m/m amplitude, therelative error Err(εa, cycle) depends on the investigation point, but itremains always between 2.3 and 2.8 % for a compression test andbetween 2.8 and 3.2 % for an extension test.

Considering the error on the measured value of the equivalentYoung’s modulus (Eeq = the peak-to-peak secant modulus for thesmall unload/reload cycle, Fig. 9), the rigid rotation of the LVDTbody induces only an error of approximately 3 %, which is consid-ered to be acceptable.

Random Errors

Errors on the values of the displacements δ measured with LVDTsensors and by extension, on the axial strain, are induced by randomerrors. These errors are due:

� To the electric signal output of the transducer and to the resolu-tion of data acquisition unit (noise, hysteresis, repeatability);

� To the sensitivity of the sensors: linearity of the calibrationcurve, measurement of the calibration factor, accuracy of thecalibration device;

� To the validity of the postulated hypothesis of homogeneousstrain field development during the test;

� To the accuracy of the measurement of the initial specimensize.

During repeated measurements of a given distance δ, these ran-dom errors lead to a scatter of measurements around a mean valuemδ. An indication of this scatter is given by the standard deviationσδ, which represents the precision of the measured displacement δ.

FIG. 10—Relative errors on the measured value of the axial strain in-duced by the rotation of the LVDT for triaxial compression and extensiontests up to large strains (a) and evolution of random errors with the axialstrain (b).

The electrical output of the LVDT is linear; therefore, the mea-sured distance δ is given by the following relation:

δ = S × E (3)

where S is the sensitivity of the LVDT (cm/V) and E the output(V). S and E are considered independent random variables (ap-proximated by normal distributions) each one represented by themean (mS and mE) and by the standard deviation (σS and σE). Byapplication of the method of central moments to the deterministicrelation (3), the mean and the standard deviation of the variableδ can be found as function of the means and standard deviations ofthe input variables S and E (Ghiocel and Lungu 1975). Therefore,the mean value, mδ, and the standard deviation, σδ, of the randomvariable δ, are:

mδ = mS × mE (4)

σδ =√

(mS)2(σE)2 + (mE)2(σS)2 (5)

The standard deviation σδcan be expressed as a function of themδ if the mean value mE is replaced by the ratio mδ/mS .

The mean mS is given by the slope of the best fit calibration line ofthe LVDT. The accuracy of the calibration device and the resolutionof the transducer are taken into account for the estimation of the



TABLE 1—Statistical parameters of the sensitivity and the electricaloutput for the LVDTs.

LVDT mS (cm/V) σS (cm/V) σE (V)

�1T and �2T 1.0909 7 × 10−3 2 × 10−5

�1B and �2B 0.9591 7 × 10−3 2 × 10−5

standard deviation σS , while the resolution of the data acquisitionunit gives an assessment of σE . For the transducers �T and �B,the current values of mS , σS , and σE used for the computation ofthe random errors are given in Table 1.

The local axial strain εa, mes is determined by the relation (2).Considering the components of this relation as independent ran-dom variables, each one represented by the average mδ and by thestandard deviation σδ, the precision of the axial strain obtainedby using this device can be estimated by the standard deviation,σεa, mes, of the random function εa, mes. A detailed description of thecalculation (based on the method of central moments) is given byIbraim (1998). For axial strains up to 5 × 10−5 m/m, the preci-sion expressed in terms of the standard deviation, σεa, mes, is around5 × 10−6 m/m (Fig. 10b). The standard deviation increases withthe strain level.

The relative error induced by these random errors on the mea-sured value of the initial Young’s modulus or equivalent Young’smodulus, if small unload/reload cycles are applied at different in-vestigation points, is around 10 % for axial strain levels up to3–5 × 10−5 m/m.

Test Results

Several triaxial tests were performed on Hostun RF sand speci-mens using this new axial strain measurement system. Two triaxialtests will be presented in this paper. Hostun RF sand is a com-mon testing material for some European laboratories, and all thespecifications have been given by Flavigny et al. (1990).

Figure 11 presents the results of an isotropic compression teston a specimen with a fabrication relative density, Dr , of 81 %. Thestrain was evaluated with the new local system of measurement andwith an internal LVDT sensor (�h) placed on the rigid top plate ofthe specimen (internal means located in the triaxial cell).

A very good agreement is observed between the measurementsmade in the lower quarter of the specimen by the �1B and �2B

FIG. 11—Isotropic compression test on Hostun RF sand.

transducers (Fig. 11a). Some differences, up to 10 %, were recordedbetween �1T and �2T . They were probably caused by the lack ofthe homogeneity in the higher quarter of the specimen density (thedry pluviation technique was used for the specimen fabrication).The axial displacement recorded by the internal LVDT (�h) resultsin a higher value of axial strain than that obtained by the localsystem (Fig. 11b). The gap between the internal and local axialstrains increases with the effective mean pressure, p′. When p′reaches 550 kPa, the local strain represents almost 70 % of theinternal one.

The second test is a triaxial compression test from an initialisotropic effective confining pressure, p′

o, of 100 kPa (specimenwith relative density, Dr , of 81 %). Again, the importance of thelocal system of measurement for the stiffness evaluation is high-lighted. The stress-strain response presented in Fig. 12b shows thatthe internal and the external (an LVDT placed external to the triaxialcell) measurement systems underestimate the initial stiffness of thesoil. For the external measure, there is no separation between thedisplacement of the specimen and the compliance and bedding er-rors. The internal measurement corrects only the compliance errors.

Good agreement between the local measurements made bythe LVDTs diametrically opposite “1” and “2” is also observed(Fig. 12c). The Strains 1 and 2 do not seem to be affected bymeasurements made in different top and bottom vertical planes (at25◦). At the same time, the quality and the continuity of the curvesindicate that the friction between the core and the body of the lo-cal LVDTs is negligible. It should be noted that the local systemremains operational also for large strains, up to 0.13 m/m (Fig. 12a).

The initial Young’s modulus Emax can be given for strain levels upto 2–3 × 10−5 m/m (Fig. 12d). The slope of the average line givesan initial stiffness around 180 MPa. The evolution of the secantYoung’s modulus with the strain level is presented in Fig. 13. Dueto the precision of the measurement system, an important scatter ofdata is observed for axial strains below 2 × 10−5 m/m. In spite of thisscatter of data, the stiffness of the sand appears to exhibit a plateauat strain levels up to 2–3 × 10−5 m/m (around 180 MPa). However,the error in the evaluation of the stiffness at 2–3 × 10−5 m/m axialstrain is around 10 %, which appears to be in agreement with theprevious estimation given by the random errors.

An extensive experimental program has been performed for theassessment of the elastic properties of the Hostun RF sand byapplication of quasi-static axial cyclic loading of small ampli-tude at different strain and stress levels (Ibraim 1998). Due to the



FIG. 12—Stress-strain behavior for a drained triaxial compression test on Hostun RF sand.

FIG. 13—Strain-dependent stiffness of Hostun RF sand specimen eval-uated with the new local axial strain system of measurement.

considerable volume of data, the analysis of the results, and thusthe assessment of the performance of the local device, will be con-sidered in a separate communication.

Conclusions

A local system of measurement of axial strains for triaxial appa-ratus using four LVDTs is described in this paper. This new deviceis characterized by some innovative solutions:

� A flexible metal plate is used to attach the body of the LVDTto an independent support;

� The rod of the transducer simply rests on the local target, thereis a nonrigid rod/target connection;

� The targets are pins driven through the membrane into thespecimen.

These solutions make possible the use of the axial device forthe investigation of the soil behavior from small strains, some10−5 m/m, up to large strains, 10–15 × 10−2 m/m without pertur-bations of the specimen radial deformation and tilting/barrelling.

The systematic error on the measured value of the axial straininduced by the rigid rotation of the LVDT body has been assessedin terms of a relative error. For very small initial axial strains (com-pression or extension tests), this relative error is around 2.8 %.Then, with the evolution of the axial strain, it reaches 2.3 % forcompression test and 3.2 % for extension test. However, a correc-tion algorithm could be considered.

For axial strains up to 5 × 10−5 m/m, the precision of the devicegiven by an assessment of the random errors is around 5 × 10−6.

Acknowledgements

The technical staff of the Department of Civil Engineering of theEcole Nationale des Travaux Publics de l’Etat de Lyon, in particularMr. M. Pernoud and Mr. G. Prevost, provided the necessary helpand assistance with the development of the new local system ofmeasurement of axial displacements.



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New Local System of Measurement of Axial Strains for Triaxial Apparatus Using LVDT

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