Local Deformation Transducers Research Articles

Dynamic properties of lightweight foamed glass and their effect on railway vibration

Abstract Deformation properties of lightweight coarse grained material from recycled foamed glass have been determined from large-scale triaxial tests on prismatic specimens with dimensions 40 cm × 40 cm × 80 cm. Deformations were measured locally using vertical and horizontal local deformation transducers. Monotonic and cyclic loading at small to medium strain range were conducted. Three load sequences representing the expected conditions of use of lightweight material as vibration-reducing material in railway geotechnics have been used. Results indicate strong effect of brittle cellular structure of tested material as well as confining pressure dependency of elastic threshold shear strain and damping ratio. The results were used to assess the applicability of empirical formulas for shear modulus of granular materials to lightweight foamed glass. The parameters determined from the laboratory tests were further used in numerical analysis of railway dynamic response. The results of the numerical simulations show that replacement of fill in track embankment by lightweight material could improve the dynamic response of the track in reducing the vibration.

Particle-scale insight into transitional behaviour of gap-graded materials – small-strain stiffness and frequency response

This study aims to develop a fundamental understanding of the role of fine particles on the small-strain stiffness of gap-graded granular soils. Stiffness was measured using cyclic triaxial probes, which give a measure of static stiffness, and dynamic wave propagation data, from which the dynamic stiffness can be measured. Assemblies of loosely packed spherical particles were considered. In the laboratory, local deformation transducers were used to measure the static stiffness, while the dynamic stiffness was calculated from stress wave velocities, measured using planar piezoelectric elements. To relate the particle-scale responses to the overall soil stiffness, complementary discrete element method (DEM) simulations were performed in which both static and dynamic stiffnesses were measured. Both the laboratory and the DEM data indicate that at low fines contents (< 30%) the stiffness decreases with increasing fines content. When the fines content increases from 30% to 35% there is a sharp increase in stiffness with increasing fines content; this is understood to mark the transition point at which the fines start to contribute significantly to the overall behaviour. Analyses of the frequency domain response of shear wave signals revealed that the lowpass frequency increases significantly at this transition point. This observation can be used to develop experimental interpretation protocols to assess to what extent fines are contributing to the overall soil stiffness.

Axial and Lateral Small Strain Measurement of Soils in Compression Test using Local Deformation Transducer

This paper presents the development of a method using local deformation transducers (LDTs) to locally and sensitively measure small axial and lateral strains in soil in a compression test. A local strain measurement system comprising of axial and lateral LDTs was developed referring to the original LDT system and the cantilever LDT system, respectively. The LDTs were calibrated both in air and under water. Their insensitivity to pressurized water was confirmed. The calibration factors for the axial and lateral LDTs were found to be 1.695 mm/volt and 1.001 mm/volt, respectively. The performance in terms of repeatability and stability of the LDT system was evaluated. The repeatability test showed that the average standard deviation of the lateral LDT was 0.015 volt, while the stability test showed that the average standard error of the axial and lateral LDT were 3.13 × 10-5 volt and 2.65 × 10-5 volt, respectively. Unconfined compression tests were conducted on three reconstituted clay samples to examine the proposed axial and lateral LDT system. The stress-strain relationship indicates a nonlinear relationship between the axial and lateral strain of soil instead of the conventionally assumed constant relationship. The results demonstrate this nonlinear behavior even at small strain levels, which were successfully measured using a domestically built axial and lateral LDT system.

A Method of Measuring the Displacement of an Ultra-High-Performance Fiber-Reinforced Concrete by Means of Unbound Gages

A study on Ultra-High-Performance Fiber-Reinforced Concrete (UHPFRC) required accurate continuous displacement measurements to fully understand specimen compressive and split tensile behavior. From uniaxial compressive testing, load, and displacement data was acquired to develop specimen specific stress–strain diagrams from which the modulus of elasticity and strain at ultimate capacity of the material were found. Thus, a device suitable to measure the displacement and crack width opening was required during testing to gain knowledge of the behavior of UHPFRC subjected to compressive and tensile loads. The device normally used to measure average displacement is typically not used for ultimate strain conditions because of the potential LVDT damage from the often explosive compression failure of concrete specimens. Hence, this study investigated the use of Local Deformation Transducers (LDTs), which consists of strain gages attached at mid-length on a narrow strip of highly flexible and resilient material. Data collected from these gages corresponded well with UHPFRC test data collected from other institutions using more complex methods and proved to be a reliable source of measuring displacements with the intent of identifying modulus of elasticity, and concrete strains at first crack, and ultimate capacity for an UHPFRC.

Large-scale triaxial tests of dense gravel material at low confining pressures

The results of a series of large-scale triaxial tests performed on dense, prismatic gravel specimens, with a height of 50cm and a cross-section of 23cm×23cm, are described. The specimens were prepared at a density equal to approximately 95% of the maximum density at the optimum moisture content. Deformations were measured locally using vertical and horizontal local deformation transducers. Stress conditions with selected levels of very low confining pressure were used to simulate specific conditions in the case of road and railway embankments. Particular attention was paid to the bedding error at the top and the bottom ends of the specimens, and to fixing transducers onto the membrane to be used under low confining pressure. The confining pressure was applied by vacuum and varied from 10kPa to 75kPa. Unsaturated specimens were tested under drained triaxial compression using monotonic and cyclic loading with frequencies in the range of 0.5–5Hz. The effects of a large number of load cycles and of specimen preloading were investigated.

Strength and small-strain modulus of lightweight geomaterials: cement-stabilised sand mixed with compressible expanded polystyrene beads

ABSTRACT: The use of lightweight geomaterials for the construction of geotechnical structures is diverse. They are often used in the construction of embankments to reduce the bearing stress imposed on soft soil foundations. In particular, compressible small beads of expanded polystyrene (EPS) have become widely used, mixed with sandy soils and stabilised with cement. The reduction of weight due to the inclusion of such EPS beads is therefore beneficial. Nonetheless, such inclusion can degrade the fundamental strength and deformation properties of constructed geomaterials, even though they are stabilised with cement. In the present study, multiple series of triaxial compression tests were conducted using a pair of local deformation transducers (LDT), and the large-strain strength and small-strain modulus of cement-stabilised sands mixed with EPS beads were examined. The changes in the strength and deformation properties with increasing inclusion of EPS beads are examined and discussed in detail. Based on the outcome of the present study, the practical implications for design of lightweight geomaterials are also described.

Effect of Specimen Size on Quasi-Elastic Properties of Toyoura Sand in Hollow Cylinder Triaxial and Torsional Shear Tests

Abstract Quasi-elastic deformation properties of dry, dense Toyoura sand were experimentally investigated by triaxial and torsional shear tests on hollow cylindrical specimens of medium sizes (outer diameter Do=20 cm, inner diameter Di=16 or, 12 cm, and height H=30 cm) and small size (Do=10, Di=6, H=20 cm). In addition to the conventional external measurements, strains were measured locally by the newly developed pin-type local deformation transducers. The effect of specimen size on locally measured Young’s modulus Ez was insignificant. On the other hand, the locally measured values of shear modulus Gzθ with the small size specimen revealed lower reproducibility as compared with those measured with the medium size specimens, suggesting that larger specimen size is preferred in evaluating the small strain shear modulus in torsional shear tests on hollow cylindrical specimens. It was also inferred from the test results that, irrespective of the specimen size, effect of end restraint at the top cap and pedestal is significant on the externally measured values of Gzθ.

Small-Strain Stress-Strain Properties of Expanded Polystyrene Geofoam

ABSTRACT The small-strain stress-strain properties of expanded polystyrene (EPS) geofoam with densities of about 20 kg/m3 and 30 kg/m3 were evaluated by laboratory unconfined compression tests on specimens of 75 mm in diameter and 150 mm in height. Two series of tests were conducted, which were continuous monotonic loading (ML) tests and ML tests intervened by sustained creep loading and minute cycles of unload and reload. Relatively small vertical and horizontal strains were locally measured by means of a pair of local deformation transducers (LDTs) and a set of three clip gauges, respectively. The paramount importance of measuring local strains in compression tests on EPS to reliably evaluate its stress-strain properties, in particular those at relatively small strains, is demonstrated. The initial modulus, E0, and Poisson's ratio, ν0, were evaluated from initial stress-strain relations at small strains obtained by these ML tests. The tangent parameters, Etan and νtan, were also evaluated from the ML stress-strain behaviour. The equivalent parameters, Eeq and νeq, were evaluated from the stress-strain behaviour during minute cycles of unload and reload. The stress-strain behaviour is essentially linear only at small strains, and it becomes highly non-linear and a significant drop of stiffness occurs as observed in the overall stress-strain behaviour. The Poisson's ratio for inelastic deformation is found to be negative.

Evaluation of Quasi-Elastic Properties of Gravel Using a Large-Scale True Triaxial Apparatus

Abstract In order to investigate the anisotropy in the deformation characteristics of gravel, a large-scale true triaxial apparatus that can control three principal stresses independently has been newly developed. One of the two horizontal stresses is applied by means of rigid vertical platens that confine the specimen, to induce a uniform horizontal strain over the height of the specimen in that one direction. A set of local deformation transducers and proximity transducers are used to measure strains to minimize the effects of specimen corners, bedding error, and system compliance. Specimens have a prismatic rectangular shape with dimensions of 50 cm high and 25 cm × 22 cm in cross section. Using this apparatus, a couple of tests were conducted on gravel specimens prepared by manual compaction at a water content of 5.5% to reach dry densities of 2.0 and 2.2 g/cm3. At several stress states, during isotropic compression and subsequent triaxial loading, vertical and horizontal loading cycles of a very small stress amplitude were applied to evaluate the quasi-elastic deformation properties. The test results show that the small-strain quasi-elastic Young's modulus in a given direction is essentially a unique function of the normal stress in the same direction, regardless of the density of the specimen. Although this is contrary to some of the well-established models used in practice, it is consistent with results of relevant laboratory tests by others. Small-strain quasi-elastic vertical and horizontal Young's moduli exhibited effects of inherent and stress state-induced anisotropies. Performing cyclic loading tests of successively increased the stress amplitude, strain-level dependency of the equivalent Young's modulus and hysteretic damping ratio in both the vertical and horizontal directions was obtained.

Small Strain Behaviour of Dense Granular Soils by True Triaxial Tests

ABSTRACT A series of tests was conducted by using small-scale and large-scale true triaxial apparatuses (where σ1≠σ2≠σ3) in order to study small strain behaviours of dense granular soils including anisotropic deformation characteristics. These apparatuses are equipped with local deformation transducers to measure deformations of prismatic specimens in three orthogonal directions. Dense gravel specimens were prepared by manual compaction and tested in large-scale true triaxial apparatus, while dense sand specimens were prepared by air-pluviation and tested in both scales of true triaxial apparatuses. During isotropic and triaxial compression, at several stress levels, many very small vertical and horizontal cycles were applied to evaluate the quasi-elastic deformation property including Young's modulus and Poisson's ratio at small strain levels around 0.001%. Its inherent and stress-state induced anisotropy could be clearly observed for both cases of dense sand and dense gravel. The inherent anisotropy is affected by the bedding plane or heavy compaction during specimen preparation. The values of Young's moduli in the direction that was perpendicular to the bedding plane are smaller than or equal to those of Young's moduli in other orthogonal directions during isotropic compression for all the tested specimens. Discussions on anisotropic characteristics of dense granular soils including their hypo-elastic modeling are also made.

Measurement of Quasi-Elastic Stiffness Parameters of Dense Toyoura Sand in Hollow Cylinder Apparatus and Triaxial Apparatus with Bender Elements

Abstract Quasi-elastic stiffness parameters of dense Toyoura sand were measured at various stress states during similar consolidation and p′-constant shear tests in a hollow cylinder apparatus and a triaxial apparatus equipped with local deformation transducers and bender elements. Test results from these two test setups were compared. Although the Young's moduli from the triaxial apparatus were slightly lower than those from the hollow cylinder apparatus, they followed approximately the same power laws with the effective normal stresses. The shear modulus Gvh from the hollow cylinder apparatus was almost the same as that from the shear wave velocity measurement in the triaxial apparatus. The Poisson's ratios were also similar from both test setups. The vertical Young's modulus was found to be smaller than the horizontal Young's modulus. The anisotropy in Young's moduli followed a power law with the effective stress ratio. However, the Poisson's ratios were not dependent on the mean effective pressure or the shear stress level. The symmetry of the stiffness matrix was also examined.

Comparison of Young's Moduli of Dense Sand and Gravel Measured by Dynamic and Static Methods

Abstract The stiffness of soil at very small strain is a useful parameter for characterizing the non-linear stress-strain behavior of soil, which has been evaluated by both dynamic and static methods based on different principles. A new technique for measuring dynamic wave velocities of coarse material is introduced in large-scale triaxial tests on rectangular specimens with dimensions of 58 cm high and 23 × 23 cm in cross section. At the same time, static deformation properties during small-amplitude unloading and reloading cycles are measured with local deformation transducers. Young's moduli of dense sand and gravel evaluated based on the static and dynamic measurements are compared, and some discussions on anisotropy and inhomogeneities are made taking advantage of the movable feature of the new technique.

Performance Evaluation of LDTs for Use in Triaxial Tests

Abstract The performance of local deformation transducers (LDTs) is described in the light of obtaining reliable data on the stiffness of geomaterial in a small-strain range. The components of LDTs and their functions are described, including recent modifications aimed at improving performance. Resolution, working range, and performance were critically examined with special reference to the evaluation of small strain elastic behavior of soil. LDTs in a lateral direction (or simply lateral LDTs) that are able to measure lateral strains precisely are also described. LDTs can underestimate the maximum elastic modulus measured during a small unload/reload cycle of a given geomaterial for no more than 2%, while they can measure strains less than 0.0005% without amplification. LDTs also function satisfactorily under submerged conditions in pressurized water for a long duration (at least 41 days).

Deformation characteristics of a sedimentary soft mudstone from triaxial compression tests using rectangular prism specimens

A new triaxial testing system has been developed for accurately evaluating the deformation characteristics of soft rock. Axial and lateral strains were measured locally along the surfaces of a rectangular prismatic specimen by using, in total, four pairs of local deformation transducers. Sedimentary mudstone samples retrieved by block sampling at Sagamihara Test Site were first compressed isotropically to the field overburden pressure level, followed by drained triaxial compression at different axial strain rates. A series of small unload/reload cycles was applied to define elastic and plastic deformation properties at intermediate loading stages. Very large bedding errors were observed at both the top and bottom ends and at the lateral surfaces of specimens during isotropic compression, and at the ends during triaxial compression. Local strains showed approximately isotropic deformation during isotropic compression. From the results of the drained triaxial compression tests, the Young's modulus and Poisson's ratio, defined for elastic and total strain increments, and their dependences on shear stress level and strain rate were quantified. Un nouveau systeème d'essais triaxiaux a été mis au point pour l'évaluation précise des caractéristiques de déformation des roches tendres. Les contraintes axiales et latérales ont été mesurées localement sur les surfaces d'une éprouvette rectangulaire prismatique à l'aide de quatre paires de capteurs de déformation locale. Des échantillons d'argilite sédimentaire prélevés par échantillonnage par blocs sur le terrain d'essai de Sagamihara ont d'abord été comprimés de façon isotrope jusqu'à la pression des mortsterrains avant de subir des essais de compression triaxiale drainés à différents taux de contrainte axiale. On a eu recours à une série de petits cycles décharge=recharge pour déÆnir les propriétés de déformation élastique et plastique aux stades de chargement intermédiaires. On a observé une grande erreur de litage aux extrémite s supérieure et inférieure et aux surfaces latérales de l'éprouvette pendant la compression isotrope, ainsi qu'à l'extrémité supérieure pendant la compression triaxiale. Les contraintes locales ont produit une déformation approximativement isotrope pendant la compression isotrope. A partir des résultats des essais de compression triaxiale drainée, on a quantifié le module de Young et le coefficient de Poisson, définis pour les écarts de contrainte élastique et totale, et la facçon dont ils dépendent du cisaillement et de l'état de contrainte.